TWO INTERFACIAL COLLINEAR GRIFFITH CRACKS IN THERMO- ELASTIC COMPOSITE MEDIA

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1 WO INERFIL OLLINER GRIFFIH RS IN HERMO- ELSI OMOSIE MEDI h m MISHR S DS * Deme o Mheml See I Ie o eholog BHU V-5 I he oee o he le o he e e o eeg o o olle Gh e he ee o he wo ohoo mel e e e emee el. he olem ee o o gl egl eqo whh e ole g Jo oloml. Nmel omo e e o o wo ee o ohoo mel o ee l e whh e ee hogh ge. he ee o mel o emee oee o he eho o hl qe z. e e o eeg o he el he e ee o he ee le. e Wo: heml ee olle Gh S eeg elee e he l. Ioo I m egeeg le z. eleo eoe le eeg lo o eeh h le ee oe g he o eho o he e leme el he o he e he ee o he omoe mel e o heml log. Ohoo omoe mel e wel e l mel e o he lgh wegh og e. Whe e ohoo omoe mel e hgh o low emee ego he he low hogh mel. I h e mo o eeme he heml e e o he whh o e o he e he he l. he ego o hemo-el el heml e oeo o he hel o e he l le o he e egeeg mel e. og o le el e meh e he o he gl. I el oool o he ee o qe oo o e om he. M oeo o hemo-el e e how h he heml e gl he o he e me hoe wh mehl ee. Howee he e o gl eome ee o el. he oee o he el he e o l omoe e o heml mehl log eme mo eeh o e meh. Fo lzg el m e wee oe e heml e e oo o ohoo omoe mel. I 9 Sh ] eeme he e e o SIF o e le whe he he low eel o he e. Le See ] eeme he e e o o e o he l. he heml ee e le e o he he l o wo he ee *oeog ho. S. D; el.: ; S. D.

2 eeme he me ho ]. Se e o o he wo olle wee ele he Zhg 4] ohoo le e he he l. heml e o gle e el le heml e o wo llel h ee eeme Io Rege 5]. he Zhg ] he eeme he heml e ohoo og wo olle. I Io 7] ele e e o o wo llel e ohoo le e o he he l. I 7 B e l. 8] he ole he olem o eemg he heml ee leme el ohoo le og o eql olle Gh g he egl om ehqe e o leme oel e e e emee el. I Zhog e l. 9] eme he eho o wo olle emee ohoo ol g he Foe egl om ehqe e om he l mehl log o he e e. olem ele o heml e lo e o he eeh le ]-5]. I he ee le he ho he me eeo o eeme he e e o he o o olle Gh e he ee o wo ohoo hemo-el hl le ee o om he l lo o eeme he eeg eqe o eg wo ew e l eomo o he e he e-e emee el. he olem h ee ee o o eo Feholm egl eqo whh e ole mell g Jo oloml. Nmel le o he e e o he o he o ee ee legh e eee hogh gh o ee l e. Nmel le o ohe hl q eeg oe hogh ee om o he leme oel o e lo eee ghll. olem Fomlo Le oe mheml moel o wo oe homogeeo ohoo el hl le og o olle Gh e mmell he ee whe e o-oe e oe wh he e o mme o he el mel. Whe heml oo e le o he e o wo meol ohoo hl le he he emee el ol ee o -le o-oe e he e e oo. he emee o o e me o he ollowg he oo eqo he ohoo me. whee eo eeel o eh hl le. he geel olo o.. he ] = e he heml oe oee log { E ] E ]} whee e he o o. Hee we he me h h hee he Foe egl om o emee o m e we

3 . } ] ] ] ] { E E h E E h 4 Fom eqo 4 we ge ] E h ] E h 5 Fom eqo 5 he emee o oe. h I we oe h 7 whee h he ee emee o eome le oe log - he D el o he el emee o oe. 8 Fg.. Geome o he olem he elo ewee he le e e he o o emee leme omoe log eo e ge 9

4 4 whee e he el o e he e emee oee. he leme eqo o eqlm e ge he qe wh e ee o hoe o he hl le- hl le- eeel. I me h he ee he ee e oee el oml heg o eeel Fg.. Fo he ee olem he o oo o = e ge Solo o he olem Dg he olo o he olem we oe leme oel Shm 7] e B e B } { } { } {. oel o o he hl le e ge e o e o. he leme omoe e we. he oeog heml ee e 4 5

5 5. he leme eqo - e e eqo o o-l 7 B B. 8 Hee he oel o e he ollowg eel eqo ; whee e he el oo o he eqo ] 9 wh. e he eeme o. lg he o oo 8 9 we ge Bo oo 7 wh he hel o he oe eqo ge e o o Now eg o

6 whee e legh oe o mheml mlo o oo 4 5 ll le o he ollowg gl egl eqo whee

7 7. Eqo e ee o he ollowg gl egl eqo o he eemo o ow o : g 4 whee ] ` ` g e g he oo. he olo o he oe egl eqo 4 m e me 5 whee l wh ow o. Now g eqo we ge whh mle. Fom eqo we ge g. Mllg he oe eqo egg om - o we ge F L l 7! whee L g F he l le o oee zeo. Fll he e e o he e lle

8 I II lm ]. I II lm ] he eeg lle. 8 9 W ]. 4 Rel o I h eo he mel omo he ee oe o hl qe z. e e o he eeg o wo olle e he ee o wo o ohoo mel wh oe -Um Eo Boo he eo oe Bellm Eo Boo. I eh e e o mel e hl le- eo e o mel hl le-. Dg he omo he legh oee =... 9 lo he log e oee. he o o he e emee oee e e.7.5 eeel o he o mel.7.5 eeel o eo o mel. he el o o he ohoo mel -Um he ee e G 4.5. G G G D 8].he el o o he ohe oee ohoo mel Boo-Eo h ee e. 8.9 G.78. G G G Sh he 9] hoe o ohoo mel Bellm e e G G G D 8]. Fo he eo o mel he e e o he e ee hogh Fg. Fg. eeel o ee le o whee he hl qe he o oh he o mel e ee hogh Fg. 4-5 o o. he mel le o eege o he wo o mel e how hogh Fg.-7 o ee le o. I ee om Fg. h he legh o he eee oh eee. Sme e ollowe o he eo o mel Fg. wh ol eee h he le o e e o hge omleel ee o mel o. he legh o he eee Fg. 4-5.e. eo e ee he eee II ee e hemo-mehl log o oh o mel. h how h hee le ol o ogo ee whe he o he ome e loe o eh ohe. he eee o Moe II e e o e h he e ewee wo eee he ee o he ogo ee lg moe wll e eee. I II I 8

9 Nomlze Se Ie Fo Nomlze Se Ie Fo he e o eho o eeg o o mel me he eo o mel wh he eee h e he e o he eee e ome o he gll eee o he eo e. I he mel omo lo ge el emh o eeme ohe hl q eeg W o eeme he eeg eqe he e ee e. Fge 7 how h he eeg ee wh he ee o legh. he eme o eeg eee h e he l zoe ze eome lge e o whh moe eeg wll e eqe o he ogo e g l le. I ee om he Fge -5 h o mel moe e e ome o eo o mel who e lo e om Fge -7 h o he o mel he eeg hghe ome o he eo o mel e o omo o lge l zoe he wh ee o legh. 4 I II 4 8 Fg.. lo o I II. o he o mel 4 I II 4 8 Fg.. lo o I II. o he eo o mel 9

10 Nomlze Eeg Nomlze Se Ie Fo Nomlze Se Ie Fo 5 I 5 II 4 8 Fg.4. lo o I II. o he o mel 5 I 5 II 4 8 Fg.5. lo o I II. o he eo o mel Fg.. lo o W. o he o mel

11 Nomlze Eeg Fg.7. lo o W. o he eo o mel olo I he ee le he ho he hee o mo gol. he oe he ego o o olle Gh he ee o wo ohoo me e hemo-mehl log. Seo oe g he ll om o he e e o he o he. h oe he el eeo o o o he e e o wh eo e. Foh oe he ee o eeg e o ee o legh o he howg he ol o he omo o lge l zoe he o he. owlegeme he ho o he le ee he heel h o he eee eewe o he lle ggeo o he moeme o he le. he ho owlege he l o om he SIR New Delh I e he SRF heme. Nomele - Bo o o he m] - he o o heml oe oee log he eo eeel -] - emee o o o ] - Dleme omoe m] I I - Nomlze SIF o Moe I e = = eeel -] II II - Nomlze SIF o Moe II e = = eeel -] W - Nomlze eeg -] Gee lee - e emee oee G o ] - e eo log he eeel G] - She e eo G]

12 Reeee ]. Sh G.. O he gl he o heml ee e SME Jol o le Meh ]. See H. heml ee e o le le em-e mem e om he low Egeeg Fe Meh ]. See H. hemoel eo ewee wo eghog Jee o o J Soe o Mehl Egee ]. he B. Zhg X. hemoel olem o ohoo le wh wo olle Ieol Jol o Fe ]. Io S. Rege Q. heml ee o wo llel wo oe ml el hl-le he o le Meh ]. he B. Zhg X. O le hemoel olem o ohoo wh wo olle Jol o Nohwee olehl Ue ]. Io S. heml ee o wo llel e ohoo le e om he low Jol o heml See ]. B. D S. Be R.. oe o hemo-el olem o wo olle Gh ohoo mem I. J. o e le Mhem ]. Zhog X.. W B. Zhg.S. hemll og olle egle hemo-mehl el mel wh ohoo heoel le Fe Meh ]. h. Se heml e e og l le e e e emee heml See 8 4 Sl..S9-S. ]. Zh Z.-W. M Y. Zhg H.-D. Sog W.-D. G Y.-. Elo o heml ee e e oze ol heml ee ]. h. Se heml Se S Re l le wh homogeeo omel ee o heml lo heml See 8 4 Sl..S8-S9. ]. Sll L. B. Dole O. he oee M-egl o heml-el olem Ieol Jol o Fe ]. Io S. heml e e o o e ohoo le wh Ieol Jol o Fe ]. Io S. heml ee o hee le ewee wo ml el Hl-le Jol o heml See ]. leme D. L. he. R. hemoel olem o oo l J. l. Mh. So. See B ]. Shm B. heml ee eel oo em-e el ol J. l. Meh ]. D S. B. Se e o o mog el ewee oe ml e ohoo le ome & Se ]. Sh G.. he E.. omoe mel M Nho lhe Hge Nehel 98.

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