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DAMASK_EICMD/code/lattice.f90

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Fixed issue with previous commit
2014-08-14 17:51:51 +05:30
!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @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 = 6_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_maxNslip = 33_pInt, & !< max # of slip systems over lattice structures
LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures
LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part)
LATTICE_maxNnonSchmid = 6_pInt, & !< max # of non schmid contributions over lattice structures
LATTICE_maxNtrans = 36_pInt !< max # of transformations over lattice structures
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
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
real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: &
lattice_Sslip !< Schmid and non-Schmid matrices
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Sslip_v !< Mandel notation of lattice_Sslip
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_trn1, &
lattice_trd1, &
lattice_trt1, &
lattice_trn2, &
lattice_trd2, &
lattice_trt2, &
lattice_NItrans_v
real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
lattice_Atrans, &
lattice_Mtrans, &
lattice_Ttrans, &
lattice_Rtrans, &
lattice_Utrans, &
lattice_NItrans
real(pReal), allocatable, dimension(:,:), protected, public :: &
lattice_shearTwin !< characteristic twin shear
integer(pInt), allocatable, dimension(:), protected, public :: &
lattice_NnonSchmid !< total # of non-Schmid contributions for each structure
!--------------------------------------------------------------------------------------------------
! fcc
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0],pInt) !< total # of slip systems per family for fcc
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_fcc_NtransSystem = int([12, 24],pInt) !< total # of transformation systems per family for fcc
integer(pInt), parameter, private :: &
LATTICE_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc
LATTICE_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc
LATTICE_fcc_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for fcc
LATTICE_fcc_Ntrans = 36_pInt !< total # of transformations for fcc
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(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
!--------------------------------------------------------------------------------------------------
! bcc
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
LATTICE_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0], pInt) !< total # of slip systems per family for bcc
integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: &
LATTICE_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< total # of twin systems per family for bcc
integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: &
LATTICE_bcc_NtransSystem = int([0,0],pInt) !< total # of transformation 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, & !< # of non-Schmid contributions for bcc. 6 known non schmid contributions for BCC (A. Koester, A. Ma, A. Hartmaier 2012)
LATTICE_bcc_Ntrans = 0_pInt !< total # of transformations 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
!--------------------------------------------------------------------------------------------------
! hex
integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: &
lattice_hex_NslipSystem = int([ 3, 3, 3, 6, 12, 6],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) !< total # of transformation 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, & !< # of non-Schmid contributions for hex
LATTICE_hex_Ntrans = 0_pInt !< total # of transformations 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 (32? in total)
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(:,:,:), allocatable, public, protected :: &
lattice_C66
real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: &
lattice_C3333
real(pReal), dimension(:), allocatable, public, protected :: &
lattice_mu, &
lattice_nu
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_thermalConductivity33, &
lattice_thermalExpansion33, &
lattice_surfaceEnergy33
real(pReal), dimension(:), allocatable, public, protected :: &
lattice_referenceTemperature
enum, bind(c)
enumerator :: LATTICE_undefined_ID, &
LATTICE_iso_ID, &
LATTICE_fcc_ID, &
LATTICE_bcc_ID, &
LATTICE_hex_ID, &
LATTICE_ort_ID
end enum
integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: &
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_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 prec, only: &
tol_math_check
use IO, only: &
IO_open_file,&
IO_open_jobFile_stat, &
IO_countSections, &
IO_countTagInPart, &
IO_error, &
IO_timeStamp, &
IO_stringPos, &
IO_EOF, &
IO_read, &
IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_EOF
use material, only: &
material_configfile, &
material_localFileExt, &
material_partPhase
use debug, only: &
debug_level, &
debug_lattice, &
debug_levelBasic
implicit none
integer(pInt), parameter :: FILEUNIT = 200_pInt
integer(pInt) :: Nphases
character(len=65536) :: &
tag = '', &
line = ''
integer(pInt), parameter :: MAXNCHUNKS = 2_pInt
integer(pInt), dimension(1+2*MAXNCHUNKS) :: positions
integer(pInt) :: section = 0_pInt,i
real(pReal), dimension(:), allocatable :: &
CoverA, & !< c/a ratio for hex type lattice
aA, & !< lattice parameter a for fcc austenite
aM, & !< lattice paramater a for bcc martensite
cM !< lattice parameter c for bcc martensite
write(6,'(/,a)') ' <<<+- lattice init -+>>>'
write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
!--------------------------------------------------------------------------------------------------
! consistency checks
if (LATTICE_maxNslip /= maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_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_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_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_maxNinteraction /= max(&
maxval(lattice_fcc_interactionSlipSlip), &
maxval(lattice_bcc_interactionSlipSlip), &
maxval(lattice_hex_interactionSlipSlip), &
!
maxval(lattice_fcc_interactionSlipTwin), &
maxval(lattice_bcc_interactionSlipTwin), &
maxval(lattice_hex_interactionSlipTwin), &
!
maxval(lattice_fcc_interactionTwinSlip), &
maxval(lattice_bcc_interactionTwinSlip), &
maxval(lattice_hex_interactionTwinSlip), &
!
maxval(lattice_fcc_interactionTwinTwin), &
maxval(lattice_bcc_interactionTwinTwin), &
maxval(lattice_hex_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(lattice_C66(6,6,Nphases), source=0.0_pReal)
allocate(lattice_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_surfaceEnergy33 (3,3,Nphases), source=0.0_pReal)
allocate(lattice_referenceTemperature (Nphases), source=0.0_pReal)
allocate(lattice_mu(Nphases), source=0.0_pReal)
allocate(lattice_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_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_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_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(CoverA(Nphases),source=0.0_pReal)
allocate(aA(Nphases),source=0.0_pReal)
allocate(aM(Nphases),source=0.0_pReal)
allocate(cM(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
positions = IO_stringPos(line,MAXNCHUNKS)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('lattice_structure')
select case(trim(IO_lc(IO_stringValue(line,positions,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('ort','orthorombic')
lattice_structure(section) = LATTICE_ort_ID
case default
call IO_error(450_pInt,ext_msg=trim(IO_lc(IO_stringValue(line,positions,2_pInt))))
end select
case ('c11')
lattice_C66(1,1,section) = IO_floatValue(line,positions,2_pInt)
case ('c12')
lattice_C66(1,2,section) = IO_floatValue(line,positions,2_pInt)
case ('c13')
lattice_C66(1,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c22')
lattice_C66(2,2,section) = IO_floatValue(line,positions,2_pInt)
case ('c23')
lattice_C66(2,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c33')
lattice_C66(3,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c44')
lattice_C66(4,4,section) = IO_floatValue(line,positions,2_pInt)
case ('c55')
lattice_C66(5,5,section) = IO_floatValue(line,positions,2_pInt)
case ('c66')
lattice_C66(6,6,section) = IO_floatValue(line,positions,2_pInt)
case ('covera_ratio','c/a_ratio','c/a')
CoverA(section) = IO_floatValue(line,positions,2_pInt)
Modification of basic states for phase transformation
2014-08-14 18:48:33 +05:30
case ('aa', 'a_a', 'a_austenite', 'a_fcc')
Fixed issue with previous commit
2014-08-14 17:51:51 +05:30
aA(section) = IO_floatValue(line,positions,2_pInt)
Modification of basic states for phase transformation
2014-08-14 18:48:33 +05:30
case ('am', 'a_m', 'a_martensite', 'a_bcc')
Fixed issue with previous commit
2014-08-14 17:51:51 +05:30
aM(section) = IO_floatValue(line,positions,2_pInt)
case ('cm', 'c_m', 'c_martensite')
cM(section) = IO_floatValue(line,positions,2_pInt)
case ('k11')
lattice_thermalConductivity33(1,1,section) = IO_floatValue(line,positions,2_pInt)
case ('k22')
lattice_thermalConductivity33(2,2,section) = IO_floatValue(line,positions,2_pInt)
case ('k33')
lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,positions,2_pInt)
case ('thermal_expansion11')
lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,positions,2_pInt)
case ('thermal_expansion22')
lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,positions,2_pInt)
case ('thermal_expansion33')
lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,positions,2_pInt)
case ('g11')
lattice_surfaceEnergy33(1,1,section) = IO_floatValue(line,positions,2_pInt)
case ('g22')
lattice_surfaceEnergy33(2,2,section) = IO_floatValue(line,positions,2_pInt)
case ('g33')
lattice_surfaceEnergy33(3,3,section) = IO_floatValue(line,positions,2_pInt)
case ('reference_temperature')
lattice_referenceTemperature(section) = IO_floatValue(line,positions,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(206_pInt) ! checking physical significance of c/a
call lattice_initializeStructure(i, CoverA(i), aA(i), aM(i), cM(i))
enddo
deallocate(CoverA,aA,aM,cM)
end subroutine lattice_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculation of Schmid matrices, etc.
!--------------------------------------------------------------------------------------------------
subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM)
use prec, only: &
tol_math_check
use math, only: &
math_vectorproduct, &
math_tensorproduct, &
math_norm3, &
math_mul33x3, &
math_trace33, &
math_symmetric33, &
math_Mandel33to6, &
math_Mandel3333to66, &
math_Voigt66to3333, &
math_axisAngleToR, &
INRAD
use IO, only: &
IO_error
implicit none
integer(pInt), intent(in) :: myPhase
real(pReal), intent(in) :: &
CoverA, &
aA, &
aM, &
cM
real(pReal), dimension(3) :: &
sdU, snU, &
np, nn
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
integer(pInt) :: &
i,j, &
myNslip, myNtwin
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(43_pInt,el=i,ip=myPhase)
enddo
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_surfaceEnergy33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
lattice_surfaceEnergy33(1:3,1:3,myPhase))
select case(lattice_structure(myPhase))
!--------------------------------------------------------------------------------------------------
! fcc
case (LATTICE_fcc_ID)
myNslip = lattice_fcc_Nslip
myNtwin = lattice_fcc_Ntwin
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
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_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
!--------------------------------------------------------------------------------------------------
! bcc
case (LATTICE_bcc_ID)
myNslip = lattice_bcc_Nslip
myNtwin = lattice_bcc_Ntwin
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) / math_norm3(sd(1:3,i))
snU = sn(1:3,i) / math_norm3(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_tensorproduct(sdU, np)
sns(1:3,1:3,2,1,i) = math_tensorproduct(-sdU, nn)
sns(1:3,1:3,1,2,i) = math_tensorproduct(math_vectorproduct(snU, sdU), snU)
sns(1:3,1:3,2,2,i) = math_tensorproduct(math_vectorproduct(snU, -sdU), snU)
sns(1:3,1:3,1,3,i) = math_tensorproduct(math_vectorproduct(np, sdU), np)
sns(1:3,1:3,2,3,i) = math_tensorproduct(math_vectorproduct(nn, -sdU), nn)
sns(1:3,1:3,1,4,i) = math_tensorproduct(snU, snU)
sns(1:3,1:3,2,4,i) = math_tensorproduct(snU, snU)
sns(1:3,1:3,1,5,i) = math_tensorproduct(math_vectorproduct(snU, sdU), math_vectorproduct(snU, sdU))
sns(1:3,1:3,2,5,i) = math_tensorproduct(math_vectorproduct(snU, -sdU), math_vectorproduct(snU, -sdU))
sns(1:3,1:3,1,6,i) = math_tensorproduct(sdU, sdU)
sns(1:3,1:3,2,6,i) = math_tensorproduct(-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
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_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
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
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_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
!--------------------------------------------------------------------------------------------------
! orthorombic and isotropic (no crystal plasticity)
case (LATTICE_ort_ID, LATTICE_iso_ID)
myNslip = 0_pInt
myNtwin = 0_pInt
!--------------------------------------------------------------------------------------------------
! something went wrong
case default
call IO_error(450_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)/math_norm3(sd(1:3,i)) ! make unit vector
lattice_sn(1:3,i,myPhase) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
lattice_st(1:3,i,myPhase) = math_vectorproduct(lattice_sd(1:3,i,myPhase), &
lattice_sn(1:3,i,myPhase))
lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct(lattice_sd(1:3,i,myPhase), &
lattice_sn(1:3,i,myPhase))
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)/math_norm3(td(1:3,i)) ! make unit vector
lattice_tn(1:3,i,myPhase) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector
lattice_tt(1:3,i,myPhase) = math_vectorproduct(lattice_td(1:3,i,myPhase), &
lattice_tn(1:3,i,myPhase))
lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct(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
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 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) :: j,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_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 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(Rodrig/=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(1) and hexagonal(2) 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