Modélisation de l'endommagement pour la simulation d'assemblages par déformation

(1)

HAL Id: hal-01490642

https://hal.archives-ouvertes.fr/hal-01490642

Submitted on 15 Mar 2017

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished 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 destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Public Domain

Modélisation de l’endommagement pour la simulation d’assemblages par déformation

Sébastien Fayolle, Katia Mocellin, Pierre-Olivier Bouchard

To cite this version:

Sébastien Fayolle, Katia Mocellin, Pierre-Olivier Bouchard. Modélisation de l’endommagement pour la simulation d’assemblages par déformation. 8e Colloque national en calcul des structures, CSMA, May 2007, Giens, France. �hal-01490642�

(2)

^HFROORTXHQDWLRQDOHHQFDOFXOGHVVWUXFWXUHV*LHQV

VLPXODWLRQG¶DVVHPEODJHVSDUGpIRUPDWLRQ

$SSOLFDWLRQDXULYHWDJHDXWRSRLQoRQQHXU

6pEDVWLHQ)D\ROOH².DWLD0RFHOOLQ

²3LHUUH2OLYLHU%RXFKDUG

* CEMEF, Ecole des Mines de Paris CNRS/UMR 7635

1 rue Claude Daunesse,BP207, 06904 Sophia-Antipolis cedex sebastien.fayolle@ensmp.fr

RÉSUMÉ. Dans cet article la pose de rivet auto-poinçonneur a été simulée. La précision des résultats dépend directement du choix de comportement ainsi que de la précision des paramètres matériaux. Nous avons choisi d’utiliser un modèle de type élasto-plastique endommageable. L’endommagement ductile est pris en compte au travers du modèle de Lemaitre. Les paramètres matériaux, i.e. lois d’écrouissage et d’endommagement, sont identifiés en utilisant une méthode d’analyse inverse. La pose du rivet est modélisée sur le logiciel éléments finis Forge2005® en configuration 2D axisymétrique. Les simulations sont comparées à l’expérience, sur les coupes géométriques et les courbes force-déplacement.

Elles montrent une bonne corrélation. De plus, l’importance de la prise en compte de l’endommagement dans ces simulations est prouvée.

ABSTRACT. This paper deals with the numerical modelling of the self-piercing riveting process.

The accuracy of the simulations depends directly on the choice of the mechanical behaviour model as well as the accuracy of materials parameters. We have chosen a damaged elasto- plastic model. The ductile damage is taking into account through the Lemaitre damage model. The sheets and rivet material parameters, i.e. hardening and damage laws, have been identified using an inverse method. The joining process was simulated using the 2D axisymmetric version of the finite element software Forge2005. Simulations were compared to experiments on geometrical cuts and comparison of load-displacement curves, and shown good agreements. It is also shown that the use of damage in the numerical modelling of self- piercing riveting is essential.

MOTS-CLÉS: Assemblage par déformation, endommagement, éléments finis

KEYWORDS: Joining by deformation, damage, finite element

(3)

,QWURGXFWLRQ

/HULYHWDJHDXWRSRLQoRQQHXUHVWXQSURFpGpUpDOLVpjIURLGTXLVHGpFRPSRVHHQ TXDWUH pWDSHV D OH VHUUHIODQ YLHQW EORTXHU OHV W{OHV j DVVHPEOHU FRQWUH OD ERXWHUROOHE/HULYHWVHPLFUHX[SRXVVpSDUXQSRLQoRQYLHQWWUDQVSHUFHUODOHV W{OHV VXSpULHXUHV F /H ULYHW V¶pYDVH GDQV OD W{OH LQIpULHXUH HQ IRQFWLRQ GH OD IRUPH GH OD ERXWHUROOH G /H VHUUHIODQ OLEqUH OHV W{OHV HW O¶DVVHPEODJH VXELW XQ GpFKDUJHPHQWpODVWLTXH/DWHQXHPpFDQLTXHGXSRLQWG¶DVVHPEODJHREWHQXGpSHQG GH QRPEUHX[ SDUDPqWUHV OHV JpRPpWULHV GH OD ERXWHUROOH HW GX ULYHW OD IRUFH GX VHUUHIODQOHFKRL[GHVPDWpULDX[«

)LJXUHLes différentes étapes de la pose du rivetage auto-poinçonneur

/HULYHWDJHDXWRSRLQoRQQHXUDG¶DERUGIDLWO¶REMHWG¶pWXGHVH[SpULPHQWDOHVSRXU FDUDFWpULVHUO¶LQIOXHQFHGHVSDUDPqWUHVGXSURFpGpGHSRVHVXUODWHQXHPpFDQLTXH GH O¶DVVHPEODJH )X et al., 5pFHPPHQW GHV pWXGHV QXPpULTXHV RQW GpEXWp 3RUFDURet al.,$EH et al.,/¶RULJLQDOLWpGHQRWUHDSSURFKHHVWODSULVH HQ FRPSWH GH O¶HQGRPPDJHPHQW GDQV OH FRPSRUWHPHQW GHV W{OHV HW GX ULYHW

%RXFKDUGet al.,

'DQV FHW DUWLFOH RQ GpWDLOOHUD OH PRGqOH GH FRPSRUWHPHQW XWLOLVp SRXU UHSUpVHQWHU OHV W{OHV HWOHULYHW3XLV QRXVDERUGHURQV VRQLPSOpPHQWDWLRQ GDQVXQ FRGH pOpPHQW ILQLV /¶LGHQWLILFDWLRQ GHV SDUDPqWUHV PDWpULDX[ HVW SUpVHQWpH 3RXU ILQLUGHVUpVXOWDWVGHVLPXODWLRQVGHSRVHGHULYHWVRQWFRPSDUpVjO¶H[SpULHQFH

0RGqOHG¶HQGRPPDJHPHQWHWJHVWLRQGHODUXSWXUH

'DQVOHPRGqOHG¶HQGRPPDJHPHQWLVRWURSHGpFULWGDQV/HPDLWUHO¶pWDW

G¶HQGRPPDJHPHQWHVWUHSUpVHQWpSDUXQHYDULDEOHLQWHUQH D &HWWHYDULDEOHHVWXQ

VFDODLUHGRQWODYDOHXUYDULHHQWUHSRXUOHPDWpULDXVDLQHWSRXUODUXSWXUH(Q

SUDWLTXH XQH YDOHXU G¶HQGRPPDJHPHQW FULWLTXH D

c <

HVW XWLOLVpH SRXU GpFULUH OH

PRPHQWRODILVVXUDWLRQDSSDUDvW/HPRGqOHGH/HPDLWUHHVWEDVpVXUOHFRQFHSWGH

(4)

YDULDEOH HIIHFWLYH 1RXV SRXYRQV GpILQLU OH WHQVHXU GpYLDWRULTXH GHV FRQWUDLQWHV HIIHFWLYHV a HWOHFULWqUHGHSODVWLFLWpGHYRQ0LVHVFRUUHVSRQGDQWSDU V

(

⁻

^D )

=

a V

V HW ^f ( ) ^a ^V ε

=

^-

( ) ^a ^ı

−

σ

( ) ε

≤

^>@

V HVW OH GpYLDWHXU GHV FRQWUDLQWHV ^V

⁼

^ı

⁻

^WU ( ) ^ı ^ı a HVW OH WHQVHXU GHV FRQWUDLQWHV HIIHFWLYHV ^ı ^a

⁼

^ı (

⁻

^D ) ^-

( ) ^ı ^a HVW OD FRQWUDLQWH HIIHFWLYH pTXLYDOHQWH

( ) ^ı â â ^V â ^V

-

=

HW ε HVW OD GpIRUPDWLRQ SODVWLTXH pTXLYDOHQWH ^σ

( ) ^ε HVW XQH IRQFWLRQDGGLWLRQQDQWODIRQFWLRQpFURXLVVDJHLVRWURSH ^R ( ) ^ε HWODFRQWUDLQWHGHOLPLWH pODVWLTXH σ

_y

/HVORLVG¶pYROXWLRQVGHVYDULDEOHVLQWHUQHVVRQWGRQQpHVSDU

( ) ^V ( ) ^ı

İ

^S

- a

a

−

D

=

λ

HW

( )

b

S Y

D D

¸¸¹

¨¨ ·

©

§

= −

λ

>@

R λ

HVW OH PXOWLSOLFDWHXU SODVWLTXH HW b HW S

VRQW GHV SDUDPqWUHV GH OD ORL G¶HQGRPPDJHPHQW $ FHV GHX[ SDUDPqWUHV LO IDXW DMRXWHU ε

_d

TXL HVW OD YDOHXU GH GpIRUPDWLRQ pTXLYDOHQWH j SDUWLU GH ODTXHOOH O¶HQGRPPDJHPHQW V¶DPRUFH Y HVW OD IRUFHWKHUPRG\QDPLTXHDVVRFLpHjODYDULDEOHG¶HQGRPPDJHPHQWGpILQLHSDU

( ) ( ) ( ^ν ^ν ) ( ) ^- â â â ^μ â â ^κ

- a

p p

Y E

¸¸= +

¹

·

¨¨

©

§

¸¸¹

¨¨ ·

©

− § + +

=

V V

ı

ı >@

R E HVW OH PRGXOH G¶<RXQJ HW

ν

OH FRHIILFLHQW GH 3RLVVRQ a HVW OD SUHVVLRQ p K\GURVWDWLTXHpTXLYDOHQWH ^a ^p

⁼ ⁻

^WU ( ) ^ı ^a

&HPRGqOHG¶HQGRPPDJHPHQWDpWpLPSOpPHQWpGDQVOHORJLFLHOpOpPHQWVILQLV )RUJH 3RXU LQWpJUHUQXPpULTXHPHQW OHVpTXDWLRQVGpYHORSSpHVQRXVDYRQV XWLOLVp OH VFKpPD G¶(XOHU LPSOLFLWH HW XQ DOJRULWKPH GH SUpGLFWHXU pODVWLTXHFRUUHFWHXU SODVWLTXH FRXUDPPHQW XWLOLVp HQ FDOFXO GH SODVWLFLWp 'RJKUL 4XDQG O¶DOJRULWKPH G¶LQWpJUDWLRQ ORFDO D FRQYHUJp XQ PRGXOH WDQJHQW FRQVLVWDQWGLVFUHWHVWFDOFXOpDILQG¶DVVXUHUODFRQYHUJHQFHTXDGUDWLTXHGXVFKpPD G¶LQWpJUDWLRQGXFDOFXOPpFDQLTXHJOREDO6LPRet al.,

3RXUPRGpOLVHUODILVVXUDWLRQGHODW{OHVXSpULHXUHQRXVDYRQVXWLOLVpODPpWKRGH

OHV pOpPHQWV D\DQW DWWHLQW OD YDOHXU FULWLTXH G¶HQGRPPDJHPHQW %RXFKDUG et al.,

(5)

,GHQWLILFDWLRQVGHVSDUDPqWUHVPDWpULDX[

/¶LGHQWLILFDWLRQ GHV SDUDPqWUHV PDWpULDX[ LH ORLV G¶pFURXLVVDJH LVRWURSH HW G¶HQGRPPDJHPHQW HVW UpDOLVpH HQ XWLOLVDQW XQH PpWKRGH G¶DQDO\VH LQYHUVH /¶DOJRULWKPH XWLOLVp HVW EDVp VXU OHV PpWKRGHV j VWUDWpJLHV G¶pYROXWLRQ DYHF PpWD PRGqOHV

/HVGRQQpHVH[SpULPHQWDOHVRQWpWpREWHQXHVSRXUOHVW{OHVJUkFHjGHVHVVDLVGH WUDFWLRQV HW G¶LQGHQWDWLRQV 3RXU FDUDFWpULVHU OHV ULYHWV GHV HVVDLV G¶pYDVHPHQWV HW G¶pFUDVHPHQWV3RUFDURet al.RQWpWpUpDOLVpV

'HYDQW OH JUDQG QRPEUH GH SDUDPqWUHV j GpWHUPLQHU O¶LGHQWLILFDWLRQ D pWp HIIHFWXpHHQGHX[pWDSHV'DQVXQSUHPLHUWHPSVF¶HVWODORLG¶pFURXLVVDJHTXLHVW GpWHUPLQpH VXU OD SUHPLqUH SDUWLH GH OD FRXUEH LH DYDQW DSSDULWLRQ GH O¶HIIHW GH O¶HQGRPPDJHPHQW3XLVF¶HVWODORLG¶HQGRPPDJHPHQWTXLHVWLGHQWLILpHVXUODILQ GHODFRXUEH)LJXUH

)LJXUHIdentification en deux temps sur un essai de traction : AA5754-O

0RGpOLVDWLRQHWYDOLGDWLRQGHODSRVHGXULYHW

/D PRGpOLVDWLRQ GH OD SRVH GX ULYHW HVW UpDOLVpH VRXV )RUJH DYHF XQH FRQILJXUDWLRQ ' D[LV\PpWULTXH )LJXUHD /H SRLQoRQ GHVFHQG j XQH YLWHVVH GH PPVHWOHVHUUHIODQDSSOLTXHXQHIIRUWGH1/HFRQWDFWHQWUHOHVGLIIpUHQWV pOpPHQWV GH O¶DVVHPEODJH HVW SULV HQ FRPSWH DYHF XQ FRQWDFW GH FRXORPE /D FRQILJXUDWLRQGHWHVWHVWODVXLYDQWHW{OHVXSpULHXUHGHPPHQDOOLDJHG¶DOXPLQLXP 2W{OHLQIpULHXUHPPHQ$FLHU;6*/DERXWHUROOHHWOHULYHWVRQWIRXUQLVSDU

%|OOKRIIHWVRQWUpIpUHQFpV'=HW&[

/HV UpVXOWDWV GHV VLPXODWLRQV VRQW FRPSDUpV DYHF O¶H[SpULHQFH VXU OHV FRXUEHV IRUFHGpSODFHPHQW)LJXUHEHWVXUGHVFRXSHVJpRPpWULTXHV)LJXUHD

'pSODFHPHQWPP

)RUFH7

([SpULPHQWDO 1XPHULTXH

'pSODFHP HQWPP

)RUFH7

([SpULPHQWDO 1XPHULTXH

&RPSRUWHPHQWpODVWRSODVWLTXH &RPSRUWHPHQWpODVWRSODVWLTXH HQGRPPDJHDEOH

(6)

)LJXUHConfiguration 2D initiale et courbes force-déplacement

6XUOD)LJXUHERQSHXWYRLUOHVUpVXOWDWVREWHQXVDYHFHWVDQVSULVHHQFRPSWH GHO¶HQGRPPDJHPHQW2QREVHUYHTXHO¶HQGRPPDJHPHQWDGRXFLWOHFRPSRUWHPHQW GHVW{OHVHWGRQFGLPLQXHO¶HIIRUWQpFHVVDLUHjODSRVHGXULYHW(QILQGHSRVHXQH GLIIpUHQFHQRQQpJOLJHDEOHG¶HQYLURQWRQQHH[LVWHHQWUHOHVGHX[VLPXODWLRQV/D SULVH HQ FRPSWH GX FRXSODJH FRPSRUWHPHQWHQGRPPDJHPHQW SHUPHW GH PLHX[ VH UDSSURFKHUGHVUpVXOWDWVH[SpULPHQWDX[

)LJXUHGéométries numérique et expérimentale, carte d’endommagement

/D)LJXUHDUHSUpVHQWHODVXSHUSRVLWLRQGHVFRQWRXUVGHODVLPXODWLRQQXPpULTXHj XQHFRXSHGXSRLQWG¶DVVHPEODJHREWHQXH[SpULPHQWDOHPHQW8QHERQQHFRUUpODWLRQ HVWREVHUYpH/D)LJXUHEUHSUpVHQWHODUpSDUWLWLRQGHO¶HQGRPPDJHPHQWGH

/HPDLWUHGDQVO¶DVVHPEODJHILQDO1RXVSRXYRQVFRQVWDWHUTXHFHWHQGRPPDJHPHQW HVWORLQG¶rWUHQpJOLJHDEOHVXUWRXWGDQVODW{OHLQIpULHXUHHWMRXHUDXQU{OHLPSRUWDQW GDQVODWHQXHPpFDQLTXHGHO¶DVVHPEODJH

&RQFOXVLRQV

/H PRGqOH G¶HQGRPPDJHPHQW GXFWLOH GH /HPDLWUH HVW SUpVHQWp DLQVL TXH VRQ LPSOpPHQWDWLRQGDQVOHORJLFLHOpOpPHQWVILQLV)RUJH$SUqVLGHQWLILFDWLRQGHV SDUDPqWUHV PDWpULDX[ YLD XQH PpWKRGH G¶DQDO\VH LQYHUVH GHV VLPXODWLRQV ' D[LV\PpWULTXHVGHSRVHGHULYHWVRQWHIIHFWXpHV1RXVDYRQVSXYRLUTXHODSULVHHQ FRPSWHGHO¶HQGRPPDJHPHQWGDQVODPRGpOLVDWLRQGXULYHWDJHDXWRSRLQoRQQHXUHVW LPSRUWDQWHSRXUXQHPHLOOHXUHFRUUpODWLRQDYHFO¶H[SpULHQFH

'pSODFHPHQWVPP

)RUFH7

1XPpULTXHDYHFHQGRPPDJHPHQW 1XPpULTXHVDQVHQGRPPDJHPHQW ([SHULPHQWDO

5LYHW 6HUUHIODQ 3RLQoRQ

7{OHV

%RXWHUROOH

E D

D E

(7)

/H PRGqOH GpYHORSSp SHXW V¶pWHQGUH j G¶DXWUHV W\SHV G¶DVVHPEODJHV SDU GpIRUPDWLRQ SODVWLTXH FOLQFKDJH ULYHW FOLQFKp « DLQVL TX¶j OD PRGpOLVDWLRQ GH OHXU WHQXH PpFDQLTXH ILJXUH 3RXU FHOD OHV UpVXOWDWV LVVXV GH OD VLPXODWLRQ GH ULYHWDJHVRQWXWLOLVpVSRXUPLHX[PRGpOLVHUODUpVLVWDQFHGXSRLQWG¶DVVHPEODJH

)LJXUHSimulations de la tenue mécanique du point riveté

5HPHUFLHPHQWV

1RXV WHQRQV j UHPHUFLHU OH &(7,0 36$ HW %|OOKRII SRXU QRXV DYRLU IRXUQL GHVGRQQpHVH[SpULPHQWDOHVHWXQVXSSRUWILQDQFLHU

%LEOLRJUDSKLH

$EH<.DWR70RUL.-RLQDELOLW\RIDOXPLQLXPDOOR\DQGPLOGVWHHOVKHHWVE\VHOISLHUFLQJ ULYHWJournal of Materials Processing TechnologyYROS

%RXFKDUG 32 )D\ROOH 6 0RFHOOLQ . ' QXPHULFDO PRGHOLQJ RI PHFKDQLFDO MRLQLQJ SURFHVVHV ± )URP -RLQLQJ GRZQ WR 6WUXFWXUDO $QDO\VLV ,QProceedings of the Eight International Conference on Computational Structures technology/DV3DOPDVGH*UDQ

&DQDULD6SDLQS

'RJKUL , 1XPHULFDO LPSOHPHQWDWLRQ DQG DQDO\VLV RI D FODVV RI PHWDO SODVWLFLW\ PRGHOV FRXSOHG ZLWK GXFWLOH GDPDJH International Journal for Numerical Methods in EngineeringYROS

)X00DOOLFN3.(IIHFWRISURFHVVYDULDEOHVRQWKHVWDWLFDQGIDWLJXHSURSHUWLHVRIVHOI SLHUFLQJULYHWHGMRLQWVLQDOXPLQLXPDOOR\3DSHUQ6$(

/HPDLWUH-A course on damage mechanics6SULQJHU9HUODJ

3RUFDUR 5 +DQVVHQ $* /DQJVHWK 0 $DOEHUJ $ 6HOISLHUFLQJ ULYHWLQJ SURFHVV $Q H[SHULPHQWDO DQG QXPHULFDO LQYHVWLJDWLRQJournal of Materials Processing Technology YROS

6LPR -& 7D\ORU 5 &RQVLVWHQW WDQJHQW RSHUDWRUV IRU UDWH LQGHSHQGHQW HODVWRSODVWLFLW\

Computer Methods in Applied Mechanics and EngineeringYROQS

7UDFWLRQ &LVDLOOHPHQW