2330 lines
122 KiB
Fortran
2330 lines
122 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
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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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#ifndef __PGI
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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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#else
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FCC_NSLIP = 18, &
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FCC_NTWIN = 12, &
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FCC_NTRANS = 12, &
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FCC_NCLEAVAGE = 3
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#endif
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real(pReal), dimension(3+3,FCC_NSLIP), parameter :: &
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FCC_SYSTEMSLIP = reshape(real([&
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! Slip direction Plane normal ! SCHMID-BOAS notation
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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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! Slip system <110>{110}
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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)) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli
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real(pReal), dimension(3+3,FCC_NTWIN), parameter :: &
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FCC_SYSTEMTWIN = reshape(real( [&
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-2, 1, 1, 1, 1, 1, &
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1,-2, 1, 1, 1, 1, &
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1, 1,-2, 1, 1, 1, &
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2,-1, 1, -1,-1, 1, &
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-1, 2, 1, -1,-1, 1, &
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-1,-1,-2, -1,-1, 1, &
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-2,-1,-1, 1,-1,-1, &
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1, 2,-1, 1,-1,-1, &
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1,-1, 2, 1,-1,-1, &
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2, 1,-1, -1, 1,-1, &
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-1,-2,-1, -1, 1,-1, &
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-1, 1, 2, -1, 1,-1 &
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],pReal),shape(FCC_SYSTEMTWIN)) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli
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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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! Cleavage direction Plane normal
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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))
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!--------------------------------------------------------------------------------------------------
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! body centered cubic
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integer, dimension(*), parameter :: &
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BCC_NSLIPSYSTEM = [12, 12] !< # 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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#ifndef __PGI
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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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#else
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BCC_NSLIP = 24, &
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BCC_NTWIN = 12, &
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BCC_NCLEAVAGE = 3
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#endif
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real(pReal), dimension(3+3,BCC_NSLIP), parameter :: &
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BCC_SYSTEMSLIP = reshape(real([&
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! Slip direction Plane normal
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! Slip system <111>{110}
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1,-1, 1, 0, 1, 1, &
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-1,-1, 1, 0, 1, 1, &
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1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 0,-1, 1, &
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-1, 1, 1, 1, 0, 1, &
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-1,-1, 1, 1, 0, 1, &
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1, 1, 1, -1, 0, 1, &
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1,-1, 1, -1, 0, 1, &
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-1, 1, 1, 1, 1, 0, &
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-1, 1,-1, 1, 1, 0, &
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1, 1, 1, -1, 1, 0, &
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1, 1,-1, -1, 1, 0, &
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! Slip system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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],pReal),shape(BCC_SYSTEMSLIP))
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real(pReal), dimension(3+3,BCC_NTWIN), parameter :: &
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BCC_SYSTEMTWIN = reshape(real([&
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! Twin system <111>{112}
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-1, 1, 1, 2, 1, 1, &
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1, 1, 1, -2, 1, 1, &
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1, 1,-1, 2,-1, 1, &
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1,-1, 1, 2, 1,-1, &
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1,-1, 1, 1, 2, 1, &
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1, 1,-1, -1, 2, 1, &
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1, 1, 1, 1,-2, 1, &
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-1, 1, 1, 1, 2,-1, &
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1, 1,-1, 1, 1, 2, &
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1,-1, 1, -1, 1, 2, &
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-1, 1, 1, 1,-1, 2, &
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1, 1, 1, 1, 1,-2 &
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],pReal),shape(BCC_SYSTEMTWIN))
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real(pReal), dimension(3+3,BCC_NCLEAVAGE), parameter :: &
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BCC_SYSTEMCLEAVAGE = reshape(real([&
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! Cleavage direction Plane normal
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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))
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!--------------------------------------------------------------------------------------------------
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! hexagonal
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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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#ifndef __PGI
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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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#else
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HEX_NSLIP = 33, &
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HEX_NTWIN = 24
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#endif
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real(pReal), dimension(4+4,HEX_NSLIP), parameter :: &
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HEX_SYSTEMSLIP = reshape(real([&
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! Slip direction Plane normal
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! Basal systems <-1-1.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base))
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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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! 1st type prismatic systems <-1-1.0>{1-1.0} (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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! 2nd type prismatic systems <-11.0>{11.0} -- a slip; plane normals 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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! 1st type 1st order pyramidal systems <-1-1.0>{-11.1} -- plane normals depend on the 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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! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the 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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! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below)
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-1, -1, 2, 3, 1, 1, -2, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a)
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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)) !< slip systems for hex, 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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! Compression or Tension = f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981)
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-1, 0, 1, 1, 1, 0, -1, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a)
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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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!
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-1, -1, 2, 6, 1, 1, -2, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a)
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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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!
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1, 0, -1, -2, 1, 0, -1, 1, & ! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
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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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!
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1, 1, -2, -3, 1, 1, -2, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
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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)) !< twin systems for hex, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
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!--------------------------------------------------------------------------------------------------
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! body centered tetragonal
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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 (Sn) Bieler J. Electr Mater 2009
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integer, parameter :: &
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#ifndef __PGI
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BCT_NSLIP = sum(BCT_NSLIPSYSTEM) !< total # of slip systems for bct
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#else
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BCT_NSLIP = 52
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#endif
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real(pReal), dimension(3+3,BCT_NSLIP), parameter :: &
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BCT_SYSTEMSLIP = reshape(real([&
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! Slip direction Plane normal
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! Slip family 1 {100)<001] (Bravais notation {hkl)<uvw] for bct c/a = 0.5456)
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0, 0, 1, 1, 0, 0, &
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0, 0, 1, 0, 1, 0, &
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! Slip family 2 {110)<001]
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0, 0, 1, 1, 1, 0, &
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0, 0, 1, -1, 1, 0, &
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! slip family 3 {100)<010]
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0, 1, 0, 1, 0, 0, &
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1, 0, 0, 0, 1, 0, &
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! Slip family 4 {110)<1-11]/2
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1,-1, 1, 1, 1, 0, &
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1,-1,-1, 1, 1, 0, &
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-1,-1,-1, -1, 1, 0, &
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-1,-1, 1, -1, 1, 0, &
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! Slip family 5 {110)<1-10]
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1, -1, 0, 1, 1, 0, &
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1, 1, 0, 1,-1, 0, &
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! Slip family 6 {100)<011]
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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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! Slip family 7 {001)<010]
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0, 1, 0, 0, 0, 1, &
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1, 0, 0, 0, 0, 1, &
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! Slip family 8 {001)<110]
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1, 1, 0, 0, 0, 1, &
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-1, 1, 0, 0, 0, 1, &
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! Slip family 9 {011)<01-1]
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0, 1,-1, 0, 1, 1, &
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0,-1,-1, 0,-1, 1, &
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-1, 0,-1, -1, 0, 1, &
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1, 0,-1, 1, 0, 1, &
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! Slip family 10 {011)<1-11]/2
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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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! Slip family 11 {011)<100]
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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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! Slip family 12 {211)<01-1]
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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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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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! Slip family 13 {211)<-111]/2
|
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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)) !< slip systems for bct sorted by Bieler
|
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|
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!--------------------------------------------------------------------------------------------------
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! orthorhombic
|
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integer, dimension(*), parameter :: &
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ORT_NCLEAVAGESYSTEM = [1, 1, 1] !< # of cleavage systems per family for ortho
|
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|
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integer, parameter :: &
|
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#ifndef __PGI
|
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ORT_NCLEAVAGE = sum(ORT_NCLEAVAGESYSTEM) !< total # of cleavage systems for ortho
|
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#else
|
||
ORT_NCLEAVAGE = 3
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#endif
|
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|
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real(pReal), dimension(3+3,ORT_NCLEAVAGE), parameter :: &
|
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ORT_SYSTEMCLEAVAGE = reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
0, 1, 0, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
1, 0, 0, 0, 0, 1 &
|
||
],pReal),shape(ORT_SYSTEMCLEAVAGE))
|
||
|
||
|
||
enum, bind(c); enumerator :: &
|
||
lattice_UNDEFINED_ID, &
|
||
lattice_ISO_ID, &
|
||
lattice_FCC_ID, &
|
||
lattice_BCC_ID, &
|
||
lattice_BCT_ID, &
|
||
lattice_HEX_ID, &
|
||
lattice_ORT_ID
|
||
end enum
|
||
|
||
! SHOULD NOT BE PART OF LATTICE BEGIN
|
||
real(pReal), dimension(:), allocatable, public, protected :: &
|
||
lattice_mu, lattice_nu, &
|
||
lattice_damageMobility, &
|
||
lattice_massDensity, &
|
||
lattice_specificHeat
|
||
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
|
||
lattice_C66, &
|
||
lattice_thermalConductivity, &
|
||
lattice_damageDiffusion
|
||
integer(kind(lattice_UNDEFINED_ID)), dimension(:), allocatable, public, protected :: &
|
||
lattice_structure
|
||
! 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_ISO_ID, &
|
||
lattice_FCC_ID, &
|
||
lattice_BCC_ID, &
|
||
lattice_BCT_ID, &
|
||
lattice_HEX_ID, &
|
||
lattice_ORT_ID, &
|
||
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, p,i
|
||
character(len=pStringLen) :: structure = ''
|
||
|
||
write(6,'(/,a)') ' <<<+- lattice init -+>>>'; flush(6)
|
||
|
||
Nphases = size(config_phase)
|
||
|
||
allocate(lattice_structure(Nphases),source = lattice_UNDEFINED_ID)
|
||
allocate(lattice_C66(6,6,Nphases), source=0.0_pReal)
|
||
|
||
allocate(lattice_thermalConductivity (3,3,Nphases), source=0.0_pReal)
|
||
allocate(lattice_damageDiffusion (3,3,Nphases), source=0.0_pReal)
|
||
|
||
allocate(lattice_damageMobility,&
|
||
lattice_massDensity,lattice_specificHeat, &
|
||
lattice_mu, lattice_nu,&
|
||
source=[(0.0_pReal,i=1,Nphases)])
|
||
|
||
do p = 1, size(config_phase)
|
||
|
||
lattice_C66(1,1,p) = config_phase(p)%getFloat('c11')
|
||
lattice_C66(1,2,p) = config_phase(p)%getFloat('c12')
|
||
|
||
lattice_C66(1,3,p) = config_phase(p)%getFloat('c13',defaultVal=0.0_pReal)
|
||
lattice_C66(2,2,p) = config_phase(p)%getFloat('c22',defaultVal=0.0_pReal)
|
||
lattice_C66(2,3,p) = config_phase(p)%getFloat('c23',defaultVal=0.0_pReal)
|
||
lattice_C66(3,3,p) = config_phase(p)%getFloat('c33',defaultVal=0.0_pReal)
|
||
lattice_C66(4,4,p) = config_phase(p)%getFloat('c44',defaultVal=0.0_pReal)
|
||
lattice_C66(5,5,p) = config_phase(p)%getFloat('c55',defaultVal=0.0_pReal)
|
||
lattice_C66(6,6,p) = config_phase(p)%getFloat('c66',defaultVal=0.0_pReal)
|
||
|
||
structure = config_phase(p)%getString('lattice_structure')
|
||
select case(trim(structure))
|
||
case('iso')
|
||
lattice_structure(p) = lattice_ISO_ID
|
||
case('fcc')
|
||
lattice_structure(p) = lattice_FCC_ID
|
||
case('bcc')
|
||
lattice_structure(p) = lattice_BCC_ID
|
||
case('hex')
|
||
lattice_structure(p) = lattice_HEX_ID
|
||
case('bct')
|
||
lattice_structure(p) = lattice_BCT_ID
|
||
case('ort')
|
||
lattice_structure(p) = lattice_ORT_ID
|
||
case default
|
||
call IO_error(130,ext_msg='lattice_init: '//trim(structure))
|
||
end select
|
||
|
||
lattice_C66(1:6,1:6,p) = applyLatticeSymmetryC66(lattice_C66(1:6,1:6,p),structure)
|
||
|
||
lattice_mu(p) = equivalent_mu(lattice_C66(1:6,1:6,p),'voigt')
|
||
lattice_nu(p) = equivalent_nu(lattice_C66(1:6,1:6,p),'voigt')
|
||
|
||
lattice_C66(1:6,1:6,p) = math_sym3333to66(math_Voigt66to3333(lattice_C66(1:6,1:6,p))) ! Literature data is in Voigt notation
|
||
do i = 1, 6
|
||
if (abs(lattice_C66(i,i,p))<tol_math_check) &
|
||
call IO_error(135,el=i,ip=p,ext_msg='matrix diagonal "el"ement of phase "ip"')
|
||
enddo
|
||
|
||
|
||
! SHOULD NOT BE PART OF LATTICE BEGIN
|
||
lattice_thermalConductivity(1,1,p) = config_phase(p)%getFloat('thermal_conductivity11',defaultVal=0.0_pReal)
|
||
lattice_thermalConductivity(2,2,p) = config_phase(p)%getFloat('thermal_conductivity22',defaultVal=0.0_pReal)
|
||
lattice_thermalConductivity(3,3,p) = config_phase(p)%getFloat('thermal_conductivity33',defaultVal=0.0_pReal)
|
||
lattice_thermalConductivity(1:3,1:3,p) = lattice_applyLatticeSymmetry33(lattice_thermalConductivity(1:3,1:3,p),structure)
|
||
|
||
lattice_specificHeat(p) = config_phase(p)%getFloat('specific_heat',defaultVal=0.0_pReal)
|
||
lattice_massDensity(p) = config_phase(p)%getFloat('mass_density', defaultVal=0.0_pReal)
|
||
|
||
lattice_DamageDiffusion(1,1,p) = config_phase(p)%getFloat('damage_diffusion11',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion(2,2,p) = config_phase(p)%getFloat('damage_diffusion22',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion(3,3,p) = config_phase(p)%getFloat('damage_diffusion33',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion(1:3,1:3,p) = lattice_applyLatticeSymmetry33(lattice_DamageDiffusion(1:3,1:3,p),structure)
|
||
|
||
lattice_DamageMobility(p) = config_phase(p)%getFloat('damage_mobility',defaultVal=0.0_pReal)
|
||
! 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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure))
|
||
|
||
a = 0
|
||
myFamilies: do f = 1,size(Ntwin,1)
|
||
mySystems: do s = 1,Ntwin(f)
|
||
a = a + 1
|
||
select case(structure)
|
||
case('fcc','bcc')
|
||
characteristicShear(a) = 0.5_pReal*sqrt(2.0_pReal)
|
||
case('hex')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,FCC_NSLIPSYSTEM,FCC_SYSTEMTWIN,&
|
||
trim(structure),0.0_pReal)
|
||
case('bcc')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,BCC_NSLIPSYSTEM,BCC_SYSTEMTWIN,&
|
||
trim(structure),0.0_pReal)
|
||
case('hex')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,HEX_NSLIPSYSTEM,HEX_SYSTEMTWIN,&
|
||
'hex',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
|
||
|
||
if (len_trim(structure_target) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_C66_trans (target): '//trim(structure_target))
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! elasticity matrix of the target phase in cube orientation
|
||
if (structure_target(1:3) == 'hex') 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,'hex')
|
||
elseif (structure_target(1:3) == 'bcc') 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) call IO_error(0,ext_msg='lattice_nonSchmidMatrix')
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,BCC_NSLIPSYSTEM,BCC_SYSTEMSLIP,&
|
||
'bcc',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,'bcc',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, 6, 5, 3, 5, 5, 4, 5, 6, 9,10, 9,10,11,12, & ! -----> acting
|
||
2, 1, 2, 6, 4, 5, 5, 4, 6, 5, 3, 5, 9,10,11,12, 9,10, & ! |
|
||
2, 2, 1, 5, 5, 3, 5, 6, 4, 6, 5, 4, 11,12, 9,10, 9,10, & ! |
|
||
4, 6, 5, 1, 2, 2, 4, 5, 6, 3, 5, 5, 9,10,10, 9,12,11, & ! v
|
||
6, 4, 5, 2, 1, 2, 5, 3, 5, 5, 4, 6, 9,10,12,11,10, 9, & ! reacting
|
||
5, 5, 3, 2, 2, 1, 6, 5, 4, 5, 6, 4, 11,12,10, 9,10, 9, &
|
||
3, 5, 5, 4, 5, 6, 1, 2, 2, 4, 6, 5, 10, 9,10, 9,11,12, &
|
||
5, 4, 6, 5, 3, 5, 2, 1, 2, 6, 4, 5, 10, 9,12,11, 9,10, &
|
||
5, 6, 4, 6, 5, 4, 2, 2, 1, 5, 5, 3, 12,11,10, 9, 9,10, &
|
||
4, 5, 6, 3, 5, 5, 4, 6, 5, 1, 2, 2, 10, 9, 9,10,12,11, &
|
||
5, 3, 5, 5, 4, 6, 6, 4, 5, 2, 1, 2, 10, 9,11,12,10, 9, &
|
||
6, 5, 4, 5, 6, 4, 5, 5, 3, 2, 2, 1, 12,11, 9,10,10, 9, &
|
||
|
||
9, 9,11, 9, 9,11,10,10,12,10,10,12, 1, 7, 8, 8, 8, 8, &
|
||
10,10,12,10,10,12, 9, 9,11, 9, 9,11, 7, 1, 8, 8, 8, 8, &
|
||
9,11, 9,10,12,10,10,12,10, 9,11, 9, 8, 8, 1, 7, 8, 8, &
|
||
10,12,10, 9,11, 9, 9,11, 9,10,12,10, 8, 8, 7, 1, 8, 8, &
|
||
11, 9, 9,12,10,10,11, 9, 9,12,10,10, 8, 8, 8, 8, 1, 7, &
|
||
12,10,10,11, 9, 9,12,10,10,11, 9, 9, 8, 8, 8, 8, 7, 1 &
|
||
],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for fcc
|
||
!< 1: self interaction
|
||
!< 2: coplanar interaction
|
||
!< 3: collinear interaction
|
||
!< 4: Hirth locks
|
||
!< 5: glissile junctions
|
||
!< 6: Lomer locks
|
||
!< 7: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
|
||
!< 8: similar to Lomer locks in <110>{111} for two {110} planes
|
||
!< 9: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
|
||
!<10: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
|
||
!<11: crossing btw one {110} and one {111} plane
|
||
!<12: collinear btw one {110} and one {111} plane
|
||
|
||
integer, dimension(BCC_NSLIP,BCC_NSLIP), parameter :: &
|
||
BCC_INTERACTIONSLIPSLIP = reshape( [&
|
||
1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! -----> acting
|
||
2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! |
|
||
6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! |
|
||
6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v
|
||
5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & ! reacting
|
||
4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, &
|
||
4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, &
|
||
3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, &
|
||
4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, &
|
||
3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, &
|
||
5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, &
|
||
4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, &
|
||
!
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, &
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, &
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 &
|
||
],shape(BCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377
|
||
!< 1: self interaction
|
||
!< 2: coplanar interaction
|
||
!< 3: collinear interaction
|
||
!< 4: mixed-asymmetrical junction
|
||
!< 5: mixed-symmetrical junction
|
||
!< 6: edge junction
|
||
|
||
integer, 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
|
||
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
|
||
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))
|
||
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONSLIPSLIP
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONSLIPSLIP
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
case('hex')
|
||
interactionTypes = HEX_INTERACTIONSLIPSLIP
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
case('bct')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONTWINTWIN
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONTWINTWIN
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
case('hex')
|
||
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 (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure))
|
||
|
||
if(structure == 'fcc') 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 &
|
||
],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
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONSLIPTWIN
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONSLIPTWIN
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
case('hex')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONTWINSLIP
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONTWINSLIP
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
case('hex')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('bct')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
twinSystems = FCC_SYSTEMTWIN
|
||
case('bcc')
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
twinSystems = BCC_SYSTEMTWIN
|
||
case('hex')
|
||
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 (len_trim(structure_target) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
if (structure_target(1:3) /= 'bcc' .and. structure_target(1:3) /= 'hex') &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
if (structure_target(1:3) == 'hex' .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(1:3) == 'bcc' .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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('ort')
|
||
NcleavageMax = ORT_NCLEAVAGESYSTEM
|
||
cleavageSystems = ORT_SYSTEMCLEAVAGE
|
||
case('fcc')
|
||
NcleavageMax = FCC_NCLEAVAGESYSTEM
|
||
cleavageSystems = FCC_SYSTEMCLEAVAGE
|
||
case('bcc')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('bct')
|
||
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
|
||
!--------------------------------------------------------------------------------------------------
|
||
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
|
||
|
||
integer :: k
|
||
|
||
T_sym = 0.0_pReal
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_applyLatticeSymmetry33: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('iso','fcc','bcc')
|
||
do k=1,3
|
||
T_sym(k,k) = T(1,1)
|
||
enddo
|
||
case('hex')
|
||
T_sym(1,1) = T(1,1)
|
||
T_sym(2,2) = T(1,1)
|
||
T_sym(3,3) = T(3,3)
|
||
case('ort','bct')
|
||
T_sym(1,1) = T(1,1)
|
||
T_sym(2,2) = T(2,2)
|
||
T_sym(3,3) = T(3,3)
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_applyLatticeSymmetry33: '//trim(structure))
|
||
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
|
||
!--------------------------------------------------------------------------------------------------
|
||
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 :: j,k
|
||
|
||
C66_sym = 0.0_pReal
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='applyLatticeSymmetryC66: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case ('iso')
|
||
do k=1,3
|
||
do j=1,3
|
||
C66_sym(k,j) = C66(1,2)
|
||
enddo
|
||
C66_sym(k,k) = C66(1,1)
|
||
C66_sym(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
enddo
|
||
case ('fcc','bcc')
|
||
do k=1,3
|
||
do j=1,3
|
||
C66_sym(k,j) = C66(1,2)
|
||
enddo
|
||
C66_sym(k,k) = C66(1,1)
|
||
C66_sym(k+3,k+3) = C66(4,4)
|
||
enddo
|
||
case ('hex')
|
||
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(2,1) = C66(1,2)
|
||
C66_sym(1,3) = C66(1,3)
|
||
C66_sym(3,1) = C66(1,3)
|
||
C66_sym(2,3) = C66(1,3)
|
||
C66_sym(3,2) = 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 ('ort')
|
||
C66_sym(1,1) = C66(1,1)
|
||
C66_sym(2,2) = C66(2,2)
|
||
C66_sym(3,3) = C66(3,3)
|
||
C66_sym(1,2) = C66(1,2)
|
||
C66_sym(2,1) = C66(1,2)
|
||
C66_sym(1,3) = C66(1,3)
|
||
C66_sym(3,1) = C66(1,3)
|
||
C66_sym(2,3) = C66(2,3)
|
||
C66_sym(3,2) = C66(2,3)
|
||
C66_sym(4,4) = C66(4,4)
|
||
C66_sym(5,5) = C66(5,5)
|
||
C66_sym(6,6) = C66(6,6)
|
||
case ('bct')
|
||
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(2,1) = C66(1,2)
|
||
C66_sym(1,3) = C66(1,3)
|
||
C66_sym(3,1) = C66(1,3)
|
||
C66_sym(2,3) = C66(1,3)
|
||
C66_sym(3,2) = C66(1,3)
|
||
C66_sym(4,4) = C66(4,4)
|
||
C66_sym(5,5) = C66(4,4)
|
||
C66_sym(6,6) = C66(6,6)
|
||
case default
|
||
call IO_error(137,ext_msg='applyLatticeSymmetryC66: '//trim(structure))
|
||
end select
|
||
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
NtwinMax = FCC_NTWINSYSTEM
|
||
twinSystems = FCC_SYSTEMTWIN
|
||
case('bcc')
|
||
NtwinMax = BCC_NTWINSYSTEM
|
||
twinSystems = BCC_SYSTEMTWIN
|
||
case('hex')
|
||
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
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure))
|
||
|
||
select case(structure)
|
||
case('fcc')
|
||
NslipMax = FCC_NSLIPSYSTEM
|
||
slipSystems = FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = BCC_NSLIPSYSTEM
|
||
slipSystems = BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = HEX_NSLIPSYSTEM
|
||
slipSystems = HEX_SYSTEMSLIP
|
||
case('bct')
|
||
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 (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure))
|
||
if (trim(structure) == 'bct' .and. cOverA > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
|
||
if (trim(structure) == 'hex' .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(trim(structure))
|
||
|
||
case ('fcc','bcc','iso','ort','bct')
|
||
direction = system(1:3,p)
|
||
normal = system(4:6,p)
|
||
|
||
case ('hex')
|
||
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 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) call IO_error(0)
|
||
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
|
||
call IO_error(0)
|
||
K = 0.0_pReal
|
||
endif
|
||
|
||
mu = equivalent_mu(C,assumption)
|
||
nu = (1.5_pReal*K -mu)/(3.0_pReal*K+mu)
|
||
|
||
end function equivalent_nu
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Equivalent shear modulus (μ)
|
||
!> @details https://doi.org/10.1143/JPSJ.20.635
|
||
!--------------------------------------------------------------------------------------------------
|
||
function 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) call IO_error(0)
|
||
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
|
||
call IO_error(0)
|
||
mu = 0.0_pReal
|
||
endif
|
||
|
||
end function 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
|
||
real(pReal), dimension(2) :: r
|
||
real(pReal) :: lambda
|
||
|
||
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,'fcc',0.0_pReal)
|
||
if(any(dNeq(CoSy(1:3,1:3,1),math_I3))) &
|
||
call IO_error(0)
|
||
|
||
call random_number(C)
|
||
C(1,1) = C(1,1) + 1.0_pReal
|
||
C = applyLatticeSymmetryC66(C,'iso')
|
||
if(dNeq(C(6,6),equivalent_mu(C,'voigt'),1.0e-12_pReal)) &
|
||
call IO_error(0,ext_msg='equivalent_mu/voigt')
|
||
if(dNeq(C(6,6),equivalent_mu(C,'voigt'),1.0e-12_pReal)) &
|
||
call IO_error(0,ext_msg='equivalent_mu/reuss')
|
||
lambda = C(1,2)
|
||
if(dNeq(lambda*0.5_pReal/(lambda+equivalent_mu(C,'voigt')),equivalent_nu(C,'voigt'),1.0e-12_pReal)) &
|
||
call IO_error(0,ext_msg='equivalent_nu/voigt')
|
||
if(dNeq(lambda*0.5_pReal/(lambda+equivalent_mu(C,'reuss')),equivalent_nu(C,'reuss'),1.0e-12_pReal)) &
|
||
call IO_error(0,ext_msg='equivalent_nu/reuss')
|
||
|
||
end subroutine selfTest
|
||
|
||
end module lattice
|