! 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_maxNonSchmid = 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_v, & lattice_Sslip !< Schmid matrices, normal, shear direction and d x n of slip systems real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_sn, & lattice_sd, & lattice_st ! 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 :: & 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 integer(pInt), private :: & lattice_fcc_Nstructure = 0_pInt real(pReal), dimension(3+3,lattice_fcc_Nslip), parameter, private :: & lattice_fcc_systemSlip = reshape(real([& 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 = reshape([& 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal & ],[lattice_fcc_Ntwin]) !< 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 integer(pInt), parameter, private :: NnonSchmid_fcc = 0_pInt !< total # of non-Schmid contributions for fcc real(pReal), dimension(3,3,2,NnonSchmid_fcc,lattice_fcc_Nslip), parameter, private :: & lattice_nonSchmid_fcc = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_fcc,lattice_fcc_Nslip]) !< Tensor for each non-Schmid contribution 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 integer(pInt), private :: & lattice_bcc_Nstructure = 0_pInt real(pReal), dimension(3+3,lattice_bcc_Nslip), parameter, private :: & lattice_bcc_systemSlip = reshape(real([& ! 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 = reshape([& 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal, & 0.7071067812_pReal & ],[lattice_bcc_Ntwin]) integer(pInt), dimension(lattice_bcc_Nslip,lattice_bcc_Nslip), target, public :: & lattice_bcc_interactionSlipSlip = reshape(int( [& 1,3,6,6,5,4,4,2,4,2,5,4, 6,6,4,2,2,4,6,6,4,2,6,6, & ! ---> slip 3,1,6,6,4,2,5,4,5,4,4,2, 6,6,2,4,4,2,6,6,2,4,6,6, & ! | 6,6,1,3,4,5,2,4,4,5,2,4, 4,2,6,6,6,6,2,4,6,6,4,2, & ! | 6,6,3,1,2,4,4,5,2,4,4,5, 2,4,6,6,6,6,4,2,6,6,2,4, & ! v slip 5,4,4,2,1,3,6,6,2,4,5,4, 2,6,4,6,6,4,6,2,4,6,2,6, & 4,2,5,4,3,1,6,6,4,5,4,2, 4,6,2,6,6,2,6,4,2,6,4,6, & 4,5,2,4,6,6,1,3,5,4,2,4, 6,2,6,4,4,6,2,6,6,4,6,2, & 2,4,4,5,6,6,3,1,4,2,4,5, 6,4,6,2,2,6,4,6,6,2,6,4, & 4,5,4,2,2,4,5,4,1,3,6,6, 2,6,6,4,4,6,6,2,6,4,2,6, & 2,4,5,4,4,5,4,2,3,1,6,6, 4,6,6,2,2,6,6,4,6,2,4,6, & 5,4,2,4,5,4,2,4,6,6,1,3, 6,2,4,6,6,4,2,6,4,6,6,2, & 4,2,4,5,4,2,4,5,6,6,3,1, 6,4,2,6,6,2,4,6,2,6,6,4, & ! 6,6,4,2,2,4,6,6,2,4,6,6, 1,5,6,6,5,6,6,2,5,6,2,6, & 6,6,2,4,6,6,2,4,6,6,2,4, 5,1,6,6,6,5,2,6,6,5,6,2, & 4,2,6,6,4,2,6,6,6,6,4,2, 6,6,1,5,6,2,5,6,2,6,5,6, & 2,4,6,6,6,6,4,2,4,2,6,6, 6,6,5,1,2,6,6,5,6,2,6,5, & 2,4,6,6,6,6,4,2,4,2,6,6, 5,6,6,2,1,6,5,6,5,2,6,6, & 4,2,6,6,4,2,6,6,6,6,4,2, 6,5,2,6,6,1,6,5,2,5,6,6, & 6,6,2,4,6,6,2,4,6,6,2,4, 6,2,5,6,5,6,1,6,6,6,5,2, & 6,6,4,2,2,4,6,6,2,4,6,6, 2,6,6,5,6,5,6,1,6,6,2,5, & 4,2,6,6,4,2,6,6,6,6,4,2, 5,6,2,6,5,2,6,6,1,6,6,5, & 2,4,6,6,6,6,4,2,4,2,6,6, 6,5,6,2,2,5,6,6,6,1,5,6, & 6,6,4,2,2,4,6,6,2,4,6,6, 2,6,5,6,6,6,5,2,6,5,1,6, & 6,6,2,4,6,6,2,4,6,6,2,4, 6,2,6,5,6,6,2,5,5,6,6,1 & ],pInt),[lattice_bcc_Nslip,lattice_bcc_Nslip],order=[2,1]) !< Slip--slip interaction types for bcc from Lee et al. Int J Plast 15 (1999) 625-645 !< 1: self interaction !< 2: no interaction !< 3: coplanar interaction !< 4: glissile interaction !< 5: weak sessile interaction !< 6: strong sessile interaction 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 integer(pInt), parameter, private :: NnonSchmid_bcc = 0_pInt !< # of non-Schmid contributions for bcc real(pReal), dimension(3,3,2,NnonSchmid_bcc,lattice_bcc_Nslip), parameter, private :: & lattice_nonSchmid_bcc = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_bcc,lattice_bcc_Nslip]) !< Tensor for each non-Schmid contribution for bcc !-------------------------------------------------------------------------------------------------- ! hex (3+) integer(pInt), dimension(lattice_maxNslipFamily), parameter, public :: & lattice_hex_NslipSystem = int([ 3, 3, 6, 12, 6, 3],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 integer(pInt), private :: & lattice_hex_Nstructure = 0_pInt real(pReal), dimension(4+4,lattice_hex_Nslip), parameter, private :: & lattice_hex_systemSlip = reshape(real([& ! 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([& 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, 33,33,33,33,33,33,33,33,33,33,33,33, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 33,33,33,33,33,33,33,33,33,33,33,33, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 33,33,33,33,33,33,33,33,33,33,33,33, 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, 10,10,10,10,10,10, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 10,10,10,10,10,10, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 10,10,10,10,10,10, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 10,10,10,10,10,10, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 10,10,10,10,10,10, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 10,10,10,10,10,10, 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, 4 & ],pInt),[lattice_hex_Ntwin,lattice_hex_Ntwin],order=[2,1]) !< Twin--slip interaction types for hex (isotropic, 16 in total) integer(pInt), parameter, private :: NnonSchmid_hex = 0_pInt !< # of non-Schmid contributions for hex real(pReal), dimension(3,3,2,NnonSchmid_hex,lattice_hex_Nslip), parameter, private :: & lattice_nonSchmid_hex = 0.0_pReal ! reshape([],[3,3,2,NnonSchmid_hex,lattice_hex_Nslip]) !< Tensor for each non-Schmid contribution for hex public :: & lattice_init, & lattice_initializeStructure, & lattice_symmetryType, & lattice_symmetrizeC66, & lattice_configNchunks contains !-------------------------------------------------------------------------------------------------- !> @brief Module initialization !-------------------------------------------------------------------------------------------------- subroutine lattice_init use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use IO, only: & IO_open_file,& IO_open_jobFile_stat, & IO_countSections, & IO_countTagInPart, & IO_error, & IO_timeStamp use material, only: & material_configfile, & material_localFileExt, & material_partPhase use debug, only: & debug_level, & debug_lattice, & debug_levelBasic implicit none integer(pInt), parameter :: fileunit = 200_pInt integer(pInt) :: Nsections write(6,'(/,a)') ' <<<+- lattice init -+>>>' write(6,'(a)') ' $Id$' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" if (.not. IO_open_jobFile_stat(fileunit,material_localFileExt)) then ! no local material configuration present... call IO_open_file(fileunit,material_configFile) ! ... open material.config file endif Nsections = IO_countSections(fileunit,material_partPhase) lattice_Nstructure = 2_pInt + sum(IO_countTagInPart(fileunit,material_partPhase,'covera_ratio',Nsections)) ! fcc + bcc + all hex close(fileunit) 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(NnonSchmid(lattice_Nstructure)); NnonSchmid = 0_pInt allocate(lattice_Sslip(3,3,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip = 0.0_pReal allocate(lattice_Sslip_v(6,1+2*lattice_maxNonSchmid,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_pInt allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,lattice_Nstructure)); lattice_NtwinSystem = 0_pInt allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,lattice_Nstructure)) lattice_interactionSlipSlip = 0_pInt ! other:me allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,lattice_Nstructure)) lattice_interactionSlipTwin = 0_pInt ! other:me allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,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 lattice_init !-------------------------------------------------------------------------------------------------- !> @brief Calculation of Schmid matrices, etc. !-------------------------------------------------------------------------------------------------- integer(pInt) function lattice_initializeStructure(struct,CoverA) use math, only: & math_vectorproduct, & math_tensorproduct, & math_norm3, & math_trace33, & math_symmetric33, & math_Mandel33to6, & math_axisAngleToR, & INRAD 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 real(pReal), dimension(12,lattice_maxNonSchmid,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(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. NnonSchmid(myStructure) = NnonSchmid_fcc ! 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, NnonSchmid_fcc sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_fcc(1:3,1:3,1,j,i)) sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_fcc(1:3,1:3,2,j,i)) 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 ('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. NnonSchmid(myStructure) = NnonSchmid_BCC ! 5 known non schmid contributions for BCC (A. Koester, A. Ma, A. Hartmaier 2012) 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) do j = 1_pInt, NnonSchmid_bcc sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_bcc(1:3,1:3,1,j,i)) sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_bcc(1:3,1:3,2,j,i)) enddo 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 ('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. NnonSchmid(myStructure) = NnonSchmid_hex ! Currently no known non schmid contributions for hex (to be changed later) ! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexgonal 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, NnonSchmid_hex sns(1:6,j,i) = math_Mandel33to6(lattice_nonSchmid_hex(1:3,1:3,1,j,i)) sns(7:12,j,i) = math_Mandel33to6(lattice_nonSchmid_hex(1:3,1:3,2,j,i)) 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 endif 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,i,myStructure) = math_tensorproduct(lattice_sd(1:3,i,myStructure), & lattice_sn(1:3,i,myStructure)) lattice_Sslip_v(1:6,1,i,myStructure) = math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,i,myStructure))) do j = 1_pInt, NnonSchmid(myStructure) lattice_Sslip_v(1:6,2*j,i,myStructure) = sns(1:6,j,i) lattice_Sslip_v(1:6,2*j+1,i,myStructure) = sns(7:12,j,i) enddo if (abs(math_trace33(lattice_Sslip(1:3,1:3,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(structName) implicit none character(len=32), intent(in) :: structName select case(structName(1:3)) case ('fcc','bcc') lattice_symmetryType = 1_pInt case ('hex') 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(structName,C66) implicit none character(len=32), intent(in) :: structName 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(structName(1:3)) case ('iso') 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 ('fcc','bcc') 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 ('hex') 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 ('ort') 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 Number of parameters to expect in material.config section ! NslipFamilies ! NtwinFamilies ! SlipSlipInteraction ! SlipTwinInteraction ! TwinSlipInteraction ! TwinTwinInteraction !-------------------------------------------------------------------------------------------------- function lattice_configNchunks(struct) use prec, only: & pInt implicit none integer(pInt), dimension(6) :: lattice_configNchunks character(len=*), intent(in) :: struct select case(struct(1:3)) ! check first three chars of structure name case ('fcc') 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) case ('bcc') 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) case ('hex') 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) end select end function lattice_configNchunks end module lattice