Исследование полимерных материалов методом линейной дилатометрии

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Author: Клюшниченко А.Б.

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 α∆[   αK   ∂ε I   ∆[δα   + ⋅   +  δ/7  δε I 7 =  δ7  +  /   /7   ∂7   /7   7 

(1.2)

]^_ δΤ − ]jZ^b_gl l_fi_jZlmju ih ^ebg_ l_jfhdZf_ju (g_ [he__ hK), ∆x – Z[khexlgh_ jZkrbj_gb_ ih^\_kghc kbkl_fu \ _^bgbpZo nhlhyq__d α − dhwnnbpb_gl ij_h[jZah\Zgby i_j_f_s_gby i_j_iZ^Z ³k\_ll_gv´ \ ^_ckl\bl_evgh_ i_j_f_s_gb_ fdfnhlhyq_cdZ δα − Z[khexlgZy ih]j_rghklv hij_^_e_gby α ( fdfnhlhyq_cdZ ), h – jZaj_rZxsZy kihkh[ghklv baf_jbl_ey fbdjhi_j_f_s_gbc fdf δLT Z[khexlgZy ih]j_rghklv baf_j_gby ^ebgu l_jfhdZf_ju 2,5 ff). Bkoh^y ba \ur_kdZaZggh]h ^ey ih]j_rghklb hij_^_e_gby l_jfbq_kdh]h jZkrbj_gby h[jZapZ fh`gh aZibkZlv:  ∆O δ  0  /

  = 

   δ∆O   ∆O  +  δ/  +  δε I     /   /  

 / ⋅  − 7  /

   ε I δ/7   +     /

  ε I /7 δ/    +    /   

(1.3)

]^_ δ∆l ± Z[khexlgZy ih]j_rghklv ^ey ∆l b hij_^_ey_lky nhjfmehc δ∆O =

(∆[& δα ) + ⋅ (αK )

(1.4)

]^_ ∆xK – Z[khexlgh_ jZkrbj_gb_ ih^\_kghc kbkl_fu k h[jZaphf \ _^bgbpZo yq__d fgh]hwe_f_glgh]h nhlhijb_fgbdZ Ih]j_rghklv l_jfbq_kdh]h jZkrbj_gby jZkkqblZggZy ih nhjfme_ ijb ^ebg_ h[jZapZ ff g_ ij_\urZ_l Â-4.

11

KemqZcgZy ih]j_rghklv hij_^_eyxsZy oZjZdl_jgmx \_ebqbgm rmfZ kdeZ^u\Z_lky ba \b[jZpbc i_j_^Zxsboky ih^\_kghc kbkl_f_ fh^meypbb bgl_gkb\ghklb k\_lZ hk\_lbl_ey hrb[db k\yaZgghc k ^bkdj_lghklvx we_f_glh\ FWN Z lZd`_ kemqZcguo nemdlmZpbc l_jfbq_kdh]h jZkrbj_gby d_jZfbdb hl Ziijhdkbfbjmxs_]h ihebghfZ Bkoh^y ba \ujZ`_gbc ^ey kbkl_fZlbq_kdhc ih]j_rghklb \ghkys_c d\Zabebg_cgu_ bkdZ`_gby fh`gh aZibkZlv

 ∆O   ∆O   δ/ δ   =  δ/  +  ε N (7 ) 7 / / /   kbkl   

  ∆[δα    /    ∆[ ⋅α − ε N (7 )/7   +  δ/  +   − 7 δε kbkl (7 ) +  /      /    / 

(1.5)

Ijb wlhf \_ebqbgZ ih]j_rghklb g_ ij_\urZ_l Â-4. >ey rmfh\ hq_\b^gh:

  /7    ∆O  α ⋅ WQ ) ( K δ   =   − δε ke  + + σ [ + σ [  / ke   /   / / (Q − )

(

)

(1.6)

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13

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L

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I (7 ) =

D , + H[S[G ⋅ (7 − 7 )]

(2.2)

]^_ a\_ebqbgZ i_j_iZ^Z DELJ /d ± ihemrbjbgZ i_j_oh^Z L0 ± oZjZdl_jgZy l_fi_jZlmjZ i_j_oh^Z
I (7 ) =

D ⋅ G ⋅ H[S[G ⋅ (7 − 7 )] , { + H[S[G ⋅ (7 − 7 )]}

(2.3)

dhlhjZy y\ey_lky ijhba\h^ghc hl nmgdpbb 2. eb[h nmgdpb_c jZkij_^_e_gby =ZmkkZ

[

I (7 ) = D ⋅ H[S − G ⋅ (7 − 7 )

]

(2.4)

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15

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18

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Ijb gZ]j_\_ \ ^beZlhf_ljbq_kdhc ljm[_ ijhbkoh^bl j_eZdkZpby \gmlj_ggbo gZijy`_gbc ijb gZebqbb ehdZevghc ih^\b`ghklb mqZkldh\ fZdjhp_i_c b [hdh\uo ]jmii βj_eZdkZpbb

20

Bkke_^m_fZy ie_gdZ y\ey_lky ijhkluf ebg_cguf ihebf_jhf Ohjhrh \ujZ`_gguf j_eZdkZpbhgguf ijhp_kkhf ^ey g__ y\ey_lky αj_eZdkZpby dhlhjZy y\ey_lky h[jZlbfuf ijhp_kkhf lZd dZd ijb hoeZ`^_gbb kbkl_fZ \ha\jZsZ_lky \ bkoh^gh_ khklhygb_ LZdbf h[jZahf \ ijb\_^_gghf ijbf_j_ h[gZjm`_gguc wnn_dl mkZ^db h[mkeh\e_g \gmlj_ggbfb gZijy`_gbyfb ijbkmlkl\mxsbfb \ ie_gd_ IhiulZ_fky gZclb mjh\_gv wlbo gZijy`_gbc ba wdki_jbf_glZevgh hij_^_e_ggh]h l_jfbq_kdh]h jZkrbj_gby b agZq_gby fh^mey Xg]Z ^ey ZgZeh]bqgh]h ihebf_jZ \aylh]h ba ebl_jZlmju >@ Hp_gbf \gmlj_ggb_ gZijy`_gby \ ijb[eb`_gbb ^_nhjfZpbb ijhklh]h jZkly`_gby bkihevamy deZkkbq_kdmx l_hjbx \yadhmijm]hklb [4] Ij_^iheh`bf qlh \ fZl_jbZe_ bagZqZevgh ijbkmlkl\m_l ^_nhjfZpby h[mkeh\e_ggZy \gmlj_ggbf gZijy`_gb_f dhlhjZy bkq_aZ_l ijb j_eZdkZpbb gZijy`_gby \uau\Zy l_f kZfuf mkZ^dm dhlhjZy hlq_leb\h nbdkbjm_lky ijb ^beZlhf_ljbq_kdbo baf_j_gbyo Ba l_hjbb mijm]hklb ba\_klgh qlh jZkly]b\Zxs__ gZijy`_gb_ σ = F/s l_ jZ\gh jZkly]b\Zxs_c kbe_ hlg_k_gghc d iehsZ^b ihi_j_qgh]h k_q_gby h[jZapZ Fh^mev Xg]Z ih hij_^_e_gbx k\yaZg k gZijy`_gb_f b \_ebqbghc ^_nhjfZpbb khhlghr_gb_f (=

σ , ε

(2.5)

]^_ ε = ∆l/L – ^_nhjfZpby h[mkeh\e_ggZy gZijy`_gb_f Hp_gbf ^_nhjfZpbx h[mkeh\e_ggmx gZqZevgufb gZijy`_gbyfb bkoh^y ba ij_^klZ\e_gby f_lh^hf ^ey \u^_e_gby lhc qZklb j_eZdkZpbhggh]h ki_dljZ h kmi_jihabpbb j_eZdkZpbhgguo ijhp_kkh\ \ ihebf_jZo [3] i b \hkihevah\Z\rbkv ki_dljhf_ljbq_kdbf dhlhjZy h[mkeh\e_gZ j_eZdkZpb_c gZqZevguo gZijy`_gbc GZ jbk bah[jZ`_gZ qZklv l_fi_jZlmjghc aZ\bkbfhklb i_j\hc ijhba\h^ghc DELJ ih l_fi_jZlmj_ Imgdlbjhf ihf_q_gZ khklZ\eyxsZy

21

j_eZdkZpbhggh]h ki_dljZ dhlhjZy k\yaZgZ k bgl_j_kmxsbf gZk ijhp_kkhf H[hagZqbf __ f1(T) Lh]^Z bkdhfZy ^_nhjfZpby ∆O

/

=

7.

7

∫ G7 ∫ I (7 ′)G7 ′ ,

7

(2.6)

7

]^_ l_fi_jZlmju L0 b LD \u[bjZxlky hlklhysbfb ^hklZlhqgh ^Ze_dh hl oZjZdl_jghc l_fi_jZlmju bkke_^m_fhc j_eZdkZpbb < ijb[eb`_gbb fh`gh lZd`_ ihevah\Zlvky [_kdhg_qgufb ij_^_eZfb g_kfhljy gZ lh qlh l_fi_jZlmjgZy rdZeZ h]jZgbq_gZ

0.00002

α

.

0.00000

-0.00002

-0.00004 R 7

60

70

80

90

100

&

110

Jbk MqZklhd l_fi_jZlmjghc ijhba\h^ghc DELJ Zfhjnghc ihebwnbjghc ie_gdb

Lh]^Z bkoh^y ba \ujZ`_gbc b mqblu\Zy qlh fh^mev Xg]Z ? aZ\bkbl hl l_fi_jZlmju ^ey ^bnn_j_gpbZeZ hl gZijy`_gby fh`gh aZibkZlv Gσ (7 ) = σ 7′ G7 = α (7 )⋅ ( (7 )G7 , (2.7) ]^_

α (7 ) =

7

∫ I (7 ′)G7 ′ – khklZ\eyxsZy DELJ Lh]^Z ij_^iheh`b\ qlh

7

gZqZevgu_ gZijy`_gby iheghklvx j_eZdkbjmxl ijb ^hklb`_gbb g_dhlhjhc dhg_qghc l_fi_jZlmju LD ihemqbf hdhgqZl_evgh_ \ujZ`_gb_ ^ey gZqZevgh]h gZijy`_gby

22

σ =

7.

∫ ( (7 )⋅ α (7 )G7

(2.8)

7

h Fh^mev Xg]Z ^ey ZgZeh]bqguo fZl_jbZeZo \ bgl_j\Ze_ l_fi_jZlmj K 8 fh`gh hp_gblv ijbf_jgh \ =IZ IZ [5] k_q_gb_ bkihevam_fh]h -8 2 f <_ebqbgZ mkZ^db h[mkeh\e_gghc h[jZapZ ff× ff gZqZevguf gZijy`_gb_f khklZ\ey_l ijbf_jgh Lh]^Z fh`gh hp_gblv \_ebqbgm gZqZevgh]h gZijy`_gby

Â

Â

 ∆O  σ ≈   ⋅ ( = ⋅ IZ  / 

OZjZdl_jgZy kbeZ gZijy`_gby \hagbdZxsZy \ h[jZap_ G F0 = σ0 ·s ≈ qlh khhl\_lkl\m_l ]jmam ijbf_jgh \ ] Gb`gyy qZklv ih^\_kghc kbkl_fu ebg_cgh]h ^beZlhf_ljZ \_kbl ijbf_jgh ] Ba wlh]h fh`gh k^_eZlv \u\h^ qlh ijb ijh\_^_gbb wdki_jbf_glZ k fZl_jbZeZfb bf_xsbfb gbadbc fh^mev Xg]Z b fZemx iehsZ^v lj_[m_lky hp_gb\Zlv b mqblu\Zlv \ebygb_ ih^\_kghc kbkl_fu gZ h[jZa_p KbeZ \ebyxsZy gZ ih\_^_gb_ h[jZapZ kdeZ^u\Z_lky ba kbeu \gmlj_gg_]h gZijy`_gby b \_kZ gb`g_c qZklb ih^\_kghc kbkl_fu Bkoh^y ba wlh]h fh`gh \\_klb ihijZ\dm \ hij_^_e_gbb \gmlj_gg_]h gZijy`_gby

σ =σ +

Pi J V

(2.9)

K mq_lhf ihijZ\db ihemqbf mlhqg_ggh_ agZq_gb_ gZqZevgh]h \gmlj_gg_]h gZijy`_gby \ h[jZap_ σ ≈ 4·106IZ

23

0.005

∆ //

0.000

1 2

-0.005 -0.010 -0.015 -0.020 -0.025 -0.030 -0.035 7

R

&

-0.040 20

30

40

50

60

70

80

90

100

110

Jbk L_jfbq_kdh_ jZkrbj_gb_ ie_gdb N ±k gZ]jmadhc ] ±k gZ]jmadhc ] <ebygb_ ih^\_kghc kbkl_fu gZ l_jfbq_kdh_ jZkrbj_gb_ ihebf_jguo ie_ghd

ohjhrh

beexkljbjmxl

^beZlhf_ljbq_kdb_

djb\u_

ie_gdb

ihebl_ljZnlhjwlbe_g N ihemq_ggu_ ijb jZaebqghf \_k_ gb`g_c qZklb ih^\_kghc kbkl_fu Ba \ur_baeh`_ggh]h fh`gh k^_eZlv \u\h^ h g_h[oh^bfhklb mqblu\Zlv \ebygb_ gZ]jmadb ijb ^beZlhf_ljbq_kdbo bkke_^h\Zgbyo fZl_jbZeh\ k gbadbf agZq_gb_f fh^mey Xg]Z b fZehc iehsZ^vx k_q_gby h[jZapZ LZd`_ ijb bgl_jij_lZpbb ^beZlhf_ljbq_kdbo j_amevlZlh\ hkh[_ggh ijb ij_^hklZ\e_gbb aZdZaqbdm ^Zgguo h DELJ ^ey l_ogbq_kdh]h bkihevah\Zgby g_h[oh^bfh bf_lv ij_^klZ\e_gb_ h \ebygbb gZ]jmahd gZ k\hckl\Z fZl_jbZeZ Z lZd`_ h g_h[jZlbfuo ijhp_kkZo \ fZl_jbZeZo dhlhju_ bkq_aZxl ijb wdkiemZlZpbb ihke_ g_kdhevdbo l_jfhpbdeh\ gh ijb wlhf ijbkmlkl\mxl \ bkoh^ghf k\_`_ba]hlh\e_gghf fZl_jbZe_

24

<ebygb_ \eZ]b gZ l_jfbq_kdh_ jZkrbj_gb_ IDF

;ueb ijh\_^_gu ^beZlhf_ljbq_kdb_ bkke_^h\Zgby m]e_ieZklbdZ DFDM

\ bkoh^ghf khklhygbb b ihke_ m\eZ`g_gby FZl_fZlbq_kdZy h[jZ[hldZ

^beZlhf_ljbq_kdbo djb\uo ihdZau\Z_l j_adh_ baf_g_gb_ j_eZdkZpbhgguo ki_dljh\ ijb m\eZ`g_gbb fZl_jbZeZ

Bkoh^guc

∆L/L0

∆L/L0

0.0010

0.0010

0.0005

0.0005

0.0000

o

T, C 0

0.000020

50

α, K

100

150

200

0.0000

250

o

T, C 0

0.000020

-1

0.000015

0.000015

0.000010

0.000010

0.000005

M\eZ`g_gguc

50

α, K

100

150

200

250

-1

0.000005 o

o

T, C 0.000000

T, C 0.000000

0

50

100

150

200

250

0

50

100

150

200

250

Jbk Ebg_cgh_ l_jfbq_kdh_ jZkrbj_gb_ m]e_ieZklbdZ DFDM

GZ jbk ihdZaZgu djb\u_ l_jfbq_kdh]h jZkrbj_gby m]e_ieZklbdZ lbiZ DFDM \ bkoh^ghf b m\eZ`g_gghf khklhygbyo Wdki_jbf_gl ihdZau\Z_l j_adh_ baf_g_gb_ k\hckl\ fZl_jbZeZ ijb m\eZ`g_gbb Nbabq_kdmx ijbjh^m wlbo baf_g_gbc fh`gh \uykgblv agZy ij_^uklhjbx bkke_^m_fuo h[jZaph\ M\eZ`g_gb_ h[jZaph\ ijh\h^behkv \ l_jfhdZf_j_ ijb l_fi_jZlmj_ hK b \eZ`ghklb Ijb wlhf k bgl_j\Zehf ijh\h^behkv l_jfhpbdebjh\Zgb_ ± hoeZ`^_gb_ ^h dhfgZlghc l_fi_jZlmju Wlh k\yaZgh k l_f qlh iZjZee_evgh k m\eZ`g_gb_f ijh\h^beky dhgljhev khj[pbb \eZ]b

25

J_amevlZlu ^beZlhf_ljbq_kdbo baf_j_gbc ihdZau\Zxl kf_s_gb_ ibdZ DELJ khhl\_lkl\mxs_]h α-j_eZdkZpbb \ h[eZklv [he__ \ukhdbo l_fi_jZlmj Ijb wlhf ibd DELJ klZgh\blky [he__ yjdh \ujZ`_gguf gZ nhg_ \k_c djb\hc ih kjZ\g_gbx k khhl\_lkl\mxsbf ibdhf ^ey g_m\eZ`g_ggh]h h[jZapZ < ^Zgghf kemqZ_ fh`gh k^_eZlv ij_^iheh`_gb_ h ^hhl\_j`^_gbb k\yamxs_]h \ ijhp_kk_ m\eZ`g_gby ijb \ukhdhc l_fi_jZlmj_ Yjdh \ujZ`_gguc ibd DELJ ih \k_c \b^bfhklb h[mkeh\e_g lZd`_ b l_f qlh \ ijhp_kk_ ^beZlhf_ljbq_kdbo baf_j_gbc ijhbkoh^bl bgl_gkb\guc \uoh^ \eZ]b ba h[jZapZ K =IZ

Kmohc M\eZ`g_g

Jbk >Zggu_ >F:bkke_^h\Zgbc m]e_ieZklbdZ DFDM

H^gZdh >F: bkke_^h\Zgby ijh\_^_ggu_ ^ey ZgZeh]bqguo h[jZaph\ ihdZau\Zxl bgmx dZjlbgm baf_g_gby k\hckl\ m]e_ieZklbdZ Ijhp_kk khhl\_lkl\mxsbc α-j_eZdkZpbb jZa^\Zb\Z_lky gZ ijbq_f h^gZ ba _]h khklZ\eyxsbo kf_sZ_lky \ h[eZklv [he__ gbadbo l_fi_jZlmj < ebl_jZlmj_ [6] ijbgylh k\yau\Zlv wlhl n_ghf_g k qZklbqghc ieZklbnbdZpb_c wihdkb^gh]h k\yamxs_]h JZaebqguc oZjZdl_j wnn_dlh\ ijhy\eyxsboky gZ ^beZlhf_ljbq_kdbo b >F: djb\uo \ ijhp_kk_ m\eZ`g_gby fZl_jbZeZ fh`gh hibkZlv l_f qlh ijhp_kk m\eZ`g_gby \ lhf \b^_ \ dZdhf hg ijhba\h^blky \ wdki_jbf_gl_

26

hdZau\Z_l dhfie_dkgh_ \ebygb_ gZ k\hckl\Z fZl_jbZeZ Ijb wlhf kms_kl\mxl jZaebqgu_ f_oZgbafu \ha^_ckl\by \eZ]b b l_fi_jZlmju h[mkeZ\eb\Zxsb_ bgh]^Z ijhlb\hiheh`gu_ wnn_dlu baf_g_gby ^bgZfbq_kdbo b l_ieh\uo k\hckl\ >ey lh]h qlh[u mlhqgblv nbabdm \ebygby \eZ]b gZ k\hckl\Z l_jfbq_kdh]h jZkrbj_gby m]e_ieZklbdZ DFDM lj_[m_lky ih \k_c \b^bfhklb ijh\_klb ^hihegbl_evguc wdki_jbf_gl gZ bkke_^h\Zgby fZl_jbZeZ ihke_ pbdeZ m\eZ`g_gb_ kmrdZ b ijb ih\lhjghf m\eZ`g_gbb < ex[hf kemqZ_ a^_kv kms_kl\m_l rbjhdh_ ihe_ ^ey ijh\_^_gby bkke_^h\Zgbc b i_jki_dlb\ghc jZ[hlu \ h[eZklb kh\_jr_gkl\h\Zgby l_ogheh]bb ijhba\h^kl\Z b memqr_gby wdkiemZlZpbhgguo oZjZdl_jbklbd ihebf_jguo dhfihabpbhgguo fZl_jbZeh\ b dhgkljmdpbc gZ bo hkgh\_

27

=eZ\Z :gbahljhiby ebg_cgh]h jZkrbj_gby IDF

:gbahljhiby ebg_cgh]h jZkrbj_gby h^ghgZijZ\e_gguo ihebf_jguo kbkl_f 3

>beZlhf_ljbq_kdb_ bkke_^h\Zgby h^ghgZijZ\e_gguo kbkl_f hlf_qZxl jZ^bdZevgh_ hlebqb_ k\hckl\ \ ijh^hevghf b ihi_j_qghf gZijZ\e_gbyo Ih \k_c \b^bfhklb wlh h[mkeh\e_gh jZaebqb_f oZjZdl_jh\ \gmljbfhe_dmeyjgh]h b f_`fhe_dmeyjgh]h \aZbfh^_ckl\by K\hckl\Z fZl_jbZeZ \ ijh^hevghf gZijZ\e_gbb h[mkeh\e_gu dZd ijZ\beh k\hckl\Zfb hkgh\guo m]e_jh^guo p_i_c < ihi_j_qghf gZijZ\e_gbb k\hckl\Z oZjZdl_jbamxlky oZjZdl_jhf hl\_l\e_gbc hl hkgh\ghc m]e_jh^ghc p_ib Z lZd`_ \aZbfh^_ckl\byfb \ gZ^fhe_dmeyjghc kljmdlmj_ Ihkdhevdm fu bkihevam_f \ dZdhc lh f_j_ b^_Zevgmx fZl_fZlbq_kdmx fh^_ev lh fu \ijZ\_ ij_^iheh`blv qlh fZl_jbZe khklhbl ba h^bgZdh\uo kljmdlmjguo we_f_glh\ Ijb wlhf g_kfhljy gZ klZlbklbq_kdbc oZjZdl_j ijhoh`^_gby j_eZdkZpbhgguo ijhp_kkh\ [m^_f kqblZlv qlh ijb baf_g_gbb l_fi_jZlmju ]_hf_ljbq_kdb_ jZaf_ju \k_o kljmdlmjguo we_f_glh\ baf_gyxlky Z[khexlgh h^bgZdh\h < wlhf kemqZ_ \ \_s_kl\_ gZ fZdjhmjh\g_ g_ ijhbkoh^bl ^_nhjfZpbc djmq_gby b f_`keh_\h]h k^\b]Z Ijb wlhf jZkrbj_gb_ [m^_l h[mkeh\e_gh bkdexqbl_evgh baf_g_gb_f ^ebgu b rbjbgu kljmdlmjguo we_f_glh\ b bo iZjZee_evguf i_j_ghkhf LZdbf h[jZahf ebg_cgu_ jZkrbj_gby \ ijh^hevghf b ihi_j_qghf gZijZ\e_gbb fh]ml kqblZlvky g_aZ\bkbfufb g_kfhljy gZ lh qlh h[mkeh\e_gu hgb h^gbfb b l_fb `_ j_eZdkZpbhggufb ijhp_kkZfb < k\yab k baeh`_ggufb \ur_ iheh`_gbyfb fu \ijZ\_ ^bnn_j_gpbjh\Zggh jZkkfZljb\Zlv \aZbfh^_ckl\by \ ijh^hevghf b ihi_j_qghf gZijZ\e_gbb LZdbf h[jZahf [m^_f kqblZlv qlh ebg_cgh_ jZkrbj_gb_ hibku\Z_lky ijhklhc j_heh]bq_kdhc fh^_evx jbk Kfuke __

28

aZdexqZ_lky \ lhf qlh jZkrbj_gb_ dZ`^h]h ba k_]f_glh\ jZkkfZljb\Z_lky dZd baf_g_gb_ _]h ^ebgu b rbjbgu GZc^_f ba wlbo mkeh\bc ebg_cgh_ l_jfbq_kdh_ jZkrbj_gb_ ^ey ex[h]h gZijZ\e_gby 1

2

jbk Kljmdlmjguc we_f_gl h^ghgZijZ\e_gghc ihebf_jghc kbkl_fu Z[khexlgh l\zj^uc [mn_j \yadhmijm]bc we_f_gl

<\_^zf \ fZl_jbZe_ dhhj^bgZlgu_ hkb lZdbf h[jZahf jbk qlh hkv HO iZjZee_evgZ hkb \uly`db Z hkv OY i_ji_g^bdmeyjgZ _c AZdj_ibf gZqZeh dhhj^bgZl \ lhqd_ H `_kldh k\yaZgghc k fhe_dmeyjghc kljmdlmjhc Imklv lhqdZ : lZd`_ `_kldh aZdj_ie_ggZy \ fZl_jbZe_ ijb l_fi_jZlmj_ L0 jZkiheh`_gZ gZ jZkklhygbb L0 hl lhqdb H lZd qlh m]he f_`^m hkvx HO b ebgb_c bo kh_^bg_gby jZ\_g ϕ Bkke_^m_f baf_g_gb_ jZkklhygby f_`^m wlbfb lhqdZfb ijb ih\ur_gbb l_fi_jZlmju _keb l_jfbq_kdb_ jZkrbj_gby \ ijh^hevghf b ihi_j_qghf gZijZ\e_gbb ih^qbgyxlky ba\_klguf aZdhgZf ( ( ) ∆L L0 0

b(

∆L L0 90

)

khhl\_lkl\_ggh Y

y

L0+∆L

y0

ϕ

A

:

L0

0

X x0 x

jbk

HibkZgb_ ebg_cgh]h jZkrbj_gby ihkj_^kl\hf dhhj^bgZl Iheh`_gb_ lhqdb : \ \u[jZgghc kbkl_f_ dhhj^bgZl

29

ijb l_fi_jZlmj_ L0 -(x0, y0): L0= x + y

(3.1)

L=L0+∆L= ( x0 + ∆x ) 2 + ( y 0 + ∆y ) 2

(3.2)

]^_ x0=L0 cosϕ , y0=L0 sinϕ ijb l_fi_jZlmj_ L – (x, y): ]^_ x=x0+∆x ,y=y0+∆y Ijh\_^y g_dhlhju_ Ze]_[jZbq_kdb_ ij_h[jZah\Zgby ihemqbf ∆L

L ϕ

=

FRV

ϕ + ∆LL + VLQ ϕ + ∆LL −

(3.3)

>bnn_j_gpbjmy ih l_fi_jZlmj_ ^ey DELJ ihemqbf αϕ=

α FRV ϕ> + ∆LL @ + α VLQ ϕ> + ∆LL @ FRV

ϕ + ∆LL + VLQ ϕ + ∆LL

(3.4)

Nhjfmeu b hljZ`Zxl \u[jZggmx dhgp_ipbx gh bkihevah\Zgb_ bo ^ey ZiijhdkbfZpbb wdki_jbf_glZevguo ^Zgguo ijZdlbq_kdb g_\hafh`gh ld hgb \_kvfZ keh`gu <\_^_f [_ajZaf_jgmx nmgdpbx d\Z^jZl ijb\_^_gghc ^ebgu f = (1 + ∆LL0 ) 2 = //R

(3.5)

Lh]^Z ba fh`gh ihemqblv hq_gv ijhklh_ khhlghr_gb_ ijb]h^gh_ ^ey j_r_gby ZiijhdkbfZpbhgguo aZ^Zq f(ϕ,Τ) = f(0,T)cos2ϕ + f(90,T)sin2ϕ

(3.6)

Ke_^m_l hlf_lblv qlh ^ZggZy ^\mf_jgZy fh^_ev Z^_d\Zlgh hibku\Z_l b g_mihjy^hq_ggmx fhe_dmeyjgmx kljmdlmjm < wlhf kemqZ_ k\hckl\Z h^bgZdh\u \h \k_o gZijZ\e_gbyo qlh fZl_fZlbq_kdb g_ ijhlb\hj_qbl \ujZ`_gbyf 3.3, 3.4, 3.6 Ijh^hevgZy b ihi_j_qgZy hkb \ ihke_^g_f kemqZ_ fh]ml \u[bjZlvky ijhba\hevguf h[jZahf < jZ[hl_ >@ khh[sZehkv h[ bkke_^h\Zgbyo l_jfbq_kdh]h jZkrbj_gby iezgdb ba ebg_cgh]h Zfhjngh]h ihebf_jZ ² ihebdZj[hgZlZ IhebdZj[hgZlgZy ie_gdZ y\ey_lky h^ghgZijZ\e_ggh hjb_glbjh\Zgghc kbkl_fhc GZ 30

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32

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3

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(3.7)

]^_ k ±dhwnnbpb_gl Zgbahljhibb dhlhjuc \ h[s_f kemqZ_ aZ\bkbl hl l_fi_jZlmju Dhwnnbpb_gl Zgbahljhibb fh`gh hij_^_eblv ba wdki_jbf_glZ Ba \ujZ`_gby ke_^m_l qlh N=

(∆/ / ) − (∆/ / )

33

(3.8)

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34

< ijbjh^_ b l_ogbd_ fh]ml \klj_qZlvky fZl_jbZeu l_jfbq_kdh_ jZkrbj_gb_ dhlhjuo g_ hibku\Z_lky Z^_d\Zlgh baeh`_ggufb jZg__ fh^_eyfb ijb]h^gufb ^ey h^ghgZijZ\e_gguo kbkl_f b ^\mgZijZ\e_gguo Zjfbjh\Zgguo ieZklbdh\ Ih^h[guo kbkl_f fh`_l kms_kl\h\Zlv fgh`_kl\h JZkkfhljbf ebrv g_dhlhju_ 1. :jfbjh\Zggu_ ieZklbdb k g_jZ\ghf_jguf gh g_ h^ghgZijZ\e_gguf jZkij_^_e_gb_f \hehdhg ih ^\mf \aZbfgh i_ji_g^bdmeyjguf gZijZ\e_gbyf eb[h k Zjfbjh\Zgb_f \ ^\mo ijhlb\hiheh`guo gZijZ\e_gbyo \hehdgZfb jZaebqgh]h lbiZ < wlhf kemqZ_ kbkl_fZ \_^_l k_[y dZd ^\mgZijiZ\e_gguc Zjfbjh\Zgguc ieZklbd b \ lh `_ \j_fy dZd h^ghgZijZ\e_ggZy kbkl_fZ jZkrbj_gby \ gZijZ\e_gbyo h b h hlghkbl_evgh hk_c Zjfbjh\Zgby kbevgh jZaebqZxlky < wlhf kemqZ_ ih \k_c \b^bfhklb jZamfgh ihkljhblv fh^_ev \ khhl\_lkl\b_ k baeh`_gguf jZg__ i ijbgpbihf kmi_jihabpbb j_eZdkZpbhgguo ijhp_kkh\ Ijb wlhf fh^_ev ijbf_l \b^  ∆/    =  / ϕ

{ ( I (7 )+ )FRV ϕ + ( I (7 ) + )VLQ

{

[

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(3.9)

+ I (7 )⋅ + N VLQ ϕ + I (7 )

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(3.10)

2.

3.

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36

AZdexq_gb_

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37

Ebl_jZlmjZ 1. 2.

Dex_\ :K :\lhfZlbq_kdh_ j_]mebjh\Zgb_±F Wg_j]by ±k Ojbklhnhjh\ >: Dexrgbq_gdh :; :\lhfZlbabjh\Zgguc ebg_cguc

^beZlhf_lj l_abku k[ “ R_klZy ` :gbahljhiby djmlbevghc `_kldhklb ihebf_jguo dhfihabpbhgguo fZl_jbZeh\ //F_oZgbdZ dhfihablguo fZl_jbZeh\ No3 ±k 9. Dexrgbq_gdh : ; Ebg_cgh_ jZkrbj_gb_ h^ghgZijZ\e_gguo ihebf_jguo kbkl_f k[ ³NbabdZ jZ^bhnbabdZ ± gh\h_ ihdhe_gb_ \ gZmd_´±;ZjgZme Ba^Zl_evkl\h :=M ± k 10. Dexrgbq_gdh : ; :gbahljhiby ebg_cgh]h l_jfbq_kdh]h jZkrbj_gby m]e_ieZklbdZ l_abku k[ “ IylZy

38

Исследование полимерных материалов методом линейной дилатометрии

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