Fracture Mechanics: Applications and Challenges (European Structural Integrity Society)

F RA C TURE ME C HANI C S: APPLICATIONS AND CHALLENGES

Other titles in the ESIS Series EGF 1

The Behaviour of Short Fatigue Cracks Edited by K.J. Miller and E.R. de los Rios

EGF 2

The Fracture Mechanics of Welds Edited by J.G. Blauel and K.-H. Schwalbe

EGF 3

Biaxial and Multiaxial Fatigue Edited by M.W. Brown and K.J. Miller

EGF 4

The Assessment of Cracked Components by Fracture Mechanics Edited by L.H. Larsson

EGF 5

Yielding, Damage, and Failure of Anisotropic Solids Edited by J.P. Boehler

EGF 6

High Temperature Fracture Mechanisms and Mechanics

EGF 7

Environment Assisted Fatigue

EGF/ESIS 8

Fracture Mechanics Verification by Large Scale Testing

ESIS/EGF 9

Defect Assessment in Components Fundamentals and Applications

ESIS 10

Fatigue under Biaxial and Multiaxial Loading

ESIS 11

Mechanics and Mechanisms of Damage in Composites and Multi-Materials

ESIS 12

High Temperature Structural Design

ESIS 13

Short Fatigue Cracks

ESIS 14

Mixed-Mode Fatigue and Fracture

ESIS 15

Behaviour of Defects at High Temperatures

ESIS 16

Fatigue Design

ESIS 17

Mis-Matching of Welds

ESIS 18

Fretting Fatigue

ESIS 19

Impact of Dynamic Fracture of Polymers and Composites

ESIS 20

Evaluating Material Properties by Dynamic Testing

ESIS 21

Multiaxial Fatigue & Design

ESIS 22

Fatigue Design of Components. ISBN 008-043318-9

ESIS 23

Fatigue Design and Reliability. ISBN 008-043329-4

ESIS 24

Minimum Reinforcement in Concrete Members. ISBN 008-043022-8

ESIS 25

Multiaxial Fatigue and Fracture. ISBN 008-043336-7

Edited by P. Bensussan and J.P. Mascarell Edited by P. Scott and R.A. Cottis Edited by K. Kussmaul

Edited by J.G. Blauel and K.-H. Schwalbe Edited by K. Kussmaul, D.L. McDiarmid and D.F. Socie Edited by D. Baptiste Edited by L.H. Larsson Edited by K.J. Miller and E.R. de los Rios Edited by H.P. Rossmanith and K.J. Miller Edited by R.A. Ainsworth and R.P. Skelton Edited by J. Solin, G. Marquis, A. Siljander and S. Sipil~ K.-H. Schwalbe and M. Kodak Edited by R.B. Waterhouse and T.C. Lindley Edited by J.G. Williams and A. Pavan Edited by E. van Walle Edited by A. Pinian, G. Cailletand and T.C. Lindley Edited by G. Marquis and J. Solin Edited by G. Marquis and J. Solin Edited by Alberto Carpinteri Edited by E. Macha, W. B~dkowski and T. Lagoda For information on how to order titles 1-21, please contact MEP Ltd, Northgate Avenue, Bury St Edmonds, Suffolk, IP32 6BW, UK. Titles 22-25 can be ordered from Elsevier Science (http://www.elsevier.com).

F R A C T U R E MECHANICS: A P P L I C A T I O N S AND CHALLENGES Invited Papers presented at the 13 th European Conference on Fracture Editors: M. Fuentes, M. Elices, A. Martin-Meizoso and J.M. Martinez-Esnaola ESIS Publication 26 This volume contains 15 fully peer-reviewed Invited Papers presented at the 13 th European Conference on Fracture held in San Sebastian, Spain, 6-9 September 2000

2000

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First edition 2000 Library of Congress Cataloging-in-Publication Data European Conference on Fracture (13th : 2000 : San Sebasti~ha,Spain) Fracture mechanics : applications and ehallenges : invited papers presented at the 13th European Conferenee on Fraeture / editors M. Fuentes ... [et al.].-- 1st ed. p. era. -- (ESIS publication ; 26) Includes bibliographical references and index. ISBN 0-08-043699-4 (hardeover) 1. Fracture mechanics. I. Fuentes, M. II. Title. III. Series. TA409 .E78 2000 620.1' 126--de21

00-058696

A catalogue record from the British library has been applied for.

ISBN:

0 08 0 4 3 6 9 9 4

O The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.

ECF13 The 13 th European Conference on Fracture I N T E R N A T I O N A L SCIENTIFIC C O M M I T T E E M. Fuentes, CEIT, San Sebastifin, Spain M. Elices, UPM, Madrid, Spain C.M. Branco, ICEMS, Lisboa, Portugal W. Brocks, GKSS, Geesthacht, Germany A. Carpinteri, Politecnico di Torino, Italy W. Dietzel, GKSS, Geesthacht, Germany D. Firrao, Politecnico di Torino, Italy J. de Fouquet, LMPM-ENSMA, Futuroscope, France D. Frangois, ECP, Chatenay Malabry, France G. Gabetta, Eniricerche, San Donato Milanese, Italy J. Gil-Sevillano, CEIT and UN, San Sebastifin, Spain M.S. Loveday, N. Physical Lab., Teddington, UK A. Martin-Meizoso, CEIT, San Sebasti~n, Spain K.J. Miller, SIRIUS, U. Sheffield, UK A. Navarro, U. Sevilla, Spare A. Neimitz, Kielce U. Technology, Poland J. Petit, CNRS, Futuroscope, France J. Planas, UPM, Madrid, Spain K.-H. Schwalbe, GKSS, Berlin, Germany M. Steen, IAM-JRC, Petten, The Netherlands K. Wallin, VTT, Finland J.G. Williams, Imperial College, London, UK

N A T I O N A L ADVISING C O M M I T T E E M. Anglada, UPC, Barcelona, Spain J. Belzunce, U. Oviedo, Spain J. Dominguez, U. Sevilla, Spain J. Gil-Sevillano, CEIT and UN, San Sebastifin, Spain F. Guiberteau, U. Extremadura, Badajoz, Spare F. Guti6rrez-Solana, U. Cantabria, Santander, Spain A. Martinez, UPC, Barcelona, Spain C. Navarro, U. Carlos III, Madrid, Spain J.M. Rodriguez-Ibabe, CEIT and UN, San Sebastifin, Spain V. Sfinchez-G/flvez, UPM, Madrid, Spain J. Toribio, U. La Comfia, Spain A. Valiente, UPM, Madrid, Spain J. Zapatero, U. Mfilaga, Spain

ORGANISING COMMITTEE Prof. Manuel Fuentes (co-chairman), CEIT, San Sebasti~in, Spain Prof. Manuel Elices (co-chairman), UPM, Madrid, Spain Dr. Antonio Martin-Meizoso, CEIT, San Sebasti/m, Spain Dr. Jos6 Manuel Martinez-Esnaola, CEIT, San Sebasti~in, Spain Prof. Javier Llorca, UPM, Madrid, Spain Dr. Ibon Ocafia, CEIT, San Sebasti~in, Spain

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MARQUIS & SOLIN Fatigue Design of Components. ISBN: 008-043318-9 MARQUIS & SOLIN Fatigue Design and Reliability. ISBN: 008-043329-4 RAVICHANDRAN ET AL. Small Fatigue Cracks: Mechanics, Mechanisms & Applications. ISBN: 008-043011-2 RIE & PORTELLA Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials. ISBN: 008-043326-X VOYIADJIS ET AL. Damage Mechanics in Engineering Materials. ISBN: 008-043322-7 VOYIADJIS & KA'I"I'AN Advances in Damage Mechanics: Metals and Metal Matrix Composites. ISBN: 0084943601-3 WILLIAMS & PAVAN Fracture of Polymers, Composites and Adhesives ISBN: 008-043 710-9

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Foreword Fracture Stress Analysis: Some "Practical" Examples C. ATKINSON Some Aspects of Fatigue of Engineering Materials H. MUGHRABI Failures of Structures and Components which Fracture Mechanics would have Prevented D.R.H. JONES

29

Interfacial Cracking in Thin Film Structures J.M. MARTINEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE and A. MARTIN-MEIZOSO

47

Designing Against Fretting Fatigue in Aeroengines C. RUIZ and D. NOWELL

73

Aircraft Fatigue Life Extension: Development of a Mid-Life Rework Method Based on Peening G. CLARK

97

Coatings for Hot Section Gas Turbine Components J. BRESSERS, S. PETEVES and M. STEEN

115

Modeling Cyclic Deformation of Thick Thermal Barrier Coatings D. SOCIE and E. REJDA

135

Application of Fracture Mechanics on Japanese Automotive Industry T. YOSHIMURA

155

Gigacycle Fatigue of High Strength Steels Prediction and Mechanisms C. BATHIAS

163

Fatigue of Railway Axles: A Classic Problem Revisited R.A. SMITH

173

Fracture Mechanics Applied to Concrete M. ELICES, J. PLANAS and G.V. GUINEA

183

Fatigue and Fracture of Steel Bridges P. ALBRECHT and W. WRIGHT

211

Designing Against Ductile Fracture Propagation in Very High Strength Steel Gas Pipelines: A Review G. BUZZICHELLI

235

Fracture Mechanics Concepts and Structural Integrity of Filament Wound Pipes A.TORRES MARQUES, A.B. de MORAIS, J.F. SILVA and P.T. de CASTRO

253

Author Index

263

vii

This Page Intentionally Left Blank

FOREWORD In September 1998, at the 12th Biennial European Conference on Fracture, in Sheffield, the European Structural Integrity Society (ESIS) entrusted the Centro de Estudios e Investigaciones T~cnicas de Gipuzkoa (CELT), a member of the Spanish Fracture Group (GEF), with the responsibility for the organisation and hosting of the 13th Biennial European Conference on Fracture in the year 2000. The Spanish Fracture Group was established in 1984, following an initiative by Prof. M. Elices, Director of the Department of Materials Science at the Universidad Polit6cnica de Madrid. It now brings together no less than fifteen separate research teams from academia and industry whose centres are scattered throughout Spain. Mathematicians, engineers, materials scientists, physicists, chemists and medical biologists, working in the field of fracture, gather together every spring at a three day meeting for discussion and exchange of views and the presentation of their latest research and development, which is published in the proceedings of the meeting (Anales de Mecanica de la Fractura). The Group has also been successful in establishing links with researchers of other nationalities, particularly those of Spain's geographic neighbours. Three of the annual meetings had a true Iberian character and they were held at Braga/Portugal (1987), M6rida/Spain (1993) and Luso/Portugal (1996), while a fourth held at Aiguablava/Spain (1992), was attended by researchers from both sides of the Pyrenees (France and Spain). This year, the 13th ECF Conference has come to Donostia/San Sebasti&n, capital of Gipuzkoa, in Spain's historical northern industrial belt. This is the cradle of the Spanish engineering and metallurgical industry and the seat of the prestigious Engineering School of the University of Navarra (The Escuela Superior de Ingenieros which has its campus in Donostia/San Sebasti&n). Fracture studies have been carried out for over 20 years by the School of Engineering as well as by two well-established Technological Centres (CELT and INASMET). They have also contributed to the understanding of fracture phenomena as well as to the dissemination of fracture concepts between practitioners and their application to the solution of engineering problems. The organisers of the ECF 13 opted from the very beginning for an application-orientated conference. After some discussion, it was decided that most of the contributions, whether poster or oral presentations, could be classified into six groups or industrial sectors: transport, power generation, electronics, civil engineering, off-shore engineering and bioengineering. For each of the six sections two state-of-the-art plenary lectures were given. In line with current practice, the Conference Proceedings-including both the poster and oral presentations as well as the keynote lectures- have been produced, for the first time in ECF Conferences, in CD-ROM format, although the key-note papers have also been published in a hardcover volume.

Thanks are given to the ESIS Technical Committee Chairmen and membersas well as to those members of the Spanish Fracture Group (GEF)- who so generously committed their precious time to referee abstracts and to revise the final manuscripts. Special thanks are due to the contributors of papers to the Conference Proceedings and to Prof. K.J. Miller who encouraged the attendance of many international delegates. Finally, the organising committee would also like to acknowledge the support and financial assistance provided by: the Department of Economy and Tourism of the Provincial Government (Gipuzkoa), the Department of Industry, Commerce and Tourism and the Department of Education, Universities and Research of the Basque Government (Vitoria/Gasteiz), the Spanish Department of Education and Culture (Madrid), the Directorate General XII of the European Union (Brussels), Iberdrola S.A. (Bilbao), a major Spanish utility, and The Escuela Superior de Ingenieros of the University of Navarra at its campus in Donostia/San Sebastian.

The Editors

F R A C T U R E STRESS ANALYSIS: S O M E " P R A C T I C A L " E X A M P L E S C. ATKINSON

Department of Mathematics, Imperial College of Science, Technology & Medicine, London SW7 2BZ, UK ABSTRACT A variety of "commonplace" (and some not so common) actual and incipient fracture occurrences will be discussed. An attempt to predict when and if these will happen will be pursued using various tools of stress analysis and continuum mechanics.

KEYWORDS Stress analysis, large deformation, tissue expander.

INTRODUCTION We will discuss here a variety of problems related to the questions (a) will fracture occur?, (b) why did fracture occur? and (c) where would fracture initiate? We will use some of the wellknown tools of fracture mechanics and some ~ 1 ~tinuum mechanical descriptions. An accurate continuum model won't always be available so we will adapt where possible plausible models from the literature. The first situation we consider is that of a benign ovarian cyst (such as shown in Fig. 1). This has grown over a number of months, the patient presumably just believing they were getting fat. What happens to the surrounding skin when the cyst grows to the size shown? We attempt an analysis of this in section 2. A reasonable account of the stresses produced in the surrounding skin can be given by solving the equations of a membrane theory but this requires a constitutive model of the skin. This is discussed in detail also in section 2 where possible fracture initiation sites are conjectured. Our second example is shown in (Fig. 2). This is the case of an implant inserted under the skin in order to provide skin for plastic surgery at a neighbouring site. The implant is expanded by inserting saline over a period of weeks thus stretching the surrounding skin. As seen in the figure there is a hole in the skin where the filling port of the implant has been inserted. This is not so important for the surgery since this is in the region of skin to be removed. Nevertheless, we would like this hole to be stable as the implant is expanded.

2

C. A TKINSON .....~,'~"~i/

i

a

.......... ~._.............

Fig. 1

I i

.....

I

Fig. 2 Our third example is related to the subject above only now we are concerned with the integrity of the implants. We describe some crude experiments, which test implants of different crosssection to destruction and attempt to rationalise the results using fairly simple theory. The membrane theory introduced to treat the example above can be generalised to materials which are reinforced by (almost) inextensible cords. Such materials are used for packers used downhole in oil wells. These are used for loading the formation and creating both micro and macro-hydraulic fractures, the microfractures are used to determine the effect of earth stress on near well bore stress fields, and macro-fractures to improve the yield of an oil well. A brief description is given in section 4.

SKIN STRETCHED OVER AN INCLUSION The situation we try to model is that shown in Fig. 1. To simplify matters we assume that the problem is cylindrically symmetric. This is somewhat of an idealisation since the cyst does not surround the whole of the torso. At any time, the geometry of the cyst is known (or can be measured by observation) so this fits (approximately) into the theory outlined in the Appendix. Since the deformation is large we need to monitor the cylindrical coordinates (r,O,z) of the deformed configuration compared to the undeformed ones (p,O, rl). ( p =constant)

F r a c t u r e Stress A n a l y s i s . . .

3

We have the principal extension ratios 21 __ d___~, A2 =--,r dr/ p

23=

h/h o

(1)

in the direction of the meridian, lines of latitude and normal to the deformed surface (see the Appendix equation (A. 1) and dr dz

= tan w

(2)

deduced from equation (A2). Also equations (A5) and (A6) give the geometry of the deformed skin provided we know both w and 21 in terms of 2 2 . Thus

z

P=+

~

cotwd2 2,

4 =+f~ d,~2

P

-

2 sin w

(3)

and r/ = q.. f 2

p

4)], 2

(4)

2 21 sin w

A 2 is known as the maximum expansion at the centre of the cyst. When the skin encloses the

cyst we know w(22) since the equation of this surface relates r and z. Also equation (A11) (Appendix) evaluated at A 1 = A1,/~2 A2 gives, since A 2 is k n o w n , the value of A1 at any other value of /~2 as a function 21(22,A2) once the energy function W is specified (in principle we can determine this from the properties of the skin). The value A 1 is still to be determined. The behaviour of the skin when it is not in contact with the cyst is given by equation (A12). If we assume P (the pressure between the skin and the fascia) is zero then equation (A12) reduces to ----

B OW 2-O,;C1 where B is an arbitrary constant. Thus we have unknowns B , A 1 and the location A 2 = A2* at which the skin and the cyst lose contact. In addition, we have three conditions we are COS W =

assuming symmetry about z = 0. At the unknown location A 2 =/l,2" both the skin and its tangent are continuous (i.e. at A 2 in Fig. 3) and at A 1 there is an additional condition. If this condition is that A 1 is fixed so that the initial length of the membrane is given as L say. Then (A6) gives the equation

2~ sin w

p

4

C. A TKINS ON

as the third condition. By considering the axial components of the forces applied on the section A 1A2 (with P0 - 0 ) one can deduce the condition F

COS 14'

4rcph o

(6)

for the axial force acting at A 1. We still need a constitutive equation for skin to complete the equations. One candidate goes back to Fung [1] who did some simple tissue extension experiments. With strain invariants I 1 - 212 -4- 2 2 2 nt- ,~,32,I2 - 2 1 - 2 nt- 2 2 -2 nt- 2 3-2 ,

(7)

and 13 - 1, if the material is incompressible, this example energy function has W(/~l,/~L2)

-- h 0 ]l~ [ey(II-3) -1]

(8)

Y Solving the above nonlinear equations gives from ~ ' 3 - - ( 2 ' 2 2 ) -1 =h/ho the decrease in membrane thickness with position and the possibility of thinning to breaking point. Another condition here is the absolute limiting strain to which a flap of skin can be stretched in vivo called the 'blanching point' at which enough of the circulation is cut off to cause the flap to die. One other possible modification of the above theory is to consider A 2 as a parameter monitoring the growth of the cyst and allowing (or observing) L to vary. If one allows L a virtual increase 6L and calculates the corresponding change in F one can perhaps calculate the energy release in such a virtual process and relate this to any debond resistance of the skin. A

A

A2

Fig. 3

Fracture Stress Analysis...

5

TISSUE EXPANDERS Figure 2 shows the effect of a tissue expander whose base plan-form is crescent shaped after it has been under the skin for a few weeks being filled slowly with saline. The circular hole in the skin where the filling port was, seems to have expanded symmetrically so the local stress field in the membrane as seen by the hole appears to be isotropic. I was asked by a plastic-surgeon friend (Mr Oliver Fenton) which expander would fail first a thick or thin one? To investigate this Dr Peter Long, Dr Ian Atkinson and I tested various expanders to destruction. We placed the expanders on a weighing pan and proceeded to fill them with a steady stream of water recording simultaneously the pressure in bars up to failure. The results are shown in Figs. 4 and 5 for expanders with a croissant plan-form (such as used in Fig. 2) and thickness between .020 to .026 inches and .012 to .016 inches. A thinner one .007 - .011 inches thick was also tested before we monitored the results in such detail. This "experiment" was also done for expanders with a circular plan-form of a similar range of thickness.

The Croissant Exp(]nder oo

2.5

""

":

24

9

:

C~ 2 k..

9~

3

D

9

-"

:

_o22

c21-

: "

9

9

.

"

-

.

"

"

: "

:

.0

....

.9 1.8

9. o 1 ~ ,

"

....

--,Otg

""9

9

......

:

.. ....

.

115 1.4

5

10

15

2o

25

Weight of w(]ter in exp(]nder in pounds Fig. 4

The croissant of thickness .020-.026 inches broke along the ridge when filled with 171bs of water and a pressure approximately 1.6 bars (1 bar - 14.7 psi). The thinner croissant .012.016 inches withstood a much larger volume of water (261bs) and went to somewhat higher pressures approximately 2.55 bars. The thinnest croissant .007 - .011 inches had similar pressures to each but we weren't monitoring the water volume then. This one didn't fracture in such a controlled manner as the others which opened up like a croissant cracking along the ridge.

6

C. A TKINSON

The Spherical Expander .012 - . 0 1 6 and .020 .026 -

2"615

24

~.~ '"~0"-°~'"

,'

~25 "£221 E20 ...

b-,17 16 ,

":

•

~ ....

~

1.5 6 ]0 15 20 2'5 Weight of water in expander in pounds .

.

.

.

.

Fig. 5 The circular cross-section expanders both went to 261bs before they broke pretty well at any location. How do we explain these results in particular the oscillatory nature of the pressure versus the weight of water (i.e. volume) curves or were they just an artefact of our experiment? Some idea of what is going on can be deduced from the behaviour of a spherical balloon under inflation. If one assumes an undeforrned spherical membrane with initial spherical radius r0 thickness to(t o << r0) and zero initial inflation pressure then at inflation pressure P(r) the sphere has radius r thickness t. Thus there is a uniform isotropic stretch of the membrane A -- r / r o and a transverse normal stretch i 3 = t i t o . Using the argument that the work done, by the surface tractions acting over a continuous simple path between two equilibrium states (without body forces), is balanced by the change in total strain energy one can deduce that the work done by the inflation pressure to increase the sphere volume is balanced by the elastic energy stored in the membrane. If one assumes for example that the stored energy function W

depends only on an 2 with W(1)= 0 one can deduce by the above argument (e.g. Beatty [2]) the formula P(2)=

for the inflation pressure P(2).

t° dW(2) r0A~ d2

(9)

Moreover, this will have a maximum at a pressure p* and

membrane stretch /%* provided there is a solution of the equation d p / d i at the solution of 2 d2W -2 dW

d~~

d-2 = o

= 0 which will occur

(] o)

Fracture Stress Analysis...

7

For an incompressible material W(I~ ,I s ),3, 3 = ,,l-2 (since 3,1 = A x in this case) and the formula for the inflation pressure for an incompressible isotropic hyperelastic spherical membrane can be written

(11) where /71 and ]7 1 are response functions that depend on 2 and are specified for a given material. This relation between pressure versus stretch of the balloon gives first a maximum and then a minimum before failure. This is reminiscent of the behaviour of the first parts of our experimental curves but does not reproduce all aspects. The well known observations of blowing up a balloon, that considerable effort must be exerted initially and that as the balloon gets larger inflation becomes easier until the pressure increases again until the balloon bursts, describe some of the qualitative results of our experiments but not the cyclical nature of the final stages. Much work has been done on hysteresis effects, on the effect of compressibility and foamlike materials (see [2] for a review). We note that for compressible models such as the Blatz-ko model of foamed polyurethane elastomer the above formula is replaced by

where for 2 < m < 5, the normalised pressure p has an absolute maximum after which it decreases to failure. Thus the above simple description indicates that a plausible explanation of our crude experiments lies in a continuum description of the elastomer (including memory effects) and a large deformation analysis of the actual implant geometry. Some experiments of the effects of the histow of the deformation on skin have been made by Mr. Michael Masser (private communication) by putting circular plan-form implants under the skin of pigs and inflating/deflating them over a period of weeks and much work continues on this general area.

FRACTURING FOR ENHANCED OIL RECOVERY There are many instances of fracture associated with the drilling of oilwells. Hydraulic fracturing is often used to enhance the yield of an oil well by causing a major fracture in the formation which will improve the flow of oil to the well. The accurate prediction of the direction and extent of such a fracture is critically dependent upon the state of stress in the rock prior to the fracture. To determine this state of stress a sleeve fracture is sometimes first created in an open hole (one that is not yet cased). This is done by expanding an inflatable packer against the borehole wall (Fig. 6) in order to stress the formation and create a fracture. The theory of these packer membranes reinforced by inextensible cords has been developed by Atkinson and Peltier [3] based on Kydoniefs [4]. This theory uses the arguments of the Appendix together with the constraints imposed by the inextensible cords. An experimentally determined energy function for the elastomer between the cords is used by [3] together with studying the influence of different cord arrangements and suggesting design features to avoid failure of the packer. For our present purposes we note that a certain pressure is required to

8

C. A TKINSON

expand the packer (or packers) against the borehole wall and any excess pressure is applied to the formation. Determining this touch-pressure and the subsequent geometry of the contact region requires solving a nonlinear equation. Once the contact region and stress on the wellbore wall is determined the stress field in the rock can be calculated and hence a quantitative analysis of a micro-hydraulic fracturing test (Thiercelin et al [5], Atkinson et al [6]). There are a variety of other related problems. When drilling through a known fault location there are problems to do with wellbore stability as well as stress measurement. For a recent analysis of this see Atkinson and Thiercelin [7]. For fracture in a cased well one has to analyse the stress field around an inclined, cased and cemented wellbore- an account of this is given in [8] and an analysis of subsequent crack growth in [9]. Finally, in principle one can perhaps determine crack length and direction if one can make displacement measurements inside a borehole. This is because a knowledge of traction conditions there plus the displacement measurements enables the whole stress-tensor to be evaluated (given some constitutive assumptions) and then subsequent deductions made (cf. [10] for straight crack growth and [ 11 ] for some ancillary tools for curved crack analysis).

.......

i!~ ~ili'~

!

!:

Fig. 6

ACKNOWLEDGEMENTS In addition to those mentioned in the text I should acknowledge Antonis, Beth, Mafia Jesfis, Marta, Rusudan and Tina for their help in preparing this article (they know who they are). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Fung, Y.C.B. (1967) Am.J. Physiology 213, 1532-1544. Beatty, M.F. (1987) App. Mech. Rev. 40, 1699-1734. Atkinson, C. and Peltier, B. (1993) J Eng. Math. 27, 443-454. Kydoniefs, A.D. (1970) Q.J.M.A.M. 23, 481-488. Thiercelin, M., Desroches, J. and Kurkjian, A. (1994) proc. Eurock'94, 921-928. Atkinson, C. Desroches, J., Eftaxiopoulos, D. and Thiercelin, M. (2000) (To be published). Atkinson, C. and Thiercelin, M. (1997), Int. J. Frac. 83,243-273. Atkinson, C. and Eftaxiopoulos, D. (1996) 20, 549-569. Eftaxiopoulos, D. and Atkinson, C. (1996) 2no Am. Rock. Mechs. Symp: NARMS (1996)

10. 11. 12. 13.

Atkinson, C. and Aparicio, N. (1999). Int. J. Sol. Struc. 36, 4889-4899. Aparicio, N.D. and Atkinson, C. (1997) Proc. Roy. Soc. A 453, 2207-2228. Kydoniefs, A.D. (1969), Q.J.M.A.M. 22, 319-331. Pipkin, A.C. (1968) Z.Angew.Math.Phys. 19, 818-819.

1127-1134.

Fracture Stress Analysis...

9

APPENDIX Axi-symmetric deformation of an initially cylindrical membrane of uniform undeformed thickness 2ho. Since any cylindrical membrane can be deformed into a circular cylinder without extension in its surface and the membrane theory neglects bending moments, there is no loss in generality in assuming that the undeformed membrane is a circular cylinder. We follow Kydoniefs [12] and assume that ( p , O , r l ) ( p =constant) are co-ordinates in the undeformed configuration and ( r , O , z ) a r e cylindrical co-ordinates in the deformed state. ~' measures length along the meridian curve in the deformed configuration. We use co to measure the angle of intersection between the tangent to the meridian curve and the positive z axis and P is the internal pressure in the deformed membrane. It is assumed that the deformed membrane is generated by rotating a continuous curve C about the z axis. Since the deformation is axially symmetric the principal directions of strain coincide with the tangents to the meridian, the lines of latitude and the normal to the deformed surface. The principal extension ratios which correspond to these directions are 3.1,/],2,/~'3 respectively where

/]'1 ---- d____~,

dr/

~['2 = r / p ,

/]'3 = h / h 0

(A. 1)

where 2h is the variable thickness of the deformed membrane, /]'2 is, of course, the extension ratio of an azimuthal curve which initially has length pd0 and length rdO after deformation. Then dr

d~

dz ~ = cosce,

= since,

d~

(A.2)

Further if K 1 is the curvature of the meridian curve of the deformed surface than K 1 is a principal curvature of the deformed surface the other being

K1 = d(coso.)),

K 2

where

K2 = cosce

dr

(A.3)

r

A principal curvature is positive when the corresponding centre of curvature is on the same side of the surface as the inward pointing normal. Defining T1 as the stress resultant in the direction of tangents to the meridian curve (i.e. force per unit current area) and T2 as the stress resultant in the directions of the tangents to the curves of latitude, then the equations of equilibrium can be written

dr

= T 2,

K1T I + K z T 2 = P

P is the excess of the pressure on the side nearest the axis of symmetry over that on the side furthest from the axis. From equations (A.1) and (A.2) it can be deduced that

(A.4)

10

C. A TKINSON

z = + Icot cod2,2 ' P A~

~: d2 K P = +A"2sin co

(A.5)

where the positive or negative sign is chosen according to whether 22 is an increasing or decreasing function of ~ and ~ = 0 for z = 0 and A 2 is assumed to be the value of 22 at Z=0.

Also r/ = i! d22 p 21 sin co

(A.6)

Where r/ is measured from the cross-section of the undeformed body which corresponds to the cross-section z = 0 of the undeformed body. Using (A.3) in (A.4) gives d cosco rT 1 ~ + (cos co)T2 = rP dr or using ( A . 4) 1

a(rr~ cos co) dr

(A.7)

= rP

If in addition we assume strain energy/unit area of the undeformed sheet to be W(/~,l,/~2) . This assumes variation of deformation through the thickness of the sheet plus stored energy due to bending and shear in a direction normal to the surface are neglected. The Pipkin ( ) shows via a minimum energy argument that we can write T~ =

1 c3W

----,

2 2 0)]q

T2

=

1 c3W

(A.8)

/7~1 0/TL1

If we multiply (A.4) 1 by 21 we get

21 d r

(A.9)

= 022

and since 22 = r / p ( p constant)

d

21

= 21

c3W d2q c321 dr

dA,2 0 W = ----+ dr c3A,2

OW dA,1 d W . . . . 021 dr dr

(A.IO)

Fracture Stress Analysis...

11

using (A.9). Hence integrating with respect to r gives

W--J~, 1

where A is constant of integration.

c~W c~2~

----

A

This equation gives

(A.11)

21 as a function of

substituting into the equation (A.8) we have the stress resultants in terms of

22

/L2

thus

(except for the

constant A). Since 2 2 = r i p and p is constant (A.7) can be integrated to give cos(c0(22) ) where P is specified. Thus when P = P0 constant we have

cosco =

pP0222 + B

where (A.8) has been used and B is a constant to be determined.

(A.12)

This Page Intentionally Left Blank

13

SOME ASPECTS OF FATIGUE OF ENGINEERING MATERIALS HAEL MUGHRABI Institut ffir Werkstoffwissenschaften, Lehrstuhl I, Universitfit Erlangen-Nfirnberg Martensstr. 5, D-91058 Erlangen, Federal Republic of Germany ABSTRACT Fatigue failures are generally the result of repeated plastic cyclic microstrains leading ultimately to the initiation and propagation of cracks. Fatigue crack initiation (and propagation) can occur in different ways and is frequently preceded by some form of cyclic strain localization. In this presentation, examples will be given of different types of fatigue studies on a number of metallic engineering (and model) materials. The aim will be to highlight different aspects of fatigue behaviour and to illustrate different experimental approaches in the study of fatigue phenomena. Some topics of current interest will be addressed, referring to recent work on the fatigue behaviours of materials of ultrafine grain size, metal-matrix composites, a cast magnesium alloy and, finally, the high-temperature fatigue of monocrystalline nickel-base superalloys. KEYWORDS Fatigue life, ultrafine grain-size materials, metal-matrix composites, cast magnesium alloys, nickel-base superalloys, elastic compliance, damage parameter, fatigue crack initiation, fatigue crack propagation, microstructure. INTRODUCTION Fatigue fracture is one of the most common types of materials failure. It occurs in materials and components subjected to repeated cyclic loads which would normally not cause damage, if applied only once monotonically. It is now well established that fatigue damage originates from (small) repeated cyclic microstrains (in the order of 10.5 to 10-2) which ultimately lead to some form of strain localization, followed by subsequent initiation and propagation of cracks in the case of ductile materials and to almost immediate propagation of cracks in the case of less ductile high-strength materials. Thus, the behaviour of materials under cyclic loads is a subject of considerable interest, both from a fundamental and a technological point of view. Cyclic plasticity is by itself an interesting topic which deals with the cyclic stress-strain response and the underlying (bulk) microstructural processes occurring during the cyclic microplastic deformation which precedes the localized processes of initiation and spreading of fatigue damage. Figure 1 illustrates schematically the sequence of events of cyclic deformation and fatigue damage [ 1].

14

H. MUGHRABI

THE FATIGUE PROCESS CYCLIC DEFORMATION

i

FATIGUE DAMAGE

9HARDENING(SOFTENING) 9SATURATION (MICROSTRUCTURALCHANGES

STRAIN 9 LOCAUZATION /

CRACK 9 INITIATION(SURFACE)

THE BULK)

CRACK 9 PROPAGATION

/ 9STRAINLOCALIZATION ~ J

(J..Q_~JT.~.~TRANS-, INTERGRANULARPROCESSES) ~ J

BASIC DISLOCATION MECHANISMS

1

irreversible cumulative plastic strain

FATIGUE FAILURE MECHANISMS

1

crack propagation rate

Fig. 1. Sequence of events during cyclic deformation and fatigue. After Mughrabi [ 1]. In this presentation, the emphasis will be laid on the description and characterization of different types of life-limiting fatigue damage. After a short introduction to fatigue life diagrams, examples will be given of different types of fatigue studies on a number of metallic engineering (and model) materials. The aim will be to demonstrate some of the varieties of fatigue behaviours, to reveal some basic relations between microstructural processes, cyclic plasticity and fatigue failure and to illustrate different types of experimental approaches. Several topics of current interest in the author's research group will be addressed, referring in particular to recent studies on: 9 fatigue of materials of ultrafine grain size (UFG) 9 fatigue of particulate-strengthened aluminium-matrix composites 9 fatigue of a cast magnesium alloy 9 high-temperature fatigue of monocrystalline nickel-base superalloys. FATIGUE LIFE DIAGRAMS Confining ourselves to symmetric push-pull fatigue, it is important to distinguish between different kinds of strain ranges. The latter are defined as the difference between the maximum and the minimum strains and are thus equal to twice the corresponding amplitudes. Then, the total strain range Ag t is related to the sum of the elastic strain range A~el and the plastic strain range Aepl: AEt = AI3el + AEpl

(l)

It has become common practice to express the fatigue life Nf (number of cycles to failure) alternatively in terms of Aet, Aeel and Aepl through the following relations [2,3]: A~el/2 = - ~ ( 2 N f

(2)

A~., / 2 = ~f (2N r )c

(3)

P_,

and

13'f A~;t/2=_E_(2Nf )b

+ ~;'f(2Nf )c .

(4)

Some Aspects of Fatigue of Engineering Materials

15

Here, 2Nf corresponds to the number of stress reversals, E is Young's modulus, CYf and t;t are the fatigue strength and ductility coefficients, respectively, and b and c the fatigue strength and ductility exponents, respectively. Equations (2) and (3) represent the well-known fatigue life laws of Basquin and of Manson-Coffin that were originally introduced in order to describe low-amplitude long-life fatigue (HCF: high-cycle fatigue) and high-amplitude short-life fatigue (LCF: low-cycle fatigue), respectively. It should be noted that, by relating the stress range Aa via Hooke' s law to the elastic strain range At;el, the Basquin relation can be written in the form

At3"= At;el" E = cr,f(2Nf)b. 2

(5)

2

If the stress amplitude A~/2 is now plotted against log Nf, one obtains the standard W6hler or S-N curve (S" stress, N: number of cycles (to failure)). The relationships (1) to (3) are displayed best in a double-logarithmic plot of strain amplitudes versus fatigue life Nf, as shown in Fig. 2. In this plot, the total-strain fatigue life relationship appears as a curve which approaches asymptotically straight lines corresponding to the Manson-Coffin and the Basquin relationships (3) and (2) in the LCF- and HCF-limits, respectively. The slopes of these straight lines lie typically in the ranges c = -0.5 to-0.6 and b =-0.05 to-0.15 [2,3]. For 2Nf = 1, i.e. in the case of monotonic deformation, these straight lines intersect the ordinate at t;f and r respectively. It is important to note that t;f and ~f can be set approximately equal to the monotonic fracture strain and strength, respectively [2,3]. It is then immediately obvious that the prerequisites for good fatigue performance in the LCFand in the HCF-regimes are high values of fatigue ductility (t; f ) and strength (cri) coefficients, respectively. Since these requirements cannot generally be fulfilled simultaneously, a good compromise between a "ductile" low-strength and a "strong" lowductility material is a "tough" material with intermediate strength and ductility, compare Landgraf [3].

,;

/+'7

A

....

9

,

(2Ne) + 6t (2N

o

(Basquin) r

i'/"

o

o',

0 I/I 0

Q,t

Elastic

m 0,.

E

("s

~

I\

~

I

~

i~

Ii

0 I,__

tO .

.

.

.

~

u,

Plastic

~{'Manson-Coffm)

~

2Nt

Reversals to Failure (10gscale}

__

?_N~,

Fig. 2. Schematic illustration of total-strain fatigue life plot and Basquin and Manson-Coffin plots in the limits of HCF and LCF, respectively. Courtesy of Landgraf [3].

16

H. M U G H R A B I

It is interesting to note that, although the Manson-Coffin and the Basquin fatigue life laws were generally considered to apply specifically to the cases of LCF (Aeel > Aeel) and HCF (Ae~l = A~/E > Aepl) respectively, it is frequently found that the fatigue lives can be described satisfactorily over a large range, from LCF to HCF, by either of these two fatigue life laws [4,5]. In some cases, however, conceming in particular high-strength materials, unrealistic (usually too high) values of e'f, c, ~'f and b are found, compare [5]. In the following, we shall discuss examples of fatigue behaviour which are intimately related to these simple concepts. FATIGUE OF MATERIALS OF ULTRAFINE GRAIN SIZE In recent years, there has been an increasing interest in the assessment of the strength properties of ultrafine-grained (UFG) material produced by the equal-channel angular (ECA) extrusion technique, compare Valiev [6] and the proceedings of a NATO Advanced Research Workshop dedicated last year to this topic [7]. In contrast to other properties such as the grain size dependence of the flow stress that have been investigated more extensively, the fatigue behaviour has not been studied as systematically so far. Thus, systematic fatigue studies have almost been confined to copper [8] which has served as a popular model material in earlier fatigue studies on materials of conventional grain size. The earlier work of Thompson and Backofen [9] on the fatigue strengths of aluminimn, copper and a-brass in stress-controlled tests had led to the conclusion that the fatigue strength in a W6hler diagram is influenced not only by Hall-Petch strengthening but equally or even more by the cyclic slip mode. Thus, these authors noted that, in their study, the biggest improvement of the fatigue strength by grain refinement was found for a-brass which is a so-called "planar-slip" material, whereas much smaller effects were observed in the case of the "wavy-slip" materials copper and aluminium. The yield stress and tensile strength of UFG copper produced by ECA-extrusion with a typical grain size between 150 and 250 nm exceed the corresponding values of material of conventional grain size considerably [6]. Because of the enhancement of (Yi, one would therefore, in accord with Fig. 2, expect an improved fatigue performance in stress-controlled tests in an S-N plot. However, since the ductility of UFG material is generally reduced, this would not automatically imply that the fatigue performance in a strain-controlled test (in a Manson-Coffin diagram) would also be improved. The experimental fatigue life data obtained so far on UFG copper [10,11,12] are in line with these expectations. Thus, it is not surprising that Agnew et al. [11] observed a significant enhancement of the fatigue strength in stresscontrolled tests, as shown in Fig. 3a, when comparing their results with data of other authors for material of conventional grain sizes [9,13]. On the other hand, all data obtained so far in strain-controlled tests on UFG copper [10,11,12] revealed a significant reduction of fatigue life at a given plastic strain amplitude, compared to copper of conventional grain size. Figure 3b shows a Manson-Coffin plot obtained by Agnew and Weertman [ 10] in total-strain-controlled tests. The fatigue lives were found to be generally shorter than those reported earlier by Tavemelli and Coffin [ 14] on copper of conventional grain size. The reason for the disappointing plastic strain fatigue resistance lies in the inherently metastable nature of the microstructure of the severely deformed ECA-extruded material [10,11,12,15,16] which has been shown to undergo strong cyclic softening caused by partial recrystallization and grain growth, when subjected to cyclic straining at room temperature. Furthermore, while persistent slip bands (PSBs) in their usual meaning (with the so-called ladder structure), compare [ 1], do not form in UFG material, massive large-scale shear banding

Some Aspects of Fatigue of EngineeringMaterials 200

a)

9

9 ~ .... --Z"

9

180 ~ 160 <1 140

17

Agnew et al [11 ]., UFG Cu, 250 nm Thompson and Backofen [9], 0.0034 mm Lukas and Kunz [13], 0.07 mm Lukas and Kunz [13], 1.2 mm

"''''4.~

~ 120 "& 100 '~ oo r~o

80 60 4O..

b)

105 106 Number of Cycles, N

04

. . . . . . . .

i

. . . . . . . .

i

. . . . . . . .

i

. . . . . . . .

i

107

. . . . . . . .

i

',

,

,

~,

,,~

- o - S P D Cu, A g n e w and W e e r t m a n [10] +

1

* +

§

§

++

+ O F H C Cu, T a v e r n e l l i & C o f f i n [14] +

§

0.1 0.01 0.001 i

0.1

i

.......

I

1

. . . . .

,,,I

10

,

,

.....

iI

100

,

,

,,

....

I

,

1000

,

1111111

10 4

,

. . . . . .

10 s

Cycles to Failure, Nf Fig. 3. Fatigue lives of fatigued UFG copper specimens, a) S-N plot. After Agnew et al. [11 ]. b) Manson-Coffin plot. After Agnew and Weertman [ 10]. Courtesy of the authors.

Fig. 4. Large-scale shear banding and crack initiation in fatigued UFG Cu which had been given a pre-annealing treatment (170 ~ 2h). Stress axis horizontal. From Brunnbauer [12]. Courtesy of the author.

18

H. MUGHRABI

inclined at about 45 ~ to the stress axis is observed at the surface (and also in the bulk in the form of elongated planar dislocations cells). Figure 4, taken from the work of Brunnbauer [12], shows an example. Attempts to improve the stability of the metastable grain structure by a suitable annealing pretreatment have been partially successful. For example, Brunnbauer [12] has observed an enhancement of fatigue life by almost an order of magnitude in a Manson-Coffin plot for ECAextruded copper after a pre-annealing treatment at 170 ~ for 2 hours. At the same time, the "saturation" stress level was, of course, reduced but still remained above that of conventional grain-size copper. Since the processing parameters of the ECA extrusion can still be optimized by systematic variation [17], it is believed that there is still room for further improvement of the fatigue performance of single-phase material like copper. In the case of commercial metals and alloys, the prospects of obtaining enhanced fatigue resistance are probably better [ 18,19]. In particular, metals of hexagonal close-packed structure are less prone to cyclic softening [19], presumably because of the limited number of slip systems available. Hence, further efforts probably have a good potential. FATIGUE OF ALUMINIUM-MATRIX COMPOSITES The use of light metal-matrix composites (MMC) has increased in recent years because of their higher strength and improved strength-to-weight ratio. Among the mechanical properties, the fatigue behaviour is of particular interest. Here, we shall confine ourselves to the discussion of some recent observations on the T6 peak age-hardened A1203 particulate-reinforced aluminium-matrix composites AA 6061-A1203-15p-T6 and AA 6061-A1203-20p-T6, containing volume fractions of particles of fp = 15 % and fp = 20 %, respectively [20]. The MMC with the higher volume fraction of reinforcement is characterized by a higher strength but shorter fatigue lives in strain-controlled tests. In this study, a particularly interesting aspect of fatigue damage concerns the fracture and decohesion of particles, as it is revealed in variations of the non-linear (elastic) compliance of the material. It had been shown earlier that the differential Young's modulus of an undamaged material ED(~ ) =

dcy

(6)

de el

becomes noticeably stress-dependent at larger stresses in the sense that ED decreases (increases) at higher tensile (compressive) stresses [21]. This is a consequence of the anharmonicity of the atomic potential which is probed increasingly, when a material is strained to higher and higher elastic strains, giving rise to an increasingly non-linear elastic behaviour. The latter can be taken into account by adding a second-order term in Hooke's law, so that = E o .eel + k .eel

.

(7)

The constant Eo corresponds to Young's modulus in the linear Hooke approximation in the limit of vanishing G, and k is a constant which describes the deviation from linear elastic behaviour. The constant k is always negative. From Eqs. (6) and (7) follows that the differential Young's modulus is given by E D = ~Eo 2 + 4key

(8)

Some Aspects of Fatigue of EngineeringMaterials

19

Now, in the case of a damaged material, the load-bearing cross section decreases (increases) progressively with increasing tensile (compressive) stress. Therefore, in the stress-strain response curve, the tangent modulus decreases (increases) in a qualitatively similar fashion as the differential Young's modulus of the undamaged material. Thus, in a damaged material, the behaviour may be described by Eqs. (7) and (8), but then Eo and k no longer have the meaning of material constants. The difficulty is, of course, to separate the intrinsic non-linear behaviour from the additional non-linear contribution which superimposes, when the material is damaged and which can be considered as a direct measure of the damage. In the case of the fatigued aluminium-matrix MMC with a volume fraction of A1203-particles of 20%, it was found that both Eo and k (which can be determined from the shape of the hysteresis loop [20,21 ]) decrease during cycling. However, the (smaller) value of Eo in tension decreases more rapidly than the value of Eo in compression. It is found that Eo and k depend in an interesting manner on the total strain amplitude Act/2, as shown in Fig. 5 for N = Nf/2 cycles. At low amplitudes, Eo and k (in tension) are constant (Eo = 97.9 GPa, k = -502 GPa), as expected. Starting at about Act/2 = 0.004, Eo begins to decrease and becomes constant again at Act/2 = 0.007. The parameter k decreases continuously. From these results, it could be concluded that at total strain amplitudes which exceed a value of about 0.004, particle fracture occurs. This conclusion is consistent with metallographic observations of broken particles. It should be pointed out that, in an earlier study of monotonic deformation, Lloyd [22] also related a decrease in Young's modulus to an increase of the fraction of broken particles. 100 [

- 1000

98[ O

9

96

-800 -

E0 o

--o-- k

94 92

N=Nf/2

.O O

-600

fp = 20 vol. %

o . . . . "0 . o .

RT 90 ~

2

4

6

8 10 Act/2/10 -3

-400

Fig. 5. Variation of Eo and k in a fatigued aluminium-matrix composite as a function of total strain range Act, indicating particle fracture at A~t > 0.004. From Hartmann et al. [20].

In the case of MMCs, there is a difficulty to relate the variations in the non-linear compliance quantitatively to the loss of load-bearing cross section, since the Young's moduli of the matrix (~ 68 GPa) and of the particles (~ 380 GPa) differ very strongly. Moreover, since the damage is more or less homogeneously distributed internally and not in the form of discrete propagating cracks, the non-linear variations of the compliance cannot be evaluated reliably in order to obtain information on crack propagation. As will be shown in the next section, the approach described above can be applied advantageously in the case of more homogeneous materials such as the cast magnesium alloy AZ91.

H. MUGHRABI

20

FATIGUE OF THE CAST MAGNESIUM ALLOY AZ91

Fatigue Lives The magnesium alloy AZ91 has recently found, once again, much interest because of its low specific weight which makes it an ideal material for light-weight components in the automotive industry. The fatigue life data of the alloy AZ91 HP (HP: high purity), were obtained in totalstrain-controlled tests at both room temperature and at 130 ~ [23]. The data for 130~ are shown in Fig. 6. It is evident that the fatigue data can be represented equally well over the entire range of fatigue lives by either the Manson-Coffin or the Basquin fatigue life law with reasonable values of the fatigue coefficients ( ~'f, (Y'f) and exponents (c, b).

10l~:.::.:>.~ ~ --._~ _

9 A~zt/2 zx Aeel/2

T = 130 ~

I

10 -2 ~ 1 0 "3 10 -4

Manson-Coffin: 10 -5 10 -6 . . . . . . . . . . . . . . . . . . . . . . . . . . 1 101 10 2

Acpi/2

=

0.0642x(2Nf) "~

' ................................... 10 3 10 4 10 5 10 6 10 7

2Nf Fig. 6. Fatigue life data of magnesium alloy AZ91 at 130 ~

From Eisenmeier et al. [23].

Fatigue Crack Initiation at Casting Cavities The metallographic observations on fatigued AZ91 indicate that crack initiation occurs at casting contraction cavities at or near the surface, as reported by Mayer et al. [24] and Eisenmeier et al. [23,25,26]. Similar types of unusual (subsurface) crack initiation have also been observed on cast aluminium alloys [27,28]. Hence, there was an interest to explore the mechanisms of this kind of crack initiation at cavities at or just beneath the surface. For this purpose, model FEM calculations were performed by Borb61y [29] in order to determine the local stress fields and the equivalent (von Mises) plastic strains around spherical cavities situated at the surface or at different distances from the surface. Figure 7 shows as an example the distribution of the equivalent plastic strain around a spherical cavity of radius r at a distance d (measured from the centre of the pore) to the free surface (on the right) for r/(r + d) = 0.4. The external stress is applied in the z-direction. For reasons of symmetry, only one quarter of the cavity had to be considered in the calculation.

Some Aspects of Fatigue of Engineering Materials

y

..A

.

.

.

.

.

.

.

.

.

21

A

.

4

"i~" free .~ surface

0.035 0.028

4 a

4

0.021 0.014 0.007

...... .

0.000 Fig. 7. Distribution of equivalent plastic strain around near-surface cavity of solid stressed in zdirection for r/(r+d) - 0.4. Total strain in z-direction: 1%. Courtesy of Borb61y [30]. As expected, one finds equivalent plastic strains of appreciable magnitude in the immediate vicinity of the cavity, especially on that side of the cavity lying closest to the free surface, on the right-hand side. Fig. 8 shows the maximum normal stress 033 (in the z-direction), normalized with respect to the "average" stress ~av as a function of r/(r + d). This stress is maximum for r/(r + d) - 0.5, which corresponds to d = r, i.e. to a "half" cavity situated at the surface, and decreases as r/(r + d) increases to 1 (i.e. d = 0) or decreases for d > r. Thus, it is to be expected that crack initiation will occur preferentially at "open" cavities lying at the surface. On the other hand, the maximum stresses and equivalent plastic strains in the "bridge" of material between the free surface and a cavity lying just underneath the surface (r/(r + d) < 0.5) are so high that (cyclic) strain localization (along a maximally stressed slip system), leading to crack initiation, seems possible. Thus, subsurface initiation of fatigue cracks at cavities lying just beneath the surface appears to be a probable and plausible mechanism in addition to fatigue crack initiation at "open" cavities at the surface.

i

D ~

,

0.0

I

0.2

~

I

I

0.4

0.6

~

I

0.8

1.0

r / (r + d)

Fig. 8. Maximum normal stress ~533 in direction of stress axis near cavities of radius r at distances d from the surface for 0.2 < r/(r+d) < 1. Courtesy of Borb61y [30].

H. MUGHRAB1

22

Fatigue Crack Propagation, Crack Closure and Opening As described in [25,26], the propagation of fatigue cracks was studied by a combination of surface replica studies, compare [29], and measurements of compliance in order to obtain the differential stress-dependent Young's modulus ED, as defined in Eqs. (6) and (7). The modulus ED was measured both as a function of the number of cycles and also intermittently within closed hysteresis loops. As shown below, it was thus possible to obtain information on the propagation of cracks not only along the surface but also into the depth. In addition, from the "in situ" compliance measurements during a closed cycle, crack opening and crack closure stresses could be determined. Figure 9 shows a sequence of traces of cracks obtained from surface replicas taken intermittently in a fatigue test after different numbers of cycles, employing the technique first applied by Ebi [29]. This technique permits to trace back the evolution of the fatal crack to its origin shortly after its initiation. In the case of the cast magnesium alloy AZ91, obviously many small cracks initiate almost simultaneously at contraction cavities, as described before. Then, the propagation of the cracks occurs by the coalescence of these microcracks.

-"

--~"--~

N= 150

"--~

N = 300

-~

N = 705

0.3 mm

s N = 906

Fig. 9. Traces of coalescing fatigue microcracks in AZ91, forming the main crack, as observed in a sequence of surface replicas after different numbers of cycles N. Aet/2 = 5x 103, T = 20 ~ From [25,26]

The loss of load-bearing cross section is reflected directly in appropriate compliance measurements, making use of the relations (6) to (8). Thus, Fig. 10a shows an example of elastic unloadings during a cycle early in the fatigue test, when there still exists no fatigue damage. It is important to note that, in this figure, the stress ~ is plotted against the plastic strain in the linear Hooke approximation, i.e. against •pl---- 8 t - ~/Eo. In a plot of ~ versus total strain et one usually obtains (very narrow) hysteresis loops of unusual, sometimes sickleshaped form [21], which do not reveal the effects in which we are interested here. Fig. 10a shows that the slopes of the unloading paths, which are vertical in the limit of vanishing stress, decrease a little at higher tensile stresses and become slightly negative at higher compressive stresses. This is typical of the intrinsic non-linear elastic behaviour.

Some Aspects of Fatigue of EngineeringMaterials 100

23

100

a)

b) 50

50

0

~

-50 -100

0

-50

-0.'04

,

0.()0

,

,

0.04

,

-100

0.08

0.00

-

0.;2

~t-~/Eo/%

,

0.;4

,

0.06

~t-a/Eo/%

Fig. 10. Hysteresis loops in the form of c vs. (~;t- (y/Eo) of fatigued AZ91 with intermittent elastic unloadings, Act/2 = 2.25x 10-3, 20 ~ a) Early in fatigue life, N/Nf ~ 10 %. b) Late in fatigue life, N/Nf ~ 80 %. From [25,26]. Fig. 10b shows examples of intermittent elastic unloadings later in the test after fatigue damage had spread over a larger part of the cross section. Now the effects described above for the intrinsic non-linear behaviour become very much more pronounced and reflect the superposition of an appreciable additional non-linear component due to the fatigue damage. The variation during the cycle of the differential elastic modulus ED, according to Eqs. (6) and (7) (with appropriate values of Eo and k) is plotted in Fig. 11 as a function of the stress o. It should be noted that this figure shows two important features, namely the intrinsic stress dependence of ED for the specimen with closed cracks (upper line and dashed extension) and the stress dependence (with damage), after the crack has opened at a tensile stress of about +12.5 MPa (lower inclined line). Crack closure (opening) corresponds to the jump AED from the lower (upper) to the upper (lower) line at a compressive (tensile) stress of about -25 MPa (+12.5 MPa), as the stress is decreased from tensile (compressive) to compressive (tensile) values. The quotient AED/Eo represents an appropriate damage parameter which is related to the loss of load-bearing cross section [25,26]. 42 41

t~

4O

~39

L

38 37

9 compression to tension .A,tension t 9 c9nlPres~ion . . . .

-100-75

-50

-25

0

25

50

75

100

o/MPa Fig. 11. Differential elastic modulus ED (stiffness values), as determined by the intermittent elastic unloadings shown in Fig. 10b. From [25,26].

24

H. MUGHRABI

Finally, in Fig. 12, the development of the crack length is plotted, as deduced by different methods [25,26]. The damage parameter AED/Eo is approximately proportional to the length of the main crack, as observed on the replicas, up to about 80% of fatigue life and then deviates toward higher values. This behaviour reflects the fact that the crack obviously first spreads mainly along the surface and then propagates into the bulk only at a later stage. The magnitude of the deviation reflects the mean depth of the crack into the bulk. In Fig. 12, another set values of AED/Eo which were determined automatically solely from the stiffness values at the load reversal points in tension and compression are also plotted. In this case, AED is given by 2

Eo + 4kCrT - ED (O'T)'

AE D =

(9)

where ~T is the stress at the tensile reversal point and ED(CYT)the stiffness of the damaged specimen at that point. The first term refers to the undamaged specimen. The good agreement between this damage parameter and that derived from the elastic unloadings is emphasized. In summary, the experimental approach described above can be considered novel and has the merit of obtaining crack growth data (in a quasi non-destructive manner) during a standard fatigue test on a plain (unnotched) specimen without the need to use a standardized fracture mechanics specimen. The work reported here has been complemented by a mesomechanical model of fatigue crack initiation and growth which describes the fatigue crack growth and fatigue life data very satisfactorily [31 ]. 14 12

9 A

crack length from replicas AED/E0 by unloading tests

10

--

AED/E0 from stiffnesses at l tensile peak stresses # l

8

=

P

6

A~t/2 = 5 x

0

0

400

12

/ / ~

N

2

/

10 -3

T = 20 ~

4

/ J

16

~ n

<3

~ 9 I

....

800 N

,

I

1200

n

0 1600

Fig. 12. Evolution of crack length (main crack) at the surface (replicas) and in the bulk (see text), as derived from the damage parameter AED/Eo in different ways. From [25,26].

HIGH-TEMPERATURE FATIGUE OF MONOCRYSTALLINE NICKEL-BASE SUPERALLOYS As the last example in this series of studies of metal fatigue, some aspects of the fatigue of monocrystalline nickel-base superalloys will be presented and discussed. Monocrystalline nickel-base superalloys are the most important high-temperature materials used in the manufacture of turbine blades. They derive their strength from a high volume fraction (up to about 70%) of the ordered 7' precipitates, embedded coherently in the 1( matrix. These

Some Aspects of Fatigue of EngineeringMaterials

25

precipitates are initially, in the as heat-treated state, cuboidal with an edge length of about 0.5 ~tm. The high-temperature deformation of these superalloys depends markedly on temperature and stress. At intermediate temperatures up to about 850 ~ and at rather high stresses, the particles retain their cuboidal shape and are cut by the dislocations. At higher temperatures and somewhat smaller stresses, the 3" particles tend to transform to plate-like precipitates (so-called rafts) which, for all common superalloys, lie perpendicular to the stress axis in the case of tensile (creep) deformation and parallel to the stress axis in the case of compressive (creep) deformation. Usually, the rafts are found to accelerate the creep rate and thus reduce the creep strength. Also, it has been found that the rafts lying perpendicular to the stress axis enhance the fatigue crack propagation, for reviews, compare [32,33]. At not so high temperatures and consequently rather high stresses, the cyclic deformation behaviour of monocrystalline nickel-base superalloys (in strain-controlled tests) is characterized by correlated cutting of the 3" particles along crystallographic slip planes. Figure 13, from the work of Obrtlik et al. [34] on the fatigue of the alloy CMSX-4 at 700 ~ shows an example of a transmission electron microscope (TEM) picture with such crystallographic slip bands. The latter bear some resemblance to the well known persistent slip bands (PSBs) and are the cause of early fatigue damage. At higher temperatures (and lower stress levels), such "PSBs" are not observed, and the fatigue behaviour is quite different.

g=(l~l)"~x i ...... ,

.~"i.,?~i;r

i~71!~ ...............!~........ ,..y:!:~l.!. "

..........i!!i!i!

.,.

.i~.... N i~

.,..:..:, .... ~ - -

stress

2 lam

Fig. 13. TEM micrograph of ,,persistent slip bands" in the monocrystalline nickel-base superalloy CMSX-4 after fatigue at 700 ~ Stress axis horizontal. From Obrtlik et al. [34]. Courtesy of the authors.

In the work to be reported here [35,36], the isothermal high-temperature fatigue strength of monocrystalline nickel-base superalloys was studied with the aim to improve the fatigue strength. For this purpose, a high-temperature pre-deformation (ca. 0.4%) in compression was applied in order to introduce a raft structure parallel to the stress axis. Fatigue cracks that usually initiated at oxidized casting pores at the surface were effectively retarded by these 3"

26

H. MUGHRABI

rafts, and fatigue life was enhanced, as shown for one example in Fig. 14 [35]. In this case, the cyclic hardening curves (plot of A~/2 versus N) are compared for monocrystalline CMSX-6 specimens with three different y/y' morphologies, namely the cuboidal y' precipitates and y/y' raft structures lying either parallel or perpendicular to the stress axis. These raft structures had been introduced by suitable pre-deformations (in high-temperature creep) in either compression or tension, respectively. It is evident that rafts lying perpendicular to the stress axis reduced fatigue life, while rafts lying parallel to the stress axis led to a longer fatigue life. In Fig. 14, also the (negligible) mean stress (Ym is plotted, since in these experiments care was taken to compensate the mean stress. The latter always arises unavoidably as a consequence of a unidirectional pre-deformation [35] and could of course affect the fatigue behaviour, unless it is compensated as in the present case. 400

N

200

~E t3 cq~

pre-deformed in tension

without predeformation

~ i(-m~

-100

in compression . . . .

,

0

pre-deformed

,

I

2000

,

,

,

I

4000

,

,

,

I

6000

,

,

,t

8000

number of cycles, N Fig. 14. Cyclic deformation curves of fatigued specimens of the monocrystalline nickel-base superalloy CMSX-6, with three different initial y/y' microstructures (cuboidal y' particles, y/y' rafts parallel and perpendicular to the stress axis, respectively), fatigued at Aet = 0.9 % at 950 ~ with compensated mean stress am. From [35]. The reasons for the observed influence of the y/y' microstructure on the fatigue behaviour are revealed by studies of the crack propagation, as illustrated with the scanning electron micrographs (SEM) shown in Fig. 15. These micrographs were taken in sections perpendicular to the main crack plane and near the crack tips. It was found that the rafts lying perpendicular to the stress axis (Fig. 15b) provide the easiest and fastest crack paths, since the crack can avoid cutting the y' plates. On the other hand, rafts lying parallel to the stress axis (Fig. 15c) obstruct crack propagation efficiently and even induce the crack to deviate into a direction that can be almost parallel to the stress axis. In this case, the crack driving force is strongly reduced. The original cuboidal y' structure (Fig. 15a) is intermediate between these two extremes in its interaction with the crack tip. Finally, it is interesting to note that it could also be shown that the introduction of rafts lying perpendicular to the stress axis improves not only the hightemperature fatigue resistance but also the creep strength [36] for strains of some percent and can therefore be considered as generally beneficial for enhancing the high-temperature strength.

Some Aspects of Fatigue of Engineering Materials ........... , . 0 . , , .............. ~ , m ,. . . ........... . . . . . . . . . . . .................................................................... :.

....

j~i;..::~::~::z:::~i:;~:.:..~i:~:~!~

':.~i~ ......

9~:~i~ii!~,~.. ~i~|'I|i

~:; 9 . ~

!!~]~ '"

':: .............

9 ~.-:.::~i~

~ ~.i.... :ii :.,,~ ,~ ~ .

::

~

~

~ ..... . . . . . . . . . . . . . . . . . . . "

~

................... !;Q;::

........~9 ~ : 9 ~ 9

'~ ~ . ~

:~ ~i~i~. ~

,

,~.,......

.~"

"~:~,,..::.i

~"

' .:::":: :. . ::i:::i :;:. :~..::;:::h.:..........

..

~

:~:.:::

":;:~.............~7.:::!-Y~: ~::~,

~.....-.~

....

::

: 9..........~9 ........ .......................~

~

!, ~

.

27

........~ : ~ :'i~ .... ~ 9 .... ~9149 9 ...... 9 9149149

~

~;

.~..".gi~+ ~

~@'.".'h~ii~: ...:

:

9

:~::~::: . :::: " '

,, ~..n :i~ i~i~i~] ~ ~

~#

~g

~

~ . : : ~ :

~ ~i~ia z

:

.am

Fig. 15. SEM micrographs of fatigued CMSX-4 specimens showing interaction of fatigue crack tips with different initial ~,/~,'microstructures. See text for details. From [35].

CONCLUDING REMARKS Fatigue damage can occur in widely different forms. The examples presented in this work were selected to illustrate some aspects of this variety of fatigue behaviour and to highlight some of the dominant microstructural mechanisms. At the same time, examples were given of different experimental approaches, emphasizing some recent developments in the quantitative assessment of fatigue damage.

ACKNOWLEDGMENTS The author is grateful to his co-workers who contributed to this article through their dedicated work over the years. Sincere thanks go to Gerd Eisenmeier, Heinz Werner H6ppel and Waltraud Kr~nzlein for their help in the preparation of the manuscript. The financial support of Deutsche Forschungsgemeinschaft through several research grants is acknowledged gratefully.

REFERENCES 1. Mughrabi, H. (1985). In: Dislocations and Properties of Real Materials (Conf. Proc.), Book No. 323, pp. 244-262. The Institute of Metals, London. 2. Morrow, JoDean (1965). In: Internal Friction, Damping and Cyclic Plasticity, ASTM STP 378, pp. 45-84. American Society for Testing and Materials. 3. Landgraf, R.W. (1970). In: Achievements of High Fatigue Resistance in Metals and Alloys, ASTM STP 467, pp. 3-36. American Society for Testing and Materials. 4. Luk~t~, P., Klesnil, M. and Pol~k, J. (1974). Mater. Sci. Eng. 15, 239-245. 5. Mughrabi, H. (1996). In: Proc of Sixth Internat. Fatigue Congress FATIGUE '96, Vol. 1, pp. 57-68, Lfitjering, G. and Nowack, H. (Eds.). Pergamon. 6. Valiev, R.Z. (1997). Mater. Sci. Eng. A 234-236, 59-66. 7. Lowe, T.C. and Valiev, R.Z. (Eds.), (2000). Investigations and Applications of Severe Plastic Deformation. Kluwer Academic Publishers. 8. Mughrabi, H. (2000). In: Investigations and Applications of Severe Plastic Deformation, pp. 241-253, Lowe, T.C. and Valiev, R.Z. (Eds.). Kluwer Academic Publishers. 9. Thompson, A.W. and Backofen, W.A. (1971),Acta metall. 19, 597-606. 10. Agnew, S.R. and Weertman, J.R. (1998). Mater. Sci. Eng. A 244, 145-153. 11. Agnew, S.R., Vinogradov, A. Yu., Hashimoto, S. and Weertman, J.R. (1999). J. of Electronic Materials 28, 1038-1044.

28

H. MUGHRABI

12. Brunnbauer, M. (2000). Diplom-Ingenieur Thesis, Universit/~t Erlangen-Ntirnberg. 13. Luk~ig,P. and Kunz, L. (1987). Mater. Sci. Eng. 85, 67-75. 14. Tavernelli, J.F. and Coffin, L.F. (1959). Trans. Am. Soc. Metals 51,438-453. 15. Vinogradov, A., Kaneko, Y., Kitagawa, K., Hashimoti, S. and Valiev, R.Z. (1998). Mater. Sci. Forum 269-272, 987-992. 16. Hashimoto, S., Kaneko, Y., Kitagawa, K., Vinogradov, A. and Valiev, R.Z. (1999). Mater. Sci. Forum 312-314, 593-598. 17. Oh-ishi, K., Horita, Z., Furukawa, M., Nemeto, M. and Langdon, T.G. (1998). Metall. Mater. Trans. A, 29A, 2011-2013. 18. Stolyarov, V.V., Latysh, V.V., Valiev, R.Z., Zhu, Y.T. and Lowe, T.C. (2000). In: Investigations and Applications of Severe Plastic Deformation, pp. 367-372, Lowe, T.C. and Valiev, R.Z. Kluwer Academic Publishers. 19. Vinogradov, A. (2000). Personal communication. 20. Hartmann, O., Biermann, H. and Mughrabi, H. (1998). In: Low Cycle Fatigue and ElastoPlastic Behaviour of Materials, pp. 431-436, Rie, K.-T. and Portella, P.D. (Eds.), Elsevier Science Ltd. 21. Sommer, C., Christ, H.-J. and Mughrabi, H. (1991). Acta. metall, mater. 39, 1177-1187. 22. Lloyd, D.J. (1991). Acta metall, mater. 39, 59-71. 23. Eisenmeier, G., Ottmtiller, M., H6ppel, H.W. and Mughrabi, H. (1999). In: FATIGUE '99, Proc. of the Seventh International Fatigue Congress, Vol. 1, pp. 253-258, Wu X.-R. and Wang Z.G. (Eds.). Higher Education Press, Beijing and EMAS Ltd., West Midlands. 24. Mayer, H.R., Lipowsky, H., Papakyriarou, M., R6sch, R., Stich, A., Zettl, B. and StanzlTschegg, E. (1999). Fatigue Fract. Engng. Mater. Struct. 22, 591-599. 25. Eisenmeier, G., Mughrabi, H., H6ppel, H.W. and Ding, H.Z. (2000). In: DFG-Kolloquium 2000 "Lebensdauervorhersage", pp. 153-164. Deutscher Verband ftir Materialforschung und -prtifung e.V. 26. Eisenmeier, G., Holzwarth, B., H6ppel, H.W. and Mughrabi, H. (2000). To appear in Proceedings of lCSMA 12, Special Volume of Mater. Sci. Eng. A. 27. Couper, M.J., Neeson, A.E. and Griffiths, J.R. (1990). Fatigue Fract. Engng. Mater. Struct. 13, 213-227. 28. Ting, J.C. and Lawrence, Jr., V. (1993). Fatigue Fract. Engng. Mater. Struct. 16, 631-647. 29. Ebi, G. (1987). Doctorate Thesis, Rheinisch Westf~ilische Technische Hochschule Aachen. 30. Borb61y, A. (1999). Unpublished work. 31. Ding, H.-Z., Eisenmeier, G. and Mughrabi, H. (2000). In: Proceedings of the Fourth International Conference FATIGUE 2000 "Fatigue and Durability Assessment of Materials, Components and Structures", pp. 209-217, Bache, M.R., Blackmore, P.A., Draper, J., Edwards, J.U., Robert, P. and Yates, J.R. (Eds.). EMAS Ltd. 32. Mughrabi, H. (1996). In: Johannes Weertman TMS Symposium, pp. 267-278, Arsenault, R.J., Cole, D., Gross, R., Kostorz, G., Liaw, P., Parameswaran, S. and Sizek, H. (Eds.). TMS, Warrendale, Pa., USA. 33. Mughrabi, H. (1999). In: FATIGUE '99, Proc. of the Seventh International Fatigue Congress, Vol. 3, pp. 1967-1976, Wu, X.-R. and Wang, Z.G. (Eds.). Higher Education Press, Beijing and EMAS Ltd., West Midlands, UK. 34. Obrtlik, K., Luke,, P. and Pol/tk, J. (1998). In: Proc. of Int. Conf. on Low Cycle Fatigue and Elasto-Plastic Behaviour of Materials, pp. 33-38, Rie, K.-T. and Portella, P.D. (Eds.). Elsevier Science Ltd. 35. Ott, M. and Mughrabi, H. (1999). Mater. Sci. Eng. A 272, 24-30. 36. Tetzlaff, U., Nicolas, M. and Mughrabi, H. (2000). In: Proceedings of EUROMAT '99, Munich, 1999, Vol. 10, in press. Wiley-VCH.

29

FAILURES OF STRUCTURES AND COMPONENTS W H I C H FRACTURE MECHANICS WOULD HAVE PREVENTED

D.R.H. JONES

Department of Engineering, Universityof Cambridge, TrumpingtonStreet Cambridge CB2 1PZ, UK

ABSTRACT Fracture Mechanics is a generic and powerful design tool. However, the experience of the author suggests that there is a lack of application of fracture mechanics in many areas. The present paper serves to highlight these problems of technology transfer using as illustrations four case studies of practical situations in which the use of fracture mechanics at the design stage would have avoided failure or the potential for failure. The case studies are as follows. (1) The fracture of a polyurethane foam insulation layer which led to the scrapping of three liquid methane bulk carriers. (2) The collapse of a wooden balustrade in a student residence which resulted in serious injury to five people. (3) The explosion of a perspex pressure vessel during its initial hydrotest. (4) The high-temperature embrittlement of Corten steel, which led to the complete replacement of all six furnace flues in a new power station. KEYWORDS Balustrade, Corten steel, furnace flue, perspex, polyurethane foam, pressure vessel, tanks, wood. INTRODUCTION Fracture Mechanics is a generic and powerful design tool. However, the experience of the author suggests that there is a lack of application of fracture mechanics in many areas. The present paper serves to highlight these problems of technology transfer using as illustrations four case studies of practical situations in which the use of fracture mechanics at the design stage would have avoided failure or the potential for failure. The case studies are as follows. (1) The fracture of a polyurethane foam insulation layer which led to the scrapping of three liquid methane bulk carriers. (2) The collapse of a wooden balustrade in a student residence which resulted in serious injury to five people. (3) The explosion of a perspex pressure vessel during its initial hydrotest. (4) The high-temperature embrittlement of Corten steel, which led to the complete replacement of all six furnace flues in a new power station.

30

D.R.H. JONES

FRACTURE OF POLYURETHANE FOAM INSULATION IN LIQUID METHANE

TANKS

Introduction

Figure 1 is a schematic half-section through a tank used for storing liquid methane at atmospheric pressure. Because methane boils a t - 1 6 2 ~ the tank is made from an aluminium alloy in order to avoid any risk of brittle failure. Even so, it is considered necessary to have a second line of defence should the tank spring a leak. This is achieved by placing the tank into a leak-proof mild-steel jacket, and inserting a layer of thermal insulation into the space between the two. The jacket is thereby protected from the cooling effect of the methane, and the temperature of the steel is kept above the brittle-ductile transition temperature. But what happens if the tank springs a leak? If the insulation is porous (like fibreglass matting) then the liquid methane will flow through the insulation to the wall of the jacket and will boil off. As a result the jacket will cool down to -162 ~ and may fail by brittle fracture. To avoid this possibility the inner wall of the jacket is coated with a layer of closed-cell foam made from rigid polyurethane (PUR). The tank is then lowered into the jacket and the assembly gap is filled with fibreglass matting. The theory is that if the tank leaks the flow of methane will be arrested by the closed-cell structure of the PUR and the jacket will be protected.

'" ~--C"

::::::::::::::::::::::::::

--I

.~Fibreglass

0.15 ------~ 0.10 - - - - - - -

Rigid ~ "

l i

matting

~-.

PU

foam Mild

steel jacket

Dry nitrogen "

:i:Z 9

;..,.,,, ~

9 Illi,l!i:'"

Ili

Aluminium alloy tank

,:

_

l•l,,?!.:"

9

-o"

9

.;;.j

ii1"

i

Balsa wood

supportpads

Fig. 1. Schematic half-section through a typical liquid methane storage tank using closed-cell polyurethane foam for thermal insulation/secondary containment. Typical dimensions in m.

Failures of Structures and Components...

31

This system has been used in ships designed for the bulk carriage of liquid methane. In such applications, the mild-steel jacket surrounding the tank is the single hull of the ship itself. It is vital in order to protect the structural integrity of the hull that the PUR provides effective containment. However, incidents have occurred where the PUR has cracked, compromising the integrity of the hull. In one reported instance, three brand-new bulk carriers had to be written-off as a result of multiple cracking of the PUR foam layer. Thermal stresses in the foam

Under normal operating conditions, the temperature of the foam decreases linearly with distance through the layer, as shown in Fig. 2. The foam wants to contract as it gets cold, but is prevented from doing so by the rigid steel wall of the jacket to which it is stuck. The temperature differential AT generates a biaxial tensile stress ty in the plane of the layer which is given by (xA~ o" = ~

(1)

(]-o)

i I I I

! I I I

I

I

I-I

Steel plate

l~ll I

/

/Foam

Io'1

/

I~1 ! ! ! I

I !

I

!

A

o (t)

_t

L/:

I

1..

Fig. 2. Temperature and thermal stress in the foam layer.

t)

D.R.H. JONES

32

o~, E and v are respectively the coefficient of thermal expansion, Young's modulus and Poisson's ratio of the foam. Figure 2 also shows the variation of stress with distance through the layer. It is non-linear because Young's modulus for polyurethane (PU) increases as the temperature decreases. The thermal stress is a maximum at the inner surface of the PUR layer. Polymers behave as elastic-brittle solids provided they are colder than about 0.75T [1], where T is the glass-transition temperature. For PUR, T = 100 ~ [1], or 373 K. One would therefore expect elastic-brittle behaviour below about 280 K (7 ~ Presumably the foam failed by brittle cracking when the maximum thermal stress reached the fracture stress of the foam. In order to check this hypothesis we first list the relevant data for a typical PUR foam as used in cryogenic applications [ 1]. Cell size --. 0.5 mm. Thermal expansion coefficient a -- 10-4 ~ Poisson's ratio v --- 0.3. Young's modulus E --- 34 MPa at-100 ~ Fracture stress @ = 1.4 MPa at-100 ~ Plane strain fracture toughness KI~ = 0.05 MPa~/m at -100 ~ Referring to Fig. 2, reasonable estimates of temperature are T~ -- 0~ T2 = -100~ and AT(t) ~- 100~ For a temperature differential of this magnitude, Eqn (1) predicts that or(t) = 0.5 MPa. However, this value for the maximum stress is substantially less than the fracture stress of-- 1.4 MPa expected at-100~ This means that, on a simple basis, the foam should not have fractured in service. In order to understand why the foam did in fact break it is necessary to analyse the problem using fracture mechanics.

Fracture mechanics analysis It is a simple matter to estimate the size of a critical defect in the foam layer by using the standard LEFM equation K,~ = o ' ~

(2)

Since KI~ -- 0.05 MPa~/m and o(t) - 0.5 MPa, then a -- 3 mm. This is a small defect and is only of the order of six times the typical cell size (0.5 mm). It is important to note that the method of applying the foam to the interior of the hull was conducive to the presence of defects. The foam was delivered through a hand-held nozzle as a gas-blown froth and was applied in layers about 25 mm thick. In practice this method is likely to result in considerable variation in cell size and the introduction of defects. The most reasonable explanation for the formation of cracks in the foam layer is therefore that small defects (introduced into the foam at the time of application) became critical as the temperature of the foam fell during charging with liquid methane. The most probable location for crack initiation would have been the inner face of the foam where the thermal stress was a maximum (and where surface defects of size a as opposed to buried defects of size 2a would have been critical). In the incidents which were reported, cracks had

Failures of Structures and Components...

33

propagated through the full thickness of the layer (although it is not obvious that this should occur in the present strain-controlled situation). Conclusions Considerable financial loss has resulted from the cracking of rigid polyurethane foam in liquid methane insulation/containment systems. This has been caused by a combination of the very low fracture toughness of PUR foam at low temperature and the likelihood that the method of applying the foam will introduce defects exceeding the critical size for crack propagation. An elementary knowledge of fracture mechanics would have suggested that the use of plain (un-reinforced) PUR in the present situation was fundamentally unsound. COLLAPSE OF A WOODEN BALUSTRADE

Introduction A student residence built approximately 30 years ago has eight balconies which are accessed from public areas in the building. Each balcony is flanked by a pair of brick walls between which is secured a balustrade fabricated from wooden components. Five years ago, while a number of people were gathered on a second-floor balcony, the balustrade gave way. As a consequence, five people fell to the ground below and were injured. The failure was caused by the propagation of pre-existing cracks in the balustrade while people were leaning against the top rail.

Design and construction of the balustrade Figures 3 to 5 are reproductions of scale drawings of the balustrade prepared during the failure investigation. The balustrades had originally been dimensioned in inches and these units are retained here (1 inch = 25.40 mm). The numbers on the drawings are identified as follows: 1, end post (31 inch long); 2, baluster; 3, top rail (105 inch long); 4, top stringer; 5, bottom stringer; 6, kick board; 7, rebate groove; 8, blind mortise; 9, tenon; 10, 2-inch nail (head at outer face of baluster); 11, 2-inch nail (head at inner face of baluster); 12, galvanised steel fixing bracket cemented into brick wall; 13, steel coach screw (1/4 inch diameter). The drawings show that the application of a horizontal force to the top rail will tend to initiate a longitudinal crack in the end post at the root of the tenon. Under load-controlled conditions such a crack would run along the grain of the end post from top to bottom. This in turn would open-out the mortises for the stringers. The tenon at the end of each stringer is retained by a single nail (and possibly glue) and should detach relatively easily. Full separation of the balustrade from the retained part of the end post would occur by torsional fracture of the joint between end post and kick board. Because the end post provides the connection between the top rail and the balcony walls, it is a safety-critical component. However, for aesthetic reasons, the post was given an L-shaped cross section which halved the width of the tenon and also halved the load required to initiate and propagate a longitudinal crack.

D.R.H. JONES

34

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Fig. 3. Elevation of the balustrade as seen by an observer standing on the balcony and looking outwards. The top and bottom of the balustrade are respectively 39 and 6 inch above the balcony floor. There is a total of 24 balusters along the length of the balustrade (not all shown).

Details of the failure In spite of these design errors, it appears unlikely that cracks would initiate from the root of the tenon under normal service loads. However, the presence of wood stain on the fracture surfaces of the failed end posts indicates that the balustrade collapsed because of pre-existing cracks. These cracks were at least 8 inches long at the time of the most recent timber treatment. Cracks presumably developed over a period of time through exposure to the weather. This hypothesis was confirmed by a high incidence of cracks in the other balustrades. Figure 6 shows an 18-inch crack observed in one of the other balustrades. The crack path is identical to that observed in the failed end posts (Fig. 7). In order to add weight to the failure scenario, double cantilever beam tests were carried out on new end posts under displacement control. The measured crack propagation forces for representative crack lengths were comparable to the combined lateral force delivered by five people leaning on the top rail.

Failures of Structures and Components...

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35

3

,...

40

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(a)

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Fig. 4. (a) Cross-section drawn on A-A (see Fig. 3) looking at the left-hand end of the balustrade. (b) Cross-section drawn on B-B (see Fig. 3) looking at the left-hand end of the balustrade. (c) Exploded view showing joints.

36

D.R.H. JONES

~

3

12

v//d

13

Fig. 5. A horizontal outward force applied to the top rail tends to split the end post.

.......

............~ '~.....~ ~

!~iii~i~,~i,i i!~ ~i~'~i !~!~'~''i~84 ~'~'~'~'~ i ,~ 'i "! iiii,i~84,,~

Fig. 6. An 18-inch crack in another balustrade.

Failures of Structures and Components...

37

Fig. 7. The crack path in a failed end post. Conclusions

The collapse of the balustrade was caused by the propagation of pre-existing cracks in the end posts, which are safety-critical components. The collapse was caused by a lack of awareness by both architect and maintenance personnel of the poor along-grain fracture toughness of wood, the potential sources of crack-opening forces in the design, the propensity of externally exposed timber to develop cracks and the significance of cracks once developed for the integrity of the structure.

D.R.H. JONES

38

EXPLOSION OF A PERSPEX PRESSURE VESSEL DURING INITIAL HYDROTEST

Introduction Figure 8 shows the general arrangement drawing for an experimental rig which is designed for studying the propagation of buckling in externally pressurised tubes. A long open-ended tubular specimen is placed on the horizontal axis of the rig with the ends emerging through pressure seals. The rig is partially filled with water and the space above the water is filled with nitrogen. The nitrogen is pressurised until a buckle propagates along the length of the specimen. The volumes of water and nitrogen in the rig can be adjusted to produce the loading compliance necessary to achieve stable propagation of the buckle. Halfway along the rig is a flanged perspex connector which allows the propagation of the buckle to be observed directly using a high-speed camera. Unfortunately, the perspex connector exploded during the initial hydrotest at a pressure of only one-half of the design hydrotest pressure.

Design data Figure 9 shows detailed drawings of the connector. Relevant design data are given as follows. Note that mechanical property data are take from the supplier's literature (except for values of fracture toughness). Internal diameter of cylindrical portion 2B = 154 mm. External diameter of cylindrical portion 2A = 255 mm. Mean diameter of O-ring seal = 195 ram. External diameter of flange = 356 ram. Length of cylindrical portion = 350 mm. Thickness of flange = 50 mm. Radius of fillet between flange and cylindrical portion = 5 mm. Flange bolting: twelve 12 mm bolts equispaced on a 320 mm pcd. Forming process: casting. Poisson's ratio v = 0.38. Young's modulus E = 2760 MPa (minimum), 3540 MPa (average). Tensile strength of= 62 MPa (minimum), 77 MPa (average). Plane strain fracture toughness Kic = 0.8 to 1.75 MPa~/m [2]. Working pressure = 7 MPa gauge. Hydraulic test pressure = 8.6 MPa gauge. Failure pressure = 4.8 MPa gauge.

Failure analysis Figure 10 is a photograph of the perspex connector taken after the explosion. Detailed visual inspection of the fracture surface indicated that the fracture initiated as a hoop stress tensile failure in the cylindrical portion and subsequently propagated towards each flange. The hoop stress crh in the cylindrical portion can be calculated from the standard result for thick-walled tubes [3]

i

U

tj

i I

t "

h ~ ~---~,~z~,~

I

~ ~[

',1

ii I

t

[ ~t ~

Failures of Structures and Components...

ll!!

t--" Ill O I,tl tlJ tt~

Fig. 8. General arrangement drawing of the experimental rig.

Z O

tu tD

39

i_0~ tl,~

® -~,~

,-~_ tt.

|

x X

r

450.00

-

A @ -

30.0'

@320 00

I

Filename PERSPEX

SECTION

x-x

Project 690 Perspex Part Pressure Tested at 1200 psi

Fig. 9. Drawings of the perspex connector.

Failures of Structures and Components...

41

:,,~iiii!!i 84

J ~ ' ~

i~!i84 i!i ~,~i!,i~!~!

:i~ iii~ii!!i~

....~.:'!~i'F!i!i',i!ii!~,ii~!::::::!!:'~:~:ii ..:

%

Fig. 10. Photograph of the perspex connector taken after the explosion.

( B ) 2 A2+r2 o"h = p A2 _ B E

(3)

where p is the internal gauge pressure and r is the radius at which the stress is calculated. The hoop stress is a maximum at the bore of the tube, with r = B and A2 + B z o"h = p B---'-'A2 _ T = 2.13p

(4)

The hoop stress is a minimum at the external surface of the tube, with r = A and 2B 2 crh = p B-------------A2 _ ~ = 1.13p

(5)

The most probable site for failure initiation is therefore the bore of the tube. Eqn (4) gives a hoop stress of 10 MPa at the failure pressure. minimum tensile strength given by the suppliers.

This is one-sixth of the

The complete connector including flanges was modelled axisymmetrically using the Abaqus finite element package. The model took into account the radial pressure loading on the bore, the axial pressure loading on the end face of the flange within the O-ring seal, and the bolting force (treated as a uniform circumferential loading). Calculations were performed for an internal gauge pressure of 7 MPa (the working pressure). Figure 11 shows the boundary conditions and mesh employed and Figure 12 shows the resulting displacements.

D.R.H. J O N E S

42

.22 i

,

I

:I

1 I

iAIA

,iiA

!

Fig. 11. Axisymmetric finite element model of the connector. The bolting force is in newtons for an internal gauge pressure of 7 MPa.

'[~t.dd.J_F~ ; ; ' I v n r

Fig. 12. Displacements of the connector for an internal gauge pressure of 7 MPa. The displacements clearly show the twisting of the flange caused by the eccentric loading of the bolting force. Near the junction of cylinder and flange the hoop strain at the bore is some 20% greater than in the main cylindrical portion. Predictably, the maximum von Mises stress is located at the fillet between cylinder and flange. However, the stress at the fillet is only some 40% greater than the hoop stress at the bore of the main cylindrical portion. On the basis of the additional 20% hoop strain near the flange, the maximum hoop stress at the bore is estimated to be 12 MPa at the failure pressure. This is still only one-fifth of the minimum tensile strength. However, a fracture mechanics analysis using Eqn (2) with a fracture toughness of 1 MPa~/m and a hoop stress of 12 MPa gives a critical defect size a of 2.2 mm at the failure pressure. At the operating pressure the critical defect size would only be 1.0 mm. No information is available on the level of residual stress, although the connector was reported to have been stress relieved aider casting. If one assumes an additional 12 MPa of residual stress, the critical defect size at the failure pressure is reduced to just 0.6 ram. A defect of this size would be difficult to find under production conditions in such a large volume. In addition, it would be easy to introduce longitudinal scratches in the bore of the connector during routine handling and use.

Failures of Structures and Components...

43

Conclusions The most probable explanation for the failure is that a critical defect was present in the wall of the perspex connector. The connector was a standard item manufactured for flow visualisation in pressurised systems. The designers had clearly used a stress-based rather than a fracture-mechanics based approach with entirely predictable consequences.

CRACKING OF FURNACE FLUES IN A POWER STATION

Introduction Figure 13 is a general view of a furnace flue in a modern power station. The power station has six coal-fired boilers arranged in a single row. The combustion gases from each boiler are discharged at a height of 104 m above ground level into a flue, which takes the gases down into a horizontal duct leading to the smoke stack. The flue is connected to the horizontal duct by expansion bellows, which means that the whole weight of the flue (380 tonne) has to be suspended from structural steelwork at the top of the boiler house. The suspension hangers are clearly visible in Fig. 13. Figure 14 is a view of a flue before the external cladding and lagging were added. The point of attachment of the suspension hangers to the shell of the flue is clearly visible. The method of support introduces appreciable self-weight stresses into the upper part of the flue. After 30,000 hours of operation, cracks were detected in circumferential butt welds in the shell and concerns were raised over the structural integrity of the flues.

Design data Relevant design data are given below. Length of flue = 51 m. Diameter of flue = 13 m. Plate thickness = 6 or 12 mm. Weight of flue = 380 tonne. Operating temperature = 400 to 460 ~ Material: Corten HT steel. Material composition (weight %)" C, 0.10; Si, 0.40; Mn, 0.40; S, 0.010; P, 0.09; Cr, 0.90; Ni, 0.20; V, 0.04; Cu, 0.30. Yield stress = 440 MPa. Charpy impact energy at 20 ~ -- 80 J (as received). Charpy impact energy at 20 ~ = 4 J (after 30,000 hours at 430 ~ Plane strain fracture toughness at 20 ~ = 30 MPa~/m.

Structural integrity assessment The main cause for concern derived from the very poor value of Charpy impact energy which was observed in test samples removed from the flue. After 30,000 hours in service at 430 ~

D.R.H. JONES

44

Ilk ~!ii~i!i~iiiii~iiiiiiii!!i!!i

:~.~,ii~:~: ~: 84

!~

~i~I.~.!I.~...

~i .... ~

i

,~.~.~i~i~ii!i~iii!ilili!i~i,i~

i!i i i i i

!!iiiiiii,, iii

.......

i

~i i 9~i~~ii i~~i~i!~ii~~i!~ i~ ~ ~ ~i!~~.~"i~ ~~i~ ~ ~ ,~ ~i/~ ~ ~:~ ~~ ~ ~ ~ ~~ ~~ ~ ~ ~ i ~ ~:~:i ~:~ i ii i~ :~ ~: ~

Fig. 13. General view of one of the furnace flues.

!I~! .....

Failures of Structures and Components...

45

the 20 ~ impact energy had decreased from 80 J to only 4 J. Corten HT steel had been selected because of its adequate elevated temperature creep strength and good oxidation resistance. However, in the absence of molybdenum additions, it is well known that Corten steel undergoes severe temper embrittlement in the range 380 - 570 ~ because of the high phosphorus content. Valid KI~ values of approximately 30 MPa~/m were obtained from centre-cracked specimens of 12 mm plate removed from a flue.

Fig. 14. View of one of the furnace flues before the external cladding and lagging were added. Note the expansion bellows at the bottom and the suspension hangers near the top.

Finite element analysis indicated primary tensile membrane stresses as follows. 0 20 40 60

-

20 40 60 80

MPa MPa MPa MPa

13 m • 13 5 m x 5m 5mx 5m 2m• 2m

m areas. areas. areas. areas.

46

D.R.H. JONES

Using Eqn (2) with a fracture toughness of 30 MPa~/m one obtains critical through-thickness crack lengths 2a as follows. 20 MPa 40 MPa 60 MPa 80 MPa

1.4 m. 0.36 m. 0.16 m. 0.09 m.

It is clear that, at all stress levels, the critical crack length is much less than the linear extent of the stressed area. Although the external stiffening beams had the potential to arrest propagating cracks, there was sufficient concern that the flues might fail at plant shutdown temperature that the decision was taken to replace them all with a steel that was not susceptible to temper embrittlement.

CONCLUSION The four case studies presented in this paper show that design based on fracture mechanics has a vital role to play in a wide range of situations, in many cases well removed from the areas in which fracture mechanics methodolgy has become firmly established. More effective technology transfer is essential to help prevent continuing failures which could otherwise be avoided using existing knowledge.

ACKNOWLEDGEMENTS The failure investigations described in this paper were carried out in collaboration with my colleagues John Horsfall, Peter Long, Doug Marriott, Jo Strydom and Ferdie van Zyl, to whom my thanks are due for many happy and stimulating discussions. REFERENCES

.

Gibson, L. J. and Ashby, M. F. (1989). Cellular Solids- Structure and Properties. Pergamon, Oxford. Hertzberg, R. W. (1989). Deformation and Fracture Mechanics o f Engineering Materials. Third edition, Wiley, New York. Jones, D. R. H. (1993). Engineering Materials 3 - Materials Failure Analysis. Pergamon, Oxford.

47

INTERFACIAL CRACKING IN THIN FILM STRUCTURES J.M. MART~qEZ-ESNAOLA, J.M. S/kNCHEZ, M.R. ELIZALDE, A. MART1N-MEIZOSO

Centro de Estudios e Investigaciones TOcnicas de Gipuzkoa (CELT), Paseo de Manuel Lardizdba115, 20018 San Sebastidn, Spain, and Escuela Superior de Ingenieros, University of Navarra, Apdo. 1674, 20080 San Sebastidn, Spain ABSTRACT Interfacial fracture is a critical failure mode identified in reliability tests of multilayer thin film structures used in microelectronics. This paper reviews the main techniques developed so far to measure interfacial toughness in thin film sandwich structures, together with the models used to extract the fracture parameters of the interface. This background is used to present Cross Sectional Nanoindentation (CSN), a new mechanical test specifically designed for measuring the fracture toughness of thin film interfaces. The main advantages of this new technique are the high spatial resolution, which makes it suitable for studying patterned structures, and the direct observation of the interfacial crack front, not possible with other test configurations. A numerical model based on the elastic theory of plates has been used to calculate the interfacial toughness for ceramic-ceramic systems from CSN test results. Closed form analytical solutions, developed for two limiting cases, are consistent with the numerical approach. The CSN technique has been successfully applied to silicon nitride - silicon oxide thin films, commonly used as electrical isolators in microelectronic devices.

KEYWORDS Microelectronics reliability, thin films, interface toughness, Cross Sectional Nanoindentation. INTRODUCTION The breakthrough achieved in microprocessor performance during the last decades is directly related to the higher resolution capacity of the new integration technologies. To increase the speed and functionality of integrated circuits (IC) with still lower production costs, each IC generation incorporates new materials and deposition technologies together with a dramatic reduction in feature size (e.g., the thickness of interconnection lines is below 0.25 gm). The reliability assessment of these devices, containing multilayer thin film structures, is an active field of research that deals with different technological issues not the least being of thermomechanical nature. Figure 1 shows a simplified scheme of a modern integrated circuit. This structure contains metallic, ceramic and polymer thin films (TF) with a stacking sequence predetermined by the

48

J.M. MART[NEZ-ESNAOLA, J.M. S.,~NCHEZ, M.R. ELIZALDE, MART[N-MEIZOSO

electrical functionality. However, this deposition sequence is not always optimised from the mechanical point of view. Residual stresses arise from two main sources: stresses due to the tendency of thin films to shrink or expand once they are deposited on the substrate ("intrinsic stresses" [1,2]) and those produced by the differences in the thermal expansion coefficients between different TF materials [3]. These stresses, that can be as high as 1 GPa [4], produce thin film and interfacial fractures that lead to short-circuit failures not only in production but also during device operation. Interfacial cracking is one of the most important failure modes found in integrated circuits. It is typically observed in ceramic-ceramic interfaces used in multilayer interconnect structures (Fig. l a), and in the polymer-ceramic interfaces occurring in packaging flip-chip interconnections (Fig. l b). Although each case requires a specific study to identify the root cause, interfacial cracking is generally governed by the development of residual stresses [5], together with the lack of chemical compatibility between dissimilar materials and low surface roughness [6-8].

J board

crack ] ~ __1W SiO2 A1-Cu Si02

[W~

l

integrated[ circuit ",4

particulate reinforced epoxy

1/TiN solder bump

cracks (a)

(b)

Fig. 1. Typical delamination failures found in IC structures: (a) SiO2-TiN interfacial fracture in the multilayer interconnect structure; (b) epoxy-die and epoxy-board cracks in the flip-chip structure. Another example of electrical failure induced by brittle fracture is found in SiO2 trenches between aluminium pads in multilevel interconnect structures (Fig. 2). In this case, SiO2 cracking is due to stresses developed by thermal expansion misfit between SiO2 and A1 structures. This type of failure has a typical dependence on feature size. SiO2 trench cracking is more likely to occur as the trench thickness increases because the stored elastic energy scales with feature volume and the surface energy with the area. The first step to address fracture induced electrical failures in complex TF sandwich structures is to measure the basic thin film material and interfacial properties. However, this is not straightforward, since conventional tests are not directly applicable to thin films 1 micron thick or less. The first part of this article includes a review of the techniques applied so far to measure interfacial fracture strength in thin film structures and the models developed to interpret such tests. Although the loading mode is different for each test, all of them share the basic fracture mechanics problem of interfacial crack propagation, which is a topic of current

Interfacial Cracking in Thin Films Structures

49

debate. The second part of the paper gathers the main conclusions of the theoretical analyses developed to address this problem. Finally, the advantages and disadvantages of each of these techniques will be compared with Cross Sectional Nanoindentation (CSN) [9], an indentation technique recently developed to measure fracture toughness of ceramic-ceramic thin film interfaces.

silicon s u b s t r a t e ~ crack

1 .

/i

'~

SiO2 thin film

.

board Fig. 2. Brittle fracture of SiO2 trenches.

THIN FILM INTERFACIAL FRACTURE TESTS Two basic capabilities are required for a test to be suitable for measuring thin film adhesion: firstly, that a sharp pre-crack can be induced at the interface of interest, and secondly, that the loading modes used for crack growth must be known. A variety of fracture tests have been designed for evaluating interfacial adhesion of thick coatings (0.04 to 1 mm thick) [ 10] or fibre reinforced composites with fibre radius in the range of 40 to 150 ~m [11]. However, these techniques are not directly applicable to thin films (1 micron thick or less) because they are not able to produce controllable cracks at the interface of interest. Presently, the techniques used for measuring interfacial toughness in thin films can be classified in six groups: stub-pull tests, peeling tests, blistering tests, laser spallation tests, bending tests, and indentation-scratching tests. Stub-Pull Tests

In stub-pull test methods, delamination is produced by bonding an actuator to the film surface by means of an adhesive, followed by loading until the interface fails (Fig. 3). The interfacial surface energy, Fg, is then calculated as p2 h Fg = 27rZKa 4

(1)

where P is the applied load, K is the film bulk modulus, a is the actuator radius and h is the film thickness. An important drawback of this technique is that misalignment between the stub and the interface is always present leading to uneven loading and uncontrolled bending moments. In addition, the maximum load that can be applied is limited by the strength of the adhesive, that is a parameter with a large scatter due to the presence of flaws produced by its

50

J.M. MARTiNEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MARTIN-MEIZOSO

inhomogeneous distribution on the wafer surface or by inappropriate curing conditions [12]. However, these methods are easy to apply and are currently used as quick turn monitors as they give a qualitative estimation of the interfacial strength.

~

P

b adhesive ---..~

-~ thin film

Fig. 3. The Stub-Pull test.

Peeling Tests

The basic peeling test configuration is shown in Fig. 4. After producing a sharp pre-crack at the interface of interest, a force is applied to the thin film with a specific loading angle with respect to the interface [13]. However, pre-cracking and loading are limited by the film thickness, being not suitable for films 1 micron thick or less. Recently, a new technique applicable to thin films has been developed based on the well-known phenomenon of "spontaneous peeling" [ 14]. In this technique, the thin film on the substrate is stressed by depositing onto the film a second super-layer of material having a large intrinsic stress, such as Nb [ 15], Cr or Ni [ 16]. The test specimen is shown in Fig. 5, where the sandwich structure corresponds to a typical multilayer interconnection. The interfacial fracture energy, Fi, is estimated from elastic finite elements simulations, since no analytical solutions are available so far for this cracking configuration. The resulting expressions have the non-dimensional form [16]:

o-2(1 - v 2)hcr = F~ tanh 2 F 2 ~

(2)

where, Ecr is the super-layer elastic modulus, o-is the intrinsic residual stress, hcr is the Cr film thickness, AL is the total intact length of the interface, and F1 and F2 are polynomial functions of hcr.

0

" "~

1 film

est,,

strate

~

Fig. 4. Peeling test basic configuration.

lnterfacial Cracking in Thin Films Structures

2....~.~~~ symmetryplane Cr AL/2 SiO TiN A1-C;

51

h

siliconsubstrate Fig. 5. Peeling test adapted to thin film structures.

1-'i

Experimental results show that is very sensitive to the elastic properties of the Cr thin film, so far not well determined. Another disadvantage of this technique is related to the complex fabrication of test specimens, consisting of an array of lines, that could not be representative of the IC configuration. It is also not clear whether the high temperature used in the Cr deposition process affects the original structure of the interface of interest.

Blistering Tests

In this case, the stress used to produce delamination is applied by means of a gas that is forced against the thin film through a window opened in the substrate (Fig. 6) [ 17,18].

d ...........

.....; ; , , d

......................

I p'"

P+AP

BULGE

BLISTER

Fig. 6. Scheme of the blistering test. A linear elastic analysis allows the calculation of Fi as Fi = p d ~cv 4 + 5 2 7r 4 + 4 2

(3)

where P is the applied pressure, d is the corresponding film deflection, n'v is a non-dimensional coefficient which accounts for the shape of the bulge, and 2 is defined by 2

=

qo-o

(4)

52

J.M. MART[NEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MARTiN-MEIZOSO

where c~ and C2 are geometric parameters which account for the shape of the window, M is the film biaxial modulus (M = El(1 - v) for an isotropic film), or0 is the film residual stress and r is the radius of the window. The blister test limitations are related to the stiffness of the test apparatus. Any compliance in the pressure set up can produce large scattering of results. One result that questions the validity of blister methods is that the interfacial energy release rate depends on the crack length showing an R-curve behaviour that could be induced by the test itself.

Laser Spallation Tests In these tests, the interface of interest is stressed by means of a pressure wave produced by a laser pulse lasting few nanoseconds. The rear surface of the substrate is coated with a material with high light absorption coefficient (Au) that converts the laser radiation into thermal energy. Explosive evaporation of the gold thin film generates a shock wave through the substrate towards the interface of interest. Finally, the interaction between wave fronts and the thin film produces spallation, i.e., thin film fracture and delamination (Fig. 7). Confining fused quartz plate

Interface

Thin film

Pulsing laser

Pressure wave \ Energy absorbing gold film

Si substrate

Fig. 7. Laser spallation test. Modelling of laser spallation is very complex and involves heat absorption and transfer phenomena, as well as elastic wave propagation in different media. The expressions used to calculate the peak tensile stress, ors,normal to the interface, have the form [ 19,20]: ~r~ = 2 poC(Uo - u~ )

(5)

where p0 is the film density, c is the velocity of the stress wave, u0 is the initial jump-off velocity and uk is the first pull-back velocity of the film. These film surface velocities are accurately measured by laser Doppler interferometry. However, the validity of such measurements is still under research. The main drawback of the technique is that the pressure wave cannot be controlled to separate delamination from thin film cracking. Therefore, the calculated stress is used in both fracture mechanisms and not only in debonding.

Interfacial Cracking in Thin Films Structures

53

Bending Tests Bending tests are specially appropriate for studying interfacial fracture energy in sandwich structures [21,22]. The test configuration (Fig. 8a) allows steady state crack propagation once the debond has extended sufficiently far from the vertical pre-crack. Under these conditions, the critical energy release rate can be calculated as

Fi=

Eb2H 3

F

,,-~

(6)

where P is the applied load, L is the moment span, E and v are the Young's modulus and the Poisson's ratio of the substrate, respectively, b is the beam width, H is the beam thickness, and F is a function that depends on the crack length to moment span ratio (a/L), a parameter related to the elastic misfit (the first Dundurs' parameter, or, see Eq. (11)) and the film to beam thickness ratio (h/H). The corresponding mode mixity angle is close to 50 ~

P/2

_ ~

m

P/2

H

K 2a

substrate

i

L ~

(a)

. [~-~'Notch \ S1wafer /-"] Cu }liffusionbonded notch

_ k

~

~

Sibea

2a T ;~ Si substrate / interface crack t _ l

i THIN FILM STRUCTURE

(b)

Fig. 8. Four-point bending test: (a) basic set up; (b) adaptation to thin film sandwiches. One practical problem of bending tests is that controlled precracking is more difficult as the thin film thickness decreases. Thus, the extension of bending tests to films about 1 micron thick has required the design of a new specimen [23]. In this sample, a rigid silicon beam with the same thickness as the substrate is adhered on top of the thin film structure by Cu diffusion bonding or by the use of polymer adhesives (Fig. 8b). A notch machined on the silicon beam generates on loading a sharp precrack that deflects towards the interface of interest. The critical energy release rate for this configuration is given by

Fi =

21PZL2(1- v 2) 2EbZH3

(7)

54

J.M. MARTiNEZ-ESNAOLA, J.M. S.4NCHEZ, M.R. ELIZALDE, MARTiN-MEIZOSO

Although these tests are commonly used for assessing interfacial toughness, some practical issues need to be pointed out. Firstly, friction at the loading points changes the loading configuration and it is difficult to avoid. Nevertheless, friction effects can be accounted for by measuring the compliance histeresis [ 10]. Another drawback is related to the high temperature used for Cu diffusion bonding, which, in addition, is a time consuming operation. When Cu is substituted by polymer adhesives, similar problems to those found in stub-pull tests are found, i.e., misalignment, lack of reproducibility and the load limit imposed by the polymer fracture strength (a parameter that depends on the random size distribution of defects that appears on curing). Indentation and Scratching Tests

The use of depth sensing indenters for studying thin film mechanical properties is profusely reported in the literature. Among these techniques, nanoindentation has proved to be a powerful tool for obtaining properties such as hardness and elastic modulus of thin films [24,25]. This technique has also been adapted to monitor thin film adhesion by using two basic configurations: indentation perpendicular to the film surface and scratching. Vickers indentation from the top of the thin film has been reported to produce controlled delamination for a variety of material combinations [26,27]. Figure 9 shows the typical cracking pattern found in these experiments. The delamination crack driving force is obtained from the combined effect of intrinsic residual stresses and those produced by indentation leading to a complex analytical expression for the strain energy release rate [26].

indenter ~

plastic zone

--~ (Yr Q'~~'x~~ crack

SUBSTRATE

~r ~ ~ h film

Fig. 9. The indentation test. The main practical problem of this technique is that the cracking pattern is not reproduced for thinner or more brittle films commonly used in modem integrated circuits. In this case, indentation induced damage is a complex phenomenon, comprising simultaneous thin film shattering and delamination, which is not yet well understood [28]. Scratching is also widely used for film adhesion assessment [29-31]. The basic test set up is shown in Fig. 10. A conical diamond tip is driven both horizontally and vertically into the film until a delamination crack is produced. Several elastic models have been proposed for this simple geometrical configuration to estimate the critical energy release rate, F/, from the critical horizontal component of the load, P [32]:

Interfacial Cracking in Thin Films Structures

55

p2 Fi

_

8E (L tan,6' + a) 2h

(8)

where E- is the plane strain elastic modulus of the film ( E = E l ( l - v z) ), 2a is the width of the scratch corresponding to the delamination onset and h is the film thickness. These models also lead to equations that correlate the interfacial toughness with the geometry of the spall as alL ---~0 " Fi = 0.35Eh

I /4

(9)

Like top-down indentation, scratch test modelling is only possible if very simple crack configurations are assumed. Difficulties arise as the crack pattern becomes more complicated. In many situations, scratching does not produce such simple spalls, but a complex cracking pattern with shattering of both the thin film and the substrate.

A (delamination 1~3 a r e a )

scratch mark

L

Fig. 10. The scratching test. Some modifications of the basic scratching test have been recently developed to simplify its cracking pattern [33]. This new technique, known as line scratching, uses a wedge-shaped indenter tip that is driven horizontally at a constant depth into the end of a lithographically developed line of the film (Fig. 11). After cracking onset, the indenter keeps pushing the delaminated portion of the line until the compressive strain energy is relaxed by either interfacial crack propagation or film buckling. Crack propagation is then modelled by considering the non-adhered end of the line as a simple beam in compression: r,i = el ~(1- v ~) 2Eb2 h

(10)

where Pt is the critical tangential load, b is the line width, h is the line thickness, and E and v are the elastic modulus and the Poisson's ratio of the film, respectively.

56

J.M. MARTINEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MART)N-MEIZOSO

-~ Asymmetric diamond wedge Lfilm ~h Thermal SiO2 Carbon precrack SILICON SUBSTRATE

Fig. 11. Line-scratching test. This approach also has severe limitations. For instance, the results critically depend on the indenter movement accuracy. Any change in the indenter movement direction results in friction between the film and the substrate, a situation that models do not account for. Moreover, sample fabrication is complex and requires special processing, out of the standard thin film processing routes. MODELLING OF INTERFACIAL FRACTURE Theoretical analyses of cracks in bimaterial systems and their interactions with the interface have been developed by a number of authors for isotropic and anisotropic elastic materials (see, for example, Refs. [34-39]). For the case of a crack meeting an interface, the stress singularity is of the type r -s , with 0 < s < 1, where s depends on the elastic properties of the materials bonded together, and r is the distance to the crack tip [40-43]. For a crack crossing the interface, in addition to the typical r -~/2 singularity at the crack tips, a different kind of singularity appears at the point at which the crack faces cross the interface [44,45]. Another classical problem of fracture mechanics that has been investigated for years since the first works of Bogy [46], and Hein and Erdogan [47] is that of the singular stress fields at bimaterial edges. This is also of interest in microelectronic devices where the circuitry is placed very close to the edges, as these regions are prone to crack initiation, leading to delaminations that in turn threatens electric signals. Very recently, attention has been given again to this problem for combinations of elastic and elastic-plastic (bilinear) materials [48,49]. The combination of asymptotic analyses and finite element calculations indicate that the two modes of singular stresses (with different orders of singularity) are relevant for a correct description of the stress field in the entire zone of practical interest. Of particular interest is the case of a crack lying along an interface between dissimilar materials. It has been known since the work of England [50], Erdogan [51 ], and Malyshev and Salganik [52] that the elastic analysis predicts the interpenetration of the crack faces, which is, of course, unsatisfactory from the physical point of view. A number of models have then been developed to re-examine the problem [53-60] as well as to predict the tendency of the crack to propagate along the interface or to kink into one of the adjoining materials [61-66]. The elastic mismatch between the two materials can be rationalised in terms of two nondimensional parameters, the so-called Dundurs' parameters [67],

Interfacial Cracking in Thin Films Structures m

57

n

a = ~' (h"2 + l ) - ~ 2 ( / q +1) =_ E,_ - E2_ and f l = ~ (/c2 - 1 ) - ~ 2 ( K " - 1 ) /'/l (K'2 "1-1) +//2 (K'I "~" 1) E 1 + E 2 ,u~(K" 2 "4-1) +//2 (K'I -j- 1)

(11)

where subscripts 1 and 2 refer to the two materials, ~'= 3 - 4 v for plane strain and ~" - ( 3 - v)/(l + v) for plane stress, /a = E/[2(1 + v)], E is Young's modulus, v is Poisson's ratio, E = E / ( 1 - v 2) in plane strain and E = E in plane stress. Note that a = , 8 = 0 homogeneous materials.

for

The interpenetration of the crack faces is reflected mathematically by an oscillatory stress singularity such that the singular tractions ahead of the interface crack can be normalised as 0"22 "}- i0"12 =

(K I +

iK. )(270") q/2 r ie

(12)

where KI and KII are the stress intensity factors in modes I and II, respectively, and e = (1/2er)ln[(1-fl)/(1 +/5')]. However, this anomalous behaviour does not appear in terms of the energy release rate, which is given by = ~ E*

(K2 + K 2 ) ' with E * =

+

The relative amount of mode II to mode I loading at the interface measured through the phase angle, ~, defined as ~ = tan -1 ( K , / K I ) the definition of ~ is slightly more complicated involving a length note that ~ can be nonzero even when the external loading is normal to the elastic mismatch.

(13) (mode mixity) is usually for ,6' = 0 (when fl ~ O, scale). It is interesting to to the interface plane, due

The admissible values of a and/5, assuming v > 0, lie within a parallelogram enclosed by a = + l and a - 4 , 6 ' = + 1 in the (cr, fl) plane. Most combinations of materials of practical interest give small values of,6'(falling between 0 and a / 4 ) [68]; in addition, it is found that the effect of nonzero/5' is of secondary importance (see, for example, Eq. (13)). Consequently, most of the analyses have been performed for /5' = 0, so that the square root singularity is retained at the crack tip, see Eq. (12). Crack advance along the interface is characterised by a critical value of the energy release rate for the interface crack, G = F ( ~ ) , where F is the interfacial fracture energy which, in general, must be determined by experiment. Thus the interface toughness is not a single material parameter but a function of the phase angle of loading. Typically, F is found to be a monotonically increasing function of the phase angle. A phenomenological relation has been proposed for this dependence in the form [68]

FINI = 1 + tan 2(1- 2 ) ~

(14)

where 1-'1is the mode I toughness and 2 is a coefficient that reflects the interface roughness and the plasticity in the adjoining materials. There is no mixed mode effect if 2 = 1, but a strong dependence exists when 2 is small.

58

J.M. MARTiNEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MARTiN-MEIZOSO

The main contributions to F are given by (i) the decohesion resistance (work of fracture) of the interface F0, (ii) plastic deformation, which often accompanies crack extension, and (iii) friction along contacting crack faces [2]. A brief summary of the more fundamental results on these topics will be given in the following sections.

The Effect of Plasticity Continuum mechanics models have been developed to estimate the plasticity contribution to interface toughness, particularly for systems where either the film or the substrate is elasticplastic (metal/ceramic interfaces). These models incorporate a local fracture criterion to characterise microscopic aspects of the fracture process within the plastic zone. Two of these models will be briefly reviewed here: the embedded process zone (EPZ) model of Needleman [69,70] and Tvergaard and Hutchinson [71,72]; and the plasticity-free strip model of Suo, Shih and Varias [73], referred to as the SSV model. In the EPZ model a traction-separation law ( o - - d ) characterising the interface fracture process is embedded in the continuum description of the two adjoining solids as a boundary condition along the interface line. The two more important parameters characterising the fracture process in this model are the work of fracture per unit area of interface, F0, and the peak stress needed to cause interface separation, 6- (Fig. 12a). In the SSV model, an elastic, plasticity-free strip of thickness t is imposed between the line of the crack and the plastic zone, with the same elastic properties as the material that yields (Fig. 12b). Due to the elastic region surrounding the crack, the stress singularity is retained, and the condition for rupture is the requirement that the energy release rate should attain the work of fracture. These interface parameters (F0 and 6-, or t) constitute a phenomenological characterisation of the zone where the separation takes place along the interface, and must be obtained by fitting model predictions to experimental measurements.

Plastic zone

Plastic zone Metal~ t //

Metal

Cer~r^

Ceramic

Fo

8 (a)

(b)

Fig. 12. Schematic of two plasticity models for the interface crack: (a) EPZ model; (b) SSV model.

lnterfacial Cracking in Thin Films Structures

59

A unified model (the Unified Zone Model, UZM) has also been proposed to combine the capabilities of the EPZ and SSV models, by incorporating both the elastic zone of thickness t in the metal and the traction-separation relation at the interface. When the length of the process zone, d, is very small compared to t, d << t, the SSV model is dominant. At the other limit, when d >> t, the elastic zone has a minor influence and the EPZ model holds. All these models result in complicated functional relationships of the form [2,71,72] Fi/F o = F(O/cry ,N, E2 / E , ,h/R o , g/)

(15)

where Gy is the yield stress of the metal, N is the strain hardening exponent, h is the metal layer thickness, and R0 is a characteristic length representative of the plastic zone size, R o oc E1Fo/cr 2 . (The ratio O/cry is replaced by t/cry in the SSV model). There is also an influence of cry/Ei, vl and v~, but these have a minor effect [74]. Some general results can be summarised as follows: (i) Roughly speaking, plastic dissipation is negligible for weak interfaces, 0/cry < 3. (ii) If the height of the plastic zone is sufficiently small compared to h, the ratio Fi/F 0 is approximately independent of h. On the other hand, in the limit of very thin metal films, plastic dissipation becomes a negligible fraction of F0. Only in these two limiting cases, one can speak of a thickness-independent interface toughness. (iii) Theoretical and experimental work on the elastic-plastic interface crack problem has revealed a strong mixed mode effect due to plasticity, which results in an increase in toughness with increasing proportions of mode II [75-81 ]. This is not surprising as for a given value of G, the plastic zone in mode II loading is approximately twice as large as that for mode I. In view of the relevance of the plasticity contribution to interface toughness in bimaterial systems involving metals, it is to be expected that strain gradient plasticity effects [82] should play an important role as the micrometer scale is approached. Note that the conventional plasticity theory predicts interface stresses that are less than about 3 or 4 times ~y, depending on N (or an elastic strip thickness, in the SSV model, on the order of a small fraction of a micron for strong interfaces, scale at which the validity of conventional plasticity is uncertain) [83]. The size-dependent effect would increase the flow stress levels, which should result in higher stresses on the interface in the fracture process zone, and therefore the models could be extended to stronger interfaces.

Friction A third contribution to interface toughness due to contact between crack faces has also been proposed [84], which depends on roughness and the friction coefficient. This is a well-known toughening mechanism in other systems such as fibre pullout in composites, characterised by the frictional shear stress and the debond energy of the interface. However, this effect does not appear to account for the strong toughness dependence on mode-mixity when one of the solids has appreciable ductility [76].

60

J.M. MARTiNEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MARTIN-MEIZOSO

Crack Path

An interesting practical problem is that of the preference of an interface crack to continue along the interface or to kink into one of the adjoining materials. This depends on the relative energy release rates for continued extension of the debond, Gi, and for crack kinking, Gs. The ratio G i / G s is a function of the elastic mismatch, the phase angle of loading and the kink angle [63], and therefore G i / a s max results in a function of or, fland ~. If Fi and Fs denote the interface toughness and the substrate toughness, respectively, then the crack path can be predicted by comparing the ratio G i / G max to the ratio F i / F ~ . If F i / F s < G i/Gsmax the interface crack will tend to keep growing at the interface, while if the

inequality is reversed, then crack kinking will be favoured (Fig. 13a). The analysis also gives the minimum value of the toughness ratio, F s/F i , needed to ensure that the crack will not leave the interface for all combinations of loading (Fig. 13b). For smaller values of F~/F~, there is a range, 0 _<~ _ ~ .... the interface crack will kink into material 2. Note that the analysis also applies for kinking into material 1, using - a and -/5', see Eq. (11).

A

75

= - 0.5

60 C /-

(Fs[Fi)min 2.5 (no kink) 2

90

c

t

~

J

13=0

45

30 15 0

,

0.5

|

|

| ~

i

1

i

I

0.5 i

,

,

i

i

,

= l

1 1.5 2 Relative toughness, Fs I Fi

(a)

=

2.5

!

I

-0.75

-0.5

..

1

-0.25

v2

E2,

0

0

t

I

I

I

0.25

0.5

0.75

(b)

Fig. 13. Diagram of crack path prediction for interface cracks with fl = 0" (a) value of the phase angle below which the crack stays at the interface; (b) minimum substrate toughness for crack propagation along the interface for all phase angles of loading. After [63].

Residual Stresses

The influence of residual stresses on interface delamination has been analysed using combinations of analytical and numerical procedures [85-89]. Under tensile residual stresses, delaminations preferentially initiate at specimen edges and propagate into the material. In the case of pre-compressed films, and in the absence of external loading, decohesion only occurs if the film buckles above an initial interface separation. This produces a stress intensification at the perimeter of the interface crack, which can result in delamination and eventual spalling

Interfacial Cracking in Thin Films Structures

61

[85]. When the film is subject to external loading (as in top indentation), delamination can also occur without buckling [86]. The crack path analysis has also been extended to account for the influence of in-plane stresses in the substrate parallel to the interface [65]. The analysis shows that tensile in-plane stresses tend to cause cracks to depart from the interface, while compressive in-plane stresses stabilise interface cracks. CROSS SECTIONAL NANOINDENTATION Cross Sectional Nanoindentation (CSN) is a new technique for thin film adhesion characterisation [9]. The main difference between CSN and other indentation-based techniques is that the indentation is carried out in a cross section of the IC structure inside the silicon substrate (Fig. 14). The technique has been successfully applied to measure the fracture toughness of SiO2-SixNy interfaces, identified as the origin of critical damage in modern integrated circuitry.

SiN SiO2

Si substrate

(a)

(b)

Fig. 14. Schematic of (a) the CSN test configuration, and (b) orientation and placement of the indentation. Scanning electron microscopy of the indentation zone allows direct observation of the CSN delamination crack path (Fig. 15), whereas optical microscopy is used to obtain a top view of the crack extension along the SiO2-SixNy interface (Fig. 16). As shown in Fig. 15, once the crack has reached the interface of interest, the interfacial crack growth is governed by the rate of penetration of the diamond tip, that is used as a wedge for interfacial crack opening. Calculation of the interfacial fracture toughness, Fi, from CSN tests is based on the energy release rate concept. For a given tip displacement, crack arrest occurs when the strain energy release rate of the silicon nitride thin film, G, equals the interfacial surface energy Fi [90]. G is calculated from the thin film maximum deflection produced by CSN, the delamination area (obtained from SEM and optical microscopy measurements) and the elastic modulus of the SixNy thin film (a value of 171+5 GPa has been measured by using the Oliver & Pharr method [91]).

62

J.M. MART[NEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MARTiN-MEIZOSO

Acc.V Spol Magn 20.0 kV 3.2 2000x

Dol WD 1' BSE 10.0

[

10 lain

Fig. 15. SEM back-scattered micrograph showing delamination produced by CSN (crosssection view).

71.....

Fig. 16. Optical micrograph of the same test shown in Fig. 15. Delamination area is measured by comparing the fringe pattern observed in this picture with the distance measured in crosssection by SEM (wafer top view). The maximum thin film deflection produced by CSN is calculated from the load vs. tip displacement records and the Berkovich diamond tip geometry (Fig. 17). Cracking onset is related to a sudden tip movement that is identified in such curves by a jump in displacement at constant load. No further plastic deformation occurs once the crack has propagated to the interface of interest. Furthermore, a set of indentations carried out below the delamination threshold has confirmed that no significant deflection is produced in the film during the substrate plastic deformation. Therefore, the maximum indenter tip displacement in depth under load, A, can be divided into two components (Fig. 18): A = 8~ + 8~

(16)

Interfacial Cracking in Thin Films Structures

63

where ~ is the residual depth after unloading corresponding to the plastic response of the silicon substrate and c~ is the tip displacement responsible for thin film deflection. Finally, the SixNythin film deflection is calculated as u 0 = 5 d tan 65.3 ~

(17)

where u0 is the maximum thin film displacement in the y-axis, and the 65.3 ~ angle comes from the Berkovich tip geometry. Y ~.

~Applied

load

o~ 65.3~

wedge

SiN

Si substrate

Fig. 17. Scheme showing the correspondence between diamond tip displacement, A, and lateral silicon nitride thin film displacement after delamination onset, u0. interfacial delamination _ 4 ......

t2.ZA

60

~ 5o ~ 4 ~ i load ~~. 20 30 < , 10

.

~I

/'

/~ad

iI

_N__ 4oo N8oo

,,lOO

Tip displacement (nm)

Fig. 18. Load vs. tip displacement curve corresponding to the test shown in Figs. 15 and 16. Delamination is detected as a sudden jump in the diamond tip displacement.

CSN Modelling Figure 19 shows the plate model of a CSN experiment. The film is modelled as an axisymmetric (circular) plate with its edge clamped and an inner ring, at a distance b from the centre, with fixed vertical displacements u0. The loading condition is described by the load (or displacement) of the inner ring. For details about the stress analysis the reader is referred to classical elasticity texts (see, for example, [92]). In the case of a thin plate, Crzz,e,z and ~ are neglected. Using the radial and circumferential bending moments (Mr and Mo) and taking into

64

J.M. MART]NEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MART]N-MEIZOSO

account that the twisting moment Mro = 0, because of symmetry, the elastic strain energy of the plate can be written as [9]

!

2

U = D(1- v2-----~ (M~ + M o - 2~klrMo)rdr

(18)

where D : Eh3/[12(1 - v2)] is the flexural rigidity of the plate.

Yi !~l i"

a

.z

u0

W

I "'

"N~~~ T (a)

- - ~ i ~ b ~ - ~ - - - a - - ~ .... r "

"~

(b)

Fig. 19. Schematic of (a) the effect of a CSN experiment on the deflection of the film, and (b) the plate model for a CSN experiment. Obviously half the plate (a semicircular blister) will have approximately one-half of this energy. This does not affect the debonding energy G, defined by the ratio G =-(aU/OA)u ~ where A is the debonded area, because the area increment is also one-half of that for the case of a complete circular blister. The partial derivative is estimated numerically by calculating the strain energies corresponding to two plates with slightly different radii a and a + Aa. In the CSN experiment, only a semicircle is delaminated, therefore the circumferential stresses on the diametrical section are removed. The problem with a diametrical section of the plate is that part of the circumferential stresses croa are relaxed (in fact, they become zero at the new free edge). Thus, the elastic strain energy is reduced in comparison with one-half of the energy of the complete plate. Based on Eq. (18), the model can compute the contribution of the different moments (and therefore, stresses) to the elastic energy, U, and to the energy release rate, G. The difference between the radial component of the energy and the total energy (or the corresponding contributions to G) is within 20% for b/a > 0.1 and within 6% for b/a > 0.2. For the case of half a circle, some of the circumferential stresses are partially released. Therefore, the above figures for the energy variation should be regarded as upper bounds. The computer model has been validated against the simple case of a point load at the centre of a circular blister (b = 0), which can be solved analytically to give G = 8Du 2/a4 [9]. This simple case has been approximated in the numerical formulation as a limit case where the ratio b/a is very small (e.g., 0.001). The resulting values of G match the analytical solution with a relative error less than 0.01%. In order to estimate the influence of the partial relaxation of the circumferential stresses in the plate when a semicircular geometry is considered, the plate has also been modelled as an assembly of tapered beams of variable moment of inertia l ( r ) , as shown in Fig. 20. Using the bending theory of beams, only radial stresses ~r are considered and then all the circumferential stresses are neglected. The imposed displacement u0 at r = b can be replaced by an unknown bending moment M0 and an unknown point load F0 applied at r = b, see Fig. 21. Then, the

Interfacial Cracking in Thin Films Structures

65

bending moment along the beam, M ( r ) , can be calculated in terms of Mo and Fo, and the curvature is given by

u"= .El(r) . . .Eah . 3

,with b < r < a

r + F o 1-

(19)

The above differential equation can be solved using the boundary conditions: At r = b , u= uo and u ' = 0 At r = a , u = 0 and u' = 0

(20)

to obtain

2uo

U=(l+/7,)lnA+2(l-A)

Eln 2 l ,/r/ I

+ in r a

ln2 1-A

/

1 -r- + ~ + 1 a 2(1-2)

1

(21)

where 2 = b/a. Then the curvature is given by

Un=

2uo

a2[(1 + 2)lnA + 2(1 A)] -

1-A

1

I(r) = - .......................

9

r

a

(22)

arh 3 12

Fig. 20. Plate modelled as an assembly of tapered beams.

m m m

o

Fig. 21. Loading configuration assumed for the assembly of tapered beams. The elastic strain energy stored in the semicircular plate, a = er, is calculated using Eq. (22) as U=

where

E 5 D(1- vZ)eru2 F(A) [j I (- r ) u .2(r)dr= 2 a 2b

(23)

66

J.M. MART]NEZ-ESNAOLA, J.M. S,SNCHEZ, M.R. ELIZALDE, MART]N-MEIZOSO 1+2` In / 2, 1-2. [(1 + 2`) In A + 2(1-2`)]2 21n2, +

F(2`)

(24)

Then the energy release rate is given by 1 ((~U'~

a

_ D(I-

).o -

/

v 2)u 2 ( l _ 2,)4 2 F

(a-b)'

+

A

(25)

Figure 22 shows the energy release rates calculated using the circular plate model and the two analytical approximations (point load and assembly of tapered beams). Each of the analytical solutions constitutes a good approximation of the more accurate plate solution for a different range of aspect ratios 2, = b/a. For small values of A, 2` < 0.2, the point load solution is accurate within 10%, while for large values of 2`, 2` > 0.4, the assembly of tapered beams provides values which are accurate within 10%. In the intermediate range, 0.2 < 2` < 0.4, the maximum of the two analytical approximations can be used with an error less than 15%. For very large values of 2, (very large indentation wedges) the situation diverges more from that of a thin plate in bending. In that case, the shear stresses Crrzmay have a non-negligible influence on the strain energy and therefore on the value of G. This may explain the unexpected behaviour of G for values of 2, greater than about 0.9. 2.5

-

o

-

Circular plate - Tapered beams

...... "

1.5

(.9 (.9

0.5

.-"~

,,o.,,.,,,,""""""

,"

0

0

8Duo

Point load

Go-(a_b )4 I

I

I

I

I

I

I

I

I

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

X = b/a

Fig. 22. Comparison of G values resulting from the plate model and the analytical approximations.

CSN Results CSN experimental results showed that Fi values depend on the distance from the indentation to the interface, Fig. 23. The interfacial fracture toughness is a material property, and thus, a constant for a given combination of materials. Therefore, the reason for this behaviour must be found in one of the model limitations. The indentations must be carried out far away from the interface to avoid interactions between the crack and the stress-strain field induced by

67

Interfacial Cracking in Thin Films Structures

indentation. Under these circumstances, the effect of the indentation stress concentration on interfacial crack growth is negligible. This is clearly not fulfilled by indentations placed at a distance to the interface similar to the indentation size. Therefore, as a general recommendation, CSN tests must be carried out at a distance to the interface larger than the indentation size. The F; values obtained from these tests are between 1.2 and 1.8 J/m 2. The same thin film structure was tested using the four-point bending technique [23] and a value of 1.65 J/m 2 was obtained, result that is in fairly good agreement with the mean value of CSN results. 4 ~E 3 v

~2 O z

1 0

I

0

I

I

I

1

I

I

2

I

3

I

i

I

4

i

5

6

Distance to Si/SiO2 interface, d (gm) Fig. 23. Dependence of F; on the distance from the indentation mark to the interface. Other important result is the confirmation of the linear correlation between the delamination area and the maximum lateral thin film displacement after CSN delamination (Fig. 24). This result gives validity to one strong model hypothesis, i.e., that the interfacial crack grows to relax the elastic strain energy stored in the outer silicon nitride thin film, see Eq. (25).

j

~""3000 E ,~2500 ~ 2000 m

= o 1500 ,m

E o

1000

500 0

I

0

l

1

I

I

2

i

I

3

I

4

Uo (lam)

Fig. 24. Delamination area vs. maximum lateral displacement produced in the silicon nitride thin film by CSN testing. Experimental results agree with model predictions. The high resolution of the Nanoindenter II | diamond tip positioning system has suggested the adaptation of the CSN test to study patterned structures. Preliminary CSN qualitative results from indentations carried out in real integrated circuits show promising results in identifying zones susceptible to mechanical failure. This is a new capability not possible with any other test configuration.

68

J.M. MARTiNEZ-ESNAOLA, J.M. SANCHEZ, M.R. ELIZALDE, MART[N-MEIZOSO

CONCLUDING REMARKS Table 1 summarises the most important characteristics of the adhesion tests included in this review. Although some of them are suitable for qualitative assessment of some specific structures, a standardised procedure applicable to all film thicknesses and material combinations used in integrated circuits is still lacking. Table 1. Comparison of delamination test methods Stub-pull

Peeling

Blistering

Laser Spallation

Bending

Indentation / Scratching

CSN

Precracking facility Steady state crack growth

No

No

Yes

No

Yes

No

Yes

No

Yes

Yes

No

Yes

No

Yes

Spatial resolution

No

No

No

Limited

No

Yes

Yes

Special specimens

No

Yes

Yes

No

Yes

No

No

Throughput time Crack front observation Use of adhesives

Short

Long

Long

Short

Long

Short

Short

No

No

No

No

No

No

Yes

Yes

No

No

No

Yes

No

No

The main drawback of tests as peeling, blistering or bending is the use of complex test pieces that are expensive and time consuming. The production of such test pieces often requires changes with respect to conventional IC fabrication procedures, which raises the concem about the likely change of interfacial performance of these structures. The use of polymer adhesives (as in the case of stub-pull and bending tests) is also a source of test errors. These adhesives present a random distribution of flaws after curing that affect their fracture strength and have also been identified as source of misalignment. Another experimental issue is found in tests such as stub-pull and laser spallation, because the pressure wave not only produces delamination but also uncontrolled shattering of the film. Indentation tests are a natural choice for IC testing as they do not use any adhesives and require a short time to be carried out, which makes them suitable for IC production quality control. Additionally, indentation methods can be applied to IC materials without any special processing and allow testing of patterned structures because of their high spatial resolution capability. However, indentations carried out from top of the thin film produce a random cracking pattern not well understood yet. Cross Sectional Nanoindentation (CSN) has been successful in producing a controlled local cracking of ceramic-ceramic interfaces. An additional capability of the CSN technique is that it allows direct measurement of the delamination area and actual observation of the interfacial crack front, which can be used to study interfacial cracking micromechanisms. The CSN technique applied to blanket wafers gives a quantitative measurement of thin film ceramicceramic interfacial adhesion and has the potential for identifying the weakest interface of a thin film structure by interaction with indentation induced cracks. Furthermore, CSN is a quick

lnterfacial Cracking in Thin Films Structures

69

method that can be applied, up to now qualitatively, to a wide range of materials and structures due to its high spatial resolution. Preliminary results obtained for metal-ceramic thin film interfaces and for patterned structures are encouraging. The CSN models developed so far are based on linear elastic fracture mechanics and predict a linear relationship between the delamination area and the film lateral deflection that has been confirmed by the experimental results. However, the model assumptions are not fulfilled for indentations carried out at distances to the interface lower than the indentation size. Another model limitation is found when the silicon nitride thin film breaks during the test. The model is being extended to overcome this latter limitation. Additional refinements of the technique are required for the application of CSN to other material combinations, such as ceramic-metal, ceramic-polymer, or polymer-metal interfaces. A basic problem common to all adhesion test methods is the lack of a complete understanding of plastic phenomena induced by interfacial cracking. Although finite elements simulations are used in basic parametric studies involving plasticity, analytical solutions are only available in the elastic regime. Moreover, there is a lack of reliable measurements of basic mechanical properties of thin films, specially the yield stress and the hardening exponent. ACKNOWLEDGEMENTS The authors wish to thank the financial support of the Intel Corporation Research Council through the project entitled "Cross Sectional Nanoindentation for Thin Film Interface Adhesion Characterisation", for the realisation of this work. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

Nix, W.D. (1989) Metall. Trans. A 20A, 2217. Evans, A.G. and Hutchinson, J.W. (1995) Acta Metall. Mater. 43, 2507. Shen, Y.L., Suresh, S. and Blech, I.A. (1996) J. Appl. Phys. 80, 1388. Lee, J., Ma, Q., Marieb, T., Mack, A.S., Fujimoto, H., Flinn, P., Woolery, B. and Keys, L. (1995). In: Materials Reliability in Microelectronics V, MRS Proceedings 391, from [5]. Liu, X.H., Suo, Z., Ma, Q. and Fujimoto, H. (1998). In: Materials Reliability in Microelectronics VII1, pp. 313-324, Bravman, J.C., Marieb, T.N., Lloyd, J.R. and Korhonen, M.A. (Eds). Materials Research Society, Warrendale. Ma, Q. (1997)Jr. Mater. Res. 12, 840. Shih, C.F., Chen, W.T., Cotterell, B., Lahiri, S.K. and Zhang, Y.W. (1998). In: Electronic Packaging Materials Science X, pp. 3-13, Belton, D.J., Gaynes, M., Jacobs, E.G., Pearson, R. and Wu, T. (Eds). Materials Research Society, Warrendale. Ma, Q., Bumgarner, J., Fujimoto, H., Lane, M. and Dauskardt, R.H. (1997). In: Materials Reliability in Microelectronics VII, pp. 3-14, Clement, J.J., Keller, R.R., Krisch, K.S., Sanchez Jr., J.E. and Suo, Z. (Eds). Materials Research Society, Pittsburgh. S~nchez, J.M., E1-Mansy, S., Sun, B., Sherban, T., Fang, N., Pantuso, D., Ford, W., Elizalde, M.R., Martinez-Esnaola, J.M., Martin-Meizoso, A., Gil-Sevillano, J., Fuentes, M. and Maiz, J. (1999) Acta mater. 47, 4405. Evans, A.G., Rtihle, M., Dalgleish, B.J. and Charalambides, P.G. (1990) Metall. Trans. A 21A, 2419. Charalambides, P.G. and Evans, A.G. (1989) J. Am. Ceram. Soc. 72, 746.

70 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50.

J.M. MART]NEZ-ESNAOLA, J.M. StiNCHEZ, M.R. ELIZALDE, MART]N-MEIZOSO

Atkinson, A. and Guppy, R. (1991) Mat. Sci. and Tech., 7, 1031. Kim, K.S. and Aravas, N. (1988) Int. J. Solids Structures 24, 417. Kendall, K. (1971)J. Phys. D: Appl. Phys. 4, 1186. Gupta, V. and Pronin, A. (1995)J. Am. Ceram. Soc. 78, 1397. He, M.Y., Xu, F., Clarke, D.R., Ma, Q. and Fujimoto, H. (1997). In: Materials Reliability in Microelectronics VII, pp. 15-26, Clement, J.J., Keller, R.R., Krisch, K.S., Sanchez Jr., J.E. and Suo, Z. (Eds). Materials Research Society, Pittsburgh. Hohlfelder, R.J., Luo, H., Vlassak, J.J., Chidsey, C.E.D. and Nix, W.D. (1997). In: Thin Films: Stresses and Mechanical Properties VI, pp. 115-120, Gerberich, W.W., Gao, H., Sundgren, J.E. and Baker, S.P. (Eds). Materials Research Society, Pittsburgh. Cotterell, B. and Chen, Z. (1997) Int. J. Fracture 86, 191. Vossen, J.L., Mittal, K.L. (Eds) (1978) ASTM STP 640, 122, from [20]. Gupta, V., Argon, A.S., Parks, D.M. and Cornie, J.A. (1992) J. Mech. Phys. Solids 40, 141. Charalambides, P.G., Lund, J., McMeeking, R.M. and Evans, A.G. (1989) J. Appl. Mech. 111, 77. Dalgleish, B.J., Trumble, K.P. and Evans, A.G. (1989) Acta. Metall. 37, 1923. Dauskardt, R.H., Lane, M., Ma, Q. and Krishna, N. (1998) Engng. Fracture Mech. 61, 141. Pharr, G.M., Oliver, W.C. and Brotzen, J. (1992) J. Mater. Res. 3, 613. Cook, R.F. and Pharr, G.M. (I 994) J. Hard Mater. fi, 179. Marshall, D.B. and Evans, A.G. (1984) J. Appl. Phys. 56, 2632. Rossington, C., Evans, A.G., Marshall, D.B. and Khuri-Yakub, B.T. (1984) J. Appl. Phys. 56, 2639. Kriese, M.D., Moody, N.R. and Gerberich, W.W. (1998). In: Fundamentals of Nanoindentation and Nanotribology, pp. 365-370, Moody, N.R., Gerberich, W.W., Burnham, N. and Baker, S.P. (Eds). Materials Research Society, Warrendale. Rickerby, D.S. (1988) Surf. Coat. Tech. 36, 541. Steinmann, P.A. and Hintermann, H.E. (1989)J. Vac. Sci. Technol. A 7, 2267. Venkataraman, S.K., Nelson, J.C., Hsieh, A.J., Kohlstedt, D.L. and Gerberich, W.W. (1993) J. Adhes. Sci. Technol. 7, 1279. Thouless, M.D. (1998) Engng. Fracture Mech. 61, 75. Kriese, M.D., Boismier, D.A., Moody, N.R. and Gerberich, W.W. (1998) Engng. Fracture Mech. 61, 1. Cook, T.S. and Erdogan, F. (1972) Int. J. Engng. Science 10, 677. Atkinson, C. and Eftaxiopoulos, D.A. (1991) int. J. Fracture fi0, 159. Beom, H.G. and Atluri, S.N. (I 995) Engng. Fracture Mech. 52, 777. Blanco, C., Martinez-Esnaola, J.M., Atkinson, C. and Bastero, J.M. (1995) Int. J. Fracture 71, 99. Wang, X.M., Gao, S. and Shen, Y.P. (1996) Engng. Fracture Mech. 53, 107. Sung, J.C., Liou, J.Y. and Lin, Y.Y. (1996) J. Appl. Mech. 63, 190. Zak, A.R. and Williams, M.L. (1963) Jo Appl. Mech. 30, 142. Bogy, D.B. (1971) J. Appl. Mech. 38, 911. Ting, T.C.T. and Hoang, P.H. (1984) Int. J. Solids Structures 20, 439. Chen, D.H. and Harada, K. (1996) int. J. Fracture 81, 147. Erdogan, F. and Biricikoglu, V. (1973) Int. J. Engng. Science 11,745. Romeo, A. and Ballarini, R. (1995) J. Appl. Mech. 62, 614. Bogy, D.B. (1968) J. Appl. Mech. 35, 460. Hein, V.L. and Erdogan, F. (1971) Int. J. Fract. Mech. 7, 317. Liu, X.H., Suo, Z. and Ma, Q. (1999) Acta mater. 47, 67. Savruk, M.P., Shkarayev, S. and Madenci, E. (1999) Theor. Appl. Fracture Mech. 31,203. England, A.H. (1965) J. Appl. Mech. 32, 400.

Interracial Cracking in Thin Films Structures

51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92.

71

Erdogan, F. (1965) J. Appl. Mech. 32, 403. Malyshev, B.M. and Salganik, R.L. (1965) Int. J. Fracture Mech. 1, 114. Comninou, M. (1977) J. Appl. Mech. 44, 631. Comninou, M. (1977)J. Appl. Mech. 44, 780. Atkinson, C. (1982) Int. J. Fracture 18, 161. Atkinson, C. (1982) Int. J. Fracture 19, 131. Rice, J.R. (1988) J. Appl. Mech. 55, 98. Ni, L. and Nemat-Nasser, S. (1992) Quarterly of Appl. Math. 50, 305. Atkinson, C., Bastero, C. and Sfinchez, M.I. (1994) Int. J. Fracture 67, 231. Choi, S.R., Chong, C.H. and Chai, Y.S. (1994) Int. J. Fracture 67, 143. Hayashi, K. and Nemat-Nasser, S. (1981)J. Appl. Mech. 48, 520. Hayashi, K. and Nemat-Nasser, S. (1981) J. Appl. Mech. 48, 529. He, M.Y. and Hutchinson, J.W. (I 989) J. Appl. Mech. 56, 270. Miller, G.R. and Stock, W.L. (1989)J. Appl. Mech. 56, 844. He, M.Y., Bartlett, A., Evans, A.G. and Hutchinson, J.W. (1991) J. Am. Ceram. Soc. 74, 767. Wang, T.C. (1994) Int. J. Solids Structures 31,629. Dundurs, J. (1969)J. Appl. Mech. 36, 650. Hutchinson, J.W. and Suo, Z. (1991) Advances in Appl. Mech. 29, 63. Needleman, A. (1987)J. Appl. Mech. 54, 525. Needleman, A. (i 990) J. Mech. Phys. Solids 38, 289. Tvergaard, V. and Hutchinson, J.W. (1992) J. Mech. Phys. Solids 40, 1377. Tvergaard, V. and Hutchinson, J.W. (1993) J. Mech. Phys. Solids 41, 1119. Suo, Z., Shih, C.F. and Varias, A.G. (1993) Acta Metall. Mater. 41,151. Wei, Y. and Hutchinson, J.W. (1997) J. Mech. Phys. Solids 45, 1137. Cao, H.C. and Evans, A.G. (1989) Mech. Mater. 7, 295. Liechti, K.M. and Chai, Y.S. (1992) J. Appl. Mech. 59, 295. Thouless, M.D. (1990) Acta Metall. Mater. 38, 1135. Shih, C.F. and Asaro, R.J. (1988) J. Appl. Mech. 55, 299. Zywicz, E. and Parks, D.M. (1992) J. Mech. Phys. Solids 40, 511. Bose, K. and Ponte Castafieda, P. (1992) J. Mech. Phys. Solids 40, 1053. Shih, C.F. (1991) Mater. Sci. Engng. A143, 77. Fleck, N.A. and Hutchinson, J.W. (1997) Advances in Appl. Mech. 33,295. Hutchinson, J.W. and Evans, A.G. (2000) Acta mater. 48, 125. Evans, A.G. and Hutchinson, J.W. (1989) Acta Metall. 37, 909. Evans, A.G. and Hutchinson, J.W. (1984) Int. J. Solids Structures 20, 455. Marshall, D.B. and Evans, A.G. (1984)J. Appl. Phys. 56, 2632. Thouless, M.D., Evans, A.G., Ashby, M.F. and Hutchinson, J.W. (1987) Acta Metall. 35, 1333. Hu, M.S., Thouless, M.D. and Evans, A.G. (1988) Acta Metall. 36, 1301. Drory, M.D., Thouless, M.D. and Evans, A.G. (1988) Acta Metall. 36, 2019. Obreimoff, J.W. (1930) Proc. R. Soc. A 127, 290. Oliver, W.C. and Pharr, G.M. (1992)J. Mater. Res. 7, 1564. Young, W.C. (1989). Roark's Formulas for Stress & Strain. McGraw-Hill, New York.

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73

D E S I G N I N G AGAINST FRETTING FATIGUE IN A E R O E N G I N E S C. Ruiz D. Nowell Oxford UTC for Solid Mechanics Department of Engineering Science University of Oxford Parks Road Oxford OX1 3PJ

ABSTRACT Gas turbines used for aircraft propulsion incorporate a large number of mechanical joints, where fretting fatigue is an important design consideration. Chief amongst them are the dovetail and firtree joints between blades and disks, particularly in the fan assembly and in the low pressure stages of the compressor where the operating temperature is sufficiently low to exclude the possibility of creep. This paper reviews some early designs and, after a brief description of the mechanics of fretting fatigue, presents current research of direct application to design. KEYWORDS Fretting, wear, dovetail joints, contact mechanics, fatigue. INTRODUCTION Failures of many mechanical components result from fatigue, a term attributed to Poncelet who, according to Timoshenko [1] spoke of the 'fatigue' of metals under repeated action of compression and tension to the workers of Metz in 1839. The importance of the problem led to the development of design rules based on service experience even before the first systematic studies were conducted by W6hler between 1860 and 1910. Although the work of W6hler and other investigators in the first decades of the last century helped to understand the basic mechanics of the process, fatigue still remains as one of the most important causes of failure and, not surprisingly, is still a rich field for academic and industrial research. Thus, Manson [2], observed that the number of scientific publications on fatigue has grown at such a rate that to conduct a comprehensive bibliographical survey and to read all new relevant publications would virtually prevent any newcomer to the field from doing any original work. On the other hand, the service experience accumulated over many years has been

74

C. RUIZ, D. NOWELL

incorporated into design rules which, when followed, suffice to avoid fatigue failures in most situations. This does not deny the value of fundamental research in the subject and of providing fatigue data for new materials. There are, however, many situations where just good engineering judgement is not an adequate safeguard against failure. Fretting fatigue is one of them. Fretting occurs when two bodies held together undergo a small localised relative displacement, typically of the order of 10 Nm. It differs from normal wear in that the displacements are much smaller and that any wear debris remains trapped between the two surfaces in contact. Well known examples of fretting fatigue are found in bolted or riveted joints, wheels and pulleys shrunk onto shafts, splined couplings and dovetail and firtree joints between blades and disks in rotating turbines and compressors. As in conventional fatigue, simple design rules are sufficient to prevent fretting fatigue in most situations [3] but do not provide a quantifiable measure of strength and do not therefore help when it is required to optimise the design or to ensure the integrity of critical components.

Fig. 1. A modern high by-pass ratio aero-engine showing components susceptible to fretting fatigue damage. [Rolls-Royce] The gas turbines used for aircraft propulsion contain a large number of elements where fatigue fretting needs to be considered as a design criterion, even if it may be subsequently dismissed in some cases. The roots of the fan blades may sustain centrifugal forces of the order of 10 MN. The high levels of bulk stress and contact pressure between the disk and the blade root together with the relative displacements that occur as the engine goes through its operational cycle make fretting fatigue an important if not the main design criterion. The possibility of a blade root failure could have catastrophic consequences and necessitates the inclusion of a containment shielding whose weight represents a loss of load carrying capacity and an increase in fuel consumption. Any improvement in the life of the fixing or in the accuracy with which the strength is assessed has an important bearing on the integrity and overall cost of the engine.

Designing Against Fretting Fatigue in Aeroengines

75

In contrast, splined shafts are designed primarily for stiffness and are subjected to relatively low stress levels with the result that fretting fatigue is seldom an important consideration. A similar conclusion applies to the roots of turbine blades where creep rather than fatigue become the dominant criterion. As discussed later, both firtree and dovetail roots are used to fix the blades on to the disks, the former being preferred for turbines and the former for compressors. Typical designs are illustrated in figure 2.

Oov:e, Qil.

Fig. 2. Typical firtree and dovetail configuration for blade roots. Contact between blade and disk in a firtree joint depends on the manufacturing tolerances and may vary over the lifetime of the engine as a result of wear or deformation of the flanks. The dovetail, which may be regarded as a single tooth firtree, presents a simpler problem while lessons learnt from its study remain applicable to other geometry. Designing against fretting fatigue of splined couplings, bolted flanged joints, gears, bearings and other mechanical elements involving interference fits in aeroengines largely follows conventional rules and will not be discussed further in this paper. The design of blade root joints, particularly in the low temperature compressor stages and front fan, on the other hand is peculiar to these machines and presents an important challenge. This paper will concentrate on the treatment of dovetail joints, of which there may be several hundred in a given engine. FUNDAMENTAL ASPECTS OF FRETTING FATIGUE The existence of a no-slip region in fretting fatigue was identified by Johnson and O'Connor [4,5] who showed that fretting damage resulted from the microslip that occur at the edges of the areas of contact. Nishioka and Hirakawa [6-10] conducted an extensive series of investigations from which they concluded that initiation and propagation cracks responded to different factors. Crack initiation was found to depend mainly on the contact stresses and occurred in the vicinity of the high localised stress concentrations caused by the frictional forces between the surfaces in contact. Crack propagation on the other hand responded to the bulk stress field away from the surface. They also confirmed the results of Field and Waters [11, 12] who observed that fretting fatigue damage depended on both the slip amplitude and

76

C. R UIZ, D. NO WELL

the bulk stresses and ascribed fretting damage to high strain fatigue of the micro-junctions between the contacting surfaces which were critically strained by the relative displacement. When this exceeds a critical value, the microfunctions break. High strain fatigue no longer occurs and the mechanism of fretting gives way to conventional wear. The net effect on the fretting fatigue strength was that this decreased with increasing slip amplitude until a point was reached where abrasive wear governed the process and the strength increased again. The work of O'Connor and his collaborators in Oxford [ 13,14,15] helped to set the basis for much of our present understanding and pointed out most of the problems addressed by current research. Their main conclusions may be summarised as follows:Cracks initiate at the edge of the surfaces in contact where microjoints between asperites are formed and relative slip causes localised high strain fatigue. ii.

In the absence of a bulk propagating stress fretting damage has a negligible effect on the fatigue strength.

iii

As the fretting process continues the real areas of contact grow fewer but increase in size, the contact stress field extends over a larger volume of material and larger cracks appear provided that the bulk stress is sufficiently high.

Work on the mechanics of fretting fatigue has continued since the pioneering work of O'Connor in parallel to that on the materials aspects of the problem. It has been generally recognised that the fretting fatigue process can be divided into three distinct phases: (i) (ii) (iii)

Crack initiation Short crack propagation Long crack propagation

Stage (iii) is most amenable to analysis, since LEFM usually applies and progress in the 1970s 1980s has made evaluation of stress intensity factors under rapidly varying contact stress fields reasonably routine [16, 17]. In any practical fretting problem crack loading is almost always non-proportional and mixed-mode for part of the cycle, and this can lead to complications. However, in many applications the long crack propagation phase accounts for a relatively small proportion of the total component life. In contrast, the crack initiation phase is relatively complex to analyse. There is an inevitable dependence on local conditions at the contact interface and it ma be necessary to consider the contact at an asperity level. Hills and Nowell [18, 19] have highlighted a number of important length scales which must be considered in any analysis of the initiation problem. A number of attempts have been made to apply global stress or displacement based parameters to the prediction of initiation life. Ruiz et al. [20] proposed a criteria based on the density of energy dissipation multiplied by the direct stress component parallel to the surface. Nowell and Hills [21 ] showed that this parameter appeared to work well in a different geometry from that considered in [20]. More recently, stress-based criteria have been proposed, using multiaxial fatigue initiation parameters have been proposed [22, 23]. Fouvry et al. [24] have employed a volume averaging approach, using the Dang Van criterion [25] and have shown that this can give more realistic life predictions for cases where the stress field varies very rapidly. The short

Designing Against Fretting Fatigue in Aeroengines

77

crack phase (ii) has received relatively little attention until recently, but Nowell and Arafijo have proposed a crack arrest criterion for short cracks, which provides an alternative explanation for the size effect noted in [26]. EVOLUTION OF THE DESIGN OF BLADE ROOTS The ancestry of the modern turbine can be traced back to the radial flow steam turbine designed by Parsons in 1894 [27]. This machine and all the subsequent models incorporated blades attached to the disks by means of mechanical joints similar to those currently used. The same methods, i.e., T-slots, dovetails and firtrees, have been used in rotating machinery ever since [28, 29]. Rudimentary rules for the design of such joints are found in early treatises on mechanical design [30]. Although the design criteria were based only on average bearing, shear and bending stresses, the weakening effect of sharp reentrant corners was already recognised. As early as 1906, Gentsch [31] offered guidance on the design of dovetails and provided several examples, not always to be imitated too closely, since as in the one shown in figure 3, no attention has been paid to stress concentration, fretting or

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78

C. R UIZ, D. NO WELL

Engineering in 1924 [32] G. F. Swain, Professor of Civil Engineering in Harvard University went as far as disputing the conclusions reached by the photoelastic work of Coker and Filon [33] who confirmed that the theoretical value of the stress concentration factor for a circular hole in an infinitely large plate was 3, regardless of the hole diameter on the grounds that 'as the diameter of the hole becomes zero the value of the ratio becomes unity. Any formula which does not give this result must be erroneous ... (The writer) has no time for such illusory mathematical recreations'. The work of Coker and Filon over several decades, compiled in [33], was however taken seriously by more enlightened engineers, in particular by Stodola, who published in the 1920s what has come to be regarded as the definitive treatise on steam and gas turbines [34]. Stodola recognised the importance of fretting fatigue, describing a method of fixing that 'reduced the danger of rubbing in reaction turbines by punching with a steel die a depression into the end of the bronze bucket, figure 4. This

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Fig. 4. Blade root and top in Brown Bovery turbine of 1920 [34] leaves an extremely thin wall of metal which in rubbing is ground away.' T-slots and ways of reinforcing the bucket root were also discussed in connection with an A.E.G. turbine featuring a tapering root width (Figure 5(a)). The effect of rounding the corners was shown to increase the strength of the dovetail as measured by the impact energy required to break the blade (Figure 5(b)). The cylindrical root, favoured by de Laval, was seen as a logical progression in an attempt to minimise stress concentrations at the corners (Figure 5(c)). The main design principles set up by Stodola have remained virtually unchanged. They are:Limits are set to the average stress, the contact (crushing) stress and the peak stress. The latter is based on the elastic stress concentration factor usually determined by photoelasticity. All corners are rounded and clearance is specified between the two elements at the ends of the flanks in contact. Fretting damage, leading to crack initiation, should be reduced by means of antifretting coatings, lower contact pressures or reduced slip. Crack growth should be prevented by reducing the bulk tensile stress in the region liable to fretting.

Designing Against Fretting Fatigue in Aeroengines

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80

C. R UIZ, D. NO WELL

Small-scale testing is attractive, of course, because of its relatively low cost. A number of attempts have been made to develop small-scale rigs. Most of this work, still unpublished, has included four blades in a section of a disc and double or single back-to-back blades in a sheet modelling the disc. In these tests, concern has been with geometrical similarity between the corresponding stress fields and the displacement between blade and disc. Backto-back specimens, of the type shown in figure 6 have been designed to overcome this problem [37, 38, 20].

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Fig. 6. General arrangement of test piece and typical dovetail profile Material Ti-6A1-4V [20] The test piece in [20] was designed taking as reference the results obtained from the photoelastic analysis of a 600 mm diameter epoxy spinning disc with simulated blades. The stress trajectories, isoclinics and isochromatics were found with the disc spinning at 2000 r.p.m, from photographs obtained by means of a stroboscopic lamp. The experimental results were checked against a 2-D finite element code developed in Oxford for that purpose [37, 39]. Any of the modern commercial non-linear codes currently in use, such as ABAQUS, have since been found to be preferable since they are, in principle, capable of analysing 3-D geometries. Test pieces similar to the one shown in figure 6 with various aspect ratios, cutout depth, profiles and with one or three pairs of back-to-back blades were machined from the same photoelastic material (Araldite CT200) used for the spinning disc and loaded in a polariscope by means of a biaxial flame. Typical results are compared in figure 7.

Designing Against Fretting Fatigue in Aeroengines

~

81

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3 bl.ode

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,-L_I

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300 ~4kN

Fig. 7. Comparison between isochromatic fringes for spinning disc and test piece with one pair of back-to-back blades (a) and with three pairs, (b). From figure 7, it is apparent that the fringe patterns in the one pair back-to-back do not agree entirely with those found in the spinning test. The fringes tend to extend further round the interface towards the rear of the dovetail, the maximum fringe orders occurring at the dovetail corners as well as on the front load bearing face. Qualitatively this would seem to be due to the greater ease with which the dovetail can open up producing bending stresses at the radiused corners. Also the bulk fringes are diffused over a greater area and follow the interface less closely. Attempts to improve the fringe pattern in this basic geometry proved to be unsuccessful. Following the idea presented of dovetail opening it was thought that greater rigidity against this type of motion should improve the fringes. However, this spread the maximum fringes

82

C. R UIZ, D. NO WELL

over greater areas, shifting them toward the rear face. This caused the bulk fringes to move away from the interface producing a definitely less representative specimen. Radiusing the transition between the dovetail and the ends causes the dovetail to open even further, resulting in a greater localisation of stress at the rear. It was finally concluded that simple modifications to this model would not produce the results required. In contrast, the three pair back-to-back test piece agrees better with the spinning disc results, the only difference being the proximity of the lower order fringes to the dovetail contour. All the tests performed between 1983 and 1988 in Oxford used the three pair back-to-back test piece shown in figure 6. However, the one pair back-to-back was shown later to provide satisfactory results [40] and is currently preferred since it is much cheaper and it is easier to set in the testing machine. As previously discussed, slip between surfaces in contact plays an essential role in the phenomena of fretting and of wear. The slip can be calculated by finite elements but a limitation of all the computer codes arises from the need to assume a value of the coefficient of friction which, in the case of Oxford code [39] remains fixed during the calculation. Since friction strongly affects the behaviour of the joint, it is necessary to repeat the analysis for several values or to deduce the correct value from the fatigue test. Furthermore, the program is only an idealised model, whose accuracy depends on the importance of factors such as surface irregularities, machining imperfections, eccentricity of loading, etc., requiring experimental guidance and validation. Besides this function, experimental work also helps to ascertain the nonlinear load-displacement of the joint upon load cycling, of particular importance for the study of vibration damping. The most valuable information to be obtained from an experiment would be the amount of relative slip and separation at the contact surface since this can be incorporated into the numerical analysis, resolving the uncertainties described in the foregoing. Ruiz, Post and Gzarnek [41] used the high sensitivity Moire interferometric technique originally developed by Post [42] to study the displacements of blade and simulated disc in a dovetail joint. The technique involves illuminating a 1200 lines/mm diffraction grating fixed to the test piece with two laser beams. The resulting interference pattern, shown in figure 8, provides a map of loci of equal displacement. The difference in displacement between the points on one fringe and those on an adjacent fringe is 0.4 ~m. A similar technique, with an interferometer incorporating a pulsed laser has been used to provide real-time interferograms while the test piece is under cyclic loading [43]. In the experiment described in [41 ], the test piece, shown in figure 9, was subjected to a load of 4.5 kN along the axis of the blades,

Designing Against Fretting Fatigue in Aeroengines

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thickness 3ram

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Fig. 9. General arrangement of test piece used for interferometric measurement of displacement. Material Mild Steel [41] giving a nominal stress on the blade stem of 250 MPa. The average slip along the straight flanks was 20 t.tm. None of the pairs of points in contact stuck together. For this condition any surface damage would be strictly due to wear rather than to a true fretting mechanism. Refinements to the interferometric technique have been introduced in recent years with the result that it is now possible to obtain displacement maps automatically with a sensitivity better than 10 nm [44, 45]. The technique is not, however, used very often since the purpose of the experiments was fulfilled by validating the results of the finite element codes which provide accurate information with minimal effort and cost [46]. Typical results for the test piece of figure 6 under biaxial loads of 20, 40 and 80 kN and friction coefficients 0.5 and 1.5 are shown in figures 10, 11 and 12 [39].

84

C. R UIZ, D. NO WELL

Contact is normally made only along the straight section of the flank, as shown in figure 10 for the three loading conditions and values of the friction coefficient. As the disc loading increases, the dovetail opens up and allows increasing slip. For tx = 1.5 there is a dramatic change as the central part of the flank, sticking at low loads, begins to slip. This is accompanied by a separation at the root and top ends and is reflected in a change in the shear stress distribution.

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Fig. 10. Calculated interface conditions for Ti-6A1-4V dovetail. The stress distribution on the disc along the dovetail is plotted in figure 10. It will be observed that (1) for a given value of the friction coefficient, decreasing the disc load results in shifting the normal stress away from the straight flank, reducing its maximum value; (2) as the friction decreases the maximum normal stress increases and the tangential stress decreases.

Designing Against Fretting Fatigue in Aeroengines

N =0.5 20kN

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Fig. 11. Stress distribution in disc along dovetail (a) 20 kN disc load, (b) 40 kN, (c) 80 kN Figure 12 shows the stress distribution along the dovetail for the central blade. The normal and shear stresses are obviously the same as for the disc but the peak tangential stress is now located near the top with a low value towards the root.

86

C. R UIZ, D. NO WELL

....................................................................................................................................... .

=

, ...............................

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Fig. 12. Stress distribution in blade along dovetail (a) 20 kN disc load, (b) 40 kN, (c) 80 kN. TESTING MACHINES Having designed a test piece that reproduces the stress and displacement condition prevailing in the rotating disc assembly, it remains to design a testing machine capable of applying a biaxial load. Such machines are not new. An example, used for creep testing of plastic sheets, is described by Johnson and Khan [47]. In common of all the other designs known to the author [48, 49], this machine consists of two pairs of identical actuators fixed to a rigid square frame as shown diagrammatically in figure 13(a). The use of four actuators, when only two working against reactive anchors on opposite sides of the frame would seem to be sufficient, is to prevent the expansion of the test piece under load resulting in a displacement of the centroid and hence in sideways loading.

Designing Against Fretting Fatigue in Aeroengines

87

],,..cycLic load on /+ j o c k s (o)

(b)

(C)

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Fig. 13. Alternative types of testing machine (a) Conventional machine with 4 actuators, (b) static/cyclic, (c) cyclic/cyclic with two floating actuators.

88

C. R UIZ, D. NO WELL

It follows from the early photoelastic studies that the centrifugal forces on the disc have a relatively small effect on the peak stresses, which depend mainly on the blades. This observation would imply that crack initiation might be entirely governed by blade loading. The disc load would, on the other hand, affect crack propagation. It would therefore be possible to study at least the process of crack initiation by applying a cyclic load to the blades using a conventional single axis fatigue machine while maintaining the disc under a fixed load. To this end a lightweight loading flame with a short stroke hydraulic jack free to follow the oscillatory movement of the test piece was designed [37]. This arrangement is shown schematically in figure 13 (b). As long as the displacement is small the change in extension of the springs does not cause a significant variation in the supporting force. The dynamic load on the specimen depends on the mass suspended, the spring stiffness, the vibration amplitude and frequency and can be minimised by tuning. The third type of testing machine, figure 13 (c), has been used successfully in Oxford for over a decade [40]. In this machine the vertical actuator is supported through a spring and damper arrangement on a cruciform structure and the horizontal actuator is suspended from a rectangular frame also through springs. It is important to ensure that the specimen is always loaded along two perpendicular axes with minimum bending, torsion and shear applied at the ends. To achieve this end, the machine was modelled as a system of lumped masses and springs and tuned to minimise the displacement of the centre of the specimen. Moving masses, i.e., piston, actuator rod, dynamometer and active clamp, must be kept as light as possible in all fatigue testing machines. In this biaxial arrangement the centre of the specimen must remain fixed in space, otherwise the vertical motion of the specimen will result in the oscillation of the whole horizontal actuator. Likewise, a horizontal displacement will cause the vertical actuator to rock. Thus, the reacting clamp and supporting beam must also be very light without sacrificing stiffness. The operating frequency is normally kept below 10 Hz, sufficient in practice to provide data for the low cycle fatigue problems that may arise during operation. The normal engine operational cycle consists of starting and warming up, rise to full power for take off, reduction to cruising conditions after the short take off period, idling prior to landing, and a power surge when thrust reversal is applied on landing before taxiing and final engine shutdown. The stress amplitude corresponding to each part of the cycle defines the magnitude of the blade and disc loads applied by the testing machine. The total number of cycles in any testing programme does not normally exceed 500,000. In addition to this cyclic loading, fluid flow round the blades causes these to vibrate at high frequencies. The combination of the low frequency high amplitude load cycles and of this high frequency vibration is known to have a pronounced effect on the fatigue strength of the blade root.[50] To model this phenomenon, the machine of figure 13(c) may be modified. The vertical actuator remains the same as in the original machine but the horizontal actuator, which applies the loading to the blades, is replaced by a balanced pair of identical actuators. The reason for this is that the test piece is now loaded at two different frequencies, a low frequency of less than 1 Hz to reproduce the low cycle fatigue process and a high frequency component applied only to the blades, at 10 - 50 Hz to model the blade vibration. It is therefore no longer possible to tune the mass-and-spring model so as to minimise the lateral loading applied to the specimen. Blade vibration may be induced with a third actuator.

Designing Against Fretting Fatigue in Aeroengines

89

FAILURE ANALYSIS OF DOVETAILS UNDER LCF LOADING Referring to figure 10, rubbing at the blade/disc interface may result in wear when the coefficient of friction and the loads are sufficiently low to cause slip or in fretting. Wear damage takes the form of pits and scratches. Both constitute stress raisers and hence accelerate the process of fatigue crack initiation but they are not as severe as the fretting damage found as the loads and friction coefficient increase and a stick/slip contact condition arises. A series of tests using Ti-6A1-4V (IMI 829) sheets to represent the disc and high strength steel blades (FV535) have been conducted to explore the difference between both processes. When tested under a disc load cycling between 2 and 20 kN the damage is spread over a fairly narrow band near the top of the dovetail, as shown in figure 14 and over irregular patches near the root. Referring to figures 10 and 11 the narrow band corresponds to a region of low stresses in a state of 'slip'. The worst damage occurs at the highly stressed region of the flank adjoining the radiused transition which is in a 'stick' state. As the load increases damage occurs much earlier and the distinction between damaged and undamaged zones is much sharper, as shown in figure 15.

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.

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Fig. 14. Surface damage of the disc dovetail. Disc load 2-20 kN, 91,000 cycles [52] In figure 15 there is an indication of a narrow pitted band at the top separated from the undamaged surface by dark lines. Traces of oxidised abrasive particles, removed from the central band were found along these lines. At the bottom of the dovetail there is a wide, dark, pitted band. The transition between the damaged and the undamaged region is much sharper.

90

C. R UIZ, D. NO WELL

:::::::::::::::::::::::::::::::....

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Fig. 15. Surface damage of the disc dovetail. Disc load 4-80 kN, 39,800 cycles [52] The damage appears to be worse near the root. Two reasons may be suggested for this:1. Pitting results from the abrasive particles retained at the root of the dovetail. 2. The shear stress is greater near the root than towards the top. (See figure 11). It has been suggested [20, 40, 41] that fretting damage depends on the product of the shear stress times the relative displacement between the points in contact, i.e., on the work done by the friction force. At the edge of the stick zone, a combination of high shear and beginning of slip cause tearing of the microwelds between surface asperities and result in fretting damage, as has been previously discussed. Close examination of the damaged zone - figure 16 - reveals the existence of two bands of score marks.

Designing Against Fretting Fatigue in Aeroengines

91

Fig. 16. Close examination of fretting damage with S.E.M. (a) zone in contact (b) zone near edge [52] The score marks start from the top side of the crack while the other side is pitted. The crack starts at the boundary between stick and slip or slip and separation and, as it grows, the surface compliance changes with a consequent shift of the stick/slip boundary. Further evidence of the intense surface activity that takes place during crack initiation is provided by the micrograph of figure 17. A number of small cracks, with a length of less than 0.1 mm, can be seen. One has grown to a length of about 0.5 mm and another longer crack has resulted from the junction of several small ones:

Fig. 17. Fatigue cracks in Ti-6A1-4V disc.

92

C. R UIZ, D. NO WELL

The location of the major fatigue crack, drawn in figure 11, does not coincide with that of the peak stresses. This is not surprising when one considers that for the fretting fatigue process can be subdivided into a first stage of crack initiation, which is governed by the shear stress and slip amplitude, and a second stage of crack growth which is more likely to depend on the tensile stress applied to the crack tip. As seen in figure 17, a large number of small cracks start in the slip zone near the stick/slip boundary, where shear stress and slip combine to give a high value of the friction work but only one of them grows to a size sufficient to bring about the final fracture. Figure 11 suggests that the process of growth is governed by the peak tensile stress. As seen in figure 12, the tensile load in the blade where the worst fretting damage is found, i.e. near the root, is very low. This is the reason why the failure is always located in the disc in the low cycle fatigue tests without high frequency blade vibration. Towards the top of the blade where the tensile stress is higher, there is considerably less fretting damage and crack initiation is therefore a very slow process which would take considerably longer than it takes for a crack to start and to grow in the more critical region near the dovetail root in the disk. EFFECT OF BLADE VIBRATION To induce the vibration of the blade, the principal actuators in the modified machine can apply a sinusoidally cycling force with an amplitude of up to 5 kN at a frequency of up to 50 Hz. The bending moment at the blade root depends on the position of the shaker and the length and stiffness of the test piece and its attachments to the testing machine. In spite of the difficulty presented by the need to model the whole assembly, consisting of the hydraulic jack, the linkages between jack and test piece, the test piece itself, the shakers and the frame of the testing machine, a detailed finite element analysis has been performed. The loads applied to the test piece are instead calculated from the signals provided by strain gauges fixed to the blades and to the disc in the test piece. The testing programme is still at an early stage and no final conclusions have yet been reached. It would appear however that the high frequency component of the stress is much lower than the low frequency component and the overall state of stress of the disc remains similar to the one described in figure 11. The only significant differences are that as a result of the bending moment and the amount of slip at the blade/disc interfaces increases and the tangential stress amplitude in the blade at the neck of the dovetail also increases. The result is a tendency for failures to occur in the blade rather than in the disc. HIGH TEMPERATURE TESTS AND JOINTS BETWEEN METALS AND CERAMICS A few remarks follow on this topic, of interest when dealing with the last stages of the compressor and with the turbine. Tests conducted in Oxford with Ti-6A1-4V specimens have shown that failure is no longer governed by fretting. At temperatures of 600~ and above the titanium alloy is soon oxidized. The friction coefficient then drops to less than 0.2 and contact conditions are such that only slip and hence conventional wear occur. Because the oxice layer protects the surface from further damage, crack initiation is retarded and crack propagation, when it takes place, is the result of creep or of the combination of creep with fatigue. [51 ].

Designing Against Fretting Fatigue in Aeroengines

93

High strength ceramics and in particular silicon nitride are still being regarded as possible materials for the fabrication of components exposed to high temperatures, such as turbine blades, bearings and shrouds. These components may be joined to metals through interlocking joints where the possibility of wear and fretting must be considered. The mechanism of crack growth under cyclic loading in ceramics is still known only imperfectly but it is generally agreed that the time during which the maximum load is maintained is as important as the actual number of cycles. Also, at high temperatures, wear and oxidation result in an intermediate layer with good lubrication properties separating the ceramic component from the metal base [53, 54]. Fretting is irrelevant. Since it is creep rather than cyclic fatigue that is mainly responsible for the propagation of cracks, it follows that the test can be simplified to include wear damage and static loading. In the testing method proposed by Wang and Ruiz [54, 55], a pad, pressed against the face in tension of a ceramic beam under static bending, oscillates at a frequency of 40 Hz and an amplitude of 0.5 mm. The whole assembly is maintained at constant temperature inside a furnace. The residual strength and Weibull modulus of the ceramic beam after a specified time is then measured by means of a three-point bending test. CONCLUSION The basic mechanisms involved in fretting, fretting fatigue and wear are now fairly well understood but quantitatively accurate models of these phenomena have not yet been fully developed. The state of stress, the relative displacement of the surfaces in contact, the materials and environmental conditions all affect the strength of the joint. As a result of the service experience acquired over almost one century, designers have acquired sufficient engineering judgment to avoid fretting fatigue in conventional situations but the challenge presented by modern high efficiency lightweight machines such as aeroengines requires a more scientific approach. An accurate stress, strain and displacement analysis is pivotal to such a treatment. It has been shown that the contact stresses and the relative displacements can be calculated using finite elements or some other approach but, in common with other problems in the presence of stress singularities, the mathematical model does not necessarily reflect a reality complicated by features such as surface irregularities, anisotropy of the materials in contact, local plasticity and the possible presence of non-metallic layers. A problem, peculiar to finite elements, is that the mesh size effects the results. For these reasons, the state of stress and displacement cannot be known with absolute certainty. This being the case, it follows that the quantification of the crack initiation stage presents a rather daunting challenge. Once the crack has started, the crack propagation follows better established rules and there is no reason why the current state of knowledge of conventional fatigue should not suffice to treat the fretting fatigue case. The biaxial test described here provides the only known practical valid alternative to full scale engine testing since it reproduces the conditions prevailing in service and includes both low cycle fatigue and high frequency vibration when required. Although it has only been applied to dovetail joints, there is no reason why it should not be used to provide basic design data for other types of joints.

C. R UIZ, D. NOWIzLL

94

The distinction has been made between fretting fatigue and the wear damage combined with fatigue or creep that governs failure at elevated temperatures. REFERENCES

.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.

Timoshenko, S.P.,(1953) History of Strength of Materials, McGraw-Hill, New York Manson, S.S. (1965) Exp. Mechanics 7, 193 Ruiz, C. and Koenigsberger, F. (1970) Design for Strength and Production. Macmillan, London O'Connor, J.J. and Johnson, K.L. (1963) Wear. 6, 118 Johnson, K.L. and O'Connor, J.J. (1964) Proc. I. Mech.E 178(3J), 7 Nishioka, K. and Hirakawa, K. (1968) Bull. J.S.M.E. 11(45), 437 Nishioka, K. and Hirakawa, K. (1969) Bull. J.S.M.E. 12(51), 397 Nishioka, K. and Hirakawa, K. (1969) Bull. J.S.M.E. 12(51), 408 Nishioka, K. and Hirakawa, K. (1969) Bull. J.S.M.E. 12(52), 692 Nishioka, K. and Hirakawa, K. (1972) Bull. J.S.M.E. 15(80), 135 Field, J. and Waters, D. (1967) N.E.L. Report 275 Field, J. and Waters, D. (1968) N.E.L. Report 340 O'Connor, J.J. and Wright, G.P. (1971) Int.J.Eng.Sci. 9, 555 O'Connor, J.J. and Wright, G.P. (1972) Proc.I.Mech.E. 186, 827 Bramhall, R. (1973) Studies in Fretting Fatigue, D.Phil. Thesis, Oxford University Edwards, P.R., Ryman, R.J., and Cook, R. (1977) Fracture mechanics prediction of fretting fatigue under constant amplitude loading RAE Technical report 77056 Nowell, D., Hills, D.A., and O'Connor, J.J. (1987) An analysis of fretting fatigue, Proc. I.Mech.E. Conference on Tribology, London, July 1987, C131/87, I.Mech.E, London Hills, D.A., and Nowell, D. (1994) Mechanics offretting fatigue, Kluwer, Dordrecht Nowell, D., Hills, D.A., and Moobola, R. (2000) in Fretting Fatigue: current technology and practices, ASTM STP 1367, D.W. Hoeppner, V. Chandrasekaran, and C.B. Elliott, Eds, ASTM, 141 Ruiz, C., Boddington, P.H.B. and Chen, K.C. (1984) Exp. Mechanics, 24, 208 Nowell, D., and Hills, D.A. (1990) Wear, 136, 329 Szolwinski, M.P., and Farris, T.N. (1996) Wear, 198, 93 Neu, R.W., Pape, J.A., and Swalla-Michaud, D.R. (2000) in ASTM STP 1367, D.W. Hoeppner, V. Chandrasekaran, and C.B. Elliott, Eds, ASTM, 369 Fouvry, S., Kapsa, P, and Vincent, L. (2000) in ASTM STP 1367, D.W. Hoeppner, V. Chandrasekaran, and C.B. Elliott, Eds, ASTM, 167 Dang Van, K., Griveau, B., and Message, O. (1989) in Biaxial and multiaxial fatigue, ed M.W. Brown and K.J. Miller, Mech. Eng. Pubs., London, 479 Nowell, D., and Aradjo, J.A. (1999) Int. Jnl Fatigue, 21,947 Spratt, P. (1958) The marine steam engine, in Singer, C., Holmyard, E.J., Hall, A.R. and Williams, T.I., A History of Technology, Vol V, Clarendon Press, Oxford Bryant, L. (1978) The internal combustion engine, in Williams, T.I., A History of Technology, Vol VII, Clarendon Press, Oxford Smith, A. (1978). The steam turbine loc. cit. ref. 17

Designing Against Fretting Fatigue in Aeroengines 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55.

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Bach, C. (1895) Die Maschinen-Elemente, Verlag de J.G. Gottaschen Buchhandlung, Stuttgart Gentsch, W. (1906) Steam Turbines, Longmans, London Swain, G.F. (1924) in Structural Engineering - Strength of Materials, McGraw Hill, New York Coker, E.G. and Filon, L.N.G. (1931) A Treatise on Photoelasticity, Cambridge U.P., Cambridge Stodola, A (1927) Steam and Gas Turbines, McGraw-Hill, New York. Owen, M.J. and Dudley (1966) J. Strain Analysis, 1, 121 Leshenski, S.J. (1974) Exp. Mechanics 14, 251 Boddington, P.H.B. and Ruiz, C. (1983) in Proc. ASME Int. Conference on Advances in Life Prediction Methods, Albany. Boddington, P.H.B. (1982) Fatigue Failure Mechanisms in Dovetail Blade Root Fixings, D.Phil. Thesis, Oxford University Boddington, P.H.B., Chen, K.C. and Ruiz, C. (1985) Computers and Structures, 20, 731 He, M.J. and Ruiz, C. (1989) Exp. Mechanics, 29, 126 Ruiz, C., Post, D. and Czarnek, R. (1985) J. Applied Mechanics, 52, 109 Post, D. (1983), Exp. Mechanics, 23, 203 Ruiz, C., Webb, P.H. and Post, D. (1986) in AGARD-CP-399 Poon, C.Y., Kujawinska, M. and Ruiz, C (1993) J. Strain Analysis, 28, 79 Poon, C.Y., Kujawinska, M. and Ruiz, C. (1993) Exp. Mechanics, 33, 234 Hibbitt, Karlson and Sorensen Inc. (1999) ABAQUS Manual, Rhode Island Johnson, A.E. and Khan (1965), in Developments in Materials Testing in Machine Design, Proc. I.Mech.E., 180(3A), 97. Instron Ltd., B iaxial Testing Machines Manufacturers Information MTS Inc., Biaxial Testing Machines Manufacturers Information LCF + HCF Ruiz, C. and Chen, K.C. (1986) in Int. Conf. Fatigue and Applications, C241-86, I.Mech.E., London, 187 Chen, K.C. (1985) Fatigue of dovetail joints, D.Phil. Thesis, Oxford University. Wang, Z.P. and Ruiz, C. (1990) Matls. Science and Engineering, A127, 105. Wang, Z.P. and Ruiz, C. (1990) Wear, 140, 107 Wang, Z.P. and Ruiz, C. (1989), J. Am. Ceram. Soc., 72, 1076.

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97

A I R C R A F T F A T I G U E LIFE EXTENSION: D E V E L O P M E N T OF A MID-LIFE R E W O R K M E T H O D B A S E D ON P E E N I N G

G. CLARK Airframes and Engines Division DSTO Aeronautical and Maritime Research Laboratory 506 Lorimer Street, Fishermans Bend, VIC 3027, Australia

ABSTRACT This paper highlights some of the ways in which (a) changes in aircraft design and maintenance, (b) changes in the materials used in aircraft construction, are leading to increased focus on small surface defects. The examples given here concem military aviation, which involves higher stresses, lower safety factors and higher risk rates than are acceptable for civil aviation. However, the changes discussed are also becoming important in civil applications. Aeronautical and Maritime Research Laboratory (AMRL) has developed a rework method in which a surface layer which has been damaged by cracking, or by other methods, can be removed in a controlled manner- a crucial factor when reworking critical parts where a small error can lead to extremely expensive repairs. The clean surface can then be peened using a controlled technique which produces minimal damage on the surface and maximises the Life Improvement Factor (LIF) for the process. The method is now being applied to fleet aircraft. KEYWORDS Fatigue, cracking, aluminium alloys, crack growth, life extension, aircraft.

INTRODUCTION Background Fatigue remains a significant cause of failure in aircraft components. To manage it, a series of changes in design approach have been used; the original method - design on a static strength basis - gave way to building in redundant load paths in the structure, and then to retiring aircraft before the risk of failure rises too far. Current management approaches rely on various combinations of inspection and early retirement to keep the structure safe. At the same time, structural optimisation and the use of high-strength materials have increased the number of parts or regions which are highly stressed, and which are therefore intrinsically intolerant of fatigue damage. Arising from these changes, one factor, more than any other, has attracted the attention of the fatigue research community over the years- the sensitivity of fatigue life to small cracks, and

98

G. CLARK

hence to surface condition and processing. Aircraft fatigue lives are dominated by this surface condition, and numerous early failures of aircraft bear witness to the presence of unexpected surface damage from manufacture, assembly, foreign object impact, maintenance procedures and other sources never adequately factored into the original design. In modem military aircraft (and in some parts on civil aircraft) life-enhancing surface treatments are applied to critical areas. The aim of this paper is to discuss the implications of using such treatments, and to highlight the sensitivity of aircraft structure to very smallsometimes apparently innocuous - changes in surface condition. The paper will show how the careful application of such treatments can give extended life in service if used judiciously. The example discussed is based on the use of glass bead peening of aluminium alloys on RAAF F/A-18 aircraft. The use of peening on aluminium alloys, rather than steels, is less well-established. Here, mechanical damage from the peening occurs in the form of laps and folds, as well as damage from any poor bead geometries. Such damage has the potential to negate the beneficial effects of the residual compressive stresses which make the process so effective as a means of retarding fatigue crack development. Uncertainty about the effectiveness of peening on some RAAF aircraft led to AMRL research which focussed on the effect of this surface damage, and which explored methods of minimising the damage in order to optimise the peening process. The research showed that at high fatigue stresses, where peening is least effective as a life extension process, there is potential for poor peening to provide little Life Improvement Factor (LIF); indeed values less than one (i.e life reduction) have been observed for severe peening. AMRL developed guidelines for limiting the range of peening conditions to the optimal conditions for life extension, and produced significant improvements in LIF values using this process. Based on this research, AMRL also developed a rework method in which a surface layer which has been damaged by cracking, or by other methods, can be removed in a controlled manner- a crucial factor when reworking critical parts where a small error can lead to extremely expensive repairs. It is planned to use the AMRL approach as a mid-life rework procedure for identified fatigueprone regions; by eliminating the most likely failure location, this could extend airframe life to an extent governed by the next-most-critical region. This paper summarises the research and observations which led to these developments, and highlights the cautionary approach which is necessary when considering any potential surface change on aircraft materials. This paper highlights some of the ways in which changes in aircraft design and maintenance, and changes in the materials used in aircraft construction, are leading to increased focus on the role of small surface defects in fatigue life determination. The examples given here concern military aviation, which involves higher stresses, lower safety factors and higher risk rates than are acceptable for civil aviation. However, the changes discussed are also becoming important in civil applications. SMALL DEFECTS

A Brief History of Changes in Aircraft Design Philosophy The traditional view of defects in a i r c r a f t - as unwelcome and unpredictable problems u is perhaps understandable when one considers the various philosophies upon which aircraft structural integrity has been based. Prior to the 1950's, aircraft were designed to handle a

99

Aircraft Fatigue Life Extension...

specified static load, and tests were performed to demonstrate this capability. This tended to encourage the view that each aircraft should continue to perform its function indefinitely. Manufacturing defects were considered to be controllable by the application of good practice, and while fatigue was a matter of some concern, it too was handled by the adoption of"good design practice" i.e. minimising stress concentration factors, rather than by specification. There is always pressure to improve aircraft efficiency by increasing performance and reducing aircraft weight. Since a small increase in stress produces a significant reduction in fatigue life, the result, with hindsight, was inevitable. The loss in 1954 of two de Havilland COMET aircraft (Fig.l) [1 ], and various military aircraft (e.g. the loss of three USAF B-47's in 1958) focussed world attention on aircraft durability. The COMET accidents led to one of the most exhaustive failure analysis investigations ever undertaken, and these accidents provided the impetus for a major change in approach to aircraft d e s i g n - for the first time, durability (in terms of fatigue life) became a design requirement and to deal with it, two approaches were adopted. These still feature in the majority of aircraft flying today, viz:

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Fig. 1. The breakup of COMET G-AL YP focussed attention on aircraft durability; the fatigue crack origin at a hole near an antenna aperture is marked.

Safe-life design is based on achieving a specified safe operational life; a test aircraft subjected to fatigue loading must reach several times its design life under a load spectrum typical of its operational usage, in order to cover the scatter in life which is expected across the fleet. Failsafe design, on the other hand, is based on redundancy such as having multiple load paths in

100

G. CLARK

the structure; after failure of any single load-bearing element, the aircraft must be able to fly until an inspection will reveal the presence of the failed member. The inherent safety of the fail-safe approach has led to its widespread use for civil transport aircraft.

~

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Fig. 2. A manufacturing anomaly in the Wing Pivot Fitting from a USAF F-111, which led to widespread acceptance of the need to maintain aircraft by regular, planned non-destructive inspection. The disadvantage of the safe-life and fail-safe design approaches is that they still rely upon good (or at least consistent) manufacturing and design practice to ensure s a f e t y - as a result, the so-called "rogue" flaw can still lead to loss of the aircraft, as occurred when an undetected crack-like manufacturing defect (Fig. 2) led to the loss of a USAF F-111 aircraft in 1969, during Australia's negotiations to purchase this aircraft type. After this accident, the US F111 fleet had to be grounded for six months pending development of a solution, which was the development of a program of regular inspections and proof tests by which the continued safety of the aircraft could be assured. Ultimately, this led to the development of the USAF Aircraft Structural Integrity Program (ASIP) which adopted concepts which are usually described as the Durability and Damage Tolerance approach to design and maintenance. These concepts are now widely implemented in military aircraft design and maintenance, and recognise that: aircraft contain defects originating during manufacture, and they must be designed and maintained to fly safely despite the presence of these defects, (ii) continued aircraft operation needs to be based on regular non-destructive inspections (NDI) of critical areas of the airframe, (iii) the safe period between inspections must be based on fracture mechanics considerations (e.g. crack growth), taking into account all loading and environmental factors, and the limit of detectability of cracks for the NDI technique used.

(i)

The effect of this recognition has been to focus attention on the development of NDI and on defect assessment. Defects are detected during testing and in service and, in order to ensure that the in-service inspection program remains adequate, there is now a need to determine not just the general nature of a defect, but why it occurred as it did, how long it had been there, and how fast it had been developing. Defect assessment based on fracture surface analysis

Aircraft Fatigue Life Extension...

101

must provide this information and Australia has invested much effort in this area, supporting an excellent record in managing fleet cracking. For example, an awareness of the concepts described above permitted the satisfactory life-extension of the Aermacchi MB326H jet trainer. This exercise required allowing the aircraft to continue flying while containing cracks, based on regular monitoring of crack length. ...... ,

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Figure 3. Fracture surface of a fatigue crack which led to fracture in an F-111 Wing Pivot Fitting during periodic testing. The growth history of the 3mm deep crack, as represented by the labels (flights) was determined at AMRL using quantitative fractography [2]. Laboratory testing programs played an important role in developing confidence in this approach, highlighting the benefits obtainable using a combination of NDI and defect assessment. Similarly, the use of quantitative fractography techniques [2,3] pioneered at AMRL, in which the fatigue markings on the crack surface are matched with the aircraft's flight load history, has permitted the adoption of regular inspection programs which have allowed the continued safe operation of critical components in Australia's F-111 fleet. As an example, Figure 3 shows the surface of a fatigue crack which caused the fracture of a wing in a test - - a test designed to reveal the presence of precisely this type of defect; the use of quantitative fractography at AMRL made it possible to determine the relationship between crack length and flight history.

Changing view of Maintenance Economics The concept of durability is associated with the idea that an aircraft has an economic l i f e eventually, the cost of maintenance, such as repair of cracks and other progressive damage such as corrosion, will represent an unacceptable burden, and the design needs to address this

102

G. CLARK

economic lifetime. It is widely acknowledged that the purchase price of a military aircraft and its systems represents only about one-third of aircraft life cycle costs. Maintenance can absorb 50% of the total life-cycle cost of the aircraft, leading to widespread interest in methods of reducing maintenance costs; the structural design philosophy changes of the last decade are being followed by similar dramatic changes in approach to component and system maintenance management. Recent easing of military tensions worldwide have already led to substantial cutbacks in expenditure on new military systems, and there will inevitably be more emphasis on prolonging the service life of older aircraft. The RAAF and DSTO already have a good record in this a r e a - an example is provided by DSTO's unrivalled experience in the use of bonded composite patches to repair cracks or reinforce airframes [4]. More than 50 different types of these repairs and reinforcements are currently installed on RAAF aircraft, and the expertise developed at AMRL is currently being transferred to many military and civil aviation users worldwide. Changes in design and construction. Large, monolithic components, such as the 7050-T73651 high-strength aluminium alloy used in RAAF F/A-18 bulkheads, illustrate a trend in aircraft design. These highly complex components are very well optimised at the design stage, to ensure full exploitation of materials properties. Naturally, the better the stress optimisation, the lower the weight of the component. However, this optimisation can lead to much of the component being critical in terms of fracture potential, with many fracture-critical locations. In practice, a well-designed modern aircraft will have many critical areas, all operating at high stresses.

A high level of structural optimisation leads to: (a) higher fatigue crack growth rates (b) smaller critical crack sizes, and (c) statistically, many more potential failure sites. As a result, the growth of small cracks (up to a few millimetres in depth) can fully control the fatigue life of the structure, and this makes structural integrity very much more dependent on the nature and condition of the surface and the material condition at the surface. Initial defects can often define the fatigue life of the structure, particularly where steps have been taken to reduce the severity of the more usual stress-concentrating features. Since stresses may be uniformly high, crack initiation in large, well-optimised components can often be observed on relatively flat, featureless surfaces- in the failure of a test bulkhead, the dominant crack was only slightly larger than a large number of cracks of similar size, on flat surfaces.. If the initiating features are inclusions, the situation shown in Fig 4 can arise, where cracking starts at many points on the surface, and grows locally. Neighbouring cracks link up as shown in Fig 4, leading to apparently rapid crack growth along the surface. The early stages of cracking in the ligaments show patches of accelerated crack growth where separate cracks have joined; this is consistent with the observations of Grandt et al (5) and Heath and Grandt (6). The linkage of cracks in this way can have a complex effect on fatigue life; while the surface growth is clearly accelerated by linkage, the presence of cracks distributed along the load line can lead to strain sharing and substantial reductions in growth rate. The detailed geometry and microstructure will determine the overall effect.

Aircri$ Fafigre Ltfe Extension ...

103

Fig. 4. Two examples of small surface cracks linking out-of-plane. (a) shows,fatigue crack growthfrom a surface-breaking inclusion, followed by linkage. Multiple linkuges(clear1-v .shown in @))can accelerate crack growth while shielding by neighbowing cracks can retard crack growth.

Fig. 5. A range of microstructures observed ut various positions throiigh plate thickness in F/A-18 bulkhead material. Note the duplex (large/small grain) structures present.

104

G. CLARK

Significance of material and surface condition A detailed analysis [7] of the initial defects in the RAAF F/A- 18 fleet, and in test articles used in design validation revealed a wide range of potential fatigue crack initiators. The material in the wing-carry through bulkheads is a 7050-T73651 aluminium alloy, in which the critical crack length in some areas is approximately 6mm, meaning that the use of safety-byinspection methods is impractical, and the structural integrity of the aircraft is managed on a safe-life basis. The rolling reduction of the material during production is limited, since the plate must remain thick enough for machining of the full 150mm thickness. As a result, the material in the centre is only mildly disrupted by rolling, and the microstructure of the material in the finished bulkhead can vary significantly (Fig 5); it varies from a small, equiaxed grain structure at the surface to a coarse duplex structure in the central region.

Grain b o u n d a r y elchin~ initiation

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Fig. 6. Two examples of cracking at etch pits located at grain boundaries. In this case, the etching is a pretreatment for the IVD coating which is clearly visible. The initial defects were identified as: (a)

(b)

Grain boundary penetrations were the most common initiating defect observed in AMRL test bulkheads. They were produced by the IVD coating process; it appears that the bulkhead was subject to an etching process for cleaning prior to coating the bulkhead with IVD aluminium. This etching had produced numerous sharp deep grainboundary penetrations which because of the large size of the grains had considerable surface length. These penetrations, along with the more favourable growth of fatigue cracks along the precipitate-free zones adjacent to the grain boundaries, allowed rapid development of fatigue cracking (Figure 6). The potential severity of this type of defect is linked to the type of microstructure of the bulkhead material, particularly the boundaries between the large grains and the smaller grains. Large inclusions were the source of some cracks, but the overall influence of these inclusions is not fully known at this stage. Inclusions of 30-50 ~m found to be effective crack initiators were generally elongated or "Y" shaped with a thickness-tolength ratio of approximately 1:5. "Y" shaped particles are typical of inclusions that have precipitated at grain boundary triple-points or where dendrite arms intersect each other during solidification. Also observed, and typical of casting defects, were the multiply-connected inclusions not dispersed by subsequent hot-rolling operations. In many cases these multiply-connected inclusions were observed to be associated with the

Aircraft Fatigue Life Extension...

(c)

105

porosity; this is typical of their having formed at the original ingot grain boundary interfaces and in the interdendritic spaces. On machined surfaces, the inclusions will tend to be the prime initiation sites for cracking (Fig 7), but, as shown in Fig 8, their effectiveness in starting fatigue cracks may be far less than that of a surface etch pit or other externally imposed damage. Porosity: This type of defect has occasionally been found to initiate fatigue cracks in some full-scale fatigue tests. The pores are a feature of the original cast billet which were not sealed up during subsequent hot rolling operations.

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Fig. 7. Two examples of fatigue cracking from inclusions (a) fracture surface (b) crack visible on surface.

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Fig. 8. Despite the presence of a large inclusion, the fatigue crack initiates from a surface etch pit. (d) The limited rolling reduction permissible when manufacturing the thick plate from which bulkheads can be machined leads to difficulties in producing a sound microstructure in the central part of the plate. The primary failure in one fatigue test was from the flange radius, where a porosity-initiated crack was found to have grown from the outer face of the bulkhead and would probably have caused failure in another 9% of life. Improvements in manufacturing processes have reduced the incidence of

G. CLARK

106

(d)

(e)

porosity to the stage where it would rarely be involved in fatigue crack development, although (Fig.9) porosity may be seen on a fatigue fracture surface. Machining indentations: Coarse machining marks were observed to initiate cracking in one fatigue test. In an AMRL test article, machining marks remained in areas that were not polished during strain-gauge fitting. These marks were deepest in the re-entrant radii behind the bulkhead flange and it was from one of these marks that the critical crack initiated. Smaller irregularities at the free surface.

Fig. 9. surface.

The progress of a fatigue crack may reveal the presence of porosity beneath the

Crack development from initial defects. The development of a fatigue crack often exhibits near-exponential growth, as illustrated in Figs 10 and 11. Interestingly, his behaviour extends to cases involving complex loading sequences, and across a range of materials and growth rates. In essence, we can describe the cracking process as; log a = b.life + c where a is crack depth, and life is a continuous measure of service experience. Clearly, at zero life, the crack size is ao, the initial defect size (c = log ao). The exponent b represents the response of the material to the stress conditions which drive the crack i.e it is a function of stress, spectrum severity and material crack growth behaviour.

Aircraft Fatigue Life Extension...

107

100 ~. 19aftupper ----!1-- 19aft lower ----O--- 19 fwd upper ---s .... 19tkvd lower

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Fig. 11. Crack growth from initial defects (whose size is shown as the zero life condition) in 7050 aluminium alloy. In this case, initiation occurs at intermetallic particles near the surface.

This simple representation of crack growth is surprisingly useful [7]; in analysing cracking found during tear-down of a trainer aircraft wing, with fatigue cracks at many hole locations, it proved possible to characterise the crack growth simply by observing the initial defect size and the final crack size (at whatever stage of life that wing was removed from service). The exponent b was found to correlate well with the stressing severity of each particular hole location (Fig.12), even across the range of flying done by different aircraft. In one analysis the value of the exponent was measured for cracks growing from a variety of locations; the highest values were used to identify the most critical locations in the component [8].

G. CLARK

108 100

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Fig. 12. Crack depth vs service data for several cracks at various hole locations in service aircraft. Two cracks were measured in detail fractographically, and for the rest, crack growth estimates were made by joining the measured initial and final defect sizes. Note that four families of curves can be identified, associated with the four hole locations. AF1410

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Fig. 13. The use of crack growth measurements, rather than total fatigue life, allows better discrimination between factors which affect crack growth. In this case, two different slopes readily identify different spectrum effects. The value of ao corresponds to the initial defect size. The size of the initial defect size can be difficult to estimate. Yang and Manning [9] defined an "equivalent initial flaw size" (EIFS) as an artificial initial crack size which, when grown under service growth conditions, duplicates the actual crack size at a particular time. Where the defect is a single feature, such as a pit, nick or intermetallic particle the approach adopted in AMRL research has followed the

Aircraft Fatigue Life Extension...

109

procedure used by Grandt et al [ 10], i.e. the size was taken to be the ellipse which fits around the boundaries. Where the defect is very long (along the surface) in comparison with its other dimensions, the maximum defect depth was taken as the effective depth and the defect was treated as an edge crack. The initial defect size has a major effect on total fatigue life, and tests designed to identify the effect of various parameters on fatigue will often require many specimens to be tested to overcome the variability in initial defect size. In recent work [ 11 ], the values of exponent b have been used in a systematic way to identify the effects of different loading spectra on fatigue crack growth; the value of b is a reliable, appropriate and sensitive indicator of the crack growth response, and by focussing on the critical growth rate, without the high variability in initial defect size, factors influencing the growth rate can be identified very easily. The example shown (Fig 13) shows the difference between the two spectrum conditions very clearly as a change in the growth slope, and required far fewer tests than would normally be required. SURFACE REWORK FOR LIFE EXTENSION Peening with shot or with glass beads is well established as a means of increasing fatigue life, although its use on high-strength aluminium alloys was rather unusual at the time the RAAF was purchasing F/A-18 aircraft. Research at AMRL, anticipating the likely significance of surface condition, showed that the likely depth of the compressive residual stresses under the surface was approximately 200 gm. The effect of these stresses in retarding crack growth is indicated in Fig. 14, which shows that the retardation effect is still noticeable when the crack tip has moved beyond the compressive stress layer; the effect of the compressive stresses which still act further back across the crack faces is still significant. 1 -.

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Fig. 14. Reduced crack growth rate at peened surface. Note the retardation applies to cracks substantially deeper than the depth of the compressive stress layer (typically 200 micrometre). A detailed examination of the crack length/cycles data (Fig 15) shows the characteristic slowing of the crack as it extends into the residual stress layer, and the slow rise in growth

G. CLARK

110

rate to reach the original (unpeened) growth rate. In this case, however, the initial defect size is substantially greater than in the unpeened samples, indicating that the effects of peening in aluminium alloys are a balance between reduced life as a result of damage to the surface, and the reduction in growth rate from the compressive stresses.

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Aircraft Fatigue Life Extension...

111

The surface condition of bulkheads as received in the RAAF fleet is shown in Fig. 16; the surface is heavily damaged, with material laps and folds, as well as embedded glass beads. Anticipating that rework of some areas might be necessary, AMRL developed a rework/repair process which is based on: (a) removing the damaged layer, including any fatigue cracking which may have developed, and (b) peening using tightly controlled conditions (e.g. no recycling of glass beads, restricted Almen intensity range, nozzle perpendicular, use of peen dye to monitor coverage) The process [ 12] is illustrated in Fig. 17. A key element is being able to remove a controlled amount of material from a critical component. The removal process must be able to polish off fractions of a millimetre of material, ensuring that no areas are left with inadequate polishing, and that no excessive material removal takes place. The approach taken is to use a springloaded punch to make indentations of the required depth in the cleaned-up surface. These indentations are then polished away. ......::::~i~ii~iiii!iiii::ii.:i~i~ii.:iiiii~ii::ii~iii!i~:!i~iii[i~i~iiii!ii!i!ii!~ii~ii!~!!~! ~l1 .

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Fig. 17. AMRL Reworkprocess, in which the damaged surface, including any fatigue crackJng is removed prior to re-peening. Early in RAAF F/A-18 fleet operation, there was a requirement to rework a particular geometrical feature in one of the main carry-through bulkheads. Since the original peening was being removed, there was an opportunity to use the more tightly controlled peening method to guarantee future fatigue resistance. Figure 18 shows the difference between the original peened surface and the finished surface; the reworked surface features much less damage in the form of laps and folds. Figure 19 shows the regions being reworked.

G. CLARK

112

A number of studies have been conducted to establish the useable bounds of the AMRL process; it has so far been demonstrated that the process may be used several times during the life of a component to fully restore the original fatigue life (e.g Fig 20). The only practical limit is when too much material has been removed, or when too many applications of the method increase the likelihood of failure from an intemal defect. Current work is developing guidelines to identify the relative growth rates of intemal defects. It is planned to use the AMRL approach as a mid-life rework procedure for identified fatigue-prone regions; by eliminating the most likely failure location, this could extend airframe life to an extent govemed by the next-most-critical region. ..........................

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Fig. 18. (a) Example of peened surface on RAAF F/A-18 fleet (b) Peened finish from AMRL process. ,i~~ i ~

Fig. 19. Rework of RAAF F/A-18bulkheads using AMRL peeningprocess. The damaged material (i.e. material with poor peening and~or any crack growth from the peened surface) was removed, and a high-quality peening method used to restore full fatigue life.

Aircraft Fatigue Life Extension...

113

Australia and Canada are jointly investigating the lives of their F/A-18 fleets, and in this collaborative program, the AMRL rework method has been used to extend the fatigue test life of various bulkheads. To achieve appropriate lives from service aircraft, the method will be used on the RAAF and CF fleet. Current work is investigating alternative methods of fatigue crack retardation, such as laser shock peening, which promise to provide improved residual stress depth and distribution, with minimal surface damage compared to mechanical methods. 40000 35000 30000 25000 20000 1 5 0 0 0

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Fig. 20. Use of AMRL procedure to recover fatigue life. CONCLUSION The presence of small surface or near-surface features is usually the factor which determines the safe fatigue life of an aircraft fleet; the potential benefits of research into the initial quality state of the material (i.e. the nature, distribution and behaviour of initial defects) offers major savings by extending the useful safe and economic lives of military aircraft. A life extension method based on surface rework has been developed and is being used for local life extension on RAAF aircraft. ACKNOWLEDGEMENTS The author wishes to acknowledge material supplied by P K Sharp, J Q Clayton, S A Barter and A F Cox.

REFERENCES [11

U.K. Ministry of Transport and Civil Aviation, HMSO, London (1955) Report of the

[2]

Cox, A.F., Kepert, J.L. and Clark, G. (1989),Accident and Failure Analysis: Learning from Experience, Proc. Australian Aeronautical Conference, I.E.Aust, Melbourne.

Court of Inquiry into the Accidents to Comet G-ALYP and G-ALYY.

114

[3]

[4]

[5] [6] [7]

[8] [9] [10]

[11] [12]

G. CLARK

Goldsmith, N.T. and Clark, G. (1990).Analysis and Interpretation of Aircraft Component Defects Using Quantitative Fractography, in Evaluation and Techniques in Fractography, Strauss, B.M. and Putatunda, S.K. (Eds), STP 1085, American Society for Testing and Materials, Philadelphia, USA. Baker, A.A. (1984) Repair of cracked or defective metallic components with advanced fibre composites m an overview of Australian work, Composite Structures 2, 153-181. Grandt, A.F.Jr, Perez, R. and Tritsch, D.E. (1984) Cyclic Growth and Coalescence of Multiple Fatigue Cracks, in Advances in Fracture Research (Fracture 84) ICF Vol 3 539.42 (062)/ADV Vol 3. Heath, B. J. and Grandt, A. F. Jr., (1984) Stress-Intensity Factors for Coalescing and Single Corner Flaws Along a Hole Bore in a Plate, Engineering Fracture Mechanics, 19 No 4. pp 665-673. Clark, G., Barter, S.A. and Goldsmith, N.T. (1993)Influence of initial defect conditions on structural fatigue in RAAF aircraft, in Durability and Structural Reliability of Airframes, Blom, A (ed), EMAS, Warley. Clark, G., Jost, G.S. and Young, G. (1997) Recovery of the RAAF MB326H Fleet; the Tale of an Aging Trainer Fleet, in Fatigue in New and Ageing Aircraft, Poole, P and Cook, R (Eds.) EMAS, Warley. Yang, J.N. and Manning, S.D., (1990) Demonstration of Probabilistic-Based Durability Analysis Method for Metallic Airframes, Journal of Aircraft, 27, No 2. Grandt, A.F. Jr, Scheumann, T.D., Todd, R.E. and Hinkle, A.J., (1993) Modeling the Influence of Initial Material Inhomogeneities on the Fatigue Life of Notched Components, Fatigue and Fracture of Engineering Materials and Structures, 16, No 2, pp 199-213. Cox, A.F., private communication Sharp, P.K, Clayton, J.Q. and Clark, G., (1994) The Fatigue Resistance of Peened 7050-T7451 Aluminium Alloy-Repair and Re-Treatment of a Component Surface, Fat & Fract Eng Mats & Struct. 17(3), 243-252.

115

COATINGS F O R H O T SECTION GAS TURBINE C O M P O N E N T S J. Bressers, S. Peteves and M. Steen Institute for Advanced Materials, Joint Research Centre, EC P.O. Box 2, 1755 ZG Petten, The Netherlands

ABSTRACT Components in the hot section of gas turbines are protected from the environment by oxidation-resistant coatings while thermal barrier coatings are applied to reduce the metal operating temperature of blades and vanes. The integrity of these protective coatings is an issue of major concern in current gas turbine designs. Premature cracking of the protective layer in oxidation-resistant coatings and of the interface in thermal barrier coating systems has become one of the life limiting factors of coated components in gas turbines. Following a brief overview of the state-of-the-art of coated material systems with respect to coating types and their status of application, the fracture mechanisms and mechanics of coated systems are presented and discussed.

KEYWORDS Gas turbines, hot section components, oxidation-resistant coatings, aluminides, overlays, thermal barrier coatings, residual stress, fracture mechanisms and mechanics.

INTRODUCTION In fossil fuel-based energy production systems the gas turbine has become the workhorse for power generation. In electric power generation gas turbines are anticipated to contribute the major fraction to the growth of electric power capacity between now and 2030 [ 1]. Compared to other fossil fuel-based energy technologies, gas turbines rank high in terms of relative cost of capital investment, greenhouse gas emissions and versatility in terms of decentralised power production. In aircraft propulsion there is no alternative for the gas turbine. The performance of gas turbines for power generation and for aircraft propulsion has steadily increased since their inception. Improvements in specific fuel consumption and efficiency, as well as in thrust-to-weight ratio in the case of aero-engines have been accomplished through increased engine operating temperatures, improved designs and through the use of better materials. Turbine entry temperatures (TET) have steadily increased over the past 35 years, as

116

J. BRESSERS, S. PETEVES, M. STEEN

shown in Fig. 1 together with the corresponding increase in efficiency [2]. Blade surface temperatures today reach levels of about 1100~ in aero-engines and somewhat lower in large power generation turbines. 1965 1500 1400 1300 1200 -

1970

1975

1980

1985

1990

1995

t

I

I

I

i

I

50

~- 3 5 ~

~oo-

30

lO0O - - ~ _ _ _ . . ~ 900 v 800 700 600 500 . 1965

2000

25 "6 20

~

- 15 .

1970

.

.

1975

.

1980

.

10

1985

1990

1995

2000

Year

Fig. 1. Evolution of the turbine entry temperature and the concomitant efficiency (simple cycle) of industrial gas turbines in the last 30 years [2]. Modem gas turbines represent one of the most demanding and sophisticated applications for materials, in particular with respect to the combustor chamber and the blades/vanes of the high pressure stage of the turbine. Since the introduction of nickel-based superalloys, increased temperature and stress capability have been achieved by incrementally optimising the chemical composition and by improving the processing methods toward precision casting and the production of cleaner alloys, see Fig. 2. The chemical composition of single crystal superalloys used today has been optimised for structural performance at the service temperature, by adding

1350 1300 Thermai

0.,

1250 1200

Bar~

1150

11oo 1050

~ 0

.

Directionaily Solidified Alloys ~ .

-

I000 9SO

.... J

900

Conventionally Alloys

~

850 800 750 1940

~-

Single Crystal AlLoys

~--

Cast

W r o u g h t Alloys i

!

1

i

1950

1960

1970

1980

,,

!

i

1990

2000

2010

Year

Fig. 2. Material temperature benefit achieved through base alloy development and improved processing methods of nickel-based superalloys for gas turbine blades. A further temperature gain of 50-100~ is possible by using "designed-in" thermal barrier coatings [3].

Coatingsfor Hot Section Gas Turbine Components

117

in refractory elements like Ta, W and Re at the expense of Ni and Cr. The corresponding decrease in the intrinsic environmental resistance has been countered by applying oxidationand corrosion-resistant coatings. Thermal barrier coatings (TBCs) on the other hand are effective in reducing the metal operating temperature in both blades/vanes and combustor chambers by lowering the heat flux across the component wall. The use of TBCs either allows to reduce the amount of cooling air required to maintain a constant metal temperature, or to increase the temperature difference between the hot gas and the metal at a constant amount of cooling air. A characteristic common to all coated materials is the presence of interfaces between material constituents that have different thermo-physical and mechanical properties. The role of the interface is to provide adherence of the coating to the substrate. As opposed to TBC systems, interface failure is not an issue of concern in oxidation-corrosion resistant coatings. The latter predominantly fail by premature cracking of the coating layer, exposing the substrate alloy to incipient cracking and to attack by the oxidising environment. The integrity of protective coatings is an issue of major concern in modern gas turbines. Coatings indeed serve as the primary thermal-mechanical fatigue crack initiation site at turbine operating conditions. The durability of the coating system thus has become one of the primary life limiting factors of coated blades and vanes.

COATING TYPES AND STATUS OF APPLICATION

Oxidation-resistant Coatings Coatings have historically been developed to provide protection of components located in the hot section of the turbine against oxidation and hot corrosion. Since diffusion coatings were first applied to gas turbine blades in 1957 [4], the demand on coatings for hot section components in the high-pressure stage of the turbine has evolved from hot corrosion resistance to oxidation resistance, in line with the increase in service temperature over the years. Today, coatings against oxidation are used in the first and second stage blades/vanes of most advanced gas turbines. Also the internal cooling passages in the hotter parts of the blades require oxidation protection by coatings. There are two standard coating groups: diffusion coatings including aluminides and modified aluminides; and overlay coatings of the MCrA1Y type including aluminised MCrA1Y's. The coating systems are all designed to form stable, continuous and slow growing protective alumina scales that limit material consumption and the loss of component section, and also prevent internal oxidation along grain boundaries of the substrate alloy. Diffusion coating is a surface modification process wherein the coating species is partly diffused into the substrate to form a protective layer, following the deposition of the coating elements on the surface by means of pack-cementation or some other technique. Alternative methods are chemical vapour deposition or slurry deposition. The superalloy is typically modified to a depth of 10 ~tm to 100 ~tm from the surface, depending on the type of coating and the process parameters selected. The aluminide layer may grow outwards (high-activity pack) or inwards (low-activity pack); in the latter case some substrate alloy components are incorporated in the coating. The phase providing A1 for the formation of the protective alumina

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J. BRESSERS, S. PETEVES, M. STEEN

scale is 13-NiA1. The cyclic loss of the protective oxide as a result of thermal cycling is an important degradation mechanism of aluminide coatings. The thermal cycling resistance has been improved by the addition of reactive elements like Y and Hf. Alloying 13-NiA1 coatings with Si has also been shown to greatly improve the cyclic oxidation and hot corrosion resistance, although silicon additions have the disadvantage of reducing coating ductility. Incorporating Pt in aluminide diffusion coatings improves the oxidation and hot corrosion/sulphidation resistance. The platinum forms an aluminide (PtAI2) and remains concentrated in the surface region of the coating, thereby decreasing the activity of A1 and hence its reaction with the oxidising atmosphere. Overlay coatings, frequently deposited by plasma spraying, are of the MCrA1Y type where M can be Ni, Co or a combination of the two. MCrA1Ys have the advantage of offering compositional flexibility. The concentrations of A1 and Cr can be varied so as to optimise the resistance against low-temperature hot corrosion (rich in Cr) or against high-temperature hot corrosion and oxidation (rich in A1). Other elements such as Si, Hf, Ta and Pt are added in order to further improve corrosion resistance and to increase the resistance against spalling. The addition of Re also improves the cyclic oxidation and hot corrosion resistance, as well as the resistance against thermal fatigue cracking. Contrary to diffusion coatings, overlay coatings do not consume the substrate material. This represents an advantage with respect to the repair of turbine components since stripping of a diffusion coating can lead to an appreciable reduction in cross section of the component. MCrA1Y coatings are sometimes used in the overaluminised version, particularly when they are applied to the outer surface of turbine blades in combination with an aluminide diffusion coating in the internal cooling passages. Overaluminised MCrA1Y's have an excellent oxidation resistance up to very high temperatures, but are more prone to thermal fatigue in the colder parts of the blade than the non-aluminised versions. Table 1. Generic information on protective coating types used on superalloy hot gas path components

Phase(s) responsible Oxidation properties Oxide spalling Hot corrosion Interdiffusional and phase stability thermal shock resistance mechanical properties Thickness range (~tm) Service temperature (~ Application process

Aluminide ~-NiAI -A1203 former -excellent for high-temp, oxidation severe poor -severe interdiffusion of A1 into substrate -favours cr phase formation poor

MCrA1Y [~-NiA1 -A1203 former -excellent for high-temp, oxidation moderate

brittle, poor 25-100 815-1150

good 125-500 815-1150

Vapour phase reaction pack cementation - above the pack - CVD - slurry

Thermal spray -air/vacuum -HVOF Vapour deposition electron beam sputtering

-

good good good

-

-

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119

Table 1 provides an overview of the types of coatings currently used for hot section structures together with typical thicknesses, temperature range of use, deposition methods and properties. Excellent overviews for further reading on coatings are provided in references [5-10].

Thermal barrier coatings TBCs were introduced several decades ago to thermally insulate the combustor chamber and transition pieces [11]. By the early 1980s TBCs had entered service on the vane platforms of aircraft gas turbine engines. By the late 1980s TBCs were applied on blade airfoils and platforms of specific aero-engines. Only recently have TBCs been applied to blades and vanes of stationary gas turbines for power generation. At the early stages - referred to as the "Protective mode" in Table 2 - the coatings were used to basically protect the underlying alloy and extend the lives of the components. Presently, TBCs are used in the "Enhanced mode", resulting in reduced cooling flow and emissions [2,12]. The ultimate goal is to take full advantage of the increased temperature capability of TBCs, and to increase the surface temperature of the coated blade by some 50-100~ However, in view of the significant effect on component life in case of TBC failure, "designing-in" of TBCs to cash in the full temperature capability requires that a full understanding of TBC system behaviour be achieved. Table 2. Application modes of TBCs Time Past "Protective Mode" Present "Enhanced Mode" Future "Designed-in Mode"

Benefits Minimisation of hot spots Improvement in life Reduced emissions Non catastrophic damage in the case of TBC loss Increase TET Increased efficiency, Reduced emissions Constant or reduced cooling Loss of TBC is not accommodated and flow can have catastrophic consequences

Engine Conditions TET constant Cooling flow constant TET constant Reduced cooling flow

TBCs currently in use in gas turbines are 6-8wt% Yttria-stabilised Zirconia (YSZ). The ceramic layer is deposited on a metallic coating - the bondcoat (BC) - that imparts good adhesion to the TBC and that protects the superalloy substrate from oxidation and corrosion effects. The bondcoat frequently is either an MCrA1Y overlay coating or a Pt-modified aluminide diffusion coating which under service conditions produce a protective, thermally grown alumina oxide (TGO) scale. Typical thicknesses of the ceramic top coat are in the range 125-200 lam in blades and up to 500 lam in combustors [ 13]. TBCs applied by means of electron beam physical vapour deposition (EB-PVD) are favoured for application in aero-engine blades and vanes. In EB-PVD the ceramic coating grows in the form of columnar grains on the bond coat, with individual grains strongly bonded at their base but weakly bonded to each other, providing good thermal strain tolerance. The smooth surface finish is advantageous in terms of blade aero-dynamics, and it is claimed that the resistance to erosion exceeds that of air plasma sprayed (APS) TBCs [3]. APS ceramic coatings are deposited in sequential layers to achieve the desired thickness, resulting in a microstructure of individual platelets formed from the droplets impinging on the surface during the spraying process. Cross sections through APS and EB-PVD deposited TBCs are compared in Fig. 3.

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J. BRESSERS, X PETEVES, M. STEEN

References [ 14-17] provide recent publications for further reading on TBCs.

Substrate m~ll:

I "

I

9

.

Fig. 3. Cross section through EB-PVD and APS-deposited TBCs

INTERNAL STRESSES AND EXTERNAL LOADS Internal stresses in coated systems

Processing two or more materials with different thermo-elastic properties into a composite gives rise to residual stresses. Different sources of residual stresses have been identified: quenching, thermal expansion mismatch, and stresses related with phase transformations. In plasma sprayed coatings residual stresses originate from the large temperature differences between the substrate and the sprayed particles during the deposition process. Tensile quenching stresses develop as the result of constrained contraction of the particles when they strike the surface and adhere to the substrate. In extreme cases quenching stresses can reach levels of several tens of MPa's [18]. Following the application of coatings a heat treatment is usually applied to the coated part, for example to establish good bonding by creating a diffusion zone between overlay coating and substrate. The heat treatment reduces the residual stresses resulting from the processing step to negligible levels relative to the residual stress resulting from thermal expansion mismatch during subsequent cooling. Upon cooling from the heat treatment temperature, the CTE (coefficient of thermal expansion, ~x) mismatch between the coating material, c, and the substrate material, s, introduces residual stresses in the coating that are tensile or compressive, depending on whether C~cis smaller or larger than C~s. The level of the mismatch residual stresses can be approximated by = Atx. AT. [E/(1-v)]

(1)

where E and v are the Young modulus and Poisson ratio of the coating. Relatively high levels of residual stresses have been reported. For example, compressive stresses of about 200 MPa in a Pt-modified aluminide coating on CMSX6 substrate at ambient temperature are quoted in [19], while a CoNiCrA1Y overlay coating on SRR99 was reported to nearly carry 250 MPa tensile residual stress in the coating layer at ambient temperature in the as-processed state [20]. In service, residual stresses are anticipated to gradually decrease, for example as the result of

121

Coatings for Hot Section Gas Turbine Components

the evening out of compositional differences between coating and substrate due to interdiffusion in diffusion coatings, as the result of cracking etc. Residual stresses in TBCs are crucially important, as the release of the corresponding strain energy stored in the coating drives cracking and finally spallation of the ceramic top coat. It has been demonstrated that phase transformation and quenching stresses are insignificant compared with mismatch stresses [18]. The CTE mismatch between the ceramic topcoat, the TGO, the bond coat (BC) and the superalloy base material (C~Tao < avsz < O~Bc< or > O~s) generates residual stresses upon cooling from the last processing step (annealing). In the case of plasma spraying mismatch stresses in the ceramic top coat are in-plane compressive and can be quite large, depending on the cooling profile, the geometry and the thickness of the individual layers of the TBC. Nevertheless, inelastic processes occur such as micro-cracking, splat sliding, plastic and creep flow which drastically reduce the magnitude of the theoretically calculated stresses. FEM calculations that account for micro-cracking of the ceramic top coat typically show stress levels of 5-10 MPa, in line with residual stress measurements [21]. However, the major source of internal stresses in thermal barrier coated systems is the TGO at the bond coat/ceramic top coat interface. The presence of a continuous thin (= llam) TGO layer on the bond coat, grown prior to the deposition of the ceramic, is a prerequisite for adherence of the EB-PVD ceramic top coat. In the case of APS-deposited ceramic top coats, the TGO grows during exposure in service, its presence and form depending on the bond coat oxidation characteristics and the processing details. The TGO is under very high (in-plane) residual compression, with stresses that can reach levels as high as 2-5 GPa. This has been demonstrated by FEM calculations [21-23], and validated recently by a number of piezospectroscopy measurement techniques [24-26]. The substantial compressive residual stress that develops in the TGO upon cooling due to thermal strain mismatch only is shown in Fig. 4 [27].

500

o -500

~usubstrate -~

L_

+ b o n d coat

-~ -1000 "0

"~ -I500

/

m

~9 -2000 -2500 0

1000

2000

3000

4000

5000

6000

7000

cooling time (s)

Fig. 4. Example of calculated in-plane residual stresses in an APS TBC system upon cooling from a stress-free temperature of 1080~ to room temperature (only thermal strain mismatch has been considered as the source for residual stress) [27].

J. BRESSERS, S. PETEVES, M. STEEN

122

The largest fraction of the TGO related stress stems from the CTE mismatch between ceramic top coat, TGO and bond coat. A significant portion, estimated at -- 30% of the total of the TGO related stress, develops due to its constrained growth at the BC/YSZ interface. In this context, interfacial roughness is of immense consideration, as it is also well known for thin oxide films. The rough surface of the bond coat offers the necessary mechanical locking for APS-deposited TBC coatings, whereas micro-roughness at the ceramic top coat/bond coat interface in EBPVD coatings often develops either due to processing artefacts or micro-structural instabilities. Calculations have shown that tensile and compressive out-of-plane stresses respectively develop at the peak sites and at the valleys of the rough interface, see Fig. 5 [21,22,27]. These out-of-plane stresses in the ceramic promote delamination cracking, in particular of APSdeposited TBC coatings.

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Fig. 5. Calculated profile of radial stress along a path perpendicular to the TGO/ceramic top coat interface that passes, from left to right, through a 'peak' and a 'valley' in the bond coat, and comparison with the radial stress across a planar interface [27]. The evolution of the residual stresses with thermal-mechanical cycling may totally change the above-described situation of the as-deposited state, in a qualitative and also quantitative sense. For example, stresses in the TGO may increase initially, due to the continuous growth of the oxide, and relax after a while due to cracking of the oxide or due to incremental loss of its adhesive strength with the bond coat, a scenario more likely to occur in EB-PVD coated TBC systems. If one accounts for a slow oxidation process, then the residual stresses in the TGO will remain relatively constant. Creep of the bond coat and of the ceramic top coat, combined with continued growth of the TGO may as well degenerate the peak tensile stresses and cause the compressive stresses in the valleys to reverse to tensile, creating favourable fracture initiation sites [21]. Other processes like sintering of the ceramic after long exposures at high temperatures and compositional changes will also contribute to changing the internal stress field.

Stresses resulting from external loads Components in the hot gas path of gas turbines are exposed to a variety of mechanical loads, including static and dynamic bending due to the combustion gas stream, thermally induced

Coatings for Hot Section Gas Turbine Components

123

stresses resulting from temperature differences over the components' cross section, and centrifugal stresses on rotating parts. The component must be designed to withstand the corresponding failure modes i.e. high cycle fatigue, thermal fatigue, excessive deformation and creep. In current blade/vane and combustor designs thermal fatigue cracking is a major cause of failure, in particular when frequent start-stop cycles are experienced like in aero-engine gas turbines and in peak-load shaving gas turbines for electricity generation. The stress state and stress/strain levels caused by external loads on the component can be calculated by means of thermal and mechanical analysis. The lack of adequate materials data for input into constitutive models, and the redistribution of stresses in service as the result of local deformation and cracking prohibit exact predictions of the stresses and strains in the uncoated component. Even if an approximation, the outcome of such analyses is instrumental in our understanding of deformation and fracture of coated materials. Consider for example the aeroengine blade with the cross- section shown in Fig. 6. The thermal strains in the internally cooled blade are due to the fast temperature changes during a typical flight cycle and to the internal constraint of the material. Finite element analysis shows vastly different thermal strain-temperature histories

Temp.

Fig. 6. Cross section through an aero-engine blade. Strain-temperature loops for the pressure side and for the leading edge of the blade typical of a flight mission are the irregular cycles. The rectangular loops represent the simulations used in TMF laboratory tests. for different parts of the blade, as illustrated in Fig. 6 by the irregularly shaped cycles in the strain-temperature plots. The fully compressive out-of-phase cycle typical of the pressure side of the blade represents a hot-spot condition that is particularly damaging to protective coatings. Such loading conditions can be reproduced in the laboratory by means of thermo-mechanical fatigue tests, applying the idealised rectangular cycles shown in Fig. 6 for testing specimens in order to simulate in-service loading conditions. The superposition on the residual stress on the stresses generated by the externally applied loads gives rise to highly complex stress fields that vary within the time frame of a single loading cycle, as well as over longer time frames due to time dependent internal degradation processes in the coating material. The corresponding stress fields acting on the various coating layers and at the interfaces are accessible by means of numerical modelling. The example in Fig. 7 illustrates that upon thermo-mechanical loading of

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J. BRESSERS, S. PETEVES, M. STEEN

the coated system to simulate a typical industrial gas turbine blade, very modest stresses on the substrate alloy are accompanied by high axial stresses in the bond coat and in the ceramic top coat when the mechanical strain imposed on the system reaches maxima (points A and B). The extremely high compressive stresses present in the TGO at the onset as the result of the thermal mismatch are actually relaxed during thermo-mechanical cycling. The availability of numerical modelling results is of great help in the interpretation of the fracture mechanisms established by means of experimental testing.

500 ...a- Substrate ---b- TBC

400

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2

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o

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lw

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0.25

0.5

0.75

t~ m

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time (h)

Fig. 7. Example of calculated axial stresses acting on the various constituents of a TBC coated test specimen during thermo-mechanical loading. A single thermo-mechanical fatigue cycle with a hold time at the maximum cycle temperature typical of an industrial gas turbine blade, was applied. A planar interface between the bond coat and the TGO is assumed. TBC in this figure stands for the ceramic YSZ top coat.

FRACTURE MECHANISMS AND MECHANICS In the case of oxidation-resistant coatings the coating layer acts as a reservoir of A1 for the formation of the protective alumina scale. A1 depletion due to cyclic oxidation, spallation of the oxide and diffusion of oxide forming elements continues until the A1 content of the coating layer has dropped below the critical level necessary for continued protection. The process of A1 depletion has been modelled and used as the basis of a method to predict the useful life of the coated system [28]. Premature cracking of the coating due to thermal-mechanical fatigue frequently undermines this ideal scenario of sustained protection since cracks in the coating not only allow oxygen ingress and attack of the superalloy base material, but by growing into the substrate also endanger the component's structural function. In components protected by thermal barrier coatings the failure mode currently of most concern is large scale delamination that results in the ceramic top coat spalling off from the underlying bondcoat.

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125

Premature Cracking of Oxidation-resistant Coatings Two modes of coating fracture are generally observed upon testing of coated specimens under simulated in-service conditions i.e. brittle fracture and ductile, time dependent fatigue cracking. Examples of both fracture modes are shown in Fig. 8.

....9.............. .

.

.

.

.

.

.

.

.

a

.

.

.

.

.

.

.

.

.

.

.

.

.

.

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Fig. 8. Different types of protective coating failure following thermo-mechanical fatigue cycling, a. Brittle cracking in a Sermaloy 1515 coating deposited on CM186 [29] b. Time dependent fatigue cracking in a CoNiCrA1Y+Pt coating on CMSX4 [30]. c. Longitudinal cross section of the same system as in b, showing rumpling of the coating layer. The original coating surface coincides with the bottom of the troughs in the figure.

Brittle coating fracture. Brittle fracture is triggered when the strain on the coating exceeds the strain-to-fracture limit at temperatures below the ductile-to-brittle transition temperature (DBTT). Both the DBTT and the absolute strain-to-fracture at temperatures below the DBTT depend on such factors as the coating type, its chemical composition, the type of substrate (polycrystalline, directionally solidified or single crystalline), and coating thickness. In particular diffusion coating behaviour has been shown to critically depend on the coating process, its heat treatment route and on composition. Increasing the A1 content and modifying the coating by adding Pt generally shifts the DBTT to higher temperatures [31-34]. A similar effect is reported upon increasing coating thickness [35,36]. The strain to first cracking of aluminide coatings also critically depends on thickness, with thicker coatings displaying a substantially reduced strain to fracture [37]. Thicker coatings tend to have higher aluminium contents with correspondingly higher hardness and lower ductility. Decoupling the effects of thickness and of A1 content, a nearly threefold increase of the strain to first cracking below the DBTT was recently shown as the result of decreasing the A1 content from 34% to 24% in aluminide coatings of similar thickness deposited on a second generation single crystal nickelbase alloy, see Fig. 9 [38]. The brittle behaviour of diffusion coatings is linked to the presence of intermetallic phases such as NiA1. At low temperature only three independent slip systems operate in NiA1, whereas a minimum of five is required for generalised plastic deformation by the Von Mises criterion. The DBTT in polycrystalline NiA1 is a consequence of the onset of thermally activated deformation processes such as dislocation climb [39]. Most of the physical and mechanical

126

J. BRESSERS, X PETEVES, M. STEEN

properties of I3-NiA1 depend on the stoichiometry within the single phase regime, with most of the properties exhibiting a minimum or maximum at, or very near to the stoichiometric composition, which would explain the relatively large effects on the DBTT when adding other elements to the aluminide coating. The DBTT and the strain-to-first cracking are expected to vary when applying the same coating to different substrates. Factors such as grain size and strain rate also have an effect on the mechanical behaviour of 13-NiA1, and hence on aluminide coatings. The same mechanism responsible for the DBTT in NiA1 is believed to be responsible for the increase in fracture toughness with increasing temperature.

1 1 c "~

1

2 4 , 4 % - Pack

1

A 3 0 , 3 % - Pack

~c

c

93 4 % - gas p h a s e

T. . . . . . j

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C C 0

200

400

temp

600

800

1000

(~

Fig. 9. Strain to fracture (in %) of aluminide coatings with different A1 content and similar thickness of--65 lam, deposited on a second generation single crystal nickel-based alloy [38]. Finally, it should be noted that since diffusion-type coatings are metastable by nature, their composition, structure and mechanical properties will change with thermal exposure during operation in the turbine. Therefore the ductility limit and the DBTT are expected to change with time at temperature. The characteristics of MCrA1Y overlay coatings are known to be very dependent on composition, and to a lesser degree on heat treatment and processing route. Because of the different processing route from diffusion coatings, coating behaviour is by-and-large independent of the substrate. The aluminium content has a large effect in CoCrA1Y coatings, with high aluminium contents resulting in high values of DBTT and vice versa [40]. Also, high chromium levels in the coating favour higher DBTT values, while additions of nickel generally result in higher ductility levels and in considerably lower DBTTs. This latter effect is mainly due to NiA1 having a lower DBTT than CoAl and as such, the relative volume fractions of NiA1 and CoAl have to be considered in understanding the effects of compositional variations on the DBTT of MCrA1Y coatings. Superplastic behaviour has been reported for some NiCoCrA1Y coatings [41,42] at temperatures in excess of 800-850~ and has been ascribed to the small grain size of the equiaxed I3-NiA1 in the y microstructure. In the brittle fracture regime the coating fails by a series of approximately equidistant cracks that span the entire circumference of the test specimen [43,44]. Brittle, multiple coating cracking can be rationalised using the fracture mechanics approach proposed by Nairn and Kim

Coatings for Hot Section Gas Turbine Components

127

[45]. The approach relates the in-situ coating fracture toughness to the applied strain to the first crack and to subsequent cracking. It is based on energy release rate concepts to estimate the strain (or stress) to first cracking and to predict the coating crack density. The energy release rate for the first crack is given by G = [EcEo + C1 (Of,s - O~c) AT] 2 C2 tc

(2)

where 80 is the applied strain, o~ and ~ are the linear coefficients of thermal expansion of the substrate and the coating, respectively, and AT is the temperature increment measured from the reference state (i.e. the equilibrium temperature at which there is no residual thermal stress). C1 and C2 are constants depending on Young's modulus, Poisson's ratio and thickness of the substrate (Es, Vs and ts) and of the coating (Ec, Vc and tc). This approach was used to estimate the fracture toughness of the aluminide coating investigated in [43] and to predict the effect of coating thickness and residual stress on first cracking [46]. In line with experimental observations, the model correctly predicts that the strain to first cracking of the coating increases with decreasing coating thickness.

Time dependent fatigue fracture. Even if the limit for brittle cracking of the coating is not exceeded, oxidation-resistant coatings still can fail prior to achieving their critical A1 level for oxidation protection by a process of time dependent fatigue cracking that results from the interplay between mechanical load and oxidation effects at high temperature. Despite the fact that the strain to brittle fracture of MCrA1Y coatings generally exceeds that of diffusion coatings, under thermal-mechanical cycling conditions the life of diffusion coated alloys can exceed the life of overlay coatings in this particular regime of time dependent fatigue cracking [47]. Therefore, absolute ductility levels and DBTTs are by no means the only criteria to be taken into consideration in coating selection. In the absence of brittle failure, the dominant mechanisms of degradation of protective coatings exposed to high temperature and thermal-mechanical fatigue are oxidation, surface roughening and cracking. The repetition of a process of irregular build-up of oxide at the high temperature part of the thermal-mechanical cycle, followed by subsequent oxide cracking and spallation at the low temperature end of the cycle is likely to cause irregular surface roughening. Frequently however, the evolving surface roughness takes the form of periodic rumples or wrinkles, as illustrated in Fig. 8c. Periodic rumpling has been observed in both aluminide and overlay coatings [48-50]. This is in line with the prediction that free, plane surfaces limiting a solid under homogeneous tensile, compressive or shear stress develop periodic roughness undulations, driven by balancing the energy reduction due to formation of the morphological distortions and the increase in free energy due to increased surface formation [51]. Initial surface roughening by compressive shear cracking and spallation of the oxide forming on top of the aluminide coating, followed by irreversible creep has also been invoked to explain the growth of rumples [52]. As illustrated in Fig. 8b and 8c, cracks are frequently associated with the troughs of the rumpled coating surface. Troughs are predicted to be higher strained in compression (tension) relative to the hills when the coating is under compression (tension). [53]. Cracking at the troughs therefore can be explained in the case of thermal-mechanical fatigue cycles that cause compression in the coating at the high temperature part of the cycle, and tension at the low temperature part. The role of rumpling as one of the drivers of coating cracking is corroborated by the observation of a substantial reduction of bond coat cracking in specimens where rumpling of the bond coating was suppressed by the presence of a thin ceramic topcoat layer [54].

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J. BRESSERS, S. PETEVES, M. STEEN

Very little work has been published concerning the mechanisms at the scale of the microstructure that are driving time-dependent crack initiation and growth in the coating during thermal-mechanical fatigue. In thermal-mechanical loading conditions that promote premature coating cracking, cracks appear early in the coating life. Preferred nucleation sites are the outer coating surface and, in the case of plasma sprayed overlay coatings, also bulk porosity. In aluminide coatings I3-NiA1 grain boundaries are the preferred growth path of cracks. Detailed analysis of populations of micro-cracks in an aluminide coating suggests that cracking in the deeper coating layers can also be related to the periodic variations in the solidification structure of the substrate material, such as by the secondary interdendrite spacing [55]. Crack densities in the coating generally are much higher than in the uncoated substrate material under similar loading conditions, which may speed up crack growth as the result of crack coalescence [47,56] and thereby result in a reduced lifetime relative to uncoated material.

Delamination/Spallation of Thermal Barrier Coatings Due to their disparity, TBC systems exhibit multiple failure mechanisms, the majority of which lead to spallation of the ceramic coating from the underlying bond-coated alloy. Prevalent mechanisms that contribute to failure are driven by (i) chemical effects, (ii) foreign object damage, (iii) edge and geometry effects, and (iv) build-up of strain energy in the TGO. Chemical effects are related to Al-depletion of the bond coat and Ni-diffusion through the TGO, both resulting in the formation of spinels in, or in the vicinity of the TGO, causing brittleness and finally delamination [57]. Of particular relevance in the environment of some industrial gas turbines is molten-salt or gaseous corrosion, leading to attack of the ceramic and the bond-coat and eventually contributing to cracking of the ceramic. Foreign object damage [3] can erode the coating, introduce high shear and tensile stresses in it or facilitate hot spot conditions, all of which are sufficient causes for spallation. Edge and geometry effects are related with the singularity at the edges of dissimilar material interfaces, for example at cooling holes [58]. The most frequently claimed operating mechanism for failure is the release of strain energy stored in the TGO, in conjunction with the imperfections at its interfaces. This mechanism will be addressed in more detail below. Some of the failure mechanisms are well understood and appropriately described; several though that are seen in service or in development engines are not reproduced in laboratory assessments. Furthermore, although the cause of failure may be understood, the various steps involved in the sequence of events that ultimately results in delamination and spallation are not substantiated in detail for every single mechanism. For example, how does the conversion of a uniform TGO scale to mixed alumina and spinel phases lead to failure? Is it because of the reduced fracture resistance of the YSZ-spinel/TGO interface relative to that of YSZ/TGO, or because the volumetric change associated with the constrained spinel formation leads to extensive cracking? Similarly, experience gained in-service and in laboratory testing shows that the failure modes of APS and EB-PVD coatings are different. Observations indicate that the final fracture path in APS coated systems is through the TBC, near the TBC/TGO interface. In EB-PVD coated systems failure usually occurs along the TGO/BC interface, although nominally similar EB-PVD TBCs have been reported to fail within the TGO as well as along the TGO/TBC interface. Evidently the growth and the mechanical properties of TGO scales play a critical role in the durability of TBCs, since failure of the TBCs is related to the presence, growth and mechanical integrity of this buried interfacial scale. The driving force for cracking and finally spalling is

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129

the strain energy stored in the TGO. The TGO, typically alumina growing at the BC/TBC interface, is subjected to large mismatch and growth induced stresses, as discussed previously. Redistribution of these stresses, in concurrence with external thermal and mechanical loads and relaxation processes, provides the drive for nucleating and extending cracks. The main differences between APS and EB-PVD coatings are the ratio of the in-plane modulus to the out-of-plane modulus of the YSZ top coat (high ratio for the APS and low ratio for the EBPVD), and the lower toughness of the APS YSZ and the much rougher YSZ/BC interface of APS coatings relative to EB-PVD TBCs. Crack nucleation sites are still surmised rather than substantiated by observations. Sites that are assumed to be prone to cracking are linked with processing inhomogeneities, with microunbonded interfacial regions and with defects related with high temperature diffusional processes. Where such defects are present the local stress field can induce crack nuclei and subsequent crack growth. Obviously the most critical stress field is linked with the TGO interfaces. Stress levels can be amplified by the interface roughness as illustrated in Fig. 5, by undulations and wrinkling of the BC/TGO interface and by thickness variations of the TGO. The different stages of the failure sequence can be summarised as follows, see Fig. 10: (1) Interfacial micro-debonds and microcracks develop from imperfections in the ceramic, in the TGO and at their interfaces, and grow and coalesce to form a critical defect size, (2) This defect then can trigger either (a) edge type delamination or (b) buckling type delamination and finally (3) Spallation.

TGO BC

Defect I

I.uckleH

Spallation I

Fig. 10. Sequence of events leading to spallation of the ceramic topcoat in an EBPVD coated material. Crack coalescence from an array of heterogeneities in TBCs has been recently investigated [59]. For simplicity here the discussion refers to a thin single layer coating only, i.e. TGO on top of the BC. The likelihood of both edge-delamination and buckle delamination is assessed by considering the steady state (i.e. crack independent) energy release rate [60-63].

130

J. BRESSERS, S. PETEVES, M. STEEN 1 --V 2

GO= ~ c r 2 t 2E

(3)

where E and v are the Young's modulus and Poisson's ratio of the thin coating, cy is the stress and t is the thickness of the coating. Edge delamination is expected when G O >.- Fi(~)

(4)

where 1-'i is the interface (coating/substrate) toughness that depends on the mode mixity, ~. The mode mixity, ~t, defines the relative contributions of the opening and shear modes to cracking. Fi is generally significantly larger in near-mode II loading conditions than in mode I for metal/ceramic interfaces. The buckling phenomenon and buckle propagation in thin compressed films are characterised by the following three non-dimensional indices. 1. A buckling index

1-i = O - vZ )cr b 2 Et

(5)

where 2b is the initial debond length. Buckling occurs at a critical value of 1.22. 2. An adhesion index Z=~

El-',

(6)

where FI is the mode I interface toughness (i.e. ~=0). Buckles propagate when Z > 1.9. 3. A mode mixity index ;k that depends on the interface roughness and friction of the interface. For a smooth frictionless interface X = 1. Typical values for F~ are in the range of 1-10 J/m 2 and for ;L about 0.3 [64,65]. Based on these indices, the conditions for TGO buckling, propagation and arrest can be specified, as show in Fig. 11. Similarly the effects of thermal cycling can be inferred by considering, for example, that the thickness of the TGO, t, will increase with time at high temperature, 1-'i will decrease due to segregation of impurities at the interface and/or moisture effects, whereas ~, is usually found to increase upon cyclic growth of the TGO. The effects of the YSZ layer on buckling have also been investigated for EB-PVD structures, even accounting for the 1-2 lam thick region of dense polycrystalline YSZ between the TGO and the columnar YSZ structure, see Fig.3a. A detailed synopsis of the results of this work is beyond the scope of this paper; its focus has been the edge-delamination and buckling of the TGO, at the TGO/BC interface, as influenced by the in-plane stiffness of the YSZ. Some of the highlights of this analysis are shown in Fig. 12.

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131

Buckle Propagation

~

t(1-v)EF i 9

i. Buckling

(l-vZ)(cr/E)(b/t)

z

Fig. 11. A map showing the regions of buckling and buckle propagation according to the indices defined in the text. As the residual stress or mechanical load increase, the conditions for buckling are satisfied ( point a -> b ), followed by an abrupt jump (b -> c) and stable propagation (c -> d). After [60,62] Depending on the combinations of the thickness of the columnar EB-PVD ceramic, and its inplane to out-of-plane modulus ratio, conditions exist which exclude both edge-delamination and buckling, for a given size of the initial defect and the mode II interface toughness.

1-" iI

O"~

r.~

~ ~

r

~=

Buckling

%

Ein_plane/Eout_of_plane (Y SZ) Fig.12. Schematic of a fail-safe map for combinations of YSZ (columnar structure) thickness and modulus ratio, showing the conditions favouring edge delamination, buckling or for fail safe operation, b is half the initial debond length, 1-'II is the mode II interface toughness (~=90~ After [63]. Although the features that govern spallation are understood, a spalling criterion as that described for buckling has still to be established. Cracking of the TGO is thought to occur

132

J. BRESSERS, S. PETEVES, M. STEEN

when the in-plane tensile stress in the apex of the buckled TGO exceeds the fracture strength of the TGO. On the other hand the buckle delamination front may kink out of the interface into the TGO, depending on the ratio of the interface toughness, F1 and the toughness of the TGO (--- 20 J/m 2) as well as on the mode mixity, ~ [61 ]. Concepts that are based on the mechanics of interface cracking to describe delamination and buckling of residually stressed coatings are instrumental to rationalise some TBC failures [65, 66]. The key elements are the relative values of the toughness of the interfaces, TGO and YSZ, the elastic energy stored in the TGO due to its residual compression, the stiffness of the ceramic and the mode mixity at the interface.

CONCLUSION The integrity of coatings that protect components from oxidation and excessive temperatures in the hot section part of aero-engines and industrial gas turbines has become one of the primary life limiting factors, in particular for coated blades and vanes. In conditions of brittle coating failure, mechanics of materials concepts offer a useful framework for analysing coating behaviour and for capturing the effect of various system parameters. In oxidation-resistant coatings, an analysis based on the energy release rate can be used to predict the onset of multiple cracking failures. In combination with experimental calibration, the analysis enables to predict the in-situ fracture toughness of the coating and the effect of coating system variables like coating thickness and residual stress on the coating performance. Similarly, in the case of thermal barrier coating systems, the conditions for safe operation or failure can be derived from the critical conditions for buckling and delamination of thermally grown oxide layers, and the effect of the presence of the ceramic top coat layer on TGO failure can be predicted. Failure of oxidation-resistant coatings due to thermal-mechanical fatigue has another dimension in that the actual cracking process involves time dependent deformation and oxidation effects. Fatigue cracking of these coatings has received little attention, in particular concerning the micro mechanisms and the mechanics of crack growth.

REFERENCES 1. 2. 3. 4.

5. 6.

Sofia, A. (1999). In: Europe 2010, Futures and Scenarios, pp. 29-35, The IPTS Report no.38, European Commission. Stringer, J. (1998). In: Gas Turbine Materials Technology, pp. 3-12, Maziasz, P.J. et al. (Eds.). ASM, Metals park, OH. Morrell, P. and Rickerby, D.S. (1997). In: Thermal Barrier Coatings, pp. 20-1 to 20-9, AGARD Report 823, NATO. Goward, G.W. and Cannon, L.W. (1988). Paper no. 87-GT-50 presented at the Gas Turbine Conference and Exhibition, May 31-June 4, Anaheim, Ca. American Society of Mechanical Engineers, New York. Proceedings of the Conference on Protective Coating Systems for High-Temperature Gas Turbine Components, (1986) Mat.Sci. and Tech. 2, 193. Wood, J.H., Foster, A.D., Schilke, P.W., (1989). Paper 89-GT-239 presented at the Gas Turbine and Aeroengine Congress and Exposition, June 4-8, Toronto, Canada. American Society of Mechanical Engineers, New York.

Coatingsfor Hot Section Gas Turbine Components 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37.

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Goward, G.W. (1992). In: Proceedings 3rd International Symposium on high Temperature Corrosion and Protection of Materials, Streiff, R., Stringer, J., Krutenat, R.C. and Caillet, M., (Eds.). M6vrel, R. (1989) Mat.Sci.and Eng., A120, 13. Bernstein, H.L. Russell, J.A., Scheirer, S.T., Hsu, L.L. and Van Roode, M. (1991). EPRI Report GS 7334-L, Palo Alto, California. McMinn, A. (1987). EPRI Report AP-5078, Palo Alto, California. Bose, S. and DeMasi-Marcin, J. (1995). In: Thermal Barrier Coatings Workshop, pp. 6377, NASA-CP-3312, NASA Lewis Research Centre, Cleveland, OH. Trubelja, M.F. (1999). Pratt & Whitney ATS TBC Development Program, ATS Annual Program Review Meeting, Pittsburgh, PA. Wing, R. (2000) Materials World, 3, 10. Proceedings 85th meeting of the AGARD Structures and Materials Panel. (1998) Thermal Barrier Coatings, AGARD Report 823, NATO. Proceedings of the TBC Workshop. (1997) NASA Lewis Research Center, Cleveland, OH., May 19-21. Thermal Bamer Coatings Workshop Proceedings. (1995) NASA Conference Publication 3312, NASA Lewis Research Center, Cleveland, OH. Meier, S.M. and Gupta, D.K. (1994) J. Eng. Gas Turbine Power, 116, 250. Clyne, T.W. and Gill, S.C. (1996) J. Thermal Spray Tech., 5, 401. Moretto, P. Bressers, J. and Arrell, D.J. (1999) Materials Science and Engineering A272, 310. Sequeira, A.D., Moretto, P. and Bressers, J. (1999) Materials Science Forum, in press. Freborg, A.M., Ferguson, B.L., Brindley, and W.J., Petrus, G.J. (1998). In: Thermal Barrier Coatings, pp. 17/1 - 17/9, AGARD Report 823, NATO. Cheng, J., Jordan, E.H., Barber, B. and Gell, M. (1998) Acta Mater., 16, 5839. Tzimas, E., Muellejans, H., Peteves, S.D. and Bressers, J. (2000) Acta Mater., in press. Sergo, V. and Clarke, D.R. (1998) J. Am. Ceram. Soc., 81, 3237. Wen, Q., Lipkin, D.M. and Clarke, D.R. (1998) J. Am. Ceram. Soc., 81, 3345. Lance, M.J. (1998). Ph.D Thesis, Rutgers University, New Bruswick, NJ. Tzimas, E., Stamos, V., Peteves, S.D. and Bressers, J. (1999). In: Mechanical Properties of Films, Coatings and Interfacial Materials, UEF Conference, 27 June-2 July, 1999, I1 Ciocco, Italy. Chan, K.S., Sastry Cheruvu, N. and Leverant, G.R. (1998). Paper no. 98-GT-478 presented at the International Gas Turbine and Aeroengine Congress and Exhibition, June 2-5, Stockholm, Sweden. De Haan, F., Timm, J., Peteves, S.D., Bressers, J., Hughes, P.M., Moss, S.J., Johnson, P. and Henderson, M., accepted for presentation at the Conference Superalloys 2000. Bressers, J., Timm, J., Unpublished results. Goward, G.W. (1970) Journal of Metals, 31. Goward, G.W. (1976). Symposium on Properties of High-Temperature Alloys, pp. 806823, Las Vegas, USA. Brandis, H., Lehnert, G., Schmidt, W. (1981) Thyssen Edelstahl Tech. Rev., 7 (1),82. Vogel, D., Newman, L., Deb, P. and Boone, D.H. (1987) Materials Science and Engineering, 88, 227. Wahl, G., Schmackner, F., Metzger, R. and Nicholl, A.R. (1981). In: Proc. 8th CVD Intern. Conf., Paris, pp.685-692. Hancock, P., Chien, H.H., Nicholls, J.R. and Stephenson, D.J. (1990) Surface and Coatings Technology, 43144, 359. Betz, W., Huff, H. and Track, W., (1976) Z. Werkstoffiechnik 7, 161.

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38. Affeldt, E.E. (1999) Euromat 99, Sep.27-30, Munich, Germany. 39. Noebe, R.D., Bowman, R.R., Nathal, M.V., (1993) International Material Reviews, 38, 193. 40. Boone, D.H. (1977) Airco Temescal Data Sheets, Airco Inc., Berkeley, Ca, USA. 41. Veys, J.M., Rivi~re, A. and M6vrel, R. (1988), "In: Proc. 1st Plasma Technik Symposium (Luzern), 2, pp.115-123, Eschnauer, H. et al., (Eds.). 42. Hebsur, M.G. and Miner, R.V. (1986) Materials Science and Engineering, 83, 239. 43. Bressers, J., Timm, J., Williams, S.W., Affeldt, E.E. and Bennett, A. (1996). In: Thermomechanical Fatigue Behaviour of Materials: Second Volume, pp.56-67, Verrilli, M.J. and Castelli, M.G. (Eds), ASTM-STP 1263, American Society for Testing and Materials, Philadelphia, USA. 44. Bressers, J., Timm, J., Affeldt, E.E. and Bennett, A. (1996). In: Thermal Mechanical Fatigue of Aircraft Engine Materials, pp.9-1 to 9-10, AGARD Report CP-569, NATO. 45. Nairn, J.A. and Kim, S.-R. (1992) Eng.Fract.Mech., 42,195. 46. Martinez-Esnaola, J.M., Arana, M., Bressers, J., Timm, J., Martin-Meisozo, A., Bennett, A. and Affeldt, E.E. (1996). In: Thermomechanical Fatigue Behaviour of Materials: Second Volume, pp.68-81, Verrilli, M.J. and Castelli, M.G. (Eds.), ASTM-STP 1263, American Society for Testing and Materials, Philadelphia, USA. 47. Bressers, J., Ostolaza, K. and Arana, M. (1996). In: Elevated Temperature Coatings: Science and Technology H, pp. 275-285, Dahotre, N.B. and Hampikian, J.M. (Eds.), The Minerals, Metals and Materials Society, Pennsylvania, USA. 48. Pennefather, P.C. and Boone, D.H. (1995) Surf. Coat.technol.,76, 47. 49. Peichl, L. and Bettridge, D.F. (1994) In: Materials for Advanced Power Engineering, pp.717-727, Coutsouradis, D. (Ed.). Kluwer Academic Publishers, The Netherlands. 50. Deb, P., Boone, D.H. and Manley, T.F. (1987) J. Vac.Sci.Technol., A5, 3366. 51. Grilhe, J. (1993) Acta metall.mater., 41,909-913. 52. Holmes, J.W. and McClintock, F.A. (1990). Metallurgical Transactions A, 21A, 1209. 53. Pidduck, A.J., Robbins, D.J., Cullis, A.G., Leong, W.Y. and Pitt, A.M. (1992) Thin Solid Films, 222, 78. 54. Zhang, Y.H., Withers, P.J., Fox, M.D. and Knowles, D.M. (1999) Materials Science and Engineering, 15, 1031. 55. Ostolaza, K.M., Johnson, P.K., Arana, M. and Bressers, J. (1996). Anales de la Mecanica de la Fractura, 13, 272. 56. Johnson, P.K., Arana, M., Ostolaza, K.M. and Bressers, J. (1997). Paper no. 97-GT-236, presented at the International Gas Turbine & Aeroengine Congress and Exhibition, Orlando, American Society of Mechanical Engineers, New York. 57. Shilington, E.A.G. and Clarke, D.R. (1999) Acta Mater, 47,1297. 58. Nissley, D.M. (1997) J. Thermal Spray Tech., 6, 91. 59. Evans, A.G., Hutchinson, J.W. and He, M.Y. (1999) Acta Mater., 47, 1513. 60. Clarke, D.R., Meier, G., Hutchinson, J.W. and Evans, A.G. (1998), Assertions and Hypotheses about Failure Mechanisms in TBCs, presented at the TBC Workshop, Irrsee, Germany, May 29-31. 61. Wang, J.S. and Evans, A.G. (1999) Acta Mater., 47, 699. 62. Wang, J.S. and Evans, A.G. (1998) Acta Mater., 46, 4993. 63. Choi, S.R., Hutchinson, J.W. and Evans, A.G. (1999) Mech. of Mater., 31,431. 64. Evans, A.G., Hutchinson, J.W. and Wei, Y. (1999) Acta Mater., 47, 4093. 65. Hutchinson, J.W. and Suo, Z. (1992) Adv. Appl. Mech., 29, 63. 66. Rice, J.R. (1998) J.Appl.Mech., 55, 98.

135

M O D E L I N G CYCLIC D E F O R M A T I O N OF T H I C K T H E R M A L B A R R I E R

COATINGS Darrell Socie and Edwin Rejda Mechanical Engineering Department University of Illinois at Urbana-Champaign 1206 West Green, Urbana, Illinois 61873, USA

ABSTRACT A cyclic deformation study of plasma-sprayed ceramic coatings for diesel engine applications was conducted. Coatings were tested independent of a substrate. Irreversible deformation was observed in all of the coating materials tested and under all conditions, including room temperature and tests conducted at very low cyclic strains. This behavior can lead to tensile fractures upon unloading from a compressive thermomechanical cycle. A model describing the irreversible strain behavior based on the combined sliding and closing of pre-existing micro cracks is proposed and compared with experimental results. The model has been used to produce a failure map for combinations of strain, strain rate and temperature that will lead to coating fractures during a thermomechanical cycle in a diesel engine. KEYWORDS ceramic coatings, deformation, fatigue, fracture INTRODUCTION Recent years has shown an increase in the use of ceramic coatings for insulating and protecting components for high temperature service. The performance of these materials in the gas turbine industry is well documented. [1-3] Of these coatings, the most successful has been plasma sprayed yttria zirconia (Y2Oa-ZrO2) onto a thin bond coat such as MCrA1Y (M = Ni, Co, NiCo). Thermal and mechanical fatigue tests of ceramic coatings have traditionally been "on-subsrtate" tests of thin (0.01-0. lmm) coatings where the failure mode has been delamination. [4-5]. Recently there has been an emphasis on the development of thick thermal barrier coatings (TTBC) for diesel engine applications. In a diesel engine, a ceramic coating/piston substrate assembly will undergo thermal and mechanical cycling where the coating is expected to remain in compression to take advantage of the high compressive strength. Failure of the coating is caused nonlinear deformation processes during the compressive loading cycle which result in a tensile stress being developed in the coating substrate assembly when the coating is cooled back to ambient temperature. EXPERIMENTAL PROCEDURE Uniaxial tension and compression tests were performed in this investigation. The TTBC specimens were prepared from powders of 8% Y203-ZrO2 having a mean particle size approximately 60 ~tm. A thin carbon steel shaft, 8.5 mm diameter 75 mm long, onto which two stainless steel ends were press fitted was fabricated as indicated in Fig. 1. The

136

D. SOCIE, E. REJDA

powders were then plasma sprayed onto this substrate. Specimens were then machined to remove excess coating material to produce a specimen with uniform dimensions. At this point the specimens were placed into a solution of 1:1 H20:HNO3 to dissolve out the carbon steel shaft. A tubular specimen of the bulk coating material remained with a wall thickness of 1.5 mm bonded to the stainless steel ends. The stainless steel ends could then be gripped in a standard testing system to perform thermomechanical fatigue tests. Details are given in reference 6. The coatings are sprayed with a bulk porosity level of about 15%. This reduces the thermal conductivity by as much as a factor of three compared to solid Y203-ZrO2. This results in the complex microstructure shown in Fig. 2. The macroscopic porosity is interconnected and has a size of about 100 ~tm. In addition there is a continuous network of microcracks that permits sliding and compaction during cyclic loading. Tensile strength of this coating is only 25 MPa while the compression strength is 500 MPa.

. . . .

-

~i]b~

:

-.,

,~ ,r

"!f ,

.

Carbon Steel Substrate

Stainless Steel Ends

Fig. 1 Test specimen

0E10012

~.;?i:.~,,,' ::::1.0n~:

:-:Our,

Fig. 2 Coating micro structure

EXPERIMENTAL OBSERVATIONS A series of fatigue tests were conducted at room temperature in cyclic tension and compression loading with the results shown in Fig. 3. All of these tests were conducted in stress control. Three sets of data are shown. The open squares represent fatigue tests tested only in tension, R = 0 loading. The solid squares represent tests conducted only in compression and the lines indicate tests conducted at various R ratios in combined tension and compression loading. The top of the line indicates the maximum tensile stress in the loading cycle and the bottom of the line indicates the compression stress. These tests were conducted with the same maximum stress as the R=0 tension tests but with different compressive stresses. A large difference between tensile and compression behavior is clearly shown in Fig. 3. Both tension and compression fatigue strengths are about 40% of

Modeling CyclicDeformation...

137

the static strength. The results show that the fatigue life is only dependent on the maximum tensile stress reached in the cycle and not the stress range. Two distinct failure modes are observed for this material. One failure mode is activated by the compressive loads and another by the tensile loads. The material starts out with microcracks formed during the plasma spraying process. These cracks are oriented both parallel and perpendicular to the loading direction. They correspond to microcracks between individual platelets of the ceramic as well as cracks around the macroscopic porosity. Transverse tensile stresses are produced around the porosity during compressive loading. This leads to microcrack growth that is parallel to the applied loads. This damage grows and coalescences with other microcracks. Many parallel cracks are formed leading to a compressive instability. Final fracture occurs on shear planes in a manner similar to the formation and growth of a kink band in a composite material or by spalling. During tensile failure, microcracks perpendicular to the applied loads grow and coalesce to form a dominant crack. There does not appear to be a strong interaction between these two damage mechanisms and the tensile mechanism is activated at very low stress levels. From an engineering viewpoint this means that a small amount of tension is very damaging and may limit the life of components that are coated with this process. To assess the durability of a coating system, a model for predicting tensile stresses resulting from thermomechanical loading is needed. Cycles

100

. . . . . . . . . . . . . . . ,D, -r, D.I.I.... . . . . . ~o; t~ IX.

-loo

or) t.,. ..., 9 (/)

~ 1

~0,

9 mmm 9m m

E ..-,1

E -3oo -400

+..r:..+ l,-F~ ...... nr .-,-..-+:..tm ......... ~0~

T ~

~0,

.......... 1..... i .... I ....... "l'I .........

-200

._ x

~;~

mm

I

9

mm

-500

-600

Fig. 3 Fatigue test results

A series of deformation experiments were conducted at various temperatures up to 800 ~ Results for 600 ~ are shown in Fig. 4. The specimen was slowly heated to 600~ and then deformed to a compressive strain of -0.005. One test was immediately unloaded until failure in tension. Note that this test failed at both a tensile stress and strain. This test is indicated by the solid line in the figure. A second test was conducted where the strain was held at -.005 after loading for a period of 1 hour. The specimen was then unloaded and failure occurred with a tensile stress even though the strain was still compressive. The difference in initial loading slopes is an indication of the scatter in these plasma sprayed materials. Variations in strength and stiffness of 25% are frequently observed. Normally

138

D. SOCIE, E. REJDA

ceramic materials are considered linear elastic at this temperature and the initial linear straight line behavior is otten mistakenly considered as elastic. If the initial loading was really elastic the unloading curve would also follow the same path. But, hysteresis is clearly evident in these tests. This is an indication of some nonlinear process during the initial compression loading. A series of cyclic deformation experiments was conducted with the results given in Fig. 5. The specimen was loaded in compression to point A and then unloaded to zero stress at point B. Then the specimen was reloaded to point C and unloaded again to zero stress. This process was repeated several times as shown in the figure. Several features of this deformation are noteworthy. First the material has memory of its prior deformation. When the material is loaded from point B to C the material remembers its prior deformation at point A and deforms along a path from O to C as if the unloading from A to B never occurred. This memory was observed at each reversal point, i.e. A, C, E and G and is similar to that observed in the cyclic deformation of a metal.

30

Strain -0.006

/ "

--"

,.7". , r. ; z

//

.,~ . , , Y ' f

no holdtime 1 hour holdtime

-0.007

Strain

H

F

D

0.001

f

g, -120

Fig. 4 Holdtime experiments

B

-140

Fig. 5 Deformation at 600 ~

The unloading modulus for each of these reversals is dependant on the stress level. The shape of the unloading curves are similar. Stress-strain response similar to Fig. 5 was observed at all temperatures. The amount of permanent strain at zero stress was found to be a linear function of the applied compressive stress for both temperatures as shown in Fig. 6. The differences in permanent strain between room temperature and 600 ~ can not be explained by creep processes of the bulk ceramic because the temperatures are not high enough to activate creep mechanisms. Examination of the specimens tested at high temperatures revealed the existence of a viscous boundary phase that is shown in Fig. 7. This viscous phase is formed during the plasma spraying process. Impurities in the powders react with oxygen in the air to form glasses. The viscosity of the glassy boundary phase is lower at 600 ~ allowing the individual platelets to more easily slide relative to each other. MODELING The complicated microcracked structure of the coating material plays a dominant role in its deformation behavior. In view of these dominant effects, a model incorporating the basic

Modeling Cyclic Deformation...

139

physics of microcrack behavior was developed. In this study, four basic mechanisms were considered to drive the deformation behavior: intrinsic elasticity, microcrack opening and closure, sliding along microcrack surfaces, and microcracking in tension. The underlying assumption for the model was that each of these mechanisms made an independent contribution to the deformation such that the total strain in the coating material, o~total, could be expressed as Etotal = • elasticity -~- ~

q- ~

"~- ~

(1)

where ~etastm~,~open, ~sliding, &rackingare the contributions due to intrinsic elasticity, open cracks, sliding cracks, and additional cracking in tension, respectively. Each of these four mechanisms is discussed, in turn, in the following subsections. a n d

o. 160 140 r.~ 120

/ ~ R n o m

Temperature

"6 lOO ==

~

80 60 40

0

0

j. g.C

~ ~~

0

0

,

,

,

,

,

,

~

0.00050.001 0.0015 0.002 0.0025 0.003 0.0035 Irreversible Compressive Strain

Fig. 6 Irreversible compressive strain

Fig. 7 Viscous boundary phase

Intrinsic Elasticity The most straightforward of the deformation mechanisms is intrinsic elasticity. In this study, intrinsic elastic strain was defined as the strain that would occur in the bulk form of the coating material, i.e. without the effects of the large amounts of porosity. With this definition, the intrinsic elastic strain in the coating material could then be given directly by Hooke's Law as

~elasticity -"

cr

Eo

where o-is the applied stress and Eo is the bulk modulus of the coating material.

(2)

D. SOCIE, E. REJDA

140

Microcrack Opening and Closure The effect of open cracks on the deformation behavior is considered next. Since the complex micro structural features of the coating material make it difficult to predict the effect of open cracks analytically, the idealized case of a random distribution of open circular cracks in an elastic body was used to establish a phenomenological basis. For such a body, the effective modulus, Eopen, is reduced relative to the intrinsic modulus of the material, Eo, by the following relation [7]:

l

Eopen

_

1

Eo

/ 4N~ 1..{-

3V

,1

fopen(t~rrfln,i~rnax

(3)

where Cope, is the average length of an open crack, the ratio Nopen,/V is the number of open cracks per unit volume, and

/o,,~,,(Pmin,P ~ ) = sin ~ ,emax -sm~/~mm

(4)

where flmm and flmaxare the minimum and maximum crack orientation angles with respect to the loading direction. For a randomly cracked body, flmm= 0 and flm~ = n/2 SO Equation 4 evaluates to unity. During compressive loading of the coating material, microcrack closure occurs and can cause a decrease in both the total number of open cracks, Nopen, and the average effective crack length, Copen" The effect is the same in each case: an increasing modulus with increasing compressive stress. In tension, the opposite occurs. Initially closed cracks open, causing an increase in the number of open cracks, and partially open cracks continue to open, causing an increase in the effective crack length. Therefore, the modulus Eopen decreases with increasing tensile stress. In the present model, the effects of changing values of Nope,, and "Copena r e captured by lumping them into a single parameter, Vopen, defined as

V

_

open

-

4

ZN~176 3V

-3

(5)

which provides a measure of the strain energy interaction volume of all open cracks in the coating material. Combining Equations 3 through 5 then leads to a simple relation for the modulus of a body with open microcracks

1 __ 10+Vopen) Eopen Eo

(6)

It is now convenient to separate the effect of open cracks from the intrinsic elasticity. This can be done by fn'st multiplying Equation 6 by an incremental stress, do-, to give the total incremental strain in the microcracked body as

Modeling Cyclic Deformation...

141

do, total = d_____~ __ O-+-Qpen)do" Eopen Eo

(7)

It is then recognized that this total incremental strain has two distinct components: the incremental strain due to the intrinsic elasticity of the material and the additional incremental strain due to presence of open microcracks. Therefore, the total incremental strain in Equation 7 may also be written as

(8)

doetotat -- doeelastJcityJr-doeopen

Finally, by combining Equations 7, 8, and the differential form of Equation 2, the incremental strain due to open microcracks, d,~open, can be given by V doeopen-- ~ doEo

(9)

which can then be integrated over the load path to yield the additional strain due to open cracks. It should be noted that Vope, is a function of the current stress level.

Microcrack Sliding The effect of sliding cracks on the deformation behavior of the coating material is now considered. Before the constitutive relations for such a body are discussed, it is instructive to first analyze the local deformation behavior of a single sliding crack. By doing this, the extension to a multiply cracked body becomes more meaningful.

C~'loc~l

y/

O'locaI

U

t I I I l O'local

Fig. 8 Local stress on a microcrack

~ ~local

Fig. 9 Sliding of a microcrack

Consider the initially closed crack shown in Fig. 8 that is subjected to a local compressive stress, Crtocat,during far-field loading. By assuming that the crack has no residual stresses on its surface fi'om the result of any previous loading, the local stress can be readily decomposed into a normal and shear stress, tr, and r, on the crack plane by

or, = Crlocat sin: fl

(10)

142

D. S O C I E , E. R E J D A

r = O'1o~! sin flcos fl

(11)

where fl is the crack orientation angle and O'local and crn are taken to be positive in compression to simplit~ signs. As the local compressive stress is increased, sliding can occur at the crack surface if the shear stress, r, on the plane of the crack is greater than the resistance due to friction. In the present model, the frictional resistance stress, rf, is assumed to be governed by a simple coefficient of friction, p, such that ry =/dcr,

(12)

By combining Equations 10 through 12, the initial sliding criteria r > rf is then found to be satisfied for the following range of crack orientation angles: 0 < fl < tan-' (1 //.t)

(13)

As would be expected, the angular range of cracks involved in initial forward sliding is seen to be dependent of the coefficient of friction. As the coefficient of friction decreases, a larger angular range of cracks will be active because there will be less resistance to frictional sliding. The opposite is true when the coefficient of friction increases and less sliding activity will result. It has been shown in the literature that the average sliding displacement on a closed crack surface is proportional to the effective shear stress, reff, that is acting on the crack [8]. The effective shear stress on a crack surface is given by re~r = r -

rs

(14)

which, through use of Equations 10 through 12, can be expanded to "Ceff -- O'locai(Sin ~ cos ]~ -- iu sin 2 ~ )

(15)

It is seen from Equation 15 that the effective shear stress is an increasing function of the local stress acting on the crack and a decreasing function of the coefficient of friction. Therefore, the crack displacements that result will also be a similar function of these two variables. When the crack shown in Fig. 8 is unloaded, i.e. when the crack sliding displacements decrease, the direction of the frictional stress, rj; changes to resist the reverse sliding of the crack. Assume at the onset of unloading that the locally applied compressive stress, normal stress, shear stress, and effective shear stress on the crack surface have the values o'~ocat, or,; r ; and r,eft,' respectively, where the prime notation indicates a reference state for the crack. As unloading proceeds, the direction o f the friction stress reverses such that the applied shear stress due to sliding at the crack has to overcome both the frictional resistance and the shear stress before reverse sliding can begin. Therefore, reverse sliding will not occur until the following inequality is satisfied:

143

Modeling Cyclic Deformation... r

(16)

r e~ > r + lt cr,

where

, = O'ioca , i (sin,Coos,e7Jeff

sin ,8)

(17)

After combining Equations 10, 11, 16, and 17, it is then found that the minimum reduction in applied stress necessary to initiate reverse sliding, Ao'r~v, is given by

AO're v >

2Cr~o,:,,,utan/3 1 + / t tan fl

(18)

It can be seen from Equation 18 that the reverse sliding of a crack is dependent on three factors: the maximum stress of the cycle, the angular orientation of the crack, and the coefficient of friction. Therefore, cracks at different angles will begin to reverse slide at different reversed stresses and the entire effect will be scaled by the stress at which unloading begins. Rearranging Equation 18 and solving for the angular range of reverse sliding cracks yields the following for local compressive unloading: O< fl < tan-' [(o-,'oca,- O-,oca,)/~t(o-,'o~o, + Cr,o~o,)]

(19)

Note that the angular range of reverse sliding cracks is zero upon initial unloading and gradually increases with the reverse stress until being equal to that during initial loading when the stress is fully reversed, i.e. when OTo~Z= 0. As was the case during initial loading, the average sliding displacement of a closed crack surface is proportional to the effective shear stress that is acting on the crack. During reverse sliding, however, the sign of the friction term in Equation 15 becomes positive because the frictional resistance on the crack surface changes direction. The effective shear stress during reverse sliding, i.e. when O~ocaZ< O'~ocal- A~ev, is then given by

-

(sin p c o s p

+ usm p)

(20)

It can be seen from Equation 20 that both a decreasing local stress and/or a decreasing coefficient of friction will lower the effective shear stress on the crack. When this occurs, the corresponding displacements on the crack surface will also decrease and constitute reverse sliding. It can also be seen by comparing Equations 15 and 20, that the effective shear stress changes more rapidly with respect to the local stress during reverse sliding and that the effective shear stress at the beginning and end of the cycle are identical. This means that reverse sliding, once initiated, will proceed at a faster rate than initial forward sliding and will occur in such a way so that the crack sliding displacements are identical at the beginning and end of a compressive stress cycle. Figure 9 illustrates the effect of a single idealized sliding crack on the local deformation behavior for a compressive stress cycle that begins and ends at zero local stress. During initial compressive loading, deformation occurs with a reduced modulus due to forward sliding of the crack. Then, when the load is decreased, reverse sliding does not occur until

144

D. SOCIE, E. REJDA

the reversed stress, A~ev, is reached. Before reversed sliding initiates, the local deformation behavior is the same as that for an uncracked material. Once reverse sliding begins the local modulus decreases significantly, attaining a value even lower than that during initial loading. As just mentioned, the considerable difference in the forward and reverse sliding modulus comes from the fact that forward sliding occurs against an increasing frictional stress while reverse sliding occurs against a decreasing frictional stress. This happens in such a way that for a complete local stress cycle, idealized crack sliding generates hysteresis in the local deformation response but not an irreversible strain. It can also be seen that the state of the crack, i.e. the local stress and strain, is equivalent at the beginning and end of the cycle. Since the state of the crack does not change, further cycling between the same two local stress levels will produce a repeating hysteresis loop. With the behavior of single crack established, the deformation behavior of a body with many sliding cracks can be found by integrating the effect of cracks over various orientations. During initial compressive loading, the effective modulus of a body with randomly oriented forward sliding cracks, Efo~,~rd, is given by the following relation [9]:

1

=~

E forward where

-Cforward

L 1+

Eo

f forward(/-l, flnm

4~f~176

(21)

3V

is the average length of a forward sliding crack, the ratio Nfo~w~rd/V is the

number o f forward sliding cracks per unit volume, and

f~o~o,~(z, pm~) = ~[30sm p ~ - 5 sm 3 p ~ -3sin 5 p ~ + 30/ZCOSflmax + 5/tCOS3fl~x -- 3/ZCOS5flr~x -- 32/Z]

(22)

Upon evaluation of Equations 13, 21, and 22, it is found that the initial forward sliding modulus is an increasing function of the coefficient of friction. Therefore, when the coefficient of friction increases or decreases during loading, the initial forward sliding modulus will do so as well. A similar formulation describes the effective modulus of a body with randomly oriented reverse sliding cracks and is given by [9]:

1

E ....... where

_ _

1 Eo

E

1.at-

4zN

_3

c

..............

3V

fre ..... (]ll'i~max

(23)

-Creverse is the average length of a reverse sliding crack, the ratio Nreverse/V is the

number o f reverse sliding cracks per unit volume, and

!

L ...... (/1, flmax)= R---~[30sin/~max -- 5Sin 3/~max -- 3sin 5/~max - 30/z COSflmax -- 5/Z COS3flm,x + 3/Z COS5flmax + 32p]

(24)

145

Modeling Cyclic Deformation...

Upon evaluation of Equations 19, 23, and 24, it is found that since all reverse crack sliding activity is impeded at the onset of unloading, the modulus is equal to the intrinsic modulus of the material. Then, as unloading continues, the value of the reversed sliding modulus decreases as more and more cracks start reverse sliding. It is also seen that the reversed sliding modulus is a function of the coefficient of friction. A decrease in the coefficient of friction will decrease the reverse sliding modulus and it will be easier for reverse sliding to proceed. To incorporate the physics of sliding cracks into the model for the coating material, a few assumptions need to be made. It is first assumed that the cracks that undergo forward sliding are the same ones that undergo reverse sliding and that crack extension does not occur during the sliding process. Therefore, C--forward ~ C---r....... ~,

constant

(25)

Next, it will be assumed that the number of reverse sliding cracks is only a fraction of the forward sliding cracks such that the nature of sliding is not truly reversible. Since microcrack surfaces could become locked due to asperities or the presence of debris, their return to their initial state will be impeded upon unloading. These same cracks are then assumed to remain "locked" in place until the local stress exceeds the previously established stress at the onset of unloading. This is the memory effect shown in Fig. 5. Once this occurs, they are then allowed to once again forward slide as they did during initial loading. For simplicity, the current model assumes that the ratio of locked to initially forward sliding cracks is constant whenever the stress is lower than any previous maximum stress. The introduction of a sliding irreversibility factor, 2', is made to account for this effect and is defined as 2, =

N forward -- Nrevers e

N jo~wara

Ntockea

=~ N forward

(26)

where Ntockedis the number of cracks that are locked during any subcycle of a larger loading sequence. The parameter 2, will have a value between zero and one, depending on the amount of irreversibility that occurs from sliding cracks. It will also have an identical value during the unloading and reloading portions of a subcycle since it is assumed that locked cracks can not become free until the previously established reference stress is exceeded. The sliding irreversibility factor, 2', allows the material model to account for permanent strain during cycling since the effective number of sliding cracks is reduced during unloading. It also provides memory in the material model by vanishing after the reference stress is exceeded. The final assumption made regarding sliding crack behavior is that when the coating material unloads into tension after compressive loading, the reverse sliding cracks open. This occurs because the sliding crack surfaces, which are closed during periods of local compression, can not support a tensile normal stress. Therefore, when the coating material goes into tension, reversed sliding cracks begin to behave as open cracks and Equation 24 is replaced by

146

D. SOCIE, E. REJDA

L ......

(~max) = sin3 flmax

(27)

where flm~ maintains its value that it had at zero stress since it is assumed that no additional sliding activity occurs. Now that the assumptions regarding sliding cracks are established, the crack configurational parameters in Equations 21 and 23 can be lumped together in a similar manner as was done for the open crack case such that

--3

(28a)

4teN forwardc forward

gforward -

3V

and

--3

(28b)

Vr ...... - 4rcN ....... C ....... 3V

where Vfo,~rd and Vr. . . . . provide a measure of the strain energy interaction volume of forward and reverse sliding cracks, respectively. Combining Equations 25, 26, and 28 gives Vrev . . . .

=

Vyorwora(1 - &)

(29)

Then, by combining Equations 23, 28, and 29, the relations that describe the modulus of a body with sliding microcracks are summarized as follows:

E forwora

l [l+VforwaraO-~)fforwaraCtt, Eo

l =l[l+VforwardO-'~)fr E ....... Eo

......

flmax)]

(,L/,flmax)]

(30a)

(30b)

where 2 is used in the forward sliding equation to distinguish between forward sliding that occurs during initial loading (2 = 0) and that occurring during a reloading segment up to a previous maximum stress (0 < 2 < 1). The effects of sliding micro cracks and the intrinsic elasticity can now be separated. Multiplying Equation 30 by an incremental stress, d ~ yields the total incremental strain in a body with forward sliding micro cracks as

dE,o,., =

d_____~ = [l+Vzo~w~r.O-~Z)f~o~w~r~(~.Pmax)Jd~ r E forward

and with reverse sliding microcracks as

Eo

(31a)

Modeling Cyclic Deformation... de,o,a' = a c t = E .........

[l+Vfo~w~ra(1-A)fr ...... Eo

147

(~,/~X)]d~

(31b)

It is next recognized that the total incremental strain is composed of elastic and sliding components such that

(32)

d~tota I = dCelasticity + dc~ sliding

By combining Equations 31 and 32, and the differential form of Equation 2, the incremental strain due to forward sliding microcracks, dg..dmg#,~rd, can then be given by

d~sliding, forward "-

and the incremental strain due to reverse sliding microcracks,

d~'sliding, reverse :

(33a)

d~r

Eo

do'sliding forward,

(1- A)Vyorwa~af~. . . . . . (lll'~max) do" Eo

by (33b)

which, through the appropriate integration, will yield the additional strain in the coating material due to forward sliding cracks.

Tensile Microcracldng The remaining deformation mechanism that needs to be discussed is microcracking of the coating material in tension. Tensile microcracking will reduce the modulus and result in cracking strains that are in addition to those previously discussed from intrinsic elasticity, open cracks, and sliding cracks. In this study, the additional cracking strains in tension were approximated by subtracting the strains due to elasticity, open cracks, and sliding cracks from the total strain measured during a monotonic tensile test such that O~craclang -- O~total m O~elasticity ~ Oeopen ~ O~sliding

(34)

from which an empirical relation could be obtained. Further details on this procedure are given in the following section.

Modeling- Parameter Determination The parameter describing the effect of open cracks, Vopen, is determined first. To do this, experimental data is needed that isolates the deformation behavior due to open cracks from that due to sliding cracks and tensile microcracking. Such data is obtained by making as a function of stress from tests measurements of the initial unloading modulus, E~ such as those shown in Fig. 5.

D. SOCIE, E. REJDA

148

V

open

=

E -o -1 unloading

(35)

E~

The unloading modulus was found to be a linear function of the applied stress.

Vopen

=

(36)

mg +b

Values for Vom, range from 5 to 20. There are three parameters - ~, Vfo,.wa,.d,and 2 - that need to be determined in order to adequately describe the effect of sliding microcracks on the deformation behavior of the coating material. Since the material starts out with a dense array of microcracks ( Fig. 2 ), it is assumed that additional microcracking in compression does not significantly affect the deformation behavior until the stresses are near failure. For lower stresses, the only contributions to deformation during the compressive loading of the coating material are those due to intrinsic elasticity, open microcracks, and microcracks that are sliding. The starting point for determining the microcrack sliding parameters is with the initial compressive loading behavior. Then, with 2 equal to zero in Equation 33a, the strain due to sliding microcracks during initial compressive loading is a function of only two unknowns: the strain energy interaction volume fraction, Vfo,.~rd, and the coefficient of friction, p. Since both of these microcrack sliding parameters are unknown, an initial estimation will be made regarding the coefficient of friction. It was seen previously in Fig. 7 that the crack surfaces in the coating material contained an appreciable amount of glassy phase. Therefore, a glass-on-glass coefficient of sliding friction of p - 0.4 should serve as a reasonable first approximation [ 10]. With this initial estimate, the only remaining unknown in Equation 33a is now Vfo,.wa,.d. 0.003

0.006 A

0.005

A

.c_ 0.004

e-

[]

0.002 O00C

"o

03 0.003 ._

800C A ~

o

9

co t~

0.001

0.002 0.001 0

e-

_

0

i

_

'

20

40 60 CompressiveStress (MPa)

Fig. 10 Sliding Strain

0

0.001

0.002 0.003 0.004 0.005 0.006 Ma~mum Sliding Strain

Fig. 11 Irreversible sliding strain

In order to determine Vforwc,,.d,the sliding strain during initial compressive loading was calculated by subtracting the intrinsic elastic strain and the strain due to open cracks from the measured total strain. Results from six tests are shown in Figure 10. In the figure, each symbol represents the results from an individual test. It can be seen that the strain due to sliding microcracks is, on average, larger for the tests conducted at 800~ than those at room temperature. It can also be seen that, to a first-order approximation, the sliding strains at each temperature are approximately linear with the applied compressive stress. By

Modeling Cyclic Deformation... integrating Equation 33a, it can be seen that this linearity implies that value during initial compressive loading and is given by

,( /

149

Vfo~w~rdhas a constant

(37)

Using a linear fit to the data in Fig. 10 and applying the result to Equation 37, values of Vfo~wardwere found to be about 34 at room temperature and about 48 at 800~ These high values indicate that the effect of sliding cracks on the deformation of the coating material is indeed quite significant. By comparing the values of Vfor~rd with those of Vopenpreviously determined, it is seen that both open and sliding cracks have effects that are on the same order of magnitude. This means that both mechanisms have to be considered to accurately model the deformation behavior of the coating material. The next microcrack sliding parameter that can be determined is the sliding irreversibility factor, 2. During compressive unloading of the coating material, a portion of cracks that underwent forward sliding during initial compressive loading will remain locked in place and will result in an irreversible strain. Since the strain due to intrinsic elasticity and open cracks is dependent on only the current stress and temperature and since micro cracking only occurs in tension, the irreversible strain that occurs at zero stress is entirely due to the sliding crack behavior. Integrating Equation 33 for a compressive cycle that begins and ends at zero stress, 2 is found to be conveniently equal to

,~- C'irr

(38)

OC'max

where oC~r~is the irreversible strain at zero stress and C.~x is the maximum compressive strain occurring during the cycle. Figure 11 shows the relationship between irreversible and maximum strains for the same six immediate unloading experiments used to determine Vope,,and ~orward.Again, each symbol represents a separate specimen. It can be readily seen that the amount of irreversible strain is greater at 800~ than at room temperature. It is also seen that the irreversible strain at both temperatures is nearly proportional to the maximum sliding strain, indicating that ~, is approximately constant. Using a linear fit to the data, ~ values were found to be about 0.34 at room temperature and about 0.55 at 800~ The physical significance of these values is that, on average, 34% of the initial forward sliding activity is halted in the coating material during unloading at room temperature and 55% of the initial forward sliding activity is halted upon unloading at 800~ The increase in sliding irreversibility at high temperature may suggest that an increase in debris at sliding microcrack surfaces tends to cause more microcracks to become locked in place during unloading. Now that/z, Vforward, and 2 have been determined for the relatively fast strain rate conditions of the unloading experiments, the model needs to be extended to account for rate effects. In the present model, rate effects are included by assuming that the average coefficient of friction on sliding microcrack surfaces is a function of the sliding strain rate and the applied compressive stress level. To determine the functional form of the coefficient of friction,

D. SOCIE, E. REJDA

150

results from stress hold experiments were employed. Since the only active deformation mechanism that is contributing to increasing strains during a stress hold is that due to sliding cracks, these experiments provide a convenient way to isolate this mechanism from the others. In making calculations for the coefficient of friction, it was assumed that the previously attained Vfo,.~a,.dvalues were independent of the sliding strain rate and the applied stress level. In addition, in order to maintain sensible values for the coefficient of friction, an upper and lower bound was imposed such that 0 < / t < 0.4. Then, integration of Equation 33a could be used to determine the evolution of the coefficient of friction during the entire loading and holding segments of the stress hold experiments. From these calculations, the coefficient of friction was found to have the following form:

/t =/to + a ha

(39)

O"

~sliding is the sliding strain rate, a is the applied stress in MPa, and a and/to are

where

temperature-dependent material constants. Values of a and lto were found to be 0.0296 and 0.7862, respectively, at room temperature and 0.0284 and 0.7617 at 800~ The functional form for the coefficient of friction in Equation 39 is very similar to that found in studies on frictional sliding that occurs at very slow velocities [11-13]. Their results show that the coefficient of friction is an increasing function of the sliding speed when the speed is low. In between the low and high speeds is a region in which the coefficient of friction is relatively independent of the sliding speed. It is believed that a similar phenomenon may be dictating the coefficient of friction in the coating material. Since there are a very large number of sliding microcracks, the actual sliding velocities of individual cracks are probably quite low. Therefore, the coefficient of friction would be confined to be at most an independent function of the sliding strain rate at high strain rates or an increasing one at low strain rates.

12

0.001

20C Model

800C Model ~" ft.

8

v

6

OC Data

__ 800C

g 0.0006

20C

,3 0.ooo4

4

~- 0.0002

0

0 0

0.0005

0.001 Strain

0.0015

0.002

0

2

4

6

i

|

8

10

TenNle Stress Above Threshold (MPa)

Fig. 12 Tensile cracking strain The final deformation mechanism remaining is tensile microcracking. In order to obtain the additional strain due to this mechanism, the tensile monotonic data was compared to the

Modeling CyclicDeformation...

151

model for opening and sliding cracks. This comparison is shown in Figure 12. It is seen that the strain during tensile loading gradually deviates from the model as the tensile stress increases. This deviation is assumed to be the direct result of the additional strain due to tensile microcracking. It is also seen that there is a threshold stress o f about 2 to 3 MPa before the deviation between the model and experimental data is observed. This suggests that a minimum tensile stress is necessary before an appreciable amount of new microcracking can occur. Figure 12 also shows the relation between the additional strain due to tensile microcracking and the tensile stress above threshold. A reasonable fit to the data was found to take the following form: (40)

....,,., -_ c , ( , , _ , , o ) + C , ( , , _ , , o )

where cr is the tensile stress in MPa, Cro is the threshold, and the brackets indicate that additional microcracking is zero for any stress that is below the threshold. From the data, values for cl were found to be about 1.04 x 10 -5 and 2.51 x 10 -5 at room temperature and 800~ respectively, while values of c2 were found to be about 1.34 x 10-5 and 1.72 x 10-5 at the same respective temperatures. Table 1 Summary of model parameters and means of determination

Deformation Mechanism Intrinsic Elasticity

Experimental Measurement

Model Parameters

Reference [ 14]

Eo

Microcrack Opening/Closure

Initial Reversed Loading Modulus

m, b-->. Vo~e,,

Microcrack Sliding

Compressive Monotonic Curve

V:orw~rd

Irreversible Strain at Zero Stress

Tensile Microcracking

Creep Strain During Stress Hold

a, kto---~l.t

Tensile Monotonic Curve

CI, C2

Now that the general relation between the additional strain due to tensile microcracking and the tensile stress is established, an assumption will be made in regard to the threshold stress at which microcracking initiates upon unloading into tension after compressive loading. During compressive cycling, a certain amount of residual tension within the coating material will develop due to the irreversible sliding processes that occur. A qualitative argument can therefore be made that tensile microcracking, with the aid of residual tensile stresses, will initiate sooner during compressive unloading than it would if the coating material were loaded directly into tension. For simplicity, the current model assumes that the threshold stress is reduced to 0 MPa for any loading cycle that initiates in compression and then unloads into tension.

152

D. SOCIE, E. REJDA

VALIDATION A summary of the model parameters obtained from the experimental results is shown in Table 1. Using these parameters the model was validated by comparing the results of the model to two sets of experimental results: the immediate unloading and strain hold experiments. Assembly of the model is schematically shown in Fig. 13.

Intrinsic

Elasticity Opening

& Closure

Sliding

A•elasti c =

1

~- Ac (2)

Vopen

AI;~ =Eoo A~ (9) AE;sliding -- (] -- ~)Vsliding f(la, I~max) A~

Eo

Tensile

Cracking

A~;cracking=(C1

(33)

+C2~)Acr (40)

Fig. 13 Assembly of deformation model Stresses are incrementally computed for each time step. The model has been used in both stress and strain control. An iterative solution is needed because the coefficient of friction is a function of the sliding strain rate. Figure 14 shows a comparison between the model and experimental results for one loading case. For clarity, the model and experimental results are shown on adjacent plots. It can be seen that the model captures the qualitative and quantitative aspects of the deformation quite well. The model accounts for the nearly linear initial loading behavior, exhibits an appropriate amount of hysteresis and memory during unloading and reloading, and nearly matches the irreversible strain at zero stress and the resulting tensile stress at zero strain.

0.006

9

Strain

Experimental Result

20 0.002

0.006

Strain . 0.0~~-~

0.094

]20 . 0007

-20 .-.

-20

-40

-4o

-60

Prediction

-80

-60

"~" oo

-80

Fig. 14 Model validation The next step of the model validation involves deformation cycling with a strain hold at the maximum compressive strain that is followed by unloading to zero strain. Figurel 5 shows a comparison of the model and experimental results for experiments with a compressive

Modeling CyclicDeformation...

153

strain hold of about --0.4% at room temperature and 800~ It can be seen that the model exhibits an appropriate amount of stress relaxation during the strain hold and predicts the unloading behavior back to zero strain. Strain

-0.004

-0.003

Strain

-0.002

-0.001

0

-?.004

-20 g

10

-0.

0

-iii

. , , " .....

-30

-10 "~" -20 ~: -30 -40

-40 -50

--- Model Prediction

- - - Model Prediction

-60

room temperature

800 C

-50 -60

Fig. 15 Strain hold results As an exploratory study, the deformation model was used to predict the tensile stresses that result from a wide variety of compressive strain cycles that begin and end at zero strain. The principle aim of this exercise was to determine the effects that various loading conditions will have on the durability of the coating material and to generate failure maps which predict tensile failures of the coating material. Failure was predictued to occur whenever the tensile stress reached a magnitude of 7 MPa during unloading. Figure 16 shows the results of eight separate e x p e r i m e n t s - four isothermal and four thermomechanical- with a strain hold at the maximum compressive strain. Failures are predicted for strains and temperatuires to the right side of the solid line for isothermal cycling. Similarly, failures are predicted to the right side of the dashed line for thermomechanical tests. It can be seen that while there is only a limited amount of data available, the failures do occur reasonably close to the predicted failure surface. 800

|

*

t ', ~

o~7 0 0 ~600 500

" ~

[]

"

\ 9

~ P r e d i c t e d Failures - Iso . . . . Predicted Failures TMC 9Survivals - Iso 9 Survivals-TMC Failures - TMC

E 400 E 300 E 200 x 100 i ~

i

i

0.002 0.004 0.006 0.008 M a x i m u m C o m p r e s s i v e Strain

i

0.01

Fig. 16 Modeling Failure predictions SUMMARY

Deformation of plasma sprayed 8% Y 2 0 3 - Z r O 2 coatings have been investigated. Inelastic deformation processes produce tensile stresses during typical thermal-mechanical loading

154

D. SOCIE, E. REJDA

cycles experienced by a diesel engine component. These tensile stresses lead to early failures since the material has a very low tensile strength and tensile fatigue limit. A cyclic deformation model based on intrinsic elasticity, opening / closing of microcracks, microcrack sliding and tensile microcracking was developed. The model was used to determine combinations of strain, strain rate and temperature that are likely to result in coating fractures during thermomechanical cyclic loading.

REFERENCES 1. Miller, R.A. "Current Status of Thermal Barrier Coatings - An Overview" Surface Coating Technology, Vol. 30, 1987, pp. 1-11 2. Larson, H.J. "Thick Thermal Barrier Coatings" Proc. Twenty-Fourth Automotive Technology Development Contractors Coordination Meeting, Society of Automotive Engineers, SAE SP- 179, 1986, pp. 73-82 3. Levy, A.V. and MacAdam, S. "Durability of Ceramic Coatings in 14000 Hours Service in a Marine Diesel Engine" ASME paper 88-ICE-19, 1988 4. Miller, R.A. and Lowell, C.E. "Failure Mechanisms of Thermal Barrier Coatings Exposed to Elevated Temperatures" Thin Solid Films, Vo195, 1982, pp. 265-273 5. Fliiaggi, M.J. and Pillar, R.M. "Mechanical Testing of Plasma-Sprayed Ceramic Coatings on Metal Substrates: Interface Fracture Toughness and Interface Bond Strength Substrates Exposed to Elevated Temperatures" J. Materials Science, Vol 28, 1991, pp.5383-5395 6. Wesling, K.F. and Socie, D.F. "Fatigue of Thick Thermal Barrier Coatings" J. American Ceramics Society, Vol. 77, 1994, pp. 1863-1868 7. J.B. Walsh, "The Effect of Cracks on the Uniaxial Elastic Compression of Rocks," Journal of Geophysical Research, Vol. 70, No. 2, pp. 399-411, 1965. 8. B. Budiansky and R.J. O'Connell, "Elastic Moduli of a Cracked Solid," International Journal of Solids and Structures, Vol. 12, pp. 81-97, 1976 9. B.R. Lawn and D.B. Marshall, "Nonlinear Stress-Strain Curves for Solids Containing Closed Cracks With Friction," Journal of the Mechanics and Physics of Solids, Vol. 46, No. 1, pp. 85-113, 1998 10. Marks' Standard Handbook for Mechanical Engineers, 10th Ed., Edited by E. Avalone and T. Baumeister, McGraw-Hill, New York, 1996. 11. E. Rabinowicz, Friction and Wear of Materials. John Wiley & Sons, New York, 1965. 12. P. Solberg and J.D. Byerlee, "A Note on the Rate Sensitivity of Frictional Sliding of Westerly Granite," Journal of Geophysical Research, Vol. 89, No. B6, pp. 4203-4205, 1984. 13. T. Baumberger and L. Gauthier, "Creeplike Relaxation at the Interface between Rough Solids under Shear," Journal De Physique I, Vol. 6, pp. 1021-1030, 1996. 14. Engineering Property Data on Selected Ceramics Volume III, Single Oxides, Battelle Memorial Institute, Metals and Ceramics Information Center, 1976.

155

APPLICATION OF FRACTURE MECHANICS ON JAPANESE AUTOMOTIVE INDUSTRY

TATSUHIKO

YOSHIMURA

Depertment of Mechanical Science & Engineering,Kyushu University, 6-10-1 Hakozaki, higasi-ku,Fukuoka,Japan ABSTRACT The purpose of this paper is to survey the history of strength evaluation in the field of Japanese Automotive Industry and to discuss the present condition and the subjects of the application of fracture mechanics. KEYWORDS Fracture mechanics,automotive industry,history,reliabirity. THE DAWN & THE FIRST HALF OF THE GROWTH PEROD (1935-1965) Fig.1 shows the transition of automobile production in Japan and the US. Those technological progress can be represented in logistic curve like Fig2[1]. Then,the progress of Japanese automotive industry will be explain according to logistic curve as follows. The first automobile was produced in Japan at 1910. As a matter of fact, it began by copying the automobile of advanced Europe and US msnufacturers. And, the start of automotive industry was about 1935. At this period, Japanese automotive founder thought that they wanted to produce the automobile by power and wisdom of Japanese. In regard to the strength of the vehicle, the third arm of the first Toyota produced truck broke after only 100 km drive. We could learn the shape of the parts, but couldn't understand the background technology. Such an experience stimulated the strong desire to obtain the strength technology behind the parts by Japanese engineers themselves and it supported the progress of Japanese automotive industry. The most important subject of designers in this period is the strength and the durability of the vehicle. They studied hard and found out the parameters that showed the strength and the durability of materials and the results prompted the standardization of materials. The manufacturers tried to provide the bases of productive technology that could supply

156

T. YOSHIMURA

materials that met the standard of materials. For example, Aoyama studied minutely the relation between the hardness and the strength of steel and succeeded to take the hardness as the parameter for the standard of materials and the design [2]. Still more, he studied the relation between many kinds of heat treatment and the strength of materials. As a result, the scope of selection of materials and the heat treatment for automobile is extended very widely. THE SECOND HALF OF GROWTH PERIOD (1965-1985) According to the study of materials strength in the first half of growth period, the dispersion of the strength on the stress-strength model declined epochally and the most important subject of reliability moved to grasping stress. The improvement of load measurement technique using Strain gages and the spread of closed-loop type electro-hydraulic testing machine supported it. A lots of researchers focused on whether Miner's rule held good or not under actual loads. In 1967, Endo [3] represented the rain flow method that had become the world standard of frequency counting method of random loads. In addition, author et al. [4] proposed the logic of effective random peak method that conducts fatigue test using the wave form that small waves that does not accumulate fatigue damage are excluded. Regarding to the accelerated testing, author proposed the new method that the fatigue limit of parts could be detected in short time by applying acoustic emission[5]. Still more, Japanese automobiles were sold to the customers world wide, the measurement technique of service loads has progressed and kinds of analyzing method of load data and trouble data have been proposed[6]. Thus, the second half of growth period, the technique that predicts the strength and the durability of vehicles based on the stress-strength model and the design technique had been established. But two problems have remained. The first is that the results of average strength parts test could not predict the least strength of the mass produced parts for such as cast iron parts which strength declines extremely if they have casting defects. The second is that the accuracy of the estimation of strength of spot welds that are applied enormously for shell body which is important structural part of vehicle based on surface strain of spot weld is very bad. It is fracture mechanics that is very useful to solve the above mentioned problems. Fracture mechanics was introduced to Japan in the latter half of 1960's and captured a lots of researchers. But the dimension of vehicle parts is smaller than that of airplane or

Application of Fracture Mechanics...

157

big pressure vessel and the inspection during service is difficult to expect, so, such as crack permitted design has not been established. But it is very useful for the above mentioned two problems. The first, for the evaluation of casting defects, there are studies of Murakami et al. and author et al. and for the wide examples of practice and the easiness to handle, Murakami's the f-area method [7] has been applied widely. The second, the subject of spot welds was studied at the fatigue and durability committee of Japanese Society of Automotive Engineering as the central force from around 198618], and the study continues now. Auther et al [9]examined spot welded test pieces and L/T pillar joints of actual passenger car, Fig~3,4. Then, fatigue strength of spot welded joints represented using K0max in one line the case that KIlI is neglible small, Fig.5, but the case that K m is not negligible we must use the criterion which includes KllI, for example Kgmax,Fig.6. SATULATED PELIOD (1985-Presnt) After 1985, the production of automobiles has saturated in Japan same as the developed countries. Since then the new era that the technique to control not to come off too wide is very important has begun. Before this era, Japanese industry has adopted the quality control method positively and added the Japanese special technique that such as customer first, team, concurrent and continuos improvement are typical of. Thus it has prepared for the saturation. The Japanese customer's severity for quality and the Japanese technology that is good at looking after every nook and comer are very powerful in this saturation period. The above mentioned three kinds of technology originate in this Japanese character of "looking after every nook and comer". Since 1970, in Japan, the standardization of development has progressed based on the idea of the qualiW control. At that time, in the field of reliability and strength, evaluating components level simultaneously, not full vehicle level, the reliability has achieved applying the stress-strength model, and at the end, being arranged as a vehicle, This method is far more useful to build in the high quality in short term than the repetition of development using the whole vehicles from the beginning. But recently the quality of the US and European vehicles is improved remarkably. The jump to next logistic curve, that is, the embodiment of good quality that has not been achieved yet is now expected. For the future automotive industry, it's a big subject for management and technology that how the development term is shorten and how the high quality production which customers require is provided. So in the field of reliability and strength, this subject

15 8

T. YOSHIMURA

could not be avoided. The reduction of development term generally leads to the simplistic discussion that the experiment should be abolished and the only calculation should be applied to evaluation. But even though the development term is short, the challenge for the new design and the evaluation of production by the experiment that meets the customer's needs cannot be missed. The evaluation technique that combines hybridly the each special W field of the CAE and the experiment will be necessary. Murakami, author et al. show one example for the evaluation method of spot weld[9]. This method is that measuring the stress distribution of structure by infrared rays stress measurement equipment, applying these results as boundary condition and the CAE analysis of spot weld, we can get creatively the K value of spot welds of body structure. Still more, for the reduction of developing term, the important technique is the "technique for detecting problems". That is, it is not too much to say that at the beginning of development how to detect problems and to deal with them determine the quality of production. Regarding to this, author et al. propose the GD3(G-D-Cube) method[10]. The GD 3 stands for that Good Design, Good Discussion and Good Design Review are combined. From the standpoint that the principle of reliability is "not to change", "not to change good design and robust design" is regarded as the basis of design. On the contrary, for the changed points, engineers try to detect problems through Good Discussion based on DRBFM(Design Review Based on Failure Mode) and examining closely the results of the CAE and the experiments, they also try to detect problems through Good Design Review. I believe that applying these methods, we can break through creatively the wall of saturated reliability technology and we can find the image of the new reliability technology. 9The method, not to estimate precisely if the local part of a structure breaks or not, but to evaluate the risk of the effective whole structure and robustness. 9The method to detect problems utilizing the creativity of human being 9The more hybrid evaluation technology utilizing the good points of the experiments (detection of problems) and the CAE(evaluation) and the reconstruction of development system based on it I'm convinced that the development of these technologies leads to all the more reduction of development term of vehicles and the realization of the high quality.

Application of Fracture Mechanics...

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

Yoshimura, T. (1996) TOYOTA Technical Review 47,1,137 Aoyama, S. (1957) TOYOTA Technical Review 9,5,31 Matsuishi, M., Endo, T (1968) paper presented to Japan Soc. Mech. Engrs. Yoshimura, T et. al, (1975) Proc.Annal Reliability and Maintenability Sympsium 263 Yoshimura, T et. al. (1987) Journal of Acoustic Emission 6,3,145 Yoshimura, T et. al. (1987) Journal of the.Society of Material Science Japan 36,408 Murakami, Y (1985) JSME Journal A 54-500,688 Yuuki, R (1987) Journal of Japan S.A.E.,41,1,132 Nagai, S, Yoshimura, T, Murakami, Y. (1998) Fatigue Design and Reliabirity ESIS Publication 23,91

159

160

T. YOSHIMURA Million vehicles 1000

v Japan

100 a

1

/ I ~ 1900

10

20

30

40

i 50

60

-

70

80

I 90

Year

Fig. 1 Trend in the Number of Automobiles Produced in Japan, USA, and Korea

Fig.2 Logistic Curve

Fig,3 T-joint Pillar Specimen

Application of Fracture Mechanics...

u~

:i

530

i:

i

220

-

~

9

9

-

"

"

~

~

~

Fig.4

o

Member 3

Member 1

L-joint Pillar Specimen

. . oType A L-JO,nt [ (} Type B 9. . ATypea

30 84 ~

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~

~ 40 84 03 E

161

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i,,.. 0

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Am

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104

105

106

Number of cycles to failure N

Test Results represented b y Komax

Fig.5

9Type A L-joint [ O Type B

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Test Results represented b y Kgmax

This Page Intentionally Left Blank

163

G I G A C Y C L E FATIGUE OF HIGH S T R E N G T H STEELS PREDICTION AND M E C H A N I S M S C. BATHIAS ITMA-CNAM, 2 Rue Conte, 75003, Paris, France

ABSTRACT It was recently shown that the concept of infinite fatigue life is not correct even in BCC metals. It means that fatigue fracture can appear in metals beyond 109 cycles. From a practical point of view, the conventional fatigue limit determined between 106and 10 7 cycles does not guarantee structural integrity. In cooperation with automotive industry we study high strength steels, spring steels and carbon steels in the gigacycle regime to get the exact shape of the SN curve for very long fatigue life. In this paper, the results are discussed, the initiation mechanisms are determined, a predictive model based on defect is proposed. A generalization of gigacycle fatigue behavior is given. KEYWORDS Subsurface crack initiation, gigacycle fatigue, high strength steels, S-N curve, inclusion, modeling; prediction

INTRODUCTION Safe-life design based on the infinite-life criterion was initially developed through the 1800s and early 1900s, one of which is the stress-life or S-N approach related to the asymptotic behavior of steels. A lot of materials display a fatigue limit or "endurance" limit at a high number of cycles (typical > 106). Most other materials do not exhibit this response, instead displaying a continuously decreasing stress-life response, even at a great number of cycles (10 6 to 109), which is more correctly described by a fatigue strength at a given number of cycles. Time and cost constraints usually rule out the use of conventional fatigue tests of more than 107 cycles to check the structural materials. In contrast to conventional fatigue tests, which require a long duration of time due to the high numbers of load cycles at low frequencies (typical < 50 Hz), the proposed piezoelectric fatigue technique operates at much high frequency (about 20 KHz). Thus the required time for measurements in the high cycles fatigue range is considerably reduced. In the area of application and design, high-cycle fatigue (HCF) failures are very common. Unfortunately, they are not well understood nor there is a methodology available. The current standardized design methodologies are unable to accurately predict

164

C. BATHIAS

HCF damage. The goal of the research is to develop experimental and analytical techniques to understand the onset of HCF behavior of structural materials. In this work, high strength steels 42CrMo4 steels and spring steels with tensile strengths from 1000 MPa to 1800 MPa were tested between 105 and 109 cycles through ultrasonic fatigue test at 20KHz. The S-N curves for the steels were obtained, the specimens continued to fail over 107, even 108 stress cycles. The mechanisms of fatigue cracks have been determined thanks to microfractographic analyses on the scanning electron microscope. The fatigue strength is also estimated by the Murakami model, which has been applied to many fatigue problem of high strength steels including nonmetallic inclusions and small defects, but the model does not fit the gigacyclic fatigue well. A modified empirical equation was proposed to predict high cycle fatigue life of high strength steels. Investigations concerning long fatigue lives (>10 7 cycles) are relatively rare. The reason is obvious, the testing time and costs are too much to perform the fatigue tests of more than 108 cycles using a conventional testing machine. A possibility of accelerated tests of the structural materials (metals, alloys, composites) is considered by using high frequency cyclic loading. The experimental results shown that fatigue fracture can occur beyond 107 cycles in the steels, and the origin of this fracture is not at the surface but some distance away. In the high and low cycle range regimes, the initial site of fatigue crack are different. In the case of HCF (> 107 cycles), the initiation sites were founded at nonmetallic inclusions located in the interior of the specimen, on the other hand, the initiation sites were found at surface. A new Murakami model being evaluated the effects of nonmetallic inclusions and small defects as well as the Vickers hardness for a specified number of cycles was proposed in this study, which is able to predict the fatigue strength of high strength steels more accurately. It is concluded that the concept of infinite fatigue life in steels is not correct. SUBSURFACE- SURFACE CRACK INITIATION In general, fatigue crack initiation is understood to occur on the specimen surface. Most of the tested materials, however, clearly exhibited two kinds of fatigue crack initiation. One was at the specimen surface, and the other was in the specimen interior [1 ]. There is more and more data which shows fatigue cracks initiate from the specimen subsurface when the cyclic lives are higher (or at a lower stress level) and the initiation sites are usually associated with defects such as inclusions, pits, pores, etc [1-11]. While subsurface crack initiation behavior has been clearly detected in many materials under any testing conditions, the mechanism has not been full understood.

Gigacycle Fatigue of High Strength Steels...

165

Omezawa [1-2] and his group have investigated subsurface crack initiation behavior of high strength austenitic steels and titanium alloys at low temperature. Kanazawa [3] obtained fatigue internal fracture data of low alloy steel tested at 300-400~ up to 109 cycles. A surface-subsurface transition in crack initiation location has described at 10 7 cycles for a SG cast iron and four high strength steels [6-7]. Subsurface crack initiation was reported by Starker [9] at all stress amplitudes below a threshold value in a carbon steel under bending fatigue. Corrosion fatigue tests and fatigue tests in vacuum were carried out by Atrens et als. [10], subsurface fatigue initiation was observed for longer cyclic lives (>10 7 cycles) and lower stresses. In contrast, for short cyclic lives, fatigue cracks initiated at the surface. The internal crack initiation in HCF has been also detected by Danninger [11] for Mo alloyed sinrered steel at ultrasonic frequency (20KHz), by Murakami [4] for Cr-Mo steel under tension-compression fatigue at 30-100Hz, by Nishijima [5] for a 2Si spring steel under rotary bending at 50 Hz. While crack propagation is important in structures containing crack(s) and in LCF, the crack initiation controls fatigue life in HCF. In this investigation, the subsurface crack initiation behavior due to HCF has been studied for seven high strength low alloy steels. MATERIALS AND EXPERIMENTAL RESULTS

Materials and experimental method The materials used in this study are seven ultra-high strength steels. The chemical compositions (wt%) and the mechanical properties of the materials are given in Table 1 and 2, respectively. Table 1. Chemical composition (wt %) of the five materials discussed in this study. Materials AISI52100 Cr-Si(54SC6) Cr-Si(55SC7) Cr-V 42CrMo4

C

Mn

0.998 0.535 0.545 0.510 0.428

0.341 0.629 0.700 0.850 0.827

P

S

Si

A1

Ni

Cr

Mo

0.015 0.011 0.254 0.103 1.445 0.028 0.006 0.016 1.400 0.056 0.635 0.035 0.040 1.400 0.700 0.035 0.040 0.250 0.950 >0.15 0.012 0.024 0.254 0.023 0.173 1.026 0.024

Table 2. Mechanical properties of the five materials discussed in this study. Materials AISI52100 Cr-Si(54SC6) Cr-Si(55SC7) Cr-Si(55SC7)-TT2 Cr-V 42CrMo4UC 42CrMo4RC

E (GPa) 213 210 210 210 210 216 205

V

9 (Kg/m3) 7845 7850 7850 7850 7850 7870 7870

Rm (MPa) 2500 1692 1800 1800 1800 1530 1485

HV*30 630 510 500 590 435 465 450

166

c. BATHIAS

Fatigue testing was carried out in a piezoelectric resonance system operating at 20 KHz with zero mean stress (R =- 1) [6]. S-N curves were taken up to 101~cycles, and the fatigue crack initiation sites were characterized by using SEM. S-N curves

1000

m. 900

0 54SC6 1-" [] 55SC7 & 55SC7TT2

Transition

-.:,

X c.fJ

"

800

700 1 .E+04

................................

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................................

1 .E+07

1 .E+08

1 .E+09

1 .E+10

1 .E+I 1

Number of cycles to failure Surface fatigue fracture

Subsurface fatigue fracture

Figure 1" S-N fatigue curve for three Cr-Si high strength spring steels 850

[]

O 750

x=

700

Transition

o

800

O

[]

o O

42CrMo4RC

b

9 42CrMo4UC 650

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

Number of cycles to failure iv-

Surface fatigue fracture

Subsurface fatigue fracture

Figure 2: S-N fatigue curve for two 42CrMo4 high strength low alloy steels

Gigacycle Fatigue of High Strength Steels...

167

9 0 0

Transition

X

008~ 7 5 0

,~ .................

1.E+04

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.

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.

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,. . . . . . . . . . . . . . . . .

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,

...............

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~

1.E+09

o f c y c l e s to f a i l u r e

1.E+10

1.E+11

...............

Subsurface fatigue fracture

Figure 3: S-N fatigue curve for the Cr-V high strength spring steels Figs.l-3 represent the S-N data of six high strength steels obtained from piezoelectric resonance fatigue machine. All the materials continued to fail beyond 107 cycles. The S-N curve of the six steels consists of two zones: Period I, where a steep drop in applied stress occurs up to 106 cycles; Period II, where the curve is almost horizontal up to 108 or 109 cycles. Depending of the steel, the plateau between period I and period II is long or short. In the case of the three Cr-Si steels and the 42Cr-Mo4 RC steel, the S-N diagram display a second decrease between 10 7 and 109 cycles. It is clearly detected that S-N curves of these steels consist of two groups of failure data, one before 10 7 cycles corresponding surface fatigue fracture origin, and another after 10 7 cycles corresponding subsurface fatigue crack initiation. A surface-subsurface transition in crack initiation location is described for the high strength steels. It was revealed that the initiation site shifts from the surface to the subsurface at a definite lower stress range and the subsurface crack initiation was dominant in the long-life range.

Fatigue crack initiation sites A typical subsurface crack initiation in the 42CrMo4 low alloy steel is shown in Fig.4. The stages of crack initiation, stable crack propagation, unstable crack propagation, and final failure are well defined. All the subsurface crack initiation sites appeared flat, smooth features of facets. The fracture origin was identified by use of energy dispersive analysis. In the high-cycle regime (> 107 cycles), all the initiation sites were found at nonmetallic inclusions located in the interior of the specimen. The chemical composition of the inclusions was mostly sulphide. The inclusions range in size from 10 to 40 /1 m.

C. BA THIAS

168

MODELING OF INITIATION FROM INCLUSIONS Few models are able to predict the effect of non-metallic inclusions on fatigue strength. This may be because adequate reliable quantitative data on non-metallic are hard to obtain. Murakami and co-workers [10] have investigated the effects of defects, inclusions and inhomogeneities on fatigue strength of high strength steels and expressed the fatigue limit as functions of Vickers hardness HV (Kgf/mm 2) and the square foot of the projection area of an inclusion or small defect: ~/area (gm). The fatigue limit prediction equation proposed by Murakami is as follows:

Cyw

= C(HV +120) I ( 1 - R) 1 cc (~/area)l / 6 2

(1)

Where, C = 1.45 for a surface inclusion or defect, C = 1.56 for interior inclusion or defect c~ = 0.226 + HV x 10-4 The model does not specify the number of cycles for which the stress Cywis represented. According to experimental data, a modified empirical equation, based on Murakami model, was proposed to estimate gigacycle fatigue initiation from inclusion and small defects. This model is especially accurate for high strength steels.

Cyw= fl (HV +120) I(1- R)1 (x/area)l~ 6

Where, [3 = 3.09-0.12 log Nf 13= 2.79-0.108 log Nf

2

(2)

for interior inclusion or defect for surface inclusion or defect

Gigacycle Fatigue of High Strength Steels...

169

Figure 4: Gigacycle Fatigue Initiation on Inclusion. The size ~/area of the inclusions at the fracture origin is about 20 lam. Table 3 shows the comparison among the fatigue strength predicted by equation (2) and the experimental results in the gigacycle regime.This gigacycle prediction has been extent successfully to a nickel base alloy (N 18)

Table 3." comparison of predicted fatigue strength and experimental results. Specimen

HV Nf ~/area H (~m) O'exp C~w(2) Err.% (2) r

42CrMo

42CrM

42CrMo

42CrMo

42CrMo

SUP9

[61 465 345 450 445 465 465 5.75 e 8.76 e 7.12 e 4.92 e 2.59 ~ 4.5% +8 +5 +5 5 +8 +7 13 25 20 60.1 20 16 25 0 0 0 900 135 750 630 760 588 760 740 775 592 763 621 724 787 -4.7% +6.4 +3.3 -6.0% +0.4 +5.6 % % % %

" maximum

SUP10M [61

SUP10M [6]

N18 [61

550 2.0e+7

554 1.63e+6

14.1 0 862 862 0%

28.9 24O 883 902 +2.2%

445 500 1.45e 1.7e+ +7 8 53 25 350 650 550 780 588 762 +6.9 -2.3% %

stress applied to specimen (MPa)

(Yw(1), Cyw(2)" fatigue strength estimated by eq. (1), (2). (MPa) error %" (~w-(3"exp)/(5'exp

Cr-Si [7]

170

C. B A THIA S

CONCLUDING REMARKS

Seven high strength steels with tensile strengths from 1500 MPa to 2500 MPa were tested between 105 and 10 l~ cycles. The specimens continued to fail over 107 stress cycles. It is confirmed that S-N characteristics of the high strength steels are composed of two zones corresponding to surface and subsurface fracture modes, respectively. It was found that the S-N curves of these steels display a plateau between 106and 108 cycles and tend to drop down again in the ultra-high HCF regime (>107 or 108 cycles). Subsurface crack initiation behavior has been clearly detected in the materials from inclusions due to HCF. There is a definite stress range (or cycles regime) where the initiation location changes from the surface to the interior, i.e. at about 10 7 cycles. Subsurface crack initiation is dominant in the long-life range and may not occur until after a crack incubation period, which often constitute the majority of the total fatigue lifetime [7]. For a general point of view, it is shown that beyond 107 cycles, fatigue rupture can still occur in a large a number of alloys and even in steels. In some cases, the difference of fatigue resistance can decrease by 100, even 200 MPa, between 106 and 109 cycles to failure. According to our observations, the concept of an infinite fatigue life on an asymptotic SN curve is not correct. Under these conditions, a fatigue limit defined with a statistical analysis between 106 and 107 cycles cannot guarantee an infinite fatigue life. In the gigacycle fatigue range a piezoelectric fatigue machine has been used at 20 kHz. This means those effects of frequency and heat dissipation could be suspected. In the examples quoted, it seems that these effects are very small (the specimen temperature is less than 60~ when the fatigue life is greater than 107 cycles). Assuming that the fatigue life of engineering components and structures can range above 108 cycles, it is very important to determine safe fatigue strength for 109 cycles. From a practical point of view, the only way is using a piezoelectric fatigue machine. The very high fatigue life regime, called the gigacycle regime, requires more attention with respect to the choice of alloys and the techniques used in the prediction of endurance.

ACKNOWLEDGEMENTS The author thanks RENAULT and CREAS for financial support.

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REFERENCES

.

3.

10. 11.

Umezawa and Nagai K. (1998). Metallurgical and Materials Transactions 29A, 809-822. Umezawa and Nagai K. (1997). ISIJ International 37(12), 1170-1179. Kanazawa K. and Nishijima S. (1997). Zairyo/Journal of the society of Materials Science, Japan 46(12), 1396-1401. Murakami Y.and Nomoto T. and Ueda T. (1999). Fatigue Fract Engng Mater Struct 22, 581-590. Nishijima S. and kanazawa K. (1999). Fatigue Fract Engng Mater Struct 22, 601607. Wang Q.Y., Berard J.Y., Bathias C., et als (1999). Fatigue Fract Engng Mater Struct 22, 667-672. Wang Q.Y., Berard J.Y., Bathias C., et als (1999). Fatigue Fract Engng Mater Struct 22, 673-677. Gibert J. L. and Piehler H. R. (1993). Metallurgical and Materials Transactions 24A, 669-680. Starker P., Wohlfahrt H. and Macherauch E. (1979). In: Fatigue of Engineering Materials and Structures, ICM3, Sheffield, England, vol. 1, no.3, pp.319-327 Atrens A., Hoffelner W., Duerig T. W. and Allison J.E. (1983). Scripta Metallurgica 17, 601-606 Danninger H. et als. (1998). Z Metallkd 89, 135-141.

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FATIGUE OF RAILWAY AXLES: A CLASSIC PROBLEM REVISITED R A Smith Advanced Railway Research Centre Department of Mechanical Engineering, University of Sheffield Mappin Street, Sheffield, S1 3JD, UK ABSTRACT This paper introduces reports from two major historical railway accidents that illustrate the ways in which axle fatigue was recognised and managed in the last century. Modem, largely successful, design methods are discussed. Because of the very large number of reversals of bending stress seen by an axle in its lifetime, these designs aim for an infinite life by keeping expected service stress ranges below the fatigue limit of the material. The small number of failures of axles in service, coupled with the serious consequences of derailment at high speed, imposes the need for very expensive, but ineffectual, inspections of axles for cracks. Some gaps in our knowledge of the fatigue of axles are identified and the need for the measurement of actual service loads is emphasised. KEYWORDS Railway axles, fatigue, inspection, crack growth, life prediction, service loads.

INTRODUCTION The railway axle, an apparently humble, and on first consideration, simple, component has played a pivotal role in the development of our knowledge of fatigue. This paper will briefly review the historical importance of axle fatigue, before discussing current design methods and issues which still remain for improvements in the design and management of the fatigue life of axles. THE RISE OF THE RAILWAYS AND THE RECOGNITION OF THE FATIGUE PROBLEM The rapid spread of railways from about 1830, initiated from Britain, then to Europe, America and finally round the world, was a landmark in human progress. Speeds of travel that had previously been limited by the power of man or horse, suddenly increased, causing a significant shrinkage of journey times and immense benefits to trade and social intercourse. However, for the first time, large metal components were subjected to high stresses: stresses that changed

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R.A. SMITH

cyclically with time in the case of axles. Although some details of failures of the axles of horse drawn carriages had been observed and reported [ 1], early trains caused many more components to be exposed. These vehicles were primitive, experimental and prone to spectacular failures of parts such as axles, boilers, cranks, springs, couplings and the like, whilst a little later the infrastructure on which the trains operated demonstrated weaknesses as rails and bridges failed. The materials employed also developed; the early wrought and cast iron being replaced by steel when bulk-manufacturing methods, notably the Bessemer Converter, became available in the years after 1856. THE VERSAILLES ACCIDENT OF 1842 Although these many failures caused operational problems and inconveniences, it took a major catastrophe to initiate research into the causes of failures. The catalyst for action was the accident which occurred near Versailles [2] on the outskirts of Paris on 8 May 1842. This was the first railway accident in which major loss of life occurred. The driving axle of a fourwheeled locomotive, the leading one of two engines hauling a train of seventeen carriages, suddenly broke. Derailment followed, the fire was spilt from the wreaked engine, and six carriages which piled up into the wreckage were ignited. The exact death toll was never established; estimates varied from 60 to 100 or more, and the shock waves echoed round Europe. In exactly the same manner that happens after a major accident today, the press was quick to take a lively interest, produce large quantities of inaccurate and irrelevant comment, and to express opinion. Religious groups proclaimed that God was punishing the wicked for travelling on a Sunday, letters to newspapers proposed all kinds of preventive measures; whilst the engineers got on with sifting the evidence and analysing the underlying causes. For several years after this accident, we can find reports of discussions about the failure of railway axles in the leading technical journals of the day. It was quickly recognised that the fracture, which caused the axle to break, was unusual. The fracture surface was described as being "lamellated with large crystals" that significantly differed from the usual woody appearance of wrought iron when broken by slow bending. The erroneous idea of fatigue being caused by an internal change, or "crystallisation", has its roots in this artefact of fracture of the highly anisotropic wrought iron, essentially a composite of iron and longitudinal slag stingers. This notion was common in the literature up to the 1950's and is occasionally referred to even today. It was clearly recognised that the failure occurred after a period of satisfactory service, so that it was proposed [3] that "every railroad company to keep books, in which shall be entered the state and length of service of every axle-tree" and "experiments be made on the length of time they axles ought to remain in use". The director of a company with long experience of providing horse drawn carriages, was reported as stating [ 1] that he only allowed his (metal) axles to run a total distance of 75, 000 miles (120,000 km) before being taken out of service and strengthened by the addition of further iron bars and that this distance should be reduced if much of the running of the axle occurs in paved roads. Typical of the debates initiated was a remarkable series of meetings held at the then embryo Institution of Mechanical Engineers; meetings which have been discussed elsewhere [2,4]. But it is worth recalling here, the evidence of Joseph Glynn recorded in a paper to the Institution of Civil Engineers [5] in 1844. Glynn had survived a railway accident caused by the breaking of an axle, but he had the presence of mind to sketch the fracture surface, see Fig 1, and to describe the fracture as extending for "about 1/2 inch (12mm) in depth all round (the axle), a perfectly

Fatigue of Railway Axles...

175

smooth cleft: this annular cleaving appeared to have been produced by a constant process: the central crystallised part being gradually reduced in diameter, until it was barely able to sustain the weight, and broke to a sudden strain. The author suggests that the .... cleft is produced, by the alternate rupture and compression of the particles or fibres of the iron" and was further of the opinion "that the breaking action commences with thefirstjourney of the (train)", present authors emphasis in italics.

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Figure 1. A sketch of a broken axle made in 1844 by Glynn [5] REPORTS ARISING FROM THE PENISTONE ACCIDENT OF 1884 As far as the present author is aware, no discussion of the outcomes of an accident which occurred in 1884 near Penistone (near Sheffield in the UK), have been made in modem literature concerned with fatigue generally or even specifically with axles. Twenty-four people were killed when the driving axle of a train travelling at 80 km/hour suddenly broke, derailing the train. Investigations revealed that the engine axle had covered some 82,000 km, which for the reported wheel size of 1.905m diameter is equivalent to the order of 1.4 x 107 revolutions. The official Inspector' s Report into the accident was discussed in a book published in 1893, "Safe Working of Railways" by Stretton [6], in which many interesting observations are made. For example, it is reported that during the fourteen years between 1878 to 1892, an average of 380 axles failed each year on Britain's railways. In the period between 1881 and 1891, an average of 178 iron and 72 steel driving axles failed each year, with an average distance to failure of the order of 340,000 kilometres. (Drivingaxles were generally cranked like a car's crankshaft.) From the detailed statistics found for the year preceding the Penistone accident, "no less than one in every sixteen driving axles in use were either broken or condemned", but this huge proportion includes 3.4 times as many axles condemned by inspection than broke in service. This, of course, implies a very effective method of inspection, but unfortunately no details are given of the technique employed. Mention is however made of the remarkable way by which an axle in which a flaw had been detected was allowed to continue to run or was withdrawn from service. "If a flaw was detected, the cracked pair of wheels were scotched" (that is prevented from rotating) "and fixed to the rails in the shop, and another pair of wheels run against the pair to be tested, and if they stood the test they were considered all right"! Mention is also made of the fact that, "several railway companies specify that one out of fifty (new) axles shall be tested, and stand five blows from a weight of 2000 lbs (907 kg) falling from a height of 20 feet (6.1m), upon the axle, upon supports 3 feet 6 inches (1 m) apart, the axle

176

R.A. SMITH

being reversed after each blow. On some lines it is expected that crank axles should run 200,000 miles (320,000 km), and if they fail in less mileage, the manufacturer is required to replace them". Two remarkable features of this book are the clear identification of the progressive growth of flaws in service, and the identification of the need to investigate more exactly the kind of loadings causing the flaws to grow. Although both these ideas had been introduced previously, they were still well in advance of other contemporary reported views of fatigue. Consider the quotation," It is satisfactory to notice that a large proportion of defective driving axles were discovered and taken out of service in the shops, and, doubtless, a more careful and frequent examination will reduce the number broken in running: but still, growingflaws will exist, which no care or investigation will detect" and again, "if a steel axle is defective orflawed when new, the failure takes place at an early period in its life, and if it runs for 150,000 or 200,000 miles (say 300,000 km), there is a great probability that it may afterwards run a very great distance" "What is it that brakes the axle? As the weight resting in the axle and the pressure of steam in the pistons, are certainly not enough to account for the fracture or failure, other reasons must be looked for, and other causes examined. When an engine is running at high speed, there is a greater or less amount of oscillation; this is kept in check by the flanges of the wheel, and great strain is put on the axles. Points and crossings are generally laid to gauge or even fight, and it frequently happens that the flanges of the wheels are thus pinched, and it will be at once seen that this action must exert an enormous force upon the axle by the tendency to bend it upward in the middle. The author is of the opinion that the strains which increase growingflaws, and ultimately end in fracture, are in a very great measure due to the force communicated to the axle by the wheels and flanges. He has therefore, given this question of 'side thrust' very careful attention." (We now know that high lateral forces can occur without flange contact, which only happens in extreme and rather rare events.) DEVELOPMENTS OF EXPERIMENT AND THEORY MID 19TM CENTURY In the period between the two accidents discussed above, considerable progress was made in the empirical understanding of the fatigue phenomena largely through experimentation. For example, James and Galton [7] in a series of experiments on large iron bars, approximately 4 m long, had showed that repeated application and removal of a load could cause failure at loads equal to one third of the static breaking load. The major contributions came however from Wrhler [4,8], a German railway engineer, who addressed the problem of axle breakages. Although Wrhler's work was mainly experimental, it could be claimed that he applied scientific method in the scope and detail of his investigation. Experimental measurements were made of the strains experienced by axles in service, see Fig. 2, which showed the effect of irregularities in the track causing large dynamic loads superimposed on the rotational bending stresses. His classic experiments were however conducted on miniature axle-like specimens, loaded by steady rotating bending in purpose built machines, Fig. 2, which allowed up to 40,000 stress reversals per day. This relatively high testing frequency permitted tests up to 106 to 107 cycles These systematic studies elucidated the existence of a limiting stress range, the fatigue limit, below which fatigue failures did not occur, thus making an important contribution to fatigue avoidance by design. Other aspects, such as the effect of the stress concentration of sharp comers; the effects of combined and residual stresses were also examined.

Fatigue of Railway Axles...

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Figure 2 (Upper) W/Shler's apparatus for the measurement of service strains on railway axles, the dashed line indicates the deflected position. (Lower) WOhler' s purpose built fatigue testing machine to apply reversed bending to axle-like specimens, [4]. MODERN DESIGN FOR RAILWAY AXLES All modem design methods follow essentially the same route, see Fig. 3 and Table 1 [9]. The vertical load on the axle leads to a couple caused by the distance between the journal beating centres and the position of the vertical reaction between the wheels and rail. This is enhanced by a dynamic factor, chosen appropriately from, for example, Table 1, leading to the moments Mland M2, which are constant along the length of the axle. A proportion of the vertical load, again from a factor in Table 1, is assumed to account for lateral accelerations (for example from curves and irregularities of track), which by statics leads to a vertical couples, Q0 on the journals and Ro at the wheel/rail contact. The last two terms of the resultant moment M3 vary with position along the axle, and are shown in Fig 3 for the wheel seat position. Finally the bending stress at the position along the axle where the total superposed moment, ~ M has been calculated, is obtained by simple bending theory as: a = m ~ M y/I = m 64 ~M_/rtds

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where m is a safety factor, and the other symbols have their usual meaning in beam theory and the final line assumes a circular axle of radius, d at the section considered. Usually the diameter is a maximum under the wheel seats, D. The critical section is found by exploring combinations of position in equation (1). The diameter, d, the major axle design variable, is found by equating the maximum stress as calculated above to the appropriate material strength, the fatigue limit. Thus d must be greater than a value proportional to the cube

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Fatigue of Railway Axles...

179

root of the total moment divided by the fatigue limit, and is therefore relatively insensitive to the particular values of the above parameters. Velocity V km/h 150-200 60-160 <60

Vertical acceleration ot v 0.0027V 0.0027V 0.16

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Table 1. Vertical and horizontal accelerations as a function of velocity, truncated table extracted from Hirakawa et al, [9]. In practice, of course, axles are not simple cylindrical shapes. The relative values of the maximum diameter under the wheel seat, D, and the value in the central portion, d, causes the critical section to vary. Japanese standard designs [9] tend to produce failures by a fretting fatigue mechanism under the wheel seats, European axles tend to fail in the transition region between the two principal diameters where the transition radius is an important variable. There have been other reports of failures in the central area of the axle. The warnings enunciated by WOhler many years ago concerning the dangers of stress concentrations have been largely heeded by the detailed design of local features such as blends between varying diameter sections and other notch like discontinuities by using finite element stress analyses. Note too that the material resistance may also vary with position along the axle; the Japanese practice is to induction harden the areas under the press fit of the wheels, thus locally increasing the fatigue resistance by applying residual compressive stresses. Although cranked axles, of the kind reported in the failures of the age of steam traction described earlier, are now rarely used, there is a difference between driving and trailing axles. Not only do the applied loads vary in the two cases, but also the mechanisms necessary to transmit the drive onto driven axles naturally lead to more complicated shapes and possible stress concentrating features. THE MANAGEMENT OF AXLES IN SERVICE

In general the kind of design approach described above works well and the number of axle failures is small. Nevertheless, failures do occur, sometimes with disastrous consequences. Even if no deaths or injuries result, collateral damage and disruption to services can be very expensive. These consequences are largely determined by luck in the particular circumstances of each accident. For example, a French high-speed TGV derailed from 270 km/h at M~con-Loch6 in 1992, but there were no deaths or serious injuries. A much lower speed derailment followed by a collision, again caused by a broken axle, caused a death at the UK Rickerscote accident in 1996. However, the accident which send shockwaves through the whole of the railway industry wordwide, was the high-speed derailment of a German ICE in May 1998. A derailed coach hitting the abutments of a bridge here magnified the random nature of the consequences. A wheel, fractured by fatigue, caused 100 deaths. (We note in passing that the fatigue design of wheels is, perhaps surprisingly, even less well understood than the axle problem, but the two are clearly rather intimately connected through the loadings.) This particular accident emphasises the role played by inspections in keeping the fatigue problem at bay. To give an idea of the numbers involved, in the UK there have been about 1.6 axle failures/year over the last 25 years, out of a population of about 180,000 axles. (A similar number of new axles are introduced every year in China, where some 2.5 million wheelsets are

180

R.A. SMITH

in fleet service.) These large numbers of axles are subjected to inspections in order to try to identify cracks before failures occur. In general, the examinations are expensive, time consuming and not particularly effective in finding cracks. Furthermore, the dismantling needed to examine axles, such as the drawing off of beatings, can cause scratching damage that is sufficiently severe to cause an axle to be retired. To give an idea of the frequency of these inspections, a particular type of passenger coach in the UK is required to be ultrasonically tested after every 200 days of service, and given what is considered to be a more sensitive magnetic particle inspection every 800 days. These intervals correspond to a duty of in the order of 400,000 km per year, or about 2 x 108 revolutions of an axle per year or 4 x 106 cycles per week. The rational behind the frequency of testing, is that the largest crack which would not be detected in an inspection, should not grow to failure during the service interval to the next inspection. This implies that crack propagation calculations can be performed with sufficient accuracy to set the inspection interval. This is improbable. Leaving aside more general criticisms of the lack of accuracy of fatigue life predictions, such as SchOtz [ 10] who wrote, "Fatigue life predictions to crack initiation by the local approach and to complete failure by Miner' s rule are still unreliable and may err by a factor of 10 or more on the unconservative side", there are several difficulties which make the task even more difficult for the axle problem. The principal difficulties can be summarised: (a) Because of the lack of reliability and sensitivity of the inspection techniques, the initial crack length chosen for the life calculation must be set larger, leading to shorter intervals between inspection than really necessary. (b) The service loads are much more stochastic in nature than the well-defined hypothetical loads used for the initial design rule suggest. Additional stresses, other than cyclic bending loads, arise from dynamic loads induced by irregularities in the wheel (fiats, out-ofroundness), defects in the running surface of the rail (joints, dips, twists), lateral loads due to points and crossovers, torsional loads arising from traction changes) there is a suggestion that loss of traction allows significant free torsional vibration of an axle leading to high superimposed shear stresses). In many cases, in the absence of experimental measurement, the magnitudes and frequencies of these events are unknown, thus making cycle by cycle crack growth predictions unreliable. (c) Important inputs to fatigue calculations are material properties such as crack growth data, fatigue limits and fatigue thresholds, which are very sensitive to material condition, manufacturing route, surface treatment, orientation and load sequence. In many cases this data is lacking, particularly from large size specimens representative of axles. (d) Although there has been an enormous improvement of our understanding of the mechanisms of fatigue, debate still exists on the most appropriate modelling techniques to use in real applications. (e) Abnormal conditions may arise in service. There is debate about the best means of protecting axles from corrosion, and the extent to which coatings may hinder inspection. The interactions between fatigue and corrosion mechanisms in extending defects are still inadequately understood. Higher speeds have lead to increased examples of damage of axles from flying ballast [ 11 ], which may be of the form of crack-like indentations on axle surfaces which initiate premature failure.

Patigue of Railway Axles...

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CONCLUDING REMARKS Although railway axles have been designed and used for approaching 200 years, the severity of the mechanical environment in which they are used has increased with the much increased speeds of the last few decades. For speeds in the region of 300 km/hour, the consequences of derailment from a broken axle can be disastrous. At the same time, in order to reduce dynamic loads from unsprung mass, that is mass below the suspension of a rail vehicle, it is desirable to reduce the mass of axles as far as reasonably possible. Modern axles are therefore highly stressed safety critical components, which can be expensive to maintain in service because of the unreliability of practical methods of crack detection and sizing, and lack of adequate information on which to base rational intervals of inspection. There have been considerable recent improvements in miniaturisation of electronic devices with which service loads can be measured. The author is currently involved in projects to measure and better quantify the actual loads to which railway axles are subjected. ACKNOWLEDGMENTS

This paper is a preliminary study of an EPSRC sponsoredprojecton railwayaxle fatigue. The paper was written during the author's study leave with Prof. Y Mumkamiat KyushuUniversity,Japan, supportedby JSPS. The author is pleasedto acknowledgethe kind supportof both organisations. REFERENCES

1.

2. 3. 4. 5. 6. 7. 8.

9. 10. 11.

Edwards, H.H. (1843). The Civil Engineer and Architect's Journal VI, No 65, p48. (In the book by Stendhal (Marie-Henri Beyle), MOmories d'un Touriste (1838),we find, "La Charitr. 13 April 1837. I was passing at a good speed through the little town of La Charit6 when, to punish me for my protracted thoughts this morning about the troubles to which iron is subject, the axle of my coach broke sharply...I examined the grain of my axle; it had become coarse, apparently because it had been in use for a long time") Smith, R.A. (1990). In Fatigue 90, Proceedings of the 4thInternational Conference on Fatigue and Fatigue Thresholds, pp2033-2041, Kitagawa, H and Tanaka, T. (Eds). Materials and Components Publications Ltd., Birmingham, UK Anon. (1842), Mechanics Magazine, XXXVI, No 981, p438 (Report of orders issued by the French Minister of Public Works.) Timoshenko, S.P. (1953). Chapter VII, History of Strength of Materials, McGraw-Hill, New York (& subsequent Dover paperback edition). Glynn, J. (1844). Minutes of the Proceedings of the Institution of Mechanical Engineers, pp202-203. Stretton, C.E. (1893). Chapter V, in Safe Railway Working. Crosby, Lockwood & Son., London. James and Galton (1848). Appendix B5, In Report of the Commission to Inquire into the Use of lron to Railway Structures, London. Wrhler, A. (1858-1871). An account in English was published in Engineering 11 (1871) March 17, pp 199-200 and subsequent issues. Original German reports are in Z. Bauwesen, 8 (1858) pp 641-652, 10 (1860) pp 583-616, 16 (1866) pp 67-84 and 20 (1870) pp 73-106. Hirakawa, K., Toyama, K. and Kubota, M. (1998). International Journal of Fatigue, 20, pp135-144. Schutz, W. (1993). In Structural Failure, Product Liability and Technical Insurance, pp 49-59, Rossmanith, H.P., (Ed). Elsevier. Gravier, N., Viet, J-J. and Leluan, A (1998). In Proceedings 12thInternational Wheelset Congress, Qingdao, China. pp 133-146 China Railway Society.

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F R A C T U R E M E C H A N I C S A P P L I E D TO C O N C R E T E

M. ELICES, J.PLANAS AND G. V. GUINEA

Dep. Ciencia de Materiales, Universidad Polit~cnica de Madrid, ETS de Ingenieros de Caminos, Ciudad Universitaria, 28040 Madrid, Spain

ABSTRACT The aim of this contribution is to show the value of fracture mechanics tools in dealing with engineering fracture problems of concrete, either plain or reinforced. The first part is a review of modeling concrete fracture in tension: the suitability of linear elastic fracture mechanics (LEFM) as an asymptotic approach is considered first, followed by an outline of classical fracture models based on stress-strain relations and their associated problems of nonobjectivity. And, finally, cohesive process zone models based on stress-displacement relations are shown to be one of the simplest models capturing the essential features of fracture processes in concrete. The second part gives some practical examples of applications of fracture mechanics to concrete, mostly drawn from the authors' experience: the difference between strength and toughness in concrete is clearly shown in the example of piles. The size effect in flexural strength, unobtainable with classical strength theories, is accurately predicted with the cohesive process zone model. For plain concrete and large concrete structures such as dams, LEFM was proven suitable. Fracture in reinforced concrete is a more involved problem; nevertheless some promising results for lightly reinforced concrete beams are discussed. The paper ends with some comments on fracture of fiber reinforced concrete (FRC) and an application of this concept to the fracture of FRC tunnel lining, presented in a Japanese standard. KEYWORDS Concrete, Crack, Fracture, Cohesive Process Zone, Size Effect.

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M. ELICES, J. PLANAS, G. K GUINEA

INTRODUCTION Concrete is a universal building material with complex microstructure and behavior. In the field of fracture mechanics, it is singular in that a large number of conceptually different models have been proposed to describe its fracture, from classical linear elastic fracture mechanics to sophisticated models based on higher order continua or even on fractal geometries. And, still, fracture mechanics is rarely used in the routine design and control of concrete structures, even though these fail after concrete cracking takes place, which should call for an extensive use of fracture mechanics concepts. The reason for the infrequent use of fracture mechanics in the routine design of concrete structures is, of course, that concrete is ordinarily reinforced or prestressed. If the reinforcing or prestressing steel is properly laid out, the concrete can safely crack because the tensile stresses released from the concrete are taken over by the rebars or tendons. However, a number of cases escape the general rule, some of which are examined in this paper. Another reason for the scant use of fracture mechanics in the design of concrete structures is the computational difficulty; the usual sizes of concrete elements do not allow the use of a linear elastic fracture mechanics (LEFM) simple approach, and the designer has to resort to more involved non-linear methods. More often, the additional information does not justify this computational effort. This situation will change when simple computational programs become available. Before examining the examples of application of fracture mechanics to concrete we devote a few pages to discussing why so many models exist to describe the fracture of concrete, and to outline one of the simplest models capturing the essential features of fracture processes in concrete. MODELING CONCRETE FRACTURE IN TENSION Concrete and L E F M

At first sight, concrete seems to be a brittle material full of flaws, and LEFM the tool of choice to deal with it. It is not so. Concrete is not brittle enough for LEFM to hold for the relatively small microstructural flaws of the size, say, of the bigger aggregates. Concrete appears to be quasibrittle, a term recently coined to identify materials that show small plastic (irrecoverable) deformation after full fracture but exhibit a relatively large zone ahead of a preexisting macrocrack, the process zone (Fig. 1), where the interdependence of stresses and strains is nonlinear. Indeed, many tests on macrocracked specimens since the work of Walsh [ 1, 2] have shown that LEFM cannot be applied to concrete specimens of typical laboratory sizes (for a review, see [3]). The reason is that the nonlinear zone ahead of the crack tip is very large compared to usual specimen (or structure) dimensions. This rules out LEFM because the nonlinear zone cannot be neglected and does not concentrate in a point at the crack tip.

Fracture Mechanics Applied to Concrete

185

PROCESS ZONE

NON-LINEAR STRESS-STRAIN DEPENDENCE

Fig. 1. Process zone ahead of a pre-existing macrocrack Direct measurement of the process zone is very difficult in concrete because, contrary to the case of metals, nonlinearity is not manifested as a wide plastic zone, but as a narrow band of heterogeneous microfracture processes, including a progressive growth of microcracks which coalesce and overlap, together with aggregate pullout and associated frictional phenomena. Since the microfracture is very progressive, it is difficult to ascertain where the end of the nonlinear zone is located. In fact, the results of direct observations are strongly dependent on the resolution of the measuring method [4]. Therefore, the size of the process zone has to be estimated from some nonlinear fracture model. For ordinary concrete, the fully developed process zone (i.e. for a semi-infinite crack in an infinite body) may be as large as 0.25-0.6 m or even more, depending on the model used. This shows that for ordinary sizes LEFM does not hold. Only for large sizes, as for dams or large walls, when the size of the process zone is negligible in comparison with other relevant dimensions, does LEFM provide a reasonable approximation [5]. This also shows that natural flaws are much smaller than the fully developed nonlinear zone and thus failure in concrete is never a single-flaw initiated process, but a multiple flaw collaborative and progressive process.

Modified LEFM Approaches One of the simplest approaches to extend the applicability of LEFM tools is to represent the effect of the process zone by an equivalent elastic crack which is longer than the true crack but shorter than the true crack plus the nonlinear zone. The model is completed only after the rules for the growth of the equivalent crack are given. For concrete, various equivalent crack models have been proposed. In the simpler models only the condition for unstable crack growth (peak load) is stipulated. This is the case of the two parameter model of Jenq and Shah [6] which assumes that the peak load occurs after some stable crack growth when Kleq (the stress intensity factor at the equivalent crack tip) reaches a critical value, KIc, and the CTOD (crack tip opening displacement, equal to the opening of the equivalent crack at the initial location of the crack tip) reaches its critical value CTODc. Both Klc and CTODc are assumed to be material parameters that have to be determined experimentally. A RILEM recommendation to determine these parameters was issued in 1990 [7]. This model has been recently extended by Xu and Reinhardt who, besides slight changes in the method of

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determination of the equivalent crack extension, introduce a new parameter KIci.i which is the stress intensity factor at which the initial crack starts growing [8]. The R-curve models go one step further and propose a crack growth law assuming a relationship between the crack resisting force R (or the resisting stress intensity factor at the equivalent crack tip KR) and the equivalent crack extension Aa. This type of approach has been used by several authors. In particular, a model proposed by Bazant [9] is made to depend on only two parameters which can be determined on the basis of size effect following the RILEM recommendation issued in 1990 [10]. Recently, other authors have advocated the use of Rcurves to describe crack growth in concrete [11, 12]. However, all these models, by their very conception, can be only approximate. In fact, the Rcurves appear to depend on the geometry of the specimen and in many cases also on its size. Detailed analysis using the cohesive crack as a more approximate model showed that a given Rcurve can describe adequately the behavior of cracked specimens only over a limited range of sizes and geometries [5,13-15]. Interestingly, it was also proven that a cohesive crack model tends to an equivalent crack model for very large sizes, and then an R-curve can be uniquely defined[5, 14]. However, this is valid only when the length of the crack and the size of the body are much larger than the fully developed nonlinear zone, which, for concrete, leads to dimensions much larger than those found in laboratory testing.

Continuous Approaches

In the design of most reinforced concrete structures, the tensile strength of concrete is simply neglected. This is the so called no tension design. For plain and lightly reinforced concrete, however, and for some special cases of reinforced concrete structures (diagonal shear, torsion, punching) the contribution of concrete strength in tension has to be considered [ 16]. Since this has been long recognized, structural engineers introduced cracking of concrete in the finite element codes. The simplest, but incorrect, way of doing so is by eliminating from the finite element mesh any finite element whose stress ever exceeded the tensile strength (by setting its stiffness to zero). More sophisticated ways were devised where cracking within a finite element could occur directionally, as depicted in Fig. 2a, where it is assumed that cracking inside the element is smeared. The element is assumed to fail through an array of finely spaced cracks while the material among them was undamaged [ 17].

a

b

--~/'-FIXED ---~ BAND WIDTH

Fig. 2 Smeared cracking in one element (a) and in a crack band of fixed width (b).

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This led to relatively sophisticated orthotropic models in which cracks could open first and later close again. Moreover, it was relatively easy to implement progressive fracture by assuming a stress-strain curve with softening rather than with a sudden stress drop. It took several years to realize that such an approach was not consistent, because the solution was dependent on the chosen element size. To see why, it is enough to note that when a crack runs through an element, the energy dissipated in fracture is proportional to the area of the cross section of the cracked element, while in the stress-strain smeared cracking model, the energy dissipation is proportional to the volume of the element. If the elements are shrunk to vanishingly small dimensions, the energy dissipated becomes vanishingly small, too. The first solution to this problem came from Bazant and consisted essentially in stating clearly that given a stress-strain relation with softening, the smeared cracking had to be confined to a band of fixed width he, where the band width is to be seen as a material property, and the strain field within the band is homogeneous across its width [ 18-19]. The crack band model is essentially a fracture-based approach, since it is devised to preserve the specific fracture energy, G F, (the energy consumed in breaking a unit area) in a crack represented as a crack band, and it is computationally equivalent to the cohesive crack model to be presented later [20]. Within the context of the continuum approaches, however, it can be seen as the simplest of the models that use stress-strain softening curves in combination with localization limiters. A localization limiter is a condition imposed on the admissible solutions so that those with zero energy dissipation are automatically ruled out [21]. Bazant's crack band model introduces the localization limiter externally. More sophisticated true continuum models incorporate the localization limiter in their formulation, so the size and shape of the strain localization zone is determined as a result of the analysis of each problem, rather than imposed a priori as in the crack band approach. There are various ways of limiting the size of the fracture zone. One common way in timeindependent models is to use generalized continua, in which the postulate of local action is relaxed and it is assumed that the stress at a point depends not only on the strain evolution at that point but also on that at neighboring points. The interaction with the neighbors can extend to a finite distance (nonlocal continua) or be confined to short range interactions. In the first case, introduced in concrete by Bazant [22], the stress depends on at least one nonlocal variable which is computed as a weighted average of other local variables over a certain averaging region. In the second case, pioneered in concrete by de Borst [23, 24], the nonlocal variable depends only on the gradients (up to some order, usually the second) of the local variables. For an introduction to fracture description using nonlocal or gradient models see [3], Chapter 13. A different approach to bring classical continuum models to consistently describe fracture processes has been developed recently [25, 26, 27]. In this approach, the constitutive equation itself embodies the possibility to describe a strong discontinuity, i.e. a jump in displacements, hence also a crack. Numerically, this leads to finite elements with embedded discontinuities and are therefore akin to cohesive crack formulations; but it is also able to represent weak discontinuities (equivalent to distributed cracking) and provides a more general framework than the simple cohesive crack we next describe.

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Cohesive Zone Crack Models

Cohesive zone crack models have been developed to model the fracture process zone ahead of a crack tip and to represent fracture situations such as those sketched in Fig. 1, where the faces of the crack open while still transferring stress from one to another lip. Barenblatt [28] introduced such a model to relieve the stress singularity at the crack tip and to relate the crack growth resistance to the bond properties of the material (Fig. 3a). His approach was limited to the analysis of the critical situation in the quasi-static steady growth of a semi-infinite crack in an infinite body. The reasoning was beautifully set in such a way that the exact relationship between the atomic separation and the atomic binding force was not required; only the integral of this relationship entered the final solution for the crack growth resistance. This was possible because the analysis was limited to cases where the process zone was very small as compared to the crack and body sizes (asymptotic limit).

b

-<'-4.. 4 "4 "~

\,

Fig. 3. Various physical sources of extended cohesive forces: (a) atomic, (b) yield (dislocation) strip, (c) grain bridging, (d) fiber bridging, (e) aggregate frictional interlock, and (f) crack overlap. In a different framework, Dugdale [29] proposed a model to approximate perfect plastic yielding of the material close to the crack tip. In this model, a displacement discontinuity is allowed to take place ahead of the crack tip, which may be viewed as the creation of a pile-up of sessile dislocations (Fig. lb). The other basic assumption of this model is that the stress along the dislocation line remains constant, equal to the elastic limit of the material (justifying the alternative name of yield strip model). The original aim of the Dugdale model was to describe crack tip plasticity rather than fracture. Fracture had to be taken into account by means of an additional (external) criterion. This model should be called the Leonov-Panasyuk-Dugdale model due to the contributions of Leonov and Panasyuk [30] and Panasyuk [31 ], largely unknown in western literature. Cohesive Crack Models

To the authors' understanding, no new basic conceptual advances were produced in this type of formulation until Hillerborg and co-workers reformulated the cohesive crack concept in a model that they called fictitious crack. This model was specifically intended for cementitious materials

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[32] and implied two new essential ideas: (1) The crack description is performed at a macroscopic scale (microstructural features such as grains, fibers, preexisting microcracks and crack surface roughness are "invisible" and have to be smoothed out, i.e. homogenized); and (2) the description must be valid for any material point, not only for those close to a preexisting macrocrack tip. This extends the applicability of the model to any situation, even if no initial macroscopic crack is present. This latter statement is of paramount importance because it raises the model status from that of a special purpose descriptor of the near-tip material behavior to that of a sound general constitutive model for the material that no longer requires a preexisting crack to hold. In fact, Hillerborg's conception provides a model that can make a smooth transition from the mechanics of a continuous body to that of a cracked solid. This interpretation of the merits of Hillerborg' s approach, which may seem exaggerated to those working in the field of continuum mechanics, has been recently strengthened by the discovery that a cohesive crack is in fact an exact solution of a well posed family of continuum nonlocal models [33-35]. In the rest of this section we present an outline of the cohesive crack, starting with the simplest possible formulation and discussing its possible extensions. Standard Cohesive Crack Formulation for Concrete A cohesive crack model must be defined by the properties of the bulk material, the crack initiation condition -this is an essential specification in the extended model because in the general case no precrack exists defining the initiation point- and the crack evolution function. In the most usual formulation the assumptions regarding these aspects are much simplified, mostly to ease the computations and to exploit well established methods in LEFM. However, this formulation is by no means the only one possible. Extensions of it are outlined in a later section. The following are the most usual assumptions: a) The bulk material follows a linear elastic and isotropic stress-strain relationship, with elastic modulus E and Poisson ratio v. Note that according to our previous remarks, these values refer to the macroscopic homogenized material and must describe the behavior of the composite material. b) The crack initiates at a point when the maximum principal stress (yI at that point reaches the tensile strength ft. Moreover, the crack forms normal to the direction of the major principal stress. Note again that the tensile strength we refer to is the mean strength of a representative volume which homogenizes the influence of microstructural features: microcracks, microvoids, grains, fibers and the like. It is not the strength of the solid phase (sometimes referred to as the local strength or matrix strength, depending on the context). c) After its formation, the macrocrack opens while transferring stress from one face to another. The stress transferred, the cohesive stress, is assumed to be determined by the crack opening displacement history. For monotonic pure opening the stress transferred is normal to the crack faces, and in the simplest formulation is taken to be a unique function of the crack opening: cy = ffw)

(1)

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190

The function flw) is called the softening function ---or softening curve-- and is a non-increasing function of the crack opening. It is the essential characteristic of the cohesive crack, and has to be experimentally determined.

Features of the Softening Curve A softening function has two essential characteristics: the tensile strength, ft, which is, by definition, the stress transferred at the initiation of opening; and the specific fracture energy (or simply, the fracture energy), GF, which is the work supply required to bring completely apart the two faces of a unit surface of crack. Graphically speaking, the fracture energy is the area under the softening curve, as depicted in Fig. 4. The analytical expressions are OO

ft =f(0),

GF=

I 6dw 0

OO

-

I f(w) dw 0

(2)

These two parameters, GF andj~ are in principle measurable in experiments without any explicit hypotheses about the shape of the softening curve.

i:.

W)

1

CRACKOPENING,w

Wc

Fig. 4. Softening curve defining the cohesive crack model Another characteristic property of the softening curve is the critical crack opening Wo which is the crack opening at which the stress transferred becomes zero. The essential difference from the other two parameters ft and GF is that the determination of Wc is very elusive. If direct tension tests are used, its value may be very dependent on the resolution of the measurement devices, and in indirect tests its determination relies on the assumed shape of the softening curve. Based on ft, GF, and the elastic modulus, E, the characteristic length Ich is defined as: EGF lch- ft 2

(3)

This parameter enters the equations governing the evolution of the cohesive crack in a very particular way: if D is the characteristic size of the structure (for example, the beam depth), then the strength of geometrically similar structures depends on D/Ich. Given a material (i.e. given a softening curve) the behavior is the more brittle the larger the ratio D/lch. Conversely, given a structure and two materials with similar softening curves (same shape of the softening curve) but different values offt, GF and E, the smaller the Ich the more brittle is the behavior.

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Extensions of the Cohesive Crack The foregoing formulation of the cohesive crack is the simplest version of it. There are possible extensions that are worth considering: (1) to extend the formulation so that a singularity at the cohesive crack tip is admissible; (2) to accept a behavior other than isotropic linear elastic in the material around the crack; (3) to introduce dependence on triaxiality; and (4) to introduce a fully consistent mixed-mode formulation. The first extension has already been in use in many models dealing with brittle matrix composites, particularly with fiber reinforced ceramics and cements. At a first glance it may seem that this kind of model is different from the Hillerborg approach where no singularity is present. However, Elices and Planas pointed out that such a singularity may very well be just a mathematical approximation of a softening curve consisting of an initial spike of large strength, followed by a long tail with a much lower transferred stress [20]. This kind of softening is basic for fiber reinforced composites, where the spike corresponds to the failure of the matrix, and the tail to the pullout of the fibers. Mathematically speaking, the singularity arises when the initial spike is approximated by a Dirac 8-function. Smith indeed showed that there is a smooth transition from the non-singular model to the singular one [36]. Therefore, this extension is sound and does not require further development, except, maybe, to quantify how narrow the spike must be for the singular approximation to work within a certain degree of accuracy. The second issue may be essential in some materials. Deviation from elastic behavior was considered from the very beginning by Hillerborg as a realistic possibility, and it has been implemented by the authors, using for the material an elastoplastic hardening model with a Rankine criterion based on the maximum principal stress and an associated flow rule [37]. The computations using a perturbation approximate method showed that for a typical concrete, the influence of the inelastic strain around the cohesive crack was small. When expressed as dissipated energy, the influence was below 5 % for notched specimens of all sizes. However, the situation may be much worse for some highly ductile fiber reinforced materials, even if the matrix is brittle (see, for example, [38] and references in the last chapter Applications to fiber reinforced concrete). In these cases, the perturbation approximation is beyond question and full nonlinear analysis is required. Even if deviation from linearity is small, elastic isotropy may not be adequate for some unidirectional fibre reinforced composites. However these situations do not rule out the cohesive crack concept. They only call for an extension of the equations and of the methods of analysis. To the authors' knowledge, the third issue has never been considered at a theoretical level, and is one of the most frequently heard criticisms of the cohesive crack. However, there is no basic objection to introducing a dependence of the softening curve on the triaxial state. This may require further hypotheses regarding the loading-unloading behavior, and may lead to a model which may be difficult to verify experimentally, because the only data so far available in biaxial tests concern the effect on the strength, not on the post-peak (stable crack opening) behavior. The first exception known to the authors is the research by Tschegg, Kreuzer and Zelezny [39] on wedge-split cubes subjected to compression parallel to the crack plane. However their results have not yet led to a theoretical formulation, and further work in this direction is needed.

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The last issue requires a complete vectorial formulation of the cohesive crack to be implemented in general purpose programs, so that general loading cases can be confidently analyzed. Even though there is now a general agreement that the fracture initiates in pure opening mode (mode I, no shear), it is obvious that crack sliding displacement may take place after the crack opens and before complete fracture. The testing procedures in this field are tremendously difficult, but they went ahead of the theoretical formulation [40, 41 ]. A few models have been proposed and implemented [42, 43, 44], but they still lack strong experimental support because they have only been checked against problems in which mode I is dominating during crack propagation. APPLICATIONS TO PLAIN CONCRETE The second part of this contribution deals with some practical examples of fracture mechanics applied to concrete, mostly drawn from the authors' experience. The examples provide rational answers to problems not solved, or empirically solved, outside the realm of fracture mechanics. The difference between strength and toughness in concrete is frequently not clearly stated in concrete design, and the importance of the size effect is often neglected, or implemented numerically. Both topics are commented on below. Concrete in Piles: Strong Concrete versus Brittle Concrete [45]

Although reinforced concrete piles have proved their ability to take a great amount of punishment without structural damage, sometimes fracture occurs during hammering. A Company producing concrete piling found that the piles from one of their two pile precast factories (Factory A) occasionally showed brittle behaviour when being hammered. The design of the reinforced piles was the same as that of the other factory (Factory B). Fig. 5 shows a typical cross-section of these piles, whose length is usually 12 m. 235 - 300 mm = 12 or 20 m m

25 m m

Fig.5 Cross-section of concrete piles Concrete mixes were nominally identical for both factories, but the aggregates came from different quarries. The mechanical properties of both concretes, as measured through standard tensile and compressive tests, and Young modulus, were almost the same or even better for concrete from factory A, as shown in Table 1. No classical approach could explain the different behaviour of the two concretes, since the conventional strengths of the brittle concrete A were never below those or the well behaved concrete B. Looking for fracture parameters, the specific fracture energy G F was measured in both concretes following the procedure proposed by RILEM TC 50 [46], and taking into account additional refinements suggested by the authors [37,47-48]. Test specimens were notched beams of 100 x 100 x 850 mm.

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Table 1 - Concrete properties (28 days) Concrete Type

Compressive Strength ASTM C39 (MPa)

Tensile Strength ASTM C496 (MPa)

Elastic Modulus ASTM C469 (GPa)

A

57.5 43.5

5.7 4.5

48 36

B

Table 2 - Concrete fracture properties Concrete Type

GF,average (j/m 2)

lch (nun)

A B

103 151

152 268

Table 2 summarizes the experimental results of the specific fracture energy G F, as well as the computed values of the characteristic length. Fracture energy results clearly show that concrete B is tougher than concrete A - - even though the standard properties are almost the same--a fact that probably is at the root of the superior performance of concrete B during hammering. Several parameters have been proposed to characterize the brittleness of concrete structures. A useful one is the brittleness number [49]: D - lch

(4)

where D is a characteristic dimension of the structure. A higher brittleness number indicates increased brittleness. However, this number has not an absolute meaning because the structural dimension D is open to choice. It is useful only when comparing geometrically similar structures. Since the piles from the two factories are geometrically identical, one can in principle determine the relative brittleness of the two concretes to be 1.8. Hence concrete A may be estimated to be nearly twice as brittle as concrete B, which again supports the observed field behaviour (For this to be exact, the two concretes should display a softening curve with exactly the same shape. This is probably not so, but the existing experience with other concretes tends to show that the difference must be slight). A fractographic analysis of the broken samples revealed that, in concrete B, most of the aggregates were debonded, while in concrete A they were broken. This evidence suggests that the low toughness values of concrete A as compared with concrete B are due to its weaker aggregates. The toughness of concrete A can be improved in either of two ways: by improving the strength of aggregates, avoiding aggregate fracture and forcing the crack to bend round the aggregates, or by improving the toughness of the cementitious matrix.

M. ELICES, J. PLANAS, G. K GUINEA

194

The second solution was selected for economic reasons, and the matrix toughness was improved by fibre reinforcement. Polypropylene fibres (Concrefib| of 40 mm length were used. The concrete mix and curing procedures were as previously described. For comparison purposes another set of samples similar to concrete A, henceforth called A2 were also tested. Table 3 gives the mechanical properties of both concretes where it is shown that the increased toughness of fibre reinforced concrete is similar to that of concrete B, thus suggesting the possibility of using it for piles, even though the aggregates were still weak. Further tests on piles made with FRC showed good performance during hammering and, at present, sufficient experience has been accumulated to permit safe and economic utilization of these fibre reinforced concrete piles.

Table 3 - Mechanical properties of fiber reinforced concrete and A2 concrete Concrete Type Fibre Reinforced A2 *28 days

Compressive Tensile Strength Elastic Modulus GF Strength (MPa)* (MPa) (GPa) (J/m 2) 59.4 57.7

5.0 5.0

45 40

157 101

lch (mm) 283 162

Concrete in Test Specimens: Size Effect in Flexural Strength [50] The second example is a well known phenomenon in the concrete field. When measuring the tensile strength of concrete by means of flexure tests it appears that its value is higher than that obtained through direct tension tests [51]. In addition, it is observed that the flexural tensile strength is dependent on the size of the beam tested. Such size effect can be evaluated with an empirical expression that relates both tensile strengths (flexural and axial) with beam size, given by CEB-FIP Model Code 1990 [52]: 2.0 (D/Do) 0.7 ft = ft,fl 1+2.0 (D/Do) 0.7

(5)

where ft is the mean value of axial tensile strength, ft,fl the mean value of flexural tensile strength, D the beam depth and Do is a reference size equal to 100mm. This expression is applicable for beam depths of more than 50 mm. A further check for this expression was carried out by the authors [50]. Details of concrete manufacture and storage are given in [53]. The maximum aggregate size was 16 mm, the specimens had been stored in lime saturated water and the tests were performed with special care to avoid shrinkage during the preparation of the specimens. Table 4 shows the mechanical properties of the concrete: elastic modulus, compressive strength and splitting tensile strength, measured according to ASTM C-469, ASTM C-39 and ASTM C496, respectively. Due to the difficulty of performing direct tension tests, the tensile strength ft was estimated as equal to the splitting tensile strength fst, which is known to be only 5 to 12 percent higher [51, 54].

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Table 4. Mechanical properties of the concrete E(GPa)

fc(MPa)

ft(MPa)

39_+1 48.5_+0.4 3.9-+0.2 Errors correspond to 95% confidenceinterval

To measure the flexural strength, stable three-point bend tests on unnotched beams were performed using full weight-compensation. Two sets of beams were tested with an span to depth ratio of 4 and depths of 30 and 96mm. The thickness was 100mm for all the beams. The values obtained for the flexural tensile strength are plotted in Fig. 6, where the ordinates are made nondimensional by dividing them by ft.

:::3

25

Z

b

-11-(9 z I.U iv, I.(/) ._1

9

Experimental

.....

2.0

Model Code (CEB-FIP)

......... Limit Strength Theory 1.5

1.0

..................................................... " " : ' - : : - - - - : - - , - , .

.J LU

I

0.5

I-W

0r

0 . 0

i

1 01

i

i

i

,

i

i

i

i

i

i

I

i

i

i

i

10 2

i

Ii

I

(}-+ i

i

i

10 3

BEAM D E P T H , D (ram) Fig. 6. Size effect in maximum load for unnotched beams. (YNu=6Pu/BD; Pu = ultimate load, B=thickness, D=beam depth As shown in the figure, experimental results display the same trend as the empirical equation of the Model Code, a result unobtainable from the limit analysis theory. A prediction of the size effect was made using the cohesive fracture model. The four parameters that define a bilinear softening curve, needed for numerical computations, were obtained by the procedure developed by the authors [55], and are given in Table 5. In particular GF, wl and Wg were determined from tests on half-notched beams cast from the same batch. As outputs, peak load, load-CMOD (Crack Mouth Opening Displacement) and load-displacement curves were obtained for the two series of unnotched beams.

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Table 5. Fracture properties for the concrete of example 2 E(GPa)

ft(MPa)

GF(J/m 2)

w 1(pm)

39_+1 3.9_+0.2 126_+14 53+9 Figures are mean values and standard error, with 95% confidence.

Wg(l.tm) 42_+9

Fig. 7 shows the numerical prediction of the size effect in peak load. The agreement with experimental results deserves some comments: The experimental point for notched beams is the reference point from which all information was derived (i.e. the softening curve) and the prediction of the cohesive model should cross through this point, as it does. The encouraging result is the very good agreement for unnotched beams of the two sizes, particularly if it is realized that the two geometries---notched and unnotchedm are quite different.

2.5

unnotched ~Z 13

20

="

r z LL,I I..-. to i,t,i

--~ ~

Experimental Model Code (CEB-FIP) Cohesive Model

.

1.5

1.0

,--I

z m I-

9

notched, a~

5 ~

{)[

0.5

0.0 101

10 2 BEAM DEPTH

{}1

[--~o

(+

10 3 D, (ram)

Fig.7. Maximum load size-effect for three point bend beams notched and unnotched. CYNu=6Pu/BD; Pu= ultimate load, B=thickness, D=beam depth

Fig. 8 shows the comparison of the predicted loads and horizontal displacements at midspan with the measured ones for the unnotched beams. One may conclude that the prediction obtained using a cohesive crack model with a softening curve (determined from independent tests on notched beams), is very good, particularly if one realizes that predictions are for unnotched specimens.

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Fracture Mechanics Applied to Concrete

12000

~}

10000

-~

w

96 mm

_

~- 8000 a

0l

6000

4000 2000 _. _ ~ - ' - - - - - - :

,

0

,

[

,

I

0.1

,

~

,

,

I

,

,

~

,

0.2

I

0.3

,

,

J

,

..........

I

0.4

~

,

,

,

0.5

AL (mm) Fig. 8 Results of tests on unnotched specimens (dashed) compared with the cohesive crack model prediction based on notched specimens (solid line). Gauge length, L0 = 25mm, beam thickness = 100mm, loading span = 384mm

The cohesive crack model appears as a simple method of modeling the fracture of plain concrete specimens, with very good results. This work shows how this model not only predicts accurately the maximum loads for different geometries and sizes but is able to make reasonably good predictions of load and displacements at any instant throughout the test, even for unnotched specimens. In a cracked structure, when the size of the structure is very large, or more precisely when D/lch --->oo s D any representative dimension), the relative extent of the cohesive crack zone is negligible when compared to all the linear dimensions of the specimen. If one measures only remote field values (loads or displacements), linear elastic fracture mechanics approximately applies and the overall behavior of the structure is brittle, as stated before. Then the pre-peak deviation from linearity is negligible and the peak load situation coincides with the critical condition when the crack opening reaches the critical value Wc [5, 14]. This means that the whole softening curve is in play. However, as is well known, in this limiting case the influence of the shape of the softening curve is irrelevant, only its area, GF, matters. This is the case of very large concrete structures such as dams.

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Concrete in Dams [56-58] The classic design methodology of dams involves the use of the no-tension approach to characterize the concrete behaviour. This model assumes that concrete is not able to withstand tensile stresses and it was first formulated for the stress analysis of rocks [59]. It was argued that by neglecting the tensile strength of the material, a lower bound of failure load is obtained, and the no-tension model results are conservative when they are used in the structural design of dams. However, it has been shown [ 16] that if a certain critical dam size is exceeded, the exact no-tension solution of any cracked dam gives a larger maximum load than LEFM for any given value of the concrete fracture toughness. This is because the elastic energy stored in the regions subjected to tensile stresses can be released at the crack tip, helping the crack to propagate. If this energy is neglected in the analysis (as occurs in a no-tension models) it has to be supplied by the work of the external forces, giving rise to larger failure loads and non-conservative predictions. For very large plain concrete structures such as dams, fracture mechanics in its simplest form (LEFM) can be used. LEFM is the asymptotic solution of cohesive crack models for large sizes when considering cracked structures, as indicated above. The hypothesis of large sizes implies that the zone where the fracture processes occur is small when compared with all the characteristic dimensions of the structure, including the crack length. The fracture process zone length is controlled by the material characteristic length, Ich, given in (3), and for practical purposes it can be assumed to be of the same order of magnitude as Ich. Bruhwiler [60] measured the fracture properties of the concrete from several dams, obtaining Ich values between 1100 mm and 1700 mm. These values are fairly large for ordinary concrete, as could be anticipated by taking into account the poor tensile strength and the large aggregate size of dam concrete. Typically, a ratio of ten between the smallest structural characteristic dimension and lch is necessary to get accurate values of the failure load when using LEFM [61 ], which is the case of large dams which are already cracked, precisely the situations in which the classic no-tension approach leads to unsafe results.

'r

400 m

52.3 m -J.

Fig.9. Geometry of the double curvature arch dam considered in the example: (a) plan and elevation view, (b) central cross section (dimensions in meters)

Fracture Mechanics Applied to Concrete

199

The practical use of LEFM to study fracture of dams was delayed until the development of numerical tools capable of modeling the crack evolution in a three-dimensional structure. As an example, the analysis of a cracked double-curvature arch dam is presented. The details of the procedure can be found in [57]. The dimensions of the arch dam are indicated in Fig.9. Three hundred and eighty 20-nodded isoparametrical brick elements were used in the finite element discretization, giving a total of 2167 nodes. Both the dam and the foundation were modeled. In every cross-section of the finite element mesh, the foundation is modeled to a depth equal to the height of the dam. All the materials were assumed to behave in a linear elastic fashion. Concrete elastic modulus and density were 40 GPa and 2465 Kg/m 3. The elastic modulus of the foundation was assumed to increase with depth. Thus, the elastic modulus at the surface of the left abutment was 4 GPa whereas it was 7 GPa at the surface of the right abutment. At the bottom of the foundation, values of 13 GPa and 25 GPa were used for the right and left abutments, respectively. The forces considered in the analysis were the weight of the concrete and the hydrostatic pressure of the water in the reservoir.

Fig. 10. Initial crack configuration of the arch dam (crack face is shaded)

Fig. 11. Final crack configuration (crack face is shaded)

M. ELICES, J. PLANAS, G.V. GUINEA

200

A simulation was performed of a surface crack nucleated on the dam's upstream face. The initial crack configuration is illustrated in Fig. 10. The crack was positioned in a tilted orientation with respect to the geometry of the dam, and therefore inclined with respect to the local stress field. The final crack configuration is illustrated in Fig. 11. Five propagation steps were performed in this analysis. The history of stress intensity factors during the crack propagation is shown in Fig.12 which shows the evolution of the mode II stress intensity factors. In the initial crack configuration, the KII values change sign along the crack front. Because the crack front is allowed to turn, these factors reverse the sign, showing a tendency to compensate. As the crack continues to propagate, the mode II stress intensity factors along the crack front decrease, becoming negligible after the fourth crack propagation step. The mode I stress intensity factor increases steadily along the crack front during crack propagation. As the crack reaches the downstream face, KI, tends to be maximum at the crack front points located on the upstream face of the dam, showing the tendency of the crack to spread along this face.

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NORMALIZED POSITION ALONG CRACK FRONT Fig. 12. History of stress intensity factors

Although there is a long way to go before the three-dimensional analysis can be routinely applied in the design and evaluation of dams, the interest of the dam engineering community in getting more accurate information and the advances in computer graphics make it reasonable to expect that full three-dimensional analysis of crack evolution in concrete dams will become commonplace in the near future [43]. In the meanwhile, LEFM techniques are now widely used to analyze practical two-dimensional configurations for gravity dams [58, 62].

201

Fracture Mechanics Applied to Concrete

APPLICATIONS TO LIGHTLY REINFORCED CONCRETE BEAMS The transition from brittle to ductile behavior of a Lightly Reinforced Concrete (LRC) beam is a matter of current research in many laboratories and has recently been addressed by an ESIS committee [63]. The reason behind this is to analyze design criteria focused on avoiding brittle structural elements within concrete structures. The cohesive crack model has been used to analyze lightly reinforced beams in three-point bending [64-66]. All the analyses so far simplify the problem by assuming that a single cohesive crack forms in the central cross section while the concrete in the bulk behaves elastically and the steel is elastic-perfectly plastic. The various analyses differ in the computational method and in the way they incorporate the effect of the reinforcement. Hededal and Kroon [64] consider the classical load-displacement curve which is obtained for pullout from a rigid half-space. The action of the steel on the concrete is introduced as a force concentrated at the surface of the cohesive crack and treated as a cohesive force with a load-crack opening curve as deduced from the pullout test. The theoretical predictions compare quite realistically with their experimental results as shown in Fig.13. In making the predictions, Hededal and Kroon use material parameters determined from independent experiments, except for the bond strength which they select in each case to give a good fit of the postpeak values. The softening curve for concrete is assumed to be bilinear and is determined from tests on notched plain concrete specimens. The steel bars are threaded bars rather than conventional reinforcing steel bars. The ultimate load and the apparent elastic modulus are determined from tensile tests. Note that Hededal and Kroon use the product of the bond shear strength, Tc, and the perimeter of the reinforcement, Ps, to characterize the bond strength; Vc Ps is the shear force per unit length of reinforcement.

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202

M. ELICES, J. PLANAS, G.V. GUINEA

Ls/2 ~

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Fig. 14. Approximations analyzed by Ruiz, Elices and Planas [65, 66]: (a) concentrated forces on the crack faces; (b) concentrated forces at the center of gravity of the bond stresses; (c) distributed bond stresses.

Ruiz, Elices and Planas [65, 66] used a different numerical approach which incorporates the effect of the reinforcement by means of internal stresses. This allows the steel-concrete interaction to be located within the concrete rather than at the surface. Three options, depicted in Fig. 14, were considered. The analysis confirmed Hawkins and Hjorsetet's conclusion that perfect adherence implies a very sharp high peak [67]. However, it also turned out that this peak depends strongly on the width (diameter) of the reinforcement or, if the steel force is concentrated at a node, on the width of the elements used in the computations. The reason is that in this approach, the steel force is modeled as a nodal force, which means that the computational procedure smears this force roughly over an element width, and thus one never deals with a concentrated force but with a distributed force; if the force were really concentrated at a point, the compliance would be infinite and the peak would decrease. This model was successfully used to describe the tests on microconcrete performed by Ruiz et al. as illustrated in Fig l5. A remarkable fact is that all the parameters required to make the predictions were determined by independent tests. In particular, the bond strength "re was determined from pullout tests. A much better fit would have been achieved if the value of ~'c had been adequately selected for each test.

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204

M. ELICES, J. PLANAS, G.V. GUINEA

APPLICATIONS TO FIBER REINFORCED CEMENT AND CONCRETE Nowadays it is becoming clear that the use of fibres in cement based composites has a significant toughening effect, as clearly shown in Fig.16. With low values of fibre volume, Vf, the enhanced toughness, as measured by the area under the load-displacement curve, is much higher than the increase in the strength properties for which the fibres were originally intended in the early days of fibre reinforced concrete (FRC). With high values of Vf, a large increase of toughness and strength is recorded. This result is important since the recognition that structural behaviour is controlled not only by the compressive strength of concrete, but also by the independent material parameter fracture energy GF, a measure of the material toughness.

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Fracture macromode ls To simulate structural response in FRC by explicitly accounting for crack development in the structure, numerical tools are needed--mainly in the form of finite element codes--. The successful utilization of these tools requires input information on the material toughness.

205

Fracture Mechanics Applied to Concrete

It appears that the wake process, which dominates the energy absorption during the fracture process in these materials, can be well characterized by tensile stress versus crack opening relationships. In this respect, cohesive process zone models for cracks in FRC are briefly described in accordance with the spirit of this review, and because, to the authors' knowledge, they are the most promising ones and bear the relevant information on toughness. Fig.17 displays three sketches of the stress profile along the process zone: Fig.17a is for the cohesive process zone, as discussed before in this paper, and proved applicable to plain concrete. Fig.17b is for a brittle material bridged with fibres, according to a model by Cox and Marshall [68]. Here the height of the process region is no longer zero and stress is allowed to drop in front of the crack tip. The zero value is because the matrix is supposed to be totally brittle. Fig.17c is intended for FRC, according to a model due to Li [69].Again, the height of the process region is not negligible but the stress does not drop to zero at the crack tip because it is assumed that the cement paste has some toughness against crack growth. In practice, difficulties arise in having reliable softening functions. In the above mentioned references, and particularly in [69], some recipes are given to measure the pertinent softening function from samples of the FRC under consideration. Very often, the standard cohesive process zone model suffices and the softening curve can be obtained using the techniques reported in previous sections.

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M. ELICES, J. PLANAS, G.V. GUINEA

206

Fracture micromodels In parallel with fracture macromodels, and with equal significance, are fracture micromodels of toughening mechanisms. This knowledge will allow "engineering" the toughness property of the material. To achieve this objective mtailoring of the fibre, matrix and interface-- requires knowledge of how these three phases interact in the composite such that large amount of energy is absorbed during the fracture process. In plain concrete, crack advance may include processes such as microcracking, crack tip deflection, crack front trapping, aggregate bridging and aggregate rupture, some of which are responsible for the presence of the cohesive traction in the crack wake. In fibre reinforced concrete, additional fibre bridging mechanisms contribute to energy dissipation, i.e.; fibre-matrix interface debonding and friction sliding. Other interactions between fibre and matrix occur when fibres are randomly oriented, such as fibre yielding at bends [70], matrix spalling and snubbing [71 ]. The combined effect of aggregates and fibres acting in the crack wake was considered by Li [69] who measured and computed the softening curves of steel and polypropylene FRC's, as shown in Fig.18. The modeling combines the concepts of aggregate tension-softening (Fig.17a) and fibre bridging (Fig.17b) with further additional refinements. 8 ~"

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Fracture Mechanics Applied to Concrete

207

When fibres are brittle, as is the case of carbon fibres, the effect of bending actually leads to fibre failure at a lower bridging load than in the aligned fibre case. This cuts short the debonding and pull-out proces'ses, and leads to lower energy consumed in this bridging zone. Based on micromechanical models a novel FRC has been designed [72, 73] in which strain hardening occurs despite a relatively low fibre volume fraction (typically less than 2%). This material was called Engineered Cementitious Composite (ECC). An enlarged process region is responsible for a significant amount of energy absorption, in addition to the wake process common to all FRC's. The order of magnitude of GF is 0.01 kJ/m2, 0.1 kJ/m2, several kJ/m2, and several tens of kJ/m2 for cement, concrete, FRC and EEC, respectively. The toughness of the ECC material is competitive with some metallic materials such as aluminum alloys.

Final remarks and some examples of applications From the above discussion, it can be seen that significant advances in concrete structural performance can be gained by our increasing ability to predict their behaviour accurately via modern concrete fracture mechanics, and the emerging science and technology of systematically tailoring the concrete microstructure for enhanced fracture and cracking resistance. Since the 90' s, numerous applications of Fracture Mechanics to FRC have thrived. A feeling of recent developments can be obtained by glancing through the proceedings of the third conference on Fracture Mechanics of Concrete and concrete Structures [74]. A new design provision for FRC tunnel lining was published in Japan [75]. This is the first design provision to be fully based on the concept of fracture mechanics applied to concrete. To estimate the maximum resultant forces on the critical cross section, the existence of a crack and transmitted stresses by fibres were considered. An analysis of this procedure, together with some suggested improvements, can be seen in [76]. As another example, Maalej and Li [72] studied a reinforced concrete beam designed to limit the COD in the concrete cover ( replaced by engineered FRC) when subjected to flexural loads. The COD restriction was aimed at increasing durability of this beam element under the attack of harmful chemical substances by limiting diffusion of these substances into the beam. The design ensures that the COD of the FRC cover would not reach a critical value, CODc, even at the structural ultimate state of the beam. Furthermore, it is necessary to tailor the composite so that the FRC ultimate strain exceeds the maximum strain expected in the cover of the beam, so that strain localization would not occur. Further extensions of this model and applications to FRC cracking appear in a recent paper by Kanda, Lin and Li [77]. ACKNOWLEDGMENTS The authors gratefully acknowledge support for this research provided by the Spanish Comisi6n Interministerial de Ciencia y Tecnologfa (CICYT), under grants MAT97-1022 and MAT971007-C02-02.

208

M. ELICES, J. PLANAS, G.V. GUINEA

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211

F A T I G U E AND F R A C T U R E OF STEEL B R I D G E S PEDRO ALBRECHT

Department of Civil Engineering, University of Maryland College Park, Maryland 20742, USA WILLIAM WRIGHT

Turner-Fairbank Highway Research Center, Federal Highway Administration 6300 Georgetown Pike, McLean, Virginia, 22101 USA ABSTRACT This paper summarizes important findings, made over the last 15 years, on fatigue and fracture behavior of steel bridges. Foremost in the area of fatigue is the increased understanding that has led to (1) guidelines for preventing deformation-induced cracks, and (2) the design of steel bridges for variable-amplitude fatigue. In the area of fracture, tougher and more ductile modern steels, adopted by ASTM in its specifications during the 1990s, are beginning to replace the conventional high-strength low-alloy steels of the 1960s. Future gains in ductility may make it possible to some day characterize the fracture resistance of bridge members in terms of yielding of the net section instead of crack tip singularity parameters. KEYWORDS Steel bridges, highway, fatigue cracking, variable amplitude loading, fracture toughness, stress intensity factors, brittle fracture, ductile fracture. INTRODUCTION By the year 1985 there were "Hundreds of Bridges--Thousands of Cracks" [ 1] in the United States and by now there are many more as steel bridges in service are aging under ever increasing traffic. Fortunately, only one bridge collapse has caused catastrophic loss of human life since the 1950's. This bridge on US Highway 35 over the Ohio River at Point Pleasant, West Virginia, had three spans 116, 213 and 116 m long. The structural system consisted of trusses suspended from towers by eyebar chains. Opened to traffic in 1928, the bridge collapsed suddenly and without warning in December 1967. The brittle fracture occurred at a very small 3 mm deep by 7 mm long part-through crack in the net section of an eyebar head. After one suspension chain broke, the second chain followed as it could not support on its own the entire weight of the bridge. Thirty-seven vehicles fell onto the shore and into river, and 46 people were killed. An identical bridge located 110 km upstream was dismantled in 1969 because the eyebar joints could not be inspected. The fracture toughness of the eyebar made of heat-treated rolled carbon steel 1060 was estimated from Charpy data to be 44 M P a ~ at -1 ~ which was the temperature at the time of collapse. The eyebar shank had a yield strength of 545 MPa - - a high value even by present s t a n d a r d s - and 21% elongation in 50 mm gage length.

212

P. ALBRECHT, W. WRIGHT A

A

ELEVATION

SECTION A

Fig. ]. Interstate 1-95 Bridge over Potomac River, Washington, D.C. The overall good performance of steel bridges, despite the large number of fatigue cracks, can be attributed mainly to the US practice of building bridges that have inherent redundancy and multiple load paths. By far the largest number of cracks found in highway bridges are those induced by distortion of members and bridge cross sections. Other causes of fatigue cracking are secondary stresses, weld defects and types of details whose fatigue strength had not previously been tested. Examples of such cracks are described below. CAUSES OF FATIGUE CRACKING Cracks induced by distortion o f cross section Vertical stiffeners. Distortion-induced cracks occur mostly at vertical stiffeners that are welded to the webs of I-girders or box girders and serve as connection plates for diaphragms, cross bracing and floor beams. When the stiffener does not extend along the full depth of the web and is not attached to the flanges, the web in the gap between a stiffener end and the adjacent flange bends out of plane with each truck crossing. The crack initiates at the end of the stiffener or along the toe of the weld fillet weld that connects the web to the flange. It propagates in a horizontal plane through the thickness of the web and then as a through thickness crack that eventually curls away from the adjacent flange. Thus, imminent fracture is unlikely.

Two examples illustrate web gap cracks. The first example comes from the 6-lane bridge on Interstate 1-95 over the Potomac River south of Washington, D.C. The structural system consists of four longitudinal plate girders, transverse floor beams, and longitudinal stringers spanning between floor beams. Frown-shaped cracks were found at the top of stiffeners welded to plate girder webs (Fig. 1, Section A) and floor beam webs (Fig. 1, Elevation). These cracks were caused by end rotation of the simple supports of floor beams and stringers which, in turn, bent the webs out of their planes in the gaps. The second example is taken from a 3-span-continuous, double-box girder bridge on southbound Interstate 1-83 to east-bound Interstate 1-695 in Baltimore, Maryland. Stiffeners were welded only to the web and stopped short of both top and bottom flanges of the boxes.

Fatigue and Fracture of Steel Bridges

213

A 100 X 100 X 12 ....... ,,.._._.

CRACK

DIAPHRAGM

I

", ~

!

50 X 600 FLANGE

WEB

STIFFENER

%' ELEVATION

N

/

~_1 A

SECTION A

Fig. 2. Southbound Interstate 1-95 Bridge to Westbound Interstate 1-695, Baltimore, Maryland K-bracing diaphragms consisting of angle members were welded to every fifth stiffener on each web. Cracks induced by distortion of the cross section (Fig. 2, Elevation) formed in both the top and bottom gaps between stiffener and flange (Fig. 2, Section A). Welding stiffeners to flanges eliminates the problem of web gap cracking. And it does not lead to cracking of the tension flange because, under in-plane bending stresses, stiffeners welded to the flange have the same fatigue strength as stiffeners welded to the web [2, 3].

Horizontal gusset plates. Web gaps can also crack at the intersection of a horizontal gusset plate for lateral bracing and a vertical stiffener serving as a connection plate for diaphragm members. In this case, the web gap is horizontal and the crack initiates and propagates along the vertical stiffener-to-web weld towards the flange, in a vertical plane. Fig. 3 shows such a detail at the end of the 3-span-continuous girder bridge on Interstate 1-70 over the Patapsco River west of Baltimore, Maryland. When the detail is located in a region of large bending moment, the crack will propagate down the web and into the flange, causing the girder to fracture. This was observed in the 4-spancontinuous delta-frame twin bridges on Interstate 64 over Maury River northwest of Lexington, Virginia. At one detail, the crack severed the tension flange and extended to the top of the 1.8 m deep web. Three features provided redundant paths for redistribution of the load to adjacent girders and thus prevented bridge collapse: continuous spans, multiple girders, and diaphragms spaced 6.1 m apart along the 256.2-m length [4].

Cracks induced by secondary stresses Cracks can initiate as a result of secondary stresses not normally accounted for in the design. For example, connections of floor beams bolted to web stiffeners are often semi-rigid and transfer some moment in addition to shear. One such case is seen in Fig. 1, Elevation. The top and bottom flanges of the floor beam were coped so that the web could be connected to the

214

P. ALBRECHT, W. WRIGHT

;_ GUSSET PLATE

L A

~

LATE;RAL BRACING

DIAPHRAGM

PLAN

/-

STIFFENER WEB

GUSS E T - - ~ _ ' . . . . . . I g PLATE [ I

i

"111

l~ , I

FLANGE

stiffener. Cracks driven by the secondary bending stresses initiated at the inside corner of both copes. In another case of secondary stresses, the twin bridges on Louisiana Highway LA 1 over the Mississippi River were connected with one-panel K-truss diaphragms whose only purpose was to support a cover over the gap between the two bridges. Relative displacement of the bridges induced secondary bending stresses in the diaphragm members. As a result, cracks initiated at the coped flange of the tee-shaped chord members, a condition similar to the cracks at the coped floor beam flanges in Fig. 1, Elevation.

Cracks induced by weld defects All too often fatigue cracks initiate at welds that were not meant to resist stress. One example is the longitudinal stiffener I I welded to the lower tension portion of the SECTION A web to balance, for aesthetic reasons, the stiffener that was welded to the upper Fig. 3. Interstate 1-70 Bridge over Patapsco River compression portion to prevent buckling West of Baltimore, Maryland of the web (Fig. 4). In the Interstate 1-95 bridge over Brandywine Creek in Wilmington, Delaware, a crack A initiated at a flawed welded splice ~ and propagated across the stiffener and into the web. By the =. time the crack was detected, it had propagated down the web and -.---Girder across the entire tension flange as well as up the web to the --Longitudinol Stiffener longitudinal stiffener in --~ compression. Because the longitudinal stiffener was non~ structural, the quality of the SECTION A groove weld had not been ELEVATION controlled properly. The stiffener A is an integral part of the girder' s Fig. 4. Fatigue Crack Initiation at Groove Weld of cross section and, thus, resists Longitudinal Stiffener in Tension Portion of Web bending stresses.

-7

f

Load-bearing welds can also be flawed when they are not properly made. In one such example, a girder of the Interstate 1-79 bridge over the Ohio River northwest of Pittsburgh,

Fatigueand Fractureof SteelBridges

215

Pennsylvania, fractured from a flaw in the electroslag groove weld of the tension flange. The fracture extended from the tension flange to the compression flange. Luckily, redundancy in the structural system prevented bridge collapse. The crack was found by a boat captain sailing under the bridge.

REQUIRED FATIGUE STRENGTH In the load and resistance factor design method, the fatigue limit state says that the required fatigue strength described hereafter can not exceed the design fatigue strength described in the next section. ?'Af_< A F

(1)

According to the Bridge Design Specifications [5], the required fatigue strength consists of the stress range at a detail, Af , and the number of single truck crossings during the service life of the bridge. The stress range is defined as the difference between the maximum and minimum stresses. It is calculated in beams with the flexure formula, using the moment range M r , the moment of inertia of the s e c t i o n / , and the distance y from the elastic neutral axis to the point on the section where the crack would initiate: Af =

M

r

(2)

The axle weights and spacings of the design truck for static loading are shown in Fig. 5. For fatigue design, one design truck with a constant spacing of 9 m between the 145-kN axles is positioned on the bridge so as to produce the largest stress range. A dynamic load allowance of 15% is added to the stress range. Bridges are designed for fatigue based on the damage induced by the many different truck weights, not just the 325-kN weight of the design truck of Fig. 5. The weight distribution chosen for this purpose comes from a study by Snyder et al [6] in which a total of 27,513 trucks were weighed on 31 Interstate, U.S., and State route bridges located in seven states. Fig. 6 shows the distribution of gross truck weights ranging from 25 to 890 kN. Automobiles were excluded. Truck weights were distributed as follows: 99.47 % from 25-445 kN, 0.38 % from 445-667 kN, and 0.05 % from 667-890 kN.

35 kN 145 kN 145 kN L 4.3m ~l~ 4.3 toS.0m .I Fig. 5. Axle Weight and Spacings of Design Truck

For equal numbers of trucks, the equivalent truck weight, hereafter called the fatigue truck weight, is defined as the weight that produces the same amount of fatigue damage as is done by all trucks of the distribution, assuming that truck weights are proportional to stress ranges. It is calculated from: = I~rlimim) We

En i

1/m

(3)

216

P. ALBRECHT, W. WRIGHT t5

27, 513 Lvucks GVIdmax = 890 kN i

~10

GVWe " 239 kN

r...) Z iii :::) LIJ

rr" LL

5

0

0

20

40

60

80

GROSS VEHICLE WEIGHT. GVW/GVWmax (%)

100

Fig. 6. Histogram of Gross Truck Weights where W i = i-th gross vehicle weight n i = number of tracks of weight W~.

m = 3 = rounded value of slope of log-log S-N lines for welded details The equivalent GVW for the 27,513 trucks is W = 239 kN. The load factor for fatigue in the Bridge Design Specifications, y in Eq. 1, is then given by: y-

Wf

Wt

-

239 35+145 +145

=0.75

(4)

where W = W = weight of fatigue design truck (Eq. 3) ~fst = weight of design truck for static loading (Fig. 5) The Bridge Design Specification, in Article 6.5.1.2.2 and Table 3.4.1-1, incorrectly represents y = 0.75 as being the load factor. In reality it is the weight ratio of the fatigue truck to that of the static load truck (Eq. 4). To determine the load factor one would have to analyze the variability of the fatigue track weights, Wf, for all 31 bridges. This was not done. In the Commentary to the Bridge Design Specifications, Article C6.6.1.2.2, the load factor is acknowledged to be 1.0. It is noted that bridges are designed for fatigue using a single truck in one lane; they are designed for static loading using one truck in each lane. The frequency of the fatigue design truck is taken as the average daily truck traffic on a single lane. For a typical, 50 m long, short-span bridge on an urban Interstate highway with three lanes in each direction, the required fatigue life for 75 years of service is:

Fatigue and Fracture of Steel Bridges N -- ADTTsL "p" 365 "Ny = 9,000-0.85" 365" 75 = 209,400,000 trucks

217

(5)

where ADTTsL = average daily truck traffic on a single lane p = reduction factor for number of lanes available to trucks Ny = number of years of service DESIGN FATIGUE STRENGTH The fatigue strength of bridges is mainly a function of detail type, stress range and number of loading cycles. Maximum stress and steel type are secondary variables and, thus, are excluded from the design. The strength of all detail types included in the specifications was determined from laboratory tests of beams that were subjected to constant amplitude stress ranges. The log-log linear S-N line, for a set of data, leads to the following expression for mean fatigue life: lO b

N -

(6)

~Xf m

where N = number of cycles to failure b = intercept of log-linear mean S-N line m = slope of log-linear mean S-N line Af = stress range The Bridge Design Specifications set the design fatigue strength, AFn, at two standard deviations, 2s, on fatigue life to the left of the mean S-N line, giving:

N-

=

(7)

/lm

or, in terms of stress range:

AF

10 b-2s

N

=

_> 0.5 A F r H

(8)

where s = standard deviation on log of fatigue life m ~ 3 = rounded slope of log-log linear S-N lines; actual slopes vary from m = 3.1 to 3.4 [7] A = detail constant = intercept of design S-N line at A F - 1 M P a [5] A F = design fatigue strength AFrH = fatigue limit for constant amplitude (CA) stress range cycles 0.5 A F r H = fatigue limit for variable amplitude (VA) stress range cycles All detail types are assigned to one of eight categories in the Bridge Design Specifications: A, B, B', C, C', D, E and E' [5]. Fig. 7 shows the seven lines, each cut off at the VA fatigue limit, which is located at 0.5 AFr/_/.When the required fatigue strength is equal to or lower than the VA fatigue limit, cracks do not initiate and the detail's fatigue life becomes infinite. S-N lines for categories C and C' have the same detail constant, A; S-N lines for categories B' and C' have the same VA fatigue limit.

218

P. ALBRECHT, W. WRIGHT 5OO

500

04

E

E 200 z LU 100

B

5o

E E'

(9 Z

200 m

AB-

w m

D

20

E

10

S"-

10 s

106

50

C

ffl I-ffl

100

107

108

20 10

109

NUMBER OF CYCLES Fig. 7. Design Fatigue Strength of Steel Bridge Details

The term q) = 10 -2s/m in the numerator of Eq. 8 is the resistance factor on fatigue strength (stress range), which varies with standard deviation and slope from a high of: s = 0.221

m = 3.178

q) - 0.73

(9)

m - 3.095

q~ - 0.86

(10)

for category A plain rolled I-beams to: s = 0.101

for category E cover plates welded to the flange of an I-beam [7]. Instead of specifying separate resistance factors, one for each category, all were incorporated in the respective detail constants A, Eq. 8.

VARIABLE-AMPLITUDE FATIGUE TEST DATA Until the mid-1970s, studies on fatigue of steel bridge details were performed under CA stress range cycling. As a result, the design curves and fatigue limits reported in the literature, and later incorporated in the specifications, are strictly valid only for CA stress range cycling. Given that bridges are subjected to VA stress ranges, it is important to understand the relationship between CA and VA cycling. To this end, the findings from eight studies on VA fatigue are summarized below.

Definition of Long-Life In examining VA fatigue test data, it is useful to distinguish between tests in which the specimens failed in the finite-life regime from those that failed in the infinite-life regime. For the purpose of this review, the so-called transition life, Ntr, that separates the two regimes is taken as the number of cycles at the intersection of the design S-N line with its applicable VA fatigue limit. As the fatigue strength of a detail decreases, the transition life increases (Fig. 7). Hereafter, a specimen is said to have a long life only when it fails at a number of cycles greater than the transition life, which is a prerequisite for determining the shape of the transition between the two regimes. Knowing the VA fatigue limit of a detail, 0.5 AFT/4, and its constant, A, Eq. 8 is solved for the transition lives, Ntr, of the eight detail categories, in

Fatigue and Fracture of Steel Bridges

219

millions of cycles: Am14.6, Bm23.6, B'--28.3, C~35.1, C'--20.4, D~51.2, E--97.0, and E'~178.5x106. To determine the effect of the CA fatigue limit on VA fatigue strength, specimens must be tested to at least 5Ntr, for example: about 102• 106 for category C' transverse stiffeners and 892x 106 for category E' thick coverplates. Only then can one be assured that the VA fatigue limit is being approached. A so-called long-life factor is used in reviewing previous work to assess how far the specimens were cycled into the infinite-life regime. This factor is calculated as the largest number of cycles applied on any specimen of a series of tests divided by the applicable transition life for the detail type, N/Ntr

Yamada and Albrecht [8] Proceeding now with the literature review, Yamada and Albrecht examined the sequence effect of blocks in a VA stress-range spectrum similar to that recorded on the girders of a Maryland bridge. They tested two flange details with that spectrum m a welded cover plate with the transverse end weld ground to a 1:3 slope, and a groove-welded flange-thickness transition ground to a 1:4 slope. Control specimens were also tested under CA fatigue. As Table 1 shows, all tests were performed in the finite-life regime, N/Ntr < 1. It was found that the order of the nine blocks into which the 1,000-cycle spectrum was subdivided had no effect on the VA fatigue life. Also, the VA fatigue lives correlated well with the CA fatigue lives when the former were plotted in terms of a so-called equivalent stress range which, for equal number of cycles, causes the same damage as the stress ranges of the VA spectrum. This value was calculated as the root-mean-cube (RMC) stress range of all cycles:

I~'niAfi3 ) 1/3

Afe=

En--~

(11)

It can be shown that the equivalent stress range concept and Miner' s rule are the same when both are calculated with the same exponent, in this case m = 3 [9].

Schilling, Klippstein, Barsom, and Blake [ 10] Schilling et al investigated the effect of minimum stress, load history, and type of steel on VA fatigue strength. They tested 58 category D cover-plated tensile specimens, 59 category B welded beams, and 153 category E cover-plated beams with the welds laid in different sequences. The specimens were cycled under CA stress range as well as VA stress range based on wide-band, medium-band, and narrow-band Rayleigh spectra. Albrecht and Rubeiz' [ 11 ] analysis of the data reported by Schilling et al showed that the VA data correlated well with the CA data when plotted in terms of the RMC stress range, Eq. 1, recommended by Yamada and Albrecht [8]. Band width and minimum stress had a statistically insignificant effect on fatigue strength. All tests were conducted well within the finite life regime, N/Ntr _< 1.07 (Table 1). The longest tests were ended at 104x 106 cycles before cracks had initiated, hereafter called a

runout. Clearly, tests of beam specimens with detail types of low fatigue strength, such as those of categories D, E and E', are unsuitable for determining the transition behavior from the finitelife to the infinite-life regimes. Because beams deflect more than tensile specimens elongate, the former must be tested at much lower cyclic frequencies. Furthermore, low fatigue strength details have very long transition lives. Both factors increase the testing time of a beam with

P. ALBRECHT, W. WRIGHT

220

category E' details by a factor of about 10 as compared, for example, with tensile specimens with a category C detail. Indeed, all tests of beams with category E and E' details fell in the finite-life regime, N/Nt,. _< 1.07, and provided no insight into the transition behavior (Table 1).

Table 1. Summary of Variable-Amplitude Long-Life Fatigue Tests, in Chronological Order Ref. Type of Detail Category Longest Transition Long-life Life Test Life Factor

(• [8]

[10]

[12]

6)

(•

Ntr 6)

N/Ntr

m Beam with coverplate welded to flanges, ends ground to slope of 1:3 m Plate girder with groove-welded flange thickness transition

C

5.1

35.1

0.15

C

4.0

35.1

0.11

m Tensile specimen with one 14x50• 100 mm welded attachment m Welded beam, web-to-flange weld m Rolled beam with one 14•215 mm welded coverplate

D

26.0

51.2

0.51

B E

10.0 104

23.6 97.0

0.42 1.07

C' C'

26.7 125

20.4 20.4

1.31 6.13

E

415

97.0

4.28

E'

112

178.5

0.63

,

150

178.5

0.84

B

15.5

23.6

0.66

C' E' E'

120 120 120

26.7 178.5 178.5

4.50 0.62 0.62

B

294

23.6

12.5

C'

250

20.4

12.3

C'

252

20.4

12.4

Tensile specimen with one pair of transverse stiffeners: m automatically welded m manually welded

[15]

m Tensile specimen with two (?)x(?)x 150 mm gusset plates normal to plate

[16]

Rolled beam, each with: m three 25• 100• mm gusset plates welded to web m two 25 • 115 • 11 oo mm welded coverplates

[17]

m Tensile specimen with 2 transverse stiffeners, extra high-quality fabrication

[18]

Welded beam, each with: m three transverse stiffeners m six 25x(?)x300 mm web gusset pl. m two 25• 11 oo mm coverplates

[14]

N

m Tensile specimen with 2 transverse stiffeners, extra high-quality fabrication m Tensile specimen with two transverse stiffeners, manually welded m Tensile specimen with two 7•215 100 mm plates welded flat

E

Fatigue and Fracture of Steel Bridges

221

Albrecht and Friedland [ 12] Albrecht and Friedland were the first to test specimens under VA cycling well beyond the transition life of a typical welded bridge detail (N/Nt~ = 6.13 in Table 1). Only 2.8 % of the stress ranges in the longest life test were greater than the CA fatigue limit. Eighty-three tensile specimens with transverse stiffeners were subjected to VA loading proportional to the mean of 106 stress-range histograms of truck traffic recorded on 29 bridges in 8 states [ 13]. It was concluded that the VA fatigue limit lies below the CA fatigue limit by a factor equal to the equivalent stress range divided by the highest stress range in the spectrum. In other words, the VA fatigue limit is reached when the highest stress range is equal to the CA fatigue limit. Assuming that only the stress ranges higher than the fatigue limit contribute to crack growth, a numerical model was proposed for predicting fatigue life. This so-called equivalent stress range model overestimates VA fatigue life because, as the crack propagates, increasingly smaller stress ranges in combination with longer cracks produce ranges of the stress intensity factor that are greater than the crack growth rate threshold, A K i > AKTH. Albrecht et al [ 14] later derived the following closed-form equation for predicting the VA fatigue life with the equivalent stress range model: N--

10 b k

E~iAfi i=a

m

(12)

where a = index for stress range equal to CA fatigue limit k = index for highest stress range in spectrum

Tilly and Nunn [ 15] Tilly and Nunn tested 14 tensile specimens with category E longitudinal gusset plates under CA cycling and 7 specimens under VA cycling corresponding to a Rayleigh spectrum. The tests were performed at a frequency of 150 Hz using a resonant fatigue machine. With fatigue lives of up to 415 • 106 cycles, these tests are the longest on record and the only ones carried out into the infinite-life regime of category D, E and E' details tested in any study. The long-life factor was N/Ntr <__4.28 (Table 1). CA and VA data correlated well, and the results confirmed the concept of a VA fatigue limit [ 12]. Fisher, Mertz, and Zhong [ 16] Fisher et al tested eight beams under VA loading corresponding to a Rayleigh distribution. Each beam had three 25 mm thick web gusset plates and two 25 mm thick flange cover plates of category E' fatigue strength. Although the tests were carried out to 150 million cycles of loading, the data fell in a wide band along the sloped S-N line of the finite-life regime well short of the transition life, N/Ntr = 0.63 and 0.84 (Table 1). Despite stating that both details had category E' fatigue strength, Fisher et al calculated the number of stress range cycles that exceeded the CA fatigue limit using the value for category E B AFrH -- 34.5 M P a in the 1983 s p e c i f i c a t i o n thus obtaining 0.1 to 11.72 % of the 1,024-cycle spectrum. Albrecht and Rubeiz [ 11 ] reanalyzed the data and found much higher values of 13 to 99 % when the correct CA fatigue limit for category E' is used B AFT/_/ = 17.9 MPa. Although attaching many details to a beam saves testing time, the presence of multiple, closely spaced details precludes testing each detail to failure. Cracks were repaired as soon as they were found to keep the section from fracturing and ending the test before data could be gathered at the

222

P. ALBRECHT, W. WRIGHT

remaining details. This had two disadvantages. First, the tests of most details were ended before they could reach their full fatigue lives. Second, the repair of web gussets - - consisting of drilling a hole at both crack tips u diverted the stress flow around the repair, partially shielded the adjacent gusset plate ends from stress and, thus, increased fatigue life. Neither effect was quantified. This study provided useful information on arresting short cracks.

Klippstein and Schilling [ 17] Klippstein and Schilling performed an exploratory fatigue study with a transverse stiffener detail that had ideally contoured weld toes of low stress concentration. They tested 27 A572 steel tensile specimens under CA and 10 under a VA random-sequence stress-range spectrum corresponding to a truncated Rayleigh distribution. The specimens tested under CA had fatigue strength of Category B' and CA fatigue limit of category B. All tests were conducted in the finite-life regime, N/Ntr = 0.66 (Table 1). The CA and VA fatigue test data correlated well.

Fisher, Nussbaumer, Keating and Yen [18] Following up on their earlier study [ 16], Fisher et al tested eight more beams. Each beam had 2 category E' cover-plate ends, 12 category E' web attachment ends, and 3 category C' transverse stiffeners. As in the earlier study, the beams were subjected to VA loading corresponding to a Rayleigh distribution. The beams were tested up to 120 million cycles. Cracks grew through the thickness of either the web or flange at one of 16 coverplate ends, 20 of 96 web attachment ends, and 2 of 24 transverse stiffeners. Of the remaining details, 86 were runouts, 23 had part-through cracks that were detected visually or destructively at the end of the test, and 4 were subjected to out-of-plane bending. The long-life factors were N/Ntr = 0.62 for the gusset plates and coverplates, and N/Ntr = 4.50 for the transverse stiffeners. Only the two data points for stiffeners provided information on long-life behavior. But unlike the earlier study [ 16], one overload was applied periodically on some beams and two overloads on other beams. From the three spectra shown in [ 18], the ratio of overload stress range to RMC stress range is found to be 2.56. Judging by the results of previous S-N tests [ 14, 19] and many crack growth rate tests reported in the literature, it appears that the periodic overloads applied in the tests by Fisher et al delayed crack growth and, thus, prolonged fatigue life. Furthermore, as already described above for the data from [ 16], arresting cracks shortens fatigue life and partially shields adjacent details from the full stress range. These three life-altering effects were not quantified, and the reported fatigue lives are thus unreliable. Details were not tested to failure. Unfortunately, despite great efforts, the tests provided little information on transition behavior.

Albrecht, Lu, Jung, Liu and Cheng [14] Albrecht et al reported fatigue test data for 192 tensile specimens of the following types that were cycled under CA and VA stress ranges: transverse stiffeners of high-quality fabrication, manually welded transverse stiffeners, and manually welded 100 mm long attachments. Fig. 8 shows the data for the category C' transverse stiffeners. The data points from the CA tests are plotted with open square symbols, and those from the VA tests are plotted with solid triangular symbols. The VA tests were performed with a spectrum of stress ranges proportional to the histogram of gross truck weights, Fig. 6, from GVW/GVWmax = 12.5 to 75 %. Histogram bars above 60 % are too small to be visible. The VA fatigue lives plotted in Fig. 8, plus two more

Fatigue and Fracture of Steel Bridges

500

l lll i

i

I

, l llll

i

I

I

i lilt

I

i

i

E

E 200

Z

o~ CO UJ tr

rm

~u~

10

I

i

i

t ilil;

A 5 8 8 Steel Stiffener

-

i-I C.A., fmin = 3 M P a 9 V.A., Medium-tail, fmin = 14

,lJll

105

,

I

500 200

t c;',,ue L'm;'

100 50

_

20

Or)

I

Simplified M o d e l

tu 100 (9

50

i llil

Equivalent Stress Range Model

r

Z

I

223

V A Fatigue Limit ~be = 0.361

20

MPa

* I Jllll

I

10 6

a I J illll

I

i

I o lllll

10 7

I

I

I a lllll

10 8

10

10 9

NUMBER OF CYCLES

Fig. 8. Fatigue Strength of Manually Welded Transverse Stiffeners sets not shown here, are the longest beyond the transition life found in the literature, with N/Ntr - 12.3 (Table 1). All three sets reinforce the previous findings, that is" (1) VA and CA fatigue test data correlate well in the finite-life regime when the former are plotted in terms of the RMC stress range of the spectrum [ 10, 12, 14, 15, 17]. (2) The VA fatigue limit is located below the CA fatigue limit by a factor of equivalent stress range to highest stress range in the spectrum. In other words, when the highest stress range is at the level of the CA fatigue limit, the equivalent stress range of the spectrum is equal to the VA fatigue limit [ 12, 14]. (3) As an increasing number of VA stress ranges fall below the CA fatigue limit, the initially straight S-N line begins to curve and gradually approaches the VA fatigue limit. (4) The CA fatigue limit is unique for a given detail. But the position of the VA fatigue limit depends on the type of spectrum to which a structural detail is subjected.

FATIGUE LIFE PREDICTION IN INFINITE-LIFE REGIME The Bridge Design Specifications define the fatigue strength of a detail as a straight S-N line in the finite-life regime extending downwards to the VA fatigue limit of the infinite-life regime below which fatigue cracks do not initiate, Fig. 7. VA fatigue test data, on the other hand, show a gradual transition between the two regimens.

Equivalent Stress Range Model In a first attempt to model the gradual transition, Albrecht and Friedland [ 12] assumed that only those stress ranges of a spectrum that were higher than the CA fatigue limit propagated the crack. Albrecht et al [ 14] later derived the closed-form Eq. 12 for this equivalent stress range model, but the calculations remain tedious because the summation in the denominator must be re-calculated for all positions of the spectrum. The fatigue strength of the transverse stiffener detail, predicted with this model, is shown as a solid curve in Fig. 8. Its somewhat high position relative to the data in the infinite-life regime can be explained in terms of fracture mechanics.

P. ALBRECHT, W. WRIGHT

224

During the initial stages of growth, when the crack is still short, the combination of crack length and VA stress range produces only a few ranges of stress intensity factor greater than the threshold, AK > AKth. As the crack grows longer, more AK values exceed AKth. Accordingly, the behavior gradually changes from few to many stress ranges causing fatigue damage during the long life of the specimen. The error is not as large as one might expect because most of the life is spent growing the crack while it is short. Still the equivalent stress range model predicts fatigue life much better than does the straight-line extension. In summary, stress ranges smaller than the CA fatigue limit cause some damage, but not as much as the straight-line extension nor as little as the equivalent stress range model predicts.

Simplified Model Fatigue life prediction would be greatly simplified if the summation in the denominator of Eq. 12 could be avoided. An idea from the fracture mechanics literature yields an elegant simplification. In one of several available models, the gradual transition between the crack growth equation and the threshold value of the stress intensity factor range is given as

da n - C ( A K " - AKth ) dN

(13)

where

da/dN = crack growth rate a = crack length AK = stress intensity factor range AKth = threshold value of stress intensity factor range C, n = material constants The corresponding model for S-N data, herein called the simplified model, is then given by: lO b N

._.

A f m - (0.5 AFTH)m

(14)

where Afe = equivalent stress range of full spectrum. The simplified model, shown as a dashed curve, is compared in Fig. 8 with the straight-line extension and equivalent stress range models. The former is an upper-bound solution because it assumes that only stress ranges higher than the CA fatigue limit propagate the crack. The latter is a lower-bound solution because it assumes that all stress ranges propagate the crack. The simplified model lies between the two bounds and has the following advantages: (1) It best predicts the mean trend of the test data. (2) The closed-form Eq. 14 is valid in both the finite-life and infinite-life regimes. (3) The fatigue life is easily calculated since the equivalent stress range in Eq. 14 is that of the full spectrum and does not change with the position of the spectrum as is the case in the equivalent stress range model. Applying the simplified model to the equations of the Bridge Design Specifications gives: A N= A f 3 - (0.5 AFTH)3 (15)

225

Fatigue and Fracture of Steel Bridges 500

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NUMBER OF CYCLES Fig. 9. Comparison of Simplified Model With Design Fatigue Strength Eq. 15 is plotted with dashed curves in Fig. 9. Clearly, as A f approaches the VA fatigue limit, the simplified model predicts increasingly longer fatigue lives than does the straight-line model. In the author' s opinion, the straight-line extension model of the Bridge Design Specification, Eq. 8, should be used for designing new bridges. The extra safety margin makes up for the lack of a load factor and the uncertainties in predicting future truck traffic. The simplified model is recommended for calculations of remaining service life because the prior load history is usually known and, thus, the remaining life can be predicted more accurately.

REQUIRED FRACTURE STRENGTH While equations for stress intensity factors (SIFs) can be found in several handbooks, none has solutions directly applicable to the elastic crack tip parameter, K, for cracks in steel beams. Lacking expressions for the elastic-plastic parameters J and CTOD, users must develop their own. Presented below are approaches for estimating K for part-through and through-thickness cracks. Values of J and CTOD would have to be calculated with finite element analysis. Part-through crack SIFs for part-through cracks emanating from a stress raiser, such as a bolt hole or the toe of a fillet weld, can be calculated readily with Irwin's equation for an edge crack in a finite thickness plate: [

K - 1.12 FG/V/-~, I __2ttanna Ek ~ na 2t

(16)

The factor F c in Eq. 16 is added to Irwin's solution to account for the stress gradient in the absence of the crack [20]. The symbols are defined as follows: E k = complete elliptical integral of second kind, varying from E k = n/2 for a semi-circular crack (a/c - 1 ) to E k = 1.0 for a half-tunnel crack (a/c -- 0 )

226

P. ALBRECHT, W. WRIGHT

F G = geometry correction factor f = dead and live load stresses in beam calculated with mechanics of materials equations a = crack length in thickness direction of plate c = half-crack length along plate edge t = plate thickness Through-thickness crack Feng et al [21 ] have used finite element analysis (FEA) to calculate SIFs for (1) two-front through cracks growing down and up the web and (2) three-front through cracks growing up the web and across the tension flange of I-beams. The beams were modeled in 3-D with eight-node shell elements. Web and flanges were joined along the intersections of web and flange centerlines. Crack tips were modeled with quarter-point singularity elements. Crack tip mesh pattems were optimized to ensure that solutions are accurate and converge. Methods of extracting SIFs from FEA results were selected based on known solutions of benchmark problems. Goveming parameters for cracked I-beams were determined. SIFs for two-front cracks are a function of applied stress (bending or axial), crack length, eccentricity about centroidal axis of the I-beam, and ratio of flange area to web area. SIFs for three-front cracks are a function of applied stress, web and flange crack lengths, and ratio of flange area to web area. FEAs were performed for 2,106 combinations of crack type, loading type, crack length, eccentricity, and flange-to-web area ratio. The results were fitted with polynomial equations for ready use by engineers [21 ]. Due to lack of space, these equations are not reproduced herein.

DESIGN FRACTURE STRENGTH

Bridge Design Specifications The fracture control plan in the Bridge Design Specifications [5] aims at eliminating brittle steels from production. This is done by specifying minimum values of Charpy V-notch (CVN) toughness at tests temperatures depending on five parameters: (1) welded versus bolted construction, (2) yield strength, (3) plate thickness, (4) fracture critical versus non-fracture critical members, and (5) minimum service temperature (MST). Rather than specifying the intended values of CVN energy at the MST, the specifications call for higher CVN values at test temperatures higher than MST. This was done to reduce the cost of having to cool specimens to the MST before testing. CVN toughness/temperature values listed in the Bridge Design Specifications for 102 combinations of the five parameters were derived using equations of Klc-CVN correlation and temperature shift in the lower transition temperature region of CVN impact test results. They are not applicable to upper shelf behavior of ductile steels. Advanced steel making practice in the 1990s has made it possible to produce modem steels that are tougher than the conventional high-strength low-alloy steels of the 1960s. Ideally, such steels would provide sufficient toughness to ensure that cracks extend on the upper shelf of the toughness versus temperature curve, even at the MST. Under this condition, crack extension would be governed by yielding of the net section at the plastic limit load rather than by elastic or elastic-plastic fracture at the critical values of KCand Jc.

Fatigue and Fracture of Steel Bridges

227

Test program at Federal Highway Administration To verify this expectation, Wright and co-workers [22-25] have been testing fracture toughness specimens made of two conventional steels: (1) High-strength Low-alloy Columbium-Vanadium Structural Steel, ASTM designation A572 grade 345 (2) High-Strength Low-Alloy Structural Steel with 345 MPa Minimum Yield Point to 1O0 mm Thick, ASTM designation A588 and two modem steels: (3) High-Strength Low-Alloy Steel Plates of Structural Quality, Produced by Quenching and Self-Tempering Process (QST), ASTM designation A913 grades 345 and 450 (4) Carbon and High-Strength Low-Alloy Structural Steel Shapes, Plates and Bars and Quenched-and-Tempered Alloy Structural Steel Plates for Bridges, ASTM designation A709 HPS grade 485W The A572 and A913 steels are used for painted bridges; the A588 and A709 HPS weathering steels are used for bare, exposed bridges. Presented hereafter are the results for A572 steel, A588 steel, and the two grades of A913 steel - - 345 and 450. All tests were performed on 25.4 mm thick specimens, ASTM designation 1T C(T), with initial crack length of ao/W- 0.5. For data on 89 C(T) and 2T(CT) specimens, the reader is referred to [24, 25]. Specimen preparation, test procedure and data analysis conformed to the requirements of the Standard Test Method for Measurement of Fracture Toughness, ASTM designation E 1820. Crack length was determined from elastic unloading compliance. The specimens were tested at temperatures of-100 to +24 ~ Table 2 lists the tensile properties of the four steels measured at room temperature. The A913 grade 450 steel did not meet the required tensile strength of 550 MPa at the slower strain rate at which the authors tested the specimens. Table 2. Tensile Properties Steel Type

Yield Strength (MPa)

Tensile Strength (MPa)

Elongation in 50 mm (%)

A572 gr. 345 A588 A913 gr. 345 A913 gr. 450

428 427 428 446

589 600 516 500

23 24 34 34

Toughness at minimum service temperature (MST) Fracture toughness data are customarily presented in terms of resistance curves of the J-integral versus crack extension. In this study the data are plotted in terms of load versus load-line displacement, a format more familiar to structural engineers and better suited to characterize the ductility of tough steels. Figs. 10 and 11 show typical load-displacement plots for the 1T C(T) specimens made of the two conventional steels and the two grades of the modem A913 steel. These specimens were tested at temperatures near the MST for zone 1 (T~ = -18 ~ and above) and zone 2 (T2 =-19 to -35 ~ according to the Bridge Design Specifications. The data are compared with the predicted elastic-plastic load-displacement curve for each specimen, in the absence of crack extension. The slope of the elastic portion is given by the compliance equation for the compact specimen, ASTM specification E 1820. Neglecting strain hardening, the plastic limit load is [22]:

228

P. ALBRECHT, W. WRIGHT

where the radius of the circular segment of the slip line is

R -- ~(].052ao) 2 + 0.409(2a0b + b z) + b 2 - 1.052a 0

(18)

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229

Fatigue and Fracture of Steel Bridges

the A913 grade 345 specimen was moderately ductile and the grade 450 specimen highly ductile. Both reached the calculated limit load (Fig. 11). (2) At or near the MST for zone 1 (T~ = -18 ~ the A572 specimen still failed in brittle manner but the A588 specimen was ductile (Fig. 10). Both grades of A913 were much more ductile than their conventional steel counterparts (Fig. 11). Although the A913 grade 450 specimen exhibited two pop-ins, the specimen reached a load-line displacement at failure that was 28 times the calculated elastic displacement at the limit load, V f / V e l ' YS" In summary, the modern steel is much tougher than the conventional steels. It is emphasized that the load-displacement plots in Figs. 10 and 11 are for those specimens that exhibited the lowest toughness among replicate specimens tested at the same temperature. All other specimens of same steel/temperature combination were tougher.

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230

P. ALBRECHT, W. WRIGHT

Effect o f temperature on ductility Ductility of non-cracked members is commonly defined in terms of percent elongation attained in a tensile test or plastic rotation capacity in a flexural test. As an example of the latter, the plastic component of the rotation capacity needed to develop the plastic moment of a section is said to be three times the elastic rotation at the plastic moment [27]. In calculating the elastic component, the moment-curvature curve is assumed to be linear-elastic up to the plastic moment, followed by the plastic moment plateau. The total elastic plus plastic rotation capacity is then equal to four times the elastic rotation. This value conforms with the requirement for minimum rotation capacity of compact sections shown in Table B5.1 of the Building Design Specification [28]. Originally developed for building design, this ductility requirement applies also to bridge design.

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231

Fatigue and Fracture o f Steel Bridges

There are at present no criteria for defining minimum rotation capacity of a plate girder with a flange crack as might be found at the end of a welded cover plate. Lacking such information, the authors have classified the fracture behavior of a C(T) specimen as follows: (1) (2)

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initial portion of the load-displacement curve divided by the limit load of the specimen calculated with Eq. 17 at the initial crack length

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232

P. ALBRECHT, W. WRIGHT

The second quantity useful in characterizing ductility is the normalized maximum load, Pmax/ PL rs, where Pmaxis the load at fracture or the maximum load if the specimen did not fracture. Figs. 12 and 13 show the fracture behavior of all 1T C(T) specimens tested at temperatures ranging from -100 to +24 ~ Each data point represents one specimen. Test temperatures are defined by the symbols. Arrows attached to groups of A913 specimens indicate tests that were discontinued because the displacement exceeded the measurement capacity of the clip gage. The following was found: (1) The behavior of the A572 steel specimens varied from brittle to transition with much scatter (Fig. 12). Degree of ductility did not correlate well with test temperature. (2) A588 steel specimens tested at -32 to -73 ~ were brittle and those tested at the MST of T~ = -18 ~ and higher were ductile, suggesting that the transition from brittle to ductile occurred between-32 to-18 ~ (Fig. 12). (3) A913 steel specimens of both grades were brittle below-80 ~ and ductile above -60 ~ (Fig. 13). The test of several specimens were discontinued at 28 times the calculated elastic displacement at limit load because the clip gage had fully opened. As cited before, the modern steel is much tougher than the conventional steels. Test results of 50.8 mm thick 2T C(T) specimens are showing some decrease in ductility as one would expect [25, 26]. The ranking of the steels by degree of ductility remains unchanged though.

CONCLUSIONS Experience with fatigue cracking of bridges in service has led to improvements in the Bridge Design Specifications and, in turn, to safer bridges. Fatigue strength under variable-amplitude stress ranges induced by truck traffic is now well understood. New bridges should be designed to the straight-line model of the specifications. However, the remaining life of existing bridges should be calculated using the less conservative simplified model, which predicts more accurately the transition between the finite-life and infinite-life regimes of fatigue strength. The modern A913 and A709-HPS 485W structural steels introduced in the 1990s are much tougher than the conventional, high-strength low-alloy steels A572 and A588 from the 1960s. Judging by the progress made in steel production during the last 10 years, it is anticipated that more bridges in the future will be built from higher toughness steels providing greater ductility in the presence of fatigue cracks. Hopefully, some day, it will be possible to characterize the fracture resistance of bridge girders built of modem steels in terms of yielding of the net ligament instead of crack tip singularity parameters.

REFERENCES 1. 2. 3.

Fisher, J.W. and Mertz, D.R., "Hundreds of Bridges - Thousands of Cracks," Civil Engineering, 55-4, April 1985, 64. Albrecht, P. and Fisher, J.W. (1975). "An Engineering Analysis of Fatigue Crack Growth at Transverse Stiffeners," Int. Assoc. Struct. and Bridge Engrs., Publications, 35-1. Fisher, J.W., Albrecht, P., Yen, B.T., Klingerman, D.J. and McNamee, B.M. (1974).

Fatigue and Fracture of Steel Bridges

4.

5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.

233

"Fatigue Strength of Steel Beams with Welded Stiffeners and Attachments," NCHRP Report 147, Transportation Research Board, Washington, D.C. Albrecht, P., Brown, W.P., and Wright, W.J. (1992). "Analysis of Fatigue Cracking in 1-64 Bridges over Maury River and Kerr's Creek, Rockbridge County, Virginia." Proceedings, Southeast Regional Meeting, American Association of State Highway and Transportation Officials, Norfolk, Virginia, August, 24 p. "Bridge Design Specifications," AASHTO LRFD. (1994). American Association of State Highway and Transportation Officials, Washington, DC. Snyder, R.E., Likins, G.E. and Moses, F., "Loading Spectrum Experienced by Bridge Structures in the United States," Report No. FHWA/RD-85/012, Federal Highway Administration, McLean, Virginia, February 1985. Albrecht, P., and Simon, S. (1981). "Fatigue Notch Factors for Structural Details." Journal of the Structural Division, American Society of Civil Engineers, Vol. 107, No. ST7, July, pp. 1279-1296. Yamada, K. and Albrecht P. (1977). "Fatigue Behavior of Two Flange Details," Journal of the Structural Division, American Society of Civil Engineers, Vol. 103, No. ST4, pp. 781-791. Yamada, K., "Fatigue Behavior of Structural Components Subjected to Variable Amplitude Loading," Ph.D. Dissertation, University of Maryland, College Park, Maryland, 1975. Schilling, C.G., Klippstein, K.H., Barsom, J.M. and Blake, G.T. (1978). "Fatigue of Welded Steel Bridge Members Under Variable Amplitude Loadings," NCHRP Report 188,Transportation Research Board, Washington, D.C. Albrecht, P. and Rubeiz C. (1987). Variable-Amplitude Load Fatigue, Task A - Literature Review, Volume III- Variable-Amplitude Fatigue Behavior, Report No. FHWA-RD-87-061, Federal Highway Administration, McLean, VA, Vol. III. Albrecht, P. and Friedland, I.M. (1979). "Fatigue-Limit Effect on Variable-Amplitude Fatigue of Stiffeners," Joumal of the Structural Division, American Society of Civil Engineers, Vol. 105, No. ST12, pp. 2657-2675. Albrecht, P., and Yamada, K. (1979). "Simulation of Service Fatigue Loads for Short-Span Highway Bridges." Service Fatigue, Loads Monitoring, Simulation and Analysis, ASTM STP 671, American Society for Testing and Materials, pp. 155-177. Albrecht, P., Lu, H.Y., Jung, K.S., Liu, H.J., and Cheng, J.G. (1994). "Long-Life Variable-Amplitude Fatigue Strength of Welded Steel Bridge Details." Report No. FHWA-RD-94-108, Federal Highway Administration, McLean, Virginia. Tilly, G.P. and Nunn, D.E. (1980). "Variable Amplitude Fatigue in Relation to Highway Bridges," The Institution of Mechanical Engineers, Proceedings, Vol. 194, No. 27. Fisher, J.W., Mertz, D.R. and Zhong, A. (1983). "Steel Bridge Members Under Variable Amplitude Long Life Fatigue Loading," NCHRP Report 267, Transportation Research Board, National Research Council, Washington, D.C. Klippstein, K.H. and Schilling, C.G. (1989). "Pilot Study on the Constant and Variable Amplitude Behavior of Transverse Stiffener Weldments," Journal of Constructional Steel Research, Special Edition on Fatigue. Fisher, J.W., Nussbaumer, A., Keating, P.B., and Yen, B.T. (1993). "Resistance of Welded Details Under Variable-Amplitude Long-Life Fatigue Loading," NCHRP Report 267, Transportation Research Board, National Research Council, Washington, D.C. Abtahi, A., Albrecht, P., and Irwin, G.R. (1976). "Fatigue of Periodically Overloaded Stiffener Detail." Journal of the Structural Division, American Society of Civil Engineers, Vol. 102, ST11, November, pp. 2103-2119.

234 20. 21. 22. 23. 24. 25. 26. 27. 28.

P. ALBRECHT, W. WRIGHT

Albrecht, P., and Yamada, K. (1977). "Rapid Calculation of Stress Intensity Factors." Journal of the Structural Division, American Society of Civil Engineers, Vol. 103, No. ST2, February, pp. 377-389. Feng, D.Q., Albrecht, P. and Wright, W.J. (1996). "Stress Intensity Factors for Cracks in Bridge Girders." Report, Department of Civil Engineering, University of Maryland, College Park, Maryland, August. Hu, J.M., and Albrecht, P. (1991). "Limit Load Solution and Loading Behavior of C(T) Fracture Specimen." International Journal of Fracture, Vol. 52, pp. 19-45. Wright, W.J., Tjiang, H., and Albrecht, P. (1995). "Fracture Toughness and Ductility of High Performance Steel." Proceedings, 13th Structures Congress, American Society of Civil Engineers, Vol. 1, pp. 193-196. Tjiang, H.C., Hartmann, J.L., Wright, W.J., and Albrecht, P. (1999). "Fracture Resistance of A572, A588 and A913 Structural Steels." Turner-Fairbank Highway Research Center, Federal Highway Administration, McLean, Virginia, June, 114 p. Wright, W.J., Tjiang, H.C., Hartmann, J.L., and Albrecht, P. (2000). "Fracture Resistance of Modem Bridge Steels." Proceedings, Structures Congress 2000, American Society of Civil Engineers. Wright, W.J. (2000). "Fracture Toughness and Ductility of A709 Grade HPS-485W High Performance Steel." Work in progress. Federal Highway Administration, McLean, Virginia. "Plastic Design in Steel, a Guide and Commentary." (1991). American Society of Civil Engineers, New York, NY. "LRFD Specification for Structural Steel Buildings." (1993). American Institute of Steel Construction, Chicago, Illinois.

235

D E S I G N I N G A G A I N S T DUCTILE F R A C T U R E P R O P A G A T I O N IN V E R Y H I G H S T R E N G T H STEEL GAS PIPELINES: A R E V I E W

G. BUZZICHELLI

Cenlro Sviluppo Materiali S.p.A. 00128 Rome, Italy ABSTRACT The paper presents a review of the actual situation on the knowledge of the ductile fracture propagation (DFP) control in very high strength, large diameter pipes tested at high hoop stresses, especially in the light of the recent years activity performed by CSM in cooperation with qualified pipe producers and gas companies. The results obtained in a series of full scale tests which demonstrate the good performance of X70X l00 grade steels are first analysed in terms of traditional fracture parameters, such as the Charpy-V energy used so far for lower strength materials, without much success. Then recent efforts in the development of a 3D-FEM physical model based on CTOA (Crack Tip Opening Angle) including a process zone associated with the crack tip and the constraint effects due to the soil backfill are also illustrated in conjunction with the first promising results obtained. KEYWORDS API X70, X80 and X100 Gas Pipeline Steels, Ductile Fracture Propagation, Full Scale Ductile Fracture Propagation Test, Charpy V, Battelle DWTT, CTOA.

INTRODUCTION The world scenario, characterised by the overall increasing gas demand and the location of most important producer/consumer countries away from the sea, is evolving under the strong need of realising thorough onshore pipeline systems able to transport large quantities of gas over long distances. All existing projects under development do share some common elements such as mediuln-large pipe diameters and extremely high operating pressures (>> 100 bar), possibly associated with the presence of rich gas. However, in order an economically advantageous project could be really translated into practice, suitable materials and pipe geometries must be used. To save weight and costs very high (or ultra-high) strength steels would be preferable in theory, but limitations might occur to their application should important aspects related both to pipeline construction (i.e. field welding) and reliability be not clarified. One essential point dealing with safety is fracture arrest capability in the unlikely event that, due to natural or artificial causes, a full bore breach be produced on the pressurised pipeline.

236

G. B UZZICHELLI

The problem is not that - extremely dangerous one - of the fracture propagation in the brittle mode. The metallurgical-scientific community as well as pipe producers are fairly confident that appropriate TMCP routes and selected compositions could at least prevent steel microstructures to undergo the cleavage mode in fi'acture at low temperatures, even if moderately increasing the strength level. On the other hand a quantitative parameter for the design of service temperature is fortunately available. In fact ample evidence was gathered concerning more traditional (lower strength) materials and good indications are already there for the new (higher strength) ones, about the validity of the Battelle shear area criterion on Drop Weight Tear specimens giving good indications on the ductile/brittle transition temperature of the pipe, also for thick wall line pipes [ 1] [2], even if in a limited range of conditions. The most important problem of still uncertain solution is instead that associated with long running shear cracks driven by high pressurised gas escaping from the breach [3] [4]. The real difficulties come from two sides: one is the fabrication cycle, in the sense that achieving high levels of "toughness", by optimising steel cleanness and type of microstructures in correspondence to the (extremely) high values of mechanical strength which favour the opposite trend, is a much difficult technological target. The second has to do with the significance of traditional fracture parameters because of their limitations in describing correctly the resistance to crack propagation [5] , which reflect in turn into the difficulty of designing and evaluating appropriate materials. Charpy-V energy for example is the parameter which interpretative theories of the Ductile Fracture Propagation (DFP) phenomenon since years 70's were based upon, including the most appreciated and familiar one developed by Battelle and known under the name of BTC (Battelle Two Curve) approach [3]. This describes with an acceptable degree of precision the behaviour of medium- low strength steels even in the presence of rich gas compositions, but fails to predict arrest/propagation events in modern high strength/high toughness materials. However the development of a commonly accepted and validated design for crack arrestability is not a pure sophisticated academic question. Choosing the appropriate parameter and specifying its quantitative value may eventually bring one very close to or even beyond the technological limits associated with the candidate materials, i.e. high or ultra-high strength steels, for the new highly demanding pipeline projects. This paper gives an updating of recent experiences that, started in 1996 by CSM in cooperation with the Italian gas company SNAM on X70/XS0 steels, are now at the stage of treating the X100 case inside an European projects frame also supported by EUROPIPE and BRITISH STEEL

(CORUS).

An effort will be made to illustrate the ongoing attempts of interpreting the full scale data with the aid of other toughness parameters (CTOA), and a recently developed 3D numerical model of the complex DFP phenomenon.

EXPERIMENTAL RESULTS

The hi,@ strength / high thickness X70/X80 pipelines The scope for this initial part of the work undertaken by SNAM and CSM was based upon recognising that in the world scenario of a growing gas transportation system, pipelines technology will keep its preminent role evolving towards large quantities over long distances in high pressure regimes (> 100 bar). Quantities of interest are in the range of 15 to 30 GSM3/y over distances of the order of 2500 km or greater; diameters are medium/large ones.

Designing Against Ductile Fracture Propagation...

237

The aim of this first joint project was to look at the possibility of realising a line with commercially available linepipe materials and explains why both the initial study on diameters/pressures optimisation and the subsequent experimental work was conducted on X70/X80 materials, after verifying that the necessary wall thicknesses could be realistic. Higher grade materials, like X100, were excluded because still susceptible at that date of further improvement at an industrial scale.

Fectsibilily study A teclmical-economic analysis has been performed on a hypothetical but realistic - gas pipeline transporting 30 GSm3/year from Chardzhou (Turkmenistan) to Bratislava (Slovak Republic) and is reported in more detail elsewhere [6]. Two options were analysed with respect to design pressures: 45 bar inlet and 75 outlet pressure following a conventional design; significantly higher pressures, i.e. 100 bar inlet and 140 outlet. For the low pressure configuration, the current API X70 of common use for large diameter pipelines was selected, whilst AP! X80 was preferred for the high pressure case, having the scope of limiting the pipe wall thickness and weight. Fig. 1 COlnpares the costs located at a 56" (1422 ram) respect to the low pressure pressure option becoming linepipe.

of the two options as a function of pipe diameter. The minimum is outside diameter pipe operated at a high pressure. The difference with option with the same diameter (56") is of the order of 45%, the low more interesting at higher diameters, however not in use for gas

1.5 X

x

~1.4

-o;osT usDsm3

~1.3 Io e-

~ighPressure

Ol.2

,,m

"~ ' .......... -

Low

Pressure

.......~ _

1

A,

~=1.0

0;041 USD/Sm3

D-

0.9 44

48

52

56

60

64

68

72

Outside diameter [in] Fig. 1. Transportation cost index vs pipeline outside diameter for 30 GSm3/year at 140 bar (High Pressure) or 75 bar (Low Pressure). Absolute cost values are given in U.S. dollars (USD). Costs evaluation for the two options shows for the same diameter of 56" (Figure 2) a large shift in percentage from compression stations (low pressure), to the linepipe (high pressure). In this calculation in fact the distance between neighbouring compressor stations moves from 166 km to 447 kin, whilst the pipe wall thickness, and the cost consequently, increases by a factor of two. However in absolute terms the difference in costs between the two options comes in reality from only operational costs, the investments being almost equal in the two cases.

238

G. B UZZICHELLI

Finally, a sensitivity study performed on prices (steel, compressor station, gas fuel) has confirmed the competitiveness of the high pressure solution even with variation of single cost elements of 1020% (steel, compressors, gas fuel) also demonstrating that the long distance transportation becomes less and less convenient with lower transported volumes.

High Pressure lOaf

5%

6%

Low Pressure 8%

~%

9%

I

I Pipeline investments Station investments

,'0%

Fuel & electricity*

Other operation costs* *costs actualised over 25 years

Fig. 2. Costs splitting - Gas transportation of 30 GSm3/year at 140 bar (High Pressure) or 75 bar (Low Pressure) E x p e r i m e n t a l j u l l scale tests

According to the technical-economic feasibility study, the present research was definitely orientated towards the definition and evaluation of technical requirements of API X70 & X80 steel pipe with 56" outside diameter and wall thickness of 30.5 mm and 26 mm respectively. A first experimental activity was decided, aimed at re-assessing two most important structural integrity aspects, i.e. that related to fracture mode (brittle to ductile transition) and to DFP in pipes of such combination of geometry, in particular the high thickness and grade (high hoop stresses). Previous experiments, i.e. on XS0 materials were performed with lower thickness (< 20 mm) and lower hoop stresses (< 400 MPa), as illustrated hereinafter. The two set of pipes necessary to design and conduct the double series of West-Jefferson tests and Propagation tests were produced by ILVA-Taranto works in strict co-operation with CSM through all steel fabrication stages. The successful objective of the production of steel pipes matching tensile properties with good weldability and toughness, expressed both in terms of Charpy-V energy (> 200 J) and Battelle Drop Weight transition temperature (85% Shear Area in BDWTT at -20~ was achieved. Steels were low C, microalloyed by Nb-Mo-Ti-Ni, with extremely low Sulphur levels (< 20 ppm) and Calcium additions processed by the controlled rolling and accelerated cooling technique (TMCP). The low carbon equivalent level (< 0.40) allowed a good field weldability. The first series of tests performed on single pipes at low temperature where the pressurised water/air mixture encourages a limited propagation (West-Jefferson tests), demonstrated the validity of the well known 85% shear area Battelle design criterion even in this range of geometry/grade. The absolute good performance of these pipes was shown, as reported elsewhere [7], with fully ductile behaviour down to - 20~

Designing Against Ductile Fracture Propagation...

239

The second series of (two) tests was devoted to DFP assessment and performed in the CSM burst station of Perdasdefogu (Sardinia). Other pipes were produced, deliberately lower in toughness, in order to realise a properly differentiated lay-out in terms of CV energy for the crack propagation test. Design test pressures of 175 and 161 bar for X70 and XS0 respectively, corresponding to 408 and 440 MPa hoop stress (~ 85% and 80% yield stress) were adopted. In both cases the designed test layouts included one initiation and six test pipes of about 10 m in length with different toughness levels, adequately instrumented in order to record temperature, crack speed, gas decompression behaviour and to measure the elastic/plastic deformation field associated with the fi'acture event. The crack was initiated at the middle of the central pipe on the top generatrix by the use of a shaped explosive charge. Pressuring gas was air, as minimum differences are to be expected with respect to methane in the gas decompression behaviour at the test pressures adopted. Figures 3 and 4 report the results for X70 and X80 respectively as a function of the distance from initiation. The actual CV and DWTT energies of single pipes are also indicated, together with the measured CTOA of the material, to be used in the following discussion. 70.05 m '11.11) m

67.60 m

6.58 m n"I i

.....................................................

]

ltppershelf CharpyV(Joule) 280

toughness CTOAcI)WTT (,I/cm2)(o)

...............

850

236 900

24.9

19.4

I i

172 750

168 850

13.4

16.6

-

I

.............

228

: 280

730 17.1

I 950 I 20.6

Resetwoir

EAST Side

Fracture

' - - - - " path

Fig. 3. API 5L X70 burst test layout and result. (X70 56" x 30.5 mm pipes pressurised by air at P=175 bar. Hoop stress=408 MPa=0.85 SMYS) In the full scale propagation test on API X70 pipes, fracture arrested in the first pipe on the west side. On the east side the crack started spiralizing from the initiation point probably due to the close-to-arrest toughness energy of the initiation pipe. The initiation and the first pipe on the west side had the same Charpy V energy, about 170 J, which can be assumed as the fracture arrest toughness, for the geometry and pressure considered.

12

Ill

/~c.~Cl'VOir

69.96 ,n

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,. o.gs,,,~1

67.91 Ill

III

26

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m

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"\Z;IIII Z2

Initiation i)ipe

Ill)pershelf CharpyV(.Joule) 278 |ou,,l,huess I)WTT (,1/cm2) 906 18.7 ('T()Ac (~

Reservoir

206 781 9.4

144 553 9.4

88 386 7.9

133 539 9.3

229 788 10.4

272 976 14.6

I Fracture path

Fig. 4. API 5L X80 burst test layout and test result. (X80 56" x 26 lnln pipes pressurised by air at P=161 bar. Hoop stress=440 MPa=0.80 SMYS)

240

G. B UZZICHELLI

In the full scale propagation test on API 5L X80, the fracture propagated both on the east and west side from the onset point along the upper generatrix and arrested only in the last pipes of the test line, having nearly the same Charpy V shelf energy (272 and 278 J). It is therefore resulting as highly consistent the fact that even high thickness materials are capable to arrest fracture within a single pipe in high hoop stresses regime. Figure 5 shows crack velocity versus distance diagram together with the specific pipes CV energy values of pipes.

400

9

:.

-'

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9:

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9

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:

35o 300

30O

...........................

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0 0

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:

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>"

- 50

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0 -30

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[]

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20

0

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point [m]

Crack velocity [ m / s ] - - - c h a r p y v e n e r g y

[J[

Fig. 5. Full scale test X80, crack velocity vs distance diagram.

The X1 O0 case

A second part of the planned activity was devoted to the evaluation of X100 grade pipes with respect to ductile fracture propagation control. This is being investigated in a joint co-operation of CSM, Snare and Europipe, with the financial support of the European Coal and Steel Community

(ECSC) [8].

A full scale ductile fracture propagation test on large diameter (56" x 19.11nln), high strength steel pipes (X100) has been carried out at very high hoop stress (469 MPa, corresponding to 68% of SMYS) while a second full scale test on X100 steel grade pipe with different geometry (36"xl 6mln) is planned for the current year 2000. The 56"x19.11nm test pipes have been manufactured by Europipe GMBH in the Mtilheim UOE pipe mill, using TMCP plates produced by Dillinger Hutte. The test line was 70 in long as in the case of X70 and X80 and it was pressurised by air at 126 bar. The fracture propagation onset was caused by a shaped explosive charge on the upper pipe generatrix. The test layout is depicted in Figure 6, together with actual CV and DWTT energies and CTOAc of single pipes.

Designing Against Ductile Fracture Propagation...

I. Ill m

241

11.95 Severance ~,~"-A

lr

141

W EST Side Initiation pipe

I

I.ongitudinlds~cltl

I

Ill)pC," shdf

CharpyV (.Joule)

271

245

200

170

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284

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(.I/cm2)

689

692

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(o)

9.6

10.9

5.6

5.9

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Fracture " path

Fig. 6. X100 burst test layout and test results. (X100 56"x19.1 mm pipes pressurised by air at P=126 bar. Hoop stress=469 MPa=0.68 SMYS)

Making reference to Figure 6, the crack propagated in the East direction through the initiation pipe, the whole 170 J pipe and the subsequent 263 J pipe, arresting eventually just before the girth weld connection to the last higher toughness pipe. Due to a severance occurred on the West side of the line in correspondence of the first girth weld at the end of the initiation pipe, no crack propagation took place in this part of the test line. However, the pressure transducers data guaranteed that the severance did not affect the crack arrest O1"1the East side. The crack speed behaviour is reported in Figure 7. IFan D i a g r a m and Crack velocity on East test side~ 200

/"x. / \ / ~

180 160

i

/

\

//

\\

Ruptures of Timing Wires (TWs)

x

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--

Girth welds

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crack speed obtained fitting TWs

400 . 360 - 320

140 -~"

Crack Deviatio

120

i i i~

280 "~ N82 ~'~

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160 r

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120

40 2O 0 0

5

10

15

Distance from initiation p o i n t ( m )

20

L-~(--25 ~

0

TimingWires

Fig. 7. Fan diagram and crack speed of the East test side for Xl00, 56"x19.1 mm pipes.

This full scale test has shown again that the toughness characteristics of these X100 pipes proved enough to warrant the arrest of a long running fracture, at operating pressure over 12 MPa, corresponding to hoop stress of about 470 MPa. In particular the toughness required to arrest, 263 J of Charpy V energy, even if high, is still will within the presumable technological limits (300+350 J) for linepipe steel production. An overall important conclusion if this initial experimental work can be drawn: either the already commercially available materials of X80 grade and high thickness or the newly developed X100 ones, both fabricated via microalloying and therlno-naechanical processing route, tested in conditions typical of the long distance gas transportation technology (large diameters, very high pressures/hoop stresses) can guarantee a shear crack arrest within a single pipe.

G. B UZZICHELLI

242

DISCUSSION

The ('~haq)y- V energy The first strong indications at the practical level showing the extremely good serviceability of X80-X100 materials in very high pressure large diameter pipelines are however not in line with predictions based on CV values. In fact using the traditional BTC approach [3], the calculated CV value fbr arrest, with the exception of X70, appear to be largely underestimated, being CV=160 J for X80 and CV= 176 J for X100. This is again in line with the inforlnation accumulated in the years on the unconservative nature of CV energy fbr modern high strength (>_ X70) - high toughness (CV > 100 J) materials, required for high pressure (hoop stresses) applications in pipeline construction (o). A representatiom together with a fairly homogeneous set of data (API grade >= X80, mediumlarge diameter, high hoop stress applied) extracted from the CSM full scale burst test database and including recent results by Alliance [9] is given in Figure 8. The correlation of the actual with the predicted (BTC) values of Charpy-V energy coming from the CSM data base shows, that an empirical line with slope of about 1.5 should be drawn as the best fitting for the arrest/propagation conditions for the higher toughness steels. In effects this "correction factor" is variable and ranges as shown by the single test results, fiOln 1.17 to 1.84 in an unpredictable way. The reported results corroborate the concept that the total Charpy V energy would not in effects be available to the fiacture propagation resistance control and should not be taken as a meaningful measure in these conditions. In fact, as re-elnphasised by Rothwell in his recent paper on the history of DFP [5], being Charpy V the sum of three different - deformation, initiation and propagation - energies, it is intrinsically subjected to variation in terms of these proportions when one has to deal with different materials compositions and processing routes. Actual CharpyV energy Vs. Predicted by Battelle Two Curve Approach [CSM Database 9 tests: grade>=X80, 0D=42-56"; thick=17-20mm, P=80-118bar, Hoop stress=340-440MPa, air and natural gas (not rich)]

350

O DatabasePropagation

300

/

9Database Arrest

1:1.84

)KX70 Arrest ~" 250

~

9X80 Arrest AX80 Propagati~

~ 9 200 ~. ,_ 150 o -~

I

~ " / -

t i .-"m'" 9 , ....... Z ~

1:1.413

"" 1:1.17

/

II X100A.... t /O"Q " .Q~ID"/.O A/,@ / 1-1X100Propagation / O "O"'Q()~[~ ~ i - 3 ~ :z. ...'"C, (9 (:p~.-~r, . u ii, X70 Alli.... 1A .... t[91 ~ _QI., " ~ O " ~ ~ 3 A / OX70 Alliance1 Propag.[9] / ..'"" ~ ~.~ - O

<~ 1oo

~ ' ~ ..... o

50

..,os

o~ ~ o"

2s

o

~o 0

0

0

50

100

150

200

Predicted CharpyV energy by Battelle Two Curve Approach (J)

Fig. 8. Actual vs. Battelle Two Curve predicted Charpy V energy for high grade steel pipes (CSM database test results for API grade >= X80 compared with test results hereby described). (o) Another phenomenon disturbed the outcome of results and their interpretation based on Charpy with heavily Controlled Rolled steels of grades > X70, i.e. the occurrence of separations on the fracturing specimens (or pipes) leading eventually to the presence of splittings on the fracture surface. This phenomenon, being temperature and strain rate dependent, causes a "rising shelf' behaviour of Charpy V or Battelle DWTT transition curve and renders the evaluation of the appropriate material touahness problematic, even if generally uncorservative.

Designing Against Ductile Fracture Propagation...

243

Recent attempts to solve "theoretically" the problem, have been made by Leis et al. [10] who, basing oll instrumented Charpy V test results, worked out an empirical relationship between the total energy measured by Charpy V test and the part of that energy available for DFP resistance. The relationship found by Leis et al. has a parabolic trend and in the range of interest, from 100 up to 300 Joule, gives a correction factor from about 1 up to 1.6 of the toughness predicted by the Battelle Two Curve model. An analysis with the Leis et al.'s approach of the same data of Figure 8 gives the results reported in Figure 9. Actual CharpyV energy Vs. Predicted by Battelle TC with Leis et al. correction [CSM Database 9 tests: grade>=X80, 0D=42-56"; thick=17-20mm, P=80-118bar, Hoop stress=340-440MPa, air and natural gas (not rich)]

350

O Database Propagation 300

9Database Arrest

1:1.60

.....

/

X X70 Arrest >,

250

9X80 Arrest

-~

o

oo

< -=

100

J

, - ' " " "'"

:

.X100Arrest

J - -

........ ~

50

100

.--'""

v

o . . . . . . .

0

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..~-

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o

. . . .

150

1:1.25 .

,

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r

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,-"" A

9

A ~ 9

9

1 :0.97

0

~

200

250

Predicted CharpyV energy by Battelle TC with Leis et al. correction (J)

Fig. 9. Actual vs. Battelle TC predicted Charpy V energy with Leis et al. correction for high grade steel pipes (CSM database test results for API grade >= X80 compared with test results hereby described). Comparing the results in Figure with those obtained using the BTC, a slight improvement can be found; the correlation of the actual to the predicted Charpy V energy values shows that an empirical line with slope of about 1.25 should be drawn as the best fitting, but once again the "correction factor" is variable and ranges as shown by the single test results, from about 1 to 1.6. Another approach could be attempted in terms of Battelle DWTT specimens by following the Wilkowski's suggestion [11] of using the CV/DWTT relationship in the non-linear range shown by high strehgth / high toughness materials to calculate the "equivalent" Charpy V energy available for DFP control and then compare it with the energy predicted by the BTC model. In the author's intention this approach should take into account both the presence of separations and the full thickness effect on DFP resistance. Such analysis demonstrated similarly to the Leis et al.'s case that no relevant improvements can be obtained following Wilkowski approach rather than using the "crude" actual Charpy V datum, as shown in Figure 10. It is known in fact that, even though the large thickness size and full ligament length assure more representative plane stress/plain strain conditions and at least parts of fracture propagation at regime, the predictive models based on Battelle DWTT energy are not successful

(~

244

G. B UZZICHELLI

Equivalent actual CharpyV energy according to Wilkowski Vs. Predicted by Battelle TC [CSM Database 9 tests: grade>=X80, 0D=42-56"; thick=17-20mm, P=80-118bar, Hoop stress=340-440MPa, air and natural gas (not rich)]

300

O Database Propagation

>, 250 r =; __j.----

X X70 Arrest

> 9._'~ " 200 ~

A X80 Propagation

= =

II X100 Arrest

1:1.76

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....

i

~

i

&

9X80 Arrest

~ ~O ~50 "~ = m .=

1:1.27""

,.."" ~'"

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:

o

/...-

~

20

40

/

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100o

/

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o

.......... ....

o

,,o.2~ 9o " O " .... e~

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9 _ ~:o.74

"'1~

80 8

o'~

o

0

0

60

80

100

120

140

160

180

200

Predicted CharpyV energy by Battelle TC (J)

Fig. 10. Equivalent actual Charpy V energy according to Wilkowski vs. Battelle TC predicted Charpy V energy for high grade steel pipes (CSM database test results for API grade >= X80 compared with test results hereby described). Analysis by CTOA

A last attempt to the analysis of XS0 +X100 full scale results of this work was made through CTOA (Crack Tip Opening Angle). According to the scientific literature, CTOA is defined as the angle between the two tangents as the crack profiles in correspondence of the crack tip (Figure 11) and it can be considered an appropriate elastic-plastic fracture parameter to evaluate the material toughness with regards to the ductile crack propagation phenomenon [13]. For a given thickness and a suitable dimension of the residual ligament in front of the crack tip, CTOA is constant during stable crack growth and characteristic of the material. All that has been proved by CSM on the base of an extensive research activity made on both Three Point Bending (TPB) specimens and pipe sections; oil these last the longitudinal crack extension was produced pushing a wedge inside by a mechanical device [14]. The CTOA is defined as (see also Figure 11): (i)

(o) It was found that in order to have a reliable toughness measurement of the energy available for the propagation fracture resistance, the energy spent during the impact DWT test for the initial defomlation and initiation phase rnust be eliminated or strongly reduced by using an appropriate notch type (for example chevron, welded, statically or fatigue precracked, etc.) or by double integration of the recorded impact tbrce until the maximum load is reached [12]. This disturbing contribution, negligible for the conventional low-medium grade steels, is not easy to estimate and becomes relevant for the modern TMCP steels.

Designing Against Ductile Fracture Propagation...

245

C T O A "" 9

2.

=================================================================== ::. ~:.i: :

A CTOD

iI

?.: ::::.:: .!

2.

...........

-\

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",...,, ,,, ',,,

'N

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/,

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......~.>.. iii: .!!i.:~::i;;;~:i':i::i/(:,:ii:i'iU;::4!~::iiii~:!!iiill;:~i ~-: ~i:!:ii:<~:;i:i.:i84~i:i;!i~;:;~i-i:~:iiil:?ii~.i.~::;ii:~:;;i:i::ii!:iiii:!;i.~ii::i:7 84

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Fig. 11. Definition of CTOA. Assuming CTOA as a dominant fi'acture parameter, in the years 85's and 93's the problem of Ductile Fracture Propagation Control on gas pipelines was faced [ 15] for the first time with the use of finite element codes which introduced a more physical modelling of the whole phenomenon. A suitable Finite Element Code, named PFRAC, was developed by SwRI and partly validated .jointly with CSM [15] [16]. I51 parallel, also a simple laboratory procedure ("Two Specimen CTOA test") was fixed to measure the critical value of CTOA of a pipe material by TPB specimens broken in dynamic conditions [17]. The simple comparison of CTOA applied (CTOAa) to the pipe, calculated by FEM code in the operating conditions, and the measured CTOA of the material (CTOAc) defines an engineering method to assess the stability of steady-state ductile fracture propagation and hence the arrest/propagation conditions. As shown in Figure 12, a prediction on fracture propagation stability for a given line pipe under specific operating conditions can be performed in practice by tracing the "CTOAa vs crack speed" curve (CTOA Driving Curve). The eventual intersections of that curve with the CTOAc value indicate whether crack propagation with constant speed is possible.

CTOA c o o

/

"k

......

9

........................C T O A

Unstable propagation

Arrest

~.~

/

......

Stable propagation

Crack Speed Fig. 12. The propagation/arrest criterion using CTOA.

246

G. B UZZICHELLI

The main simplifications adopted in PFRAC were: The CTOAa evaluation was only based upon geometrical consideration at the crack flanks; no particular care was taken to simulate the process zone ahead the crack tip. A remeshing of the crack tip zone was introduced to minimize the mesh dependence of the calculated CTOAa value; >

The backfill constraint effect was taken into account by simply increasing the inertia loads of the pipe flaps. To do this, an artificial increase of the pipe wall thickness was introduced and a subsequently optimisation of the code on the base of full scale test results was performed.

In spite of that, the PFRAC code, validated using CSM full scale test results on pipes with API grade less than X80, proved to give substantially correct results in terms of arrest / propagation event even though its application to high grade / high hoop stress conditions (i.e. outside the range of validation) has given to not consistent provisional results. In order to overcome those limitations to the application of the CTOA approach also in different operating/materials conditions, CSM, jointly with the Department of Mechanical Engineering of University of Rome "Tor Vergata", is currently developing a new finite element code named PICPRO (Pipe Crack PROpagation code) with the scope of better managing the fracture mechanism and soil backfill constraint [18] [19]. Concerning the first point of modelling a Fracture Process Zone (FPZ), Figure 13a, characterized in the code by the extension A (cohesive distance), having a leading edge where maximum cohesive ibrce occurs, and a trailing edge where loads drop to zero (Figure 13b-13c), is introduced in PICRO.

.................. ~--~:::~iiTii"-(]--" /

CTON2

-.... .

.

Ductile tearing

.

L

.

b)

A ..............

F

i

/

c)

Trailing edge

/ Leading edge

Figure 13: Definition (a) and implementation (b) of the cohesive model. CTOA evaluation (c). The A-parameter is lnaterial-dependent and can be evaluated by an optimising procedure of the PICPRO FE calculation aimed at reconstructing the Force vs. Time (Displacement) diagram in a full thickness DWTT specimen [18] with a known CTOAc. Figure 14 shows an example of this optimisation procedure on a specimen cut from the arrest X100 pipe with CTOAc = 8.4 ~ A cohesive distance A equal to 20 mm is worked out independent of the mesh size (< A). The cohesive distance A has been calculated for several pipe steels with API grade X80-X100, Charpy V energies of 100-300 J and thickness 15-30 rain; results revealed that typical values of A are centred within 10-20 mm and thus comparable to the thickness value [18].

247

Designing Against Ductile Fracture Propagation... 400 =

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200 5- (.... ~ .

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c~!,_~~,% ~ ~

...<-,

100

0

i

0

,

I

1

'

I

2

'

I

3

'

I

4

'

I

5

'

I

6

'

7

Time since impact [ms]

Fig. 14. Comparison between PICPRO calculated and experimental load vs' displacement curves on DWT test of X100 arrest pipe material. The numerical analysis of the fracture propagation on DWTT specimen is not affected by mesh dimensions. A phenon~el~ological model of soil dynamics has been introduced in PICPRO to account the effect of soil backfill constraint (Figure 15a). It is assumed that the soil domain is characterised by a set of slip planes, radially oriented by respect to the buried pipe (Figure 15b) and sub-divided in a series of prismatic piles. The behaviour of each pile is considered independent of the others; therefore, one pile can move only in a fixed direction given by its axis. Each pile is modelled by means of several lumped masses linked by non-linear springs whose behaviour is in accordance with a non-linear constitutive law. The springs are active only when compression occurs and their characteristics are derived by literature as well as by energetic considerations.

Figure 15a. View of the line after the burst

248

G. B UZZICHELLI

Ejected soil

Opening

Slip line

flap

Figure 15b. Soil model based on slip lines Concerning the internal pressure decompression model, in order to avoid the complexity deriving from a fluid-structure coupled analysis, the gas decompression is calculated separately from the structural analysis. Regarding the fluid analysis, two regions are studied separately. A first onedimensional model developed by CSM is adopted accounting for the decompression ahead of the crack tip for both lean and rich gas, while a second two-dimensional model is used for the region behind the crack where flap opening occurs. The latter comes from simplified fitting of pressure maps given by pressure transducer during past full-scale propagation tests carried out by CSM. A first check of capability the PlCPRO code in reproducing the experimental phenomena has been made using the field measurements carried out during the two X80 and X100 tEll-scale fracture propagation tests mentioned above. Figure 16 shows the comparison of the interface peak pressure (contact load divided by effective area) from experimental and numerical data, relative to an instrumented section of the pipe.

0.8

a)

O.G

/

L.

.-

..9.... / ii"

a. 0.4

............. 0.2

.:::~

0

9 Exp E x p - L i n e a r fit

i

0

60

120

180

0 [3 Fig. 16. Experimental and PICPRO peak measure at the soil-to-pipe interface (Xl00 test, Prel=75bar)

Designing Against Ductile Fracture Propagation...

249

Figure 17 reports equivalent strains, from two independent measurements on XS0 pipe and PICPRO analysis, as a function of the circumferential distance from the crack line location (usually the top generatrix), showing good agreement.

16 i,I, -c:-

t-

"~

Exper

1

12

L_

\~

(/)

E

1 ""IV./' V!'|

.................................. . . . . . . . . . .1............ . . . . .V. . ,. ). i. . . .

8

.,.,.

/"

El-

2

....... :

:>

LU

-,,",-*-E x p e r F.E.N.

4

i

0

-z~

- =Au = %~: = =>

200

_ _:>

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400

Distance from fracture [mm] Fig. 17. Final equivalent plastic strains for X80 pipe. Making reference to Figure 18, tile experimental reconstruction of "flap's shape" versus time during fl,acture phenolnenon also show a good agreement with the predicted flaps development calculated by PICPRO.

800

c

400

go -400

-800

.......... U n d e f o r m e d :,~

Exp. Oms

=

Exp. 5 m s

*,

Exp. 6 m s

=

Exp. 8 m s

v

Exp. 9 m s

~4-~

F.E.M. Oms

~D~

F.E.M. 5ms

~ ~

F.E.M. 6ms

--,>~

F.E.M. 8ms

~v~

F.E.M. 9ms

.;0 ' 4;0 'Xt ml' ';~ ' ";~ Fig. 18. Flap displacements in one section tbr the X80 analysed. Times are given with respect to crack arrival. Basing upon these satisfactory descriptions of bursting pipe details, a comparison of the calculated versus experimental CTOA has been attempted on the light of full scale results of X80-X100 of the present study. Figure 19 shows that CTOAa values predicted by PICPRO fall inside the range

250

G. B UZZICHELLI

of experimental data (+ 1~ derived by the experimental reconstruction, confirming the capability of the PICPRO in the correct estimation of fracture drivingjorce in terms of CTOAa. The diagram also contains a data point from the recent results obtained by Alliance on X70 36"x14.2 nlln pipes (Alliance test 1) and described in more detail in a recent paper [19]. This test, conducted with rich gas pressurised at 120 bar (hoop stress 386 MPa) again demonstrates the successful prediction based on CTOA. Note that for sake of completeness the results of this test (indicated as "Alliance 1") are also reported in Figures 8 to 10. CTOAa by PICPRO vs. CTOAc (X80, Xl00 and Alliance tests) 20 1:1 line

18

+_1 ~

16

[]

14

9 X100 Arrest

E " 12 t~

,~

0

X80 Propagation 9 X80 Arrest

O X100 Propagation

10

9 Alliance Arrest

6 4 ~

o 4

5

6

7

8

CTOAa

9

lO

11

12

(~

Fig. 19. Capability of the PICPRO code to predict the arrest/propagation conditions for high steel grade/hoop stress or when rich gas is used.

CONCLUDING REMARKS The recent worldwide interest towards (ultra-)high strength (API grade > X80) materials for the construction of efficient large diameter / very high pressure pipelines has renewed inside the technical-scientific community the problem of Ductile Fracture Propagation (DFP) control. This is just because a validated design tool based on a correct physical description of the phenomenon and using of a meaningful and measurable parameter is still not available for all classes of steel and operating conditions. The paper has reviewed the results of recent experiments obtained by CSM, in association with SNAM and EUROPIPE, on high grade materials (up to X100) giving two sets of indications. First the full scale results show the good performance of large diameter high grade linepipes (up to X100) in controlling the ti'acture arrest within a single pipe even in extremely high pressure (up to 170 bar) - high hoop stress conditions and demonstrate the very high standard levels of steel linepipe fabrication technology. Second, the expected limits of Charpy-V and CV-related fracture parameters used in the traditional Battelle-Two-Curve (BTC) approach, have been confirmed. Fracture arrest predictions do not change substantially by the use of semi-empirical correction factors of very limited applicability. However the improved predictive capability of a new CTOA-based numerical model which contains a better description of the pipe fracturing process, has been illustrated at its well advanced developmental stage.

Designing Against Ductile Fracture Propagation...

251

The application of this model to the results of this work as well as to other recent full scale experiments reveals promising and will be adopted in the new X100 demonstration activity programmed with the financial aid of European Community for the years 2000's. A C KN O WL EDG EM ENTS Part of this work, i.e. that related to X100, was performed with the financial aid of European Coal and Steel Community (ECSC). Fruitful discussion with Mr. Giuseppe Demofonti and Gianluca Mannucci is gratefully acknowledged.

REFERENCES

1. API RP5 L3 (1996) Recommended Practicejbr conducling Drop Weight Tear Tests on Line

Pit)e.

2. Pistone, V., Demofonti, G., Junker G. (2000), 3R Int. J. 39, pp. 199 - 204. 3. Maxey, W. (1974), pp. J- 1, Proc of 5th Symposium on Line Pipe Research, AGA Ed. Houston. 4. Demotbnti, G., Pistone, P, Re, G., Vogt, G., Jones, D.G. (1995) EPRG Recommendation for (;rack Arrest Toughnessjbr High Strength Line Pipe Steels, 3R International 34. 5. Rothwell, B. (2000) Fracture propagation control for gas pipelines. Past, present and )@ture, Proc. of 3 'd Int. Conf. Pipeline Technology, Ed. by Elsevier Science, Brugge (to be publ.). 6. Pistone, V., Donati, E., Buzzichelli, G. (1999), Proceedings 7 th National ATIG Turin Conference, pp. 343-361. 7. Mannucci, G., Demolbnti, G., Galli, M.R., Spinelli, C. (1998), pp. 459-469, Proc. of IGRC98, 2,459, GRI Ed. San Diego. 8. Demotbnti, G., Mannucci, G., Spinelli, C., Barsanti, L., Hillenbrand, H.G. (2000) Large Diameter XIO0 Gas Linepipes. Fracture Propagation Evaluation by Full-Scale Burst Test", Proc. of 3 'd Int. Conf Pipeline Technology, Ed. by Elsevier Science, Brugge (to be publ.). 9. Johnson, D., Carlon, L., Eiber R. (2000) Full scale validation of the ji'acture control of a l)ipeline designed to lransport rich natural gas, Proc. of 3~d Int. Conf. Pipeline Technology, Ed. by Elsevier Science, Brugge (to be publ.). 10. Leis, B., Eiber R., Carlson L., Gilroy Scott A. (1998), pp. 723-731, Proc. of In. Pipeline Conf. ASME. 11. Wilkowski, G. M., Maxey, W. A., Eiber, R. J. (1980), Canadian Metallurgical Quarterly, 19, pp. 59-77. 12. Maxey W.A., Barnes C.R. (1990) The chevron notched drop weight tear test specimen, PRCI of AGA, Arlington, VA, Catalogue No. L51622. 13. Venzi S., Martinelli A., Re G. (1981), Proc. of Int. Cone on Analytical and Experimental Fracture Mechanics, pp. 737-756, Ed. G.Sih and M. Mirabile, Sijthoff and Noordhoff. 14. Demofonti, G., Maresca, A. (1985) Previsione del comportamento alia propagazione della .fi'allura duttile in ~vasdotti tramite prove di laboratorio, Final report for ECSC, Contract no. 7210-KE/409. 15. Demofonti G., Kanninen, M.F. (1994) AGA contracts nos. PR-15-9121 and PR-15-9209, The developmenl and validation o.[a ductile j?aclure analysis model, Final report. 16. O'Donoghue P.E., Demo*bnti G., Kanninen, M.F. et al. (1997), Int J. Pres. Ves & Piping 70, pp. 11 -25. 17. Buzzichelli, G., Demofonti, G., Venzi, S., Kanninen, M.F. (1995), Proc. Of the 2 nd Int. Conf. On Pipeline Technology, Vol. II, Ostend.

252

G. B UZZICHELLI

18. Salvini, P., Mannucci, G., Berardo, G. (1999)A Fracture Process Zone model jbr CTOA analysis, Proc. of Int. Conf. on Fracture and Damage Mechanics 1999, Queen Mary and West field College University of London, London (UK). 19. Salvini P., Berardo G., Demofonti G., Mannucci G. (2000) Numerical model qfthe backfill conslrainl e[/ecl durin~z /i'aclz.H'e l~ropagation on buried large diameter gas pipelines, Proc. of o rd Int. Colif. Pipeline Technology, Ed. Univ. Gent, Brugge (to be publ.). 20. Buzzichelli, G., Mannucci, G., Salvini, P., Eiber, R. J., Carlson, L. (2000) Ductile Fracture A~'z~est Assessment in a Gas Transmission Pipeline Using CTOA, paper submitted to the International Pipeline Conference IPC2000, Calgary (to be publ.).

253

F R A C T U R E M E C H A N I C S C O N C E P T S AND S T R U C T U R A L I N T E G R I T Y OF F I L A M E N T W O U N D PIPES Ant6nio Torres Marques*, Alfredo Balac6 de Morais**, Jogo Francisco Silva***, Paulo Tavares de Castro* * INEGI - DEMEGI - FEUP, Porto, Portugal ** SAEM - Universidade de Aveiro, Portugal *** ISEP, Porto, Portugal

ABSTRACT This paper presents a study on the interlaminar fracture of filament wound composites. Mode II End Notched Flexure (ENF) tests were performed on flat glass/polyester specimens. The tested specimens had asymmetric [+0]4 angle-ply stacking-sequences. Relatively small 0 values (0, 5 and 10~ were considered to avoid material non-linearity. The values of the critical strain energy release rates GHc from the insert were lower than those from mode II precracks, except for 0 = 0 ~ Similar values were obtained for 0 = 5 ~ and 0 = 10 ~ From mode II precracks, the GiIc values decreased from 0 = 0 ~ to 0 = 5~ and then increased again for 0 = 10~ KEYWORDS Fracture mechanics, structural integrity, filament wound pipes INTRODUCTION There has been considerable interest in the characterisation of the delamination resistance of laminated composites [1-3]. On the other hand, very few studies have been conducted the interlaminar fracture of filament wound composites [4,5]. In filament wound pipes subjected to internal or to external pressures, interlaminar fracture may occur associated to matrix cracks, leading to significant stiffness losses and to increased probability of buckling. The study of interlaminar fracture of these materials is challenging in many aspects. Firstly, they are clearly much less homogeneous than autoclaved laminates. This larger heterogeneity can be expected to result in considerable scatter, which is already relatively high for laminated composites. Secondly, typical applications of filament wound composites involve angle-ply [+0] stacking sequences. Several studies have been presented on the fracture toughness of multidirectional composites e.g. [4,6-9]. The results are often affected by delamination jumping and material non-linearities. Considerable research is still required, and the current standards are still concerned with unidirectional specimens. Thirdly, filament wound parts have curved shapes. Odzil and Carlsson [4] tested curved filament wound specimens under a modified End Notched Flexure (ENF) rig, and developed a data reduction analysis based on the Theory of Shells. They found that the critical strain energy release rate of [+0]n specimens increased when 0 varied from 30 to 55 ~ The validity of their results is, however, questionable in view of the non-linear load-displacement curves and permanent deformations [4].

254

A. TORRES MARQUES, A.B. DE MORAIS, J.F. SILVA, P.T. DE CASTRO

In this work, we have also employed the ENF test (figure 1) which, among all interlaminar fracture tests, most resembles a realistic bending stress state. For simplicity of testing and data reduction, we used flat specimens. Obviously, one may question whether a flat region is representative of an actual curved shape. Truth is, however, that actual applications involve an enormous variety of curvatures, and so the same question of representativity can be put for any specimen curvature. EXPERIMENTAL Glass/polyester parts were manufactured by filament winding with a CNC machine. The parts dimensions are shown in figure 2. The winding parameters are given in Table 1. The E-glass roving (2400 Tex), sized for Polyester resins, was supplied by VETROTEX. An isophtalic polyester resin CRYSTIC 272 was used, formulated with 2% catalyst (BUTANOX M50) and less than 0.05 % accelerator (0.4 % diluted Cobalt salt). A 25 ~tm MELINEX film was inserted at half-thickness to generate the starter crack. After winding, the part was wrapped by a peelply and put into an oven for post-cure at 80 ~ during 24 h. The mandrel was then removed and the specimens were cut from the section's larger side. The ENF tests were performed following most of the guidelines of the ESIS protocol [ 10]. The specimen widths (b) and thicknesses (2h) were around 20 and 3 mm, respectively. The distance between supports 2L and the crack length a were kept equal to 100 and 25 mm, respectively (figure 1). By sliding the specimens across the supports, three measurements have been made: the first from the insert, and the others from the cracks generated in the previous loading cycles. Each loading cycle typically implied a 25 mm propagation, as the crack tended to be arrested close to the loading anvil. Loading and unloading were performed at 3 and 6 mm/min, respectively. Unloading curves were also recorded to detect any possible non-linearity or permanent deformations that would invalidate the test results. Prior to the ENF tests, the flexural E-modulus of each specimen was measured. The compliance calibration coefficient m was also determined for some of the specimens. This requires that the initial compliance C is measured in flexural tests with crack lengths a varying from 0 to 40 mm, and that m is subsequently determined from the regression (1)

C = C O + ma 3

This method, known as experimental compliance calibration (ECC) [10], can be used to obtain the critical strain energy release rate 3ma2pr 2 F GIIc = - -

2b

N

(2)

where Pc is the critical load value and F and N are large displacement correction factors [10]. Compliance calibration is strongly recommended when testing from a mode II pre-crack, since the crack front position may be difficult to define. The actual crack length in the propagation test can be then be determined using the measured initial compliance C and the regression (1). In the present case, the position of the mode II crack was easily visible, in view of the transparency of the specimens. The ECC method was only used for verification purposes, and was always in good agreement with the corrected beam theory value Giic = 9aZPc2 F 16Eb2h 3 N

(3)

Fracture Mechanics Concepts and Structural Integrity...

255

The data reduction schemes require the load-displacement point corresponding to crack initiation. ESIS has also suggested two alternative criteria to define the critical point (figure 3): the non-linearity (NL) and the 5 % offset or maximum load (5 %/Max). In the first case, the critical point is the one where the load-displacement curve deviates from linearity. It has been shown, however, that the NL point depends on the plot scale, and that the deviation from linearity is often due to large displacements, leading to unrealistically low GiIc values [2]. The 5 %/Max criterion stipulates that a line corresponding to a compliance 5 % larger than the initial one is drawn and intersected with the actual load-displacement curve (figure 3). This intersection point will be taken as the critical point, unless it occurs at a larger displacement than the maximum load point. In this case, the critical point is the one of maximum load. This criterion usually results in higher Gim values than the visual detection ones, and may still be affected by large displacements [2]. We have therefore used the visual detection criterion to define crack initiation. As mentioned above, the transparency of the specimens made observations much easier and more accurate. RESULTS AND DISCUSSION Figures 4 to 9 show typical load-displacement curves. No significant non-linearities or permanent deformations were visible. Furthermore, the delamination was generally confined to the initial half-thickness plane. Extensive fibre bridging was observed on all specimens. Figures 10 to 12 show the results obtained for all tested specimens. As it was expected, there is considerable scatter, especially for [+10~ specimens. For the unidirectional specimens, the GHc values from the insert are slightly higher than those obtained from the mode II pre-cracks. The reverse happens in the angle-ply specimens, indicating that a more pronounced R-curve may exist. Figure 13 compares the average results for the various stacking sequences and precracks. The G.c values from the insert are significantly higher for the unidirectional specimens, while [+5~ and [+10~ specimens have nearly equal values. This shows that the standard ENF tests on unidirectional specimens from the insert may yield very optimistic toughness values for filament woud composites. The GHc values from the mode II precrack decrease from the unidirectional to the [+5~ specimens, and then increase again for the [+10~ specimens. A possible explanation for this variation could lie on the conflicting effects of the layer 0 angle on the toughening efficiency of fibre bridging and on the size of the plastic zone behind the crack tip. Bridged fibres at an increasingly inclined angle may be expected to offer less resistance to crack propagation. On the other hand, specimens with increased 0 angle will have larger matrix plasticity zones behind the crack tip, promoting, eventually, higher toughnesses. In order to confirm this analysis, further work will be conducted on angle-ply specimens with higher 0 angles. The next stage will consist in correlating the measured interlaminar strain-energy release rates GIIc with the behaviour of actual filament wound pipes under impact loading. According to Robinson and Davies [ 11 ], the impact peak load can be obtained from

I

8rc2h3Ea F = GIIc 9(3 + Va )(1 - Va )

(4)

256

A. TORRES MARQUES, A.B. DE MORAIS, J.F. SILVA, P.T. DE CASTRO

where h is the pipe wall thickness and E a and v a are the average Young's modulus and Poisson's ratio, respectively, given by Ea = (EaxialE3oop ) l/ 4

va =

V axia l + V hoop

2

(5)

(6)

The delaminated area A d of Glass/Polyester composites can be easily assessed by visual inspection, as recommended by US Air Force procedures. The delaminated area can be related to GIIc and to the measured impact energy Wi. Assuming negligible curvature [ 11 ], Wi = Giic(np - 1)A d

(7)

for a composite with np layers. CONCLUSIONS A study on the mode II interlaminar fracture of filament wound composites was described. End Notched Flexure (ENF) tests were performed on flat glass/polyester specimens with three different stacking-sequences: [0~ [+5~ and [+10~ . Considerable fibre bridging was observed in the tests, but no significant material non-linearities or delamination plane changes occurred. The GIIc values from the insert were lower than those from mode II precracks, except for the [0~ specimens. Similar values were obtained for the [+5~ and [+10~ specimens. From mode II precracks, the Giic values decreased from the [0~ to the [+5~ specimens, and then increased again for the [+10~ specimens. The conflicting effects of the layer angle on the toughening efficiency of fibre bridging and on the size of the plastic zone behind the crack tip could explain the observed variation. Further work is needed to validate the analysis and to determine the G~c value to be used for the evaluation of structural integrity of filament wound pipes after low velocity impact. REFERENCES .

2.

.

8.

9. 10. 11.

Williams JG, Davies P, Brunner AJ. ICCM-10 ConfProc, 1995, I: 71-75. Davies P, Ducept F, Brunner AJ, Blackman BRK, Morais AB. ECCM-7 Conf Proc, 1996, II: 9-15. Davies P, Blackman BRK, Brunner AJ. Applied Comp Mat, 5 (1998): 345-364. Odzil F, Carlsson LA. J Comp Mat, 34 (2000): 274-298. Davies P, Rannou F. Appl Comp Mat, 1 (1995): 333-347. Laksimi A, Benyahia AA, Benzeggagh ML, Gong XL. Comp Sci Tech, 60 (2000): 597604. Choi NS, Kinloch AJ, Williams JG. J Comp Mat, 33 (1999): 73-100. Tao JX, Sun CT. J Comp Mat, 32 (1998): 1933-1947. Polaha JJ, Davidson BD, Hudson RC, Pieracci A. J Reinf Plast Comp, 15 (1996): 141173. Protocols for interlaminar fracture testing of composites. ESIS-Polymers & Composites Task group. Edited by P. Davies, 1993. Frost SR, Cervenka A. Composites Manufacturing, 5 (1994): 73-81.

Fracture Mechanics Concepts and Structural Integrity...

FIGURES AND TABLES a

'hI L

~

L

..-,

Fig. 1. Schematic representation of the ENF test. /

350

i000

Fig. 2. Dimensions of the filament wound part from which the specimens were cut. load

5%

offset

/

Max

displacement

Fig. 3. Alternative ESIS crack initiation criteria [ 10].

257

258

A. TORRES MARQUES, A.B. DE MORAIS, J.F. SILVA, P.T. DE CASTRO 700 600 500 ~" 400 r

300

0 m

2O0 100 0 0

2

4

6

8

0

displacement (mm)

Fig. 4. Typical load-displacement for a [0~ specimen tested from the insert. 800 700 600

~, 500 " " 400 "~ 300 200 100 0 0

2

4

6

8

10

displacement (ram)

Fig. 5. Typical load-displacement for a [0~ specimen tested from a mode II precrack. 450 400 350 300 z 0

250 200

P

150 100 50 0 0

2

4

6

8

10

12

displacement(mm)

Fig. 6. Typical load-displacement for a [nt-5~ specimen tested from the insert.

Fracture Mechanics Concepts and Structural Integrity... 450 400

j

350 300 z

J

250

9

J I

/

o 200 150 100

0

2

4

6

8

lo

12

displacement (mm)

Fig. 7. Typical load-displacement for

a [-]--5~

specimen tested from a mode II precrack.

80O

700

~.

600

/

z'-" 500 "o 400

o

300

0

|

0

1

2

3

4

5

6

displacement (ram)

Fig. 8. Typical load-displacement for a [+100]4 specimen tested from the insert. 9OO 8OO 70O

A z

600 500

/

"~ 400

/

S

300 200 IO0 0 0

1

2

3

4

5

6

displacement (mm)

Fig. 9. Typical load-displacement for a [__100]4 specimen tested from a mode II precrack.

259

260

A. TORRES MARQUES, A.B. DE MORAIS, J.F. SILVA, P.T. DE CASTRO 3000 2500 2000 m Insert 9Crack 1 [] Crack 2

1500 B

1000 500

i

1

|

2

i

3

|

|

4

5

6

#specimen

Fig. 10. Results obtained for all tested [0~ specimens. 2500

2OOO

N" 1500

B

Crack Crack

1000 500

!

1

|

2

|

3

,

|

4

5

6

#specimen

Fig. 11. Results obtained for all tested [-t-5~ specimens. 3000

i

2500

20OO

li ,nse.

1500

Crack Crack

1000 500

I

i

1

2

|

3

i

4

=

5

6

#specimen

Fig. 12. Results obtained for all tested [+10~ specimens.

Fracture Mechanics Concepts and Structural Integrity...

261

3000

2500 2000

.9.0 0

l i Insert Crack 1 Crack 2

1500 1000 500 0

5 0 (deg.)

10

Fig. 13. Comparison of the average results. Table 1. Filament winding parameters used. Variable

Mandrel rotational speed Fibre tension Used rovings Number of layers Band-width

Units

Value

min -1 gTex -1

30 0.3

mm

4 5

1

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263

A U T H O R INDEX Albrecht, P. 211 Atkinson, C. 1 Bathias, C. 163 Bressers, J. 115 Buzzichelli, G. 235 Clark, G. 97 de Castro, P.T. 253 de Morais, A.B. 253 Elices, M. 183 Elizalde, M.R. 47 Guinea, G.V. 183 Jones, D.R.H. 29 Martinez-Esnaola, J.M. 47 Martin-Meizoso, A. 47 Mughrabi, H. 13

Nowell, D. 73 Peteves, S. 115 Planas, J. 183 Rejda, E. 135 Ruiz, C. 73 Sfinchez, J.M. 47 Silva, J.F. 253 Smith, R.A. 173 Socie, D. 135 Steen, M. 115 Torres Marques, A. 253 Wright, W. 211 Yoshimura, T. 155

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