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Pitsch orientation relationship for phase transformation

This commit is contained in:
Su Leen Wong 2014-08-29 13:03:48 +00:00
parent b566eed5a8
commit e8a3b7ed19
1 changed files with 98 additions and 18 deletions
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116
code/lattice.f90
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@ -23,7 +23,7 @@ module lattice
LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures
LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part)
LATTICE_maxNnonSchmid = 6_pInt, & !< max # of non schmid contributions over lattice structures
LATTICE_maxNtrans = 36_pInt !< max # of transformations over lattice structures
LATTICE_maxNtrans = 12_pInt !< max # of transformations over lattice structures
integer(pInt), allocatable, dimension(:,:), protected, public :: &
lattice_NslipSystem, & !< total # of slip systems in each family
@ -59,20 +59,13 @@ module lattice
lattice_tt
real(pReal), allocatable, dimension(:,:,:), protected, public :: &
lattice_trn1, &
lattice_trd1, &
lattice_trt1, &
lattice_trn2, &
lattice_trd2, &
lattice_trt2, &
lattice_NItrans_v
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Atrans, &
lattice_Mtrans, &
lattice_Ttrans, &
lattice_Rtrans, &
lattice_Utrans, &
lattice_Btrans, &
lattice_Qtrans, &
lattice_NItrans
real(pReal), allocatable, dimension(:,:), protected, public :: &
@ -90,13 +83,13 @@ module lattice
LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_fcc_NtransSystem = int([12, 24],pInt) !< total # of transformation systems per family for fcc
LATTICE_fcc_NtransSystem = int([12, 0],pInt) !< total # of transformation systems per family for fcc
integer(pInt), parameter, private :: &
LATTICE_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc
LATTICE_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc
LATTICE_fcc_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for fcc
LATTICE_fcc_Ntrans = 36_pInt !< total # of transformations for fcc
LATTICE_fcc_Ntrans = 12_pInt !< total # of transformations for fcc
real(pReal), dimension(3+3,LATTICE_fcc_Nslip), parameter, private :: &
LATTICE_fcc_systemSlip = reshape(real([&
@ -208,7 +201,44 @@ module lattice
2,2,2,2,2,2,2,2,2,1,1,1 &
],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for fcc
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fcc_systemTrans = reshape(real( [&
0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
0.0, 1.0, 0.0, -10.26, &
0.0, 0.0, 1.0, 10.26, &
0.0, 0.0, 1.0, -10.26, &
1.0, 0.0, 0.0, 10.26, &
1.0, 0.0, 0.0, -10.26, &
0.0, 0.0, 1.0, 10.26, &
0.0, 0.0, 1.0, -10.26, &
1.0, 0.0, 0.0, 10.26, &
1.0, 0.0, 0.0, -10.26, &
0.0, 1.0, 0.0, 10.26, &
0.0, 1.0, 0.0, -10.26 &
],pReal),[ 4_pInt,LATTICE_fcc_Ntrans])
integer(pInt), dimension(LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fcc_bainVariant = reshape(int( [&
1, 1, 1, 1, &
2, 2, 2, 2, &
3, 3, 3, 3 &
],pInt),[LATTICE_fcc_Ntrans])
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fcc_bainRot = reshape(real( [&
1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
1.0, 0.0, 0.0, 45.0, &
1.0, 0.0, 0.0, 45.0, &
1.0, 0.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0 &
],pReal),[ 4_pInt,LATTICE_fcc_Ntrans])
!--------------------------------------------------------------------------------------------------
! bcc
@ -861,8 +891,9 @@ subroutine lattice_init
call IO_error(0_pInt,ext_msg = 'LATTICE_maxNslip')
if (LATTICE_maxNtwin /= maxval([LATTICE_fcc_Ntwin,LATTICE_bcc_Ntwin,LATTICE_hex_Ntwin])) &
call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtwin')
if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) &
if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) then
call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtrans')
endif
if (LATTICE_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,&
lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid')
@ -945,6 +976,13 @@ subroutine lattice_init
allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_Rtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Utrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Btrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Qtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_NItrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_NItrans_v(6,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_NslipSystem(lattice_maxNslipFamily,Nphases),source=0_pInt)
allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,Nphases),source=0_pInt)
allocate(lattice_NtransSystem(lattice_maxNtransFamily,Nphases),source=0_pInt)
@ -1063,9 +1101,11 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
use prec, only: &
tol_math_check
use math, only: &
math_identity2nd, &
math_vectorproduct, &
math_tensorproduct, &
math_norm3, &
math_mul33x33, &
math_mul33x3, &
math_trace33, &
math_symmetric33, &
@ -1096,9 +1136,15 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
td, tn
real(pReal), dimension(lattice_maxNtwin) :: &
ts
real(pReal), dimension(3,lattice_maxNtrans) :: &
rtr, rb
real(pReal), dimension(lattice_maxNtrans) :: &
atr, ab
real(pReal), dimension(3,3,3) :: &
bainstr
integer(pInt) :: &
i,j, &
myNslip, myNtwin
myNslip, myNtwin, myNtrans
lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),&
lattice_C66(1:6,1:6,myPhase))
@ -1127,8 +1173,9 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
!--------------------------------------------------------------------------------------------------
! fcc
case (LATTICE_fcc_ID)
myNslip = lattice_fcc_Nslip
myNtwin = lattice_fcc_Ntwin
myNslip = lattice_fcc_Nslip
myNtwin = lattice_fcc_Ntwin
myNtrans = lattice_fcc_Ntrans
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)
sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)
@ -1138,6 +1185,26 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
ts(i) = lattice_fcc_shearTwin(i)
enddo
do i = 1_pInt,myNtrans
rtr(1:3,i) = lattice_fcc_systemTrans(1:3,i)
atr(i) = lattice_fcc_systemTrans(4,i)
rb(1:3,i) = lattice_fcc_bainRot(1:3,i)
ab(i) = lattice_fcc_bainRot(4,i)
enddo
bainstr = 0.0_pReal
if ((aA > 0.0_pReal) .and. (aM > 0.0_pReal) .and. (cM == 0.0_pReal)) then
bainstr(1,1,1) = aM/aA ! 3 Bain strain variants for fcc to bcc transformation
bainstr(2,2,1) = sqrt(2.0_pReal)*aM/aA
bainstr(3,3,1) = sqrt(2.0_pReal)*aM/aA
bainstr(1,1,2) = sqrt(2.0_pReal)*aM/aA
bainstr(2,2,2) = aM/aA
bainstr(3,3,2) = sqrt(2.0_pReal)*aM/aA
bainstr(1,1,3) = sqrt(2.0_pReal)*aM/aA
bainstr(2,2,3) = sqrt(2.0_pReal)*aM/aA
bainstr(3,3,3) = aM/aA
endif
lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_fcc_NslipSystem
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_fcc_NtwinSystem
lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_fcc_NtransSystem
@ -1146,7 +1213,7 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_fcc_interactionSlipTwin
lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_fcc_interactionTwinSlip
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_fcc_interactionTwinTwin
!--------------------------------------------------------------------------------------------------
! bcc
case (LATTICE_bcc_ID)
@ -1274,6 +1341,19 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myPhase))) > tol_math_check) &
call IO_error(301_pInt,myPhase,ext_msg = 'dilatational twin Schmid matrix')
enddo
do i = 1_pInt,myNtrans
lattice_Rtrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rtr(1:3,i),atr(i)*INRAD)
lattice_Utrans(1:3,1:3,i,myPhase) = bainstr(1:3,1:3,LATTICE_fcc_bainVariant(i))
lattice_Btrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rb(1:3,i),ab(i)*INRAD)
lattice_Qtrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), &
lattice_Btrans(1:3,1:3,i,myPhase))
if ((aA > 0.0_pReal) .and. (aM > 0.0_pReal) .and. (cM == 0.0_pReal)) then
lattice_NItrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), &
lattice_Utrans(1:3,1:3,i,myPhase)) - math_identity2nd(3)
lattice_NItrans_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_NItrans(1:3,1:3,i,myPhase)))
endif
enddo
end subroutine lattice_initializeStructure