diff --git a/code/lattice.f90 b/code/lattice.f90 deleted file mode 100644 index 9319a6403..000000000 --- a/code/lattice.f90 +++ /dev/null @@ -1,1452 +0,0 @@ -!-------------------------------------------------------------------------------------------------- -! $Id$ -!-------------------------------------------------------------------------------------------------- -!> @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_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