2260 lines
125 KiB
Fortran
2260 lines
125 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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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 contains lattice structure definitions including Schmid matrices for slip, twin, trans,
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! and cleavage as well as interaction among the various systems
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!--------------------------------------------------------------------------------------------------
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module lattice
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use prec
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use IO
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use config
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use math
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use rotations
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implicit none
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private
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!--------------------------------------------------------------------------------------------------
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! face centered cubic (cF)
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integer, dimension(*), parameter :: &
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FCC_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for fcc
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integer, dimension(*), parameter :: &
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FCC_NTWINSYSTEM = [12] !< # of twin systems per family for fcc
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integer, dimension(*), parameter :: &
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FCC_NTRANSSYSTEM = [12] !< # of transformation systems per family for fcc
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integer, dimension(*), parameter :: &
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FCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for fcc
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integer, parameter :: &
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FCC_NSLIP = sum(FCC_NSLIPSYSTEM), & !< total # of slip systems for fcc
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FCC_NTWIN = sum(FCC_NTWINSYSTEM), & !< total # of twin systems for fcc
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FCC_NTRANS = sum(FCC_NTRANSSYSTEM), & !< total # of transformation systems for fcc
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FCC_NCLEAVAGE = sum(FCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for fcc
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real(pReal), dimension(3+3,FCC_NSLIP), parameter :: &
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FCC_SYSTEMSLIP = reshape(real([&
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! <110>{111} systems
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0, 1,-1, 1, 1, 1, & ! B2
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-1, 0, 1, 1, 1, 1, & ! B4
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1,-1, 0, 1, 1, 1, & ! B5
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0,-1,-1, -1,-1, 1, & ! C1
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1, 0, 1, -1,-1, 1, & ! C3
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-1, 1, 0, -1,-1, 1, & ! C5
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0,-1, 1, 1,-1,-1, & ! A2
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-1, 0,-1, 1,-1,-1, & ! A3
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1, 1, 0, 1,-1,-1, & ! A6
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0, 1, 1, -1, 1,-1, & ! D1
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1, 0,-1, -1, 1,-1, & ! D4
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-1,-1, 0, -1, 1,-1, & ! D6
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! <110>{110}/non-octahedral systems
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1, 1, 0, 1,-1, 0, &
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1,-1, 0, 1, 1, 0, &
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1, 0, 1, 1, 0,-1, &
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1, 0,-1, 1, 0, 1, &
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0, 1, 1, 0, 1,-1, &
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0, 1,-1, 0, 1, 1 &
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],pReal),shape(FCC_SYSTEMSLIP)) !< fcc slip systems
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real(pReal), dimension(3+3,FCC_NTWIN), parameter :: &
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FCC_SYSTEMTWIN = reshape(real( [&
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! <112>{111} systems
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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),shape(FCC_SYSTEMTWIN)) !< fcc twin systems
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integer, dimension(2,FCC_NTWIN), parameter, public :: &
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lattice_FCC_TWINNUCLEATIONSLIPPAIR = reshape( [&
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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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],shape(lattice_FCC_TWINNUCLEATIONSLIPPAIR))
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real(pReal), dimension(3+3,FCC_NCLEAVAGE), parameter :: &
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FCC_SYSTEMCLEAVAGE = reshape(real([&
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! <001>{001} systems
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0, 1, 0, 1, 0, 0, &
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0, 0, 1, 0, 1, 0, &
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1, 0, 0, 0, 0, 1 &
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],pReal),shape(FCC_SYSTEMCLEAVAGE)) !< fcc cleavage systems
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!--------------------------------------------------------------------------------------------------
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! body centered cubic (cI)
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integer, dimension(*), parameter :: &
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BCC_NSLIPSYSTEM = [12, 12, 24] !< # of slip systems per family for bcc
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integer, dimension(*), parameter :: &
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BCC_NTWINSYSTEM = [12] !< # of twin systems per family for bcc
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integer, dimension(*), parameter :: &
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BCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for bcc
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integer, parameter :: &
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BCC_NSLIP = sum(BCC_NSLIPSYSTEM), & !< total # of slip systems for bcc
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BCC_NTWIN = sum(BCC_NTWINSYSTEM), & !< total # of twin systems for bcc
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BCC_NCLEAVAGE = sum(BCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for bcc
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real(pReal), dimension(3+3,BCC_NSLIP), parameter :: &
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BCC_SYSTEMSLIP = reshape(real([&
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! <111>{110} systems
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1,-1, 1, 0, 1, 1, & ! D1
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-1,-1, 1, 0, 1, 1, & ! C1
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1, 1, 1, 0,-1, 1, & ! B2
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-1, 1, 1, 0,-1, 1, & ! A2
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-1, 1, 1, 1, 0, 1, & ! A3
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-1,-1, 1, 1, 0, 1, & ! C3
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1, 1, 1, -1, 0, 1, & ! B4
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1,-1, 1, -1, 0, 1, & ! D4
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-1, 1, 1, 1, 1, 0, & ! A6
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-1, 1,-1, 1, 1, 0, & ! D6
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1, 1, 1, -1, 1, 0, & ! B5
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1, 1,-1, -1, 1, 0, & ! C5
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! <111>{112} systems
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-1, 1, 1, 2, 1, 1, & ! A-4
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1, 1, 1, -2, 1, 1, & ! B-3
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1, 1,-1, 2,-1, 1, & ! C-10
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1,-1, 1, 2, 1,-1, & ! D-9
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1,-1, 1, 1, 2, 1, & ! D-6
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1, 1,-1, -1, 2, 1, & ! C-5
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1, 1, 1, 1,-2, 1, & ! B-12
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-1, 1, 1, 1, 2,-1, & ! A-11
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1, 1,-1, 1, 1, 2, & ! C-2
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1,-1, 1, -1, 1, 2, & ! D-1
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-1, 1, 1, 1,-1, 2, & ! A-8
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1, 1, 1, 1, 1,-2, & ! B-7
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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),shape(BCC_SYSTEMSLIP)) !< bcc slip systems
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real(pReal), dimension(3+3,BCC_NTWIN), parameter :: &
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BCC_SYSTEMTWIN = reshape(real([&
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! <111>{112} systems
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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),shape(BCC_SYSTEMTWIN)) !< bcc twin systems
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real(pReal), dimension(3+3,BCC_NCLEAVAGE), parameter :: &
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BCC_SYSTEMCLEAVAGE = reshape(real([&
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! <001>{001} systems
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0, 1, 0, 1, 0, 0, &
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0, 0, 1, 0, 1, 0, &
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1, 0, 0, 0, 0, 1 &
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],pReal),shape(BCC_SYSTEMCLEAVAGE)) !< bcc cleavage systems
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!--------------------------------------------------------------------------------------------------
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! hexagonal (hP)
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integer, dimension(*), parameter :: &
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HEX_NSLIPSYSTEM = [3, 3, 3, 6, 12, 6] !< # of slip systems per family for hex
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integer, dimension(*), parameter :: &
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HEX_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hex
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integer, parameter :: &
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HEX_NSLIP = sum(HEX_NSLIPSYSTEM), & !< total # of slip systems for hex
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HEX_NTWIN = sum(HEX_NTWINSYSTEM) !< total # of twin systems for hex
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real(pReal), dimension(4+4,HEX_NSLIP), parameter :: &
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HEX_SYSTEMSLIP = reshape(real([&
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! <-1-1.0>{00.1}/basal systems (independent of c/a-ratio)
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2, -1, -1, 0, 0, 0, 0, 1, &
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-1, 2, -1, 0, 0, 0, 0, 1, &
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-1, -1, 2, 0, 0, 0, 0, 1, &
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! <-1-1.0>{1-1.0}/prismatic systems (independent of c/a-ratio)
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2, -1, -1, 0, 0, 1, -1, 0, &
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-1, 2, -1, 0, -1, 0, 1, 0, &
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-1, -1, 2, 0, 1, -1, 0, 0, &
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! <-11.0>{11.0}/2nd order prismatic compound systems (plane normal independent of c/a-ratio)
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-1, 1, 0, 0, 1, 1, -2, 0, &
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0, -1, 1, 0, -2, 1, 1, 0, &
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1, 0, -1, 0, 1, -2, 1, 0, &
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! <-1-1.0>{-11.1}/1st order pyramidal <a> systems (direction independent of c/a-ratio)
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-1, 2, -1, 0, 1, 0, -1, 1, &
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-2, 1, 1, 0, 0, 1, -1, 1, &
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-1, -1, 2, 0, -1, 1, 0, 1, &
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1, -2, 1, 0, -1, 0, 1, 1, &
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2, -1, -1, 0, 0, -1, 1, 1, &
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1, 1, -2, 0, 1, -1, 0, 1, &
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! <11.3>{-10.1}/1st order pyramidal <c+a> systems (direction independent of c/a-ratio)
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-2, 1, 1, 3, 1, 0, -1, 1, &
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-1, -1, 2, 3, 1, 0, -1, 1, &
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-1, -1, 2, 3, 0, 1, -1, 1, &
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1, -2, 1, 3, 0, 1, -1, 1, &
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1, -2, 1, 3, -1, 1, 0, 1, &
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2, -1, -1, 3, -1, 1, 0, 1, &
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2, -1, -1, 3, -1, 0, 1, 1, &
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1, 1, -2, 3, -1, 0, 1, 1, &
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1, 1, -2, 3, 0, -1, 1, 1, &
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-1, 2, -1, 3, 0, -1, 1, 1, &
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-1, 2, -1, 3, 1, -1, 0, 1, &
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-2, 1, 1, 3, 1, -1, 0, 1, &
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! <11.3>{-1-1.2}/2nd order pyramidal <c+a> systems
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-1, -1, 2, 3, 1, 1, -2, 2, &
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1, -2, 1, 3, -1, 2, -1, 2, &
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2, -1, -1, 3, -2, 1, 1, 2, &
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1, 1, -2, 3, -1, -1, 2, 2, &
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-1, 2, -1, 3, 1, -2, 1, 2, &
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-2, 1, 1, 3, 2, -1, -1, 2 &
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],pReal),shape(HEX_SYSTEMSLIP)) !< hex slip systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
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real(pReal), dimension(4+4,HEX_NTWIN), parameter :: &
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HEX_SYSTEMTWIN = reshape(real([&
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! <-10.1>{10.2} systems, shear = (3-(c/a)^2)/(sqrt(3) c/a)
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! tension in Co, Mg, Zr, Ti, and Be; compression in Cd and Zn
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-1, 0, 1, 1, 1, 0, -1, 2, & !
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0, -1, 1, 1, 0, 1, -1, 2, &
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1, -1, 0, 1, -1, 1, 0, 2, &
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1, 0, -1, 1, -1, 0, 1, 2, &
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0, 1, -1, 1, 0, -1, 1, 2, &
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-1, 1, 0, 1, 1, -1, 0, 2, &
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! <11.6>{-1-1.1} systems, shear = 1/(c/a)
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! tension in Co, Re, and Zr
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-1, -1, 2, 6, 1, 1, -2, 1, &
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1, -2, 1, 6, -1, 2, -1, 1, &
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2, -1, -1, 6, -2, 1, 1, 1, &
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1, 1, -2, 6, -1, -1, 2, 1, &
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-1, 2, -1, 6, 1, -2, 1, 1, &
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-2, 1, 1, 6, 2, -1, -1, 1, &
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! <10.-2>{10.1} systems, shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
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! compression in Mg
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1, 0, -1, -2, 1, 0, -1, 1, &
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0, 1, -1, -2, 0, 1, -1, 1, &
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-1, 1, 0, -2, -1, 1, 0, 1, &
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-1, 0, 1, -2, -1, 0, 1, 1, &
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0, -1, 1, -2, 0, -1, 1, 1, &
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1, -1, 0, -2, 1, -1, 0, 1, &
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! <11.-3>{11.2} systems, shear = 2((c/a)^2-2)/(3 c/a)
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! compression in Ti and Zr
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1, 1, -2, -3, 1, 1, -2, 2, &
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-1, 2, -1, -3, -1, 2, -1, 2, &
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-2, 1, 1, -3, -2, 1, 1, 2, &
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-1, -1, 2, -3, -1, -1, 2, 2, &
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1, -2, 1, -3, 1, -2, 1, 2, &
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2, -1, -1, -3, 2, -1, -1, 2 &
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],pReal),shape(HEX_SYSTEMTWIN)) !< hex twin systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
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!--------------------------------------------------------------------------------------------------
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! body centered tetragonal (tI)
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integer, dimension(*), parameter :: &
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BCT_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for bct
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integer, parameter :: &
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BCT_NSLIP = sum(BCT_NSLIPSYSTEM) !< total # of slip systems for bct
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real(pReal), dimension(3+3,BCT_NSLIP), parameter :: &
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BCT_SYSTEMSLIP = reshape(real([&
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! {100)<001] systems
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0, 0, 1, 1, 0, 0, &
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0, 0, 1, 0, 1, 0, &
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! {110)<001] systems
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0, 0, 1, 1, 1, 0, &
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0, 0, 1, -1, 1, 0, &
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! {100)<010] systems
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0, 1, 0, 1, 0, 0, &
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1, 0, 0, 0, 1, 0, &
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! {110)<1-11]/2 systems
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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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! {110)<1-10] systems
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1, -1, 0, 1, 1, 0, &
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1, 1, 0, 1,-1, 0, &
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! {100)<011] systems
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0, 1, 1, 1, 0, 0, &
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0,-1, 1, 1, 0, 0, &
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-1, 0, 1, 0, 1, 0, &
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1, 0, 1, 0, 1, 0, &
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! {001)<010] systems
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0, 1, 0, 0, 0, 1, &
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1, 0, 0, 0, 0, 1, &
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! {001)<110] systems
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1, 1, 0, 0, 0, 1, &
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-1, 1, 0, 0, 0, 1, &
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! {011)<01-1] systems
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0, 1,-1, 0, 1, 1, &
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0,-1,-1, 0,-1, 1, &
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-1, 0,-1, -1, 0, 1, &
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1, 0,-1, 1, 0, 1, &
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! {011)<1-11]/2 systems
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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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! {011)<100] systems
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1, 0, 0, 0, 1, 1, &
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1, 0, 0, 0, 1,-1, &
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0, 1, 0, 1, 0, 1, &
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0, 1, 0, 1, 0,-1, &
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! {211)<01-1] systems
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0, 1,-1, 2, 1, 1, &
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0,-1,-1, 2,-1, 1, &
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1, 0,-1, 1, 2, 1, &
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-1, 0,-1, -1, 2, 1, &
|
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0, 1,-1, -2, 1, 1, &
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0,-1,-1, -2,-1, 1, &
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-1, 0,-1, -1,-2, 1, &
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1, 0,-1, 1,-2, 1, &
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! {211)<-111]/2 systems
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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, -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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],pReal),shape(BCT_SYSTEMSLIP)) !< bct slip systems for c/a = 0.5456 (Sn), sorted by Bieler 2009 (https://doi.org/10.1007/s11664-009-0909-x)
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|
||
! SHOULD NOT BE PART OF LATTICE BEGIN
|
||
real(pReal), dimension(:), allocatable, public, protected :: &
|
||
lattice_mu, lattice_nu
|
||
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
|
||
lattice_C66
|
||
! SHOULD NOT BE PART OF LATTICE END
|
||
|
||
interface lattice_forestProjection_edge
|
||
module procedure slipProjection_transverse
|
||
end interface lattice_forestProjection_edge
|
||
|
||
interface lattice_forestProjection_screw
|
||
module procedure slipProjection_direction
|
||
end interface lattice_forestProjection_screw
|
||
|
||
public :: &
|
||
lattice_init, &
|
||
lattice_equivalent_nu, &
|
||
lattice_equivalent_mu, &
|
||
lattice_applyLatticeSymmetry33, &
|
||
lattice_SchmidMatrix_slip, &
|
||
lattice_SchmidMatrix_twin, &
|
||
lattice_SchmidMatrix_trans, &
|
||
lattice_SchmidMatrix_cleavage, &
|
||
lattice_nonSchmidMatrix, &
|
||
lattice_interaction_SlipBySlip, &
|
||
lattice_interaction_TwinByTwin, &
|
||
lattice_interaction_TransByTrans, &
|
||
lattice_interaction_SlipByTwin, &
|
||
lattice_interaction_SlipByTrans, &
|
||
lattice_interaction_TwinBySlip, &
|
||
lattice_characteristicShear_Twin, &
|
||
lattice_C66_twin, &
|
||
lattice_C66_trans, &
|
||
lattice_forestProjection_edge, &
|
||
lattice_forestProjection_screw, &
|
||
lattice_slip_normal, &
|
||
lattice_slip_direction, &
|
||
lattice_slip_transverse, &
|
||
lattice_labels_slip, &
|
||
lattice_labels_twin
|
||
|
||
contains
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Module initialization
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine lattice_init
|
||
|
||
integer :: Nphases, ph,i
|
||
class(tNode), pointer :: &
|
||
phases, &
|
||
phase, &
|
||
mech, &
|
||
elasticity
|
||
|
||
print'(/,a)', ' <<<+- lattice init -+>>>'; flush(IO_STDOUT)
|
||
|
||
! SHOULD NOT BE PART OF LATTICE BEGIN
|
||
|
||
phases => config_material%get('phase')
|
||
Nphases = phases%length
|
||
|
||
allocate(lattice_C66(6,6,Nphases), source=0.0_pReal)
|
||
|
||
allocate(lattice_mu, lattice_nu,&
|
||
source=[(0.0_pReal,i=1,Nphases)])
|
||
|
||
do ph = 1, phases%length
|
||
phase => phases%get(ph)
|
||
mech => phase%get('mechanical')
|
||
elasticity => mech%get('elastic')
|
||
lattice_C66(1,1,ph) = elasticity%get_asFloat('C_11')
|
||
lattice_C66(1,2,ph) = elasticity%get_asFloat('C_12')
|
||
lattice_C66(4,4,ph) = elasticity%get_asFloat('C_44')
|
||
|
||
lattice_C66(1,3,ph) = elasticity%get_asFloat('C_13',defaultVal=0.0_pReal)
|
||
lattice_C66(2,3,ph) = elasticity%get_asFloat('C_23',defaultVal=0.0_pReal)
|
||
lattice_C66(3,3,ph) = elasticity%get_asFloat('C_33',defaultVal=0.0_pReal)
|
||
lattice_C66(6,6,ph) = elasticity%get_asFloat('C_66',defaultVal=0.0_pReal)
|
||
|
||
lattice_C66(1:6,1:6,ph) = applyLatticeSymmetryC66(lattice_C66(1:6,1:6,ph),phase%get_asString('lattice'))
|
||
|
||
lattice_nu(ph) = lattice_equivalent_nu(lattice_C66(1:6,1:6,ph),'voigt')
|
||
lattice_mu(ph) = lattice_equivalent_mu(lattice_C66(1:6,1:6,ph),'voigt')
|
||
|
||
lattice_C66(1:6,1:6,ph) = math_sym3333to66(math_Voigt66to3333(lattice_C66(1:6,1:6,ph))) ! Literature data is in Voigt notation
|
||
do i = 1, 6
|
||
if (abs(lattice_C66(i,i,ph))<tol_math_check) &
|
||
call IO_error(135,el=i,ip=ph,ext_msg='matrix diagonal "el"ement of phase "ip"')
|
||
enddo
|
||
! SHOULD NOT BE PART OF LATTICE END
|
||
|
||
call selfTest
|
||
|
||
enddo
|
||
|
||
end subroutine lattice_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Characteristic shear for twinning
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_characteristicShear_Twin(Ntwin,structure,CoverA) result(characteristicShear)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Ntwin)) :: characteristicShear
|
||
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system list
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
integer, dimension(HEX_NTWIN), parameter :: &
|
||
HEX_SHEARTWIN = reshape( [&
|
||
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 &
|
||
],[HEX_NTWIN]) ! indicator to formulas below
|
||
|
||
a = 0
|
||
myFamilies: do f = 1,size(Ntwin,1)
|
||
mySystems: do s = 1,Ntwin(f)
|
||
a = a + 1
|
||
select case(structure)
|
||
case('cF','cI')
|
||
characteristicShear(a) = 0.5_pReal*sqrt(2.0_pReal)
|
||
case('hP')
|
||
if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='lattice_characteristicShear_Twin')
|
||
p = sum(HEX_NTWINSYSTEM(1:f-1))+s
|
||
select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
|
||
case (1) ! <-10.1>{10.2}
|
||
characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA
|
||
case (2) ! <11.6>{-1-1.1}
|
||
characteristicShear(a) = 1.0_pReal/cOverA
|
||
case (3) ! <10.-2>{10.1}
|
||
characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA
|
||
case (4) ! <11.-3>{11.2}
|
||
characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA
|
||
end select
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure))
|
||
end select
|
||
enddo mySystems
|
||
enddo myFamilies
|
||
|
||
end function lattice_characteristicShear_Twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Rotated elasticity matrices for twinning in 66-vector notation
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_C66_twin(Ntwin,C66,structure,CoverA)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(6,6), intent(in) :: C66 !< unrotated parent stiffness matrix
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(6,6,sum(Ntwin)) :: lattice_C66_twin
|
||
|
||
real(pReal), dimension(3,3,sum(Ntwin)):: coordinateSystem
|
||
type(rotation) :: R
|
||
integer :: i
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,FCC_NSLIPSYSTEM,FCC_SYSTEMTWIN,&
|
||
structure,0.0_pReal)
|
||
case('cI')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,BCC_NSLIPSYSTEM,BCC_SYSTEMTWIN,&
|
||
structure,0.0_pReal)
|
||
case('hP')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,HEX_NSLIPSYSTEM,HEX_SYSTEMTWIN,&
|
||
structure,cOverA)
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure))
|
||
end select
|
||
|
||
do i = 1, sum(Ntwin)
|
||
call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI],P=1) ! ToDo: Why always 180 deg?
|
||
lattice_C66_twin(1:6,1:6,i) = R%rotTensor4sym(C66)
|
||
enddo
|
||
|
||
end function lattice_C66_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Rotated elasticity matrices for transformation in 66-vector notation
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_C66_trans(Ntrans,C_parent66,structure_target, &
|
||
cOverA_trans,a_bcc,a_fcc)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure_target !< lattice structure
|
||
real(pReal), dimension(6,6), intent(in) :: C_parent66
|
||
real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans
|
||
|
||
real(pReal), dimension(6,6) :: C_bar66, C_target_unrotated66
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: Q,S
|
||
type(rotation) :: R
|
||
real(pReal) :: a_bcc, a_fcc, cOverA_trans
|
||
integer :: i
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! elasticity matrix of the target phase in cube orientation
|
||
if (structure_target == 'hP') then
|
||
if (cOverA_trans < 1.0_pReal .or. cOverA_trans > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='lattice_C66_trans: '//trim(structure_target))
|
||
C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal
|
||
C_bar66(1,2) = (C_parent66(1,1) + 5.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/6.0_pReal
|
||
C_bar66(3,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) + 4.0_pReal*C_parent66(4,4))/3.0_pReal
|
||
C_bar66(1,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/3.0_pReal
|
||
C_bar66(4,4) = (C_parent66(1,1) - C_parent66(1,2) + C_parent66(4,4))/3.0_pReal
|
||
C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal))
|
||
|
||
C_target_unrotated66 = 0.0_pReal
|
||
C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
|
||
C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
|
||
C_target_unrotated66(1,3) = C_bar66(1,3)
|
||
C_target_unrotated66(3,3) = C_bar66(3,3)
|
||
C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
|
||
C_target_unrotated66 = applyLatticeSymmetryC66(C_target_unrotated66,'hP')
|
||
elseif (structure_target == 'cI') then
|
||
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
|
||
call IO_error(134,ext_msg='lattice_C66_trans: '//trim(structure_target))
|
||
C_target_unrotated66 = C_parent66
|
||
else
|
||
call IO_error(137,ext_msg='lattice_C66_trans : '//trim(structure_target))
|
||
endif
|
||
|
||
do i = 1, 6
|
||
if (abs(C_target_unrotated66(i,i))<tol_math_check) &
|
||
call IO_error(135,el=i,ext_msg='matrix diagonal "el"ement in transformation')
|
||
enddo
|
||
|
||
call buildTransformationSystem(Q,S,Ntrans,cOverA_trans,a_fcc,a_bcc)
|
||
|
||
do i = 1, sum(Ntrans)
|
||
call R%fromMatrix(Q(1:3,1:3,i))
|
||
lattice_C66_trans(1:6,1:6,i) = R%rotTensor4sym(C_target_unrotated66)
|
||
enddo
|
||
|
||
end function lattice_C66_trans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Non-schmid projections for bcc with up to 6 coefficients
|
||
! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17)
|
||
! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections
|
||
integer, intent(in) :: sense !< sense (-1,+1)
|
||
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix
|
||
|
||
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem !< coordinate system of slip system
|
||
real(pReal), dimension(3) :: direction, normal, np
|
||
type(rotation) :: R
|
||
integer :: i
|
||
|
||
if (abs(sense) /= 1) error stop 'Sense in lattice_nonSchmidMatrix'
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,BCC_NSLIPSYSTEM,BCC_SYSTEMSLIP,'cI',0.0_pReal)
|
||
coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip))*real(sense,pReal) ! convert unidirectional coordinate system
|
||
nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'cI',0.0_pReal) ! Schmid contribution
|
||
|
||
do i = 1,sum(Nslip)
|
||
direction = coordinateSystem(1:3,1,i)
|
||
normal = coordinateSystem(1:3,2,i)
|
||
call R%fromAxisAngle([direction,60.0_pReal],degrees=.true.,P=1)
|
||
np = R%rotate(normal)
|
||
|
||
if (size(nonSchmidCoefficients)>0) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(1) * math_outer(direction, np)
|
||
if (size(nonSchmidCoefficients)>1) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(2) * math_outer(math_cross(normal, direction), normal)
|
||
if (size(nonSchmidCoefficients)>2) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(3) * math_outer(math_cross(np, direction), np)
|
||
if (size(nonSchmidCoefficients)>3) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(4) * math_outer(normal, normal)
|
||
if (size(nonSchmidCoefficients)>4) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(5) * math_outer(math_cross(normal, direction), &
|
||
math_cross(normal, direction))
|
||
if (size(nonSchmidCoefficients)>5) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(6) * math_outer(direction, direction)
|
||
enddo
|
||
|
||
end function lattice_nonSchmidMatrix
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-slip interaction matrix
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipBySlip(Nslip,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-slip interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NSLIP,FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 2, 2, 4, 7, 5, 3, 5, 5, 4, 6, 7, 10,11,10,11,12,13, & ! -----> acting (forest)
|
||
2, 1, 2, 7, 4, 5, 6, 4, 7, 5, 3, 5, 10,11,12,13,10,11, & ! |
|
||
2, 2, 1, 5, 5, 3, 6, 7, 4, 7, 6, 4, 12,13,10,11,10,11, & ! |
|
||
4, 7, 6, 1, 2, 2, 4, 6, 7, 3, 5, 5, 10,11,11,10,13,12, & ! v
|
||
7, 4, 6, 2, 1, 2, 5, 3, 5, 6, 4, 7, 10,11,13,12,11,10, & ! reacting (primary)
|
||
5, 5, 3, 2, 2, 1, 7, 6, 4, 6, 7, 4, 12,13,11,10,11,10, &
|
||
3, 5, 5, 4, 6, 7, 1, 2, 2, 4, 7, 6, 11,10,11,10,12,13, &
|
||
6, 4, 7, 5, 3, 5, 2, 1, 2, 7, 4, 6, 11,10,13,12,10,11, &
|
||
6, 7, 4, 7, 6, 4, 2, 2, 1, 5, 5, 3, 13,12,11,10,10,11, &
|
||
4, 6, 7, 3, 5, 5, 4, 7, 6, 1, 2, 2, 11,10,10,11,13,12, &
|
||
5, 3, 5, 6, 4, 7, 7, 4, 6, 2, 1, 2, 11,10,12,13,11,10, &
|
||
7, 6, 4, 6, 7, 4, 5, 5, 3, 2, 2, 1, 13,12,10,11,11,10, &
|
||
|
||
10,10,12,10,10,12,11,11,13,11,11,13, 1, 8, 9, 9, 9, 9, &
|
||
11,11,13,11,11,13,10,10,12,10,10,12, 8, 1, 9, 9, 9, 9, &
|
||
10,12,10,11,13,11,11,13,11,10,12,10, 9, 9, 1, 8, 9, 9, &
|
||
11,13,11,10,12,10,10,12,10,11,13,11, 9, 9, 8, 1, 9, 9, &
|
||
12,10,10,13,11,11,12,10,10,13,11,11, 9, 9, 9, 9, 1, 8, &
|
||
13,11,11,12,10,10,13,11,11,12,10,10, 9, 9, 9, 9, 8, 1 &
|
||
],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for fcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
|
||
!< 1: self interaction --> alpha 0
|
||
!< 2: coplanar interaction --> alpha copla
|
||
!< 3: collinear interaction --> alpha coli
|
||
!< 4: Hirth locks --> alpha 1
|
||
!< 5: glissile junctions I --> alpha 2
|
||
!< 6: glissile junctions II --> alpha 2*
|
||
!< 7: Lomer locks --> alpha 3
|
||
!< 8: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
|
||
!< 9: similar to Lomer locks in <110>{111} for two {110} planes
|
||
!<10: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
|
||
!<11: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
|
||
!<12: crossing btw one {110} and one {111} plane
|
||
!<13: collinear btw one {110} and one {111} plane
|
||
|
||
integer, dimension(BCC_NSLIP,BCC_NSLIP), parameter :: &
|
||
BCC_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 3, 6, 6, 7, 5, 4, 2, 4, 2, 7, 5, 18,18,11, 8, 9,13,17,14,13, 9,17,14, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &! -----> acting (forest)
|
||
3, 1, 6, 6, 4, 2, 7, 5, 7, 5, 4, 2, 18,18, 8,11,13, 9,14,17, 9,13,14,17, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &! |
|
||
6, 6, 1, 3, 5, 7, 2, 4, 5, 7, 2, 4, 11, 8,18,18,17,14, 9,13,17,14,13, 9, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &! |
|
||
6, 6, 3, 1, 2, 4, 5, 7, 2, 4, 5, 7, 8,11,18,18,14,17,13, 9,14,17, 9,13, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &! v
|
||
7, 5, 4, 2, 1, 3, 6, 6, 2, 4, 7, 5, 9,17,13,14,18,11,18, 8,13,17, 9,14, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &! reacting (primary)
|
||
4, 2, 7, 5, 3, 1, 6, 6, 5, 7, 4, 2, 13,14, 9,17,18, 8,18,11, 9,14,13,17, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &
|
||
5, 7, 2, 4, 6, 6, 1, 3, 7, 5, 2, 4, 17, 9,14,13,11,18, 8,18,17,13,14, 9, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &
|
||
2, 4, 5, 7, 6, 6, 3, 1, 4, 2, 5, 7, 14,13,17, 9, 8,18,11,18,14, 9,17,13, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &
|
||
5, 7, 4, 2, 2, 4, 7, 5, 1, 3, 6, 6, 9,17,14,13,13,17,14, 9,18,11, 8,18, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &
|
||
2, 4, 7, 5, 5, 7, 4, 2, 3, 1, 6, 6, 13,14,17, 9, 9,14,17,13,18, 8,11,18, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &
|
||
7, 5, 2, 4, 7, 5, 2, 4, 6, 6, 1, 3, 17, 9,13,14,17,13, 9,14,11,18,18, 8, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &
|
||
4, 2, 5, 7, 4, 2, 5, 7, 6, 6, 3, 1, 14,13, 9,17,14, 9,13,17, 8,18,18,11, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &
|
||
|
||
19,19,10, 8, 9,12,16,15, 9,12,16,15, 1,20,24,24,23,22,21, 2,23,22, 2,21, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
|
||
19,19, 8,10,16,15, 9,12,16,15, 9,12, 20, 1,24,24,22,23, 2,21,22,23,21, 2, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
|
||
10, 8,19,19,12, 9,15,16,15,16,12, 9, 24,24, 1,20,21, 2,23,22, 2,21,23,22, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
|
||
8,10,19,19,15,16,12, 9,12, 9,15,16, 24,24,20, 1, 2,21,22,23,21, 2,22,23, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
|
||
9,12,16,15,19,19,10, 8,12, 9,16,15, 23,21,22, 2, 1,24,20,24,23, 2,22,21, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
|
||
12, 9,15,16,10, 8,19,19,16,15,12, 9, 21,23, 2,21,24, 1,24,20, 2,23,21,22, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
|
||
16,15, 9,12,19,19, 8,10,15,16, 9,12, 22, 2,23,22,20,24, 1,24,22,21,23, 2, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
|
||
15,16,12, 9, 8,10,19,19, 9,12,15,16, 2,22,21,23,24,20,24, 1,21,22, 2,23, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
|
||
12, 9,16,15,12, 9,16,15,19,19,10, 8, 23,21, 2,22,23, 2,21,22, 1,24,24,20, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
|
||
9,12,15,16,16,15,12, 9,10, 8,19,19, 21,23,22, 2, 2,23,22,21,24, 1,20,24, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
|
||
16,15,12, 9, 9,12,15,16, 8,10,19,19, 2,22,23,21,21,22,23, 2,24,20, 1,24, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
|
||
15,16, 9,12,15,16, 9,12,19,19, 8,10, 22, 2,21,23,22,21, 2,23,20,24,24, 1, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
|
||
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28, 1,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,27,27,28,28,28,27,28,28,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28, 1,28,28,27,28,28,28,28,27,28,28,27,28,28,27,28,28,28,27,28,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28, 1,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28, 1,28,28,28,28,27,28,28,27,28,28,27,28,28,28,27,28,28, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28, 1,28,28,27,28,28,28,28,27,27,28,28,28,27,28,28,28, &
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28, 1,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28, 1,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28, 1,28,28,28,28,27,27,28,28,28,27,28,28,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28, 1,28,28,27,28,28,27,28,28,28,27,28,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28, 1,28,28,28,28,28,28,27,28,28,28,27, &
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28, 1,28,28,28,28,27,28,28,28,27,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28, 1,28,28,27,28,28,28,27,28,28, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28, 1,27,28,28,28,27,28,28,28, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,27, 1,28,28,28,27,28,28,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28,27,28,28, 1,28,28,28,27,28,28, &
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28, 1,28,28,28,27,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28, 1,28,28,28,27, &
|
||
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,27,27,28,28,28, 1,28,28,28, &
|
||
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,27,28,28,28, 1,28,28, &
|
||
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28, 1,28, &
|
||
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28, 1 &
|
||
],shape(BCC_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for bcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
|
||
!< 1: self interaction --> alpha 0
|
||
!< 2: collinear interaction --> alpha 1
|
||
!< 3: coplanar interaction --> alpha 2
|
||
!< 4-7: other coefficients
|
||
!< 8: {110}-{112} collinear and perpendicular planes --> alpha 6
|
||
!< 9: {110}-{112} collinear --> alpha 7
|
||
!< 10-24: other coefficients
|
||
!< 25: {110}-{123} collinear
|
||
!< 26: {112}-{123} collinear
|
||
!< 27: {123}-{123} collinear
|
||
!< 28: other interaction
|
||
|
||
integer, dimension(HEX_NSLIP,HEX_NSLIP), parameter :: &
|
||
HEX_INTERACTIONSLIPSLIP = reshape( [&
|
||
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, & ! -----> acting (forest)
|
||
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
|
||
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, & ! reacting (primary)
|
||
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 &
|
||
],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for hex (onion peel naming scheme)
|
||
|
||
integer, dimension(BCT_NSLIP,BCT_NSLIP), parameter :: &
|
||
BCT_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 2, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! -----> acting
|
||
2, 1, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! |
|
||
! |
|
||
6, 6, 4, 5, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! v
|
||
6, 6, 5, 4, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! reacting
|
||
|
||
12, 12, 11, 11, 9, 10, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
|
||
12, 12, 11, 11, 10, 9, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
|
||
|
||
20, 20, 19, 19, 18, 18, 16, 17, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 16, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 17, 16, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 17, 17, 16, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
|
||
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 25, 26, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
|
||
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 26, 25, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
|
||
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 36, 37, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 36, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 36, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 37, 36, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
|
||
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 49, 50, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
|
||
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 50, 49, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
|
||
|
||
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 64, 65, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
|
||
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 65, 64, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
|
||
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 81, 82, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 81, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 81, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 82, 81, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 100,101,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,100,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,100,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,100,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,100,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,100,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,100,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,101,100, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 121, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 121, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 121, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 144,145,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,144,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,144,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,144,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,144,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,144,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,144,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,145,144, 168,168,168,168,168,168,168,168, &
|
||
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,169,170,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,169,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,169,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,170,169,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 &
|
||
],shape(BCT_INTERACTIONSLIPSLIP))
|
||
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
interactionTypes = FCC_INTERACTIONSLIPSLIP
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
case('cI')
|
||
interactionTypes = BCC_INTERACTIONSLIPSLIP
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
case('hP')
|
||
interactionTypes = HEX_INTERACTIONSLIPSLIP
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
case('tI')
|
||
interactionTypes = BCT_INTERACTIONSLIPSLIP
|
||
NslipMax = BCT_NSLIPSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipBySlip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Twin-twin interaction matrix
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TwinByTwin(Ntwin,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Ntwin),sum(Ntwin)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NTWIN,FCC_NTWIN), parameter :: &
|
||
FCC_INTERACTIONTWINTWIN = reshape( [&
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
|
||
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 &
|
||
],shape(FCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for fcc
|
||
|
||
integer, dimension(BCC_NTWIN,BCC_NTWIN), parameter :: &
|
||
BCC_INTERACTIONTWINTWIN = reshape( [&
|
||
1,3,3,3,3,3,3,2,3,3,2,3, & ! -----> acting
|
||
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
|
||
3,3,3,2,1,3,3,3,3,2,3,3, & ! reacting
|
||
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 &
|
||
],shape(BCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for bcc
|
||
!< 1: self interaction
|
||
!< 2: collinear interaction
|
||
!< 3: other interaction
|
||
integer, dimension(HEX_NTWIN,HEX_NTWIN), parameter :: &
|
||
HEX_INTERACTIONTWINTWIN = reshape( [&
|
||
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting
|
||
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
|
||
2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting
|
||
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 &
|
||
],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
interactionTypes = FCC_INTERACTIONTWINTWIN
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
case('cI')
|
||
interactionTypes = BCC_INTERACTIONTWINTWIN
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
case('hP')
|
||
interactionTypes = HEX_INTERACTIONTWINTWIN
|
||
NtwinMax = HEX_NTWINSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TwinByTwin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Trans-trans interaction matrix
|
||
!> details only active trans systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TransByTrans(Ntrans,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active trans systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for trans-trans interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
|
||
real(pReal), dimension(sum(Ntrans),sum(Ntrans)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtransMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NTRANS,FCC_NTRANS), parameter :: &
|
||
FCC_INTERACTIONTRANSTRANS = reshape( [&
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
|
||
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 &
|
||
],shape(FCC_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for fcc
|
||
|
||
if(structure == 'cF') then
|
||
interactionTypes = FCC_INTERACTIONTRANSTRANS
|
||
NtransMax = FCC_NTRANSSYSTEM
|
||
else
|
||
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure))
|
||
end if
|
||
|
||
interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TransByTrans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-twin interaction matrix
|
||
!> details only active slip and twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
|
||
Ntwin !< number of active twin systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Nslip),sum(Ntwin)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax, &
|
||
NtwinMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NTWIN,FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPTWIN = reshape( [&
|
||
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> twin (acting)
|
||
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
|
||
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
|
||
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
|
||
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
|
||
2,2,2,1,1,1,3,3,3,3,3,3, &
|
||
2,2,2,3,3,3,1,1,1,3,3,3, &
|
||
3,3,3,2,2,2,1,1,1,3,3,3, &
|
||
3,3,3,3,3,3,1,1,1,2,2,2, &
|
||
3,3,3,2,2,2,3,3,3,1,1,1, &
|
||
2,2,2,3,3,3,3,3,3,1,1,1, &
|
||
3,3,3,3,3,3,2,2,2,1,1,1, &
|
||
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4 &
|
||
],shape(FCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for fcc
|
||
!< 1: coplanar interaction
|
||
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
|
||
!< 3: other interaction
|
||
integer, dimension(BCC_NTWIN,BCC_NSLIP), parameter :: &
|
||
BCC_INTERACTIONSLIPTWIN = reshape( [&
|
||
3,3,3,2,2,3,3,3,3,2,3,3, & ! -----> twin (acting)
|
||
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
|
||
2,3,3,3,3,3,3,2,3,3,2,3, & ! slip (reacting)
|
||
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, &
|
||
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4 &
|
||
],shape(BCC_INTERACTIONSLIPTWIN)) !< 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
|
||
!< 4: other interaction with slip family {123}
|
||
|
||
integer, dimension(HEX_NTWIN,HEX_NSLIP), parameter :: &
|
||
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 (acting)
|
||
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 (reacting)
|
||
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 &
|
||
],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
interactionTypes = FCC_INTERACTIONSLIPTWIN
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
case('cI')
|
||
interactionTypes = BCC_INTERACTIONSLIPTWIN
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
case('hP')
|
||
interactionTypes = HEX_INTERACTIONSLIPTWIN
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
NtwinMax = HEX_NTWINSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipByTwin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-trans interaction matrix
|
||
!> details only active slip and trans systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
|
||
Ntrans !< number of active trans systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-trans interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
|
||
real(pReal), dimension(sum(Nslip),sum(Ntrans)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax, &
|
||
NtransMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NTRANS,FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPTRANS = reshape( [&
|
||
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> trans (acting)
|
||
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
|
||
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
|
||
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
|
||
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
|
||
2,2,2,1,1,1,3,3,3,3,3,3, &
|
||
2,2,2,3,3,3,1,1,1,3,3,3, &
|
||
3,3,3,2,2,2,1,1,1,3,3,3, &
|
||
3,3,3,3,3,3,1,1,1,2,2,2, &
|
||
3,3,3,2,2,2,3,3,3,1,1,1, &
|
||
2,2,2,3,3,3,3,3,3,1,1,1, &
|
||
3,3,3,3,3,3,2,2,2,1,1,1, &
|
||
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4 &
|
||
],shape(FCC_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for fcc
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
interactionTypes = FCC_INTERACTIONSLIPTRANS
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
NtransMax = FCC_NTRANSSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipByTrans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Twin-slip interaction matrix
|
||
!> details only active twin and slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin, & !< number of active twin systems per family
|
||
Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Ntwin),sum(Nslip)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtwinMax, &
|
||
NslipMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(FCC_NSLIP,FCC_NTWIN), parameter :: &
|
||
FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc
|
||
|
||
integer, dimension(BCC_NSLIP,BCC_NTWIN), parameter :: &
|
||
BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc
|
||
|
||
integer, dimension(HEX_NSLIP,HEX_NTWIN), parameter :: &
|
||
HEX_INTERACTIONTWINSLIP = reshape( [&
|
||
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 (acting)
|
||
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 (reacting)
|
||
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 &
|
||
],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
interactionTypes = FCC_INTERACTIONTWINSLIP
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
case('cI')
|
||
interactionTypes = BCC_INTERACTIONTWINSLIP
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
case('hP')
|
||
interactionTypes = HEX_INTERACTIONTWINSLIP
|
||
NtwinMax = HEX_NTWINSYSTEM
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TwinBySlip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for slip
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
integer :: i
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('cI')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hP')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('tI')
|
||
NslipMax = BCT_NSLIPSYSTEM
|
||
slipSystems = BCT_SYSTEMSLIP
|
||
case default
|
||
allocate(NslipMax(0))
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Nslip)
|
||
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
|
||
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for slip')
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for twinning
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_twin(Ntwin,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Ntwin)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: twinSystems
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
integer :: i
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
twinSystems = FCC_SYSTEMTWIN
|
||
case('cI')
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
twinSystems = BCC_SYSTEMTWIN
|
||
case('hP')
|
||
NtwinMax = HEX_NTWINSYSTEM
|
||
twinSystems = HEX_SYSTEMTWIN
|
||
case default
|
||
allocate(NtwinMax(0))
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
|
||
call IO_error(145,ext_msg='Ntwin '//trim(structure))
|
||
if (any(Ntwin < 0)) &
|
||
call IO_error(144,ext_msg='Ntwin '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Ntwin)
|
||
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
|
||
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for twin')
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for twinning
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_trans(Ntrans,structure_target,cOverA,a_bcc,a_fcc) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure_target !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: devNull
|
||
real(pReal) :: a_bcc, a_fcc
|
||
|
||
if (structure_target /= 'cI' .and. structure_target /= 'hP') &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
if (structure_target == 'hP' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
|
||
call IO_error(131,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
if (structure_target == 'cI' .and. (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal)) &
|
||
call IO_error(134,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA,a_fcc,a_bcc)
|
||
|
||
end function lattice_SchmidMatrix_trans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for cleavage
|
||
!> details only active cleavage systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_cleavage(Ncleavage,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ncleavage !< number of active cleavage systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,3,sum(Ncleavage)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ncleavage)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: cleavageSystems
|
||
integer, dimension(:), allocatable :: NcleavageMax
|
||
integer :: i
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NcleavageMax = FCC_NCLEAVAGESYSTEM
|
||
cleavageSystems = FCC_SYSTEMCLEAVAGE
|
||
case('cI')
|
||
NcleavageMax = BCC_NCLEAVAGESYSTEM
|
||
cleavageSystems = BCC_SYSTEMCLEAVAGE
|
||
case default
|
||
allocate(NcleavageMax(0))
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0)) &
|
||
call IO_error(145,ext_msg='Ncleavage '//trim(structure))
|
||
if (any(Ncleavage < 0)) &
|
||
call IO_error(144,ext_msg='Ncleavage '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Ncleavage,NcleavageMax,cleavageSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Ncleavage)
|
||
SchmidMatrix(1:3,1:3,1,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
SchmidMatrix(1:3,1:3,2,i) = math_outer(coordinateSystem(1:3,3,i),coordinateSystem(1:3,2,i))
|
||
SchmidMatrix(1:3,1:3,3,i) = math_outer(coordinateSystem(1:3,2,i),coordinateSystem(1:3,2,i))
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_cleavage
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip direction of slip systems (|| b)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_direction(Nslip,structure,cOverA) result(d)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: d
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
d = coordinateSystem(1:3,1,1:sum(Nslip))
|
||
|
||
end function lattice_slip_direction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Normal direction of slip systems (|| n)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_normal(Nslip,structure,cOverA) result(n)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: n
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
n = coordinateSystem(1:3,2,1:sum(Nslip))
|
||
|
||
end function lattice_slip_normal
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Transverse direction of slip systems (|| t = b x n)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_transverse(Nslip,structure,cOverA) result(t)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: t
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
t = coordinateSystem(1:3,3,1:sum(Nslip))
|
||
|
||
end function lattice_slip_transverse
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Labels for slip systems
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_labels_slip(Nslip,structure) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('cI')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hP')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('tI')
|
||
NslipMax = BCT_NSLIPSYSTEM
|
||
slipSystems = BCT_SYSTEMSLIP
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
labels = getLabels(Nslip,NslipMax,slipSystems)
|
||
|
||
end function lattice_labels_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Return 3x3 tensor with symmetry according to given crystal structure
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function lattice_applyLatticeSymmetry33(T,structure) result(T_sym)
|
||
|
||
real(pReal), dimension(3,3) :: T_sym
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: T
|
||
character(len=*), intent(in) :: structure
|
||
|
||
|
||
T_sym = 0.0_pReal
|
||
|
||
select case(structure)
|
||
case('cF','cI')
|
||
T_sym(1,1) = T(1,1)
|
||
T_sym(2,2) = T(1,1)
|
||
T_sym(3,3) = T(1,1)
|
||
case('hP','tI')
|
||
T_sym(1,1) = T(1,1)
|
||
T_sym(2,2) = T(1,1)
|
||
T_sym(3,3) = T(3,3)
|
||
end select
|
||
|
||
end function lattice_applyLatticeSymmetry33
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Return stiffness matrix in 6x6 notation with symmetry according to given crystal structure
|
||
!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function applyLatticeSymmetryC66(C66,structure) result(C66_sym)
|
||
|
||
real(pReal), dimension(6,6) :: C66_sym
|
||
|
||
real(pReal), dimension(6,6), intent(in) :: C66
|
||
character(len=*), intent(in) :: structure
|
||
|
||
integer :: i,j
|
||
|
||
|
||
C66_sym = 0.0_pReal
|
||
|
||
select case(structure)
|
||
case ('cF','cI')
|
||
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1); C66_sym(3,3) = C66(1,1)
|
||
C66_sym(1,2) = C66(1,2); C66_sym(1,3) = C66(1,2); C66_sym(2,3) = C66(1,2)
|
||
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4); C66_sym(6,6) = C66(4,4) ! isotropic C_44 = (C_11-C_12)/2
|
||
case ('hP')
|
||
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1)
|
||
C66_sym(3,3) = C66(3,3)
|
||
C66_sym(1,2) = C66(1,2)
|
||
C66_sym(1,3) = C66(1,3); C66_sym(2,3) = C66(1,3)
|
||
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4)
|
||
C66_sym(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
case ('tI')
|
||
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1)
|
||
C66_sym(3,3) = C66(3,3)
|
||
C66_sym(1,2) = C66(1,2)
|
||
C66_sym(1,3) = C66(1,3); C66_sym(2,3) = C66(1,3)
|
||
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4)
|
||
C66_sym(6,6) = C66(6,6)
|
||
end select
|
||
|
||
do i = 1, 6
|
||
do j = i+1, 6
|
||
C66_sym(j,i) = C66_sym(i,j)
|
||
enddo
|
||
enddo
|
||
|
||
end function applyLatticeSymmetryC66
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Labels for twin systems
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_labels_twin(Ntwin,structure) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
|
||
real(pReal), dimension(:,:), allocatable :: twinSystems
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
twinSystems = FCC_SYSTEMTWIN
|
||
case('cI')
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
twinSystems = BCC_SYSTEMTWIN
|
||
case('hP')
|
||
NtwinMax = HEX_NTWINSYSTEM
|
||
twinSystems = HEX_SYSTEMTWIN
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
|
||
call IO_error(145,ext_msg='Ntwin '//trim(structure))
|
||
if (any(Ntwin < 0)) &
|
||
call IO_error(144,ext_msg='Ntwin '//trim(structure))
|
||
|
||
labels = getLabels(Ntwin,NtwinMax,twinSystems)
|
||
|
||
end function lattice_labels_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Projection of the transverse direction onto the slip plane
|
||
!> @details: This projection is used to calculate forest hardening for edge dislocations
|
||
!--------------------------------------------------------------------------------------------------
|
||
function slipProjection_transverse(Nslip,structure,cOverA) result(projection)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
|
||
|
||
real(pReal), dimension(3,sum(Nslip)) :: n, t
|
||
integer :: i, j
|
||
|
||
n = lattice_slip_normal (Nslip,structure,cOverA)
|
||
t = lattice_slip_transverse(Nslip,structure,cOverA)
|
||
|
||
do i=1, sum(Nslip); do j=1, sum(Nslip)
|
||
projection(i,j) = abs(math_inner(n(:,i),t(:,j)))
|
||
enddo; enddo
|
||
|
||
end function slipProjection_transverse
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Projection of the slip direction onto the slip plane
|
||
!> @details: This projection is used to calculate forest hardening for screw dislocations
|
||
!--------------------------------------------------------------------------------------------------
|
||
function slipProjection_direction(Nslip,structure,cOverA) result(projection)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
|
||
|
||
real(pReal), dimension(3,sum(Nslip)) :: n, d
|
||
integer :: i, j
|
||
|
||
n = lattice_slip_normal (Nslip,structure,cOverA)
|
||
d = lattice_slip_direction(Nslip,structure,cOverA)
|
||
|
||
do i=1, sum(Nslip); do j=1, sum(Nslip)
|
||
projection(i,j) = abs(math_inner(n(:,i),d(:,j)))
|
||
enddo; enddo
|
||
|
||
end function slipProjection_direction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief build a local coordinate system on slip systems
|
||
!> @details Order: Direction, plane (normal), and common perpendicular
|
||
!--------------------------------------------------------------------------------------------------
|
||
function coordinateSystem_slip(Nslip,structure,cOverA) result(coordinateSystem)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
|
||
select case(structure)
|
||
case('cF')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('cI')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hP')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('tI')
|
||
NslipMax = BCT_NSLIPSYSTEM
|
||
slipSystems = BCT_SYSTEMSLIP
|
||
case default
|
||
allocate(NslipMax(0))
|
||
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
|
||
|
||
end function coordinateSystem_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Populate reduced interaction matrix
|
||
!--------------------------------------------------------------------------------------------------
|
||
function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
reacting_used, & !< # of reacting systems per family as specified in material.config
|
||
acting_used, & !< # of acting systems per family as specified in material.config
|
||
reacting_max, & !< max # of reacting systems per family for given lattice
|
||
acting_max !< max # of acting systems per family for given lattice
|
||
real(pReal), dimension(:), intent(in) :: values !< interaction values
|
||
integer, dimension(:,:), intent(in) :: matrix !< interaction types
|
||
real(pReal), dimension(sum(reacting_used),sum(acting_used)) :: buildInteraction
|
||
|
||
integer :: &
|
||
acting_family_index, acting_family, acting_system, &
|
||
reacting_family_index, reacting_family, reacting_system, &
|
||
i,j,k,l
|
||
|
||
do acting_family = 1,size(acting_used,1)
|
||
acting_family_index = sum(acting_used(1:acting_family-1))
|
||
do acting_system = 1,acting_used(acting_family)
|
||
|
||
do reacting_family = 1,size(reacting_used,1)
|
||
reacting_family_index = sum(reacting_used(1:reacting_family-1))
|
||
do reacting_system = 1,reacting_used(reacting_family)
|
||
|
||
i = sum( acting_max(1: acting_family-1)) + acting_system
|
||
j = sum(reacting_max(1:reacting_family-1)) + reacting_system
|
||
|
||
k = acting_family_index + acting_system
|
||
l = reacting_family_index + reacting_system
|
||
|
||
if (matrix(i,j) > size(values)) call IO_error(138,ext_msg='buildInteraction')
|
||
|
||
buildInteraction(l,k) = values(matrix(i,j))
|
||
|
||
enddo; enddo
|
||
enddo; enddo
|
||
|
||
end function buildInteraction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Build a local coordinate system on slip, twin, trans, cleavage systems
|
||
!> @details Order: Direction, plane (normal), and common perpendicular
|
||
!--------------------------------------------------------------------------------------------------
|
||
function buildCoordinateSystem(active,potential,system,structure,cOverA)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
active, & !< # of active systems per family
|
||
potential !< # of potential systems per family
|
||
real(pReal), dimension(:,:), intent(in) :: &
|
||
system
|
||
character(len=*), intent(in) :: &
|
||
structure !< lattice structure
|
||
real(pReal), intent(in) :: &
|
||
cOverA
|
||
real(pReal), dimension(3,3,sum(active)) :: &
|
||
buildCoordinateSystem
|
||
|
||
real(pReal), dimension(3) :: &
|
||
direction, normal
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system matrix
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
if (structure == 'tI' .and. cOverA > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
|
||
if (structure == 'hP' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
|
||
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
|
||
|
||
a = 0
|
||
activeFamilies: do f = 1,size(active,1)
|
||
activeSystems: do s = 1,active(f)
|
||
a = a + 1
|
||
p = sum(potential(1:f-1))+s
|
||
|
||
select case(structure)
|
||
|
||
case ('cF','cI','tI')
|
||
direction = system(1:3,p)
|
||
normal = system(4:6,p)
|
||
|
||
case ('hP')
|
||
direction = [ system(1,p)*1.5_pReal, &
|
||
(system(1,p)+2.0_pReal*system(2,p))*sqrt(0.75_pReal), &
|
||
system(4,p)*cOverA ] ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(p/a)])
|
||
normal = [ system(5,p), &
|
||
(system(5,p)+2.0_pReal*system(6,p))/sqrt(3.0_pReal), &
|
||
system(8,p)/cOverA ] ! plane (hkil)->(h (h+2k)/sqrt(3) l/(p/a))
|
||
|
||
case default
|
||
call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure))
|
||
|
||
end select
|
||
|
||
buildCoordinateSystem(1:3,1,a) = direction/norm2(direction)
|
||
buildCoordinateSystem(1:3,2,a) = normal /norm2(normal)
|
||
buildCoordinateSystem(1:3,3,a) = math_cross(direction/norm2(direction),&
|
||
normal /norm2(normal))
|
||
|
||
enddo activeSystems
|
||
enddo activeFamilies
|
||
|
||
end function buildCoordinateSystem
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Helper function to define transformation systems
|
||
! Needed to calculate Schmid matrix and rotated stiffness matrices.
|
||
! @details: set c/a = 0.0 for fcc -> bcc transformation
|
||
! set a_Xcc = 0.0 for fcc -> hex transformation
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
Ntrans
|
||
real(pReal), dimension(3,3,sum(Ntrans)), intent(out) :: &
|
||
Q, & !< Total rotation: Q = R*B
|
||
S !< Eigendeformation tensor for phase transformation
|
||
real(pReal), intent(in) :: &
|
||
cOverA, & !< c/a for target hex structure
|
||
a_bcc, & !< lattice parameter a for target bcc structure
|
||
a_fcc !< lattice parameter a for parent fcc structure
|
||
|
||
type(rotation) :: &
|
||
R, & !< Pitsch rotation
|
||
B !< Rotation of fcc to Bain coordinate system
|
||
real(pReal), dimension(3,3) :: &
|
||
U, & !< Bain deformation
|
||
ss, sd
|
||
real(pReal), dimension(3) :: &
|
||
x, y, z
|
||
integer :: &
|
||
i
|
||
real(pReal), dimension(3+3,FCC_NTRANS), parameter :: &
|
||
FCCTOHEX_SYSTEMTRANS = reshape(real( [&
|
||
-2, 1, 1, 1, 1, 1, &
|
||
1,-2, 1, 1, 1, 1, &
|
||
1, 1,-2, 1, 1, 1, &
|
||
2,-1, 1, -1,-1, 1, &
|
||
-1, 2, 1, -1,-1, 1, &
|
||
-1,-1,-2, -1,-1, 1, &
|
||
-2,-1,-1, 1,-1,-1, &
|
||
1, 2,-1, 1,-1,-1, &
|
||
1,-1, 2, 1,-1,-1, &
|
||
2, 1,-1, -1, 1,-1, &
|
||
-1,-2,-1, -1, 1,-1, &
|
||
-1, 1, 2, -1, 1,-1 &
|
||
],pReal),shape(FCCTOHEX_SYSTEMTRANS))
|
||
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
|
||
FCCTOBCC_SYSTEMTRANS = reshape([&
|
||
0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
|
||
0.0,-1.0, 0.0, 10.26, &
|
||
0.0, 0.0, 1.0, 10.26, &
|
||
0.0, 0.0,-1.0, 10.26, &
|
||
1.0, 0.0, 0.0, 10.26, &
|
||
-1.0, 0.0, 0.0, 10.26, &
|
||
0.0, 0.0, 1.0, 10.26, &
|
||
0.0, 0.0,-1.0, 10.26, &
|
||
1.0, 0.0, 0.0, 10.26, &
|
||
-1.0, 0.0, 0.0, 10.26, &
|
||
0.0, 1.0, 0.0, 10.26, &
|
||
0.0,-1.0, 0.0, 10.26 &
|
||
],shape(FCCTOBCC_SYSTEMTRANS))
|
||
|
||
integer, dimension(9,fcc_Ntrans), parameter :: &
|
||
FCCTOBCC_BAINVARIANT = reshape( [&
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0 &
|
||
],shape(FCCTOBCC_BAINVARIANT))
|
||
|
||
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
|
||
FCCTOBCC_BAINROT = reshape([&
|
||
1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0 &
|
||
],shape(FCCTOBCC_BAINROT))
|
||
|
||
if (a_bcc > 0.0_pReal .and. a_fcc > 0.0_pReal .and. dEq0(cOverA)) then ! fcc -> bcc transformation
|
||
do i = 1,sum(Ntrans)
|
||
call R%fromAxisAngle(FCCTOBCC_SYSTEMTRANS(:,i),degrees=.true.,P=1)
|
||
call B%fromAxisAngle(FCCTOBCC_BAINROT(:,i), degrees=.true.,P=1)
|
||
x = real(FCCTOBCC_BAINVARIANT(1:3,i),pReal)
|
||
y = real(FCCTOBCC_BAINVARIANT(4:6,i),pReal)
|
||
z = real(FCCTOBCC_BAINVARIANT(7:9,i),pReal)
|
||
|
||
U = (a_bcc/a_fcc)*math_outer(x,x) &
|
||
+ (a_bcc/a_fcc)*math_outer(y,y) * sqrt(2.0_pReal) &
|
||
+ (a_bcc/a_fcc)*math_outer(z,z) * sqrt(2.0_pReal)
|
||
Q(1:3,1:3,i) = matmul(R%asMatrix(),B%asMatrix())
|
||
S(1:3,1:3,i) = matmul(R%asMatrix(),U) - MATH_I3
|
||
enddo
|
||
elseif (cOverA > 0.0_pReal .and. dEq0(a_bcc)) then ! fcc -> hex transformation
|
||
ss = MATH_I3
|
||
sd = MATH_I3
|
||
ss(1,3) = sqrt(2.0_pReal)/4.0_pReal
|
||
sd(3,3) = cOverA/sqrt(8.0_pReal/3.0_pReal)
|
||
|
||
do i = 1,sum(Ntrans)
|
||
x = FCCTOHEX_SYSTEMTRANS(1:3,i)/norm2(FCCTOHEX_SYSTEMTRANS(1:3,i))
|
||
z = FCCTOHEX_SYSTEMTRANS(4:6,i)/norm2(FCCTOHEX_SYSTEMTRANS(4:6,i))
|
||
y = -math_cross(x,z)
|
||
Q(1:3,1,i) = x
|
||
Q(1:3,2,i) = y
|
||
Q(1:3,3,i) = z
|
||
S(1:3,1:3,i) = matmul(Q(1:3,1:3,i), matmul(matmul(sd,ss), transpose(Q(1:3,1:3,i)))) - MATH_I3 ! ToDo: This is of interest for the Schmid matrix only
|
||
enddo
|
||
else
|
||
call IO_error(132,ext_msg='buildTransformationSystem')
|
||
endif
|
||
|
||
end subroutine buildTransformationSystem
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief select active systems as strings
|
||
!--------------------------------------------------------------------------------------------------
|
||
function getlabels(active,potential,system) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
active, & !< # of active systems per family
|
||
potential !< # of potential systems per family
|
||
real(pReal), dimension(:,:), intent(in) :: &
|
||
system
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
character(len=:), allocatable :: label
|
||
|
||
integer :: i,j
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system matrix
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
i = 2*size(system,1) + (size(system,1) - 2) + 4 ! 2 letters per index + spaces + brackets
|
||
allocate(character(len=i) :: labels(sum(active)), label)
|
||
|
||
a = 0
|
||
activeFamilies: do f = 1,size(active,1)
|
||
activeSystems: do s = 1,active(f)
|
||
a = a + 1
|
||
p = sum(potential(1:f-1))+s
|
||
|
||
i = 1
|
||
label(i:i) = '['
|
||
direction: do j = 1, size(system,1)/2
|
||
write(label(i+1:i+2),'(I2.1)') int(system(j,p))
|
||
label(i+3:i+3) = ' '
|
||
i = i + 3
|
||
enddo direction
|
||
label(i:i) = ']'
|
||
|
||
i = i +1
|
||
label(i:i) = '('
|
||
normal: do j = size(system,1)/2+1, size(system,1)
|
||
write(label(i+1:i+2),'(I2.1)') int(system(j,p))
|
||
label(i+3:i+3) = ' '
|
||
i = i + 3
|
||
enddo normal
|
||
label(i:i) = ')'
|
||
|
||
labels(s) = label
|
||
|
||
enddo activeSystems
|
||
enddo activeFamilies
|
||
|
||
end function getlabels
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Equivalent Poisson's ratio (ν)
|
||
!> @details https://doi.org/10.1143/JPSJ.20.635
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_equivalent_nu(C,assumption) result(nu)
|
||
|
||
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
|
||
character(len=*), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
|
||
real(pReal) :: K, mu, nu
|
||
|
||
logical :: error
|
||
real(pReal), dimension(6,6) :: S
|
||
|
||
|
||
if (IO_lc(assumption) == 'voigt') then
|
||
K = (C(1,1)+C(2,2)+C(3,3) +2.0_pReal*(C(1,2)+C(2,3)+C(1,3))) &
|
||
/ 9.0_pReal
|
||
elseif(IO_lc(assumption) == 'reuss') then
|
||
call math_invert(S,error,C)
|
||
if(error) error stop 'matrix inversion failed'
|
||
K = 1.0_pReal &
|
||
/ (S(1,1)+S(2,2)+S(3,3) +2.0_pReal*(S(1,2)+S(2,3)+S(1,3)))
|
||
else
|
||
error stop 'invalid assumption'
|
||
endif
|
||
|
||
mu = lattice_equivalent_mu(C,assumption)
|
||
nu = (1.5_pReal*K -mu)/(3.0_pReal*K+mu)
|
||
|
||
end function lattice_equivalent_nu
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Equivalent shear modulus (μ)
|
||
!> @details https://doi.org/10.1143/JPSJ.20.635
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_equivalent_mu(C,assumption) result(mu)
|
||
|
||
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
|
||
character(len=*), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
|
||
real(pReal) :: mu
|
||
|
||
logical :: error
|
||
real(pReal), dimension(6,6) :: S
|
||
|
||
|
||
if (IO_lc(assumption) == 'voigt') then
|
||
mu = (1.0_pReal*(C(1,1)+C(2,2)+C(3,3)) -1.0_pReal*(C(1,2)+C(2,3)+C(1,3)) +3.0_pReal*(C(4,4)+C(5,5)+C(6,6))) &
|
||
/ 15.0_pReal
|
||
elseif(IO_lc(assumption) == 'reuss') then
|
||
call math_invert(S,error,C)
|
||
if(error) error stop 'matrix inversion failed'
|
||
mu = 15.0_pReal &
|
||
/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
|
||
else
|
||
error stop 'invalid assumption'
|
||
endif
|
||
|
||
end function lattice_equivalent_mu
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Check correctness of some lattice functions.
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine selfTest
|
||
|
||
real(pReal), dimension(:,:,:), allocatable :: CoSy
|
||
real(pReal), dimension(:,:), allocatable :: system
|
||
|
||
real(pReal), dimension(6,6) :: C, C_cF, C_cI, C_hP, C_tI
|
||
real(pReal), dimension(3,3) :: T, T_cF, T_cI, T_hP, T_tI
|
||
real(pReal), dimension(2) :: r
|
||
real(pReal) :: lambda
|
||
integer :: i
|
||
|
||
|
||
call random_number(r)
|
||
|
||
system = reshape([1.0_pReal+r(1),0.0_pReal,0.0_pReal, 0.0_pReal,1.0_pReal+r(2),0.0_pReal],[6,1])
|
||
CoSy = buildCoordinateSystem([1],[1],system,'cF',0.0_pReal)
|
||
if(any(dNeq(CoSy(1:3,1:3,1),math_I3))) error stop 'buildCoordinateSystem'
|
||
|
||
do i = 1, 10
|
||
call random_number(C)
|
||
C_cF = applyLatticeSymmetryC66(C,'cI')
|
||
C_cI = applyLatticeSymmetryC66(C,'cF')
|
||
C_hP = applyLatticeSymmetryC66(C,'hP')
|
||
C_tI = applyLatticeSymmetryC66(C,'tI')
|
||
|
||
if (any(dNeq(C_cI,transpose(C_cF)))) error stop 'SymmetryC66/cI-cF'
|
||
if (any(dNeq(C_cF,transpose(C_cI)))) error stop 'SymmetryC66/cF-cI'
|
||
if (any(dNeq(C_hP,transpose(C_hP)))) error stop 'SymmetryC66/hP'
|
||
if (any(dNeq(C_tI,transpose(C_tI)))) error stop 'SymmetryC66/tI'
|
||
|
||
if (any(dNeq(C(1,1),[C_cF(1,1),C_cF(2,2),C_cF(3,3)]))) error stop 'SymmetryC_11-22-33/c'
|
||
if (any(dNeq(C(1,2),[C_cF(1,2),C_cF(1,3),C_cF(2,3)]))) error stop 'SymmetryC_12-13-23/c'
|
||
if (any(dNeq(C(4,4),[C_cF(4,4),C_cF(5,5),C_cF(6,6)]))) error stop 'SymmetryC_44-55-66/c'
|
||
|
||
if (any(dNeq(C(1,1),[C_hP(1,1),C_hP(2,2)]))) error stop 'SymmetryC_11-22/hP'
|
||
if (any(dNeq(C(1,3),[C_hP(1,3),C_hP(2,3)]))) error stop 'SymmetryC_13-23/hP'
|
||
if (any(dNeq(C(4,4),[C_hP(4,4),C_hP(5,5)]))) error stop 'SymmetryC_44-55/hP'
|
||
|
||
if (any(dNeq(C(1,1),[C_tI(1,1),C_tI(2,2)]))) error stop 'SymmetryC_11-22/tI'
|
||
if (any(dNeq(C(1,3),[C_tI(1,3),C_tI(2,3)]))) error stop 'SymmetryC_13-23/tI'
|
||
if (any(dNeq(C(4,4),[C_tI(4,4),C_tI(5,5)]))) error stop 'SymmetryC_44-55/tI'
|
||
|
||
call random_number(T)
|
||
T_cF = lattice_applyLatticeSymmetry33(T,'cI')
|
||
T_cI = lattice_applyLatticeSymmetry33(T,'cF')
|
||
T_hP = lattice_applyLatticeSymmetry33(T,'hP')
|
||
T_tI = lattice_applyLatticeSymmetry33(T,'tI')
|
||
|
||
if (any(dNeq0(T_cF) .and. math_I3<1.0_pReal)) error stop 'Symmetry33/c'
|
||
if (any(dNeq0(T_hP) .and. math_I3<1.0_pReal)) error stop 'Symmetry33/hP'
|
||
if (any(dNeq0(T_tI) .and. math_I3<1.0_pReal)) error stop 'Symmetry33/tI'
|
||
|
||
if (any(dNeq(T(1,1),[T_cI(1,1),T_cI(2,2),T_cI(3,3)]))) error stop 'Symmetry33_11-22-33/c'
|
||
if (any(dNeq(T(1,1),[T_hP(1,1),T_hP(2,2)]))) error stop 'Symmetry33_11-22/hP'
|
||
if (any(dNeq(T(1,1),[T_tI(1,1),T_tI(2,2)]))) error stop 'Symmetry33_11-22/tI'
|
||
|
||
enddo
|
||
|
||
call random_number(C)
|
||
C(1,1) = C(1,1) + C(1,2) + 0.1_pReal
|
||
C(4,4) = 0.5_pReal * (C(1,1) - C(1,2))
|
||
C = applyLatticeSymmetryC66(C,'cI')
|
||
if(dNeq(C(4,4),lattice_equivalent_mu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_mu/voigt'
|
||
if(dNeq(C(4,4),lattice_equivalent_mu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_mu/reuss'
|
||
|
||
lambda = C(1,2)
|
||
if(dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'voigt')), &
|
||
lattice_equivalent_nu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_nu/voigt'
|
||
if(dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'reuss')), &
|
||
lattice_equivalent_nu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_nu/reuss'
|
||
|
||
end subroutine selfTest
|
||
|
||
end module lattice
|