!* $Id$ !************************************ !* Module: LATTICE * !************************************ !* contains: * !* - Lattice structure definition * !* - Slip system definition * !* - Schmid matrices calculation * !************************************ MODULE lattice !*** Include other modules *** use prec, only: pReal,pInt implicit none !************************************ !* Lattice structures * !************************************ integer(pInt) lattice_Nhexagonal, & ! # of hexagonal lattice structure (from tag CoverA_ratio) lattice_Nstructure ! # of lattice structures (1: fcc,2: bcc,3+: hexagonal) integer(pInt), parameter :: lattice_maxNslipFamily = 4 ! max # of slip system families over lattice structures integer(pInt), parameter :: lattice_maxNtwinFamily = 4 ! max # of twin system families over lattice structures integer(pInt), parameter :: lattice_maxNslip = 48 ! max # of slip systems over lattice structures integer(pInt), parameter :: lattice_maxNtwin = 24 ! max # of twin systems over lattice structures integer(pInt), parameter :: lattice_maxNinteraction = 20 ! max # of interaction types (in hardening matrix part) integer(pInt), pointer, dimension(:,:) :: interactionSlipSlip, & interactionSlipTwin, & interactionTwinSlip, & interactionTwinTwin ! Schmid matrices, normal, shear direction and d x n of slip systems real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Sslip real(pReal), allocatable, dimension(:,:,:) :: lattice_Sslip_v real(pReal), allocatable, dimension(:,:,:) :: lattice_sn, & lattice_sd, & lattice_st ! rotation and Schmid matrices, normal, shear direction and d x n of twin systems real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Qtwin real(pReal), allocatable, dimension(:,:,:,:) :: lattice_Stwin real(pReal), allocatable, dimension(:,:,:) :: lattice_Stwin_v real(pReal), allocatable, dimension(:,:,:) :: lattice_tn, & lattice_td, & lattice_tt ! characteristic twin shear real(pReal), allocatable, dimension(:,:) :: lattice_shearTwin ! number of slip and twin systems in each family integer(pInt), allocatable, dimension(:,:) :: lattice_NslipSystem, & lattice_NtwinSystem ! interaction type of slip and twin systems among each other integer(pInt), allocatable, dimension(:,:,:) :: lattice_interactionSlipSlip, & lattice_interactionSlipTwin, & lattice_interactionTwinSlip, & lattice_interactionTwinTwin !============================== fcc (1) ================================= integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_fcc_NslipSystem = (/12, 0, 0, 0/) integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_fcc_NtwinSystem = (/12, 0, 0, 0/) integer(pInt), parameter :: lattice_fcc_Nslip = 12 ! sum(lattice_fcc_NslipSystem) integer(pInt), parameter :: lattice_fcc_Ntwin = 12 ! sum(lattice_fcc_NtwinSystem) integer(pInt) :: lattice_fcc_Nstructure = 0_pInt real(pReal), dimension(3+3,lattice_fcc_Nslip), parameter :: lattice_fcc_systemSlip = & reshape((/& ! Slip system <110>{111} Sorted according to Eisenlohr & Hantcherli 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 & /),(/3+3,lattice_fcc_Nslip/)) real(pReal), dimension(3+3,lattice_fcc_Ntwin), parameter :: lattice_fcc_systemTwin = & reshape((/& ! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli -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 & /),(/3+3,lattice_fcc_Ntwin/)) real(pReal), dimension(lattice_fcc_Ntwin), parameter :: lattice_fcc_shearTwin = & reshape((/& ! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812, & 0.7071067812 & /),(/lattice_fcc_Ntwin/)) integer(pInt), target, dimension(lattice_fcc_Nslip,lattice_fcc_Nslip) :: lattice_fcc_interactionSlipSlip = & reshape((/& ! Interaction types ! 1 --- self interaction ! 2 --- coplanar interaction ! 3 --- collinear interaction ! 4 --- Hirth locks ! 5 --- glissile junctions ! 6 --- Lomer locks 1,2,2,4,6,5,3,5,5,4,5,6, & 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, & 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 & /),(/lattice_fcc_Nslip,lattice_fcc_Nslip/)) integer(pInt), target, dimension(lattice_fcc_Ntwin,lattice_fcc_Nslip) :: lattice_fcc_interactionSlipTwin = & reshape((/& 1,1,1,2,2,1,1,2,2,2,1,2, & 1,1,1,2,2,1,1,2,2,2,1,2, & 1,1,1,2,2,1,1,2,2,2,1,2, & 2,2,1,1,1,1,2,1,2,1,2,2, & 2,2,1,1,1,1,2,1,2,1,2,2, & 2,2,1,1,1,1,2,1,2,1,2,2, & 1,2,2,2,1,2,1,1,1,2,2,1, & 1,2,2,2,1,2,1,1,1,2,2,1, & 1,2,2,2,1,2,1,1,1,2,2,1, & 2,1,2,1,2,2,2,2,1,1,1,1, & 2,1,2,1,2,2,2,2,1,1,1,1, & 2,1,2,1,2,2,2,2,1,1,1,1 & /),(/lattice_fcc_Ntwin,lattice_fcc_Nslip/)) integer(pInt), target, dimension(lattice_fcc_Nslip,lattice_fcc_Ntwin) :: lattice_fcc_interactionTwinSlip = 0 integer(pInt), target, dimension(lattice_fcc_Ntwin,lattice_fcc_Ntwin) :: lattice_fcc_interactionTwinTwin = & reshape((/& 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, & 2,2,2,1,1,1,2,2,2,2,2,2, & 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 & /),(/lattice_fcc_Ntwin,lattice_fcc_Ntwin/)) !============================== bcc (2) ================================= integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_bcc_NslipSystem = (/12,12,24, 0/) integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_bcc_NtwinSystem = (/12, 0, 0, 0/) integer(pInt), parameter :: lattice_bcc_Nslip = 48 ! sum(lattice_bcc_NslipSystem) integer(pInt), parameter :: lattice_bcc_Ntwin = 12 ! sum(lattice_bcc_NtwinSystem) integer(pInt) :: lattice_bcc_Nstructure = 0_pInt real(pReal), dimension(3+3,lattice_bcc_Nslip), parameter :: lattice_bcc_systemSlip = & reshape((/& ! Slip system <111>{110} meaningful sorting? 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} meaningful sorting ? -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} meaningful sorting ? 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 & /),(/3+3,lattice_bcc_Nslip/)) ! twin system <111>{112} ! MISSING: not implemented yet -- now dummy copy from fcc !! real(pReal), dimension(3+3,lattice_bcc_Ntwin), parameter :: lattice_bcc_systemTwin = & reshape((/& ! Twin system <112>{111} Sorted according to Eisenlohr & Hantcherli -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 & /),(/3+3,lattice_bcc_Ntwin/)) real(pReal), dimension(lattice_bcc_Ntwin), parameter :: lattice_bcc_shearTwin = & reshape((/& ! Twin system {111}<112> just a dummy 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123, & 0.123 & /),(/lattice_bcc_Ntwin/)) !*** slip--slip interactions for BCC structures (2) *** integer(pInt), target, dimension(lattice_bcc_Nslip,lattice_bcc_Nslip) :: lattice_bcc_interactionSlipSlip = & reshape((/& 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,2, & 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1 & /),(/lattice_bcc_Nslip,lattice_bcc_Nslip/)) !*** slip--twin interactions for BCC structures (2) *** ! MISSING: not implemented yet integer(pInt), target, dimension(lattice_bcc_Ntwin,lattice_bcc_Nslip) :: lattice_bcc_interactionSlipTwin = & reshape((/& 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0 & /),(/lattice_bcc_Ntwin,lattice_bcc_Nslip/)) !*** twin--slip interactions for BCC structures (2) *** ! MISSING: not implemented yet integer(pInt), target, dimension(lattice_bcc_Nslip,lattice_bcc_Ntwin) :: lattice_bcc_interactionTwinSlip = & reshape((/& 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 & /),(/lattice_bcc_Nslip,lattice_bcc_Ntwin/)) !*** twin-twin interactions for BCC structures (2) *** ! MISSING: not implemented yet integer(pInt), target, dimension(lattice_bcc_Ntwin,lattice_bcc_Ntwin) :: lattice_bcc_interactionTwinTwin = & reshape((/& 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0, & 0,0,0,0,0,0,0,0,0,0,0,0 & /),(/lattice_bcc_Ntwin,lattice_bcc_Ntwin/)) !============================== hex (3+) ================================= integer(pInt), parameter, dimension(lattice_maxNslipFamily) :: lattice_hex_NslipSystem = (/ 3, 3, 6,12/) integer(pInt), parameter, dimension(lattice_maxNtwinFamily) :: lattice_hex_NtwinSystem = (/ 6, 6, 6, 6/) integer(pInt), parameter :: lattice_hex_Nslip = 24 ! sum(lattice_hex_NslipSystem) integer(pInt), parameter :: lattice_hex_Ntwin = 24 ! sum(lattice_hex_NtwinSystem) integer(pInt) :: lattice_hex_Nstructure = 0_pInt !* sorted by YJ.Ro and Philip real(pReal), dimension(4+4,lattice_hex_Nslip), parameter :: lattice_hex_systemSlip = & reshape((/& ! Basal systems <1120>{0001} (independent of c/a-ratio, Bravais notation (4 coordinate base)) 2, -1, -1, 0, 0, 0, 0, 1, & 1, 1, -2, 0, 0, 0, 0, 1, & -1, 2, -1, 0, 0, 0, 0, 1, & ! 1st type prismatic systems <1120>{1010} (independent of c/a-ratio) 2, -1, -1, 0, 0, -1, 1, 0, & 1, 1, 2, 0, 1, -1, 0, 0, & -1, 2, -1, 0, 1, 0, -1, 0, & ! 1st type 1st order pyramidal systems <1120>{1011} 2, -1, -1, 0, 0, -1, 1, 1, & 1, 1, -2, 0, 1, -1, 0, 1, & -1, 2, -1, 0, 1, 0, -1, 1, & -2, 1, 1, 0, 0, 1, -1, 1, & -1, -1, 2, 0, -1, 1, 0, 1, & 1, -2, 1, 0, -1, 0, 1, 1, & ! pyramidal system: c+a slip <2113>{1011} -- plane normals depend on the c/a-ratio 2, -1, -1, -3, 1, -1, 0, 1, & 1, 1, -2, -3, 1, 0, -1, 1, & -1, 2, -1, -3, 1, -1, 0, 1, & -2, 1, 1, -3, 1, 0, -1, 1, & -1, -1, 2, -3, 0, 1, -1, 1, & 1, -2, 1, -3, 0, -1, 1, 1, & -2, 1, 1, -3, -1, 0, 1, 1, & -1, -1, 2, -3, 0, -1, 1, 1, & 1, -2, 1, -3, 0, 1, -1, 1, & 2, -1, -1, -3, -1, 1, 0, 1, & 1, 1, -2, -3, -1, 0, 1, 1, & -1, 2, -1, -3, -1, 1, 0, 1 & /),(/4+4,lattice_hex_Nslip/)) real(pReal), dimension(4+4,lattice_hex_Ntwin), parameter :: lattice_hex_systemTwin = & reshape((/& 0, 1, -1, 1, 0, -1, 1, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a) -1, 1, 0, 1, 1, -1, 0, 2, & -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, & 2, -1, -1, -3, 2, -1, -1, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a) 1, 1, -2, -3, 1, 1, -2, 2, & !! -1, 2, -1, -3, -1, 2, -1, 2, & -2, 1, 1, -3, -2, 1, 1, 2, & -1, -1, 2, -3, -1, -1, 2, 2, & 1, -2, 1, -3, 1, -2, 1, 2, & -2, 1, 1, 6, 2, -1, -1, 1, & ! <-1-1.6>{11.1} shear = 1/(c/a) -1, -1, 2, 6, 1, 1, -2, 1, & !! 1, -2, 1, 6, -1, 2, -1, 1, & 2, -1, -1, 6, -2, 1, 1, 1, & 1, 1, -2, 6, -1, -1, 2, 1, & -1, 2, -1, 6, 1, -2, 1, 1, & 1, 0, -1, -2, 1, 0, -1, 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, & 0, -1, 1, -2, 0, -1, 1, 1, & 1, -1, 0, -2, 1, -1, 0, 1, & -1, 1, 0, -2, -1, 1, 0, 1 & /),(/4+4,lattice_hex_Ntwin/)) !* Sort? Numbering of twin system follows Prof. Tom Bieler's scheme (to be consistent with his work); but numbering in data was restarted from 1 & integer(pInt), dimension(lattice_hex_Ntwin), parameter :: lattice_hex_shearTwin = & ! indicator to formula further below reshape((/& 1, & ! {10.2}<-10.1> 1, & 1, & 1, & 1, & 1, & 2, & ! {11.2}<11.-3> 2, & 2, & 2, & 2, & 2, & 3, & ! {11.1}<-1-1.6> 3, & 3, & 3, & 3, & 3, & 4, & ! {10.1}<10.-2> 4, & 4, & 4, & 4, & 4 & /),(/lattice_hex_Ntwin/)) !* four different interaction type matrix !* 1. slip-slip interaction - 20 types !* 2. slip-twin interaction - 16 types !* 3. twin-twin interaction - 20 types !* 4. twin-slip interaction - 16 types integer(pInt), target, dimension(lattice_hex_Nslip,lattice_hex_Nslip) :: lattice_hex_interactionSlipSlip = & reshape((/& 1, 5, 5, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, & 5, 1, 5, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, & 5, 5, 1, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14,14,14,14,14,14,14, & ! 15,15,15, 2, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, & 15,15,15, 6, 2, 6, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, & 15,15,15, 6, 6, 2, 10,10,10,10,10,10, 13,13,13,13,13,13,13,13,13,13,13,13, & ! 18,18,18, 16,16,16, 3, 7, 7, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, & 18,18,18, 16,16,16, 7, 3, 7, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, & 18,18,18, 16,16,16, 7, 7, 3, 7, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, & 18,18,18, 16,16,16, 7, 7, 7, 3, 7, 7, 11,11,11,11,11,11,11,11,11,11,11,11, & 18,18,18, 16,16,16, 7, 7, 7, 7, 3, 7, 11,11,11,11,11,11,11,11,11,11,11,11, & 18,18,18, 16,16,16, 7, 7, 7, 7, 7, 3, 11,11,11,11,11,11,11,11,11,11,11,11, & ! 20,20,20, 19,19,19, 17,17,17,17,17,17, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, & 20,20,20, 19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4 & /),(/lattice_hex_Nslip,lattice_hex_Nslip/)) !* isotropic interaction at the moment integer(pInt), target, dimension(lattice_hex_Ntwin,lattice_hex_Nslip) :: lattice_hex_interactionSlipTwin = & reshape((/& 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, & 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, & 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 & /),(/lattice_hex_Ntwin,lattice_hex_Nslip/)) !* isotropic interaction at the moment integer(pInt), target, dimension(lattice_hex_Nslip,lattice_hex_Ntwin) :: lattice_hex_interactionTwinSlip = & reshape((/& 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! --> slip 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! | 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! v 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! twin 1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, & ! 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & 2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, & ! 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & 3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, & ! 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, & 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, & 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, & 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, & 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, & 4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16 & /),(/lattice_hex_Nslip,lattice_hex_Ntwin/)) integer(pInt), target, dimension(lattice_hex_Ntwin,lattice_hex_Ntwin) :: lattice_hex_interactionTwinTwin = & reshape((/& 1, 5, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & 5, 1, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & 5, 5, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & 5, 5, 5, 1, 5, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & 5, 5, 5, 5, 1, 5, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & 5, 5, 5, 5, 5, 1, 9, 9, 9, 9, 9, 9, 12,12,12,12,12,12, 14,14,14,14,14,14, & ! 15,15,15,15,15,15, 2, 6, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, & 15,15,15,15,15,15, 6, 2, 6, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, & 15,15,15,15,15,15, 6, 6, 2, 6, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, & 15,15,15,15,15,15, 6, 6, 6, 2, 6, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, & 15,15,15,15,15,15, 6, 6, 6, 6, 2, 6, 10,10,10,10,10,10, 13,13,13,13,13,13, & 15,15,15,15,15,15, 6, 6, 6, 6, 6, 2, 10,10,10,10,10,10, 13,13,13,13,13,13, & ! 18,18,18,18,18,18, 16,16,16,16,16,16, 3, 7, 7, 7, 7, 7, 11,11,11,11,11,11, & 18,18,18,18,18,18, 16,16,16,16,16,16, 7, 3, 7, 7, 7, 7, 11,11,11,11,11,11, & 18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 3, 7, 7, 7, 11,11,11,11,11,11, & 18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 3, 7, 7, 11,11,11,11,11,11, & 18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 3, 7, 11,11,11,11,11,11, & 18,18,18,18,18,18, 16,16,16,16,16,16, 7, 7, 7, 7, 7, 3, 11,11,11,11,11,11, & ! 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 4, 8, 8, 8, 8, 8, & 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 4, 8, 8, 8, 8, & 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 4, 8, 8, 8, & 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 4, 8, 8, & 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 4, 8, & 20,20,20,20,20,20, 19,19,19,19,19,19, 17,17,17,17,17,17, 8, 8, 8, 8, 8, 4 & /),(/lattice_hex_Ntwin,lattice_hex_Ntwin/)) CONTAINS !**************************************** !* - lattice_init !* - lattice_initializeStructure !**************************************** pure function lattice_symmetryType(structID) !************************************** !* maps structure to symmetry type * !* fcc(1) and bcc(2) are cubic(1) * !* hex(3+) is hexagonal(2) * !************************************** implicit none integer(pInt), intent(in) :: structID integer(pInt) lattice_symmetryType select case(structID) case (1,2) lattice_symmetryType = 1_pInt case (3:) lattice_symmetryType = 2_pInt case default lattice_symmetryType = 0_pInt end select return end function subroutine lattice_init() !************************************** !* Module initialization * !************************************** use IO, only: IO_open_file,IO_countSections,IO_countTagInPart,IO_error use material, only: material_configfile,material_partPhase implicit none integer(pInt), parameter :: fileunit = 200 integer(pInt) i,Nsections write(6,*) write(6,*) '<<<+- lattice init -+>>>' write(6,*) '$Id$' write(6,*) if(.not. IO_open_file(fileunit,material_configFile)) call IO_error(100) ! cannot open config file Nsections = IO_countSections(fileunit,material_partPhase) lattice_Nstructure = 2_pInt + sum(IO_countTagInPart(fileunit,material_partPhase,'covera_ratio',Nsections)) ! fcc + bcc + all hex ! lattice_Nstructure = Nsections + 2_pInt ! most conservative assumption close(fileunit) write(6,'(a16,x,i5)') '# sections:',Nsections write(6,'(a16,x,i5)') '# structures:',lattice_Nstructure write(6,*) allocate(lattice_Sslip(3,3,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip = 0.0_pReal allocate(lattice_Sslip_v(6,lattice_maxNslip,lattice_Nstructure)); lattice_Sslip_v = 0.0_pReal allocate(lattice_sd(3,lattice_maxNslip,lattice_Nstructure)); lattice_sd = 0.0_pReal allocate(lattice_st(3,lattice_maxNslip,lattice_Nstructure)); lattice_st = 0.0_pReal allocate(lattice_sn(3,lattice_maxNslip,lattice_Nstructure)); lattice_sn = 0.0_pReal allocate(lattice_Qtwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Qtwin = 0.0_pReal allocate(lattice_Stwin(3,3,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin = 0.0_pReal allocate(lattice_Stwin_v(6,lattice_maxNtwin,lattice_Nstructure)); lattice_Stwin_v = 0.0_pReal allocate(lattice_td(3,lattice_maxNtwin,lattice_Nstructure)); lattice_td = 0.0_pReal allocate(lattice_tt(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tt = 0.0_pReal allocate(lattice_tn(3,lattice_maxNtwin,lattice_Nstructure)); lattice_tn = 0.0_pReal allocate(lattice_shearTwin(lattice_maxNtwin,lattice_Nstructure)); lattice_shearTwin = 0.0_pReal allocate(lattice_NslipSystem(lattice_maxNslipFamily,lattice_Nstructure)); lattice_NslipSystem = 0.0_pReal allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,lattice_Nstructure)); lattice_NtwinSystem = 0.0_pReal allocate(lattice_interactionSlipSlip(lattice_maxNslip,lattice_maxNslip,lattice_Nstructure)); lattice_interactionSlipSlip = 0_pInt ! other:me allocate(lattice_interactionSlipTwin(lattice_maxNtwin,lattice_maxNslip,lattice_Nstructure)); lattice_interactionSlipTwin = 0_pInt ! other:me allocate(lattice_interactionTwinSlip(lattice_maxNslip,lattice_maxNtwin,lattice_Nstructure)); lattice_interactionTwinSlip = 0_pInt ! other:me allocate(lattice_interactionTwinTwin(lattice_maxNtwin,lattice_maxNtwin,lattice_Nstructure)); lattice_interactionTwinTwin = 0_pInt ! other:me end subroutine function lattice_initializeStructure(struct,CoverA) !************************************** !* Calculation of Schmid * !* matrices, etc. * !************************************** use prec, only: pReal,pInt use math use IO, only: IO_error implicit none character(len=*) struct real(pReal) CoverA real(pReal), dimension(3,lattice_maxNslip) :: sd = 0.0_pReal, & sn = 0.0_pReal, & st = 0.0_pReal real(pReal), dimension(3,lattice_maxNtwin) :: td = 0.0_pReal, & tn = 0.0_pReal, & tt = 0.0_pReal real(pReal), dimension(lattice_maxNtwin) :: ts = 0.0_pReal real(pReal), dimension(3) :: hex_d = 0.0_pReal, & hex_n = 0.0_pReal integer(pInt), dimension(lattice_maxNslipFamily) :: myNslipSystem = 0_pInt integer(pInt), dimension(lattice_maxNtwinFamily) :: myNtwinSystem = 0_pInt integer(pInt) :: i,myNslip,myNtwin,myStructure = 0_pInt logical :: processMe integer(pInt) lattice_initializeStructure processMe = .false. select case(struct(1:3)) ! check first three chars of structure name case ('fcc') myStructure = 1_pInt myNslipSystem = lattice_fcc_NslipSystem ! size of slip system families myNtwinSystem = lattice_fcc_NtwinSystem ! size of twin system families myNslip = lattice_fcc_Nslip ! overall number of slip systems myNtwin = lattice_fcc_Ntwin ! overall number of twin systems lattice_fcc_Nstructure = lattice_fcc_Nstructure + 1_pInt ! count fcc instances if (lattice_fcc_Nstructure == 1_pInt) then ! me is first fcc structure processMe = .true. do i = 1,myNslip ! calculate slip system vectors sd(:,i) = lattice_fcc_systemSlip(1:3,i)/dsqrt(math_mul3x3(lattice_fcc_systemSlip(1:3,i),lattice_fcc_systemSlip(1:3,i))) sn(:,i) = lattice_fcc_systemSlip(4:6,i)/dsqrt(math_mul3x3(lattice_fcc_systemSlip(4:6,i),lattice_fcc_systemSlip(4:6,i))) st(:,i) = math_vectorproduct(sd(:,i),sn(:,i)) enddo do i = 1,myNtwin ! calculate twin system vectors and (assign) shears td(:,i) = lattice_fcc_systemTwin(1:3,i)/dsqrt(math_mul3x3(lattice_fcc_systemTwin(1:3,i),lattice_fcc_systemTwin(1:3,i))) tn(:,i) = lattice_fcc_systemTwin(4:6,i)/dsqrt(math_mul3x3(lattice_fcc_systemTwin(4:6,i),lattice_fcc_systemTwin(4:6,i))) tt(:,i) = math_vectorproduct(td(:,i),tn(:,i)) ts(i) = lattice_fcc_shearTwin(i) enddo interactionSlipSlip => lattice_fcc_interactionSlipSlip interactionSlipTwin => lattice_fcc_interactionSlipTwin interactionTwinSlip => lattice_fcc_interactionTwinSlip interactionTwinTwin => lattice_fcc_interactionTwinTwin endif case ('bcc') myStructure = 2_pInt myNslipSystem = lattice_bcc_NslipSystem ! size of slip system families myNtwinSystem = lattice_bcc_NtwinSystem ! size of twin system families myNslip = lattice_bcc_Nslip ! overall number of slip systems myNtwin = lattice_bcc_Ntwin ! overall number of twin systems lattice_bcc_Nstructure = lattice_bcc_Nstructure + 1_pInt ! count bcc instances if (lattice_bcc_Nstructure == 1_pInt) then ! me is first bcc structure processMe = .true. do i = 1,myNslip ! calculate slip system vectors sd(:,i) = lattice_bcc_systemSlip(1:3,i)/dsqrt(math_mul3x3(lattice_bcc_systemSlip(1:3,i),lattice_bcc_systemSlip(1:3,i))) sn(:,i) = lattice_bcc_systemSlip(4:6,i)/dsqrt(math_mul3x3(lattice_bcc_systemSlip(4:6,i),lattice_bcc_systemSlip(4:6,i))) st(:,i) = math_vectorproduct(sd(:,i),sn(:,i)) enddo do i = 1,myNtwin ! calculate twin system vectors and (assign) shears td(:,i) = lattice_bcc_systemTwin(1:3,i)/dsqrt(math_mul3x3(lattice_bcc_systemTwin(1:3,i),lattice_bcc_systemTwin(1:3,i))) tn(:,i) = lattice_bcc_systemTwin(4:6,i)/dsqrt(math_mul3x3(lattice_bcc_systemTwin(4:6,i),lattice_bcc_systemTwin(4:6,i))) tt(:,i) = math_vectorproduct(td(:,i),tn(:,i)) ts(i) = lattice_bcc_shearTwin(i) enddo interactionSlipSlip => lattice_bcc_interactionSlipSlip interactionSlipTwin => lattice_bcc_interactionSlipTwin interactionTwinSlip => lattice_bcc_interactionTwinSlip interactionTwinTwin => lattice_bcc_interactionTwinTwin endif case ('hex') if (CoverA >= 1.0_pReal) then ! checking physical significance of c/a lattice_hex_Nstructure = lattice_hex_Nstructure + 1_pInt ! count instances of hex structures myStructure = 2_pInt + lattice_hex_Nstructure ! 3,4,5,.. for hex myNslipSystem = lattice_hex_NslipSystem ! size of slip system families myNtwinSystem = lattice_hex_NtwinSystem ! size of twin system families myNslip = lattice_hex_Nslip ! overall number of slip systems myNtwin = lattice_hex_Ntwin ! overall number of twin systems processMe = .true. ! converting from 4 axes coordinate system (a1=a2=a3=c) to ortho-hexgonal system (a, b, c) do i = 1,myNslip hex_d(1) = lattice_hex_systemSlip(1,i)*1.5_pReal ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(c/a)] hex_d(2) = (lattice_hex_systemSlip(1,i)+2.0_pReal*lattice_hex_systemSlip(2,i))*(0.5_pReal*dsqrt(3.0_pReal)) hex_d(3) = lattice_hex_systemSlip(4,i)*CoverA hex_n(1) = lattice_hex_systemSlip(5,i) ! plane (hkil)->(h (h+2k)/sqrt(3) l/(c/a)) hex_n(2) = (lattice_hex_systemSlip(5,i)+2.0_pReal*lattice_hex_systemSlip(6,i))/dsqrt(3.0_pReal) hex_n(3) = lattice_hex_systemSlip(8,i)/CoverA sd(:,i) = hex_d/dsqrt(math_mul3x3(hex_d,hex_d)) sn(:,i) = hex_n/dsqrt(math_mul3x3(hex_n,hex_n)) st(:,i) = math_vectorproduct(sd(:,i),sn(:,i)) enddo do i = 1,myNtwin hex_d(1) = lattice_hex_systemTwin(1,i)*1.5_pReal hex_d(2) = (lattice_hex_systemTwin(1,i)+2.0_pReal*lattice_hex_systemTwin(2,i))*(0.5_pReal*dsqrt(3.0_pReal)) hex_d(3) = lattice_hex_systemTwin(4,i)*CoverA hex_n(1) = lattice_hex_systemTwin(5,i) hex_n(2) = (lattice_hex_systemTwin(5,i)+2.0_pReal*lattice_hex_systemTwin(6,i))/dsqrt(3.0_pReal) hex_n(3) = lattice_hex_systemTwin(8,i)/CoverA td(:,i) = hex_d/dsqrt(math_mul3x3(hex_d,hex_d)) tn(:,i) = hex_n/dsqrt(math_mul3x3(hex_n,hex_n)) tt(:,i) = math_vectorproduct(td(:,i),tn(:,i)) select case(lattice_hex_shearTwin(i)) ! from Christian & Mahajan 1995 p.29 case (1) ! {10.2}<-10.1> ts(i) = (3.0_pReal-CoverA*CoverA)/dsqrt(3.0_pReal)/CoverA case (2) ! {11.2}<11.-3> ts(i) = 2.0_pReal*(CoverA*CoverA-2.0_pReal)/3.0_pReal/CoverA case (3) ! {11.1}<-1-1.6> ts(i) = 1.0_pReal/CoverA case (4) ! {10.1}<10.-2> ts(i) = (4.0_pReal*CoverA*CoverA-9.0_pReal)/4.0_pReal/dsqrt(3.0_pReal)/CoverA end select enddo interactionSlipSlip => lattice_hex_interactionSlipSlip interactionSlipTwin => lattice_hex_interactionSlipTwin interactionTwinSlip => lattice_hex_interactionTwinSlip interactionTwinTwin => lattice_hex_interactionTwinTwin endif end select if (processMe) then if (myStructure > lattice_Nstructure) & call IO_error(666,0,0,0,'structure index too large') ! check for memory leakage do i = 1,myNslip ! store slip system vectors and Schmid matrix for my structure lattice_sd(:,i,myStructure) = sd(:,i) lattice_st(:,i,myStructure) = st(:,i) lattice_sn(:,i,myStructure) = sn(:,i) lattice_Sslip(:,:,i,myStructure) = math_tensorproduct(sd(:,i),sn(:,i)) lattice_Sslip_v(:,i,myStructure) = math_Mandel33to6(math_symmetric3x3(lattice_Sslip(:,:,i,myStructure))) enddo do i = 1,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure lattice_td(:,i,myStructure) = td(:,i) lattice_tt(:,i,myStructure) = tt(:,i) lattice_tn(:,i,myStructure) = tn(:,i) lattice_Stwin(:,:,i,myStructure) = math_tensorproduct(td(:,i),tn(:,i)) lattice_Stwin_v(:,i,myStructure) = math_Mandel33to6(math_symmetric3x3(lattice_Stwin(:,:,i,myStructure))) lattice_Qtwin(:,:,i,myStructure) = math_AxisAngleToR(tn(:,i),180.0_pReal*inRad) lattice_shearTwin(i,myStructure) = ts(i) enddo lattice_NslipSystem(1:lattice_maxNslipFamily,myStructure) = myNslipSystem ! number of slip systems in each family lattice_NtwinSystem(1:lattice_maxNtwinFamily,myStructure) = myNtwinSystem ! number of twin systems in each family lattice_interactionSlipSlip(1:myNslip,1:myNslip,myStructure) = interactionSlipSlip(1:myNslip,1:myNslip) lattice_interactionSlipTwin(1:myNtwin,1:myNslip,myStructure) = interactionSlipTwin(1:myNtwin,1:myNslip) lattice_interactionTwinSlip(1:myNslip,1:myNtwin,myStructure) = interactionTwinSlip(1:myNslip,1:myNtwin) lattice_interactionTwinTwin(1:myNtwin,1:myNtwin,myStructure) = interactionTwinTwin(1:myNtwin,1:myNtwin) endif lattice_initializeStructure = myStructure ! report my structure index back end function END MODULE