.!(+%**#/!01!! 50+%02'#I! #!"#$! %1! #'01*%&%*6! *#/1.+! %/! ($%&$! c.-/)d1! ^.,-'-1! %1! 011-4#,! *.! ,#7#/,! ./! + DI!( !" !%1!*$#!,#5%0*.+%&!1*+#11!*#/1.+;!6!%1!,040)#! C0'1.!(+%**#/!01!! #N-%50'#/*!"./!^%1#1!1*+#11I!C0'1.!(+%**#/!01!! + DI!( !" !%1!*$#!,#5%0*.+%&!1*+#11!*#/1.+;!6!%1!,040)#! + DI!(!" !%1!*$#!,#5%0*.+%&!1*+#11!*#/1.+;!6!%1!,040)#! #11I!C0'1.!(+%**#/!01!! (+%**#/!01!!+ DI!(!" !%1!*$#!,#5%0*.+%&!1*+#11!*#/1.+;!6!%1!,040)#! + DI!(!" !%1!*$#!,#5%0*.+%&!1*+#11!*#/1.+;!6!%1!,040)#! .+! %/! ($%&$! c.-/)d1! ^.,-'-1! %1! 011-4#,! *.! ,#7#/,! ./! #/1.+!($%&$! %/! ($%&$! c.-/)d1! %1!%1! 011-4#,! *.! ,#7#/,! ./!*#47#+0*-+#;! =$#! #5.'-*%./! .3! ,%1'.&0*%./! ,#/1%*6! $! %1! +#'0*#,! *.! *$#! #N-%50'#/*! 5%1&.7'01*%&! #'01*%&%*6! *#/1.+! %/! ($%&$! c.-/)d1! 50+%02'#I! #!"#$! %1!^.,-'-1! +!*6!%/!*#/1.+! %/! c.-/)d1! ($%&$! c.-/)d1! ^.,-'-1! ^.,-'-1! %1! 011-4#,! 011-4#,! *.! ,#7#/,! *.! ./! ,#7#/,! ./! ^.,-'-1! %1! 011-4#,! *.! ,#7#/,! ./! 1*+0%/! +0*#I! %/&'-,#1! *$#! 5%1&.7'01*%&! ,6/04%&! +#&.5#+6! 0/,! *$#! 1*0*%&! +#&.5#+6! ($%&$! 077#0+! 0*! $%)$! ,%1'.&0*%./! ,#/1%*6! $! %1! +#'0*#,! *.! *$#! #N-%50'#/*! 5%1&.7'01*%&! .3! ,#/1%*6! $! =$#! %1! +#'0*#,! *.! 5%1&.7'01*%&! *#47#+0*-+#;! #5.'-*%./! .3!#N-%50'#/*! ,%1'.&0*%./! ,#/1%*6! $! %1! +#'0*#,! *.!%*! *$#! #N-%50'#/*! 1'.&0*%./! ./!,%1'.&0*%./! .3! ,%1'.&0*%./! ,#/1%*6! $!,#/1%*6! %1! +#'0*#,! $! %1! *.! +#'0*#,! *$#! #N-%50'#/*! *.!*$#! *$#! #N-%50'#/*! 5%1&.7'01*%&! 5%1&.7'01*%&! *#47#+0*-+#;!G0+04#*#+1!! I!*$#!1#&./,!%/50+%0/*J!#N-%50'#/*!1*+#11!; # ? # ! ;!=$#!70+04#*#+1!& !%1!*#47#+0*-+#! 0!3 0!3 0!3 7'#! 4! 7+%/&%7'#! 1*+#11J! 1*+#11J! ;9+#17#&*%5#'6! !;9%#0!3 %! *$#! # ! %! %/50+%0/*J! *$#! 3%+1*! %/50+%0/*J! ; # <=0!3 ; # <=0!3 # 0!3 0!3 0!3 %into ; # ! %! *$#! 3%+1*! %/50+%0/*J! ; # <=0!3 # 40O%4-4! 7+%/&%7'#! 1*+#11J! ;#9 0!3 # ! %! *$#! 3%+1*! %/50+%0/*J! ; # <=0!3 # +%/&%7'#! 1*+#11J! 0!3 &%7'#! 1*+#11J! ;9 0!3 !%*$#! %!3%+1*! *$#! 3%+1*! %/50+%0/*J! ; # <=0!3 : . + software partner to release the new integrated model the first invariant: % % % 9 % % % %% 0!3 #/*!1*+#11!; J!#N-%50'#/*!1*+#11!; # ? # ! # ;!=$#!70+04#*#+1!& ? # ! ;!=$#!70+04#*#+1!& !%1!*#47#+0*-+#! !%1!*#47#+0*-+#! ,#7#/,#/*!& !%1!1*+0%/!+0*#!,#7#/,#/*!0/,!& !%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! % % 0!3 & ' 0!3 >! I!*$#!1#&./,!%/50+%0/*J!#N-%50'#/*!1*+#11!; # ? # ! ;!=$#!70+04#*#+1!& !%1!*#47#+0*-+#! -%50'#/*!1*+#11!; # ? # ! ;!=$#!70+04#*#+1!& !%1!*#47#+0*-+#! . 0!3 . + + commercially available software. Meanwhile, an example of the the second invariant: equivalent stress The 0!3 % % 0'#/*!1*+#11!; # ? # ! ;!=$#!70+04#*#+1!& !%1!*#47#+0*-+#! % . + .: . + + #!,#7#/,#/*!0/,!& #/*!0/,!& '!%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! '!%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! *$#!+#7+#1#/*0*%./!.3!*(.!,%33#+#/*!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! ,#7#/,#/*!& !%1!1*+0%/!+0*#!,#7#/,#/*!0/,!& !%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! 7#/,#/*!0/,!& !%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! model performance is shown below for AA7075 B-Pillar. Two parameters α1 is temperature dependent α2 is strain rate & ' ' /,#/*!0/,!&'!%1!&./1*0/*;!=$#!*$+##!%/50+%0/*1!*.)#*$#+!#/02'#! *!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! !,%33#+#/*!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! ,-&*%'#!,040)#;!=$#!70+04#*#+1!'(I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! *$#!+#7+#1#/*0*%./!.3!*(.!,%33#+#/*!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! pressings were carried out. One with a non-optimised blank to dependent and α3 is constant. The three invariants together #+#/*!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! /*!,040)#!4#&$0/%141I!/04#'6!)+0%/!2.-/,0+6!,040)#!0/,! 04#*#+1!'(I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! (I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! 0+#!*#47#+0*-+#!%/,#7#/,#/*;!=$#!,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! ,-&*%'#!,040)#;!=$#!70+04#*#+1!'(I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! induce splitting in different locations for model validation. The enable the representation of two different damage mechanisms, #+1!'(I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! !'(I!')!0+#!3-/&*%./1!.3!*#47#+0*-+#!0/,!70+04#*#+1!fYI!gI!h! ,#/*;!=$#!,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! ,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! #N-0'! *.! U! 0*! *$#! %/%*%0'! 1*0*#!pressing .3! *$#! ,#3.+40*%./;! *$#!an ,040)#! '#5#'!blank +#0&$#1! second was carriedW$#/! out with optimised to U;RI! %*! %1! 0+#!*#47#+0*-+#!%/,#7#/,#/*;!=$#!,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! namely grain boundary damage and ductile damage. The !=$#!,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! #!,040)#!70+04#*#+!,#3%/#,!%/!`N-0*%./!CRD!%1!011-4#,!*.!2#! 1*0*#! $#! ,#3.+40*%./;! .3! *$#! ,#3.+40*%./;! W$#/! *$#! W$#/! ,040)#! *$#!'#5#'! ,040)#! +#0&$#1! '#5#'!U;RI! +#0&$#1! %*! %1!U;RI! %*! %1! 011-4#,!*$0*!30%'-+#!*0B#1!7'0&#!%/!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! achieve a successful part. parameters η1, η2 are functions of temperature and parameters #N-0'! *.! U! 0*! *$#! %/%*%0'! 1*0*#! .3! *$#! ,#3.+40*%./;! W$#/! *$#! ,040)#! '#5#'! +#0&$#1! U;RI! %*! %1! !! .3! ,#3.+40*%./;! W$#/! *$#! ,040)#! '#5#'! +#0&$#1!U;RI! U;RI!%*!%*!%1!%1! *$#!*$#! ,#3.+40*%./;! W$#/! *$#! ,040)#! '#5#'! +#0&$#1! /!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! 1!7'0&#!%/!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! η3, ϕ, Δ are temperature independent. The damage parameter 0&&-4-'0*%./I!01!*$#!,040)#!%/&+#01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! 011-4#,!*$0*!30%'-+#!*0B#1!7'0&#!%/!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! 0&#!%/!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! !%/!*$#!40*#+%0';!T-#!*.!*$#!#O7./#/*%0'!/0*-+#!.3!*$#!,040)#! 40)#!%/&+#01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! #01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! defined in Equation (7) is assumed to be equal to 0 at the initial 0&&-4-'0*%./I!01!*$#!,040)#!%/&+#01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! &0/!2#!.4%**#,;! !%/&+#01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! &+#01#1!3+.4!U;R!*.!P;UI!*$#!1*+0%/!%/&+#4#/*!%1!/#)'%)%2'#!0/,! state of the deformation. When the damage level reaches 0.7, it &0/!2#!.4%**#,;! ]#&#/*'6I!E=F!$01!&.''02.+0*#,!(%*$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! .+0*#,!(%*$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! *$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! is assumed that failure takes place in the material. Due to the ]#&#/*'6I!E=F!$01!&.''02.+0*#,!(%*$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! %/*#)+0*#,!4.,#'!%/*.!&.44#+&%0''6!050%'02'#!1.3*(0+#;!^#0/($%'#I!0/!#O047'#!.3!*$#!4.,#'! ,!(%*$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! 44#+&%0''6!050%'02'#!1.3*(0+#;!^#0/($%'#I!0/!#O047'#!.3!*$#!4.,#'! '6!050%'02'#!1.3*(0+#;!^#0/($%'#I!0/!#O047'#!.3!*$#!4.,#'! exponential nature of the damage accumulation, as the damage (%*$!`LE!)+.-7I!G041*047!1.3*(0+#!70+*/#+!*.!+#'#01#!*$#!/#(! %/*#)+0*#,!4.,#'!%/*.!&.44#+&%0''6!050%'02'#!1.3*(0+#;!^#0/($%'#I!0/!#O047'#!.3!*$#!4.,#'! <