223031012
/
DAMASK_EICMD
mirror of https://github.com/achalhp/DAMASK_EICMD.git
1
0
Fork 0
Code Issues Projects Releases Wiki Activity
DAMASK_EICMD/code/lattice.f90

2273 lines
136 KiB
Fortran
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

!--------------------------------------------------------------------------------------------------
!> @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
0, 1,-1, 1, 1, 1, &
-1, 0, 1, 1, 1, 1, &
1,-1, 0, 1, 1, 1, &
0,-1,-1, -1,-1, 1, &
1, 0, 1, -1,-1, 1, &
-1, 1, 0, -1,-1, 1, &
0,-1, 1, 1,-1,-1, &
-1, 0,-1, 1,-1,-1, &
1, 1, 0, 1,-1,-1, &
0, 1, 1, -1, 1,-1, &
1, 0,-1, -1, 1,-1, &
-1,-1, 0, -1, 1,-1 &
],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 :: &
lattice_thermalConductivity33, &
lattice_thermalExpansion33, &
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
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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
use numerics, only: &
worldrank
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_thermalConductivity33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_thermalExpansion33 (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')
lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_expansion22')
lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt)
case ('thermal_expansion33')
lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt)
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
lattice_thermalConductivity33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalConductivity33(1:3,1:3,myPhase))
lattice_thermalExpansion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_thermalExpansion33(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 prec, only: &
prec_isNaN
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(prec_isNaN(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
Reference in New Issue View Git Blame Copy Permalink