Residual stresses in a ceramic-metal composite - Hal

Residual stresses in a ceramic-metal composite Vincent Cazajus, Sebastien Seguy, H´el`ene Welemane, Moussa Karama

To cite this version: Vincent Cazajus, Sebastien Seguy, H´el`ene Welemane, Moussa Karama. Residual stresses in a ceramic-metal composite. Applied Mechanics and Materials, Trans Tech Publications, 2011, vol. 146, pp. 185-196. .

HAL Id: hal-00784294 https://hal.archives-ouvertes.fr/hal-00784294 Submitted on 4 Feb 2013

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destin´ee au d´epˆot et `a la diffusion de documents scientifiques de niveau recherche, publi´es ou non, ´emanant des ´etablissements d’enseignement et de recherche fran¸cais ou ´etrangers, des laboratoires publics ou priv´es.

Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible.

This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID: 6574

To link to this article: DOI:10.4028/www.scientific.net/AMM.146.185 http://dx.doi.org/10.4028/www.scientific.net/AMM.146.185

To cite this version:

Cazajus, Vincent and Seguy, Sebastien and Welemane, Hélène and Karama, Moussa Residual stresses in a ceramic-metal composite. (2011) Applied Mechanics and Materials, vol. 146 . pp. 185-196. ISSN 1662-7482

Any correspondence concerning this service should be sent to the repository administrator: [email protected]

5HVLGXDOVWUHVVHVLQDFHUDPLFPHWDOFRPSRVLWH  

&D]DMXV96HJX\6+:HOHPDQH.DUDPD0  

8QLYHUVLWpGH7RXORXVH,137(1,7/*3

$YHQXHG¶$]HUHL[%3±7$5%(6&HGH[)5$1&( 

8QLYHUVLWpGH7RXORXVH,16$7*0±,&$DYHQXHGH5DQJXHLO 7RXORXVHFHGH[ 

PRXVVDNDUDPD#HQLWIUVHEDVWLHQVHJX\#LQVDWRXORXVHIU 

 .H\ZRUGVWKHUPRPHFKDQLFDODQDO\VLV&HUDPLFPHWDOUHVLGXDOVWUHVVHVQXPHULFDOVLPXODWLRQV

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±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d> :K/Ed ZD/    &/>>ZDd>       /ŶƚĞƌĨĂĐĞƐ     DĞƚĂůůŝnjĞĚƐƵƌĨĂĐĞ )LJXUH0LFURVWUXFWXUHRIWKHFHUDPLFWRPHWDOEUD]HGDVVHPEO\



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



)LOOHU0HWDO/(9@

@ 6WDLQOHVVVWHHO

    







7HPSHUDWXUHƒ&  )LJXUH0HWDOSODVWLF\LHOGVWUHVVHYROXWLRQGHSHQGLQJRQWHPSHUDWXUH                           

 



7DEOH0HFKDQLFDODQGWKHUPDOSURSHUWLHVRIHDFKFRPSRQHQWDFFRUGLQJWRWHPSHUDWXUH$OXPLQD $ )LOOHU0HWDO)0 6WDLQOHVV6WHHO66  @















66















3RLVVRQUDWLR 7ƒ& 















$















)0>@















66















&RHIILFLHQWRI7KHUPDO([SDQVLRQu uƒ&  7ƒ& 















$















)0>@















66















@















)0>@















66



























7HQVLOH6WUHQJWK03D  66









7HQVLOHIDLOXUHVWUDLQ 66







  

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

9RQ0LVHVVWUHVV03D 

 

0HWDO

&HUDPLF

(ODVWLF



(ODVWRSODVWLF SHUIHFWIORZ



(ODVWRSODVWLF KDUGHQDEOH

      









  'LVWDQFHDORQJWKHIUHHVLGHVXUIDFHPP     )LJXUH5HVLGXDOVWUHVVGLVWULEXWLRQDORQJWKHDVVHPEO\IUHHVLGHVXUIDFH DFFRUGLQJWRWKHPHWDOOLFPDWHULDOVFRQVWLWXWLYHODZV    /HW H[DPLQH QRZ WKH HYROXWLRQ RI VWUHVV GXULQJ WKH FRROLQJ SKDVH DFFRUGLQJ WR WKH WZR ELEOLRJUDSKLFSODVWLF\LHOGVWUHVVJLYHQIRUWKHILOOHUPHWDOE\/HY\>@DQG/RYDWR>@)LJ )RU ERWKFDVHVWKHILOOHUPHWDOH[KLELWVDORZ\LHOGVWUHVVYDOXHLQWKHKLJKWHPSHUDWXUHVUDQJHƒ& ƒ&  DQG FRQVHTXHQWO\ WKH SODVWLF EHKDYLRXU TXLFNO\ RFFXUV 7KH VWUDLQ LQGXFHG E\ WKH WKHUPDO H[SDQVLRQFRHIILFLHQWGLIIHUHQFHEHWZHHQWKHDOXPLQDDQGWKHVWDLQOHVVVWHHOSDUWDUHWKHQELJJHULQ WKHILOOHUPHWDOSDUWWKDQLQWKHRWKHUFRPSRQHQWV&RQVHTXHQWO\WKHUHVLGXDOVWUHVVHVDUHTXLWHVPDOO ZLWKLQ WKH DVVHPEO\ DW KLJK WHPSHUDWXUH EHFDXVH WKH\ DUH OLPLWHG WR WKH \LHOG VWUHVV LQ WKH ILOOHU PHWDODQGDVVRFLDWHGWRORZVWUDLQVYDOXHVLQPHWDODQGFHUDPLF)LJ  

0D[LPXP9RQ0LVHVVWUHVV03D 

 

)LOOHU0HWDO/(9@



)LOOHU0HWDO/29$72>@

       









7HPSHUDWXUHƒ& 











  )LJXUH0D[LPXP9RQ0LVHVVWUHVVRQWKHIUHHVLGHVXUIDFHDFFRUGLQJWRIXUQDFHWHPSHUDWXUHDQG ILOOHUPHWDOPHFKDQLFDOSURSHUWLHV     ,Q WKH ORZ WHPSHUDWXUHV UDQJH XQGHU ƒ&  WKH \LHOG VWUHVV YDOXH IRU ERWK GDWD LQFUHDVH VLJQLILFDQWO\DQGLQGXFHELJJHUVWUHVVHVGXULQJFRROLQJ)LJ +RZHYHUWKHEHKDYLRXUGHSHQGVRQ WKH\LHOGVWUHVVFKRVHQ)RUWKHGDWDJLYHQE\/RYDWR>@ZHREVHUYHWKHVDPHIHDWXUHVDVIRUKLJK WHPSHUDWXUH DV WKH ILOOHU \LHOG VWUHVV UHPDLQV WKH VLJQLILFDQW SDUDPHWHU HYHQ LI LWV YDOXH LQFUHDVH ZLWK WHPSHUDWXUH 7KH ILOOHU PHWDO \LHOG VWUHVV JLYHQ E\ /HY\ >@ JHWV XSSHU WKDQ WKH PHWDO RQH EHWZHHQDQGƒ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ƒ&  $V WKLV JUDGLHQW UHPDLQV TXLWH QHJOLJLEOH ƒ&  DOO DORQJ WKH FRROLQJ VWUHVVHV UHVSRQVHVZLWKERWKK\SRWKHVHVDUHTXLWHVLPLODUGXULQJWKHSURFHVV)LJ DQGDWWKHILQDOVWDJH UHVLGXDO VWUHVVHV RQ )LJ   7KH XQLIRUP FRROLQJ K\SRWKHVLV VHHPV WKHQ VXIILFLHQW IRU WKH QXPHULFDOWKHUPDODQDO\VLV 

7KHUPDOORDGLQJ

0HWDO

5HYROXWLRQD[LV

&HUDPLF

6WDQG

/HJHQGƒ& 

)LOOHU 0HWDO



 )LJXUH0D[LPDOWHPSHUDWXUHJUDGLHQWLQWKHFHUDPLFPHWDO DVVHPEO\IURPWKHWKHUPDODQDO\VLV   0D[LPXP9RQ0LVHVVWUHVV03D 

 

8QLIRUPFRROLQJ



7KHUPDODQDO\VLV

      





7HPSHUDWXUHƒ&  









)LJXUH0D[LPDOVWUHVVHYROXWLRQDFFRUGLQJWRIXUQDFHWHPSHUDWXUHDQGFRROLQJFRQGLWLRQV 

9RQ0LVHVVWUHVV03D 

           

 )LOOHU 0HWDO &HUDPLF 0HWDO  8QLIRUPFRROLQJ   7KHUPDODQDO\VLV                 'LVWDQFHDORQJWKHIUHHVLGHVXUIDFHPP  

)LJXUH5HVLGXDOVWUHVVGLVWULEXWLRQDORQJWKHIUHHVLGHVXUIDFH GHSHQGLQJRQFRROLQJFRQGLWLRQV 



9RQ0LVHVVWUHVV03D 

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

9RQ0LVHVVWUHVV03D 

 7KHVH UHVXOWV DUH FRUUHODWHG E\ H[LVWLQJ GDWD >@ ,Q RUGHU WR UHGXFH WKH UHVLGXDO VWUHVVHV LQ FHUDPLFPHWDODVVHPEOLHVLWLVWKHQUHFRPPHQGHGWRWDNH+$DQG5H[WDVVPDOODVSRVVLEOHDQG+66 DVELJDVSRVVLEOHDVWKHILOOHUPHWDOKHLJKW+)0 LVXVXDOO\OLPLWHGE\WKHEUD]LQJSURFHVV   $VHFRQGIDFWRULDO DQDO\VLVKDVEHHQGRQHIRUWKHSLSHGHVLJQ5LQW ZLWKDIL[HGILOOHUPHWDO KHLJKW+)0 PP 7KHIDFWRUVFRQVLGHUHGLQWKLVFDVHDUHWKHKHLJKWVRIEDVHPDWHULDOV+$+66  DQGWKHSLSHWKLFNQHVV5H[W5LQW RIWKHF\OLQGHU7DE   7DEOH*HRPHWULFDOIDFWRUVOHYHOPP D IXOOF\OLQGHUGHVLJQ±E SLSHGHVLJQ  D     E      5H[W    5LQW +66    5H[W   +)0    +66   +$    +$     )LJXUHVKRZVWKDWWKHODWWHUSDUDPHWHULVWKHPRVWLPSRUWDQWIDFWRUZKLFKFRQWUROVWKHUHVLGXDO VWUHVVHVOHYHOLQWKHDVVHPEO\,QGHHGWKHLQIOXHQFHRIDOXPLQDDQGVWDLQOHVVVWHHOKHLJKWVLVTXLWH QHJOLJLEOH)RUWKLVJHRPHWU\LWLVWKHQQHFHVVDU\WROLPLWDVPXFKDVSRVVLEOHWKHSLSHWKLFNQHVVRI WKHF\OLQGHU      0HDQYDOXH 3LSHWKLFNQHVV5H[W5LQW    $OXPLQD+HLJKW+$  6WDLQOHVV6WHHO+HLJKW+66                 *HRPHWULFDOIDFWRUVOHYHO7DE     )LJXUH*HRPHWULFDOIDFWRUVHIIHFWVRQPD[LPDOVWUHVVRIWKHSLSHGHVLJQ   &RQFOXVLRQ   7KLV SDSHU KDV VWXGLHG WKURXJK D QXPHULFDO DSSURDFK WKH GLIIHUHQW IDFWRUV WKDW LQIOXHQFH WKH VWUHVV GHYHORSPHQW DQG WKHLU ILQDO YDOXH RQ FHUDPLF PHWDO EUD]HG DVVHPEOLHV 7KHVH QXPHULFDO UHVXOWVDUHLQDFFRUGDQFHZLWKH[SHULPHQWDOREVHUYDWLRQVRQVXFKSLHFHVE\SUHGLFWLQJIRUH[DPSOH WKHORFDOLVDWLRQRIWKHPD[LPXPVWUHVVLQWKHFHUDPLFQHDUWKHLQWHUIDFHZLWKWKHILOOHUPHWDO  ,QFHUDPLFPHWDODVVHPEOLHVWKHWKHUPRPHFKDQLFDOEHKDYLRXURIWKHFRPSRQHQWVDQGHVSHFLDOO\ WKH SODVWLF FRQWULEXWLRQ RI PHWDOOLF PDWHULDOV KDYH D VLJQLILFDQW LQIOXHQFH RQ WKH UHVLGXDO VWUHVVHV UHSDUWLWLRQ DQG WKHLU PD[LPXP YDOXHV 6WUHVVHV HYROXWLRQ GXULQJ WKH FRROLQJ LV FRQWUROOHG E\ WKH

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pFDQLTXH GHV DVVHPEODJHV FDOFXO GHV FRQWUDLQWHV UpVLGXHOOHV GDQV OHV DVVHPEODJHV FpUDPLTXHPpWDO REWHQXV SDU EUDVDJH UpDFWLI HW FDUDFWpULVDWLRQ PpFDQLTXHGHVLQWHUIDFHV3K'7KHVLV(FROH3RO\WHFKQLTXH >@ 0XQ] ' 6FNXKU 0$ @ /RYDWR *  5KpRORJLH GHV MRLQWV EUDVpV  pWXGH H[SpULPHQWDOH HW GpWHUPLQDWLRQ SDU PpWKRGHLQYHUVH3K'7KHVLV(FROH1DWLRQDOH6XSpULHXUHGHV0LQHVGH3DULV