!-------------------------------------------------------------------------------------------------- !> @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 ! BEGIN DEPRECATED 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 = 1_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 lattice_Qtrans, & !< Total rotation: Q = R*B lattice_Strans, & !< Eigendeformation tensor for phase transformation lattice_Stwin, & lattice_Qtwin real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_sn, & !< normal direction of slip system lattice_st, & !< sd x sn lattice_sd, & !< slip direction of slip system lattice_Stwin_v, & 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_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 real(pReal), allocatable, dimension(:,:,:), private :: & lattice_tn, & lattice_td, & lattice_tt ! END DEPRECATED !-------------------------------------------------------------------------------------------------- ! 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],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 = sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc LATTICE_fcc_Ntwin = 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 = sum(lattice_fcc_NtransSystem), & !< total # of transformation systems for fcc LATTICE_fcc_Ncleavage = 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 ! SCHMID-BOAS notation 0, 1,-1, 1, 1, 1, & ! B2 -1, 0, 1, 1, 1, 1, & ! B4 1,-1, 0, 1, 1, 1, & ! B5 0,-1,-1, -1,-1, 1, & ! C1 1, 0, 1, -1,-1, 1, & ! C3 -1, 1, 0, -1,-1, 1, & ! C5 0,-1, 1, 1,-1,-1, & ! A2 -1, 0,-1, 1,-1,-1, & ! A3 1, 1, 0, 1,-1,-1, & ! A6 0, 1, 1, -1, 1,-1, & ! D1 1, 0,-1, -1, 1,-1, & ! D4 -1,-1, 0, -1, 1,-1 & ! D6 ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Nslip]) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli character(len=*), dimension(1), parameter, public :: LATTICE_FCC_SLIPFAMILY_NAME = & ['<0 1 -1>{1 1 1}'] 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 character(len=*), dimension(1), parameter, public :: LATTICE_FCC_TWINFAMILY_NAME = & ['<-2 1 1>{1 1 1}'] 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],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 = sum(lattice_bcc_NslipSystem), & !< total # of slip systems for bcc LATTICE_bcc_Ntwin = 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 = sum(lattice_bcc_NtransSystem), & !< total # of transformation systems for bcc LATTICE_bcc_Ncleavage = 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]) character(len=*), dimension(2), parameter, public :: LATTICE_BCC_SLIPFAMILY_NAME = & ['<1 -1 1>{0 1 1}', & '<1 -1 1>{2 1 1}'] 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]) character(len=*), dimension(1), parameter, public :: LATTICE_BCC_TWINFAMILY_NAME = & ['<1 1 1>{2 1 1}'] 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],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 = sum(lattice_hex_NslipSystem), & !< total # of slip systems for hex LATTICE_hex_Ntwin = 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 = sum(lattice_hex_NtransSystem), & !< total # of transformation systems for hex LATTICE_hex_Ncleavage = 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 character(len=*), dimension(6), parameter, public :: LATTICE_HEX_SLIPFAMILY_NAME = & ['<1 1 . 1>{0 0 . 1} ', & '<1 1 . 1>{1 0 . 0} ', & '<1 0 . 0>{1 1 . 0} ', & '<1 1 . 0>{-1 1 . 1} ', & '<1 1 . 3>{-1 0 . 1} ', & '<1 1 . 3>{-1 -1 . 2}'] 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 character(len=*), dimension(4), parameter, public :: LATTICE_HEX_TWINFAMILY_NAME = & ['<-1 0 . 1>{1 0 . 2} ', & '<1 1 . 6>{-1 -1 . 1}', & '<1 0 . -2>{1 0 . 1} ', & '<1 1 . -3>{1 1 . 2} '] 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],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 = sum(lattice_bct_NslipSystem), & !< total # of slip systems for bct LATTICE_bct_Ntwin = 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 = sum(lattice_bct_NtransSystem), & !< total # of transformation systems for bct LATTICE_bct_Ncleavage = 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 #if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800 use, intrinsic :: iso_fortran_env, only: & compiler_version, & compiler_options #endif use IO, only: & IO_error, & IO_timeStamp use config, only: & config_phase implicit none integer(pInt) :: Nphases character(len=65536) :: & tag = '' integer(pInt) :: i,p real(pReal), dimension(:), allocatable :: & temp, & 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 write(6,'(/,a)') ' <<<+- lattice init -+>>>' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" Nphases = size(config_phase) 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(temp66(6,6,Nphases), source=0.0_pReal) allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal) allocate(lattice_trans_C3333(3,3,3,3,Nphases), source=0.0_pReal) allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients allocate(lattice_thermalConductivity33 (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_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_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_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) 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_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) do p = 1, size(config_phase) tag = config_phase(p)%getString('lattice_structure') select case(trim(tag)) case('iso','isotropic') lattice_structure(p) = LATTICE_iso_ID case('fcc') lattice_structure(p) = LATTICE_fcc_ID case('bcc') lattice_structure(p) = LATTICE_bcc_ID case('hex','hexagonal') lattice_structure(p) = LATTICE_hex_ID case('bct') lattice_structure(p) = LATTICE_bct_ID case('ort','orthorhombic') lattice_structure(p) = LATTICE_ort_ID end select tag = 'undefined' tag = config_phase(p)%getString('trans_lattice_structure',defaultVal=tag) select case(trim(tag)) case('bcc') trans_lattice_structure(p) = LATTICE_bcc_ID case('hex','hexagonal') trans_lattice_structure(p) = LATTICE_hex_ID end select lattice_C66(1,1,p) = config_phase(p)%getFloat('c11',defaultVal=0.0_pReal) lattice_C66(1,2,p) = config_phase(p)%getFloat('c12',defaultVal=0.0_pReal) lattice_C66(1,3,p) = config_phase(p)%getFloat('c13',defaultVal=0.0_pReal) lattice_C66(2,2,p) = config_phase(p)%getFloat('c22',defaultVal=0.0_pReal) lattice_C66(2,3,p) = config_phase(p)%getFloat('c23',defaultVal=0.0_pReal) lattice_C66(3,3,p) = config_phase(p)%getFloat('c33',defaultVal=0.0_pReal) lattice_C66(4,4,p) = config_phase(p)%getFloat('c44',defaultVal=0.0_pReal) lattice_C66(5,5,p) = config_phase(p)%getFloat('c55',defaultVal=0.0_pReal) lattice_C66(6,6,p) = config_phase(p)%getFloat('c66',defaultVal=0.0_pReal) temp66(1,1,p) = config_phase(p)%getFloat('c11_trans',defaultVal=0.0_pReal) temp66(1,2,p) = config_phase(p)%getFloat('c12_trans',defaultVal=0.0_pReal) temp66(1,3,p) = config_phase(p)%getFloat('c13_trans',defaultVal=0.0_pReal) temp66(2,2,p) = config_phase(p)%getFloat('c22_trans',defaultVal=0.0_pReal) temp66(2,3,p) = config_phase(p)%getFloat('c23_trans',defaultVal=0.0_pReal) temp66(3,3,p) = config_phase(p)%getFloat('c33_trans',defaultVal=0.0_pReal) temp66(4,4,p) = config_phase(p)%getFloat('c44_trans',defaultVal=0.0_pReal) temp66(5,5,p) = config_phase(p)%getFloat('c55_trans',defaultVal=0.0_pReal) temp66(6,6,p) = config_phase(p)%getFloat('c66_trans',defaultVal=0.0_pReal) CoverA(p) = config_phase(p)%getFloat('c/a',defaultVal=0.0_pReal) CoverA_trans(p) = config_phase(p)%getFloat('c/a_trans',defaultVal=0.0_pReal) a_fcc(p) = config_phase(p)%getFloat('a_fcc',defaultVal=0.0_pReal) a_bcc(p) = config_phase(p)%getFloat('a_bcc',defaultVal=0.0_pReal) lattice_thermalConductivity33(1,1,p) = config_phase(p)%getFloat('thermal_conductivity11',defaultVal=0.0_pReal) lattice_thermalConductivity33(2,2,p) = config_phase(p)%getFloat('thermal_conductivity22',defaultVal=0.0_pReal) lattice_thermalConductivity33(3,3,p) = config_phase(p)%getFloat('thermal_conductivity33',defaultVal=0.0_pReal) temp = config_phase(p)%getFloats('thermal_expansion11',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(1,1,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion22',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(2,2,1:size(temp),p) = temp temp = config_phase(p)%getFloats('thermal_expansion33',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T) lattice_thermalExpansion33(3,3,1:size(temp),p) = temp lattice_specificHeat(p) = config_phase(p)%getFloat( 'specific_heat',defaultVal=0.0_pReal) lattice_vacancyFormationEnergy(p) = config_phase(p)%getFloat( 'vacancyformationenergy',defaultVal=0.0_pReal) lattice_vacancySurfaceEnergy(p) = config_phase(p)%getFloat( 'vacancyvolume',defaultVal=0.0_pReal) lattice_vacancyVol(p) = config_phase(p)%getFloat( 'vacancysurfaceenergy',defaultVal=0.0_pReal) lattice_hydrogenFormationEnergy(p) = config_phase(p)%getFloat( 'hydrogenformationenergy',defaultVal=0.0_pReal) lattice_hydrogenSurfaceEnergy(p) = config_phase(p)%getFloat( 'hydrogensurfaceenergy',defaultVal=0.0_pReal) lattice_hydrogenVol(p) = config_phase(p)%getFloat( 'hydrogenvolume',defaultVal=0.0_pReal) lattice_massDensity(p) = config_phase(p)%getFloat( 'mass_density',defaultVal=0.0_pReal) lattice_referenceTemperature(p) = config_phase(p)%getFloat( 'reference_temperature',defaultVal=0.0_pReal) lattice_DamageDiffusion33(1,1,p) = config_phase(p)%getFloat( 'damage_diffusion11',defaultVal=0.0_pReal) lattice_DamageDiffusion33(2,2,p) = config_phase(p)%getFloat( 'damage_diffusion22',defaultVal=0.0_pReal) lattice_DamageDiffusion33(3,3,p) = config_phase(p)%getFloat( 'damage_diffusion33',defaultVal=0.0_pReal) lattice_DamageMobility(p) = config_phase(p)%getFloat( 'damage_mobility',defaultVal=0.0_pReal) lattice_vacancyfluxDiffusion33(1,1,p) = config_phase(p)%getFloat( 'vacancyflux_diffusion11',defaultVal=0.0_pReal) lattice_vacancyfluxDiffusion33(2,2,p) = config_phase(p)%getFloat( 'vacancyflux_diffusion22',defaultVal=0.0_pReal) lattice_vacancyfluxDiffusion33(3,3,p) = config_phase(p)%getFloat( 'vacancyflux_diffusion33',defaultVal=0.0_pReal) lattice_vacancyfluxMobility33(1,1,p) = config_phase(p)%getFloat( 'vacancyflux_mobility11',defaultVal=0.0_pReal) lattice_vacancyfluxMobility33(2,2,p) = config_phase(p)%getFloat( 'vacancyflux_mobility22',defaultVal=0.0_pReal) lattice_vacancyfluxMobility33(3,3,p) = config_phase(p)%getFloat( 'vacancyflux_mobility33',defaultVal=0.0_pReal) lattice_PorosityDiffusion33(1,1,p) = config_phase(p)%getFloat( 'porosity_diffusion11',defaultVal=0.0_pReal) lattice_PorosityDiffusion33(2,2,p) = config_phase(p)%getFloat( 'porosity_diffusion22',defaultVal=0.0_pReal) lattice_PorosityDiffusion33(3,3,p) = config_phase(p)%getFloat( 'porosity_diffusion33',defaultVal=0.0_pReal) lattice_PorosityMobility(p) = config_phase(p)%getFloat( 'porosity_mobility',defaultVal=0.0_pReal) lattice_hydrogenfluxDiffusion33(1,1,p) = config_phase(p)%getFloat( 'hydrogenflux_diffusion11',defaultVal=0.0_pReal) lattice_hydrogenfluxDiffusion33(2,2,p) = config_phase(p)%getFloat( 'hydrogenflux_diffusion22',defaultVal=0.0_pReal) lattice_hydrogenfluxDiffusion33(3,3,p) = config_phase(p)%getFloat( 'hydrogenflux_diffusion33',defaultVal=0.0_pReal) lattice_hydrogenfluxMobility33(1,1,p) = config_phase(p)%getFloat( 'hydrogenflux_mobility11',defaultVal=0.0_pReal) lattice_hydrogenfluxMobility33(2,2,p) = config_phase(p)%getFloat( 'hydrogenflux_mobility22',defaultVal=0.0_pReal) lattice_hydrogenfluxMobility33(3,3,p) = config_phase(p)%getFloat( 'hydrogenflux_mobility33',defaultVal=0.0_pReal) lattice_equilibriumVacancyConcentration(p) = config_phase(p)%getFloat( 'vacancy_eqcv',defaultVal=0.0_pReal) lattice_equilibriumHydrogenConcentration(p) = config_phase(p)%getFloat( 'hydrogen_eqch',defaultVal=0.0_pReal) 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 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))bcc transformation') enddo case (LATTICE_hex_ID) c11bar = (lattice_C66(1,1,myPhase) + lattice_C66(1,2,myPhase) + 2.0_pReal*lattice_C66(4,4,myPhase))/2.0_pReal c12bar = (lattice_C66(1,1,myPhase) + 5.0_pReal*lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase))/6.0_pReal c33bar = (lattice_C66(1,1,myPhase) + 2.0_pReal*lattice_C66(1,2,myPhase) + 4.0_pReal*lattice_C66(4,4,myPhase))/3.0_pReal c13bar = (lattice_C66(1,1,myPhase) + 2.0_pReal*lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase))/3.0_pReal c44bar = (lattice_C66(1,1,myPhase) - lattice_C66(1,2,myPhase) + lattice_C66(4,4,myPhase))/3.0_pReal c14bar = (lattice_C66(1,1,myPhase) - lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase)) & /(3.0_pReal*sqrt(2.0_pReal)) A = c14bar**(2.0_pReal)/c44bar B = c14bar**(2.0_pReal)/(0.5_pReal*(c11bar - c12bar)) temp66(1,1,myPhase) = c11bar - A temp66(1,2,myPhase) = c12bar + A temp66(1,3,myPhase) = c13bar temp66(3,3,myPhase) = c33bar temp66(4,4,myPhase) = c44bar - B temp66(1:6,1:6,myPhase) = lattice_symmetrizeC66(trans_lattice_structure(myPhase),& temp66(1:6,1:6,myPhase)) lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(temp66(1:6,1:6,myPhase)) temp66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_trans_C3333(1:3,1:3,1:3,1:3,myPhase)) do i = 1_pInt, 6_pInt if (abs(temp66(i,i,myPhase))hex transformation') enddo end select end select forall (i = 1_pInt:3_pInt) & lattice_thermalExpansion33 (1:3,1:3,i,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_thermalExpansion33 (1:3,1:3,i,myPhase)) lattice_thermalConductivity33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_thermalConductivity33 (1:3,1:3,myPhase)) lattice_DamageDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_DamageDiffusion33 (1:3,1:3,myPhase)) lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_vacancyfluxDiffusion33 (1:3,1:3,myPhase)) lattice_vacancyfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_vacancyfluxMobility33 (1:3,1:3,myPhase)) lattice_PorosityDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_PorosityDiffusion33 (1:3,1:3,myPhase)) lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_hydrogenfluxDiffusion33(1:3,1:3,myPhase)) lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),& lattice_hydrogenfluxMobility33 (1:3,1:3,myPhase)) select case(lattice_structure(myPhase)) !-------------------------------------------------------------------------------------------------- ! fcc case (LATTICE_fcc_ID) myNslip = lattice_fcc_Nslip myNtwin = lattice_fcc_Ntwin myNtrans = lattice_fcc_Ntrans myNcleavage = lattice_fcc_Ncleavage do i = 1_pInt,myNslip ! assign slip system vectors sd(1:3,i) = lattice_fcc_systemSlip(1:3,i) sn(1:3,i) = lattice_fcc_systemSlip(4:6,i) enddo do i = 1_pInt,myNtwin ! assign twin system vectors and shears td(1:3,i) = lattice_fcc_systemTwin(1:3,i) tn(1:3,i) = lattice_fcc_systemTwin(4:6,i) ts(i) = lattice_fcc_shearTwin(i) enddo do i = 1_pInt, myNcleavage ! assign cleavage system vectors cd(1:3,i) = lattice_fcc_systemCleavage(1:3,i)/norm2(lattice_fcc_systemCleavage(1:3,i)) cn(1:3,i) = lattice_fcc_systemCleavage(4:6,i)/norm2(lattice_fcc_systemCleavage(4:6,i)) ct(1:3,i) = math_crossproduct(cd(1:3,i),cn(1:3,i)) enddo ! Phase transformation select case(trans_lattice_structure(myPhase)) case (LATTICE_bcc_ID) ! fcc to bcc transformation do i = 1_pInt,myNtrans Rtr(1:3,1:3,i) = math_axisAngleToR(lattice_fccTobcc_systemTrans(1:3,i), & ! Pitsch rotation lattice_fccTobcc_systemTrans(4,i)*INRAD) Btr(1:3,1:3,i) = math_axisAngleToR(lattice_fccTobcc_bainRot(1:3,i), & ! Rotation of fcc to Bain coordinate system lattice_fccTobcc_bainRot(4,i)*INRAD) xtr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(1:3,i),pReal) ytr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(4:6,i),pReal) ztr(1:3,i) = real(LATTICE_fccTobcc_bainVariant(7:9,i),pReal) Utr(1:3,1:3,i) = 0.0_pReal ! Bain deformation if ((a_fcc > 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, intrinsic :: & IEEE_arithmetic 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(IEEE_is_NaN(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 function lattice_C66_twin(Ntwin,C66,structure,CoverA) use IO, only: & IO_error use math, only: & INRAD, & math_axisAngleToR, & math_Mandel3333to66, & math_Mandel66to3333, & math_rotate_forward3333 implicit none integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(6,6), intent(in) :: C66 real(pReal), intent(in) :: cOverA real(pReal), dimension(6,6,sum(Ntwin)) :: lattice_C66_twin real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem real(pReal), dimension(3,3) :: R integer(pInt) :: i select case(structure) case('fcc') coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_FCC_SYSTEMTWIN,pInt),structure) case('bcc') coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_BCC_SYSTEMTWIN,pInt),structure) case('hex','hexagonal') !ToDo: "No alias policy": long or short? coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_HEX_SYSTEMTWIN,pInt),'hex',cOverA) case default call IO_error(130_pInt,ext_msg=trim(structure)//' (lattice_C66_twin)') end select do i = 1, sum(Ntwin) R = math_axisAngleToR(coordinateSystem(1:3,2,i), 180.0_pReal * INRAD) ! ToDo: Why always 180 deg? lattice_C66_twin(1:6,1:6,i) = math_Mandel3333to66(math_rotate_forward3333(math_Mandel66to3333(C66),R)) enddo end function function lattice_C66_trans(Ntrans,C66_parent,structure_parent,cOverA_parent, & C66_target,structure_target,cOverA_target) use IO, only: & IO_error use math, only: & INRAD, & math_axisAngleToR, & math_Mandel3333to66, & math_Mandel66to3333, & math_rotate_forward3333 implicit none integer(pInt), dimension(:), intent(in) :: Ntrans !< number of active twin systems per family character(len=*), intent(in) :: & structure_target, & !< lattice structure structure_parent !< lattice structure real(pReal), dimension(6,6), intent(in) :: C66_target, C66_parent real(pReal), intent(in) :: cOverA_parent, cOverA_target real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans, C_bar66, C_target_unrotated66 real(pReal), dimension(3,3,sum(Ntrans)) :: coordinateSystem real(pReal), dimension(3,3) :: R real(pReal) :: A, B integer(pInt) :: i ! if (trim(structure_parent) == 'fcc' .and. trim(structure_target) == 'hex') then ! C_bar66(1,1) = (C66_parent(1,1) + C66_parent(1,2) + 2.0_pReal*C66_parent(4,4))/2.0_pReal ! C_bar66(1,2) = (C66_parent(1,1) + 5.0_pReal*C66_parent(1,2) - 2.0_pReal*C66_parent(4,4))/6.0_pReal ! C_bar66(3,3) = (C66_parent(1,1) + 2.0_pReal*C66_parent(1,2) + 4.0_pReal*C66_parent(4,4))/3.0_pReal ! C_bar66(1,3) = (C66_parent(1,1) + 2.0_pReal*C66_parent(1,2) - 2.0_pReal*C66_parent(4,4))/3.0_pReal ! C_bar66(4,4) = (C66_parent(1,1) - C66_parent(1,2) + C66_parent(4,4))/3.0_pReal ! C_bar66(1,4) = (C66_parent(1,1) - C66_parent(1,2) - 2.0_pReal*C66_parent(4,4)) /(3.0_pReal*sqrt(2.0_pReal)) ! A = C_bar(1,4)**2.0_pReal/C_bar66(4,4) ! B = C_bar(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2))) ! C_target_unrotated66(1,1) = C_bar66(1,1) - A ! C_target_unrotated66(1,2) = C_bar66(1,2) + A ! C_target_unrotated66(1,3) = C_bar66(1,3) ! C_target_unrotated66(3,3) = C_bar66(3,3) ! C_target_unrotated66(4,4) = C_bar66(4,4) - B ! C_target_unrotated66 = lattice_symmetrizeC66(LATTICE_HEX_ID,C_target_unrotated) ! elseif (trim(structure_parent) == 'fcc' .and. trim(structure_target) == 'bcc') then ! C_target_unrotated66 = C_parent66 ! endif ! do i = 1_pInt, 6_pInt ! if (abs(C_target_unrotated66(i,i)) 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 end function ! ! 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) ! ! "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) function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix) use math, only: & INRAD, & math_tensorproduct33, & math_crossproduct, & math_mul33x3, & math_axisAngleToR implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family real(pReal), dimension(6), intent(in) :: nonSchmidCoefficients integer(pInt), intent(in) :: sense !< sense (-1,+1) real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem real(pReal), dimension(:), allocatable :: direction real(pReal), dimension(:), allocatable :: normal,np integer(pInt) :: i if (abs(sense) /= 1_pInt) write(6,*) 'mist' coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_BCC_SYSTEMSLIP,pInt),'bcc') coordinateSystem(1:3,1,sum(Nslip)) = coordinateSystem(1:3,1,sum(Nslip)) *real(sense,pReal) nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'bcc') do i = 1_pInt,sum(Nslip) direction = coordinateSystem(1:3,1,i) normal = coordinateSystem(1:3,2,i) np = math_mul33x3(math_axisAngleToR(+direction,60.0_pReal*INRAD), normal) nonSchmidMatrix(1:3,1:3,i) & = nonSchmidMatrix(1:3,1:3,i) & + nonSchmidCoefficients(1) * math_tensorproduct33(direction, np) & + nonSchmidCoefficients(2) * math_tensorproduct33(math_crossproduct(normal, direction), normal) & + nonSchmidCoefficients(3) * math_tensorproduct33(math_crossproduct(np, direction), np) & + nonSchmidCoefficients(4) * math_tensorproduct33(normal, normal) & + nonSchmidCoefficients(5) * math_tensorproduct33(math_crossproduct(normal, direction), & math_crossproduct(normal, normal)) & + nonSchmidCoefficients(6) * math_tensorproduct33(direction, direction) enddo end function lattice_nonSchmidMatrix !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced slip-slip interaction matrix !> ToDo: prefix "2" needed as long as deprecated array lattice_interactionSlipSlip exists !-------------------------------------------------------------------------------------------------- function lattice_interactionSlipSlip2(Nslip,interactionValues,structure) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< interaction values slip-slip character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Nslip),sum(Nslip)) :: lattice_interactionSlipSlip2 integer(pInt), dimension(:), allocatable :: NslipMax integer(pInt), dimension(:,:), allocatable :: interactionSlipSlip select case(structure) case('fcc') interactionSlipSlip = LATTICE_FCC_INTERACTIONSLIPSLIP NslipMax = LATTICE_FCC_NSLIPSYSTEM case('bcc') interactionSlipSlip = LATTICE_BCC_INTERACTIONSLIPSLIP NslipMax = LATTICE_BCC_NSLIPSYSTEM case('hex','hexagonal') !ToDo: "No alias policy": long or short? interactionSlipSlip = LATTICE_HEX_INTERACTIONSLIPSLIP NslipMax = LATTICE_HEX_NSLIPSYSTEM case('bct') interactionSlipSlip = LATTICE_BCT_INTERACTIONSLIPSLIP NslipMax = LATTICE_BCT_NSLIPSYSTEM case default call IO_error(132_pInt,ext_msg=trim(structure)//' (slip slip interaction)') end select if (any(Nslip(1:size(Nslip)) - Nslip < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntrans '//trim(structure)) lattice_interactionSlipSlip2 = & buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionSlipSlip) end function lattice_interactionSlipSlip2 !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced twin-twin interaction matrix !> ToDo: prefix "2" needed as long as deprecated array lattice_interactionTwinTwin exists !-------------------------------------------------------------------------------------------------- function lattice_interactionTwinTwin2(Ntwin,interactionValues,structure) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< interaction values twin-twin character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Ntwin),sum(Ntwin)) :: lattice_interactionTwinTwin2 integer(pInt), dimension(:), allocatable :: NtwinMax integer(pInt), dimension(:,:), allocatable :: interactionTwinTwin select case(structure) case('fcc') interactionTwinTwin = LATTICE_FCC_INTERACTIONTWINTWIN NtwinMax = LATTICE_FCC_NTWINSYSTEM case('bcc') interactionTwinTwin = LATTICE_BCC_INTERACTIONTWINTWIN NtwinMax = LATTICE_BCC_NTWINSYSTEM case('hex','hexagonal') !ToDo: "No alias policy": long or short? interactionTwinTwin = LATTICE_HEX_INTERACTIONTWINTWIN NtwinMax = LATTICE_HEX_NTWINSYSTEM case default call IO_error(132_pInt,ext_msg=trim(structure)//' (twin twin interaction)') end select if (any(Ntwin(1:size(Ntwin)) - Ntwin < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntrans '//trim(structure)) lattice_interactionTwinTwin2 = & buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTwinTwin) end function lattice_interactionTwinTwin2 !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced slip-twin interaction matrix !> ToDo: prefix "2" needed as long as deprecated array lattice_interactionTwinTwin exists !-------------------------------------------------------------------------------------------------- function lattice_interactionSlipTwin2(Nslip,Ntwin,interactionValues,structure) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< interaction values twin-twin character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Nslip),sum(Ntwin)) :: lattice_interactionSlipTwin2 integer(pInt), dimension(:), allocatable :: NslipMax integer(pInt), dimension(:), allocatable :: NtwinMax integer(pInt), dimension(:,:), allocatable :: interactionSlipTwin select case(structure) case('fcc') interactionSlipTwin = LATTICE_FCC_INTERACTIONSLIPTWIN NslipMax = LATTICE_FCC_NSLIPSYSTEM NtwinMax = LATTICE_FCC_NTWINSYSTEM case('bcc') interactionSlipTwin = LATTICE_BCC_INTERACTIONSLIPTWIN NslipMax = LATTICE_BCC_NSLIPSYSTEM NtwinMax = LATTICE_BCC_NTWINSYSTEM case('hex','hexagonal') !ToDo: "No alias policy": long or short? interactionSlipTwin = LATTICE_HEX_INTERACTIONSLIPTWIN NslipMax = LATTICE_HEX_NSLIPSYSTEM NtwinMax = LATTICE_HEX_NTWINSYSTEM case default call IO_error(132_pInt,ext_msg=trim(structure)//' (slip twin interaction)') end select if (any(Ntwin(1:size(Ntwin)) - Ntwin < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntrans '//trim(structure)) lattice_interactionSlipTwin2 = & buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionSlipTwin) end function lattice_interactionSlipTwin2 !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced twin-slip interaction matrix !> ToDo: prefix "2" needed as long as deprecated array lattice_interactionTwinTwin exists !-------------------------------------------------------------------------------------------------- function lattice_interactionTwinSlip2(Ntwin,Nslip,interactionValues,structure) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< interaction values twin-twin character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(sum(Ntwin),sum(Nslip)) :: lattice_interactionTwinSlip2 integer(pInt), dimension(:), allocatable :: NslipMax integer(pInt), dimension(:), allocatable :: NtwinMax integer(pInt), dimension(:,:), allocatable :: interactionTwinSlip select case(structure) case('fcc') interactionTwinSlip = LATTICE_FCC_INTERACTIONTWINSLIP NtwinMax = LATTICE_FCC_NTWINSYSTEM NslipMax = LATTICE_FCC_NSLIPSYSTEM case('bcc') interactionTwinSlip = LATTICE_BCC_INTERACTIONTWINSLIP NtwinMax = LATTICE_BCC_NTWINSYSTEM NslipMax = LATTICE_BCC_NSLIPSYSTEM case('hex','hexagonal') !ToDo: "No alias policy": long or short? interactionTwinSlip = LATTICE_HEX_INTERACTIONTWINSLIP NtwinMax = LATTICE_HEX_NTWINSYSTEM NslipMax = LATTICE_HEX_NSLIPSYSTEM case default call IO_error(132_pInt,ext_msg=trim(structure)//' (slip twin interaction)') end select if (any(Ntwin(1:size(Ntwin)) - Ntwin < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntrans '//trim(structure)) lattice_interactionTwinSlip2 = & buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTwinSlip) end function lattice_interactionTwinSlip2 !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced trans-trans interaction matrix !> ToDo: prefix "2" needed as long as deprecated array lattice_interactionTransTrans exists !-------------------------------------------------------------------------------------------------- function lattice_interactionTransTrans2(Ntrans,interactionValues,structure,targetStructure) use IO, only: & IO_error implicit none integer(pInt), dimension(:), intent(in) :: Ntrans !< number of active twin systems per family real(pReal), dimension(:), intent(in) :: interactionValues !< interaction values twin-twin character(len=*), intent(in) :: & structure, & !< lattice structure of parent crystal targetStructure !< lattice structure of transformed crystal real(pReal), dimension(sum(Ntrans),sum(Ntrans)) :: lattice_interactionTransTrans2 integer(pInt), dimension(:), allocatable :: NtransMax integer(pInt), dimension(:,:), allocatable :: interactionTransTrans if (trim(structure) == 'fcc' .and. trim(targetStructure) == 'hex') then interactionTransTrans = lattice_fccToHex_interactionTransTrans NtransMax = lattice_fcc_Ntrans else call IO_error(132_pInt,ext_msg=trim(structure)//' => '//trim(targetStructure)) end if if (any(Ntrans(1:size(Ntrans)) - Ntrans < 0_pInt)) & call IO_error(145_pInt,ext_msg='Ntrans '//trim(structure)) lattice_interactionTransTrans2 = & buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTransTrans) end function lattice_interactionTransTrans2 !-------------------------------------------------------------------------------------------------- !> @brief Calculates Schmid matrix for active slip systems !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix) use prec, only: & tol_math_check use IO, only: & IO_error use math, only: & math_trace33, & math_tensorproduct33 implicit none integer(pInt), dimension(:), intent(in) :: Nslip !< number of active slip systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(3,3,sum(Nslip)) :: SchmidMatrix real(pReal), intent(in), optional :: & cOverA real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem integer(pInt) :: i select case(structure) case('fcc') coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_FCC_SYSTEMSLIP,pInt),structure) case('bcc') coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_BCC_SYSTEMSLIP,pInt),structure) case('hex','hexagonal') !ToDo: "No alias policy": long or short? coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_HEX_SYSTEMSLIP,pInt),'hex',cOverA) case('bct') coordinateSystem = buildCoordinateSystem(Nslip,int(LATTICE_BCT_SYSTEMSLIP,pInt),structure,cOverA) case default call IO_error(130_pInt,ext_msg=trim(structure)//' (lattice_SchmidMatrix_slip)') end select do i = 1, sum(Nslip) SchmidMatrix(1:3,1:3,i) = math_tensorproduct33(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) & call IO_error(0_pInt,i,ext_msg = 'dilatational Schmid matrix for slip') enddo end function lattice_SchmidMatrix_slip !-------------------------------------------------------------------------------------------------- !> @brief Calculates Schmid matrix for active twin systems !-------------------------------------------------------------------------------------------------- function lattice_SchmidMatrix_twin(Ntwin,structure,cOverA) use IO, only: & IO_error use math, only: & math_tensorproduct33 implicit none integer(pInt), dimension(:), intent(in) :: Ntwin !< number of active twin systems per family character(len=*), intent(in) :: structure !< lattice structure real(pReal), dimension(3,3,sum(Ntwin)) :: lattice_SchmidMatrix_Twin real(pReal), intent(in), optional :: & cOverA real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem integer(pInt) :: i select case(structure) case('fcc') coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_FCC_SYSTEMTWIN,pInt),structure) case('bcc') coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_BCC_SYSTEMTWIN,pInt),structure) case('hex','hexagonal') !ToDo: "No alias policy": long or short? coordinateSystem = buildCoordinateSystem(Ntwin,int(LATTICE_HEX_SYSTEMTWIN,pInt),'hex',cOverA) case default call IO_error(130_pInt,ext_msg=trim(structure)//' (lattice_SchmidMatrix_twin)') end select do i = 1, sum(Ntwin) lattice_SchmidMatrix_twin(1:3,1:3,i) = & math_tensorproduct33(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i)) enddo end function lattice_SchmidMatrix_twin !-------------------------------------------------------------------------------------------------- !> @brief Populates reduced interaction matrix !-------------------------------------------------------------------------------------------------- pure function buildInteraction(activeA,activeB,maxA,maxB,values,matrix) implicit none integer(pInt), dimension(:), intent(in) :: & activeA, & !< number of active systems as specified in material.config activeB, & !< number of active systems as specified in material.config maxA, & !< number of maximum available systems maxB !< number of maximum available systems real(pReal), dimension(:), intent(in) :: values !< interaction values integer(pInt), dimension(:,:), intent(in) :: matrix !< full interaction matrix real(pReal), dimension(sum(activeA),sum(activeB)) :: buildInteraction integer(pInt) :: & index_myFamily, index_otherFamily, & mf, ms, of, os myFamilies: do mf = 1_pInt,size(activeA,1) index_myFamily = sum(activeA(1:mf-1_pInt)) mySystems: do ms = 1_pInt,activeA(mf) otherFamilies: do of = 1_pInt,size(activeB,1) index_otherFamily = sum(activeB(1:of-1_pInt)) otherSystems: do os = 1_pInt,activeB(of) buildInteraction(index_myFamily+ms,index_otherFamily+os) = & values(matrix(sum(maxA(1:mf-1))+ms, sum(maxB(1:of-1))+os)) enddo otherSystems; enddo otherFamilies; enddo mySystems;enddo myFamilies end function buildInteraction !-------------------------------------------------------------------------------------------------- !> @brief build a local coordinate system in a slip, twin, trans, cleavage system !> @details: Order: Direction, plane (normal), and common perpendicular !-------------------------------------------------------------------------------------------------- pure function buildCoordinateSystem(active,system,structure,cOverA) use math, only: & math_crossproduct implicit none integer(pInt), dimension(:), intent(in) :: & active integer(pInt), dimension(:,:), intent(in) :: & system character(len=*), intent(in) :: & structure !< lattice structure real(pReal), intent(in), optional :: & cOverA real(pReal), dimension(3,3,sum(active)) :: & buildCoordinateSystem real(pReal), dimension(3) :: & direction, normal integer(pInt) :: & ir, & !< index in reduced matrix ig, & !< index in full matrix mf, & !< index of my family ms !< index of my system in current family ir = 0_pInt myFamilies: do mf = 1_pInt,size(active,1) mySystems: do ms = 1_pInt,active(mf) ir = ir + 1_pInt ig = sum(system(:,1:mf-1))+ms select case(trim(structure)) case ('fcc','bcc') direction = real(system(1:3,ig),pReal) normal = real(system(4:6,ig),pReal) case ('hex') ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)]) direction = [ real(system(1,ig),pReal)*1.5_pReal, & (real(system(1,ig),pReal)+2.0_pReal*real(system(2,ig),pReal))*sqrt(0.75_pReal), & real(system(4,ig),pReal)*CoverA ] ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) normal = [ real(system(5,ig),pReal), & (real(system(5,ig),pReal)+2.0_pReal*real(system(6,ig),pReal))/ sqrt(3.0_pReal), & real(system(8,ig),pReal)/CoverA ] case ('bct') direction = [real(system(1:2,ig),pReal),real(system(3,ig),pReal)*CoverA] normal = [real(system(4:5,ig),pReal),real(system(6,ig),pReal)/CoverA] end select buildCoordinateSystem(1:3,1,ir) = direction/norm2(direction) ! make unit vector buildCoordinateSystem(1:3,2,ir) = normal/norm2(normal) ! make unit vector buildCoordinateSystem(1:3,3,ir) = math_crossproduct(direction,normal) enddo mySystems enddo myFamilies end function buildCoordinateSystem end module lattice