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DAMASK_EICMD
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DAMASK_EICMD/src/lattice.f90

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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief defines lattice structure definitions, slip and twin system definitions, Schimd matrix
!> calculation and non-Schmid behavior
!--------------------------------------------------------------------------------------------------
module lattice
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), parameter, public :: &
LATTICE_maxNslipFamily = 13_pInt, & !< max # of slip system families over lattice structures
LATTICE_maxNtwinFamily = 4_pInt, & !< max # of twin system families over lattice structures
LATTICE_maxNtransFamily = 2_pInt, & !< max # of transformation system families over lattice structures
LATTICE_maxNcleavageFamily = 3_pInt !< max # of transformation system families over lattice structures
integer(pInt), allocatable, dimension(:,:), protected, public :: &
lattice_NslipSystem, & !< total # of slip systems in each family
lattice_NtwinSystem, & !< total # of twin systems in each family
lattice_NtransSystem, & !< total # of transformation systems in each family
lattice_NcleavageSystem !< total # of transformation systems in each family
integer(pInt), allocatable, dimension(:,:,:), protected, public :: &
lattice_interactionSlipSlip, & !< Slip--slip interaction type
lattice_interactionSlipTwin, & !< Slip--twin interaction type
lattice_interactionTwinSlip, & !< Twin--slip interaction type
lattice_interactionTwinTwin, & !< Twin--twin interaction type
lattice_interactionSlipTrans, & !< Slip--trans interaction type
lattice_interactionTransSlip, & !< Trans--slip interaction type
lattice_interactionTransTrans !< Trans--trans interaction type
real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: &
lattice_Sslip, & !< Schmid and non-Schmid matrices
lattice_Scleavage !< Schmid matrices for cleavage systems
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Sslip_v, & !< Mandel notation of lattice_Sslip
lattice_Scleavage_v !< Mandel notation of lattice_Scleavege
real(pReal), allocatable, dimension(:,:,:), protected, public :: &
lattice_sn, & !< normal direction of slip system
lattice_sd, & !< slip direction of slip system
lattice_st !< sd x sn
! rotation and Schmid matrices, normal, shear direction and d x n of twin systems
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Stwin, &
lattice_Qtwin
real(pReal), allocatable, dimension(:,:,:), protected, public :: &
lattice_Stwin_v, &
lattice_tn, &
lattice_td, &
lattice_tt
real(pReal), allocatable, dimension(:,:,:), protected, public :: &
lattice_Strans_v, & !< Eigendeformation tensor in vector form
lattice_projectionTrans !< Matrix for projection of slip to fault-band (twin) systems for strain-induced martensite nucleation
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Qtrans, & !< Total rotation: Q = R*B
lattice_Strans !< Eigendeformation tensor for phase transformation
real(pReal), allocatable, dimension(:,:), protected, public :: &
lattice_shearTwin, & !< characteristic twin shear
lattice_shearTrans !< characteristic transformation shear
integer(pInt), allocatable, dimension(:), protected, public :: &
lattice_NnonSchmid !< total # of non-Schmid contributions for each structure
!--------------------------------------------------------------------------------------------------
! face centered cubic
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],pInt) !< # of slip systems per family for fcc
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< # of twin systems per family for fcc
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_fcc_NtransSystem = int([12, 0],pInt) !< # of transformation systems per family for fcc
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_fcc_NcleavageSystem = int([3, 4, 0],pInt) !< # of cleavage 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 = 12_pInt, & !sum(lattice_fcc_NtransSystem), & !< total # of transformation systems for fcc
LATTICE_fcc_Ncleavage = 7_pInt !sum(lattice_fcc_NcleavageSystem) !< total # of cleavage systems for fcc
real(pReal), dimension(3+3,LATTICE_fcc_Nslip), parameter, private :: &
LATTICE_fcc_systemSlip = reshape(real([&
! Slip direction Plane normal ! SCHMID-BOAS notation
0, 1,-1, 1, 1, 1, & ! B2
-1, 0, 1, 1, 1, 1, & ! B4
1,-1, 0, 1, 1, 1, & ! B5
0,-1,-1, -1,-1, 1, & ! C1
1, 0, 1, -1,-1, 1, & ! C3
-1, 1, 0, -1,-1, 1, & ! C5
0,-1, 1, 1,-1,-1, & ! A2
-1, 0,-1, 1,-1,-1, & ! A3
1, 1, 0, 1,-1,-1, & ! A6
0, 1, 1, -1, 1,-1, & ! D1
1, 0,-1, -1, 1,-1, & ! D4
-1,-1, 0, -1, 1,-1 & ! D6
],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Nslip]) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli
real(pReal), dimension(3+3,LATTICE_fcc_Ntwin), parameter, private :: &
LATTICE_fcc_systemTwin = reshape(real( [&
-2, 1, 1, 1, 1, 1, &
1,-2, 1, 1, 1, 1, &
1, 1,-2, 1, 1, 1, &
2,-1, 1, -1,-1, 1, &
-1, 2, 1, -1,-1, 1, &
-1,-1,-2, -1,-1, 1, &
-2,-1,-1, 1,-1,-1, &
1, 2,-1, 1,-1,-1, &
1,-1, 2, 1,-1,-1, &
2, 1,-1, -1, 1,-1, &
-1,-2,-1, -1, 1,-1, &
-1, 1, 2, -1, 1,-1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ntwin]) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli
real(pReal), dimension(3+3,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fccTohex_systemTrans = reshape(real( [&
-2, 1, 1, 1, 1, 1, &
1,-2, 1, 1, 1, 1, &
1, 1,-2, 1, 1, 1, &
2,-1, 1, -1,-1, 1, &
-1, 2, 1, -1,-1, 1, &
-1,-1,-2, -1,-1, 1, &
-2,-1,-1, 1,-1,-1, &
1, 2,-1, 1,-1,-1, &
1,-1, 2, 1,-1,-1, &
2, 1,-1, -1, 1,-1, &
-1,-2,-1, -1, 1,-1, &
-1, 1, 2, -1, 1,-1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ntrans])
real(pReal), dimension(LATTICE_fcc_Ntwin), parameter, private :: &
LATTICE_fcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) !< Twin system <112>{111} ??? Sorted according to Eisenlohr & Hantcherli
integer(pInt), dimension(2_pInt,LATTICE_fcc_Ntwin), parameter, public :: &
LATTICE_fcc_twinNucleationSlipPair = reshape(int( [&
2,3, &
1,3, &
1,2, &
5,6, &
4,6, &
4,5, &
8,9, &
7,9, &
7,8, &
11,12, &
10,12, &
10,11 &
],pInt),[2_pInt,LATTICE_fcc_Ntwin])
integer(pInt), dimension(LATTICE_fcc_Nslip,lattice_fcc_Nslip), parameter, public :: &
LATTICE_fcc_interactionSlipSlip = reshape(int( [&
1,2,2,4,6,5,3,5,5,4,5,6, & ! ---> slip
2,1,2,6,4,5,5,4,6,5,3,5, & ! |
2,2,1,5,5,3,5,6,4,6,5,4, & ! |
4,6,5,1,2,2,4,5,6,3,5,5, & ! v slip
6,4,5,2,1,2,5,3,5,5,4,6, &
5,5,3,2,2,1,6,5,4,5,6,4, &
3,5,5,4,5,6,1,2,2,4,6,5, &
5,4,6,5,3,5,2,1,2,6,4,5, &
5,6,4,6,5,4,2,2,1,5,5,3, &
4,5,6,3,5,5,4,6,5,1,2,2, &
5,3,5,5,4,6,6,4,5,2,1,2, &
6,5,4,5,6,4,5,5,3,2,2,1 &
],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Nslip],order=[2,1]) !< Slip--slip interaction types for fcc
!< 1: self interaction
!< 2: coplanar interaction
!< 3: collinear interaction
!< 4: Hirth locks
!< 5: glissile junctions
!< 6: Lomer locks
integer(pInt), dimension(LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin), parameter, public :: &
LATTICE_fcc_interactionSlipTwin = reshape(int( [&
1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip
3,3,3,1,1,1,2,2,2,3,3,3, &
2,2,2,1,1,1,3,3,3,3,3,3, &
2,2,2,3,3,3,1,1,1,3,3,3, &
3,3,3,2,2,2,1,1,1,3,3,3, &
3,3,3,3,3,3,1,1,1,2,2,2, &
3,3,3,2,2,2,3,3,3,1,1,1, &
2,2,2,3,3,3,3,3,3,1,1,1, &
3,3,3,3,3,3,2,2,2,1,1,1 &
],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for fcc
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Nslip), parameter, public :: &
LATTICE_fcc_interactionTwinSlip = 1_pInt !< Twin--Slip interaction types for fcc
integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Ntwin), parameter,public :: &
LATTICE_fcc_interactionTwinTwin = reshape(int( [&
1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
2,2,2,1,1,1,2,2,2,2,2,2, & ! v twin
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
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
integer(pInt), dimension(LATTICE_fcc_Nslip,LATTICE_fcc_Ntrans), parameter, public :: &
LATTICE_fccTohex_interactionSlipTrans = reshape(int( [&
1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> trans
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip
3,3,3,1,1,1,2,2,2,3,3,3, &
2,2,2,1,1,1,3,3,3,3,3,3, &
2,2,2,3,3,3,1,1,1,3,3,3, &
3,3,3,2,2,2,1,1,1,3,3,3, &
3,3,3,3,3,3,1,1,1,2,2,2, &
3,3,3,2,2,2,3,3,3,1,1,1, &
2,2,2,3,3,3,3,3,3,1,1,1, &
3,3,3,3,3,3,2,2,2,1,1,1 &
],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Ntrans],order=[2,1]) !< Slip--trans interaction types for fcc
integer(pInt), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Nslip), parameter, public :: &
LATTICE_fccTohex_interactionTransSlip = 1_pInt !< Trans--Slip interaction types for fcc
integer(pInt), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans), parameter,public :: &
LATTICE_fccTohex_interactionTransTrans = reshape(int( [&
1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> trans
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
2,2,2,1,1,1,2,2,2,2,2,2, & ! v trans
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1 &
],pInt),[LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans],order=[2,1]) !< Trans--trans interaction types for fcc
real(pReal), dimension(LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fccTohex_shearTrans = sqrt(2.0_pReal)/4.0_pReal
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fccTobcc_systemTrans = reshape([&
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 &
],[ 4_pInt,LATTICE_fcc_Ntrans])
integer(pInt), dimension(9,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fccTobcc_bainVariant = reshape(int( [&
1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
1, 0, 0, 0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 1, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0 &
],pInt),[ 9_pInt, LATTICE_fcc_Ntrans])
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: &
LATTICE_fccTobcc_bainRot = reshape([&
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 &
],[ 4_pInt,LATTICE_fcc_Ntrans])
real(pReal), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans), parameter, private :: & ! Matrix for projection of shear from slip system to fault-band (twin) systems
LATTICE_fccTobcc_projectionTrans = reshape(real([& ! For ns = nt = nr
0, 1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 1,-1, 0, 0, 0, 0, 0, 0, &
0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 1,-1, 0, 0, 0, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 1,-1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 1,-1, 0, 0, 0, 0, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, &
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, &
0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 0 &
],pReal),[LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans],order=[2,1])
real(pReal), parameter, private :: &
LATTICE_fccTobcc_projectionTransFactor = sqrt(3.0_pReal/4.0_pReal)
real(pReal), parameter, public :: &
LATTICE_fccTobcc_shearCritTrans = 0.0224
integer(pInt), dimension(2_pInt,LATTICE_fcc_Ntrans), parameter, public :: &
LATTICE_fccTobcc_transNucleationTwinPair = reshape(int( [&
4, 7, &
1, 10, &
1, 4, &
7, 10, &
2, 8, &
5, 11, &
8, 11, &
2, 5, &
6, 12, &
3, 9, &
3, 12, &
6, 9 &
],pInt),[2_pInt,LATTICE_fcc_Ntrans])
real(pReal), dimension(3+3,LATTICE_fcc_Ncleavage), parameter, private :: &
LATTICE_fcc_systemCleavage = reshape(real([&
! Cleavage direction Plane normal
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1, &
0, 1,-1, 1, 1, 1, &
0,-1,-1, -1,-1, 1, &
-1, 0,-1, 1,-1,-1, &
0, 1, 1, -1, 1,-1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ncleavage])
!--------------------------------------------------------------------------------------------------
! body centered cubic
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], pInt) !< # of slip systems per family for bcc
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< # of twin systems per family for bcc
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_bcc_NtransSystem = int([0,0],pInt) !< # of transformation systems per family for bcc
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_bcc_NcleavageSystem = int([3,6,0],pInt) !< # of cleavage systems per family for bcc
integer(pInt), parameter, private :: &
LATTICE_bcc_Nslip = 24_pInt, & !sum(lattice_bcc_NslipSystem), & !< total # of slip systems for bcc
LATTICE_bcc_Ntwin = 12_pInt, & !sum(lattice_bcc_NtwinSystem), & !< total # of twin systems for bcc
LATTICE_bcc_NnonSchmid = 6_pInt, & !< total # of non-Schmid contributions for bcc (A. Koester, A. Ma, A. Hartmaier 2012)
LATTICE_bcc_Ntrans = 0_pInt, & !sum(lattice_bcc_NtransSystem), & !< total # of transformation systems for bcc
LATTICE_bcc_Ncleavage = 9_pInt !sum(lattice_bcc_NcleavageSystem) !< total # of cleavage systems for bcc
real(pReal), dimension(3+3,LATTICE_bcc_Nslip), parameter, private :: &
LATTICE_bcc_systemSlip = reshape(real([&
! Slip direction Plane normal
! Slip system <111>{110}
1,-1, 1, 0, 1, 1, &
-1,-1, 1, 0, 1, 1, &
1, 1, 1, 0,-1, 1, &
-1, 1, 1, 0,-1, 1, &
-1, 1, 1, 1, 0, 1, &
-1,-1, 1, 1, 0, 1, &
1, 1, 1, -1, 0, 1, &
1,-1, 1, -1, 0, 1, &
-1, 1, 1, 1, 1, 0, &
-1, 1,-1, 1, 1, 0, &
1, 1, 1, -1, 1, 0, &
1, 1,-1, -1, 1, 0, &
! Slip system <111>{112}
-1, 1, 1, 2, 1, 1, &
1, 1, 1, -2, 1, 1, &
1, 1,-1, 2,-1, 1, &
1,-1, 1, 2, 1,-1, &
1,-1, 1, 1, 2, 1, &
1, 1,-1, -1, 2, 1, &
1, 1, 1, 1,-2, 1, &
-1, 1, 1, 1, 2,-1, &
1, 1,-1, 1, 1, 2, &
1,-1, 1, -1, 1, 2, &
-1, 1, 1, 1,-1, 2, &
1, 1, 1, 1, 1,-2 &
! Slip system <111>{123}
! 1, 1,-1, 1, 2, 3, &
! 1,-1, 1, -1, 2, 3, &
! -1, 1, 1, 1,-2, 3, &
! 1, 1, 1, 1, 2,-3, &
! 1,-1, 1, 1, 3, 2, &
! 1, 1,-1, -1, 3, 2, &
! 1, 1, 1, 1,-3, 2, &
! -1, 1, 1, 1, 3,-2, &
! 1, 1,-1, 2, 1, 3, &
! 1,-1, 1, -2, 1, 3, &
! -1, 1, 1, 2,-1, 3, &
! 1, 1, 1, 2, 1,-3, &
! 1,-1, 1, 2, 3, 1, &
! 1, 1,-1, -2, 3, 1, &
! 1, 1, 1, 2,-3, 1, &
! -1, 1, 1, 2, 3,-1, &
! -1, 1, 1, 3, 1, 2, &
! 1, 1, 1, -3, 1, 2, &
! 1, 1,-1, 3,-1, 2, &
! 1,-1, 1, 3, 1,-2, &
! -1, 1, 1, 3, 2, 1, &
! 1, 1, 1, -3, 2, 1, &
! 1, 1,-1, 3,-2, 1, &
! 1,-1, 1, 3, 2,-1 &
],pReal),[ 3_pInt + 3_pInt ,LATTICE_bcc_Nslip])
real(pReal), dimension(3+3,LATTICE_bcc_Ntwin), parameter, private :: &
LATTICE_bcc_systemTwin = reshape(real([&
! Twin system <111>{112}
-1, 1, 1, 2, 1, 1, &
1, 1, 1, -2, 1, 1, &
1, 1,-1, 2,-1, 1, &
1,-1, 1, 2, 1,-1, &
1,-1, 1, 1, 2, 1, &
1, 1,-1, -1, 2, 1, &
1, 1, 1, 1,-2, 1, &
-1, 1, 1, 1, 2,-1, &
1, 1,-1, 1, 1, 2, &
1,-1, 1, -1, 1, 2, &
-1, 1, 1, 1,-1, 2, &
1, 1, 1, 1, 1,-2 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_bcc_Ntwin])
real(pReal), dimension(LATTICE_bcc_Ntwin), parameter, private :: &
LATTICE_bcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal)
integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Nslip), parameter, public :: &
LATTICE_bcc_interactionSlipSlip = reshape(int( [&
1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! ---> slip
2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! |
6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! |
6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v slip
5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, &
4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, &
4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, &
3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, &
4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, &
3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, &
5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, &
4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, &
!
6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, &
4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, &
3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, &
3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, &
4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, &
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, &
4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, &
3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, &
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 &
],pInt),[lattice_bcc_Nslip,lattice_bcc_Nslip],order=[2,1]) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377
!< 1: self interaction
!< 2: coplanar interaction
!< 3: collinear interaction
!< 4: mixed-asymmetrical junction
!< 5: mixed-symmetrical junction
!< 6: edge junction
integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin), parameter, public :: &
LATTICE_bcc_interactionSlipTwin = reshape(int( [&
3,3,3,2,2,3,3,3,3,2,3,3, & ! ---> twin
3,3,2,3,3,2,3,3,2,3,3,3, & ! |
3,2,3,3,3,3,2,3,3,3,3,2, & ! |
2,3,3,3,3,3,3,2,3,3,2,3, & ! v slip
2,3,3,3,3,3,3,2,3,3,2,3, &
3,3,2,3,3,2,3,3,2,3,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,3,2,2,3,3,3,3,2,3,3, &
2,3,3,3,3,3,3,2,3,3,2,3, &
3,3,3,2,2,3,3,3,3,2,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,2,3,3,2,3,3,2,3,3,3, &
!
1,3,3,3,3,3,3,2,3,3,2,3, &
3,1,3,3,3,3,2,3,3,3,3,2, &
3,3,1,3,3,2,3,3,2,3,3,3, &
3,3,3,1,2,3,3,3,3,2,3,3, &
3,3,3,2,1,3,3,3,3,2,3,3, &
3,3,2,3,3,1,3,3,2,3,3,3, &
3,2,3,3,3,3,1,3,3,3,3,2, &
2,3,3,3,3,3,3,1,3,3,2,3, &
3,3,2,3,3,2,3,3,1,3,3,3, &
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1 &
],pInt),[LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for bcc
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Nslip), parameter, public :: &
LATTICE_bcc_interactionTwinSlip = 1_pInt !< Twin--slip interaction types for bcc @todo not implemented yet
integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin), parameter, public :: &
LATTICE_bcc_interactionTwinTwin = reshape(int( [&
1,3,3,3,3,3,3,2,3,3,2,3, & ! ---> twin
3,1,3,3,3,3,2,3,3,3,3,2, & ! |
3,3,1,3,3,2,3,3,2,3,3,3, & ! |
3,3,3,1,2,3,3,3,3,2,3,3, & ! v twin
3,3,3,2,1,3,3,3,3,2,3,3, &
3,3,2,3,3,1,3,3,2,3,3,3, &
3,2,3,3,3,3,1,3,3,3,3,2, &
2,3,3,3,3,3,3,1,3,3,2,3, &
3,3,2,3,3,2,3,3,1,3,3,3, &
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1 &
],pInt),[LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for bcc
!< 1: self interaction
!< 2: collinear interaction
!< 3: other interaction
real(pReal), dimension(3+3,LATTICE_bcc_Ncleavage), parameter, private :: &
LATTICE_bcc_systemCleavage = reshape(real([&
! Cleavage direction Plane normal
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1, &
1,-1, 1, 0, 1, 1, &
1, 1, 1, 0,-1, 1, &
-1, 1, 1, 1, 0, 1, &
1, 1, 1, -1, 0, 1, &
-1, 1, 1, 1, 1, 0, &
1, 1, 1, -1, 1, 0 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_bcc_Ncleavage])
!--------------------------------------------------------------------------------------------------
! hexagonal
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
lattice_hex_NslipSystem = int([ 3, 3, 3, 6, 12, 6, 0, 0, 0, 0, 0, 0, 0],pInt) !< # of slip systems per family for hex
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
lattice_hex_NtwinSystem = int([ 6, 6, 6, 6],pInt) !< # of slip systems per family for hex
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_hex_NtransSystem = int([0,0],pInt) !< # of transformation systems per family for hex
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_hex_NcleavageSystem = int([3,0,0],pInt) !< # of cleavage systems per family for hex
integer(pInt), parameter, private :: &
LATTICE_hex_Nslip = 33_pInt, & !sum(lattice_hex_NslipSystem), & !< total # of slip systems for hex
LATTICE_hex_Ntwin = 24_pInt, & !sum(lattice_hex_NtwinSystem), & !< total # of twin systems for hex
LATTICE_hex_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for hex
LATTICE_hex_Ntrans = 0_pInt, & !sum(lattice_hex_NtransSystem), & !< total # of transformation systems for hex
LATTICE_hex_Ncleavage = 3_pInt !sum(lattice_hex_NcleavageSystem) !< total # of cleavage systems for hex
real(pReal), dimension(4+4,LATTICE_hex_Nslip), parameter, private :: &
LATTICE_hex_systemSlip = reshape(real([&
! Slip direction Plane normal
! Basal systems <11.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base))
2, -1, -1, 0, 0, 0, 0, 1, &
-1, 2, -1, 0, 0, 0, 0, 1, &
-1, -1, 2, 0, 0, 0, 0, 1, &
! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio)
2, -1, -1, 0, 0, 1, -1, 0, &
-1, 2, -1, 0, -1, 0, 1, 0, &
-1, -1, 2, 0, 1, -1, 0, 0, &
! 2nd type prismatic systems <10.0>{11.0} -- a slip; plane normals independent of c/a-ratio
0, 1, -1, 0, 2, -1, -1, 0, &
-1, 0, 1, 0, -1, 2, -1, 0, &
1, -1, 0, 0, -1, -1, 2, 0, &
! 1st type 1st order pyramidal systems <11.0>{-11.1} -- plane normals depend on the c/a-ratio
2, -1, -1, 0, 0, 1, -1, 1, &
-1, 2, -1, 0, -1, 0, 1, 1, &
-1, -1, 2, 0, 1, -1, 0, 1, &
1, 1, -2, 0, -1, 1, 0, 1, &
-2, 1, 1, 0, 0, -1, 1, 1, &
1, -2, 1, 0, 1, 0, -1, 1, &
! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the c/a-ratio
2, -1, -1, 3, -1, 1, 0, 1, &
1, -2, 1, 3, -1, 1, 0, 1, &
-1, -1, 2, 3, 1, 0, -1, 1, &
-2, 1, 1, 3, 1, 0, -1, 1, &
-1, 2, -1, 3, 0, -1, 1, 1, &
1, 1, -2, 3, 0, -1, 1, 1, &
-2, 1, 1, 3, 1, -1, 0, 1, &
-1, 2, -1, 3, 1, -1, 0, 1, &
1, 1, -2, 3, -1, 0, 1, 1, &
2, -1, -1, 3, -1, 0, 1, 1, &
1, -2, 1, 3, 0, 1, -1, 1, &
-1, -1, 2, 3, 0, 1, -1, 1, &
! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below)
2, -1, -1, 3, -2, 1, 1, 2, & ! sorted according to similar twin system
-1, 2, -1, 3, 1, -2, 1, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a)
-1, -1, 2, 3, 1, 1, -2, 2, &
-2, 1, 1, 3, 2, -1, -1, 2, &
1, -2, 1, 3, -1, 2, -1, 2, &
1, 1, -2, 3, -1, -1, 2, 2 &
],pReal),[ 4_pInt + 4_pInt,LATTICE_hex_Nslip]) !< slip systems for hex sorted by A. Alankar & P. Eisenlohr
real(pReal), dimension(4+4,LATTICE_hex_Ntwin), parameter, private :: &
LATTICE_hex_systemTwin = reshape(real([&
! Compression or Tension =f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981)
1, -1, 0, 1, -1, 1, 0, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a)
-1, 0, 1, 1, 1, 0, -1, 2, &
0, 1, -1, 1, 0, -1, 1, 2, &
-1, 1, 0, 1, 1, -1, 0, 2, &
1, 0, -1, 1, -1, 0, 1, 2, &
0, -1, 1, 1, 0, 1, -1, 2, &
!
2, -1, -1, 6, -2, 1, 1, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a)
-1, 2, -1, 6, 1, -2, 1, 1, &
-1, -1, 2, 6, 1, 1, -2, 1, &
-2, 1, 1, 6, 2, -1, -1, 1, &
1, -2, 1, 6, -1, 2, -1, 1, &
1, 1, -2, 6, -1, -1, 2, 1, &
!
-1, 1, 0, -2, -1, 1, 0, 1, & !! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
1, 0, -1, -2, 1, 0, -1, 1, &
0, -1, 1, -2, 0, -1, 1, 1, &
1, -1, 0, -2, 1, -1, 0, 1, &
-1, 0, 1, -2, -1, 0, 1, 1, &
0, 1, -1, -2, 0, 1, -1, 1, &
!
2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
-1, 2, -1, -3, -1, 2, -1, 2, &
-1, -1, 2, -3, -1, -1, 2, 2, &
-2, 1, 1, -3, -2, 1, 1, 2, &
1, -2, 1, -3, 1, -2, 1, 2, &
1, 1, -2, -3, 1, 1, -2, 2 &
],pReal),[ 4_pInt + 4_pInt ,LATTICE_hex_Ntwin]) !< twin systems for hex, order follows Prof. Tom Bieler's scheme; but numbering in data was restarted from 1
integer(pInt), dimension(LATTICE_hex_Ntwin), parameter, private :: &
LATTICE_hex_shearTwin = reshape(int( [& ! indicator to formula further below
1, & ! <-10.1>{10.2}
1, &
1, &
1, &
1, &
1, &
2, & ! <11.6>{-1-1.1}
2, &
2, &
2, &
2, &
2, &
3, & ! <10.-2>{10.1}
3, &
3, &
3, &
3, &
3, &
4, & ! <11.-3>{11.2}
4, &
4, &
4, &
4, &
4 &
],pInt),[LATTICE_hex_Ntwin])
integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Nslip), parameter, public :: &
LATTICE_hex_interactionSlipSlip = reshape(int( [&
1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! ---> slip
2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
! v slip
6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
!
12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
!
20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
!
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, &
!
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 &
!
],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Nslip],order=[2,1]) !< Slip--slip interaction types for hex (onion peel naming scheme)
integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Ntwin), parameter, public :: &
LATTICE_hex_interactionSlipTwin = reshape(int( [&
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! --> twin
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
! v
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
!
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
!
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
!
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
!
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 &
!
],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Ntwin],order=[2,1]) !< Slip--twin interaction types for hex (isotropic, 24 in total)
integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Nslip), parameter, public :: &
LATTICE_hex_interactionTwinSlip = reshape(int( [&
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! --> slip
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, &
!
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
!
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
!
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 &
],pInt),[LATTICE_hex_Ntwin,LATTICE_hex_Nslip],order=[2,1]) !< Twin--twin interaction types for hex (isotropic, 20 in total)
integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Ntwin), parameter, public :: &
LATTICE_hex_interactionTwinTwin = reshape(int( [&
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! ---> twin
2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v twin
2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, &
2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, &
!
6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
!
12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, &
!
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 &
],pInt),[lattice_hex_Ntwin,lattice_hex_Ntwin],order=[2,1]) !< Twin--slip interaction types for hex (isotropic, 16 in total)
real(pReal), dimension(4+4,LATTICE_hex_Ncleavage), parameter, private :: &
LATTICE_hex_systemCleavage = reshape(real([&
! Cleavage direction Plane normal
2,-1,-1, 0, 0, 0, 0, 1, &
0, 0, 0, 1, 2,-1,-1, 0, &
0, 0, 0, 1, 0, 1,-1, 0 &
],pReal),[ 4_pInt + 4_pInt,LATTICE_hex_Ncleavage])
!--------------------------------------------------------------------------------------------------
! body centered tetragonal
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_bct_NslipSystem = int([2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ],pInt) !< # of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_bct_NtwinSystem = int([0, 0, 0, 0], pInt) !< # of twin systems per family for bct
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_bct_NtransSystem = int([0,0],pInt) !< # of transformation systems per family for bct
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_bct_NcleavageSystem = int([0,0,0],pInt) !< # of cleavage systems per family for bct
integer(pInt), parameter, private :: &
LATTICE_bct_Nslip = 52_pInt, & !sum(lattice_bct_NslipSystem), & !< total # of slip systems for bct
LATTICE_bct_Ntwin = 0_pInt, & !sum(lattice_bct_NtwinSystem), & !< total # of twin systems for bct
LATTICE_bct_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for bct
LATTICE_bct_Ntrans = 0_pInt, & !sum(lattice_bct_NtransSystem), & !< total # of transformation systems for bct
LATTICE_bct_Ncleavage = 0_pInt !sum(lattice_bct_NcleavageSystem) !< total # of cleavage systems for bct
real(pReal), dimension(3+3,LATTICE_bct_Nslip), parameter, private :: &
LATTICE_bct_systemSlip = reshape(real([&
! Slip direction Plane normal
! Slip family 1 {100)<001] (Bravais notation {hkl)<uvw] for bct c/a = 0.5456)
0, 0, 1, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
! Slip family 2 {110)<001]
0, 0, 1, 1, 1, 0, &
0, 0, 1, -1, 1, 0, &
! slip family 3 {100)<010]
0, 1, 0, 1, 0, 0, &
1, 0, 0, 0, 1, 0, &
! Slip family 4 {110)<1-11]/2
1,-1, 1, 1, 1, 0, &
1,-1,-1, 1, 1, 0, &
-1,-1,-1, -1, 1, 0, &
-1,-1, 1, -1, 1, 0, &
! Slip family 5 {110)<1-10]
1, -1, 0, 1, 1, 0, &
1, 1, 0, 1,-1, 0, &
! Slip family 6 {100)<011]
0, 1, 1, 1, 0, 0, &
0,-1, 1, 1, 0, 0, &
-1, 0, 1, 0, 1, 0, &
1, 0, 1, 0, 1, 0, &
! Slip family 7 {001)<010]
0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 0, 1, &
! Slip family 8 {001)<110]
1, 1, 0, 0, 0, 1, &
-1, 1, 0, 0, 0, 1, &
! Slip family 9 {011)<01-1]
0, 1,-1, 0, 1, 1, &
0,-1,-1, 0,-1, 1, &
-1, 0,-1, -1, 0, 1, &
1, 0,-1, 1, 0, 1, &
! Slip family 10 {011)<1-11]/2
1,-1, 1, 0, 1, 1, &
1, 1,-1, 0, 1, 1, &
1, 1, 1, 0, 1,-1, &
-1, 1, 1, 0, 1,-1, &
1,-1,-1, 1, 0, 1, &
-1,-1, 1, 1, 0, 1, &
1, 1, 1, 1, 0,-1, &
1,-1, 1, 1, 0,-1, &
! Slip family 11 {011)<100]
1, 0, 0, 0, 1, 1, &
1, 0, 0, 0, 1,-1, &
0, 1, 0, 1, 0, 1, &
0, 1, 0, 1, 0,-1, &
! Slip family 12 {211)<01-1]
0, 1,-1, 2, 1, 1, &
0,-1,-1, 2,-1, 1, &
1, 0,-1, 1, 2, 1, &
-1, 0,-1, -1, 2, 1, &
0, 1,-1, -2, 1, 1, &
0,-1,-1, -2,-1, 1, &
-1, 0,-1, -1,-2, 1, &
1, 0,-1, 1,-2, 1, &
! Slip family 13 {211)<-111]/2
-1, 1, 1, 2, 1, 1, &
-1,-1, 1, 2,-1, 1, &
1,-1, 1, 1, 2, 1, &
-1,-1, 1, -1, 2, 1, &
1, 1, 1, -2, 1, 1, &
1,-1, 1, -2,-1, 1, &
-1, 1, 1, -1,-2, 1, &
1, 1, 1, 1,-2, 1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_bct_Nslip]) !< slip systems for bct sorted by Bieler
integer(pInt), dimension(LATTICE_bct_Nslip,LATTICE_bct_Nslip), parameter, public :: &
LATTICE_bct_interactionSlipSlip = reshape(int( [&
1, 2, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, &
2, 1, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, &
!
6, 6, 4, 5, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, &
6, 6, 5, 4, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, &
!
12, 12, 11, 11, 9, 10, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
12, 12, 11, 11, 10, 9, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
!
20, 20, 19, 19, 18, 18, 16, 17, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 16, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 17, 16, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 17, 17, 16, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
!
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 25, 26, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 26, 25, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
!
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 36, 37, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 36, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 36, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 37, 36, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
!
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 49, 50, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 50, 49, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
!
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 64, 65, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 65, 64, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
!
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 81, 82, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 81, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 81, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 82, 81, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
!
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 100,101,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,100,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,100,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,100,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,100,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,100,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,100,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,101,100, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
!
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 121, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 121, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 121, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
!
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 144,145,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,144,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,144,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,144,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,144,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,144,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,144,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,145,144, 168,168,168,168,168,168,168,168, &
!
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,169,170,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,169,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,169,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,170,169,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 &
],pInt),[lattice_bct_Nslip,lattice_bct_Nslip],order=[2,1])
!--------------------------------------------------------------------------------------------------
! isotropic
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_iso_NslipSystem = int([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],pInt) !< # of slip systems per family for iso
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_iso_NtwinSystem = int([0, 0, 0, 0], pInt) !< # of twin systems per family for iso
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_iso_NtransSystem = int([0, 0],pInt) !< # of transformation systems per family for iso
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_iso_NcleavageSystem = int([3,0,0],pInt) !< # of cleavage systems per family for iso
integer(pInt), parameter, private :: &
LATTICE_iso_Nslip = 0_pInt, & !sum(lattice_iso_NslipSystem), & !< total # of slip systems for iso
LATTICE_iso_Ntwin = 0_pInt, & !sum(lattice_iso_NtwinSystem), & !< total # of twin systems for iso
LATTICE_iso_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for iso
LATTICE_iso_Ntrans = 0_pInt, & !sum(lattice_iso_NtransSystem), & !< total # of transformation systems for iso
LATTICE_iso_Ncleavage = 3_pInt !sum(lattice_iso_NcleavageSystem) !< total # of cleavage systems for iso
real(pReal), dimension(3+3,LATTICE_iso_Ncleavage), parameter, private :: &
LATTICE_iso_systemCleavage = reshape(real([&
! Cleavage direction Plane normal
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_iso_Ncleavage])
!--------------------------------------------------------------------------------------------------
! orthorhombic
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_ortho_NslipSystem = int([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ],pInt) !< # of slip systems per family for ortho
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_ortho_NtwinSystem = int([0, 0, 0, 0], pInt) !< # of twin systems per family for ortho
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_ortho_NtransSystem = int([0, 0],pInt) !< # of transformation systems per family for ortho
integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: &
LATTICE_ortho_NcleavageSystem = int([1,1,1],pInt) !< # of cleavage systems per family for ortho
integer(pInt), parameter, private :: &
LATTICE_ortho_Nslip = 0_pInt, & !sum(lattice_ortho_NslipSystem), & !< total # of slip systems for ortho
LATTICE_ortho_Ntwin = 0_pInt, & !sum(lattice_ortho_NtwinSystem), & !< total # of twin systems for ortho
LATTICE_ortho_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for ortho
LATTICE_ortho_Ntrans = 0_pInt, & !sum(lattice_ortho_NtransSystem), & !< total # of transformation systems for ortho
LATTICE_ortho_Ncleavage = 3_pInt !sum(lattice_ortho_NcleavageSystem) !< total # of cleavage systems for ortho
real(pReal), dimension(3+3,LATTICE_ortho_Ncleavage), parameter, private :: &
LATTICE_ortho_systemCleavage = reshape(real([&
! Cleavage direction Plane normal
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1 &
],pReal),[ 3_pInt + 3_pInt,LATTICE_ortho_Ncleavage])
integer(pInt), parameter, public :: &
LATTICE_maxNslip = 52_pInt, &
!LATTICE_maxNslip = maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_Nslip,\
! LATTICE_bct_Nslip,LATTICE_iso_Nslip,LATTICE_ortho_Nslip]), & !< max # of slip systems over lattice structures
LATTICE_maxNtwin = 24_pInt, &
!LATTICE_maxNtwin = maxval([LATTICE_fcc_Ntwin,LATTICE_bcc_Ntwin,LATTICE_hex_Ntwin,\
! LATTICE_bct_Ntwin,LATTICE_iso_Ntwin,LATTICE_ortho_Ntwin]), & !< max # of twin systems over lattice structures
LATTICE_maxNnonSchmid = 6_pInt, &
!LATTICE_maxNtwin = maxval([LATTICE_fcc_NnonSchmid,LATTICE_bcc_NnonSchmid,\
! LATTICE_hex_NnonSchmid,LATTICE_bct_NnonSchmid,\
! LATTICE_iso_NnonSchmid,LATTICE_ortho_NnonSchmid]), & !< max # of non-Schmid contributions over lattice structures
LATTICE_maxNtrans = 12_pInt, &
!LATTICE_maxNtrans = maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans,\
! LATTICE_bct_Ntrans,LATTICE_iso_Ntrans,LATTICE_ortho_Ntrans]),&!< max # of transformation systems over lattice structures
LATTICE_maxNcleavage = 9_pInt, &
!LATTICE_maxNcleavage = maxval([LATTICE_fcc_Ncleavage,LATTICE_bcc_Ncleavage,\
! LATTICE_hex_Ncleavage,LATTICE_bct_Ncleavage,\
! LATTICE_iso_Ncleavage,LATTICE_ortho_Ncleavage]) !< max # of cleavage systems over lattice structures
LATTICE_maxNinteraction = 182_pInt !< max # of interaction types (in hardening matrix part)
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_C66, lattice_trans_C66
real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: &
lattice_C3333, lattice_trans_C3333
real(pReal), dimension(:), allocatable, public, protected :: &
lattice_mu, &
lattice_nu, &
lattice_trans_mu, &
lattice_trans_nu
real(pReal), dimension(:,:,:,:), allocatable, public, protected :: & ! with higher-order parameters (e.g. temperature-dependent)
lattice_thermalExpansion33
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_thermalConductivity33, &
lattice_damageDiffusion33, &
lattice_vacancyfluxDiffusion33, &
lattice_vacancyfluxMobility33, &
lattice_porosityDiffusion33, &
lattice_hydrogenfluxDiffusion33, &
lattice_hydrogenfluxMobility33
real(pReal), dimension(:), allocatable, public, protected :: &
lattice_damageMobility, &
lattice_porosityMobility, &
lattice_massDensity, &
lattice_specificHeat, &
lattice_vacancyFormationEnergy, &
lattice_vacancySurfaceEnergy, &
lattice_vacancyVol, &
lattice_hydrogenFormationEnergy, &
lattice_hydrogenSurfaceEnergy, &
lattice_hydrogenVol, &
lattice_referenceTemperature, &
lattice_equilibriumVacancyConcentration, &
lattice_equilibriumHydrogenConcentration
enum, bind(c)
enumerator :: LATTICE_undefined_ID, &
LATTICE_iso_ID, &
LATTICE_fcc_ID, &
LATTICE_bcc_ID, &
LATTICE_hex_ID, &
LATTICE_bct_ID, &
LATTICE_ort_ID
end enum
integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: &
lattice_structure, trans_lattice_structure
integer(pInt), dimension(2), parameter, private :: &
lattice_NsymOperations = [24_pInt,12_pInt]
real(pReal), dimension(4,36), parameter, private :: &
lattice_symOperations = reshape([&
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry
0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, &
0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry
-0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
-0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
-0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, &
0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
-0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, &
0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, &
0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, &
-0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, &
!
1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations
0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry
0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, &
0.0_pReal, 0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, -0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, &
0.0_pReal, 0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.0_pReal, -0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, &
0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry
-0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, &
0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
-0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, &
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal &
],[4,36]) !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36
! use this later on to substitute the matrix above
! if self.lattice == 'cubic':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ],
! [ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ],
! [ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
! [ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ],
! [ 0.5, 0.5, 0.5, 0.5 ],
! [-0.5, 0.5, 0.5, 0.5 ],
! [-0.5, 0.5, 0.5,-0.5 ],
! [-0.5, 0.5,-0.5, 0.5 ],
! [-0.5,-0.5, 0.5, 0.5 ],
! [-0.5,-0.5, 0.5,-0.5 ],
! [-0.5,-0.5,-0.5, 0.5 ],
! [-0.5, 0.5,-0.5,-0.5 ],
! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ],
! [-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ],
! [-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ],
! [-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ],
! ]
! elif self.lattice == 'hexagonal':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ],
! [-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ],
! [ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ],
! [ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ],
! [ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ],
! [ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ],
! [ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
! [-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ],
! ]
! elif self.lattice == 'tetragonal':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! [ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
! [ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ],
! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ],
! ]
! elif self.lattice == 'orthorhombic':
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! [ 0.0,1.0,0.0,0.0 ],
! [ 0.0,0.0,1.0,0.0 ],
! [ 0.0,0.0,0.0,1.0 ],
! ]
! else:
! symQuats = [
! [ 1.0,0.0,0.0,0.0 ],
! ]
public :: &
lattice_init, &
lattice_qDisorientation, &
LATTICE_fcc_ID, &
LATTICE_bcc_ID, &
LATTICE_bct_ID, &
LATTICE_hex_ID
contains
!--------------------------------------------------------------------------------------------------
!> @brief Module initialization
!--------------------------------------------------------------------------------------------------
subroutine lattice_init
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
use IO, only: &
IO_open_file,&
IO_open_jobFile_stat, &
IO_countSections, &
IO_error, &
IO_timeStamp, &
IO_EOF, &
IO_read, &
IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue
use material, only: &
material_configfile, &
material_localFileExt, &
material_partPhase
use debug, only: &
debug_level, &
debug_lattice, &
debug_levelBasic
implicit none
integer(pInt), parameter :: FILEUNIT = 200_pInt
integer(pInt) :: Nphases
character(len=65536) :: &
tag = '', &
line = ''
integer(pInt), allocatable, dimension(:) :: chunkPos
integer(pInt) :: section = 0_pInt,i
real(pReal), dimension(:), allocatable :: &
CoverA, & !!!!!!< c/a ratio for low symmetry type lattice
CoverA_trans, & !< c/a ratio for transformed hex type lattice
a_fcc, & !< lattice parameter a for fcc austenite
a_bcc !< lattice paramater a for bcc martensite
write(6,'(/,a)') ' <<<+- lattice init -+>>>'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
!--------------------------------------------------------------------------------------------------
! consistency checks (required since ifort 15.0 does not support sum/maxval in parameter definition)
if (LATTICE_maxNslip /= maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_Nslip,LATTICE_bct_Nslip])) &
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])) &
call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtrans')
if (LATTICE_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,&
lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid')
if (LATTICE_fcc_Nslip /= sum(lattice_fcc_NslipSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Nslip')
if (LATTICE_bcc_Nslip /= sum(lattice_bcc_NslipSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Nslip')
if (LATTICE_hex_Nslip /= sum(lattice_hex_NslipSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Nslip')
if (LATTICE_bct_Nslip /= sum(lattice_bct_NslipSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Nslip')
if (LATTICE_fcc_Ntwin /= sum(lattice_fcc_NtwinSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntwin')
if (LATTICE_bcc_Ntwin /= sum(lattice_bcc_NtwinSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntwin')
if (LATTICE_hex_Ntwin /= sum(lattice_hex_NtwinSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntwin')
if (LATTICE_bct_Ntwin /= sum(lattice_bct_NtwinSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Ntwin')
if (LATTICE_fcc_Ntrans /= sum(lattice_fcc_NtransSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntrans')
if (LATTICE_bcc_Ntrans /= sum(lattice_bcc_NtransSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntrans')
if (LATTICE_hex_Ntrans /= sum(lattice_hex_NtransSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntrans')
if (LATTICE_bct_Ntrans /= sum(lattice_bct_NtransSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Ntrans')
if (LATTICE_fcc_Ncleavage /= sum(lattice_fcc_NcleavageSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ncleavage')
if (LATTICE_bcc_Ncleavage /= sum(lattice_bcc_NcleavageSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ncleavage')
if (LATTICE_hex_Ncleavage /= sum(lattice_hex_NcleavageSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ncleavage')
if (LATTICE_bct_Ncleavage /= sum(lattice_bct_NcleavageSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Ncleavage')
if (LATTICE_iso_Ncleavage /= sum(lattice_iso_NcleavageSystem)) &
call IO_error(0_pInt,ext_msg = 'LATTICE_iso_Ncleavage')
if (LATTICE_maxNinteraction /= max(&
maxval(lattice_fcc_interactionSlipSlip), &
maxval(lattice_bcc_interactionSlipSlip), &
maxval(lattice_hex_interactionSlipSlip), &
maxval(lattice_bct_interactionSlipSlip), &
!
maxval(lattice_fcc_interactionSlipTwin), &
maxval(lattice_bcc_interactionSlipTwin), &
maxval(lattice_hex_interactionSlipTwin), &
! maxval(lattice_bct_interactionSlipTwin), &
!
maxval(lattice_fcc_interactionTwinSlip), &
maxval(lattice_bcc_interactionTwinSlip), &
maxval(lattice_hex_interactionTwinSlip), &
! maxval(lattice_bct_interactionTwinSlip), &
!
maxval(lattice_fcc_interactionTwinTwin), &
maxval(lattice_bcc_interactionTwinTwin), &
maxval(lattice_hex_interactionTwinTwin))) &
! maxval(lattice_bct_interactionTwinTwin))) &
call IO_error(0_pInt,ext_msg = 'LATTICE_maxNinteraction')
!--------------------------------------------------------------------------------------------------
! read from material configuration file
if (.not. IO_open_jobFile_stat(FILEUNIT,material_localFileExt)) & ! no local material configuration present...
call IO_open_file(FILEUNIT,material_configFile) ! ... open material.config file
Nphases = IO_countSections(FILEUNIT,material_partPhase)
if(Nphases<1_pInt) &
call IO_error(160_pInt,Nphases, ext_msg='No phases found')
if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then
write(6,'(a16,1x,i5)') ' # phases:',Nphases
endif
allocate(lattice_structure(Nphases),source = LATTICE_undefined_ID)
allocate(trans_lattice_structure(Nphases),source = LATTICE_undefined_ID)
allocate(lattice_C66(6,6,Nphases), source=0.0_pReal)
allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal)
allocate(lattice_trans_C66(6,6,Nphases), source=0.0_pReal)
allocate(lattice_trans_C3333(3,3,3,3,Nphases), source=0.0_pReal)
allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients
allocate(lattice_thermalConductivity33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_damageDiffusion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_vacancyfluxDiffusion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_vacancyfluxMobility33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_PorosityDiffusion33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_hydrogenfluxDiffusion33(3,3,Nphases), source=0.0_pReal)
allocate(lattice_hydrogenfluxMobility33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_damageMobility ( Nphases), source=0.0_pReal)
allocate(lattice_PorosityMobility ( Nphases), source=0.0_pReal)
allocate(lattice_massDensity ( Nphases), source=0.0_pReal)
allocate(lattice_specificHeat ( Nphases), source=0.0_pReal)
allocate(lattice_vacancyFormationEnergy ( Nphases), source=0.0_pReal)
allocate(lattice_vacancySurfaceEnergy ( Nphases), source=0.0_pReal)
allocate(lattice_vacancyVol ( Nphases), source=0.0_pReal)
allocate(lattice_hydrogenFormationEnergy( Nphases), source=0.0_pReal)
allocate(lattice_hydrogenSurfaceEnergy ( Nphases), source=0.0_pReal)
allocate(lattice_hydrogenVol ( Nphases), source=0.0_pReal)
allocate(lattice_referenceTemperature ( Nphases), source=300.0_pReal)
allocate(lattice_equilibriumVacancyConcentration(Nphases), source=0.0_pReal)
allocate(lattice_equilibriumHydrogenConcentration(Nphases),source=0.0_pReal)
allocate(lattice_mu(Nphases), source=0.0_pReal)
allocate(lattice_nu(Nphases), source=0.0_pReal)
allocate(lattice_trans_mu(Nphases), source=0.0_pReal)
allocate(lattice_trans_nu(Nphases), source=0.0_pReal)
allocate(lattice_NnonSchmid(Nphases), source=0_pInt)
allocate(lattice_Sslip(3,3,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_Sslip_v(6,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_Scleavage(3,3,3,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_Scleavage_v(6,3,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_sd(3,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_st(3,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_sn(3,lattice_maxNslip,Nphases),source=0.0_pReal)
allocate(lattice_Qtwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_Stwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_Stwin_v(6,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_td(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_tt(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_tn(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal)
allocate(lattice_shearTrans(lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Qtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Strans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_Strans_v(6,lattice_maxNtrans,Nphases),source=0.0_pReal)
allocate(lattice_projectionTrans(lattice_maxNtrans,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)
allocate(lattice_NcleavageSystem(lattice_maxNcleavageFamily,Nphases),source=0_pInt)
allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionSlipTrans(lattice_maxNslip,lattice_maxNtrans,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionTransSlip(lattice_maxNtrans,lattice_maxNslip,Nphases),source=0_pInt) ! other:me
allocate(lattice_interactionTransTrans(lattice_maxNtrans,lattice_maxNtrans,Nphases),source=0_pInt) ! other:me
allocate(CoverA(Nphases),source=0.0_pReal)
allocate(CoverA_trans(Nphases),source=0.0_pReal)
allocate(a_fcc(Nphases),source=0.0_pReal)
allocate(a_bcc(Nphases),source=0.0_pReal)
rewind(fileUnit)
line = '' ! to have it initialized
section = 0_pInt ! - " -
do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= material_partPhase) ! wind forward to <Phase>
line = IO_read(fileUnit)
enddo
do while (trim(line) /= IO_EOF) ! read through sections of material part
line = IO_read(fileUnit)
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') then ! stop at next part
line = IO_read(fileUnit, .true.) ! reset IO_read
exit
endif
if (IO_getTag(line,'[',']') /= '') then ! next section
section = section + 1_pInt
endif
if (section > 0_pInt) then
chunkPos = IO_stringPos(line)
tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key
select case(tag)
case ('lattice_structure')
select case(trim(IO_lc(IO_stringValue(line,chunkPos,2_pInt))))
case('iso','isotropic')
lattice_structure(section) = LATTICE_iso_ID
case('fcc')
lattice_structure(section) = LATTICE_fcc_ID
case('bcc')
lattice_structure(section) = LATTICE_bcc_ID
case('hex','hexagonal')
lattice_structure(section) = LATTICE_hex_ID
case('bct')
lattice_structure(section) = LATTICE_bct_ID
case('ort','orthorhombic')
lattice_structure(section) = LATTICE_ort_ID
case default
call IO_error(130_pInt,ext_msg=trim(IO_lc(IO_stringValue(line,chunkPos,2_pInt))))
end select
case('trans_lattice_structure')
select case(trim(IO_lc(IO_stringValue(line,chunkPos,2_pInt))))
case('bcc')
trans_lattice_structure(section) = LATTICE_bcc_ID
case('hex','hexagonal','hcp')
trans_lattice_structure(section) = LATTICE_hex_ID
end select
case ('c11')
lattice_C66(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c12')
lattice_C66(1,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c13')
lattice_C66(1,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c22')
lattice_C66(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c23')
lattice_C66(2,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c33')
lattice_C66(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c44')
lattice_C66(4,4,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c55')
lattice_C66(5,5,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c66')
lattice_C66(6,6,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c11_trans')
lattice_trans_C66(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c12_trans')
lattice_trans_C66(1,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c13_trans')
lattice_trans_C66(1,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c22_trans')
lattice_trans_C66(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c23_trans')
lattice_trans_C66(2,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c33_trans')
lattice_trans_C66(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c44_trans')
lattice_trans_C66(4,4,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c55_trans')
lattice_trans_C66(5,5,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c66_trans')
lattice_trans_C66(6,6,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('covera_ratio','c/a_ratio','c/a')
CoverA(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('c/a_trans','c/a_martensite','c/a_mart')
CoverA_trans(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('a_fcc')
a_fcc(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('a_bcc')
a_bcc(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_conductivity11')
lattice_thermalConductivity33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_conductivity22')
lattice_thermalConductivity33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_conductivity33')
lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_expansion11')
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(1,1,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('thermal_expansion22')
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(2,2,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('thermal_expansion33')
do i = 2_pInt, min(4,chunkPos(1)) ! read up to three parameters (constant, linear, quadratic with T)
lattice_thermalExpansion33(3,3,i-1_pInt,section) = IO_floatValue(line,chunkPos,i)
enddo
case ('specific_heat')
lattice_specificHeat(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyformationenergy')
lattice_vacancyFormationEnergy(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancysurfaceenergy')
lattice_vacancySurfaceEnergy(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyvolume')
lattice_vacancyVol(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenformationenergy')
lattice_hydrogenFormationEnergy(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogensurfaceenergy')
lattice_hydrogenSurfaceEnergy(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenvolume')
lattice_hydrogenVol(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('mass_density')
lattice_massDensity(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('reference_temperature')
lattice_referenceTemperature(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('damage_diffusion11')
lattice_DamageDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('damage_diffusion22')
lattice_DamageDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('damage_diffusion33')
lattice_DamageDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('damage_mobility')
lattice_DamageMobility(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_diffusion11')
lattice_vacancyfluxDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_diffusion22')
lattice_vacancyfluxDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_diffusion33')
lattice_vacancyfluxDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_mobility11')
lattice_vacancyfluxMobility33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_mobility22')
lattice_vacancyfluxMobility33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancyflux_mobility33')
lattice_vacancyfluxMobility33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('porosity_diffusion11')
lattice_PorosityDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('porosity_diffusion22')
lattice_PorosityDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('porosity_diffusion33')
lattice_PorosityDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('porosity_mobility')
lattice_PorosityMobility(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_diffusion11')
lattice_hydrogenfluxDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_diffusion22')
lattice_hydrogenfluxDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_diffusion33')
lattice_hydrogenfluxDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_mobility11')
lattice_hydrogenfluxMobility33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_mobility22')
lattice_hydrogenfluxMobility33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogenflux_mobility33')
lattice_hydrogenfluxMobility33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('vacancy_eqcv')
lattice_equilibriumVacancyConcentration(section) = IO_floatValue(line,chunkPos,2_pInt)
case ('hydrogen_eqch')
lattice_equilibriumHydrogenConcentration(section) = IO_floatValue(line,chunkPos,2_pInt)
end select
endif
enddo
do i = 1_pInt,Nphases
if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) &
.and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(131_pInt,el=i) ! checking physical significance of c/a
if ((CoverA(i) > 2.0_pReal) &
.and. lattice_structure(i) == LATTICE_bct_ID) call IO_error(131_pInt,el=i) ! checking physical significance of c/a
call lattice_initializeStructure(i, CoverA(i), CoverA_trans(i), a_fcc(i), a_bcc(i))
enddo
deallocate(CoverA,CoverA_trans,a_fcc,a_bcc)
end subroutine lattice_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculation of Schmid matrices, etc.
!--------------------------------------------------------------------------------------------------
subroutine lattice_initializeStructure(myPhase,CoverA,CoverA_trans,a_fcc,a_bcc)
use prec, only: &
tol_math_check
use math, only: &
math_crossproduct, &
math_tensorproduct33, &
math_mul33x33, &
math_mul33x3, &
math_transpose33, &
math_trace33, &
math_symmetric33, &
math_Mandel33to6, &
math_Mandel3333to66, &
math_Voigt66to3333, &
math_axisAngleToR, &
INRAD, &
MATH_I3
use IO, only: &
IO_error, &
IO_warning
implicit none
integer(pInt), intent(in) :: myPhase
real(pReal), intent(in) :: &
CoverA, &
CoverA_trans, &
a_fcc, &
a_bcc
real(pReal), dimension(3) :: &
sdU, snU, &
np, nn
real(pReal), dimension(3,3) :: &
sstr, sdtr, sttr
real(pReal), dimension(3,lattice_maxNslip) :: &
sd, sn
real(pReal), dimension(3,3,2,lattice_maxNnonSchmid,lattice_maxNslip) :: &
sns
real(pReal), dimension(3,lattice_maxNtwin) :: &
td, tn
real(pReal), dimension(lattice_maxNtwin) :: &
ts
real(pReal), dimension(lattice_maxNtrans) :: &
trs
real(pReal), dimension(3,lattice_maxNtrans) :: &
xtr, ytr, ztr
real(pReal), dimension(3,3,lattice_maxNtrans) :: &
Rtr, Utr, Btr, Qtr, Str
real(pReal), dimension(3,lattice_maxNcleavage) :: &
cd, cn, ct
integer(pInt) :: &
i,j, &
myNslip = 0_pInt, myNtwin = 0_pInt, myNtrans = 0_pInt, myNcleavage = 0_pInt
real(pReal) :: c11bar, c12bar, c13bar, c14bar, c33bar, c44bar, A, B
lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),&
lattice_C66(1:6,1:6,myPhase))
lattice_mu(myPhase) = 0.2_pReal *( lattice_C66(1,1,myPhase) &
- lattice_C66(1,2,myPhase) &
+ 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
lattice_nu(myPhase) = ( lattice_C66(1,1,myPhase) &
+ 4.0_pReal*lattice_C66(1,2,myPhase) &
- 2.0_pReal*lattice_C66(4,4,myPhase)) &
/( 4.0_pReal*lattice_C66(1,1,myPhase) &
+ 6.0_pReal*lattice_C66(1,2,myPhase) &
+ 2.0_pReal*lattice_C66(4,4,myPhase))! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt
lattice_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel
do i = 1_pInt, 6_pInt
if (abs(lattice_C66(i,i,myPhase))<tol_math_check) &
call IO_error(135_pInt,el=i,ip=myPhase,ext_msg='matrix diagonal "el"ement of phase "ip"')
enddo
! Elasticity matrices for transformed phase
select case(lattice_structure(myPhase))
case (LATTICE_fcc_ID)
select case(trans_lattice_structure(myPhase))
case (LATTICE_bcc_ID)
lattice_trans_C66(1:6,1:6,myPhase) = lattice_C66(1:6,1:6,myPhase)
lattice_trans_mu(myPhase) = lattice_mu(myPhase)
lattice_trans_nu(myPhase) = lattice_nu(myPhase)
lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase) = lattice_C3333(1:3,1:3,1:3,1:3,myPhase)
lattice_trans_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase))
do i = 1_pInt, 6_pInt
if (abs(lattice_trans_C66(i,i,myPhase))<tol_math_check) &
call IO_error(135_pInt,el=i,ip=myPhase,ext_msg='matrix diagonal "el"ement of phase "ip" in fcc-->bcc transformation')
enddo
case (LATTICE_hex_ID)
c11bar = (lattice_C66(1,1,myPhase) + lattice_C66(1,2,myPhase) + 2.0_pReal*lattice_C66(4,4,myPhase))/2.0_pReal
c12bar = (lattice_C66(1,1,myPhase) + 5.0_pReal*lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase))/6.0_pReal
c33bar = (lattice_C66(1,1,myPhase) + 2.0_pReal*lattice_C66(1,2,myPhase) + 4.0_pReal*lattice_C66(4,4,myPhase))/3.0_pReal
c13bar = (lattice_C66(1,1,myPhase) + 2.0_pReal*lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase))/3.0_pReal
c44bar = (lattice_C66(1,1,myPhase) - lattice_C66(1,2,myPhase) + lattice_C66(4,4,myPhase))/3.0_pReal
c14bar = (lattice_C66(1,1,myPhase) - lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase)) &
/(3.0_pReal*sqrt(2.0_pReal))
A = c14bar**(2.0_pReal)/c44bar
B = c14bar**(2.0_pReal)/(0.5_pReal*(c11bar - c12bar))
lattice_trans_C66(1,1,myPhase) = c11bar - A
lattice_trans_C66(1,2,myPhase) = c12bar + A
lattice_trans_C66(1,3,myPhase) = c13bar
lattice_trans_C66(3,3,myPhase) = c33bar
lattice_trans_C66(4,4,myPhase) = c44bar - B
lattice_trans_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(trans_lattice_structure(myPhase),&
lattice_trans_C66(1:6,1:6,myPhase))
lattice_trans_mu(myPhase) = 0.2_pReal *( lattice_trans_C66(1,1,myPhase) &
- lattice_trans_C66(1,2,myPhase) &
+ 3.0_pReal*lattice_trans_C66(4,4,myPhase))
lattice_trans_nu(myPhase) = ( lattice_trans_C66(1,1,myPhase) &
+ 4.0_pReal*lattice_trans_C66(1,2,myPhase) &
- 2.0_pReal*lattice_trans_C66(4,4,myPhase)) &
/( 4.0_pReal*lattice_trans_C66(1,1,myPhase) &
+ 6.0_pReal*lattice_trans_C66(1,2,myPhase) &
+ 2.0_pReal*lattice_trans_C66(4,4,myPhase))
lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_trans_C66(1:6,1:6,myPhase))
lattice_trans_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase))
do i = 1_pInt, 6_pInt
if (abs(lattice_trans_C66(i,i,myPhase))<tol_math_check) &
call IO_error(135_pInt,el=i,ip=myPhase,ext_msg='matrix diagonal "el"ement of phase "ip" in fcc-->hex transformation')
enddo
end select
end select
forall (i = 1_pInt:3_pInt) &
lattice_thermalExpansion33 (1:3,1:3,i,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalExpansion33 (1:3,1:3,i,myPhase))
lattice_thermalConductivity33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalConductivity33 (1:3,1:3,myPhase))
lattice_DamageDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_DamageDiffusion33 (1:3,1:3,myPhase))
lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase))
lattice_vacancyfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_vacancyfluxMobility33 (1:3,1:3,myPhase))
lattice_PorosityDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_PorosityDiffusion33 (1:3,1:3,myPhase))
lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase))
lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase))
select case(lattice_structure(myPhase))
!--------------------------------------------------------------------------------------------------
! fcc
case (LATTICE_fcc_ID)
myNslip = lattice_fcc_Nslip
myNtwin = lattice_fcc_Ntwin
myNtrans = lattice_fcc_Ntrans
myNcleavage = lattice_fcc_Ncleavage
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)
enddo
do i = 1_pInt,myNtwin ! assign twin system vectors and shears
td(1:3,i) = lattice_fcc_systemTwin(1:3,i)
tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
ts(i) = lattice_fcc_shearTwin(i)
enddo
do i = 1_pInt, myNcleavage ! assign cleavage system vectors
cd(1:3,i) = lattice_fcc_systemCleavage(1:3,i)/norm2(lattice_fcc_systemCleavage(1:3,i))
cn(1:3,i) = lattice_fcc_systemCleavage(4:6,i)/norm2(lattice_fcc_systemCleavage(4:6,i))
ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i))
enddo
! Phase transformation
select case(trans_lattice_structure(myPhase))
case (LATTICE_bcc_ID) ! fcc to bcc transformation
do i = 1_pInt,myNtrans
Rtr(1:3,1:3,i) = math_axisAngleToR(lattice_fccTobcc_systemTrans(1:3,i), & ! Pitsch rotation
lattice_fccTobcc_systemTrans(4,i)*INRAD)
Btr(1:3,1:3,i) = math_axisAngleToR(lattice_fccTobcc_bainRot(1:3,i), & ! Rotation of fcc to Bain coordinate system
lattice_fccTobcc_bainRot(4,i)*INRAD)
xtr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(1:3,i),pReal)
ytr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(4:6,i),pReal)
ztr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(7:9,i),pReal)
Utr(1:3,1:3,i) = 0.0_pReal ! Bain deformation
if ((a_fcc > 0.0_pReal) .and. (a_bcc > 0.0_pReal)) then
Utr(1:3,1:3,i) = (a_bcc/a_fcc)*math_tensorproduct33(xtr(1:3,i), xtr(1:3,i)) + &
sqrt(2.0_pReal)*(a_bcc/a_fcc)*math_tensorproduct33(ytr(1:3,i), ytr(1:3,i)) + &
sqrt(2.0_pReal)*(a_bcc/a_fcc)*math_tensorproduct33(ztr(1:3,i), ztr(1:3,i))
endif
Qtr(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), Btr(1:3,1:3,i))
Str(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), Utr(1:3,1:3,i)) - MATH_I3
enddo
case (LATTICE_hex_ID)
sstr(1:3,1:3) = MATH_I3
sstr(1,3) = sqrt(2.0_pReal)/4.0_pReal
sdtr(1:3,1:3) = MATH_I3
if (CoverA_trans > 1.0_pReal .and. CoverA_trans < 2.0_pReal) then
sdtr(3,3) = CoverA_trans/sqrt(8.0_pReal/3.0_pReal)
endif
sttr = math_mul33x33(sdtr, sstr)
do i = 1_pInt,myNtrans
xtr(1:3,i) = lattice_fccTohex_systemTrans(1:3,i)/norm2(lattice_fccTohex_systemTrans(1:3,i))
ztr(1:3,i) = lattice_fccTohex_systemTrans(4:6,i)/norm2(lattice_fccTohex_systemTrans(4:6,i))
ytr(1:3,i) = -math_crossproduct(xtr(1:3,i), ztr(1:3,i))
Rtr(1:3,1,i) = xtr(1:3,i)
Rtr(1:3,2,i) = ytr(1:3,i)
Rtr(1:3,3,i) = ztr(1:3,i)
Qtr(1:3,1:3,i) = Rtr(1:3,1:3,i)
Str(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), math_mul33x33(sttr, math_transpose33(Rtr(1:3,1:3,i))))
Str(1:3,1:3,i) = Str(1:3,1:3,i) - MATH_I3
trs(i) = lattice_fccTohex_shearTrans(i)
enddo
case default
Qtr = 0.0_pReal
Str = 0.0_pReal
end select
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
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_fcc_NcleavageSystem
lattice_NnonSchmid(myPhase) = lattice_fcc_NnonSchmid
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_fcc_interactionSlipSlip
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
lattice_interactionSlipTrans(1:myNslip,1:myNtrans,myPhase) = lattice_fccTohex_interactionSlipTrans
lattice_interactionTransSlip(1:myNtrans,1:myNslip,myPhase) = lattice_fccTohex_interactionTransSlip
lattice_interactionTransTrans(1:myNtrans,1:myNtrans,myPhase) = lattice_fccTohex_interactionTransTrans
lattice_projectionTrans(1:myNtrans,1:myNtrans,myPhase) = LATTICE_fccTobcc_projectionTrans*&
LATTICE_fccTobcc_projectionTransFactor
!--------------------------------------------------------------------------------------------------
! bcc
case (LATTICE_bcc_ID)
myNslip = lattice_bcc_Nslip
myNtwin = lattice_bcc_Ntwin
myNtrans = lattice_bcc_Ntrans
myNcleavage = lattice_bcc_Ncleavage
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1:3,i) = lattice_bcc_systemSlip(1:3,i)
sn(1:3,i) = lattice_bcc_systemSlip(4:6,i)
sdU = sd(1:3,i) / norm2(sd(1:3,i))
snU = sn(1:3,i) / norm2(sn(1:3,i))
! "np" and "nn" according to Gröger_etal2008, Acta Materialia 56 (2008) 5412–5425, table 1 (corresponds to their "n1" for positive and negative slip direction respectively)
np = math_mul33x3(math_axisAngleToR(sdU,60.0_pReal*INRAD), snU)
nn = math_mul33x3(math_axisAngleToR(-sdU,60.0_pReal*INRAD), snU)
! Schmid matrices with non-Schmid contributions according to Koester_etal2012, Acta Materialia 60 (2012) 3894–3901, eq. (17) ("n1" is replaced by either "np" or "nn" according to either positive or negative slip direction)
sns(1:3,1:3,1,1,i) = math_tensorproduct33(sdU, np)
sns(1:3,1:3,2,1,i) = math_tensorproduct33(-sdU, nn)
sns(1:3,1:3,1,2,i) = math_tensorproduct33(math_crossproduct(snU, sdU), snU)
sns(1:3,1:3,2,2,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), snU)
sns(1:3,1:3,1,3,i) = math_tensorproduct33(math_crossproduct(np, sdU), np)
sns(1:3,1:3,2,3,i) = math_tensorproduct33(math_crossproduct(nn, -sdU), nn)
sns(1:3,1:3,1,4,i) = math_tensorproduct33(snU, snU)
sns(1:3,1:3,2,4,i) = math_tensorproduct33(snU, snU)
sns(1:3,1:3,1,5,i) = math_tensorproduct33(math_crossproduct(snU, sdU), math_crossproduct(snU, sdU))
sns(1:3,1:3,2,5,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), math_crossproduct(snU, -sdU))
sns(1:3,1:3,1,6,i) = math_tensorproduct33(sdU, sdU)
sns(1:3,1:3,2,6,i) = math_tensorproduct33(-sdU, -sdU)
enddo
do i = 1_pInt,myNtwin ! assign twin system vectors and shears
td(1:3,i) = lattice_bcc_systemTwin(1:3,i)
tn(1:3,i) = lattice_bcc_systemTwin(4:6,i)
ts(i) = lattice_bcc_shearTwin(i)
enddo
do i = 1_pInt, myNcleavage ! assign cleavage system vectors
cd(1:3,i) = lattice_bcc_systemCleavage(1:3,i)/norm2(lattice_bcc_systemCleavage(1:3,i))
cn(1:3,i) = lattice_bcc_systemCleavage(4:6,i)/norm2(lattice_bcc_systemCleavage(4:6,i))
ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i))
enddo
lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_bcc_NslipSystem
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_bcc_NtwinSystem
lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_bcc_NtransSystem
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_bcc_NcleavageSystem
lattice_NnonSchmid(myPhase) = lattice_bcc_NnonSchmid
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_bcc_interactionSlipSlip
lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_bcc_interactionSlipTwin
lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_bcc_interactionTwinSlip
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_bcc_interactionTwinTwin
!--------------------------------------------------------------------------------------------------
! hex (including conversion from miller-bravais (a1=a2=a3=c) to miller (a, b, c) indices)
case (LATTICE_hex_ID)
myNslip = lattice_hex_Nslip
myNtwin = lattice_hex_Ntwin
myNtrans = lattice_hex_Ntrans
myNcleavage = lattice_hex_Ncleavage
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1,i) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*&
0.5_pReal*sqrt(3.0_pReal)
sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA
sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal)
sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA
enddo
do i = 1_pInt,myNtwin ! assign twin system vectors and shears
td(1,i) = lattice_hex_systemTwin(1,i)*1.5_pReal
td(2,i) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*&
0.5_pReal*sqrt(3.0_pReal)
td(3,i) = lattice_hex_systemTwin(4,i)*CoverA
tn(1,i) = lattice_hex_systemTwin(5,i)
tn(2,i) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal)
tn(3,i) = lattice_hex_systemTwin(8,i)/CoverA
select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29
case (1_pInt) ! <-10.1>{10.2}
ts(i) = (3.0_pReal-CoverA*CoverA)/sqrt(3.0_pReal)/CoverA
case (2_pInt) ! <11.6>{-1-1.1}
ts(i) = 1.0_pReal/CoverA
case (3_pInt) ! <10.-2>{10.1}
ts(i) = (4.0_pReal*CoverA*CoverA-9.0_pReal)/4.0_pReal/sqrt(3.0_pReal)/CoverA
case (4_pInt) ! <11.-3>{11.2}
ts(i) = 2.0_pReal*(CoverA*CoverA-2.0_pReal)/3.0_pReal/CoverA
end select
enddo
do i = 1_pInt, myNcleavage ! cleavage system vectors
cd(1,i) = lattice_hex_systemCleavage(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
cd(2,i) = (lattice_hex_systemCleavage(1,i)+2.0_pReal*lattice_hex_systemCleavage(2,i))*&
0.5_pReal*sqrt(3.0_pReal)
cd(3,i) = lattice_hex_systemCleavage(4,i)*CoverA
cd(1:3,1) = cd(1:3,i)/norm2(cd(1:3,i))
cn(1,i) = lattice_hex_systemCleavage(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
cn(2,i) = (lattice_hex_systemCleavage(5,i)+2.0_pReal*lattice_hex_systemCleavage(6,i))/sqrt(3.0_pReal)
cn(3,i) = lattice_hex_systemCleavage(8,i)/CoverA
cn(1:3,1) = cn(1:3,i)/norm2(cn(1:3,i))
ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i))
enddo
lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_hex_NslipSystem
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_hex_NtwinSystem
lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_hex_NtransSystem
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_hex_NcleavageSystem
lattice_NnonSchmid(myPhase) = lattice_hex_NnonSchmid
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_hex_interactionSlipSlip
lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_hex_interactionSlipTwin
lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_hex_interactionTwinSlip
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_hex_interactionTwinTwin
!--------------------------------------------------------------------------------------------------
! bct
case (LATTICE_bct_ID)
myNslip = lattice_bct_Nslip
myNtwin = lattice_bct_Ntwin
myNcleavage = lattice_bct_Ncleavage
do i = 1_pInt,myNslip ! assign slip system vectors
sd(1:2,i) = lattice_bct_systemSlip(1:2,i)
sd(3,i) = lattice_bct_systemSlip(3,i)*CoverA
sn(1:2,i) = lattice_bct_systemSlip(4:5,i)
sn(3,i) = lattice_bct_systemSlip(6,i)/CoverA
sdU = sd(1:3,i) / norm2(sd(1:3,i))
snU = sn(1:3,i) / norm2(sn(1:3,i))
enddo
lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_bct_NslipSystem
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_bct_NtwinSystem
lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_bct_NtransSystem
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_bct_NcleavageSystem
lattice_NnonSchmid(myPhase) = lattice_bct_NnonSchmid
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_bct_interactionSlipSlip
!--------------------------------------------------------------------------------------------------
! orthorhombic (no crystal plasticity)
case (LATTICE_ort_ID)
myNslip = 0_pInt
myNtwin = 0_pInt
myNtrans = 0_pInt
myNcleavage = lattice_ortho_Ncleavage
do i = 1_pInt, myNcleavage ! assign cleavage system vectors
cd(1:3,i) = lattice_iso_systemCleavage(1:3,i)/norm2(LATTICE_ortho_systemCleavage(1:3,i))
cn(1:3,i) = lattice_iso_systemCleavage(4:6,i)/norm2(LATTICE_ortho_systemCleavage(4:6,i))
ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i))
enddo
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_iso_NcleavageSystem
!--------------------------------------------------------------------------------------------------
! isotropic (no crystal plasticity)
case (LATTICE_iso_ID)
myNslip = 0_pInt
myNtwin = 0_pInt
myNtrans = 0_pInt
myNcleavage = lattice_iso_Ncleavage
do i = 1_pInt, myNcleavage ! assign cleavage system vectors
cd(1:3,i) = lattice_iso_systemCleavage(1:3,i)/norm2(lattice_iso_systemCleavage(1:3,i))
cn(1:3,i) = lattice_iso_systemCleavage(4:6,i)/norm2(lattice_iso_systemCleavage(4:6,i))
ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i))
enddo
lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_iso_NcleavageSystem
!--------------------------------------------------------------------------------------------------
! something went wrong
case default
call IO_error(130_pInt,ext_msg='lattice_initializeStructure')
end select
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
lattice_sd(1:3,i,myPhase) = sd(1:3,i)/norm2(sd(1:3,i)) ! make unit vector
lattice_sn(1:3,i,myPhase) = sn(1:3,i)/norm2(sn(1:3,i)) ! make unit vector
lattice_st(1:3,i,myPhase) = math_crossproduct(lattice_sd(1:3,i,myPhase), &
lattice_sn(1:3,i,myPhase))
lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct33(lattice_sd(1:3,i,myPhase), &
lattice_sn(1:3,i,myPhase)) ! calculate Schmid matrix d \otimes n
do j = 1_pInt,lattice_NnonSchmid(myPhase)
lattice_Sslip(1:3,1:3,2*j ,i,myPhase) = sns(1:3,1:3,1,j,i)
lattice_Sslip(1:3,1:3,2*j+1,i,myPhase) = sns(1:3,1:3,2,j,i)
enddo
do j = 1_pInt,1_pInt+2_pInt*lattice_NnonSchmid(myPhase)
lattice_Sslip_v(1:6,j,i,myPhase) = &
math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,j,i,myPhase)))
enddo
if (abs(math_trace33(lattice_Sslip(1:3,1:3,1,i,myPhase))) > tol_math_check) &
call IO_error(0_pInt,myPhase,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix')
enddo
do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure
lattice_td(1:3,i,myPhase) = td(1:3,i)/norm2(td(1:3,i)) ! make unit vector
lattice_tn(1:3,i,myPhase) = tn(1:3,i)/norm2(tn(1:3,i)) ! make unit vector
lattice_tt(1:3,i,myPhase) = math_crossproduct(lattice_td(1:3,i,myPhase), &
lattice_tn(1:3,i,myPhase))
lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct33(lattice_td(1:3,i,myPhase), &
lattice_tn(1:3,i,myPhase))
lattice_Stwin_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myPhase)))
lattice_Qtwin(1:3,1:3,i,myPhase) = math_axisAngleToR(tn(1:3,i),180.0_pReal*INRAD)
lattice_shearTwin(i,myPhase) = ts(i)
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_Qtrans(1:3,1:3,i,myPhase) = Qtr(1:3,1:3,i)
lattice_Strans(1:3,1:3,i,myPhase) = Str(1:3,1:3,i)
lattice_Strans_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Strans(1:3,1:3,i,myPhase)))
lattice_shearTrans(i,myPhase) = trs(i)
enddo
do i = 1_pInt,myNcleavage ! store slip system vectors and Schmid matrix for my structure
lattice_Scleavage(1:3,1:3,1,i,myPhase) = math_tensorproduct33(cd(1:3,i),cn(1:3,i))
lattice_Scleavage(1:3,1:3,2,i,myPhase) = math_tensorproduct33(ct(1:3,i),cn(1:3,i))
lattice_Scleavage(1:3,1:3,3,i,myPhase) = math_tensorproduct33(cn(1:3,i),cn(1:3,i))
do j = 1_pInt,3_pInt
lattice_Scleavage_v(1:6,j,i,myPhase) = &
math_Mandel33to6(math_symmetric33(lattice_Scleavage(1:3,1:3,j,i,myPhase)))
enddo
enddo
end subroutine lattice_initializeStructure
!--------------------------------------------------------------------------------------------------
!> @brief Symmetrizes stiffness matrix according to lattice type
!--------------------------------------------------------------------------------------------------
pure function lattice_symmetrizeC66(struct,C66)
implicit none
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct
real(pReal), dimension(6,6), intent(in) :: C66
real(pReal), dimension(6,6) :: lattice_symmetrizeC66
integer(pInt) :: j,k
lattice_symmetrizeC66 = 0.0_pReal
select case(struct)
case (LATTICE_iso_ID)
forall(k=1_pInt:3_pInt)
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
lattice_symmetrizeC66(k,k) = C66(1,1)
lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
end forall
case (LATTICE_fcc_ID,LATTICE_bcc_ID)
forall(k=1_pInt:3_pInt)
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
lattice_symmetrizeC66(k,k) = C66(1,1)
lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4)
end forall
case (LATTICE_hex_ID)
lattice_symmetrizeC66(1,1) = C66(1,1)
lattice_symmetrizeC66(2,2) = C66(1,1)
lattice_symmetrizeC66(3,3) = C66(3,3)
lattice_symmetrizeC66(1,2) = C66(1,2)
lattice_symmetrizeC66(2,1) = C66(1,2)
lattice_symmetrizeC66(1,3) = C66(1,3)
lattice_symmetrizeC66(3,1) = C66(1,3)
lattice_symmetrizeC66(2,3) = C66(1,3)
lattice_symmetrizeC66(3,2) = C66(1,3)
lattice_symmetrizeC66(4,4) = C66(4,4)
lattice_symmetrizeC66(5,5) = C66(4,4)
lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
case (LATTICE_ort_ID)
lattice_symmetrizeC66(1,1) = C66(1,1)
lattice_symmetrizeC66(2,2) = C66(2,2)
lattice_symmetrizeC66(3,3) = C66(3,3)
lattice_symmetrizeC66(1,2) = C66(1,2)
lattice_symmetrizeC66(2,1) = C66(1,2)
lattice_symmetrizeC66(1,3) = C66(1,3)
lattice_symmetrizeC66(3,1) = C66(1,3)
lattice_symmetrizeC66(2,3) = C66(2,3)
lattice_symmetrizeC66(3,2) = C66(2,3)
lattice_symmetrizeC66(4,4) = C66(4,4)
lattice_symmetrizeC66(5,5) = C66(5,5)
lattice_symmetrizeC66(6,6) = C66(6,6)
case (LATTICE_bct_ID)
lattice_symmetrizeC66(1,1) = C66(1,1)
lattice_symmetrizeC66(2,2) = C66(1,1)
lattice_symmetrizeC66(3,3) = C66(3,3)
lattice_symmetrizeC66(1,2) = C66(1,2)
lattice_symmetrizeC66(2,1) = C66(1,2)
lattice_symmetrizeC66(1,3) = C66(1,3)
lattice_symmetrizeC66(3,1) = C66(1,3)
lattice_symmetrizeC66(2,3) = C66(1,3)
lattice_symmetrizeC66(3,2) = C66(1,3)
lattice_symmetrizeC66(4,4) = C66(4,4)
lattice_symmetrizeC66(5,5) = C66(4,4)
lattice_symmetrizeC66(6,6) = C66(6,6) !J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
case default
lattice_symmetrizeC66 = C66
end select
end function lattice_symmetrizeC66
!--------------------------------------------------------------------------------------------------
!> @brief Symmetrizes 2nd order tensor according to lattice type
!--------------------------------------------------------------------------------------------------
pure function lattice_symmetrize33(struct,T33)
implicit none
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct
real(pReal), dimension(3,3), intent(in) :: T33
real(pReal), dimension(3,3) :: lattice_symmetrize33
integer(pInt) :: k
lattice_symmetrize33 = 0.0_pReal
select case(struct)
case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID)
forall(k=1_pInt:3_pInt) lattice_symmetrize33(k,k) = T33(1,1)
case (LATTICE_hex_ID)
lattice_symmetrize33(1,1) = T33(1,1)
lattice_symmetrize33(2,2) = T33(1,1)
lattice_symmetrize33(3,3) = T33(3,3)
case (LATTICE_ort_ID,lattice_bct_ID)
lattice_symmetrize33(1,1) = T33(1,1)
lattice_symmetrize33(2,2) = T33(2,2)
lattice_symmetrize33(3,3) = T33(3,3)
case default
lattice_symmetrize33 = T33
end select
end function lattice_symmetrize33
!--------------------------------------------------------------------------------------------------
!> @brief figures whether unit quat falls into stereographic standard triangle
!--------------------------------------------------------------------------------------------------
logical pure function lattice_qInSST(Q, struct)
use, intrinsic :: &
IEEE_arithmetic
use math, only: &
math_qToRodrig
implicit none
real(pReal), dimension(4), intent(in) :: Q ! orientation
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct ! lattice structure
real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q
Rodrig = math_qToRodrig(Q)
if (any(IEEE_is_NaN(Rodrig))) then
lattice_qInSST = .false.
else
select case (struct)
case (LATTICE_bcc_ID,LATTICE_fcc_ID)
lattice_qInSST = Rodrig(1) > Rodrig(2) .and. &
Rodrig(2) > Rodrig(3) .and. &
Rodrig(3) > 0.0_pReal
case (LATTICE_hex_ID)
lattice_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. &
Rodrig(2) > 0.0_pReal .and. &
Rodrig(3) > 0.0_pReal
case default
lattice_qInSST = .true.
end select
endif
end function lattice_qInSST
!--------------------------------------------------------------------------------------------------
!> @brief calculates the disorientation for 2 unit quaternions
!--------------------------------------------------------------------------------------------------
pure function lattice_qDisorientation(Q1, Q2, struct)
use prec, only: &
tol_math_check
use math, only: &
math_qMul, &
math_qConj
implicit none
real(pReal), dimension(4) :: lattice_qDisorientation
real(pReal), dimension(4), intent(in) :: &
Q1, & ! 1st orientation
Q2 ! 2nd orientation
integer(kind(LATTICE_undefined_ID)), optional, intent(in) :: & ! if given, symmetries between the two orientation will be considered
struct
real(pReal), dimension(4) :: dQ,dQsymA,mis
integer(pInt) :: i,j,k,s,symmetry
integer(kind(LATTICE_undefined_ID)) :: myStruct
!--------------------------------------------------------------------------------------------------
! check if a structure with known symmetries is given
if (present(struct)) then
myStruct = struct
select case (struct)
case(LATTICE_fcc_ID,LATTICE_bcc_ID)
symmetry = 1_pInt
case(LATTICE_hex_ID)
symmetry = 2_pInt
case default
symmetry = 0_pInt
end select
else
symmetry = 0_pInt
myStruct = LATTICE_undefined_ID
endif
!--------------------------------------------------------------------------------------------------
! calculate misorientation, for cubic and hexagonal structure find symmetries
dQ = math_qMul(math_qConj(Q1),Q2)
lattice_qDisorientation = dQ
select case(symmetry)
case (1_pInt,2_pInt)
s = sum(lattice_NsymOperations(1:symmetry-1_pInt))
do i = 1_pInt,2_pInt
dQ = math_qConj(dQ) ! switch order of "from -- to"
do j = 1_pInt,lattice_NsymOperations(symmetry) ! run through first crystal's symmetries
dQsymA = math_qMul(lattice_symOperations(1:4,s+j),dQ) ! apply sym
do k = 1_pInt,lattice_NsymOperations(symmetry) ! run through 2nd crystal's symmetries
mis = math_qMul(dQsymA,lattice_symOperations(1:4,s+k)) ! apply sym
if (mis(1) < 0.0_pReal) & ! want positive angle
mis = -mis
if (mis(1)-lattice_qDisorientation(1) > -tol_math_check &
.and. lattice_qInSST(mis,LATTICE_undefined_ID)) lattice_qDisorientation = mis ! found better one
enddo; enddo; enddo
case (0_pInt)
if (lattice_qDisorientation(1) < 0.0_pReal) lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg
end select
end function lattice_qDisorientation
end module lattice
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