Etude - Using Abaqus to Model Delamination in Fiber Reinforced Composite Materials

Visit the Resource Center for more SIMULIA customer papers 

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

6,08/,$&RPPXQLW\&RQIHUHQFH



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

 0RGHOGHVFULSWLRQ $GLVFUHWHGHVFULSWLRQRIWKHIDEULFLVEXLOWXVLQJDPHVKRI'DQG'HOHPHQWV)LJXUH  ZKHUHDXQLWFHOOUHSUHVHQWVWKH\DUQLQWHUYDOLQWKHIDEULF-DXIIUHVHWDO $IWHUDVHULHVRI PHFKDQLFDOWHVWVWKHDSSURSULDWHSURSHUWLHVRIWKHFRPSRVLWHIDEULFFDQEHREWDLQHGDQG LPSOHPHQWHGLQWRWKHK\EULGPRGHOYLDDXVHUGHILQHGPDWHULDOVXEURXWLQHWRFDSWXUHWKH PHFKDQLFDOEHKDYLRURIWKHIDEULF 

 )LJXUH3ULQFLSOHRIWKHGLVFUHWHPHVRVFRSLFPRGHOLQJXVLQJDFRPELQDWLRQRI 'DQG'HOHPHQWV  7KH'DQG'HOHPHQWVLQWKHIDEULFPRGHODUHFRQYHQWLRQDOVKHOO65 HOHPHQWVDQG%  EHDPHOHPHQWVUHVSHFWLYHO\7KHOHYHORIUHILQHPHQWLVEDVHGRQWKHPHDVXUHGXQLWFHOOVL]H $EDTXV([SOLFLWVLPXODWLRQVRIDSXQFKGLHVHWXSDUHXVHGWRIRUPWKHIDEULFVWDFNLQWRWKHVKDSH RIWKHGLH)LJXUH 7KHH[SOLFLWIRUPXODWLRQLVXVHGIRUWKHVHIRUPLQJVLPXODWLRQVGXHWRWKH PRUHUREXVWFRQWDFWDOJRULWKPVUHODWLYHWRWKHLPSOLFLWIRUPXODWLRQ

 6,08/,$&RPPXQLW\&RQIHUHQFH



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

 )LJ6KHDUDQJOHFRQWRXULQGHJUHHIRUWKHRULHQWDWLRQ 

6,08/,$&RPPXQLW\&RQIHUHQFH



  )LJXUH([SORGHGYLHZRIFRQVWLWXHQWVRIDPHWHUFRPSRVLWHZLQGWXUELQH EODGH 7KHDELOLW\WRSUHGLFWGHODPLQDWLRQW\SHIDLOXUHLQFRPSRVLWHSDUWVLVDYDOXDEOHWRROLQWKHGHVLJQ DQGRSWLPL]DWLRQSURFHVV0RGHOLQJRIWKLVW\SHRIIDLOXUHFDQEHGRQHWKURXJKFRKHVLYHEHKDYLRU 'HILQLQJFRKHVLYHEHKDYLRUEHWZHHQFRQWDFWLQJVXUIDFHLVDPHDQVWRFRQVLGHUWKHLQLWLDOERQG VWUHQJWKEHWZHHQDGMDFHQWOD\HUVDQGWRSUHGLFWWKHSRVVLEOHIDLOXUHRIWKDWERQGGXHWRYDULRXV ORDGLQJFRQGLWLRQV7KHLPSRUWDQFHRIGHILQLQJWKHERQGVWUHQJWKLVGHPRQVWUDWHGLQ)LJXUH XVLQJDWZROD\HUVSHFLPHQWKDWLVORDGHGLQFRPSUHVVLRQD ,QDILVWFDVHE FRKHVLRQLVQRW GHILQHGEHWZHHQWKHWZROD\HUVDQGHDFKOD\HUDFWVLQGHSHQGHQWRIWKHRWKHUDVWKHV\VWHPLV VXEMHFWHGWRLQSODQHFRPSUHVVLRQ,QWKHVHFRQGLQVWDQFHF FRKHVLYHSURSHUWLHVDUHGHILQHG EHWZHHQWKHWZROD\HUVDQGWKHFRXSRQUHPDLQVERQGHGDQGEXFNOHVRXWRISODQHGXHWRWKH FRPSUHVVLYHORDG

 )LJXUH7ZROD\HUFRXSRQPRGHOVKRZLQJD FRPSUHVVLYHORDGLQJERXQGDU\ FRQGLWLRQVDQGWKHUHVXOWLQJERQGLQJE ZLWKRXWFRKHVLYHSURSHUWLHVDQGF ZLWK FRKHVLYHVXUIDFHSURSHUWLHV  

 6,08/,$&RPPXQLW\&RQIHUHQFH



7KHVWUHQJWKRIWKHERQGLVDSDUDPHWHUZKLFKFDQEHH[SHULPHQWDOO\REWDLQHG6WDQGDUGL]HGDQG QRQVWDQGDUGL]HGFRPSRVLWHFRXSRQWHVWVFDQEHFRQGXFWHGWRGHWHUPLQHWKHLQWHUODPLQDUIUDFWXUH SURSHUWLHVRIFRPSRVLWHODPLQDWHVWRVLPXODWHGHODPLQDWLRQIDLOXUH7KLVUHVHDUFKLVDZRUNLQ SURJUHVVVRK\SRWKHWLFDOERQGVWUHQJWKLVFXUUHQWO\EHLQJXVHGWRGHPRQVWUDWHWKHSRWHQWLDOYDOXH RIWKHSURSRVHGPHWKRGRORJ\LQFDSWXULQJWKHGHODPLQDWLRQRIDFRPSRVLWHSO\VWDFN

 0DWHULDOFKDUDFWHUL]DWLRQ %ULWWOHIUDFWXUHLQDQLVRWURSLFPDWHULDOZLOORFFXULQDWOHDVWWZRVWDJHVFUDFNLQLWLDWLRQDQGFUDFN SURSDJDWLRQ%RUHVL$3 2QFHFUDFNLQLWLDWLRQKDVRFFXUUHGDQGDIODZKDVGHYHORSHGLQ WKHPDWHULDOFUDFNSURSDJDWLRQFDQVXEVHTXHQWO\RFFXUDVDIXQFWLRQRIWKHORDGLQJFRQGLWLRQVDQG WKHPDWHULDOSURSHUWLHV7KHUHDUHWKUHHSXUHPRGHVRIFUDFNSURSDJDWLRQLQDQLVRWURSLFPDWHULDO DVVKRZQLQ)LJXUH

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

6,08/,$&RPPXQLW\&RQIHUHQFH



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

9DOXH

//HQJWK 

PPLQ 

E:LGWK 

WRPPWRLQ 

DR(IIHFWLYH,QVHUW/HQJWK 

PPLQ 

K7KLFNQHVV 

WRPPWRLQ 

 6SHFLPHQVDUHDWWDFKHGWRWKHJULSVRIDORDGVHQVLQJGHYLFHVXFKWKDWVOLSSLQJZLOOQRWRFFXU$ ORDGLVWKHQDSSOLHGZLWKDFURVVKHDGGLVSODFHPHQWUDWHEHWZHHQDQGPPPLQDQGORDG GLVSODFHPHQWGDWDDUHUHFRUGHG$QRSWLFDOPLFURVFRSHRURWKHURSWLFDOPHWKRGPD\EHXVHGWR UHFRUGDQGPHDVXUHWKHGHODPLQDWLRQOHQJWK,IIDLOXUHKDVRFFXUUHGDWWKHPLGSODQHRIWKHSOLHV DQGQRVOLSSLQJRUGHERQGLQJRIWKHDWWDFKPHQWPHWKRGVLVYLVLEOHWKHQWKHVDPSOHVKRXOGDSSHDU VLPLODUWR)LJXUH

 6,08/,$&RPPXQLW\&RQIHUHQFH



 )LJXUH([DPSOHRI0RGH,7HVW=ZLFN  7KH0RGLILHG%HDP7KHRU\WKH&RPSOLDQFH&DOLEUDWLRQDQGWKH0RGLILHG&RPSOLDQFH &DOLEUDWLRQDUHDOOPHWKRGVXVHGWRFDOFXODWHWKHLQWHUODPLQDUIUDFWXUHWRXJKQHVVGXHWRSXUH PRGH,IDLOXUH7KHEHDPWKHRU\XVHGWRFDOFXODWHVWUDLQHQHUJ\UHOHDVHUDWHV*,IRUWKLVORDGLQJ FRQGLWLRQLVJLYHQE\  ‫ܩ‬ூ ൌ

ଷ௉ఋ ଶ௕௔

 

ZKHUH 3 ORDG G ORDGSRLQWGLVSODFHPHQW E VSHFLPHQZLGWK D GHODPLQDWLRQOHQJWK (TXDWLRQDVVXPHVDEXLOWLQFRQGLWLRQZKHUHWKHGRXEOHFDQWLOHYHUEHDPLVFODPSHGDWWKH GHODPLQDWLRQIURQW%HFDXVHWKHDFWXDOWHVWLQJDOORZVIRUURWDWLRQDWWKLVHQGRIWKHEHDPD PRGLILHGYHUVLRQRIWKHEHDPWKHRU\LVXVHGDQGWKHVWUDLQHQHUJ\UHOHDVHUDWHLVJLYHQE\ ‫ܩ‬ூ ൌ

ଷ௉ఋ

 

ଶ௕ሺ௔ାȁοȁሻ

ZKHUH'PD\EHGHWHUPLQHGH[SHULPHQWDOO\E\JHQHUDWLQJDOHDVWVTXDUHVSORWRIWKHFXEHURRWRI FRPSOLDQFH& DVDIXQFWLRQRIGHODPLQDWLRQOHQJWK)LJXUH $670' 

6,08/,$&RPPXQLW\&RQIHUHQFH



 )LJXUH0RGLILHGEHDPWKHRU\$670'  

 )LQLWHHOHPHQWVLPXODWLRQV 1RZWKDWWKHH[SHULPHQWDOPHWKRGVIRUGHWHUPLQLQJPRGH,IUDFWXUHFKDUDFWHULVWLFVRIILEHU UHLQIRUFHGSRO\PHUPDWUL[FRPSRVLWHVKDYHEHHQSUHVHQWHGVLPXODWLRQVRIIUDFWXUHWHVWLQJ ZLOOEHSUHVHQWHG6XFKVLPXODWLRQVFDQEHXVHGWRSURYLGHIHHGEDFNWRWKHGHVLJQSURFHVV E\SUHGLFWLQJFUDFNLQLWLDWLRQDQGSURSDJDWLRQWKURXJKFRPSRVLWHVWUXFWXUHVXSRQORDGLQJ %RQGVWUHQJWKSURSHUWLHVEHWZHHQDGMDFHQWSOLHVDUHGHILQHGXVLQJFRQWDFWWKURXJKFRKHVLYH VXUIDFHV,QOLHXRIPHFKDQLFDOWHVWGDWDLQWKHFXUUHQWUHVHDUFKIUDFWXUHSURSHUWLHVIURP 6LPXOLD DUHXVHGWRGHPRQVWUDWHWKHSURSRVHGPHWKRGRORJ\ 

0DWHULDO2ULHQWDWLRQV

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

 )LJXUH&XUYHGSODWHPDWHULDORULHQWDWLRQZLWKD JOREDOFRRUGLQDWHV\VWHP DQGE GLVFUHWHFRRUGLQDWHV\VWHP  6,08/,$&RPPXQLW\&RQIHUHQFH



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

6,08/,$&RPPXQLW\&RQIHUHQFH



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

;ĂͿ

;ďͿ

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

 6,08/,$&RPPXQLW\&RQIHUHQFH



7DEOH9HFWRUSO\(/70DWHULDO3URSHUWLHV 0DWHULDO3URSHUW\

9DOXH

( ( 1X * * *

1PP  1PP   1PP  1PP  1PP 

 ϯϱ ϯϬ

>ŽĂĚ;EͿ

Ϯϱ ϮϬ ϭϱ ŽŶǀĞŶƚŝŽŶĂů

ϭϬ

ŽŶƚŝŶƵƵŵ

ϱ Ϭ Ϭ

Ϯ

ϰ

ϲ

ϴ ϭϬ ϭϮ ŝƐƉůĂĐĞŵĞŶƚ;ŵŵͿ

ϭϰ

ϭϲ

ϭϴ

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

6,08/,$&RPPXQLW\&RQIHUHQFH 



;ďͿ

;ĂͿ

    

)LJXUH'RXEOHFDQWLOHYHUEHDPFRQWRXUVXVLQJD FRQYHQWLRQDOVKHOOV DQGE FRQWLQXXPVKHOOV

)XUWKHUUHVHDUFKLVSODQQHGWREHFRQGXFWHGWRUHSOLFDWHFRPSRVLWHIUDFWXUHWHVWVIRURWKHUPRGHVRI IDLOXUH&RUUHODWLRQEHWZHHQFRQYHQWLRQDODQGFRQWLQXXPVKHOOHOHPHQWVLQWKHVHVLPXODWLRQVZLOO DOVREHH[SORUHG

 &RQFOXVLRQV )DLOXUHFULWHULDDQGGDPDJHSURSHUWLHVZHUHLQYHVWLJDWHGWRPRGHOGHODPLQDWLRQVLQFRPSRVLWH SDUWV'HODPLQDWLRQVGXHWR0RGH,IDLOXUHZHUHPRGHOHGXVLQJ$EDTXV6WDQGDUGDQGVKRZ SURPLVHDVDPHWKRGIRUFDSWXULQJWKHGHODPLQDWLRQSKHQRPHQRQRIODPLQDWHGFRPSRVLWHVXVLQJ ERWKFRQYHQWLRQDODQGFRQWLQXXPVKHOOHOHPHQWV 

 5HIHUHQFHV  3XFN$6FKXUPDQQ+)DLOXUH$QDO\VLVRI)53/DPLQDWHVE\PHDQVRI3K\VLFDOO\%DVHG 3KHQRPHQRORJLFDO0RGHOV&RPSRVLWHV6FLHQFHDQG7HFKQRORJ\  &KULVWHQVHQ506WUHVV%DVHG