- Email: [email protected]
Modeling fatigue behavior of quasi-isotropic laminates
Available online www.sciencedirect.com Available online atat www.sciencedirect.com
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Procedia Engineering !
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Abstract ^):(,@&!A&B)7($#!$?!C@)6(D(6$:#$;(%!%)#A$+9&;$UO!5)8(+):&6!3&#&!6:@'(&'I!@6(+,!6(U!6:)%_(+,!6&C@&+%&64!*U;&#(8&+:)5! #&6@5:6!6B$3!:B):!:B&#&!(6!)!6(,+(?(%)+:!6:)%_(+,!6&C@&+%&!&??&%:!$+!8$+$:$+(%!)+'!%O%5(%!;&#?$#8)+%&!$?!5)8(+):&64! MB$@,B!AO!%B)+,(+,!:B&!6:)%_(+,!6&C@&+%&!:B&!'(??&#&+%&!A&:3&&+!?)(5@#&!6:#&+,:B!$?!:B&!6:#$+,&6:!)+'!3&)_&6:!5)OD @;6! #&)%B&6! $+5O! :$! `! 0/! aI! :B&! '(??&#&+%&! A&:3&&+! ?):(,@&! 5(7&6! .%O%5&6! :$! ?)(5@#&1! (+%#&)6&'! `! 0---a! (+! 6$8&! 5$)'(+,!#&,($+64!<+!)''(:($+I!A$:B!5(+&)#!)+'!6(,8$(')5!?@+%:($+6!3&#&!&U)8(+&'!:$!8$'&5!:B&!?):(,@&!5(?&!A&B)7($#4!!
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1. Introduction d@)6(D(6$:#$;(%! %$8;$6(:&! 5)8(+):&6! )#&! 3('&5O! @6&'! (+! B(,B! ;&#?$#8)+%&! 6:#@%:@#)5! );;5(%):($+64! "#&7($@6!#&6&)#%B&6!6B$3&'!)!6(,+(?(%)+:!6:)%_(+,!6&C@&+%&!&??&%:!$+!:B&!8$+$:$+(%!)+'!?):(,@&!6:#&+,:B! $?!C@)6(D(6$:#$;(%!5)8(+):&6!'@&!:$!(+:)8(+)#!6:#&66!+&)#!:B&!?#&&!&',&6!$?!5)8(+):&6!.*',&!&??&%:1!e0DWf4!! MB&#&! )#&! 8)+O! (+7&6:(,):($+! $+! :&+6(5&! A&B)7($#! $?! C@)6(D(6$:#$;(%! 5)8(+):&64! ^@#:B$#&I! 6$8&! #&6&)#%B!B)6!6:@'(&'!:B&6&!5)8(+):&6!@+'&#!?):(,@&!5$)'(+,!eVIgf4!<+:&#&6:(+,5OI!5)8(+):&6!8(,B:!&UB(A(:! '(??&#&+:!:#&+'!@+'&#!8$+$:$+(%!)+'!%O%5(%!5$)'(+,h!3B&+!:3$!5)8(+):&6!)#&!&U)8(+&'I!)!5)8(+):&!3(:B! ! P!=$##&6;$+'(+,!)@:B$#4!M&54i!jZXDYX0D[[/[[-0h!?)Ui!jZXDYX0D[[/[[YX4! E-mail addressi!)A)'O)+kO)B$$4%$84!
1877–7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.615
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Z. Razavi Hesabi et al. / Physics Engineering 10 (2011) 3764–3768 Author name / Procedia Engineering 00 (2011) 000–000
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References 0D /D
=4!M4!H&#)_$7(%BI!.0ZZg1I!m>&%B)+(%6!$?!^(A#$@6!=$8;$6(:&6nI!S+(7(:O!$?!o(#,(+()4! F4! N#O)+! "(;&6I! ]4! L4! "),)+$I! .0Zg-1I! m<+:)8(+)#! 6:#&66&6! (+! %$8;$6(:&! 5)8(+):&6! @+'&#! @+(?$#8! )U()5! &U:&+6($+nI! p4! =$8;$6(:&!>):&#()56I![i!WYX4! YD =4!M4!H&#)_$7(%BI!.0ZX01I!mT+!:B&!F&5):($+6B(;!A&:3&&+!*+,(+&&#(+,!"#$;&#:(&6!)+'!Q&5)8(+):($+!$?!=$8;$6(:&!>):&#()56nI!p4! =$8;$6(:&!>):&#()56I!0Wi!YYVDY[X4! [D >(::&56:&':! =! )+'! N&%_&#! q! ./--[1I! <+:)8(+)#! 6:#&66! %$+%&+:#):($+6! (+! 5)O&#&'! 6:#@%:@#&6! D! ;)#:!):!YXI!0-YgD0-V/4! WD RB(+r(! T,(B)#)I! ]$A@$! M)_&')I! R):$6B(! K$A)O)6B(IJ_(#)! K$A)O)%B(I! m*??&%:6! $?! 6:)%_(+,! 6&C@&+%&! $+! 8(%#$6%$;(%! ?):(,@&! ')8),&! '&7&5$;8&+:! (+! C@)6(D(6$:#$;(%! =^F"! 5)8(+):&6! 3(:B! (+:)8(+)#D:$@,B&+&'! 5)OnI! =$8;$6(:&6! R%(&+%&! )+'! M&%B+$5$,OI!0ZZZI!;;-0YXgD0YZX4! VD R!>)55O!)+'!p!>!=$5&8)+4!>$+$:$+(%!)+'!?):(,@&!5$)'(+,!A&B)7($#!$?!C@)6(D(6$:#$;(%!,#);B(:&9&;$UO!5)8(+):&!&8A&''&'!3(:B! ;(&G$&5&%:#(%!6&+6$#4!R8)#:!>):!R:#@%:4!g!.0ZZX1!X//2XY/4! gD =4!p)O):B&&#:B)!)+'!p4!"4!H4!q&AA&#I!.0ZZ[1I!m*??&%:!$?!6:)%_(+,!6&C@&+%&!)+'!:B(%_+&66!$+!:B&!(+:)8(+)#!6:#&66&6!?$#!C@)6(D (6$:#$;(%!5)8(+):&'!;5):&6!3(:B!)!B$5&nI!=$8;$6(:&6!R%(&+%&!)+'!M&%B+$5$,OI!V-0DV004!! XD >4! =)##$5I! ^4! *55O(+I! Q4! K@r)36_(I! mR:)%_(+,! 6&C@&+%&! &??&%:! $+! :&+6(5&! )+'! ?):(,@&! 6:#&+,:B! $?! 6O88&:#(%! 5)8(+):&6nI! "$5O8!s!"$5O8&#!=$8;$6(:&6I!7$54YI!]$40I!0ZZWI!;;40DZ4! ZD J4! R4! =B&+! )+'! N4! H)##(6I! m^):(,@&! (+'@%&'! ')8),&! 8&%B)+(686! (+! %)#A$+! ?(A#&D#&(+?$#%&'! ;5)6:(%! %$8;$6(:&6nI! p$@#+)5! $?! >):&#()56!6%(&+%&I!/XI!0ZZYI!;;!/-0YD/-/g4! 0-D p(:&+'#)! R4! M):&I! Jr(:! Q4! K&5_)#! 4! R:(??+&66! '&,#)'):($+! 8$'&5! ?$#! A()U()5! A#)('&'! %$8;$6(:&6! @+'&#! ?):(,@&! 5$)'(+,4! =$8;$6(:&6i!")#:!N!YZ!./--X1!W[X2WWW4! 00D p(:&+'#)! R4! M):&I! Jr(:! Q4! K&5_)#I! p$B+! Q4! qB(:%$8A4! *??&%:! $?! A#)('! )+,5&! $+! ?):(,@&! ;&#?$#8)+%&! $?! A()U()5! A#)('&'! %$8;$6(:&64!<+:&#+):($+)5!p$@#+)5!$?!^):(,@&!/X!./--V1!0/YZ20/[g4! !
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!!!!!!!!!!"#$%&'()!*+,(+&&#(+,!!--!./-001!---2---! Physics Engineering 10 (2011) 3764–3768 3334&56&7(%$895$%):&9;#$%&'()
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Abstract ^):(,@&!A&B)7($#!$?!C@)6(D(6$:#$;(%!%)#A$+9&;$UO!5)8(+):&6!3&#&!6:@'(&'I!@6(+,!6(U!6:)%_(+,!6&C@&+%&64!*U;&#(8&+:)5! #&6@5:6!6B$3!:B):!:B&#&!(6!)!6(,+(?(%)+:!6:)%_(+,!6&C@&+%&!&??&%:!$+!8$+$:$+(%!)+'!%O%5(%!;&#?$#8)+%&!$?!5)8(+):&64! MB$@,B!AO!%B)+,(+,!:B&!6:)%_(+,!6&C@&+%&!:B&!'(??&#&+%&!A&:3&&+!?)(5@#&!6:#&+,:B!$?!:B&!6:#$+,&6:!)+'!3&)_&6:!5)OD @;6! #&)%B&6! $+5O! :$! `! 0/! aI! :B&! '(??&#&+%&! A&:3&&+! ?):(,@&! 5(7&6! .%O%5&6! :$! ?)(5@#&1! (+%#&)6&'! `! 0---a! (+! 6$8&! 5$)'(+,!#&,($+64!<+!)''(:($+I!A$:B!5(+&)#!)+'!6(,8$(')5!?@+%:($+6!3&#&!&U)8(+&'!:$!8$'&5!:B&!?):(,@&!5(?&!A&B)7($#4!!
! ! b!/-00!"@A5(6B&'!AO!*56&7(&#!c:'4!R&5&%:($+!)+'9$#!;&&#D#&7(&3!@+'&#!#&6;$+6(A(5(:O!$?!<=>00! ! Keywords: d@)6(D(6$:#$;(%!c)8(+):&I!^):(,@&!c$)'(+,I!=O%5(%!c$)'(+,4!
1. Introduction d@)6(D(6$:#$;(%! %$8;$6(:&! 5)8(+):&6! )#&! 3('&5O! @6&'! (+! B(,B! ;&#?$#8)+%&! 6:#@%:@#)5! );;5(%):($+64! "#&7($@6!#&6&)#%B&6!6B$3&'!)!6(,+(?(%)+:!6:)%_(+,!6&C@&+%&!&??&%:!$+!:B&!8$+$:$+(%!)+'!?):(,@&!6:#&+,:B! $?!C@)6(D(6$:#$;(%!5)8(+):&6!'@&!:$!(+:)8(+)#!6:#&66!+&)#!:B&!?#&&!&',&6!$?!5)8(+):&6!.*',&!&??&%:1!e0DWf4!! MB&#&! )#&! 8)+O! (+7&6:(,):($+! $+! :&+6(5&! A&B)7($#! $?! C@)6(D(6$:#$;(%! 5)8(+):&64! ^@#:B$#&I! 6$8&! #&6&)#%B!B)6!6:@'(&'!:B&6&!5)8(+):&6!@+'&#!?):(,@&!5$)'(+,!eVIgf4!<+:&#&6:(+,5OI!5)8(+):&6!8(,B:!&UB(A(:! '(??&#&+:!:#&+'!@+'&#!8$+$:$+(%!)+'!%O%5(%!5$)'(+,h!3B&+!:3$!5)8(+):&6!)#&!&U)8(+&'I!)!5)8(+):&!3(:B! ! P!=$##&6;$+'(+,!)@:B$#4!M&54i!jZXDYX0D[[/[[-0h!?)Ui!jZXDYX0D[[/[[YX4! E-mail addressi!)A)'O)+kO)B$$4%$84!
1877–7058 © 2011 Published by Elsevier Ltd. doi:10.1016/j.proeng.2011.04.615
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Z. Razavi Hesabi et al. / Physics Engineering 10 (2011) 3764–3768 Author name / Procedia Engineering 00 (2011) 000–000
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Z. Razavi Hesabi et al. / Physics Engineering 10 (2011) 3764–3768 !
[4!Conclusions J! 6(,+(?(%)+:! 6&C@&+%&! &??&%:! $+! 8$+$:$+(%! )+'! %O%5(%! ;&#?$#8)+%&! $?! C@)6(D(6$:#$;(%! 5)8(+):&6! 3&#&! $A6&'!'@&!:$!&',&!&??&%:4!<:!3)6!?$@+'!:B):i!!! D!d@)6(D(6$:#$;(%!5)8(+):&6!3(:B!eZ-9[W9-9D[Wf6!)+'!e[W9D[W9-9Z-f6!5)OD@;I!6B$3&'!:B&!A&6:!)+'!:B&!3$#6:! :&+6(5&! 6:#&+,:B! A&:3&&+! 6(U! 6&C@&+%&6I! #&6;&%:(7&5O4! =B)+,(+,! :B&! 6:)%_(+,! 6&C@&+%&! 5&'! :$! 0/a! '(??&#&+%&!(+!:&+6(5&!6:#&+,:B4!R)8&!:#&+'!3)6!$A6&'!(+!?):(,@&!:&6:4! D! MB&! 6(G&! &??&%:! &+B)+%&6! )6! #&'@%&64! <+! $:B&#! 3$#'6I! :B$@,B! AO! %B)+,(+,! :B&! 6:)%_(+,! 6&C@&+%&! :B&! '(??&#&+%&! A&:3&&+! ?)(5@#&! 6:#&+,:B! $?! :B&! 6:#$+,&6:! )+'! 3&)_&6:! 5)OD@;6! #&)%B&6! $+5O! :$! `! 0/! aI! :B&! '(??&#&+%&!A&:3&&+!?):(,@&!5(7&6!(+%#&)6&'!)58$6:!0-!?$5'6!(+!6$8&!5$)'(+,!#&,($+64! D!MB&!6(,8$(')5!.N$5:G8)+!?@+%:($+1!);;&)#6!:$!A&!)+!&U%&55&+:!?(:!?$#!RD]!'(),#)8!$?!C@)6(D(6$:#$;(%! 5)8(+):&64!!!!
References 0D /D
=4!M4!H&#)_$7(%BI!.0ZZg1I!m>&%B)+(%6!$?!^(A#$@6!=$8;$6(:&6nI!S+(7(:O!$?!o(#,(+()4! F4! N#O)+! "(;&6I! ]4! L4! "),)+$I! .0Zg-1I! m<+:)8(+)#! 6:#&66&6! (+! %$8;$6(:&! 5)8(+):&6! @+'&#! @+(?$#8! )U()5! &U:&+6($+nI! p4! =$8;$6(:&!>):&#()56I![i!WYX4! YD =4!M4!H&#)_$7(%BI!.0ZX01I!mT+!:B&!F&5):($+6B(;!A&:3&&+!*+,(+&&#(+,!"#$;&#:(&6!)+'!Q&5)8(+):($+!$?!=$8;$6(:&!>):&#()56nI!p4! =$8;$6(:&!>):&#()56I!0Wi!YYVDY[X4! [D >(::&56:&':! =! )+'! N&%_&#! q! ./--[1I! <+:)8(+)#! 6:#&66! %$+%&+:#):($+6! (+! 5)O&#&'! 6:#@%:@#&6! D! ;)#:!
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