!-------------------------------------------------------------------------------------------------- ! $Id$ !-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @brief defines lattice structure definitions, slip and twin system definitions, Schimd matrix !> calculation and non-Schmid behavior !-------------------------------------------------------------------------------------------------- module lattice use prec, only: & pReal, & pInt implicit none private integer(pInt), parameter, public :: & LATTICE_maxNslipFamily = 6_pInt, & !< max # of slip system families over lattice structures LATTICE_maxNtwinFamily = 4_pInt, & !< max # of twin system families over lattice structures LATTICE_maxNtransFamily = 2_pInt, & !< max # of transformation system families over lattice structures LATTICE_maxNslip = 33_pInt, & !< max # of slip systems over lattice structures LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part) LATTICE_maxNnonSchmid = 6_pInt, & !< max # of non schmid contributions over lattice structures LATTICE_maxNtrans = 12_pInt !< max # of transformations over lattice structures integer(pInt), allocatable, dimension(:,:), protected, public :: & lattice_NslipSystem, & !< total # of slip systems in each family lattice_NtwinSystem, & !< total # of twin systems in each family lattice_NtransSystem !< total # of transformation systems in each family integer(pInt), allocatable, dimension(:,:,:), protected, public :: & lattice_interactionSlipSlip, & !< Slip--slip interaction type lattice_interactionSlipTwin, & !< Slip--twin interaction type lattice_interactionTwinSlip, & !< Twin--slip interaction type lattice_interactionTwinTwin !< Twin--twin interaction type real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: & lattice_Sslip !< Schmid and non-Schmid matrices real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & lattice_Sslip_v !< Mandel notation of lattice_Sslip real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_sn, & !< normal direction of slip system lattice_sd, & !< slip direction of slip system lattice_st !< sd x sn ! rotation and Schmid matrices, normal, shear direction and d x n of twin systems real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & lattice_Stwin, & lattice_Qtwin real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_Stwin_v, & lattice_tn, & lattice_td, & lattice_tt real(pReal), allocatable, dimension(:,:,:), protected, public :: & lattice_NItrans_v real(pReal), allocatable, dimension(:,:,:,:), protected, public :: & lattice_Rtrans, & lattice_Utrans, & lattice_Btrans, & lattice_Qtrans, & lattice_NItrans real(pReal), allocatable, dimension(:,:), protected, public :: & lattice_shearTwin !< characteristic twin shear integer(pInt), allocatable, dimension(:), protected, public :: & lattice_NnonSchmid !< total # of non-Schmid contributions for each structure !-------------------------------------------------------------------------------------------------- ! fcc integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0],pInt) !< total # of slip systems per family for fcc integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & LATTICE_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_fcc_NtransSystem = int([12, 0],pInt) !< total # of transformation systems per family for fcc integer(pInt), parameter, private :: & LATTICE_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc LATTICE_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc LATTICE_fcc_NnonSchmid = 0_pInt, & !< total # of non-Schmid contributions for fcc LATTICE_fcc_Ntrans = 12_pInt !< total # of transformations for fcc real(pReal), dimension(3+3,LATTICE_fcc_Nslip), parameter, private :: & LATTICE_fcc_systemSlip = reshape(real([& ! Slip direction Plane normal 0, 1,-1, 1, 1, 1, & -1, 0, 1, 1, 1, 1, & 1,-1, 0, 1, 1, 1, & 0,-1,-1, -1,-1, 1, & 1, 0, 1, -1,-1, 1, & -1, 1, 0, -1,-1, 1, & 0,-1, 1, 1,-1,-1, & -1, 0,-1, 1,-1,-1, & 1, 1, 0, 1,-1,-1, & 0, 1, 1, -1, 1,-1, & 1, 0,-1, -1, 1,-1, & -1,-1, 0, -1, 1,-1 & ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Nslip]) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli real(pReal), dimension(3+3,LATTICE_fcc_Ntwin), parameter, private :: & LATTICE_fcc_systemTwin = reshape(real( [& -2, 1, 1, 1, 1, 1, & 1,-2, 1, 1, 1, 1, & 1, 1,-2, 1, 1, 1, & 2,-1, 1, -1,-1, 1, & -1, 2, 1, -1,-1, 1, & -1,-1,-2, -1,-1, 1, & -2,-1,-1, 1,-1,-1, & 1, 2,-1, 1,-1,-1, & 1,-1, 2, 1,-1,-1, & 2, 1,-1, -1, 1,-1, & -1,-2,-1, -1, 1,-1, & -1, 1, 2, -1, 1,-1 & ],pReal),[ 3_pInt + 3_pInt,LATTICE_fcc_Ntwin]) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli real(pReal), dimension(LATTICE_fcc_Ntwin), parameter, private :: & LATTICE_fcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) !< Twin system <112>{111} ??? Sorted according to Eisenlohr & Hantcherli integer(pInt), dimension(2_pInt,LATTICE_fcc_Ntwin), parameter, public :: & LATTICE_fcc_twinNucleationSlipPair = reshape(int( [& 2,3, & 1,3, & 1,2, & 5,6, & 4,6, & 4,5, & 8,9, & 7,9, & 7,8, & 11,12, & 10,12, & 10,11 & ],pInt),[2_pInt,LATTICE_fcc_Ntwin]) integer(pInt), dimension(LATTICE_fcc_Nslip,lattice_fcc_Nslip), parameter, public :: & LATTICE_fcc_interactionSlipSlip = reshape(int( [& 1,2,2,4,6,5,3,5,5,4,5,6, & ! ---> slip 2,1,2,6,4,5,5,4,6,5,3,5, & ! | 2,2,1,5,5,3,5,6,4,6,5,4, & ! | 4,6,5,1,2,2,4,5,6,3,5,5, & ! v slip 6,4,5,2,1,2,5,3,5,5,4,6, & 5,5,3,2,2,1,6,5,4,5,6,4, & 3,5,5,4,5,6,1,2,2,4,6,5, & 5,4,6,5,3,5,2,1,2,6,4,5, & 5,6,4,6,5,4,2,2,1,5,5,3, & 4,5,6,3,5,5,4,6,5,1,2,2, & 5,3,5,5,4,6,6,4,5,2,1,2, & 6,5,4,5,6,4,5,5,3,2,2,1 & ],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Nslip],order=[2,1]) !< Slip--slip interaction types for fcc !< 1: self interaction !< 2: coplanar interaction !< 3: collinear interaction !< 4: Hirth locks !< 5: glissile junctions !< 6: Lomer locks integer(pInt), dimension(LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin), parameter, public :: & LATTICE_fcc_interactionSlipTwin = reshape(int( [& 1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin 1,1,1,3,3,3,3,3,3,2,2,2, & ! | 1,1,1,2,2,2,3,3,3,3,3,3, & ! | 3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip 3,3,3,1,1,1,2,2,2,3,3,3, & 2,2,2,1,1,1,3,3,3,3,3,3, & 2,2,2,3,3,3,1,1,1,3,3,3, & 3,3,3,2,2,2,1,1,1,3,3,3, & 3,3,3,3,3,3,1,1,1,2,2,2, & 3,3,3,2,2,2,3,3,3,1,1,1, & 2,2,2,3,3,3,3,3,3,1,1,1, & 3,3,3,3,3,3,2,2,2,1,1,1 & ],pInt),[LATTICE_fcc_Nslip,LATTICE_fcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for fcc !< 1: coplanar interaction !< 2: screw trace between slip system and twin habit plane (easy cross slip) !< 3: other interaction integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Nslip), parameter, public :: & LATTICE_fcc_interactionTwinSlip = 1_pInt !< Twin--Slip interaction types for fcc integer(pInt), dimension(LATTICE_fcc_Ntwin,LATTICE_fcc_Ntwin), parameter,public :: & LATTICE_fcc_interactionTwinTwin = reshape(int( [& 1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 1,1,1,2,2,2,2,2,2,2,2,2, & ! | 2,2,2,1,1,1,2,2,2,2,2,2, & ! v twin 2,2,2,1,1,1,2,2,2,2,2,2, & 2,2,2,1,1,1,2,2,2,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,1,1,1,2,2,2, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1, & 2,2,2,2,2,2,2,2,2,1,1,1 & ],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for fcc real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fcc_systemTrans = reshape(real( [& 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 & ],pReal),[ 4_pInt,LATTICE_fcc_Ntrans]) integer(pInt), dimension(LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fcc_bainVariant = reshape(int( [& 1, 1, 1, 1, & 2, 2, 2, 2, & 3, 3, 3, 3 & ],pInt),[LATTICE_fcc_Ntrans]) real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter, private :: & LATTICE_fcc_bainRot = reshape(real( [& 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 & ],pReal),[ 4_pInt,LATTICE_fcc_Ntrans]) !-------------------------------------------------------------------------------------------------- ! bcc integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & LATTICE_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0], pInt) !< total # of slip systems per family for bcc integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & LATTICE_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< total # of twin systems per family for bcc integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_bcc_NtransSystem = int([0,0],pInt) !< total # of transformation systems per family for bcc integer(pInt), parameter, private :: & LATTICE_bcc_Nslip = 24_pInt, & ! sum(lattice_bcc_NslipSystem), & !< total # of slip systems for bcc LATTICE_bcc_Ntwin = 12_pInt, & ! sum(lattice_bcc_NtwinSystem) !< total # of twin systems for bcc LATTICE_bcc_NnonSchmid = 6_pInt, & !< # of non-Schmid contributions for bcc. 6 known non schmid contributions for BCC (A. Koester, A. Ma, A. Hartmaier 2012) LATTICE_bcc_Ntrans = 0_pInt !< total # of transformations for bcc real(pReal), dimension(3+3,LATTICE_bcc_Nslip), parameter, private :: & LATTICE_bcc_systemSlip = reshape(real([& ! Slip direction Plane normal ! Slip system <111>{110} 1,-1, 1, 0, 1, 1, & -1,-1, 1, 0, 1, 1, & 1, 1, 1, 0,-1, 1, & -1, 1, 1, 0,-1, 1, & -1, 1, 1, 1, 0, 1, & -1,-1, 1, 1, 0, 1, & 1, 1, 1, -1, 0, 1, & 1,-1, 1, -1, 0, 1, & -1, 1, 1, 1, 1, 0, & -1, 1,-1, 1, 1, 0, & 1, 1, 1, -1, 1, 0, & 1, 1,-1, -1, 1, 0, & ! Slip system <111>{112} -1, 1, 1, 2, 1, 1, & 1, 1, 1, -2, 1, 1, & 1, 1,-1, 2,-1, 1, & 1,-1, 1, 2, 1,-1, & 1,-1, 1, 1, 2, 1, & 1, 1,-1, -1, 2, 1, & 1, 1, 1, 1,-2, 1, & -1, 1, 1, 1, 2,-1, & 1, 1,-1, 1, 1, 2, & 1,-1, 1, -1, 1, 2, & -1, 1, 1, 1,-1, 2, & 1, 1, 1, 1, 1,-2 & ! Slip system <111>{123} ! 1, 1,-1, 1, 2, 3, & ! 1,-1, 1, -1, 2, 3, & ! -1, 1, 1, 1,-2, 3, & ! 1, 1, 1, 1, 2,-3, & ! 1,-1, 1, 1, 3, 2, & ! 1, 1,-1, -1, 3, 2, & ! 1, 1, 1, 1,-3, 2, & ! -1, 1, 1, 1, 3,-2, & ! 1, 1,-1, 2, 1, 3, & ! 1,-1, 1, -2, 1, 3, & ! -1, 1, 1, 2,-1, 3, & ! 1, 1, 1, 2, 1,-3, & ! 1,-1, 1, 2, 3, 1, & ! 1, 1,-1, -2, 3, 1, & ! 1, 1, 1, 2,-3, 1, & ! -1, 1, 1, 2, 3,-1, & ! -1, 1, 1, 3, 1, 2, & ! 1, 1, 1, -3, 1, 2, & ! 1, 1,-1, 3,-1, 2, & ! 1,-1, 1, 3, 1,-2, & ! -1, 1, 1, 3, 2, 1, & ! 1, 1, 1, -3, 2, 1, & ! 1, 1,-1, 3,-2, 1, & ! 1,-1, 1, 3, 2,-1 & ],pReal),[ 3_pInt + 3_pInt ,LATTICE_bcc_Nslip]) real(pReal), dimension(3+3,LATTICE_bcc_Ntwin), parameter, private :: & LATTICE_bcc_systemTwin = reshape(real([& ! Twin system <111>{112} -1, 1, 1, 2, 1, 1, & 1, 1, 1, -2, 1, 1, & 1, 1,-1, 2,-1, 1, & 1,-1, 1, 2, 1,-1, & 1,-1, 1, 1, 2, 1, & 1, 1,-1, -1, 2, 1, & 1, 1, 1, 1,-2, 1, & -1, 1, 1, 1, 2,-1, & 1, 1,-1, 1, 1, 2, & 1,-1, 1, -1, 1, 2, & -1, 1, 1, 1,-1, 2, & 1, 1, 1, 1, 1,-2 & ],pReal),[ 3_pInt + 3_pInt,LATTICE_bcc_Ntwin]) real(pReal), dimension(LATTICE_bcc_Ntwin), parameter, private :: & LATTICE_bcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Nslip), parameter, public :: & LATTICE_bcc_interactionSlipSlip = reshape(int( [& 1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! ---> slip 2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! | 6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! | 6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v slip 5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & 4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, & 4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, & 3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, & 4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, & 3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, & 5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, & 4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, & ! 6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, & 4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, & 3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, & 3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, & 4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, & 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, & 4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, & 3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, & 6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, & 6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 & ],pInt),[lattice_bcc_Nslip,lattice_bcc_Nslip],order=[2,1]) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377 !< 1: self interaction !< 2: coplanar interaction !< 3: collinear interaction !< 4: mixed-asymmetrical junction !< 5: mixed-symmetrical junction !< 6: edge junction integer(pInt), dimension(LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin), parameter, public :: & LATTICE_bcc_interactionSlipTwin = reshape(int( [& 3,3,3,2,2,3,3,3,3,2,3,3, & ! ---> twin 3,3,2,3,3,2,3,3,2,3,3,3, & ! | 3,2,3,3,3,3,2,3,3,3,3,2, & ! | 2,3,3,3,3,3,3,2,3,3,2,3, & ! v slip 2,3,3,3,3,3,3,2,3,3,2,3, & 3,3,2,3,3,2,3,3,2,3,3,3, & 3,2,3,3,3,3,2,3,3,3,3,2, & 3,3,3,2,2,3,3,3,3,2,3,3, & 2,3,3,3,3,3,3,2,3,3,2,3, & 3,3,3,2,2,3,3,3,3,2,3,3, & 3,2,3,3,3,3,2,3,3,3,3,2, & 3,3,2,3,3,2,3,3,2,3,3,3, & ! 1,3,3,3,3,3,3,2,3,3,2,3, & 3,1,3,3,3,3,2,3,3,3,3,2, & 3,3,1,3,3,2,3,3,2,3,3,3, & 3,3,3,1,2,3,3,3,3,2,3,3, & 3,3,3,2,1,3,3,3,3,2,3,3, & 3,3,2,3,3,1,3,3,2,3,3,3, & 3,2,3,3,3,3,1,3,3,3,3,2, & 2,3,3,3,3,3,3,1,3,3,2,3, & 3,3,2,3,3,2,3,3,1,3,3,3, & 3,3,3,2,2,3,3,3,3,1,3,3, & 2,3,3,3,3,3,3,2,3,3,1,3, & 3,2,3,3,3,3,2,3,3,3,3,1 & ],pInt),[LATTICE_bcc_Nslip,LATTICE_bcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for bcc !< 1: coplanar interaction !< 2: screw trace between slip system and twin habit plane (easy cross slip) !< 3: other interaction integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Nslip), parameter, public :: & LATTICE_bcc_interactionTwinSlip = 1_pInt !< Twin--slip interaction types for bcc @todo not implemented yet integer(pInt), dimension(LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin), parameter, public :: & LATTICE_bcc_interactionTwinTwin = reshape(int( [& 1,3,3,3,3,3,3,2,3,3,2,3, & ! ---> twin 3,1,3,3,3,3,2,3,3,3,3,2, & ! | 3,3,1,3,3,2,3,3,2,3,3,3, & ! | 3,3,3,1,2,3,3,3,3,2,3,3, & ! v twin 3,3,3,2,1,3,3,3,3,2,3,3, & 3,3,2,3,3,1,3,3,2,3,3,3, & 3,2,3,3,3,3,1,3,3,3,3,2, & 2,3,3,3,3,3,3,1,3,3,2,3, & 3,3,2,3,3,2,3,3,1,3,3,3, & 3,3,3,2,2,3,3,3,3,1,3,3, & 2,3,3,3,3,3,3,2,3,3,1,3, & 3,2,3,3,3,3,2,3,3,3,3,1 & ],pInt),[LATTICE_bcc_Ntwin,LATTICE_bcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for bcc !< 1: self interaction !< 2: collinear interaction !< 3: other interaction !-------------------------------------------------------------------------------------------------- ! hex integer(pInt), dimension(LATTICE_maxNslipFamily), parameter, public :: & lattice_hex_NslipSystem = int([ 3, 3, 3, 6, 12, 6],pInt) !< # of slip systems per family for hex integer(pInt), dimension(LATTICE_maxNtwinFamily), parameter, public :: & lattice_hex_NtwinSystem = int([ 6, 6, 6, 6],pInt) !< # of slip systems per family for hex integer(pInt), dimension(LATTICE_maxNtransFamily), parameter, public :: & LATTICE_hex_NtransSystem = int([0,0],pInt) !< total # of transformation systems per family for hex integer(pInt), parameter , private :: & LATTICE_hex_Nslip = 33_pInt, & ! sum(lattice_hex_NslipSystem), !< total # of slip systems for hex LATTICE_hex_Ntwin = 24_pInt, & ! sum(lattice_hex_NtwinSystem) !< total # of twin systems for hex LATTICE_hex_NnonSchmid = 0_pInt, & !< # of non-Schmid contributions for hex LATTICE_hex_Ntrans = 0_pInt !< total # of transformations for hex real(pReal), dimension(4+4,LATTICE_hex_Nslip), parameter, private :: & LATTICE_hex_systemSlip = reshape(real([& ! Slip direction Plane normal ! Basal systems <11.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base)) 2, -1, -1, 0, 0, 0, 0, 1, & -1, 2, -1, 0, 0, 0, 0, 1, & -1, -1, 2, 0, 0, 0, 0, 1, & ! 1st type prismatic systems <11.0>{10.0} (independent of c/a-ratio) 2, -1, -1, 0, 0, 1, -1, 0, & -1, 2, -1, 0, -1, 0, 1, 0, & -1, -1, 2, 0, 1, -1, 0, 0, & ! 2nd type prismatic systems <10.0>{11.0} -- a slip; plane normals independent of c/a-ratio 0, 1, -1, 0, 2, -1, -1, 0, & -1, 0, 1, 0, -1, 2, -1, 0, & 1, -1, 0, 0, -1, -1, 2, 0, & ! 1st type 1st order pyramidal systems <11.0>{-11.1} -- plane normals depend on the c/a-ratio 2, -1, -1, 0, 0, 1, -1, 1, & -1, 2, -1, 0, -1, 0, 1, 1, & -1, -1, 2, 0, 1, -1, 0, 1, & 1, 1, -2, 0, -1, 1, 0, 1, & -2, 1, 1, 0, 0, -1, 1, 1, & 1, -2, 1, 0, 1, 0, -1, 1, & ! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the c/a-ratio 2, -1, -1, 3, -1, 1, 0, 1, & 1, -2, 1, 3, -1, 1, 0, 1, & -1, -1, 2, 3, 1, 0, -1, 1, & -2, 1, 1, 3, 1, 0, -1, 1, & -1, 2, -1, 3, 0, -1, 1, 1, & 1, 1, -2, 3, 0, -1, 1, 1, & -2, 1, 1, 3, 1, -1, 0, 1, & -1, 2, -1, 3, 1, -1, 0, 1, & 1, 1, -2, 3, -1, 0, 1, 1, & 2, -1, -1, 3, -1, 0, 1, 1, & 1, -2, 1, 3, 0, 1, -1, 1, & -1, -1, 2, 3, 0, 1, -1, 1, & ! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below) 2, -1, -1, 3, -2, 1, 1, 2, & ! sorted according to similar twin system -1, 2, -1, 3, 1, -2, 1, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a) -1, -1, 2, 3, 1, 1, -2, 2, & -2, 1, 1, 3, 2, -1, -1, 2, & 1, -2, 1, 3, -1, 2, -1, 2, & 1, 1, -2, 3, -1, -1, 2, 2 & ],pReal),[ 4_pInt + 4_pInt,LATTICE_hex_Nslip]) !< slip systems for hex sorted by A. Alankar & P. Eisenlohr real(pReal), dimension(4+4,LATTICE_hex_Ntwin), parameter, private :: & LATTICE_hex_systemTwin = reshape(real([& ! Compression or Tension =f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981) 1, -1, 0, 1, -1, 1, 0, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a) -1, 0, 1, 1, 1, 0, -1, 2, & 0, 1, -1, 1, 0, -1, 1, 2, & -1, 1, 0, 1, 1, -1, 0, 2, & 1, 0, -1, 1, -1, 0, 1, 2, & 0, -1, 1, 1, 0, 1, -1, 2, & ! 2, -1, -1, 6, -2, 1, 1, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a) -1, 2, -1, 6, 1, -2, 1, 1, & -1, -1, 2, 6, 1, 1, -2, 1, & -2, 1, 1, 6, 2, -1, -1, 1, & 1, -2, 1, 6, -1, 2, -1, 1, & 1, 1, -2, 6, -1, -1, 2, 1, & ! -1, 1, 0, -2, -1, 1, 0, 1, & !! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a) 1, 0, -1, -2, 1, 0, -1, 1, & 0, -1, 1, -2, 0, -1, 1, 1, & 1, -1, 0, -2, 1, -1, 0, 1, & -1, 0, 1, -2, -1, 0, 1, 1, & 0, 1, -1, -2, 0, 1, -1, 1, & ! 2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a) -1, 2, -1, -3, -1, 2, -1, 2, & -1, -1, 2, -3, -1, -1, 2, 2, & -2, 1, 1, -3, -2, 1, 1, 2, & 1, -2, 1, -3, 1, -2, 1, 2, & 1, 1, -2, -3, 1, 1, -2, 2 & ],pReal),[ 4_pInt + 4_pInt ,LATTICE_hex_Ntwin]) !< twin systems for hex, order follows Prof. Tom Bieler's scheme; but numbering in data was restarted from 1 integer(pInt), dimension(LATTICE_hex_Ntwin), parameter, private :: & LATTICE_hex_shearTwin = reshape(int( [& ! indicator to formula further below 1, & ! <-10.1>{10.2} 1, & 1, & 1, & 1, & 1, & 2, & ! <11.6>{-1-1.1} 2, & 2, & 2, & 2, & 2, & 3, & ! <10.-2>{10.1} 3, & 3, & 3, & 3, & 3, & 4, & ! <11.-3>{11.2} 4, & 4, & 4, & 4, & 4 & ],pInt),[LATTICE_hex_Ntwin]) integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Nslip), parameter, public :: & LATTICE_hex_interactionSlipSlip = reshape(int( [& 1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! ---> slip 2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | 2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! | ! v slip 6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & 6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & 6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! 12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & 12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, & ! 20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & 20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, & ! 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, & 30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, & ! 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, & 42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 & ! ],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Nslip],order=[2,1]) !< Slip--slip interaction types for hex (32? in total) integer(pInt), dimension(LATTICE_hex_Nslip,LATTICE_hex_Ntwin), parameter, public :: & LATTICE_hex_interactionSlipTwin = reshape(int( [& 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! --> twin 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! | ! v 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & 9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & ! 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & 13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & ! 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & 17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, & ! 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, & 21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 & ! ],pInt),[LATTICE_hex_Nslip,LATTICE_hex_Ntwin],order=[2,1]) !< Slip--twin interaction types for hex (isotropic, 24 in total) integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Nslip), parameter, public :: & LATTICE_hex_interactionTwinSlip = reshape(int( [& 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! --> slip 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin 1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & 2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, & ! 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & 3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, & ! 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, & 4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 & ],pInt),[LATTICE_hex_Ntwin,LATTICE_hex_Nslip],order=[2,1]) !< Twin--twin interaction types for hex (isotropic, 20 in total) integer(pInt), dimension(LATTICE_hex_Ntwin,LATTICE_hex_Ntwin), parameter, public :: & LATTICE_hex_interactionTwinTwin = reshape(int( [& 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! ---> twin 2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! | 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v twin 2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! 6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, & ! 12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, & 12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, & ! 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, & 20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 & ],pInt),[lattice_hex_Ntwin,lattice_hex_Ntwin],order=[2,1]) !< Twin--slip interaction types for hex (isotropic, 16 in total) real(pReal), dimension(:,:,:), allocatable, public, protected :: & lattice_C66 real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: & lattice_C3333 real(pReal), dimension(:), allocatable, public, protected :: & lattice_mu, & lattice_nu real(pReal), dimension(:,:,:), allocatable, public, protected :: & lattice_thermalConductivity33, & lattice_thermalExpansion33, & lattice_surfaceEnergy33 real(pReal), dimension(:), allocatable, public, protected :: & lattice_referenceTemperature enum, bind(c) enumerator :: LATTICE_undefined_ID, & LATTICE_iso_ID, & LATTICE_fcc_ID, & LATTICE_bcc_ID, & LATTICE_hex_ID, & LATTICE_ort_ID end enum integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: & lattice_structure integer(pInt), dimension(2), parameter, private :: & lattice_NsymOperations = [24_pInt,12_pInt] real(pReal), dimension(4,36), parameter, private :: & lattice_symOperations = reshape([& 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! cubic symmetry operations 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, & ! 2-fold symmetry 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, & 0.0_pReal, 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, & 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, & 0.0_pReal, -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, & 0.0_pReal, 0.7071067811865476_pReal, -0.7071067811865476_pReal, 0.0_pReal, & 0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & ! 3-fold symmetry -0.5_pReal, 0.5_pReal, 0.5_pReal, 0.5_pReal, & 0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & -0.5_pReal, -0.5_pReal, 0.5_pReal, 0.5_pReal, & 0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & -0.5_pReal, 0.5_pReal, -0.5_pReal, 0.5_pReal, & 0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & -0.5_pReal, 0.5_pReal, 0.5_pReal, -0.5_pReal, & 0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & ! 4-fold symmetry 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & -0.7071067811865476_pReal, 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, & 0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, & 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & -0.7071067811865476_pReal, 0.0_pReal, 0.7071067811865476_pReal, 0.0_pReal, & 0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, & 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, & -0.7071067811865476_pReal, 0.0_pReal, 0.0_pReal, 0.7071067811865476_pReal, & 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, & ! hexagonal symmetry operations 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, & ! 2-fold symmetry 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, & 0.0_pReal, 0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, & 0.0_pReal, -0.5_pReal, 0.866025403784439_pReal, 0.0_pReal, & 0.0_pReal, 0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, & 0.0_pReal, -0.866025403784439_pReal, 0.5_pReal, 0.0_pReal, & 0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & ! 6-fold symmetry -0.866025403784439_pReal, 0.0_pReal, 0.0_pReal, 0.5_pReal, & 0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, & -0.5_pReal, 0.0_pReal, 0.0_pReal, 0.866025403784439_pReal, & 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal & ],[4,36]) !< Symmetry operations as quaternions 24 for cubic, 12 for hexagonal = 36 ! use this later on to substitute the matrix above ! if self.lattice == 'cubic': ! symQuats = [ ! [ 1.0,0.0,0.0,0.0 ], ! [ 0.0,1.0,0.0,0.0 ], ! [ 0.0,0.0,1.0,0.0 ], ! [ 0.0,0.0,0.0,1.0 ], ! [ 0.0, 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2) ], ! [ 0.0, 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2) ], ! [ 0.0, 0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2) ], ! [ 0.0, 0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2) ], ! [ 0.0, 0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], ! [ 0.0,-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0 ], ! [ 0.5, 0.5, 0.5, 0.5 ], ! [-0.5, 0.5, 0.5, 0.5 ], ! [-0.5, 0.5, 0.5,-0.5 ], ! [-0.5, 0.5,-0.5, 0.5 ], ! [-0.5,-0.5, 0.5, 0.5 ], ! [-0.5,-0.5, 0.5,-0.5 ], ! [-0.5,-0.5,-0.5, 0.5 ], ! [-0.5, 0.5,-0.5,-0.5 ], ! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], ! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], ! [-0.5*math.sqrt(2), 0.0, 0.5*math.sqrt(2), 0.0 ], ! [-0.5*math.sqrt(2), 0.0,-0.5*math.sqrt(2), 0.0 ], ! [-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0, 0.0 ], ! [-0.5*math.sqrt(2),-0.5*math.sqrt(2), 0.0, 0.0 ], ! ] ! elif self.lattice == 'hexagonal': ! symQuats = [ ! [ 1.0,0.0,0.0,0.0 ], ! [ 0.0,1.0,0.0,0.0 ], ! [ 0.0,0.0,1.0,0.0 ], ! [ 0.0,0.0,0.0,1.0 ], ! [-0.5*math.sqrt(3), 0.0, 0.0, 0.5 ], ! [-0.5*math.sqrt(3), 0.0, 0.0,-0.5 ], ! [ 0.0, 0.5*math.sqrt(3), 0.5, 0.0 ], ! [ 0.0,-0.5*math.sqrt(3), 0.5, 0.0 ], ! [ 0.0, 0.5,-0.5*math.sqrt(3), 0.0 ], ! [ 0.0,-0.5,-0.5*math.sqrt(3), 0.0 ], ! [ 0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], ! [-0.5, 0.0, 0.0, 0.5*math.sqrt(3) ], ! ] ! elif self.lattice == 'tetragonal': ! symQuats = [ ! [ 1.0,0.0,0.0,0.0 ], ! [ 0.0,1.0,0.0,0.0 ], ! [ 0.0,0.0,1.0,0.0 ], ! [ 0.0,0.0,0.0,1.0 ], ! [ 0.0, 0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], ! [ 0.0,-0.5*math.sqrt(2), 0.5*math.sqrt(2), 0.0 ], ! [ 0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], ! [-0.5*math.sqrt(2), 0.0, 0.0, 0.5*math.sqrt(2) ], ! ] ! elif self.lattice == 'orthorhombic': ! symQuats = [ ! [ 1.0,0.0,0.0,0.0 ], ! [ 0.0,1.0,0.0,0.0 ], ! [ 0.0,0.0,1.0,0.0 ], ! [ 0.0,0.0,0.0,1.0 ], ! ] ! else: ! symQuats = [ ! [ 1.0,0.0,0.0,0.0 ], ! ] public :: & lattice_init, & lattice_qDisorientation, & LATTICE_fcc_ID, & LATTICE_bcc_ID, & LATTICE_hex_ID contains !-------------------------------------------------------------------------------------------------- !> @brief Module initialization !-------------------------------------------------------------------------------------------------- subroutine lattice_init use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use prec, only: & tol_math_check use IO, only: & IO_open_file,& IO_open_jobFile_stat, & IO_countSections, & IO_countTagInPart, & IO_error, & IO_timeStamp, & IO_stringPos, & IO_EOF, & IO_read, & IO_lc, & IO_getTag, & IO_isBlank, & IO_stringPos, & IO_stringValue, & IO_floatValue, & IO_EOF use material, only: & material_configfile, & material_localFileExt, & material_partPhase use debug, only: & debug_level, & debug_lattice, & debug_levelBasic implicit none integer(pInt), parameter :: FILEUNIT = 200_pInt integer(pInt) :: Nphases character(len=65536) :: & tag = '', & line = '' integer(pInt), parameter :: MAXNCHUNKS = 2_pInt integer(pInt), dimension(1+2*MAXNCHUNKS) :: positions integer(pInt) :: section = 0_pInt,i real(pReal), dimension(:), allocatable :: & CoverA, & !< c/a ratio for hex type lattice aA, & !< lattice parameter a for fcc austenite aM, & !< lattice paramater a for bcc martensite cM !< lattice parameter c for bcc martensite write(6,'(/,a)') ' <<<+- lattice init -+>>>' write(6,'(a)') ' $Id$' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" !-------------------------------------------------------------------------------------------------- ! consistency checks if (LATTICE_maxNslip /= maxval([LATTICE_fcc_Nslip,LATTICE_bcc_Nslip,LATTICE_hex_Nslip])) & call IO_error(0_pInt,ext_msg = 'LATTICE_maxNslip') if (LATTICE_maxNtwin /= maxval([LATTICE_fcc_Ntwin,LATTICE_bcc_Ntwin,LATTICE_hex_Ntwin])) & call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtwin') if (LATTICE_maxNtrans /= maxval([LATTICE_fcc_Ntrans,LATTICE_bcc_Ntrans,LATTICE_hex_Ntrans])) then call IO_error(0_pInt,ext_msg = 'LATTICE_maxNtrans') endif if (LATTICE_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,& lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid') if (LATTICE_fcc_Nslip /= sum(lattice_fcc_NslipSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Nslip') if (LATTICE_bcc_Nslip /= sum(lattice_bcc_NslipSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Nslip') if (LATTICE_hex_Nslip /= sum(lattice_hex_NslipSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Nslip') if (LATTICE_fcc_Ntwin /= sum(lattice_fcc_NtwinSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntwin') if (LATTICE_bcc_Ntwin /= sum(lattice_bcc_NtwinSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntwin') if (LATTICE_hex_Ntwin /= sum(lattice_hex_NtwinSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntwin') if (LATTICE_fcc_Ntrans /= sum(lattice_fcc_NtransSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_fcc_Ntrans') if (LATTICE_bcc_Ntrans /= sum(lattice_bcc_NtransSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_bcc_Ntrans') if (LATTICE_hex_Ntrans /= sum(lattice_hex_NtransSystem)) & call IO_error(0_pInt,ext_msg = 'LATTICE_hex_Ntrans') if (LATTICE_maxNinteraction /= max(& maxval(lattice_fcc_interactionSlipSlip), & maxval(lattice_bcc_interactionSlipSlip), & maxval(lattice_hex_interactionSlipSlip), & ! maxval(lattice_fcc_interactionSlipTwin), & maxval(lattice_bcc_interactionSlipTwin), & maxval(lattice_hex_interactionSlipTwin), & ! maxval(lattice_fcc_interactionTwinSlip), & maxval(lattice_bcc_interactionTwinSlip), & maxval(lattice_hex_interactionTwinSlip), & ! maxval(lattice_fcc_interactionTwinTwin), & maxval(lattice_bcc_interactionTwinTwin), & maxval(lattice_hex_interactionTwinTwin))) & call IO_error(0_pInt,ext_msg = 'LATTICE_maxNinteraction') !-------------------------------------------------------------------------------------------------- ! read from material configuration file if (.not. IO_open_jobFile_stat(FILEUNIT,material_localFileExt)) & ! no local material configuration present... call IO_open_file(FILEUNIT,material_configFile) ! ... open material.config file Nphases = IO_countSections(FILEUNIT,material_partPhase) if(Nphases<1_pInt) & call IO_error(160_pInt,Nphases, ext_msg='No phases found') if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then write(6,'(a16,1x,i5)') ' # phases:',Nphases endif allocate(lattice_structure(Nphases),source = LATTICE_undefined_ID) allocate(lattice_C66(6,6,Nphases), source=0.0_pReal) allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal) allocate(lattice_thermalConductivity33(3,3,Nphases), source=0.0_pReal) allocate(lattice_thermalExpansion33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_surfaceEnergy33 (3,3,Nphases), source=0.0_pReal) allocate(lattice_referenceTemperature (Nphases), source=0.0_pReal) allocate(lattice_mu(Nphases), source=0.0_pReal) allocate(lattice_nu(Nphases), source=0.0_pReal) allocate(lattice_NnonSchmid(Nphases), source=0_pInt) allocate(lattice_Sslip(3,3,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_Sslip_v(6,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_sd(3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_st(3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_sn(3,lattice_maxNslip,Nphases),source=0.0_pReal) allocate(lattice_Qtwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_Stwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_Stwin_v(6,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_td(3,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_tt(3,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_tn(3,lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal) allocate(lattice_Rtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Utrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Btrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_Qtrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_NItrans(3,3,lattice_maxNtrans,Nphases),source=0.0_pReal) allocate(lattice_NItrans_v(6,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_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,Nphases),source=0_pInt) ! other:me allocate(lattice_interactionSlipTwin(lattice_maxNslip,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me allocate(lattice_interactionTwinSlip(lattice_maxNtwin,lattice_maxNslip,Nphases),source=0_pInt) ! other:me allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,Nphases),source=0_pInt) ! other:me allocate(CoverA(Nphases),source=0.0_pReal) allocate(aA(Nphases),source=0.0_pReal) allocate(aM(Nphases),source=0.0_pReal) allocate(cM(Nphases),source=0.0_pReal) rewind(fileUnit) line = '' ! to have it initialized section = 0_pInt ! - " - do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= material_partPhase) ! wind forward to line = IO_read(fileUnit) enddo do while (trim(line) /= IO_EOF) ! read through sections of material part line = IO_read(fileUnit) if (IO_isBlank(line)) cycle ! skip empty lines if (IO_getTag(line,'<','>') /= '') then ! stop at next part line = IO_read(fileUnit, .true.) ! reset IO_read exit endif if (IO_getTag(line,'[',']') /= '') then ! next section section = section + 1_pInt endif if (section > 0_pInt) then positions = IO_stringPos(line,MAXNCHUNKS) tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key select case(tag) case ('lattice_structure') select case(trim(IO_lc(IO_stringValue(line,positions,2_pInt)))) case('iso','isotropic') lattice_structure(section) = LATTICE_iso_ID case('fcc') lattice_structure(section) = LATTICE_fcc_ID case('bcc') lattice_structure(section) = LATTICE_bcc_ID case('hex','hexagonal') lattice_structure(section) = LATTICE_hex_ID case('ort','orthorombic') lattice_structure(section) = LATTICE_ort_ID case default call IO_error(450_pInt,ext_msg=trim(IO_lc(IO_stringValue(line,positions,2_pInt)))) end select case ('c11') lattice_C66(1,1,section) = IO_floatValue(line,positions,2_pInt) case ('c12') lattice_C66(1,2,section) = IO_floatValue(line,positions,2_pInt) case ('c13') lattice_C66(1,3,section) = IO_floatValue(line,positions,2_pInt) case ('c22') lattice_C66(2,2,section) = IO_floatValue(line,positions,2_pInt) case ('c23') lattice_C66(2,3,section) = IO_floatValue(line,positions,2_pInt) case ('c33') lattice_C66(3,3,section) = IO_floatValue(line,positions,2_pInt) case ('c44') lattice_C66(4,4,section) = IO_floatValue(line,positions,2_pInt) case ('c55') lattice_C66(5,5,section) = IO_floatValue(line,positions,2_pInt) case ('c66') lattice_C66(6,6,section) = IO_floatValue(line,positions,2_pInt) case ('covera_ratio','c/a_ratio','c/a') CoverA(section) = IO_floatValue(line,positions,2_pInt) case ('aa', 'a_a', 'a_austenite', 'a_fcc') aA(section) = IO_floatValue(line,positions,2_pInt) case ('am', 'a_m', 'a_martensite', 'a_bcc') aM(section) = IO_floatValue(line,positions,2_pInt) case ('cm', 'c_m', 'c_martensite') cM(section) = IO_floatValue(line,positions,2_pInt) case ('k11') lattice_thermalConductivity33(1,1,section) = IO_floatValue(line,positions,2_pInt) case ('k22') lattice_thermalConductivity33(2,2,section) = IO_floatValue(line,positions,2_pInt) case ('k33') lattice_thermalConductivity33(3,3,section) = IO_floatValue(line,positions,2_pInt) case ('thermal_expansion11') lattice_thermalExpansion33(1,1,section) = IO_floatValue(line,positions,2_pInt) case ('thermal_expansion22') lattice_thermalExpansion33(2,2,section) = IO_floatValue(line,positions,2_pInt) case ('thermal_expansion33') lattice_thermalExpansion33(3,3,section) = IO_floatValue(line,positions,2_pInt) case ('g11') lattice_surfaceEnergy33(1,1,section) = IO_floatValue(line,positions,2_pInt) case ('g22') lattice_surfaceEnergy33(2,2,section) = IO_floatValue(line,positions,2_pInt) case ('g33') lattice_surfaceEnergy33(3,3,section) = IO_floatValue(line,positions,2_pInt) case ('reference_temperature') lattice_referenceTemperature(section) = IO_floatValue(line,positions,2_pInt) end select endif enddo do i = 1_pInt,Nphases if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) & .and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(206_pInt) ! checking physical significance of c/a call lattice_initializeStructure(i, CoverA(i), aA(i), aM(i), cM(i)) enddo deallocate(CoverA,aA,aM,cM) end subroutine lattice_init !-------------------------------------------------------------------------------------------------- !> @brief Calculation of Schmid matrices, etc. !-------------------------------------------------------------------------------------------------- subroutine lattice_initializeStructure(myPhase,CoverA,aA,aM,cM) use prec, only: & tol_math_check use math, only: & math_identity2nd, & math_vectorproduct, & math_tensorproduct, & math_norm3, & math_mul33x33, & math_mul33x3, & math_trace33, & math_symmetric33, & math_Mandel33to6, & math_Mandel3333to66, & math_Voigt66to3333, & math_axisAngleToR, & INRAD use IO, only: & IO_error implicit none integer(pInt), intent(in) :: myPhase real(pReal), intent(in) :: & CoverA, & aA, & aM, & cM real(pReal), dimension(3) :: & sdU, snU, & np, nn real(pReal), dimension(3,lattice_maxNslip) :: & sd, sn real(pReal), dimension(3,3,2,lattice_maxNnonSchmid,lattice_maxNslip) :: & sns real(pReal), dimension(3,lattice_maxNtwin) :: & td, tn real(pReal), dimension(lattice_maxNtwin) :: & ts real(pReal), dimension(3,lattice_maxNtrans) :: & rtr, rb real(pReal), dimension(lattice_maxNtrans) :: & atr, ab real(pReal), dimension(3,3,3) :: & bainstr real(pReal), dimension(3,3,lattice_maxNtrans) :: & ub integer(pInt) :: & i,j, & myNslip, myNtwin, myNtrans lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),& lattice_C66(1:6,1:6,myPhase)) lattice_mu(myPhase) = 0.2_pReal *( lattice_C66(1,1,myPhase) & - lattice_C66(1,2,myPhase) & + 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 lattice_nu(myPhase) = ( lattice_C66(1,1,myPhase) & + 4.0_pReal*lattice_C66(1,2,myPhase) & - 2.0_pReal*lattice_C66(4,4,myPhase)) & /( 4.0_pReal*lattice_C66(1,1,myPhase) & + 6.0_pReal*lattice_C66(1,2,myPhase) & + 2.0_pReal*lattice_C66(4,4,myPhase))! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5 lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt lattice_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel do i = 1_pInt, 6_pInt if (abs(lattice_C66(i,i,myPhase)) 0.0_pReal) .and. (aM > 0.0_pReal) .and. (cM == 0.0_pReal)) then bainstr(1,1,1) = aM/aA ! 3 Bain strain variants for fcc to bcc transformation bainstr(2,2,1) = sqrt(2.0_pReal)*aM/aA bainstr(3,3,1) = sqrt(2.0_pReal)*aM/aA bainstr(1,1,2) = sqrt(2.0_pReal)*aM/aA bainstr(2,2,2) = aM/aA bainstr(3,3,2) = sqrt(2.0_pReal)*aM/aA bainstr(1,1,3) = sqrt(2.0_pReal)*aM/aA bainstr(2,2,3) = sqrt(2.0_pReal)*aM/aA bainstr(3,3,3) = aM/aA endif ub(1:3,1:3,i) = bainstr(1:3,1:3,LATTICE_fcc_bainVariant(i)) ! Pitsch OR enddo 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_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 !-------------------------------------------------------------------------------------------------- ! bcc case (LATTICE_bcc_ID) myNslip = lattice_bcc_Nslip myNtwin = lattice_bcc_Ntwin myNtrans = lattice_bcc_Ntrans 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) / math_norm3(sd(1:3,i)) snU = sn(1:3,i) / math_norm3(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_tensorproduct(sdU, np) sns(1:3,1:3,2,1,i) = math_tensorproduct(-sdU, nn) sns(1:3,1:3,1,2,i) = math_tensorproduct(math_vectorproduct(snU, sdU), snU) sns(1:3,1:3,2,2,i) = math_tensorproduct(math_vectorproduct(snU, -sdU), snU) sns(1:3,1:3,1,3,i) = math_tensorproduct(math_vectorproduct(np, sdU), np) sns(1:3,1:3,2,3,i) = math_tensorproduct(math_vectorproduct(nn, -sdU), nn) sns(1:3,1:3,1,4,i) = math_tensorproduct(snU, snU) sns(1:3,1:3,2,4,i) = math_tensorproduct(snU, snU) sns(1:3,1:3,1,5,i) = math_tensorproduct(math_vectorproduct(snU, sdU), math_vectorproduct(snU, sdU)) sns(1:3,1:3,2,5,i) = math_tensorproduct(math_vectorproduct(snU, -sdU), math_vectorproduct(snU, -sdU)) sns(1:3,1:3,1,6,i) = math_tensorproduct(sdU, sdU) sns(1:3,1:3,2,6,i) = math_tensorproduct(-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 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_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 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 lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_hex_NslipSystem lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_hex_NtwinSystem lattice_NtransSystem(1:lattice_maxNtransFamily,myPhase) = lattice_hex_NtransSystem lattice_NnonSchmid(myPhase) = lattice_hex_NnonSchmid lattice_interactionSlipSlip(1:myNslip,1:myNslip,myPhase) = lattice_hex_interactionSlipSlip lattice_interactionSlipTwin(1:myNslip,1:myNtwin,myPhase) = lattice_hex_interactionSlipTwin lattice_interactionTwinSlip(1:myNtwin,1:myNslip,myPhase) = lattice_hex_interactionTwinSlip lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myPhase) = lattice_hex_interactionTwinTwin !-------------------------------------------------------------------------------------------------- ! orthorombic and isotropic (no crystal plasticity) case (LATTICE_ort_ID, LATTICE_iso_ID) myNslip = 0_pInt myNtwin = 0_pInt myNtrans = 0_pInt !-------------------------------------------------------------------------------------------------- ! something went wrong case default call IO_error(450_pInt,ext_msg='lattice_initializeStructure') end select do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure lattice_sd(1:3,i,myPhase) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector lattice_sn(1:3,i,myPhase) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector lattice_st(1:3,i,myPhase) = math_vectorproduct(lattice_sd(1:3,i,myPhase), & lattice_sn(1:3,i,myPhase)) lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct(lattice_sd(1:3,i,myPhase), & lattice_sn(1:3,i,myPhase)) do j = 1_pInt,lattice_NnonSchmid(myPhase) lattice_Sslip(1:3,1:3,2*j ,i,myPhase) = sns(1:3,1:3,1,j,i) lattice_Sslip(1:3,1:3,2*j+1,i,myPhase) = sns(1:3,1:3,2,j,i) enddo do j = 1_pInt,1_pInt+2_pInt*lattice_NnonSchmid(myPhase) lattice_Sslip_v(1:6,j,i,myPhase) = & math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,j,i,myPhase))) enddo if (abs(math_trace33(lattice_Sslip(1:3,1:3,1,i,myPhase))) > tol_math_check) & call IO_error(0_pInt,myPhase,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix') enddo do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure lattice_td(1:3,i,myPhase) = td(1:3,i)/math_norm3(td(1:3,i)) ! make unit vector lattice_tn(1:3,i,myPhase) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector lattice_tt(1:3,i,myPhase) = math_vectorproduct(lattice_td(1:3,i,myPhase), & lattice_tn(1:3,i,myPhase)) lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct(lattice_td(1:3,i,myPhase), & lattice_tn(1:3,i,myPhase)) lattice_Stwin_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myPhase))) lattice_Qtwin(1:3,1:3,i,myPhase) = math_axisAngleToR(tn(1:3,i),180.0_pReal*INRAD) lattice_shearTwin(i,myPhase) = ts(i) if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myPhase))) > tol_math_check) & call IO_error(301_pInt,myPhase,ext_msg = 'dilatational twin Schmid matrix') enddo do i = 1_pInt,myNtrans lattice_Rtrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rtr(1:3,i),atr(i)*INRAD) lattice_Utrans(1:3,1:3,i,myPhase) = ub(1:3,1:3,i) lattice_Btrans(1:3,1:3,i,myPhase) = math_axisAngleToR(rb(1:3,i),ab(i)*INRAD) lattice_Qtrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), & lattice_Btrans(1:3,1:3,i,myPhase)) lattice_NItrans(1:3,1:3,i,myPhase) = math_mul33x33(lattice_Rtrans(1:3,1:3,i,myPhase), & lattice_Utrans(1:3,1:3,i,myPhase)) - math_identity2nd(3) lattice_NItrans_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_NItrans(1:3,1:3,i,myPhase))) enddo end subroutine lattice_initializeStructure !-------------------------------------------------------------------------------------------------- !> @brief Symmetrizes stiffness matrix according to lattice type !-------------------------------------------------------------------------------------------------- pure function lattice_symmetrizeC66(struct,C66) implicit none integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(6,6), intent(in) :: C66 real(pReal), dimension(6,6) :: lattice_symmetrizeC66 integer(pInt) :: j,k lattice_symmetrizeC66 = 0.0_pReal select case(struct) case (LATTICE_iso_ID) forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2) lattice_symmetrizeC66(k,k) = C66(1,1) lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2)) end forall case (LATTICE_fcc_ID,LATTICE_bcc_ID) forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2) lattice_symmetrizeC66(k,k) = C66(1,1) lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4) end forall case (LATTICE_hex_ID) lattice_symmetrizeC66(1,1) = C66(1,1) lattice_symmetrizeC66(2,2) = C66(1,1) lattice_symmetrizeC66(3,3) = C66(3,3) lattice_symmetrizeC66(1,2) = C66(1,2) lattice_symmetrizeC66(2,1) = C66(1,2) lattice_symmetrizeC66(1,3) = C66(1,3) lattice_symmetrizeC66(3,1) = C66(1,3) lattice_symmetrizeC66(2,3) = C66(1,3) lattice_symmetrizeC66(3,2) = C66(1,3) lattice_symmetrizeC66(4,4) = C66(4,4) lattice_symmetrizeC66(5,5) = C66(4,4) lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2)) case (LATTICE_ort_ID) lattice_symmetrizeC66(1,1) = C66(1,1) lattice_symmetrizeC66(2,2) = C66(2,2) lattice_symmetrizeC66(3,3) = C66(3,3) lattice_symmetrizeC66(1,2) = C66(1,2) lattice_symmetrizeC66(2,1) = C66(1,2) lattice_symmetrizeC66(1,3) = C66(1,3) lattice_symmetrizeC66(3,1) = C66(1,3) lattice_symmetrizeC66(2,3) = C66(2,3) lattice_symmetrizeC66(3,2) = C66(2,3) lattice_symmetrizeC66(4,4) = C66(4,4) lattice_symmetrizeC66(5,5) = C66(5,5) lattice_symmetrizeC66(6,6) = C66(6,6) case default lattice_symmetrizeC66 = C66 end select end function lattice_symmetrizeC66 !-------------------------------------------------------------------------------------------------- !> @brief Symmetrizes 2nd order tensor according to lattice type !-------------------------------------------------------------------------------------------------- pure function lattice_symmetrize33(struct,T33) implicit none integer(kind(LATTICE_undefined_ID)), intent(in) :: struct real(pReal), dimension(3,3), intent(in) :: T33 real(pReal), dimension(3,3) :: lattice_symmetrize33 integer(pInt) :: j,k lattice_symmetrize33 = 0.0_pReal select case(struct) case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID) forall(k=1_pInt:3_pInt) lattice_symmetrize33(k,k) = T33(1,1) case (LATTICE_hex_ID) lattice_symmetrize33(1,1) = T33(1,1) lattice_symmetrize33(2,2) = T33(1,1) lattice_symmetrize33(3,3) = T33(3,3) case (LATTICE_ort_ID) lattice_symmetrize33(1,1) = T33(1,1) lattice_symmetrize33(2,2) = T33(2,2) lattice_symmetrize33(3,3) = T33(3,3) case default lattice_symmetrize33 = T33 end select end function lattice_symmetrize33 !-------------------------------------------------------------------------------------------------- !> @brief figures whether unit quat falls into stereographic standard triangle !-------------------------------------------------------------------------------------------------- logical pure function lattice_qInSST(Q, struct) use math, only: & math_qToRodrig implicit none real(pReal), dimension(4), intent(in) :: Q ! orientation integer(kind(LATTICE_undefined_ID)), intent(in) :: struct ! lattice structure real(pReal), dimension(3) :: Rodrig ! Rodrigues vector of Q Rodrig = math_qToRodrig(Q) if (any(Rodrig/=Rodrig)) then lattice_qInSST = .false. else select case (struct) case (LATTICE_bcc_ID,LATTICE_fcc_ID) lattice_qInSST = Rodrig(1) > Rodrig(2) .and. & Rodrig(2) > Rodrig(3) .and. & Rodrig(3) > 0.0_pReal case (LATTICE_hex_ID) lattice_qInSST = Rodrig(1) > sqrt(3.0_pReal)*Rodrig(2) .and. & Rodrig(2) > 0.0_pReal .and. & Rodrig(3) > 0.0_pReal case default lattice_qInSST = .true. end select endif end function lattice_qInSST !-------------------------------------------------------------------------------------------------- !> @brief calculates the disorientation for 2 unit quaternions !-------------------------------------------------------------------------------------------------- pure function lattice_qDisorientation(Q1, Q2, struct) use prec, only: & tol_math_check use math, only: & math_qMul, & math_qConj implicit none real(pReal), dimension(4) :: lattice_qDisorientation real(pReal), dimension(4), intent(in) :: & Q1, & ! 1st orientation Q2 ! 2nd orientation integer(kind(LATTICE_undefined_ID)), optional, intent(in) :: & ! if given, symmetries between the two orientation will be considered struct real(pReal), dimension(4) :: dQ,dQsymA,mis integer(pInt) :: i,j,k,s,symmetry integer(kind(LATTICE_undefined_ID)) :: myStruct !-------------------------------------------------------------------------------------------------- ! check if a structure with known symmetries is given if (present(struct)) then myStruct = struct select case (struct) case(LATTICE_fcc_ID,LATTICE_bcc_ID) symmetry = 1_pInt case(LATTICE_hex_ID) symmetry = 2_pInt case default symmetry = 0_pInt end select else symmetry = 0_pInt myStruct = LATTICE_undefined_ID endif !-------------------------------------------------------------------------------------------------- ! calculate misorientation, for cubic(1) and hexagonal(2) structure find symmetries dQ = math_qMul(math_qConj(Q1),Q2) lattice_qDisorientation = dQ select case(symmetry) case (1_pInt,2_pInt) s = sum(lattice_NsymOperations(1:symmetry-1_pInt)) do i = 1_pInt,2_pInt dQ = math_qConj(dQ) ! switch order of "from -- to" do j = 1_pInt,lattice_NsymOperations(symmetry) ! run through first crystal's symmetries dQsymA = math_qMul(lattice_symOperations(1:4,s+j),dQ) ! apply sym do k = 1_pInt,lattice_NsymOperations(symmetry) ! run through 2nd crystal's symmetries mis = math_qMul(dQsymA,lattice_symOperations(1:4,s+k)) ! apply sym if (mis(1) < 0.0_pReal) & ! want positive angle mis = -mis if (mis(1)-lattice_qDisorientation(1) > -tol_math_check & .and. lattice_qInSST(mis,LATTICE_undefined_ID)) lattice_qDisorientation = mis ! found better one enddo; enddo; enddo case (0_pInt) if (lattice_qDisorientation(1) < 0.0_pReal) lattice_qDisorientation = -lattice_qDisorientation ! keep omega within 0 to 180 deg end select end function lattice_qDisorientation end module lattice