! Copyright 2011-13 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 .
!
!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @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
!> @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_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
integer(pInt), allocatable, dimension(:,:), protected, public :: &
lattice_NslipSystem, & !< total # of slip systems in each family
lattice_NtwinSystem !< total # of twin 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_shearTwin !< characteristic twin shear
integer(pInt), private :: &
lattice_Nhexagonal, & !< total # of hexagonal lattice structure (from tag CoverA_ratio)
lattice_Nstructure !< total # of lattice structures (1: fcc,2: bcc,3+: hexagonal)
integer(pInt), dimension(:,:), pointer, private :: &
interactionSlipSlip, &
interactionSlipTwin, &
interactionTwinSlip, &
interactionTwinTwin
integer(pInt), allocatable, dimension(:), protected, public :: &
lattice_NnonSchmid !< total # of non-Schmid contributions for each structure
!--------------------------------------------------------------------------------------------------
! fcc (1)
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), 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
integer(pInt), private :: &
lattice_fcc_Nstructure = 0_pInt
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_corellationTwinSlip = 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), target, 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), target, 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), target, public :: &
lattice_fcc_interactionTwinSlip = 0_pInt !< Twin--Slip interaction types for fcc
integer(pInt), dimension(lattice_fcc_Ntwin,lattice_fcc_Ntwin), target, 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 (2)
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), 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)
integer(pInt), private :: &
lattice_bcc_Nstructure = 0_pInt
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), target, 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), target, 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), target, public :: &
lattice_bcc_interactionTwinSlip = 0_pInt !< Twin--slip interaction types for bcc @todo not implemented yet
integer(pInt), dimension(lattice_bcc_Ntwin,lattice_bcc_Ntwin), target, 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 (3+)
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), 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
integer(pInt), private :: &
lattice_hex_Nstructure = 0_pInt
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), target, 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), target, 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), target, 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), target, 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)
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(pInt), dimension(:), allocatable, public, protected :: &
lattice_structure
integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: &
lattice_structureID
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_Cslip_66
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 ],
! ]
character(len=*), parameter, public :: &
LATTICE_iso_label = 'iso', &
LATTICE_fcc_label = 'fcc', &
LATTICE_bcc_label = 'bcc', &
LATTICE_hex_label = 'hex', &
LATTICE_ort_label = 'ort'
public :: &
lattice_init, &
lattice_initializeStructure, &
lattice_symmetryType, &
lattice_symmetrizeC66, &
lattice_configNchunks, &
lattice_qDisorientation, &
LATTICE_undefined_ID, &
LATTICE_iso_ID, &
LATTICE_fcc_ID, &
LATTICE_bcc_ID, &
LATTICE_hex_ID, &
LATTICE_ort_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
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333
implicit none
integer(pInt), parameter :: FILEUNIT = 200_pInt
integer(pInt) :: Nsections
character(len=32) :: &
structure = ''
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
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_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,&
lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid')
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
Nsections = IO_countSections(FILEUNIT,material_partPhase)
lattice_Nstructure = 2_pInt + sum(IO_countTagInPart(FILEUNIT,material_partPhase,'covera_ratio',Nsections)) ! fcc + bcc + all hex
allocate(lattice_structure(Nsections), source=0_pInt)
allocate(lattice_structureID(Nsections), source=LATTICE_undefined_ID)
allocate(lattice_Cslip_66(6,6,Nsections),source=0.0_pReal)
allocate(CoverA(Nsections), 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
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')
structure = IO_lc(IO_stringValue(line,positions,2_pInt))
select case(structure(1:3))
case(LATTICE_iso_label)
lattice_structureID(section) = LATTICE_iso_ID
case(LATTICE_fcc_label)
lattice_structureID(section) = LATTICE_fcc_ID
case(LATTICE_bcc_label)
lattice_structureID(section) = LATTICE_bcc_ID
case(LATTICE_hex_label)
lattice_structureID(section) = LATTICE_hex_ID
case(LATTICE_ort_label)
lattice_structureID(section) = LATTICE_ort_ID
case default
!there should be an error here
end select
case ('c11')
lattice_Cslip_66(1,1,section) = IO_floatValue(line,positions,2_pInt)
case ('c12')
lattice_Cslip_66(1,2,section) = IO_floatValue(line,positions,2_pInt)
case ('c13')
lattice_Cslip_66(1,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c22')
lattice_Cslip_66(2,2,section) = IO_floatValue(line,positions,2_pInt)
case ('c23')
lattice_Cslip_66(2,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c33')
lattice_Cslip_66(3,3,section) = IO_floatValue(line,positions,2_pInt)
case ('c44')
lattice_Cslip_66(4,4,section) = IO_floatValue(line,positions,2_pInt)
case ('c55')
lattice_Cslip_66(5,5,section) = IO_floatValue(line,positions,2_pInt)
case ('c66')
lattice_Cslip_66(6,6,section) = IO_floatValue(line,positions,2_pInt)
case ('covera_ratio')
CoverA(section) = IO_floatValue(line,positions,2_pInt)
end select
endif
enddo
if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then
write(6,'(a16,1x,i5)') ' # phases:',Nsections
write(6,'(a16,1x,i5,/)') ' # structures:',lattice_Nstructure
endif
allocate(lattice_NnonSchmid(lattice_Nstructure), source=0_pInt)
allocate(lattice_Sslip(3,3,1+2*lattice_maxNnonSchmid,lattice_maxNslip,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_Sslip_v(6,1+2*lattice_maxNnonSchmid,lattice_maxNslip,lattice_Nstructure),source = 0.0_pReal)
allocate(lattice_sd(3,lattice_maxNslip,lattice_Nstructure),source=0.0_pReal)
allocate(lattice_st(3,lattice_maxNslip,lattice_Nstructure),source=0.0_pReal)
allocate(lattice_sn(3,lattice_maxNslip,lattice_Nstructure),source=0.0_pReal)
allocate(lattice_Qtwin(3,3,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_Stwin(3,3,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_Stwin_v(6,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_td(3,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_tt(3,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_tn(3,lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_shearTwin(lattice_maxNtwin,lattice_Nstructure),source= 0.0_pReal)
allocate(lattice_NslipSystem(lattice_maxNslipFamily,lattice_Nstructure), source=0_pInt)
allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,lattice_Nstructure), source=0_pInt)
allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,lattice_Nstructure), source=0_pInt)! other:me
allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,lattice_Nstructure), source=0_pInt)! other:me
allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,lattice_Nstructure), source=0_pInt)! other:me
allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,lattice_Nstructure), source=0_pInt)! other:me
do i = 1_pInt,Nsections
lattice_structure(i) = lattice_initializeStructure(lattice_structureID(i), CoverA(i)) ! get structure
lattice_Cslip_66(1:6,1:6,i) = lattice_symmetrizeC66(lattice_structureID(i),lattice_Cslip_66(1:6,1:6,i))
lattice_Cslip_66(1:6,1:6,i) = math_Mandel3333to66(math_Voigt66to3333(lattice_Cslip_66(1:6,1:6,i))) ! Literature data is Voigt, DAMASK uses Mandel
enddo
deallocate(CoverA)
end subroutine lattice_init
!--------------------------------------------------------------------------------------------------
!> @brief Calculation of Schmid matrices, etc.
!--------------------------------------------------------------------------------------------------
integer(pInt) function lattice_initializeStructure(struct_ID,CoverA)
use math, only: &
math_vectorproduct, &
math_tensorproduct, &
math_norm3, &
math_mul33x3, &
math_trace33, &
math_symmetric33, &
math_Mandel33to6, &
math_axisAngleToR, &
INRAD
use IO, only: &
IO_error
implicit none
integer(kind(LATTICE_fcc_ID)), intent(in) :: struct_ID
real(pReal), intent(in) :: CoverA
real(pReal), dimension(3) :: sdU = 0.0_pReal, &
snU = 0.0_pReal, &
np = 0.0_pReal, &
nn = 0.0_pReal
real(pReal), dimension(3,lattice_maxNslip) :: sd = 0.0_pReal, &
sn = 0.0_pReal
real(pReal), dimension(3,3,2,lattice_maxNnonSchmid,lattice_maxNslip) :: sns = 0.0_pReal
real(pReal), dimension(3,lattice_maxNtwin) :: td = 0.0_pReal, &
tn = 0.0_pReal
real(pReal), dimension(lattice_maxNtwin) :: ts = 0.0_pReal
integer(pInt), dimension(lattice_maxNslipFamily) :: myNslipSystem = 0_pInt
integer(pInt), dimension(lattice_maxNtwinFamily) :: myNtwinSystem = 0_pInt
integer(pInt) :: i,j,myNslip,myNtwin,myStructure = 0_pInt
logical :: processMe
processMe = .false.
select case(struct_ID)
case (LATTICE_fcc_ID)
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.
lattice_NnonSchmid(myStructure) = lattice_fcc_NnonSchmid ! Currently no known non Schmid contributions for FCC (to be changed later)
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)
do j = 1_pInt,lattice_fcc_NnonSchmid
sns(1:3,1:3,1,j,i) = 0.0_pReal
sns(1:3,1:3,2,j,i) = 0.0_pReal
enddo
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
interactionSlipSlip => lattice_fcc_interactionSlipSlip
interactionSlipTwin => lattice_fcc_interactionSlipTwin
interactionTwinSlip => lattice_fcc_interactionTwinSlip
interactionTwinTwin => lattice_fcc_interactionTwinTwin
endif
case (LATTICE_bcc_ID)
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.
lattice_NnonSchmid(myStructure) = lattice_bcc_NnonSchmid
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 = math_mul33x3(math_axisAngleToR(sdU,60.0_pReal*INRAD), snU)
nn = math_mul33x3(math_axisAngleToR(-sdU,60.0_pReal*INRAD), snU)
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
interactionSlipSlip => lattice_bcc_interactionSlipSlip
interactionSlipTwin => lattice_bcc_interactionSlipTwin
interactionTwinSlip => lattice_bcc_interactionTwinSlip
interactionTwinTwin => lattice_bcc_interactionTwinTwin
endif
case (LATTICE_hex_ID)
if (CoverA < 1.0_pReal .or. CoverA > 2.0_pReal) call IO_error(206_pInt) ! 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.
lattice_NnonSchmid(myStructure) = lattice_hex_NnonSchmid ! Currently no known non Schmid contributions for hex (to be changed later)
! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexagonal system (a, b, c)
do i = 1_pInt,myNslip
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
do j = 1_pInt,lattice_hex_NnonSchmid
sns(1:3,1:3,1,j,i) = 0.0_pReal
sns(1:3,1:3,2,j,i) = 0.0_pReal
enddo
enddo
do i = 1_pInt,myNtwin
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
interactionSlipSlip => lattice_hex_interactionSlipSlip
interactionSlipTwin => lattice_hex_interactionSlipTwin
interactionTwinSlip => lattice_hex_interactionTwinSlip
interactionTwinTwin => lattice_hex_interactionTwinTwin
case default
processMe = .false.
myStructure = 0_pInt
end select
if (processMe) then
if (myStructure > lattice_Nstructure) &
call IO_error(666_pInt,myStructure,ext_msg = 'structure index out of bounds') ! check for memory leakage
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
lattice_sd(1:3,i,myStructure) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector
lattice_sn(1:3,i,myStructure) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
lattice_st(1:3,i,myStructure) = math_vectorproduct(lattice_sd(1:3,i,myStructure), &
lattice_sn(1:3,i,myStructure))
lattice_Sslip(1:3,1:3,1,i,myStructure) = math_tensorproduct(lattice_sd(1:3,i,myStructure), &
lattice_sn(1:3,i,myStructure))
do j = 1_pInt,lattice_NnonSchmid(myStructure)
lattice_Sslip(1:3,1:3,2*j ,i,myStructure) = sns(1:3,1:3,1,j,i)
lattice_Sslip(1:3,1:3,2*j+1,i,myStructure) = sns(1:3,1:3,2,j,i)
enddo
do j = 1_pInt,1_pInt+2_pInt*lattice_NnonSchmid(myStructure)
lattice_Sslip_v(1:6,j,i,myStructure) = &
math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,j,i,myStructure)))
enddo
if (abs(math_trace33(lattice_Sslip(1:3,1:3,1,i,myStructure))) > 1.0e-8_pReal) &
call IO_error(0_pInt,myStructure,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,myStructure) = td(1:3,i)/math_norm3(td(1:3,i)) ! make unit vector
lattice_tn(1:3,i,myStructure) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector
lattice_tt(1:3,i,myStructure) = math_vectorproduct(lattice_td(1:3,i,myStructure), &
lattice_tn(1:3,i,myStructure))
lattice_Stwin(1:3,1:3,i,myStructure) = math_tensorproduct(lattice_td(1:3,i,myStructure), &
lattice_tn(1:3,i,myStructure))
lattice_Stwin_v(1:6,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myStructure)))
lattice_Qtwin(1:3,1:3,i,myStructure) = math_axisAngleToR(tn(1:3,i),180.0_pReal*INRAD)
lattice_shearTwin(i,myStructure) = ts(i)
if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myStructure))) > 1.0e-8_pReal) &
call IO_error(0_pInt,myStructure,i,0_pInt,ext_msg = 'dilatational twin Schmid matrix')
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:myNslip,1:myNtwin,myStructure) = interactionSlipTwin(1:myNslip,1:myNtwin)
lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myStructure) = interactionTwinSlip(1:myNtwin,1:myNslip)
lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myStructure) = interactionTwinTwin(1:myNtwin,1:myNtwin)
endif
lattice_initializeStructure = myStructure ! report my structure index back
end function lattice_initializeStructure
!--------------------------------------------------------------------------------------------------
!> @brief Maps structure to symmetry type
!> @details fcc(1) and bcc(2) are cubic(1) hex(3+) is hexagonal(2)
!--------------------------------------------------------------------------------------------------
integer(pInt) pure function lattice_symmetryType(struct_ID)
implicit none
integer(kind(LATTICE_fcc_ID)), intent(in) :: struct_ID
select case(struct_ID)
case (LATTICE_fcc_ID,LATTICE_bcc_ID)
lattice_symmetryType = 1_pInt
case (LATTICE_hex_ID)
lattice_symmetryType = 2_pInt
case default
lattice_symmetryType = 0_pInt
end select
return
end function lattice_symmetryType
!--------------------------------------------------------------------------------------------------
!> @brief Symmetrizes stiffness matrix according to lattice type
!--------------------------------------------------------------------------------------------------
pure function lattice_symmetrizeC66(struct_ID,C66)
implicit none
integer(kind(LATTICE_fcc_ID)), intent(in) :: struct_ID
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_ID)
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)
end select
end function lattice_symmetrizeC66
!--------------------------------------------------------------------------------------------------
!> @brief figures whether unit quat falls into stereographic standard triangle
!--------------------------------------------------------------------------------------------------
logical pure function lattice_qInSST(Q, symmetryType)
use math, only: &
math_qToRodrig
implicit none
real(pReal), dimension(4), intent(in) :: Q ! orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q
Rodrig = math_qToRodrig(Q)
if (any(Rodrig/=Rodrig)) then
lattice_qInSST = .false.
else
select case (symmetryType)
case (1_pInt)
lattice_qInSST = Rodrig(1) > Rodrig(2) .and. &
Rodrig(2) > Rodrig(3) .and. &
Rodrig(3) > 0.0_pReal
case (2_pInt)
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
!--------------------------------------------------------------------------------------------------
function lattice_qDisorientation(Q1, Q2, symmetryType)
use prec, only: &
tol_math_check
use math, only: &
math_qMul, &
math_qConj
real(pReal), dimension(4) :: lattice_qDisorientation
real(pReal), dimension(4), intent(in) :: Q1, & ! 1st orientation
Q2 ! 2nd orientation
integer(pInt), intent(in) :: symmetryType ! Type of crystal symmetry; 1:cubic, 2:hexagonal
! 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
dQ = math_qMul(math_qConj(Q1),Q2)
lattice_qDisorientation = dQ
select case (symmetryType)
case (0_pInt)
if (lattice_qDisorientation(1) < 0.0_pReal) &
lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg
case (1_pInt,2_pInt)
s = sum(lattice_NsymOperations(1:symmetryType-1_pInt))
do i = 1_pInt,2_pInt
dQ = math_qConj(dQ) ! switch order of "from -- to"
do j = 1_pInt,lattice_NsymOperations(symmetryType) ! run through first crystal's symmetries
dQsymA = math_qMul(lattice_symOperations(1:4,s+j),dQ) ! apply sym
do k = 1_pInt,lattice_NsymOperations(symmetryType) ! 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,symmetryType)) &
lattice_qDisorientation = mis ! found better one
enddo; enddo; enddo
end select
end function lattice_qDisorientation
!--------------------------------------------------------------------------------------------------
!> @brief Number of parameters to expect in material.config section
! NslipFamilies
! NtwinFamilies
! SlipSlipInteraction
! SlipTwinInteraction
! TwinSlipInteraction
! TwinTwinInteraction
! NnonSchmid
!--------------------------------------------------------------------------------------------------
function lattice_configNchunks(struct_ID)
use prec, only: &
pInt
implicit none
integer(pInt), dimension(7) :: lattice_configNchunks
integer(kind(LATTICE_fcc_ID)) :: struct_ID
select case(struct_ID)
case (LATTICE_fcc_ID)
lattice_configNchunks(1) = count(lattice_fcc_NslipSystem > 0_pInt)
lattice_configNchunks(2) = count(lattice_fcc_NtwinSystem > 0_pInt)
lattice_configNchunks(3) = maxval(lattice_fcc_interactionSlipSlip)
lattice_configNchunks(4) = maxval(lattice_fcc_interactionSlipTwin)
lattice_configNchunks(5) = maxval(lattice_fcc_interactionTwinSlip)
lattice_configNchunks(6) = maxval(lattice_fcc_interactionTwinTwin)
lattice_configNchunks(7) = lattice_fcc_NnonSchmid
case (LATTICE_bcc_ID)
lattice_configNchunks(1) = count(lattice_bcc_NslipSystem > 0_pInt)
lattice_configNchunks(2) = count(lattice_bcc_NtwinSystem > 0_pInt)
lattice_configNchunks(3) = maxval(lattice_bcc_interactionSlipSlip)
lattice_configNchunks(4) = maxval(lattice_bcc_interactionSlipTwin)
lattice_configNchunks(5) = maxval(lattice_bcc_interactionTwinSlip)
lattice_configNchunks(6) = maxval(lattice_bcc_interactionTwinTwin)
lattice_configNchunks(7) = lattice_bcc_NnonSchmid
case (LATTICE_hex_ID)
lattice_configNchunks(1) = count(lattice_hex_NslipSystem > 0_pInt)
lattice_configNchunks(2) = count(lattice_hex_NtwinSystem > 0_pInt)
lattice_configNchunks(3) = maxval(lattice_hex_interactionSlipSlip)
lattice_configNchunks(4) = maxval(lattice_hex_interactionSlipTwin)
lattice_configNchunks(5) = maxval(lattice_hex_interactionTwinSlip)
lattice_configNchunks(6) = maxval(lattice_hex_interactionTwinTwin)
lattice_configNchunks(7) = lattice_hex_NnonSchmid
end select
end function lattice_configNchunks
end module lattice