Residual Stress and Its Effects on Fatigue and Fracture: Proceedings of a Special Symposium held within the 16th European Conference of Fracture - ECF16, Alexandroupolis, Greece, 3-7 July, 2006

Residual Stress and Its Effects on Fatigue and Fracture

Residual Stress and Its Effects on Fatigue and Fracture Proceedings of a Special Symposium held within the 16th European Conference of Fracture – ECF16, Alexandroupolis, Greece, 3-7 July 2006

Edited by A.G. Youtsos Joint Research Centre Petten, The Netherlands

A C.I.P. Catalogue record for this book is available from the Library of Congress.

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Symposium on Residual Stress and its Effects on Fatigue and Fracture Alexandroupolis, Greece July 2006 Organized by A.G. Youtsos

Symposium Chair: A.G. Youtsos Institute for Energy, Westerduinweg 3, NL 1755 LE Petten, The Netherlands Phone: +31-224-565262, FAX : +31-224-565628 E-mail: [email protected] Symposium Co-chair: P.J. Withers Manchester Materials Science Centre, Grosvenor St., Manchester, MI 7HS, UK Phone: +44-161 306 8872, FAX: +44-161 200 3636 E-mail: [email protected]

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Preface of ECF16 Chairman Emmanuel E. Gdoutos

The “16th European Conference of Fracture,” (ECF16) was held in the beautiful town of Alexandroupolis, Greece, site of the Democritus University of Thrace, July 3-7, 2006. Within the context of ECF16 forty six special symposia and sessions were organized by renowned experts from around the world. The present volume is devoted to the symposium on “Residual Stress and its Effects on Fatigue and Fracture,” organized by Dr. A.G. (Tassos) Youtsos of the European Joint Research Center in Petten, The Netherlands. I am greatly indebted to Tassos who undertook the difficult task to organize this symposium and edit the symposium volume. Started in 1976, the European Conference of Fracture (ECF) takes place every two years in a European country. Its scope is to promote world-wide cooperation among scientists and engineers concerned with fracture and fatigue of solids. ECF16 was under the auspices of the European Structural Integrity Society (ESIS) and was sponsored by the American Society of Testing and Materials, the British Society for Stain Measurement, the Society of Experimental Mechanics, the Italian Society for Experimental Mechanics and the Japanese Society of Mechanical Engineers. ECF16 focused in all aspects of structural integrity with the objective of improving the safety and performance of engineering structures, components, systems and their associated materials. Emphasis was given to the failure of nanostructured materials and nanostructures and micro- and nanoelectromechanical systems (MEMS and NEMS). The technical program of ECF16 was the product of hard work and dedication of the members of the Scientific Advisory Board, the pillars of ECF16, to whom I am greatly indebted. As chairman of ECF16 I am honored to have them on the Board and work closely with them for the success of ECF16. ECF16 has been attended by more than nine hundred participants, while more than eight hundred papers have been presented, far more than any other previous ECF over a thirty year period. I am happy and proud to have welcomed in Alexandroupolis wellknown experts, colleague, friends, old and new acquaintances who came from around the world to discuss problems related to the analysis and prevention of failure in structures. The tranquility and peacefulness of the small town of Alexandroupolis provided an ideal environment for a group of scientists and engineers to gather and interact on a personal basis. I wish to thank very sincerely the editor Dr. A.G. Youtsos for the excellent appearance of this volume and the authors for their valuable contributions. Finally, a special word of thanks goes to Mrs. Nathalie Jacobs of Springer who accepted my proposal to publish this special volume and her kind and continuous collaboration and support.

Emmanuel. E. Gdoutos Chairman, ECF16 January 2006 Xanthi, Greece

vi

Preface of the Symposium Chairman A.G. Youtsos Residual stresses originate from the elastic accommodation of misfits between different regions in a structure. In practice it is unlikely that any engineering component is entirely free from residual stress because of the material processing, fabrication and service load history. The interaction between the misfit and its elastic accommodation in the surrounding material determines the magnitude of the resultant residual stress and its length-scale. In order to assess the influence of residual stress on the fracture behaviour of a structure, it is essential to quantify the residual stress field over the length-scales of concern from a structural integrity viewpoint. Simplified fracture mechanics based assessment methods are widely used by industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected degradation of engineering components under normal and abnormal service loads. In many cases, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. Various procedures provide upper bound residual profiles for various classes of welded joints that can be used in fracture assessments, but these often give very conservative results. Recently, the option to use more realistic profiles has been adopted, but only where such profiles are based on finite element residual stress simulations supported by detailed residual stress measurements. Rapid advances in the capability of residual stress measurement techniques, such as the contour and deep hole drilling techniques as well as the neutron and synchrotron X-ray diffraction methods, now readily allow residual stresses and strains to be mapped on defined planes within a structure. Oral presentations of this symposium have been grouped in three topic areas and four technical sessions covering theoretical/numerical and experimental analyses of residual stress and its effects on fatigue and fracture. I wish to thank all those who have assisted in the preparation of this symposium. Furthermore, I wish to thank very sincerely the ECF16 Chairman, Professor Emmanuel E. Gdoutos for his enthusiastic support to its organization. Finally I wish to thank Ms. Nathalie Jacobs and Ms. Anneke Pot of Springer for their kind support toward publication of these Proceedings by Springer.

A.G. Youtsos Symposium Chairman March 2006 Petten, The Netherlands

vii

Table of Contents

Organizers

v

Preface of ECF16 Chairman

vi

Preface of Symposium Chairman

vii

Session: Residual Stress Analysis by Modelling Techniques – I Residual Stress Numerical Simulation of Two Dissimilar Metal Weld Junctions P. Gilles, L. Nouet, J. Devaux, and P. Duranton . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Finite Element Simulation of Welding in Pipes: A Sensitivity Analysis D.E. Katsareas, C. Ohms, and A.G. Youtsos . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

Residual Stress Prediction in Letterbox-Type Repair Welds L.K. Keppas, N.K. Anifantis, D.E. Katsareas, and A.G. Youtsos . . . . . . . . . . . . . . 27 Viscosity Effect on Displacements and Residual Stresses of a Two-Pass Welding Plate W. El Ahmar, and J.-F. Jullien . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

Session: Residual Stress Analysis by Experimental Methods Evaluation of Novel Post Weld Heat Treatment in Ferritic Steel Repair Welds based on Neutron Diffraction C. Ohms, D. Neov, A.G. Youtsos, and R.C. Wimpory . . . . . . . . . . . . . . . . . . . . .

55

High-Resolution Neutron Diffraction for Residual Strain/Stress Investigations P. Mikula, and M. Vrána . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Effects of the Cryogenic Wire Brushing on the Surface Integrity and the Fatigue Life Improvements of the AISI 304 Stainless Steel Ground Components N. Ben Fredj, A. Djemaiel, A. Ben Rhouma, H. Sidhom, and C. Braham . . . .

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Surface Integrity in High Speed Machining of Ti-6wt.%Al-4wt.%V Alloy J.D. Puerta Velásquez, B. Bolle, P. Chevrier, and A. Tidu . . . . . . . . . . . . . . . . .

87

ix

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Table of Contents

The Present and the New HFR-Petten SANS Facility O. Uca, C. Ohms, and A.G. Youtsos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

97

Session: Residual Stress Analysis by Modelling Techniques – II Sensitivity of Predicted Residual Stresses to Modelling Assumptions S.K. Bate, R. Charles, D. Everett, D. O’Gara, A. Warren, and S. Yellowlees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

105

Welding Effects on Thin Stiffened Panels T.T. Chau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

117

Evaluation of Residual Stresses in Ceramic and Polymer Matrix Composites Using Finite Element Method K. Babski, T. Boguszewski, A. Boczkowska, M. Lewandowska, W. Swieszkowski, and K.J. Kurzydlowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Phase Transformation and Damage Elastoplastic Multiphase Model for Welding Simulation T. Wu, M. Coret, and A. Combescure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

149

Session: Residual Stress Effects on Fatigue and Fracture Identification of Residual Stress Length Scales in Welds for Fracture Assessment P.J. Bouchard, and P.J. Withers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163

Interaction of Residual Stress with Mechanical Loading in a Ferritic Steel A. Mirzaee-Sisan, M.C. Smith, C.E. Truman, and D.J. Smith . . . . . . . . . . . . . .

177

Effects of Residual Stresses on Crack Growth In Aluminum Alloys B. Kumar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

189

Effect of Reflection Shot Peening and Fine Grain Size on Improvement of Fatigue Strength for Metal Bellows H.Okada, A.Tange, and K. Ando . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

201

Surface Crack Development in Transformation Induced Fatigue of SMA Actuators D.C. Lagoudas, O.W. Bertacchini, and E. Patoor . . . . . . . . . . . . . . . . . . . . . . . . .

209

Assessment of Defects under Combined Primary and Residual Stresses A.H. Sherry, J. Quinta da Fonseca, K. Taylor, and M.R. Goldthorpe . . . . . . .

223

Author Index

233

Session: Residual Stress Analysis by Modelling Techniques – I

RESIDUAL STRESS NUMERICAL SIMULATION OF TWO DISSIMILAR METAL WELD JUNCTIONS Philippe Gilles and Ludovic Nouet AREVA NP Tour AREVA Paris la Défense 92084, France

Josette Devaux and Pascal Duranton, ESI-France ESI-France Le Discover, 84 Bd. Vivier Merle 69485 Lyon France In nuclear reactors such as Pressurized Water Reactors (PWR), heavy section components made in low alloy steel are connected with stainless steel piping systems. The dissimilar metal weld (DMW) junctions are performed following a special manufacturing procedure to ensure a good resistance of the joint. However, several experiences from the field confirm sensitivity to fatigue, corrosion or the existence of low toughness areas in this type of junction. Fatigue, corrosion and brittle fracture risks are enhanced by tensile residual stress fields, therefore reliable determination of residual stress fields in DMWs are of importance. The high level of residual stresses due to manufacturing process is greatly reduced by a post weld heat treatment (PWHT); however a full relief is impossible at the interface between weld material and the ferritic steel because of the difference in dilatation coefficients of these materials In the present work a full numerical simulation of residual stress fields was conducted on two different Dissimilar Metal Weld mock-ups manufactured respectively for the two EC projects BIMET and ADIMEW. The paper recalls the experimental residual strain measurements performed on the 6” (BIMET) and 16” (ADIMEW) DMW junctions, details the features of the numerical simulations and compares numerical predictions to the measurements. Furthermore in both cases, the effect of the PWHT on the residual stress fields has been investigated numerically. Introduction In the framework of the European Community Research and Development Programme two projects (DG-RTD programmes BIMET, C. Faidy et al. [1] and ADIMEW, C. Faidy [2]) have been sponsored on the fracture behaviour of cracked stainless steel/ferritic steel bimetallic welds. In each of these projects, the mock-ups were (at least) duplicated: one in which a surface notch was machined in the buttering parallel and close to the ferritic interface for the fracture test and another one for residual stresses evaluation and material characterization. Residual stress measurements were performed using the neutron diffraction technique [3] across the piping thickness in the buttering, weld and the HAZ of the base material. In the ADIMEW project, residual stress measurements were also carried out on the surface by the Hole Drilling method [4] and verifications were also made later by the Cut-Compliance method [5]. The BIMET project has been launched to examine the feasibility of the ADIMEW project which aimed to perform a large scale fracture test on a 16” pipe at 300°C. For BIMET several tubular mock-ups of 6” have been manufactured following an US nuclear

3 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 3–13. © 2006 Springer.

4

Gilles et al.

specification. The BIMET weld connects an A508 ferritic steel pipe section to a 304 stainless steel pipe section and is a type 308 austenitic vee join with type 308/309L buttering laid on the ferritic pipe. In the ADIMEW project, two DMW specimens have been manufactured: one for a 4-point bending fracture test and one for the experimental determination of welding residual stresses and the generation of material property data. The ADIMEW mock-ups were much larger than the BIMET ones, but the type is similar: an A508 ferritic steel pipe section is joined to a 316 stainless steel pipe section with a 308 filler metal vee connection. A 308/309 SS buttering is applied on the ferritic pipe. This paper presents numerical simulations of the welding process of the BIMET 6” and the 16” ADIMEW Dissimilar Metal Weld mock-ups. The calculations were performed by ESI and AREVA-NP for different modelling of the material behaviour. Mock-ups and residual stress measurements The BIMET tubular mock-ups (Fig. 1) had a length of 393 mm and outer and inner diameters of 168 and 118 mm (25 mm thick). Two mock-ups with two different notch depths were used for fracture testing and one for material characterisation and residual stress measurements.

200

200

30

25

304L

A508

168

118

25 deg

6

Figure 1: BIMET Dissimilar Weld Metal Junction mock-up The ADIMEW mock-ups (Fig. 2) were much larger than the BIMET ones, the final external diameter and thickness being respectively 453 and 51 mm. To guarantee the quality of the DMWs, a considerable experience and high degree of quality control has been required within the weld manufacturing process, in accordance with AREVA-NP basic nuclear specification.

Residual Stress Numerical Simulation

$

/

Ø 467

530

Ø 339

Ø 321

Ø 467

510

5

3RLQWDJH

Figure 2: ADIMEW Dissimilar Weld Metal Junction mock-up (before machining) Residual stress measurements The Neutron Diffraction (ND) technique has been applied by the Institute of Energy (IEJRC) to determine the residual stress fields non-destructively and through thickness. Neutron diffraction stress measurements are based on the Bragg principle illustrated on Fig. 3 (taken from [6]): an incident neutron of wavelength O is scattered by a crystalline lattice in such a way, that diffraction peaks occur in scattering directions 2Thkl , where the combination of O, Thkl and the observed lattice distance dhkl fulfill the following equation:

Ȝ

 2 d hkl sin ș hkl

İ

sinș 0 1 sinș

(1) The scattered neutrons are counted by means of an appropriate neutron detector and after analysis of the neutron count profile the scattering angle 2Thkl is determined. The residual strain in the measurement direction (bi-section of the incoming and diffracted beams) is obtained by measuring the scattering angles on a stress-free companion specimen (2T0) and on the sample exhibiting residual stress. (2) NEUTRON SOURCE SLIT INCOMING BEAM

MEASURING DIRECTION

SAMPLING VOLUME DIFFRACTED BEAM

SAMPLE

24

DETECTOR

SLIT

Figure 3. Bragg scattering of neutrons from the shaded area to measure the lattice spacing in the indicated measuring direction

6

Gilles et al.

Strains are measured in three orthogonal directions (ideally the principal directions) at each location of interest, and by using Hooke’s law residual stresses can then readily be determined. Four points should be emphasized about the ND technique: ƒ Reference scattering measurements have to be performed on a stress-free reference sample. ƒ The reflection planes depend on the structure of the materials: (110) for the ferrite, (200) for the austenite in weld and buttering, (111) for the austenite in the HAZ. ƒ Neutron diffraction test data represent average values of residual stresses over a gauge parallelipipedic volume the size of which lies in the 3 to 10 mm range. ƒ The determination of the residual stresses at any location within the material the strains have to be measured in at least three independent directions at this location. In BIMET and ADIMEW, the measurements revealed a strong (200)-texture within the weld and buttering layer. Because of this unfavourable texture, in the axial direction half of the weld pool could not be tested. In BIMET the gauge volume was: 4 x 4 x 5 to 4 x 4 3 x 10 mm . In ADIMEW, the gauge volume was larger. Methodology of numerical simulation of welding of dissimilar metal joints Main features of the methodology The methodology developed by AREVA-NP in simulating the welding of dissimilar metal weld joints is defined by the following features: ƒ ƒ ƒ ƒ ƒ

Heat input modelling by 3D computation of temperature fields induced by a moving source, the source being calibrated on sizes of the melted zone and the HAZ. Accurate representation of the material behaviour, accounting for cyclic strain hardening, phase transformations, tempering effects and creep. Simulation of the mock-up entire welding process, from buttering stage to weld groove filling using a Thermo-Metallurgical-Mechanical model (TMM) and a pass by pass automatic procedure. Simulation of the machining by simple material removal Simulation of the PWHT using a creep law

Thermal and thermo-metallurgical SYSWELD“ software [7].

computations

have

been

performed

using

Heat input characterization It is assumed that uncoupled quasi-static thermoelasticity equations are applicable here, since thermal dissipation phenomena in metals are insignificant, thus the transient thermal problem is solved first. A welding process is characterized by its welding energy E = U.I / v (where I and U are respectively the welding intensity and voltage and v the torch speed) and the preheat temperature. Only a fraction of this energy is transferred to the weld material, the heat input into the deposited material is given by the expression:

QR

Ș˜

UI v(t)

(1)

The efficiency coefficient K is characteristic of the welding process and is obtained trough calibration of the size of the melted zone, the size of the Heat Affected Zone and/or measured thermal cycles. In the present study the temperature measurements

Residual Stress Numerical Simulation

7

available for the ADIMEW case were not considered as reliable since the measurement locations were too far from the weld pool. For the calibration, elementary computations are performed using a 3D quasi stationary approach. The 3D computation allows accounting for the displacement of the torch. The calibration is carried out for each type of welding: 4 in our case, first and second / third buttering layers, root pass and filling passes. This 3D calibration gives a characteristic thermal cycle which will be applied on the corresponding deposited bead. The size and shape of the heat source have to be determined trough these inverse computations. However the influence of these factors is much lower than the welding parameters. For a welding process with filler material, a volume heat source is recommended and a cylindrical shape has been selected in this study. This approach gives representative heating rates and which are almost the same all along the border of the deposited material. This is illustrated in Figure 4 for the root pass deposit. The temperatures exceed 1800°C, which is beyond the fusion temperature and may be considered as the maximum temperature reached in the deposited weld material.

Figure 4. Calibration of the heat input applied to the root pass Material behavior The second key step in the welding simulation is the characterization of the behavior of the materials involved in the welding process. The following properties and behavior laws have to be determined from room temperature to fusion temperature. ƒ

Thermo physical properties: thermal conductivity, specific heat and density. The latent heat and phase transformation heat have been neglected.

ƒ

Phase transformation phenomena: ferritic phases o solid austenitic phase during heating and the reverse during cooling (creation of bainite and martensite), the solidification of the austenitic phase in 308 austenitic stainless steel.

ƒ

Tempering effects on quenched ferritic parts which reduce the yield strength below 400°C.

ƒ

Mechanical characteristics: the thermal expansion coefficient for the thermal strain computation, the elastoplastic behavior laws used for stress computation

8

Gilles et al.

during welding and the creep laws for stress computation during the Post Weld Heat Treatment simulation. For the ferritic steel (A508) this had to be done for the austenite and ferritic phases. The characterization has been also conducted for the austenitic steels 304L (BIMET) and 316L (ADIMEW) as well as for the buttering materials (308/309L). All these results have been taken from private data bases. In the frame of a cooperative action with INSA-Lyon, EDF and the French Safety Authorities, the behavior of all the ferritic phases of the 16MND5 ferritic steel (A508 in US standards) has been characterized (see for details on phase transforms [8]) and a similar work has been conducted on austenitic steel [9]. Heating transformations are characterized by the temperatures of start and arrest of the austenitization which depend on the heating rate. The cooling transformations are characterized Continuous Cooling Transformation diagrams. In SYSWELD, the phase transformations are computed using the Leblond model ([10], [11]). The modelling of phase transformations allows to obtain good predictions of the size of the HAZ, which is of interest for checking the quality of temperature calculations, but do not affect predictions in the weld. The stress-strain laws are extrapolated up to 20% of plastic strain. The data related to the cyclic behaviour of the materials as function of temperature being too scarce, an isotropic cyclic behaviour of the materials has been assumed. Discretization of the multipass welding process The two DMW joints are axisymmetric, but the thermal loading is local and one should use a 3D model for the step by step computation of the stresses in the weld beads under a heating source moving along the pipe circumference. However in a thick pipe, the weld deposit do not change the overall pipe geometry and the stress state is mainly induced by the effects of thermal cycle applied to the bead or to the neighbouring ones and the restrain imposed by the cold structure. If we except the restart point, each of the beads on a given circumference is subjected to the same boundary conditions, and therefore an axisymmetric model of the weld deposit is likely to be representative. We considered then 2D axisymmetric models. The self restraint effect of the cold parts during welding is taken into account by appropriate boundary conditions: fixed end displacements are applied during the heating phase and free boundary conditions during the cooling phase. The mock-ups have been meshed using quadratic elements. The use of quadratic elements increases the size of the problem, but they give much better results than linear elements (for the same number of nodes) at locations where stress gradients are high like at the material interfaces. Simulation of the welding steps The bead-by-bead (BBB) simulation of the buttering and weld deposition has been performed for the two DMW joints. The deposit of a pass is modeled trough the “activation” of the group of elements representing the pass cross section. All of these elements have to be generated from the beginning of the meshing procedure and remain inactive until the time at which the weld pass to which they belong is deposited. The deposit of the beads follows the weld-pass sequence described in the welding records. The deactivation and activation of elements during the simulation is achieved through the “birth & death of elements” technique: the deactivation or “death” is achieved by multiplying their material characteristics (conductivity or stiffness for thermal or mechanical analysis, respectively) by a strong reduction factor. A same type of approach has been used by other researchers as Katsareas for example [11]. The main difference between the two cases is that no PWHT has been applied to the BIMET mock-up (as stated in [1]), but on a PWHT of 6 hours at 600°C has been applied to the ADIMEW mock-up before the final machining.

Residual Stress Numerical Simulation

9

As shown on Figure 5b, the BIMET simulation based on our database characteristics (BBB_charact2) overestimates largely the measurements. This is mainly due to the selection of an isotropic strain hardening and to an identified bias in our austenitic stainless steel data base which contains data corresponding to pre hardened materials. We performed a second simulation (inoxHR_NoPWHT) accounting for the hardening recovery phenomenon which appears during cooling of the austenitic material. The results are much closer to the measured values, thus the hardening recovery has been considered in all the BIMET results presented in the following. In the ADIMEW computations our austenitic steel data base is better suited for describing the 316L behavior and hardening recovery of the ferritic phase during austenitization has been considered. On this graph, is also drawn the result (Cooling_computation) of a simulation of simple cooling from the PWHT temperature (600°C). These results are much lower than the measured values, which invalidates the hypothesis of a full stress relief at 600°C. However, the inoxHR_NoPWHT result overestimates the results in the ferritic side which will be discussed in the § on PWHT effect. Simulation of machining The machining is modelled making the element strength to vanish: the Young modulus is decreased to a very low value and Poisson ratio is set to zero. Only the removal of material and its consequences on stress redistribution is taken into account. The heating due to machining is neglected.

Figure 5. Discretization of the structure and comparison of computational hypotheses in the BIMET case Comparisons between predictions and measurements All the comparisons presented in this paragraph are made in terms of strains. The comparison on strains is more suited for a comparison with measurements and allows separating potential uncertainties on measurements. Figures 6 (a to d) show the comparison between measured and computed strains in the BIMET mock-up. Figures 7 (a to d) display the same type of results for the ADIMW mock-up. The computed results presented in this paragraph represent averages of strains over a gage volume as in the measurement: the selected “gage” section are squares of 4x4 mm for BIMET and 5x5 for ADIMEW.

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Gilles et al.

Figure 6. Comparison of strain predictions with ND measurements in BIMET mock-up In BIMET configuration, the agreement between predicted strains and measured ones is good in general. Comparisons have been carried out on four different lines parallel to the pipe axis: at 3, 9.3 mm, 15.7 and 22 mm from the outer surface. We present comparisons along the 3 and 15.7 lines, but the trends are the same on the other ones. The trough thickness axial bending is overestimated in the ferritic section. On the contrary on hoop strains the agreement is better in the ferritic than in the austenitic section. But in weld and buttering computed and measured strain distributions are pretty close to each other. The same conclusions may be drawn on stress distributions from figure 5b. The same type of comparison has been conducted for the ADIMEW case. The results presented in Figure 7 shows an excellent agreement, except for an erratic axial strain measurement in the groove. In the ADIMEW project, it has been concluded concerning neutron diffraction measurements that the results were much more reliable in the circumferential direction and in general radial and axial values should be disregarded in the welded zone. In the ADIMEW computations the good results obtained on the 316L side are explained by the fact that hardening at high level of strains has been truncated: this is a rough technique, but a more refined description with hardening recovery would have lead to the same result. The strains (or stress) distributions are similar in both DMWs: ƒ Axial direction: trough thickness bending and 3 levels along the DMW, medium in the austenitic stainless steel, low in the weld, high in ferritic steel. ƒ Circumferential direction: trough thickness membrane and bending (membrane being dominant) and 3 levels along the DMW, negative in the austenitic

11

Residual Stress Numerical Simulation

stainless steel, positive in the weld, negative in ferritic steel and lower than in the austenitic part. The circumferential bending distribution is relatively more important in the smaller DMW. ND_Mes_12,75mm BeadByBead_Av

Axial strains: Measures / Simulations (12.75mm)

ADIMEW / hoop strains: Measures / Simulations (12.75mm)

316L

Weld 2000

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-40

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20

40

60

Figure 7. Comparison of strain predictions with ND measurements in ADIMEW mock-up Analysis of the effect of the Post Weld Heat Treatment BIMET: axial stresses in the middle of the buttering 500

ADIMEW / axial stresses in the middle of the buttering 450

Stress measurement

400

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ADIMEW / hoop stresses : Measures / Simulations (Butterring)

InoxHR_Av_withPWH T

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Measurements BeadByBead_NoPWHT_Av

700

BeadByBead_withPWHT_Av

600

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500

stress (MPa)

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30

depth (mm)

-400 0

25

-150

100 0 -100 -200

distance from the outer surface (mm)

-300

400 300 200

-100 5

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depth (mm)

Root

0

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0

Invalid measure ??

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BIMET – Middle of the buttering

25

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-200

ADIMEW– Middle of the buttering

Figure 8. PWHT effect on trough thickness axial and hoop stress distributions in BIMET and ADIMEW mock-ups Figure 8 shows the influence of the Post Weld Heat Treatment on the residual stresses in the buttering. We observe that: ƒ

Again the agreement between measurement and computations is good: in ADIMEW on which PWHT has been applied, the computations with PWHT are in closer agreement with the measurements and in BIMET, were no PWHT as

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been applied, the predictions without and with PWHT embraces the measurements. ƒ

The shape of the stress distributions is about the same in both DMWs.

ƒ

The stress relief seems more important in the large DMW.

ƒ

The stress relief reduces more the axial stresses in general, but the PWHT is far from being effective: the maximum percentage of stress reduction is 40%!

ƒ

On the inner wall of the DMW, the axial stress is compressive even after PWHT, but the circumferential stress in the weld is tensile. Conclusions

A simulation of the mock-up entire manufacturing process, from buttering stage to final machining and PWHT of two DMWs was undertaken using a Thermo-MetallurgicalMechanical model and a pass by pass automatic procedure. We may conclude from this study, that: ƒ Predicted strains are in good agreement with Neutron Diffraction measurements on BIMET and ADIMEW mock-ups. The quality of the comparison has been improved since bearing on strains averaged on the gage volume. ƒ These results could be improved provided more detailed characterization of the cyclic strain hardening behavior is performed. ƒ Assuming PWHT is applied on both mock-ups, the stress profiles are very similar in both DMW mock-ups. In the larger DMW junction. ƒ The stress relief has a limited efficiency but non negligible on the axial stresses: the PWHT relief mainly an axial bending moment. The assumption of total relief after PWHT underestimates significantly the stress levels. ƒ In both DMWs, on the inner wall in the weld and the buttering, the axial stress is compressive and the circumferential stress is tensile. Acknowledgments The authors would like to thank DG-RTD of the European Commission for its support to the two EC R&D programs BIMET and ADIMEW. References 1.

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

Faidy C., Chas G., Bhandari S., Sainte-Catherine C., Hurst R., Nevasmaa P., Schwalbe K., Brocks W., Lidbury D. and Wiesner C.: “BIMET: Structural Integrity of Bi-Metallic Components“. Proc. of the “FISA’97 Conference”, Luxembourg, 17-19 November (1997). Faidy C., “Structural integrity of dissimilar welds – ADIMEW project overview” In Proceedings of PVP 2004, ASME Pressure Vessel and Piping Conference, USA (2004). Ohms C., Youtsos A. G., Textures and Microstructures, Vol. 33, pp. 243 – 262 (1999). Beaney E M: “Accurate measurement of residual stress on any steel using the centre hole method“ Strain, 9999-106, April (1976). Schindler H. J: “Residual stress effects on crack growth mechanisms and structural integrity', 9th Conf. on Mechanical Behaviour of Materials, Geneva, Switzerland, 2529, May 2003. Ohms C., Katsareas D. E., Wimpory R. C., Hornak P., Youtsos, A. G., “Residual stress analysis in a thick dissimilar metal weld based on neutron diffraction”, PVP Vol. 479, ASME Pressure Vessel and Piping Conference, USA, July 2004. SYSWELD“, User’s reference manual. ESI-group, 9 rue des Solets, BP 80112, 94513, Rungis, France.

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8.

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Vincent Y., Petit-Grostabussiat S. and Jullien J-F, “Thermal, Metallurgical and Mechanical Simulations and Experimental Validation of the Residual Stresses in the Heat-Affected Zone”, in Mathematical modeling of weld phenomena, H. Cerjak Ed., Maney Publihing (2002) . 9. Depradeux L. and Jullien J.-F., “Numerical Simulations of Thermomechanical Phenomena During TIG Welding and Experimental Validation on Analytical Tests of Increasing Complexity”, Proceedings of the 7th conference on Numerical Analysis of Weldability , Seggau Graz, Austria, Sept. (2003). 10. Leblond J.- B., Mottet G. and Devaux J.-C. , “A theoretical and numerical approach to the plastic behaviour of steels during phase transformations, I & II”, J. Mech. Phys. Solids, 34, p. 395-432 (1986). 11 Leblond J.-B., Devaux J. and Devaux J.-C, “Mathematical modelling of transformation plasticity in steels - I : Case of ideal-plastic phases - II : Coupling with strain hardening phenomena”, Int. Jour. of Plasticity, 5, p. 551-571 (1989). 12 Katsareas D. and Youtsos A., “Residual stress prediction in Dissimilar Metal Pipe Joints using the Finite Element Method”, Materials Science Forum Vols 490-491, pp. 53-61 (2005)

FINITE ELEMENT SIMULATION OF WELDING IN PIPES: A SENSITIVITY ANALYSIS

D.E. Katsareas Machine Design Laboratory Mechanical Engineering & Aeronautics Department University of Patras Rion, GR-26010 Greece C. Ohms and A.G. Youtsos High Flux Reactor Unit Institute for Energy, EC-JRC PO2, 1755 ZG Petten, The Netherlands

ABSTRACT Thermal cycling, high heating rates, high temperature peaks and inter-pass and post weld cooling are parameters that largely affect residual stress generation in and around welds. A multi-pass weld joining two pipes made of different materials is simulated using 2-D axi-symmetric finite element analysis. The proposed methodology for weld simulation incorporates the well-known birth of elements technique and follows the prescribed temperature approach for heat input modeling. The effect of various aspects of modeling, on the accuracy of predicted residual strains, is investigated through a series of sensitivity tests, using a 2-D axi-symmetric model. Radiation, creep and heat input model selection, have a significant impact on results, but phase change, convective cooling and pipe contact are not as important. Results are also compared to neutron diffraction measurements obtained from the literature. Welding electrode start/stop effects on predicted residual strains are found to be significant, after a limited 3-D analysis, which justifies further investigation. Introduction Residual stresses influence considerably nuclear power plant component integrity, by affecting service-induced crack initiation and even crack propagation. This influence can be even more severe under the presence of corrosion mechanisms, like inter-granular stress corrosion cracking in austenitic steel pipes. Such failure mechanisms are common in stainless steel piping used in pressurized water reactors. As early as 1979 [1] residual stresses in pipes due to welding have been investigated experimentally. Faure and Leggatt [2] utilized destructive test methods, like the center-hole and layering methods, to determine the residual stress fields in austenitic-ferritic pipe welded joints. The common trend in industry, when developing a welding procedure specification, is to base it on a large number of costly and complicated experiments.

15 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 15–26. © 2006 Springer.

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Computer simulation of welding and finite element prediction of residual stresses present a cost effective and more efficient alternatives to the engineer/designer of welds, as long as these methods have been validated and proven in the field. Finite element simulations are in general supplementing the experimental tests for the evaluation of welding residual stresses. As early as 1978 [3-8] two and three-dimensional models of welds have been used for pipe welded joints. Lindgren [9] has shown that over the last 25 years of recorded weld simulation efforts, FE model sizes have increased by a factor of 104. This dramatic increase was allowed, off course, by a similar increase in computer power and clearly illustrates the continuous effort for model refinement and increase in accuracy. This effort reflects the trend in industry to shift the welding residual stress evaluation from an experimental to a computational based procedure. Fricke et al [10] have developed FERESA, a finite element code based on ABAQUS, dedicated to welding simulation and residual stress predictions and validated it by analyzing an austenitic pipe weld using 2-D and 3-D models. It is common practice among researchers to develop in-house finite element codes for weld simulation. Such codes, though, lack the universality of commercially available software, which is favored by the industry. This is due to the fact that, residual stress analysis procedures based on them can be readily transferred to industrial applications. In the present paper, a multi-pass weld joining two pipes made of different materials is simulated using 2-D axi-symmetric and 3-D solid finite element models. The proposed methodology for weld simulation incorporates the well-known birth of elements technique and follows the prescribed temperature approach for heat input modeling. The effects of various aspects of modeling, on predicted residual strains, are summarized through a series of sensitivity tests, using the 2-D model [11-13]. It is concluded that contact analysis, simulating the assembly of the two pipes, convective cooling and phase change, when incorporated into the model have very little or no effect on predicted residual strains, whereas the radiation boundary condition, creep and heat input load due to welding modeling need to be considered carefully in the FE model. Predicted residual strains are also compared to neutron diffraction measurements [14]. The limited 3-D analysis, using a coarse FE mesh and lumping of weld passes in order to minimize computational cost, concentrates on the effect that the welding electrode start/stop has on predicted strains along the circumference of the pipe. It is found that there is a strong indication of such an effect that justifies a more detailed and thorough 3-D investigation. The ultimate goal of the present analysis is to determine the level of simulation detail, which can be implemented under a realistic computational cost, but at the same time achieving the industrial requirement of accuracy, regarding residual stress predictions. The results obtained from the current analysis, illustrate the main objective of the present work, which is the development of an efficient numerical tool for simulating welded joints and predicting residual stresses in industrial applications. The efficiency is highly appreciated since simulation time is of paramount importance, if the proposed method is to be used as a welding simulation and residual stress prediction tool for industrial R&D. Low CPU times, small manageable FE models and off-the-self commercial FE codes used on non-high-end computers are the advantages that will make the proposed method attractive to weld designers and CAE engineers in relevant industries. Finite element models For the sensitivity analysis conducted in this paper, a dissimilar metal pipe weld (DMW) is investigated. This is comprised of an austenitic stainless steel pipe (316L) and a ferritic low alloy steel pipe (A508), joined together via a 96-pass gas tungsten arc manual weld. The pipe assembly shown in Fig. 1a was designed and manufactured for the purposes of research projects ADIMEW and NESCIII. Both projects were focused on the structural integrity assessment and evaluation of welded steel components, acknowledging at the

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same time the important role of residual stresses by launching a computational and experimental round robin for their evaluation. Material properties, welding parameters and a detailed account of the manufacturing stages followed for the fabrication of the DMW can be found in [11-13]. The weld pass sequence is illustrated in Fig. 1b, whereas a macrograph of the weld cross-section together with weld groove dimensions is presented in Fig. 2b.

Figure 1. (a) Geometry of the DMW pipe assembly and (b) weld pass sequence For the finite element analysis of the DMW pipe two models are used, a 2-D axisymmetric one, depicted in Fig. 2a and a 3-D solid model, presented in Fig. 3b. Details on the 2-D mesh can be found in [12-13]. Figure 2 shows the mesh of the complete pipe assembly, which includes the two pipes, weld and buttering prior to final machining. In this case the solid mesh of Fig. 3b is generated by sweeping the 2-D mesh of Fig. 3a o o along the pipe circumference (360 ), using a 30 step. Convergence tests have shown o that a circumferential step of 30 is sufficient without significantly compromising the accuracy of predicted residual strains. Early in the investigation, though, it was evident that this treatment is very time consuming and computationally expensive for the class of industrial problems represented here by the DMW pipe. The reason why the 3-D model is not based on the 2-D mesh of Fig. 2a is the extremely high computational cost that would have. The 2-D structural analysis, using the mesh of Fig. 2 (26000 degrees of freedom), takes about 8 hours on an Intel P4 computer at 1.8GHz with 512MB RAM. The corresponding 3-D model would have 700000 degrees of freedom, which would have rendered a 3-D analysis impractical. The coarse mesh of Fig. 3a has only 576 nodes and 175 elements. This produces a 3-D model (see Fig. 3b) having a total of 2100 20-node brick elements and 9324 nodes. The analysis time using the mesh of Fig. 3b is about 14 hours on the same computer. It is stressed that, if the computational cost is not sufficiently low, a 3-D analysis is simply not feasible in a realistic time frame. The elements used for the 3-D thermal analysis have a “consistent” specific heat matrix. Simplifications and assumptions are the same as for the 2-D model [11-13]. The only difference being the axi-symmetry assumption, which in 2-D implies that each weld pass is “deposited” in one go. It is understood that this is not true during weld deposition, because each weld pass is laid on the circumference of the pipe in an incremental o manner, so that geometrical axi-symmetry is valid only when a weld pass is complete (360 ). On the other hand thermal load axi-symmetry is never fulfilled, since the welding electrode, which is the source of the heat input, is continuously orbiting the pipe. Under this assumption o each weld pass is a complete 360 ring, which when cooled applies an unrealistic “strangling” force on the pipe. It is the effect of this major assumption on predicted

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residual strains that is of great interest here. The finite element mesh used for the structural analysis is identical to the one used for the thermal analysis.

Figure 2. (a) 2-D axi-symmetric finite element model and (b) weld macrograph The former is generated by the later, changing only the elements to quadratic isoparametric 20-node brick elements, for which the 14-point integration rule is used. The number of degrees of freedom per node also changes from one (temperature) for thermal to 3 degrees of freedom (x, y and z translation) for the structural analysis. The material model used is multi-linear kinematic hardening, fitting the equivalent stress – plastic strain curves obtained from [13]. Although the buttering (see Figs. 1 and 2) consisted of two different stainless steels (308L and 309L), it is treated as homogeneous. The pipe assembly is allowed to expand/contract freely in the current model, using only rigid body motion preventive supports. Post-buttering and post-weld machining are simulated by simply removing (killing) the corresponding elements, using the “birth and death of elements” technique. Creep and metallurgical phase transformations are not incorporated in the described finite element model.

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Figure 3. (a) 2-D coarse mesh used to generate it and (b) 3-D solid finite element model In the following finite element analyses, the heat input due to welding was simulated using the so-called “prescribed temperature approach”. A prescribed temperature load, equal to the solidification temperature of the weld material, is applied over a volume, representing the melted weld pool. The characteristic time (T), for which the prescribed temperature is applied, is regulated by the size of the melt pool and more specifically its length (L). For the 2-D simulation, this characteristic time is the heating period or the period during which a node is in the melt pool. In the 3-D simulation, each weld pass is descretized into 12 increments (30o each). Each pass increment represents the melted weld pool, as it moves at the same speed S as the welding electrode. Thus each weld pass increment ideally has the shape and dimensions of the melted weld pool. The characteristic time is obtained by dividing the length of the pool (2ʌr/12, where r is the radial coordinate in respect of the axis of the pipe) by the traveling speed (S) of the electrode. Multi-pass welding simulation The simulation procedure that is followed in the 3-D approach is incremental, as is the real process of weld pass deposition. This is the major difference between this approach and a 2-D axi-symmetric approximation, described in detail in references [11, 13]. In a full 3-D simulation, each weld pass is descretized in increments, which are “deposited” sequentially along the circumference of the pipe. “Deposited” means, in numerical terms, activated and that refers to the elements that constitute the weld pass increment. These elements, although generated from the beginning of the meshing procedure (no elements are generated during the analysis), remain inactive until the moment in time Tiact when the weld pass increment they belong to is “deposited”. The deactivation and activation of elements during the simulation is achieved through the “birth & death of elements” technique, a feature common to many commercial FE codes. For the multipass weld considered here, the simulation procedure for the transient thermal and static structural analysis, is described in Tables 1 and 2, respectively.

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Table 1. Welding simulation procedure steps for the 3-D transient thermal analysis step 1 2 3 4 5 6 7 8 9 10

Action Mesh complete structure including weld to be deposited. Set free convection to all free surfaces and initial temperature to room temperature. De-activate all weld elements. st st Activated elements belonging to the 1 (out of N) increment of the 1 weld pass. st Apply prescribed temperature (equal to melting temperature) on 1 pass increment nodes. Perform non-linear transient thermal analysis. Heating duration is equal to characteristic time. Remove all loads from current increment nodes. nd st st Repeat steps 3-6 for the 2 increment of the 1 pass (until the 1 pass is completely deposited), using as initial condition for the transient thermal analysis (step 5) the solution obtained from the previous pass increment. Remove all thermal loads and allow it to cool under free convection until the pipe temperature reaches the inter-pass temperature. nd Repeat steps 3-8 for the 2 pass, until the weld is completely deposited. Remove all temperature loads and allow free convection cooling, to room temperature (uniform).

Each ith pass increment is a complete transient thermal analysis, starting at time point i th T act, using as input the results from the (i-1) pass increment analysis and stopping at i+1 time point T act. During each of these transient analyses the number of time steps is fixed using manual time stepping. The great advantage of manual time stepping is the absolute control that the analyst has over his finite element temporal analysis. Before starting the simulation, the whole structure including the weld is meshed. The elements corresponding to the weld are “killed”. Elements corresponding to the 1st weld pass increment are activated. A constant temperature load, equal to the solidification temperature of the weld material, is applied on the nodes of these elements, for the i i+1 st duration (T act - T act, where for the 1 increment i=1) of the increment (heating period). Using an initial temperature equal to room temperature and a free convection boundary condition over all free surfaces, the 1st transient non-linear thermal analysis of the 1st pass increment is performed starting at time point T1act and ending at time point T2act, nd using a fixed number of time steps (manual time stepping). Before moving to the 2 pass increment, the temperature load is removed from nodes belonging to the 1st increment elements, allowing them to cool under free convection during analysis of the 2nd increment. For the 2nd pass increment the procedure is repeated (activation of corresponding elements, application of temperature load, transient analysis), the only difference being that as an initial condition the resulting temperature distribution of the 1 st st increment is used. The procedure goes on until the 1 weld pass is complete. What follows is a series of transient thermal analyses, that simulate the inter-pass cooling period between the 1st and 2nd weld passes, in order to achieve a uniform temperature distribution over the pipe equal to the inter-pass temperature. The procedure is repeated for all weld passes until the full weld is “deposited”. What follows is a series of transient thermal analyses, that simulate final cooling to room temperature. Melting and annealing of the pipe material as well as re-melting of deposited weld material is not simulated by this procedure. It is assumed that the temperature field is not dependent on the displacement field or in other words, the heat produced due to dissipation or internal friction, is negligible when compared to the heat input due to welding. It is also assumed that the thermal transient evolves much faster than the resulting changes in the displacement field. This is an uncoupled quasi-static thermoelasticity problem, where the thermal and mechanical problems are treated separately. The mechanical analysis is a close follow-through of the transient thermal analysis (the mesh

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must be identical to the thermal analysis mesh) and is constituted by a sequence of static mechanical analyses, equal in number to the time steps of the thermal analysis. Each mechanical analysis uses as load, the temperature field predicted in the corresponding time point of the transient thermal analysis and as initial displacement field, the result of the previous mechanical analysis. The final mechanical analysis, which corresponds to a completely cooled down structure, produces the residual stress field. Computed thermal strains are based on the current temperature load and the reference temperature. In order for activated elements, representing the weld, to be stress-free as is the real case, the weld material reference temperature is set to the solidification temperature. The base material reference temperature is set to room temperature. To initiate the analysis, the temperature field obtained from the 1st time step of the transient thermal analysis of the 1st weld pass increment, is applied as a temperature load and a static non-linear mechanical analysis is performed. Using as initial displacement the nd result of the preceding mechanical analysis, the temperature field, obtained from the 2 st time step of the transient thermal analysis of the 1 weld pass, is applied as a temperature load and static non-linear mechanical analysis is performed. This is repeated for all time steps of the transient thermal analysis performed for the 1st weld nd st pass increment. For the 2 increment of the 1 weld pass, the procedure is repeated (activation of corresponding elements, application of temperature fields, obtained from all time steps of the thermal analyses, as thermal loads and execution of equal number of restarting static mechanical analyses). The procedure goes on until the 1st weld pass is laid. When all weld passes are active the weld is complete and cooled and the resulting stress field is the residual stress field. In order to reduce analysis time, there is the possibility to solve mechanical analyses corresponding to a selection of thermal load steps. Contribution of mechanical analyses to the built up of residual stresses is not of the same importance. Mechanical analysis steps, which have an insignificant effect in the predicted residual stress, may be omitted thus considerably reducing the overall computational cost. Table 2. Welding simulation procedure steps for the 3-D static structural analysis step 1 2 3 4 5 6 7 8 9 10

Action Mesh complete structure including weld to be deposited using identical mesh to corresponding thermal analysis (set pipe reference temperature to room). Set nodal constrains to prevent rigid body motion. Initial stress field is zero (stressfree). De-activate all elements belonging to the weld (set weld reference temperature to activation temperature). st st Activated elements belonging to the 1 increment of the 1 weld pass. st st st Apply temperature field obtained from 1 time step of 1 increment of 1 pass of transient thermal analysis, as temperature load. Perform non-linear static structural analysis. st st Repeat steps 5-6 for all time steps of the 1 increment of 1 pass, using as initial stress the result of the previous static structural analysis. nd st st Repeat steps 4-7 for the 2 increment of the 1 pass (repeat until 1 pass is completely deposited). nd Repeat steps 4-8 for the 2 pass (repeat until weld is completely deposited). After the complete weld is active, continue using as temperature load the results of the cooling steps of the transient thermal analysis until uniform room temperature is achieved. The final result is the residual stress field.

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Results and discussion The results obtained from the current analysis, are separated into two groups. The first group, are results of a 2-D sensitivity analysis, performed using a detailed pass-by-pass FE simulation of the weld (see Fig. 2a), investigating the effect of various aspects of modeling on the predicted residual strains. The second group of results were obtained after a 3-D simulation of the DMW (see Fig. 3b), but using a much coarser mesh and following a more computationally efficient technique known as lumping, in order to minimize analysis time. Lumping is an effective technique for reducing analysis time during multi-pass weld simulation. Instead of performing a pass-by-pass analysis, the weld passes are grouped and each group (lump of passes) is treated as a single pass. The technique is effective and accurate only when the passes are grouped following the right strategy, which is largely based on the pass sequence (see Fig. 1b). Finding this strategy is always a matter of numerical tests. Figure 3a shows the mesh that resulted from a series of numerical tests in order to obtain an optimum strategy for a lump-bylump analysis. It is concluded that 6 lumps are sufficient for the weld and 1 for the buttering. The lump-by-lump mesh has 175 elements and 576 nodes and much fewer analysis steps than the pass-by-pass mesh of Fig. 2, thus reducing considerably the analysis time without significantly compromising the accuracy of predicted strains. The aim of the 3-D analysis is to show if the effect of the 2-D axi-symmetry assumption on predicted residual strains is so significant as to justify a full scale pass-by-pass 3-D analysis of the DMW. Results obtained using the 2-D axi-symmetric model of Fig. 2a are directly compared to neutron diffraction measurements obtained from the literature [14], in the hoop direction at distances 4.25mm (see Fig. 4a) and 12.75mm (see Fig. 4b) from the external pipe surface. This particular analysis involves a detailed pass-by-pass simulation of the weld and buttering deposition. It can be seen that there is a good correlation between predictions and measurements, which though is degrading near the internal pipe surface. The exact reason for this has not been identified, but assumptions like axi-symmetry, disregard of metallurgical phase transformation, creep and heat affected zone simulation, could have played a significant role.

Figure 4. Measured [14] vs. predicted hoop residual strains, 4.25mm (a) and 12.75mm (b) under the external pipe surface, using the 2-D axi-symmetric model of Fig. 2

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This items need to be addressed separately in order to draw final conclusions regarding the efficiency of the proposed method. A complete account of these results and comparison to neutron diffraction measurements of residual strains and stresses, in all directions and at 6 different depths from the pipe surface, can be found in references [11, 13].

Figure 5. Sensitivity of predicted residual hoop strain, at 4.25mm (a) and 46.75mm (b) under the external pipe surface, on radiation boundary condition, steady-state creep modeling and an alternative heat input model (heat generation rate) An extensive set of sensitivity tests have been performed, using the 2-D axi-symmetric model of Fig. 2a in conjunction with a lumping scheme to reduce analysis time, in order to investigate the effect of the detail level of the FE model on the predicted residual strain. Figure 5 illustrates the effect that radiation heat transfer modeling has on predicted hoop strain distribution, 4.25mm (see Fig. 5a) and 46.75mm (see Fig. 5b) from the external pipe surface. A difference of almost 700ȝm/m is observed, but only near the internal surface of the pipe (Fig. 5b). Creep simulation (steady-state) has a significant effect near the external and internal surfaces, but only in the weld region. As it is expected, creep reduces tensile strain, during the PWHT stage of the DMW fabrication process. As mentioned earlier the welding simulation performed here, incorporates the prescribed temperature approach for heat input idealization.

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Figure 6. Orbital distribution of residual strains, 4.25mm under the external pipe surface on the weld centerline (a) and axial residual strains, 4,25mm under the external pipe surface, at 4 different radial cross-sections (b) An alternative approach is modeling the heat input due to welding as heat generation rate per unit volume, the results of which are also shown in Fig. 5. It is observed that the later approach predicts lower tensile strains, not only in the hoop but in all directions, not shown here. This is attributed to the fact that the prescribed temperature approach introduces much higher heating rates than the heat generation approach and as such simulates more closely the abrupt heat input during welding. Simulations performed incorporating phase change (solidification of melted weld pool) and contact (during pipe assembly) modeling and varying heat transfer coefficients (but always in the free convection regime) had insignificant effects on the predicted strains using the basic FE model (solid curves in Fig. 5). Figures 6 and 7 present results obtained using the 3-D solid model of Fig. 3b. A first look of residual strain distributions along a circumferential path (see Fig. 6a), having its center on the intersection of the axis of the DMW with the weld center-plane (see Fig. 1a) and a radius of 222.25mm, shows a significant orbital variation of axial (800ȝm/m) and radial (300ȝm/m) strains. A more complete picture is presented in Fig. 6b, where residual axial strain distributions o o o o are shown at 4 radial cross-sections (0 , 90 , 180 and 270 ), 4.25mm under the external o surface of the pipe. It can be seen that, 90 after the start point of each weld pass (0o), the axial strain drops almost 500ȝm/m over the whole weld region and then increase gradually as one moves along the circumference. Similar behavior (increasing instead of decreasing strain) is observed in the hoop direction, 29.75mm (see Fig. 7a) and 4.25mm (see Fig. 7b) under the external surface of the pipe. These results are a clear indication that there is a welding electrode start/stop effect on the predicted residual strains. The sensitivity of predicted strains on this start/stop effect can only be investigated through 3D analysis using a more detailed solid FE model.

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Figure 7. 3D predictions of hoop residual strains, 29.75mm (a) and 4,25mm (b) under the external pipe surface, at 4 different radial cross-sections Conclusions The proposed methodology is successfully applied on a dissimilar metal pipe weld, typical in the nuclear industry and through comparison of predicted strains to neutron diffraction measurements, proved its potential as a welding simulation and residual stress prediction tool. Items to be resolved in future work that apparently affect the accuracy of this method are the axi-symmetry assumption, metallurgical phase transformation and creep modeling. Sensitivity tests have shown that creep, radiation boundary condition and heat input modeling need special attention and cannot be neglected in the simulation, whereas phase change, contact analysis and convective cooling have an insignificant effect on the accuracy of predicted strains. Limited 3-D analysis indicates that there is a welding electrode start/stop effect on predicted strains that cannot be disregarded. The strength of this effect should be investigated by performing a more thorough 3-D simulation, using a detailed solid model of the DMW. Acknowledgments The authors would like to thank the steering committees of NESCIII and ADIMEW projects for making available data from this project. The research presented in this report was conducted under the financial support of the Institute for Energy, JRC-IE, Petten, NL, through Study Contract SC320226. References 1. 2. 3.

Ellingson, W.A. and Shack, W.J., “Residual stress measurements on multipass weldments of stainless steel piping”, Experiment. Mech., 19, 317-323(1979). Faure, F. and Leggatt, R.H., “Residual stresses in austenitic stainless steel primary coolant pipes and welds of pressurized water reactor”, Int. J. Pressure Vessels Piping, 65, 265-275(1996). Rybicki, E. and Stonesifer, R., “Computation of residual stresses due to multi-pass welds in piping systems”, ASME J. Press. Vessel Technol., 101, 149-154(1979).

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13. 14.

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Brust, F.W. and Rybicki, E., “A computational model of backlay welding for controlling residual stresses in welded pipes”, ASME J. Press. Vessel Technol., 103, 226-232(1981). Rybicki, E. and McGuire, P.A., “A computational model for improving weld residual stresses in small diameter pipes by induction heating”, ASME J. Press. Vessel Technol., 103, 294-299(1981). Koch, R., Rybicki, E. and Strttan, R., “A computational temperature analysis for induction heating of welded pipes”, J. Engng. Mater. Technol., 107, 148-153(1985). Josefson, B.L. and Karlsson, C.T., “FE-calculated stresses in a multi-pass buttwelded pipe – a simplified approach”, Int. J. Pressure Vessels Piping, 38, 227243(1989). Karlsson, R. and Josefson, B., “Three-dimensional finite element analysis of temperature and stresses in a single-pass butt-welded pipe”, ASME J. Press. Vessel Technol., 112, 76-84(1990). Lindgren, L.E., “Finite element modeling and simulation of welding – part 1: Increased complexity”, J. Therm. Stress, 24, 141-192(2001). Fricke, S., Keim, E. and Schmidt, “Numerical weld modeling – a method for calculating weld-induced residual stresses”, J., Nucl. Engng. Design, 206, 139150(2001). Katsareas, D.E., Ohms, C. and Youtsos, A.G., “Structural integrity assessment of nuclear safety related welded components”, Proceedings of the International Conference on the Influence of Traditional Mathematics and Mechanics on Modern Science and Technology, edited by G.C. Sih and C.P. Spyropoulos, Eptalofos ABEM, 111-123(Messini 2004). Katsareas, D.E., Ohms, C. and Youtsos, A.G., “On the performance of a commercial finite element code in multi-pass welding simulation”, Proceedings of the 2004 ASME/JSME Pressure Vessels and Piping Conference, edited by M.A. Porter and T. Sato, ASME, PVP-Vol. 477, 29-37(San Diego 2004). Katsareas, D.E. and Youtsos, A.G., “Welding residual stresses in a bimetallic pipe joint using the finite element method”, Int. J. Pressure Vessels Piping, submitted for publication (2005). Ohms, C., Katsareas, D.E., Wimpory, R.C., Hornak, P. and Youtsos, A.G., “Residual Stress Analysis in Thick Dissimilar Metal Weld based on Neutron Diffraction”, Proceedings of the 2004 ASME/JSME Pressure Vessels and Piping Conference, edited by M.A. Porter and T. Sato, ASME, PVP-Vol. 479, 85-92(San Diego 2004).

RESIDUAL STRESS PREDICTION IN LETTERBOXTYPE REPAIR WELDS L.K. Keppasa, N.K. Anifantisa, D.E. Katsareasa, and A.G. Youtsosb a

Machine Design Laboratory, Mechanical & Aeronautics Engineering Dept, University of Patras, GR-26010 Rion, Greece b

High Flux Reactor Unit, Institute for Energy, EC-JRC PO2, 1755 ZG Petten, The Netherlands

ABSTRACT The influence of various modelling aspects on the prediction of residual stresses in a 3-bead letterbox-type repair weld is investigated in the present work. The repair is performed on a 2¼CrMo low alloy ferritic steel plate, containing a machined central groove of 9mm depth, 200mm length and 14mm width. Three weld beads are deposited in the groove using AL CROMO S 225 2¼CrMo electrodes. The repaired region is considerably long and narrow to enable a 2D plane strain analysis. Using the commercial finite element code ANSYS and the very well known “birth and death” technique, the effect of material hardening rule, different heat input models such as prescribed temperature and heat generation rate approach, radiation boundary conditions and coefficient of convective cooling on the evaluation of residual stress field is examined in a sensitivity analysis frame work. Finite element 2D mesh and time step size are optimised affording useful information for a future 3D analysis. Metallurgical phase transformation effects are not included in the model, although it is general knowledge that its role in the formation of a residual stress field might be quite significant for ferritic steels. Recorded data for temperature and thermal strain histories are used to validate predictions obtained by finite element computer simulation. Comparisons reveal a good agreement between predicted and recorded temperature and thermal strain histories. Material hardening rule affects remarkably the results whereas the implication of radiation boundary conditions has a small contribution on the predicted results. Introduction Repair welds are commonly carried out in industry on components where flaws or defects have been detected in weldments during inspection. These defects arise from initial fabrication or in service conditions and degenerate the 27 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 27–39. © 2006 Springer.

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efficiency of welded joints. The objective of a repair is to remedy the degradation of the component and thereby to extend the life of ageing plants. Part of the weld metal containing the defect is excavated through machining. Then the groove, which has usually letterbox geometry, is filled with weld material of the same composition as the parent material. The type of repair can vary from filling a localized shallow excavation, to welding deep excavations that can extend around a significant proportion of a structure. However, in some cases the repair processes may have a detrimental effect on the residual lifetime of the component. This can be due to metallurgical changes in the component material in the vicinity of the repair on account of extremely high residual stresses which are inevitably introduced during the repair. Indeed, in the construction of new plants and for their continued operation, local repair welds are undertaken, so it is necessary to be able to underwrite these for safe operation. As a result, the success of such a repair is ambiguous if no particular concern is undertaken. This concern encompasses thoroughly designed repair process and subsequent post weld heat treatment (PWHT) in order to alleviate the residual stresses associated with the repair. Consequently, a complete knowledge of residual stresses distribution on weld joint components is of great importance for accurate structural integrity assessments. Many researchers over the last two decades have paid attention to measure and predict satisfactorily the residual stresses in weldments. Dong et al [1] inferred that residual stresses in weld repairs typically exhibit strong threedimensional features, depending on both component and repair geometry. In a subsequent study [2] the same researchers examined several weld repair cases, using both advanced numerical modelling and experimental measurement techniques. The main remarks of this study were that repair welds increase the magnitude of transverse residual stresses along the weldments and the shorter the repair length the greater the increase in transverse stresses. Moreover, welding parameters such as bead lumping, heat content and pass sequencing play more important role when analyzing repair than initial fabrication welds. Ohms et al [3-4] used a novel and very promising non-destructive method, in order to evaluate large welded components, like dissimilar metal welded pipe joints and RPV walls, used in the nuclear industry, within the context of structural integrity assessment. They used the neutron diffraction method to measure residual stresses, induced in such components during welding and compared successfully their results to data of other experimental and computational methods. Bouchard et al. [5] who implemented measurements to obtain the through thickness residual stress profiles in repair welded stainless steel pipes, using neutron diffraction, deep hole and surface hole techniques. The measurements revealed that the trend of the residual stress profile in repaired welds was the opposite of that referring to the fabrication weld and the axial and transverse stresses along the weld line have approximately the same magnitude, inducing high bi-axial tension. Lant et al [6] concentrated on practical weld repair procedures for low alloy steels. They suggest nickel based

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29

filler welds for emergency or unforeseen weld repairs to hardenable ferritic steel components of power plants. Finite elements simulations of welding utilizing the same methodology as the one proposed in the present study can be found in [7] where cases of single and multi-pass welding are examined as well as dissimilar metal welds and the effect of PWHT on the residual stresses have been studied. Several researchers have conducted numerical analyses incorporating PWHT and creep effects in their models. The main scope of these studies is the examination of hot-cracking risk during the PWHT or during the operation under real conditions. Recently, Soanes et al [8] used a 2D-axisymetric model to simulate a repair in a steam header to tube/plate weld. The residual stress analysis was followed by a series of PWHT analyses to optimize these stresses and to maximize the integrity life. Weld simulation involves complicated aspects of modeling like metallurgical phase transformation, temperature dependent material properties, creep, phase change, radiation, heat input models, etc. Lindgren in his review [9] demonstrates the complexity of weld simulation models if aspects such as solidstate phase transformations and hot-cracking are involved in order to achieve a more accurate analysis. The most common approach is to ignore the microstructure change and assume that the material properties depend only on the temperature. Zhu and Chao [10] investigated the effect of each temperature dependent material property on the transient temperature, residual stresses and distortion in computational simulation of welding process using a 3D-plate model. They inferred that only the yield stress variation should be rigorously determined for correct predictions of residual stresses and distortions. The proposed study investigates a letterbox type 3-bead repair weld, on a low alloy low carbon steel panel. This simple in design repair weld plays the role of a benchmark problem on which the proposed welding simulation technique is tested and validated, by comparison with residual stress measurements. A series of 2D sensitivity analyses of the predicted residual stresses on various aspects of the finite element modeling are performed. Aspects such as, material hardening rule, heat input models, radiation boundary conditions and coefficient of convective cooling have been involved in the models and their effects on the residual stress prediction are assessed. Finite Element Simulation of Welding A 2D half model mesh with iso-parametric 8-node plane strain elements was constructed, assuming that the longitudinal to the weld bead centre-plane is a plane of symmetry. The same mesh was used for the thermal and mechanical sensitivity analyses. Mesh convergence tests were conducted using coarser and finer meshes before selecting the current mesh as appropriate for residual stress predictions. Figure 1 presents four different meshes examined in the mesh convergence test. It is assumed that the temperature field is not dependent on the displacement field (the heat produced due to dissipation or internal friction, is negligible when compared

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to the heat input due to welding). Thus the present is treated as an uncoupled thermo-elasticity problem. It is also assumed that the thermal transient evolves much faster than the resulting changes in the displacement field, thus the present is treated as an uncoupled quasi-static thermo-elasticity problem. In this treatment the mechanical part of the analysis is a series of static analyses that use as an initial displacement field, the one produced by the previous mechanical analysis and as a thermal load, the temperature field at the corresponding time point that was produced by the transient thermal analysis. Both parent plate and weld bead material behaviors were modeled using various hardening rules such as bilinear and multi-linear kinematc hardening and multi-linear isotropic hardening. The effects of creep strain, metallurgical phase transformation and phase change are not incorporated in the present model.

a) 327 nodes

b) 707 nodes

c) 1962 nodes

d) 4031 nodes

Figure 1: 2-D plane strain FE models.

Heat input H in welding terminology is the amount of energy (heat) entering the component per weld pool unit volume. The Electric Power of the welding machine is normally estimated by multiplying the Welding Current I by the Arc Voltage V P=VxI

(1)

In the present case V and I are given, consequently P = 600 x 29 =17400 Watt. Not all of this Heat Input is used for heating the welded component, but a good part of it is wasted as heat losses (e.g. due to radiation etc.) and for the phase change process as latent heat. The part of H that reaches the component is controlled by another welding parameter, which is called Weld Efficiency C. For the present analysis a “common practice” value of 0.75 is taken. Thus the Effective Heat Input Heff that heats the specimen (heating rate) is Heff = C x P

(2)

thus Heff = 0.75 x 17400 = 13050 Watt. In the present finite element analysis, the heat input due to welding was simulated as heat generation rate per unit volume. Therefore, it is requisite to calculate the weld pool volume, making a series of assumptions. Supposing that after the completion of weld bead deposition, the groove is perfectly charged and there is no overfill, the weld metal cross section has trapezoidal scheme with an area of A = 13 x 9 = 117 mm2 and each bead cross section is approximately Ab = 117 / 3 = 39 mm2. It is also assumed that the weld pool length is L = 20 mm, so the weld pool volume

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31

is given by multiplying the bead cross sectional area by the weld pool length U = 39 x 20 = 780 mm3. Finally, the heat generation rate per unit volume HR is given dividing the effective heat input Heff by the weld pool volume HR = 13050 / 780 = 16.73 W/mm2.

Figure 2: Base plate dimensions

Figure 3: Welding sequence

A more simplified approach that was also followed during the reported analysis was the so-called “prescribed temperature approach”. Instead of applying the heat generation rate per unit volume load, a prescribed temperature load is applied over the same volume of material. This temperature corresponds to the melting point of the weld material, namely 1450 0C. The time for which the “prescribed temperature” is applied is the time the weld pool needs to come through a specific cross section. Since the weld pool length is 20 mm and the electrode travel speed is 50 cm/min or 8.33 mm/sec (see Table 1), the “prescribed temperature” application time (heating time) is th = 20 / 8.33 = 2.4 sec and for reasons of simplicity it is taken th = 2.5 sec. Specimen Welding machine Total number of weld passes Pre-heating temperature [oC] Inter-pass temperature [oC] Welding current [A] Arc voltage [V] Electrode diameter [mm] Electrode travel speed [cm/min]

Test-Plate+PL1+PL2+PL3 LINCOLN DC1500 For Submerged Arc 3 per plate 150 250 600 29 4,00 50

Table 1: Welding parameters

Thermocouple

Position

TC1 TC2

X 10 / Y 0 / Z 0 X 0 / Y-12 / Z 20

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TC3 TC4

X 0 / Y 15 / Z 20 X 0 / Y +32.5 / Z 20

Table 2: Thermocouple positions

Transient temperature and strains as well as residual stress predictions using the methods described above, are presented in the next chapter. It is mentioned that the “prescribed temperature approach” is the standard method used for the convergence tests and sensitivity analysis. The Letterbox Repair Weld

327 nodes / 2 min 707 nodes / 24 min 1962 nodes / 57 min 4031 nodes /128 min

120 100 80 60

Section x=0 , z=14 mm

40 20 0 -20 -40 -60

weld

plate

-80

100

Transverse Residual Stress (MPa)

Transverse Residual Stress (MPa)

Four identical machined 2¼CrMo base plates (1 test plate and 3 sample plates), 400mm x 200mm x 20mm, containing a central cavity, 218mm x 14mm at the opening, 200mm x 12mm at the base, and 9mm deep, were manufactured (Fig. 2). The plates were not heat treated to remove fabrication residual stresses prior to welding. A 3-pass submerged arc weld was deposited along each plate cavity, as shown in Fig. 3. The welding conditions for each pass are given in Table 1. Each pass was allowed to cool to the specified interpass temperature of 150oC, before proceeding with the next. The base plate was pre-heated to 150oC before welding commenced and was fully free to expand. The base plate material is DIN 17175, grade 10CrMo9-10, low alloy steel and the electrodes used were AL CROMO S 225 2¼CrMo, 4mm diameter. Stress-strain data, for the base plate parent material and filler material at different temperatures, as well as for thermal and physical properties can be found in reference [11].

60 40 20 0 -20

0

2

4

6

8

10 12 14 16 18 20 22 24

Distance from Centreline (mm)

Figure 4: Mesh convergence

weld

plate

-40 -60 -80

-100

280 steps / 57 min 100 steps / 10 min 55 steps / 4 min 49 steps / 3 min 43 steps / 2 min

80

Section x=0 , z=14 mm 0

2

4

6

8

10 12 14 16 18 20 22 24

Distance from Centreline (mm)

Figure 5: Time step convergence

A set of thermocouples (Table 2) and strain gauges had been placed at specific positions on the top and bottom surface of the plates to record the transient temperatures and strains during weld bead deposition. Temperature data can be used to control the finite element models as they indicate the cooling time and inter-pass temperature as well as the transient strain data to validate the numerical results of 2-D and 3-D analyses.

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Results and Discussion

Prescribed Temperature Heat Generation Rate

400 300

Transverse Residual Stress (MPa)

Transverse Residual Stress (MPa)

Mesh and time step convergence Simulation time is of paramount importance if the proposed method is to be used as a welding simulation and residual stress prediction tool for industrial R&D. Low CPU times, small manageable FE models and off-the-self commercial FE codes used on non-high-end computers are the advantages that will make the proposed method attractive to weld designers and CAE engineers in relevant industries. Figure 4 presents a comparison for the predicted transverse residual stress along the section x=0, z=14mm as they have been calculated with four different mesh densities (see Fig. 1).

Weld Centreline

200 100 0 -100 -200

Plate

-300

Weld

Prescribed Temperature Heat Generation Rate

120 80

Section x=0 , z = 14 mm

40 0 -40 -80

Plate

Weld

-120

-400

-160

-500

-200

-600 0

2

4

6

8

10

12

14

16

18

Distance from bottom surface (mm)

20

Figure 6: Transverse residual stress along weld centreline

0

2

4

6

8

10 12 14 16 18 20 22 24

Distance from centerline (mm)

Figure 7: Transverse residual stress, x=0, z=14mm

The legend shows the number of nodes and the corresponding solution time for the mechanical analysis. Simulations performed on a 3GHz Intel Pentium IV with 512 MB RAM. Although the 4031-nodes mesh is considerably finer from the 1962-nodes mesh, there is negligible difference between the corresponding residual stresses. This comparison indicates as optimum the 1962-modes mesh. Comparing these meshes to the 707-nodes mesh, the diagram reveals remarkable discrepancies within the weld region. The 327 nodes mesh is completely inadequate for the analysis. Results presented below concerning the residual stress prediction by utilizing different heat input models are based on the 1962-nodes mesh.

Keppas et al.

200

Section x=0 , z = 14 mm

100 0 -100 -200

Weld

Plate

-300

1200

Prescribed Temperature Heat Generation Rate

1000

Section x=0 , z = 14 mm

800 600 400

Weld

Prescribed Temperature Heat Generation Rate

300

Longitudinal Residual Stress (MPa)

Through thickness Residual Stress (MPa)

34

200

Plate

0

-400 0

2

4

6

8

10 12 14 16 18 20 22 24

Distance from centerline (mm)

Figure 8: Through-thickness residual stress: x=0, z=14mm

0

10

20

30

40

50

60

70

80

Distance from centerline (mm)

90 100

Figure 9: Longitudinal residual stress: x=0, z=14mm

In an effort to reduce the simulation time, a time step convergence is necessary, affording useful information before proceeding to a full 3-D analysis. In Fig. 5, several cases of step numbers used for the analysis are compared. Each weld bead deposition is descritized in a number of heating and cooling periods and each period in a number of time steps. Starting from 280 time steps the step size is increased reducing the total number of steps up to 43. Figure 5 shows that with 100 steps the processing time is decreased from 57 to 10 minutes (1962-nodes mesh), giving acceptable residual stress results. Trying to achieve shorter simulation times, the step number falls down to 55 and finally to the limit value of 49 using longer time steps for the heating periods. It is remarkable here that decreasing the steps from 280 to 49 the effect on the residual stress prediction is negligible, but the simulation time has been decreased from 57 min to 3 sec. Apparently, the optimum combination is that of 49 steps and longer steps can be used for the heating periods. This valuable conclusion will be reclaimed in a future 3D analysis. Prescribed temperature vs. heat generation rate approach Two different approaches were followed for the finite element idealization of the heat input load due to welding. The “heat generation rate approach” and the “prescribed temperature approach”. Figures 10 and 11 depict the predicted temperature transient using these methods. It is clear that the “heat generation rate approach” prediction using the realistic value of 0.75 for the welding efficiency come in great accordance with the recorded thermal cycle for the thermocouples (see Fig. 12). On the other hand the “prescribed temperature approach” which is based on the weld pool temperature and geometry during welding underestimates the pick temperatures during welding.

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Residual Stress Prediction

900 st

1 pass

Temperature ( 0C)

800

rd

3 pass

700

nd

2 pass

600 500 400 300 200 100

0

TC1 TC2 TC3 TC4

Temperature ( 0C)

900

240 480 720 960 1200 1440 1680 1920 2160 2400 2640 2880

Time (sec)

Figure 10: Thermal cycle: heat generation rate

800 700 600

st

1 pass

nd

2 pass

rd

3 pass

TC1 TC2 TC3 TC4

500 400 300 200 100

0

240 480 720 960 1200 1440 1680 1920 2160 2400 2640 2880

Time(sec)

Figure 11: Thermal cycle: Prescribed temperature

Diagrams in Figs. 6-9 depict the predicted components of residual stresses along the weld centreline and section x=0, z=14, respectively, giving an overall view of the residual stress distribution in the specimen. In these figures results obtained by the two methods are compared. It can be seen that the transverse residual stress is the most sensitive to the heat input method (Figs. 6-7). The other two stress components do not noticeably influenced by the heat input method used in the analysis. “Heat generation rate approach” yields higher absolute values for the transverse residual stress.

Figure 12: Recorded thermal cycle

Figure 13: Transient strain prediction

A preliminary assessment of the validity of the predicted results and the reliability of each heat input approach could be extracted through the comparative graph in Fig. 13. The predictions come in good agreement with the recorded data for the plate number 2. In both cases, the transverse strain is tensile during the weld bead deposition and the transverse residual strain is compressive. The “prediction curve of “prescribed temperature approach” follows better the trend of the recorded curve and the heat generation method derives higher absolute residual strain. However, no definite conclusions can be drawn unless residual stress measurements are available. It is mentioned that “prescribed temperature approach” is the method used in the following analyses.

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Material hardening rule Both parent plate and weld bead material behaviors were modeled using various hardening laws such as bilinear and multi-linear kinematc hardening and multi-linear isotropic hardening. Bilinear kinematic hardening assumes that the total stress range is equal to twice the yield stress, so that the Bauschinger effect is included. This option is recommended for generally small-strain use for materials that obey von Mises yield criteria, which includes most metals, and of course the case under investigation and it is not recommended for large-strain applications. A more accurate modeling of material behavior is based on the definition of a number of stress- strain data corresponding to the points of the real strain – real stress curves instead of specifying the elastic and tangent moduli. This alternative can be combined with kinematic or isotropic hardening laws deriving the multi-linear kinematic hardening and multi-linear isotropic hardening laws, respectively. The Multi-linear Kinematic Hardening option uses the Besseling model, also called the sub-layer or overlay model, so that the Bauschinger effect is included. It also uses Rice's model where the total plastic strains remain constant by scaling the sub-layers. This option is suitable for small-strain analyses and cyclic load histories. The Multi-linear Isotropic Hardening option uses the von Mises yield criteria coupled with an isotropic work hardening assumption. The main difference between this option and the Multi-linear Kinematic Hardening is that this option is not recommended for cyclic or highly non-proportional load histories in smallstrain analyses. It is, however, recommended for large strain analyses. Transverse Residual Stress (MPa)

160

Weld

Plate

140

Longitudinal Residual Stress (MPa)

Bilinear Kinematic Multilinear Kinematic Multilinear Isotropic

180

Section x=0 , z=17 mm

120 100 80 60 40 20 0

0

4

8

12

16

20

24

28

32

Distance from Centreline (mm)

36

Figure 14: Hardening rule influence: transverse stress

40

1200

Bilinear Kinematic Multilinear Kinematic Multilinear Isotropic

1000

Section x=0 , z=17 mm

800

Weld

Plate

600

400

200 0

4

8

12

16

20

24

28

32

Distance from Centreline (mm)

36

40

Figure 15: Hardening rule influence: longitudinal stress

Results are provided in Figs.14 and 15 for two components of residual stress. Bilinear and multi-linear kinematic hardening predictions are very close each other. One can say that if data for exact behaviour of the material are not available the usage of bilinear rule yields acceptable results. However, the isotropic hardening option raises significantly the residual stress, mainly the transverse component within the weld material. As aforementioned, this option is suitable for large strain analysis and non-cyclic loading, consequently is this

37

Residual Stress Prediction

Transverse Residual Stress (MPa)

prediction rather unrealistic this prediction. This cross section (x=0, z=17mm) corresponds to the case of the largest difference between the predictions. film coefficient film coefficient 2o (Watt / m . C) 10 15* 20 25 30 40

Weld

Plate Section x=0 , z=14 mm

Transverse Residual Stress (MPa)

140

100 80 60 40 20 0 -20 -40 -60 -80 -100 -120 -140 -160

No radiation Radiation (H  ) Radiation (H  )

120 100

Section x=0, z=17 mm

80 60 40 20

Weld

Plate

0 -20

0

2

4

6

8

10 12 14 16 18 20 22 24

0

Figure 16: Influence of convection film coefficient

4

8

12

16

20

24

28

32

36

40

Distance from Centreline (mm)

Distance from Centreline (mm)

Figure 17: Effect of incorporating radiation boundary conditions into the FE

Convective cooling and radiation boundary conditions Convection is the prevailing mechanism for heat transfer from the specimen to the ambient. In the present problem free convection is the case. The magnitude of film coefficient may influence the residual stresses. Figure 16 indicates as appropriate the range 15-20 Watt/m2 0C for the film coefficient value. In the present analysis the value 15 was used. It is obviously acceptable since the predicted thermal cycle comes in agreement with the recorded thermal cycle (see Fig. 12) Figure 17 illustrates the effect of incorporating the radiation boundary condition on the predicted residual stress components. The radiation boundary condition was applied only on the weld bead free surfaces and it was idealized as an open enclosure radiation to the ambient, which was set at room temperature. It is noted that radiation between two or more surfaces (e.g. between the deposited weld bead and the robotic welder) would normally be more severe. Two radiation cases are tested with emissivities equal to İ=0.5 and İ=0.8 (1 is the maximum value), respectively. It is clear that, even in the severest case, radiation has not significant impact on predicted residual stresses. Conclusions x

x

x

Material hardening rule used in analysis has a significant effect on the predicted values of weld residual stresses. The more realistic is the kinematic hardening rule since it refers to small displacements and cyclic load history. The radiation boundary condition does not affect considerably the temperature predictions and therefore may safely be ignored. Convection is the dominant mechanism of heat transfer from the plate to the environment and the optimum film coefficient value is 15Watt/m2.oC. Heat input model incorporated in analysis appears remarkable influence on the results. It primarily affects the transverse residual stress.

38

x

x x

Keppas et al.

The 2D model yields valuable information concerning the mesh configuration and optimisation of the numerical solution. Solution parameters such as the number of load steps required for the heating and cooling period to achieve reliable solution in brief time, can be determined prior to a 3D analysis. Transient temperatures during welding are accurately predicted using the heat generation rate method. A good agreement is revealed between the recorded and predicted values of transient strain. However, no definite conclusion can be drawn regarding the accuracy of the proposed methodology, unless residual strains-stresses are compared to experimental data.

Acknowledgements The authors would like to thank the steering committee of NET for making available data from this project. The research presented in this paper was conducted under the financial support of the Institute for Energy, JRC-IE, Petten, NL, through Study Contract SC320226_One Year Extension. References [1] [2] [3]

[4]

[5]

[6] [7]

Dong P, Zhang J, Bouchard PJ, “Effects of repair weld length on residual stress distribution”, Trans ASME J Press Vessel Technology 124,1, 7480, 2002 Dong P.,Hong J.K., Bouchard P.J. “Analysis of residual stresses at weld repairs”, Int J.Pressure Vessels Piping 82,4, 258-269, 2005 Ohms C., Katsareas D.E., Wimpory R.C., Hornak P., & Youtsos A.G, Residual stress analysis in RPV & piping welded components based on neutron diffraction, Proceedings of the 12th International Conference on Experimental Mechanics, C. Pappalettere (Ed), ISBN-88-386-62738, Bari (Italy), August 29 2004. Ohms C., Katsareas D.E., Wimpory R.C., Hornak P., & Youtsos A.G, Residual stress analysis in a thick dissimilar metal based on neutron diffraction, Proceedings of the 2004 ASME/ JSME Pressure Vessels and Piping Conference, PVP-Vol. 479, ISBN-0-7918-4674-1, pp. 85-92, San Diego (California), July 25-29 2004 Bouchard P.J., George D., Santisteban J.R, Bruno G., Dutta M., Edwards L., Kingston E., Smith D.J. “Measurement of residual stresses in a stainless steel pipe girth weld containing long and short repairs”, Int J. Pressure Vessels Piping 82,4,299-310, 2005 Lant T., Robinson D.L., Spafford B., Storesund J., “Review of weld repair procedures for low alloy steels designed to minimize the risk of future cracking”, Int J. Pressure Vessels Piping 78, 813-818, 2001 Katsareas D.E., & Youtsos A.G., Recent advances in IE-JRC on finite element prediction of residual stresses in welds, Proceedings of the 6th International Conference for Mesomechanics, G.C. Sih, T.B. Kermanidis & S.G. Pantelakis (Eds), ISBN-960-88104-0-X, p. 358-370, Patras (Greece), May 31 2004.

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[8] [9] [10] [11]

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Soanes T.P.T., Bell W., Vibert A.J., “Optimizing residual stresses at a repair in a steam header to tubeplate weld”, Int J. Pressure Vessels and Piping 82,4 311-318, 2005 Lindgren L.E., “Finite element modeling and simulation of welding. Part I: increased complexity”, J. Therm. Stress 24 141-192, 2001 Zhu X.K., Chao Y.J, “Effects of temperature-dependent material properties on welding simulation”, Computers and Structures 80, 11, 967-976, 2002 NET – TG2 Auxiliary Round Robin 3-Bead Repair Weld Finite Element Simulation Protocol – V1, 2005

VISCOSITY EFFECT ON DISPLACEMENTS AND RESIDUAL STRESSES OF A TWO-PASS WELDING PLATE

W. EL Ahmar, and J.-F. Jullien LaMCoS, CNRS UMR 5514, INSA-Lyon 20 Avenue Albert Einstein, 69621 Villeurbanne, Lyon, France. Email: [email protected], [email protected] Keywords Heat source, Thermal exchanges, Welding viscosity, 3D Simulation, Stainless steel.

ABSTRACT The highly localized transient heat and strongly nonlinear temperature fields in both heating and cooling processes cause nonuniform thermal expansion and contraction, and thus result in plastic deformation in the weld and surrounding areas. Consequently, residual stress, strain and distortion are permanently produced in the welded structures. High tensile residual stresses are known to promote fracture and fatigue, while compressive residual stresses may induce undesired, and often unpredictable, global or local buckling during or after the welding. It is particularly evident with large and thick panels, as used in the construction of nuclear building. These adversely affect the fabrication, assembly, and service life of the structures. Therefore, prediction and control of residual stresses and distortion from the welding process are extremely important for the nuclear installation’s security. This study focuses on the three-thermo-mechanical behavior of 316L stainless steel, during a TIG welding process. In this paper, we investigate the effect of the heat modeling source, thermal exchanges and viscous property on experimental and numerical results. Therefore, a parallel experimental and numerical study is carried out on an industrial 24-25 mock-up benchmark [4], a test more representative of a real welding operation, considering repair welding, is implemented to validate threedimensional numerical effect. The TIG process, with 316L material filler, is considered. Comparative analyses through numerical simulations using finite element code (version 7.4 code_Aster from EDF) are performed. Introduction A two pass weld using the TIG process with 316L material filler is made along the groove (see Figure 2) of a low-carbon austenitic stainless steel (type 316LNSPH) plate in the longitudinal direction. We usually named this test as “24-25” mock-up. The weld begins on the appendix (see Figure 1) and ends 10mm from the plate edges. The welding

41 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 41–51. © 2006 Springer.

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parameters used for the trial are U = 9V, I = 155A, and a welding speed of 0,667 mm.s-1. The plate is lying on three points in its lower face as shown in Figure 1. Temperatures are continuously recorded during the welding, using thermocouples (Type K (±15%)) in same points of the plate surface (see Figure 4a). Welding parameters (Tension, Intensity, traveling speed of the torch) are also continuously recorded during the test. After cooling of the second pass, the residual stresses in the middle section perpendicular to the welding direction of the plates are measured with X-rays (±50MPa). NB: The role of the thermocouple T4 and the captor D6 is to verify the symmetry of thermal and mechanical fields in the plate. Table 1 presents the chemical composition of the used material (316L SPH). Comp.

C

Si

Mn

316L SPH

0.024

0.38

1.76

P

S

Cr

Ni

0.023 0.001 17.31 12.05

Mo

N

2.55

0.07

Table 1: Chemical composition of the 316L material Geometry and boundary conditions The experiment specimen is a plate with dimensions: 270 x 200 x 30 mm. The Figure 1 presents the geometry of the plate, which supports with three points on its lower face. The Figure 2 presents the groove geometry. 200

270 Welding direction

APPENDIX 30

Figure 1 : Geometry of the plate (mm)

Figure 2: Groove geometry (mm).

Numerical simulations An uncoupled 3D thermo-mechanical analysis is considered in this study. The thermal analysis is performed at first, during which the time-dependent temperature field is saved for the subsequent mechanical analysis (stresses, displacements) [6]. Due to the symmetry of the plate, only one-half was modeled (we suppose no heat exchange on the plane of symmetry (adiabatic thermal boundary conditions)).

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The mesh consists of quadratic prismatic elements, with 1800 HEXA20; five quadratic elements are set through the thickness. To perform the thermal analysis, we consider at the first stage of the numerical process a quasi-stationary problem, in order to adjust faster the parameters of the heat input. The arc efficiency term K is determined to take into account the losses. Afterwards, the non-stationary thermal process is considered from the beginning of the heating to the end of the cooling. The transient time-dependent temperature field is then used as thermal loading to complete the three-dimensional mechanical analysis. Modeling of the heat input For the modeling of the heat source, it is of course possible to consider different types of mathematical models, from surface, like a Gaussian heat source, to volumetric, like the double ellipsoid from(see Figure 3). Different types of modeling of the heat source have been considered for the thermal steady state calculation, with an efficiency parameter K fitted to adjust the simulated temperatures considering the measured ones, on some points of the surface plate (see Figure 5a). We conclude that the way that the heat flux density was spread (in surface or in volume) had little effect on the macroscopic thermomechanical simulation results if: x The net total heat flux KUI is the same. x The dimensions of the modeling source are in the same order than the dimensions impact of the heat flow on the plate surface (see Figure 3).

Figure 3a: 2D Gaussian Figure 3b: 3D Gaussian Figure 3c: 3D double source source ellipsoïde source Figure 3: Thermal filed gives by different modelings source and comparison with experimental weld-pool For that raison, the chosen of heat source modeling for the 3-Dimensionnal transient thermal calculation was rather simple: we modeled the heat flux density by a volumetric mathematical function (Q=f1(x,y,z).f2(t)(see Figure 4)) that it is constant in space and vary with time. Such modeling of heat input flux gives as a triangular aspect of heat source (see Figure 4) and its powerful point that it allows as to do welding simulation with any FE software.

Figure 4: Mathematical function of heat flux modeling for “24-25” mock-up

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Thermal exchanges In a welding simulation, all material properties are usually taken as functions of temperature. But, because is difficult to obtain them and as there is a big uncertainty regarding data accuracy it was considered useful to investigate in what extent the temperature dependence of material data affects the thermo-mechanical analysis results. In order to see the effects of numerical values of thermal losses properties (radiation and convective), many analyses were conducted employing different emissivity and a convective coefficient values and type of structures. In conclusion, the effect of thermal losses (SL) on the temperature and mechanical simulations fields is very small for thick welding steel structures. The sensitivity of thermal losses (SL) on the numerical result depends on the heat input (Q), material conductivity (Ȝ), dimensions of perpendicular section to the weld direction (L/e) and welding velocity (v): SL=f(Q, Ȝ, L/e, v). Therefore, there is no need for a more precise (and complicate) losses parameters identification for thick welding steel structures simulation. Thermal adjustment Figures 5b & 5c compare the evolution of measured and calculated temperatures, for the transient analyses. The temperatures measured in the thermocouples were used to fit the heat input modeling, and that is why there is a very good agreement with the experimental results. No temperature measurement was possible closer to the fusion line. Thermal adjustment/P1 ǃ=80%

TEMPERATURES (°C)

1000

800

600

Measur NWS

400

200

0 200

300

400

TIME 500 (s)

600

Figure 5b : Thermal adjustment (1

700

st

800

pass)

Thermal adjustment/P2 ǃ=80%

1000

TEMPERATURES (°C)

800

600

Measur NWS

400

200

0 200

Figure 5a: Thermal instrumentation (mm)

300

400

TIME 500(s)

600

700

800

Figure 5c : Thermal adjustment (2 nd pass)

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Mechanical analysis Different modelings of 24-25 mock-up are considered in this study [1]. A complete threedimensional simulation is performed; firstly without considered time-dependant plasticity, Bilinear kinematics hardening (C) or Bilinear isotropic hardening (I). Secondly taking into account, time-dependant plasticity for high temperatures, by the use of an elastoviscoplastic with kinematics hardening and Norton viscosity (V-C). For the second pass and after cooling, all the numerical results are compared to experimental results given by a similar mock-up.

Mechanical proprieties All requisite material characteristic data including their temperature dependency have been deduced form characterization of the 316L steel in our laboratory [3]. Dilatation tests provided expansion coefficient, and traction tests(see Figure 6) at various temperatures have been realized in order to obtain elasto-plastic data from 20°C to 1000°C, that is: Young’s modulus, yield stress, linear hardening’s modulus. Viscoplastic data have been deduced from creeping and relaxing tests above 500°C, as viscosity effect was not taken into account below this temperature (Q = 0 for T<500°C). The yield of vicoplastic flow is set to zero for T > 1000°C, the behavior is then purely viscoplastic above this temperature. 20°C

200°C

400°C

600°C

800°C

900°C

1000°C

Figure 6: Tensile behaviors of 316L “INSA”, private database (BIFE) [3] Welding process involve a combination of heating and cooling operations which commonly induce mechanical cyclic loads. Measurement analyses show us, that stress range changed in plastic zones with the increase of the number of cycles as shown in Figure 8. 316L have a nonlinear hardening behavior as shown in Figure 7. In this study, we were simplified the real mechanical behavior on a bilinear mechanical law. Therefore, the bilinear kinematic hardening strain range is constant with the increase of cycle number.

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450

24-25 : SIXX Residual stress

400

One 316L cyclic CHAB tension test at 20°C

350 300

Stress (MPa)

150 0 -150

2P

250

4P

200 150 m

100

-300

13 5m

Stress (MPa)

300

50

-450 -0,03

-0,02

-0,01

Strain 0,00

0,01

0,02

0,03

0 -100

0,04

Figure 7: The 316L cyclic tension test at room temperature

X(mm) 0

-50

50

100

Figure 8: The effect of cyclic loads on the SIXX residual stress

Displacements Captor D3 (see Figure 9a) provides the displacement under the fusion line, on the centre. The calculated transient vertical displacement on D3 position, relative to the two passes[7], compared to the measured ones, as shown in Figures 9b and 9c, is satisfactory agreement. In particular, considering viscosity in the material behavior reduce error between calculation and experiment. NB : The three-dimensional effects, which result in flexion effects, are well reproduced. UZ/D3/P1

DISPLACEMENT (micron)

100 0

Measur Z

-100

Y

C

-200 -300

X

I

-400 -500

V- I

-600 -700 0

500

1000

1500

2000

Figure 9 b : D3 displacement (1

TIME (s)

pass)

UZ/D3/P2

100

DISPLACEMENT (micron)

st

0

Measur

Z Y

-100

C

-200 X

-300

I

-400 -500

V- I

-600 -700 0

Figure 9a: Displacement instrumentation (mm)

500

1000

1500

2000

Figure 9c : D3 displacement (2 nd pass)

TIME (s)

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47

Residual Stresses The shape and level of calculated residual stresses in a horizontal median plan (Figure 10), shows that the stress state is mainly longitudinal. The repartition of longitudinal stresses is close to the repartition of tangential residual stresses. The level of transverse residual stresses is lower, and other components of the residual stress tensor are negligible. The stress gradient through the thickness is low. Flexion effects in the longitudinal direction seem to have a non-negligible influence on the final stress state. To validate the numerical simulation we need same experimental measurements for comparing. The Figure10 shows us that SIXX and SIYY are the tow important components of the stress tensor. So after cooling of the second pass only, the SIXX and SIYY residual stresses in the perpendicular middle section to the welding direction of the plate are measured with X-rays diffraction technique (±50MPa). In this paper we will particularly focus our study in the most important component of the stress tensor; the longitudinal residual stress: SIXX.

Figure 10: Residual stress tensor (1st pass)

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Experimental results Figures 11a and 11b represent respectively the longitudinal residual stresses (in the direction of the weld), and the transverse residual stresses. The measured residual stress field (relative to another similar mock-up with 4 passes) is mainly longitudinal, in the welding direction, with a typical pattern of tensile stresses near the weld and compressive stresses in the edges. Longitudinal stress is a tensile stress at the weld centerline, and drop to compressive values about 30mm from the centerline, reaching approximately –200MPa. The transverse tensile stress is much lower, even in the centerline. It is for common use to neglect viscous effects when simulations of welding are performed, mainly because viscous parameters are difficult to obtain [8], [9]. For this reason we make two same tests but with different speeds to test the effect of viscosity on the residual state of stress as shown in Figure 11. We conclude that the viscosity (synonym of the speed of torch) has a neglect effect on the longitudinal and transversal residual stresses. 24-25 : SIXX Residual stress

400

350

150

250

150 100

50

50

X(mm) 0

-50

50

0 -100

100

Figure 11a : Longitudinal stress X-rays nd measurement (2 pass)

2*V

200

100

0 -100

V=40mm/min

m

2*V

13 5m

Stress (MPa)

200

300

V=40mm/min 13 5m m

Stress (MPa)

300 250

24-25 : SIYY Residual stress

400

350

X(mm) 0

-50

50

100

Figure 11b : Transversal stress X-rays measurement (2nd pass)

Figure 11: Effect of torch speed on the measurement of residual stress (SIXX, SIYY) Numerical analyses 400

100

I 0

-100

Measur

200

m

200

SIXX/2nd pass/X=135mm/UP face

300

13 5m

C

Longitudinal Residual Stress (MPa)

SIXX/1st pass/X=135mm/UP face

300

13 5m m

Longitudinal Residual Stress (MPa)

400

100

C

0

I

-100

V- I

-200 -300

-200

V- I

-300

0

20

40

60

80

100

y (mm)

Figure 12a: Longitudinal stress (1 st pass)

0

20

40

60

80

100

y (mm)

Figure 12b: Longitudinal stress (2 nd pass)

Figure12: Effect of hardening model on the residual stress SIXX

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The isotropic hardening (I) assumption does not properly describe the Bauschinger effect and the springback during the reverse loading [2]. Another way to simplify the evolution of the yield stress surface, without changing its shape and size during plastic deformation, is by assuming the initial yield stress surface to translate in the stress field. The Bilinear Kinematic hardening (C) option (see Figure 12) assumes the total stress range is equal to twice the yield stress, so that the Bauschinger effect is included. Figure 12b compares the longitudinal residual stress calculated using different hardening models. The energy input during cyclic hardening material model depends on the selected type of law. The ranking of models as function of increasing amplitude of residual stresses in plastic zones and displacements in specimen is as follows: 1. Bilinear Isotropic Hardening material model (I) 2. Bilinear Isotropic Hardening material model with viscous data (V-I) 3. Bilinear Kinematic Hardening material model (C) We conclude that the viscous data have a localized effect in the HAZ zone, which is a very good agreement with the experimental results (see Figure 10). If viscous data are not available, it seems better to use bilinear kinematic hardening (C) for calculating residual stresses during simulating multipasse welding. On the other hand, isotropic hardening would lead to an increasing of the residual stress after each cycle. Therefore, elastoplastic with bilinear kinematic hardening (C), can then be used with quite enough confidence to simulate multipasse welding. Conclusions In the thermal analysis, different modelings of the heat source have been considered for the thermal steady state calculation, with an efficiency parameter K fitted to adjust the simulated temperatures considering the measured ones. In the conclusion, two axioms were emerging: A1- The way that the heat flux density was spread (in surface or in volume) had little effect on the macroscopic thermo-mechanical simulation results if: x The net total heat flux KUI is the same. x The dimensions of the modeling source are in the same order than the dimensions impact of the heat flow on the plate surface. A2- The sensitivity of thermal losses (SL) on the numerical result depends on the heat input (Q), material conductivity (Ȝ), dimensions of perpendicular section to the weld direction (L/e) and welding velocity (v): SL=f(Q, Ȝ, L/e, v). Therefore, there is no need for a more precise (and complicate) losses parameters identification for thick welding steel structures simulation. In the mechanical analysis, 24-25 mock-up allow us to test the effect of viscosity on displacements and stresses results, the different conclusions are: x The stress state is mainly longitudinal. x The energy input during cyclic hardening material model depends on the selected type of low. The ranking of models as a function of increasing amplitude of residual stresses in plastic zones and displacements in specimen is as follows: 1. Bilinear Isotropic Hardening material model (I) 2. Bilinear Isotropic Hardening material model with viscous data (V-I) 3. Bilinear Kinematic Hardening material model (C)

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x x x x x

The isotropic hardening law is unsuitable for analyzing cyclic welding load histories. Considering viscosity in the material behavior, reduce error between calculation and experiment displacements. Measurement analyses show us that the viscosity (synonym of the torch speed) has a neglect effect on the longitudinal and transversal residual stresses. Numerical analyses show us that the viscosity have a localized effect in the HAZ zone. If viscous data are not available, elastoplastic modeling with bilinear kinematic hardening (C) can gives a good agreement between the experiments and the finite element simulations.

Acknowledgments We thank FRAMATOME-ANP, EDF/SEPTEN, ESI-Group and EADS/CCR for their funding of this research effort and CEA, EDF/R&D for their experimental support. References 1.

El-ahmar, W., J-F.Jullien, “ 3D Simulation of Multipass Welding Austenitic Stainless Steel Plate”, MCWASP-XI Conference, Opio , May. 2006.

2.

El-ahmar, W., J-F.Jullien, P.Gilles, “Reliability of hardening model to predict the welding residual stresses”, 3rd Intl Conference, Budapest , April. 2006.

3.

El-ahmar, W., Base de données 316L, Comportement des matériaux situés dans la zone affectée thermiquement lors d’une opération de soudage, Note INSA Lyon, N° : INSAVALOR257.8A401

4.

Ayrault D., Blanchot O., Maquettes instrumentées de soudage multi-passe. Base de données expérimentale destinée à la validation de calculs.Projet : intégrité mécanique des tuyauteries fiche-action : CEA/EDF 2425, DECS/UTA /02-RT – 07.

5.

Y.Vincent, J-F.Jullien, P.Gilles, “Thermo-mechanical consequences of phase transformations in heat-affected zone using a cyclic uniaxial test,” International Journal of Solids and Structures, 42 (2005) 4077-4098.

6.

L.Depradeux, J-F.Jullien, “Experimental and numerical simulation of thermomechanical phenomena during a TIG welding process,” J.Phys.IV France 120 (2004) 697-704

7.

X.Desroches, ”Note méthodologique sur la simulation numérique du soudage multipasses, ” HI-75/01/017/A, EDF R&D.

8.

L.E.Lindgren, “Finite element modelling and simulation of welding, Part 1: increased complexity,” Journal of thermal stresses, 24, 2001, p.141-192.

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9.

51

L.E.Lindgren, “Finite element modelling and simulation of welding, Part 2: improved material modelling,” Journal of thermal stresses, 24, 2001, p.195-131.

Session: Residual Stress Analysis by Experimental Methods

EVALUATION OF NOVEL POST WELD HEAT TREATMENT IN FERRITIC STEEL REPAIR WELDS BASED ON NEUTRON DIFFRACTION

C. Ohms, D. Neov, A.G. Youtsos EC-JRC-IE, High Flux Reactor Unit PO Box 2, 1755 ZG Petten, Netherlands R.C. Wimpory Hahn-Meitner-Institute, Glienicker Str. 100 14109 Berlin, Germany

ABSTRACT The occurrence of cracks in – normally welded – components with safety relevance in, e.g. nuclear installations or in the (petro-)chemical industry, is not an unusual event. In most cases such cracking is detected in periodic inspections prior to complete failure of the component. Sometimes a detected defect necessitates repair of the damaged component to facilitate its further operation. Repairing of a crack would normally be performed by excavating of the material surrounding the crack and subsequent filling of the excavation by welding. However, such a repair welding process leaves the component in a sensitive state in that it generates a complicated residual stress pattern and that the heat affected zone of the weld might become very susceptible to the formation of new cracking [1]. Post weld heat treatment of a repaired component can be an option to mitigate the damaging impact of the welding process. Through heat treatments residual stresses can be severely reduced or redistributed to obtain stress fields around the weld deemed less detrimental. At the same time a heat treatment process could positively influence the HAZ sensitivity for further cracking. In any case, a thorough assessment of the welding process is necessary to ensure a safe continued operation of the repaired component. In this context letterbox repair welds applied to thin ferritic steel plates to simulate repair of postulated shallow cracks have been manufactured. The excavations of postulated cracks for these experiments were filled with 20 to 30 welding passes. Components have been made available in the as welded state and after the application of PWHT. Two different heat treatment processes are compared: a. a full scale treatment, where the entire test piece has been subjected to an elevated temperature for several hours in order to significantly reduce the residual stresses, and b. an alternative treatment whereby the heat is applied locally for a short period of time in order to redistribute the stresses in a controlled manner.

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In this paper the experimental determination of these residual stresses in the as welded and in the heat-treated states is presented. Such measurements have been performed by neutron diffraction at the High Flux Reactor (HFR) of the Joint Research Centre of the European Commission in Petten, the Netherlands. The principle of residual stress measurements by neutron diffraction is introduced [2] and the particular considerations for performing such measurements in multi-pass butt welds are briefly outlined [3]. The experimental approach is presented and explained and an outline is given on the data analyses. Results are depicted in the form of comparison between the as received and the heat treated stress states. The derived data facilitate conclusions on the effects and effectiveness of the applied heat treatments and they also demonstrate that neutron diffraction is a very suitable tool for non-destructive analysis of internal residual stress fields in such welded components of considerable thickness. In addition, the method is well suited for the validation of predictive numerical models.

Introduction Pipes, vessels and other safety critical parts in industrial installations are – generally speaking – subjected to high thermal and mechanical loads for extended periods. When catastrophic failure of such components cannot be tolerated in view of the consequences involved, regular inspection of the plant is necessary. In case flaws and/or defects are revealed in the course of such an inspection, the need for component repair or replacement needs to be carefully assessed. Replacement of an entire damaged component may not be possible because of its size, shape, accessibility or economic value. In such cases, when the presence of a flaw cannot be tolerated for further operation, one would have to repair the component. Repair welds are manufactured by excavation around and removal of defective material and refilling the excavation by a series of weld beads. Such repair welds are applied in power and (petro-)chemical industry, but also elsewhere. Unfortunately, such repair welding introduces significant residual stresses in the area, where the repair is applied. In addition, a zone of high sensitivity to further cracking might be generated. This can once again lead to cracking and/or failure of the repaired component [1]. This paper deals with the experimental assessment of repair welding residual stresses by neutron diffraction. In addition to the as welded state, two different types of heat treatment have been assessed – a standard post-weld heat treatment (PWHT) with the entire component subjected to a high temperature for several hours, and a localized thermal shock based alternative approach (APWT), which rather serves to redistribute the stresses than mitigate them, the latter being a novel approach taking account of the possibility that a repaired component might be too big in size for a standard PWHT. All investigations were performed on mock-ups for weld repairs, since neutron diffraction is a technique that cannot be applied in situ. As neutron diffraction is the technique applied for stress measurement, the basic principles of this method are first outlined within the following section. At the same time the particularities of measuring stresses in welded components are briefly explained. Following this, specimen procurement and the applied heat treatments are described in the next section. As the different heat treatments have been applied in the context of different projects and experimental campaigns, the specimens and the repair welds are actually different in size and shape. The assessment of the standard PWHT is actually part of ongoing research at the time of drafting of this paper. For this reason the

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corresponding account is kept relatively short. Nevertheless, the data presented herein give a very good impression of the difference between the effects of the standard PWHT and the APWT. Subsequently the experimental procedures are described and the locations where tests have been performed within the specimens are shown. A brief account is given on the data analysis procedure and finally the experimental results obtained for the as repaired and for the heat treated components are shown. The paper is completed with a discussion on the effectiveness of the different heat treatments examined and some concluding remarks. Some preliminary recommendations are given for real applications.

The Neutron Diffraction Technique Techniques for exploring matter with neutrons have been developed over the past 50 to 60 years. The application of neutron diffraction for analysis of residual stresses in crystalline materials is still relatively young as it emerged only in the early 80’s. For this reason, and because only a limited number of facilities exists in the world, its application is not as widespread as the well-known and closely related X-ray diffraction technique. The most unique feature of the technique is that it can measure non-destructively threedimensional residual stress fields deep within crystalline materials with good spatial resolution. Like X-ray diffraction the technique is based on Bragg’s equation:

nO

2d ˜ sin T

where O is the neutron wavelength, d the crystallographic lattice spacing and T the diffraction angle. Hence the technique facilitates the measurement of lattice spacing in crystalline materials through measurement of the diffraction angle T. Figure 1 below illustrates the set-up of such a diffraction measurement. Additional measurements taken from a free-ofstrain specimen (d0, T0) from identical material facilitate the calculation of strain H through

H

sin T 0 1, sin T

which in turn allows for measurement of strain without precise knowledge of the neutron wavelength, provided instrument settings, including neutron wavelength, are identical for measurements of both strained and reference specimen. Eq. (2) is derived from eq. (1) together with the definition of strain. The sampling volume, i.e. the volume from which an individual measurement is taken, is defined by the cross section of the incoming and diffracted beams (see Fig. 1). By changing the size of the slits one can modify size (and shape) of the sampling volume. The direction, in which the lattice spacing is measured, is by default the bi-sector of the incoming and diffracted neutron beams.

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NEUTRON SOURCE SLIT INCOMING BEAM

MEASURING DIRECTION

SAMPLING VOLUME DIFFRACTED BEAM

SAMPLE

24

DETECTOR

SLIT

Figure 1. Sketch of a neutron diffraction measurement Strain measurements obtained in three mutually orthogonal directions, called x, y and z here for simplicity, facilitate the calculation of residual stress at the test location via the generalized Hooke’s law:

Vx

E QE Hx  (H x  H y  H z ) ; 1 Q (1  Q )(1  2Q )

accordingly, Vy and Vz are derived. In case x, y and z coincide with the principal stress directions, the thus derived Vx, Vy and Vz are the principal stresses. It lies in the nature of residual stresses that they vary with location. Therefore measurements are normally made at various locations within an area of interest. This is facilitated through moving the specimen relative to the sampling volume, which remains fixed in space. Particularities of measurements in butt weld fusion zones In general, the application of multi-pass welding introduces material inhomogeneities in the fusion and heat-affected zones. These inhomogeneities are present in form of local variation of chemical composition, microstructure and strain history of the material. This implies a local variation of the stress free reference lattice spacing (d0), which would need to be determined individually for every test location and direction in order to obtain exactly correct strain values through Eq. (2). This normally requires the availability and destruction of companion test pieces manufactured to the same specifications as the specimen under investigation [3]. For the purpose of the reported herein investigations it was decide to relax the requirement of determining special reference lattice distance variations for two reasons. At first in particular with ferritic materials as investigated here such local variations tend to be relatively small compared to the mechanical strains/stresses induced by the repair

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welding process. Secondly, the purpose of these investigations was the study of the impact of post-weld heat treatments, i.e. specimens have been tested before and after application of the respective heat treatment and thus the main focus here is to estimate and present changes in the stress fields obtained by these heat treatments. Such changes are less effected by reference variations than the absolute stress values. Specimen procurement The specimens for testing a conventional full scale PWHT were manufactured from the ferritic steel DIN17175 grade 10CrMo9-10. Plates of dimensions 200×100×20 mm were machined and for the application of the repair of a postulated crack an excavation of about 90 mm length, 30 mm width and 15 mm depth was machined in the centre of each plate. The plate excavations were subsequently filled with 18 welding passes employing the submerged arc welding technique. The pre-heating temperature was specified to be 200°C. The interpass temperature was 250°C. The exact dimensions of the plate excavation and the sequence of welding is shown in Figs. 2 and 3 below. Following welding and cooling down of the specimens, the excess material was ground down to 0.5 mm remaining thickness, and the ground surface was sand flushed with fine grained grinding paper. Subsequently a PWHT was performed whereby the entire specimen was kept at ~750°C for about 8 hours. Specimens were available in the as welded and in the heat-treated state.

Figure 2.

Plate dimensions and position of the weld groove.

Figure 3.

Transverse section of the 18 bead weld with a scheme of the deposition sequence.

The investigations on the APWT were actually performed in a different project context and for this reason the specimens are not of the same shape as the specimens produced for the investigations on the full-scale heat treatment. These specimens were manufactured from the ferritic steel grade A533B. The base plate in this case was 25 mm thick and 300×300 mm wide. The excavation of the postulated small repair in this case was 12 mm deep and about 70×20 mm across and was filled with 26 welding passes. The pre-heating temperature again was 200°. Figure 4 below depicts the actual cross section of the excavation and the bead sequence applied. The entire excess material was ground away subsequent to welding and cooling down. In this case only one specimen was manufactured. Therefore neutron diffraction measurements had to be made on this specimen prior to APWT and again on the same specimen after application of the APWT. The APWT consisted in the application of a localized thermal shock, which would induce plastic flow in order to obtain a modified residual stress field. In this case two heating pads of 30 mm diameter were applied on the welded surface on either side of the weld. The pads were boosted to a temperature of about 600°C and this

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temperature was held for about 15 sec. Subsequently the specimen was allowed to cool down freely. Finally the same specimen was tested again by neutron diffraction in order to establish the modification accomplished by this alternative heat treatment.

Figure 4. Cross-section of the 26 bead weld with a scheme of the deposition sequence. Measurement procedures 18 bead weld with full scale PWHT at about 750°C As stated before, the measurements presented here are part of an ongoing campaign. For this reason and in order to keep things short only a few of the measurements performed in these test campaigns are shown. Nevertheless, the results given below are fully conclusive in the context of this paper. Neutron diffraction testing has been performed at the Large Component Neutron Diffraction facility at beam tube HB4 of the HFR. At this facility a pyrolytic graphite double monochromator is installed for neutron wavelength selection. An AECL-Canada type 32wire neutron detector registers the diffracted neutrons. Cadmium masks in the incoming and diffracted beams determine the neutron beams’ size and therefore the sampling volume. A nominal neutron wavelength of 0.257 nm was used for these measurements. The sampling volume was 3×3×8 mm3. Measurement times for an individual test ranged from ten minutes to one hour. Data were collected in form of neutron counts versus scattering angle, and the analysis was done by fitting a Gaussian to every diffraction peak. Measurements in two specimens are presented here, an as welded test piece and a companion specimen, which has received a normal PWHT at 750°C for 8 hours. Two scans were performed in each specimen. One scan was made along a line located at 3 mm below the welded surface and running orthogonal to the welding direction across the weld at mid-length of the specimen. The other scan was made along a second line also at 3 mm below the welded surface, running parallel to the welding direction through the centre of the weld. Measurements were taken at intervals of 8 mm covering the entire width and length of the specimen. In order to facilitate the calculation of stresses in accordance with eq. (3), measurements have been taken in the welding longitudinal, welding transverse and plate normal directions for every test location.

Evaluation of Novel Post Weld Heat Treatment

61

With the above neutron wavelength, measurements were taken from the ferritic (110) reflection plane, which rendered diffraction angles 2T in the vicinity of 78°. As there was no separate test piece available for reference measurements, the reference scattering angle was determined based on measurements taken from the heat treated specimen, because of the low variation of the lattice spacings measured there. 26 bead weld with application of localized thermal shock as APWT Neutron diffraction testing has been performed using the large Combined Powder and Stress Diffractometer at beam tube HB5 of the HFR. At this facility a copper monochromator is installed for neutron wavelength selection. An Ordela type 1150N single wire position sensitive neutron detector is operated at this facility. Cadmium masks in the incoming and diffracted beams determine the neutron beams’ size and therefore the sampling volume. Also here a nominal neutron wavelength of 0.257 nm 3 was used for the measurements. The sampling volume was 5×4×8 mm . (Remark: The larger sampling volume was used here in order to compensate for attenuation due to the larger thickness of this specimen.) Therefore measurement times for an individual test were kept in the same range, ten minutes to one hour. Data collection and analysis obviously is identical to the HB4 facility. Measurements on one and the same specimen are presented here, the first series in the as welded state and the second series after application of the APWT. Several scans were performed in this specimen. All of them were made along lines running through the thickness of the plate, from the welded surface down to the opposite surface, where the base metal had remained intact. One of these lines is located at the very centre of the weld; the other lines are away from this line by 10 and 30 mm. At 10 mm distance the line would still crosses the weld pool, while at 30 mm distance the line is entirely within the base metal. Measurements were taken at intervals of 1 or 2 mm covering the entire thickness of the specimen. In order to facilitate the calculation of stresses in accordance with eq. (3), measurements have been taken in the welding longitudinal, welding transverse and plate normal directions for every test location. Here again measurements were taken from the ferritic (110) reflection plane, which rendered in this case diffraction angles 2T in the vicinity of 77.3°. (NB: On both machines wavelengths were not calibrated, as this is not necessary for the determination of strains using eq. (2). Therefore the nominal wavelengths given are not completely accurate, which accounts for the difference in the scattering angles.) A base material specimen cut from a corner of the plate was used for measuring reference values. Figure 5 below shows the specimen installed at the facility for measurements in the welding longitudinal direction.

Figure 5. 26 bead set-up at HFR/HB5 for measuring the welding longitudinal direction.

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Measurement results In both cases measurements have been performed on the ferritic (110) diffraction plane. Suitable elastic constants for calculating stresses in accordance with eq. (3), to be used when deriving stresses from strain measurements performed by diffraction methods on this lattice plane, have been obtained from the literature [5], i.e., E110=220 GPa and Q110=0.28. All stress data presented below have been calculated using these values for E and Q. 18 bead weld with full scale PWHT at about 750°C Two sets of measurement results obtained from the as welded and the heat-treated specimen are presented in Fig. 6 and 7. Figure 6 shows longitudinal residual stresses measured along the line across the weld at mid-length, while in Fig. 7 the distribution of longitudinal stresses over the line parallel to the welding direction are depicted. Both Figs. 6 and 7 indicate that the welding residual stresses have been almost completely relieved by this conventional heat treatment whereby the entire specimen is subjected to a high temperature for several hours. In the as welded component, welding longitudinal stresses near the weld fusion line, along both lines, were found to be around 300 to 400 MPa in tension in the as welded test piece. Normal stresses across whole cross sections of components must integrate to 0, i.e., tensile and compressive stresses must be found. The stress distribution for the as welded test piece in Fig. 6 reflects this with high tensile stresses within the weld and high compressive stresses in the base material. Nevertheless, these stresses do not balance since the test locations do not cover a full cross section. No such condition exists for the scan presented in Fig. 7, where scanning direction and stress direction coincide. Both data sets exhibit a significant drop of the tensile residual stresses in the centre of the weld. This will be subject to further investigation, as this research activity is ongoing. Nevertheless, the assumption is made that this dip is related to the welding sequence shown in Fig. 3, where the final bead was actually applied in the centre of the weld, which can have reduced the stresses at the test locations just underneath this final bead. 400

residual stress [MPa]

300 200 100 0 -100 -200

As welded

-300

8 hours PWHT 750C

-400 -50

-40

-30

-20

-10

0

10

20

30

40

50

distance from weld centre

Figure 6. Longitudinal residual stresses in 18 bead weld – scan across the weld at midlength at 3 mm below welded surface.

Evaluation of Novel Post Weld Heat Treatment

63

500

residual stress [MPa]

400 300 200 100 0

As welded

-100

8 hours PWHT 750C -200

-120 -100

-80

-60

-40

-20

0

20

40

60

80

100

distance from weld centre

Figure 7. Longitudinal residual stresses in 18 bead weld – scan through the weld parallel to welding direction at 3 mm below welded surface. 26 bead weld with localized thermal shock at about 600°C Four sets of measurement results obtained from the as welded and the heat-treated specimen are presented in Fig. 8, 9, 10 and 11. A more comprehensive account on measurements performed on the as welded component, including some numerical stress predictions, is given in [5]. Figures 8 and 9 show the through thickness distribution at weld centre of residual stresses measured in the welding longitudinal and transverse directions respectively. Figures 10 and 11 show corresponding measurements along a through thickness line 30 mm away from weld centre. The latter is roughly the position, where one of the heating pads was placed when applying the APWT. The data are presented such that test locations near the welded surface are on the left (distance from welded surface 0), and locations on the back face of the specimen, where there is only base material, are on the right. 800

residual stress [MPa]

700 600 500 400 300 200 100

longitudinal as rec.

0

longitudinal APWT

-100 0

5

10

15

20

25

distance from welded surface [mm]

Figure 8. Longitudinal residual stresses in 26 bead weld – through thickness scan across at weld centre; as welded and heat-treated specimen.

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Ohms et al.

800

residual stress [MPa]

700 600 500 400 300 200 100

transverse as rec. transverse APWT

0 -100 0

5

10

15

20

25

distance from welded surface [mm]

Figure 9. Transverse residual stresses in 26 bead weld – through thickness scan across at weld centre; as welded and heat-treated specimen. What can be seen from Figs. 8 and 9 is, that the as welded plate experienced very high tensile residual stresses, both in the welding longitudinal and transverse directions; locally the data suggest more than 700 MPa. This is particularly the case for the fusion zone and the heat affected zone, whereas in the base material underneath the weld stresses drop to significantly lower values. The next thing that can be seen is that the APWT managed to reduce the longitudinal stresses within the fusion zone significantly. At the top surface a remaining value of 100 MPa was observed and the maximum value found just underneath the fusion zone in the heat affected zone was reduced to 500 MPa. The outcome is different for the transverse direction though. The already high tensile stresses in the weld were slightly increased by the APWT, and also stresses in the base material underneath the weld were measurably raised. Similar observations were made at 10 mm away from the centre of the weld. These data are not depicted here in view of restrictions in space. 800 700 residual stress [MPa]

600

longitudinal as rec.

500

longitudinal APWT

400 300 200 100 0 -100 -200 0

5

10

15

20

25

distance from welded surface [mm]

Figure 10. Longitudinal residual stresses in 26 bead weld – through thickness 30 mm from weld centre in base metal; as welded and heat-treated specimen.

Evaluation of Novel Post Weld Heat Treatment

65

800

residual stress [MPa]

700 600 500 400 300 200 100

transverse as rec.

0

transverse APWT

-100 0

5

10

15

20

25

distance from welded surface [mm]

Figure 11. Transverse residual stresses in 26 bead weld – through thickness 30 mm from weld centre in base metal; as welded and heat-treated specimen. Figures 10 and 11 show how residual stresses developed after APWT at a location underneath one of the heating pads. For the welding longitudinal direction the situation is reversed now. Surface stresses that had originally found to be slightly compressive, have been turned into strong tensile stresses of up to 500 MPa. Near the back of the specimen again the change in stresses is rather small. For the transverse stresses, as before the values have risen as a consequence of the APWT. And again the transverse stresses were reaching considerable magnitudes of up to 700 MPa near the welded surface. Conclusions A study of the impact of different post-weld heat treatments on the residual stress fields around letterbox repair welds in ferritic steel plates has been performed experimentally by means of neutron diffraction. A standard PWHT at 750°C in a furnace has been investigated in addition to an alternative method, whereby heat was only applied locally in terms of a thermal shock in order to redistribute stresses in a predetermined manner. Such a procedure might become relevant in cases, where the repaired component is too big to be put into a furnace or it cannot be removed from the place, where it is installed. For both heat treatment cases measurements of residual stresses within and near the fusion zone have been performed before and after application of the heat treatment. Based on the data presented above the following conclusions can be drawn: 1.

Almost complete relief of residual stresses is accomplished by a normal heat treatment, whereby the specimen is kept at temperatures in the vicinity of or even higher than half the melting temperature of the material for several hours.

2.

Contrary to that, the alternative method described above did not result in overall stress relief but only locally and in one direction. At various locations and directions stresses were found to be increased, at some places even substantially, reaching values probably near the yield stress of the material.

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3.

Nevertheless, the results obtained were to be expected based on the geometry, which was applied in the APWT. This particular geometry was actually chosen to achieve the reduction of longitudinal stresses in the fusion zone that was found in the measurement. Numerical stress predictions by Institute de Soudure, yet unpublished, actually show similar results.

Based on the above, at first glance one could conclude that the application of such an APWT is not helpful, because the partial reduction of stress comes at the cost of a significant increase elsewhere. However, one also has to say that it is clear that a fullscale standard PWHT is in many cases simply not possible. An APWT as presented here has the advantage that it can be applied under almost any circumstances and that its impact is quite predictable. It is clear that the APWT geometry applied here does not necessarily render an acceptable result in terms of stress relief, when considering that the repaired component is to go back into operation. Hence there is need for further investigations in this direction, eventually investigating more complex APWT set-ups, in order to establish whether satisfactory solutions can be found without placing the entire component into a furnace. Acknowledgments The authors wish to express their gratitude to all those without whose contribution this work would not have been possible. The partners of the research project ENPOWER, co-financed by them and the European Commission, should be mentioned here and in particular Mr. D. Lawrjaniec from Institute de Soudure. From amongst the partners of the European Network NET the authors wish to single out the contribution of Mr. D. Pettene from Belleli Energy, which manufactured and heat treated a large number of specimens for these investigations. References 1.

2. 3.

4. 5.

Boucher, C., Bourchard, P.J., Brown, B., Smith, D., Lawrjaniec, D., Hein, H., Truman, C., Smith, M., Ohms, C., Dauda, T.A., Cardamone, D. and Youtsos, A.G., “Management of Nuclear Plant Operation by Optimising Weld Repairs – Enpower Project Overview”, in: Proceedings of the ASME Pressure Vessels and Piping Conference 2005, Volume 6, Materials and Fabrication, ASME, New York, 2005, ISBN 0-7918-4191-X, pp. 355-360. Hutchings, M.T., Krawitz, A.D., editors, Measurement of residual and applied stress using neutron diffraction, Kluwer Academic Publishers, Dordrecht, Boston, London, 1992. Ohms, C., Youtsos, A.G. and van den Idsert, P., in: Proceedings of Baltica V – International Symposium on Condition and Life Management for Power Plants, edited by S. Hietanen & P. Auerkari, VTT Technical Research Centre, Espoo, Finland, June 2001, Vol. 2, 487-497. Eigenmann, B., Macherauch, E., Mat.-wiss. u. Werkstofftech., Vol. 27, 1996, pp. 426-437. Ohms, C., Wimpory, R.C., Neov, D., Lawrjaniec, D. and Youtsos, A.G., “ENPOWER – Investigations by neutron diffraction and finite element analyses on Residual stress Formation in repair welds applied to ferritic steel plates”, in: Proceedings of the ASME Pressure Vessels and Piping Conference 2005, Volume 6, Materials and Fabrication, ASME, New York, 2005, ISBN 0-7918-4191-X, pp. 385-393.

HIGH-RESOLUTION NEUTRON DIFFRACTION FOR RESIDUAL STRAIN/STRESS INVESTIGATIONS

P. Mikula and M. Vrána Nuclear Physics Institute and Research Centre ěež, plc. 250 68 ěež, Czech Republic

ABSTRACT In this paper, attractive properties of unconventional and high-resolution neutron diffraction performances exploiting cylindrically bent perfect (BPC) Si-crystal monochromators documented by experimental results, are presented. They permit high or even ultrahigh-resolution of macro- and microstrain scanning of bulk polycrystalline materials. The diffractometer using a dispersive type multiple reflection monochromator can operate with the resolution of the backscattering device, however, at a rather small monochromator take-off angle. Introduction By a simple implementation of the bent-perfect-crystal (BPC) elements on conventional scattering devices one can considerably benefit from real or/and momentum space focusing, especially for small slit-like samples. When working with open beams (without Soller collimators) the diffraction devices equipped with the BPC-elements can be dramatically superior to the conventional devices with flat mosaic crystals and Soller collimators [1-3]. Moreover, position sensitive detectors can be used instead of usually used multidetector systems. In some cases, a simultaneous use of both momentum space focusing (resulting in a high resolution) and real space focusing (resulting in a high luminosity) is possible. The drawback of such focusing diffraction performances (with the exception of the dispersive monochromators) is that the high resolution is achieved in a limited range of scattering angles. Therefore, they need not be useful for powder diffractometry generally, namely when samples of larger dimensions have to be investigated. On the other hand, in the case of strain/stress measurements, when the changes of the position of one or more diffraction lines and their profiles have to be studied, focusing techniques are not avoidable because they permit one to carry out such experiments even at the medium power neutron sources [4-7]. Cylindrically Bent Perfect Si-Crystal Monochromator versus a Hot Pressed GeMosaic Monochromator As there is a lack of experimental evidence of a direct comparison of different monochromators at defined experimental conditions, we carried out a comparison of a widely used hot pressed Ge crystal with a sandwich of two BPC Si slabs. For the

67 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 67–75. © 2006 Springer.

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experiment we used a Ge(511)- crystal of the dimensions of 70x12x8 mm3 (length x height x thickness) with the planes (311) at <=9.5o and the Si(211)-BPC sandwich of 200x30x(2x4) mm3 with the planes (311) at <=10o (< is the angle of the lattice plane with respect to the main face of the crystal). Therefore, for a correct comparison just asymmetric diffraction geometry of the monochromators on the lattice planes (311) was chosen. The specific experimental conditions were determined by the parameters of our diffractometer, the cut and dimension of the Ge and Si crystals and the employed slits: the maximum 2TM-angle was 60o, collimation of the incident polychromatic beam Do = 20´, monochromator-slit distance LMS=175 cm, slit dimensions of 2x1 mm2 (width x height), a fixed radius of RSi=8.5 m of the Si sandwich (no focusing optimization was carried out) and cross-section of the incident polychromatic beam of 50x12 mm2. The neutron current passing through the slit was measured for several take-off angles and in all cases the neutron current from the bent Si surpassed the current corresponding to the Ge counterpart (as can be seen from the example shown in Figure 1). Further in the next step, using a solid D-Fe polycrystalline sample of the diameter )=2 mm, the diffraction profiles Fe(110) and Fe(211) were measured by a position sensitive detector for a fixed bending radius of the BPC Si-monochromator RSi=8.5 m (see Figure 2 which is related to the results obtained for 2TM =60o). As a result of focusing effects, the difference in the maximum peak intensity and FWHM of the profiles in favour of the bent Si sandwich is evident. For experimental results taken at other take-off angles, see [3]. 0

0

1,5x10

5

240 = 50 , RSi = 8.5 m

5

5,0x10

4

0,0 33,0

33,5

34,0

34,5

240 = 60 , RSi = 8.5 m

5

FWHM 31.33´ 13.18´

Ge (311)-mosaic crystal Si (311)-bent crystal

Intensity / 30 s

Intensity / 30 s

Ge(311)-mosaic crystal Si(311)-bent crystal 1,0x10

1,5x10

FWHM 28.08´ 12.53´

35,0

35,5

1,0x10

5

5,0x10

4

0,0 38,0

36,0

38,5

39,0

39,5

40,0

40,5

41,0

Z0 / deg

Z0 / deg

Figure 1. Comparison of the current of monochromatic neutrons passing through the 2 2x1 mm slit situated at the distance LMS=175 cm for two monochromator take-off angles 2TM and RSi = 8.5 m. 1000

2000

0

0

240 = 60 , RSi = 8.5 m

240 = 60 , RSi = 8.5 m

Intensity / 10 800 s

800

Intensity / 10 800 s

M-Si(311) + S-Fe(110) M-Ge(311) + S-Fe(110)

1500

FWHM 15.83´ 21.28´

1000

500

FWHM 34.82´ 44.21´

600 400 200 0

0 46,5

M-Si(311) + S-Fe(211) M-Ge(311) + S-Fe(211)

47,0

47,5

48,0

48,5

24S / deg

49,0

49,5

50,0

50,5

87

88

89

90

91

92

93

94

95

24S / deg

Figure 2. Comparison of diffraction profiles of the Dҏ-Fe(110) and D-Fe(211) reflections of o a polycrystalline sample taken at 2TM=60 . FWHM is in minutes of arc.

High-Resolution Neutron Diffraction

69

Strain Measurement by the Energy-Dispersive Neutron Transmission Diffraction (EDNTD) The EDNTD method is based on the measurement of a decrease of beam intensity transmitted through the sample in dependence on the wavelength. The edge in this dependence can be observed when passing through the limit of O=2dhkl, below which the particular reflection planes (hkl) begin to scatter neutrons. It means that no angular dependence of scattering is measured and only the integrated intensity of this particular reflection can be determined from the transmitted beam for each value of O The microstructure parameters can be then extracted from O-dependence of the transmission coefficient T(O) = ((IS(O) – IB(O)) / ((IW(O) – IB(O)) ,

(1)

Relative amplitude

where IW(O), IS(O) and IB(O) are the intensity dependencies of the direct beam (without the sample), the direct beam passing through the sample and the background, respectively. During the last years we tested several modifications of the high resolution EDNTD based on Bragg diffraction optics [8,9] and the most efficient modification [10] employing a one dimensional high-resolution Bent perfect crystal position sensitive detector (1d-PSD) for monochromator PSD detector Slit data acquisition is described in the O!O 'T0 following part. This simplest EDNTD setting (see Figure 3) exploiting Bragg OO diffraction optics which is convenient for the use at steady state reactors is based O  Polycrystalline T0 on the following ideas [10]: sample There is a strong angular-wavelength correlation of neutrons reflected by a bent monochromator crystal (a particular Figure 3. Scheme of the EDNTD wavelength O corresponds to a particular performance. 'TM of the beam), which is then used for intensity vs. O scanning. This correlation enables the conversion of the Odependence of the scattered intensity 1,0 into the spatial dependence. This Standard sample reduction 40 % 0,8 conversion is sufficiently linear, providing reduction 90 % thus possibility to use a one-dimensional 0,6 PSD for an effective collection of data. It can be described as: 0,4 a. Focusing in real space: The monochromator of horizontal bending 0,2 radius RM selects a monochromatic 0,0 beam and focuses the neutrons onto a narrow slit. The focal length of the bent -0,2 crystal monochroator (in the symmetric 250 260 270 280 reflection geometry is given by the len´s Channel number formula Figure 4. Bragg edges of the standard sample and plastically deformed (by cold rolling) ARMCO steel samples after thickness reduction. The corresponding FWHM values are 8x10-4 rad, 1.4x10-3 rad -3 and 1.6x10 rad, respectively.

fM= (RM/2) sin TM.

(2)

b. Correlation angle-wavelength: There is a strong correlation TOin the converging beam passing through the slit as

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O O0[1-'TM (1-LMS/2fM) cot TM] ,

(3)

which can be manipulated by changing RM and/or the monochromator-sample distance LMS. No Soller collimators are used. c. Simultaneous data acquisition by a position sensitive detector: The PSD situated at a distance LSD from the sample measures I('T) via 'Tҏ = 'x / LSD (x is represented by the channel number). The amplitude of the Bragg edge depends on the thickness of the sample, however, with the increased thickness a multiple scattering effect can be observed resulting in the smaller inclination of the edge. Similarly, the finite thickness tM and the bending radius RM of the monochromator as well as the slit width W relax the strict correlation (3) and induce a blurring of the position 'x of the Bragg edge on the PSD. Together with the spatial resolution of the detector they all determine the instrumental resolution. For details see [10]. Figure 4 shows the Bragg edges for a standard annealed sample as well as two plastically deformed ones and the suitability of this method for high resolution strain measurements. As FWHM of the edges we take the FWHM of the Gaussian function in the cumulative normal function used for fitting the shape of the diffraction edges. In comparison with the conventional method based on scattering angle analysis this one permits a considerably higher sensitivity to the edge shifts (due to the change of the lattice spacing) brought about by macrostresses. Figure 5 shows a practical example of the use of the EDNTD method for investigation of microstrains in prestrained steel samples [11]. 0.38

prestrain 0%

0.38

0.36

transmission

transmission

0.40

0.36 0.34

prestrain 5%

0.34 0.32 0.30

0.32 0.28 1.520 1.522 1.524 1.526 1.528 1.530 1.532 wavelength (Å)

0.38

transmission

0.36

prestrain 10%

0.34 0.32 0.30 0.28 1.5201.5221.5241.5261.5281.5301.532 wavelength (Å)

microstrain

1/2 (10-3)

1.520 1.522 1.524 1.526 1.528 1.530 1.532 wavelength (Å)

1.50 1.25 1.00 0.75 0.50

diffraction edge diffraction profile

0.25 0.00 0

5

10 15 prestrain (%)

20

Figure 5. Bragg edges for different prestrained low carbon steel samples and the mean microstrain dependences on the applied prestrain obtained from the evaluation procedure developed for EDNTD method as well as for Bragg-diffraction-profile broadening (for the sake of comparison).

High-Resolution Neutron Diffraction

71

Conventional Method of Strain Measurements Using Bragg-Diffraction-AngleAnalysis (BDAA) Diffractometer Employing the BPC-Monochromator In the case of the beam monochromatized by a BPC monochromator and a polycrystalline sample the ('d/d)-resolution of the diffractometer is determined by the divergenceҏ '(2TS) of the output beam. Similarly to the previous case, the rays of the beam are also TO correlated according to

'(2TS) = 'T M [2aSM (1 – LMS /2fM) - 1],

(4)

'OO = '(2TS) cot T M (1 – LMS /2fM) / [2aSM (1 – LMS /2fM) - 1],

(5)

where aSM = -tan TS/tan TM is the dispersion parameter. However, for the radius RM, RM = 2 LMS / [sin TM (2 – 1/ aSM ) ],

(6)



'T0

Polycrystalline sample 'TM

(hkl)

Cd-slits

Bent perfect crystal monochromator 1d-PSD

Figure 6. Scheme of the powder diffractometer using a BPC monochromator in combination with a position sensitive detector which is advantageously used in strain/stress measurements.

'Ҟ(2TS)=0 and a (quasi)-parallel and highly luminous diffracted beam from the sample is obtained which can be directly analyzed by a position sensitive detector [12] (see Figure 6). The blurring of the beam parallelity is brought about by a nonnegligible thickness tM of the monochromator and its curvature (responsible for a nonnegligible effective mosaicity) and the finite width W of the irradiated gauge volume. They contribute to the instrumental resolution by uncertainties 'D2t and 'D2w as 'D2t = 2(tM / RM) aSM / tan TM, 'D2W

= W(2 aSM - 1)/ LMS.

(7)

It should be pointed out that contrary to the diffractometer employing a mosaic monochromator where a minimum 'd-resolution takes place for tan TS = -(1/2)tan TM, a o high resolution usually required in the vicinity of 2TS = 90 can be easily achieved in this case even with much smaller monochromator take-off angles, simply by setting the optimum curvature of the BPC-monochromator. Depending on the parameters tM, RM,T M and W, the BDAA-diffractometer performances provide the resolution in 'd/d (taken from the FWHM of the diffraction profile) typically in the range of (1-4)x10-3 and a good luminosity permitting one their effective use for strain/stress measurements even at the medium flux neutron sources [13]. Figure 7 displays an example of the strain components (see scanning line) in the vicinity of the 10 mm wide and 3.5 mm high weld deposited pass. The gauge volume of 3x2x2 mm3 was situated in the middle of the plate and the scanning was carried out perpendicularly to the pass. The axes x,y and z are parallel to the longest edge of the plate, the medium wide edge and the shortest edge, respectively.

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Figure 7. A diagram displaying the course of the welding, the photo of the plate of 15Ch2MFA with the six fold welding path and the marked scanning line and the strain components versus the distance from the welded pass (welding material - Inconel 52).

Dispersive Multiple Reflection Monochromator for Ultra-High Resolution Strain Diffractometer The effects of multiple Bragg reflections in a deformed single crystal can be observed when more than one set of planes are simultaneously operative for a given wavelength

Figure 8. Schematic diagram of a twostep multiple Bragg reflection simulating a weak or forbidden reflection. The numbers 1,2 and 3 correspond to the primary, secondary and tertiary reflection planes, respectively.

Figure 9. TT scan with the crystal slab (the largest face parallel to (110) ) set for (hhh)1 reflections in the symmetric transmission geometry.

i.e. when more than two reciprocal lattice points are at the Ewald sphere [14,15]. Multiple reflection effects can result in reducing the intensity of a strong primary reflection or increasing the intensity of a weak primary reflection. The extreme case is the effect of simulation of forbidden primary reflection occurring in r1 by a successive co-operation of the two allowed reflections - secondary and tertiary occurring in r2 and r3 (see Figure 8). All these reflections are defined by the scattering vectors g1, g2 and g3, respectively. Then, the doubly reflected beam has the same direction as the one that could have been reflected by the particular primary set of planes. Scattering vectors g2 and g3 are in relation to g1 as g1 = g2 + g3. It follows from the crystal symmetry that when a secondary

High-Resolution Neutron Diffraction

73

Fe(220) FWHM = 5.90(16) / '

Fe(211) FWHM = 6.35(09) / '

120

S45C steel Exp.data Fit Gauss 1 Gauss 2 Gauss 3

100

Relative intensity

60

Fe(110) FWHM = 7.13 (07) / '

Relative intensity

Relative intensity

80

Fe(200) FWHM = 6.43(13) / '

reflection fulfils the Bragg condition simultaneously with the primary one, there exists automatically a tertiary reflection defined by g3 = g1 – g2 [16]. 80 Using bent prefect crystals we determined several strong double60 reflection processes on several pairs of lattice planes which are mutually in the dispersive geometry [17]. In 40 relation to the value of bending radius, the obtained doubly reflected 20 beam has however a narrow bandwidth 'OO of 10-4 -10-3 and 'T0 collimation of the order of minute of 45,0 45,5 46,0 66,0 66,5 83,5 84,0 109,5 110,0 110,5 arc. It is clear that in comparison with 2TS / deg the conventional single reflection Figure 10. Examples of the D-Fe profiles monochromators the monochromatic obtained on the diffractometer equipped with a neutron current is lower proposition sensitive detector and the multiple portionally to a smaller 'Oand 'T reflection monochromator. spread. New experimental studies of the multiple reflection monochromator proved the possibility of using it for high or ultra-high resolution monochromatization. For our test we used the double-reflection process based on two pairs of 153/1-3-1 and -31-1/513 reflections at O= 0.156 nm which was realized in a cylindrically bent Si-crystal set for diffraction in symmetric transmission geometry at T=30o (see Figure 9) [17]. Then, as a first step, the resolution properties of the diffractometer equipped with such a monochromator were tested. Figure 10 shows D-Fe diffraction profiles taken with a diffractometer performance employing this multiple reflection monochromator (without using any Soller collimators and with a 2 mm wide sample) which demonstrates its resolution abilities. The profiles were taken by a PSD detector with the 1.5 mm spatial resolution and situated at the distance of 1.42 m from the sample. Using only FWHM of the diffraction profiles, the resolution in 'd/d calculated 100

40

20

80

S45C steel Exp. data Fit Gauss 1 Gauss 2

60 40 20

0 43

44

45

46

2 T / deg

47

48

Figure 11. Induction-hardened S45C steel diffraction profile taken at the distance of 8 mm from the rod axis with the fitted profiles related to the perlitic, ferritic and martensitic phases.

0 43

44

45

46

47

48

2 T / deg Figure 12. Induction-hardened S45C steel diffraction profile taken at the distance of 6 mm from the rod axis with the fitted profiles related to the ferritic and martensitic phases.

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from our results is of about 8x10-4 in the vicinity for 2TS § 90o. But an estimation of the contribution coming from the width of the sample together with the detector spatial resolution gives a comparable uncertainty value. Therefore, it is expected that the intrinsic instrument resolution would be better than 5x10-4. Thus, it follows from the obtained results that at the high-flux sources the strains can be measured with the sensitivity of 10-5 in a large range of scattering angles. In the next step, the diffractometer equipped with this monochromator was used for investigation of Fe-reflections of an induction hardened S45C steel rod ()=20 mm) having different phase composition at different distances from the rod axis. The gauge volume was determined by 2 mm wide slits in the incident as well as diffracted beam. Fig. 11 displays the diffraction profile obtained at the distance of 8 mm from the axis. Similarly, Figure 12 displays the diffraction profile obtained at the distance of 6 mm from the axis. Thanks to the used high-resolution monochromatic beam, after a fitting procedure we could reliably determine contributions of the individual phases. Finally, it can be stated that diffractometers employing multiple reflection monochromator can provide very high resolution at low monochromator take-off angles. As can be also seen from Figure 8, in many cases of the double reflection process, one reflection of the pair can be realised at a large diffraction angle approaching the back-scattering and therefore the resolution of such a diffractometer can be comparable to back-scattering instruments. For adjustment of optimum parameters (the crystal cut, the thickness and the bending radius) of the monochromator and of the performance of the whole scattering device Monte Carlo simulations would be desirable [18]. Conclusions Several high-resolution diffractometer performances equipped with the BPCmonochromators for residual strain/stress scanning are presented. First off all, it is shown that in comparison with the conventional mosaic counterpart, the focusing BPCmonochromator provides higher resolution as well as a higher neutron flux delivered at the sample. However, a vertically focusing assembly can further improve the efficiency of the diffractometer. The Energy-Dispersive Neutron Transmission Diffraction performance is mostly suitable for measurements of one strain component in the in-situ studies of samples under an external thermomechanical load e.g. in a tension/compression rig. For determination of the stress tensor the inclination sin2<method should be used. The performance based on the method of Bragg-DiffractionAngle-Analysis (BDAA) is at present widely spread, because it provides a sufficient neutron current as well as the 'd/d resolution and can be efficiently used even at the medium power neutron sources. The diffractometer performance employing MRmonochromator can provide very high resolution at a rather low take-off angles. The resolution comparable to that of back-scattering instruments can be approached. Of course, they can be efficiently used namely at high-flux neutron sources. It should be noted that in our case the resolution shown by the MR-monochromator is higher than that presented in Figure 10 which was practically determined by the spatial resolution of the position sensitive detector and the width of the irradiated volume of the sample. Acknowledgements These studies were supported by the projects AV0Z10480505, MSM2672244501 and GA-CR 202/06/0601.

High-Resolution Neutron Diffraction

75

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11.

12. 13. 14. 15. 16. 17. 18.

Kulda, J., Wagner, V., Mikula, P. and Šaroun, J. ”Comparative Tests of Neutron Monochromators Using Elastically Bent Silicon and Mosaic Crystals”, Nucl. Instrum. Methods in Phys. Research, A 338, 60-64 (1994). Popovici, M. and Yelon, W.B., “Focusing Monochromators for Neutron Diffraction,” J. Neutron Research 3, 1-25 (1995). Vrána, M., Mikula, P. and Lebech, B. “Direct Comparison of Plastically Deformed Ge Mosaic Crystal and Bent Perfect Si Crystal for Neutron Monochromatization”, Physica B, 350, e663-e666 (2004). Vrána, M., Lukáš, P., Mikula, P. and Kulda, J., ”Bragg Diffraction Optics in High Resolution Strain Measurements,” Nucl. Instrum. Methods in Phys. Research, A 338, 125-131 (1994). Mikula, P., Vrána, M., Lukáš, P., Šaroun, J., Strunz, P., Wagner, V., and Alefeld, B., ”Bragg Optics for Strain/Stress Measurement Techniques”, Physica B 213-214, 845847 (1995). Mikula, P., Vrána, M., Lukáš, P., Šaroun, J., Strunz, P., Ullrich, H.J. and Wagner, V., “Neutron Diffractometer Exploiting Bragg Diffraction Optics - A High Resolution Strain Scanner”, Proc. of the 5th Int. Conf. on Residual Stresses ICRS-5, June 1618, 1997, Linköping, Sweden, editted by T. Ericsson, M. Odén and A. Andersson, Vol. 2, p. 721-725. Lukáš, P., KouĜil, Z., Strunz, P., Mikula, P., Vrána, M. and Wagner, V., ”Microstrain Characterization of Metals Using High-Resolution Neutron Diffraction”, Physica B, 234-236, 956-958 (1997). Wagner, V., KouĜil, Z., Lukáš, P. Mikula, P., and Vrána, M., ”Residual Strain/Stress Analysis by Means of Energy Dispersive Neutron Transmission Diffraction”, SPIE 2867, 168-171 (1997). Mikula, P., Wagner, V. and Vrána, M., “Bragg Diffraction Optics for EnergyDispersive Neutron-Transmission Diffraction”, Physica B, 283, 403-405 (2000). Mikula, P., Wagner, V., Vrána, M. and Lukáš, P., “Residual Strain/Stress Analysis by Means of Energy-Dispersive Neutron Transmission Diffraction”, Proc. of 6th Int. IOM Communications, Vol. 1, p. 1124-1128, Strunz, P., Lukáš, P., Mikula, P., Wagner, V., KouĜil, Z. and Vrána, M., “Data Evaluation Procedure for Energy-Dispersive Neutron-Transmission-Diffraction Geometry”, Proc. of the 5th Int. Conference on Residual Stresses ICRS-5, June 16-18, 1997, Linköping, Sweden, editted by T. Ericsson, M. Odén and A. Andersson, Vol. 2, p. 688-693. Mikula, P., Vrána, M., Lukáš, P., Šaroun, J. and Wagner, V., “High-Resolution Neutron Powder Diffractometry on Samples of Small Dimensions”, Materials Science Forum, 228-231, 269-274 (1996). Mikula, P. and Wagner, V., “Strain Scanning Using a Neutron Guide Diffractometer”, Materials Science Forum, 347-349, 113-118 (2000). Renninger, M., “Die verbotenen Reflexe von Diamant, Silicium and Germanium”, Zeitschrift für Kristallographie, 113, 99-103 (1960). Moon, R.M. and Shull, C.G., “The Effects of Simultaneous Reflections on SingleCrystal Neutron Diffraction Intensities”, Acta Cryst. 17, 805-812 (1964). Chang, Shih-Lin, “Multiple Diffraction of X-rays in Crystals”, Springer Verlag, 1984. Mikula, P., Vrána, M. and Wagner, V., “On a Possible Use of Multiple Bragg Reflections for High Resolution Monochromatization of Neutrons”, Physica B, 350, e667-e670 (2004). Šaroun, J., and Kulda J., “RESTRAX – a Program for TAS Resolution Calculation and Scan Profile Simulation”, Physica B, 234-236, 1102-1104 (1997).

EFFECTS OF THE CRYOGENIC WIRE BRUSHING ON THE SURFACE INTEGRITY AND THE FATIGUE LIFE IMPROVEMENTS OF THE AISI 304 STAINLESS STEEL GROUND COMPONENTS

N. Ben Fredj, A. Djemaiel, A. Ben Rhouma, H. Sidhom Laboratoire de Mécanique Matériaux et Procédés, ESSTT, 5, Av. Taha Hussein Tunis, Tunisia C. Braham Laboratoire d’Ingénierie des Matériaux ENSAM, 151 Boulevard de l’Hôpital, 75013 Paris, France

ABSTRACT In this investigation, ground surface integrity and fatigue behavior improvements of the AISI 304 SS resulting from the application of wire brushing at ambient and low temperatures were investigated. It was found that the cold work hardening generated by the cryogenic brushing increases the levels of the compressive residual stresses comparatively to the dry brushing and therefore, results on higher nucleation fatigue lifetime of mechanical components having undergone this treatment. On the other hand the propagation fatigue lifetime of these components was found to be extended by plastic induced martensite formed at the tips of the nucleated fatigue cracks. The realized improvement rates expressed in terms of endurance limits at 2x106 cycles comparatively to the ground state are 47% for the dry brushing conditions and 72% for the cryogenic brushing. Introduction Nowadays, increasing the productivity of machining processes is more and more required in manufacturing. As for the grinding, which remains the mostly used finishing process, working with high removal rates is essential to reduce the cost of ground components. Nevertheless, grinding with high removal rates, suggests the generation of finished surfaces under coarse grinding conditions, particularly, characterized by high feed rates and deep depths of cut. Unfortunately, it has been shown [1,2] that these conditions affect significantly the ground surfaces integrity by inducing thermal microcracks and high level tensile residual stresses and therefore, reduce significantly the in service lifetime of ground components. In order to cure this problem and improve the ground surface quality, several solutions were proposed [3-5]. Among these solutions, fine grinding has been proven to offer the possibility of generating surfaces with limited

77 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 77–86. © 2006 Springer.

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damages. However, this solution is not compatible with the aspired high process productivity. The other solution, proposed to reduce the ground surface damages, is the application of the liquid nitrogen as coolant [6-9]. Results of investigations having tested this cooling technique has shown that the realized improvements regarding of the ground surface integrity remain limited. N. Ben Fredj et al. [9] and A. Ben Rhouma et al. [10] have indicated that substantial improvements of the ground surfaces quality can be realized by the application of wire brushing to these surfaces. It was pointed out that this low cost and easy to implement process increases significantly the endurance limit and the stress cracking corrosion resistance of ground surfaces having undergo this treatment. However, it is thought that the realized improvements can be optimized, particularly, in the case of unstable steels like the AISI 304 SS by carrying brushing at very low temperatures. This can be provided by the application of liquid nitrogen during the brushing operation. This is thought to favor the formation of the plastic induced martensite, which is generated at low temperatures (below 38°C) and high deformation rates [11, 12]. In this study, an experimental setup was developed to elucidate the effects of the cryogenic wire brushing on the fatigue crack nucleation and propagation of the AISI 304 SS ground surfaces. The role of the residual stresses distributions and the plastic induced martensite on the fatigue cracks nucleation and propagation mechanisms of the AISI 304 SS was particularity investigated.

Experimental The material used in this study was AISI 304 SS for which the chemical composition is given in table 1. A notched fatigue-bending specimen with a stress concentration factor of Kt =1.6 was selected (Fig. 1). The main advantage of this geometry is the localized crack initiation at the notch root. The notch was machined into the sample on an NC milling machine using an endmill having a diameter of 8 mm. Specimens were subsequently subjected to a stress relief annealing treatment (i.e., heating at 1050 °C over the course of 1 h followed by air cooling) before being ground and/or wire brushed. Only the notch was ground using a V-shaped grinding wheel. The grinding conditions are summarized in Table 2. The experimental setup used for the wire-brushing experiments is shown in schematic form in Fig. 2. An SS wire brush was used for the experiments. This brush was set on a conventional milling machine. During the wire-brushing process, the wires were effectively compressed by 3% of their length (i.e., the surface of the notch was set at 2.4 mm from the inner end of the wires). The experimental conditions under which the brushing tests were conducted are listed in Table 3. Fatigue tests were conducted using an MTS 50 testing machine under a frequency of 15Hz and a loading ratio of 0.1. The stare case method was used to evaluate the fatigue limit at 2x106 cycles.

Figure 1. Geometry of fatigue test specimen (Kt=1.6, all dimensions are in mm)

Effects of the Cryogenic Wire Brushing

Table 2. Grinding conditions Grinding mode Grinding wheel Stock removal rate Wheel speed Work speed Depth of cut Environment Workpiece material Dresser Dressing depth Cross feed Environment

Plunge surface grinding, down cut 99 A 46 M 7 V 10 N with V shape 3 Z’=30mm /mm.min Vs =30m/s vw= 5 m/min a= 6—m Soluble oil (20%), 7.2 l/min AISI 304 Stainless Steel Single point diamond dresser 0.01 mm 0.2 mm/rev Dry

Figure 2. Schematic view of the wire brushing experimental setup and parameters

Table 3. Brushing conditions Wire material Brush diameter Wire diameter Wire length Brush rotational speed Work speed Number of passes Percentage of effective wire compression Environment

Stainless steel D= 230mm I= 0.1mm l= 80mm Vs= 800, 1250, 2000 rpm Vf= 50 mm/min N= 3, 5, 10 passes 3% Dry, Liquid nitrogen

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80

Results Effect of the cryogenic wire brushing condition on the surface quality • Surface roughness Brushing under low temperatures results in a higher resistance of the work material to the plastic deformation. Therefore, the material removal by the successive passes of the brush wires on the work surface is minimized under these conditions. Consequently, the initially preexisting grinding groves are partially erased by the steel wires and only a slight total roughness differences between the ground (Ra=2.2—m, Rt=16.5—m) and the cryogenic brushed (Ra=1.95—m, Rt=11.5—m) states are noticed. However, brushing under dry condition significantly deforms plastically the brushed surfaces and therefore, generates a completely different finished surface morphology than the ground one. In this case, significant total roughness differences between the ground and the wire brushed surfaces are observed (Ra=1.74—m, Rt=11.03—m). • Superficial hardening Microhardness profiles measured at a cross sectional area of the of the wire brushed surfaces under dry and cryogenic environments put in evidence that brushing induces superficial cold work hardening (depth less 100—m) with a level, which is as important as the brushing temperature is low (figure 3).

350 Cryogenic wire brushing Dry wire brushing

Micro-hardness Hv0.05

300

250

200

150

100 0

50

100

150

200

250

300

350

Depth below the surface —m

Figure 3. Hardening of the near wire brushed surface

ƒ Plastic Induced Martensite The formation of plastic induced martensite D’ is favored by the cold work hardening generated by the cryogenic wire brushing. This can be clearly grasped from the X-ray diffraction picks of austenite J and martensite D’ given by figure 4-a. On the other hand the wire brushing carried out under dry condition induces an increase of the interface temperature between the steel wires and the brushed surface (about 85°C), which is enough high to prevent the formation of the plastic induced matensite. This is well

Effects of the Cryogenic Wire Brushing

81

confirmed by the X-ray diffraction picks given by figure 4-b as no picks corresponding to the D’ phase could be detected.

Figure 4. Phases analysis by X-ray diffraction of the near brushed surface layers

x Residual stress Wire brushing redistributes the tensile residual stresses fields generated by the grinding process and put in compression the upper layers of the brushed surfaces (figure 5). This redistribution is thought to be very beneficial to the fatigue life of mechanical components subjected to cyclic loading. Figure 5 shows that the maximum level of the compressive residual stress generated by the cryogenic brushing (-1200MPa) is almost twice as high as the level reached under dry brushing (-560MPa). Fatigue behavior of cryogenic wire brushed surfaces Superficial cold work hardening associated to the compressive residual stress fields generated under cryogenic wire brushing, improves substantially the resistance of ground components to fatigue crack nucleation and propagation (figure 6). Moreover, the formed plastic induced martensite by cryogenic wire brushing, is found to contribute

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significantly at increasing the levels of the compressive residual stresses and therefore, delays the fatigue cracks nucleation. On the other hand, the plastic induced martensite D’ at the brushed surface upper layers is thought to control the fatigue cracks that initiate at D’/J interfaces (figure 7). These short cracks contributes to the formation of a diffused fracture network. This network delays the formation of cracks with critical sizes that can propagate and conduct to the fracture of the fatigue tested specimen (figure 8 ). Moreover, the formed plastic induced martensite by the cyclic loading at the tips of the nucleated fatigue crack, contributes to slow down the crack propagation speed and to stop it in some cases (figure 9). Figure 10 shows that the main fatigue crack is formed by short cracks coalescence and by obstacle bypassing of the martensitic D’ plaques.

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Figure 9. Blocking of the fatigue crack propagation by the plastic induced martensite formed by the high deformation rates at the tips of the fatigue crack nucleated at slip bands (electro-polished specimens)

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Figure 2. Coalesence of short fatigue cracks Conclusions Substantial improvement of the fatigue life of the AISI 304 SS ground surfaces could be realized by the application of cryogenic wire brushing (72%). This improvement is thought to be, mainly, the consequence of the high level of the compressive residual stresses induced by both clod work hardening at low temperature and volume change associated to the formation of the plastic induced martensite. These stresses delay the surface fatigue cracks nucleation. On the other hand, the application of the cryogenic cooling during wire brushing of the AISI 304 SS surfaces was found to be very beneficial as short and small fatigue cracks are formed in this case. On the other hand, the formed plastic induced martensite at the tips of the fatigue cracks was observed to block the propagation of the cracks. Thus, the propagation fatigue life can be increased by the cryogenic wire brushing.

References 1. 2. 3.

4.

5.

Malkin, S., (1989), Grinding Technology Theory and Application of Machining with Abrasives, Ellis Horwood Limited, pp. 111-12. R. Snoeys, M. Maris and J. Peters, Thermally Induced Damages in Grinding, Ann. CIRP 27 (Vol.2), (1978) pp 571-576. K. V. Kumar, R.R. Matarrese, E. Ratterman, Control of Residual Stress in th Production Grinding with CBN, SEA Technical Paper Series n°890979, 40 Annual Earthmoving Industry Conference Peoria, Illinois, April 11-13, 1989. N. Ben Fredj, Y. Ichida, K. Kishi, X. Lei, Wear Mechanism of CBN Wheels in Creep Feed Grinding, Proceedings of the first China-Japan International Conference on Progress of Cutting and Grinding, Beijin, (1992), pp. 227-32. E.R. de lois, A. Walley, M.T. Milan and G. Hammersley, Fatigue Crack Initiation and Propagation on Shot-Peened Surfaces in A316 Stainless Steel, International Journal of Fatigue, 17 (995), pp. 493-99.

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6. S. Paul, A.B. Chattopadhyay, (1996), The Effect of the Cryogenic Cooling on Grinding Forces, Int. J. Mach. Tools Manufact. Vol 36, 1, pp. 63- 72. 7. S. Paul, P.P. Bandyopadhyay, A.B. Chattopadhyay, (1993), Effects of Cryo-Cooling in Grinding Steels, Journal of Material Processing Technology, Vol 37, pp. 791-800. 8. S. Paul, A.B. Chattopadhyay, (1995) Effects of Cryogenic Cooling by liquid Nitrogen Jet on Forces, Temperature and Surface Residual Stresses in Grinding Steels, Cryogenics, Vol 35, 8, pp. 515-523. 9. Nabil Ben Fredj, Habib Sidhom, Chedly Braham, Ground surface improvement of the austenitic stainless steel AISI 304 using cryogenic cooling, Surface and Coatings Technology, in press. 10. A. Ben Rhouma, C. Braham, M.E. Fitzpatrick, J. Lédion, H. Sidhom, (2001), Effects of Surface Preparation on Pitting Resistance, Residual Stress, and Stress Corrosion Cracking in Austenitic Stainless Steel, Journal of Materials Engineering and Performances, Vol. 10(5,) pp. 507-514. 11. Z. Tourki, H. Bargui and H. Sidhom, The kinetic of induced martensitic formation and its effect on forming limit curves in the AISI 304 stainless steel, Journal of Materials Processing Technology, Volume 166, Issue 3, 20 August 2005, pp. 330-336 12. Jacques Stolarz, Natacha Baffie, Thierry Magnin, Fatigue short crack behavior in metastable autenitic stainless Steels with different grain sizes, Materials science and engineering, (2001) A319-321, pp. 521-526.

SURFACE INTEGRITY IN HIGH SPEED MACHINING OF Ti-6wt.%Al-4wt.%V ALLOY J.D. Puerta Velásquez1,2,*, B. Bolle1,2, P. Chevrier2,3 , and A. Tidu1,2 1 Laboratoire d’Etude des Textures et Applications aux Matériaux (LETAM), F-57045 Metz, France 2 Ecole Nationale D’Ingénieurs de Metz (ENIM), F-57045 Metz , France 3 Laboratoire de Physique et Mécanique des Matériaux (LPMM), F-57012 Metz, France *

Corresponding author: J.D. Puerta Velásquez, email: [email protected]

ABSTRACT Surface integrity of commercial Ti-6wt.%Al-4wt.%V alloy after high speed machining has been investigated. Scanning electron microscopy reveals highly deformed grains in the obtained surface, turned in the direction of the cutting tool passage. X-ray diffraction confirms the intense deformation of the machined surface and shows a crystallographic texture modification. The metallurgical observations do not reveal any phase transformation and no evidence of formation of a white layer has been noticed. A preliminary study of the residual stress reveals a strong influence of machining parameters on the residual stress in obtained surface. Introduction Titanium alloys are very interesting materials for industrial applications because of their elevated mechanical resistance having a low density and their excellent corrosion resistance, even at high temperatures. Despite these features, utilisation of titanium alloys is still limited because of their poor machinability, intimately bound to their thermal and chemical properties [1]. In fact, low thermal conductivity of titanium hinds the evacuation of heat generated during cutting process, leading to temperature rise of the workpiece. Furthermore, the high chemical reactivity of titanium, which increases with high temperature, produces an early damage of the cutting tools, affecting the final quality of the obtained surface as well as increases in production costs.

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High speed machining is widely appreciated in industry for its high quality and surface finishing in the obtained parts. Nevertheless, erroneous selection of cutting parameters can generate poor surface finishing. Surface integrity can be defined as a measure of the quality of a machined workpiece and it includes roughness, crystallographic texture, residual stress and metallurgy of the obtained surface [2]. The presence of residual stresses and residual stress gradients in surface of parts under fatigue conditions are recognised as important factor affecting their life. Generally it is accepted that the presence of compressive residual stresses in surface is beneficial for work-piece lifetime and the residual tensile stresses can lead to crack propagation and final failure of the work-piece. The aim of this work is to study the surface integrity in high speed machining of Ti-6wt.%Al-4wt.%V alloy. Experimental High speed machining tests were performed on a Ti-6wt.%Al-4wt.%V titanium alloy (typical chemical composition given in Table 1). High speed milling test been performed with a five continuous axis milling machine Huron (Gambin 120 CR) equipped with an electro-spindle developed by S2M Company. All tests were performed using an external microlubrication. A solid carbide coated tool has been used (solid carbide tool Leclerc 2, ref. K6310-10, coating TiAlN, 2 teeth, diameter 10 mm, helix angle 25°, rake angle 4°, clearance angle 10°, overall length 66 mm, shrink fitted length 32 mm, tool holder HSK 50 modified) machining parameters are given in Table 2. Table 1. Typical chemical composition of Ti-6wt.%Al-4wt.%V alloy (ASTM grade 5 titanium). Element % wt

Ti

Al

Base 5.5 – 6.75

V

Fe

O

3.5 – 4.5

<0.25

<0.2

Table 2. Machining parameters of the cutting test. Feed rate Vf [mm/min]

Deep of cut ap [mm]

480

0.5

Cutting speed Vc [m/min] 113

3980

637

0.5

150

5573

892

0.5

210

7165

1146

0.5

270

8758

1401

0.5

330

Spindle speed N [tr/min] 3000

C

N

H

<0.08 <0.05 <0.01

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Machined surfaces were characterised by X-ray diffraction (XRD). Measurements were carried out on a texture goniometer equipped with a curved position sensitive detector (CPS120, Inel). The XRD patterns, crystallographic texture and residual stresses were obtained using Cu KD radiation (O = 1.5418 Å) emitted by a rotating anode (Rigaku RU300). An isotropic model, so-called sin2\ method, was used to determine residual stress. Detailed explanation of this method is given in [2]. Obtained surfaces were also analysed by scanning electron microscopy (SEM) using a 6500F JEOL FEG. The samples were cut at 90° from the machined surface to observe cross-sectional plane in order to evaluate the possible microstructural modifications beneath the obtained surface. Results and discussion As-received material The as-received material is a two-phase (DE)titanium alloy, composed of equiaxed Ti Į grains (hcp) surrounded by Ti ȕ grains (fcc) (Fig. 1). An XRD is shown in Figure 2. Using XRD quantitative phase analysis, the starting material is composed of 8% of titanium E phase.

Figure 1. Microstructure of the as-received material (dark grains corresponds to Ti D and light grains to Ti E phase).

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Intensity (A.U.)

00.2

Ti D Ti E

10.1

110

10.0

10.3

10.2

30

35

40

45

50

55

2T (°)

11.2

11.0

200

60

65

211 20.0

70

75

20.1

80

Figure 2. XRD pattern of the as-received material. Ti D and Ti E phase and (hkl) planes are indicated. Microstructural modifications The microstructure of the material beneath the machined surface was observed by SEM. Obtained images reveal a high deformation of the grains at the machined surface. Following the Ti E grains from the machined surface to the bulk material it is possible to see a strong deformation gradient in a depth of few microns: at the free surface the grains are dragged and turned in the direction of the cutting tool passage. The deformation rapidly a decrease in the first line of grains (those that were in contact with the cutting tool) until the next line that seems undeformed.

Machining direction Figure 3. Cross-section of a machined surface obtained at Vc = 330 m.min-1 (free surface is in the bottom of the picture).

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Previous studies shows that during machining titanium alloys an overheated layer of hardened material can be produced on the top of the surface [1,2] (generally called white layer). Produced white layer can be softer or harder than the base materials [1,2]. In present study no evidence white layer was observed in the machined surface, whatever the cutting speed was, contrary to it has been reported in literature for similar material al machining conditions. XRD examination Samples were also evaluated by XRD. The analysis of XRD patterns leads to determinate the effect of cutting tool passage in the obtained surface. Figure 4 presents the XRD pattern of the machined surface obtained at the higher and the lower cutting speed, as well as the one of the as-received material. The examination of the peak shape shows a general broadening from all peaks in the patterns of the machined surface. This broadening increases with the higher cutting speeds. Generally the broadening of the peaks in the XRD patterns has been associated to high lattice deformation of the crystallites involved during X-ray measurements. In present study the broadening of the peaks and can be understood as a consequence of the high plastic deformation produced by cutting process on the machined surface. If we consider the intensity of the peaks, it is possible to see a modification of the intensity ratios between the more intense peaks of the Ti D phase (peaks (00.2) and (10.1)) that appears from a cutting speed of 210 m.min-1. The modification of the intensities of the different peaks is a consequence of a modification of the crystallographic texture in the studied material. The influence of the cutting speed on the crystallographic texture of the machined surfaces will be presented in the next section.

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Ti E

Intensity (A.U.)

10.1

00.2

Ti D

As received material

30

35

40

Vc = 113 m.min

-1

Vc = 330 m.min

-1

45

50

55

2T (°)

60

65

70

75

80

Figure 4. XRD patterns of as-received material and machined surfaces at different cutting speeds. Theoretical XRD patterns of Ti D and Ti E phases are given on the top of the figure. Phase identification performed for all XRD patterns shows the presence of Ti D and Ti E phases. The presence of only the same phases observed in the asreceived material leads confirms the electronic microscope observations, which do not reveals the formation of any white layer on the machined surface. The presence of a white layer has been related to the machining process performed during longs periods, under dry machining conditions or machining carried out in abusive manner [2,4]. It leads to important rises of the temperature at the machined surface during the contact with the cutting tool, followed by a rapid cooling after the tool passage. During abusive machining the heating and cooling rates can that be similar to those of the quenching conditions, and local phase transformations can take place and white layers can be generated [5]. The absence of white layers in obtained machined surfaces seems to indicate that the thermal conditions during present test were softer than those reported in previous works. Crystallographic texture modifications Crystallographic texture was evaluated by XRD. Figure 5 presents the pole figures of crystallographic planes (10.0), (00.2) and (10.1) of the Ti D phase for the as-received material and the machined surfaces at two different cutting

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speeds. The measured pole figures reveals that after the cutting tool passage a strong texture is produced in the machined surface. Obtained texture is composed by a majority basal orientation ((00.2) planes perpendicular to the surface). A secondary orientation component is observed and reflects a rotation of the crystallites in the direction of the cutting tool passage, leading to obtain a second (00.2) pole turned from the basal majority component. The turning angle of the new component increases with the increase of the cutting speed. (10.0)

(00.2)

(10.1)

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MD 1.9

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MD

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Figure 5. Crystallographic texture of as-received material and the machined surface for different cutting speed (MD: machining direction). Residual Stress Previous work on a low alloyed steel shows that residual stress evolves rapidly from tensile stress to compressive stress in the first ten microns beneath the machined surface [2]. In present study a preliminary study of residual stress has been carried out in the machined surfaces. Linear correlation between the cutting speed and the residual stress was revealed. Lower cutting speed leads to compressive residual stress. Higher cutting speed causes the residual stress to change from compression to tensile. (Fig. 6).

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0 200

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Figure 6. Residual stress in machined surfaces for different cutting speeds. Conclusions In present work a study of the surface integrity in high speed machining of Ti6Al(wt.%)-4V(wt.%) has been presented. In relation to the results obtained some main conclusions can be defined: 1. High speed machining produces a surface composed by highly deformed grains turned in the direction of the cutting tool passage. 2. No evidence of white layer formation on the obtained surface has been observed. 3. A strong crystallographic texture in generated by high speed machining with a majority basal orientation. 4. A linear relation between residual stress and cutting speed was observed. Compressive residual stress was observed for the lower cutting speed. Increasing the cutting speed leads to an increase in the residual stress and changes the compressive to tensile residual stress. Acknowledgements Authors are grateful with Région Lorraine in France that supports this research program. References 1. Ezugwu, E.O. and Wang, Z.M., “Titanium alloys and their machinability – a review”, J. Mater. Process Tech., 68, 262-274 (1997).

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2. Chevrier, P., Tidu, A., Bolle, B., Cezard, P. and Tinnes, J.P., “ Investigation of surface integrity in high speed end milling of a low alloyed steel” Int. J. Mach. Tools & Manu., 43, 1135-1142, (2003). 3. Che-Haron, C.H. “Tool life and surface integrity in turning titanium alloy “, J. Mater. Process Tech., 118, 231-237 (2001). 4. Che-Haron, C. H., Jawaid A. “The effect of machining on surface integrity of titanium alloy Ti-6%Al-4%V”, J. Mater. Process Tech., 166 (issue 2), 188192, (2004). 5. Reissig L., Völkl R., Mills M.J., Glatzel U. “Investigation of near surface structure in order to determinate process-temperatures during different machining processes of Ti6Al4V”, Scripta Materialia 50 (issue 1) 121-126 (2004).

The present and the new HFR-Petten SANS facility O. Ucaa,b, C. Ohmsa, and A.G. Youtsosa, High Flux Reactor Unit, Institute for Energy, EC-JRC, PO2, 1755 ZG Petten, NL b [email protected]

a

ABSTRACT A great deal of the properties of materials is influenced by phenomena taking place in the sub-micron region. Scattering techniques play an important role for obtaining structural information. Small-Angle Neutron-Scattering (SANS) is one such scattering technique by which one can obtain structural information of the material being studied. Structural information here means size and form of the object under investigation. In a SANS experiment one collects data as a function of the momentum transfer which is proportional to the scattering angle. The probed length scales by SANS varies from a few nanometres to 600 nanometres. In this paper we present the present status of the SANS facility with a preliminary measurement on core-shell particles. Furthermore, we look at the future perspectives of upgrading the facility to enhance the neutron flux at the sample position

Introduction The Small-Angle Neutron-Scattering facility at the 45 MW High-Flux Reactor in Petten, the Netherlands, is constructed in the late eighties. It is a medium size SANS instrument -3 -1 -1 covering a Q range of 5x10 Å to 0.4 Å . The instrument has been constructed with a double crystal monochromator consisting of six pairs of Pyrolytic Graphite crystals giving a monochromatic beam of 4.75 Å. The present SANS machine uses the HB3 radial 4 2 beam tube. The flux at the sample position is for the current case ~10 n/cm /s. The instrument has a length of 10 meters. The two dimensional position sensitive detector can be moved from 90 to 425 cm, Alf and Zurita [1] and Vlak et al. [2]. After the construction of the facility the scientific activities were stopped due to several nonscientific reasons. In recent years there has been effort to make the facility become operational.

Experimental In Figure 1, the present SANS setup is shown. Part of the neutrons from the reactor enters the beam tube of length Lb, diameter db and divergency Įb. After the beam tube

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the neutrons enter the in-pile collimator of length Lii, diameter, di and divergency Įii that is defined as di/Lii. Thus neutron beams having an angle between -Įii/2 and Įii/2 radians are

2-D detector Sample col. (Ls, Ds) (Lm, Dm)

Beam shutter

Double monochromator

In-pile col.

Beam tube

Lii

(Lb, Db) Reactor core

Lb (Li, Di)

Figure 1 The present SANS setup. passed to the next section. Next to the in-pile collimator we have the beam shutter of length Lb. From this point on the white neutron beam enters the double monochromator where it is monochromatized. The transmission part of the monochromator is characterized by the pair (Lm, Įm). After the monochromator the beam passes through the sample collimator of length Ls , diameter ds and divergency Įs. Finally, it impinges on the sample. In Figure 2 one can see the SANS spectrum obtained from scattering from core-shell particles. The particles are solved in h12-cyclohexane with a volume fraction of 2% and the core consists of SiO2. These systems are well characterized with other techniques. The core has a Guinier radius of 70±8 Å [3]. The number of recorded neutrons per unit time scattered into a detector pixel, I(Q), is described by

I (Q )

I 0 :K T Vs

w6 (Q ) w:

(1)

where I0 is the incident flux, :the solid angle subtended by a pixel,K the detector efficiency T the transmission of the sample, Vs the volume of the sample which is -1 illuminated by the beam and ˜6˜:(Q) is the differential cross-section in cm [4]. For small Q, ˜6˜:(Q) can be described by the well known Guinier approximation [4]:

w6 (Q) w:

 ( QRg ) 2 2

2

N V 'U e

3

(2)

The Present and the New HFR-Petten SANS Facility

99

30

I (a.u.)

25 20 15 10 5 0.01

0.02

0.03

0.04

0.05

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Q (Å )

Figure 2 Sans spectrum from SiO2 solved in h12-cyclohexane. The volume fraction of the particles is 2 %.

where N is the number concentration of the particles, V the volume of the particles,

'Uthe scattering length density and Rg the radius of gyration. By substituting Eq.(2) in Eq.(1) and taking the logarithm one can write:

log( I (Q))

c

R g2

3

(3)

Q

2

where c contains all the other variables other than Q and Rg. Therefore, it is not necessary to bring the scattering curve on an absolute scale in order to determine the radius of gyration. Absolute calibration changes the intercept with the y-axis, which is useful for deriving other information, but not needed for determining Rg. In Figure 3, log(I(Q)) is plotted vs. Q2. A linear fit is made for the initial part of the curve which gives a slope of -1077.3 and hence from Eq.(3), a radius of gyration of 57 Å. The actual value varies as indicated above between 62 and 78 Å. So the measured value is certainly not far away. The reason for the deviation can be attributed to aging effects, since the sample is very old.

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3.4 3.2 log(I) (a.u)

3 2.8 2.6 2.4 2.2 2 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

Q2 (Å-2) 2 Figure 3 Log(I(Q)) versus Q . The slope of the linear fit is –1077.3 giving a radius of gyration of 57 Å.

The sample-detector distance and the wavelength of the neutrons in the experiment was 300 cm, 4.75 Å respectively. Upgrading the SANS facility In this section we will discuss the possibility of increasing the flux at the sample position of the SANS facility. The main components/characteristics of the instrument are: 1. The initial flux, which is extracted from the reactor pool. 2. The moderator. 3. The in-pile collimator 4. The neutron guide 5. Monochromatization of the beam 6. Sample collimator 7. Sample station 8. Flight tube 9. The two-dimensional position sensitive detector. For the purpose of upgrading only points 1, 2, 4 and 5 are important. It is evident that a higher initial flux is favorable. The flux at the entrance of the HB10 radial beam tube is two times higher than the HB3 radial beam tube, which is the present tube for the facility. So moving the facility to the new beam tube will double the flux. At the moment, the instrument uses neutrons of 4.75 Å at room temperature. The neutrons from the reactor follow a Maxwell-Boltzamn distribution. Therefore it is favorable to use a cold source for increasing the flux. The monochromatization of a white beam can be done by several methods. These are: double-crystal monochromator, velocity selector and polycrystalline BeO filter Aswal, [5]. Although, it is used in SANS facilities, the BeO filter is not a good choice because of the asymmetric wavelength distribution around the mean wavelength. The velocity selector

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gives a higher flux compared to the double monochromator. However, with a velocity selector one has the choice to continuously tune the wavelength form 2 Å to 25 Å Rosta [6]. The neutron guide will have a transmission of 1 for neutrons above the cutoff wavelength, Oc and for neutrons whose paths are inclined at angles less than the critical angle Tc to the nominal beam direction. For 4.75 A and 58Ni, Tc=9.64 10-3 rad Crawford [7] and Baruchel et al. [8]. Therefore, the divergency of the in-pile collimator has to match the divergency of the guides.

Conclusions We have presented measurement on well-characterized core-shell particles. The measured radius of gyration is in reasonable accordance with the value determined by other techniques. The intensity scale is in arbitrary units. However, this has no effect for determination of the radius of gyration. In future we plan to do measurements on other well-characterized samples to calibrate the instrument on an absolute scale. Moving the SANS instrument to the HB10 radial beam tube and installing a neutron guide and a cold source while replacing the double monochromator with a velocity selector, offers possibilities to enhance the neutron flux at the sample position.

References 1. Ahlf, J. and Zurita, A. (editors), High Flux reactor (HFR) Petten- characterization of the installation and the irradiation facilities, Report No. EUR 15151 EN, 1992 2. Vlak, W.A.H.M., Dijk C. , Slagter, S., The ECN Small- Angle Neutron Scattering facility, Report No. ECN-PB-89-3 3. Versetelle, T., Vlak, W.A.H.M., Vrij, A., Small-Angle Neutron Scattering from colloidal dispersions, Report No. ECN-I-90-044 4. King, S.M., Small-Angle Neutron Scattering, chapter 7, in Modern Techniques for Polymer Characterization edited by Pethrick, R.A. and Dawkins, J.V., 1999, John Wiley & Sons Ltd 5. Aswal, V. K.,, Journal of Applied Crystallography 33, 118-125, 2000 6. Rosta L., Physica B 174, 562-565, 1991 7. Crawford, R. K. and Carpenter, J.M ., J. Appl. Cryst,. 2, 589-601,1988 8. Baruchel. J. et al. (editors), Neutron and synchrotron radiation for condensed matter studies, HERCULES, volume 1, p. 125-126

Session: Residual Stress Analysis by Modelling Techniques – II

Sensitivity of Predicted Residual Stresses To Modelling Assumptions S. K. Bate1, R. Charles1, D. Everett2, D. O’Gara1, A. Warren1, and S. Yellowlees1 1 Serco Assurance, 2Rolls-Royce 1 Walton House, 404 The Quadrant, Birchwood Park, Warrington, Cheshire, WA3 6AT [email protected]

ABSTRACT The use of numerical techniques to simulate the welding process is not new and the increase in computing power has seen the size and complexity of the models increase. Such features mean that in some cases simplifications and assumptions have to be made to approximate residual stresses. A programme of work is now underway to develop a procedure for residual stress prediction which will account for how the various simplifications and assumptions affect the magnitude of predicted stresses, and to identify the limitations of the various modelling techniques. This paper describes how variations of the heat source representation and the material cyclic hardening behaviour affect the predicted residual stresses in an austenitic single weld bead-on-plate specimen. Introduction The treatment of residual stresses in welded components is considered in defect assessment procedures such as R6 [1], BS7910 [2] and API579 [3]. R6, for example, considers three approaches for determining the as-welded residual stress distribution. The first approach, Level 1, is a simple estimate of stresses which enable an initial conservative assessment of a defect to be made. The second approach, Level 2, uses published compendia that characterises bounding profiles for different types of weldments. The third approach, Level 3, entails the use of analysis coupled with experimental measurements to define the detailed spatial distribution of residual stress. The assessor should first try to apply Levels 1 and 2; however these may lead to insufficient margins in the assessment. There may also be cases where a more comprehensive understanding of the residual stress field is required and the Level 3 approach has to be used. The use of analytical, mainly finite element, and experimental approaches to characterise weld residual stresses is fairly widespread but the limitations to these

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methods are not fully known and they need to be recognised. However, when the two approaches are combined, and the results corroborate each other sufficiently well, the resulting residual stress distribution can be confidently used for assessment. The use of numerical techniques to simulate the welding process is not new and the increase in computing power has seen the size and complexity of the models increase. Such features mean that in some cases simplifications and assumptions have to be made to approximate residual stresses. Thus there is an uncertainty in the accuracy of these methods which tends to suggest that conservative approximations, i.e. upper bound residual stress profiles, have still to be relied upon in many cases when carrying out structural integrity assessments. A programme of work is now underway to develop a procedure for residual stress prediction which will account for how the various simplifications and assumptions affect the magnitude of predicted stresses, and to identify the limitations of the various modelling techniques. This will include heat source representation, material behaviour in terms of high temperature annealing, cyclic hardening or softening, creep, and phase transformations. Supporting experimental data are required in order to validate the predictions and a series of mock-ups will be manufactured to enable measurements to be carried out. Use will also be made of benchmarks which are the subject of round-robin exercises which combine analytical predictions with various measurement techniques. Initial work has considered an austenitic single weld bead-on-plate specimen; see Figure 1 below, which is one of the benchmarks being studied within the NET European network. This paper describes the analytical work that has been carried out to investigate how various assumptions on modelling the bead on plate specimen affect the predicted residual stresses. In each of the cases considered, a 3-dimenensional finite element representation of the plate has been used for the analysis. The cases presented in this paper are: (a) Varying the geometric parameters defining the Goldak [4] heat source model. (b) Varying the weld efficiency. (c) The effect of different material hardening models and annealing. Bead on Plate Specimen Four bead-on-plate specimens were manufactured for the NET Task Group 1 by Mitsui Babcock in July 2003. The specimens were nominally identical, but it was recommended that only one be analysed (Specimen A11). A schematic representation of the plate, nominally 17mm thick, is shown in Figure 1.

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A longitudinal macrograph of the bead-on-plate specimen is shown in Figure 3. It can be seen from this figure that the weld bead size is not uniform along the length, particularly at the end where the weld was started. This may be explained by a one second dwell (approx.) between striking the arc and beginning the traverse. It was noted that the size of the fusion boundary could be variable, even with an automated weld process. There were also some concerns that the test bead sizes were larger than the actual specimen bead sizes: it was the test bead macrographs that were used in the assessments.

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Figure 3 Longitudinal Cross Sectional Macrograph of Bead-on-Plate Specimen Temperature dependant material properties for both the plate and weld bead (both thermal and mechanical) up to high temperatures (1400oC) were supplied in the NET benchmark protocol [5] as were the basic welding parameters. The following parameters were provided: Heat Input = 633 J/mm Weld Speed = 2.27 mm/s An initial efficiency of 80% was assumed. Temperatures at nine locations on the plate were monitored during the welding process and these data were made available for comparison. Sensitivity to Heat Source Representation The heat source representation was defined using the SYSWELD [6] heat source fitting tool (HSF). A volumetric heat source defined by a double ellipsoid is advised to simulate welding processes with material deposition (consistent with recommendations of Goldak [4]. The double ellipsoid model uses the following equation to define the power density (q) inside the front and rear regions of the heat source, where 1 and 2 denotes these regions respectively:

q1,2 x,y,z,t

6 3 f 1,2 Q abc1,2 ʌ ʌ

3 x 2

e

a

2

3 z  v  IJ t 2

3 y 2

e

b

2

e

c12, 2

(1) where, a, b and c describe the dimensions of the heat source, Q is the power input from the welding source, v is the welding velocity, t is the time, t is a lag factor defining the position of the heat source at t=0 and f defines the fraction of the heat deposited in either

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region, where f1 + f2 = 2. Figure 4 shows the configuration of the double ellipsoid heat source.

Figure 4 Diagrammatic representation of the double ellipsoid heat source model as defined by Goldak [5] (The heat source moves in the positive z direction) The parameters defining the Goldak heat source are based upon a steady state heat transfer analysis and comparing the predicted weld molten zone with a macrograph of the actual weld, see Figure 6 and temperatures with thermocouple measurements. These calculations can be readily performed using the HSF provided that this information is available.

Figure 5 Comparison of macrograph with predicted fusion zone

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An initial, base case was determined by using the welding parameters provided and then adjusting the Goldak geometric parameters until a good match was achieved with the macrograph and thermocouple measurements provided. Sensitivity analyses were then carried out to examine the affect of the different geometric parameters in the Goldak model on the size of the predicted fusion zone. The heat input was the same for all these cases. The temperatures at three locations (which matched thermocouple positions); two on the top surface 7.5mm and 11.5mm from the weld centre-line and one at the centre on the bottom surface of the plate, were compared. These showed that the geometric parameters affected the size of the predicted fusion zone. However the differences in the temperatures at the three locations were relatively small. The parameters, ‘c1’, ‘c2’ and ‘a’, see Figure 4 have little effect on the predicted temperatures at the thermocouple positions. However, increasing the parameter ‘b’ affected the temperatures local to the weld. The two cases which produced the smallest and largest fusion zone were then selected to examine the effect of the molten zone size on the predicted residual stress. The predicted stresses were compared to the case where the predicted fusion zone was wellmatched to the macrograph, see Figure 5. The predictions showed that most variation in stress occurred local to the weld which may be important in the prediction of crack initiation or the fracture assessment of small defects. Sensitivity to Weld Efficiency Two cases examined the effect of the assumed weld efficiency on the predicted fusion zone and temperatures in the plate. The geometric parameters were kept consistent with that obtained for the well-matched macrograph. Increasing (to 95%) and decreasing (to 65%) the weld efficiency, hence changing the power, increased and decreased the size of the predicted fusion zone respectively. Similarly the temperatures at the three monitored locations increased and decreased with respect to the base case. A third case was examined whereby the power and hence heat input was reduced. The geometric parameters were then adjusted until the predicted fusion zone determined using the HSF tool matched the macrograph. The resulting residual stresses were compared with those for the base case. Figure 6 shows the through-wall variation of stresses at the intersection of lines A and D (i.e. weld start position) shown in Figure 1. It can be seen that stresses under predict those of the base line case even though the predicted fusion zone agreed with the macrograph.

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TWA 600 500

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Figure 6 Comparison of predicted stresses: through-wall variation on the weld centreline at the intersection of line D with Line A Sensitivity to Material Hardening Models The stress analyses carried out in the above sensitivity studies were based on the Isotropic hardening model. The analysis of the base case was repeated but using the Kinematic hardening model. The Kinematic hardening model in SYSWELD requires the use of a bilinear representation of the material hardening curve, and therefore some interpretation of how to fit this to the actual material properties curves was required. It was also found that the Kinematic hardening model in SYSWELD was slightly unstable and would not run with some combinations of properties. In particular, the use of elasticperfectly plastic materials properties caused problems and therefore generally a small hardening value needed to be introduced to counteract this. Figure 7 shows the Isotropic and Kinematic representation used for the parent material over the temperature range of interest. The predicted stresses using these two representations are shown in Figure 8, and it can be seen that they are much lower when a Kinematic hardening model is used. Further sensitivity analyses were carried out using the finite element code ABAQUS [7]. These analyses studied various combinations for representing the Isotropic and Kinematic hardening models and also included a representation using the combined Isotropic/Kinematic hardening model available in ABAQUS. The representations used for the parent material are shown in Figure 9.

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Figure 7 SYSWELD Analyses - Parent Material D2 700 Isotropic Longitudinal Kinematic Longitudinal Isotropic Transverse

600

Kinematic Transverse Isotropic Thru Wall Kinematic Thru Wall

500

Stress (MPa)

400

300

200

100

0 -60

-40

-20

0

20

40

60

80

100

120

-100

-200 Distance (mm)

Figure 8 Comparison of the Predicted Stresses using Isotropic and Kinematic Hardening SYSWELD Analysis

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800 700 600

stress /MPa

500 400 tabular data (ISO1) simple bilinear (KIN1) SYSWELD properties (KIN2) upper bound (KIN3) best fit bilinear (KIN4, ISO2) elastic-perfectly plastic (KIN5,ISO3) combined hardening by parameters (COM1)

300 200 100 0 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

plastic strain

o Figure 9 Comparisons of Stress-Strain Relations (Parent Material at 20 C)

ABAQUS Analyses The stresses within the weld bead were compared along a path running parallel with the top surface of the plate. Figure 10 shows the transverse stresses for each of the cases considered. 700 ISO1

ISO2

ISO3

KIN1

KIN2

KIN3

KIN4

KIN5

400

COM1

COM2

300

COM3

600

S11 /MPa

500

200 100 0 0

10

20

30

40

50

60

70

-100 -200 -300 distance /mm

Figure 10 Comparison of predicted transverse residual stresses - ABAQUS Analyses These sensitivity analyses showed that: x

The magnitude of the residual stress field is strongly dependent on the material hardening representation used, with Isotropic hardening giving rise to the

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x

x

x

x

largest residual stresses, and Kinematic hardening producing much smaller stresses (more than a factor of 2). Using a combined hardening model gives residual stresses between the two. The use of different bilinear approximations to represent plasticity influences residual stress levels less strongly than the hardening law these values are used with. Kinematic hardening models with a hardening slope in the stress-strain curve can predict lower residual stresses than elastic-perfectly plastic representations (using either isotropic or Kinematic hardening). For Kinematic hardening, a small change in the material properties at high temperatures (i.e. by adding a nominal hardening slope to improve numerical stability), can give rise to significant variability in the predicted residual stresses. These properties are generally not measured due to difficulties testing materials at high temperatures with such low strength. Annealing resets the plastic strain to zero at the annealing temperature, but does not generally have much effect on the resulting residual stress for this single pass weld.

Conclusions The Goldak model is currently the most commonly used heat source representation. Sensitivity analyses have been carried out to investigate the effect of the Goldak parameters on the prediction of (i) the weld fusion zone, and (ii) temperatures, in an austenitic single-bead-on-plate specimen. x It has been shown that differing weld fusion zones can be obtained for the same power input by changing the Goldak input parameters. This emphasizes the need to have a weld macrograph showing the true size and shape of the weld fusion zone. The temperatures predicted in the plate were largely unaffected by these changes to the Goldak input parameters. x

Changing the weld efficiency, and hence power input, has a greater effect on temperature distribution in the plate than changes to the Goldak input parameters. This also had the greatest effect on the predicted local stresses and plastic strains in the plate.

Sensitivity analyses have been carried out to demonstrate the effect of various material hardening models on the predicted residual stress in the specimen. It was shown that: x The magnitude of the residual stress field is strongly dependent on the material hardening representation used, with isotropic hardening giving rise to the largest residual stresses, and Kinematic hardening producing much smaller stresses (more than a factor of 2). Using a combined hardening model gives residual stresses between the two. x

The use of different bilinear approximations to represent plasticity influences residual stress levels less strongly than the hardening law these values are used with.

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x

Kinematic hardening models with a hardening slope in the stress-strain curve can predict lower residual stresses than elastic-perfectly plastic representations (using either Isotropic or Kinematic hardening).

x

For Kinematic hardening, a small change in the material properties at high temperatures (i.e. by adding a nominal hardening slope to improve numerical stability), can give rise to significant variability in the predicted residual stresses. These properties are generally not measured due to difficulties testing materials at high temperatures with such low strength.

x

Annealing resets the plastic strain to zero at the annealing temperature, but does not generally have much effect on the resulting residual stress for this single pass weld.

Ultimately, the validity of the finite element analysis model can only be achieved by comparing the predicted stresses to those that have been measured. The NET roundrobin benchmark includes a significant amount of measurement using various techniques and these will be reported by the network group at a later date. References R6 - Revision 4, Assessment of the integrity of structures containing defects, British Energy, September 2000. BS7910:1999, Guide on methods for assessing the acceptability of flaws in metallic structures, BSI 10-2000. Fitness-for-Service, API Recommended Practice 579, First Edition, January 2000. Goldak J., Chakravarti, A. and Bibby, M., Metallurgical Transactions, vol. 15B, 229–305, June 1984. British Energy, Protocol for Finite Element Simulations of the NET Single Bead-on-Plate Test Specimen. NET_modelling_protocol-6, June 2004 SYSWELD Version 2004, ESI Group ABAQUS Version 6.4-1, Linear and Non-Linear FE Analysis Package, ABAQUS Inc., USA, 2003.

WELDING EFFECTS ON THIN STIFFENED PANELS

T.T. Chau AREVA (Technicatome), Aix-en-Provence, France Numerical Simulation of Welding Committee (AFM/SNS), Paris, France

ABSTRACT The major problems due to welding effects are the residual stresses and distortions of which the levels affect more or less the resistance and lifetime of welded structure. In steel industry and particularly in shipbuilding, during these last few decades, thin plates are used more and more in ship construction in order to lighten the structure weight. Unfortunately, excessive distortions occurred on these thin stiffened panels and straightening works must be executed in respecting the limit tolerance fixed by the Quality Standard of Ship Construction. These futil works reduce Productivity and Quality, increase Construction Cost and get longer Fabrication Delay. Thus, it is necessary to evaluate, control and minimize the distortion and stress levels of thin welded panels before welding assembly operations. In this paper, a short presentation of the Methodology and its industrial applications in shipbuilding are presented for two panels of a Chemical Parcel Tanker (1996) and a large “Testing” Panel in full scale of a Passsengers Ship (2002). The numerical results due to welding effects so obtained within short computer-time (three hours and half for a 3D FE model of more than two million of degrees of freedom) ) on a linear FEM software were verified with measured stress values and identified with the buckling state of the “Testing” Panel before and after welding operations by photographies. Introduction The excessive distortion of several thin stiffened panels due to welding effects may seriously affect the Fabrication Cost and Delay of a Ship. As an example, early in 1991 in France, it was noted down that for the construction of a passenger-ship, the Shipyard has lost about 90000 skilled man-hours for straightening works and in U.S.A, the Navy estimated an additional cost of US$3.4 million per destroyer, as reported in the Welding Journal published in August 1995. Carried out from RD studies in 1991-1995 [1], the Methodology of numerical simulation of arc welding, based on a metallurgical concept, had been presented successively in 1992 [2], 1999 [3], 2000 [4], 2003 [5,6], 2004 [7], reviewed and updated in 2005 [8]. Two industrial applications of the methodology in shipbuilding are described in this paper using its main basic assumptions for verifying the excessive distortions due to welding effects occurred on thin welded stiffened plate panels. The first application one was in 1996 [9] for two thin stiffened panels of a chemical parcel tanker in Fabrication stage and the second one was in 2002 [10] for a large thin deck panel of a passengers ship for the Performance RD project .

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Short presentation of the Methodology for Numerical Simulation of Arc Welding The Methodology has been developed on a Metallurgical Concept [2-8] issued from two main diagrams of mild steel (usual ordinary iron-carbon steels): metallurgical phase transformation diagram and dilatation diagram. METALLURGICAL PHASE TRANSFORMATION DIAGRAM The typical characteristics of iron-carbon steels are the phases changes (solid-liquidsolid) under high temperatures going with the crystalline transformation (ferriteaustenite). Figure 1 below shows an approximate correspondence of the thermal zones with the peak temperatures of phase changes in a butt welded joint [11]. DILATATION DIAGRAM The behaviour of iron-carbon steel in solid phases (ferrite and austenite) is illustrated in the following dilatation diagram on which we denoted four specific peak temperatures (Tf, Tc, Ta and To) and mentioned three main thermal zones (FZ, HAZ and NHAZ) created during welding process (Figure 2) [12].

where : To Ta Tc Tf

: ambient temperature (°C) : peak temperature at the beginning of phase transformation in heating cycle (°C) : peak temperature at the beginning of melt liquid transformation in heating cycle(°C) : fusion temperature = maximum temperature at melting zone center in heating cycle (°C) OA : non heat affected zone (NHAZ), limited by To and Ta ABC : heat affected zone (HAZ), transition thermal zone limited by Ta and Tc CF : fusion zone (FZ), limited by Tf and Tc METALLURGICAL CONCEPT The Metallurgical Concept, based on two main diagrams of iron-carbon steel, is illustrated in the following Schematic Analysis (Figure 3) [2-8].

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Figure 3 : Schematic analysis of the Metallurgical Concept of Arc Welding process for iron-carbon steels [2-8]

SOLIDIFICATION TIME OF THE MELT METAL IN THE FUSION ZONE At the end of the heating cycle, the cooling cycle starts immediately in all parts of the work-piece after a solidification time of the melt weld pool [11]:

L.Hnet St =  2S k U C (Tmax  To)2 where : = heat of fusion (J / mm3) 3 = 2 J/mm (for steels) Hnet = heat net input (J / mm) = K U.I / V K = welding efficiency U , I = arc voltage (Volt), arc current (Ampere) V = welding speed (mm / s) To = ambient temperature or initial temperature (°C) Tmax = peak temperature at fusion zone centre (°C) St = solidification time (s) UC = volumetric specific heat (J / mm3/°C) = 0.0044 J/mm3.°C (for steels) k = thermal conductivity of the metal (J / mm / s / °C) = 0.028 J/mm/s/°C (for steels) L

(1)

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COOLING RATES The cooling rate (by air cooling) of iron-carbon steel at any given point P mainly depends on the heat net input energy Hnet , the peak temperature Tp at this point, the ambient temperature To and the thickness t of the work-piece. The definition of “thin” or “thick” of the thickness of the work-piece is determined by the following criterion [11] :

W = t [ U C(Tp  To ) e Hnet ]1/2

(2)

Hence, in shipbuilding :

W 0.6 < W W

< 0.6 : o thin plate ( up to 6 mm ) < 0.9 : o medium plate ( 6 to 19 mm ) > 0.9 : o thick plate ( 19 mm and up )

x Jhaveri et al.'s formula for thin plate [11,13] :

R = 2S k UC (Tp  To )3 ( t / Hnet )2

(3)

x Adams Jr.'s formula for thick plate [11,14] :

R = 2S k (Tp  To )2 / Hnet

(4)

x For medium plate : the cooling rate may be obtained by mean of these two extreme values (within 15% max error) [11]. BASIC ASSUMPTIONS ) Base time : The base time to be considered in the methodology is the time at the end of the cooling cycle where the temperatures are stabilized at the ambient temperature and the final deformation of the work-piece does not change anymore. 2) Sizes of thermal zones : The size of three main thermal zones created by heating during welding depend on the peak temperatures (Tf, Tc, Ta and To) and may be determined by the Adams’ formula [11,14] :

(Tmax – Tp)

Hnet

y =  x  (Tmax – To) (Tp – To) (2S e UC t) 1/2

where :

(5)

y

= distance of the given point from the fusion zone centre or from the front of maximum temperatures (mm) Tp = peak temperature at the given point P (°C) e = basis of natural logarithm = 2.718

t

= plate thickness (mm)

Note : The limits of fusion zone (FZ) and of heat affected zone (HAZ) are thus determined by applying the above formula with the values of Tmax = Tf , Tp = Tc (for FZ) and Tp = Ta (for HAZ).

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3) Effective shrinkages in three main thermal zones : At the end of the cooling cycle, the effective shrinkages in three main thermal zones, are resulting as follows:

D (NHAZ) = D (ferrite)  D (ferrite) = 0 D (HAZ) = D (ferrite)  D (austenite) = D (D)  D (J) z 0 D (FZ) = 0  D (austenite) =  D (J) z 0

(6) (7) (8)

4) Shrinkage forces : The shrinkage forces, developed in the weldment, are due in fact to the difference of dilatation and contraction coefficients of the metal inside the thermal zones between two cycles:

Fsh (NHAZ) = S (NHAZ) x E x D (NHAZ) x 'T(NHAZ) Fsh (HAZ) = S (HAZ) x E x D (HAZ) x 'T(HAZ) z 0 Fsh (FZ) = S (FZ) x E x D (FZ) x 'T(FZ) z 0

0

(9) (10) (11)

where : S = section of thermal zone (mm²) 'T = thermal gradient in thermal zone (°C) E = Young’s modulus, supposed unchanged in three thermal zones (N/mm²) For iron-carbon steels, as the contraction coefficient D(austenite) in cooling cycle is stronger than the dilatation coefficient D(ferrite) in heating cycle, the shrinkage forces developed in the weldment are compressive in three directions. So, thanks to these compressive shrinkage forces, metals are strongly assembled together. By the above relation (9), no shrinkage force is developed in the non heat affected zone (NHAZ). 5) Elastic and Plastic domains : In the above Schematic Analysis on Figure 3, the nonheat affected zone (NHAZ) has no change in its physical and mechanical properties during two cycles (heating and cooling). This thermal zone, representing besides a large part of the whole welded assembly, remains in the elastic domain, before and after welding. Therefore, all deformations (strains and stresses) occurring in this zone are assumed to be submitted to the Hooke’s law. In other zones (smaller Fusion and Heat affected zones), the deformations are produced in the plastic domain and so, they are not considered in the analyses of linear elastic FEM calculation results. 6) Mechanism of excessive distortion of a welded plate : The final distortion of the welded assembly is resulting from the difference of deformations in three main thermal zones during two cycles (heating and cooling). So, the excessive distortion of a welded plate is due to the buckling effect reached on the plate when the contraction forces developed in the weldment exceed the effective buckling limit of the plate (i.e of the NHAZ of the welded plate). 7) Effective buckling limit of an elastic plate : That is the effective capacity of its resistance against the buckling compressive force, taking into account all the residual states accumulated onto the plate during all the preparation works such as cutting, rolling, planing, shot-peening (Fig.4) etc. before welding assembly operations [2-8] and it is evaluated by the modified Euler-Bryan’s formula as below :

V *cr

K c .E.

S 2 .E

§t· . ¨ ¸ 12 (1  Q 2 ) © b ¹

2 (12)

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where :

Kc = >teff /t@² Kc = corrector coefficient, estimated to be (0.75 < Kc < 1);

(13)

= 0,75 for “coil” platings (updated value [8] issued from the RD project [10])

teff = effective thickness of the plate (mm) ; E = Bryan’s coefficient, depending upon the ratio (a/b), the boundary conditions and the mode shape of the plate ;

a,b,t = length, width and initial thickness of the plate (mm) ; E = Young’s modulus of material of the plate (N/mm²) ;

Q = Poisson’s ratio. x In shipbuilding, the coil platings of deck and bulkhead stiffened panels are generally assumed to be under one of these two cases of boundary conditions (Fig. 4 and 5):

8) Idealization of welded joint sections and building up 3D finite element models : Two of the most used welded joints for fabrication of stiffened panels are Fillet and Butt welds. For both welded-joint modelings, their sections are simplified and idealized into perfect triangular sections of weld deposit metal (for simple and multi-pass welds). In steel industry and in shipbuilding, welded joints are generally realized on machine by automation, these idealized sections are assumed to be constant along the weld line and 3D FE models are then built up from 2D sections by extrusion along the weld length (Fig. 6 to 11).

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9) Effective peak temperatures distributions on thermal zone limits : In welding process, the cooling cycle starts up soon after the solidification time St of the melt metal in the fusion zone, so that at any point P in the work piece, the temperature Tp drops down to a lower level by the cooling rate effect during this very short time. So, effective temperatures T’p are defined by the relation taking account of the cooling rate Rp at this point P :

T’p = Tp – Rp Tp St

(14)

The effective peak temperatures ( T’f , T’c , T’a ) are then calculated and applied on nodes of the limit lines of three thermal zones along the welded joint of the model by the temperature distribution curves (Figure 12) defined as below :

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Figure 12 : Example of effective peak temperatures distributions on three thermal zone limits of two alternate welded-joints 10) Thermo-elastic analysis : Temperature field is applied to the 3D FE model so being created (with isostatic boundary conditions on some nodes). Thermo-elastic calculation is then performed on a linear FEM software. Stress and strength results are thus analysed only for elastic zones NHAZ of the assembly, which are the large elastic parts of the model without phase changes during two heating and cooling cycles during the welding process. The buckling state of the panel plate is reached when the effective buckling limit of the plate is overpassed by the compressive stresses due to welding effects. The principles of linear stress analysis are illustrated in the following Figure 13 [5-8].

Figure 13 : Principles of linear thermo-elastic stress analysis of thin plates according to the Quality Standard of Ship Construction [21]

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Application of the Methodology on Deck and Bulkhead panels of a Chemical Parcel Tanker

That was a Chemical Parcel Tanker of 36700 dwt (Fig.14) [9], the first one of a series of three tankers to be built by the Shipyard [16]. Main characteristics of the ship are as below : Length overall = 176.70 m ; Depth = 16.20 m ; Service speed = 16.2 knots Breadth = 31.20 m ; Draught = 11.85 m ; Number of tanks = 48 + 6 deck tanks

In Fabrication stage, the superstructure had 6 upper decks to be built up from the main deck F. Arc welding operations have been realized simultaneously on board for assembling of deck H plate panels and of bulkhead plate panels at frame 40 (Fig.15) [9]. x After welding assembly operations, the problem of excessive distortion in wave shapes was stated occurring on thin panels of bulkhead of 5 mm thick, located in the central part (Fig.16) at frame 40. x The straightening works (by flame) were executed on these thin distorted bulkhead panels, and the phenomenon due to welding effects appeared again, but this time, on deck H panels of 7mm thick. x And then, after straightening on panels of deck H, distortion reappeared again just on bulkhead panels (at frame 40) having been already straightened and so on, such as in a vicious circle between action and reaction of thin straightened panels. x After checking up the ship on site, two FE models of deck and bulkhead have been proposed and realized taking account of the geometry data and materials of the panels and the welding parameters of the welding assembly process into the calculation by application of the Methodology for determining the origine of these excessive distortions in order to reduce these defects. Informations about design and welding parameters are presented in tables below, FE models of deck and bulkhead and corresponding numerical results (Figures 16-19).

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MODEL OF DECK PANEL Design parameters

Arc welding parameters

Plate thickness th = 7 mm Plate length a = 3200 mm Plate width b=700 mm + 350 mm Stiffener (HP) = 100 mm x 6 mm ½ T beam = 490 x 7 / 160 x 10

Characteristics of mild steel (E24) Young’s modulus E =210 000MPa Poisson’s ratio Q = 0.3 3 Mass density U = 7.8510 g/mm3 Ferrite dilatation coefficient : 5 D(D) = 1.20 10 /°C Austenite contraction coefficient :

D(J) = 1.65 105 /°C

Stiffeners HP

½ T beam

Chain intermittent alternate Fillet weld

Continuous fillet weld

Heat net input energy : H net = 840J/mm/s v = 5 mm/s Welding speed Weld size (throat) a = 3.5 mm

Heat net input energy : H net = 1 575 J/mm/s Welding speed v = 3.3 mm/s Weld size (throat) a = 4 mm

Specific peak temperatures of mild steel (E24)

FE model of deck panel

Fusion temperature :

Volume elements (6, 8 nodes) :

Tf = 1520 °C Limit fusion zone temperature : Tc = 1020 °C Limit heat-affected zone temperature : Ta = 720 °C Ambient tempearture: To = 20 °

= 35 450 = 54 954 Total of nodes Total of degrees of freedom : = 158 665 Total boundary conditions :

=

6 197

(symmetries and supports)

MODEL OF BULKHEAD PANEL Design parameters

Arc welding parameters Stiffeners HP Chain intermittent alternate Fillet weld

Plate thickness th = 5 mm Plate length a = 2800 mm Plate width b = 600 mm + 350 mm Stiffener (HP) = 100 mm x 7 mm

Heat net input energy : H net = 840 J/mm/s Welding speed v = 5 mm/s Weld size (throat) a = 3.5 mm

½ V Butt Continuous V butt weld Heat net input energy : H net = 3060 J/mm/s Welding speed v = 1.6 mm/s Weld size (root) a = 4.8 mm Weld size ‘angle) = 60°

Welding Effects on Thin Stiffened Panels

Characteristics of mild steel (E24)

Same values for :

Specific peak temperatures of mild steel (E24)

Same values for :

E , Q , U , D(D) , D(J)

Tf , Tc, Ta , To

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FE model of bulkhead panel Volume elements (6, 8 nodes) : = 22 070 Total of nodes = 33 335 Total of degrees of freedom : = 99 332 Total boundary conditions : 673 = (symmetries and supports)

Application of the Methodology on the “Testing” Panel The Performance RD project has been realized (2001-2002) by Principia Marine with the cooperation of the “Chantiers de l”Atlantique” Shipyard [10]. The main objectives of the task 1-4.2 were to identify the fondamental mechanism of excessive distortion of thin welded panels, to verify the solution for reducing Fabrication Cost and Delay and to validate the Methodology. The “testing” panel which was composed of three “coil” platings (Fig.22), has been cut out from a “coil” roll issued from metallurgy. Before welding assembly operations, “coil” platings had to be submitted to the preparation works such as uncoiling, planishing, cutting, shot-peening, machining etc. (Fig.20).

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Figure 20 : Additional stress-strain states occurred from prepation works onto “coil” platings before welding assembly operations in shipbuilding [6-7] Design parameters

Arc welding parameters Stiffeners HP (AS Twin-Arc)

Plate thickness th = 6 mm 2 Plates length a = 17 m 1 Plate length a = 15 m Plate width b= 2m Stiffener (HP) = 120 mm x 6 mm

Characteristics of mild steel (E24)

Same values for :

E , Q , U , D(D) , D(J)

½ V Butt (AS Tandem)

Chain continuous & discontinuous Fillet weld (from plate centre to extremities)

Continuous V Butt weld (one pass one side)

Heat net input energy : H net = 4,7 kJ/cm/s Welding speed v = 4,5 cm/s Weld size (throat) a = 2.5 mm

Heat net input energy : H net = 18 kJ/cm/s Welding speed v = 1.8 cm/s Weld size (angle) = 0° Gap = 1.5 mm

Specific peak temperatures of mild steel (E24)

FE model of deck panel Volume elements (6, 8 nodes) : = 692 900 Total of nodes = 523 684 Total of degrees of freedom : = 2 078 694 Total boundary conditions : = 6 Computer time = 3h30 (SGI Origin 200)

Same values for :

Tf , Tc, Ta , To

MEASUREMENTS Method

: Blind “hole” drilling method

Equipment : Drilling device (MTS3000) Data recorder system (MGC 3 ways) 9 Measurement points/ plate : 3 sensitive gauges (rosette) / point

Equipment : Laser “tachymeter” 3 Measurement lines : Continuous and distant from the first free edge of the panel : d = 16 mm ; 853 mm ; 1753 mm

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NUMERICAL RESULTS

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Conclusions and Perspectives 1) Effective elastic thickness of coil plating : In steel industry and particularly in shipbuilding, all of coil platings for construction have their effective thickness, in elasticity domain, thinner than its initial value : the outer surface layers of plate are plastified by hardening effects during all preration works before welding assembly operations (Fig. 44).

Figure 44 : Schematic analysis showing the evolution of stress-strain states of “coil” plating during fabrication process in shipbuilding [6,7]

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2) Coefficient corrector of the effective buckling limit of coil plating : For coil platings in ship fabrication, the updated value of corrector coefficient obtained by measurements on the “testing” panel in full scale [10] : Kc = 0.75 3) Welding effects on coil platings : The “real” welding effects result the difference of stress-strain states of coil plating before and after welding assembly operations (Fig.44). 4) Initial state of welded plate in numerical simulation of arc welding : The stress-strain states due to welding effects are obtained from numerical simulation of arc welding without initial state ( Vo = 0 ; Ho = 0 ) (Fig.44) 5) Validation of the Methodology : The Methodology has been applied with success for two times (1996 and 2002) on three numerical models in full scales : the buckling and out-of-buckling states of bulkhead and deck plate panels of the Chemical Tanker and the “Testing” Panel were confirmed by numerical results (Figs. 16, 18, 36 and photos 5, 6). 6) Advantages of uses of the Methodology : the Methodology presents following advantages of uses so that it may be applicable to [6-8] :









Linear elastic analysis (linear FEM software) with short computer time (3h30 for 2 million of dof [19] ) Any metallic structures (2D and 3D) Any structure size (small and large) Any plate thickness (thin and thick) Any welding energy (low and high) Any welded joint section (T, fillet, V and double V butt) Any single and multiple pass weld Any welding technique (one-pass-one-side or one-pass-two-sides) Any welding sequence (in sequence or not, in same direction or inverse) Any welded joint (continuous, discontinuous, intermittent, alternate, simultaneous) Any welding speed (low and high) Any welding process (tandem, twin-arc) All steel industries (naval, automobile, railways, nuclear, on-offshore, aerospace).

7) Optimization procedure for thin welded plate panels : In design stage, the Methodology may help Designer Engineer to optimize, within a short time, his welded structure sizes (thickness, length, breadth), weld sizes (fillet, butt) and Constructor Engineer to optimize, without excessive dostortion, his welding process (energy, electric current intensity and tension, welding speed, welding sequence, welded joint types) by means of successive numerical simulations performed on differents 3D finite-element models (Fig.45). 8) Perspectives : The principles of the Methodology may be applicable to other new thermal joining techniques such as Laser and Hybrid-laser welding processes by using an adequate adaptation (Fig.46).

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Acknowledgments « ... Homage to Shipbuilders for their courage in attempting to overcome without and with success the welding effects ... » Thanks to the French Ministry of Research and Industry, to French Shipyards (Chantiers de l’Atlantique C.A.T and Ex-Ateliers et Chantiers du Havre A.C.H) and to the active cooperation of working group : ƒ Chantiers de l’Atlantique : J.P. Guellec ƒ Principia Marine : T.T. Chau , E. Rauline , A. Guerrier , (ex-IRCN) G. Babaud & F. Besnier

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References [1] Chau, T.T., « Etude des déformations des structures planes des ponts et des cloisons de navire en vue de diminuer les travaux de redressage», Final Technical Report, 1991-1995, IRCN/SEA 95013, 1 rue de la Noë, 44321 Nantes, France. [2] Chau, T.T. & Masson, J.C., « Une méthode d’évaluation des contraintes et des déformations résiduelles dans les assemblages d’éléments métalliques soudés d’épaisseurs moyennes », Proc., ATMA 1992, 207-233, 19-21 (1992) [3] Chau, T.T., Paradis, A., Masson J.C., « A simple method for evaluating the 3D welding effects on thin stiffened panel assemblies in shipbuilding», Proc.,3rd International Conference on Marine Technology, ODRA’99, Szczecin, Poland, Marine Technology III, 485-530 (1999). WIT Press: [email protected] [4] Chau, T.T. & Besnier, F., «Optimization of thin stiffened plate panels in th shipbuilding», Proc. 6 Int. Symposium on Marine Engineering, ISME Tokyo 2000. [5] Chau, T.T. & Besnier, F., «Numerical simulation of welding in shipbuilding», Proc. th 5 Int. Conf. on Marine Technology, ODRA’03, Szczecin, Poland, Marine Technology V, 3-20, (2003). WIT Press: [email protected] [6] Chau, T.T, Raulline, E., Guerrier, A., Babaud, G., Besnier, F., « Simulation numérique du soudage à l’arc en construction navale», Proc. 1st Technical Meeting on Numerical Simulation of Welding, AFM/SNS, Paris, France, (2003). [7] Chau, T.T, Babaud, G., Besnier, F., « Une méthode de simulation numérique du soudage à l’arc dans l’industrie métallique », Proc. of Engineering Mechanics Today EMT, Hochiminh City, organized by LMS Ecole Polytechnique (France) and Institute of Applied Mechanics (Vietnam), (2004). [8] Chau, T.T., «A metallurgical Concept for Numerical Simulation of Arc Welding», Proc. ASME PVP 2005, Denver,Colorado, USA, paper N°71654, 17-21 July (2005). [9] Chau, T.T., Jancart, F., Bechepay, G., «About the welding effects on thin stiffened th panel assemblies in shipbuilding», Proc.4 Int. Conf. Technology, ODRA’01, Szczecin, Poland, Marine Technology IV, (2001). [email protected] [10] Performance RD project, 2001-2002, Task 1-4.2, « Mesures et prédictions des déformations et des contraintes apparaissant lors de l’élaboration d’une nappe à partir de tôles « coils », IRCN Convention N°00290-6020, Document N°02RC65 (Juillet 2002), Principia Marine (ex-IRCN), Nantes, France, (2002). [11] American Welding Handbook, 1, Welding Metallurgy, 4,90-124, A.W.S, USA (1987). [12] Leblond, J.B., Mottet, G., Devaux J.C., « A theoretical and numerical approach to the plastic behaviour of steels during phase transformations. Derivation of general relations», J. Mech. Phys. Solids, 34, 395-409 (1986) [13] Jhaveri, P., Moffatt, W.G., Adams, C.M. Jr., «The effect of plate thickness and radiation on heat flow in welding and cutting», Welding journal, 41, 12-16 (1962). [14] Adams, C.M. Jr., «Cooling rates and peak temperatures in fusion welding», Welding J. Research Suppl., 210-215 (1958). [15] Timoshenko, S., «Strength of Materials», 4, D. Van Nostrand Company Inc. Princeton, New Jersey, USA (1941). [16] Ex-A.C.H French Shipyard (Ateliers et Chantiers du Havre). [17] Master-Series V7m2 (EDS-PLM Solutions, USA) [18] PERMAS V4.0 INTES France (INTES GmbH, Stuttgart, Germany) [19] SGI Origin 200 Computer, USA. [20] ASTM : American Society of Testings and Materials. [21] IRCN 31/1081 Quality Standard for Ship Construction (ex-French Shipbuilding Research Institute), Principia Marine, 1 rue de la Noë, Nantes, France. http//www.principia.fr [22] Stauffer, H. & Hackl, H., «Laser-Hybrid welding – A powerful joining technology», Proc. 7th Int. Aachen Welding Conference, Germany, 477-488, May 3-4 (2001)

EVALUATION OF RESIDUAL STRESSES IN CERAMIC AND POLYMER MATRIX COMPOSITES USING FINITE ELEMENT METHOD K. Babski, T. Boguszewski, A. Boczkowska, M. Lewandowska, W. Swieszkowski*, and K.J. Kurzydlowski Division of Materials Design Faculty of Materials Science and Engineering Warsaw University of Technology Woloska 141, 02-507 Warsaw, POLAND e-mail: [email protected]

ABSTRACT The aim of the study was to evaluate the residual stresses in polymer – ceramic composites using the Finite Element Method (FEM). The effect of the composite structure on the residual stresses built up was also analyzed. The ceramic matrix composites were made of porous SiO2 ceramic infiltrated with urea – urethane elastomer. In the infiltration process liquid mixture of the substrates is incorporated into ceramic pores using the vacuum pressure and elevated temperature. This results in thermal stresses being generated since the thermal expansions of the elastomer and ceramics are different upon cooling to ambient temperature. A bis-glycidylmethylmethacrylate (bis-GMA) polymeric matrix with the ceramic fillers, which is used for dental restoration, was also investigated. During the restoration the matrix polymerizes and shrinks. The shrinkage again results in strains, which lead to restoration failure by de-bonding at the composite-tooth interface. The fillers are added to the polymeric matrix to reduce the material shrinkage. The effect of the fillers on the residual stresses at composite-tooth and resin-ceramic filler interfaces has been evaluated in the present study. Both composite materials were analysed using the Finite Element Method employing the Ansys software. A linear and isotropic properties have been assumed for the ceramic and polymer components. For infiltrated composite (CMC) the simulations of both thermal and external loading of material were carried out. The models were subjected to thermal load o o simulating the cooling from fabrication (120 C) to room temperature (20 C), followed by compressive straining. For the dental restoration polymer matrix composite (PMC) the polymerization shrinkage of the composite was modelled using temperature-dependent expansion. The analysis of distribution of principal stresses in the CMC shows that a change of temperature leads to buildup of high tensile stresses in elastomeric phase and both tensile and compressive stresses in the ceramic pre-form. It was found that the thermal stresses present in composite mostly reduce the maximum values of tensile stresses in ceramics. It can be advantageous and result in an increase of composite toughness. The FE results obtained for the PMC show the effect of the resin shrinkage on the residual stresses at the resin-ceramic filler interface, which can cause de-bonding.

139 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 139–148. © 2006 Springer.

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Various fillers have been examined in terms of the efficiency in the reduction of these residual stresses. In more general sense, the present studies show the potential application of the finite element method in investigation of the residual stresses in different types of the composite materials. The future work will be concentrated on the experimental validation of the numerical results.

Introduction Composites are complex materials which comprise of multiple phases (components) of different thermal and mechanical properties. By combining such components as metals, ceramics, glasses, and polymers, one can produce new functional and construction materials with superior properties which could be tailored for the specific applications. However, due to the mismatch in the properties of their constituents, composite are prone to build-up of residual stresses. This is in particular true to the thermal stresses arising due to mismatch in thermal expansion coefficients. These thermal stresses might be generated either during manufacturing process, more precisely during the cooling from fabrication temperature, or due to thermal cycling in in-service conditions. They, in general, can improve the properties of the composites. However, they can also have detrimental effect on their performance. This calls for their control over manufacturing and in-service conditions. The widely used ceramic–polymer composites with enhanced properties commonly consist of ceramic particles or fibres embedded in a polymeric matrix. This type of composite is used in dentistry as a dental filling material. However, one of the main problems influencing longevity of polymeric-ceramic based dental restorations is shrinkage of the polymeric resin. As the resin matrix polymerizes it shrinks and for large cavities the composite material might be pulled away from the cavity walls. This in turn, leads to restoration failure by de-bonding at the composite-tooth interface [1,2]. The second type of ceramic-polymer composites is material with the microstructure of two interpenetrating phases. These composites exhibit high initial compressive strength and stiffness together with the afterwards ability to sustain large deformations due to combining the ceramic stiffness and rubbery elasticity of elastomer [3,4]. A material with such properties can be potentially used as shock absorber or force sensor. Composites with interpenetrating structure can also provide some functional properties in case the piezoelectric ceramic is being used. Such structures exhibit better piezoelectric parameters and are lightweight comparing to bulk ceramic. This can make them useful for a host of sensor and actuator, e.g. hydrostatic sonar sensors [5]. For the both composites the thermal expansions of the elastomer and ceramics are different upon cooling to ambient temperature and thermal stresses are generated. Moreover, the elastomer shrinks as a consequence of its transformation from the mixture of substrates in the liquid to the solid states. These two phenomena result in buildup of considerable residual stresses. The aim of the study was to evaluate the residual stresses in polymer – ceramic composites using the Finite Element Method (FEM). The effect of the composite structure, defined in terms of the volume fraction, size and shape of constituents, on the residual stresses built up was also analyzed.

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Materials and Methods Ceramic-elastomer composites were made by infiltration process that consists in incorporation of liquid elastomer into the open pores of ceramics perform (Fig.1). Such materials as: porous SiO2 ceramic made of sintered fractioned quartz sand and polynitrille urea-urethane elastomer (PNMU) were used. The open porosity of pre-form was approximately 40% and closed porosity was negligibly low. Basic properties of the components are listed in Table 1.

Fig. 1. SEM images of: a) fracture surface of porous ceramics, b) plane section of ceramic -elastomer composite.

Table 1. Mechanical properties of SiO2 ceramics and PNMU elastomer. material property E [MPa] Q O [1/K]

SiO2

PNMU

67000 0,19 0,6 ˜ 10-6

18 0,49997 160 ˜ 10-6

Infiltration process was conducted at elevated temperature and vacuum in order to decrease the viscosity of elastomer substrates mixture to fully fill up the pores. The curing reaction of elastomer was conducted at the temperature of 120oC. Since the thermal expansion coefficients of ceramic and elastomer differ, the thermal residual stresses can be induced during cooling to ambient temperature. Arising residual stresses can cause micro cracks and debonding at the ceramic elastomer interface. A moderate residual stresses and good adhesion of components can also effect on brittle cracking of ceramics and enhance mechanical properties [6,7]. In fact, the composites modelled here exhibit greater apparent stiffness and about 400% higher compression strength comparing to the porous ceramic [3]. The Finite Element Method and Ansys 9.0 software were used to model the residual stresses. The FEM models were developed assuming 6 and 4 –fold planar symmetry. In the modelling the volume fractions, size of particles and necks between ceramic grains were assumed according to average values measured for series of samples via image analysis. Fig. 2 shows the modelled structure and a corresponding unit cell used in FEM analyses.

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Fig. 2. Modelled structure and elementary unit cell used in FEM analysis.

The unit cell was subjected to loading under three conditions: (a) thermal, (b) external compressive and (c) combined compressive and thermal loadings. The distribution of principal and equivalent von Mises stresses were analysed. A bis-glycidylmethylmethacrylate (bis-GMA) polymeric matrix with the ceramic fillers of different shapes, which is used for dental restoration [8], was investigated. Two numerical models were developed. The macro model of tooth-composite was used to study interaction between tooth and the composite filling. The composite properties were selected based on the data published in literature [9]. These properties change during polymerization of the composite. The Table 2 lists Young’s modulus and volumetric shrinkage of the composite as a factor of time. The tooth was assumed to have constant elastic, isotropic and uniform material properties (Table 3) [9]. The micro model was used to analyse residual stresses in the composite itself during it polymerization. The material properties of the resin are shown in the Table 4. The ceramic fillers properties was constant in time (Table 3). Volumetric contribution of ceramic in the composite was of about 45 %.

Table 2. Material properties of the composites. Time [min]

Volumetric shrinkage [%]

Young Modulus [GPa]

Poisson ratio

0

0

0,04

0.45

5

1.93

0,7

0.3

10

2.31

3,8

0.21

15

2.41

5,4

0.21

30

2.41

5,4

0.21

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Table 3. Material properties of the tooth and ceramic fillers. Material

Young Modulus [GPa]

Poisson ratio

Tooth

186

0.3

Ceramic

400

0.3

Table 4. Material properties of the resin. Time [min] Volumetric shrinkage [%]

Modulus [GPa]

Poisson ratio

5

4

0,19

0.45

12

6

0,388

0.35

30

7

0,467

0.25

To evaluate the residual stresses in the models, the Finite Element Method was used. The polymerization of the composite in the both models was simulated by temperaturedependent expansion of the composite based on temperature/shrinkage calibration of the models performed according to the method presented by Boguszewski et al [10].The analysis was made in the Ansys 9.0 - FE software program. There SOLID92 - 10 nodes element was used. The geometry of the models is presented in Fig.3.

a)

b) Fig. 3. FEM model of: a) composite – tooth system, b) resin – ceramic system.

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Results As it is shown in SEM images of real composite structure, the necks between grains of ceramics are the main object of concern because mainly due to their fracture the composite looses its stiffness and strength. The calculated distribution of residual thermal stresses in area of one of the necks is shown in Fig. 4. The plots show maximum (V1) and minimum(V3) principal stresses in porous skeleton.

Fig. 4. The distribution of: a) maximum (V1) and b) minimum(V3) principal stress in ceramics. The high stresses concentration occurs in the area of the neck (Fig. 3). There are also concentration and discontinuities of stresses at the interface of components. Since the model of real structure is idealised the values of stresses can be used only to show a tendency of arising residual stresses The values of stresses are normalised by the elasticity modulus of composite. The changes of V1, V3 principal stresses and von Mises equivalent stresses along the paths (according to Fig. 5) are illustrated in Figs. 6 and 7.

Fig. 5. Paths used in stress distribution anlayses.

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Fig. 6. Spatial variation in V1, V3 principal stresses in the ceramics filler. It was found that thermal stresses present in composite mostly reduce the maximum values of tensile stresses in volume of ceramic neck under external load. Since ceramic materials have much better compressive than tensile strength the local increase of compressive stresses can improve resistance for brittle cracking and strength of the composite [4,11]. The local concentration of stresses, especially at the boundary surface can lead to debonding between ceramics and elastomer.

Fig. 7. Changes of von Mises equivalent stress in ceramics.

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Due to polymerization shrinkage, the high residual stresses arise in the whole compositetooth model. The highest values of these stresses are at the tooth composite interface (Fig. 8).

a) in whole model

b) in the composite

Fig. 8. Map of von Mises stress distribution in the composite – tooth system (a) and in the composite itself (b).

The von Mises stresses have also been calculated for the resin-ceramic model (Fig. 9). The stresses distribution maps show the high concentration of the stresses at the interface between polymeric resin and ceramics with the highest values in the polymer (Fig. 9b)- see also Table 5. Moreover, the highest stress concentrations for the models are located at the interfaces between different materials.

a) in whole model

b) in the resin

Fig. 9. Map of von Mises stress distribution in the whole resin - ceramic system (a) and in the resin itself (b).

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Table 5. Results of the maximum stresses in two models.

Model

Material

Maximum von Mises stresses at the end of the polymerization process [MPa]

tooth

11.8

composites

4.8

resin-ceramic

resin

7

composite

ceramic

3.3

tooth-composites

Summary The result of the studies show that presence of the residual stresses in the composites with brittle ceramic matrix mostly reduce maximum values of tensile stresses introduced under external load. The presence of calculated residual stresses can locally decrease the tensile stresses. It can improve resistance for brittle cracking of ceramic. High values of the stresses at the interfaces between the ceramic and elastomer would cause debonding of phases or relaxation in elastomer. They may also cause local microcracking. Such phenomena may be a concern of further analysis and material properties selection. Regarding the analysis of dental restoration composite, the influence of the composite shrinkage due to polymerization on built-up residual stresses was investigated using a 3D elastic models in Finite Element Method. The results of the tooth-composite system which are similar to one in the literature [9], shows high residual stresses at the interfaces between the tooth and composite. This high stresses may result in debonding of the restoration. This can be an explanation of the failure of the dental restoration. As the composite (resin matrix) polymerizes it shrinks and for large cavities the composite material might be pulled away from the cavity walls. This in turn, leads to restoration failure by de-bonding at the composite-tooth interface. The FE calculation of stresses in the ceramic-resin system was carried on. The value of residual stress after light activated polymerization process have been estimated by this method. The high residual stresses are located at the interfaces between ceramic filler and polymeric matrix. This can also results in microcracking at the interfaces and failure of the restoration. One of the possible ways to reduce these stresses could be changing the volumetric contributions, size and shape of fillers in the composite to find the optimum structure of the dental restoration. In general, the present studies show the potential application of the finite element method in investigation of the residual stresses in different types of the composite materials. The future work will be concentrated on the experimental validation of the numerical results.

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References 1.

P.F. Hubsch, J. Middelton, J. Knox, “A finite element analysis of the stress at the restoration-tooth interface, comparing inlays and bulk fillings”, Biomaterials 21 (2000) 1015-1019. 2. B.S. Dauviller, M.P. Aarnts, A.J. Feilzer, “ Modelling of the viscoelastic behavior of dental light-activated resin composites during curing”, Dental Materials 19 (2003) 277-285. 3. K. Konopka, A. Boczkowska, K. Batorski, M. Szafran, K.J. Kurzydlowski (2004). Microstructure and properties of novel ceramic – polymer composites. Materials Letters 58: 3857-3862 4. Y. Podrezov, S. Firstov, M. Szafran, K. Kurzydlowski, „Non-elastic behaviors of high-porosity ceramics and ceramic –polymer composites for medical applications” E-MRS Fall Meeting 2003, conference proceedings 5. R. Ramesch, H. Kara, C.R. Bowen, “Finie element modelling of dense and porous ceramic disc hydrophones”’ Ultrasonics 43 (2004) 173-181 6. F. Hild, A. Burr, F.A. Leckie, “Matrix cracking and debonding of ceramic matrix composites”, Int. J. Solids Structures Vol. 33, No 8, pp.1209-1220 (1996) 7. K. Konopka, A. Boczkowska, K. Batorski, K.J.Kurzydáowski, M. Szafran, „Propagacja pĊkniĊcia w kompozycie o osnowie ceramiki porowatej SiO2 infiltrowanej elastomerem”, Kompozyty 3(2002), (108) 8. A. Versluis, D. Tantbirojn, M.R. Pintado, R. Delong, W.H. Douglas, “Residual shrinkage stress distributions in molar after composite restoration”, Dental Materials (2004) 20, 554-564. 9. M. Barink, P.C.P. Van der Mark, W.M.M. Fennis, R.H. Kuijs, C.M. Kreulen, N. Verdonschot, “A tree-dimensional finite element model of the polymerization process in dental restorations”, Biomaterials 24 (2003) 1427-1435. 10. T. Boguszewski, W. Swieszkowski, M. Lewandowska, K. Kurzydlowski, ”Shrinkage of dental polymeric composites“, e-Polymers, 2004 11. G. Grabowski, L. Stobierski, “Modelowanie rozkáadu naprĊĪeĔ cieplnych w materiaáach ceramicznych na przykáadzie kmpozytu SiC-TiB2”, XXXI Szkoáa InĪynierii Materiaáowej, Kraków (2003) p. 413-418

PHASE TRANSFORMATION AND DAMAGE ELASTOPLASTIC MULTIPHASE MODEL FOR WELDING SIMULATION T. WU, M. CORET, AND A. COMBESCURE LaMCoS, CNRS UMR 5514, National Institute of Applied Sciences, Lyon 20 av A. Einstein, 69621 Villeurbanne Cedex, France [email protected], [email protected], [email protected] ABSTRACT The aim of the article is to study and develop welding numerical models in the phase transformation and damage condition. The models are based on the study of damage concept in the multiphasic behavior, which occurs by welding process. The core of models or constitutive equations is the coupling between ductile damage, small strain elasticity, finite visco-plasticity and phase transformation. Based on the theory of thermodynamics and continuum damage mechanics (CDM), constitutive equations are built to describe damage growth and crack appearance during and after welding. The thermodynamics of irreversible processes with state variables is used as a framework to develop the phase coupling model. The related numerical aspects concern both the local integration scheme of the constitutive equations and the global resolution strategies. In this study, the majority of efforts are devoted to the theoretical developing of damage model. In addition, the models are implemented in computing software MATLAB® and CEA CAST3M® finite element code, and some calculations are presented to further explain the models in the end of the article. Introduction Under certain conditions, damage and phase transformation phenomenon exist simultaneously during welding process. For example, the welding of 16MND5 (French nuclear ferrite steel) or 15Cr-5Ni (martensitic stainless steel) components in the manufacture of nuclear equipment produces phase transformation phenomenon during heating and cooling stages, while damages induced by welding usually happen during cooling stage of welding. It is means that mechanics properties of components or structures are affected by damage or even fracture induced by welding. Thus, it is really significative to use numerical modeling method to analysis and predict welding results, including the distribution of residual stress and damage. According to numerical results, the adjustments of the process parameters are implemented before doing the real experiments and manufacture processes in order to save time and money. However, now there is no evidence of a model that is able to predict the damage induced by welding process. One observes high spatial and temporal gradients as well as phase transformations. Such situations imply to cope with a diversity of damage models and add complexity to standard constitutive equations. The model contains three main ingredients: continuum damage mechanics, transformation plasticity and multiphase behavior. A graphic representation of these coupling mechanisms (Figure 1) was given

149 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 149–160. © 2006 Springer.

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by Inoue [1]. Although some authors proposed to take all these phenomena into account in a common framework, we consider the influences of mechanics on thermics (arrow No. 4) and of mechanics on metallurgy (arrow No. 6) as second-order effects, since it has been observed that for such steels the influence of the stress state on the transformation diagrams is small. This assumption enables us to solve the thermometallurgical problem independently of the mechanical one. M. Coret and A. Combescure have done some work about such coupling mechanical behaviors under without damage condition [2-5]. Our study of damage factor coupling with other thermometallurgical and mechanical problems is based on their previous work.

Figure 1. Coupling mechanisms [1] To model the behavior of damage of continuous medium, the modeling of the damage can be done according to two different approaches. One rests on a micromechanical approach whereas the other uses a phenomenological macroscopic one. The micromechanical approach uses the method of localization-homogenization, which makes it possible to go down on smaller scales from the structure (grain, system of slip) to describe the elementary mechanisms of the damage. For this micromechanical aspect, mechanisms are to be implemented in order to determine the required sizes. For example, the process of homogenization consists in determining the macroscopic sizes of volume representative element from those of basic cells by taking suitable averages. Although such an approach seems to be closer to reality of material, it is not easily realizable for the metal structural calculation. The computing time is extremely long because of the number considerable of equations. The other approach of modeling is purely phenomenologic. It is founded on the introduction of variables of state associated with the various phenomena revealed by the experimentation. These phenomena are described within the framework of the thermodynamics of the irreversible processes [6]. There are still two approaches, which can be underlined. One is gained through physical inspiration. GURSON, ROUSSELIER, GELIN, BENNANI, PICART and others developed certain such kinds of models. The other comes from phenomenologic and macroscopic inspiration: KACHANOV, RABOTNOV, CHABOCHE and LEMAITRE built up this kind of damage model. The physical approach is based on a growth rate of the cavities inside a matrix with the elastoplastic behavior. By construction, this theory supposes the isotropy of the damage and uses a scalar variable to describe the volume fraction of the cavities.

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Definition of Damage The theory of the continuum damage mechanics is based on the assumption of the difference of scale between the micro-damage (microcracks and microvoids) and the Representative Volume Element (RVE). The damage analysis gives criteria for the creation of mesocracks, and then fracture mechanics is used to describe the phenomena. It is important to use a unique formulation to describe the different damage processes. It is based on the assumption that damage is driven by plastic strains, elastic strain energy and by an instability process. The macroscale scalar variable is defined to describe damage [7, 8]:

D

SD S

(1)

where S is the original surface, and SD is the damaged surface.

D 0 D 1

:

Undamaged material

:

Fully broken material in parts

0  D 1 :

Failure occurs but crack does not happen

In the model, it is important and clearly understood to adopt the unique macro variable to describe the damage phenomena. Such damage macro variable is obtained through two approaches: 1) to integrate the unique micro damage variable (regard no difference between the damage in the austenitic phase and one in the martensitic phase); 2) to unify two micro damage variable (the ductile damage of the austenitic phase and the ductile damage of the martensitic phase) into one damage variable. For phasetransformation material, such as martensite stainless steel, there exist both martensitic phase and austenitic phase simultaneously during the specific heating or cooling stages. In order to closer the reality, it is necessary to describe the two different phases respectively. The Representative Volume Element (RVE) and microdamage are two scales of materials. In fact, the RVE consists of inclusions and matrix (the austenitic phase and the martensitic phase), and microdamage (microcracks and microvoids) distribute in inclusions and matrix (Figure 2). In our model, the damage in the inclusions (martensite) is regarded different from damage in the matrix (austenite). The damage in martensitic phase is marked by DĮ, and the damage in austenitic phase is noted by DȖ. In microscale approach, the local damage variable at one point is defined by:

DP

dS D dS

(2)

And the macroscale variable of damage can be given and developed by microscale definition of damage one.

D

S DJ S DD  S S

1 1 dS D  ³ D dS D J ³ S S S S

1 1 DP dS  ³ D DP dS J ³ S S S S (3)

DD [ s  DJ (1  [ s ) where [ s is the surface fraction of martensitic phase.

It was known that the damage variable is defined and deduced from the surface fraction, while the phase fraction of material is defined by the volume fraction. Therefore, in order to derive the constitutive equations of damage in phase transformation, we set up a bridge between both of them by formula:

D DD [ s  DJ (1  [ s ) DD [V

2

3

2

 DJ (1  [V 3 )

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RVE

n

S

Microvoids& Microcracks Parameter D

Martensite inclusions

Austenite

Figure 2. Damage variable and RVE Phase transformation The phase transformations often play a dominating role in the modeling of certain thermomechanical problems. Solid-state phase transformation causes the macroscopic geometric change because these different types of crystalline structures have different densities, which is so-called transformation-induced volumetric strain. This deformation can be explained by two micromechanical mechanisms of Greenwood and Johnson and of Magee. The transformations are strongly dependent not only on the speed of cooling but also on the composition in elements of alloys. Two types of diagrams are used by the researchers of the heat treatments to represent these transformations simply: Timetemperature transformation (TTT) diagrams are obtained by fast cooling of austenite then maintenance at constant temperature; continuous cooling transformation (CCT) diagrams represents the transformations during cooling at constant speed. In our research, we focus on the transformation from austenite to martensite after welding. The martensitic transformation should be treated separately comparing other transformations, because it was considered as independent of time. The empirical law of Koistinen and Marburger gives the voluminal fraction of martensite according to the temperature. The theoretical justification of this equation was given by Magee:

zD

zJ (1  e

 E Ms T

)

(4)

where zĮ and zȖ are voluminal proportion of martensite and austenite respectively; Ms is martensite start temperature; ȕ is coefficient depend on material; T represents temperature. On the one hand, from a mechanical point of view, the phase transformations are complex phenomena that induced constraints growth or release. On the other hand, the application of pressure modified both the energy stored in material and the structure of the material, and caused the deformation’s changes in macroscale (Figure 3). Therefore, the influence of the stress on the transformations of phases can not be neglected to some extent. It was shown that extremely high pressures about the hundreds MPa lead to notable effects on the kinetics of transformations [9]. Further more, even a low macroscopic constraint applied, lower than the yield stress of the softest phase, an additional deformation, called “TRansformation-Induced Plasticity” (TRIP), can be

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observed during the transformation (Figure 4). Leblond’s transformation plasticity model [10,11,12] is presented to further explain the TRIP as follows:

E pt



3'H JthD

§ 6 eq · ˜ S ˜ h¨¨ y ¸¸ ˜ ln z ˜ z ©6 ¹

V Jy

:

Difference of thermal deformations between the two phases.

:

Macroscopic von Mises equivalent stress.

:

Homogenized ultimate stress.

z

:

Volume proportion of phase D .

S

:

Deviator of the macroscopic stress.

'H JthD

6

eq

6

y

§ 6 eq h ¨¨ y ©6

· : ¸¸ ¹

(5)

Term that translates the non-linearity of the plasticity of

transformation, defined by:

§ 6 eq h ¨¨ y ©6

· ¸¸ ¹

1

1,

if

7 6 eq 1 (  ), 2 6y 2

if

6eq 1 d 6y 2 6 eq 1 ! 2 6y

For most situations, the following simplified formulation also leads to content effects:

E pt



3'H JthD

V Jy

˜ S ˜ ln z ˜ z

(6)

The equivalent TRIP strain can be gained from the integral of the TRIP’ rate:

E

t1

pt ³ E dt

pt eq

t0

t1

³ t0

3'H JthD

V Jy

˜ S ˜ ln z ˜ zdt

(7)

th

If we consider that 'H J D is constant and the cooling rates of different time keep same during the transformation, we have:

Eeqpt

IS

2 IV eq 3

(8)

with t1

I

 3' H

th J D

1

³ V J ˜ ln z ˜ z ˜ dt y

Const ( positive )

t0

This equation shows the direct relationship between the equivalent TRIP strain and the equivalent stress: the transformation-induced plastic strain is proportional to the level of the equivalent stress in von Mises’ sense. Furthermore, in the case of small loads, the strain is proportional to the applied stress [3].

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Figure 3. Free dilatometries of martensitic transformation [3] Figure 4. Total strain with loading ( V 70MPa ) [3] Mesoscopic Damage Model The mesoscopic model, which we introduced, is much more numerically oriented and ignores a priori constitutive law for each phase, and it developed based on the method of localization-homogenization. The homogenizing procedure used is the Taylor’s localization law, which assumes homogeneous deformations in a heterogeneous medium with nonlinear behavior. This law provides the closest possible match with Leblond’s theoretical case for elastoplastic phases. Such approach, called micro-macro, consists of staring from the behavior of each phase and working back to the macroscopic behavior of the material. After the localization, the behavior of each phase can be treated respectively, without coupling. Such model provides the freedom to choose the behavior type of each phase. It seems more reasonable not only to adopt different material properties but also to use the different types of behaviors for the austenitic and martensitic phases. Therefore, as other behaviors, our mesoscopic damage model adopts two damage variables corresponding to phase Į and phase Ȗ to further describe the damage during the phase transformation between martensite and austenite. We suppose that the material have two types solid solution: Į type solid solution and Ȗ type solid solution. The martensite, ferrite and bainite have the same Į type solid solution while the austenite is Ȗ type solid solution. In this model, we use martensitic phase to replace other Į type phases. We adopt the following variables for the fraction of phase: zĮ is the volume fraction of phase Į. And then, the volume fraction of phase Ȗ is zȖ. In addition, we regard that the damage in the Į phase DĮ is different from that in the Ȗ phase DȖ, and DĮ is no coupling with DȖ. The approach was based on the Voigt model with equal repartition of strains in all phases of the multiphase composite.

H

H i ( i D ,J

)

(9)

Based on the principle of localization mentioned above, we split the total strain ratio into two parts, one coming from the total microscopic strain rate of the phases, and the other representing the plastic transformation strain rate. Thus:

Phase Transformation and Damage Elastoplastic Multiphase Model

E tot

H  E pt

155

(10)

In our model, classical plasticity and transformation plasticity are assumed to be uncoupled, which is true for small strain. Thus, the homogenization law for stress is:

zV ¦ ¦ DJ i

i

(11)

i

,

In addition, the homogenization law for damage is presented in Equation 4. Such modeling scheme provides great flexibility in the calculation. Thus, arbitrary constitutive laws, including different models of transformations plasticity rates and damage governing equations can be selected for each phase. Therefore, the equations of the mesomodel can be developed as follows. The strain equations are:

E tot H  E pt i Hi Hie  Hithm  Hivp i

(12) (13)

The transformation plasticity strain rate is given by Equation 6. For each phase’s behavior, various behavioral models were tested. Here, in order to focus on the interpretation of various coupling behavior clearly, we choose the same type of plastic hardening model (including isotropic and kenimatic hardening) for two phases, although adopting different models for each phase is closer to the reality. Material properties, including the damage parameters, should choose different data according to the various phase materials. The elastic and thermomertallurgical strains are:

Hie

H 1 (T )V i  [H ithm (T )  H ithm (Tref )]

(14)

with

H ithm D i (T ) ˜ TI Tref

H ithm D i (T ) ˜ TI  zD 'H D J

for

J

for

D

phase phase

Our coupling model for each phase is developed on the base of method of local state in the thermodynamics of irreversible process [8, 9]. The various state’s laws of the phases can deduced from the state potential of each phase and the partial differentials of each tot phase’s pseudo-potential also can lead to flux variables. The totally internal energy e e-th-met , viscoplastic (including consists of elastic and thermometallurgic internal energy e isotropic and kenimatic hardening) internal energy eypi-vpk, and internal energy induced by tr phase-transformation e as the following equation shown: e

e tot (H , T , p, D , D, z )

e

e ethmet (H , T , D, z )  e vpivpk (T , p, D , D, z )  e tr (T , z )

(15)

After the partial differential of the internal energy, the state relations (isotropic strain hardening variable Ri, back stress Xi, release ratio of elastic energy -Yi) for each phase are:

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156

Ri

weitot wDi

ci (T )(1  Di )>1  exp(J i pi )@

weitot wD i

(16)

2 g i (T )bi (1  Di )D i 3

(17)

ª º 1 1 1 e e Ai (T )H i : H i  g i (T )bi D i : D i  ci (T ) « pi  exp(J i pi )» Ji 2 3 ¬ ¼

(18)

Xi

 Yi

weitot wpi

The pseudo-potential of dissipation

Mi

is the function of all the dual variables:

M i M i (V i , Ak , gradT , Yi , k ; H e , Vk , T , Di ) The damage potential

(19)

MiD can be defined by: M iD

Y Si ( i ) s i 1 ( si  1)(1  Di ) S i

(20)

Si and si: Characteristic coefficients of materials to describe damage, usually are the functions of temperature. The yield function of each phase can be written:

Ri J 2 (V i  X i )   V yi 1  Di 1 D i

f i (V i , Ri , X i , Di )

fi

(21)

then Fi

fi 

V yi

bi Si (T ) Y ai [  i ]s i ( T ) 1 Ri2  J 22 ( X i )  2(1  Di ) 2(1  Di ) [ si (T )  1](1  Di ) Si (T )

:

(22)

The yield stress of phase i.

The whole of the selected variables and the potentials previously defined lead to a thermodynamically acceptable model whose general formulation is presented as follows. The viscoplastic flow:

Hip

wMi wV i

D

D

Vi  Xi 3 p i 2 1  Di J 2 (V i  X i )

(23)

The evolution of the internal variable associated with isotropic hardening:

ri



wMi wRi

ui Fi

ni

(24)

The evolution of the internal variable associated with kinematic hardening:

D



wMi wX i

D

D

3 p i Vi  Xi 2 1  D i J 2 (V i  X i )

(25)

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The evolution of the damage variable:

D i



Si Y ( i ) si (1  Di ) S i

wM i wYi

(26)

Numerical Analysis As far as the numerical analysis is concerned, the first step is to computer the coupled transient temperature and metallurgical phase field. The second one is stress and strain field computation and then the states of each phase (stresses, strains, internal variables, damage ...) are output. At the end, we can homogenize the strains and stresses, displacements and damages. In order to explain the models, we give elementary calculations of examples in this part. These calculations are implemented in Matlab 6.5, and they can illustrate directly the damage evolution and other coupling behaviors. Here, we introduce the “Satoh” type test that an uniaxial bar is clamped on the top and bottom and simultaneously suffer thermal loading. The test consists of austenitizing and martensitizing with cooling homogeneously a test piece whose longitudinal displacements are restrained. Thus can be used to induce the same or similar phenomena as that can be observed in welding heat-affected zone (HAZ). This led us to choose this type of test in the framework of this study for the analysis. The test contains several complex coupled phenomena, and they are thermal (temperature), metallurgical (phase-transformation) and mechanical (strain-stress, damage) behaviors. In our calculation, the total strain is partitioned as follows tot (for Satoh test, E =0):

E tot

E e  E thm  E pc  E pt

(27)

e thm is the macroscopic thermowhere E is the macroscopic elastic strain, E metallurgical strain, Epc is the classical macroscopic plastic strain and Ept is the transformation-induced-plasticity strain.

>z D

E thm where Tref

J

J

 zD D D @(T  T

Tref

T

20qC

Thermal strain difference between the two phases: 'H DJ20qC

0.011

Thermal expansion coefficient of the austenitic phase ( Tref

DJ

(28)

)  zJ 'H DJref

6

1000qC ):

9

22.6 u 10  2.52 u 10 ˜ T

Thermal expansion coefficient of the martensitic phase: D D 12.35 u 10 6  7.710 9 ˜ T ( T d 350qC ); D D 15 u 10 6 ( 350qC  T  700qC ) The beginning temperature of martensitic transformation: Ms 400qC We suppose the bar has the elasticity and perfect plasticity that the Young’s modulus and yield stress depend on temperature, which is given in Table 1. The temperature loading of the bar is from 1000°C to 20°C with T = 9.8°C/s. The phase-transformation model adopts Magee’s model as shown in Equation 5 and Figure 5. The martensitic phase transformation occurs at temperature 400°C and the proportion of austenitic

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phase quickly increases, near to 0 at ambient temperature. The TRIP, related to macroscopic stress, is calculated according to Leblond’s model (Equation 6).

T (°C) E (GPa)

0

100

200

400

600

700

800

900

1000

208

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135

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32

30

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20

140 130 (MPa) m=martensite, a=austenite

120

110

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ıym (MPa)

ıya

Table 1. Material properties It is generally accepted that the additional flow induced by the TRIP strain plays a significant role in the evolution of the stress during structural transformations. Our results can verify this point and various strains are presented in Figure 6. The TRIP strain is dominating comparing others, and such big value is because of the large macroscopic stress at low temperature. Furthermore, the TRIP strain that comes from the damagemechanical model is smaller a little than one gained from the usual strain-stress model (without damage) because of the decline of stress in damage condition. Although TRIP notably affects the stress via changing elastic stress in elastic stage, it changes the stress little in plastic stage because of perfect plasticity. In fact, the thermal strain has observable effect to the stress in “Satoh” test, but the metallurgical stain from austenite to martensite weakens this effect because its volume increases whereas the thermal strain is negative.

Figure 5. Proportion of each phase

Figure 6. Various strains vs. temperature

From the Figure 7, it is observed that both austenite and martensite are yield at the beginning of their existed stage (martensite, near to 400°C). Generally, the austenitic component of stress is much lower than the martensite’s because of the big difference of yield stresses. It is evident that damage decreases the effective stress, especially for martensitic component. For austenitic component, it is not large effect whether coupling damage or not. Thus is caused by its smaller damage variable (Figure 8). Before phase transformation, the all variables of martensite equal to zero and the mechanical behavior is entirely predominated by single austenitic phase. With the development of phase transformation, the martensite plays more and more role not only in evolution of stress

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but also to the damage’s growth. At the end of phase-transformation stage, the macroscopic stress increases slowly or even decreases because of damage’s effect. In this calculation, there are lacking for accurate material data about damage because the calibration test is still going on and can be finished soon. However, the numerical results give an interesting in-depth insight about complicated phenomena coupling with damage.

Figure 7. Comparing stress with/without damage

Figure 8. Damage variables

Conclusion and prospective The objective of this study is to develop the damage model to describe damage during the cooling in welding process, and it was accomplished in the aspect of theoretical derivation. Comparing the traditional model of damage, which does not take the phase transformation into account, our new mesoscopic damage model has its own advantage: it is free to choose the behavior for each phase whereas it is difficult or impossible to choose the reasonable parameters for various-phase material through traditional model. The model coupled thermal, metallurgical and mechanical behaviors can be used to predict not only the strain and stress fields but also the damage distribution in welded work piece. In fact, the numerical results, especially stress, through the coupled damage model, are closer to material’s state than that through the model coupled without damage. The specific test of “Satoh” type is adopted to imitate the real welding process as a matter of simplification. In this case, virtually all the thermo-mechanical and thermometallurgical phenomena, which can be observed in the HAZ, are present simultaneously. For that reason, the Satoh tests are very useful in validating the constitutive relations used to describe the mechanical evolution in the HAZ. The comparative analyses of the calculations and the experiments should be implemented after the completeness of calibration test of damage and welding damage experimental. Acknowledgments This research is one part of project INZAT4 sponsored by EDF-SEPTEN, FRAMTOMEANP, ESI-GROUP, EADS-CCR, Rhône-Alps, and INSA-Lyon, so we thank their financial and technical supports.

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References 1.

Inoue T, Wang Z. Coupling between stress, temperature, and metallic structures during processes involving phases transformations. Materials Science and Technology, 1: 845–50,1985. 2. Coret, M., Etude experimentale et simulation de la plasticite de transformation et du comportement multiphase de l’acier de cuve 16MND5 sous chargement multiaxial anisotherme, These, LMT-Cachan, Paris, France, 2001. 3. Coret, M., Calloch, S. and Combescure, A., Experimental study of the phase transformation plasticity of 16MND5 low carbon steel induced by proportional and nonproportional biaxial loading paths, European Journal of Mechanics - A/Solids, vol. 23, 823-842, 2004. 4. Coret, M., Calloch, S. and Combescure, A., Experimental study of the phase transformation plasticity of 16MND5 low carbon steel under multiaxial loading,International Journal of Plasticity, vol. 18, 1707-1727, 2002. 5. Coret, M., and Combescure, A., A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading, International Journal of Mechanical Sciences, vol. 44, 1947-1963, 2002. 6. Germain, P., Nguyen, Q.S., Suquet, S., Continuum thermodynamics, J. Applied Mechanics, ASME, vol. 50, 1010-1020, 1983. 7. Chaboche, J.L., Description thermodynamique et phénoménologique de la viscoplasticité cyclique avec endommagement, Thèse de Doctorat Es-Science, Paris, VI, 1978. 8. Lemaitre, J. and Chaboche, J. L., Mechanics of Materials, Cambridge University Press, Cambridge, 1994. 9. Aliage, C., Massoni, E., Louin. J.C., and Denis. S., 3D finite element simulation of residuel stresses and distorsions of cooling workpieces. In 3rd international conference on quenching and control of distorson, Prague, Czech Republic, 1999. 10. Leblond, J., Devaux, J., Devaux, J., Mathematical modelling of transformation plasticity in steel i. case of ideal-plastic phases. Int. J. Plasticity 5, 551–572, 1989. 11. Leblond, J., Devaux, J., Devaux, J., Mathematical modelling of transformation plasticity in steel i. coupling with strain hardening phenomena. Int. J. Plasticity 5, 573–591, 1989. 12. Vincent, Y., Jullien, J.F., Gilles, P., Thermo-mechanical consquences of phase transformation in the heat-affected zone using a cyclic uniaxial test, International Journal of Solid and Structures, Elsevier Ltd, 4077-4098,July 2005.

Session: Residual Stress Effects on Fatigue and Fracture

IDENTIFICATION OF RESIDUAL STRESS LENGTH SCALES IN WELDS FOR FRACTURE ASSESSMENT

P. J. Bouchard British Energy Barnwood, Gloucester GL4 3RS, UK [email protected] P. J. Withers Manchester Materials Science Centre, University of Manchester Grosvenor Street, Manchester M1 7HS, UK [email protected]

ABSTRACT Residual stresses originate from the elastic accommodation of misfits between different regions in a structure. The interaction between the misfit and the restraint of the surrounding structure determines the magnitude of the resultant residual stress and its length-scale. This paper defines the residual stress length-scales that must be considered in engineering fracture mechanics analyses for welded joints by identifying the crack length-scale of concern. This information is used to estimate measurement length-scale requirements to quantify the stress field and the length-scale that must be represented in finite element weld residual stress simulations.

Introduction Residual stresses originate from the elastic accommodation of misfits between different regions in a structure. In practice it is unlikely that any engineering component is entirely free from residual stress because of the material processing, fabrication and service load history. The interaction between the misfit and its elastic accommodation in the surrounding material determines the magnitude of the resultant residual stress and its length-scale. In order to assess the influence of residual stress on the fracture behaviour of a structure, it is essential to quantify the residual stress field over the length-scales of concern from a structural integrity viewpoint. Simplified fracture mechanics based assessment methods, such as the R6 procedure [1], are widely used by industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected

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degradation of engineering components under normal and abnormal service loads. In many cases, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. Multi-pass welding introduces a complex residual stress field in the fabricated structure that varies in 3 dimensions over a range of macro length-scales [2]. However, for simplified engineering fracture assessments, a representative stress profile along a line through the wallthickness is required. This is assumed to apply across the full width of the crack. The R6 procedure provides upper bound (Level 2) residual profiles for various classes of welded joint that can be used in fracture assessments, but these often give very conservative results. Recently, the option to use more realistic (Level 3) profiles has been introduced into R6, but only where such profiles are based on finite element weld residual stress simulations supported by detailed residual stress measurements with the caveat that fracture analysis sensitivity studies on residual stress levels must be performed. Rapid advances in the capability of residual stress measurement techniques, such as the contour method and synchrotron X-ray diffraction, now readily allow residual stresses and strains in welded structures to be mapped on defined planes within a structure [3]. Recent experimental and analytical studies have revealed the importance of short length-scale residual stress variations arising from weld bead sequence effects, weld bead start/stops and stress concentrating features, for example [4]. When such stress modulations are significant from a fracture analysis standpoint it is vital that measurement techniques are sufficiently refined to capture the stress field length-scales of concern. This paper tackles the question of how to identify appropriate length-scales for characterising weld residual stress distributions for use in engineering fracture assessments. First, the principles for decomposing a residual stress profile along a line through a body into linear and self-equilibrated components are defined. Secondly, the minimum crack length of structural concern, amin, for engineering fracture assessment is discussed with particular reference to welded steel structures. Classical stress intensity factor solutions for self-equilibrated stress fields are then used to infer the shortest residual stress wavelength, w, and more specifically the minimum tensile zone length, wten, of concern. This information is then used to estimate the measurement lengthscale, g, required to capture the essential features of the stress field, and the lengthscale that must be represented in finite element weld simulations.

Stress Decomposition If a body is free from all external constraints, that is no forces or moments are applied to any of its external surfaces, then the self-equilibrated 3-dimensional stress distribution is by definition a residual stress field. In order to understand the origin and length-scale of residual stresses [2], as well as their treatment within fracture assessment procedures such as R6 [1], it is useful to decompose the local residual stress profile along a line within the body into membrane, ı m , through-section bending, ı b , and self-equilibrated, ı se , component stress contributions. Consider an arbitrary cut plane dividing the body into two halves, Figure 1a. To satisfy force equilibrium the net force acting normal to the cut plane, F, must be zero, that is the stress acting normal to the surface must equal zero when integrated across the entire surface. Likewise the moments, M1 and M2, acting around arbitrary orthogonal axes within the plane must be equal to zero.

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In engineering fracture assessments it is usual to consider the distribution of stress along a line through a body, rather than the 2-dimensional distribution across a plane, whether the stress is derived from a series of measurements or by continuum analysis. In this case, the force, f, and moments, m1 and m2, acting on the sub-domain (Figure 1b) need not be zero. M2

M1

m1

m2

F

m2 f m1

M2

M1 (a)

(b)

'y

V z (x / t) x=0

xna

0

x

t

x

my fz

Vm

Vb x=t

0

Vse

V z (x / t) (c)

(d)

Figure 1. a) Force and moments on a cut plane, b) force and moments on sub-domain of cut plane, c) sub-domain case of a thin strip through the wall-thickness of a pressure vessel cut perpendicular to the cylinder axis (z), and d) axial stress field along the wall section strip decomposed into the membrane, bending and self-equilibrated components. For example consider the case of a non-stress relieved circumferential butt weld in a cylindrical pressure vessel where the axial (z direction) stress distribution, V z ( x / t ) , acting on a thin strip of width 'y, passing through the wall-thickness of a cylindrical vessel of thickness t, is known (see Figure 1c). The net axial force, fz, for this case often approximates to zero but strictly it is the total force, Fz, acting over a cross-section of the entire vessel that must equal zero. In contrast the bending moment, my, for such a circumferential butt weld residual stress profile is usually non-zero, it being balanced by “tourniquet” moments distributed around the vessel circumference.

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The net force, fz, acting on the thin strip is obtained by integrating the axial stress field V z ( x / t ) over the strip from one surface of the body to the other (x = 0 to t). t

fz 'y

³

§x· ©t ¹

(1)

V z ¨ ¸dx

0

The membrane, or average stress, acting over the strip is given by:

fz

Vm

(2)

t 'y

The resultant bending moment acting over the rectangular strip is given by: t

my

'y

³

§x· ©t ¹

V z ¨ ¸.( x  x na ).dx

0

(3)

where xna is the distance of the neutral axis from the surface x = 0, that is xna = t/2. Using simple beam bending theory, this bending moment can be equated to a linear stress profile having a peak surface value at position x = 0 defined by:

Vb

6m y

(4)

t 2 'y

The remaining self-equilibrated component of stress along the line is then given by:

V se t

noting that

³

0

§x· ©t ¹

§x· ©t ¹

§x· ©t ¹

V z ¨ ¸ V m  2 ¨ ¸V b

V se ¨ ¸dx 0 and

t

³

0

§x· ©t ¹

V se ¨ ¸.x.dx

(5)

0

(6)

The three components are illustrated schematically in Figure 1d.

Self-Equilibrated Stress Length-scale

Often the self-equilibrated component of residual stress along a line (from eqn 5) can be decomposed further into a fundamental stress distribution having a characteristic wavelength wf | t, and higher-order distributions having shorter wavelengths wh | t/2, t/4 etc.. The fundamental stress distribution develops from local restraint of the section wallthickness to weld bead thermo-mechanical cycles. Shorter length-scale self-equilibrated stress fluctuations can be associated with weld bead to bead variations, weld bead start/stop concentrations, localised stresses at geometric singularities (weld root, cap and weld toe) and microstructure phase transformation effects.

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Figure 2. a) Sketch of a bead on plate weld, and b) the predicted transverse stresses (ydirection) along a through-thickness line (x-direction) at mid-length showing the fundamental and shorter length-scale stress fluctuations Shorter length-scale variations are often predicted by finite element (FE) weld residual stress simulation procedures. Sometimes these are artefacts of the modelling approach. For example, Figure 2b illustrates a predicted through-wall weld residual stress profile [5] for the bead-on-plate weld shown in Figure 2a. Short wavelength stress fluctuations are evident in the region x = 0 – 6 mm. When the FE results are volumetrically averaged over a 3 mm diameter sphere, these fluctuations are effectively filtered out. This averaged profile has been analysed using eqns 1 – 6 to identify the self-equilibrated stress distribution. Inspection of this profile in Figure 2 shows that it has a wavelength of the order of the thickness (actually about 0.8t over the region x = 1.5 to 15.5 mm); therefore this is the fundamental component of self-equilibrated stress. Subtracting the averaged profile from the baseline profile can isolate the shorter length-scale stress fluctuations evident in the baseline FE distribution. Inspection of this profile indicates a wavelength of about t/4 for the stress perturbation in the region x = 2 – 6 mm. It is of

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interest to note that this is the region where material discontinuities have been introduced into the FE model, namely a weld metal - base metal boundary and 100% plastic strain annealing when transient welding temperatures exceed 850oC [5]. In reality, material properties will vary over a short length-scale at the weld fusion boundary and plastic strain annealing will vary with temperature and distance from the weld. Thus this particular short length-scale stress perturbation is judged to be mainly an artefact of the FE weld modelling strategy. 1.2 1.0

Self-equilibrated cos(w=t)

0.8

Self-equilibrated, cos(w=2t) - bend

Normalised Stress

0.6 0.4 0.2 0.0 -0.2 0.0

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-0.4 -0.6 -0.8 -1.0 -1.2 x/t

(a) 1.2 Unrestrained cos(w=t) Restrained cos(w=t) Unrestrained cos(w=2t)-bend

1.0 0.8

Normalised K

0.6 K <0 for a/w ten > for 2.6

0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8

0.0

0.1

0.2

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K <0 for a/w ten > 1.56 K <0 for a/w ten > 1.56

-1.0

a/t

(b) Figure 3. a) Self-equilibrated stress profiles in a finite width plate, normalised by the peak stress and thickness, b) stress intensity factors normalised by the peak value and thickness, for restrained and unrestrained remote boundary conditions. For fracture assessment purposes the significance of shorter length-scale selfequilibrated components of stress depends on the length-scale of the crack, a, compared with the length-scale of the distribution. In this context the most important characteristic length-scale of a self-equilibrated stress distribution is the extent of the tensile zone, wten,

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in the locality of the crack of concern. Practically, this length-scale is often easier to identify than the overall distribution wavelength. The importance of the ratio a/wten is illustrated below using analytical stress intensity factor, K, solutions for cracks in residual stress fields found in the compendium of Tada, Paris and Irwin [6].

Figure 4. a) Cosine residual stress profile with a periodic array of cracks spacing 2S, b) cosine residual stress profile with periodic array of cracks spacing 4S, c) stress intensity factors normalised by the peak value of K and the tensile zone ½-length, wten, for cases a) and b).

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Consider the simple case of a self-equilibrated stress distribution across a finite plate thickness, t, defined by a cosine distribution (see Figure 3a):

§x· ©t ¹

§ 2Sx · ¸ © t ¹

V se ¨ ¸ V 0 cos ¨

(7)

The wavelength of this distribution is w = t, but for surface breaking defects the tensile length-scale of concern is wten = w/4 = t/4. The analytical stress intensity factor solution for an unrestrained plate with this stress distribution is shown in Figure 3b. The stress intensity factor, K, falls below zero for a/t > 0.65 or a/wten > 2.60. However, for the case of a plate with transverse restraint, K falls below zero for a/t > 0.39 or a/wten > 1.56. Another self-equilibrated stress distribution of interest can be derived by considering the superposition of a bending component of stress and a compensating counter-bending cosine distribution of wavelength 2t as shown in Fig. 3a

ª 12 § 2x · § ʌx · º §x· ı se ¨ ¸ ı 0 « 2 ¨1  ¸» ¸  cos ¨ t ʌ © t ¹¼ ¹ © ©t¹ ¬

(8)

The wavelength of this distribution, based on the central region (x/t = 0.12 to 0.88), is w = 0.76t, but for a crack breaking the surface at x = 0, the tensile length-scale of concern is wten = 0.116t. The analytical stress intensity factor solution for an unrestrained plate with this composite stress distribution is shown in Figure 3b. Note that for this shorter wavelength case K falls below zero for a/t > 0.18, that is for a/wten >1.56. The effect of global restraint on K for self-equilibrated stress fields can be further illustrated using analytical solutions cited in [6] for a periodic array of cracks located in cosine distributions of residual stress in an infinite plate (Figure 4a and Figure 4b). K falls to zero at a/wten = 1.56 for the residual stress short wavelength case whereas the longer wavelength stress distribution falls to zero more slowly at a/wten = 2, see Figure 4c. Thus the shorter the wavelength of the residual stress distribution, the more highly restrained are the boundary conditions and the more rapidly K tends to zero with a/wten. Some other forms of self-equilibrating residual stress fields in an infinite plate are illustrated in Figure 5a. The analytical K solutions [6] for these cases are plotted as a function of a/wten in Figure 5b. These stress profiles, by definition, have a long wavelength (approaching infinity). Nonetheless it is seen that K reduces to d 10% of the peak K at a/wten = 2 for all cases. It can be inferred from the above evidence that K becomes insignificant when the depth of a surface breaking crack exceeds about twice the length of the local residual stress tensile zone (a > 2 wten) for self-equilibrating stress fields having a wavelength less than | 0.8 t. Similarly for embedded defects, K becomes insignificant when a/wten > 2 for a wide range of residual stress distributions. Examining the predicted self-equilibrated stress profile in Figure 2 and applying the above criterion implies that cracks longer than about 3.5 mm will be immune to the high order stress fluctuation between x = 2 and 6 mm that has a tensile zone length-scale, wten | 1.75 mm. This type of assessment can be used to judge the shortest wavelength self-equilibrated component of stress that needs to be quantified by measurement or FE prediction.

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1.2 F2 stress distribution F3 stress distribution F4 stress distribution F5 stress distribution

1.0

Normalised Stress

0.8 0.6 0.4 0.2 0.0 -0.2 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

-0.4 -0.6 -0.8 -1.0 x/w ten

(a) 1.2 F2 stress distribution F3 stress distribution F4 stress distribution F5 stress distribution

1.0

Normalised K

0.8 0.6

All Ks < 0.1 for a/w ten > 2

0.4 0.2 0.0 0.0 -0.2 -0.4

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

K <0 for a/w ten > 1.78 a/w ten

(b) Figure 5. a) Self-equilibrated residual stress distributions in an infinite plate normalised by the peak stress and wten , the tensile zone ½-length, b) stress intensity factors for the stress profiles (from [6]). The important conclusions arising from these illustrative examples are: a) It is useful to consider decomposition of the self-equilibrated residual stress distribution, Vse, from eqns 5 and 6, into fundamental (wf | t) and shorter wavelength components (wh d ½ t). b) The length-scale of the residual stress tensile zone, wten, at the crack location is a key parameter. c) For surface breaking cracks, self-equilibrating stress fields having a wavelength less than | 0.8 t can be ignored when surface crack depth, a > 2wten, where wten is the tensile zone length-scale. d) For embedded cracks, self-equilibrating stress fields can be ignored when the embedded crack ½-length of concern, a, is greater than 2wten, where wten is the tensile zone ½-length-scale.

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Crack Length-scale

Engineering fracture mechanics is concerned with the continuum behaviour of structures containing cracks under internal and external applied loads. The minimum length-scale, amin, of such cracks – variously described as macro-cracks, engineering cracks, or structural cracks - is usually at least an order of magnitude greater than the material grain size. This microstructural definition of crack length-scale suggests that, for typical steel components, engineering fracture mechanics is concerned with crack sizes, amin t 0.25 – 2.5 mm. The R6 defect assessment procedure [1] was originally developed by the UK power generation industry to underwrite the structural integrity of steel pressure vessels, pipework systems and welded plant. In these types of structure, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. Metallurgical defects (e.g. porosity and inclusions) associated with the original fabrication procedure are generally not of sufficient size to be of structural concern. However, fabrication defects having a length-scale related to the weld bead depth, for example lack of fusion defects and liquation cracks, are classified as macrocracks where typically amin t 1 – 5 mm depending on the welding process and welding heat input. In engineering practice, R6 fracture analyses are performed to assess crack-like indications found and sized during manufacture or in-service by non-destructive examination (NDE). For example, thread-like surface indications are frequently identified using dye penetrant or magnetic particle inspection techniques. However, volumetric techniques such as eddy current and ultrasonics must be used to identify whether such indications are crack-like, that is whether they have a measurable through-wall extent. For safety-critical or high integrity applications, fitness-for-service structural integrity assessments usually concede the presence in the structure of a crack having dimensions equal to the largest defect that might have been undetected by the inspection technique. Thus amin is related to the inspection technique capability for the material and the structural geometry (thickness). In the nuclear power industry, amin for ultrasonic techniques generally is taken to be 3 mm depth by 30 mm length for ferritic welds, and 5 mm depth by 50 mm long crack for austenitic welds. However, the capability for austenitics may be better depending on the section thickness, proximity of weld metal and access for inspection using different angled probes. Of course, inservice inspections can reveal crack-lengths much longer than these minimum sizes, for example see [7]. Measurement Length-scale

When quantifying detailed weld residual stress distributions (e.g. R6 level 3 profiles) for fracture assessment of defects by embarking on measurement procedures or performing FE weld simulations, it is important to consider the residual length-scales of significance. Clearly one would not expect to reconstruct features in a stress profile having a lengthscale smaller than the spatial resolution (gauge length) of the measurement technique. First the crack minimum length-scale, amin, should be defined based on the structural integrity problem of concern. This length-scale is used to judge the shortest wavelength of the self-equilibrated stress that needs to be quantified, that is wten t 0.5 amin. It is then desirable to estimate the measurement gauge dimensions needed to capture this stress wavelength to a specified precision.

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Consider the simple case of an idealised cosine self-equilibrated stress profile (eqn 7) to be characterised using a residual stress measurement technique that samples evenly over a gauge length, g (i.e. ‘top-hat’ sensor response). The smearing error in the measured value, introduced by using a finite sized gauge length, is determined by evaluating the difference between the mean value and the cosine function point value. This error can be readily expressed as a per cent fraction of the cosine function value at any distance x1 from the surface.

err ( g , x1 ) 100% .

§ 2Sx1 · V o V o cos ¨ ¸ © t ¹ g

³

x1  g 2

x1  g 2

§ 2Sx · cos ¨ ¸ .dx © t ¹

(9)

§ 2Sx1 · V o cos ¨ ¸ © t ¹

There are two cases of particular interest: a) where the influence of the gauge size on the measurement is likely to be greatest, that is when the measurement volume is fully immersed in the component and centred where d 2V / dx 2 is a maximum at the cosine turning point ( dV / dx 0 ) where x1 = t/2, and b) the error in measurements near the peak at the surface (x1 = 0) using a gauge measurement volume that is just fully immersed and centred at x1 = g/2. However, it is of interest to note that, for the cosine stress function assumed, eqn 9 can be simplified to the following error expression that is a function of g alone.

ª t § Sg ·º sin ¨ err ( g ) 100% .«1 ¸» S g © t ¹¼ ¬

(10)

This error function is plotted versus g/t in Figure 6 and is independent of position, x1, through the wall section.

Error function (% peak value)

100 90 80 70 60 50 40 30 20 10 0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

g/t

Figure 6. Error function for a cosine residual stress distribution using a top-hat measurement gauge dimension, g

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It is seen that using a gauge size, g = t/4 (i.e. w/4), can give a 10% error in stress magnitude at any point along the profile. This result demonstrates that the loss in accuracy for near surface measurements is equal to the maximum loss of accuracy (at x1 = t/2) for the cosine distribution considered here. However it should be noted that the effective gauge decreases in size when the gauge is only partially immersed in the sample improving somewhat the error. The above analysis provides a conservative estimate of accuracy because it assumes top-hat sensor response over the gauge length. In practice, neutron and synchrotron diffraction measurement techniques use a diamond shaped gauge volume which means that the extent of the gauge does not sample evenly. Substantially better resolution and accuracy can be achieved for these sampling conditions (i.e. the ‘effective gauge length’ is smaller than the gauge dimensions), especially when measurements are made with significant overlap and advanced deconvolution techniques are used to reduce the smearing effect discussed here [8]. Finally it is worth noting that the measurement length-scale has no influence on the linear membrane and bending components of the stress profile. Nonetheless, there must be sufficient measurement points along the measurement line to define a profile that can be integrated accurately. In summary the main conclusions relating to measurement length-scale are: a) Measurement length-scale is unimportant if linear components of local residual stress, ı m and ı b , alone are required, but there must be enough measurement points along the line to define a profile that can be integrated accurately. b) If the functional form of the local self-equilibrated residual stress field is known or can be estimated, the effective gauge length can be chosen to achieve a defined degree of peak stress accuracy. c) For an idealised measurement technique with a top-hat sensor response, a nominal gauge dimension set equal to ¼ of the stress wavelength can capture the stress peak of a self-equilibrated cosine distribution to within 10%. In practice, where diamond gauge shapes are used, it is usually possible to use larger gauge dimensions, especially if deconvolution procedures are employed to recover some of the amplitude of variation lost by smoothing [8]. Example

The principles developed above can be applied to determine the measurement lengthscales required to quantify the expected bead-on-plate weld self-equilibrated residual stress profile shown in Figure 2. This weld is made from austenitic stainless steel for which it is reasonable to assume an inspection crack depth (i.e. largest defect that might have been missed by ultrasonic inspection) amin = 5 mm. This determines that selfequilibrated components of residual stress having a tensile zone, wten < 2.5 mm can be ignored for fracture assessment purposes. Examining the predicted profile in Figure 2, it is evident that the short wavelength perturbation between region x = 0 – 6 mm can be discounted (wh = 4 mm, wten = 1.75 mm). However, it is important that the measurement procedure is designed to capture the fundamental self-equilibrated profile (wf = 14 mm, wten = 8.5 mm). This can be achieved to an accuracy of within 10%, by choosing a tophat measurement gauge length, g d 3.5 mm (i.e. g d 0.25 wf,). It is of interest to note that a gauge length <1 mm would be required to capture the higher order distribution (wh = 4 mm) for 10% accuracy.

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Conclusions

The self-equilibrated component of stress along a line through a body can be dissociated from the total profile by decomposition using force and moment equilibrium. This component of stress can be decomposed further into a fundamental self-equilibrated distribution having wf d t and higher order distributions with wh d t/2. From a crack driving force perspective, the important length-scale of a self-equilibrated component of residual stress along a line is the size of the tensile zone, wten. The minimum length-scale of a crack, amin, in a welded steel component that is of concern for fracture assessment can be defined in terms of either the microstructural unit (grain size), weld bead depth, or largest size that might be missed by volumetric non-destructive inspection. In fracture assessments self-equilibrating stress fields can be ignored when the tensile zone lengthscale wten < amin/2 for embedded cracks and also for surface breaking cracks when w < | 0.8t. When measuring residual stress profiles suitable gauge dimensions can be chosen to achieve a required degree of peak stress accuracy if the functional form of the selfequilibrated stress field is known or estimated. For example, an idealised top-hat sampling gauge dimension g = w/4 can capture the stress peak of a self-equilibrated cosine distribution to within 10%, although in diffraction measurements where diamond shaped gauges are used, significantly greater sensitivity can be obtained, especially when combined with advanced analysis techniques. The guidelines developed in this paper can be applied to define the residual stress length-scales of concern for fracture assessment purposes and provide a conservative estimate of the measurement gauge dimensions needed to capture the identified residual stress profile to a required accuracy. Acknowledgements

This paper is published with the permission of British Energy Generation Limited. P.J. Withers acknowledges the support of a Royal Society-Wolfson Merit Award. References

1. 2. 3. 4.

5. 6. 7.

R6 Revision 4, Assessment of the Integrity of Structures Containing Defects, British Energy Generation Ltd., Gloucester UK (2004). Bouchard, P. J. and Withers P. J., “The Appropriateness of Residual Stress Length Scales in Structural Integrity”, J Neutron Research, 12(1-3):81-91 (2004). Withers, P. J., Turski, M., Edwards, L., Bouchard, P.J., and Buttle D., “Recent Advances in Residual Stress Measurement”, Sub. to Int J. Pres. Ves. & Piping. Bouchard, P. J., Santisteban, J. R., Edwards, L., Turski, M., Pratihar, S. and Withers, P. J., “Residual Stress Measurements Revealing Weld Bead Start and Stop Effects in Single and Multi-pass Weld-runs”. In: Proc. ASME PVP2005, Denver, Colorado (2005). Dennis, R.J. and Leggatt, N.A., “Optimisation of Weld Modelling Techniques, Beadon-Plate Analysis”, to be presented at ASME PVP2006, Vancouver, July 2006. Tada, H., Paris, P. C. and Irwin, G. R., The Stress Analysis of Cracks Handbook, Third edition, American Society of Mechanical Engineers, New York (2000). Exworthy, L. F., Ellis, B. J. C. and Flewitt, P. E. J., “An Evaluation of the Nature and Origin of Cracking and the Implications for the Repair Strategy”. In: Boiler Shell Weld Repair Sizewell A Nuclear Power Station, I. Mech. E. Seminar Publication 1999-14. Prof. Eng. Publishing, London, pp 9-32 (1999).

176

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Xiong, Y. S. and Withers, P. J., “Statistical Learning Methods for the Reconstruction of Underlying Strain Profiles Measured by Diffraction using Large Sampling Volumes”, Sub. to J Appl. Cryst. (2006).

INTERACTION OF RESIDUAL STRESS WITH MECHANICAL LOADING IN A FERRITIC STEEL A. Mirzaee-Sisan1, M.C. Smith2, C.E. Truman1, and D.J. Smith1 1 Department of Mechanical Engineering University of Bristol, Bristol BS8 1TR 2 Engineering Division, British Energy Generation Ltd Barnett Way, Gloucester, GL4

ABSTRACT The effect of residual stresses generated by load history on fracture has been investigated through experimental and numerical studies. In this paper the application of a “local approach” to determine the change in applied load to cause fracture is described. Then the R6 defect assessment procedure is presented. The effect of tensile residual stress on brittle fracture of ferritic steel type A533B at -150qC is explored. The modified J-integral, Jmod has been also used to estimate the combined crack driving force during loading to fracture of the specimens containing tensile residual stresses ahead of a crack/notch. It is shown that by having more accurate estimates of driving force created by the residual stresses leads to increased agreement between experiments and assessment. Introduction In the context of structural integrity if a part of component had an initial elastic residual stress field of and is subjected to an in-service load the driving force on the structure would be the sum of the residual stress and the service stress. By adding a tensile residual stress to an in-service load, the part can be locally overloaded and there would be risk of failure. Residual stresses can be generated in a component in different stages of life of the component, i.e manufacturing, processing or assembly. Failure assessment of welded structures has been given more interest because of vulnerability of weldments to cracks. A review of the treatment of residual stresses in the defect assessment of welded structures has been discussed by Budden and Sharples [1]. The purpose of the work presented in this paper is to understand and quantify interactions between residual stresses and fracture. A series of fracture tests were carried to study the effect of combined residual stress and additional primary load on brittle fracture. The R6 defect assessment procedure was used to assess the experimental data, and the assessment predictions were compared both with test data and with the results of non-linear cracked body analyses using the modified J-integral, Jmod. Materials and Experiments The material used in this study was A533B low alloy steel plate in the form of two blocks with dimensions of 520 × 230 × 230 mm. The transition fracture toughness behaviour of this plate material has been extensively characterised in a number of studies (eg [2]). Of particular significance in this A533B material was the presence of a banded area in the

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middle of the plate. The banded area was an indication of regions of higher carbon equivalent. The area was a preferential site for both carbide precipitation and formation of non-metallic inclusions. Modified single edge notched bend, SEN(B), specimens were extracted in such way that the crack tips of the A533B specimens were located at the middle of the plates. The test temperatures were chosen to be -150qC and the mechanical properties at the test temperature was obtained by extrapolation from higher temperatures. The extrapolation was conducted in two steps: 1) Fitting a quadratic temperature variation to the available yield data 2) Shifting an available stress-strain curve, e.g. the -90qC stress-strain curve by o Vy-150 - Vy-90 to establish the stress-strain curve at -150 C In-plane loading was applied to the A533B-AEA modified SEN(B) specimens using a procedure similar to that developed by Cotton [3]. Initially the specimens had a machined notch of 12.5 mm depth at mid length, with two ‘V’ grooved notches at the ends of the specimens. A sharp notch of width 0.1 mm and depth 2.5 mm was then introduced at the root of the machined notch using electro discharge machining (EDM) in eight specimens to achieve a crack length, a, of 15 mm. These specimens were then tested to establish the baseline fracture behaviour in the absence of residual stresses. In the remaining five specimens the EDM notch was introduced after a residual stress field had been generated in the specimens by in-plane loading. A schematic of the loading is shown in Fig. 1. A compressive load of 73 kN was applied at room temperature and then the specimen was unloaded. The design and loading of the specimens was such that the bending moment and compressive load produced permanent local deformation at the notch. Consequently, a tensile residual stress field was created at the notch tip in each specimen on unloading. After introducing the EDM notch the specimens were cooled to -150qC and loaded to fracture. The complete loading cycle is abbreviated to CUCF, corresponding to Compression (in-plane loading)-UnloadCooling-load to Fracture.

Figure 1 Schematic of modified single edge notch bend, SEN(B), specimen and in-plane loading (dimensions in mm) Figure 2 shows the experimental results for the A533B modified SEN(B) specimens at 150qC. The results are plotted in terms of apparent fracture toughness (peak applied

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primary stress intensity factor) against failure probability, for EDM-notched SEN(B) specimens in the as-received (AR) condition, and containing a residual stress field. The probability of failure for the experimental results is based on the following estimate [4], Pf = (i-0.5)/N

(1)

where N represents the sample size and i the order number. The statistical distribution of the experimental results demonstrates that the average apparent fracture toughness of the specimens reduces by approximately 40 % in the presence of residual stress. 1.0

Probability of failure,%

0.8

0.6

0.4

AR CUCF Calibrated (Ko=73.57, Kmin=31) Shifted (AR-Kres) Predicted based on KJmod

0.2

0.0 0

20

40

60

80

100

120

KI-MPa.m0.5

Figure 2. Probability of failure of A533B fracture tests at -150ºC, with predicted probability based on Kres and Jmod Finite Element Analysis In-plane loading was modelled using two different parts defined in ABAQUS/CAE [5], one representing a SEN(B) specimen and the other representing a loading fixture as a rigid body. Too many small elements were required to simulate the contact in the ‘V’ shape loading fixture and ‘V’ shaped groove and therefore the ‘V’ grooved notches in the specimens and ‘V’ shape wedges as loading fixtures were not modelled. This assumption made it possible to reduce the number of elements required for the simulation substantially. A cylindrical rigid body was the loading fixture. A three dimensional 8-noded linear brick element, C3D8R, with reduced integration was used for the SEN(B) model. Due to the existence of two planes of symmetry, only a quarter of the SEN(B) was modelled. Elastic-plastic material behaviour with isotropic hardening was used during in-plane loading and unloading, except for an area close to the longitudinal edge of the specimen where the material was considered elastic since the stress field in this region was not in our interest. This assumption did not affect the notch tip stresses and allowed a substantial reduction in the number of elements required.

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1600 After In-plane loading, Unloading

Normal stress to notch, MPa

1400 1200

Introducing crack by changing boundary condition Introducing notch by removing elements

1000

Introducing notch by removing elements and submodelling

800 600 400 200 0 -200 -400 0

5

10

15

20

25

30

35

Distance from notch root, mm Figure 3. Residual stress distribution after in-plane loadingand introducing a crack The simulation of in-plane loading consisted of a cycle of compression by in-plane loading, unloading and the introduction of a notch, cooling and finally loading to fracture, CUCF. The simulation was carried out in five different steps. The first step modelled the compression of a modified SEN(B) containing a shallow notch and loading the specimen in the axial direction to 73 kN, using room temperature material properties for the A533B steel. The second step consisted of removing the applied load. To validate the finite element simulation of the in-plane loading procedure, a strain gauge was attached in the longitudinal axis of a SEN(B) specimen. The variation of longitudinal strain was recorded and compared with numerical results in compression and unloading steps and excellent agreement found. As explained earlier a sharp notch of length 2.5 mm was introduced at the notch root using the EDM process in order to determine the fracture toughness of the specimens at low temperature. Introducing a sharp notch was simulated in the following step after generating a residual stress field. Different approaches were followed for introducing a sharp notch: 1. Changing the boundary condition at the symmetry plane 2. Removing elements with thickness of 0.1 mm using a) a quarter model and b) a quarter model in conjunction with sub modelling technique. Figure 2 clearly demonstrates a tensile residual stress field created at the notch tip of the modified SEN(B) after compression and unloading. Following the introduction of the 2.5 mm sharp notch the stresses at the notch tip increases by a factor of two. There is no significant difference between introducing a sharp notch by changing the boundary condition or by removing element in this problem. The refinement of the mesh used in submodelling at the notch tip also did not alter the magnitude of the stresses. The final step of the CUCF cycle was applied using three point bending in order to fracture the specimen. This was modelled by introducing another cylindrical rigid body, positioned on the top surface of the SEN(B). The specimen was subjected to three-point bending by applying a displacement on the top rigid body.

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The predicted stresses from the final loading were used to determine the probability of failure using a “local approach” analysis. The details of this are described elsewhere [6]. The general scheme in failure prediction using the modified local approach is that the Weibull parameters in the Beremin [7] type model, calibrated to the as-received data, should predict the failure following complex interaction of residual and applied stresses. Their calibration to the as-received results is shown in Figure 4. To estimate probability of fracture a routine was performed via post-processing the results from the finite element simulation at final stage of loading to fracture. The results from the analysis are shown in Figure 4, and demonstrate that for the same failure probability lower values of fracture toughness were obtained. 1.0

Probability of failure- %

0.8

0.6 Calibrated parameters, 3 Vo=0.01 mm , m=4

0.4

Vu=10GPa,Vmin=2.85GPa AR CUCF FE-AR, Calibrated FE-CUCF, Predicted

0.2

0.0 0

20

40

60

80

100

120

KI- MPa.m0.5 Figure 4 Comparison of probability of failure local approach prediction with experiments

Assessments Using R6 Procedure The R6 defect assessment procedure was used to assess the experimental data [8]. An integrity assessment of a structure considers all sources of loading which may increase the risk of failure. The loads acting on a structure may be categorised as primary or secondary [9]. Primary loads are those that contribute to plastic collapse, while secondary loads do not. Stresses due to mechanical loading such as pressure, applied forces, self-weight, or long–range structural constraint are categorised as primary loads. Stresses due to temperature variation or short and medium range welding residual stresses are often considered as secondary stresses. Both primary and secondary loads contribute to crack-tip fracture [9]. Primary Load Alone: R6 assesses proximity to failure in a structure using two parameters, Kr and Lr. Kr is a measure of proximity to fracture and Lr is a measure of proximity to plastic collapse. For primary load alone, K r and Lr are defined by: Kr

K Ip K mat

(2)

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Papplied

Lr

(3)

PLimit

where K Ip is the linear elastic stress intensity factor due to the applied primary loads, Papplied is the applied primary load, K mat , is the material fracture toughness, and Plim it is the perfectly plastic limit load of the structure. In this study the only primary load is that applied by the test machine. K Ip and limit load were calculated using standard solutions for SEN(B) specimens. Assessment points (Lr, Kr) are plotted on the failure assessment diagram. Failure is predicted to occur when assessment points are on or outside the failure assessment line, defined by: Kr f ( Lr )

f ( Lr ) for Lr  Lr max 0 for Lr !Lr max

(4)

Lr max is the collapse cut-off of the failure assessment line. It depends on the 0.2% proof

stress,

V y , and ultimate strength, ̣ V u , and is defined as : Lr max

§ V y  Vu · ¨ ¸ ¨ ¸ 2 © ¹

(5)

Vy

The function f ( Lr ) can be estimated using three different options [8], with decreasing levels of conservatism. The Option 1 or general failure assessment diagram may be used for materials without discontinuous yielding, and is described by: f1( Lr )

[1  0.5Lr 2 ]1 / 2 [0.3  0.7 exp(0.6Lr 6 )]

(6)

If detailed uniaxial stress-strain data for the material are available then an Option 2, material-specific failure assessment diagram may be defined by: f 2 ( Lr )

ª EH ref Lr 3V y «  « LrV y 2 EH ref ¬

º » » ¼

1 / 2

.

(7)

V y are the Young’s modulus and 0.2 % proof stress respectively and H ref is the true strain at a true stress LrV y . where E and

An Option 3, material- and geometry-specific failure assessment diagram may be derived using the results of a non-linear cracked body analysis, using the relationship: f 3 ( Lr )

(Je / J )

(8)

where Je and J are the elastic and elastic-plastic values of the J-integral at a given Lr. Both Option 1 and Option 2 failure assessment diagrams were constructed for A533B, the latter using the inferred stress-strain curve for -150ºC. The two diagrams differ little

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for Lr<0.6. Since the region of interest for the A533B tests lies below Lr=0.6, subsequent assessments of these tests all use the Option 1 failure assessment diagram.

Kr and Lr were calculated at -170ºC and -150ºC using equations (2) and (3). The fracture toughness, K mat , was chosen as the average of the experimental elastic stress intensity factor at failure for each test and specimen type. The limit loads for the SEN(B) specimens with an EDM notch or a fatigue pre-crack were assumed to be identical. The resulting (Lr, Kr) points are plotted on the Option 1 failure assessment diagram in Figure 5, which shows that the assessment points for the tests lie both inside and outside the R6 diagram, with the mean (Lr, Kr) at failure close to the failure assessment line. This is as expected for R6 used as a best estimate failure prediction tool.

Combined Primary and Secondary Loads: Under these conditions, from:

Kr

K Ip Ks  I U K mat Kmat

K r is calculated (9)

s

where K I is the elastic stress intensity factor due to the secondary loads, and ȡ is a factor covering interactions. The other parameters remain unchanged R6 also gives an alternative but equivalent definition of Kr as Kr

( K 1p  VK1s ) / K mat

(10)

where the factor V now covers interactions. The two definitions are based on the same underlying approach, with the V approach introduced more recently. Two methods are given in R6 for evaluation of U or V as described below. The calculation of V is described first, since its formulation makes it easier to separate the different effects of plasticity on secondary crack driving force. R6 of course contains equivalent approaches for calculation of U. The U-based approaches were used in the assessments.

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F(Lr) Option-1

1.6

AR

1.4

Simple

1.2

Detailed-(KIS-FOP)

Kr

1

Detailed-(KJS=KIS) Detailed-(KJ=KJmod)

0.8

KJ=KJmod-(No rho factor)

0.6 AVG-CUCF-Exp AVG exp (CUCF)

0.4 0.2 0 0

0.2

0.4

0.6

0.8

1

1.2

1.4

Lr

Figure 5 FAD curves for A533B at -150qC under pure primary load and combined primary and secondary stresses introduced by in-plane loading The tests for CUCF conditions were chosen to explore the interaction between primary and residual stress. This set of experiments was chosen because the residual stress field showed little through-thickness variation. This allowed the evaluation of the secondary stress intensity factor, K Is s using two dimensional finite element models. Two different routes were used: (i) a simplified analysis using a elastic cracked body analysis where only elastic calculations of K1s are needed and (ii) a detailed procedure to calculate an effective stress intensity factor or crack driving force, K Js , for the secondary loading alone in this case using the modified J-integral, Jmod [10] The Jmod routine can only evaluate 2D-dimensional problems. The R6 simplified procedure is straightforward to apply to combined residual stress and primary load, provided that it is possible to make an estimate of K Is . In this study K Is was calculated using finite element analysis. The residual stress normal to the crack plane were extracted from the uncracked body residual stress simulations, and K Is was calculated by applying these stresses as crack face pressure loading in an elastic cracked body analysis. K Is was estimated to be 45.9 MPa.m0.5. Given an estimate of K Is , ȡ follows from formulae given in [8].

In the application of the detailed procedure there are again two parts: evaluation of followed by evaluation of ȡ. Of the three routes offered to evaluate applicable to a weld residual stress field: an evaluation of body analysis and evaluation of

K Js ,

K Js , only two are

K Js from a non-linear cracked

K Js by applying a first order plasticity correction to K Is .

Residual Stress with Mechanical Loading in a Ferritic Steel

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Four R6 assessments of the combined loading tests were performed: (i) using the simplified calculation of U, (ii) applying a first order plasticity correction to K Is in order to estimate K Js .(iii) calculating K Js using the modified J-integral Jmod and (iv) calculating KJ for combined loading directly using Jmod. The details of the Jmod are presented by Mirzaee-Sisan etal [11] In all cases Kmat was taken to be the average elastic stress intensity factor at failure for the as-received spark-eroded SEN(B) specimens tested at -150qC. The resulting (Lr, Kr) points are plotted on the Option 1 failure assessment diagram in Figure 5, which shows that all the combined loading assessments are conservative, with the predicted failure load (indexed via Lr) lower than the mean achieved failure load. Also all the combined loading assessments are more conservative than the assessment for as-received specimens with no residual stresses. Finally, the conservatism of the combined loading assessments falls as more sophisticated routes are used to estimate Kr.

Probability of Failure The scatter of cleavage fracture toughness data can be described by fitting a curve to the actual fracture toughness data. Then further load history effects can be determined from this calibration curve. A probability model based on experimental toughness data is used to describe the distribution of cleavage toughness in (AR) and following in-plane loading.

Pf

ª § KK min 1  exp« ¨¨ «¬ © K 0  K min

· ¸¸ ¹

4

º » »¼

(11)

The fitting parameters were Kmin and Ko in equation 11, obtained by calibrating equation 11 to predict the as-received toughness and were The calibrated parameters were found to be Kmin=73.57, K0= 31 MPa.m0.5. The probability of failure of CUCF data, by replacing K

by K mod , where K mod is the crack driving force calculated by the Jmod routine at

different level of primary loads. Then the Jmod routine was applied to find J s  p during reloading to fracture and converted to K mod

EJ mod /(1  Q 2 ) . The probability of failure in

presence of residual stresses was calculated using equation 11 with the same calibrated parameters as explained earlier. Figure 2 illustrates the predictions and compares them to the experimental results obtained. Good agreement was observed between the experiments and prediction. Another approach to predicting the effect of in-plane loading is to shift the fitted curve to AR data by magnitude of

K Js at zero primary load. Figure 2 compares both predictions.

The difference between two predictions increases with increasing primary load. Shifting the AR curve implies that the effect of secondary stresses K Js is constant during loading to fracture while Jmod shows that the effect of secondary load decrease as primary load increases.

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Discussion and Concluding Remarks The combined loading assessments still retain more pessimism than those for the asreceived specimens with no residual stress, even if the crack driving force is calculated explicitly using Jmod. There are a number of possible reasons for this: x

The residual stresses may have been over-estimated by the FE models. However, there are no confirmatory residual stress measurements for the preloaded specimens, and the predicted residual stress field obviously depends on both the assumed material yield strength and the hardening behaviour (kinematic or isotropic hardening). Isotropic hardening was assumed, here, based upon previous studies of pre-compressed notched specimens which concluded that this hardening model gave the most accurate predictions [12].

x

The intrinsic scatter in transition fracture toughness. Only five combined load specimens were tested, which may be insufficient to accurately define the mean apparent toughness.

x

Jmod evaluated for a simultaneously opened crack may be an underestimate of the crack driving force for a crack that opens progressively to its tip [13]. The final 2.5 mm of the crack was inserted progressively using EDM. This may have affected the crack driving force, since the crack resides in a region of high tensile stress, and some plastic energy dissipation may have occurred during EDM machining.

x

The mechanical pre-strain cycle may possibly have affected the population of cleavage initiation sites ahead of the notch, and so changed the baseline fracture toughness.

x

Notwithstanding these uncertainties, it is clear that moving to a more accurate estimate of the secondary crack driving force and its interaction with primary loads leads to considerably reduced pessimism in the R6 assessments.

Acknowledgments The work reported in this paper was supported through ENPOWER (Management of Nuclear Plant by Optimising Repair Welds), a three-year collaborative research project that started in December 2001, co-funded by the European Commission Nuclear Fission Safety Programme (5th Framework) and the project partners, Mitsui Babcock, University of Bristol, Institut de Soudure, JRC Petten, Framatome-ANP, Usinor Industeel, and British Energy. References [1] Budden, P. J. and Sharples, J. K. (2003) Comprehensive structural Integrity, 7.07, Elsevier Ltd. [2] T. Ingham, N. Knee, I. Milne and E. Morland, Fracture toughness in the transition regime for A533B-1 steel: Prediction of large specimen results from specimen tests, Risley Nuclear Power Development Laboratories, ND-R-1354(R), July1987. [3] C. Cotton, A candidate test-piece to investigate creep crack growth in a residual stress field, M.Sc. Thesis, University of Sheffield, UK. 1997. [4] Khalili, A. and Kromp K., “Statistical properties of Weibull estimators,” J. Mat. Sci, 26, pp. 6741-6752. 1991.

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[5] ABAQUS Users Manuals, Hibbit, Karlsson and Sorenson Inc., HKS Inc., 1080 Main Street, Pawtucket, RI 02680-4847, USA. (2002) [6] Mirzaee-Sisan, A., Mahmoudi, A-H, Truman, C.E. and Smith, D.J. “Application of the local approach to predict load history effects in ferritic steels”, Proceedings of Pressure Vessels and Piping Conference , paper 71706, 2005 [7] Beremin, F.M. A local criterion for cleavage fracture of a nuclear pressure vessel steel, J. Met. Trans., 14A, 2277-2287, 1983 [8] R6, Revision 4: Assessment of the Integrity of Structures containing Defects, British Energy Generation Ltd, September 2000. [9] P.J. Budden and J.K. Sharples, Comprehensive structural Integrity, 7.07, pp.245-287, Edited by R.A. Ainsworth, K. –H. Schwalbe, Elsevier Ltd. 2003. [10] Y. Lei, ENPOWER Task 7.2: The Crack driving force for cases Non-monotonic loading, British Energy Report E/REP/BDBB/0034/GEN/03, Revision 00, December 2003. [11] Mirzaee-Sisan, A., Truman, C.E., Smith D.J. and Smith, M.C., “ENPOWER WP7.4: Effect of residual stress load-history on fracture”, British Energy Report E/REP/BDBB/0077/GEN/05, Decemeber 2005 [12] M.R. Goldthorpe,ENPOWER WP7 Task 7.3-B: Comparison of estimates of crack driving force for defects in a plate slit-weld, E/REP/ATEC/0061/GEN/05. [13] M.Turski High temperature creep cavitation cracking under the action of residual stress in 316H stainless steel. University of Manchester, Manchester, UK.2004.

EFFECTS OF RESIDUAL STRESSES ON CRACK GROWTH IN ALUMINUM ALLOYS B. Kumar† † National Institute of Aviation Research, Wichita State University Wichita State University Wichita, KS 67260 USA ABSTRACT It is well known that mechanical surface treatments such as shot peening can significantly improve the fatigue behavior of highly stressed metallic components. This increase in fatigue and corrosion performance occurs because of the thin layer of residual stresses created by the shot peening process. Literature [1, 2 & 3] is replete with information on the increase in fatigue life with peening but there is little information in open literature on the crack initiation and growth in the shot peened materials. The measurement of fatigue crack growth through this layer of compressive stress field which is less than 0.01” (~ 0.6mm) thick is a challenge. The present study highlights the attempts to detect crack initiation and measure crack growth in the heavily deformed surface layers, using several measurement techniques of the following aluminum alloys: 7050-T7451 & 7075-T7351. To produce specimens with short cracks several specimen geometries proposed by Suresh & Ritchie [3] were prospected and after several tests it was found that the hourglass coupon with a scratch, the Eccentrically Loaded Single Edge Notched Coupons ESE(T) coupons and the double edge notch coupons DENT(T) similar to the one used by Everett et al [4] would be most appropriate. Several measurement techniques were used in order to detect crack initiation in the hourglass coupons. It was found that the ACPD and eddy current methods were more reliable than the non-contact surface measurement techniques used. The ESE(T) coupons were used to determine the effects of shot peening on crack growth rates, and the results indicate that the effects of peening did not sufficiently retard crack growth for the specimen geometry chosen. Currently work is being conducted to fabricate specimens such that the initial crack is fully embedded in a zone of compressive stresses using the DENT(T) specimen geometry. Understanding the influence of compressive residual stresses and how it affects the fracture mode is central to any investigation on how it may be utilized to improve fatigue resistance of the material. Thus, quantifying and measurement of the residual stress field was also conducted to help better understand its influence on crack growth. Introduction The safe life approach for design and life cycle management of rotorcraft structures subjected to fatigue cycling incorporate safety factors to guard against fatigue failures during service. The components as a result are retired after a finite service life based on statistical crack initiation criterion, leading to pre-mature retirement of components. The damage tolerant methodology is currently being strongly advocated for the rotorcraft structures since the main cause of typical failures are related to fatigue cracking. Rotorcraft structures/components undergo some form of surface treatment such as shot peening to improve fatigue & corrosion resistance. The improvement in fatigue life occurs due to the shallow layer of compressive residual stresses that are generated near

189 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 189–200. © 2006 Springer.

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the surface. This layer of the compressive stress helps in retarding crack growth in cases of tensile fatigue loading. The determination of crack growth rate for the aluminum alloys in the residual stress layer is important to not only to accurately predict the life of the components but to also better understand the effects of the shallow layer of residual stresses on fatigue crack initiation and crack growth rates. There have been numerous studies on the effect of shot peening and how it affects fatigue life, but there is a growing need to determine the crack growth interaction with residual compressive stresses. This investigation is a part of the research effort being conducted as a part of the FAA RotorCraft Damage Tolerance (RCDT) program. The investigation of short fatigue cracks in metals has been a subject of considerable interest during the past decade, however very few studies have been dedicated to the problem of short crack growth in shot peened material [2, 4 & 5]. One of the reasons is the difficulty in monitoring a short crack in the heavily deformed surface layer. During the course of the investigation the fatigue crack growth characteristics of short cracks and their interaction with the residual stress field were investigated. The determination of crack growth rates, where initiation could be subsurface is a challenging problem. Therefore several measurements techniques were used in an attempt to detect crack initiation. The objective of this research effort was to obtain a measure of the improvement in fatigue endurance in the shot peened material by detecting crack initiation and crack growth through the heavily deformed surface layers. Material The two materials being used for this study were both Aluminum alloys: Al 7050-T7451 & Al7075-T7351. Table 1 provides the chemical composition (wt %) of the two alloys. Table 1: Aluminum 7050 and 7075 – Composition Eleme nts Al 7050 Al 7075

Si

Fe

Cu

Mn

Mg

Cr

Zn

Ti

Ni

Zr

Pb

B

0.1 2 0.0 8

0.1 5 0.1 5

2.6

0.1 0 0.0 2

2.6

0.0 4 0.1 9

6.7

0.0 6 0.0 38

0.0 4 0.0 1

0.1 5 0.0 1

-na-

-na-

0.0 01

0.00 1

1.6 6

2.4 9

5.8 2

Specimen types The specimens that were used to evaluate the effect of shot peening on the fatigue endurance are the hourglass shaped with KT =1.0, and the eccentrically loaded single edge (ESE(T)) specimen shown in figures 1 & 2. The KT = 1. 0 specimens had a minimum width of 1.0 inch (25.4 mm) and gage section of 3.30 inches (84 mm). The specimens had a scratch along the width at the center of the specimen. The scratch on the specimen surface was made using a knife edge in a specially designed fixture. The average depth of the scratch on first batch of specimens was 0.010 inches (0.25 mm). The ESE(T) coupons were 3.00 inch (76.2 mm) wide and 0.25 inch ( 6.35 mm) thick.

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The fatigue tests were conducted on MTS servo-hydraulic test frames of 22 Kip capacity. The maximum stress was 45 Ksi and a stress ratio R = 0.50 at a frequency of 2 Hz was used for the hourglass coupons. To detect crack initiation/propagation the tests were stopped at several intervals and measurements made using the following instruments: Aramis™ photogrammetry system, Istra™ ESPI system, Eddy current inspections, Visual measurement, Laser Extensometer and the Alternating Current Potential Drop method (ACPD). The ESE(T) coupons were tested in separate batches, since some of them were precracked to a length of approximately 0.10” and then shot peened, while, others were shot peened without pre-cracking. The ESE(T) specimens were shot peened on the surface only and the hourglass specimens were peened everywhere except the gripping region. The shot peening intensity used for both the hourglass coupons and the ESE(T) coupons was the same as at 0.077 ~ 0.079 Almen scale. Cast steel shots with 230R or 0.0230 inch (0.58 mm) diameter. The coverage was 100 and 200% for the hourglass coupons and 100% coverage for the ESE(T) coupons. Aramis™ and ISTRA™ Testing The fundamental principle of Aramis™ is based on the fact that the distribution of the gray scale of a rectangular area in the undeformed state corresponds to the distribution of gray scale values of the same area in the deformed state and ISTRA program was developed for the control of ESPI-sensors and for the evaluation of speckle interferograms. During the test the region around the notch as shown in figure 1 was

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monitored. Static measurements were conducted by loading the specimen to the maximum load of the fatigue cycle were conducted and measurements made using both the systems. This was done at several intervals including the first one at zero cycles (reference condition), and then after 18x103, 20 x103, 21 x103, 22 x103, 23 x103, 24 x103, 3 3 3 25 x10 , 26 x10 and 27 x10 cycles till failure. The Y-strain (loading direction) through the width of the specimen was evaluated at every interval. It should be noted that the specimens are shot peened so the strain values correspond to the load applied, implying zero strain at zero load. It does not account for the residual strains that were present on the surface of the specimen. The results of Istra measurement at several intervals for one specimen are shown in figure 3. The plots show the strains around the notch measured through the width of the specimen. The higher strains near the edges are due to crack initiation and growth at those locations. 6.00

5

Y- Strain

4.00

3 Initial Test 20,000 cycles 22,000 cycles 24,000 cycles 25,000 cycles 26,000 cycles 27,000 cycles

2.00

1

0.00 -5

0

5

10 Notch Length

15

20

25

Figure 3 : Y- strain at the scratch measured by Istra equipment Compliance, Visual and Eddy Current Probe Measurement The following three methods were also used to determine crack initiation and growth: compliance change, visual measurement and eddy current method. The compliance measurements were made using a laser extensometer. The scratch opening displacement at the center of the coupon was monitored. The two edges of the hourglass coupons were monitored using an optical microscope capable of 160X magnification. The crack growth along the width (inside the notch) was difficult to monitor. The crack length was over 0.010” before it could be observed. The eddy current hand held probe was used to determine the crack initiation in the hourglass coupons. The specimens were inspected before being installed in test frame they were then again inspected after being loaded to the maximum load of the fatigue cycle, and further inspections were carried out every 2,000 cycles till a crack was detected. A comparison of the measurement equipment on detecting crack initiation and growth are provided is provided in figure 4. The cycles to initiation detection and cycles for the

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propagation are shown in the figure along with the percentage of the total life spent in the initiation stage.

Figure 4: Comparison measurement techniques used to determine crack initiation in the hourglass coupons Fatigue crack growth testing The ESE(T) coupons were tested in three batches for both the 7050 and 7075 alloys. The batches were: (a) unpeened specimens (b) pre-cracked specimens with crack lengths approximately 0.10” inches (2.54 mm), which were then shot peened and (c) shot-peened without pre-cracking. For the pre-cracked specimens initial testing was conducted at a stress ratio R of 0.1 and stress intensity less than 7.8 Ksi-in½. The specimens were then removed and sent for shot peening region around the notches as shown in figure 2 was shot peened for 100% coverage of the peened area. The results of the testing are shown in figures 5 through 12. Figures 5 through 8 present the results of the Al 7050-T7451 and Figures 9 through 12 of Al 7075-T7351. Figure 5 and 9 show the complete data of the three batches of Al 7050 and 7075 materials. Figures 6 and 10 compare the results of the pristine material with the pre-cracked and shot peened specimens for both alloys. Figures 7 and 11 compare the pristine and un-cracked and shot peened specimens again for the two alloys. Finally figures 8 and 12 show the results of the pre-cracked and un-cracked shot peened specimens for Al 7050 and Al 7075 alloys.

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Da_Dn Vs. Delta K 1.00E-03

1.00E-04

Da/Dn

1.00E-05

Filled symbol-show indicate the pristine and unpeened specimens The rest are results of shot peened specimens both pre-cracked and uncracked

1.00E-06

1.00E-07

1.00E-08 1.00

10.00

100.00

Delta K Ksi-in1/2

Figure 5: The results of the Al 7050-T7451 full data.

Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2

Figure 6: Comparison of the pristine with the pre-cracked shot peened Al 7050 The results indicate that the effects of the shot peening the surface had minimal effect on the crack growth for both alloys, in the range of the ¨K and da/dN tested. Crack length measurement of the un-cracked shot peened specimens while the crack is very small was extremely difficult and unreliable, the data presented here only represents the region were accurate crack length measurements could be made. Also the pre-cracked specimens has crack lengths were greater than 0.10” (2.54 mm) which is much greater than the residual stress zone depth. Further only the surfaces and not the edges which were shot peened. It was also noted that none of the specimens showed any signs of crack tunneling.

Effects of Residual Stresses in Aluminum Alloys

Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2 7050-E

7050-04

7050-07

7050-08

Figure 7: Comparison of the pristine with the un-cracked shot peened Al 7050 Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2

Figure 8: Comparison of the pre-cracked and un-cracked shot peened Al 7050 Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

Filled symbol-show indicate the pristine and unpeened specimens The rest are results of shot peened specimens both pre-cracked and uncracked 1.00E-06

1.00E-07 1.00

10.00

Delta K Ksi-in1/2

Figure 9: The results of the Al 7075-T7351 full data

100.00

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Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2

Figure 10: Comparison of the pristine with the pre-cracked shot peened Al 7075. Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2

Figure 11: Comparison of the pristine with the un-cracked shot peened Al 7075 Da_Dn Vs. Delta K 1.00E-03

Da/Dn

1.00E-04

1.00E-05

1.00E-06

1.00E-07 1.00

10.00

100.00

Delta K Ksi-in1/2

. Figure 12: Comparison of the pre-cracked and un-cracked shot peened Al 7075.

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Fractographic Measurements Detailed fractographic investigation was carried out though here only the results of the fatigue crack length and the associated area of the fatigue cracks are presented. The area measurements of Al 7075 T-7351 specimens and Al 7050 T-7451 are provided in table 4. The results of the detailed fractographic study currently underway will be published separately. The fatigue area and the crack lengths of the fractured specimens were determined from the SEM micrographs of the fracture surfaces. Low magnification images of the entire fracture surface of the specimens were examined at 18 to 23X. These images were then ® montaged as shown in Figure 13. The images were then analyzed using AnalySIS software and the required measurements obtained the results are presented in table 4.

Figure 13: Montage image of the fracture surface Table 4: Fatigue crack length and area for the 7075 specimens Al Alloys Average Average Average Average Al 7075-T7351 Fatigue Area Crack Length Crack Length Cycles to [in2] Edge I [in] Edge II [in] failure 100% 23,000 0.0741 0.1856 0.1167 coverage 200% 28,154 0.0692 0.1797 0.1087 coverage Al 7050-T7451 100% coverage 200% coverage

28,925

0.0855

0.2025

0.1423

24,614

0.0775

0.2132

0.1047

Residual Stress Measurements To determine the influence of the residual stresses on the fatigue crack growth of the shot peened aluminum alloys it is necessary to determine the residual stress profile versus depth. Therefore the measurement of the residual stress was carried out on Al 7050-T7451 alloys with 100% and 200% coverage. The measurements were made using the X-ray diffraction technique. The vertical error bars indicate the variation in the values from different samples. The errors involved with the measurements are not included. Conclusions The measurement of small crack growth through the thin layer of residual stresses, in the shot peened materials presents a formidable challenge. The research effort has focused on several surface measurement methods, the non-contact methods such as ESPI™ and Aramis™ are of limited use as they are expensive and time exhaustive. The

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compliance method used by Sharpe et al [6] utilized a laser based interferometric strain/displacement gage to monitor small crack growth displacement gages of very high resolution which provided a compliance measurement to determine small crack growth in titanium alloys. The displacement gage used during this investigation was the laser extensometer and the resolution was not high enough to determine small changes in the CMOD, thereby limiting the use of the compliance method to determine crack growth using the currently available equipment. Table 6. Residual stress along depth in 100 and 200% peened Al 7050 T-7451 Residual Stress Ksi (std. dev) Residual Stress Ksi (std. dev) Depth in 100% coverage 200% coverage 0.0000 -31.95 ± 4.89 -38.60 ± 1.0 0.0010

-41.19 ± 1.80

-47.55 ± 1.5

0.0020

-50.48

-49.40 ± 2.1

0.0030

-48.52 ± 3.07

0.0040

-52.94

0.0060

-29.75 ± 5.44

0.0070 0.0100

-4.52 ± 1.72

0.001

0.003

0.005

-46.20 ± 4.0 -18.70 ± 3.6 -5.00 ± 3.5

0.007

0.009

0.011

0.013

0.015

0

Residual Stress [Ksi]

-10

-20

-30

-40

-50

Scratch Depth Initial specimens

-60

100% Coverage 200% Coverage

-70

0

0.002

0.004

0.006 0.008 Depth [in]

0.01

0.012

0.014

Figure 14: Residual stress profile in the 100% and 200% peened Al 7050-T7451 alloy

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Table 6. Residual stress along depth in 100 and 200% peened Al 7050 T-7451 Residual Stress Ksi (std. dev) Residual Stress Ksi (std. dev) Depth in 100% coverage 200% coverage 0.0000 -31.95 ± 4.89 -38.60 ± 1.0 0.0010

-41.19 ± 1.80

-47.55 ± 1.5

0.0020

-50.48

-49.40 ± 2.1

0.0030

-48.52 ± 3.07

0.0040

-52.94

0.0060

-29.75 ± 5.44

0.0070 0.0100

-4.52 ± 1.72

-46.20 ± 4.0 -18.70 ± 3.6 -5.00 ± 3.5

Though the Istra and Aramis provided detailed information about the displacement field around the notch they are unable to provide sufficient resolution at the notches to determine very small changes in crack length. The usefulness of these methods is limited, especially in the hourglass coupons where the crack growth is the thickness direction (S-L) making it difficult to monitor the crack from the front. The ACPD technique to measure small crack growth has been used by several researchers (8, 9 & 10). In the current research the probe used was a handheld one requiring periodic stopping of the test to make measurements and sliding the probe along the width of the specimen the method was successful in detecting crack initiation. The technique would be better used if the ACPD probes are fixed on the specimen. For the Aluminum material this requires ultrasonic welding (9). Further work using ACPD and a different gage is currently underway. The results of the testing of the ESE(T) specimens show that there was little if any difference on crack growth rates (for the range of testing) of both the Al 7050 and 7075 alloys. Specimens with no pre-cracks showed little difference between the unpeened and peened materials. One of the reasons was it was difficult to measure crack initiation on these specimens. Once the crack was measurable crack length was already greater than ~ 0.01” (0.254 mm). The crack had already grown past the compressive residual zone. Also it must be mentioned that the edges of the samples were not peened only the surfaces were peened. The determination of the fatigue crack growth rates in the shot peened material, requires not only the cracks/flaws be small enough to be completely embedded in the compressive stress zones, it also requires measurement techniques which are able to detect the very small changes in crack length. Area measurement of the fractured specimens did not provide the correlation with fatigue life as expected. One of the reason was the substantial crack growth occurs very rapidly towards the end of the fatigue life. It was not possible to identify regions when transition between slow growth and rapid crack growth occurs from images taken at 20~25X. After viewing several fracture surfaces it was clear that are multiple crack initiation sites and ratcheting was present on the fracture surfaces of most specimens. This indicates that the fatigue area rather than just crack length is a better indicator of fatigue life. The measurement of the surface profile and its correlation with the stable crack growth in the shot peened specimens would help in the identification of the region where the transition occurs from stable or slow crack growth to rapid crack growth.

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Although progress was made during the course of this study, continued research and effort are required to be able to develop crack growth data on the shot peened material which can be used by the design engineers. Acknowledgments This research was sponsored by FAA (Federal Aviation Administration). The encouragement and guidance of Dr. Melvin Kanninen of Galaxy Scientific is deeply appreciated. The author also appreciates with gratitude to Dr Dy Le the technical monitor of the Rotor Craft Damage Tolerance program for his support and thanks him for this opportunity. References 1.

Fuchs H.O. (1986) Shot peening Mechanical Engineer’s Handbook Pages 941-951, John Wiley and Sons, Inc. 2. KocaĔda, D., KocaĔda, S., and Tomazek, H. “Description of Short Crack Growth in Shot-Peened Medium Carbon Steel,” Fatigue & Fracture of Engineering Materials & Structures: Vol 21, pp 977-985, 1998. 3. Suresh S., & Ritchie R. O., “Propagation of Short Fatigue Cracks,” International Metals Reviews, 1984, Vol.29, No. 6. 4. Turnbull, A., De Ls Rios, E. R., Tait, R. B., Laurant, C., and Boabaid, J.,S., “Improving the Fatigue Resistance of Waspaloy by Shot Peening” Fatigue & Fracture of Engineering Materials & Structures: Vol 21:pp 1513-1524, 1998. 5. Everett Jr., R. A., Mathews, W.T., Prabhakaran, R., Newman, Jr., J. C., and Dubberly, M.J., “The Effects of Shot and Laser Peening on the Crack Growth and Fatigue Life in 2024 Aluminum Alloy and 4340 Steel” NASA/TM-2001-210843, ARLTR-2363. 6. Masaki K., Ochi. Y., and Matsumura. T. “Initiation and propagation behaviour of fatigue cracks in hard-shot peened Type 316L steel in high cycle fatigue” Fatigue Fract Engng Mater Struct 27, 1137-1145. 7. Sharpe W. N. Jr., Jira R. J., and Larsen J. M., “Real Time Measurement of smallCrack Opening Behavior Using an Interferometric Strain/Displacement Gage. 8. Verpoest I., Aernoudt E., Deruyttere A., & Neyrick M., “An Improved A.C. Potential Drop Method For Detecting Surface Microcracks During Fatigue Tests of Unnotched Specimens,” Fatigue and Fracture of Engineering Materials and Structures: Vol. 3, pp 203-217, 1981. 9. Sanjay Tiku PhD. Dissertation, “Micro-Mechanical Damage Accumulation in Airframe Materials and Structural Components” Universitý De Montréal 1997. 10. Dai Y., Marchand N., & Hongoh M., “Study of Fatigue Crack Initiation and Growth in Titanium Alloys Using An ACPD Technique,” Canadian Aeronautics and Space Journal: Vol. 39, No. 1, pp 35-44, 1993.

Effect of Reflection Shot Peening and Fine Grain Size on Improvement of Fatigue Strength for Metal Bellows H. OKADA*, A. TANGE* , AND K. ANDO** *NHK SPRING CO., LTD., KANAGAWA᧩PREF JAPAN **YOKOHAMA NATIONAL UNIVERSITY, KANAGAWA᧩PREF, JAPAN

ABSTRACT In this study various approaches were applied to bellows to confirm the effect on improving the fatigue strength as follows. As for the effect of the grain size, the re-crystallized materials after cold working are employed. The effect of high strength is studied by using the SUS631 stainless steel so called precipitation hardened semi-austenitic stainless steel. The shot peening process used with reflection plate is also studied to see the effect of residual stress on fatigue strength. Introduction Generally speaking, metal bellows (hereinafter described as bellows) is well-known for a mechanical part with the abilities of sealing and elasticity [1]. Figure 1 shows the appearance of bellows and sectional shape cut in axis. In automotive industry, the non-leakage sealing has recently been demanded due to the high reliability of the system. Then, it moves away from seals of the polymeric materials such as rubbers to a metallic seal such as bellows. In particular, the bellows with small bore and heavy thickness are expecting a seal of small high pressure pump. However, until now, it has been difficult to achieve the fatigue strength for required specifications in most cases. In order to increase the fatigue strength of automotive parts, the authors have made clear that the required processes and factors in order to improve fatigue strength [2], are (a) to increase the Vickers Hardness of the component as much as possible, (b) to introduce as high as possible compressive residual stress , and (c) to fine a grain diameter as fine as possible. The specimen and experimental conditions The specimen and method to decrease grain diameter Fatigue test specimen is U-shaped forming bellows. The manufacturing processes of bellows are to set the tube of which diameter is the same as inner diameter of bellows, to the mold divided into two. The interval of mold is contracted with giving internal pressure to the inside of the tube. It must be cautious to form the bellows without the buckling during the processes. This manufacturing process of bellows can be well-known as hydraulic bulge forming process, as shown in Figure 2. A cold-rolled working (thickness is reduced from 0.15mm to 0.13mm) is given to the welding pipe by spinning. Bright Annealing (it is hereafter described as a BA) is carried out in order to have the work-hardened material annealed. The grain diameter is adjusted by changing BA temperature after cold working. The BA temperature can be chosen five conditions (10300C, 10000C, 9800C, 9500C, and 9000C). The BA holding time is always four minutes.

201 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 201–207. © 2006 Springer.

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The materials The material is austenitic stainless steel SUS304 and precipitation hardened semi-austenitic stainless steel SUS631. The static strength can be increased by the aging hardening carried out after hydraulic bulge forming process. Shot peening processes It is known that the shot peening have an effect on improving fatigue strength [3]㧚However, it seems to be difficult to obtain a large compressive residual stress on the inner surface of bellows by the normal shot peening process㧚In order to obtain the effect of shot peening on the inner surface of bellows, the shot peening processes by using an air blasting machine and a reflective plate, are developed㧚The reflection plate shown in Figure 3, is installed to the nozzle, in order to apply the shots effectively to the inside surface of bellows [4]. As the bellows are normally used under the compressive status, the tensile stress occurs at the outside of outer diameter and inside of inner diameter, which can be the origin of fatigue fracture in most cases. Therefore, the shot peening should be done in those area. Table 1 shows shot peening conditions. The pressure is from 0.1 MPa to 0.5 MPa. The nozzle diameter is 8mm in case of inner, 9mm (normal size) in case of outer. The shot materials used is glass beads (550HV). The glass beads diameter used are from 38ȝm to 215ȝm. The shot peening processes are carried out under the condition that the nozzle is fixed. The turning bellows can be moved from the top to the bottom four times within two minutes. After that, the direction of bellows is made up-down reverse, and it goes in the same action for two minutes. The total shot peening time is, therefore, four minutes. The outside of the outer diameter was also shot peened for two minutes by using the standard nozzle without reflection plate.

     



Figure1. Metal bellows

Improvement of Fatigue Strength for Metal Bellows

Pipe Welding Ǿ18.4×0.15㨠

Spinning ˳ 18.4×0.13t

BA 1030͠×4min

Bellows Forming

Low Temperature Annealing 510͠×60min

203

Pre-setting

Figure 2. Manufacturing process of bellows

Table 1 Conditions of shot peening processes Pressure㧔MPa㧕 Peening time (s㧕 Nozzle diamater (mm) G㨘ass beads size㧔ȝm㧕 Hardness

0.1㨪0.5 Outer diameter 120 Inner diameter 240 Outer diameter 9 Inner diameter 8 38㨪215 550HV

Figure 3. Reflection shot peening system Experimental results and discussions The results of grain diameter Figure 4 shows the relationship between the BA temperature and grain diameter. The grain diameter tends to decrease in proportion with decreasing BA temperature. It can be said that the grain diameter of both 9500C and 9000C shows no significant differences. It can be also said that the minimum grain

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diameter by adjusting of the BA temperature is about 11 ȝm. Figure 5 shows the relationship between the grain diameter and fatigue strength of the bellows. The fatigue strength is the longest in case of 12.4 ȝm (BA temperature is 9500C). The fatigue strength is the shortest in case of 35 ȝm (BA temperature is 10300C). When the grain diameter is 11 ȝm (BA temperature is 9000C), the fatigue strength is shorter than 12.4 ȝm. It can be thought that the reason why the fatigue strength is shorter at 11ȝm is the distortion of bellows caused by unsuitable forming pressure, which may induce stress concentration. Then, when the data of grain diameter 11ȝm is deleted, the relationship between the grain diameter and fatigue strength of the bellows, can be arranged as, 12.4 ȝm㧪21 ȝm㧪24 ȝm㧪35 ȝm. It can be realized that the fatigue strength increases in proportion with decreasing grain diameter [5]. The ratio of single grain diameter to thickness is denoted by d/t. It can be calculated as 0.27 for grain diameter 35 ȝm and thickness 0.13 mm. This condition shows the shortest fatigue strength. It is 0.10 for grain diameter 12.4 ȝm and thickness 0.13mm. This condition shows the longest fatigue strength. It is difficult to say that the reason why the fatigue strength is improved is the smaller grain diameter or the smaller d/t which means the smaller grain size per thickness ratio. Then, the fatigue tests are carried out under the conditions of thickness of 0.15 mm, 0.3 mm, and 0.5 mm, and grain diameter of 40 ȝm and 13 ȝm. The fatigue test is carried out by the cantilever beam. The tested number of specimen is two in all conditions. The fatigue test condition is the completely reversed stress, R= -1. The deflection is constant and adjusted by the set length to correspond to constant stress amplitude, 472 MPa. 40 35

Grain diameter ᧤ȝ ᨩ᧥

35 30 25 20 15 10

30 25 20

10 5

0 880

900

920

940

960

980

1000

1020

1.E+04

1.E+05

0.5t/13ȝm

0.3t/40ȝm

0.5t/40ȝm

1.E+06

1.E+05

1.E+04

1.E+07

Figure5 Relationship between grain diameter and number of cycles᧤stress condition:491±377MPa᧥ 1.E+06

Number of cycles to failure (cycles)

0.3t/13ȝm

1.E+06

Number of cycles to failure (cycles)

Figure4ᇫRelationship between grain diameter and BA temperature

0.15t/40ȝm

non-fracture(n=3)

0

1040

BA temperature ᧤ഒ᧥

0.15t/13ȝm

non-fracture(n=1)

35ȝᨩ 24ȝᨩ 21ȝᨩ 12.4ȝᨩ 11ȝᨩ lower curve

15

5

Number of cycles to failure (cycles)

Grain diameter ᧤ȝ ᨩ᧥

40

y = 1E+06x-1.3665 1.E+05

1.E+04

1.E+03 0 13ȝm

40ȝm

1.E+03

(1)ᇫResults of fatigue test ᧤0±472MPa)

5

10

15

20

25

Ratio of one grain diameter and thicknes (%)

(2) Relationship between ratio of one grain diameter and thickness and fatigue strength

Figure 6 Results of thin plate fatigue test

30

Improvement of Fatigue Strength for Metal Bellows

205

It can be seen from Figure 6 (1) that the fatigue strength tends to increase in proportion with increasing the thickness when grain diameter is the same. When the thickness is the same excluding the thickness 0.15mm, the fatigue strength tends to increase in proportion with decreasing the grain diameter. This is the same result as for the bellows. It can be thought that the fatigue strength is rather dependent on the ratio of grain diameter and thickness, d/t, than on the absolute value of grain diameter. Figure 6 (2) shows the relationship between d/t and fatigue strength. The fatigue strength tends to increase in proportion with decreasing d/t. This tendency is more remarkable in case of a smaller d/t. Therefore, the reason why the fatigue strength was improved by decreasing grain diameter could be that the fatigue crack size in stage I is short compared to the thickness. The results of high hardness Figure 7 shows the hardness distribution of bellows before and after age hardening. The age hardening condition is 4800C, and one hour. The outer diameter (it is hereafter described as a top) is harder in comparison with inner diameter (it is hereafter described as a bottom) because of work hardening effect. It can be seen that the hardness of the bellows increases overall by age hardening. Especially, this tendency is more remarkable in case of the top. This is due to the inter-metallic compound Ni3Al is separated out from the martensite by age hardening after the stress-induced martensite is generated by the bellows forming processing [6]. Figure 8 shows the hardness distributions of the bellows of SUS631 and SUS304 with the same processing and BA temperature㧚 The hardness of SUS631 bellows become high in all area, comparing with the SUS304 bellows. Because of the age hardening, it becomes possible to increase the hardness of the SUS631. The shot peening process is applied to this SUS631 bellows with high strength and smaller grain size. 600 600 550

After aging

500 450 400 350

550

SUS631

500

SUS304

450 400 350 300

300

250

250

200 0

200 0

2

4

6

8

10

12

14

16

18

20

5

10

15

20

Outer dia.᧤1ᨺ 6᧥ᇫᇫᇫᇫEffective dia.᧤7ᨺ 12᧥ᇫᇫInner dia.᧤13ᨺ 18᧥

Outer dia.(1 ᨺ 6) ᇫ Effective dia.(7 ᨺ 12) ᇫ Inner dia.(13 ᨺ 18)

Figure8 Hardness distribution of bellows

-200 -300 -400

Residual stress

-500 -600 -700 0

0.1

0.2

0.3

0.4

0.5

0.6

Pressure (MPa) (1)ᇫRelationship between residual stress and ᇫᇫᇫpressure (glass beads size 97ȝm)

0 Residual stress (MPa)

42 41 40 39 38 37 36 35 34 33 32

Free length

Free length (mm)

0 -100

-100

42 41 40

Free length

-200

39 38 37 36 35

-300 -400

Residual stress

-500

34 33 32

-600 -700 0

50

100

150

200

250

Glass beads size (ȝm) (2) Relationship between residual stress and glass beads size (pressure0.3MPa)

Figure 9. Relationship among shot peening conditions, residual stress and free length

Free length (mm)

Figure7 Hardness distribution of bellows

Residual stress (MPa)

Hardness ᧤HV0.2)

Hardness ᧤HV0.2)

Before aging

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The results of reflection shot peening Figure 9 (1) and (2) show the relationship between the projection pressure, the glass beads size which is one of the most important factors in the shot peening condition, the residual stress of the surface, and the free length of bellows. The optimum residual stress distribution is the larger and deeper compressive residual stress. The best shot peening method is stress double shot peening, but is single shot peening in this case. The optimum shot peening conditions were decided by the relationship between residual stress, the free length of the bellows, projection pressure and glass beads size in the past experiments. It was obtained that the fatigue strength can be improved by the depth of residual stress, comparing with the value of surface residual stress [4]. Then, it can be said that the recommendable shot peening conditions are to have deeper residual stress distributions, even if residual stress of surface is somewhat low. The high free length bellows can be suitable to have the impact of shot peening. It can be said that the recommendable shot peening conditions are the glass beads size, 97ȝm and the projection pressure, 0.3 MPa. When shot peened to the different material bellows in the same condition, the residual stress is SUS304 -350 MPa, and SUS631is -500 MPa. The compressive residual stress of SUS631 is about 40% larger than that of SUS304. This is due to that the hardness of SUS631 is higher than that of SUS304 [7].

800

Stress amplitude (MPa)

700 600

585MPa

500

500MPa 430MPa

400 300 SUS304/35ȝm 200

240MPa

SUS304/12.4ȝm SUS304/12.4ȝm/SP

100

SUS631/12ȝm/SP

Stress ratio R=0

0 1.E+04

1.E+05

1.E+06

1.E+07

Number of cycles to failure (cycles)

Figure10 S-N diagram

1.E+08

Improvement of Fatigue Strength for Metal Bellows

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Figure 10 shows the fatigue test results of the bellows of SUS631, and shows the fatigue test results of SUS304 with 35ȝm and 12.4 ȝm. The bellows where the fatigue strength of 107 cycles is the lowest is SUS304 with the grain diameter 35ȝm, and the fatigue strength is 240 MPa. The bellows where the fatigue strength of 107 cycles is the second lowest is SUS304 with the grain diameter 12.4ȝm and 430 MPa. The bellows where the fatigue strength of 107 cycles is the third lowest is SUS304 with the grain diameter 12.4ȝm and shot peening, and 500 MPa. The bellows where the fatigue strength of 107 cycles is the highest is SUS631 with the grain diameter 12ȝm and shot peening, and 585MPa [8]. It can be said that fatigue strength of 107 cycles was improved by 2.4 times by using this practice. The fatigue strength can be improve by (a) decreasing of a grain diameter, (b) increasing of the Vickers Hardness by using SUS631 and (c) introducing of high compressive residual stress by using reflection shot peening. Conclusions By applying fatigue strength improvement processes proposed by the author, to the metal bellows, it can be realized that this process is applicable to the bellows with thin thickness, 0.13mm. It is found that the fatigue strength of 107 cycles is improved by 2.4 times by decreasing of grain diameter, and applying SUS631 stainless steel and the reflection shot peening to the inside. The result of obtaining is shown as follows. 1) It is clear that the impact of the grain diameter to thickness ratio on fatigue strength is larger than that of the absolute value of the grain size. 2) In the relationship between the hardness and fatigue strength, SUS631 have larger compressive residual stress to show higher fatigue strength, comparing with SUS304. This is due to the hardness of which SUS631 is higher. 3) It is clarified that the reflection shot peening is effective as the processing of the inside of the bellows with small bore diameter. References 1. 2. 3. 4. 5. 6. 7. 8.

T.Mitsushiba, a vacuum, 26-10 (1983), 757. H.Ishigami, K.Matsui, A.Tange and K.Ando, High Pressure Institute of Japan,38-4(2000),205-215. M.Hirose, Shot peening, Seibundo shinkosha (1964),48. H.Okada, A.Tange, K.Ando, Transaction of Japan Society for Spring Research,46(2001),27-31. H.Okada, K.Ando, Transaction of Japan Society for Spring Research,48(2003),1-6. M.Usui, T.Kaumaru, Technical report of Nisshin Steel,18(1968),40-50. H.Okada, A.Tange, K.Ando, High Pressure Institute of Japan,41-5(2003),19-28. H.Okada, A.Tange, K.Ando, Transaction of Japan Society for Spring Research,49(2004),1-7

SURFACE CRACK DEVELOPMENT IN TRANSFORMATION INDUCED FATIGUE OF SMA ACTUATORS

D.C. Lagoudas, O.W. Bertacchini, Aerospace Engineering Department Texas A&M University College Station, TX 77843-3141, USA E. Patoor Laboratoire de Physique et Mécanique des Matériaux UMR CNRS 7554/ENSAM Metz, 4 rue Augustin Fresnel 57078 Metz, France ABSTRACT This paper is based on the study of a post mortem analysis of shape memory alloy (SMA) actuators undergoing thermally induced martensitic phase transformation fatigue under various stress levels. Fatigue life results were obtained for both complete and partial phase transformation cycles applied to the SMA actuators. The thermal cyclic loading was induced by forced fluid convection cooling in order to increase the cycling frequency to approximately 1Hz, resulting to corrosion assisted fatigue. The combination of corrosion and reversible phase transformation under stress led to the formation of circular cracks on the surface of the cylindrical SMA wire actuators, which eventually saturated in a periodical distribution. In order to understand the stress field contributions to the microcracking in the presence of eigenstrains, a shear lag model was developed. The model accounts for eigenstrains introduced by corrosion, plastic strain accumulation with the number of cycles and the cyclic phase transformation strain. Comparison of the model predictions with crack spacing reached at fatigue failure is carried out and the reduction of fatigue life of SMA actuators under a corrosive environment is discussed. Introduction SMAs have seen growing use in the mechanical, medical and aerospace industries over the last decade [1]. The thermomechanical response of NiTi SMAs subject to various mechanical and thermal loads resulting in a cyclic phase transformation has been widely investigated [2-4]. However, most of the results pertain to a limited number of cycles and mainly focus on the development and stability of two-way transformation strain and the evolution of plastic strain. Mechanical fatigue properties of SMAs have been primarily studied based on the pseudoelastic response of SMAs with some key results presented by Tobushi et al. [5] and Miyazaki et al. [6]. However, thermally induced transformation fatigue is a more recent subject, where the applied level of stress has a major influence on the development of plastic strains and therefore on a low cycle fatigue performance of

209 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 209–222. © 2006 Springer.

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SMA actuators (Bigeon and Morin [7], De Araujo et al. [8], Lagoudas et al. [9], Cuellar et al. [10]). The applied stress during the thermally induced phase transformation favors the growth of certain martensitic variants and enforces elongation of the SMA actuator during cooling below the martensitic start temperature. Upon heating, these variants transform back into the austenitic parent phase inducing strain recovery. Such transformation conditions induce an evolution of the microstructure with the number of cycles leading to a modification of the performance of the actuator (Lagoudas et al. [9], Tamura et al. [11], Morgan and Friend [12]). Recent studies by Hornbogen and Eggeler [13, 14] focus on the role of surface quality in the fatigue life of shape memory alloys. The non-reversible plastic strain developed upon transformation cycles is permanently modifying the surface morphology and can nucleate surface cracks without assistance of inclusions or grain boundaries throughout cycled domain boundaries. Surface defects under an applied stress generate stress concentrations leading to a cyclic growth of these defects. Due to a large reversible transformation strain under applied stress, shape memory alloys are used as high energy density actuators. However, their actuation frequency is highly limited by the heat transfer rate upon cooling [15]. Fluid convection is a way to increase the frequency but the environment may become corrosive under certain conditions [16]. In the presence of a fluid environment containing an electrolyte, the applied electrical current used to heat up the SMA actuator will induce corrosion. The corrosive environment is able to penetrate the material through the fractured passivation layer, which ceases to be a barrier for corrosion due to microcracking induced by the cyclic thermal loading. These corrosion barriers have been studied and observed in SMAs for heat treatments between 300-600°C [17, 18]. In the present work, we briefly present the experimental set up and the fatigue results of thermally induced martensitic phase transformation under various stress levels for TiNiCu SMAs. Fatigue results are obtained for both complete and partial transformation cycles. A post mortem microstructural evaluation is conducted on the failed specimens. The microstructure reveals a unique periodical crack pattern on the surface with creation of a superficial brittle layer. An analysis is made to define the parameters of this embrittlement phenomenon. A shear lag model accounting for inelastic strains is applied to characterize and identify what drives the failure of this corrosive brittle layer on the surface of SMA actuators leading to ultimate actuator failure. Experiments and selected results TiNiCu (Ti.40Ni.10Cu, wt.%) SMA wires of 0.6 mm (0.024 in.) diameter were used to perform the present fatigue study. The gauge length of the specimens was approximately 200 mm (8 in.). The SMA wires were annealed for 15 minutes at 550°C to allow partial recrystallization and optimization of shape memory effect and fatigue properties [9]. This study relied on isobaric (isostress) thermally induced phase transformation cycles. The experimental setup was previously utilized [19] for the purpose of testing SMA NiTi actuators with “dead” loads under thermal actuation cycles, in the presence of fluid forced convection. The SMA actuators were heated through resistive heating and were cooled through a chilled, forced fluid convection cooling. Several applied stress levels were used in the isobaric experiments performed in the range between 54 MPa and 247 MPa. The measured data were the relative displacements of the two ends of the actuators during the thermal cycles using LVTD transducers. Upon heating and cooling, each phase (austenite and martensite) reached an endpoint of transformation, where no strain recovery was observed anymore. Such

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thermal cycles allowed to achieve complete transformation cycles (major loops) for the different stress levels. Partial transformation cycles were then possible by applying a percentage of the maximum recoverable strain for the considered stress level. In this study, we carried out fatigue experiments for complete transformation cycles (100% of maximum recoverable strain) and for partial transformation cycles with a50% of the maximum recoverable strain) [9]. The repeated thermal cycles were conducted until final failure of the specimens. The transformation temperatures of the SMA wires were measured using differential scanning calorimetry (DSC) and they are reported in Table 1. Austenitic transformation temperatures

Martensitic transformation temperatures

As = 54.4qC

Ms = 46.7qC

Af = 60.6qC Mf = 39.5qC Table 1. Transformation temperatures for TiNiCu SMA wires from stress free DSC measurement.

0.08

0.04

0.07

0.035

0.06

0.03

0.05

0.025

Strain

S tra in

Figures 1 and 2 show two typical transformation induced thermal fatigue results corresponding to 100% and 50% of the total amount of recoverable transformation strain, respectively. The applied stress level is 154 MPa. One can observe from Figure 2 a larger strain measurement for each 1000 cycle increment. These measurements were used to recalibrate the percentage of transformation strain as it changes with the number of cycles. The results in these two figures give a good indication of rapid plastic strain build up, while the recoverable strain suffers from a decrease initially before it stabilizes. An important feature is the lifespan extension when going from major to a minor transformation loop.

0.04 0.03

(a) (a)

(b) (b) (c)

0.02 0.015

0.02

0.01

0.01

0.005

(c)

0

0

0

500

1000

1500

2000

2500

Cycles

Figure 1. Complete transformation: H-N curve for a constant applied stress of 154 MPa. The different curves show the total strain in the martensitic phase (a), austenitic phase (b) and transformation strain (c).

0

5000 10000 15000 20000 25000 30000 35000

Cycles

Figure 2. Partial transformation: H-N curve for a constant applied stress of 154 MPa. The different curves show the total strain in the martensitic phase (a), austenitic phase (b) and transformation strain (c).

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A summary of all fatigue results is given in Figures 3 and 4. Figure 3 reports transformation strain and plastic strain accumulation as a function of the constant applied load, while Figure 4 is a Wohler representation of the fatigue life obtained for major and minor loops experiments. 1000

0.05

Externally applied stress (MPa)

Plastic strain-Major loops Transformation strain-Major loops Plastic strain-Minor loops Transformation strain-Minor loops

0.06

Strain

0.04 0.03 0.02 0.01 0 0

50

100

150

200

250

Externally applied stress (MPa)

Figure 3. Evolution of plastic and transformation strains with respect to the externally applied load.

100

Major loops Power (Major loops) 10 1000

10000

Minor loops Power (Minor loops)

Number of cycles

100000

Figure 4. Wohler curve for complete and partial transformations.

Microstructural Observations The key observation for fatigued specimens was a distribution of periodic circular cracks on both segments of broken SMA actuators. Figure 5 is an SEM micrograph of a post mortem SMA actuator exhibiting this particular microcracking structure.

Figure 5. SEM micrograph of a SMA actuator with periodical circular cracks (total length = 8 mm, crack spacing | 180 Pm). The fracture surface can be seen on the right hand side of the specimen. Complete transformation cycles, applied stress 247 MPa. It seems plausible that, under cyclic phase transformation, the protective surface oxide layer on the SMA wires is fragmented and oxide free martensitic variants are exposed to the environment, which is a mixture of water and glycol, with an electric current passing through the SMA actuator during every cycle. This corrosive environment leads to the creation of a SMA brittle layer saturated with cyclically formed and inserted oxides. This proposed surface embrittlement mechanism is supported by the observation of a thickness of embrittlement related to the lifespan of the SMA actuators. Figures 6 and 7 characterize the brittle superficial layer formed during the thermal cycles. The thickness of that layer appears to increase from a40Pm to a70Pm when the number of cycles increases from a1200 cycles to a15000 cycles under the same applied stress. Composition analysis of the SMA brittle layer has not been carried out yet. However, similar conditions have been identified with a preponderant formation of TiO2 oxide [16, 17]. The superficial formation of TiO2 generates a depletion of Ti content in the sub-layer. The result is a Ni rich region at the interface SMA/oxide layer [16, 17]. From now on and for simplicity of further modeling, we will consider cyclic formation and insertion of only TiO2 oxide in the SMA actuators.

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Figure 8. Schematic of the periodical microcraking pattern and identification of a representative volume element. With the corrosion phenomenon occurring during fatigue testing, the brittle layer is continuously developing at the surface of the SMA actuators. The observation of periodical crack spacing appears to relate to a saturated distance between the circular cracks and their depth. This distance and depth vary with different parameters such as the applied stress, the amount of transformation strain, and the number of cycles. The periodicity was identified around the failure location with averaging spacing from a100 Pm to a400 Pm. The depths of the brittle layer vary from a30 Pm to a100 Pm. Figure 8 qualitatively summarizes the identification process of the periodicity with the definition of the representative volume element that will be of interest in the next section of this work. Figures 9 and 10 report the actual measurement of the depth of the brittle layer while the measured crack spacing is described in Figure 11. Figures 9 and 10 indicate the influences of both the stress level and the amount of transformation strain on the depth of the brittle layer, closely related to the fatigue life of the actuators. Figure 11 shows how two different transformation strains affect the periodical crack spacing.

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120

Major loops 154MPa Major loops 192MPa Major loops 247MPa

110 100

B rittle la y e r th ic k n e s s (m ic ro n s )

B r ittle la y e r th ic k n e s s ( m ic r o n s )

120

90 80 70 60 50 40 30 20 -15

-10

-5

0

5

10

15

Position on wire relative to the fracture surface (mm)

Figure 9. Brittle layer profile around failure location. Complete transformation conditions (Major loops).

Minor loops 106MPa Minor loops 154MPa Minor loops 192MPa Minor loops 247MPa

110 100 90 80 70 60 50 40 30 20 -15

-10

-5

0

5

10

Position on wire relative to the fracture surface (mm)

Figure 10. Brittle layer profile around failure location. Partial transformation conditions (Minor loops).

450

Crack spacing (microns)

400

Crack spacing evolution in major loops Crack spacing evolution in minor loops

350 300 250 200 150 100 100

150

200

250

Applied stress (MPa)

Figure 11. Crack spacing as a function of the applied stress. Shear Lag Modeling of SMA Actuators with Circular Microcracks The representative volume element (RVE) shown in Figure 8 is analyzed using a shear lag model in this section.

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Figure 12. Free body diagrams for TiNiCu core and brittle surface layer for the shear lag model. Force equilibrium over the respective averaged cross section areas yields:

w V zzf wz w V zzm wz Where

cf

and

 

2 W Re 2c f

(1)

0

 R  e cm

W

(2)

0

cm are the TiNiCu core and brittle surface layer volume fractions (the

same as area fractions), respectively. In order to reduce the number of unknowns in the above equations, one starts with the shear stress-strain constitutive relations:

wurf wuzf  wz wr f

f

m

V rzf and wurm wuzm  P Af wz wr

V rzm P Am

(3)

m

Where ur , u z , ur and u z are the displacements components for the fiber and matrix, respectively, and where

P Af

and

P Am

are the respective axial shear moduli for the fiber

and matrix. Consistent with the shear lag approximation, a negligible variation of radial displacements along the fiber axis is assumed [20]:

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wu m wu m wurf wu f  z and r  z wz wr wz wr

(4)

This reduces equations (3) to the following form: m V rzf and wuz wr P Af

wuzf wr

V rzm P Am

(5)

The shear stress distribution is now assumed to be of the form [21]:

V rzf W ( z )

r and m V rz Re

r ½ W ( z) ­R e  cf ® ¾ R  e ¿ cm ¯ r

(6)

Following the work of McCartney [22], one can easily define the interfacial shear stress at r R  e as proportional to the difference between the average axial displacements of the matrix and the fiber, i.e.:



W ( z ) * u zm ( z )  u zf ( z )



(7)

With the constant *given by:

cm ­° c c ·½ 1 § 1 1  R  e ® m f  m ¨¨ ln  1  m ¸¸°¾ 2 ¹ ¿° ¯° 4 P A 2 P A © cm c f

*

(8)

Assuming different eigenstrains for the TiNiCu core, due to phase transformation and plastic strain accumulation, and the brittle layer due to the formation of oxide, denoted by

H inf

m

and H in , respectively, the constitutive equations for the axial strains are given by:

H zzf Where



Q Af E

E Af

f A

V

and

f rr

 V TTf 

E Am

V zzf E

f A

 H inf and H zzm



Q Am E

m A

V

are axial Young’s moduli, and

m rr

Q Af

 V TTm  and

Q Am

V zzm E

m A

 H inm

(9)

are axial Poisson’s

ratios for the core and surface layer, respectively. Averaging equations (9a) and (9b) over the cross section yields:

H zzf

V zzf E Af

 H inf and H zzm

V zzm E Am

 H inm

We also have the following kinematic relations for infinitesimal strains:

(10)

Transformation Induced Fatigue of SMA Actuators

H zzf

wu zf and H zzm wz

wuzm wz

217

(11)

Averaging equations (11a) and (11b) and combining them with equations (1), (2), (7), (8) and (10), we can show that the interfacial shear stress W ( z ) satisfies the following second order ordinary differential equation:

d 2W ( z ) dz 2

k 2W ( z )

(12)

Where:

k2

2 E A* 2

 R  e K EAf EAm

, E A*

cm c · 1 § 1 1  m ¨ ln  1  m ¸ (13) f 4P A 2P A ¨© cm c f 2 ¸¹

c f E Af  cm E Am and K

Upon integration of equation (12) and use of equations (1) and (2), the average stresses in the core and surface layer are of the form:

V zzf ( z ) 

V zzm ( z )

2   Ae kz  Bekz  D f k  R  e

(14)

cf 2  Ae  kz  Be kz  Dm  k  R  e cm

(15)

Integration of the above equations leads to the following expression for the average displacements:

u zzf ( z )

u zzm ( z ) Where



D 2 Ae  kz  Be kz  ff z  F f f  k  R  e EA EA 2

cf D 2 Ae  kz  Be kz  mm z  Fm  m k  R  e E A cm EA 2

A , B , D f , Dm , Ff

and

Fm are

(16)

(17)

constants to be determined from the boundary

conditions. The boundary conditions are defined by the externally applied load conditions, by the validity of equation (7) at

z

G 2

and by the perfect bonding

assumption at the interface, as well as symmetry requirements for the RVE. They are given below:

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Figure 13. Schematic describing the boundary conditions for the selected RVE.

z

x

r V

m zz

G 2 ( z )  E AmH inm

V zzf ( z )  E Af H inf



0

(18)

V0

(19)

W ( z ) * u zzm ( z )  uzzf ( z )

z

x



(20)

0 (21)

W ( z) 0 f zz

( z)

0

(22)

u zzm ( z )

0

(23)

u

The material parameters for the model are given in Table 2. TiNiCu core Surface layer Austenite axial Young’s 67.9 69.5 modulus (GPa) Martensite axial Young’s 16 18.1 modulus (GPa) Austenite axial shear 26 26.7 modulus (GPa) Martensite axial shear 6.2 7.0 modulus (GPa) Poisson’s ratio 0.3 0.29 Table 2. Material parameters for TiNiCu core and surface layer. The shear lag modeling results are shown in Figures 14 and 15 for SMA actuators initially loaded under 154 MPa. The periodical cracks induce a high stress concentration at the boundary of each unit cell. The concentration factors are 1.63 and 1.86 in complete and partial transformation, respectively, as it can be seen in the figures for

z

G 2

.

Transformation Induced Fatigue of SMA Actuators

TiNiCu core: zero eigenstrains Surface layer: zero eigenstrains

TiNiCu core: non-zero eigenstrains Surface layer: non-zero eigenstrains

300

Axial stress (MPa)

250 200 150 100 50 0 -0.1

-0.05

0

0.05

0.1

Axial position for crack spacing = 200 microns TiNiCu core: zero eigenstrains

TiNiCu core: non-zero eigenstrains

Surface layer: zero eigenstrains

Surface layer: non-zero eigenstrains

300

Axial stress (MPa)

250 200 150 100 50 0 -0.15

-0.1

-0.05

0

0.05

0.1

0.15

219

Figure 14. Axial stress profile between two circular microcracks for crack spacing: δ = 200 μ m in complete transformation (total eigenstrain in the TiNiCu core 7%), external load = 154 MPa, thickness of cracked brittle layer = 65 μ m, eigenstrain in surface layer = 5%. Figure 15. Axial stress profile between two circular microcracks for crack spacing: δ = 300 μ m in partial transformation (total eigenstrain in the TiNiCu core of 4%), external load = 154 MPa, thickness of cracked brittle layer = 80 μ m, eigenstrain in surface layer = 3%.

Axial position for crack spacing = 300 microns

Eigenstrains for the unbroken SMA core are determined from the fatigue data previously obtained (transformation strain plus accumulated plastic strain). The embrittlement of the surface layer is most likely to reduce the contribution from the recoverable strain and therefore reduce the amount of accumulated plastic strain. Based on the proposed embrittlement mechanism, the amount of transformation strain is driving the level of crack spacing saturation of the surface layer with cyclic oxide insertion. This means that the higher the amount of transformation strain is, the faster saturation is reached and the higher the difference between TiNiCu core and surface layer eigenstrains is. Therefore, a parametric study is conducted to determine the amount of eigenstrain in the brittle layer. Eigenstrain values of 5% and 3% are obtained for complete and partial transformation cycles, respectively, and eigenstrain mismatches of 2% and 1% between the brittle layer and the core are identified. The shear lag results are computed in the martensitic phase, where the eigenstrains are maximum and yield a threshold value for the stress level inducing crack in the brittle layer. In both complete transformation (major loops) and partial transformation (minor loops), an almost identical stress level is attained as indicated in Figures 14 and 15, which most likely leads to the ultimate fracture of the brittle surface layer. The increase in the axial stress from the purely elastic solution (zero

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eigenstrains in both SMA core and surface layer), which is included for comparison purpose, indicates the influence of inelastic strains on the axial stress development in the brittle surface layer. One can also see from Figures 14 and 15 how the inelastic strains influence the stress reduction in the TiNiCu core for both complete and partial transformation cycles. Conclusion In this paper, a study on the thermomechanical transformation induced fatigue of SMAs under various stress levels was conducted. Complete and partial phase transformation cycles were applied. Corrosion assisted fatigue was identified using microstructural evaluation of post mortem SMA actuators. The microstructure revealed a periodical distribution of circular cracks on the cylindrical surface of the actuators. The crack distribution was related to the creation of a SMA brittle layer saturated with cyclically formed and inserted oxides. A surface embrittlement mechanism was proposed and supported by the observation of a brittle layer related to the lifespan of SMA actuators. The crack spacing was related to the amount of transformation strain applied to the SMA actuators. A shear lag model accounting for inelastic strains was derived to evaluate the stress field leading to the formation of the observed circular cracks developed in the SMA brittle layer. The amount of transformation strain, and therefore of eigenstrain mismatch, was related to the crack spacing. Occurring faster in the case of complete phase transformation cycles, the saturation of the surface layer was recognized to accelerate the damage process of the TiNiCu actuators leading to premature failure. In the case of partial phase transformation cycles, saturation was slower, leading to a thicker brittle layer with larger crack spacing. The combination of the saturation of the surface layer with the stress concentration occurring at each crack location, where the active cross section is reduced, was most likely responsible for accelerating the ultimate failure of SMA actuators and therefore reducing their fatigue life.

Acknowledgments The authors would like to acknowledge the support of the Texas Institute for Intelligent Bio-Nano Materials and Structures for Aerospace Vehicles (TiiMS) and of the Region Lorraine from France. This effort is the result of a joint research program between the Aerospace Engineering Department at Texas A&M University and the Laboratoire de Physique et Mécanique des Matériaux (LPMM) at the Ecole Nationale Supérieure d’Arts et Métiers (ENSAM). References 1. Birman, V., “Review of Mechanics of Shape Memory Alloy Structures”, Applied Mechanics Reviews, Vol. 50 (11), 629-645, (1997). 2. Hebda, D. and White, S. R., “Effect of Training Conditions and Extended Thermal Cycling on Nitinol Two-way Shape Memory Behavior”, Smart Materials and Structures Vol. 4, 298-304, (1995). 3. Bo, Z. and Lagoudas, D. C., “Thermomechanical Modeling of Polycrystalline SMAs under Cyclic Loading, Part III: Evolution of Plastic Strains and Two-Way Memory Effect”, Int. J. Eng. Sci., 1175-1203, (1999).

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4. Lim, T. J. and McDowell, D. L., “Degradation of a Ni-Ti alloy During Cyclic Loading”, Proceedings of the North American Conference on Smart Structures and Materials, SPIE, Orlando, Florida, 153-165, (1994). 5. Tobushi, H., Hachisuka, T., Hashimoto, T., Yamada, S., “Cyclic deformation and fatigue of a TiNi shape-memory alloy wire subjected to rotating bending”, Journal of Engineering Materials and Technology 120, 64-70, (1998). 6. Miyazaki, S., Mizukoshi, K., Ueki, T., Sakuma, T., Liu, Y., “Fatigue life of Ti–50 at.% Ni and Ti–40Ni–10Cu (at.%) shape memory alloy wires”, Material Science and Engineering A 273-275, 658-663, (1999). 7. Bigeon, M. and Morin, M., “Thermomechanical study of the stress assisted two way memory effect fatigue in TiNi and CuZnAl wires”, Scripta Materialia Vol.35 (N°12), 13731378, (1996). 8. C.J. De Araujo, M. Morin, G. Guénin, “Electro-thermomechanical behaviour of a Ti45.0Ni-5.0Cu (at.%) alloy during shape memory cycling”, Material Science and Engineering., A 273-275, 305-309, (1999). 9. Lagoudas, D. C., Li, C., Miller, D. A., Rong, L., “Thermomechanical transformation fatigue of SMA actuators”, Proceedings of SPIE, Vol. 3992, 420-429, (2000). 10. López Cuéllar, E., Guénin, Morin, G. M., “Study of the stress-assisted two-way memory effect of a Ti–Ni–Cu alloy using resistivity and thermoelectric power techniques”, Materials Science and Engineering A, Volume 358, Issues 1-2, 350-355, (2003). 11. Tamura, H., Mitose, K., Suzuki, Y., “Fatigue Properties of Ti-Ni Shape Memory Alloy Springs”, J. Phys. IV, Vol. 5, C8, 617, (1995). 12. Morgan, N.B., Friend, C.M., “A review of shape memory stability in NiTi alloys”, J. Phys. IV, C11, 325-332, (2001). 13. Hornbogen, E. and Eggeler, G., “Surface Aspects in Fatigue of Shape Memory Alloys (SMA)”, Materialwissenschaft und Werkstofftechnik, Volume 35, Issue 5 , 255-259, (2004). 14. Hornbogen, E., “Review Thermo-mechanical fatigue of shape memory alloys”, Journal of Material Science, Vol. 39, 385-399, (2004). 15. Miller, D. A., “Thermomechanical characterization of plastic deformation and transformation fatigue in Shape Memory alloys”, PhD thesis, Texas A&M University, (2000). 16. Shabalovskaya S. A., “Surface, corrosion and biocompatibility aspects of Nitinol as an implant material”, Bio-Medical Materials and Engineering, Vol. 12, 69–109, (2002). 17. Firstov, G.S., Vitchev, R.G., Kumar, H., Blanpain, B., Van Humbeeck, J., “Surface oxidation of NiTi shape memory alloy”, Biomaterials, Vol. 23, 4863-4871, (2002). 18. Ishida, A. and Sato, M., “Thickness effect on shape memory behavior of Ti50.0at.%Ni thin film”, Acta Mat., Vol. 51, 5571-5578, (2003).

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19. Bertacchini, O., Lagoudas, D., Patoor, E., “Fatigue life characterization of shape memory alloys undergoing thermomechanical cyclic loading”, Proceedings of SPIE, Vol. 5053, 612-624, (2003). 20. Nairn, J.A., “On the use of shear-lag methods for analysis of stress transfer in unidirectional composites”, Mechanics of Materials, vol. 26, 63-80, (1997). 21. McCartney, L. N., “New Theoretical Model of Stress Transfer between Fibre and Matrix in a Uniaxially Fibre-Reinforced Composite”, Proc. R. Soc. Lond., vol. A425, 215244, (1989). 22. McCartney, L. N., “Analytical Models of Stress Transfer in Unidirectional Composites and Cross-Ply Laminates, and Their Application to the Prediction of Matrix/Transverse Cracking”, Local Mechanics Concepts for Composite Material Systems, Proc. IUTAM Symposium, Blacksburg, VA, 251-258, (1991).

ASSESSMENT OF DEFECTS UNDER COMBINED PRIMARY AND RESIDUAL STRESSES

A.H. Sherry, J. Quinta da Fonseca, K. Taylor, and M.R. Goldthorpe Materials Performance Centre University of Manchester Manchester M60 1QD United Kingdom ABSTRACT Residual stresses can provide a significant contribution to the crack driving force for defects associated with non stress-relieved welds. Structural integrity assessment methods are available which provide detailed guidance for the assessment of such defects under the combined influence of primary and residual stresses. However, in some circumstances these methods may be unduly conservative due, in part, to an over-estimation of the crack driving force contribution from the residual stress, KJs. This paper describes a programme of experimental and supporting analytical work undertaken to better characterise the influence of residual stress levels on KJs for cracks in a high strength, low toughness aluminium alloy. The work is based on a compact specimen in which a highly tensile residual stress field is mechanically induced through a compressive preload prior to fatigue pre-cracking. Different approaches to numerically simulate crack development within the residual stress field are explored by finite element analysis and, where possible, numerical data are compared with experimental measurements of crack opening displacement for different crack lengths. The results demonstrate that progressive crack insertion in finite element models provides a than instantaneous crack insertion. In addition, progressive crack insertion leads to maximum values KJs which are approximately 30% below those derived using the instantaneous method. The implications of these results for structural integrity assessments are discussed. Introduction The stability of defects in engineering components is assessed using the principles of fracture mechanics in which the driving force for crack initiation is compared with the fracture toughness of the material. Where the former exceeds the latter, crack initiation is predicted to occur. The derivation of the crack driving force (KJ) requires that all contributions to the stress acting on the defect be acknowledged. These include primary loads, which contribute to plastic collapse, and in many cases secondary loads, including thermal and residual stresses. Residual stresses are self-balancing internal stresses that develop during the manufacture and/or operation of engineering components. It 223 A.G. Youtsos (ed.), Residual Stress and Its Effects on Fatigue and Fracture, 223–232. © 2006 Springer.

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is critical that the influence of residual stresses on crack driving forces is understood and that validated guidance is available for the correct derivation of KJ under different combinations of primary and secondary load. The R6 defect assessment method [1] provides a number of approaches for the assessment of residual stresses on defect behaviour within the framework of a failure assessment diagram (FAD) approach. These methods, described in Section II.6 of R6, partition the elastic CDF into components due to primary (KIp) and secondary loads (KIs) alongside a plasticity correction factor (U or V). The calculation of these parameters requires an estimate of the elastic-plastic crack driving force due to the secondary stresses (KJs). This estimate is made either via: (a) elastic-plastic cracked-body Finite Element Analysis (FEA), (b) elasticplastic uncracked-body FEA, or (c) a plastic zone size correction to the crack length to modify KIs. This paper presents the results of a combined experimental and numerical programme to study residual stress effects on crack behaviour in laboratory specimens. The influence of residual stress on Crack Opening Displacement (COD) and KJs is assessed in preloaded and fatigue precracked aluminium alloy samples, with accompanying three-dimensional, elastic-plastic FEA. The CDF is derived using a recently developed FEA post processor which takes full account of the effect of prior plasticity on the J-integral [2]. Experimental The material used in this study was a wrought aluminium alloy AL2024-T351. The yield stress and fracture toughness values for this material are 370 MPa and 30 MPa—m, respectively. This high ratio of yield stress to fracture toughness enables laboratory-scale specimens to be used to study ductile fracture in the small-scale yielding regime where residual stresses have a significant influence on fracture

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The work was undertaken on a preloaded and pre-cracked compact tension (PL-CT) specimen developed specifically to study residual stress effects on fracture. Ten 25 mm thick, blunt-notch PL-CT specimens were machined according to the geometry shown in Fig. 1(a). The specimen is characterised by shallow scallops positioned on the load-line on both upper and lower surfaces to enable the accurate application of a compressive preload to the specimen via loading pins in order to generate a mechanically-induced residual stress at the root. Specimens were preloaded in compression to a total applied displacement of 1.75 mm. Following preloading, a spark-eroded notch, with diameter 0.75 mm and length between 0.5 to 1.0 mm, was inserted at the root of the blunt notch to ensure that the fatigue pre-crack developed close to the mid-plane of the specimen. Specimens were precracked in fatigue using an initial compressive load range of 0 to 5 kN, providing an initial 'KJ of approximately 10 MPa—m. The specimens were precracked to different crack lengths, these being nominally 2, 3 and 4 mm ahead of the blunt notch. A typical fatigue crack introduced into the residual stress region is illustrated in Figure 1(b). An optical microscope equipped with a digital camera was used to image the spark-eroded notch and the fatigue precracks in each of the specimens at a magnification of u200. Cracks were imaged at both surfaces and near the midplane of the specimen (following sectioning). Images were combined to provide a montage of the crack using digital image manipulation software and the composite images analysed using a routine written for MatlabTM that measured the Crack Opening Displacement (COD) along the full crack flank. Finite Element Analysis Three dimensional FEA calculations were carried out using ABAQUS, Version 6.3 [3]. The model consisted of 1,668 full integration elements of type C3D8 and took advantage of two planes of symmetry: one through the mid-thickness of the specimen and the other the plane lying in the middle of the notch. Eight layers of elements were used through the specimen half thickness modelled, with the element sides decreasing in size towards the free surface to accommodate the reduction to zero of through-thickness stress. The mesh was more refined in the region of the notch root. For a distance of 5 mm ahead of the notch tip, the model used regular element sides, each of length 0.25 mm, in order to allow a crack to be inserted to specified, regular lengths. Material properties were derived from standard tensile tests as Young’s modulus E = 73.7 GPa, Poisson’s ratio Q = 0.34 and the 0.2% proof stress V0.2 | 350 MPa. Flow behaviour was assumed to be isotropic, von Mises, with a multi-linear strain hardening law, with work hardening properties taken as those relating to the L-direction in the plate.

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The nodes on the two planes of symmetry were restrained from displacing in the respective normal directions. A slave contact surface was set up on the surface of the shallow scallop. The loading pin was simulated by means of a rigid master contact surface that is allowed displace only in the vertical (2) direction. Preloading was simulated by downward displacement of the rigid master surface. The latter was then removed to simulate relaxation of the preload. A single node that lies on both planes of symmetry was fully restrained to prevent any further rigid body motion. Following the relaxation of preload, full through-thickness cracks were introduced into the residual stress field directly ahead of the notch tip to simulate the spark-eroded notch and fatigue pre-crack. This was accomplished by removal of the constraints on the relevant nodes on the plane of symmetry. The lengths of the cracks studied were a = 1, 2, 3, 4 and 5 mm, measured from the tip of the blunt notch. These were introduced either ‘simultaneously’ or ‘progressively’. (a) a=5.00 mm, Simultaneous, z/t=0.50 a=5.00 mm, Progressive, z/t=0.50 a=4.00 mm, Simultaneous, z/t=0.50 a=4.00 mm, Progressive, z/t=0.50 a=3.00 mm, Simultaneous, z/t=0.50 a=3.00 mm, Progressive, z/t=0.50 a=2.00 mm, Simultaneous, z/t=0.50 a=2.00 mm, Progressive, z/t=0.50 a=1.00 mm, Simultaneous, z/t=0.50 a=1.00 mm, Progressive, z/t=0.50

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(b) a=5.00 mm, Simultaneous, z/t=0.00 a=5.00 mm, Progressive, z/t=0.00 a=4.00 mm, Simultaneous, z/t=0.00 a=4.00 mm, Progressive, z/t=0.00 a=3.00 mm, Simultaneous, z/t=0.00 a=3.00 mm, Progressive, z/t=0.00 a=2.00 mm, Simultaneous, z/t=0.00 a=2.00 mm, Progressive, z/t=0.00 a=1.00 mm, Simultaneous, z/t=0.00 a=1.00 mm, Progressive, z/t=0.00

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Figure 2 Predicted COD for simultaneous (solid lines) and progressive (dashed lines) cracks at (a) surface (b) mid-plane

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In the simultaneous cases, the whole of the crack face was introduced in one analysis step by removal of constraints on all relevant nodes, albeit using several increments to unload the crack face and redistribute the stresses within the model. Five separate analyses were conducted to cover the crack lengths studied. In the analysis modelling the progressive case, the crack was introduced fully through the specimen thickness but at one element side at a time starting at the original notch tip using individual loading steps. Each loading step used several loading increments to unload the new portion of crack face. For each crack length, the J-integral was calculated using the JEDI post processor [2] which uses the equivalent domain integral to correctly account for the influence of prior plastic strain on the J-integral. Here, the final strain at any point within the domain integral is partitioned into initial (due to pre-loading) and subsequent components. This leads to path-independent results for J. The elastic-plastic crack driving force for residual stress acting alone, KJs, was determined using the plane strain expression KJs = [EJs/(1-Q2)]1/2. After relaxation of the preload, the direct stress acting normal to the plane of the notch, at the centroid of each element forming part of the potential crack face, was written to the ABAQUS ‘.dat’ output file. These results were processed in a spreadsheet and subsequently applied as distributed loads to the crack faces of the same elements in five separate, pre-cracked, elastic FEA of the PL-CT geometry for all crack lengths. The ABAQUS J-integral procedure was used to determine Jels. Results Finite element predictions for COD for simultaneously and progressively created crack faces in the presence of the residual stress field are illustrated in Fig. 2(a) for the specimen surface and Fig. 2(b) at the mid-plane. Results are provided for the five different crack lengths. The CODs for the progressively introduced cracks are consistently smaller than the simultaneous cases. This is more apparent at the specimen surface than at the mid-plane. For a = 1 to 3 mm close to the crack tip, the COD for the progressive case is about half that of simultaneous. The crack opening profile for the progressively developed cracks is relatively straight: showing a fairly constant crack opening angle. On the other hand, simultaneously created cracks show more intense opening at the elements immediately behind the crack tip. Comparisons of measured COD data with instantaneous growth demonstrated that the FEA consistently over-predicted the COD values, particularly at the crack tip. Comparisons of measured CODs with predictions for progressive growth are illustrated in Fig. 3(a) for the specimen surface and Fig. 3(b) for the mid-plane. First, for the surface measurements, comparisons are made for a = 2.0 to 3.75 mm. For the three shortest surface cracks, the measurements, though scattered are reasonably well predicted by the FEA. For the longer cracks, the FEA tends to under-predict the experimentally measured CODs. This is particularly acute for measurement ‘AS01_D’, with has a total length of

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spark-eroded notch and fatigue crack of 3.75 mm. Secondly, Fig. 3(b) compares mid-thickness measurements for a = 4.3 to 4.68 mm with predictions at similar total crack lengths. Whilst there is some scatter in the measured results depicted by symbols, the curves from the finite element results are generally in good agreement with corresponding measurements. Figure 4 illustrates the results for crack driving force (CDF) at the mid-plane of the specimen derived using: (i) the superposition principle, (ii) JEDI for instantaneously introduced cracks and (iii) JEDI for progressively introduced cracks. The CDFs for the progressive crack are consistently smaller than that derived using the superposition principle and for the simultaneously introduced. This is most apparent for a=1 mm and 2 mm, where the CDF for the progressive case is about 70 to 75% of that for simultaneous. This behaviour is consistent with the results for crack opening displacement, as highlighted in Fig. 2(b). For the longer cracks, this difference between simultaneous and progressive is not as great. This might be because the crack tip experiences a much reduced or even compressive uncracked stress as crack length increases. (a) a=3.75mm, Progressive, z/t=0.50 a=3.25mm, Progressive, z/t=0.50 a=3.00mm, Progressive, z/t=0.50 a=2.50mm, Progressive, z/t=0.50 a=2.00mm, Progressive, z/t=0.50 AS01_D_avg, a_tot=3.78mm AS06_U_avg, a_tot=3.31mm AS09_D_avg, a_tot=3.14mm AS04_D_avg, a_tot=2.93mm AS05_D_avg, a_tot=2.56mm AS03_D_avg, a_tot=2.09mm

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(b) a=4.75mm, Progressive, z/t=0.00 a=4.50mm, Progressive, z/t=0.00 a=4.25mm, Progressive, z/t=0.00 AS04_M_avg, a_tot=4.68mm AS08_M_avg, a_tot=4.60mm AS02_M_avg, a_tot=4.49mm AS06_M_avg, a_tot=4.46mm AS01_M_avg, a_tot=4.30mm

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Figure 3 Predicted and measured COD for progressive cracks at (a) surface (b) mid-plane

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It is worth noting that the residual stress field due to preload gives a peak CDF of about 32.5 MPa—m for the simultaneous a = 2 mm crack. This is larger than the specified minimum fracture toughness: so such specimens might be expected to initiate ductile crack growth with little additional (primary) loading. For the progressively introduced a = 2 mm crack the CDF is nearly 24.0 MPa—m. Here, a larger additional primary loading would be required to cause ductile initiation. Discussion Figures 2(a) and (b) has demonstrated the significant difference between the predicted COD generated for defects introduced simultaneously versus progressively. The main reason for this difference is that for the progressively introduced crack, plastic strain is accumulated along the crack length during crack development. Conversely, for the simultaneously introduced crack, pleastic strain is only accumulated at the crack tip. Figure 5 illustrates that the distribution of equivalent plastic strain ahead of the notch tip (generated by preloading) is largely unchanged due to the introduction of a crack into the model in a simultaneous manner. The plastic strain is only increased in the first two elements ahead of the new crack tip, leading to a large crack tip opening displacement, Fig. 2(a,b). Conversely, there is marked difference in the plastic strain in the wake of the crack introduced in a progressive manner. Here the plastic strain is increased locally above that due to the preload. The comparison between these experimental data and the numerical results for progressive cracks at mid-thickness are particularly encouraging, Fig. 3(b). They provide useful experimental validation for this approach for simulating crack development in numerical analyses. These results demonstrate that it is important to simulate adequately the process by which cracks develop in real structures. For progressive cracking processes such as stress corrosion cracking (SCC), creep and (in the current work) fatigue, the progressive introduction of a crack into a FE model by stepped nodal release is most appropriate. Such slow crack growth in a residual stress field consumes elastic strain energy, since the developing crack leaves a plastic wake behind the current crack tip. Conversely, for pre-existing cracks or rapid crack development (e.g. local brittle zones, hydrogen cracking), the simultaneous approach to introduce a crack into an FE model may be more appropriate. The instantaneous approach to crack introduction in the FE model always gives a higher COD profile behind the crack. In line with this observation, crack driving forces KJs based on JEDI for instantaneous cracks are shown to be larger than for cracks introduced progressively, Fig. 4. These observations have important practical consequences. For the accurate assessment of the initiation condition for slowly growing cracks in engineering structures, it is more appropriate to model the progressive introduction of the crack into the model. Conservative results would, however, be obtained using the instantaneous

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approach. Conversely, it is important to note that the progressive approach could reduce conservatisms in Leak-before-Break (LbB) assessments, since the crack opening area is minimised, Fig. 12. In this case, conservative results would be obtained using the progressive approach. 35

z/t=0.000, K(Elastic) z/t=0.000, KJ(Simul)

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Figure 5 Distribution of equivalent plastic strain after inserting 2 mm long crack simultaneously and progressively into the preload residual stress field Conclusions This paper has presented the results of a series of experimental measurements of Crack Opening Displacement in preloaded and pre-cracked compact tension specimens of a high strength, low toughness aluminium alloy. The experimental

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results have been compared with three-dimensional finite element predictions. In addition, the crack driving force for cracks of differing lengths has been calculated using the JEDI post-processing code. The following conclusions have been made as a result of this work. 1.

2. 3. 4.

5.

6.

7.

8.

9.

The preloading of the compact tension specimen creates a region of high tensile stress over the first one to two millimetres ahead of the notch, followed by a large reduction over the next 3 mm or so. The ensuing maximum peak compressive stress occurs at about 6 mm ahead of the notch tip. There is good agreement between experimentally measured and numerically calculated surface displacements resulting from the preloading. There is generally good agreement between the predictions of crack opening displacement profile for the progressively created cracks and the experimental measurements at mid-thickness. At the specimen surface there is generally less agreement between measurement and prediction, with a tendency for the FEA to underpredict the measurements particularly at the beginning of the fatigue crack near the spark-eroded notch. For 1 mm and 2 mm long cracks, the CDF is maximum at mid-thickness and slowly decreases until very close to the near surface, where it then falls rapidly. For longer cracks, the peak CDF at occurs nearer the free surface, consistent with the pattern of uncracked residual stresses. The CDF for the progressively introduced crack is always smaller than the simultaneous case. This is most apparent for the shortest cracks that lie in the intense tensile stress directly ahead of the notch, where the CDF for the progressive case is about 70 to 75% of that for simultaneous. For the shorter cracks, the JEDI calculated, elastic-plastic results for the simultaneous cases tend to be slightly smaller than the elastic estimates of CDF. For the longest cracks, the finite element cracked body results for the simultaneous cases are in good agreement the elastic estimates of CDF. The preloading gives a peak CDF of about 32.5 MPa—m for the simultaneously introduced 2 mm long crack. This is larger than the minimum fracture toughness and so such specimens might be expected to fail with little additional (primary) loading. For the progressively introduced 2 mm long crack, the CDF is nearly 24 MPa m. Here, a larger additional primary loading would be required to break the specimen. The results have practical implications for the assessment of initiation for slowly growing cracks, where assessments would be more accurate using progressive crack introduction. Acknowledgments

The authors are grateful to Mr D W Beardsmore (Serco Assurance) for the supply of the JEDI post processor, and to Serco Assurance and the Royal Society for their support of this work through the Industry Fellowship scheme.

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References 1. R6: Assessment of the integrity of structures containing defects, British Energy Generation Limited, Revision 4 (2001). 2. Beardsmore, D,W. and Sherry, A.H., “Allowance for residual stresses and material interfaces when calculating J in and close to welded joints”, ASME Press. Vess. Piping, 464, 11-21 (2003). 3. ABAQUS/Standard Users Manual Version 6.3, Hibbitt, Karlsson and Sorensen Inc, 1080 Main Street, Pawtucket, Rhode Island (2003).

Author Index

A Ando, K........................................ 201 Anifantis, N.K................................. 27 B Babski, K. .................................... 139 Bate, S.K. .................................... 105 Bertacchini, O.W. ........................ 209 Boczkowska, A. ........................... 139 Boguszewski, T. .......................... 139 Bolle, B. ......................................... 87 Bouchard, P.J.............................. 163 Braham, C. .................................... 77 C Charles, R. .................................. 105 Chau, T.T. ................................... 117 Chevrier, P. ................................... 87 Combescure, A............................ 149 Coret, M....................................... 149 D Devaux, J. ....................................... 3 Djemaiel, Abdelkahader ................ 77 Duranton, P. .................................... 3

K Katsareas, D.E......................... 15, 27 Keppas, L.K. .................................. 27 Kumar, B...................................... 189 Kurzydlowski, K.J......................... 139 L Lagoudas, D.C............................. 209 Lewandowska, M. ........................ 139 M Mikula, P. ....................................... 67 Mirzaee-Sisan, A. ....................... 177 N Neov, D. ........................................ 55 Nouet, L. .......................................... 3 O O’Gara, D..................................... 105 Ohms, C............................. 15, 55, 97 Okada, H...................................... 201 P Patoor, E...................................... 209 Puerta Velásquez, J.D. .................. 87

E El Ahmar, Walid............................. 41 Everett, D. ................................... 105

Q Quinta da Fonseca, J................... 223

F Fredj, Nabil ben ............................. 77

R Rhouma, Amir ben......................... 77

G Gilles, Ph. ........................................ 3 Goldthorpe, M.R. ......................... 223

S Sherry, A.H. ................................. 223 Sidhom, Habib ............................... 77 Smith, D.J. ................................... 177 Smith, M.C. .................................. 177 Swieszkowski, W. ........................ 139

J Jullien, J.-F. ................................... 41

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234

Author Index

T Tange, A.......................................201 Taylor, K. ......................................223 Tidu, A. ...........................................87 Truman, C.E. ................................177

W Warren, A..................................... 105 Wimpory, R.C. ............................... 55 Withers, P.J. ................................ 163 Wu, T. .......................................... 149

U Uca, O. ...........................................97

Y Yellowlees, S................................ 105 Youtsos A.G................. 15, 27, 55, 97

V Vrána, M.........................................67