Pitsch orientation relationship for phase transformation
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Su Leen Wong
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112
code/lattice.f90
112
code/lattice.f90
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@ -23,7 +23,7 @@ module lattice
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LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures
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LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part)
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LATTICE_maxNnonSchmid = 6_pInt, & !< max # of non schmid contributions over lattice structures
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LATTICE_maxNtrans = 36_pInt !< max # of transformations over lattice structures
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LATTICE_maxNtrans = 12_pInt !< max # of transformations over lattice structures
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integer(pInt), allocatable, dimension(:,:), protected, public :: &
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lattice_NslipSystem, & !< total # of slip systems in each family
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@ -59,20 +59,13 @@ module lattice
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lattice_tt
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real(pReal), allocatable, dimension(:,:,:), protected, public :: &
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lattice_trn1, &
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lattice_trd1, &
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lattice_trt1, &
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lattice_trn2, &
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lattice_trd2, &
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lattice_trt2, &
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lattice_NItrans_v
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real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
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lattice_Atrans, &
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lattice_Mtrans, &
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lattice_Ttrans, &
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lattice_Rtrans, &
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lattice_Utrans, &
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lattice_Btrans, &
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lattice_Qtrans, &
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lattice_NItrans
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real(pReal), allocatable, dimension(:,:), protected, public :: &
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@ -90,13 +83,13 @@ module lattice
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LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc
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integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
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LATTICE_fcc_NtransSystem = int([12, 24],pInt) !< total # of transformation systems per family for fcc
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LATTICE_fcc_NtransSystem = int([12, 0],pInt) !< total # of transformation systems per family for fcc
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integer(pInt), parameter, private :: &
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LATTICE_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc
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LATTICE_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc
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LATTICE_fcc_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for fcc
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LATTICE_fcc_Ntrans = 36_pInt !< total # of transformations for fcc
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LATTICE_fcc_Ntrans = 12_pInt !< total # of transformations for fcc
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real(pReal), dimension(3+3,LATTICE_fcc_Nslip), parameter, private :: &
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LATTICE_fcc_systemSlip = reshape(real([&
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@ -208,7 +201,44 @@ module lattice
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2,2,2,2,2,2,2,2,2,1,1,1 &
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],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for fcc
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real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
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LATTICE_fcc_systemTrans = reshape(real( [&
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0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
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0.0, 1.0, 0.0, -10.26, &
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0.0, 0.0, 1.0, 10.26, &
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0.0, 0.0, 1.0, -10.26, &
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1.0, 0.0, 0.0, 10.26, &
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1.0, 0.0, 0.0, -10.26, &
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0.0, 0.0, 1.0, 10.26, &
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0.0, 0.0, 1.0, -10.26, &
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1.0, 0.0, 0.0, 10.26, &
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1.0, 0.0, 0.0, -10.26, &
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0.0, 1.0, 0.0, 10.26, &
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0.0, 1.0, 0.0, -10.26 &
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],pReal),[ 4_pInt,LATTICE_fcc_Ntrans])
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integer(pInt), dimension(LATTICE_fcc_Ntrans), parameter, private :: &
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LATTICE_fcc_bainVariant = reshape(int( [&
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1, 1, 1, 1, &
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2, 2, 2, 2, &
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3, 3, 3, 3 &
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],pInt),[LATTICE_fcc_Ntrans])
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real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
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LATTICE_fcc_bainRot = reshape(real( [&
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1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
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1.0, 0.0, 0.0, 45.0, &
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1.0, 0.0, 0.0, 45.0, &
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1.0, 0.0, 0.0, 45.0, &
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0.0, 1.0, 0.0, 45.0, &
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0.0, 1.0, 0.0, 45.0, &
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0.0, 1.0, 0.0, 45.0, &
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0.0, 1.0, 0.0, 45.0, &
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0.0, 0.0, 1.0, 45.0, &
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0.0, 0.0, 1.0, 45.0, &
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0.0, 0.0, 1.0, 45.0, &
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0.0, 0.0, 1.0, 45.0 &
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],pReal),[ 4_pInt,LATTICE_fcc_Ntrans])
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!--------------------------------------------------------------------------------------------------
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! bcc
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@ -861,8 +891,9 @@ subroutine lattice_init
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call IO_error(0_pInt,ext_msg = 'LATTICE_maxNslip')
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if (LATTICE_maxNtwin /= maxval([LATTICE_fcc_Ntwin,LATTICE_bcc_Ntwin,LATTICE_hex_Ntwin])) &
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call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtwin')
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if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) &
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if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) then
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call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtrans')
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endif
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if (LATTICE_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,&
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lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid')
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@ -945,6 +976,13 @@ subroutine lattice_init
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allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal)
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allocate(lattice_Rtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_Utrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_Btrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_Qtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_NItrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_NItrans_v(6,lattice_maxNtrans,Nphases),source=0.0_pReal)
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allocate(lattice_NslipSystem(lattice_maxNslipFamily,Nphases),source=0_pInt)
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allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,Nphases),source=0_pInt)
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allocate(lattice_NtransSystem(lattice_maxNtransFamily,Nphases),source=0_pInt)
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@ -1063,9 +1101,11 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
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use prec, only: &
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tol_math_check
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use math, only: &
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math_identity2nd, &
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math_vectorproduct, &
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math_tensorproduct, &
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math_norm3, &
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math_mul33x33, &
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math_mul33x3, &
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math_trace33, &
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math_symmetric33, &
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@ -1096,9 +1136,15 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
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td, tn
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real(pReal), dimension(lattice_maxNtwin) :: &
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ts
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real(pReal), dimension(3,lattice_maxNtrans) :: &
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rtr, rb
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real(pReal), dimension(lattice_maxNtrans) :: &
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atr, ab
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real(pReal), dimension(3,3,3) :: &
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bainstr
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integer(pInt) :: &
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i,j, &
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myNslip, myNtwin
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myNslip, myNtwin, myNtrans
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lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),&
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lattice_C66(1:6,1:6,myPhase))
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@ -1127,8 +1173,9 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
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!--------------------------------------------------------------------------------------------------
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! fcc
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case (LATTICE_fcc_ID)
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myNslip = lattice_fcc_Nslip
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myNtwin = lattice_fcc_Ntwin
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myNslip = lattice_fcc_Nslip
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myNtwin = lattice_fcc_Ntwin
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myNtrans = lattice_fcc_Ntrans
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do i = 1_pInt,myNslip ! assign slip system vectors
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sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)
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sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)
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@ -1138,6 +1185,26 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
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tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
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ts(i) = lattice_fcc_shearTwin(i)
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enddo
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do i = 1_pInt,myNtrans
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rtr(1:3,i) = lattice_fcc_systemTrans(1:3,i)
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atr(i) = lattice_fcc_systemTrans(4,i)
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rb(1:3,i) = lattice_fcc_bainRot(1:3,i)
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ab(i) = lattice_fcc_bainRot(4,i)
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enddo
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bainstr = 0.0_pReal
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if ((aA > 0.0_pReal) .and. (aM > 0.0_pReal) .and. (cM == 0.0_pReal)) then
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bainstr(1,1,1) = aM/aA ! 3 Bain strain variants for fcc to bcc transformation
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bainstr(2,2,1) = sqrt(2.0_pReal)*aM/aA
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bainstr(3,3,1) = sqrt(2.0_pReal)*aM/aA
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bainstr(1,1,2) = sqrt(2.0_pReal)*aM/aA
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bainstr(2,2,2) = aM/aA
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bainstr(3,3,2) = sqrt(2.0_pReal)*aM/aA
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bainstr(1,1,3) = sqrt(2.0_pReal)*aM/aA
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bainstr(2,2,3) = sqrt(2.0_pReal)*aM/aA
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bainstr(3,3,3) = aM/aA
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endif
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lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_fcc_NslipSystem
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lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_fcc_NtwinSystem
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lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_fcc_NtransSystem
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@ -1274,6 +1341,19 @@ subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
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if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myPhase))) > tol_math_check) &
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call IO_error(301_pInt,myPhase,ext_msg = 'dilatational twin Schmid matrix')
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enddo
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do i = 1_pInt,myNtrans
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lattice_Rtrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rtr(1:3,i),atr(i)*INRAD)
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lattice_Utrans(1:3,1:3,i,myPhase) = bainstr(1:3,1:3,LATTICE_fcc_bainVariant(i))
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lattice_Btrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rb(1:3,i),ab(i)*INRAD)
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lattice_Qtrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), &
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lattice_Btrans(1:3,1:3,i,myPhase))
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if ((aA > 0.0_pReal) .and. (aM > 0.0_pReal) .and. (cM == 0.0_pReal)) then
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lattice_NItrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), &
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lattice_Utrans(1:3,1:3,i,myPhase)) - math_identity2nd(3)
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lattice_NItrans_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_NItrans(1:3,1:3,i,myPhase)))
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endif
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enddo
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end subroutine lattice_initializeStructure
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