1322 lines
73 KiB
Fortran
1322 lines
73 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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! $Id$
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!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief defines lattice structure definitions, slip and twin system definitions, Schimd matrix
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!> calculation and non-Schmid behavior
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!--------------------------------------------------------------------------------------------------
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module lattice
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use prec, only: &
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pReal, &
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pInt
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implicit none
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private
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integer(pInt), parameter, public :: &
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LATTICE_maxNslipFamily = 6_pInt, & !< max # of slip system families over lattice structures
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LATTICE_maxNtwinFamily = 4_pInt, & !< max # of twin system families over lattice structures
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LATTICE_maxNslip = 33_pInt, & !< max # of slip systems over lattice structures
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LATTICE_maxNtwin = 24_pInt, & !< max # of twin systems over lattice structures
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LATTICE_maxNinteraction = 42_pInt, & !< max # of interaction types (in hardening matrix part)
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LATTICE_maxNnonSchmid = 6_pInt !< max # of non schmid contributions over lattice structures
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integer(pInt), allocatable, dimension(:,:), protected, public :: &
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lattice_NslipSystem, & !< total # of slip systems in each family
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lattice_NtwinSystem !< total # of twin systems in each family
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integer(pInt), allocatable, dimension(:,:,:), protected, public :: &
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lattice_interactionSlipSlip, & !< Slip--slip interaction type
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lattice_interactionSlipTwin, & !< Slip--twin interaction type
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lattice_interactionTwinSlip, & !< Twin--slip interaction type
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lattice_interactionTwinTwin !< Twin--twin interaction type
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real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: &
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lattice_Sslip !< Schmid and non-Schmid matrices
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real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
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lattice_Sslip_v !< Mandel notation of lattice_Sslip
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real(pReal), allocatable, dimension(:,:,:), protected, public :: &
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lattice_sn, & !< normal direction of slip system
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lattice_sd, & !< slip direction of slip system
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lattice_st !< sd x sn
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! rotation and Schmid matrices, normal, shear direction and d x n of twin systems
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real(pReal), allocatable, dimension(:,:,:,:), protected, public :: &
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lattice_Stwin, &
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lattice_Qtwin
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real(pReal), allocatable, dimension(:,:,:), protected, public :: &
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lattice_Stwin_v, &
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lattice_tn, &
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lattice_td, &
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lattice_tt
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real(pReal), allocatable, dimension(:,:), protected, public :: &
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lattice_shearTwin !< characteristic twin shear
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integer(pInt), allocatable, dimension(:), protected, public :: &
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lattice_NnonSchmid !< total # of non-Schmid contributions for each structure
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!--------------------------------------------------------------------------------------------------
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! fcc
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integer(pInt), dimension(lattice_maxNslipFamily), parameter, public :: &
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LATTICE_fcc_NslipSystem = int([12, 0, 0, 0, 0, 0],pInt) !< total # of slip systems per family for fcc
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integer(pInt), dimension(lattice_maxNtwinFamily), parameter, public :: &
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lattice_fcc_NtwinSystem = int([12, 0, 0, 0],pInt) !< total # of twin systems per family for fcc
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integer(pInt), parameter, private :: &
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lattice_fcc_Nslip = 12_pInt, & ! sum(lattice_fcc_NslipSystem), & !< total # of slip systems for fcc
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lattice_fcc_Ntwin = 12_pInt, & ! sum(lattice_fcc_NtwinSystem) !< total # of twin systems for fcc
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lattice_fcc_NnonSchmid = 0_pInt !< total # of non-Schmid contributions for fcc
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real(pReal), dimension(3+3,lattice_fcc_Nslip), parameter, private :: &
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lattice_fcc_systemSlip = reshape(real([&
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! Slip direction Plane normal
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0, 1,-1, 1, 1, 1, &
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-1, 0, 1, 1, 1, 1, &
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1,-1, 0, 1, 1, 1, &
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0,-1,-1, -1,-1, 1, &
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1, 0, 1, -1,-1, 1, &
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-1, 1, 0, -1,-1, 1, &
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0,-1, 1, 1,-1,-1, &
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-1, 0,-1, 1,-1,-1, &
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1, 1, 0, 1,-1,-1, &
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0, 1, 1, -1, 1,-1, &
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1, 0,-1, -1, 1,-1, &
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-1,-1, 0, -1, 1,-1 &
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],pReal),[ 3_pInt + 3_pInt,lattice_fcc_Nslip]) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli
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real(pReal), dimension(3+3,lattice_fcc_Ntwin), parameter, private :: &
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lattice_fcc_systemTwin = reshape(real( [&
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-2, 1, 1, 1, 1, 1, &
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1,-2, 1, 1, 1, 1, &
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1, 1,-2, 1, 1, 1, &
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2,-1, 1, -1,-1, 1, &
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-1, 2, 1, -1,-1, 1, &
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-1,-1,-2, -1,-1, 1, &
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-2,-1,-1, 1,-1,-1, &
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1, 2,-1, 1,-1,-1, &
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1,-1, 2, 1,-1,-1, &
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2, 1,-1, -1, 1,-1, &
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-1,-2,-1, -1, 1,-1, &
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-1, 1, 2, -1, 1,-1 &
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],pReal),[ 3_pInt + 3_pInt ,lattice_fcc_Ntwin]) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli
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real(pReal), dimension(lattice_fcc_Ntwin), parameter, private :: &
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lattice_fcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal) !< Twin system <112>{111} ??? Sorted according to Eisenlohr & Hantcherli
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integer(pInt), dimension(2_pInt,lattice_fcc_Ntwin), parameter, public :: &
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lattice_fcc_twinNucleationSlipPair = reshape(int( [&
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2,3, &
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1,3, &
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1,2, &
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5,6, &
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4,6, &
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4,5, &
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8,9, &
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7,9, &
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7,8, &
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11,12, &
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10,12, &
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10,11 &
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],pInt),[2_pInt,lattice_fcc_Ntwin])
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integer(pInt), dimension(lattice_fcc_Nslip,lattice_fcc_Nslip), parameter, public :: &
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lattice_fcc_interactionSlipSlip = reshape(int( [&
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1,2,2,4,6,5,3,5,5,4,5,6, & ! ---> slip
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2,1,2,6,4,5,5,4,6,5,3,5, & ! |
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2,2,1,5,5,3,5,6,4,6,5,4, & ! |
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4,6,5,1,2,2,4,5,6,3,5,5, & ! v slip
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6,4,5,2,1,2,5,3,5,5,4,6, &
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5,5,3,2,2,1,6,5,4,5,6,4, &
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3,5,5,4,5,6,1,2,2,4,6,5, &
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5,4,6,5,3,5,2,1,2,6,4,5, &
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5,6,4,6,5,4,2,2,1,5,5,3, &
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4,5,6,3,5,5,4,6,5,1,2,2, &
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5,3,5,5,4,6,6,4,5,2,1,2, &
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6,5,4,5,6,4,5,5,3,2,2,1 &
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],pInt),[lattice_fcc_Nslip,lattice_fcc_Nslip],order=[2,1]) !< Slip--slip interaction types for fcc
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!< 1: self interaction
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!< 2: coplanar interaction
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!< 3: collinear interaction
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!< 4: Hirth locks
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!< 5: glissile junctions
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!< 6: Lomer locks
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integer(pInt), dimension(lattice_fcc_Nslip,lattice_fcc_Ntwin), parameter, public :: &
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lattice_fcc_interactionSlipTwin = reshape(int( [&
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1,1,1,3,3,3,2,2,2,3,3,3, & ! ---> twin
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1,1,1,3,3,3,3,3,3,2,2,2, & ! |
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1,1,1,2,2,2,3,3,3,3,3,3, & ! |
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3,3,3,1,1,1,3,3,3,2,2,2, & ! v slip
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3,3,3,1,1,1,2,2,2,3,3,3, &
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2,2,2,1,1,1,3,3,3,3,3,3, &
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2,2,2,3,3,3,1,1,1,3,3,3, &
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3,3,3,2,2,2,1,1,1,3,3,3, &
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3,3,3,3,3,3,1,1,1,2,2,2, &
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3,3,3,2,2,2,3,3,3,1,1,1, &
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2,2,2,3,3,3,3,3,3,1,1,1, &
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3,3,3,3,3,3,2,2,2,1,1,1 &
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],pInt),[lattice_fcc_Nslip,lattice_fcc_Ntwin],order=[2,1]) !< Slip--twin interaction types for fcc
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!< 1: coplanar interaction
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!< 2: screw trace between slip system and twin habit plane (easy cross slip)
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!< 3: other interaction
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integer(pInt), dimension(lattice_fcc_Ntwin,lattice_fcc_Nslip), parameter, public :: &
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lattice_fcc_interactionTwinSlip = 1_pInt !< Twin--Slip interaction types for fcc
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integer(pInt), dimension(lattice_fcc_Ntwin,lattice_fcc_Ntwin), parameter,public :: &
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lattice_fcc_interactionTwinTwin = reshape(int( [&
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1,1,1,2,2,2,2,2,2,2,2,2, & ! ---> twin
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1,1,1,2,2,2,2,2,2,2,2,2, & ! |
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1,1,1,2,2,2,2,2,2,2,2,2, & ! |
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2,2,2,1,1,1,2,2,2,2,2,2, & ! v twin
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2,2,2,1,1,1,2,2,2,2,2,2, &
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2,2,2,1,1,1,2,2,2,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,1,1,1,2,2,2, &
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2,2,2,2,2,2,2,2,2,1,1,1, &
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2,2,2,2,2,2,2,2,2,1,1,1, &
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2,2,2,2,2,2,2,2,2,1,1,1 &
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],pInt),[lattice_fcc_Ntwin,lattice_fcc_Ntwin],order=[2,1]) !< Twin--twin interaction types for fcc
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!--------------------------------------------------------------------------------------------------
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! bcc
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integer(pInt), dimension(lattice_maxNslipFamily), parameter, public :: &
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lattice_bcc_NslipSystem = int([ 12, 12, 0, 0, 0, 0], pInt) !< total # of slip systems per family for bcc
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integer(pInt), dimension(lattice_maxNtwinFamily), parameter, public :: &
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lattice_bcc_NtwinSystem = int([ 12, 0, 0, 0], pInt) !< total # of twin systems per family for bcc
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integer(pInt), parameter, private :: &
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lattice_bcc_Nslip = 24_pInt, & ! sum(lattice_bcc_NslipSystem), & !< total # of slip systems for bcc
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lattice_bcc_Ntwin = 12_pInt, & ! sum(lattice_bcc_NtwinSystem) !< total # of twin systems for bcc
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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)
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real(pReal), dimension(3+3,lattice_bcc_Nslip), parameter, private :: &
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lattice_bcc_systemSlip = reshape(real([&
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! Slip direction Plane normal
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! Slip system <111>{110}
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1,-1, 1, 0, 1, 1, &
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-1,-1, 1, 0, 1, 1, &
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1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 1, 0, 1, &
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-1,-1, 1, 1, 0, 1, &
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1, 1, 1, -1, 0, 1, &
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1,-1, 1, -1, 0, 1, &
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-1, 1, 1, 1, 1, 0, &
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-1, 1,-1, 1, 1, 0, &
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1, 1, 1, -1, 1, 0, &
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1, 1,-1, -1, 1, 0, &
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! Slip system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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! Slip system <111>{123}
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! 1, 1,-1, 1, 2, 3, &
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! 1,-1, 1, -1, 2, 3, &
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! -1, 1, 1, 1,-2, 3, &
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! 1, 1, 1, 1, 2,-3, &
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! 1,-1, 1, 1, 3, 2, &
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! 1, 1,-1, -1, 3, 2, &
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! 1, 1, 1, 1,-3, 2, &
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! -1, 1, 1, 1, 3,-2, &
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! 1, 1,-1, 2, 1, 3, &
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! 1,-1, 1, -2, 1, 3, &
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! -1, 1, 1, 2,-1, 3, &
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! 1, 1, 1, 2, 1,-3, &
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! 1,-1, 1, 2, 3, 1, &
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! 1, 1,-1, -2, 3, 1, &
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! 1, 1, 1, 2,-3, 1, &
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! -1, 1, 1, 2, 3,-1, &
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! -1, 1, 1, 3, 1, 2, &
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! 1, 1, 1, -3, 1, 2, &
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! 1, 1,-1, 3,-1, 2, &
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! 1,-1, 1, 3, 1,-2, &
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! -1, 1, 1, 3, 2, 1, &
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! 1, 1, 1, -3, 2, 1, &
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! 1, 1,-1, 3,-2, 1, &
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! 1,-1, 1, 3, 2,-1 &
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],pReal),[ 3_pInt + 3_pInt ,lattice_bcc_Nslip])
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real(pReal), dimension(3+3,lattice_bcc_Ntwin), parameter, private :: &
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lattice_bcc_systemTwin = reshape(real([&
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! Twin system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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],pReal),[ 3_pInt + 3_pInt,lattice_bcc_Ntwin])
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real(pReal), dimension(lattice_bcc_Ntwin), parameter, private :: &
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lattice_bcc_shearTwin = 0.5_pReal*sqrt(2.0_pReal)
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integer(pInt), dimension(lattice_bcc_Nslip,lattice_bcc_Nslip), parameter, public :: &
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lattice_bcc_interactionSlipSlip = reshape(int( [&
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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
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2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! |
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6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! |
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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
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5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, &
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4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, &
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4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, &
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3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, &
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4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, &
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3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, &
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5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, &
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4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, &
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!
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6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, &
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6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, &
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4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, &
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3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, &
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3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, &
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4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, &
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6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, &
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6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, &
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4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, &
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3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, &
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6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, &
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6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 &
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],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
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!< 1: self interaction
|
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!< 2: coplanar interaction
|
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!< 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), 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
|
||
|
||
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
|
||
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
|
||
|
||
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_maxNnonSchmid /= maxval([lattice_fcc_NnonSchmid,lattice_bcc_NnonSchmid,&
|
||
lattice_hex_NnonSchmid])) call IO_error(0_pInt,ext_msg = 'LATTICE_maxNnonSchmid')
|
||
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)
|
||
|
||
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_mu(Nphases), source=0.0_pReal)
|
||
allocate(lattice_nu(Nphases), source=0.0_pReal)
|
||
|
||
allocate(lattice_NnonSchmid(Nphases), source=0_pInt)
|
||
allocate(lattice_Sslip(3,3,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal)
|
||
allocate(lattice_Sslip_v(6,1+2*lattice_maxNnonSchmid,lattice_maxNslip,Nphases),source=0.0_pReal)
|
||
allocate(lattice_sd(3,lattice_maxNslip,Nphases),source=0.0_pReal)
|
||
allocate(lattice_st(3,lattice_maxNslip,Nphases),source=0.0_pReal)
|
||
allocate(lattice_sn(3,lattice_maxNslip,Nphases),source=0.0_pReal)
|
||
|
||
allocate(lattice_Qtwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
allocate(lattice_Stwin(3,3,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
allocate(lattice_Stwin_v(6,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
allocate(lattice_td(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
allocate(lattice_tt(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
allocate(lattice_tn(3,lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
|
||
allocate(lattice_shearTwin(lattice_maxNtwin,Nphases),source=0.0_pReal)
|
||
|
||
allocate(lattice_NslipSystem(lattice_maxNslipFamily,Nphases),source=0_pInt)
|
||
allocate(lattice_NtwinSystem(lattice_maxNtwinFamily,Nphases),source=0_pInt)
|
||
|
||
allocate(lattice_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)
|
||
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 <Phase>
|
||
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
|
||
!there will be an error here
|
||
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)
|
||
if (CoverA(section) < 1.0_pReal .or. CoverA(section) > 2.0_pReal) call IO_error(206_pInt) ! checking physical significance of c/a
|
||
end select
|
||
endif
|
||
enddo
|
||
|
||
if (iand(debug_level(debug_lattice),debug_levelBasic) /= 0_pInt) then
|
||
write(6,'(a16,1x,i5)') ' # phases:',Nphases
|
||
endif
|
||
|
||
do i = 1_pInt,Nphases
|
||
call lattice_initializeStructure(i, CoverA(i))
|
||
enddo
|
||
|
||
deallocate(CoverA)
|
||
|
||
end subroutine lattice_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Calculation of Schmid matrices, etc.
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine lattice_initializeStructure(myPhase,CoverA)
|
||
use prec, only: &
|
||
tol_math_check
|
||
use math, only: &
|
||
math_vectorproduct, &
|
||
math_tensorproduct, &
|
||
math_norm3, &
|
||
math_mul33x3, &
|
||
math_trace33, &
|
||
math_symmetric33, &
|
||
math_Mandel33to6, &
|
||
math_Mandel3333to66, &
|
||
math_Voigt66to3333, &
|
||
math_axisAngleToR, &
|
||
INRAD
|
||
use IO, only: &
|
||
IO_error
|
||
|
||
implicit none
|
||
integer(pInt), intent(in) :: myPhase
|
||
real(pReal), intent(in) :: CoverA
|
||
|
||
real(pReal), dimension(3) :: &
|
||
sdU, snU, &
|
||
np, nn
|
||
real(pReal), dimension(3,lattice_maxNslip) :: &
|
||
sd, sn
|
||
real(pReal), dimension(3,3,2,lattice_maxNnonSchmid,lattice_maxNslip) :: &
|
||
sns
|
||
real(pReal), dimension(3,lattice_maxNtwin) :: &
|
||
td, tn
|
||
real(pReal), dimension(lattice_maxNtwin) :: &
|
||
ts
|
||
integer(pInt) :: &
|
||
i,j, &
|
||
myNslip, myNtwin
|
||
|
||
lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),lattice_C66(1:6,1:6,myPhase))
|
||
lattice_mu(myPhase) = 0.2_pReal * (lattice_C66(1,1,myPhase) - lattice_C66(1,2,myPhase) + 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
||
lattice_nu(myPhase) = (lattice_C66(1,1,myPhase) + 4.0_pReal*lattice_C66(1,2,myPhase) - 2.0_pReal*lattice_C66(4,4,myPhase)) &
|
||
/ (4.0_pReal*lattice_C66(1,1,myPhase) + 6.0_pReal*lattice_C66(1,2,myPhase) + 2.0_pReal*lattice_C66(4,4,myPhase)) ! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
||
lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt
|
||
lattice_C66(1:6,1:6,myPhase) = math_Mandel3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel
|
||
|
||
|
||
select case(lattice_structure(myPhase))
|
||
!--------------------------------------------------------------------------------------------------
|
||
! fcc
|
||
case (LATTICE_fcc_ID)
|
||
myNslip = lattice_fcc_Nslip
|
||
myNtwin = lattice_fcc_Ntwin
|
||
do i = 1_pInt,lattice_fcc_Nslip ! assign slip system vectors
|
||
sd(1:3,i) = lattice_fcc_systemSlip(1:3,i)
|
||
sn(1:3,i) = lattice_fcc_systemSlip(4:6,i)
|
||
enddo
|
||
do i = 1_pInt,lattice_fcc_Ntwin ! assign twin system vectors and shears
|
||
td(1:3,i) = lattice_fcc_systemTwin(1:3,i)
|
||
tn(1:3,i) = lattice_fcc_systemTwin(4:6,i)
|
||
ts(i) = lattice_fcc_shearTwin(i)
|
||
enddo
|
||
lattice_NslipSystem(1:lattice_maxNslipFamily,myPhase) = lattice_fcc_NslipSystem
|
||
lattice_NtwinSystem(1:lattice_maxNtwinFamily,myPhase) = lattice_fcc_NtwinSystem
|
||
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
|
||
do i = 1_pInt,lattice_bcc_Nslip ! 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 = math_mul33x3(math_axisAngleToR(sdU,60.0_pReal*INRAD), snU)
|
||
nn = math_mul33x3(math_axisAngleToR(-sdU,60.0_pReal*INRAD), snU)
|
||
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,lattice_bcc_Ntwin ! 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_NnonSchmid(myPhase) = lattice_bcc_NnonSchmid
|
||
lattice_interactionSlipSlip(1:lattice_bcc_Nslip,1:lattice_bcc_Nslip,myPhase) = &
|
||
lattice_bcc_interactionSlipSlip
|
||
lattice_interactionSlipTwin(1:lattice_bcc_Nslip,1:lattice_bcc_Ntwin,myPhase) = &
|
||
lattice_bcc_interactionSlipTwin
|
||
lattice_interactionTwinSlip(1:lattice_bcc_Ntwin,1:lattice_bcc_Nslip,myPhase) = &
|
||
lattice_bcc_interactionTwinSlip
|
||
lattice_interactionTwinTwin(1:lattice_bcc_Ntwin,1:lattice_bcc_Ntwin,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
|
||
do i = 1_pInt,lattice_hex_Nslip ! 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,lattice_hex_Ntwin ! 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_NnonSchmid(myPhase) = lattice_hex_NnonSchmid
|
||
lattice_interactionSlipSlip(1:lattice_hex_Nslip,1:lattice_hex_Nslip,myPhase) = &
|
||
lattice_hex_interactionSlipSlip
|
||
lattice_interactionSlipTwin(1:lattice_hex_Nslip,1:lattice_hex_Ntwin,myPhase) = &
|
||
lattice_hex_interactionSlipTwin
|
||
lattice_interactionTwinSlip(1:lattice_hex_Ntwin,1:lattice_hex_Nslip,myPhase) = &
|
||
lattice_hex_interactionTwinSlip
|
||
lattice_interactionTwinTwin(1:lattice_hex_Ntwin,1:lattice_hex_Ntwin,myPhase) = &
|
||
lattice_hex_interactionTwinTwin
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! orthorombic and isotropic (no crystal plasticity)
|
||
case (LATTICE_ort_ID, LATTICE_iso_ID)
|
||
myNslip = 0_pInt
|
||
myNtwin = 0_pInt
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! something went wrong
|
||
case default
|
||
print*, 'error'
|
||
end select
|
||
|
||
|
||
do i = 1_pInt,myNslip ! store slip system vectors and Schmid matrix for my structure
|
||
lattice_sd(1:3,i,myPhase) = sd(1:3,i)/math_norm3(sd(1:3,i)) ! make unit vector
|
||
lattice_sn(1:3,i,myPhase) = sn(1:3,i)/math_norm3(sn(1:3,i)) ! make unit vector
|
||
lattice_st(1:3,i,myPhase) = math_vectorproduct(lattice_sd(1:3,i,myPhase), &
|
||
lattice_sn(1:3,i,myPhase))
|
||
lattice_Sslip(1:3,1:3,1,i,myPhase) = math_tensorproduct(lattice_sd(1:3,i,myPhase), &
|
||
lattice_sn(1:3,i,myPhase))
|
||
do j = 1_pInt,lattice_NnonSchmid(myPhase)
|
||
lattice_Sslip(1:3,1:3,2*j ,i,myPhase) = sns(1:3,1:3,1,j,i)
|
||
lattice_Sslip(1:3,1:3,2*j+1,i,myPhase) = sns(1:3,1:3,2,j,i)
|
||
enddo
|
||
do j = 1_pInt,1_pInt+2_pInt*lattice_NnonSchmid(myPhase)
|
||
lattice_Sslip_v(1:6,j,i,myPhase) = &
|
||
math_Mandel33to6(math_symmetric33(lattice_Sslip(1:3,1:3,j,i,myPhase)))
|
||
enddo
|
||
if (abs(math_trace33(lattice_Sslip(1:3,1:3,1,i,myPhase))) > tol_math_check) &
|
||
call IO_error(0_pInt,myPhase,i,0_pInt,ext_msg = 'dilatational slip Schmid matrix')
|
||
enddo
|
||
do i = 1_pInt,myNtwin ! store twin system vectors and Schmid plus rotation matrix for my structure
|
||
lattice_td(1:3,i,myPhase) = td(1:3,i)/math_norm3(td(1:3,i)) ! make unit vector
|
||
lattice_tn(1:3,i,myPhase) = tn(1:3,i)/math_norm3(tn(1:3,i)) ! make unit vector
|
||
lattice_tt(1:3,i,myPhase) = math_vectorproduct(lattice_td(1:3,i,myPhase), &
|
||
lattice_tn(1:3,i,myPhase))
|
||
lattice_Stwin(1:3,1:3,i,myPhase) = math_tensorproduct(lattice_td(1:3,i,myPhase), &
|
||
lattice_tn(1:3,i,myPhase))
|
||
lattice_Stwin_v(1:6,i,myPhase) = math_Mandel33to6(math_symmetric33(lattice_Stwin(1:3,1:3,i,myPhase)))
|
||
lattice_Qtwin(1:3,1:3,i,myPhase) = math_axisAngleToR(tn(1:3,i),180.0_pReal*INRAD)
|
||
lattice_shearTwin(i,myPhase) = ts(i)
|
||
if (abs(math_trace33(lattice_Stwin(1:3,1:3,i,myPhase))) > tol_math_check) &
|
||
call IO_error(301_pInt,myPhase,ext_msg = 'dilatational twin Schmid matrix')
|
||
enddo
|
||
|
||
end subroutine lattice_initializeStructure
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Symmetrizes stiffness matrix according to lattice type
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function lattice_symmetrizeC66(struct,C66)
|
||
|
||
implicit none
|
||
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct
|
||
real(pReal), dimension(6,6), intent(in) :: C66
|
||
real(pReal), dimension(6,6) :: lattice_symmetrizeC66
|
||
integer(pInt) :: j,k
|
||
|
||
lattice_symmetrizeC66 = 0.0_pReal
|
||
|
||
select case(struct)
|
||
case (LATTICE_iso_ID)
|
||
forall(k=1_pInt:3_pInt)
|
||
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
|
||
lattice_symmetrizeC66(k,k) = C66(1,1)
|
||
lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
end forall
|
||
case (LATTICE_fcc_ID,LATTICE_bcc_ID)
|
||
forall(k=1_pInt:3_pInt)
|
||
forall(j=1_pInt:3_pInt) lattice_symmetrizeC66(k,j) = C66(1,2)
|
||
lattice_symmetrizeC66(k,k) = C66(1,1)
|
||
lattice_symmetrizeC66(k+3_pInt,k+3_pInt) = C66(4,4)
|
||
end forall
|
||
case (LATTICE_hex_ID)
|
||
lattice_symmetrizeC66(1,1) = C66(1,1)
|
||
lattice_symmetrizeC66(2,2) = C66(1,1)
|
||
lattice_symmetrizeC66(3,3) = C66(3,3)
|
||
lattice_symmetrizeC66(1,2) = C66(1,2)
|
||
lattice_symmetrizeC66(2,1) = C66(1,2)
|
||
lattice_symmetrizeC66(1,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,1) = C66(1,3)
|
||
lattice_symmetrizeC66(2,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,2) = C66(1,3)
|
||
lattice_symmetrizeC66(4,4) = C66(4,4)
|
||
lattice_symmetrizeC66(5,5) = C66(4,4)
|
||
lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
case (LATTICE_ort_ID)
|
||
lattice_symmetrizeC66(1,1) = C66(1,1)
|
||
lattice_symmetrizeC66(2,2) = C66(2,2)
|
||
lattice_symmetrizeC66(3,3) = C66(3,3)
|
||
lattice_symmetrizeC66(1,2) = C66(1,2)
|
||
lattice_symmetrizeC66(2,1) = C66(1,2)
|
||
lattice_symmetrizeC66(1,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,1) = C66(1,3)
|
||
lattice_symmetrizeC66(2,3) = C66(2,3)
|
||
lattice_symmetrizeC66(3,2) = C66(2,3)
|
||
lattice_symmetrizeC66(4,4) = C66(4,4)
|
||
lattice_symmetrizeC66(5,5) = C66(5,5)
|
||
lattice_symmetrizeC66(6,6) = C66(6,6)
|
||
case default
|
||
lattice_symmetrizeC66 = C66
|
||
end select
|
||
|
||
end function lattice_symmetrizeC66
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief 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
|