!-------------------------------------------------------------------------------------------------- !> @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 = 13_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_maxNcleavageFamily = 3_pInt !< max # of transformation system families 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 lattice_NcleavageSystem !< 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 lattice_interactionSlipTrans, & !< Slip--trans interaction type lattice_interactionTransSlip, & !< Trans--slip interaction type lattice_interactionTransTrans !< Trans--trans interaction type real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: & lattice_Sslip, & !< Schmid and non-Schmid matrices lattice_Scleavage !< Schmid matrices for cleavage systems real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & lattice_Sslip_v, & !< Mandel notation of lattice_Sslip lattice_Scleavage_v !< Mandel notation of lattice_Scleavege 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_Strans_v, & !< Eigendeformation tensor in vector form lattice_projectionTrans !< Matrix for projection of slip to fault-band (twin) systems for strain-induced martensite nucleation real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & lattice_Qtrans, & !< Total rotation: Q = R*B lattice_Strans !< Eigendeformation tensor for phase transformation real(pReal), allocatable, dimension(:,:), protected, public :: & lattice_shearTwin, & !< characteristic twin shear lattice_shearTrans !< characteristic transformation shear integer(pInt), allocatable, dimension(:), protected, public :: & lattice_NnonSchmid !< total # of non-Schmid contributions for each structure !-------------------------------------------------------------------------------------------------- ! face centered cubic integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],pInt) !< # of slip systems per family for fcc integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< # of twin systems per family for fcc integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_fcc_NtransSystem = int([12, 0],pInt) !< # of transformation systems per family for fcc integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: & LATTICE_fcc_NcleavageSystem = int([3, 4, 0],pInt) !< # of cleavage 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 = 12_pInt, & !sum(lattice_fcc_NtransSystem), & !< total # of transformation systems for fcc LATTICE_fcc_Ncleavage = 7_pInt !sum(lattice_fcc_NcleavageSystem) !< total # of cleavage systems 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(3+3,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fccTohex_systemTrans = 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_Ntrans]) 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 integer(pInt), dimension(LATTICE_fcc_Nslip,LATTICE_fcc_Ntrans), parameter, public :: & LATTICE_fccTohex_interactionSlipTrans = reshape(int( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> trans 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_Ntrans],order=[2,1]) !< Slip--trans interaction types for fcc integer(pInt), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Nslip), parameter, public :: & LATTICE_fccTohex_interactionTransSlip = 1_pInt !< Trans--Slip interaction types for fcc integer(pInt), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans), parameter,public :: & LATTICE_fccTohex_interactionTransTrans = reshape(int( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> trans 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 trans 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_Ntrans,LATTICE_fcc_Ntrans],order=[2,1]) !< Trans--trans interaction types for fcc real(pReal), dimension(LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fccTohex_shearTrans = sqrt(2.0_pReal)/4.0_pReal real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fccTobcc_systemTrans = reshape([& 0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3) 0.0, 1.0, 0.0, -10.26, & 0.0, 0.0, 1.0, 10.26, & 0.0, 0.0, 1.0, -10.26, & 1.0, 0.0, 0.0, 10.26, & 1.0, 0.0, 0.0, -10.26, & 0.0, 0.0, 1.0, 10.26, & 0.0, 0.0, 1.0, -10.26, & 1.0, 0.0, 0.0, 10.26, & 1.0, 0.0, 0.0, -10.26, & 0.0, 1.0, 0.0, 10.26, & 0.0, 1.0, 0.0, -10.26 & ],[ 4_pInt,LATTICE_fcc_Ntrans]) integer(pInt), dimension(9,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fccTobcc_bainVariant = reshape(int( [& 1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3) 1, 0, 0, 0, 1, 0, 0, 0, 1, & 1, 0, 0, 0, 1, 0, 0, 0, 1, & 1, 0, 0, 0, 1, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 1, 0, 1, 0, 0, 0, 0, 1, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0, & 0, 0, 1, 1, 0, 0, 0, 1, 0 & ],pInt),[ 9_pInt, LATTICE_fcc_Ntrans]) real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fccTobcc_bainRot = reshape([& 1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant 1.0, 0.0, 0.0, 45.0, & 1.0, 0.0, 0.0, 45.0, & 1.0, 0.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 1.0, 0.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0, & 0.0, 0.0, 1.0, 45.0 & ],[ 4_pInt,LATTICE_fcc_Ntrans]) real(pReal), dimension(LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans), parameter, private :: & ! Matrix for projection of shear from slip system to fault-band (twin) systems LATTICE_fccTobcc_projectionTrans = reshape(real([& ! For ns = nt = nr 0, 1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, & -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, & 1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, & 0, 0, 0, 0, 1,-1, 0, 0, 0, 0, 0, 0, & 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, & 0, 0, 0, 1,-1, 0, 0, 0, 0, 0, 0, 0, & 0, 0, 0, 0, 0, 0, 0, 1,-1, 0, 0, 0, & 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, & 0, 0, 0, 0, 0, 0, 1,-1, 0, 0, 0, 0, & 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, & 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, & 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 0 & ],pReal),[LATTICE_fcc_Ntrans,LATTICE_fcc_Ntrans],order=[2,1]) real(pReal), parameter, private :: & LATTICE_fccTobcc_projectionTransFactor = sqrt(3.0_pReal/4.0_pReal) real(pReal), parameter, public :: & LATTICE_fccTobcc_shearCritTrans = 0.0224 integer(pInt), dimension(2_pInt,LATTICE_fcc_Ntrans), parameter, public :: & LATTICE_fccTobcc_transNucleationTwinPair = reshape(int( [& 4, 7, & 1, 10, & 1, 4, & 7, 10, & 2, 8, & 5, 11, & 8, 11, & 2, 5, & 6, 12, & 3, 9, & 3, 12, & 6, 9 & ],pInt),[2_pInt,LATTICE_fcc_Ntrans]) real(pReal), dimension(3+3,LATTICE_fcc_Ncleavage), parameter, private :: & LATTICE_fcc_systemCleavage = reshape(real([& ! Cleavage direction Plane normal 0, 1, 0, 1, 0, 0, & 0, 0, 1, 0, 1, 0, & 1, 0, 0, 0, 0, 1, & 0, 1,-1, 1, 1, 1, & 0,-1,-1, -1,-1, 1, & -1, 0,-1, 1,-1,-1, & 0, 1, 1, -1, 1,-1 & ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ncleavage]) !-------------------------------------------------------------------------------------------------- ! body centered cubic integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & LATTICE_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], pInt) !< # of slip systems per family for bcc integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & LATTICE_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< # of twin systems per family for bcc integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_bcc_NtransSystem = int([0,0],pInt) !< # of transformation systems per family for bcc integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: & LATTICE_bcc_NcleavageSystem = int([3,6,0],pInt) !< # of cleavage 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, & !< total # of non-Schmid contributions for bcc (A. Koester, A. Ma, A. Hartmaier 2012) LATTICE_bcc_Ntrans = 0_pInt, & !sum(lattice_bcc_NtransSystem), & !< total # of transformation systems for bcc LATTICE_bcc_Ncleavage = 9_pInt !sum(lattice_bcc_NcleavageSystem) !< total # of cleavage systems 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 real(pReal), dimension(3+3,LATTICE_bcc_Ncleavage), parameter, private :: & LATTICE_bcc_systemCleavage = reshape(real([& ! Cleavage direction Plane normal 0, 1, 0, 1, 0, 0, & 0, 0, 1, 0, 1, 0, & 1, 0, 0, 0, 0, 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, 1, 0, & 1, 1, 1, -1, 1, 0 & ],pReal),[ 3_pInt + 3_pInt,LATTICE_bcc_Ncleavage]) !-------------------------------------------------------------------------------------------------- ! hexagonal integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & lattice_hex_NslipSystem = int([ 3, 3, 3, 6, 12, 6, 0, 0, 0, 0, 0, 0, 0],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) !< # of transformation systems per family for hex integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: & LATTICE_hex_NcleavageSystem = int([3,0,0],pInt) !< # of cleavage 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, & !< total # of non-Schmid contributions for hex LATTICE_hex_Ntrans = 0_pInt, & !sum(lattice_hex_NtransSystem), & !< total # of transformation systems for hex LATTICE_hex_Ncleavage = 3_pInt !sum(lattice_hex_NcleavageSystem) !< total # of cleavage systems 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 (onion peel naming scheme) 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(4+4,LATTICE_hex_Ncleavage), parameter, private :: & LATTICE_hex_systemCleavage = reshape(real([& ! Cleavage direction Plane normal 2,-1,-1, 0, 0, 0, 0, 1, & 0, 0, 0, 1, 2,-1,-1, 0, & 0, 0, 0, 1, 0, 1,-1, 0 & ],pReal),[ 4_pInt + 4_pInt,LATTICE_hex_Ncleavage]) !-------------------------------------------------------------------------------------------------- ! body centered tetragonal integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & LATTICE_bct_NslipSystem = int([2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ],pInt) !< # of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009 integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & LATTICE_bct_NtwinSystem = int([0, 0, 0, 0], pInt) !< # of twin systems per family for bct integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_bct_NtransSystem = int([0,0],pInt) !< # of transformation systems per family for bct integer(pInt), dimension(LATTICE_maxNcleavageFamily), parameter, public :: & LATTICE_bct_NcleavageSystem = int([0,0,0],pInt) !< # of cleavage systems per family for bct integer(pInt), parameter, private :: & LATTICE_bct_Nslip = 52_pInt, & !sum(lattice_bct_NslipSystem), & !< total # of slip systems for bct LATTICE_bct_Ntwin = 0_pInt, & !sum(lattice_bct_NtwinSystem), & !< total # of twin systems for bct LATTICE_bct_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for bct LATTICE_bct_Ntrans = 0_pInt, & !sum(lattice_bct_NtransSystem), & !< total # of transformation systems for bct LATTICE_bct_Ncleavage = 0_pInt !sum(lattice_bct_NcleavageSystem) !< total # of cleavage systems for bct real(pReal), dimension(3+3,LATTICE_bct_Nslip), parameter, private :: & LATTICE_bct_systemSlip = reshape(real([& ! Slip direction Plane normal ! Slip family 1 {100)<001] (Bravais notation {hkl) @brief Module initialization !-------------------------------------------------------------------------------------------------- subroutine lattice_init use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use IO, only: & IO_open_file,& IO_open_jobFile_stat, & IO_countSections, & IO_error, & IO_timeStamp, & IO_EOF, & IO_read, & IO_lc, & IO_getTag, & IO_isBlank, & IO_stringPos, & IO_stringValue, & IO_floatValue use material, only: & material_configfile, & material_localFileExt, & material_partPhase use debug, only: & debug_level, & debug_lattice, & debug_levelBasic use numerics, only: & worldrank implicit none integer(pInt), parameter :: FILEUNIT = 200_pInt integer(pInt) :: Nphases character(len=65536) :: & tag = '', & line = '' integer(pInt), allocatable, dimension(:) :: chunkPos integer(pInt) :: section = 0_pInt,i real(pReal), dimension(:), allocatable :: & CoverA, & !!!!!!< c/a ratio for low symmetry type lattice CoverA_trans, & !< c/a ratio for transformed hex type lattice a_fcc, & !< lattice parameter a for fcc austenite a_bcc !< lattice paramater a for bcc martensite mainProcess: if (worldrank == 0) then write(6,'(/,a)') ' <<<+- lattice init -+>>>' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" endif mainProcess !-------------------------------------------------------------------------------------------------- ! consistency checks (required since ifort 15.0 does not support sum/maxval in parameter definition) if (LATTICE_maxNslip /= maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_Nslip,LATTICE_bct_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_bct_Nslip /= sum(lattice_bct_NslipSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bct_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_bct_Ntwin /= sum(lattice_bct_NtwinSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bct_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_bct_Ntrans /= sum(lattice_bct_NtransSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Ntrans') if (LATTICE_fcc_Ncleavage /= sum(lattice_fcc_NcleavageSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ncleavage') if (LATTICE_bcc_Ncleavage /= sum(lattice_bcc_NcleavageSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ncleavage') if (LATTICE_hex_Ncleavage /= sum(lattice_hex_NcleavageSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ncleavage') if (LATTICE_bct_Ncleavage /= sum(lattice_bct_NcleavageSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bct_Ncleavage') if (LATTICE_iso_Ncleavage /= sum(lattice_iso_NcleavageSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_iso_Ncleavage') if (LATTICE_maxNinteraction /= max(& maxval(lattice_fcc_interactionSlipSlip), & maxval(lattice_bcc_interactionSlipSlip), & maxval(lattice_hex_interactionSlipSlip), & maxval(lattice_bct_interactionSlipSlip), & ! maxval(lattice_fcc_interactionSlipTwin), & maxval(lattice_bcc_interactionSlipTwin), & maxval(lattice_hex_interactionSlipTwin), & ! maxval(lattice_bct_interactionSlipTwin), & ! maxval(lattice_fcc_interactionTwinSlip), & maxval(lattice_bcc_interactionTwinSlip), & maxval(lattice_hex_interactionTwinSlip), & ! maxval(lattice_bct_interactionTwinSlip), & ! maxval(lattice_fcc_interactionTwinTwin), & maxval(lattice_bcc_interactionTwinTwin), & maxval(lattice_hex_interactionTwinTwin))) & ! maxval(lattice_bct_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(trans_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_trans_C66(6,6,Nphases), source=0.0_pReal) allocate(lattice_trans_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_damageDiffusion33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_vacancyfluxDiffusion33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_vacancyfluxMobility33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_PorosityDiffusion33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_hydrogenfluxDiffusion33(3,3,Nphases), source=0.0_pReal) allocate(lattice_hydrogenfluxMobility33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_damageMobility ( Nphases), source=0.0_pReal) allocate(lattice_PorosityMobility ( Nphases), source=0.0_pReal) allocate(lattice_massDensity ( Nphases), source=0.0_pReal) allocate(lattice_specificHeat ( Nphases), source=0.0_pReal) allocate(lattice_vacancyFormationEnergy ( Nphases), source=0.0_pReal) allocate(lattice_vacancySurfaceEnergy ( Nphases), source=0.0_pReal) allocate(lattice_vacancyVol ( Nphases), source=0.0_pReal) allocate(lattice_hydrogenFormationEnergy( Nphases), source=0.0_pReal) allocate(lattice_hydrogenSurfaceEnergy ( Nphases), source=0.0_pReal) allocate(lattice_hydrogenVol ( Nphases), source=0.0_pReal) allocate(lattice_referenceTemperature ( Nphases), source=300.0_pReal) allocate(lattice_equilibriumVacancyConcentration(Nphases), source=0.0_pReal) allocate(lattice_equilibriumHydrogenConcentration(Nphases),source=0.0_pReal) allocate(lattice_mu(Nphases), source=0.0_pReal) allocate(lattice_nu(Nphases), source=0.0_pReal) allocate(lattice_trans_mu(Nphases), source=0.0_pReal) allocate(lattice_trans_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_Scleavage(3,3,3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_Scleavage_v(6,3,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_shearTrans(lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Qtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Strans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Strans_v(6,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_projectionTrans(lattice_maxNtrans,lattice_maxNtrans,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_NcleavageSystem(lattice_maxNcleavageFamily,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(lattice_interactionSlipTrans(lattice_maxNslip,lattice_maxNtrans,Nphases),source=0_pInt) ! other:me allocate(lattice_interactionTransSlip(lattice_maxNtrans,lattice_maxNslip,Nphases),source=0_pInt) ! other:me allocate(lattice_interactionTransTrans(lattice_maxNtrans,lattice_maxNtrans,Nphases),source=0_pInt) ! other:me allocate(CoverA(Nphases),source=0.0_pReal) allocate(CoverA_trans(Nphases),source=0.0_pReal) allocate(a_fcc(Nphases),source=0.0_pReal) allocate(a_bcc(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 chunkPos = IO_stringPos(line) tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key select case(tag) case ('lattice_structure') select case(trim(IO_lc(IO_stringValue(line,chunkPos,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('bct') lattice_structure(section) = LATTICE_bct_ID case('ort','orthorhombic') lattice_structure(section) = LATTICE_ort_ID case default call IO_error(130_pInt,ext_msg=trim(IO_lc(IO_stringValue(line,chunkPos,2_pInt)))) end select case('trans_lattice_structure') select case(trim(IO_lc(IO_stringValue(line,chunkPos,2_pInt)))) case('bcc') trans_lattice_structure(section) = LATTICE_bcc_ID case('hex','hexagonal','hcp') trans_lattice_structure(section) = LATTICE_hex_ID end select case ('c11') lattice_C66(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c12') lattice_C66(1,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c13') lattice_C66(1,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c22') lattice_C66(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c23') lattice_C66(2,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c33') lattice_C66(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c44') lattice_C66(4,4,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c55') lattice_C66(5,5,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c66') lattice_C66(6,6,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c11_trans') lattice_trans_C66(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c12_trans') lattice_trans_C66(1,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c13_trans') lattice_trans_C66(1,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c22_trans') lattice_trans_C66(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c23_trans') lattice_trans_C66(2,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c33_trans') lattice_trans_C66(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c44_trans') lattice_trans_C66(4,4,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c55_trans') lattice_trans_C66(5,5,section) = IO_floatValue(line,chunkPos,2_pInt) case ('c66_trans') lattice_trans_C66(6,6,section) = IO_floatValue(line,chunkPos,2_pInt) case ('covera_ratio','c/a_ratio','c/a') CoverA(section) = IO_floatValue(line,chunkPos,2_pInt) case ('c/a_trans','c/a_martensite','c/a_mart') CoverA_trans(section) = IO_floatValue(line,chunkPos,2_pInt) case ('a_fcc') a_fcc(section) = IO_floatValue(line,chunkPos,2_pInt) case ('a_bcc') a_bcc(section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_conductivity11') lattice_thermalConductivity33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_conductivity22') lattice_thermalConductivity33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_conductivity33') lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_expansion11') lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_expansion22') lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('thermal_expansion33') lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('specific_heat') lattice_specificHeat(section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyformationenergy') lattice_vacancyFormationEnergy(section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancysurfaceenergy') lattice_vacancySurfaceEnergy(section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyvolume') lattice_vacancyVol(section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenformationenergy') lattice_hydrogenFormationEnergy(section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogensurfaceenergy') lattice_hydrogenSurfaceEnergy(section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenvolume') lattice_hydrogenVol(section) = IO_floatValue(line,chunkPos,2_pInt) case ('mass_density') lattice_massDensity(section) = IO_floatValue(line,chunkPos,2_pInt) case ('reference_temperature') lattice_referenceTemperature(section) = IO_floatValue(line,chunkPos,2_pInt) case ('damage_diffusion11') lattice_DamageDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('damage_diffusion22') lattice_DamageDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('damage_diffusion33') lattice_DamageDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('damage_mobility') lattice_DamageMobility(section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_diffusion11') lattice_vacancyfluxDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_diffusion22') lattice_vacancyfluxDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_diffusion33') lattice_vacancyfluxDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_mobility11') lattice_vacancyfluxMobility33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_mobility22') lattice_vacancyfluxMobility33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancyflux_mobility33') lattice_vacancyfluxMobility33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('porosity_diffusion11') lattice_PorosityDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('porosity_diffusion22') lattice_PorosityDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('porosity_diffusion33') lattice_PorosityDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('porosity_mobility') lattice_PorosityMobility(section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_diffusion11') lattice_hydrogenfluxDiffusion33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_diffusion22') lattice_hydrogenfluxDiffusion33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_diffusion33') lattice_hydrogenfluxDiffusion33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_mobility11') lattice_hydrogenfluxMobility33(1,1,section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_mobility22') lattice_hydrogenfluxMobility33(2,2,section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogenflux_mobility33') lattice_hydrogenfluxMobility33(3,3,section) = IO_floatValue(line,chunkPos,2_pInt) case ('vacancy_eqcv') lattice_equilibriumVacancyConcentration(section) = IO_floatValue(line,chunkPos,2_pInt) case ('hydrogen_eqch') lattice_equilibriumHydrogenConcentration(section) = IO_floatValue(line,chunkPos,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(131_pInt,el=i) ! checking physical significance of c/a if ((CoverA(i) > 2.0_pReal) & .and. lattice_structure(i) == LATTICE_bct_ID) call IO_error(131_pInt,el=i) ! checking physical significance of c/a call lattice_initializeStructure(i, CoverA(i), CoverA_trans(i), a_fcc(i), a_bcc(i)) enddo deallocate(CoverA,CoverA_trans,a_fcc,a_bcc) end subroutine lattice_init !-------------------------------------------------------------------------------------------------- !> @brief Calculation of Schmid matrices, etc. !-------------------------------------------------------------------------------------------------- subroutine lattice_initializeStructure(myPhase,CoverA,CoverA_trans,a_fcc,a_bcc) use prec, only: & tol_math_check use math, only: & math_crossproduct, & math_tensorproduct33, & math_mul33x33, & math_mul33x3, & math_transpose33, & math_trace33, & math_symmetric33, & math_Mandel33to6, & math_Mandel3333to66, & math_Voigt66to3333, & math_axisAngleToR, & INRAD, & MATH_I3 use IO, only: & IO_error, & IO_warning implicit none integer(pInt), intent(in) :: myPhase real(pReal), intent(in) :: & CoverA, & CoverA_trans, & a_fcc, & a_bcc real(pReal), dimension(3) :: & sdU, snU, & np, nn real(pReal), dimension(3,3) :: & sstr, sdtr, sttr 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 real(pReal), dimension(lattice_maxNtrans) :: & trs real(pReal), dimension(3,lattice_maxNtrans) :: & xtr, ytr, ztr real(pReal), dimension(3,3,lattice_maxNtrans) :: & Rtr, Utr, Btr, Qtr, Str real(pReal), dimension(3,lattice_maxNcleavage) :: & cd, cn, ct integer(pInt) :: & i,j, & myNslip = 0_pInt, myNtwin = 0_pInt, myNtrans = 0_pInt, myNcleavage = 0_pInt real(pReal) :: c11bar, c12bar, c13bar, c14bar, c33bar, c44bar, A, B 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)) 0.0_pReal) .and. (a_bcc > 0.0_pReal)) then Utr(1:3,1:3,i) = (a_bcc/a_fcc)*math_tensorproduct33(xtr(1:3,i), xtr(1:3,i)) + & sqrt(2.0_pReal)*(a_bcc/a_fcc)*math_tensorproduct33(ytr(1:3,i), ytr(1:3,i)) + & sqrt(2.0_pReal)*(a_bcc/a_fcc)*math_tensorproduct33(ztr(1:3,i), ztr(1:3,i)) endif Qtr(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), Btr(1:3,1:3,i)) Str(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), Utr(1:3,1:3,i)) - MATH_I3 enddo case (LATTICE_hex_ID) sstr(1:3,1:3) = MATH_I3 sstr(1,3) = sqrt(2.0_pReal)/4.0_pReal sdtr(1:3,1:3) = MATH_I3 if (CoverA_trans > 1.0_pReal .and. CoverA_trans < 2.0_pReal) then sdtr(3,3) = CoverA_trans/sqrt(8.0_pReal/3.0_pReal) endif sttr = math_mul33x33(sdtr, sstr) do i = 1_pInt,myNtrans xtr(1:3,i) = lattice_fccTohex_systemTrans(1:3,i)/norm2(lattice_fccTohex_systemTrans(1:3,i)) ztr(1:3,i) = lattice_fccTohex_systemTrans(4:6,i)/norm2(lattice_fccTohex_systemTrans(4:6,i)) ytr(1:3,i) = -math_crossproduct(xtr(1:3,i), ztr(1:3,i)) Rtr(1:3,1,i) = xtr(1:3,i) Rtr(1:3,2,i) = ytr(1:3,i) Rtr(1:3,3,i) = ztr(1:3,i) Qtr(1:3,1:3,i) = Rtr(1:3,1:3,i) Str(1:3,1:3,i) = math_mul33x33(Rtr(1:3,1:3,i), math_mul33x33(sttr, math_transpose33(Rtr(1:3,1:3,i)))) Str(1:3,1:3,i) = Str(1:3,1:3,i) - MATH_I3 trs(i) = lattice_fccTohex_shearTrans(i) enddo case default Qtr = 0.0_pReal Str = 0.0_pReal end select lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_fcc_NslipSystem lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_fcc_NtwinSystem lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_fcc_NtransSystem lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_fcc_NcleavageSystem lattice_NnonSchmid(myPhase) = lattice_fcc_NnonSchmid lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_fcc_interactionSlipSlip lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_fcc_interactionSlipTwin lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_fcc_interactionTwinSlip lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_fcc_interactionTwinTwin lattice_interactionSlipTrans(1:myNslip,1:myNtrans,myPhase) = lattice_fccTohex_interactionSlipTrans lattice_interactionTransSlip(1:myNtrans,1:myNslip,myPhase) = lattice_fccTohex_interactionTransSlip lattice_interactionTransTrans(1:myNtrans,1:myNtrans,myPhase) = lattice_fccTohex_interactionTransTrans lattice_projectionTrans(1:myNtrans,1:myNtrans,myPhase) = LATTICE_fccTobcc_projectionTrans*& LATTICE_fccTobcc_projectionTransFactor !-------------------------------------------------------------------------------------------------- ! bcc case (LATTICE_bcc_ID) myNslip = lattice_bcc_Nslip myNtwin = lattice_bcc_Ntwin myNtrans = lattice_bcc_Ntrans myNcleavage = lattice_bcc_Ncleavage do i = 1_pInt,myNslip ! assign slip system vectors sd(1:3,i) = lattice_bcc_systemSlip(1:3,i) sn(1:3,i) = lattice_bcc_systemSlip(4:6,i) sdU = sd(1:3,i) / norm2(sd(1:3,i)) snU = sn(1:3,i) / norm2(sn(1:3,i)) ! "np" and "nn" according to Gröger_etal2008, Acta Materialia 56 (2008) 5412–5425, table 1 (corresponds to their "n1" for positive and negative slip direction respectively) np = math_mul33x3(math_axisAngleToR(sdU,60.0_pReal*INRAD), snU) nn = math_mul33x3(math_axisAngleToR(-sdU,60.0_pReal*INRAD), snU) ! Schmid matrices with non-Schmid contributions according to Koester_etal2012, Acta Materialia 60 (2012) 3894–3901, eq. (17) ("n1" is replaced by either "np" or "nn" according to either positive or negative slip direction) sns(1:3,1:3,1,1,i) = math_tensorproduct33(sdU, np) sns(1:3,1:3,2,1,i) = math_tensorproduct33(-sdU, nn) sns(1:3,1:3,1,2,i) = math_tensorproduct33(math_crossproduct(snU, sdU), snU) sns(1:3,1:3,2,2,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), snU) sns(1:3,1:3,1,3,i) = math_tensorproduct33(math_crossproduct(np, sdU), np) sns(1:3,1:3,2,3,i) = math_tensorproduct33(math_crossproduct(nn, -sdU), nn) sns(1:3,1:3,1,4,i) = math_tensorproduct33(snU, snU) sns(1:3,1:3,2,4,i) = math_tensorproduct33(snU, snU) sns(1:3,1:3,1,5,i) = math_tensorproduct33(math_crossproduct(snU, sdU), math_crossproduct(snU, sdU)) sns(1:3,1:3,2,5,i) = math_tensorproduct33(math_crossproduct(snU, -sdU), math_crossproduct(snU, -sdU)) sns(1:3,1:3,1,6,i) = math_tensorproduct33(sdU, sdU) sns(1:3,1:3,2,6,i) = math_tensorproduct33(-sdU, -sdU) enddo do i = 1_pInt,myNtwin ! assign twin system vectors and shears td(1:3,i) = lattice_bcc_systemTwin(1:3,i) tn(1:3,i) = lattice_bcc_systemTwin(4:6,i) ts(i) = lattice_bcc_shearTwin(i) enddo do i = 1_pInt, myNcleavage ! assign cleavage system vectors cd(1:3,i) = lattice_bcc_systemCleavage(1:3,i)/norm2(lattice_bcc_systemCleavage(1:3,i)) cn(1:3,i) = lattice_bcc_systemCleavage(4:6,i)/norm2(lattice_bcc_systemCleavage(4:6,i)) ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i)) enddo lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_bcc_NslipSystem lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_bcc_NtwinSystem lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_bcc_NtransSystem lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_bcc_NcleavageSystem lattice_NnonSchmid(myPhase) = lattice_bcc_NnonSchmid lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_bcc_interactionSlipSlip lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_bcc_interactionSlipTwin lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_bcc_interactionTwinSlip lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_bcc_interactionTwinTwin !-------------------------------------------------------------------------------------------------- ! hex (including conversion from miller-bravais (a1=a2=a3=c) to miller (a, b, c) indices) case (LATTICE_hex_ID) myNslip = lattice_hex_Nslip myNtwin = lattice_hex_Ntwin myNtrans = lattice_hex_Ntrans myNcleavage = lattice_hex_Ncleavage do i = 1_pInt,myNslip ! assign slip system vectors sd(1,i) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)] sd(2,i) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*& 0.5_pReal*sqrt(3.0_pReal) sd(3,i) = lattice_hex_systemSlip(4,i)*CoverA sn(1,i) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) sn(2,i) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/sqrt(3.0_pReal) sn(3,i) = lattice_hex_systemSlip(8,i)/CoverA 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 do i = 1_pInt, myNcleavage ! cleavage system vectors cd(1,i) = lattice_hex_systemCleavage(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)] cd(2,i) = (lattice_hex_systemCleavage(1,i)+2.0_pReal*lattice_hex_systemCleavage(2,i))*& 0.5_pReal*sqrt(3.0_pReal) cd(3,i) = lattice_hex_systemCleavage(4,i)*CoverA cd(1:3,1) = cd(1:3,i)/norm2(cd(1:3,i)) cn(1,i) = lattice_hex_systemCleavage(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) cn(2,i) = (lattice_hex_systemCleavage(5,i)+2.0_pReal*lattice_hex_systemCleavage(6,i))/sqrt(3.0_pReal) cn(3,i) = lattice_hex_systemCleavage(8,i)/CoverA cn(1:3,1) = cn(1:3,i)/norm2(cn(1:3,i)) ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i)) 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_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_hex_NcleavageSystem 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 !-------------------------------------------------------------------------------------------------- ! bct case (LATTICE_bct_ID) myNslip = lattice_bct_Nslip myNtwin = lattice_bct_Ntwin myNcleavage = lattice_bct_Ncleavage do i = 1_pInt,myNslip ! assign slip system vectors sd(1:2,i) = lattice_bct_systemSlip(1:2,i) sd(3,i) = lattice_bct_systemSlip(3,i)*CoverA sn(1:2,i) = lattice_bct_systemSlip(4:5,i) sn(3,i) = lattice_bct_systemSlip(6,i)/CoverA sdU = sd(1:3,i) / norm2(sd(1:3,i)) snU = sn(1:3,i) / norm2(sn(1:3,i)) enddo lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_bct_NslipSystem lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_bct_NtwinSystem lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_bct_NtransSystem lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_bct_NcleavageSystem lattice_NnonSchmid(myPhase) = lattice_bct_NnonSchmid lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_bct_interactionSlipSlip !-------------------------------------------------------------------------------------------------- ! orthorhombic (no crystal plasticity) case (LATTICE_ort_ID) myNslip = 0_pInt myNtwin = 0_pInt myNtrans = 0_pInt myNcleavage = lattice_ortho_Ncleavage do i = 1_pInt, myNcleavage ! assign cleavage system vectors cd(1:3,i) = lattice_iso_systemCleavage(1:3,i)/norm2(LATTICE_ortho_systemCleavage(1:3,i)) cn(1:3,i) = lattice_iso_systemCleavage(4:6,i)/norm2(LATTICE_ortho_systemCleavage(4:6,i)) ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i)) enddo lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_iso_NcleavageSystem !-------------------------------------------------------------------------------------------------- ! isotropic (no crystal plasticity) case (LATTICE_iso_ID) myNslip = 0_pInt myNtwin = 0_pInt myNtrans = 0_pInt myNcleavage = lattice_iso_Ncleavage do i = 1_pInt, myNcleavage ! assign cleavage system vectors cd(1:3,i) = lattice_iso_systemCleavage(1:3,i)/norm2(lattice_iso_systemCleavage(1:3,i)) cn(1:3,i) = lattice_iso_systemCleavage(4:6,i)/norm2(lattice_iso_systemCleavage(4:6,i)) ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i)) enddo lattice_NcleavageSystem(1:lattice_maxNcleavageFamily,myPhase) = lattice_iso_NcleavageSystem !-------------------------------------------------------------------------------------------------- ! something went wrong case default call IO_error(130_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)/norm2(sd(1:3,i)) ! make unit vector lattice_sn(1:3,i,myPhase) = sn(1:3,i)/norm2(sn(1:3,i)) ! make unit vector lattice_st(1:3,i,myPhase) = math_crossproduct(lattice_sd(1:3,i,myPhase), & lattice_sn(1:3,i,myPhase)) lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct33(lattice_sd(1:3,i,myPhase), & lattice_sn(1:3,i,myPhase)) ! calculate Schmid matrix d \otimes n 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)/norm2(td(1:3,i)) ! make unit vector lattice_tn(1:3,i,myPhase) = tn(1:3,i)/norm2(tn(1:3,i)) ! make unit vector lattice_tt(1:3,i,myPhase) = math_crossproduct(lattice_td(1:3,i,myPhase), & lattice_tn(1:3,i,myPhase)) lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct33(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 do i = 1_pInt,myNtrans lattice_Qtrans(1:3,1:3,i,myPhase) = Qtr(1:3,1:3,i) lattice_Strans(1:3,1:3,i,myPhase) = Str(1:3,1:3,i) lattice_Strans_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Strans(1:3,1:3,i,myPhase))) lattice_shearTrans(i,myPhase) = trs(i) enddo do i = 1_pInt,myNcleavage ! store slip system vectors and Schmid matrix for my structure lattice_Scleavage(1:3,1:3,1,i,myPhase) = math_tensorproduct33(cd(1:3,i),cn(1:3,i)) lattice_Scleavage(1:3,1:3,2,i,myPhase) = math_tensorproduct33(ct(1:3,i),cn(1:3,i)) lattice_Scleavage(1:3,1:3,3,i,myPhase) = math_tensorproduct33(cn(1:3,i),cn(1:3,i)) do j = 1_pInt,3_pInt lattice_Scleavage_v(1:6,j,i,myPhase) = & math_Mandel33to6(math_symmetric33(lattice_Scleavage(1:3,1:3,j,i,myPhase))) enddo 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 (LATTICE_bct_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) = C66(6,6) !J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962 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) :: 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_bct_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 prec, only: & prec_isNaN 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(prec_isNaN(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 and hexagonal 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