From 591a82de260d5689d9067eebae8580a6b6f9ed92 Mon Sep 17 00:00:00 2001 From: Su Leen Wong Date: Thu, 14 Aug 2014 12:21:51 +0000 Subject: [PATCH] Fixed issue with previous commit --- code/lattice.f90 | 1469 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 1469 insertions(+) create mode 100644 code/lattice.f90 diff --git a/code/lattice.f90 b/code/lattice.f90 new file mode 100644 index 000000000..d71445661 --- /dev/null +++ b/code/lattice.f90 @@ -0,0 +1,1469 @@ +!-------------------------------------------------------------------------------------------------- +! $Id$ +!-------------------------------------------------------------------------------------------------- +!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH +!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH +!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH +!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH +!> @brief defines lattice structure definitions, slip and twin system definitions, Schimd matrix +!> calculation and non-Schmid behavior +!-------------------------------------------------------------------------------------------------- +module lattice + use prec, only: & + pReal, & + pInt + + implicit none + private + integer(pInt), parameter, public :: & + LATTICE_maxNslipFamily = 6_pInt, & !< max # of slip system families over lattice structures + LATTICE_maxNtwinFamily = 4_pInt, & !< max # of twin system families over lattice structures + LATTICE_maxNtransFamily = 2_pInt, & !< max # of transformation system families over lattice structures + LATTICE_maxNslip = 33_pInt, & !< max # of slip systems over lattice structures + LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures + LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part) + LATTICE_maxNnonSchmid = 6_pInt, & !< max # of non schmid contributions over lattice structures + LATTICE_maxNtrans = 36_pInt !< max # of transformations over lattice structures + + integer(pInt), allocatable, dimension(:,:), protected, public :: & + lattice_NslipSystem, & !< total # of slip systems in each family + lattice_NtwinSystem, & !< total # of twin systems in each family + lattice_NtransSystem !< total # of transformation systems in each family + + integer(pInt), allocatable, dimension(:,:,:), protected, public :: & + lattice_interactionSlipSlip, & !< Slip--slip interaction type + lattice_interactionSlipTwin, & !< Slip--twin interaction type + lattice_interactionTwinSlip, & !< Twin--slip interaction type + lattice_interactionTwinTwin !< Twin--twin interaction type + + real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: & + lattice_Sslip !< Schmid and non-Schmid matrices + + real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & + lattice_Sslip_v !< Mandel notation of lattice_Sslip + + real(pReal), allocatable, dimension(:,:,:), protected, public :: & + lattice_sn, & !< normal direction of slip system + lattice_sd, & !< slip direction of slip system + lattice_st !< sd x sn + +! rotation and Schmid matrices, normal, shear direction and d x n of twin systems + real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & + lattice_Stwin, & + lattice_Qtwin + + real(pReal), allocatable, dimension(:,:,:), protected, public :: & + lattice_Stwin_v, & + lattice_tn, & + lattice_td, & + lattice_tt + + real(pReal), allocatable, dimension(:,:,:), protected, public :: & + lattice_trn1, & + lattice_trd1, & + lattice_trt1, & + lattice_trn2, & + lattice_trd2, & + lattice_trt2, & + lattice_NItrans_v + + real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & + lattice_Atrans, & + lattice_Mtrans, & + lattice_Ttrans, & + lattice_Rtrans, & + lattice_Utrans, & + lattice_NItrans + + real(pReal), allocatable, dimension(:,:), protected, public :: & + lattice_shearTwin !< characteristic twin shear + + integer(pInt), allocatable, dimension(:), protected, public :: & + lattice_NnonSchmid !< total # of non-Schmid contributions for each structure + +!-------------------------------------------------------------------------------------------------- +! fcc + integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & + LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0],pInt) !< total # of slip systems per family for fcc + + integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & + LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc + + integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & + LATTICE_fcc_NtransSystem = int([12, 24],pInt) !< total # of transformation systems per family for fcc + + integer(pInt), parameter, private :: & + LATTICE_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc + LATTICE_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc + LATTICE_fcc_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for fcc + LATTICE_fcc_Ntrans = 36_pInt !< total # of transformations for fcc + + real(pReal), dimension(3+3,LATTICE_fcc_Nslip), parameter, private :: & + LATTICE_fcc_systemSlip = reshape(real([& + ! Slip direction Plane normal + 0, 1,-1, 1, 1, 1, & + -1, 0, 1, 1, 1, 1, & + 1,-1, 0, 1, 1, 1, & + 0,-1,-1, -1,-1, 1, & + 1, 0, 1, -1,-1, 1, & + -1, 1, 0, -1,-1, 1, & + 0,-1, 1, 1,-1,-1, & + -1, 0,-1, 1,-1,-1, & + 1, 1, 0, 1,-1,-1, & + 0, 1, 1, -1, 1,-1, & + 1, 0,-1, -1, 1,-1, & + -1,-1, 0, -1, 1,-1 & + ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Nslip]) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli + + real(pReal), dimension(3+3,LATTICE_fcc_Ntwin), parameter, private :: & + LATTICE_fcc_systemTwin = reshape(real( [& + -2, 1, 1, 1, 1, 1, & + 1,-2, 1, 1, 1, 1, & + 1, 1,-2, 1, 1, 1, & + 2,-1, 1, -1,-1, 1, & + -1, 2, 1, -1,-1, 1, & + -1,-1,-2, -1,-1, 1, & + -2,-1,-1, 1,-1,-1, & + 1, 2,-1, 1,-1,-1, & + 1,-1, 2, 1,-1,-1, & + 2, 1,-1, -1, 1,-1, & + -1,-2,-1, -1, 1,-1, & + -1, 1, 2, -1, 1,-1 & + ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ntwin]) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli + + real(pReal), dimension(LATTICE_fcc_Ntwin), parameter, private :: & + LATTICE_fcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) !< Twin system <112>{111} ??? Sorted according to Eisenlohr & Hantcherli + + integer(pInt), dimension(2_pInt,LATTICE_fcc_Ntwin), parameter, public :: & + LATTICE_fcc_twinNucleationSlipPair = reshape(int( [& + 2,3, & + 1,3, & + 1,2, & + 5,6, & + 4,6, & + 4,5, & + 8,9, & + 7,9, & + 7,8, & + 11,12, & + 10,12, & + 10,11 & + ],pInt),[2_pInt,LATTICE_fcc_Ntwin]) + + integer(pInt), dimension(LATTICE_fcc_Nslip,lattice_fcc_Nslip), parameter, public :: & + LATTICE_fcc_interactionSlipSlip = reshape(int( [& + 1,2,2,4,6,5,3,5,5,4,5,6, & ! ---> slip + 2,1,2,6,4,5,5,4,6,5,3,5, & ! | + 2,2,1,5,5,3,5,6,4,6,5,4, & ! | + 4,6,5,1,2,2,4,5,6,3,5,5, & ! v slip + 6,4,5,2,1,2,5,3,5,5,4,6, & + 5,5,3,2,2,1,6,5,4,5,6,4, & + 3,5,5,4,5,6,1,2,2,4,6,5, & + 5,4,6,5,3,5,2,1,2,6,4,5, & + 5,6,4,6,5,4,2,2,1,5,5,3, & + 4,5,6,3,5,5,4,6,5,1,2,2, & + 5,3,5,5,4,6,6,4,5,2,1,2, & + 6,5,4,5,6,4,5,5,3,2,2,1 & + ],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Nslip],order=[2,1]) !< Slip--slip interaction types for fcc + !< 1: self interaction + !< 2: coplanar interaction + !< 3: collinear interaction + !< 4: Hirth locks + !< 5: glissile junctions + !< 6: Lomer locks + integer(pInt), dimension(LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin), parameter, public :: & + LATTICE_fcc_interactionSlipTwin = reshape(int( [& + 1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin + 1,1,1,3,3,3,3,3,3,2,2,2, & ! | + 1,1,1,2,2,2,3,3,3,3,3,3, & ! | + 3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip + 3,3,3,1,1,1,2,2,2,3,3,3, & + 2,2,2,1,1,1,3,3,3,3,3,3, & + 2,2,2,3,3,3,1,1,1,3,3,3, & + 3,3,3,2,2,2,1,1,1,3,3,3, & + 3,3,3,3,3,3,1,1,1,2,2,2, & + 3,3,3,2,2,2,3,3,3,1,1,1, & + 2,2,2,3,3,3,3,3,3,1,1,1, & + 3,3,3,3,3,3,2,2,2,1,1,1 & + ],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for fcc + !< 1: coplanar interaction + !< 2: screw trace between slip system and twin habit plane (easy cross slip) + !< 3: other interaction + integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Nslip), parameter, public :: & + LATTICE_fcc_interactionTwinSlip = 1_pInt !< Twin--Slip interaction types for fcc + + integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Ntwin), parameter,public :: & + LATTICE_fcc_interactionTwinTwin = reshape(int( [& + 1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin + 1,1,1,2,2,2,2,2,2,2,2,2, & ! | + 1,1,1,2,2,2,2,2,2,2,2,2, & ! | + 2,2,2,1,1,1,2,2,2,2,2,2, & ! v twin + 2,2,2,1,1,1,2,2,2,2,2,2, & + 2,2,2,1,1,1,2,2,2,2,2,2, & + 2,2,2,2,2,2,1,1,1,2,2,2, & + 2,2,2,2,2,2,1,1,1,2,2,2, & + 2,2,2,2,2,2,1,1,1,2,2,2, & + 2,2,2,2,2,2,2,2,2,1,1,1, & + 2,2,2,2,2,2,2,2,2,1,1,1, & + 2,2,2,2,2,2,2,2,2,1,1,1 & + ],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for fcc + + + +!-------------------------------------------------------------------------------------------------- +! bcc + integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & + LATTICE_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0], pInt) !< total # of slip systems per family for bcc + + integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & + LATTICE_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< total # of twin systems per family for bcc + + integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & + LATTICE_bcc_NtransSystem = int([0,0],pInt) !< total # of transformation systems per family for bcc + + integer(pInt), parameter, private :: & + LATTICE_bcc_Nslip = 24_pInt, & ! sum(lattice_bcc_NslipSystem), & !< total # of slip systems for bcc + LATTICE_bcc_Ntwin = 12_pInt, & ! sum(lattice_bcc_NtwinSystem) !< total # of twin systems for bcc + LATTICE_bcc_NnonSchmid = 6_pInt, & !< # of non-Schmid contributions for bcc. 6 known non schmid contributions for BCC (A. Koester, A. Ma, A. Hartmaier 2012) + LATTICE_bcc_Ntrans = 0_pInt !< total # of transformations for bcc + + real(pReal), dimension(3+3,LATTICE_bcc_Nslip), parameter, private :: & + LATTICE_bcc_systemSlip = reshape(real([& + ! Slip direction Plane normal + ! Slip system <111>{110} + 1,-1, 1, 0, 1, 1, & + -1,-1, 1, 0, 1, 1, & + 1, 1, 1, 0,-1, 1, & + -1, 1, 1, 0,-1, 1, & + -1, 1, 1, 1, 0, 1, & + -1,-1, 1, 1, 0, 1, & + 1, 1, 1, -1, 0, 1, & + 1,-1, 1, -1, 0, 1, & + -1, 1, 1, 1, 1, 0, & + -1, 1,-1, 1, 1, 0, & + 1, 1, 1, -1, 1, 0, & + 1, 1,-1, -1, 1, 0, & + ! Slip system <111>{112} + -1, 1, 1, 2, 1, 1, & + 1, 1, 1, -2, 1, 1, & + 1, 1,-1, 2,-1, 1, & + 1,-1, 1, 2, 1,-1, & + 1,-1, 1, 1, 2, 1, & + 1, 1,-1, -1, 2, 1, & + 1, 1, 1, 1,-2, 1, & + -1, 1, 1, 1, 2,-1, & + 1, 1,-1, 1, 1, 2, & + 1,-1, 1, -1, 1, 2, & + -1, 1, 1, 1,-1, 2, & + 1, 1, 1, 1, 1,-2 & + ! Slip system <111>{123} + ! 1, 1,-1, 1, 2, 3, & + ! 1,-1, 1, -1, 2, 3, & + ! -1, 1, 1, 1,-2, 3, & + ! 1, 1, 1, 1, 2,-3, & + ! 1,-1, 1, 1, 3, 2, & + ! 1, 1,-1, -1, 3, 2, & + ! 1, 1, 1, 1,-3, 2, & + ! -1, 1, 1, 1, 3,-2, & + ! 1, 1,-1, 2, 1, 3, & + ! 1,-1, 1, -2, 1, 3, & + ! -1, 1, 1, 2,-1, 3, & + ! 1, 1, 1, 2, 1,-3, & + ! 1,-1, 1, 2, 3, 1, & + ! 1, 1,-1, -2, 3, 1, & + ! 1, 1, 1, 2,-3, 1, & + ! -1, 1, 1, 2, 3,-1, & + ! -1, 1, 1, 3, 1, 2, & + ! 1, 1, 1, -3, 1, 2, & + ! 1, 1,-1, 3,-1, 2, & + ! 1,-1, 1, 3, 1,-2, & + ! -1, 1, 1, 3, 2, 1, & + ! 1, 1, 1, -3, 2, 1, & + ! 1, 1,-1, 3,-2, 1, & + ! 1,-1, 1, 3, 2,-1 & + ],pReal),[ 3_pInt + 3_pInt ,LATTICE_bcc_Nslip]) + + real(pReal), dimension(3+3,LATTICE_bcc_Ntwin), parameter, private :: & + LATTICE_bcc_systemTwin = reshape(real([& + ! Twin system <111>{112} + -1, 1, 1, 2, 1, 1, & + 1, 1, 1, -2, 1, 1, & + 1, 1,-1, 2,-1, 1, & + 1,-1, 1, 2, 1,-1, & + 1,-1, 1, 1, 2, 1, & + 1, 1,-1, -1, 2, 1, & + 1, 1, 1, 1,-2, 1, & + -1, 1, 1, 1, 2,-1, & + 1, 1,-1, 1, 1, 2, & + 1,-1, 1, -1, 1, 2, & + -1, 1, 1, 1,-1, 2, & + 1, 1, 1, 1, 1,-2 & + ],pReal),[ 3_pInt + 3_pInt,LATTICE_bcc_Ntwin]) + + real(pReal), dimension(LATTICE_bcc_Ntwin), parameter, private :: & + LATTICE_bcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) + + integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Nslip), parameter, public :: & + LATTICE_bcc_interactionSlipSlip = reshape(int( [& + 1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! ---> slip + 2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! | + 6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! | + 6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v slip + 5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & + 4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, & + 4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, & + 3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, & + 4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, & + 3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, & + 5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, & + 4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, & + ! + 6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, & + 6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, & + 4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, & + 3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, & + 3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, & + 4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, & + 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, & + 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, & + 4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, & + 3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, & + 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, & + 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 & + ],pInt),[lattice_bcc_Nslip,lattice_bcc_Nslip],order=[2,1]) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377 + !< 1: self interaction + !< 2: coplanar interaction + !< 3: collinear interaction + !< 4: mixed-asymmetrical junction + !< 5: mixed-symmetrical junction + !< 6: edge junction + integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin), parameter, public :: & + LATTICE_bcc_interactionSlipTwin = reshape(int( [& + 3,3,3,2,2,3,3,3,3,2,3,3, & ! ---> twin + 3,3,2,3,3,2,3,3,2,3,3,3, & ! | + 3,2,3,3,3,3,2,3,3,3,3,2, & ! | + 2,3,3,3,3,3,3,2,3,3,2,3, & ! v slip + 2,3,3,3,3,3,3,2,3,3,2,3, & + 3,3,2,3,3,2,3,3,2,3,3,3, & + 3,2,3,3,3,3,2,3,3,3,3,2, & + 3,3,3,2,2,3,3,3,3,2,3,3, & + 2,3,3,3,3,3,3,2,3,3,2,3, & + 3,3,3,2,2,3,3,3,3,2,3,3, & + 3,2,3,3,3,3,2,3,3,3,3,2, & + 3,3,2,3,3,2,3,3,2,3,3,3, & + ! + 1,3,3,3,3,3,3,2,3,3,2,3, & + 3,1,3,3,3,3,2,3,3,3,3,2, & + 3,3,1,3,3,2,3,3,2,3,3,3, & + 3,3,3,1,2,3,3,3,3,2,3,3, & + 3,3,3,2,1,3,3,3,3,2,3,3, & + 3,3,2,3,3,1,3,3,2,3,3,3, & + 3,2,3,3,3,3,1,3,3,3,3,2, & + 2,3,3,3,3,3,3,1,3,3,2,3, & + 3,3,2,3,3,2,3,3,1,3,3,3, & + 3,3,3,2,2,3,3,3,3,1,3,3, & + 2,3,3,3,3,3,3,2,3,3,1,3, & + 3,2,3,3,3,3,2,3,3,3,3,1 & + ],pInt),[LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for bcc + !< 1: coplanar interaction + !< 2: screw trace between slip system and twin habit plane (easy cross slip) + !< 3: other interaction + integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Nslip), parameter, public :: & + LATTICE_bcc_interactionTwinSlip = 1_pInt !< Twin--slip interaction types for bcc @todo not implemented yet + + integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin), parameter, public :: & + LATTICE_bcc_interactionTwinTwin = reshape(int( [& + 1,3,3,3,3,3,3,2,3,3,2,3, & ! ---> twin + 3,1,3,3,3,3,2,3,3,3,3,2, & ! | + 3,3,1,3,3,2,3,3,2,3,3,3, & ! | + 3,3,3,1,2,3,3,3,3,2,3,3, & ! v twin + 3,3,3,2,1,3,3,3,3,2,3,3, & + 3,3,2,3,3,1,3,3,2,3,3,3, & + 3,2,3,3,3,3,1,3,3,3,3,2, & + 2,3,3,3,3,3,3,1,3,3,2,3, & + 3,3,2,3,3,2,3,3,1,3,3,3, & + 3,3,3,2,2,3,3,3,3,1,3,3, & + 2,3,3,3,3,3,3,2,3,3,1,3, & + 3,2,3,3,3,3,2,3,3,3,3,1 & + ],pInt),[LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for bcc + !< 1: self interaction + !< 2: collinear interaction + !< 3: other interaction + + +!-------------------------------------------------------------------------------------------------- +! hex + integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & + lattice_hex_NslipSystem = int([ 3, 3, 3, 6, 12, 6],pInt) !< # of slip systems per family for hex + + integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & + lattice_hex_NtwinSystem = int([ 6, 6, 6, 6],pInt) !< # of slip systems per family for hex + + integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & + LATTICE_hex_NtransSystem = int([0,0],pInt) !< total # of transformation systems per family for hex + + integer(pInt), parameter , private :: & + LATTICE_hex_Nslip = 33_pInt, & ! sum(lattice_hex_NslipSystem), !< total # of slip systems for hex + LATTICE_hex_Ntwin = 24_pInt, & ! sum(lattice_hex_NtwinSystem) !< total # of twin systems for hex + LATTICE_hex_NnonSchmid = 0_pInt, & !< # of non-Schmid contributions for hex + LATTICE_hex_Ntrans = 0_pInt !< total # of transformations for hex + + real(pReal), dimension(4+4,LATTICE_hex_Nslip), parameter, private :: & + LATTICE_hex_systemSlip = reshape(real([& + ! Slip direction Plane normal + ! Basal systems <11.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base)) + 2, -1, -1, 0, 0, 0, 0, 1, & + -1, 2, -1, 0, 0, 0, 0, 1, & + -1, -1, 2, 0, 0, 0, 0, 1, & + ! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio) + 2, -1, -1, 0, 0, 1, -1, 0, & + -1, 2, -1, 0, -1, 0, 1, 0, & + -1, -1, 2, 0, 1, -1, 0, 0, & + ! 2nd type prismatic systems <10.0>{11.0} -- a slip; plane normals independent of c/a-ratio + 0, 1, -1, 0, 2, -1, -1, 0, & + -1, 0, 1, 0, -1, 2, -1, 0, & + 1, -1, 0, 0, -1, -1, 2, 0, & + ! 1st type 1st order pyramidal systems <11.0>{-11.1} -- plane normals depend on the c/a-ratio + 2, -1, -1, 0, 0, 1, -1, 1, & + -1, 2, -1, 0, -1, 0, 1, 1, & + -1, -1, 2, 0, 1, -1, 0, 1, & + 1, 1, -2, 0, -1, 1, 0, 1, & + -2, 1, 1, 0, 0, -1, 1, 1, & + 1, -2, 1, 0, 1, 0, -1, 1, & + ! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the c/a-ratio + 2, -1, -1, 3, -1, 1, 0, 1, & + 1, -2, 1, 3, -1, 1, 0, 1, & + -1, -1, 2, 3, 1, 0, -1, 1, & + -2, 1, 1, 3, 1, 0, -1, 1, & + -1, 2, -1, 3, 0, -1, 1, 1, & + 1, 1, -2, 3, 0, -1, 1, 1, & + -2, 1, 1, 3, 1, -1, 0, 1, & + -1, 2, -1, 3, 1, -1, 0, 1, & + 1, 1, -2, 3, -1, 0, 1, 1, & + 2, -1, -1, 3, -1, 0, 1, 1, & + 1, -2, 1, 3, 0, 1, -1, 1, & + -1, -1, 2, 3, 0, 1, -1, 1, & + ! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below) + 2, -1, -1, 3, -2, 1, 1, 2, & ! sorted according to similar twin system + -1, 2, -1, 3, 1, -2, 1, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a) + -1, -1, 2, 3, 1, 1, -2, 2, & + -2, 1, 1, 3, 2, -1, -1, 2, & + 1, -2, 1, 3, -1, 2, -1, 2, & + 1, 1, -2, 3, -1, -1, 2, 2 & + ],pReal),[ 4_pInt + 4_pInt,LATTICE_hex_Nslip]) !< slip systems for hex sorted by A. Alankar & P. Eisenlohr + + real(pReal), dimension(4+4,LATTICE_hex_Ntwin), parameter, private :: & + LATTICE_hex_systemTwin = reshape(real([& + ! Compression or Tension =f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981) + 1, -1, 0, 1, -1, 1, 0, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a) + -1, 0, 1, 1, 1, 0, -1, 2, & + 0, 1, -1, 1, 0, -1, 1, 2, & + -1, 1, 0, 1, 1, -1, 0, 2, & + 1, 0, -1, 1, -1, 0, 1, 2, & + 0, -1, 1, 1, 0, 1, -1, 2, & +! + 2, -1, -1, 6, -2, 1, 1, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a) + -1, 2, -1, 6, 1, -2, 1, 1, & + -1, -1, 2, 6, 1, 1, -2, 1, & + -2, 1, 1, 6, 2, -1, -1, 1, & + 1, -2, 1, 6, -1, 2, -1, 1, & + 1, 1, -2, 6, -1, -1, 2, 1, & +! + -1, 1, 0, -2, -1, 1, 0, 1, & !! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) + 1, 0, -1, -2, 1, 0, -1, 1, & + 0, -1, 1, -2, 0, -1, 1, 1, & + 1, -1, 0, -2, 1, -1, 0, 1, & + -1, 0, 1, -2, -1, 0, 1, 1, & + 0, 1, -1, -2, 0, 1, -1, 1, & +! + 2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a) + -1, 2, -1, -3, -1, 2, -1, 2, & + -1, -1, 2, -3, -1, -1, 2, 2, & + -2, 1, 1, -3, -2, 1, 1, 2, & + 1, -2, 1, -3, 1, -2, 1, 2, & + 1, 1, -2, -3, 1, 1, -2, 2 & + ],pReal),[ 4_pInt + 4_pInt ,LATTICE_hex_Ntwin]) !< twin systems for hex, order follows Prof. Tom Bieler's scheme; but numbering in data was restarted from 1 + + integer(pInt), dimension(LATTICE_hex_Ntwin), parameter, private :: & + LATTICE_hex_shearTwin = reshape(int( [& ! indicator to formula further below + 1, & ! <-10.1>{10.2} + 1, & + 1, & + 1, & + 1, & + 1, & + 2, & ! <11.6>{-1-1.1} + 2, & + 2, & + 2, & + 2, & + 2, & + 3, & ! <10.-2>{10.1} + 3, & + 3, & + 3, & + 3, & + 3, & + 4, & ! <11.-3>{11.2} + 4, & + 4, & + 4, & + 4, & + 4 & + ],pInt),[LATTICE_hex_Ntwin]) + + integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Nslip), parameter, public :: & + LATTICE_hex_interactionSlipSlip = reshape(int( [& + 1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! ---> slip + 2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | + 2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | + ! v slip + 6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & + 6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & + 6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & + ! + 12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & + 12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & + 12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & + ! + 20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + 20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + 20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + 20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & + ! + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, & + 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, & + ! + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, & + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, & + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, & + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, & + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, & + 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 & + ! + ],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Nslip],order=[2,1]) !< Slip--slip interaction types for hex (32? in total) + + integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Ntwin), parameter, public :: & + LATTICE_hex_interactionSlipTwin = reshape(int( [& + 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! --> twin + 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | + 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | + ! v + 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip + 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & + 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & + ! + 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & + 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & + 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & + ! + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & + ! + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & + ! + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & + 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 & + ! + ],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Ntwin],order=[2,1]) !< Slip--twin interaction types for hex (isotropic, 24 in total) + + integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Nslip), parameter, public :: & + LATTICE_hex_interactionTwinSlip = reshape(int( [& + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! --> slip + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin + 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & + ! + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & + ! + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & + ! + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & + 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 & + ],pInt),[LATTICE_hex_Ntwin,LATTICE_hex_Nslip],order=[2,1]) !< Twin--twin interaction types for hex (isotropic, 20 in total) + + integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Ntwin), parameter, public :: & + LATTICE_hex_interactionTwinTwin = reshape(int( [& + 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! ---> twin + 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | + 2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | + 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v twin + 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & + 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & + ! + 6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + 6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + 6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & + ! + 12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, & + 12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, & + 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, & + 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, & + 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, & + 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, & + ! + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, & + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, & + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, & + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, & + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, & + 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 & + ],pInt),[lattice_hex_Ntwin,lattice_hex_Ntwin],order=[2,1]) !< Twin--slip interaction types for hex (isotropic, 16 in total) + real(pReal), dimension(:,:,:), allocatable, public, protected :: & + lattice_C66 + real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: & + lattice_C3333 + real(pReal), dimension(:), allocatable, public, protected :: & + lattice_mu, & + lattice_nu + real(pReal), dimension(:,:,:), allocatable, public, protected :: & + lattice_thermalConductivity33, & + lattice_thermalExpansion33, & + lattice_surfaceEnergy33 + real(pReal), dimension(:), allocatable, public, protected :: & + lattice_referenceTemperature + enum, bind(c) + enumerator :: LATTICE_undefined_ID, & + LATTICE_iso_ID, & + LATTICE_fcc_ID, & + LATTICE_bcc_ID, & + LATTICE_hex_ID, & + LATTICE_ort_ID + end enum + integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: & + lattice_structure + + +integer(pInt), dimension(2), parameter, private :: & + lattice_NsymOperations = [24_pInt,12_pInt] + +real(pReal), dimension(4,36), parameter, private :: & + lattice_symOperations = reshape([& + 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations + 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry + 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, & + 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, & + 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, & + 0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, & + 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, & + 0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry + -0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & + 0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & + -0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & + 0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & + -0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & + 0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & + -0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & + 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry + 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & + -0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & + 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, & + 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & + -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, & + 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, & + 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, & + -0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, & + 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations + 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry + 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & + 0.0_pReal, 0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, & + 0.0_pReal, -0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, & + 0.0_pReal, 0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, & + 0.0_pReal, -0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, & + 0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry + -0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & + 0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, & + -0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, & + 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal & + ],[4,36]) !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36 + + ! use this later on to substitute the matrix above + ! if self.lattice == 'cubic': + ! symQuats = [ + ! [ 1.0,0.0,0.0,0.0 ], + ! [ 0.0,1.0,0.0,0.0 ], + ! [ 0.0,0.0,1.0,0.0 ], + ! [ 0.0,0.0,0.0,1.0 ], + ! [ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ], + ! [ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ], + ! [ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ], + ! [ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ], + ! [ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], + ! [ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], + ! [ 0.5, 0.5, 0.5, 0.5 ], + ! [-0.5, 0.5, 0.5, 0.5 ], + ! [-0.5, 0.5, 0.5,-0.5 ], + ! [-0.5, 0.5,-0.5, 0.5 ], + ! [-0.5,-0.5, 0.5, 0.5 ], + ! [-0.5,-0.5, 0.5,-0.5 ], + ! [-0.5,-0.5,-0.5, 0.5 ], + ! [-0.5, 0.5,-0.5,-0.5 ], + ! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + ! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + ! [-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ], + ! [-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ], + ! [-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ], + ! [-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ], + ! ] + ! elif self.lattice == 'hexagonal': + ! symQuats = [ + ! [ 1.0,0.0,0.0,0.0 ], + ! [ 0.0,1.0,0.0,0.0 ], + ! [ 0.0,0.0,1.0,0.0 ], + ! [ 0.0,0.0,0.0,1.0 ], + ! [-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ], + ! [-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ], + ! [ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ], + ! [ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ], + ! [ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ], + ! [ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ], + ! [ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], + ! [-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], + ! ] + ! elif self.lattice == 'tetragonal': + ! symQuats = [ + ! [ 1.0,0.0,0.0,0.0 ], + ! [ 0.0,1.0,0.0,0.0 ], + ! [ 0.0,0.0,1.0,0.0 ], + ! [ 0.0,0.0,0.0,1.0 ], + ! [ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], + ! [ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], + ! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + ! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], + ! ] + ! elif self.lattice == 'orthorhombic': + ! symQuats = [ + ! [ 1.0,0.0,0.0,0.0 ], + ! [ 0.0,1.0,0.0,0.0 ], + ! [ 0.0,0.0,1.0,0.0 ], + ! [ 0.0,0.0,0.0,1.0 ], + ! ] + ! else: + ! symQuats = [ + ! [ 1.0,0.0,0.0,0.0 ], + ! ] + + public :: & + lattice_init, & + lattice_qDisorientation, & + LATTICE_fcc_ID, & + LATTICE_bcc_ID, & + LATTICE_hex_ID + +contains + +!-------------------------------------------------------------------------------------------------- +!> @brief Module initialization +!-------------------------------------------------------------------------------------------------- +subroutine lattice_init + use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) + use prec, only: & + tol_math_check + use IO, only: & + IO_open_file,& + IO_open_jobFile_stat, & + IO_countSections, & + IO_countTagInPart, & + IO_error, & + IO_timeStamp, & + IO_stringPos, & + IO_EOF, & + IO_read, & + IO_lc, & + IO_getTag, & + IO_isBlank, & + IO_stringPos, & + IO_stringValue, & + IO_floatValue, & + IO_EOF + use material, only: & + material_configfile, & + material_localFileExt, & + material_partPhase + use debug, only: & + debug_level, & + debug_lattice, & + debug_levelBasic + + implicit none + integer(pInt), parameter :: FILEUNIT = 200_pInt + integer(pInt) :: Nphases + character(len=65536) :: & + tag = '', & + line = '' + integer(pInt), parameter :: MAXNCHUNKS = 2_pInt + integer(pInt), dimension(1+2*MAXNCHUNKS) :: positions + integer(pInt) :: section = 0_pInt,i + real(pReal), dimension(:), allocatable :: & + CoverA, & !< c/a ratio for hex type lattice + aA, & !< lattice parameter a for fcc austenite + aM, & !< lattice paramater a for bcc martensite + cM !< lattice parameter c for bcc martensite + + write(6,'(/,a)') ' <<<+- lattice init -+>>>' + write(6,'(a)') ' $Id$' + write(6,'(a15,a)') ' Current time: ',IO_timeStamp() +#include "compilation_info.f90" + +!-------------------------------------------------------------------------------------------------- +! consistency checks + if (LATTICE_maxNslip /= maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_Nslip])) & + call IO_error(0_pInt,ext_msg = 'LATTICE_maxNslip') + if (LATTICE_maxNtwin /= maxval([LATTICE_fcc_Ntwin,LATTICE_bcc_Ntwin,LATTICE_hex_Ntwin])) & + call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtwin') + if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) & + call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtrans') + if (LATTICE_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,& + lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid') + + if (LATTICE_fcc_Nslip /= sum(lattice_fcc_NslipSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Nslip') + if (LATTICE_bcc_Nslip /= sum(lattice_bcc_NslipSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Nslip') + if (LATTICE_hex_Nslip /= sum(lattice_hex_NslipSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Nslip') + + if (LATTICE_fcc_Ntwin /= sum(lattice_fcc_NtwinSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntwin') + if (LATTICE_bcc_Ntwin /= sum(lattice_bcc_NtwinSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntwin') + if (LATTICE_hex_Ntwin /= sum(lattice_hex_NtwinSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntwin') + + if (LATTICE_fcc_Ntrans /= sum(lattice_fcc_NtransSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntrans') + if (LATTICE_bcc_Ntrans /= sum(lattice_bcc_NtransSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntrans') + if (LATTICE_hex_Ntrans /= sum(lattice_hex_NtransSystem)) & + call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntrans') + + if (LATTICE_maxNinteraction /= max(& + maxval(lattice_fcc_interactionSlipSlip), & + maxval(lattice_bcc_interactionSlipSlip), & + maxval(lattice_hex_interactionSlipSlip), & + ! + maxval(lattice_fcc_interactionSlipTwin), & + maxval(lattice_bcc_interactionSlipTwin), & + maxval(lattice_hex_interactionSlipTwin), & + ! + maxval(lattice_fcc_interactionTwinSlip), & + maxval(lattice_bcc_interactionTwinSlip), & + maxval(lattice_hex_interactionTwinSlip), & + ! + maxval(lattice_fcc_interactionTwinTwin), & + maxval(lattice_bcc_interactionTwinTwin), & + maxval(lattice_hex_interactionTwinTwin))) & + call IO_error(0_pInt,ext_msg = 'LATTICE_maxNinteraction') + +!-------------------------------------------------------------------------------------------------- +! read from material configuration file + if (.not. IO_open_jobFile_stat(FILEUNIT,material_localFileExt)) & ! no local material configuration present... + call IO_open_file(FILEUNIT,material_configFile) ! ... open material.config file + Nphases = IO_countSections(FILEUNIT,material_partPhase) + + if(Nphases<1_pInt) & + call IO_error(160_pInt,Nphases, ext_msg='No phases found') + + if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then + write(6,'(a16,1x,i5)') ' # phases:',Nphases + endif + + allocate(lattice_structure(Nphases),source = LATTICE_undefined_ID) + allocate(lattice_C66(6,6,Nphases), source=0.0_pReal) + allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal) + allocate(lattice_thermalConductivity33(3,3,Nphases), source=0.0_pReal) + allocate(lattice_thermalExpansion33 (3,3,Nphases), source=0.0_pReal) + allocate(lattice_surfaceEnergy33 (3,3,Nphases), source=0.0_pReal) + allocate(lattice_referenceTemperature (Nphases), source=0.0_pReal) + + allocate(lattice_mu(Nphases), source=0.0_pReal) + allocate(lattice_nu(Nphases), source=0.0_pReal) + + allocate(lattice_NnonSchmid(Nphases), source=0_pInt) + allocate(lattice_Sslip(3,3,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal) + allocate(lattice_Sslip_v(6,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal) + allocate(lattice_sd(3,lattice_maxNslip,Nphases),source=0.0_pReal) + allocate(lattice_st(3,lattice_maxNslip,Nphases),source=0.0_pReal) + allocate(lattice_sn(3,lattice_maxNslip,Nphases),source=0.0_pReal) + + allocate(lattice_Qtwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal) + allocate(lattice_Stwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal) + allocate(lattice_Stwin_v(6,lattice_maxNtwin,Nphases),source=0.0_pReal) + allocate(lattice_td(3,lattice_maxNtwin,Nphases),source=0.0_pReal) + allocate(lattice_tt(3,lattice_maxNtwin,Nphases),source=0.0_pReal) + allocate(lattice_tn(3,lattice_maxNtwin,Nphases),source=0.0_pReal) + + allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal) + + allocate(lattice_NslipSystem(lattice_maxNslipFamily,Nphases),source=0_pInt) + allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,Nphases),source=0_pInt) + allocate(lattice_NtransSystem(lattice_maxNtransFamily,Nphases),source=0_pInt) + + allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,Nphases),source=0_pInt) ! other:me + allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me + allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,Nphases),source=0_pInt) ! other:me + allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me + + allocate(CoverA(Nphases),source=0.0_pReal) + allocate(aA(Nphases),source=0.0_pReal) + allocate(aM(Nphases),source=0.0_pReal) + allocate(cM(Nphases),source=0.0_pReal) + + rewind(fileUnit) + line = '' ! to have it initialized + section = 0_pInt ! - " - + do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= material_partPhase) ! wind forward to + line = IO_read(fileUnit) + enddo + + do while (trim(line) /= IO_EOF) ! read through sections of material part + line = IO_read(fileUnit) + if (IO_isBlank(line)) cycle ! skip empty lines + if (IO_getTag(line,'<','>') /= '') then ! stop at next part + line = IO_read(fileUnit, .true.) ! reset IO_read + exit + endif + if (IO_getTag(line,'[',']') /= '') then ! next section + section = section + 1_pInt + endif + if (section > 0_pInt) then + positions = IO_stringPos(line,MAXNCHUNKS) + tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key + select case(tag) + case ('lattice_structure') + select case(trim(IO_lc(IO_stringValue(line,positions,2_pInt)))) + case('iso','isotropic') + lattice_structure(section) = LATTICE_iso_ID + case('fcc') + lattice_structure(section) = LATTICE_fcc_ID + case('bcc') + lattice_structure(section) = LATTICE_bcc_ID + case('hex','hexagonal') + lattice_structure(section) = LATTICE_hex_ID + case('ort','orthorombic') + lattice_structure(section) = LATTICE_ort_ID + case default + call IO_error(450_pInt,ext_msg=trim(IO_lc(IO_stringValue(line,positions,2_pInt)))) + end select + case ('c11') + lattice_C66(1,1,section) = IO_floatValue(line,positions,2_pInt) + case ('c12') + lattice_C66(1,2,section) = IO_floatValue(line,positions,2_pInt) + case ('c13') + lattice_C66(1,3,section) = IO_floatValue(line,positions,2_pInt) + case ('c22') + lattice_C66(2,2,section) = IO_floatValue(line,positions,2_pInt) + case ('c23') + lattice_C66(2,3,section) = IO_floatValue(line,positions,2_pInt) + case ('c33') + lattice_C66(3,3,section) = IO_floatValue(line,positions,2_pInt) + case ('c44') + lattice_C66(4,4,section) = IO_floatValue(line,positions,2_pInt) + case ('c55') + lattice_C66(5,5,section) = IO_floatValue(line,positions,2_pInt) + case ('c66') + lattice_C66(6,6,section) = IO_floatValue(line,positions,2_pInt) + case ('covera_ratio','c/a_ratio','c/a') + CoverA(section) = IO_floatValue(line,positions,2_pInt) + case ('aa', 'a_a', 'a_austenite') + aA(section) = IO_floatValue(line,positions,2_pInt) + case ('am', 'a_m', 'a_martensite') + aM(section) = IO_floatValue(line,positions,2_pInt) + case ('cm', 'c_m', 'c_martensite') + cM(section) = IO_floatValue(line,positions,2_pInt) + case ('k11') + lattice_thermalConductivity33(1,1,section) = IO_floatValue(line,positions,2_pInt) + case ('k22') + lattice_thermalConductivity33(2,2,section) = IO_floatValue(line,positions,2_pInt) + case ('k33') + lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,positions,2_pInt) + case ('thermal_expansion11') + lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,positions,2_pInt) + case ('thermal_expansion22') + lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,positions,2_pInt) + case ('thermal_expansion33') + lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,positions,2_pInt) + case ('g11') + lattice_surfaceEnergy33(1,1,section) = IO_floatValue(line,positions,2_pInt) + case ('g22') + lattice_surfaceEnergy33(2,2,section) = IO_floatValue(line,positions,2_pInt) + case ('g33') + lattice_surfaceEnergy33(3,3,section) = IO_floatValue(line,positions,2_pInt) + case ('reference_temperature') + lattice_referenceTemperature(section) = IO_floatValue(line,positions,2_pInt) + end select + endif + enddo + + do i = 1_pInt,Nphases + if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) & + .and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(206_pInt) ! checking physical significance of c/a + call lattice_initializeStructure(i, CoverA(i), aA(i), aM(i), cM(i)) + enddo + + deallocate(CoverA,aA,aM,cM) + +end subroutine lattice_init + + +!-------------------------------------------------------------------------------------------------- +!> @brief Calculation of Schmid matrices, etc. +!-------------------------------------------------------------------------------------------------- +subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM) + use prec, only: & + tol_math_check + use math, only: & + math_vectorproduct, & + math_tensorproduct, & + math_norm3, & + math_mul33x3, & + math_trace33, & + math_symmetric33, & + math_Mandel33to6, & + math_Mandel3333to66, & + math_Voigt66to3333, & + math_axisAngleToR, & + INRAD + use IO, only: & + IO_error + + implicit none + integer(pInt), intent(in) :: myPhase + real(pReal), intent(in) :: & + CoverA, & + aA, & + aM, & + cM + + real(pReal), dimension(3) :: & + sdU, snU, & + np, nn + real(pReal), dimension(3,lattice_maxNslip) :: & + sd, sn + real(pReal), dimension(3,3,2,lattice_maxNnonSchmid,lattice_maxNslip) :: & + sns + real(pReal), dimension(3,lattice_maxNtwin) :: & + td, tn + real(pReal), dimension(lattice_maxNtwin) :: & + ts + integer(pInt) :: & + i,j, & + myNslip, myNtwin + + lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),& + lattice_C66(1:6,1:6,myPhase)) + lattice_mu(myPhase) = 0.2_pReal *( lattice_C66(1,1,myPhase) & + - lattice_C66(1,2,myPhase) & + + 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 + lattice_nu(myPhase) = ( lattice_C66(1,1,myPhase) & + + 4.0_pReal*lattice_C66(1,2,myPhase) & + - 2.0_pReal*lattice_C66(4,4,myPhase)) & + /( 4.0_pReal*lattice_C66(1,1,myPhase) & + + 6.0_pReal*lattice_C66(1,2,myPhase) & + + 2.0_pReal*lattice_C66(4,4,myPhase))! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 + lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt + lattice_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel + do i = 1_pInt, 6_pInt + if (abs(lattice_C66(i,i,myPhase))[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)] + sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*& + 0.5_pReal*sqrt(3.0_pReal) + sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA + sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) + sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal) + sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA + enddo + do i = 1_pInt,myNtwin ! assign twin system vectors and shears + td(1,i) = lattice_hex_systemTwin(1,i)*1.5_pReal + td(2,i) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*& + 0.5_pReal*sqrt(3.0_pReal) + td(3,i) = lattice_hex_systemTwin(4,i)*CoverA + tn(1,i) = lattice_hex_systemTwin(5,i) + tn(2,i) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/sqrt(3.0_pReal) + tn(3,i) = lattice_hex_systemTwin(8,i)/CoverA + select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29 + case (1_pInt) ! <-10.1>{10.2} + ts(i) = (3.0_pReal-CoverA*CoverA)/sqrt(3.0_pReal)/CoverA + case (2_pInt) ! <11.6>{-1-1.1} + ts(i) = 1.0_pReal/CoverA + case (3_pInt) ! <10.-2>{10.1} + ts(i) = (4.0_pReal*CoverA*CoverA-9.0_pReal)/4.0_pReal/sqrt(3.0_pReal)/CoverA + case (4_pInt) ! <11.-3>{11.2} + ts(i) = 2.0_pReal*(CoverA*CoverA-2.0_pReal)/3.0_pReal/CoverA + end select + enddo + lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_hex_NslipSystem + lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_hex_NtwinSystem + lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_hex_NtransSystem + lattice_NnonSchmid(myPhase) = lattice_hex_NnonSchmid + lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_hex_interactionSlipSlip + lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_hex_interactionSlipTwin + lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_hex_interactionTwinSlip + lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_hex_interactionTwinTwin + +!-------------------------------------------------------------------------------------------------- +! orthorombic and isotropic (no crystal plasticity) + case (LATTICE_ort_ID, LATTICE_iso_ID) + myNslip = 0_pInt + myNtwin = 0_pInt + +!-------------------------------------------------------------------------------------------------- +! something went wrong + case default + call IO_error(450_pInt,ext_msg='lattice_initializeStructure') + end select + + + do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure + lattice_sd(1:3,i,myPhase) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector + lattice_sn(1:3,i,myPhase) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector + lattice_st(1:3,i,myPhase) = math_vectorproduct(lattice_sd(1:3,i,myPhase), & + lattice_sn(1:3,i,myPhase)) + lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct(lattice_sd(1:3,i,myPhase), & + lattice_sn(1:3,i,myPhase)) + do j = 1_pInt,lattice_NnonSchmid(myPhase) + lattice_Sslip(1:3,1:3,2*j ,i,myPhase) = sns(1:3,1:3,1,j,i) + lattice_Sslip(1:3,1:3,2*j+1,i,myPhase) = sns(1:3,1:3,2,j,i) + enddo + do j = 1_pInt,1_pInt+2_pInt*lattice_NnonSchmid(myPhase) + lattice_Sslip_v(1:6,j,i,myPhase) = & + math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,j,i,myPhase))) + enddo + if (abs(math_trace33(lattice_Sslip(1:3,1:3,1,i,myPhase))) > tol_math_check) & + call IO_error(0_pInt,myPhase,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix') + enddo + do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure + lattice_td(1:3,i,myPhase) = td(1:3,i)/math_norm3(td(1:3,i)) ! make unit vector + lattice_tn(1:3,i,myPhase) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector + lattice_tt(1:3,i,myPhase) = math_vectorproduct(lattice_td(1:3,i,myPhase), & + lattice_tn(1:3,i,myPhase)) + lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct(lattice_td(1:3,i,myPhase), & + lattice_tn(1:3,i,myPhase)) + lattice_Stwin_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myPhase))) + lattice_Qtwin(1:3,1:3,i,myPhase) = math_axisAngleToR(tn(1:3,i),180.0_pReal*INRAD) + lattice_shearTwin(i,myPhase) = ts(i) + if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myPhase))) > tol_math_check) & + call IO_error(301_pInt,myPhase,ext_msg = 'dilatational twin Schmid matrix') + enddo + +end subroutine lattice_initializeStructure + + +!-------------------------------------------------------------------------------------------------- +!> @brief Symmetrizes stiffness matrix according to lattice type +!-------------------------------------------------------------------------------------------------- +pure function lattice_symmetrizeC66(struct,C66) + + implicit none + integer(kind(LATTICE_undefined_ID)), intent(in) :: struct + real(pReal), dimension(6,6), intent(in) :: C66 + real(pReal), dimension(6,6) :: lattice_symmetrizeC66 + integer(pInt) :: j,k + + lattice_symmetrizeC66 = 0.0_pReal + + select case(struct) + case (LATTICE_iso_ID) + forall(k=1_pInt:3_pInt) + forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2) + lattice_symmetrizeC66(k,k) = C66(1,1) + lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2)) + end forall + case (LATTICE_fcc_ID,LATTICE_bcc_ID) + forall(k=1_pInt:3_pInt) + forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2) + lattice_symmetrizeC66(k,k) = C66(1,1) + lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4) + end forall + case (LATTICE_hex_ID) + lattice_symmetrizeC66(1,1) = C66(1,1) + lattice_symmetrizeC66(2,2) = C66(1,1) + lattice_symmetrizeC66(3,3) = C66(3,3) + lattice_symmetrizeC66(1,2) = C66(1,2) + lattice_symmetrizeC66(2,1) = C66(1,2) + lattice_symmetrizeC66(1,3) = C66(1,3) + lattice_symmetrizeC66(3,1) = C66(1,3) + lattice_symmetrizeC66(2,3) = C66(1,3) + lattice_symmetrizeC66(3,2) = C66(1,3) + lattice_symmetrizeC66(4,4) = C66(4,4) + lattice_symmetrizeC66(5,5) = C66(4,4) + lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2)) + case (LATTICE_ort_ID) + lattice_symmetrizeC66(1,1) = C66(1,1) + lattice_symmetrizeC66(2,2) = C66(2,2) + lattice_symmetrizeC66(3,3) = C66(3,3) + lattice_symmetrizeC66(1,2) = C66(1,2) + lattice_symmetrizeC66(2,1) = C66(1,2) + lattice_symmetrizeC66(1,3) = C66(1,3) + lattice_symmetrizeC66(3,1) = C66(1,3) + lattice_symmetrizeC66(2,3) = C66(2,3) + lattice_symmetrizeC66(3,2) = C66(2,3) + lattice_symmetrizeC66(4,4) = C66(4,4) + lattice_symmetrizeC66(5,5) = C66(5,5) + lattice_symmetrizeC66(6,6) = C66(6,6) + case default + lattice_symmetrizeC66 = C66 + end select + + end function lattice_symmetrizeC66 + +!-------------------------------------------------------------------------------------------------- +!> @brief Symmetrizes 2nd order tensor according to lattice type +!-------------------------------------------------------------------------------------------------- +pure function lattice_symmetrize33(struct,T33) + + implicit none + integer(kind(LATTICE_undefined_ID)), intent(in) :: struct + real(pReal), dimension(3,3), intent(in) :: T33 + real(pReal), dimension(3,3) :: lattice_symmetrize33 + integer(pInt) :: j,k + + lattice_symmetrize33 = 0.0_pReal + + select case(struct) + case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID) + forall(k=1_pInt:3_pInt) lattice_symmetrize33(k,k) = T33(1,1) + case (LATTICE_hex_ID) + lattice_symmetrize33(1,1) = T33(1,1) + lattice_symmetrize33(2,2) = T33(1,1) + lattice_symmetrize33(3,3) = T33(3,3) + case (LATTICE_ort_ID) + lattice_symmetrize33(1,1) = T33(1,1) + lattice_symmetrize33(2,2) = T33(2,2) + lattice_symmetrize33(3,3) = T33(3,3) + case default + lattice_symmetrize33 = T33 + end select + + end function lattice_symmetrize33 + + +!-------------------------------------------------------------------------------------------------- +!> @brief figures whether unit quat falls into stereographic standard triangle +!-------------------------------------------------------------------------------------------------- +logical pure function lattice_qInSST(Q, struct) + use math, only: & + math_qToRodrig + + implicit none + real(pReal), dimension(4), intent(in) :: Q ! orientation + integer(kind(LATTICE_undefined_ID)), intent(in) :: struct ! lattice structure + real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q + + Rodrig = math_qToRodrig(Q) + if (any(Rodrig/=Rodrig)) then + lattice_qInSST = .false. + else + select case (struct) + case (LATTICE_bcc_ID,LATTICE_fcc_ID) + lattice_qInSST = Rodrig(1) > Rodrig(2) .and. & + Rodrig(2) > Rodrig(3) .and. & + Rodrig(3) > 0.0_pReal + case (LATTICE_hex_ID) + lattice_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. & + Rodrig(2) > 0.0_pReal .and. & + Rodrig(3) > 0.0_pReal + case default + lattice_qInSST = .true. + end select + endif + +end function lattice_qInSST + + +!-------------------------------------------------------------------------------------------------- +!> @brief calculates the disorientation for 2 unit quaternions +!-------------------------------------------------------------------------------------------------- +pure function lattice_qDisorientation(Q1, Q2, struct) + use prec, only: & + tol_math_check + use math, only: & + math_qMul, & + math_qConj + + implicit none + real(pReal), dimension(4) :: lattice_qDisorientation + real(pReal), dimension(4), intent(in) :: & + Q1, & ! 1st orientation + Q2 ! 2nd orientation + integer(kind(LATTICE_undefined_ID)), optional, intent(in) :: & ! if given, symmetries between the two orientation will be considered + struct + + real(pReal), dimension(4) :: dQ,dQsymA,mis + integer(pInt) :: i,j,k,s,symmetry + integer(kind(LATTICE_undefined_ID)) :: myStruct + +!-------------------------------------------------------------------------------------------------- +! check if a structure with known symmetries is given + if (present(struct)) then + myStruct = struct + select case (struct) + case(LATTICE_fcc_ID,LATTICE_bcc_ID) + symmetry = 1_pInt + case(LATTICE_hex_ID) + symmetry = 2_pInt + case default + symmetry = 0_pInt + end select + else + symmetry = 0_pInt + myStruct = LATTICE_undefined_ID + endif + + +!-------------------------------------------------------------------------------------------------- +! calculate misorientation, for cubic(1) and hexagonal(2) structure find symmetries + dQ = math_qMul(math_qConj(Q1),Q2) + lattice_qDisorientation = dQ + + select case(symmetry) + + case (1_pInt,2_pInt) + s = sum(lattice_NsymOperations(1:symmetry-1_pInt)) + do i = 1_pInt,2_pInt + dQ = math_qConj(dQ) ! switch order of "from -- to" + do j = 1_pInt,lattice_NsymOperations(symmetry) ! run through first crystal's symmetries + dQsymA = math_qMul(lattice_symOperations(1:4,s+j),dQ) ! apply sym + do k = 1_pInt,lattice_NsymOperations(symmetry) ! run through 2nd crystal's symmetries + mis = math_qMul(dQsymA,lattice_symOperations(1:4,s+k)) ! apply sym + if (mis(1) < 0.0_pReal) & ! want positive angle + mis = -mis + if (mis(1)-lattice_qDisorientation(1) > -tol_math_check & + .and. lattice_qInSST(mis,LATTICE_undefined_ID)) lattice_qDisorientation = mis ! found better one + enddo; enddo; enddo + case (0_pInt) + if (lattice_qDisorientation(1) < 0.0_pReal) lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg + end select + +end function lattice_qDisorientation + +end module lattice