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DAMASK_EICMD
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DAMASK_EICMD/code/lattice.f90

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! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!##############################################################
!* $Id$
!************************************
!* Module: LATTICE *
!************************************
!* contains: *
!* - Lattice structure definition *
!* - Slip system definition *
!* - Schmid matrices calculation *
!************************************
MODULE lattice
!*** Include other modules ***
use prec, only: pReal,pInt
implicit none
!************************************
!* Lattice structures *
!************************************
integer(pInt) lattice_Nhexagonal, & ! # of hexagonal lattice structure (from tag CoverA_ratio)
lattice_Nstructure ! # of lattice structures (1: fcc,2: bcc,3+: hexagonal)
integer(pInt), parameter :: lattice_maxNslipFamily = 4 ! max # of slip system families over lattice structures
integer(pInt), parameter :: lattice_maxNtwinFamily = 4 ! max # of twin system families over lattice structures
integer(pInt), parameter :: lattice_maxNslip = 48 ! max # of slip systems over lattice structures
integer(pInt), parameter :: lattice_maxNtwin = 24 ! max # of twin systems over lattice structures
integer(pInt), parameter :: lattice_maxNinteraction = 20 ! max # of interaction types (in hardening matrix part)
integer(pInt), pointer, dimension(:,:) :: interactionSlipSlip, &
interactionSlipTwin, &
interactionTwinSlip, &
interactionTwinTwin
! Schmid matrices, normal, shear direction and d x n of slip systems
real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Sslip
real(pReal), allocatable, dimension(:,:,:) :: lattice_Sslip_v
real(pReal), allocatable, dimension(:,:,:) :: lattice_sn, &
lattice_sd, &
lattice_st
! rotation and Schmid matrices, normal, shear direction and d x n of twin systems
real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Qtwin
real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Stwin
real(pReal), allocatable, dimension(:,:,:) :: lattice_Stwin_v
real(pReal), allocatable, dimension(:,:,:) :: lattice_tn, &
lattice_td, &
lattice_tt
! characteristic twin shear
real(pReal), allocatable, dimension(:,:) :: lattice_shearTwin
! number of slip and twin systems in each family
integer(pInt), allocatable, dimension(:,:) :: lattice_NslipSystem, &
lattice_NtwinSystem
! interaction type of slip and twin systems among each other
integer(pInt), allocatable, dimension(:,:,:) :: lattice_interactionSlipSlip, &
lattice_interactionSlipTwin, &
lattice_interactionTwinSlip, &
lattice_interactionTwinTwin
!============================== fcc (1) =================================
integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_fcc_NslipSystem = (/12, 0, 0, 0/)
integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_fcc_NtwinSystem = (/12, 0, 0, 0/)
integer(pInt), parameter :: lattice_fcc_Nslip = 12 ! sum(lattice_fcc_NslipSystem)
integer(pInt), parameter :: lattice_fcc_Ntwin = 12 ! sum(lattice_fcc_NtwinSystem)
integer(pInt) :: lattice_fcc_Nstructure = 0_pInt
real(pReal), dimension(3+3,lattice_fcc_Nslip), parameter :: lattice_fcc_systemSlip = &
reshape((/&
! Slip system <110>{111} Sorted according to Eisenlohr & Hantcherli
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 &
/),(/3+3,lattice_fcc_Nslip/))
real(pReal), dimension(3+3,lattice_fcc_Ntwin), parameter :: lattice_fcc_systemTwin = &
reshape((/&
! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli
-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 &
/),(/3+3,lattice_fcc_Ntwin/))
real(pReal), dimension(lattice_fcc_Ntwin), parameter :: lattice_fcc_shearTwin = &
reshape((/&
! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812, &
0.7071067812 &
/),(/lattice_fcc_Ntwin/))
integer(pInt), target, dimension(lattice_fcc_Nslip,lattice_fcc_Nslip) :: lattice_fcc_interactionSlipSlip = &
reshape((/&
! Interaction types
! 1 --- self interaction
! 2 --- coplanar interaction
! 3 --- collinear interaction
! 4 --- Hirth locks
! 5 --- glissile junctions
! 6 --- Lomer locks
1,2,2,4,6,5,3,5,5,4,5,6, &
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, &
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 &
/),(/lattice_fcc_Nslip,lattice_fcc_Nslip/))
integer(pInt), target, dimension(lattice_fcc_Ntwin,lattice_fcc_Nslip) :: lattice_fcc_interactionSlipTwin = &
reshape((/&
1,1,1,2,2,1,1,2,2,2,1,2, &
1,1,1,2,2,1,1,2,2,2,1,2, &
1,1,1,2,2,1,1,2,2,2,1,2, &
2,2,1,1,1,1,2,1,2,1,2,2, &
2,2,1,1,1,1,2,1,2,1,2,2, &
2,2,1,1,1,1,2,1,2,1,2,2, &
1,2,2,2,1,2,1,1,1,2,2,1, &
1,2,2,2,1,2,1,1,1,2,2,1, &
1,2,2,2,1,2,1,1,1,2,2,1, &
2,1,2,1,2,2,2,2,1,1,1,1, &
2,1,2,1,2,2,2,2,1,1,1,1, &
2,1,2,1,2,2,2,2,1,1,1,1 &
/),(/lattice_fcc_Ntwin,lattice_fcc_Nslip/))
integer(pInt), target, dimension(lattice_fcc_Nslip,lattice_fcc_Ntwin) :: lattice_fcc_interactionTwinSlip = 0
integer(pInt), target, dimension(lattice_fcc_Ntwin,lattice_fcc_Ntwin) :: lattice_fcc_interactionTwinTwin = &
reshape((/&
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, &
2,2,2,1,1,1,2,2,2,2,2,2, &
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 &
/),(/lattice_fcc_Ntwin,lattice_fcc_Ntwin/))
!============================== bcc (2) =================================
integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_bcc_NslipSystem = (/12,12,24, 0/)
integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_bcc_NtwinSystem = (/12, 0, 0, 0/)
integer(pInt), parameter :: lattice_bcc_Nslip = 48 ! sum(lattice_bcc_NslipSystem)
integer(pInt), parameter :: lattice_bcc_Ntwin = 12 ! sum(lattice_bcc_NtwinSystem)
integer(pInt) :: lattice_bcc_Nstructure = 0_pInt
real(pReal), dimension(3+3,lattice_bcc_Nslip), parameter :: lattice_bcc_systemSlip = &
reshape((/&
! Slip system <111>{110} meaningful sorting?
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} meaningful sorting ?
-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} meaningful sorting ?
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 &
/),(/3+3,lattice_bcc_Nslip/))
! twin system <111>{112}
! MISSING: not implemented yet -- now dummy copy from fcc !!
real(pReal), dimension(3+3,lattice_bcc_Ntwin), parameter :: lattice_bcc_systemTwin = &
reshape((/&
! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli
-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 &
/),(/3+3,lattice_bcc_Ntwin/))
real(pReal), dimension(lattice_bcc_Ntwin), parameter :: lattice_bcc_shearTwin = &
reshape((/&
! Twin system {111}<112> just a dummy
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123, &
0.123 &
/),(/lattice_bcc_Ntwin/))
!*** slip--slip interactions for BCC structures (2) ***
integer(pInt), target, dimension(lattice_bcc_Nslip,lattice_bcc_Nslip) :: lattice_bcc_interactionSlipSlip = &
reshape((/&
1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2, &
2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1 &
/),(/lattice_bcc_Nslip,lattice_bcc_Nslip/))
!*** slip--twin interactions for BCC structures (2) ***
! MISSING: not implemented yet
integer(pInt), target, dimension(lattice_bcc_Ntwin,lattice_bcc_Nslip) :: lattice_bcc_interactionSlipTwin = &
reshape((/&
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0 &
/),(/lattice_bcc_Ntwin,lattice_bcc_Nslip/))
!*** twin--slip interactions for BCC structures (2) ***
! MISSING: not implemented yet
integer(pInt), target, dimension(lattice_bcc_Nslip,lattice_bcc_Ntwin) :: lattice_bcc_interactionTwinSlip = &
reshape((/&
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 &
/),(/lattice_bcc_Nslip,lattice_bcc_Ntwin/))
!*** twin-twin interactions for BCC structures (2) ***
! MISSING: not implemented yet
integer(pInt), target, dimension(lattice_bcc_Ntwin,lattice_bcc_Ntwin) :: lattice_bcc_interactionTwinTwin = &
reshape((/&
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0, &
0,0,0,0,0,0,0,0,0,0,0,0 &
/),(/lattice_bcc_Ntwin,lattice_bcc_Ntwin/))
!============================== hex (3+) =================================
integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_hex_NslipSystem = (/ 3, 3, 6,12/)
integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_hex_NtwinSystem = (/ 6, 6, 6, 6/)
integer(pInt), parameter :: lattice_hex_Nslip = 24 ! sum(lattice_hex_NslipSystem)
integer(pInt), parameter :: lattice_hex_Ntwin = 24 ! sum(lattice_hex_NtwinSystem)
integer(pInt) :: lattice_hex_Nstructure = 0_pInt
!* sorted by A. Alankar & P. Eisenlohr
real(pReal), dimension(4+4,lattice_hex_Nslip), parameter :: lattice_hex_systemSlip = &
reshape((/&
! Basal systems <1120>{0001} (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 <1120>{1010} (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, &
! 1st type 1st order pyramidal systems <1120>{1011} -- plane normals depend on the c/a-ratio
2, -1, -1, 0, 0, 1, -1, 1, &
1, 1, -2, 0, -1, 1, 0, 1, &
-1, 2, -1, 0, -1, 0, 1, 1, &
-2, 1, 1, 0, 0, -1, 1, 1, &
-1, -1, 2, 0, 1, -1, 0, 1, &
1, -2, 1, 0, 1, 0, -1, 1, &
! pyramidal system: c+a slip <2113>{1011} -- plane normals depend on the c/a-ratio
-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, &
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 &
/),(/4+4,lattice_hex_Nslip/))
real(pReal), dimension(4+4,lattice_hex_Ntwin), parameter :: lattice_hex_systemTwin = &
reshape((/&
0, 1, -1, 1, 0, -1, 1, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a)
-1, 1, 0, 1, 1, -1, 0, 2, &
-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, &
2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
1, 1, -2, -3, 1, 1, -2, 2, & !!
-1, 2, -1, -3, -1, 2, -1, 2, &
-2, 1, 1, -3, -2, 1, 1, 2, &
-1, -1, 2, -3, -1, -1, 2, 2, &
1, -2, 1, -3, 1, -2, 1, 2, &
-2, 1, 1, 6, 2, -1, -1, 1, & ! <-1-1.6>{11.1} shear = 1/(c/a)
-1, -1, 2, 6, 1, 1, -2, 1, & !!
1, -2, 1, 6, -1, 2, -1, 1, &
2, -1, -1, 6, -2, 1, 1, 1, &
1, 1, -2, 6, -1, -1, 2, 1, &
-1, 2, -1, 6, 1, -2, 1, 1, &
1, 0, -1, -2, 1, 0, -1, 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, &
0, -1, 1, -2, 0, -1, 1, 1, &
1, -1, 0, -2, 1, -1, 0, 1, &
-1, 1, 0, -2, -1, 1, 0, 1 &
/),(/4+4,lattice_hex_Ntwin/)) !* Sort? Numbering of twin system follows Prof. Tom Bieler's scheme (to be consistent with his work); but numbering in data was restarted from 1 &
integer(pInt), dimension(lattice_hex_Ntwin), parameter :: lattice_hex_shearTwin = & ! indicator to formula further below
reshape((/&
1, & ! {10.2}<-10.1>
1, &
1, &
1, &
1, &
1, &
2, & ! {11.2}<11.-3>
2, &
2, &
2, &
2, &
2, &
3, & ! {11.1}<-1-1.6>
3, &
3, &
3, &
3, &
3, &
4, & ! {10.1}<10.-2>
4, &
4, &
4, &
4, &
4 &
/),(/lattice_hex_Ntwin/))
!* four different interaction type matrix
!* 1. slip-slip interaction - 20 types
!* 2. slip-twin interaction - 16 types
!* 3. twin-twin interaction - 20 types
!* 4. twin-slip interaction - 16 types
integer(pInt), target, dimension(lattice_hex_Nslip,lattice_hex_Nslip) :: lattice_hex_interactionSlipSlip = &
reshape((/&
1, 5, 5, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, &
5, 1, 5, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, &
5, 5, 1, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, &
!
15,15,15, 2, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, &
15,15,15, 6, 2, 6, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, &
15,15,15, 6, 6, 2, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, &
!
18,18,18, 16,16,16, 3, 7, 7, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, &
18,18,18, 16,16,16, 7, 3, 7, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, &
18,18,18, 16,16,16, 7, 7, 3, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, &
18,18,18, 16,16,16, 7, 7, 7, 3, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, &
18,18,18, 16,16,16, 7, 7, 7, 7, 3, 7, 11,11,11,11,11,11,11,11,11,11,11,11, &
18,18,18, 16,16,16, 7, 7, 7, 7, 7, 3, 11,11,11,11,11,11,11,11,11,11,11,11, &
!
20,20,20, 19,19,19, 17,17,17,17,17,17, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, &
20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4 &
/),(/lattice_hex_Nslip,lattice_hex_Nslip/))
!* isotropic interaction at the moment
integer(pInt), target, dimension(lattice_hex_Ntwin,lattice_hex_Nslip) :: lattice_hex_interactionSlipTwin = &
reshape((/&
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, &
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, &
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 &
/),(/lattice_hex_Ntwin,lattice_hex_Nslip/))
!* isotropic interaction at the moment
integer(pInt), target, dimension(lattice_hex_Nslip,lattice_hex_Ntwin) :: lattice_hex_interactionTwinSlip = &
reshape((/&
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! --> slip
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! v
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! twin
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, &
!
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, &
!
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, &
!
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16 &
/),(/lattice_hex_Nslip,lattice_hex_Ntwin/))
integer(pInt), target, dimension(lattice_hex_Ntwin,lattice_hex_Ntwin) :: lattice_hex_interactionTwinTwin = &
reshape((/&
1, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
5, 1, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
5, 5, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
5, 5, 5, 1, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
5, 5, 5, 5, 1, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
5, 5, 5, 5, 5, 1, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, &
!
15,15,15,15,15,15, 2, 6, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
15,15,15,15,15,15, 6, 2, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
15,15,15,15,15,15, 6, 6, 2, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
15,15,15,15,15,15, 6, 6, 6, 2, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
15,15,15,15,15,15, 6, 6, 6, 6, 2, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, &
15,15,15,15,15,15, 6, 6, 6, 6, 6, 2, 10,10,10,10,10,10, 13,13,13,13,13,13, &
!
18,18,18,18,18,18, 16,16,16,16,16,16, 3, 7, 7, 7, 7, 7, 11,11,11,11,11,11, &
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 3, 7, 7, 7, 7, 11,11,11,11,11,11, &
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 3, 7, 7, 7, 11,11,11,11,11,11, &
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 3, 7, 7, 11,11,11,11,11,11, &
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 3, 7, 11,11,11,11,11,11, &
18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 7, 3, 11,11,11,11,11,11, &
!
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 4, 8, 8, 8, 8, 8, &
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 4, 8, 8, 8, 8, &
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 4, 8, 8, 8, &
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 4, 8, 8, &
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 4, 8, &
20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 4 &
/),(/lattice_hex_Ntwin,lattice_hex_Ntwin/))
CONTAINS
!****************************************
!* - lattice_init
!* - lattice_initializeStructure
!****************************************
pure function lattice_symmetryType(structID)
!**************************************
!* maps structure to symmetry type *
!* fcc(1) and bcc(2) are cubic(1) *
!* hex(3+) is hexagonal(2) *
!**************************************
implicit none
integer(pInt), intent(in) :: structID
integer(pInt) lattice_symmetryType
select case(structID)
case (1,2)
lattice_symmetryType = 1_pInt
case (3:)
lattice_symmetryType = 2_pInt
case default
lattice_symmetryType = 0_pInt
end select
return
end function
subroutine lattice_init()
!**************************************
!* Module initialization *
!**************************************
use IO, only: IO_open_file,IO_countSections,IO_countTagInPart,IO_error
use material, only: material_configfile,material_partPhase
use debug, only: debug_verbosity
implicit none
integer(pInt), parameter :: fileunit = 200
integer(pInt) i,Nsections
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '<<<+- lattice init -+>>>'
write(6,*) '$Id$'
write(6,*)
!$OMP END CRITICAL (write2out)
if(.not. IO_open_file(fileunit,material_configFile)) call IO_error(100) ! cannot open config file
Nsections = IO_countSections(fileunit,material_partPhase)
lattice_Nstructure = 2_pInt + sum(IO_countTagInPart(fileunit,material_partPhase,'covera_ratio',Nsections)) ! fcc + bcc + all hex
! lattice_Nstructure = Nsections + 2_pInt ! most conservative assumption
close(fileunit)
if (debug_verbosity > 0) then
!$OMP CRITICAL (write2out)
write(6,'(a16,x,i5)') '# phases:',Nsections
write(6,'(a16,x,i5)') '# structures:',lattice_Nstructure
write(6,*)
!$OMP END CRITICAL (write2out)
endif
allocate(lattice_Sslip(3,3,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip = 0.0_pReal
allocate(lattice_Sslip_v(6,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip_v = 0.0_pReal
allocate(lattice_sd(3,lattice_maxNslip,lattice_Nstructure)); lattice_sd = 0.0_pReal
allocate(lattice_st(3,lattice_maxNslip,lattice_Nstructure)); lattice_st = 0.0_pReal
allocate(lattice_sn(3,lattice_maxNslip,lattice_Nstructure)); lattice_sn = 0.0_pReal
allocate(lattice_Qtwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Qtwin = 0.0_pReal
allocate(lattice_Stwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin = 0.0_pReal
allocate(lattice_Stwin_v(6,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin_v = 0.0_pReal
allocate(lattice_td(3,lattice_maxNtwin,lattice_Nstructure)); lattice_td = 0.0_pReal
allocate(lattice_tt(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tt = 0.0_pReal
allocate(lattice_tn(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tn = 0.0_pReal
allocate(lattice_shearTwin(lattice_maxNtwin,lattice_Nstructure)); lattice_shearTwin = 0.0_pReal
allocate(lattice_NslipSystem(lattice_maxNslipFamily,lattice_Nstructure)); lattice_NslipSystem = 0.0_pReal
allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,lattice_Nstructure)); lattice_NtwinSystem = 0.0_pReal
allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,lattice_Nstructure)); lattice_interactionSlipSlip = 0_pInt ! other:me
allocate(lattice_interactionSlipTwin(lattice_maxNtwin,lattice_maxNslip,lattice_Nstructure)); lattice_interactionSlipTwin = 0_pInt ! other:me
allocate(lattice_interactionTwinSlip(lattice_maxNslip,lattice_maxNtwin,lattice_Nstructure)); lattice_interactionTwinSlip = 0_pInt ! other:me
allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,lattice_Nstructure)); lattice_interactionTwinTwin = 0_pInt ! other:me
end subroutine
function lattice_initializeStructure(struct,CoverA)
!**************************************
!* Calculation of Schmid *
!* matrices, etc. *
!**************************************
use prec, only: pReal,pInt
use math
use IO, only: IO_error
implicit none
character(len=*) struct
real(pReal) CoverA
real(pReal), dimension(3,lattice_maxNslip) :: sd = 0.0_pReal, &
sn = 0.0_pReal, &
st = 0.0_pReal
real(pReal), dimension(3,lattice_maxNtwin) :: td = 0.0_pReal, &
tn = 0.0_pReal, &
tt = 0.0_pReal
real(pReal), dimension(lattice_maxNtwin) :: ts = 0.0_pReal
real(pReal), dimension(3) :: hex_d = 0.0_pReal, &
hex_n = 0.0_pReal
integer(pInt), dimension(lattice_maxNslipFamily) :: myNslipSystem = 0_pInt
integer(pInt), dimension(lattice_maxNtwinFamily) :: myNtwinSystem = 0_pInt
integer(pInt) :: i,myNslip,myNtwin,myStructure = 0_pInt
logical :: processMe
integer(pInt) lattice_initializeStructure
processMe = .false.
select case(struct(1:3)) ! check first three chars of structure name
case ('fcc')
myStructure = 1_pInt
myNslipSystem = lattice_fcc_NslipSystem ! size of slip system families
myNtwinSystem = lattice_fcc_NtwinSystem ! size of twin system families
myNslip = lattice_fcc_Nslip ! overall number of slip systems
myNtwin = lattice_fcc_Ntwin ! overall number of twin systems
lattice_fcc_Nstructure = lattice_fcc_Nstructure + 1_pInt ! count fcc instances
if (lattice_fcc_Nstructure == 1_pInt) then ! me is first fcc structure
processMe = .true.
do i = 1,myNslip ! calculate slip system vectors
sd(:,i) = lattice_fcc_systemSlip(1:3,i)/sqrt(math_mul3x3(lattice_fcc_systemSlip(1:3,i),lattice_fcc_systemSlip(1:3,i)))
sn(:,i) = lattice_fcc_systemSlip(4:6,i)/sqrt(math_mul3x3(lattice_fcc_systemSlip(4:6,i),lattice_fcc_systemSlip(4:6,i)))
st(:,i) = math_vectorproduct(sd(:,i),sn(:,i))
enddo
do i = 1,myNtwin ! calculate twin system vectors and (assign) shears
td(:,i) = lattice_fcc_systemTwin(1:3,i)/sqrt(math_mul3x3(lattice_fcc_systemTwin(1:3,i),lattice_fcc_systemTwin(1:3,i)))
tn(:,i) = lattice_fcc_systemTwin(4:6,i)/sqrt(math_mul3x3(lattice_fcc_systemTwin(4:6,i),lattice_fcc_systemTwin(4:6,i)))
tt(:,i) = math_vectorproduct(td(:,i),tn(:,i))
ts(i) = lattice_fcc_shearTwin(i)
enddo
interactionSlipSlip => lattice_fcc_interactionSlipSlip
interactionSlipTwin => lattice_fcc_interactionSlipTwin
interactionTwinSlip => lattice_fcc_interactionTwinSlip
interactionTwinTwin => lattice_fcc_interactionTwinTwin
endif
case ('bcc')
myStructure = 2_pInt
myNslipSystem = lattice_bcc_NslipSystem ! size of slip system families
myNtwinSystem = lattice_bcc_NtwinSystem ! size of twin system families
myNslip = lattice_bcc_Nslip ! overall number of slip systems
myNtwin = lattice_bcc_Ntwin ! overall number of twin systems
lattice_bcc_Nstructure = lattice_bcc_Nstructure + 1_pInt ! count bcc instances
if (lattice_bcc_Nstructure == 1_pInt) then ! me is first bcc structure
processMe = .true.
do i = 1,myNslip ! calculate slip system vectors
sd(:,i) = lattice_bcc_systemSlip(1:3,i)/sqrt(math_mul3x3(lattice_bcc_systemSlip(1:3,i),lattice_bcc_systemSlip(1:3,i)))
sn(:,i) = lattice_bcc_systemSlip(4:6,i)/sqrt(math_mul3x3(lattice_bcc_systemSlip(4:6,i),lattice_bcc_systemSlip(4:6,i)))
st(:,i) = math_vectorproduct(sd(:,i),sn(:,i))
enddo
do i = 1,myNtwin ! calculate twin system vectors and (assign) shears
td(:,i) = lattice_bcc_systemTwin(1:3,i)/sqrt(math_mul3x3(lattice_bcc_systemTwin(1:3,i),lattice_bcc_systemTwin(1:3,i)))
tn(:,i) = lattice_bcc_systemTwin(4:6,i)/sqrt(math_mul3x3(lattice_bcc_systemTwin(4:6,i),lattice_bcc_systemTwin(4:6,i)))
tt(:,i) = math_vectorproduct(td(:,i),tn(:,i))
ts(i) = lattice_bcc_shearTwin(i)
enddo
interactionSlipSlip => lattice_bcc_interactionSlipSlip
interactionSlipTwin => lattice_bcc_interactionSlipTwin
interactionTwinSlip => lattice_bcc_interactionTwinSlip
interactionTwinTwin => lattice_bcc_interactionTwinTwin
endif
case ('hex')
if (CoverA >= 1.0_pReal) then ! checking physical significance of c/a
lattice_hex_Nstructure = lattice_hex_Nstructure + 1_pInt ! count instances of hex structures
myStructure = 2_pInt + lattice_hex_Nstructure ! 3,4,5,.. for hex
myNslipSystem = lattice_hex_NslipSystem ! size of slip system families
myNtwinSystem = lattice_hex_NtwinSystem ! size of twin system families
myNslip = lattice_hex_Nslip ! overall number of slip systems
myNtwin = lattice_hex_Ntwin ! overall number of twin systems
processMe = .true.
! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexgonal system (a, b, c)
do i = 1,myNslip
hex_d(1) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]
hex_d(2) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*(0.5_pReal*sqrt(3.0_pReal))
hex_d(3) = lattice_hex_systemSlip(4,i)*CoverA
hex_n(1) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a))
hex_n(2) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal)
hex_n(3) = lattice_hex_systemSlip(8,i)/CoverA
sd(:,i) = hex_d/sqrt(math_mul3x3(hex_d,hex_d))
sn(:,i) = hex_n/sqrt(math_mul3x3(hex_n,hex_n))
st(:,i) = math_vectorproduct(sd(:,i),sn(:,i))
enddo
do i = 1,myNtwin
hex_d(1) = lattice_hex_systemTwin(1,i)*1.5_pReal
hex_d(2) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*(0.5_pReal*sqrt(3.0_pReal))
hex_d(3) = lattice_hex_systemTwin(4,i)*CoverA
hex_n(1) = lattice_hex_systemTwin(5,i)
hex_n(2) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal)
hex_n(3) = lattice_hex_systemTwin(8,i)/CoverA
td(:,i) = hex_d/sqrt(math_mul3x3(hex_d,hex_d))
tn(:,i) = hex_n/sqrt(math_mul3x3(hex_n,hex_n))
tt(:,i) = math_vectorproduct(td(:,i),tn(:,i))
select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29
case (1) ! {10.2}<-10.1>
ts(i) = (3.0_pReal-CoverA*CoverA)/sqrt(3.0_pReal)/CoverA
case (2) ! {11.2}<11.-3>
ts(i) = 2.0_pReal*(CoverA*CoverA-2.0_pReal)/3.0_pReal/CoverA
case (3) ! {11.1}<-1-1.6>
ts(i) = 1.0_pReal/CoverA
case (4) ! {10.1}<10.-2>
ts(i) = (4.0_pReal*CoverA*CoverA-9.0_pReal)/4.0_pReal/sqrt(3.0_pReal)/CoverA
end select
enddo
interactionSlipSlip => lattice_hex_interactionSlipSlip
interactionSlipTwin => lattice_hex_interactionSlipTwin
interactionTwinSlip => lattice_hex_interactionTwinSlip
interactionTwinTwin => lattice_hex_interactionTwinTwin
endif
end select
if (processMe) then
if (myStructure > lattice_Nstructure) &
call IO_error(666,0,0,0,'structure index too large') ! check for memory leakage
do i = 1,myNslip ! store slip system vectors and Schmid matrix for my structure
lattice_sd(:,i,myStructure) = sd(:,i)
lattice_st(:,i,myStructure) = st(:,i)
lattice_sn(:,i,myStructure) = sn(:,i)
lattice_Sslip(:,:,i,myStructure) = math_tensorproduct(sd(:,i),sn(:,i))
lattice_Sslip_v(:,i,myStructure) = math_Mandel33to6(math_symmetric3x3(lattice_Sslip(:,:,i,myStructure)))
enddo
do i = 1,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure
lattice_td(:,i,myStructure) = td(:,i)
lattice_tt(:,i,myStructure) = tt(:,i)
lattice_tn(:,i,myStructure) = tn(:,i)
lattice_Stwin(:,:,i,myStructure) = math_tensorproduct(td(:,i),tn(:,i))
lattice_Stwin_v(:,i,myStructure) = math_Mandel33to6(math_symmetric3x3(lattice_Stwin(:,:,i,myStructure)))
lattice_Qtwin(:,:,i,myStructure) = math_AxisAngleToR(tn(:,i),180.0_pReal*inRad)
lattice_shearTwin(i,myStructure) = ts(i)
enddo
lattice_NslipSystem(1:lattice_maxNslipFamily,myStructure) = myNslipSystem ! number of slip systems in each family
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myStructure) = myNtwinSystem ! number of twin systems in each family
lattice_interactionSlipSlip(1:myNslip,1:myNslip,myStructure) = interactionSlipSlip(1:myNslip,1:myNslip)
lattice_interactionSlipTwin(1:myNtwin,1:myNslip,myStructure) = interactionSlipTwin(1:myNtwin,1:myNslip)
lattice_interactionTwinSlip(1:myNslip,1:myNtwin,myStructure) = interactionTwinSlip(1:myNslip,1:myNtwin)
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myStructure) = interactionTwinTwin(1:myNtwin,1:myNtwin)
endif
lattice_initializeStructure = myStructure ! report my structure index back
end function
END MODULE
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