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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief contains lattice 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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!--------------------------------------------------------------------------------------------------
module lattice
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use prec
use IO
use config
use math
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use rotations
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implicit none
private
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!--------------------------------------------------------------------------------------------------
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! face centered cubic (cF)
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integer , dimension ( * ) , parameter :: &
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FCC_NSLIPSYSTEM = [ 12 , 6 ] !< # of slip systems per family for fcc
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integer , dimension ( * ) , parameter :: &
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FCC_NTWINSYSTEM = [ 12 ] !< # of twin systems per family for fcc
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integer , dimension ( * ) , parameter :: &
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FCC_NTRANSSYSTEM = [ 12 ] !< # of transformation systems per family for fcc
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integer , dimension ( * ) , parameter :: &
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FCC_NCLEAVAGESYSTEM = [ 3 ] !< # of cleavage systems per family for fcc
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integer , parameter :: &
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FCC_NSLIP = sum ( FCC_NSLIPSYSTEM ) , & !< total # of slip systems for fcc
FCC_NTWIN = sum ( FCC_NTWINSYSTEM ) , & !< total # of twin systems for fcc
FCC_NTRANS = sum ( FCC_NTRANSSYSTEM ) , & !< total # of transformation systems for fcc
FCC_NCLEAVAGE = sum ( FCC_NCLEAVAGESYSTEM ) !< total # of cleavage systems for fcc
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real ( pReal ) , dimension ( 3 + 3 , FCC_NSLIP ) , parameter :: &
FCC_SYSTEMSLIP = reshape ( real ( [ &
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! <110>{111} systems
0 , 1 , - 1 , 1 , 1 , 1 , & ! B2
- 1 , 0 , 1 , 1 , 1 , 1 , & ! B4
1 , - 1 , 0 , 1 , 1 , 1 , & ! B5
0 , - 1 , - 1 , - 1 , - 1 , 1 , & ! C1
1 , 0 , 1 , - 1 , - 1 , 1 , & ! C3
- 1 , 1 , 0 , - 1 , - 1 , 1 , & ! C5
0 , - 1 , 1 , 1 , - 1 , - 1 , & ! A2
- 1 , 0 , - 1 , 1 , - 1 , - 1 , & ! A3
1 , 1 , 0 , 1 , - 1 , - 1 , & ! A6
0 , 1 , 1 , - 1 , 1 , - 1 , & ! D1
1 , 0 , - 1 , - 1 , 1 , - 1 , & ! D4
- 1 , - 1 , 0 , - 1 , 1 , - 1 , & ! D6
! <110>{110}/non-octahedral systems
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1 , 1 , 0 , 1 , - 1 , 0 , &
1 , - 1 , 0 , 1 , 1 , 0 , &
1 , 0 , 1 , 1 , 0 , - 1 , &
1 , 0 , - 1 , 1 , 0 , 1 , &
0 , 1 , 1 , 0 , 1 , - 1 , &
0 , 1 , - 1 , 0 , 1 , 1 &
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] , pReal ) , shape ( FCC_SYSTEMSLIP ) ) !< fcc slip systems
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real ( pReal ) , dimension ( 3 + 3 , FCC_NTWIN ) , parameter :: &
FCC_SYSTEMTWIN = reshape ( real ( [ &
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! <112>{111} systems
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- 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 &
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] , pReal ) , shape ( FCC_SYSTEMTWIN ) ) !< fcc twin systems
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integer , dimension ( 2 , FCC_NTWIN ) , parameter , public :: &
lattice_FCC_TWINNUCLEATIONSLIPPAIR = reshape ( [ &
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2 , 3 , &
1 , 3 , &
1 , 2 , &
5 , 6 , &
4 , 6 , &
4 , 5 , &
8 , 9 , &
7 , 9 , &
7 , 8 , &
11 , 12 , &
10 , 12 , &
10 , 11 &
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] , shape ( lattice_FCC_TWINNUCLEATIONSLIPPAIR ) )
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real ( pReal ) , dimension ( 3 + 3 , FCC_NCLEAVAGE ) , parameter :: &
FCC_SYSTEMCLEAVAGE = reshape ( real ( [ &
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! <001>{001} systems
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0 , 1 , 0 , 1 , 0 , 0 , &
0 , 0 , 1 , 0 , 1 , 0 , &
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1 , 0 , 0 , 0 , 0 , 1 &
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] , pReal ) , shape ( FCC_SYSTEMCLEAVAGE ) ) !< fcc cleavage systems
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!--------------------------------------------------------------------------------------------------
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! body centered cubic (cI)
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integer , dimension ( * ) , parameter :: &
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BCC_NSLIPSYSTEM = [ 12 , 12 , 24 ] !< # of slip systems per family for bcc
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integer , dimension ( * ) , parameter :: &
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BCC_NTWINSYSTEM = [ 12 ] !< # of twin systems per family for bcc
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integer , dimension ( * ) , parameter :: &
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BCC_NCLEAVAGESYSTEM = [ 3 ] !< # of cleavage systems per family for bcc
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integer , parameter :: &
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BCC_NSLIP = sum ( BCC_NSLIPSYSTEM ) , & !< total # of slip systems for bcc
BCC_NTWIN = sum ( BCC_NTWINSYSTEM ) , & !< total # of twin systems for bcc
BCC_NCLEAVAGE = sum ( BCC_NCLEAVAGESYSTEM ) !< total # of cleavage systems for bcc
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real ( pReal ) , dimension ( 3 + 3 , BCC_NSLIP ) , parameter :: &
BCC_SYSTEMSLIP = reshape ( real ( [ &
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! <111>{110} systems
1 , - 1 , 1 , 0 , 1 , 1 , & ! D1
- 1 , - 1 , 1 , 0 , 1 , 1 , & ! C1
1 , 1 , 1 , 0 , - 1 , 1 , & ! B2
- 1 , 1 , 1 , 0 , - 1 , 1 , & ! A2
- 1 , 1 , 1 , 1 , 0 , 1 , & ! A3
- 1 , - 1 , 1 , 1 , 0 , 1 , & ! C3
1 , 1 , 1 , - 1 , 0 , 1 , & ! B4
1 , - 1 , 1 , - 1 , 0 , 1 , & ! D4
- 1 , 1 , 1 , 1 , 1 , 0 , & ! A6
- 1 , 1 , - 1 , 1 , 1 , 0 , & ! D6
1 , 1 , 1 , - 1 , 1 , 0 , & ! B5
1 , 1 , - 1 , - 1 , 1 , 0 , & ! C5
! <111>{112} systems
- 1 , 1 , 1 , 2 , 1 , 1 , & ! A-4
1 , 1 , 1 , - 2 , 1 , 1 , & ! B-3
1 , 1 , - 1 , 2 , - 1 , 1 , & ! C-10
1 , - 1 , 1 , 2 , 1 , - 1 , & ! D-9
1 , - 1 , 1 , 1 , 2 , 1 , & ! D-6
1 , 1 , - 1 , - 1 , 2 , 1 , & ! C-5
1 , 1 , 1 , 1 , - 2 , 1 , & ! B-12
- 1 , 1 , 1 , 1 , 2 , - 1 , & ! A-11
1 , 1 , - 1 , 1 , 1 , 2 , & ! C-2
1 , - 1 , 1 , - 1 , 1 , 2 , & ! D-1
- 1 , 1 , 1 , 1 , - 1 , 2 , & ! A-8
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1 , 1 , 1 , 1 , 1 , - 2 , & ! B-7
! Slip system <111>{123}
1 , 1 , - 1 , 1 , 2 , 3 , &
1 , - 1 , 1 , - 1 , 2 , 3 , &
- 1 , 1 , 1 , 1 , - 2 , 3 , &
1 , 1 , 1 , 1 , 2 , - 3 , &
1 , - 1 , 1 , 1 , 3 , 2 , &
1 , 1 , - 1 , - 1 , 3 , 2 , &
1 , 1 , 1 , 1 , - 3 , 2 , &
- 1 , 1 , 1 , 1 , 3 , - 2 , &
1 , 1 , - 1 , 2 , 1 , 3 , &
1 , - 1 , 1 , - 2 , 1 , 3 , &
- 1 , 1 , 1 , 2 , - 1 , 3 , &
1 , 1 , 1 , 2 , 1 , - 3 , &
1 , - 1 , 1 , 2 , 3 , 1 , &
1 , 1 , - 1 , - 2 , 3 , 1 , &
1 , 1 , 1 , 2 , - 3 , 1 , &
- 1 , 1 , 1 , 2 , 3 , - 1 , &
- 1 , 1 , 1 , 3 , 1 , 2 , &
1 , 1 , 1 , - 3 , 1 , 2 , &
1 , 1 , - 1 , 3 , - 1 , 2 , &
1 , - 1 , 1 , 3 , 1 , - 2 , &
- 1 , 1 , 1 , 3 , 2 , 1 , &
1 , 1 , 1 , - 3 , 2 , 1 , &
1 , 1 , - 1 , 3 , - 2 , 1 , &
1 , - 1 , 1 , 3 , 2 , - 1 &
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] , pReal ) , shape ( BCC_SYSTEMSLIP ) ) !< bcc slip systems
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real ( pReal ) , dimension ( 3 + 3 , BCC_NTWIN ) , parameter :: &
BCC_SYSTEMTWIN = reshape ( real ( [ &
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! <111>{112} systems
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- 1 , 1 , 1 , 2 , 1 , 1 , &
1 , 1 , 1 , - 2 , 1 , 1 , &
1 , 1 , - 1 , 2 , - 1 , 1 , &
1 , - 1 , 1 , 2 , 1 , - 1 , &
1 , - 1 , 1 , 1 , 2 , 1 , &
1 , 1 , - 1 , - 1 , 2 , 1 , &
1 , 1 , 1 , 1 , - 2 , 1 , &
- 1 , 1 , 1 , 1 , 2 , - 1 , &
1 , 1 , - 1 , 1 , 1 , 2 , &
1 , - 1 , 1 , - 1 , 1 , 2 , &
- 1 , 1 , 1 , 1 , - 1 , 2 , &
1 , 1 , 1 , 1 , 1 , - 2 &
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] , pReal ) , shape ( BCC_SYSTEMTWIN ) ) !< bcc twin systems
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real ( pReal ) , dimension ( 3 + 3 , BCC_NCLEAVAGE ) , parameter :: &
BCC_SYSTEMCLEAVAGE = reshape ( real ( [ &
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! <001>{001} systems
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0 , 1 , 0 , 1 , 0 , 0 , &
0 , 0 , 1 , 0 , 1 , 0 , &
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1 , 0 , 0 , 0 , 0 , 1 &
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] , pReal ) , shape ( BCC_SYSTEMCLEAVAGE ) ) !< bcc cleavage systems
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!--------------------------------------------------------------------------------------------------
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! hexagonal (hP)
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integer , dimension ( * ) , parameter :: &
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HEX_NSLIPSYSTEM = [ 3 , 3 , 6 , 12 , 6 ] !< # of slip systems per family for hex
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integer , dimension ( * ) , parameter :: &
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HEX_NTWINSYSTEM = [ 6 , 6 , 6 , 6 ] !< # of slip systems per family for hex
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integer , parameter :: &
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HEX_NSLIP = sum ( HEX_NSLIPSYSTEM ) , & !< total # of slip systems for hex
HEX_NTWIN = sum ( HEX_NTWINSYSTEM ) !< total # of twin systems for hex
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real ( pReal ) , dimension ( 4 + 4 , HEX_NSLIP ) , parameter :: &
HEX_SYSTEMSLIP = reshape ( real ( [ &
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! <-1-1.0>{00.1}/basal systems (independent of c/a-ratio)
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2 , - 1 , - 1 , 0 , 0 , 0 , 0 , 1 , &
- 1 , 2 , - 1 , 0 , 0 , 0 , 0 , 1 , &
- 1 , - 1 , 2 , 0 , 0 , 0 , 0 , 1 , &
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! <-1-1.0>{1-1.0}/prismatic systems (independent of c/a-ratio)
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2 , - 1 , - 1 , 0 , 0 , 1 , - 1 , 0 , &
- 1 , 2 , - 1 , 0 , - 1 , 0 , 1 , 0 , &
- 1 , - 1 , 2 , 0 , 1 , - 1 , 0 , 0 , &
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! <-1-1.0>{-11.1}/1. order pyramidal <a> systems (direction independent of c/a-ratio)
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- 1 , 2 , - 1 , 0 , 1 , 0 , - 1 , 1 , &
- 2 , 1 , 1 , 0 , 0 , 1 , - 1 , 1 , &
- 1 , - 1 , 2 , 0 , - 1 , 1 , 0 , 1 , &
1 , - 2 , 1 , 0 , - 1 , 0 , 1 , 1 , &
2 , - 1 , - 1 , 0 , 0 , - 1 , 1 , 1 , &
1 , 1 , - 2 , 0 , 1 , - 1 , 0 , 1 , &
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! <11.3>{-10.1}/1. order pyramidal <c+a> systems (direction independent of c/a-ratio)
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- 2 , 1 , 1 , 3 , 1 , 0 , - 1 , 1 , &
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- 1 , - 1 , 2 , 3 , 1 , 0 , - 1 , 1 , &
- 1 , - 1 , 2 , 3 , 0 , 1 , - 1 , 1 , &
1 , - 2 , 1 , 3 , 0 , 1 , - 1 , 1 , &
1 , - 2 , 1 , 3 , - 1 , 1 , 0 , 1 , &
2 , - 1 , - 1 , 3 , - 1 , 1 , 0 , 1 , &
2 , - 1 , - 1 , 3 , - 1 , 0 , 1 , 1 , &
1 , 1 , - 2 , 3 , - 1 , 0 , 1 , 1 , &
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1 , 1 , - 2 , 3 , 0 , - 1 , 1 , 1 , &
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- 1 , 2 , - 1 , 3 , 0 , - 1 , 1 , 1 , &
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- 1 , 2 , - 1 , 3 , 1 , - 1 , 0 , 1 , &
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- 2 , 1 , 1 , 3 , 1 , - 1 , 0 , 1 , &
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! <11.3>{-1-1.2}/2. order pyramidal <c+a> systems
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- 1 , - 1 , 2 , 3 , 1 , 1 , - 2 , 2 , &
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1 , - 2 , 1 , 3 , - 1 , 2 , - 1 , 2 , &
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2 , - 1 , - 1 , 3 , - 2 , 1 , 1 , 2 , &
1 , 1 , - 2 , 3 , - 1 , - 1 , 2 , 2 , &
- 1 , 2 , - 1 , 3 , 1 , - 2 , 1 , 2 , &
- 2 , 1 , 1 , 3 , 2 , - 1 , - 1 , 2 &
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] , pReal ) , shape ( HEX_SYSTEMSLIP ) ) !< hex slip systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
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real ( pReal ) , dimension ( 4 + 4 , HEX_NTWIN ) , parameter :: &
HEX_SYSTEMTWIN = reshape ( real ( [ &
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! <-10.1>{10.2} systems, shear = (3-(c/a)^2)/(sqrt(3) c/a)
! tension in Co, Mg, Zr, Ti, and Be; compression in Cd and Zn
- 1 , 0 , 1 , 1 , 1 , 0 , - 1 , 2 , & !
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0 , - 1 , 1 , 1 , 0 , 1 , - 1 , 2 , &
1 , - 1 , 0 , 1 , - 1 , 1 , 0 , 2 , &
1 , 0 , - 1 , 1 , - 1 , 0 , 1 , 2 , &
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0 , 1 , - 1 , 1 , 0 , - 1 , 1 , 2 , &
- 1 , 1 , 0 , 1 , 1 , - 1 , 0 , 2 , &
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! <11.6>{-1-1.1} systems, shear = 1/(c/a)
! tension in Co, Re, and Zr
- 1 , - 1 , 2 , 6 , 1 , 1 , - 2 , 1 , &
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1 , - 2 , 1 , 6 , - 1 , 2 , - 1 , 1 , &
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2 , - 1 , - 1 , 6 , - 2 , 1 , 1 , 1 , &
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1 , 1 , - 2 , 6 , - 1 , - 1 , 2 , 1 , &
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- 1 , 2 , - 1 , 6 , 1 , - 2 , 1 , 1 , &
- 2 , 1 , 1 , 6 , 2 , - 1 , - 1 , 1 , &
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! <10.-2>{10.1} systems, shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
! compression in Mg
1 , 0 , - 1 , - 2 , 1 , 0 , - 1 , 1 , &
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0 , 1 , - 1 , - 2 , 0 , 1 , - 1 , 1 , &
- 1 , 1 , 0 , - 2 , - 1 , 1 , 0 , 1 , &
- 1 , 0 , 1 , - 2 , - 1 , 0 , 1 , 1 , &
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0 , - 1 , 1 , - 2 , 0 , - 1 , 1 , 1 , &
1 , - 1 , 0 , - 2 , 1 , - 1 , 0 , 1 , &
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! <11.-3>{11.2} systems, shear = 2((c/a)^2-2)/(3 c/a)
! compression in Ti and Zr
1 , 1 , - 2 , - 3 , 1 , 1 , - 2 , 2 , &
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- 1 , 2 , - 1 , - 3 , - 1 , 2 , - 1 , 2 , &
- 2 , 1 , 1 , - 3 , - 2 , 1 , 1 , 2 , &
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- 1 , - 1 , 2 , - 3 , - 1 , - 1 , 2 , 2 , &
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1 , - 2 , 1 , - 3 , 1 , - 2 , 1 , 2 , &
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2 , - 1 , - 1 , - 3 , 2 , - 1 , - 1 , 2 &
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] , pReal ) , shape ( HEX_SYSTEMTWIN ) ) !< hex twin systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
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!--------------------------------------------------------------------------------------------------
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! body centered tetragonal (tI)
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integer , dimension ( * ) , parameter :: &
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BCT_NSLIPSYSTEM = [ 2 , 2 , 2 , 4 , 2 , 4 , 2 , 2 , 4 , 8 , 4 , 8 , 8 ] !< # of slip systems per family for bct
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integer , parameter :: &
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BCT_NSLIP = sum ( BCT_NSLIPSYSTEM ) !< total # of slip systems for bct
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real ( pReal ) , dimension ( 3 + 3 , BCT_NSLIP ) , parameter :: &
BCT_SYSTEMSLIP = reshape ( real ( [ &
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! {100)<001] systems
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0 , 0 , 1 , 1 , 0 , 0 , &
0 , 0 , 1 , 0 , 1 , 0 , &
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! {110)<001] systems
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0 , 0 , 1 , 1 , 1 , 0 , &
0 , 0 , 1 , - 1 , 1 , 0 , &
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! {100)<010] systems
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0 , 1 , 0 , 1 , 0 , 0 , &
1 , 0 , 0 , 0 , 1 , 0 , &
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! {110)<1-11]/2 systems
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1 , - 1 , 1 , 1 , 1 , 0 , &
1 , - 1 , - 1 , 1 , 1 , 0 , &
- 1 , - 1 , - 1 , - 1 , 1 , 0 , &
- 1 , - 1 , 1 , - 1 , 1 , 0 , &
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! {110)<1-10] systems
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1 , - 1 , 0 , 1 , 1 , 0 , &
1 , 1 , 0 , 1 , - 1 , 0 , &
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! {100)<011] systems
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0 , 1 , 1 , 1 , 0 , 0 , &
0 , - 1 , 1 , 1 , 0 , 0 , &
- 1 , 0 , 1 , 0 , 1 , 0 , &
1 , 0 , 1 , 0 , 1 , 0 , &
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! {001)<010] systems
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0 , 1 , 0 , 0 , 0 , 1 , &
1 , 0 , 0 , 0 , 0 , 1 , &
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! {001)<110] systems
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1 , 1 , 0 , 0 , 0 , 1 , &
- 1 , 1 , 0 , 0 , 0 , 1 , &
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! {011)<01-1] systems
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0 , 1 , - 1 , 0 , 1 , 1 , &
0 , - 1 , - 1 , 0 , - 1 , 1 , &
- 1 , 0 , - 1 , - 1 , 0 , 1 , &
1 , 0 , - 1 , 1 , 0 , 1 , &
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! {011)<1-11]/2 systems
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1 , - 1 , 1 , 0 , 1 , 1 , &
1 , 1 , - 1 , 0 , 1 , 1 , &
1 , 1 , 1 , 0 , 1 , - 1 , &
- 1 , 1 , 1 , 0 , 1 , - 1 , &
1 , - 1 , - 1 , 1 , 0 , 1 , &
- 1 , - 1 , 1 , 1 , 0 , 1 , &
1 , 1 , 1 , 1 , 0 , - 1 , &
1 , - 1 , 1 , 1 , 0 , - 1 , &
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! {011)<100] systems
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1 , 0 , 0 , 0 , 1 , 1 , &
1 , 0 , 0 , 0 , 1 , - 1 , &
0 , 1 , 0 , 1 , 0 , 1 , &
0 , 1 , 0 , 1 , 0 , - 1 , &
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! {211)<01-1] systems
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0 , 1 , - 1 , 2 , 1 , 1 , &
0 , - 1 , - 1 , 2 , - 1 , 1 , &
1 , 0 , - 1 , 1 , 2 , 1 , &
- 1 , 0 , - 1 , - 1 , 2 , 1 , &
0 , 1 , - 1 , - 2 , 1 , 1 , &
0 , - 1 , - 1 , - 2 , - 1 , 1 , &
- 1 , 0 , - 1 , - 1 , - 2 , 1 , &
1 , 0 , - 1 , 1 , - 2 , 1 , &
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! {211)<-111]/2 systems
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- 1 , 1 , 1 , 2 , 1 , 1 , &
- 1 , - 1 , 1 , 2 , - 1 , 1 , &
1 , - 1 , 1 , 1 , 2 , 1 , &
- 1 , - 1 , 1 , - 1 , 2 , 1 , &
1 , 1 , 1 , - 2 , 1 , 1 , &
1 , - 1 , 1 , - 2 , - 1 , 1 , &
- 1 , 1 , 1 , - 1 , - 2 , 1 , &
1 , 1 , 1 , 1 , - 2 , 1 &
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] , pReal ) , shape ( BCT_SYSTEMSLIP ) ) !< bct slip systems for c/a = 0.5456 (Sn), sorted by Bieler 2009 (https://doi.org/10.1007/s11664-009-0909-x)
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interface lattice_forestProjection_edge
module procedure slipProjection_transverse
end interface lattice_forestProjection_edge
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interface lattice_forestProjection_screw
module procedure slipProjection_direction
end interface lattice_forestProjection_screw
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public :: &
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lattice_init , &
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lattice_equivalent_nu , &
lattice_equivalent_mu , &
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lattice_symmetrize_33 , &
lattice_symmetrize_C66 , &
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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 , &
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lattice_slip_transverse , &
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lattice_labels_slip , &
lattice_labels_twin
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contains
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!--------------------------------------------------------------------------------------------------
!> @brief Module initialization
!--------------------------------------------------------------------------------------------------
subroutine lattice_init
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print '(/,1x,a)' , '<<<+- lattice init -+>>>' ; flush ( IO_STDOUT )
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call selfTest
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end subroutine lattice_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Characteristic shear for twinning
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!--------------------------------------------------------------------------------------------------
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function lattice_characteristicShear_Twin ( Ntwin , lattice , CoverA ) result ( characteristicShear )
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integer , dimension ( : ) , intent ( in ) :: Ntwin !< number of active twin systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( sum ( Ntwin ) ) :: characteristicShear
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integer :: &
a , & !< index of active system
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p , & !< index in potential system list
f , & !< index of my family
s !< index of my system in current family
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integer , dimension ( HEX_NTWIN ) , parameter :: &
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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 &
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] , [ HEX_NTWIN ] ) ! indicator to formulas below
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a = 0
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myFamilies : do f = 1 , size ( Ntwin , 1 )
mySystems : do s = 1 , Ntwin ( f )
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a = a + 1
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select case ( lattice )
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case ( 'cF' , 'cI' )
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characteristicShear ( a ) = 0.5_pReal * sqrt ( 2.0_pReal )
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case ( 'hP' )
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if ( cOverA < 1.0_pReal . or . cOverA > 2.0_pReal ) &
call IO_error ( 131 , ext_msg = 'lattice_characteristicShear_Twin' )
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p = sum ( HEX_NTWINSYSTEM ( 1 : f - 1 ) ) + s
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select case ( HEX_SHEARTWIN ( p ) ) ! from Christian & Mahajan 1995 p.29
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case ( 1 ) ! <-10.1>{10.2}
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characteristicShear ( a ) = ( 3.0_pReal - cOverA ** 2 ) / sqrt ( 3.0_pReal ) / CoverA
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case ( 2 ) ! <11.6>{-1-1.1}
characteristicShear ( a ) = 1.0_pReal / cOverA
case ( 3 ) ! <10.-2>{10.1}
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characteristicShear ( a ) = ( 4.0_pReal * cOverA ** 2 - 9.0_pReal ) / sqrt ( 4 8.0_pReal ) / cOverA
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case ( 4 ) ! <11.-3>{11.2}
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characteristicShear ( a ) = 2.0_pReal * ( cOverA ** 2 - 2.0_pReal ) / 3.0_pReal / cOverA
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end select
case default
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call IO_error ( 137 , ext_msg = 'lattice_characteristicShear_Twin: ' / / trim ( lattice ) )
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end select
enddo mySystems
enddo myFamilies
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end function lattice_characteristicShear_Twin
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!--------------------------------------------------------------------------------------------------
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!> @brief Rotated elasticity matrices for twinning in 6x6-matrix notation
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!--------------------------------------------------------------------------------------------------
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function lattice_C66_twin ( Ntwin , C66 , lattice , CoverA )
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integer , dimension ( : ) , intent ( in ) :: Ntwin !< number of active twin systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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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
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real ( pReal ) , dimension ( 3 , 3 , sum ( Ntwin ) ) :: coordinateSystem
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type ( tRotation ) :: R
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integer :: i
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select case ( lattice )
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case ( 'cF' )
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coordinateSystem = buildCoordinateSystem ( Ntwin , FCC_NSLIPSYSTEM , FCC_SYSTEMTWIN , &
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lattice , 0.0_pReal )
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case ( 'cI' )
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coordinateSystem = buildCoordinateSystem ( Ntwin , BCC_NSLIPSYSTEM , BCC_SYSTEMTWIN , &
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lattice , 0.0_pReal )
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case ( 'hP' )
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coordinateSystem = buildCoordinateSystem ( Ntwin , HEX_NSLIPSYSTEM , HEX_SYSTEMTWIN , &
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lattice , cOverA )
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case default
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call IO_error ( 137 , ext_msg = 'lattice_C66_twin: ' / / trim ( lattice ) )
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end select
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do i = 1 , sum ( Ntwin )
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call R % fromAxisAngle ( [ coordinateSystem ( 1 : 3 , 2 , i ) , PI ] , P = 1 ) ! ToDo: Why always 180 deg?
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lattice_C66_twin ( 1 : 6 , 1 : 6 , i ) = R % rotStiffness ( C66 )
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enddo
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end function lattice_C66_twin
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!--------------------------------------------------------------------------------------------------
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!> @brief Rotated elasticity matrices for transformation in 6x6-matrix notation
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!--------------------------------------------------------------------------------------------------
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function lattice_C66_trans ( Ntrans , C_parent66 , lattice_target , &
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cOverA_trans , a_fcc , a_bcc )
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integer , dimension ( : ) , intent ( in ) :: Ntrans !< number of active twin systems per family
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character ( len = 2 ) , intent ( in ) :: lattice_target !< Bravais lattice (Pearson symbol)
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: C_parent66
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real ( pReal ) , optional , intent ( in ) :: cOverA_trans , a_fcc , a_bcc
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real ( pReal ) , dimension ( 6 , 6 , sum ( Ntrans ) ) :: lattice_C66_trans
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real ( pReal ) , dimension ( 6 , 6 ) :: C_bar66 , C_target_unrotated66
real ( pReal ) , dimension ( 3 , 3 , sum ( Ntrans ) ) :: Q , S
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type ( tRotation ) :: R
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integer :: i
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!--------------------------------------------------------------------------------------------------
! elasticity matrix of the target phase in cube orientation
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if ( lattice_target == 'hP' . and . present ( cOverA_trans ) ) then
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! https://doi.org/10.1063/1.1663858 eq. (16), eq. (18), eq. (19)
! https://doi.org/10.1016/j.actamat.2016.07.032 eq. (47), eq. (48)
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if ( cOverA_trans < 1.0_pReal . or . cOverA_trans > 2.0_pReal ) &
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call IO_error ( 131 , ext_msg = 'lattice_C66_trans: ' / / trim ( lattice_target ) )
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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 ) )
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C_target_unrotated66 = 0.0_pReal
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C_target_unrotated66 ( 1 , 1 ) = C_bar66 ( 1 , 1 ) - C_bar66 ( 1 , 4 ) ** 2 / C_bar66 ( 4 , 4 )
C_target_unrotated66 ( 1 , 2 ) = C_bar66 ( 1 , 2 ) + C_bar66 ( 1 , 4 ) ** 2 / C_bar66 ( 4 , 4 )
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C_target_unrotated66 ( 1 , 3 ) = C_bar66 ( 1 , 3 )
C_target_unrotated66 ( 3 , 3 ) = C_bar66 ( 3 , 3 )
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C_target_unrotated66 ( 4 , 4 ) = C_bar66 ( 4 , 4 ) - C_bar66 ( 1 , 4 ) ** 2 / ( 0.5_pReal * ( C_bar66 ( 1 , 1 ) - C_bar66 ( 1 , 2 ) ) )
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C_target_unrotated66 = lattice_symmetrize_C66 ( C_target_unrotated66 , 'hP' )
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elseif ( lattice_target == 'cI' . and . present ( a_fcc ) . and . present ( a_bcc ) ) then
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if ( a_bcc < = 0.0_pReal . or . a_fcc < = 0.0_pReal ) &
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call IO_error ( 134 , ext_msg = 'lattice_C66_trans: ' / / trim ( lattice_target ) )
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C_target_unrotated66 = C_parent66
else
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call IO_error ( 137 , ext_msg = 'lattice_C66_trans : ' / / trim ( lattice_target ) )
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endif
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do i = 1 , 6
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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
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call buildTransformationSystem ( Q , S , Ntrans , cOverA_trans , a_fcc , a_bcc )
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do i = 1 , sum ( Ntrans )
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call R % fromMatrix ( Q ( 1 : 3 , 1 : 3 , i ) )
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lattice_C66_trans ( 1 : 6 , 1 : 6 , i ) = R % rotStiffness ( C_target_unrotated66 )
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enddo
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end function lattice_C66_trans
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!--------------------------------------------------------------------------------------------------
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!> @brief Non-schmid projections for bcc with up to 6 coefficients
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! https://doi.org/10.1016/j.actamat.2012.03.053, eq. (17)
! https://doi.org/10.1016/j.actamat.2008.07.037, table 1
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!--------------------------------------------------------------------------------------------------
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function lattice_nonSchmidMatrix ( Nslip , nonSchmidCoefficients , sense ) result ( nonSchmidMatrix )
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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
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real ( pReal ) , dimension ( 1 : 3 , 1 : 3 , sum ( Nslip ) ) :: coordinateSystem !< coordinate system of slip system
real ( pReal ) , dimension ( 3 ) :: direction , normal , np
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type ( tRotation ) :: R
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integer :: i
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if ( abs ( sense ) / = 1 ) error stop 'Sense in lattice_nonSchmidMatrix'
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coordinateSystem = buildCoordinateSystem ( Nslip , BCC_NSLIPSYSTEM , BCC_SYSTEMSLIP , 'cI' , 0.0_pReal )
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coordinateSystem ( 1 : 3 , 1 , 1 : sum ( Nslip ) ) = coordinateSystem ( 1 : 3 , 1 , 1 : sum ( Nslip ) ) * real ( sense , pReal ) ! convert unidirectional coordinate system
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nonSchmidMatrix = lattice_SchmidMatrix_slip ( Nslip , 'cI' , 0.0_pReal ) ! Schmid contribution
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do i = 1 , sum ( Nslip )
direction = coordinateSystem ( 1 : 3 , 1 , i )
normal = coordinateSystem ( 1 : 3 , 2 , i )
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call R % fromAxisAngle ( [ direction , 6 0.0_pReal ] , degrees = . true . , P = 1 )
np = R % rotate ( normal )
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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
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end function lattice_nonSchmidMatrix
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!--------------------------------------------------------------------------------------------------
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!> @brief Slip-slip interaction matrix
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!> @details only active slip systems are considered
!> @details https://doi.org/10.1016/j.actamat.2016.12.040 (fcc: Tab S4-1, bcc: Tab S5-1)
!> @details https://doi.org/10.1016/j.ijplas.2014.06.010 (hex: Tab 3b)
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_SlipBySlip ( Nslip , interactionValues , lattice ) result ( interactionMatrix )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
real ( pReal ) , dimension ( : ) , intent ( in ) :: interactionValues !< values for slip-slip interaction
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , dimension ( sum ( Nslip ) , sum ( Nslip ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NslipMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NSLIP , FCC_NSLIP ) , parameter :: &
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FCC_INTERACTIONSLIPSLIP = reshape ( [ &
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1 , 2 , 2 , 4 , 7 , 5 , 3 , 5 , 5 , 4 , 6 , 7 , 10 , 11 , 10 , 11 , 12 , 13 , & ! -----> acting (forest)
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2 , 1 , 2 , 7 , 4 , 5 , 6 , 4 , 7 , 5 , 3 , 5 , 10 , 11 , 12 , 13 , 10 , 11 , & ! |
2 , 2 , 1 , 5 , 5 , 3 , 6 , 7 , 4 , 7 , 6 , 4 , 12 , 13 , 10 , 11 , 10 , 11 , & ! |
4 , 7 , 6 , 1 , 2 , 2 , 4 , 6 , 7 , 3 , 5 , 5 , 10 , 11 , 11 , 10 , 13 , 12 , & ! v
2021-05-09 14:31:21 +05:30
7 , 4 , 6 , 2 , 1 , 2 , 5 , 3 , 5 , 6 , 4 , 7 , 10 , 11 , 13 , 12 , 11 , 10 , & ! reacting (primary)
2021-05-09 14:28:43 +05:30
5 , 5 , 3 , 2 , 2 , 1 , 7 , 6 , 4 , 6 , 7 , 4 , 12 , 13 , 11 , 10 , 11 , 10 , &
3 , 5 , 5 , 4 , 6 , 7 , 1 , 2 , 2 , 4 , 7 , 6 , 11 , 10 , 11 , 10 , 12 , 13 , &
6 , 4 , 7 , 5 , 3 , 5 , 2 , 1 , 2 , 7 , 4 , 6 , 11 , 10 , 13 , 12 , 10 , 11 , &
6 , 7 , 4 , 7 , 6 , 4 , 2 , 2 , 1 , 5 , 5 , 3 , 13 , 12 , 11 , 10 , 10 , 11 , &
4 , 6 , 7 , 3 , 5 , 5 , 4 , 7 , 6 , 1 , 2 , 2 , 11 , 10 , 10 , 11 , 13 , 12 , &
5 , 3 , 5 , 6 , 4 , 7 , 7 , 4 , 6 , 2 , 1 , 2 , 11 , 10 , 12 , 13 , 11 , 10 , &
7 , 6 , 4 , 6 , 7 , 4 , 5 , 5 , 3 , 2 , 2 , 1 , 13 , 12 , 10 , 11 , 11 , 10 , &
10 , 10 , 12 , 10 , 10 , 12 , 11 , 11 , 13 , 11 , 11 , 13 , 1 , 8 , 9 , 9 , 9 , 9 , &
11 , 11 , 13 , 11 , 11 , 13 , 10 , 10 , 12 , 10 , 10 , 12 , 8 , 1 , 9 , 9 , 9 , 9 , &
10 , 12 , 10 , 11 , 13 , 11 , 11 , 13 , 11 , 10 , 12 , 10 , 9 , 9 , 1 , 8 , 9 , 9 , &
11 , 13 , 11 , 10 , 12 , 10 , 10 , 12 , 10 , 11 , 13 , 11 , 9 , 9 , 8 , 1 , 9 , 9 , &
12 , 10 , 10 , 13 , 11 , 11 , 12 , 10 , 10 , 13 , 11 , 11 , 9 , 9 , 9 , 9 , 1 , 8 , &
13 , 11 , 11 , 12 , 10 , 10 , 13 , 11 , 11 , 12 , 10 , 10 , 9 , 9 , 9 , 9 , 8 , 1 &
] , shape ( FCC_INTERACTIONSLIPSLIP ) ) !< Slip-slip interaction types for fcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
2021-05-07 14:01:30 +05:30
!< 1: self interaction --> alpha 0
!< 2: coplanar interaction --> alpha copla
!< 3: collinear interaction --> alpha coli
!< 4: Hirth locks --> alpha 1
!< 5: glissile junctions I --> alpha 2
!< 6: glissile junctions II --> alpha 2*
!< 7: Lomer locks --> alpha 3
!< 8: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
!< 9: similar to Lomer locks in <110>{111} for two {110} planes
!<10: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
!<11: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
!<12: crossing btw one {110} and one {111} plane
!<13: collinear btw one {110} and one {111} plane
2020-02-25 22:02:49 +05:30
2020-03-10 18:15:00 +05:30
integer , dimension ( BCC_NSLIP , BCC_NSLIP ) , parameter :: &
2019-04-13 04:16:27 +05:30
BCC_INTERACTIONSLIPSLIP = reshape ( [ &
2021-05-24 00:42:31 +05:30
1 , 3 , 6 , 6 , 7 , 5 , 4 , 2 , 4 , 2 , 7 , 5 , 18 , 18 , 11 , 8 , 9 , 13 , 17 , 14 , 13 , 9 , 17 , 14 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , & ! -----> acting (forest)
3 , 1 , 6 , 6 , 4 , 2 , 7 , 5 , 7 , 5 , 4 , 2 , 18 , 18 , 8 , 11 , 13 , 9 , 14 , 17 , 9 , 13 , 14 , 17 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , & ! |
6 , 6 , 1 , 3 , 5 , 7 , 2 , 4 , 5 , 7 , 2 , 4 , 11 , 8 , 18 , 18 , 17 , 14 , 9 , 13 , 17 , 14 , 13 , 9 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , & ! |
6 , 6 , 3 , 1 , 2 , 4 , 5 , 7 , 2 , 4 , 5 , 7 , 8 , 11 , 18 , 18 , 14 , 17 , 13 , 9 , 14 , 17 , 9 , 13 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , & ! v
7 , 5 , 4 , 2 , 1 , 3 , 6 , 6 , 2 , 4 , 7 , 5 , 9 , 17 , 13 , 14 , 18 , 11 , 18 , 8 , 13 , 17 , 9 , 14 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , & ! reacting (primary)
4 , 2 , 7 , 5 , 3 , 1 , 6 , 6 , 5 , 7 , 4 , 2 , 13 , 14 , 9 , 17 , 18 , 8 , 18 , 11 , 9 , 14 , 13 , 17 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , &
5 , 7 , 2 , 4 , 6 , 6 , 1 , 3 , 7 , 5 , 2 , 4 , 17 , 9 , 14 , 13 , 11 , 18 , 8 , 18 , 17 , 13 , 14 , 9 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , &
2 , 4 , 5 , 7 , 6 , 6 , 3 , 1 , 4 , 2 , 5 , 7 , 14 , 13 , 17 , 9 , 8 , 18 , 11 , 18 , 14 , 9 , 17 , 13 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , &
5 , 7 , 4 , 2 , 2 , 4 , 7 , 5 , 1 , 3 , 6 , 6 , 9 , 17 , 14 , 13 , 13 , 17 , 14 , 9 , 18 , 11 , 8 , 18 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , &
2 , 4 , 7 , 5 , 5 , 7 , 4 , 2 , 3 , 1 , 6 , 6 , 13 , 14 , 17 , 9 , 9 , 14 , 17 , 13 , 18 , 8 , 11 , 18 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , &
7 , 5 , 2 , 4 , 7 , 5 , 2 , 4 , 6 , 6 , 1 , 3 , 17 , 9 , 13 , 14 , 17 , 13 , 9 , 14 , 11 , 18 , 18 , 8 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , &
4 , 2 , 5 , 7 , 4 , 2 , 5 , 7 , 6 , 6 , 3 , 1 , 14 , 13 , 9 , 17 , 14 , 9 , 13 , 17 , 8 , 18 , 18 , 11 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , &
19 , 19 , 10 , 8 , 9 , 12 , 16 , 15 , 9 , 12 , 16 , 15 , 1 , 20 , 24 , 24 , 23 , 22 , 21 , 2 , 23 , 22 , 2 , 21 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , &
19 , 19 , 8 , 10 , 16 , 15 , 9 , 12 , 16 , 15 , 9 , 12 , 20 , 1 , 24 , 24 , 22 , 23 , 2 , 21 , 22 , 23 , 21 , 2 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , &
10 , 8 , 19 , 19 , 12 , 9 , 15 , 16 , 15 , 16 , 12 , 9 , 24 , 24 , 1 , 20 , 21 , 2 , 23 , 22 , 2 , 21 , 23 , 22 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , &
8 , 10 , 19 , 19 , 15 , 16 , 12 , 9 , 12 , 9 , 15 , 16 , 24 , 24 , 20 , 1 , 2 , 21 , 22 , 23 , 21 , 2 , 22 , 23 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , &
9 , 12 , 16 , 15 , 19 , 19 , 10 , 8 , 12 , 9 , 16 , 15 , 23 , 21 , 22 , 2 , 1 , 24 , 20 , 24 , 23 , 2 , 22 , 21 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , &
12 , 9 , 15 , 16 , 10 , 8 , 19 , 19 , 16 , 15 , 12 , 9 , 21 , 23 , 2 , 21 , 24 , 1 , 24 , 20 , 2 , 23 , 21 , 22 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , &
16 , 15 , 9 , 12 , 19 , 19 , 8 , 10 , 15 , 16 , 9 , 12 , 22 , 2 , 23 , 22 , 20 , 24 , 1 , 24 , 22 , 21 , 23 , 2 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , &
15 , 16 , 12 , 9 , 8 , 10 , 19 , 19 , 9 , 12 , 15 , 16 , 2 , 22 , 21 , 23 , 24 , 20 , 24 , 1 , 21 , 22 , 2 , 23 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , &
12 , 9 , 16 , 15 , 12 , 9 , 16 , 15 , 19 , 19 , 10 , 8 , 23 , 21 , 2 , 22 , 23 , 2 , 21 , 22 , 1 , 24 , 24 , 20 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , &
9 , 12 , 15 , 16 , 16 , 15 , 12 , 9 , 10 , 8 , 19 , 19 , 21 , 23 , 22 , 2 , 2 , 23 , 22 , 21 , 24 , 1 , 20 , 24 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , &
16 , 15 , 12 , 9 , 9 , 12 , 15 , 16 , 8 , 10 , 19 , 19 , 2 , 22 , 23 , 21 , 21 , 22 , 23 , 2 , 24 , 20 , 1 , 24 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , &
15 , 16 , 9 , 12 , 15 , 16 , 9 , 12 , 19 , 19 , 8 , 10 , 22 , 2 , 21 , 23 , 22 , 21 , 2 , 23 , 20 , 24 , 24 , 1 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 26 , 28 , 28 , &
2021-06-01 02:32:51 +05:30
2021-05-24 00:42:31 +05:30
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , &
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , &
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , &
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 27 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 1 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 1 , 28 , 28 , 28 , 27 , 28 , 28 , &
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , 27 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , 27 , &
28 , 28 , 28 , 25 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 27 , 28 , 28 , 28 , 1 , 28 , 28 , 28 , &
28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 1 , 28 , 28 , &
28 , 25 , 28 , 28 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 1 , 28 , &
25 , 28 , 28 , 28 , 28 , 28 , 28 , 25 , 28 , 25 , 28 , 28 , 28 , 28 , 28 , 26 , 26 , 28 , 28 , 28 , 28 , 26 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 27 , 28 , 28 , 28 , 28 , 28 , 28 , 27 , 28 , 28 , 28 , 1 &
2021-05-09 14:28:43 +05:30
] , shape ( BCC_INTERACTIONSLIPSLIP ) ) !< Slip-slip interaction types for bcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
2021-05-07 14:07:08 +05:30
!< 1: self interaction --> alpha 0
!< 2: collinear interaction --> alpha 1
!< 3: coplanar interaction --> alpha 2
2021-05-09 14:28:43 +05:30
!< 4-7: other coefficients
2021-05-24 00:42:31 +05:30
!< 8: {110}-{112} collinear and perpendicular planes --> alpha 6
!< 9: {110}-{112} collinear --> alpha 7
2021-05-09 14:28:43 +05:30
!< 10-24: other coefficients
2021-05-24 00:42:31 +05:30
!< 25: {110}-{123} collinear
!< 26: {112}-{123} collinear
!< 27: {123}-{123} collinear
2021-05-20 20:34:47 +05:30
!< 28: other interaction
2020-02-25 22:02:49 +05:30
2020-03-10 18:15:00 +05:30
integer , dimension ( HEX_NSLIP , HEX_NSLIP ) , parameter :: &
2019-04-13 04:16:27 +05:30
HEX_INTERACTIONSLIPSLIP = reshape ( [ &
2021-12-04 07:20:53 +05:30
! basal prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
2021-12-07 23:40:24 +05:30
1 , 2 , 2 , 3 , 4 , 4 , 9 , 10 , 9 , 9 , 10 , 9 , 20 , 21 , 22 , 22 , 21 , 20 , 20 , 21 , 22 , 22 , 21 , 20 , 47 , 47 , 48 , 47 , 47 , 48 , & ! -----> acting (forest)
2 , 1 , 2 , 4 , 3 , 4 , 10 , 9 , 9 , 10 , 9 , 9 , 22 , 22 , 21 , 20 , 20 , 21 , 22 , 22 , 21 , 20 , 20 , 21 , 47 , 48 , 47 , 47 , 48 , 47 , & ! | basal
2 , 2 , 1 , 4 , 4 , 3 , 9 , 9 , 10 , 9 , 9 , 10 , 21 , 20 , 20 , 21 , 22 , 22 , 21 , 20 , 20 , 21 , 22 , 22 , 48 , 47 , 47 , 48 , 47 , 47 , & ! |
! v
7 , 8 , 8 , 5 , 6 , 6 , 11 , 12 , 11 , 11 , 12 , 11 , 23 , 24 , 25 , 25 , 24 , 23 , 23 , 24 , 25 , 25 , 24 , 23 , 49 , 49 , 50 , 49 , 49 , 50 , & ! reacting (primary)
8 , 7 , 8 , 6 , 5 , 6 , 12 , 11 , 11 , 12 , 11 , 11 , 25 , 25 , 24 , 23 , 23 , 24 , 25 , 25 , 24 , 23 , 23 , 24 , 49 , 50 , 49 , 49 , 50 , 49 , & ! prism
8 , 8 , 7 , 6 , 6 , 5 , 11 , 11 , 12 , 11 , 11 , 12 , 24 , 23 , 23 , 24 , 25 , 25 , 24 , 23 , 23 , 24 , 25 , 25 , 50 , 49 , 49 , 50 , 49 , 49 , &
18 , 19 , 18 , 16 , 17 , 16 , 13 , 14 , 14 , 15 , 14 , 14 , 26 , 26 , 27 , 28 , 28 , 27 , 29 , 29 , 27 , 28 , 28 , 27 , 51 , 52 , 51 , 51 , 52 , 51 , &
19 , 18 , 18 , 17 , 16 , 16 , 14 , 13 , 14 , 14 , 15 , 14 , 28 , 27 , 26 , 26 , 27 , 28 , 28 , 27 , 29 , 29 , 27 , 28 , 51 , 51 , 52 , 51 , 51 , 52 , &
18 , 18 , 19 , 16 , 16 , 17 , 14 , 14 , 13 , 14 , 14 , 15 , 27 , 28 , 28 , 27 , 26 , 26 , 27 , 28 , 28 , 27 , 29 , 29 , 52 , 51 , 51 , 52 , 51 , 51 , &
18 , 19 , 18 , 16 , 17 , 16 , 15 , 14 , 14 , 13 , 14 , 14 , 29 , 29 , 27 , 28 , 28 , 27 , 26 , 26 , 27 , 28 , 28 , 27 , 51 , 52 , 51 , 51 , 52 , 51 , & ! 1. pyr<a>
19 , 18 , 18 , 17 , 16 , 16 , 14 , 15 , 14 , 14 , 13 , 14 , 28 , 27 , 29 , 29 , 27 , 28 , 28 , 27 , 26 , 26 , 27 , 28 , 51 , 51 , 52 , 51 , 51 , 52 , &
18 , 18 , 19 , 16 , 16 , 17 , 14 , 14 , 15 , 14 , 14 , 13 , 27 , 28 , 28 , 27 , 29 , 29 , 27 , 28 , 28 , 27 , 26 , 26 , 52 , 51 , 51 , 52 , 51 , 51 , &
44 , 45 , 46 , 41 , 42 , 43 , 37 , 38 , 39 , 40 , 38 , 39 , 30 , 31 , 32 , 32 , 32 , 33 , 34 , 35 , 32 , 32 , 32 , 36 , 53 , 54 , 55 , 53 , 54 , 56 , &
46 , 45 , 44 , 43 , 42 , 41 , 37 , 39 , 38 , 40 , 39 , 38 , 31 , 30 , 36 , 32 , 32 , 32 , 35 , 34 , 33 , 32 , 32 , 32 , 56 , 54 , 53 , 55 , 54 , 53 , &
45 , 46 , 44 , 42 , 43 , 41 , 39 , 37 , 38 , 39 , 40 , 38 , 32 , 36 , 30 , 31 , 32 , 32 , 32 , 33 , 34 , 35 , 32 , 32 , 56 , 53 , 54 , 55 , 53 , 54 , &
45 , 44 , 46 , 42 , 41 , 43 , 38 , 37 , 39 , 38 , 40 , 39 , 32 , 32 , 31 , 30 , 36 , 32 , 32 , 32 , 35 , 34 , 33 , 32 , 53 , 56 , 54 , 53 , 55 , 54 , &
46 , 44 , 45 , 43 , 41 , 42 , 38 , 39 , 37 , 38 , 39 , 40 , 32 , 32 , 32 , 36 , 30 , 31 , 32 , 32 , 32 , 33 , 34 , 35 , 54 , 56 , 53 , 54 , 55 , 53 , &
44 , 46 , 45 , 41 , 43 , 42 , 39 , 38 , 37 , 39 , 38 , 40 , 33 , 32 , 32 , 32 , 31 , 30 , 36 , 32 , 32 , 32 , 35 , 34 , 54 , 53 , 56 , 54 , 53 , 55 , &
44 , 45 , 46 , 41 , 42 , 43 , 40 , 38 , 39 , 37 , 38 , 39 , 34 , 35 , 32 , 32 , 32 , 36 , 30 , 31 , 32 , 32 , 32 , 33 , 53 , 54 , 56 , 53 , 54 , 55 , & ! 1. pyr<c+a>
46 , 45 , 44 , 43 , 42 , 41 , 40 , 39 , 38 , 37 , 39 , 38 , 35 , 34 , 33 , 32 , 32 , 32 , 31 , 30 , 36 , 32 , 32 , 32 , 55 , 54 , 53 , 56 , 54 , 53 , &
45 , 46 , 44 , 42 , 43 , 41 , 39 , 40 , 38 , 39 , 37 , 38 , 32 , 33 , 34 , 35 , 32 , 32 , 32 , 36 , 30 , 31 , 32 , 32 , 55 , 53 , 54 , 56 , 53 , 54 , &
45 , 44 , 46 , 42 , 41 , 43 , 38 , 40 , 39 , 38 , 37 , 39 , 32 , 32 , 35 , 34 , 33 , 32 , 32 , 32 , 31 , 30 , 36 , 32 , 53 , 55 , 54 , 53 , 56 , 54 , &
46 , 44 , 45 , 43 , 41 , 42 , 38 , 39 , 40 , 38 , 39 , 37 , 32 , 32 , 32 , 33 , 34 , 35 , 32 , 32 , 32 , 36 , 30 , 31 , 54 , 55 , 53 , 54 , 56 , 53 , &
44 , 46 , 45 , 41 , 43 , 42 , 39 , 38 , 40 , 39 , 38 , 37 , 36 , 32 , 32 , 32 , 35 , 34 , 33 , 32 , 32 , 32 , 31 , 30 , 54 , 53 , 55 , 54 , 53 , 56 , &
68 , 68 , 69 , 66 , 66 , 67 , 64 , 64 , 65 , 64 , 65 , 65 , 60 , 61 , 61 , 60 , 62 , 62 , 60 , 63 , 63 , 60 , 62 , 62 , 57 , 58 , 58 , 59 , 58 , 58 , &
68 , 69 , 68 , 66 , 67 , 66 , 65 , 64 , 64 , 65 , 64 , 64 , 62 , 62 , 60 , 61 , 61 , 60 , 62 , 62 , 60 , 63 , 63 , 60 , 58 , 57 , 58 , 58 , 59 , 58 , &
69 , 68 , 68 , 67 , 66 , 66 , 64 , 65 , 64 , 64 , 65 , 64 , 63 , 60 , 62 , 62 , 60 , 61 , 61 , 60 , 62 , 62 , 60 , 63 , 58 , 58 , 57 , 58 , 58 , 59 , &
68 , 68 , 69 , 66 , 66 , 67 , 64 , 64 , 65 , 64 , 64 , 65 , 60 , 63 , 63 , 60 , 62 , 62 , 60 , 61 , 61 , 60 , 62 , 62 , 59 , 58 , 58 , 57 , 58 , 58 , & ! 2. pyr<c+a>
68 , 69 , 68 , 66 , 67 , 66 , 65 , 64 , 64 , 65 , 64 , 64 , 62 , 62 , 60 , 63 , 63 , 60 , 62 , 62 , 60 , 61 , 61 , 60 , 58 , 59 , 58 , 58 , 57 , 58 , &
69 , 68 , 68 , 67 , 66 , 66 , 64 , 65 , 64 , 64 , 65 , 64 , 61 , 60 , 62 , 62 , 60 , 63 , 63 , 60 , 62 , 62 , 60 , 61 , 58 , 58 , 59 , 58 , 58 , 57 &
2022-01-13 21:12:05 +05:30
] , shape ( HEX_INTERACTIONSLIPSLIP ) ) !< Slip-slip interaction types for hex (onion peel naming scheme)
!< 10.1016/j.ijplas.2014.06.010 table 3
!< 10.1080/14786435.2012.699689 table 2 and 3
2022-01-13 21:53:09 +05:30
!< index & label & description
!< 1 & S1 & basal self-interaction
!< 2 & 1 & basal/basal coplanar
!< 3 & 3 & basal/prismatic collinear
!< 4 & 4 & basal/prismatic non-collinear
!< 5 & S2 & prismatic self-interaction
!< 6 & 2 & prismatic/prismatic
!< 7 & 5 & prismatic/basal collinear
!< 8 & 6 & prismatic/basal non-collinear
!< 9 & - & basal/pyramidal <a> non-collinear
!< 10 & - & basal/pyramidal <a> collinear
!< 11 & - & prismatic/pyramidal <a> non-collinear
!< 12 & - & prismatic/pyramidal <a> collinear
!< 13 & - & pyramidal <a> self-interaction
!< 14 & - & pyramidal <a> non-collinear
!< 15 & - & pyramidal <a> collinear
!< 16 & - & pyramidal <a>/prismatic non-collinear
!< 17 & - & pyramidal <a>/prismatic collinear
!< 18 & - & pyramidal <a>/basal non-collinear
!< 19 & - & pyramidal <a>/basal collinear
!< 20 & - & basal/1. order pyramidal <c+a> semi-collinear
!< 21 & - & basal/1. order pyramidal <c+a>
!< 22 & - & basal/1. order pyramidal <c+a>
!< 23 & - & prismatic/1. order pyramidal <c+a> semi-collinear
!< 24 & - & prismatic/1. order pyramidal <c+a>
!< 25 & - & prismatic/1. order pyramidal <c+a> semi-coplanar?
!< 26 & - & pyramidal <a>/1. order pyramidal <c+a> coplanar
!< 27 & - & pyramidal <a>/1. order pyramidal <c+a>
!< 28 & - & pyramidal <a>/1. order pyramidal <c+a> semi-collinear
!< 29 & - & pyramidal <a>/1. order pyramidal <c+a> semi-coplanar
!< 30 & - & 1. order pyramidal <c+a> self-interaction
!< 31 & - & 1. order pyramidal <c+a> coplanar
!< 32 & - & 1. order pyramidal <c+a>
!< 33 & - & 1. order pyramidal <c+a>
!< 34 & - & 1. order pyramidal <c+a> semi-coplanar
!< 35 & - & 1. order pyramidal <c+a> semi-coplanar
!< 36 & - & 1. order pyramidal <c+a> collinear
!< 37 & - & 1. order pyramidal <c+a>/pyramidal <a> coplanar
!< 38 & - & 1. order pyramidal <c+a>/pyramidal <a> semi-collinear
!< 39 & - & 1. order pyramidal <c+a>/pyramidal <a>
!< 40 & - & 1. order pyramidal <c+a>/pyramidal <a> semi-coplanar
!< 41 & - & 1. order pyramidal <c+a>/prismatic semi-collinear
!< 42 & - & 1. order pyramidal <c+a>/prismatic semi-coplanar
!< 43 & - & 1. order pyramidal <c+a>/prismatic
!< 44 & - & 1. order pyramidal <c+a>/basal semi-collinear
!< 45 & - & 1. order pyramidal <c+a>/basal
!< 46 & - & 1. order pyramidal <c+a>/basal
!< 47 & 8 & basal/2. order pyramidal <c+a> non-collinear
!< 48 & 7 & basal/2. order pyramidal <c+a> semi-collinear
!< 49 & 10 & prismatic/2. order pyramidal <c+a>
!< 50 & 9 & prismatic/2. order pyramidal <c+a> semi-collinear
!< 51 & - & pyramidal <a>/2. order pyramidal <c+a>
!< 52 & - & pyramidal <a>/2. order pyramidal <c+a> semi collinear
!< 53 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 54 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 55 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 56 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a> collinear
!< 57 & S3 & 2. order pyramidal <c+a> self-interaction
!< 58 & 16 & 2. order pyramidal <c+a> non-collinear
!< 59 & 15 & 2. order pyramidal <c+a> semi-collinear
!< 60 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 61 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a> collinear
!< 62 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 63 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 64 & - & 2. order pyramidal <c+a>/pyramidal <a> non-collinear
!< 65 & - & 2. order pyramidal <c+a>/pyramidal <a> semi-collinear
!< 66 & 14 & 2. order pyramidal <c+a>/prismatic non-collinear
!< 67 & 13 & 2. order pyramidal <c+a>/prismatic semi-collinear
!< 68 & 12 & 2. order pyramidal <c+a>/basal non-collinear
!< 69 & 11 & 2. order pyramidal <c+a>/basal semi-collinear
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2020-03-10 18:15:00 +05:30
integer , dimension ( BCT_NSLIP , BCT_NSLIP ) , parameter :: &
2019-04-13 04:16:27 +05:30
BCT_INTERACTIONSLIPSLIP = reshape ( [ &
2021-05-24 00:42:31 +05:30
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 ) )
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select case ( lattice )
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case ( 'cF' )
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interactionTypes = FCC_INTERACTIONSLIPSLIP
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NslipMax = FCC_NSLIPSYSTEM
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case ( 'cI' )
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interactionTypes = BCC_INTERACTIONSLIPSLIP
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NslipMax = BCC_NSLIPSYSTEM
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case ( 'hP' )
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interactionTypes = HEX_INTERACTIONSLIPSLIP
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NslipMax = HEX_NSLIPSYSTEM
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case ( 'tI' )
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interactionTypes = BCT_INTERACTIONSLIPSLIP
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NslipMax = BCT_NSLIPSYSTEM
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case default
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call IO_error ( 137 , ext_msg = 'lattice_interaction_SlipBySlip: ' / / trim ( lattice ) )
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end select
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interactionMatrix = buildInteraction ( Nslip , Nslip , NslipMax , NslipMax , interactionValues , interactionTypes )
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end function lattice_interaction_SlipBySlip
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!--------------------------------------------------------------------------------------------------
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!> @brief Twin-twin interaction matrix
!> details only active twin systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_TwinByTwin ( Ntwin , interactionValues , lattice ) result ( interactionMatrix )
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integer , dimension ( : ) , intent ( in ) :: Ntwin !< number of active twin systems per family
real ( pReal ) , dimension ( : ) , intent ( in ) :: interactionValues !< values for twin-twin interaction
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , dimension ( sum ( Ntwin ) , sum ( Ntwin ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NtwinMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NTWIN , FCC_NTWIN ) , parameter :: &
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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
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integer , dimension ( BCC_NTWIN , BCC_NTWIN ) , parameter :: &
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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
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!< 1: self interaction
!< 2: collinear interaction
!< 3: other interaction
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integer , dimension ( HEX_NTWIN , HEX_NTWIN ) , parameter :: &
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HEX_INTERACTIONTWINTWIN = reshape ( [ &
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! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
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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 , & ! |
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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 <-10.1>{10.2}
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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 , &
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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 , &
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6 , 6 , 6 , 6 , 6 , 6 , 5 , 5 , 5 , 4 , 5 , 5 , 8 , 8 , 8 , 8 , 8 , 8 , 14 , 14 , 14 , 14 , 14 , 14 , & ! <11.6>{-1-1.1}
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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 , &
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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 , &
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12 , 12 , 12 , 12 , 12 , 12 , 11 , 11 , 11 , 11 , 11 , 11 , 10 , 10 , 10 , 9 , 10 , 10 , 15 , 15 , 15 , 15 , 15 , 15 , & ! <10.-2>{10.1}
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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 , &
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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 , &
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20 , 20 , 20 , 20 , 20 , 20 , 19 , 19 , 19 , 19 , 19 , 19 , 18 , 18 , 18 , 18 , 18 , 18 , 17 , 17 , 17 , 16 , 17 , 17 , & ! <11.-3>{11.2}
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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
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select case ( lattice )
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case ( 'cF' )
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interactionTypes = FCC_INTERACTIONTWINTWIN
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NtwinMax = FCC_NTWINSYSTEM
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case ( 'cI' )
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interactionTypes = BCC_INTERACTIONTWINTWIN
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NtwinMax = BCC_NTWINSYSTEM
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case ( 'hP' )
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interactionTypes = HEX_INTERACTIONTWINTWIN
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NtwinMax = HEX_NTWINSYSTEM
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case default
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call IO_error ( 137 , ext_msg = 'lattice_interaction_TwinByTwin: ' / / trim ( lattice ) )
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end select
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interactionMatrix = buildInteraction ( Ntwin , Ntwin , NtwinMax , NtwinMax , interactionValues , interactionTypes )
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end function lattice_interaction_TwinByTwin
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!--------------------------------------------------------------------------------------------------
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!> @brief Trans-trans interaction matrix
!> details only active trans systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_TransByTrans ( Ntrans , interactionValues , lattice ) result ( interactionMatrix )
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integer , dimension ( : ) , intent ( in ) :: Ntrans !< number of active trans systems per family
real ( pReal ) , dimension ( : ) , intent ( in ) :: interactionValues !< values for trans-trans interaction
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character ( len = 2 ) , intent ( in ) :: lattice !<Bravais lattice (Pearson symbol) (parent crystal)
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real ( pReal ) , dimension ( sum ( Ntrans ) , sum ( Ntrans ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NtransMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NTRANS , FCC_NTRANS ) , parameter :: &
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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
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if ( lattice == 'cF' ) then
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interactionTypes = FCC_INTERACTIONTRANSTRANS
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NtransMax = FCC_NTRANSSYSTEM
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else
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call IO_error ( 137 , ext_msg = 'lattice_interaction_TransByTrans: ' / / trim ( lattice ) )
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end if
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interactionMatrix = buildInteraction ( Ntrans , Ntrans , NtransMax , NtransMax , interactionValues , interactionTypes )
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end function lattice_interaction_TransByTrans
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!--------------------------------------------------------------------------------------------------
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!> @brief Slip-twin interaction matrix
!> details only active slip and twin systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_SlipByTwin ( Nslip , Ntwin , interactionValues , lattice ) result ( interactionMatrix )
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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
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , dimension ( sum ( Nslip ) , sum ( Ntwin ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NslipMax , &
NtwinMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NTWIN , FCC_NSLIP ) , parameter :: &
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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 , & ! |
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3 , 3 , 3 , 1 , 1 , 1 , 3 , 3 , 3 , 2 , 2 , 2 , & ! v
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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 , &
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4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
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
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!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
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integer , dimension ( BCC_NTWIN , BCC_NSLIP ) , parameter :: &
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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 , &
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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 , &
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3 , 2 , 3 , 3 , 3 , 3 , 2 , 3 , 3 , 3 , 3 , 1 , &
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4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 &
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] , shape ( BCC_INTERACTIONSLIPTWIN ) ) !< Slip-twin interaction types for bcc
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!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
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!< 4: other interaction with slip family {123}
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integer , dimension ( HEX_NTWIN , HEX_NSLIP ) , parameter :: &
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HEX_INTERACTIONSLIPTWIN = reshape ( [ &
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! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
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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)
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1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 4 , & ! | basal
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1 , 1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 3 , 4 , 4 , 4 , 4 , 4 , 4 , & ! |
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! v
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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)
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5 , 5 , 5 , 5 , 5 , 5 , 6 , 6 , 6 , 6 , 6 , 6 , 7 , 7 , 7 , 7 , 7 , 7 , 8 , 8 , 8 , 8 , 8 , 8 , & ! prism
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5 , 5 , 5 , 5 , 5 , 5 , 6 , 6 , 6 , 6 , 6 , 6 , 7 , 7 , 7 , 7 , 7 , 7 , 8 , 8 , 8 , 8 , 8 , 8 , &
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9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 10 , 11 , 11 , 11 , 11 , 11 , 11 , 12 , 12 , 12 , 12 , 12 , 12 , &
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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 , & ! 1. pyr<a>
9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 10 , 11 , 11 , 11 , 11 , 11 , 11 , 12 , 12 , 12 , 12 , 12 , 12 , &
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9 , 9 , 9 , 9 , 9 , 9 , 10 , 10 , 10 , 10 , 10 , 10 , 11 , 11 , 11 , 11 , 11 , 11 , 12 , 12 , 12 , 12 , 12 , 12 , &
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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 , &
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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 , & ! 1. pyr<c+a>
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 , &
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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 , &
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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 , &
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17 , 17 , 17 , 17 , 17 , 17 , 18 , 18 , 18 , 18 , 18 , 18 , 19 , 19 , 19 , 19 , 19 , 19 , 20 , 20 , 20 , 20 , 20 , 20 , & ! 2. pyr<c+a>
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17 , 17 , 17 , 17 , 17 , 17 , 18 , 18 , 18 , 18 , 18 , 18 , 19 , 19 , 19 , 19 , 19 , 19 , 20 , 20 , 20 , 20 , 20 , 20 , &
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17 , 17 , 17 , 17 , 17 , 17 , 18 , 18 , 18 , 18 , 18 , 18 , 19 , 19 , 19 , 19 , 19 , 19 , 20 , 20 , 20 , 20 , 20 , 20 &
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] , shape ( HEX_INTERACTIONSLIPTWIN ) ) !< Slip-twin interaction types for hex
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select case ( lattice )
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case ( 'cF' )
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interactionTypes = FCC_INTERACTIONSLIPTWIN
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NslipMax = FCC_NSLIPSYSTEM
NtwinMax = FCC_NTWINSYSTEM
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case ( 'cI' )
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interactionTypes = BCC_INTERACTIONSLIPTWIN
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NslipMax = BCC_NSLIPSYSTEM
NtwinMax = BCC_NTWINSYSTEM
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case ( 'hP' )
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interactionTypes = HEX_INTERACTIONSLIPTWIN
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NslipMax = HEX_NSLIPSYSTEM
NtwinMax = HEX_NTWINSYSTEM
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case default
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call IO_error ( 137 , ext_msg = 'lattice_interaction_SlipByTwin: ' / / trim ( lattice ) )
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end select
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interactionMatrix = buildInteraction ( Nslip , Ntwin , NslipMax , NtwinMax , interactionValues , interactionTypes )
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end function lattice_interaction_SlipByTwin
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!--------------------------------------------------------------------------------------------------
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!> @brief Slip-trans interaction matrix
!> details only active slip and trans systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_SlipByTrans ( Nslip , Ntrans , interactionValues , lattice ) result ( interactionMatrix )
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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
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol) (parent crystal)
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real ( pReal ) , dimension ( sum ( Nslip ) , sum ( Ntrans ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NslipMax , &
NtransMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NTRANS , FCC_NSLIP ) , parameter :: &
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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 , &
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4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , 4 , &
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
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select case ( lattice )
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case ( 'cF' )
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interactionTypes = FCC_INTERACTIONSLIPTRANS
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NslipMax = FCC_NSLIPSYSTEM
NtransMax = FCC_NTRANSSYSTEM
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case default
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call IO_error ( 137 , ext_msg = 'lattice_interaction_SlipByTrans: ' / / trim ( lattice ) )
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end select
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interactionMatrix = buildInteraction ( Nslip , Ntrans , NslipMax , NtransMax , interactionValues , interactionTypes )
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end function lattice_interaction_SlipByTrans
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!--------------------------------------------------------------------------------------------------
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!> @brief Twin-slip interaction matrix
!> details only active twin and slip systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_interaction_TwinBySlip ( Ntwin , Nslip , interactionValues , lattice ) result ( interactionMatrix )
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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
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , dimension ( sum ( Ntwin ) , sum ( Nslip ) ) :: interactionMatrix
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integer , dimension ( : ) , allocatable :: NtwinMax , &
NslipMax
integer , dimension ( : , : ) , allocatable :: interactionTypes
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integer , dimension ( FCC_NSLIP , FCC_NTWIN ) , parameter :: &
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FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc
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integer , dimension ( BCC_NSLIP , BCC_NTWIN ) , parameter :: &
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BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc
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integer , dimension ( HEX_NSLIP , HEX_NTWIN ) , parameter :: &
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HEX_INTERACTIONTWINSLIP = reshape ( [ &
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! basal prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , & ! ----> slip (acting)
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , & ! |
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , & ! |
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , & ! v <-10.1>{10.2}
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , & ! twin (reacting)
1 , 1 , 1 , 5 , 5 , 5 , 9 , 9 , 9 , 9 , 9 , 9 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 13 , 17 , 17 , 17 , 17 , 17 , 17 , &
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , &
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , &
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , &
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , & ! <11.6>{-1-1.1}
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , &
2 , 2 , 2 , 6 , 6 , 6 , 10 , 10 , 10 , 10 , 10 , 10 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 14 , 18 , 18 , 18 , 18 , 18 , 18 , &
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , &
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , &
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , &
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , & ! <10.-2>{10.1}
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , &
3 , 3 , 3 , 7 , 7 , 7 , 11 , 11 , 11 , 11 , 11 , 11 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 15 , 19 , 19 , 19 , 19 , 19 , 19 , &
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 , &
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 , &
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 , &
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 , & ! <11.-3>{11.2}
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 , &
4 , 4 , 4 , 8 , 8 , 8 , 12 , 12 , 12 , 12 , 12 , 12 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 16 , 20 , 20 , 20 , 20 , 20 , 20 &
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] , shape ( HEX_INTERACTIONTWINSLIP ) ) !< Twin-slip interaction types for hex
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select case ( lattice )
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case ( 'cF' )
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interactionTypes = FCC_INTERACTIONTWINSLIP
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NtwinMax = FCC_NTWINSYSTEM
NslipMax = FCC_NSLIPSYSTEM
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case ( 'cI' )
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interactionTypes = BCC_INTERACTIONTWINSLIP
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NtwinMax = BCC_NTWINSYSTEM
NslipMax = BCC_NSLIPSYSTEM
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case ( 'hP' )
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interactionTypes = HEX_INTERACTIONTWINSLIP
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NtwinMax = HEX_NTWINSYSTEM
NslipMax = HEX_NSLIPSYSTEM
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case default
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call IO_error ( 137 , ext_msg = 'lattice_interaction_TwinBySlip: ' / / trim ( lattice ) )
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end select
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interactionMatrix = buildInteraction ( Ntwin , Nslip , NtwinMax , NslipMax , interactionValues , interactionTypes )
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end function lattice_interaction_TwinBySlip
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2018-08-25 22:02:55 +05:30
!--------------------------------------------------------------------------------------------------
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!> @brief Schmid matrix for slip
!> details only active slip systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_SchmidMatrix_slip ( Nslip , lattice , cOverA ) result ( SchmidMatrix )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA
real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: SchmidMatrix
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real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: coordinateSystem
real ( pReal ) , dimension ( : , : ) , allocatable :: slipSystems
integer , dimension ( : ) , allocatable :: NslipMax
integer :: i
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select case ( lattice )
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case ( 'cF' )
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NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
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case ( 'cI' )
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NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
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case ( 'hP' )
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NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
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case ( 'tI' )
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NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
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case default
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allocate ( NslipMax ( 0 ) )
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call IO_error ( 137 , ext_msg = 'lattice_SchmidMatrix_slip: ' / / trim ( lattice ) )
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end select
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if ( any ( NslipMax ( 1 : size ( Nslip ) ) - Nslip < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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if ( any ( Nslip < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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coordinateSystem = buildCoordinateSystem ( Nslip , NslipMax , slipSystems , lattice , cOverA )
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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
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2018-09-12 17:33:45 +05:30
end function lattice_SchmidMatrix_slip
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!--------------------------------------------------------------------------------------------------
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!> @brief Schmid matrix for twinning
!> details only active twin systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_SchmidMatrix_twin ( Ntwin , lattice , cOverA ) result ( SchmidMatrix )
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integer , dimension ( : ) , intent ( in ) :: Ntwin !< number of active twin systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , 3 , sum ( Ntwin ) ) :: SchmidMatrix
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real ( pReal ) , dimension ( 3 , 3 , sum ( Ntwin ) ) :: coordinateSystem
real ( pReal ) , dimension ( : , : ) , allocatable :: twinSystems
integer , dimension ( : ) , allocatable :: NtwinMax
integer :: i
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select case ( lattice )
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case ( 'cF' )
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NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
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case ( 'cI' )
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NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
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case ( 'hP' )
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NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
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case default
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allocate ( NtwinMax ( 0 ) )
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call IO_error ( 137 , ext_msg = 'lattice_SchmidMatrix_twin: ' / / trim ( lattice ) )
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end select
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if ( any ( NtwinMax ( 1 : size ( Ntwin ) ) - Ntwin < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Ntwin ' / / trim ( lattice ) )
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if ( any ( Ntwin < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Ntwin ' / / trim ( lattice ) )
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coordinateSystem = buildCoordinateSystem ( Ntwin , NtwinMax , twinSystems , lattice , cOverA )
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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
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end function lattice_SchmidMatrix_twin
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!--------------------------------------------------------------------------------------------------
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!> @brief Schmid matrix for transformation
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!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
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function lattice_SchmidMatrix_trans ( Ntrans , lattice_target , cOverA , a_fcc , a_bcc ) result ( SchmidMatrix )
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integer , dimension ( : ) , intent ( in ) :: Ntrans !< number of active twin systems per family
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character ( len = 2 ) , intent ( in ) :: lattice_target !< Bravais lattice (Pearson symbol)
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real ( pReal ) , optional , intent ( in ) :: cOverA , a_bcc , a_fcc
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real ( pReal ) , dimension ( 3 , 3 , sum ( Ntrans ) ) :: SchmidMatrix
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real ( pReal ) , dimension ( 3 , 3 , sum ( Ntrans ) ) :: devNull
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if ( lattice_target == 'hP' . and . present ( cOverA ) ) then
if ( cOverA < 1.0_pReal . or . cOverA > 2.0_pReal ) &
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call IO_error ( 131 , ext_msg = 'lattice_SchmidMatrix_trans: ' / / trim ( lattice_target ) )
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call buildTransformationSystem ( devNull , SchmidMatrix , Ntrans , cOverA = cOverA )
else if ( lattice_target == 'cI' . and . present ( a_fcc ) . and . present ( a_bcc ) ) then
if ( a_bcc < = 0.0_pReal . or . a_fcc < = 0.0_pReal ) &
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call IO_error ( 134 , ext_msg = 'lattice_SchmidMatrix_trans: ' / / trim ( lattice_target ) )
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call buildTransformationSystem ( devNull , SchmidMatrix , Ntrans , a_fcc = a_fcc , a_bcc = a_bcc )
else
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call IO_error ( 131 , ext_msg = 'lattice_SchmidMatrix_trans: ' / / trim ( lattice_target ) )
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end if
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end function lattice_SchmidMatrix_trans
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!--------------------------------------------------------------------------------------------------
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!> @brief Schmid matrix for cleavage
!> details only active cleavage systems are considered
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!--------------------------------------------------------------------------------------------------
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function lattice_SchmidMatrix_cleavage ( Ncleavage , lattice , cOverA ) result ( SchmidMatrix )
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integer , dimension ( : ) , intent ( in ) :: Ncleavage !< number of active cleavage systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , 3 , 3 , sum ( Ncleavage ) ) :: SchmidMatrix
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real ( pReal ) , dimension ( 3 , 3 , sum ( Ncleavage ) ) :: coordinateSystem
real ( pReal ) , dimension ( : , : ) , allocatable :: cleavageSystems
integer , dimension ( : ) , allocatable :: NcleavageMax
integer :: i
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select case ( lattice )
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case ( 'cF' )
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NcleavageMax = FCC_NCLEAVAGESYSTEM
cleavageSystems = FCC_SYSTEMCLEAVAGE
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case ( 'cI' )
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NcleavageMax = BCC_NCLEAVAGESYSTEM
cleavageSystems = BCC_SYSTEMCLEAVAGE
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case default
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allocate ( NcleavageMax ( 0 ) )
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call IO_error ( 137 , ext_msg = 'lattice_SchmidMatrix_cleavage: ' / / trim ( lattice ) )
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end select
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if ( any ( NcleavageMax ( 1 : size ( Ncleavage ) ) - Ncleavage < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Ncleavage ' / / trim ( lattice ) )
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if ( any ( Ncleavage < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Ncleavage ' / / trim ( lattice ) )
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coordinateSystem = buildCoordinateSystem ( Ncleavage , NcleavageMax , cleavageSystems , lattice , cOverA )
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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
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end function lattice_SchmidMatrix_cleavage
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!--------------------------------------------------------------------------------------------------
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!> @brief Slip direction of slip systems (|| b)
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!--------------------------------------------------------------------------------------------------
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function lattice_slip_direction ( Nslip , lattice , cOverA ) result ( d )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , sum ( Nslip ) ) :: d
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real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: coordinateSystem
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coordinateSystem = coordinateSystem_slip ( Nslip , lattice , cOverA )
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d = coordinateSystem ( 1 : 3 , 1 , 1 : sum ( Nslip ) )
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end function lattice_slip_direction
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!--------------------------------------------------------------------------------------------------
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!> @brief Normal direction of slip systems (|| n)
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!--------------------------------------------------------------------------------------------------
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function lattice_slip_normal ( Nslip , lattice , cOverA ) result ( n )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , sum ( Nslip ) ) :: n
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real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: coordinateSystem
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coordinateSystem = coordinateSystem_slip ( Nslip , lattice , cOverA )
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n = coordinateSystem ( 1 : 3 , 2 , 1 : sum ( Nslip ) )
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end function lattice_slip_normal
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2019-02-20 12:23:34 +05:30
!--------------------------------------------------------------------------------------------------
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!> @brief Transverse direction of slip systems (|| t = b x n)
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!--------------------------------------------------------------------------------------------------
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function lattice_slip_transverse ( Nslip , lattice , cOverA ) result ( t )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , sum ( Nslip ) ) :: t
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real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: coordinateSystem
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coordinateSystem = coordinateSystem_slip ( Nslip , lattice , cOverA )
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t = coordinateSystem ( 1 : 3 , 3 , 1 : sum ( Nslip ) )
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end function lattice_slip_transverse
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!--------------------------------------------------------------------------------------------------
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!> @brief Labels of slip systems
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!> details only active slip systems are considered
!--------------------------------------------------------------------------------------------------
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function lattice_labels_slip ( Nslip , lattice ) result ( labels )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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character ( len = : ) , dimension ( : ) , allocatable :: labels
real ( pReal ) , dimension ( : , : ) , allocatable :: slipSystems
integer , dimension ( : ) , allocatable :: NslipMax
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select case ( lattice )
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case ( 'cF' )
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NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
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case ( 'cI' )
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NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
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case ( 'hP' )
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NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
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case ( 'tI' )
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NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
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case default
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call IO_error ( 137 , ext_msg = 'lattice_labels_slip: ' / / trim ( lattice ) )
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end select
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if ( any ( NslipMax ( 1 : size ( Nslip ) ) - Nslip < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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if ( any ( Nslip < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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labels = getLabels ( Nslip , NslipMax , slipSystems )
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2019-10-10 16:41:02 +05:30
end function lattice_labels_slip
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!--------------------------------------------------------------------------------------------------
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!> @brief Return 3x3 tensor with symmetry according to given Bravais lattice
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!--------------------------------------------------------------------------------------------------
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pure function lattice_symmetrize_33 ( T , lattice ) result ( T_sym )
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real ( pReal ) , dimension ( 3 , 3 ) :: T_sym
real ( pReal ) , dimension ( 3 , 3 ) , intent ( in ) :: T
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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T_sym = 0.0_pReal
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select case ( lattice )
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case ( 'cF' , 'cI' )
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T_sym ( 1 , 1 ) = T ( 1 , 1 )
T_sym ( 2 , 2 ) = T ( 1 , 1 )
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T_sym ( 3 , 3 ) = T ( 1 , 1 )
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case ( 'hP' , 'tI' )
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T_sym ( 1 , 1 ) = T ( 1 , 1 )
T_sym ( 2 , 2 ) = T ( 1 , 1 )
T_sym ( 3 , 3 ) = T ( 3 , 3 )
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end select
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end function lattice_symmetrize_33
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!--------------------------------------------------------------------------------------------------
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!> @brief Return stiffness matrix in 6x6 notation with symmetry according to given Bravais lattice
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!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
!--------------------------------------------------------------------------------------------------
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pure function lattice_symmetrize_C66 ( C66 , lattice ) result ( C66_sym )
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real ( pReal ) , dimension ( 6 , 6 ) :: C66_sym
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: C66
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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integer :: i , j
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C66_sym = 0.0_pReal
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select case ( lattice )
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case ( 'cF' , 'cI' )
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C66_sym ( 1 , 1 ) = C66 ( 1 , 1 ) ; C66_sym ( 2 , 2 ) = C66 ( 1 , 1 ) ; C66_sym ( 3 , 3 ) = C66 ( 1 , 1 )
C66_sym ( 1 , 2 ) = C66 ( 1 , 2 ) ; C66_sym ( 1 , 3 ) = C66 ( 1 , 2 ) ; C66_sym ( 2 , 3 ) = C66 ( 1 , 2 )
C66_sym ( 4 , 4 ) = C66 ( 4 , 4 ) ; C66_sym ( 5 , 5 ) = C66 ( 4 , 4 ) ; C66_sym ( 6 , 6 ) = C66 ( 4 , 4 ) ! isotropic C_44 = (C_11-C_12)/2
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case ( 'hP' )
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C66_sym ( 1 , 1 ) = C66 ( 1 , 1 ) ; C66_sym ( 2 , 2 ) = C66 ( 1 , 1 )
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C66_sym ( 3 , 3 ) = C66 ( 3 , 3 )
C66_sym ( 1 , 2 ) = C66 ( 1 , 2 )
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C66_sym ( 1 , 3 ) = C66 ( 1 , 3 ) ; C66_sym ( 2 , 3 ) = C66 ( 1 , 3 )
C66_sym ( 4 , 4 ) = C66 ( 4 , 4 ) ; C66_sym ( 5 , 5 ) = C66 ( 4 , 4 )
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C66_sym ( 6 , 6 ) = 0.5_pReal * ( C66 ( 1 , 1 ) - C66 ( 1 , 2 ) )
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case ( 'tI' )
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C66_sym ( 1 , 1 ) = C66 ( 1 , 1 ) ; C66_sym ( 2 , 2 ) = C66 ( 1 , 1 )
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C66_sym ( 3 , 3 ) = C66 ( 3 , 3 )
C66_sym ( 1 , 2 ) = C66 ( 1 , 2 )
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C66_sym ( 1 , 3 ) = C66 ( 1 , 3 ) ; C66_sym ( 2 , 3 ) = C66 ( 1 , 3 )
C66_sym ( 4 , 4 ) = C66 ( 4 , 4 ) ; C66_sym ( 5 , 5 ) = C66 ( 4 , 4 )
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C66_sym ( 6 , 6 ) = C66 ( 6 , 6 )
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end select
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do i = 1 , 6
do j = i + 1 , 6
C66_sym ( j , i ) = C66_sym ( i , j )
enddo
enddo
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end function lattice_symmetrize_C66
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2019-10-10 16:41:02 +05:30
!--------------------------------------------------------------------------------------------------
!> @brief Labels for twin systems
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
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function lattice_labels_twin ( Ntwin , lattice ) result ( labels )
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integer , dimension ( : ) , intent ( in ) :: Ntwin !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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character ( len = : ) , dimension ( : ) , allocatable :: labels
real ( pReal ) , dimension ( : , : ) , allocatable :: twinSystems
integer , dimension ( : ) , allocatable :: NtwinMax
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select case ( lattice )
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case ( 'cF' )
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NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
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case ( 'cI' )
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NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
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case ( 'hP' )
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NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
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case default
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call IO_error ( 137 , ext_msg = 'lattice_labels_twin: ' / / trim ( lattice ) )
2019-10-10 16:41:02 +05:30
end select
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if ( any ( NtwinMax ( 1 : size ( Ntwin ) ) - Ntwin < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Ntwin ' / / trim ( lattice ) )
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if ( any ( Ntwin < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Ntwin ' / / trim ( lattice ) )
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labels = getLabels ( Ntwin , NtwinMax , twinSystems )
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2019-10-10 16:41:02 +05:30
end function lattice_labels_twin
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!--------------------------------------------------------------------------------------------------
!> @brief Projection of the transverse direction onto the slip plane
!> @details: This projection is used to calculate forest hardening for edge dislocations
!--------------------------------------------------------------------------------------------------
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function slipProjection_transverse ( Nslip , lattice , cOverA ) result ( projection )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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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
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n = lattice_slip_normal ( Nslip , lattice , cOverA )
t = lattice_slip_transverse ( Nslip , lattice , cOverA )
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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
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!--------------------------------------------------------------------------------------------------
!> @brief Projection of the slip direction onto the slip plane
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!> @details: This projection is used to calculate forest hardening for screw dislocations
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!--------------------------------------------------------------------------------------------------
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function slipProjection_direction ( Nslip , lattice , cOverA ) result ( projection )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( sum ( Nslip ) , sum ( Nslip ) ) :: projection
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real ( pReal ) , dimension ( 3 , sum ( Nslip ) ) :: n , d
integer :: i , j
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n = lattice_slip_normal ( Nslip , lattice , cOverA )
d = lattice_slip_direction ( Nslip , lattice , cOverA )
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do i = 1 , sum ( Nslip ) ; do j = 1 , sum ( Nslip )
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projection ( i , j ) = abs ( math_inner ( n ( : , i ) , d ( : , j ) ) )
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enddo ; enddo
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end function slipProjection_direction
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!--------------------------------------------------------------------------------------------------
!> @brief build a local coordinate system on slip systems
!> @details Order: Direction, plane (normal), and common perpendicular
!--------------------------------------------------------------------------------------------------
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function coordinateSystem_slip ( Nslip , lattice , cOverA ) result ( coordinateSystem )
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integer , dimension ( : ) , intent ( in ) :: Nslip !< number of active slip systems per family
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character ( len = 2 ) , intent ( in ) :: lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: cOverA !< c/a ratio
real ( pReal ) , dimension ( 3 , 3 , sum ( Nslip ) ) :: coordinateSystem
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real ( pReal ) , dimension ( : , : ) , allocatable :: slipSystems
integer , dimension ( : ) , allocatable :: NslipMax
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select case ( lattice )
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case ( 'cF' )
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NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
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case ( 'cI' )
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NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
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case ( 'hP' )
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NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
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case ( 'tI' )
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NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
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case default
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allocate ( NslipMax ( 0 ) )
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call IO_error ( 137 , ext_msg = 'coordinateSystem_slip: ' / / trim ( lattice ) )
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end select
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if ( any ( NslipMax ( 1 : size ( Nslip ) ) - Nslip < 0 ) ) &
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call IO_error ( 145 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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if ( any ( Nslip < 0 ) ) &
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call IO_error ( 144 , ext_msg = 'Nslip ' / / trim ( lattice ) )
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coordinateSystem = buildCoordinateSystem ( Nslip , NslipMax , slipSystems , lattice , cOverA )
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end function coordinateSystem_slip
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!--------------------------------------------------------------------------------------------------
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!> @brief Populate reduced interaction matrix
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!--------------------------------------------------------------------------------------------------
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function buildInteraction ( reacting_used , acting_used , reacting_max , acting_max , values , matrix )
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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
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integer :: &
acting_family_index , acting_family , acting_system , &
reacting_family_index , reacting_family , reacting_system , &
i , j , k , l
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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 )
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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 )
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i = sum ( acting_max ( 1 : acting_family - 1 ) ) + acting_system
j = sum ( reacting_max ( 1 : reacting_family - 1 ) ) + reacting_system
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k = acting_family_index + acting_system
l = reacting_family_index + reacting_system
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if ( matrix ( i , j ) > size ( values ) ) call IO_error ( 138 , ext_msg = 'buildInteraction' )
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buildInteraction ( l , k ) = values ( matrix ( i , j ) )
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enddo ; enddo
enddo ; enddo
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end function buildInteraction
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!--------------------------------------------------------------------------------------------------
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!> @brief Build a local coordinate system on slip, twin, trans, cleavage systems
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!> @details Order: Direction, plane (normal), and common perpendicular
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!--------------------------------------------------------------------------------------------------
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function buildCoordinateSystem ( active , potential , system , lattice , cOverA )
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integer , dimension ( : ) , intent ( in ) :: &
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active , & !< # of active systems per family
potential !< # of potential systems per family
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real ( pReal ) , dimension ( : , : ) , intent ( in ) :: &
system
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character ( len = 2 ) , intent ( in ) :: &
lattice !< Bravais lattice (Pearson symbol)
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real ( pReal ) , intent ( in ) :: &
cOverA
real ( pReal ) , dimension ( 3 , 3 , sum ( active ) ) :: &
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buildCoordinateSystem
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real ( pReal ) , dimension ( 3 ) :: &
direction , normal
integer :: &
a , & !< index of active system
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p , & !< index in potential system matrix
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f , & !< index of my family
s !< index of my system in current family
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if ( lattice == 'tI' . and . cOverA > 2.0_pReal ) &
call IO_error ( 131 , ext_msg = 'buildCoordinateSystem:' / / trim ( lattice ) )
if ( lattice == 'hP' . and . ( cOverA < 1.0_pReal . or . cOverA > 2.0_pReal ) ) &
call IO_error ( 131 , ext_msg = 'buildCoordinateSystem:' / / trim ( lattice ) )
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a = 0
activeFamilies : do f = 1 , size ( active , 1 )
activeSystems : do s = 1 , active ( f )
a = a + 1
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p = sum ( potential ( 1 : f - 1 ) ) + s
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select case ( lattice )
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case ( 'cF' , 'cI' , 'tI' )
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direction = system ( 1 : 3 , p )
normal = system ( 4 : 6 , p )
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case ( 'hP' )
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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))
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case default
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call IO_error ( 137 , ext_msg = 'buildCoordinateSystem: ' / / trim ( lattice ) )
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end select
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buildCoordinateSystem ( 1 : 3 , 1 , a ) = direction / norm2 ( direction )
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buildCoordinateSystem ( 1 : 3 , 2 , a ) = normal / norm2 ( normal )
buildCoordinateSystem ( 1 : 3 , 3 , a ) = math_cross ( direction / norm2 ( direction ) , &
normal / norm2 ( normal ) )
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enddo activeSystems
enddo activeFamilies
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end function buildCoordinateSystem
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!--------------------------------------------------------------------------------------------------
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!> @brief Helper function to define transformation systems
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! Needed to calculate Schmid matrix and rotated stiffness matrices.
! @details: set c/a = 0.0 for fcc -> bcc transformation
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! set a_Xcc = 0.0 for fcc -> hex transformation
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!--------------------------------------------------------------------------------------------------
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subroutine buildTransformationSystem ( Q , S , Ntrans , cOverA , a_fcc , a_bcc )
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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
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real ( pReal ) , optional , intent ( in ) :: &
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cOverA , & !< c/a for target hex lattice
a_bcc , & !< lattice parameter a for bcc target lattice
a_fcc !< lattice parameter a for fcc parent lattice
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type ( tRotation ) :: &
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R , & !< Pitsch rotation
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B !< Rotation of fcc to Bain coordinate system
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real ( pReal ) , dimension ( 3 , 3 ) :: &
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U , & !< Bain deformation
ss , sd
real ( pReal ) , dimension ( 3 ) :: &
x , y , z
integer :: &
i
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real ( pReal ) , dimension ( 3 + 3 , FCC_NTRANS ) , parameter :: &
FCCTOHEX_SYSTEMTRANS = reshape ( real ( [ &
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- 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 &
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] , pReal ) , shape ( FCCTOHEX_SYSTEMTRANS ) )
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real ( pReal ) , dimension ( 4 , fcc_Ntrans ) , parameter :: &
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FCCTOBCC_SYSTEMTRANS = reshape ( [ &
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0.0 , 1.0 , 0.0 , 1 0.26 , & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
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0.0 , - 1.0 , 0.0 , 1 0.26 , &
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0.0 , 0.0 , 1.0 , 1 0.26 , &
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0.0 , 0.0 , - 1.0 , 1 0.26 , &
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1.0 , 0.0 , 0.0 , 1 0.26 , &
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- 1.0 , 0.0 , 0.0 , 1 0.26 , &
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0.0 , 0.0 , 1.0 , 1 0.26 , &
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0.0 , 0.0 , - 1.0 , 1 0.26 , &
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1.0 , 0.0 , 0.0 , 1 0.26 , &
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- 1.0 , 0.0 , 0.0 , 1 0.26 , &
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0.0 , 1.0 , 0.0 , 1 0.26 , &
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0.0 , - 1.0 , 0.0 , 1 0.26 &
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] , shape ( FCCTOBCC_SYSTEMTRANS ) )
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integer , dimension ( 9 , fcc_Ntrans ) , parameter :: &
FCCTOBCC_BAINVARIANT = reshape ( [ &
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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 &
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] , shape ( FCCTOBCC_BAINVARIANT ) )
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real ( pReal ) , dimension ( 4 , fcc_Ntrans ) , parameter :: &
FCCTOBCC_BAINROT = reshape ( [ &
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1.0 , 0.0 , 0.0 , 4 5.0 , & ! Rotate fcc austensite to bain variant
1.0 , 0.0 , 0.0 , 4 5.0 , &
1.0 , 0.0 , 0.0 , 4 5.0 , &
1.0 , 0.0 , 0.0 , 4 5.0 , &
0.0 , 1.0 , 0.0 , 4 5.0 , &
0.0 , 1.0 , 0.0 , 4 5.0 , &
0.0 , 1.0 , 0.0 , 4 5.0 , &
0.0 , 1.0 , 0.0 , 4 5.0 , &
0.0 , 0.0 , 1.0 , 4 5.0 , &
0.0 , 0.0 , 1.0 , 4 5.0 , &
0.0 , 0.0 , 1.0 , 4 5.0 , &
0.0 , 0.0 , 1.0 , 4 5.0 &
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] , shape ( FCCTOBCC_BAINROT ) )
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if ( present ( a_bcc ) . and . present ( a_fcc ) ) then
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do i = 1 , sum ( Ntrans )
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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 )
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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 )
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Q ( 1 : 3 , 1 : 3 , i ) = matmul ( R % asMatrix ( ) , B % asMatrix ( ) )
S ( 1 : 3 , 1 : 3 , i ) = matmul ( R % asMatrix ( ) , U ) - MATH_I3
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enddo
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else if ( present ( cOverA ) ) then
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ss = MATH_I3
sd = MATH_I3
ss ( 1 , 3 ) = sqrt ( 2.0_pReal ) / 4.0_pReal
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sd ( 3 , 3 ) = cOverA / sqrt ( 8.0_pReal / 3.0_pReal )
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do i = 1 , sum ( Ntrans )
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x = FCCTOHEX_SYSTEMTRANS ( 1 : 3 , i ) / norm2 ( FCCTOHEX_SYSTEMTRANS ( 1 : 3 , i ) )
z = FCCTOHEX_SYSTEMTRANS ( 4 : 6 , i ) / norm2 ( FCCTOHEX_SYSTEMTRANS ( 4 : 6 , i ) )
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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
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end do
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else
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call IO_error ( 132 , ext_msg = 'buildTransformationSystem' )
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end if
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end subroutine buildTransformationSystem
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!--------------------------------------------------------------------------------------------------
!> @brief select active systems as strings
!--------------------------------------------------------------------------------------------------
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function getlabels ( active , potential , system ) result ( labels )
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integer , dimension ( : ) , intent ( in ) :: &
active , & !< # of active systems per family
potential !< # of potential systems per family
real ( pReal ) , dimension ( : , : ) , intent ( in ) :: &
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system
character ( len = : ) , dimension ( : ) , allocatable :: labels
character ( len = : ) , allocatable :: label
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integer :: i , j
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integer :: &
a , & !< index of active system
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p , & !< index in potential system matrix
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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 )
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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
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i = 1
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label ( i : i ) = '['
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direction : do j = 1 , size ( system , 1 ) / 2
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write ( label ( i + 1 : i + 2 ) , '(I2.1)' ) int ( system ( j , p ) )
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label ( i + 3 : i + 3 ) = ' '
i = i + 3
enddo direction
label ( i : i ) = ']'
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i = i + 1
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label ( i : i ) = '('
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normal : do j = size ( system , 1 ) / 2 + 1 , size ( system , 1 )
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write ( label ( i + 1 : i + 2 ) , '(I2.1)' ) int ( system ( j , p ) )
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label ( i + 3 : i + 3 ) = ' '
i = i + 3
enddo normal
label ( i : i ) = ')'
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labels ( a ) = label
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enddo activeSystems
enddo activeFamilies
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end function getlabels
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!--------------------------------------------------------------------------------------------------
!> @brief Equivalent Poisson's ratio (ν )
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
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pure function lattice_equivalent_nu ( C , assumption ) result ( nu )
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: C !< Stiffness tensor (Voigt notation)
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character ( len = 5 ) , intent ( in ) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
real ( pReal ) :: nu
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real ( pReal ) :: K , mu
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logical :: error
real ( pReal ) , dimension ( 6 , 6 ) :: S
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if ( IO_lc ( assumption ) == 'voigt' ) then
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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
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elseif ( IO_lc ( assumption ) == 'reuss' ) then
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call math_invert ( S , error , C )
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if ( error ) error stop 'matrix inversion failed'
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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
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error stop 'invalid assumption'
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endif
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mu = lattice_equivalent_mu ( C , assumption )
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nu = ( 1.5_pReal * K - mu ) / ( 3.0_pReal * K + mu )
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end function lattice_equivalent_nu
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!--------------------------------------------------------------------------------------------------
!> @brief Equivalent shear modulus (μ)
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
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pure function lattice_equivalent_mu ( C , assumption ) result ( mu )
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real ( pReal ) , dimension ( 6 , 6 ) , intent ( in ) :: C !< Stiffness tensor (Voigt notation)
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character ( len = 5 ) , intent ( in ) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
real ( pReal ) :: mu
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logical :: error
real ( pReal ) , dimension ( 6 , 6 ) :: S
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if ( IO_lc ( assumption ) == 'voigt' ) then
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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 ) ) ) &
/ 1 5.0_pReal
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elseif ( IO_lc ( assumption ) == 'reuss' ) then
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call math_invert ( S , error , C )
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if ( error ) error stop 'matrix inversion failed'
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mu = 1 5.0_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
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error stop 'invalid assumption'
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endif
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end function lattice_equivalent_mu
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!--------------------------------------------------------------------------------------------------
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!> @brief Check correctness of some lattice functions.
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!--------------------------------------------------------------------------------------------------
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subroutine selfTest
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real ( pReal ) , dimension ( : , : , : ) , allocatable :: CoSy
real ( pReal ) , dimension ( : , : ) , allocatable :: system
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real ( pReal ) , dimension ( 6 , 6 ) :: C , C_cF , C_cI , C_hP , C_tI
real ( pReal ) , dimension ( 3 , 3 ) :: T , T_cF , T_cI , T_hP , T_tI
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real ( pReal ) , dimension ( 2 ) :: r
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real ( pReal ) :: lambda
integer :: i
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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 ] )
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CoSy = buildCoordinateSystem ( [ 1 ] , [ 1 ] , system , 'cF' , 0.0_pReal )
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if ( any ( dNeq ( CoSy ( 1 : 3 , 1 : 3 , 1 ) , math_I3 ) ) ) error stop 'buildCoordinateSystem'
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do i = 1 , 10
call random_number ( C )
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C_cF = lattice_symmetrize_C66 ( C , 'cI' )
C_cI = lattice_symmetrize_C66 ( C , 'cF' )
C_hP = lattice_symmetrize_C66 ( C , 'hP' )
C_tI = lattice_symmetrize_C66 ( C , 'tI' )
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if ( any ( dNeq ( C_cI , transpose ( C_cF ) ) ) ) error stop 'SymmetryC66/cI-cF'
if ( any ( dNeq ( C_cF , transpose ( C_cI ) ) ) ) error stop 'SymmetryC66/cF-cI'
if ( any ( dNeq ( C_hP , transpose ( C_hP ) ) ) ) error stop 'SymmetryC66/hP'
if ( any ( dNeq ( C_tI , transpose ( C_tI ) ) ) ) error stop 'SymmetryC66/tI'
if ( any ( dNeq ( C ( 1 , 1 ) , [ C_cF ( 1 , 1 ) , C_cF ( 2 , 2 ) , C_cF ( 3 , 3 ) ] ) ) ) error stop 'SymmetryC_11-22-33/c'
if ( any ( dNeq ( C ( 1 , 2 ) , [ C_cF ( 1 , 2 ) , C_cF ( 1 , 3 ) , C_cF ( 2 , 3 ) ] ) ) ) error stop 'SymmetryC_12-13-23/c'
if ( any ( dNeq ( C ( 4 , 4 ) , [ C_cF ( 4 , 4 ) , C_cF ( 5 , 5 ) , C_cF ( 6 , 6 ) ] ) ) ) error stop 'SymmetryC_44-55-66/c'
if ( any ( dNeq ( C ( 1 , 1 ) , [ C_hP ( 1 , 1 ) , C_hP ( 2 , 2 ) ] ) ) ) error stop 'SymmetryC_11-22/hP'
if ( any ( dNeq ( C ( 1 , 3 ) , [ C_hP ( 1 , 3 ) , C_hP ( 2 , 3 ) ] ) ) ) error stop 'SymmetryC_13-23/hP'
if ( any ( dNeq ( C ( 4 , 4 ) , [ C_hP ( 4 , 4 ) , C_hP ( 5 , 5 ) ] ) ) ) error stop 'SymmetryC_44-55/hP'
if ( any ( dNeq ( C ( 1 , 1 ) , [ C_tI ( 1 , 1 ) , C_tI ( 2 , 2 ) ] ) ) ) error stop 'SymmetryC_11-22/tI'
if ( any ( dNeq ( C ( 1 , 3 ) , [ C_tI ( 1 , 3 ) , C_tI ( 2 , 3 ) ] ) ) ) error stop 'SymmetryC_13-23/tI'
if ( any ( dNeq ( C ( 4 , 4 ) , [ C_tI ( 4 , 4 ) , C_tI ( 5 , 5 ) ] ) ) ) error stop 'SymmetryC_44-55/tI'
call random_number ( T )
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T_cF = lattice_symmetrize_33 ( T , 'cI' )
T_cI = lattice_symmetrize_33 ( T , 'cF' )
T_hP = lattice_symmetrize_33 ( T , 'hP' )
T_tI = lattice_symmetrize_33 ( T , 'tI' )
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if ( any ( dNeq0 ( T_cF ) . and . math_I3 < 1.0_pReal ) ) error stop 'Symmetry33/c'
if ( any ( dNeq0 ( T_hP ) . and . math_I3 < 1.0_pReal ) ) error stop 'Symmetry33/hP'
if ( any ( dNeq0 ( T_tI ) . and . math_I3 < 1.0_pReal ) ) error stop 'Symmetry33/tI'
if ( any ( dNeq ( T ( 1 , 1 ) , [ T_cI ( 1 , 1 ) , T_cI ( 2 , 2 ) , T_cI ( 3 , 3 ) ] ) ) ) error stop 'Symmetry33_11-22-33/c'
if ( any ( dNeq ( T ( 1 , 1 ) , [ T_hP ( 1 , 1 ) , T_hP ( 2 , 2 ) ] ) ) ) error stop 'Symmetry33_11-22/hP'
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if ( any ( dNeq ( T ( 1 , 1 ) , [ T_tI ( 1 , 1 ) , T_tI ( 2 , 2 ) ] ) ) ) error stop 'Symmetry33_11-22/tI'
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enddo
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call random_number ( C )
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C ( 1 , 1 ) = C ( 1 , 1 ) + C ( 1 , 2 ) + 0.1_pReal
C ( 4 , 4 ) = 0.5_pReal * ( C ( 1 , 1 ) - C ( 1 , 2 ) )
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C = lattice_symmetrize_C66 ( C , 'cI' )
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if ( dNeq ( C ( 4 , 4 ) , lattice_equivalent_mu ( C , 'voigt' ) , 1.0e-12_pReal ) ) error stop 'equivalent_mu/voigt'
if ( dNeq ( C ( 4 , 4 ) , lattice_equivalent_mu ( C , 'reuss' ) , 1.0e-12_pReal ) ) error stop 'equivalent_mu/reuss'
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lambda = C ( 1 , 2 )
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if ( dNeq ( lambda * 0.5_pReal / ( lambda + lattice_equivalent_mu ( C , 'voigt' ) ) , &
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lattice_equivalent_nu ( C , 'voigt' ) , 1.0e-12_pReal ) ) error stop 'equivalent_nu/voigt'
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if ( dNeq ( lambda * 0.5_pReal / ( lambda + lattice_equivalent_mu ( C , 'reuss' ) ) , &
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lattice_equivalent_nu ( C , 'reuss' ) , 1.0e-12_pReal ) ) error stop 'equivalent_nu/reuss'
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end subroutine selfTest
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end module lattice