2368 lines
128 KiB
Fortran
2368 lines
128 KiB
Fortran
!--------------------------------------------------------------------------------------------------
|
||
!> @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
|
||
!> @brief contains lattice structure definitions including Schmid matrices for slip, twin, trans,
|
||
! and cleavage as well as interaction among the various systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
module lattice
|
||
use prec
|
||
use IO
|
||
use config
|
||
use math
|
||
use rotations
|
||
|
||
implicit none
|
||
private
|
||
|
||
! BEGIN DEPRECATED
|
||
integer, parameter, public :: &
|
||
LATTICE_maxNcleavageFamily = 3 !< max # of transformation system families over lattice structures
|
||
|
||
integer, allocatable, dimension(:,:), protected, public :: &
|
||
lattice_NcleavageSystem !< total # of transformation systems in each family
|
||
|
||
real(pReal), allocatable, dimension(:,:,:,:,:), protected, public :: &
|
||
lattice_Scleavage !< Schmid matrices for cleavage systems
|
||
! END DEPRECATED
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! face centered cubic
|
||
integer, dimension(2), parameter :: &
|
||
LATTICE_FCC_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for fcc
|
||
|
||
integer, dimension(1), parameter :: &
|
||
LATTICE_FCC_NTWINSYSTEM = [12] !< # of twin systems per family for fcc
|
||
|
||
integer, dimension(1), parameter :: &
|
||
LATTICE_FCC_NTRANSSYSTEM = [12] !< # of transformation systems per family for fcc
|
||
|
||
integer, dimension(2), parameter :: &
|
||
LATTICE_FCC_NCLEAVAGESYSTEM = [3, 4] !< # of cleavage systems per family for fcc
|
||
|
||
integer, parameter :: &
|
||
LATTICE_FCC_NSLIP = sum(LATTICE_FCC_NSLIPSYSTEM), & !< total # of slip systems for fcc
|
||
LATTICE_FCC_NTWIN = sum(LATTICE_FCC_NTWINSYSTEM), & !< total # of twin systems for fcc
|
||
LATTICE_FCC_NTRANS = sum(LATTICE_FCC_NTRANSSYSTEM), & !< total # of transformation systems for fcc
|
||
LATTICE_FCC_NCLEAVAGE = sum(LATTICE_FCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for fcc
|
||
|
||
real(pReal), dimension(3+3,LATTICE_FCC_NSLIP), parameter :: &
|
||
LATTICE_FCC_SYSTEMSLIP = reshape(real([&
|
||
! Slip direction Plane normal ! SCHMID-BOAS notation
|
||
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
|
||
! Slip system <110>{110}
|
||
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 &
|
||
],pReal),shape(LATTICE_FCC_SYSTEMSLIP)) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli
|
||
|
||
real(pReal), dimension(3+3,LATTICE_FCC_NTWIN), parameter :: &
|
||
LATTICE_FCC_SYSTEMTWIN = reshape(real( [&
|
||
-2, 1, 1, 1, 1, 1, &
|
||
1,-2, 1, 1, 1, 1, &
|
||
1, 1,-2, 1, 1, 1, &
|
||
2,-1, 1, -1,-1, 1, &
|
||
-1, 2, 1, -1,-1, 1, &
|
||
-1,-1,-2, -1,-1, 1, &
|
||
-2,-1,-1, 1,-1,-1, &
|
||
1, 2,-1, 1,-1,-1, &
|
||
1,-1, 2, 1,-1,-1, &
|
||
2, 1,-1, -1, 1,-1, &
|
||
-1,-2,-1, -1, 1,-1, &
|
||
-1, 1, 2, -1, 1,-1 &
|
||
],pReal),shape(LATTICE_FCC_SYSTEMTWIN)) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli
|
||
|
||
integer, dimension(2,LATTICE_FCC_NTWIN), parameter, public :: &
|
||
LATTICE_FCC_TWINNUCLEATIONSLIPPAIR = reshape( [&
|
||
2,3, &
|
||
1,3, &
|
||
1,2, &
|
||
5,6, &
|
||
4,6, &
|
||
4,5, &
|
||
8,9, &
|
||
7,9, &
|
||
7,8, &
|
||
11,12, &
|
||
10,12, &
|
||
10,11 &
|
||
],shape(LATTICE_FCC_TWINNUCLEATIONSLIPPAIR))
|
||
|
||
real(pReal), dimension(3+3,LATTICE_FCC_NCLEAVAGE), parameter :: &
|
||
LATTICE_FCC_SYSTEMCLEAVAGE = reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
0, 1, 0, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
1, 0, 0, 0, 0, 1, &
|
||
0, 1,-1, 1, 1, 1, &
|
||
0,-1,-1, -1,-1, 1, &
|
||
-1, 0,-1, 1,-1,-1, &
|
||
0, 1, 1, -1, 1,-1 &
|
||
],pReal),shape(LATTICE_FCC_SYSTEMCLEAVAGE))
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! body centered cubic
|
||
integer, dimension(2), parameter :: &
|
||
LATTICE_BCC_NSLIPSYSTEM = [12, 12] !< # of slip systems per family for bcc
|
||
|
||
integer, dimension(1), parameter :: &
|
||
LATTICE_BCC_NTWINSYSTEM = [12] !< # of twin systems per family for bcc
|
||
|
||
integer, dimension(2), parameter :: &
|
||
LATTICE_BCC_NCLEAVAGESYSTEM = [3, 6] !< # of cleavage systems per family for bcc
|
||
|
||
integer, parameter :: &
|
||
LATTICE_BCC_NSLIP = sum(LATTICE_BCC_NSLIPSYSTEM), & !< total # of slip systems for bcc
|
||
LATTICE_BCC_NTWIN = sum(LATTICE_BCC_NTWINSYSTEM), & !< total # of twin systems for bcc
|
||
LATTICE_BCC_NCLEAVAGE = sum(LATTICE_BCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for bcc
|
||
|
||
real(pReal), dimension(3+3,LATTICE_BCC_NSLIP), parameter :: &
|
||
LATTICE_BCC_SYSTEMSLIP = reshape(real([&
|
||
! Slip direction Plane normal
|
||
! Slip system <111>{110}
|
||
1,-1, 1, 0, 1, 1, &
|
||
-1,-1, 1, 0, 1, 1, &
|
||
1, 1, 1, 0,-1, 1, &
|
||
-1, 1, 1, 0,-1, 1, &
|
||
-1, 1, 1, 1, 0, 1, &
|
||
-1,-1, 1, 1, 0, 1, &
|
||
1, 1, 1, -1, 0, 1, &
|
||
1,-1, 1, -1, 0, 1, &
|
||
-1, 1, 1, 1, 1, 0, &
|
||
-1, 1,-1, 1, 1, 0, &
|
||
1, 1, 1, -1, 1, 0, &
|
||
1, 1,-1, -1, 1, 0, &
|
||
! Slip system <111>{112}
|
||
-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 &
|
||
],pReal),shape(LATTICE_BCC_SYSTEMSLIP))
|
||
|
||
real(pReal), dimension(3+3,LATTICE_BCC_NTWIN), parameter :: &
|
||
LATTICE_BCC_SYSTEMTWIN = reshape(real([&
|
||
! Twin system <111>{112}
|
||
-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 &
|
||
],pReal),shape(LATTICE_BCC_SYSTEMTWIN))
|
||
|
||
real(pReal), dimension(3+3,LATTICE_BCC_NCLEAVAGE), parameter :: &
|
||
LATTICE_BCC_SYSTEMCLEAVAGE = reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
0, 1, 0, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
1, 0, 0, 0, 0, 1, &
|
||
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, 1, 0, &
|
||
1, 1, 1, -1, 1, 0 &
|
||
],pReal),shape(LATTICE_BCC_SYSTEMCLEAVAGE))
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! hexagonal
|
||
integer, dimension(6), parameter :: &
|
||
LATTICE_HEX_NSLIPSYSTEM = [3, 3, 3, 6, 12, 6] !< # of slip systems per family for hex
|
||
|
||
integer, dimension(4), parameter :: &
|
||
LATTICE_HEX_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hex
|
||
|
||
integer, dimension(1), parameter :: &
|
||
LATTICE_HEX_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for hex
|
||
|
||
integer, parameter :: &
|
||
LATTICE_HEX_NSLIP = sum(LATTICE_HEX_NSLIPSYSTEM), & !< total # of slip systems for hex
|
||
LATTICE_HEX_NTWIN = sum(LATTICE_HEX_NTWINSYSTEM), & !< total # of twin systems for hex
|
||
LATTICE_HEX_NCLEAVAGE = sum(LATTICE_HEX_NCLEAVAGESYSTEM) !< total # of cleavage systems for hex
|
||
|
||
real(pReal), dimension(4+4,LATTICE_HEX_NSLIP), parameter :: &
|
||
LATTICE_HEX_SYSTEMSLIP = reshape(real([&
|
||
! Slip direction Plane normal
|
||
! Basal systems <-1-1.0>{00.1} (independent of c/a-ratio, Bravais notation (4 coordinate base))
|
||
2, -1, -1, 0, 0, 0, 0, 1, &
|
||
-1, 2, -1, 0, 0, 0, 0, 1, &
|
||
-1, -1, 2, 0, 0, 0, 0, 1, &
|
||
! 1st type prismatic systems <-1-1.0>{1-1.0} (independent of c/a-ratio)
|
||
2, -1, -1, 0, 0, 1, -1, 0, &
|
||
-1, 2, -1, 0, -1, 0, 1, 0, &
|
||
-1, -1, 2, 0, 1, -1, 0, 0, &
|
||
! 2nd type prismatic systems <-11.0>{11.0} -- a slip; plane normals independent of c/a-ratio
|
||
-1, 1, 0, 0, 1, 1, -2, 0, &
|
||
0, -1, 1, 0, -2, 1, 1, 0, &
|
||
1, 0, -1, 0, 1, -2, 1, 0, &
|
||
! 1st type 1st order pyramidal systems <-1-1.0>{-11.1} -- plane normals depend on the c/a-ratio
|
||
-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, &
|
||
! pyramidal system: c+a slip <11.3>{-10.1} -- plane normals depend on the c/a-ratio
|
||
-2, 1, 1, 3, 1, 0, -1, 1, &
|
||
-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, &
|
||
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, &
|
||
! pyramidal system: c+a slip <11.3>{-1-1.2} -- as for hexagonal ice (Castelnau et al. 1996, similar to twin system found below)
|
||
-1, -1, 2, 3, 1, 1, -2, 2, & ! <11.3>{-1-1.2} shear = 2((c/a)^2-2)/(3 c/a)
|
||
1, -2, 1, 3, -1, 2, -1, 2, &
|
||
2, -1, -1, 3, -2, 1, 1, 2, &
|
||
1, 1, -2, 3, -1, -1, 2, 2, &
|
||
-1, 2, -1, 3, 1, -2, 1, 2, &
|
||
-2, 1, 1, 3, 2, -1, -1, 2 &
|
||
],pReal),shape(LATTICE_HEX_SYSTEMSLIP)) !< slip systems for hex, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
|
||
|
||
real(pReal), dimension(4+4,LATTICE_HEX_NTWIN), parameter :: &
|
||
LATTICE_HEX_SYSTEMTWIN = reshape(real([&
|
||
! Compression or Tension = f(twinning shear=f(c/a)) for each metal ! (according to Yoo 1981)
|
||
-1, 0, 1, 1, 1, 0, -1, 2, & ! <-10.1>{10.2} shear = (3-(c/a)^2)/(sqrt(3) c/a)
|
||
0, -1, 1, 1, 0, 1, -1, 2, &
|
||
1, -1, 0, 1, -1, 1, 0, 2, &
|
||
1, 0, -1, 1, -1, 0, 1, 2, &
|
||
0, 1, -1, 1, 0, -1, 1, 2, &
|
||
-1, 1, 0, 1, 1, -1, 0, 2, &
|
||
!
|
||
-1, -1, 2, 6, 1, 1, -2, 1, & ! <11.6>{-1-1.1} shear = 1/(c/a)
|
||
1, -2, 1, 6, -1, 2, -1, 1, &
|
||
2, -1, -1, 6, -2, 1, 1, 1, &
|
||
1, 1, -2, 6, -1, -1, 2, 1, &
|
||
-1, 2, -1, 6, 1, -2, 1, 1, &
|
||
-2, 1, 1, 6, 2, -1, -1, 1, &
|
||
!
|
||
1, 0, -1, -2, 1, 0, -1, 1, & ! <10.-2>{10.1} shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
|
||
0, 1, -1, -2, 0, 1, -1, 1, &
|
||
-1, 1, 0, -2, -1, 1, 0, 1, &
|
||
-1, 0, 1, -2, -1, 0, 1, 1, &
|
||
0, -1, 1, -2, 0, -1, 1, 1, &
|
||
1, -1, 0, -2, 1, -1, 0, 1, &
|
||
!
|
||
1, 1, -2, -3, 1, 1, -2, 2, & ! <11.-3>{11.2} shear = 2((c/a)^2-2)/(3 c/a)
|
||
-1, 2, -1, -3, -1, 2, -1, 2, &
|
||
-2, 1, 1, -3, -2, 1, 1, 2, &
|
||
-1, -1, 2, -3, -1, -1, 2, 2, &
|
||
1, -2, 1, -3, 1, -2, 1, 2, &
|
||
2, -1, -1, -3, 2, -1, -1, 2 &
|
||
],pReal),shape(LATTICE_HEX_SYSTEMTWIN)) !< twin systems for hex, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
|
||
|
||
real(pReal), dimension(4+4,LATTICE_HEX_NCLEAVAGE), parameter :: &
|
||
LATTICE_HEX_SYSTEMCLEAVAGE = reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
2,-1,-1, 0, 0, 0, 0, 1, &
|
||
0, 0, 0, 1, 2,-1,-1, 0, &
|
||
0, 0, 0, 1, 0, 1,-1, 0 &
|
||
],pReal),shape(LATTICE_HEX_SYSTEMCLEAVAGE))
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! body centered tetragonal
|
||
integer, dimension(13), parameter :: &
|
||
LATTICE_BCT_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for bct (Sn) Bieler J. Electr Mater 2009
|
||
|
||
integer, parameter :: &
|
||
LATTICE_BCT_NSLIP = sum(LATTICE_BCT_NSLIPSYSTEM) !< total # of slip systems for bct
|
||
|
||
real(pReal), dimension(3+3,LATTICE_BCT_NSLIP), parameter :: &
|
||
LATTICE_BCT_SYSTEMSLIP = reshape(real([&
|
||
! Slip direction Plane normal
|
||
! Slip family 1 {100)<001] (Bravais notation {hkl)<uvw] for bct c/a = 0.5456)
|
||
0, 0, 1, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
! Slip family 2 {110)<001]
|
||
0, 0, 1, 1, 1, 0, &
|
||
0, 0, 1, -1, 1, 0, &
|
||
! slip family 3 {100)<010]
|
||
0, 1, 0, 1, 0, 0, &
|
||
1, 0, 0, 0, 1, 0, &
|
||
! Slip family 4 {110)<1-11]/2
|
||
1,-1, 1, 1, 1, 0, &
|
||
1,-1,-1, 1, 1, 0, &
|
||
-1,-1,-1, -1, 1, 0, &
|
||
-1,-1, 1, -1, 1, 0, &
|
||
! Slip family 5 {110)<1-10]
|
||
1, -1, 0, 1, 1, 0, &
|
||
1, 1, 0, 1,-1, 0, &
|
||
! Slip family 6 {100)<011]
|
||
0, 1, 1, 1, 0, 0, &
|
||
0,-1, 1, 1, 0, 0, &
|
||
-1, 0, 1, 0, 1, 0, &
|
||
1, 0, 1, 0, 1, 0, &
|
||
! Slip family 7 {001)<010]
|
||
0, 1, 0, 0, 0, 1, &
|
||
1, 0, 0, 0, 0, 1, &
|
||
! Slip family 8 {001)<110]
|
||
1, 1, 0, 0, 0, 1, &
|
||
-1, 1, 0, 0, 0, 1, &
|
||
! Slip family 9 {011)<01-1]
|
||
0, 1,-1, 0, 1, 1, &
|
||
0,-1,-1, 0,-1, 1, &
|
||
-1, 0,-1, -1, 0, 1, &
|
||
1, 0,-1, 1, 0, 1, &
|
||
! Slip family 10 {011)<1-11]/2
|
||
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, &
|
||
! Slip family 11 {011)<100]
|
||
1, 0, 0, 0, 1, 1, &
|
||
1, 0, 0, 0, 1,-1, &
|
||
0, 1, 0, 1, 0, 1, &
|
||
0, 1, 0, 1, 0,-1, &
|
||
! Slip family 12 {211)<01-1]
|
||
0, 1,-1, 2, 1, 1, &
|
||
0,-1,-1, 2,-1, 1, &
|
||
1, 0,-1, 1, 2, 1, &
|
||
-1, 0,-1, -1, 2, 1, &
|
||
0, 1,-1, -2, 1, 1, &
|
||
0,-1,-1, -2,-1, 1, &
|
||
-1, 0,-1, -1,-2, 1, &
|
||
1, 0,-1, 1,-2, 1, &
|
||
! Slip family 13 {211)<-111]/2
|
||
-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 &
|
||
],pReal),[ 3 + 3,LATTICE_BCT_NSLIP]) !< slip systems for bct sorted by Bieler
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! isotropic
|
||
integer, dimension(1), parameter :: &
|
||
LATTICE_ISO_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for iso
|
||
|
||
integer, parameter :: &
|
||
LATTICE_ISO_NCLEAVAGE = sum(LATTICE_ISO_NCLEAVAGESYSTEM) !< total # of cleavage systems for iso
|
||
|
||
real(pReal), dimension(3+3,LATTICE_ISO_NCLEAVAGE), parameter :: &
|
||
LATTICE_ISO_SYSTEMCLEAVAGE= reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
0, 1, 0, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
1, 0, 0, 0, 0, 1 &
|
||
],pReal),[ 3 + 3,LATTICE_ISO_NCLEAVAGE])
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! orthorhombic
|
||
integer, dimension(3), parameter :: &
|
||
LATTICE_ORT_NCLEAVAGESYSTEM = [1, 1, 1] !< # of cleavage systems per family for ortho
|
||
|
||
integer, parameter :: &
|
||
LATTICE_ORT_NCLEAVAGE = sum(LATTICE_ORT_NCLEAVAGESYSTEM) !< total # of cleavage systems for ortho
|
||
|
||
real(pReal), dimension(3+3,LATTICE_ORT_NCLEAVAGE), parameter :: &
|
||
LATTICE_ORT_SYSTEMCLEAVAGE = reshape(real([&
|
||
! Cleavage direction Plane normal
|
||
0, 1, 0, 1, 0, 0, &
|
||
0, 0, 1, 0, 1, 0, &
|
||
1, 0, 0, 0, 0, 1 &
|
||
],pReal),[ 3 + 3,LATTICE_ORT_NCLEAVAGE])
|
||
|
||
|
||
|
||
! BEGIN DEPRECATED
|
||
integer, parameter, public :: &
|
||
LATTICE_maxNcleavage = max(LATTICE_fcc_Ncleavage,LATTICE_bcc_Ncleavage, &
|
||
LATTICE_hex_Ncleavage, &
|
||
LATTICE_iso_Ncleavage,LATTICE_ort_Ncleavage)
|
||
! END DEPRECATED
|
||
|
||
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
|
||
lattice_C66
|
||
real(pReal), dimension(:,:,:,:,:), allocatable, public, protected :: &
|
||
lattice_C3333
|
||
real(pReal), dimension(:), allocatable, public, protected :: &
|
||
lattice_mu, lattice_nu
|
||
|
||
! SHOULD NOT BE PART OF LATTICE BEGIN
|
||
real(pReal), dimension(:,:,:,:), allocatable, public, protected :: & ! with higher-order parameters (e.g. temperature-dependent)
|
||
lattice_thermalExpansion33
|
||
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
|
||
lattice_thermalConductivity33, &
|
||
lattice_damageDiffusion33
|
||
real(pReal), dimension(:), allocatable, public, protected :: &
|
||
lattice_damageMobility, &
|
||
lattice_massDensity, &
|
||
lattice_specificHeat, &
|
||
lattice_referenceTemperature
|
||
! SHOULD NOT BE PART OF LATTICE END
|
||
|
||
enum, bind(c)
|
||
enumerator :: LATTICE_undefined_ID, &
|
||
LATTICE_iso_ID, &
|
||
LATTICE_fcc_ID, &
|
||
LATTICE_bcc_ID, &
|
||
LATTICE_hex_ID, &
|
||
LATTICE_bct_ID, &
|
||
LATTICE_ort_ID
|
||
end enum
|
||
|
||
integer(kind(LATTICE_undefined_ID)), dimension(:), allocatable, public, protected :: &
|
||
lattice_structure
|
||
|
||
interface lattice_forestProjection_edge
|
||
module procedure slipProjection_transverse
|
||
end interface lattice_forestProjection_edge
|
||
|
||
interface lattice_forestProjection_screw
|
||
module procedure slipProjection_direction
|
||
end interface lattice_forestProjection_screw
|
||
|
||
public :: &
|
||
lattice_init, &
|
||
LATTICE_iso_ID, &
|
||
LATTICE_fcc_ID, &
|
||
LATTICE_bcc_ID, &
|
||
LATTICE_bct_ID, &
|
||
LATTICE_hex_ID, &
|
||
LATTICE_ort_ID, &
|
||
lattice_SchmidMatrix_slip, &
|
||
lattice_SchmidMatrix_twin, &
|
||
lattice_SchmidMatrix_trans, &
|
||
lattice_SchmidMatrix_cleavage, &
|
||
lattice_nonSchmidMatrix, &
|
||
lattice_interaction_SlipBySlip, &
|
||
lattice_interaction_TwinByTwin, &
|
||
lattice_interaction_TransByTrans, &
|
||
lattice_interaction_SlipByTwin, &
|
||
lattice_interaction_SlipByTrans, &
|
||
lattice_interaction_TwinBySlip, &
|
||
lattice_characteristicShear_Twin, &
|
||
lattice_C66_twin, &
|
||
lattice_C66_trans, &
|
||
lattice_forestProjection_edge, &
|
||
lattice_forestProjection_screw, &
|
||
lattice_slip_normal, &
|
||
lattice_slip_direction, &
|
||
lattice_slip_transverse, &
|
||
lattice_labels_slip
|
||
|
||
contains
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Module initialization
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine lattice_init
|
||
|
||
integer :: Nphases
|
||
character(len=65536) :: &
|
||
tag = ''
|
||
integer :: i,p
|
||
real(pReal), dimension(:), allocatable :: &
|
||
temp, &
|
||
CoverA !< c/a ratio for low symmetry type lattice
|
||
|
||
write(6,'(/,a)') ' <<<+- lattice init -+>>>'
|
||
|
||
Nphases = size(config_phase)
|
||
|
||
allocate(lattice_structure(Nphases),source = LATTICE_undefined_ID)
|
||
allocate(lattice_C66(6,6,Nphases), source=0.0_pReal)
|
||
allocate(lattice_C3333(3,3,3,3,Nphases), source=0.0_pReal)
|
||
|
||
allocate(lattice_thermalExpansion33 (3,3,3,Nphases), source=0.0_pReal) ! constant, linear, quadratic coefficients
|
||
allocate(lattice_thermalConductivity33 (3,3,Nphases), source=0.0_pReal)
|
||
allocate(lattice_damageDiffusion33 (3,3,Nphases), source=0.0_pReal)
|
||
allocate(lattice_damageMobility ( Nphases), source=0.0_pReal)
|
||
allocate(lattice_massDensity ( Nphases), source=0.0_pReal)
|
||
allocate(lattice_specificHeat ( Nphases), source=0.0_pReal)
|
||
allocate(lattice_referenceTemperature ( Nphases), source=300.0_pReal)
|
||
|
||
allocate(lattice_mu(Nphases), source=0.0_pReal)
|
||
allocate(lattice_nu(Nphases), source=0.0_pReal)
|
||
|
||
|
||
allocate(lattice_Scleavage(3,3,3,lattice_maxNcleavage,Nphases),source=0.0_pReal)
|
||
allocate(lattice_NcleavageSystem(lattice_maxNcleavageFamily,Nphases),source=0)
|
||
|
||
allocate(CoverA(Nphases),source=0.0_pReal)
|
||
|
||
do p = 1, size(config_phase)
|
||
tag = config_phase(p)%getString('lattice_structure')
|
||
select case(trim(tag(1:3)))
|
||
case('iso')
|
||
lattice_structure(p) = LATTICE_iso_ID
|
||
case('fcc')
|
||
lattice_structure(p) = LATTICE_fcc_ID
|
||
case('bcc')
|
||
lattice_structure(p) = LATTICE_bcc_ID
|
||
case('hex')
|
||
lattice_structure(p) = LATTICE_hex_ID
|
||
case('bct')
|
||
lattice_structure(p) = LATTICE_bct_ID
|
||
case('ort')
|
||
lattice_structure(p) = LATTICE_ort_ID
|
||
end select
|
||
|
||
|
||
lattice_C66(1,1,p) = config_phase(p)%getFloat('c11',defaultVal=0.0_pReal)
|
||
lattice_C66(1,2,p) = config_phase(p)%getFloat('c12',defaultVal=0.0_pReal)
|
||
lattice_C66(1,3,p) = config_phase(p)%getFloat('c13',defaultVal=0.0_pReal)
|
||
lattice_C66(2,2,p) = config_phase(p)%getFloat('c22',defaultVal=0.0_pReal)
|
||
lattice_C66(2,3,p) = config_phase(p)%getFloat('c23',defaultVal=0.0_pReal)
|
||
lattice_C66(3,3,p) = config_phase(p)%getFloat('c33',defaultVal=0.0_pReal)
|
||
lattice_C66(4,4,p) = config_phase(p)%getFloat('c44',defaultVal=0.0_pReal)
|
||
lattice_C66(5,5,p) = config_phase(p)%getFloat('c55',defaultVal=0.0_pReal)
|
||
lattice_C66(6,6,p) = config_phase(p)%getFloat('c66',defaultVal=0.0_pReal)
|
||
|
||
|
||
CoverA(p) = config_phase(p)%getFloat('c/a',defaultVal=0.0_pReal)
|
||
|
||
lattice_thermalConductivity33(1,1,p) = config_phase(p)%getFloat('thermal_conductivity11',defaultVal=0.0_pReal)
|
||
lattice_thermalConductivity33(2,2,p) = config_phase(p)%getFloat('thermal_conductivity22',defaultVal=0.0_pReal)
|
||
lattice_thermalConductivity33(3,3,p) = config_phase(p)%getFloat('thermal_conductivity33',defaultVal=0.0_pReal)
|
||
|
||
temp = config_phase(p)%getFloats('thermal_expansion11',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T)
|
||
lattice_thermalExpansion33(1,1,1:size(temp),p) = temp
|
||
temp = config_phase(p)%getFloats('thermal_expansion22',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T)
|
||
lattice_thermalExpansion33(2,2,1:size(temp),p) = temp
|
||
temp = config_phase(p)%getFloats('thermal_expansion33',defaultVal=[0.0_pReal]) ! read up to three parameters (constant, linear, quadratic with T)
|
||
lattice_thermalExpansion33(3,3,1:size(temp),p) = temp
|
||
|
||
lattice_specificHeat(p) = config_phase(p)%getFloat( 'specific_heat',defaultVal=0.0_pReal)
|
||
lattice_massDensity(p) = config_phase(p)%getFloat( 'mass_density',defaultVal=0.0_pReal)
|
||
lattice_referenceTemperature(p) = config_phase(p)%getFloat( 'reference_temperature',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion33(1,1,p) = config_phase(p)%getFloat( 'damage_diffusion11',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion33(2,2,p) = config_phase(p)%getFloat( 'damage_diffusion22',defaultVal=0.0_pReal)
|
||
lattice_DamageDiffusion33(3,3,p) = config_phase(p)%getFloat( 'damage_diffusion33',defaultVal=0.0_pReal)
|
||
lattice_DamageMobility(p) = config_phase(p)%getFloat( 'damage_mobility',defaultVal=0.0_pReal)
|
||
enddo
|
||
|
||
do i = 1,Nphases
|
||
if ((CoverA(i) < 1.0_pReal .or. CoverA(i) > 2.0_pReal) &
|
||
.and. lattice_structure(i) == LATTICE_hex_ID) call IO_error(131,el=i) ! checking physical significance of c/a
|
||
if ((CoverA(i) > 2.0_pReal) &
|
||
.and. lattice_structure(i) == LATTICE_bct_ID) call IO_error(131,el=i) ! checking physical significance of c/a
|
||
call lattice_initializeStructure(i, CoverA(i))
|
||
enddo
|
||
|
||
end subroutine lattice_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief !!!!!!!DEPRECTATED!!!!!!
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine lattice_initializeStructure(myPhase,CoverA)
|
||
|
||
integer, intent(in) :: myPhase
|
||
real(pReal), intent(in) :: &
|
||
CoverA
|
||
|
||
integer :: &
|
||
i, &
|
||
myNcleavage
|
||
|
||
lattice_C66(1:6,1:6,myPhase) = lattice_symmetrizeC66(lattice_structure(myPhase),&
|
||
lattice_C66(1:6,1:6,myPhase))
|
||
|
||
lattice_mu(myPhase) = 0.2_pReal *( lattice_C66(1,1,myPhase) &
|
||
- lattice_C66(1,2,myPhase) &
|
||
+ 3.0_pReal*lattice_C66(4,4,myPhase)) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
||
lattice_nu(myPhase) = ( lattice_C66(1,1,myPhase) &
|
||
+ 4.0_pReal*lattice_C66(1,2,myPhase) &
|
||
- 2.0_pReal*lattice_C66(4,4,myPhase)) &
|
||
/( 4.0_pReal*lattice_C66(1,1,myPhase) &
|
||
+ 6.0_pReal*lattice_C66(1,2,myPhase) &
|
||
+ 2.0_pReal*lattice_C66(4,4,myPhase))! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
||
lattice_C3333(1:3,1:3,1:3,1:3,myPhase) = math_Voigt66to3333(lattice_C66(1:6,1:6,myPhase)) ! Literature data is Voigt
|
||
lattice_C66(1:6,1:6,myPhase) = math_sym3333to66(lattice_C3333(1:3,1:3,1:3,1:3,myPhase)) ! DAMASK uses Mandel-weighting
|
||
do i = 1, 6
|
||
if (abs(lattice_C66(i,i,myPhase))<tol_math_check) &
|
||
call IO_error(135,el=i,ip=myPhase,ext_msg='matrix diagonal "el"ement of phase "ip"')
|
||
enddo
|
||
|
||
do i = 1,3
|
||
lattice_thermalExpansion33 (1:3,1:3,i,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
|
||
lattice_thermalExpansion33 (1:3,1:3,i,myPhase))
|
||
enddo
|
||
|
||
lattice_thermalConductivity33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
|
||
lattice_thermalConductivity33 (1:3,1:3,myPhase))
|
||
lattice_DamageDiffusion33 (1:3,1:3,myPhase) = lattice_symmetrize33(lattice_structure(myPhase),&
|
||
lattice_DamageDiffusion33 (1:3,1:3,myPhase))
|
||
myNcleavage = 0
|
||
|
||
select case(lattice_structure(myPhase))
|
||
|
||
case (LATTICE_fcc_ID)
|
||
myNcleavage = lattice_fcc_Ncleavage
|
||
lattice_NcleavageSystem(1:2,myPhase) = lattice_fcc_NcleavageSystem
|
||
|
||
lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = &
|
||
lattice_SchmidMatrix_cleavage(lattice_fcc_ncleavageSystem,'fcc',covera)
|
||
|
||
case (LATTICE_bcc_ID)
|
||
myNcleavage = lattice_bcc_Ncleavage
|
||
lattice_NcleavageSystem(1:2,myPhase) = lattice_bcc_NcleavageSystem
|
||
|
||
lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = &
|
||
lattice_SchmidMatrix_cleavage(lattice_bcc_ncleavagesystem,'bcc',covera)
|
||
|
||
case (LATTICE_hex_ID)
|
||
myNcleavage = lattice_hex_Ncleavage
|
||
lattice_NcleavageSystem(1:1,myPhase) = lattice_hex_NcleavageSystem
|
||
|
||
lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = &
|
||
lattice_SchmidMatrix_cleavage(lattice_hex_ncleavagesystem,'hex',covera)
|
||
|
||
case (LATTICE_bct_ID)
|
||
|
||
case (LATTICE_ort_ID)
|
||
myNcleavage = lattice_ort_Ncleavage
|
||
lattice_NcleavageSystem(1:3,myPhase) = lattice_ort_NcleavageSystem
|
||
|
||
lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = &
|
||
lattice_SchmidMatrix_cleavage(lattice_ort_NcleavageSystem,'ort',covera)
|
||
|
||
case (LATTICE_iso_ID)
|
||
myNcleavage = lattice_iso_Ncleavage
|
||
lattice_NcleavageSystem(1:1,myPhase) = lattice_iso_NcleavageSystem
|
||
|
||
lattice_Scleavage(1:3,1:3,1:3,1:myNcleavage,myPhase) = &
|
||
lattice_SchmidMatrix_cleavage(lattice_iso_NcleavageSystem,'iso',covera)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! something went wrong
|
||
case default
|
||
call IO_error(130,ext_msg='lattice_initializeStructure')
|
||
end select
|
||
|
||
end subroutine lattice_initializeStructure
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Symmetrizes stiffness matrix according to lattice type
|
||
!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function lattice_symmetrizeC66(struct,C66)
|
||
|
||
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct
|
||
real(pReal), dimension(6,6), intent(in) :: C66
|
||
real(pReal), dimension(6,6) :: lattice_symmetrizeC66
|
||
integer :: j,k
|
||
|
||
lattice_symmetrizeC66 = 0.0_pReal
|
||
|
||
select case(struct)
|
||
case (LATTICE_iso_ID)
|
||
do k=1,3
|
||
do j=1,3
|
||
lattice_symmetrizeC66(k,j) = C66(1,2)
|
||
enddo
|
||
lattice_symmetrizeC66(k,k) = C66(1,1)
|
||
lattice_symmetrizeC66(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
enddo
|
||
case (LATTICE_fcc_ID,LATTICE_bcc_ID)
|
||
do k=1,3
|
||
do j=1,3
|
||
lattice_symmetrizeC66(k,j) = C66(1,2)
|
||
enddo
|
||
lattice_symmetrizeC66(k,k) = C66(1,1)
|
||
lattice_symmetrizeC66(k+3,k+3) = C66(4,4)
|
||
enddo
|
||
case (LATTICE_hex_ID)
|
||
lattice_symmetrizeC66(1,1) = C66(1,1)
|
||
lattice_symmetrizeC66(2,2) = C66(1,1)
|
||
lattice_symmetrizeC66(3,3) = C66(3,3)
|
||
lattice_symmetrizeC66(1,2) = C66(1,2)
|
||
lattice_symmetrizeC66(2,1) = C66(1,2)
|
||
lattice_symmetrizeC66(1,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,1) = C66(1,3)
|
||
lattice_symmetrizeC66(2,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,2) = C66(1,3)
|
||
lattice_symmetrizeC66(4,4) = C66(4,4)
|
||
lattice_symmetrizeC66(5,5) = C66(4,4)
|
||
lattice_symmetrizeC66(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
|
||
case (LATTICE_ort_ID)
|
||
lattice_symmetrizeC66(1,1) = C66(1,1)
|
||
lattice_symmetrizeC66(2,2) = C66(2,2)
|
||
lattice_symmetrizeC66(3,3) = C66(3,3)
|
||
lattice_symmetrizeC66(1,2) = C66(1,2)
|
||
lattice_symmetrizeC66(2,1) = C66(1,2)
|
||
lattice_symmetrizeC66(1,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,1) = C66(1,3)
|
||
lattice_symmetrizeC66(2,3) = C66(2,3)
|
||
lattice_symmetrizeC66(3,2) = C66(2,3)
|
||
lattice_symmetrizeC66(4,4) = C66(4,4)
|
||
lattice_symmetrizeC66(5,5) = C66(5,5)
|
||
lattice_symmetrizeC66(6,6) = C66(6,6)
|
||
case (LATTICE_bct_ID)
|
||
lattice_symmetrizeC66(1,1) = C66(1,1)
|
||
lattice_symmetrizeC66(2,2) = C66(1,1)
|
||
lattice_symmetrizeC66(3,3) = C66(3,3)
|
||
lattice_symmetrizeC66(1,2) = C66(1,2)
|
||
lattice_symmetrizeC66(2,1) = C66(1,2)
|
||
lattice_symmetrizeC66(1,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,1) = C66(1,3)
|
||
lattice_symmetrizeC66(2,3) = C66(1,3)
|
||
lattice_symmetrizeC66(3,2) = C66(1,3)
|
||
lattice_symmetrizeC66(4,4) = C66(4,4)
|
||
lattice_symmetrizeC66(5,5) = C66(4,4)
|
||
lattice_symmetrizeC66(6,6) = C66(6,6)
|
||
case default
|
||
lattice_symmetrizeC66 = C66
|
||
end select
|
||
|
||
end function lattice_symmetrizeC66
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Symmetrizes 2nd order tensor according to lattice type
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function lattice_symmetrize33(struct,T33)
|
||
|
||
integer(kind(LATTICE_undefined_ID)), intent(in) :: struct
|
||
real(pReal), dimension(3,3), intent(in) :: T33
|
||
real(pReal), dimension(3,3) :: lattice_symmetrize33
|
||
integer :: k
|
||
|
||
lattice_symmetrize33 = 0.0_pReal
|
||
|
||
select case(struct)
|
||
case (LATTICE_iso_ID,LATTICE_fcc_ID,LATTICE_bcc_ID)
|
||
do k=1,3
|
||
lattice_symmetrize33(k,k) = T33(1,1)
|
||
enddo
|
||
case (LATTICE_hex_ID)
|
||
lattice_symmetrize33(1,1) = T33(1,1)
|
||
lattice_symmetrize33(2,2) = T33(1,1)
|
||
lattice_symmetrize33(3,3) = T33(3,3)
|
||
case (LATTICE_ort_ID,lattice_bct_ID)
|
||
lattice_symmetrize33(1,1) = T33(1,1)
|
||
lattice_symmetrize33(2,2) = T33(2,2)
|
||
lattice_symmetrize33(3,3) = T33(3,3)
|
||
case default
|
||
lattice_symmetrize33 = T33
|
||
end select
|
||
|
||
end function lattice_symmetrize33
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Characteristic shear for twinning
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_characteristicShear_Twin(Ntwin,structure,CoverA) result(characteristicShear)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Ntwin)) :: characteristicShear
|
||
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system list
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
integer, dimension(LATTICE_HEX_NTWIN), parameter :: &
|
||
HEX_SHEARTWIN = reshape( [&
|
||
1, & ! <-10.1>{10.2}
|
||
1, &
|
||
1, &
|
||
1, &
|
||
1, &
|
||
1, &
|
||
2, & ! <11.6>{-1-1.1}
|
||
2, &
|
||
2, &
|
||
2, &
|
||
2, &
|
||
2, &
|
||
3, & ! <10.-2>{10.1}
|
||
3, &
|
||
3, &
|
||
3, &
|
||
3, &
|
||
3, &
|
||
4, & ! <11.-3>{11.2}
|
||
4, &
|
||
4, &
|
||
4, &
|
||
4, &
|
||
4 &
|
||
],[LATTICE_HEX_NTWIN]) ! indicator to formulas below
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure))
|
||
|
||
a = 0
|
||
myFamilies: do f = 1,size(Ntwin,1)
|
||
mySystems: do s = 1,Ntwin(f)
|
||
a = a + 1
|
||
select case(structure(1:3))
|
||
case('fcc','bcc')
|
||
characteristicShear(a) = 0.5_pReal*sqrt(2.0_pReal)
|
||
case('hex')
|
||
if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='lattice_characteristicShear_Twin')
|
||
p = sum(LATTICE_HEX_NTWINSYSTEM(1:f-1))+s
|
||
select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
|
||
case (1) ! <-10.1>{10.2}
|
||
characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA
|
||
case (2) ! <11.6>{-1-1.1}
|
||
characteristicShear(a) = 1.0_pReal/cOverA
|
||
case (3) ! <10.-2>{10.1}
|
||
characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA
|
||
case (4) ! <11.-3>{11.2}
|
||
characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA
|
||
end select
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure))
|
||
end select
|
||
enddo mySystems
|
||
enddo myFamilies
|
||
|
||
end function lattice_characteristicShear_Twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Rotated elasticity matrices for twinning in 66-vector notation
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_C66_twin(Ntwin,C66,structure,CoverA)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(6,6), intent(in) :: C66 !< unrotated parent stiffness matrix
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(6,6,sum(Ntwin)) :: lattice_C66_twin
|
||
|
||
real(pReal), dimension(3,3,sum(Ntwin)):: coordinateSystem
|
||
type(rotation) :: R
|
||
integer :: i
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_FCC_NSLIPSYSTEM,LATTICE_FCC_SYSTEMTWIN,&
|
||
trim(structure),0.0_pReal)
|
||
case('bcc')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_BCC_NSLIPSYSTEM,LATTICE_BCC_SYSTEMTWIN,&
|
||
trim(structure),0.0_pReal)
|
||
case('hex')
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,LATTICE_HEX_NSLIPSYSTEM,LATTICE_HEX_SYSTEMTWIN,&
|
||
'hex',cOverA)
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure))
|
||
end select
|
||
|
||
do i = 1, sum(Ntwin)
|
||
call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI],P=1) ! ToDo: Why always 180 deg?
|
||
lattice_C66_twin(1:6,1:6,i) = R%rotTensor4sym(C66)
|
||
enddo
|
||
|
||
end function lattice_C66_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Rotated elasticity matrices for transformation in 66-vector notation
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_C66_trans(Ntrans,C_parent66,structure_target, &
|
||
cOverA_trans,a_bcc,a_fcc)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure_target !< lattice structure
|
||
real(pReal), dimension(6,6), intent(in) :: C_parent66
|
||
real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans
|
||
|
||
real(pReal), dimension(6,6) :: C_bar66, C_target_unrotated66
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: Q,S
|
||
type(rotation) :: R
|
||
real(pReal) :: a_bcc, a_fcc, cOverA_trans
|
||
integer :: i
|
||
|
||
if (len_trim(structure_target) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_C66_trans (target): '//trim(structure_target))
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! elasticity matrix of the target phase in cube orientation
|
||
if (structure_target(1:3) == 'hex') then
|
||
if (cOverA_trans < 1.0_pReal .or. cOverA_trans > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='lattice_C66_trans: '//trim(structure_target))
|
||
C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal
|
||
C_bar66(1,2) = (C_parent66(1,1) + 5.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/6.0_pReal
|
||
C_bar66(3,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) + 4.0_pReal*C_parent66(4,4))/3.0_pReal
|
||
C_bar66(1,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/3.0_pReal
|
||
C_bar66(4,4) = (C_parent66(1,1) - C_parent66(1,2) + C_parent66(4,4))/3.0_pReal
|
||
C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal))
|
||
|
||
C_target_unrotated66 = 0.0_pReal
|
||
C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
|
||
C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
|
||
C_target_unrotated66(1,3) = C_bar66(1,3)
|
||
C_target_unrotated66(3,3) = C_bar66(3,3)
|
||
C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
|
||
C_target_unrotated66 = lattice_symmetrizeC66(LATTICE_HEX_ID,C_target_unrotated66)
|
||
elseif (structure_target(1:3) == 'bcc') then
|
||
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
|
||
call IO_error(134,ext_msg='lattice_C66_trans: '//trim(structure_target))
|
||
C_target_unrotated66 = C_parent66
|
||
else
|
||
call IO_error(137,ext_msg='lattice_C66_trans : '//trim(structure_target))
|
||
endif
|
||
|
||
do i = 1, 6
|
||
if (abs(C_target_unrotated66(i,i))<tol_math_check) &
|
||
call IO_error(135,el=i,ext_msg='matrix diagonal "el"ement in transformation')
|
||
enddo
|
||
|
||
call buildTransformationSystem(Q,S,Ntrans,cOverA_trans,a_fcc,a_bcc)
|
||
|
||
do i = 1, sum(Ntrans)
|
||
call R%fromMatrix(Q(1:3,1:3,i))
|
||
lattice_C66_trans(1:6,1:6,i) = R%rotTensor4sym(C_target_unrotated66)
|
||
enddo
|
||
|
||
end function lattice_C66_trans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Non-schmid projections for bcc with up to 6 coefficients
|
||
! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17)
|
||
! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections
|
||
integer, intent(in) :: sense !< sense (-1,+1)
|
||
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix
|
||
|
||
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem !< coordinate system of slip system
|
||
real(pReal), dimension(3) :: direction, normal, np
|
||
type(rotation) :: R
|
||
integer :: i
|
||
|
||
if (abs(sense) /= 1) call IO_error(0,ext_msg='lattice_nonSchmidMatrix')
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,LATTICE_BCC_NSLIPSYSTEM,LATTICE_BCC_SYSTEMSLIP,&
|
||
'bcc',0.0_pReal)
|
||
coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip)) *real(sense,pReal) ! convert unidirectional coordinate system
|
||
nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'bcc',0.0_pReal) ! Schmid contribution
|
||
|
||
do i = 1,sum(Nslip)
|
||
direction = coordinateSystem(1:3,1,i)
|
||
normal = coordinateSystem(1:3,2,i)
|
||
call R%fromAxisAngle([direction,60.0_pReal],degrees=.true.,P=1)
|
||
np = R%rotate(normal)
|
||
|
||
if (size(nonSchmidCoefficients)>0) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(1) * math_outer(direction, np)
|
||
if (size(nonSchmidCoefficients)>1) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(2) * math_outer(math_cross(normal, direction), normal)
|
||
if (size(nonSchmidCoefficients)>2) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(3) * math_outer(math_cross(np, direction), np)
|
||
if (size(nonSchmidCoefficients)>3) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(4) * math_outer(normal, normal)
|
||
if (size(nonSchmidCoefficients)>4) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(5) * math_outer(math_cross(normal, direction), &
|
||
math_cross(normal, direction))
|
||
if (size(nonSchmidCoefficients)>5) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
|
||
+ nonSchmidCoefficients(6) * math_outer(direction, direction)
|
||
enddo
|
||
|
||
end function lattice_nonSchmidMatrix
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-slip interaction matrix
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipBySlip(Nslip,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-slip interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 2, 2, 4, 6, 5, 3, 5, 5, 4, 5, 6, 9,10, 9,10,11,12, & ! -----> acting
|
||
2, 1, 2, 6, 4, 5, 5, 4, 6, 5, 3, 5, 9,10,11,12, 9,10, & ! |
|
||
2, 2, 1, 5, 5, 3, 5, 6, 4, 6, 5, 4, 11,12, 9,10, 9,10, & ! |
|
||
4, 6, 5, 1, 2, 2, 4, 5, 6, 3, 5, 5, 9,10,10, 9,12,11, & ! v
|
||
6, 4, 5, 2, 1, 2, 5, 3, 5, 5, 4, 6, 9,10,12,11,10, 9, & ! reacting
|
||
5, 5, 3, 2, 2, 1, 6, 5, 4, 5, 6, 4, 11,12,10, 9,10, 9, &
|
||
3, 5, 5, 4, 5, 6, 1, 2, 2, 4, 6, 5, 10, 9,10, 9,11,12, &
|
||
5, 4, 6, 5, 3, 5, 2, 1, 2, 6, 4, 5, 10, 9,12,11, 9,10, &
|
||
5, 6, 4, 6, 5, 4, 2, 2, 1, 5, 5, 3, 12,11,10, 9, 9,10, &
|
||
4, 5, 6, 3, 5, 5, 4, 6, 5, 1, 2, 2, 10, 9, 9,10,12,11, &
|
||
5, 3, 5, 5, 4, 6, 6, 4, 5, 2, 1, 2, 10, 9,11,12,10, 9, &
|
||
6, 5, 4, 5, 6, 4, 5, 5, 3, 2, 2, 1, 12,11, 9,10,10, 9, &
|
||
|
||
9, 9,11, 9, 9,11,10,10,12,10,10,12, 1, 7, 8, 8, 8, 8, &
|
||
10,10,12,10,10,12, 9, 9,11, 9, 9,11, 7, 1, 8, 8, 8, 8, &
|
||
9,11, 9,10,12,10,10,12,10, 9,11, 9, 8, 8, 1, 7, 8, 8, &
|
||
10,12,10, 9,11, 9, 9,11, 9,10,12,10, 8, 8, 7, 1, 8, 8, &
|
||
11, 9, 9,12,10,10,11, 9, 9,12,10,10, 8, 8, 8, 8, 1, 7, &
|
||
12,10,10,11, 9, 9,12,10,10,11, 9, 9, 8, 8, 8, 8, 7, 1 &
|
||
],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for fcc
|
||
!< 1: self interaction
|
||
!< 2: coplanar interaction
|
||
!< 3: collinear interaction
|
||
!< 4: Hirth locks
|
||
!< 5: glissile junctions
|
||
!< 6: Lomer locks
|
||
!< 7: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
|
||
!< 8: similar to Lomer locks in <110>{111} for two {110} planes
|
||
!< 9: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
|
||
!<10: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
|
||
!<11: crossing btw one {110} and one {111} plane
|
||
!<12: collinear btw one {110} and one {111} plane
|
||
|
||
integer, dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NSLIP), parameter :: &
|
||
BCC_INTERACTIONSLIPSLIP = reshape( [&
|
||
1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! -----> acting
|
||
2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! |
|
||
6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! |
|
||
6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v
|
||
5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & ! reacting
|
||
4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, &
|
||
4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, &
|
||
3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, &
|
||
4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, &
|
||
3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, &
|
||
5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, &
|
||
4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, &
|
||
!
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, &
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, &
|
||
4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, &
|
||
3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, &
|
||
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, &
|
||
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 &
|
||
],shape(BCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377
|
||
!< 1: self interaction
|
||
!< 2: coplanar interaction
|
||
!< 3: collinear interaction
|
||
!< 4: mixed-asymmetrical junction
|
||
!< 5: mixed-symmetrical junction
|
||
!< 6: edge junction
|
||
|
||
integer, dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NSLIP), parameter :: &
|
||
HEX_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! -----> acting
|
||
2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
|
||
2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
|
||
! ! v
|
||
6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! reacting
|
||
6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
|
||
6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
|
||
!
|
||
12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
|
||
12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
|
||
12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
|
||
!
|
||
20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
|
||
!
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, &
|
||
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, &
|
||
!
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, &
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, &
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, &
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, &
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, &
|
||
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 &
|
||
],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for hex (onion peel naming scheme)
|
||
|
||
integer, dimension(LATTICE_BCT_NSLIP,LATTICE_BCT_NSLIP), parameter :: &
|
||
BCT_INTERACTIONSLIPSLIP = reshape( [&
|
||
1, 2, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! -----> acting
|
||
2, 1, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! |
|
||
! |
|
||
6, 6, 4, 5, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! v
|
||
6, 6, 5, 4, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! reacting
|
||
!
|
||
12, 12, 11, 11, 9, 10, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
|
||
12, 12, 11, 11, 10, 9, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
|
||
!
|
||
20, 20, 19, 19, 18, 18, 16, 17, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 16, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 17, 16, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
20, 20, 19, 19, 18, 18, 17, 17, 17, 16, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
|
||
!
|
||
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 25, 26, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
|
||
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 26, 25, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
|
||
!
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 36, 37, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 36, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 36, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 37, 36, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
|
||
!
|
||
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 49, 50, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
|
||
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 50, 49, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
|
||
!
|
||
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 64, 65, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
|
||
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 65, 64, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
|
||
!
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 81, 82, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 81, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 81, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 82, 81, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
|
||
!
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 100,101,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,100,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,100,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,100,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,100,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,100,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,100,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,101,100, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
|
||
!
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 121, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 121, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 121, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
|
||
!
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 144,145,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,144,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,144,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,144,145,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,144,145,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,144,145,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,144,145, 168,168,168,168,168,168,168,168, &
|
||
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,145,144, 168,168,168,168,168,168,168,168, &
|
||
!
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,169,170,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,169,170,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,169,170,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,170,169,170,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, &
|
||
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 &
|
||
],shape(BCT_INTERACTIONSLIPSLIP))
|
||
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONSLIPSLIP
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONSLIPSLIP
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
case('hex')
|
||
interactionTypes = HEX_INTERACTIONSLIPSLIP
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
case('bct')
|
||
interactionTypes = BCT_INTERACTIONSLIPSLIP
|
||
NslipMax = LATTICE_BCT_NSLIPSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipBySlip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Twin-twin interaction matrix
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TwinByTwin(Ntwin,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Ntwin),sum(Ntwin)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NTWIN), parameter :: &
|
||
FCC_INTERACTIONTWINTWIN = reshape( [&
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
|
||
2,2,2,1,1,1,2,2,2,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1 &
|
||
],shape(FCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for fcc
|
||
|
||
integer, dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NTWIN), parameter :: &
|
||
BCC_INTERACTIONTWINTWIN = reshape( [&
|
||
1,3,3,3,3,3,3,2,3,3,2,3, & ! -----> acting
|
||
3,1,3,3,3,3,2,3,3,3,3,2, & ! |
|
||
3,3,1,3,3,2,3,3,2,3,3,3, & ! |
|
||
3,3,3,1,2,3,3,3,3,2,3,3, & ! v
|
||
3,3,3,2,1,3,3,3,3,2,3,3, & ! reacting
|
||
3,3,2,3,3,1,3,3,2,3,3,3, &
|
||
3,2,3,3,3,3,1,3,3,3,3,2, &
|
||
2,3,3,3,3,3,3,1,3,3,2,3, &
|
||
3,3,2,3,3,2,3,3,1,3,3,3, &
|
||
3,3,3,2,2,3,3,3,3,1,3,3, &
|
||
2,3,3,3,3,3,3,2,3,3,1,3, &
|
||
3,2,3,3,3,3,2,3,3,3,3,1 &
|
||
],shape(BCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for bcc
|
||
!< 1: self interaction
|
||
!< 2: collinear interaction
|
||
!< 3: other interaction
|
||
integer, dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NTWIN), parameter :: &
|
||
HEX_INTERACTIONTWINTWIN = reshape( [&
|
||
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting
|
||
2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
|
||
2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
|
||
2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v
|
||
2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting
|
||
2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, &
|
||
!
|
||
6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
|
||
!
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, &
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, &
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, &
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, &
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, &
|
||
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, &
|
||
!
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, &
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, &
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, &
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, &
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, &
|
||
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 &
|
||
],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONTWINTWIN
|
||
NtwinMax = LATTICE_FCC_NTWINSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONTWINTWIN
|
||
NtwinMax = LATTICE_BCC_NTWINSYSTEM
|
||
case('hex')
|
||
interactionTypes = HEX_INTERACTIONTWINTWIN
|
||
NtwinMax = LATTICE_HEX_NTWINSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TwinByTwin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Trans-trans interaction matrix
|
||
!> details only active trans systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TransByTrans(Ntrans,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active trans systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for trans-trans interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
|
||
real(pReal), dimension(sum(Ntrans),sum(Ntrans)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtransMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NTRANS,LATTICE_FCC_NTRANS), parameter :: &
|
||
FCC_INTERACTIONTRANSTRANS = reshape( [&
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
|
||
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
|
||
2,2,2,1,1,1,2,2,2,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,1,1,1,2,2,2, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1, &
|
||
2,2,2,2,2,2,2,2,2,1,1,1 &
|
||
],shape(FCC_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for fcc
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure))
|
||
|
||
if(structure(1:3) == 'fcc') then
|
||
interactionTypes = FCC_INTERACTIONTRANSTRANS
|
||
NtransMax = LATTICE_FCC_NTRANSSYSTEM
|
||
else
|
||
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure))
|
||
end if
|
||
|
||
interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TransByTrans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-twin interaction matrix
|
||
!> details only active slip and twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
|
||
Ntwin !< number of active twin systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Nslip),sum(Ntwin)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax, &
|
||
NtwinMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NTWIN,LATTICE_FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPTWIN = reshape( [&
|
||
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> twin (acting)
|
||
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
|
||
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
|
||
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
|
||
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
|
||
2,2,2,1,1,1,3,3,3,3,3,3, &
|
||
2,2,2,3,3,3,1,1,1,3,3,3, &
|
||
3,3,3,2,2,2,1,1,1,3,3,3, &
|
||
3,3,3,3,3,3,1,1,1,2,2,2, &
|
||
3,3,3,2,2,2,3,3,3,1,1,1, &
|
||
2,2,2,3,3,3,3,3,3,1,1,1, &
|
||
3,3,3,3,3,3,2,2,2,1,1,1, &
|
||
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4 &
|
||
],shape(FCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for fcc
|
||
!< 1: coplanar interaction
|
||
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
|
||
!< 3: other interaction
|
||
integer, dimension(LATTICE_BCC_NTWIN,LATTICE_BCC_NSLIP), parameter :: &
|
||
BCC_INTERACTIONSLIPTWIN = reshape( [&
|
||
3,3,3,2,2,3,3,3,3,2,3,3, & ! -----> twin (acting)
|
||
3,3,2,3,3,2,3,3,2,3,3,3, & ! |
|
||
3,2,3,3,3,3,2,3,3,3,3,2, & ! |
|
||
2,3,3,3,3,3,3,2,3,3,2,3, & ! v
|
||
2,3,3,3,3,3,3,2,3,3,2,3, & ! slip (reacting)
|
||
3,3,2,3,3,2,3,3,2,3,3,3, &
|
||
3,2,3,3,3,3,2,3,3,3,3,2, &
|
||
3,3,3,2,2,3,3,3,3,2,3,3, &
|
||
2,3,3,3,3,3,3,2,3,3,2,3, &
|
||
3,3,3,2,2,3,3,3,3,2,3,3, &
|
||
3,2,3,3,3,3,2,3,3,3,3,2, &
|
||
3,3,2,3,3,2,3,3,2,3,3,3, &
|
||
!
|
||
1,3,3,3,3,3,3,2,3,3,2,3, &
|
||
3,1,3,3,3,3,2,3,3,3,3,2, &
|
||
3,3,1,3,3,2,3,3,2,3,3,3, &
|
||
3,3,3,1,2,3,3,3,3,2,3,3, &
|
||
3,3,3,2,1,3,3,3,3,2,3,3, &
|
||
3,3,2,3,3,1,3,3,2,3,3,3, &
|
||
3,2,3,3,3,3,1,3,3,3,3,2, &
|
||
2,3,3,3,3,3,3,1,3,3,2,3, &
|
||
3,3,2,3,3,2,3,3,1,3,3,3, &
|
||
3,3,3,2,2,3,3,3,3,1,3,3, &
|
||
2,3,3,3,3,3,3,2,3,3,1,3, &
|
||
3,2,3,3,3,3,2,3,3,3,3,1 &
|
||
],shape(BCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for bcc
|
||
!< 1: coplanar interaction
|
||
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
|
||
!< 3: other interaction
|
||
integer, dimension(LATTICE_HEX_NTWIN,LATTICE_HEX_NSLIP), parameter :: &
|
||
HEX_INTERACTIONSLIPTWIN = reshape( [&
|
||
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! ----> twin (acting)
|
||
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
|
||
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
|
||
! v
|
||
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip (reacting)
|
||
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
|
||
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
|
||
!
|
||
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
||
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
||
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
|
||
!
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
|
||
!
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
|
||
!
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
|
||
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 &
|
||
!
|
||
],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONSLIPTWIN
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
NtwinMax = LATTICE_FCC_NTWINSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONSLIPTWIN
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
NtwinMax = LATTICE_BCC_NTWINSYSTEM
|
||
case('hex')
|
||
interactionTypes = HEX_INTERACTIONSLIPTWIN
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
NtwinMax = LATTICE_HEX_NTWINSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipByTwin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip-trans interaction matrix
|
||
!> details only active slip and trans systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
|
||
Ntrans !< number of active trans systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-trans interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
|
||
real(pReal), dimension(sum(Nslip),sum(Ntrans)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NslipMax, &
|
||
NtransMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NTRANS,LATTICE_FCC_NSLIP), parameter :: &
|
||
FCC_INTERACTIONSLIPTRANS = reshape( [&
|
||
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> trans (acting)
|
||
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
|
||
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
|
||
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
|
||
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
|
||
2,2,2,1,1,1,3,3,3,3,3,3, &
|
||
2,2,2,3,3,3,1,1,1,3,3,3, &
|
||
3,3,3,2,2,2,1,1,1,3,3,3, &
|
||
3,3,3,3,3,3,1,1,1,2,2,2, &
|
||
3,3,3,2,2,2,3,3,3,1,1,1, &
|
||
2,2,2,3,3,3,3,3,3,1,1,1, &
|
||
3,3,3,3,3,3,2,2,2,1,1,1, &
|
||
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4, &
|
||
4,4,4,4,4,4,4,4,4,4,4,4 &
|
||
],shape(FCC_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for fcc
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONSLIPTRANS
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
NtransMax = LATTICE_FCC_NTRANSSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_SlipByTrans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Twin-slip interaction matrix
|
||
!> details only active twin and slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,structure) result(interactionMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin, & !< number of active twin systems per family
|
||
Nslip !< number of active slip systems per family
|
||
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), dimension(sum(Ntwin),sum(Nslip)) :: interactionMatrix
|
||
|
||
integer, dimension(:), allocatable :: NtwinMax, &
|
||
NslipMax
|
||
integer, dimension(:,:), allocatable :: interactionTypes
|
||
|
||
integer, dimension(LATTICE_FCC_NSLIP,LATTICE_FCC_NTWIN), parameter :: &
|
||
FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc
|
||
|
||
integer, dimension(LATTICE_BCC_NSLIP,LATTICE_BCC_NTWIN), parameter :: &
|
||
BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc
|
||
|
||
integer, dimension(LATTICE_HEX_NSLIP,LATTICE_HEX_NTWIN), parameter :: &
|
||
HEX_INTERACTIONTWINSLIP = reshape( [&
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! ----> slip (acting)
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin (reacting)
|
||
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, &
|
||
!
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
|
||
!
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
|
||
!
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
|
||
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 &
|
||
],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
interactionTypes = FCC_INTERACTIONTWINSLIP
|
||
NtwinMax = LATTICE_FCC_NTWINSYSTEM
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
case('bcc')
|
||
interactionTypes = BCC_INTERACTIONTWINSLIP
|
||
NtwinMax = LATTICE_BCC_NTWINSYSTEM
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
case('hex')
|
||
interactionTypes = HEX_INTERACTIONTWINSLIP
|
||
NtwinMax = LATTICE_HEX_NTWINSYSTEM
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure))
|
||
end select
|
||
|
||
interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes)
|
||
|
||
end function lattice_interaction_TwinBySlip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for slip
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
integer :: i
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
slipSystems = LATTICE_HEX_SYSTEMSLIP
|
||
case('bct')
|
||
NslipMax = LATTICE_BCT_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCT_SYSTEMSLIP
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Nslip)
|
||
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
|
||
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for slip')
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for twinning
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_twin(Ntwin,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Ntwin)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: twinSystems
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
integer :: i
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
NtwinMax = LATTICE_FCC_NTWINSYSTEM
|
||
twinSystems = LATTICE_FCC_SYSTEMTWIN
|
||
case('bcc')
|
||
NtwinMax = LATTICE_BCC_NTWINSYSTEM
|
||
twinSystems = LATTICE_BCC_SYSTEMTWIN
|
||
case('hex')
|
||
NtwinMax = LATTICE_HEX_NTWINSYSTEM
|
||
twinSystems = LATTICE_HEX_SYSTEMTWIN
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
|
||
call IO_error(145,ext_msg='Ntwin '//trim(structure))
|
||
if (any(Ntwin < 0)) &
|
||
call IO_error(144,ext_msg='Ntwin '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Ntwin)
|
||
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
|
||
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for twin')
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for twinning
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_trans(Ntrans,structure_target,cOverA,a_bcc,a_fcc) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
|
||
character(len=*), intent(in) :: structure_target !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ntrans)) :: devNull
|
||
real(pReal) :: a_bcc, a_fcc
|
||
|
||
if (len_trim(structure_target) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
if (structure_target(1:3) /= 'bcc' .and. structure_target(1:3) /= 'hex') &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
if (structure_target(1:3) == 'hex' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
|
||
call IO_error(131,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
if (structure_target(1:3) == 'bcc' .and. (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal)) &
|
||
call IO_error(134,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
|
||
|
||
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA,a_fcc,a_bcc)
|
||
|
||
end function lattice_SchmidMatrix_trans
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Schmid matrix for cleavage
|
||
!> details only active cleavage systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_SchmidMatrix_cleavage(Ncleavage,structure,cOverA) result(SchmidMatrix)
|
||
|
||
integer, dimension(:), intent(in) :: Ncleavage !< number of active cleavage systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,3,sum(Ncleavage)) :: SchmidMatrix
|
||
|
||
real(pReal), dimension(3,3,sum(Ncleavage)) :: coordinateSystem
|
||
real(pReal), dimension(:,:), allocatable :: cleavageSystems
|
||
integer, dimension(:), allocatable :: NcleavageMax
|
||
integer :: i
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('iso')
|
||
NcleavageMax = LATTICE_ISO_NCLEAVAGESYSTEM
|
||
cleavageSystems = LATTICE_ISO_SYSTEMCLEAVAGE
|
||
case('ort')
|
||
NcleavageMax = LATTICE_ORT_NCLEAVAGESYSTEM
|
||
cleavageSystems = LATTICE_ORT_SYSTEMCLEAVAGE
|
||
case('fcc')
|
||
NcleavageMax = LATTICE_FCC_NCLEAVAGESYSTEM
|
||
cleavageSystems = LATTICE_FCC_SYSTEMCLEAVAGE
|
||
case('bcc')
|
||
NcleavageMax = LATTICE_BCC_NCLEAVAGESYSTEM
|
||
cleavageSystems = LATTICE_BCC_SYSTEMCLEAVAGE
|
||
case('hex')
|
||
NcleavageMax = LATTICE_HEX_NCLEAVAGESYSTEM
|
||
cleavageSystems = LATTICE_HEX_SYSTEMCLEAVAGE
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0)) &
|
||
call IO_error(145,ext_msg='Ncleavage '//trim(structure))
|
||
if (any(Ncleavage < 0)) &
|
||
call IO_error(144,ext_msg='Ncleavage '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Ncleavage,NcleavageMax,cleavageSystems,structure,cOverA)
|
||
|
||
do i = 1, sum(Ncleavage)
|
||
SchmidMatrix(1:3,1:3,1,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
|
||
SchmidMatrix(1:3,1:3,2,i) = math_outer(coordinateSystem(1:3,3,i),coordinateSystem(1:3,2,i))
|
||
SchmidMatrix(1:3,1:3,3,i) = math_outer(coordinateSystem(1:3,2,i),coordinateSystem(1:3,2,i))
|
||
enddo
|
||
|
||
end function lattice_SchmidMatrix_cleavage
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Slip direction of slip systems (|| b)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_direction(Nslip,structure,cOverA) result(d)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: d
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
d = coordinateSystem(1:3,1,1:sum(Nslip))
|
||
|
||
end function lattice_slip_direction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Normal direction of slip systems (|| n)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_normal(Nslip,structure,cOverA) result(n)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: n
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
n = coordinateSystem(1:3,2,1:sum(Nslip))
|
||
|
||
end function lattice_slip_normal
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Transverse direction of slip systems ( || t = b x n)
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_slip_transverse(Nslip,structure,cOverA) result(t)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,sum(Nslip)) :: t
|
||
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
|
||
t = coordinateSystem(1:3,3,1:sum(Nslip))
|
||
|
||
end function lattice_slip_transverse
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Projection of the transverse direction onto the slip plane
|
||
!> @details: This projection is used to calculate forest hardening for edge dislocations
|
||
!--------------------------------------------------------------------------------------------------
|
||
function slipProjection_transverse(Nslip,structure,cOverA) result(projection)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
|
||
|
||
real(pReal), dimension(3,sum(Nslip)) :: n, t
|
||
integer :: i, j
|
||
|
||
n = lattice_slip_normal (Nslip,structure,cOverA)
|
||
t = lattice_slip_transverse(Nslip,structure,cOverA)
|
||
|
||
do i=1, sum(Nslip); do j=1, sum(Nslip)
|
||
projection(i,j) = abs(math_inner(n(:,i),t(:,j)))
|
||
enddo; enddo
|
||
|
||
end function slipProjection_transverse
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Labels for slip systems
|
||
!> details only active slip systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_labels_slip(Nslip,structure) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
slipSystems = LATTICE_HEX_SYSTEMSLIP
|
||
case('bct')
|
||
NslipMax = LATTICE_BCT_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCT_SYSTEMSLIP
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
labels = getLabels(Nslip,NslipMax,slipSystems,structure)
|
||
|
||
end function lattice_labels_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Labels for twin systems
|
||
!> details only active twin systems are considered
|
||
!--------------------------------------------------------------------------------------------------
|
||
function lattice_labels_twin(Ntwin,structure) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: Ntwin !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
|
||
real(pReal), dimension(:,:), allocatable :: twinSystems
|
||
integer, dimension(:), allocatable :: NtwinMax
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
NtwinMax = LATTICE_FCC_NTWINSYSTEM
|
||
twinSystems = LATTICE_FCC_SYSTEMTWIN
|
||
case('bcc')
|
||
NtwinMax = LATTICE_BCC_NTWINSYSTEM
|
||
twinSystems = LATTICE_BCC_SYSTEMTWIN
|
||
case('hex')
|
||
NtwinMax = LATTICE_HEX_NTWINSYSTEM
|
||
twinSystems = LATTICE_HEX_SYSTEMTWIN
|
||
case default
|
||
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
|
||
call IO_error(145,ext_msg='Ntwin '//trim(structure))
|
||
if (any(Ntwin < 0)) &
|
||
call IO_error(144,ext_msg='Ntwin '//trim(structure))
|
||
|
||
labels = getLabels(Ntwin,NtwinMax,twinSystems,structure)
|
||
|
||
end function lattice_labels_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Projection of the slip direction onto the slip plane
|
||
!> @details: This projection is used to calculate forest hardening for screw dislocations
|
||
!--------------------------------------------------------------------------------------------------
|
||
function slipProjection_direction(Nslip,structure,cOverA) result(projection)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
|
||
|
||
real(pReal), dimension(3,sum(Nslip)) :: n, d
|
||
integer :: i, j
|
||
|
||
n = lattice_slip_normal (Nslip,structure,cOverA)
|
||
d = lattice_slip_direction(Nslip,structure,cOverA)
|
||
|
||
do i=1, sum(Nslip); do j=1, sum(Nslip)
|
||
projection(i,j) = abs(math_inner(n(:,i),d(:,j)))
|
||
enddo; enddo
|
||
|
||
end function slipProjection_direction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief build a local coordinate system on slip systems
|
||
!> @details Order: Direction, plane (normal), and common perpendicular
|
||
!--------------------------------------------------------------------------------------------------
|
||
function coordinateSystem_slip(Nslip,structure,cOverA) result(coordinateSystem)
|
||
|
||
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
real(pReal), intent(in) :: cOverA !< c/a ratio
|
||
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
|
||
|
||
real(pReal), dimension(:,:), allocatable :: slipSystems
|
||
integer, dimension(:), allocatable :: NslipMax
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure))
|
||
|
||
select case(structure(1:3))
|
||
case('fcc')
|
||
NslipMax = LATTICE_FCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_FCC_SYSTEMSLIP
|
||
case('bcc')
|
||
NslipMax = LATTICE_BCC_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCC_SYSTEMSLIP
|
||
case('hex')
|
||
NslipMax = LATTICE_HEX_NSLIPSYSTEM
|
||
slipSystems = LATTICE_HEX_SYSTEMSLIP
|
||
case('bct')
|
||
NslipMax = LATTICE_BCT_NSLIPSYSTEM
|
||
slipSystems = LATTICE_BCT_SYSTEMSLIP
|
||
case default
|
||
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure))
|
||
end select
|
||
|
||
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
|
||
call IO_error(145,ext_msg='Nslip '//trim(structure))
|
||
if (any(Nslip < 0)) &
|
||
call IO_error(144,ext_msg='Nslip '//trim(structure))
|
||
|
||
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
|
||
|
||
end function coordinateSystem_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Populates reduced interaction matrix
|
||
!--------------------------------------------------------------------------------------------------
|
||
function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
reacting_used, & !< # of reacting systems per family as specified in material.config
|
||
acting_used, & !< # of acting systems per family as specified in material.config
|
||
reacting_max, & !< max # of reacting systems per family for given lattice
|
||
acting_max !< max # of acting systems per family for given lattice
|
||
real(pReal), dimension(:), intent(in) :: values !< interaction values
|
||
integer, dimension(:,:), intent(in) :: matrix !< interaction types
|
||
real(pReal), dimension(sum(reacting_used),sum(acting_used)) :: buildInteraction
|
||
|
||
integer :: &
|
||
acting_family_index, acting_family, acting_system, &
|
||
reacting_family_index, reacting_family, reacting_system, &
|
||
i,j,k,l
|
||
|
||
do acting_family = 1,size(acting_used,1)
|
||
acting_family_index = sum(acting_used(1:acting_family-1))
|
||
do acting_system = 1,acting_used(acting_family)
|
||
|
||
do reacting_family = 1,size(reacting_used,1)
|
||
reacting_family_index = sum(reacting_used(1:reacting_family-1))
|
||
do reacting_system = 1,reacting_used(reacting_family)
|
||
|
||
i = sum( acting_max(1: acting_family-1)) + acting_system
|
||
j = sum(reacting_max(1:reacting_family-1)) + reacting_system
|
||
|
||
k = acting_family_index + acting_system
|
||
l = reacting_family_index + reacting_system
|
||
|
||
if (matrix(i,j) > size(values)) call IO_error(138,ext_msg='buildInteraction')
|
||
|
||
buildInteraction(l,k) = values(matrix(i,j))
|
||
|
||
enddo; enddo
|
||
enddo; enddo
|
||
|
||
end function buildInteraction
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief build a local coordinate system on slip, twin, trans, cleavage systems
|
||
!> @details Order: Direction, plane (normal), and common perpendicular
|
||
!--------------------------------------------------------------------------------------------------
|
||
function buildCoordinateSystem(active,potential,system,structure,cOverA)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
active, &
|
||
potential
|
||
real(pReal), dimension(:,:), intent(in) :: &
|
||
system
|
||
character(len=*), intent(in) :: &
|
||
structure !< lattice structure
|
||
real(pReal), intent(in) :: &
|
||
cOverA
|
||
real(pReal), dimension(3,3,sum(active)) :: &
|
||
buildCoordinateSystem
|
||
|
||
real(pReal), dimension(3) :: &
|
||
direction, normal
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system matrix
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
if (len_trim(structure) /= 3) &
|
||
call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure))
|
||
if (trim(structure(1:3)) == 'bct' .and. cOverA > 2.0_pReal) &
|
||
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
|
||
if (trim(structure(1:3)) == 'hex' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
|
||
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
|
||
|
||
a = 0
|
||
activeFamilies: do f = 1,size(active,1)
|
||
activeSystems: do s = 1,active(f)
|
||
a = a + 1
|
||
p = sum(potential(1:f-1))+s
|
||
|
||
select case(trim(structure(1:3)))
|
||
|
||
case ('fcc','bcc','iso','ort','bct')
|
||
direction = system(1:3,p)
|
||
normal = system(4:6,p)
|
||
|
||
case ('hex')
|
||
direction = [ system(1,p)*1.5_pReal, &
|
||
(system(1,p)+2.0_pReal*system(2,p))*sqrt(0.75_pReal), &
|
||
system(4,p)*cOverA ] ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(p/a)])
|
||
normal = [ system(5,p), &
|
||
(system(5,p)+2.0_pReal*system(6,p))/sqrt(3.0_pReal), &
|
||
system(8,p)/cOverA ] ! plane (hkil)->(h (h+2k)/sqrt(3) l/(p/a))
|
||
|
||
case default
|
||
call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure))
|
||
|
||
end select
|
||
|
||
buildCoordinateSystem(1:3,1,a) = direction/norm2(direction)
|
||
buildCoordinateSystem(1:3,2,a) = normal /norm2(normal)
|
||
buildCoordinateSystem(1:3,3,a) = math_cross(direction/norm2(direction),&
|
||
normal /norm2(normal))
|
||
|
||
enddo activeSystems
|
||
enddo activeFamilies
|
||
|
||
end function buildCoordinateSystem
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Helper function to define transformation systems
|
||
! Needed to calculate Schmid matrix and rotated stiffness matrices.
|
||
! @details: set c/a = 0.0 for fcc -> bcc transformation
|
||
! set a_Xcc = 0.0 for fcc -> hex transformation
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
Ntrans
|
||
real(pReal), dimension(3,3,sum(Ntrans)), intent(out) :: &
|
||
Q, & !< Total rotation: Q = R*B
|
||
S !< Eigendeformation tensor for phase transformation
|
||
real(pReal), intent(in) :: &
|
||
cOverA, & !< c/a for target hex structure
|
||
a_bcc, & !< lattice parameter a for target bcc structure
|
||
a_fcc !< lattice parameter a for parent fcc structure
|
||
|
||
type(rotation) :: &
|
||
R, & !< Pitsch rotation
|
||
B !< Rotation of fcc to Bain coordinate system
|
||
real(pReal), dimension(3,3) :: &
|
||
U, & !< Bain deformation
|
||
ss, sd
|
||
real(pReal), dimension(3) :: &
|
||
x, y, z
|
||
integer :: &
|
||
i
|
||
real(pReal), dimension(3+3,LATTICE_FCC_NTRANS), parameter :: &
|
||
LATTICE_FCCTOHEX_SYSTEMTRANS = reshape(real( [&
|
||
-2, 1, 1, 1, 1, 1, &
|
||
1,-2, 1, 1, 1, 1, &
|
||
1, 1,-2, 1, 1, 1, &
|
||
2,-1, 1, -1,-1, 1, &
|
||
-1, 2, 1, -1,-1, 1, &
|
||
-1,-1,-2, -1,-1, 1, &
|
||
-2,-1,-1, 1,-1,-1, &
|
||
1, 2,-1, 1,-1,-1, &
|
||
1,-1, 2, 1,-1,-1, &
|
||
2, 1,-1, -1, 1,-1, &
|
||
-1,-2,-1, -1, 1,-1, &
|
||
-1, 1, 2, -1, 1,-1 &
|
||
],pReal),shape(LATTICE_FCCTOHEX_SYSTEMTRANS))
|
||
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter :: &
|
||
LATTICE_FCCTOBCC_SYSTEMTRANS = reshape([&
|
||
0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
|
||
0.0,-1.0, 0.0, 10.26, &
|
||
0.0, 0.0, 1.0, 10.26, &
|
||
0.0, 0.0,-1.0, 10.26, &
|
||
1.0, 0.0, 0.0, 10.26, &
|
||
-1.0, 0.0, 0.0, 10.26, &
|
||
0.0, 0.0, 1.0, 10.26, &
|
||
0.0, 0.0,-1.0, 10.26, &
|
||
1.0, 0.0, 0.0, 10.26, &
|
||
-1.0, 0.0, 0.0, 10.26, &
|
||
0.0, 1.0, 0.0, 10.26, &
|
||
0.0,-1.0, 0.0, 10.26 &
|
||
],shape(LATTICE_FCCTOBCC_SYSTEMTRANS))
|
||
|
||
integer, dimension(9,LATTICE_fcc_Ntrans), parameter :: &
|
||
LATTICE_FCCTOBCC_BAINVARIANT = reshape( [&
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
1, 0, 0, 0, 1, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 1, 0, 1, 0, 0, 0, 0, 1, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0, &
|
||
0, 0, 1, 1, 0, 0, 0, 1, 0 &
|
||
],shape(LATTICE_FCCTOBCC_BAINVARIANT))
|
||
|
||
real(pReal), dimension(4,LATTICE_fcc_Ntrans), parameter :: &
|
||
LATTICE_FCCTOBCC_BAINROT = reshape([&
|
||
1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
1.0, 0.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 1.0, 0.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0, &
|
||
0.0, 0.0, 1.0, 45.0 &
|
||
],shape(LATTICE_FCCTOBCC_BAINROT))
|
||
|
||
if (a_bcc > 0.0_pReal .and. a_fcc > 0.0_pReal .and. dEq0(cOverA)) then ! fcc -> bcc transformation
|
||
do i = 1,sum(Ntrans)
|
||
call R%fromAxisAngle(LATTICE_FCCTOBCC_SYSTEMTRANS(:,i),degrees=.true.,P=1)
|
||
call B%fromAxisAngle(LATTICE_FCCTOBCC_BAINROT(:,i), degrees=.true.,P=1)
|
||
x = real(LATTICE_FCCTOBCC_BAINVARIANT(1:3,i),pReal)
|
||
y = real(LATTICE_FCCTOBCC_BAINVARIANT(4:6,i),pReal)
|
||
z = real(LATTICE_FCCTOBCC_BAINVARIANT(7:9,i),pReal)
|
||
|
||
U = (a_bcc/a_fcc)*math_outer(x,x) &
|
||
+ (a_bcc/a_fcc)*math_outer(y,y) * sqrt(2.0_pReal) &
|
||
+ (a_bcc/a_fcc)*math_outer(z,z) * sqrt(2.0_pReal)
|
||
Q(1:3,1:3,i) = matmul(R%asMatrix(),B%asMatrix())
|
||
S(1:3,1:3,i) = matmul(R%asMatrix(),U) - MATH_I3
|
||
enddo
|
||
elseif (cOverA > 0.0_pReal .and. dEq0(a_bcc)) then ! fcc -> hex transformation
|
||
ss = MATH_I3
|
||
sd = MATH_I3
|
||
ss(1,3) = sqrt(2.0_pReal)/4.0_pReal
|
||
sd(3,3) = cOverA/sqrt(8.0_pReal/3.0_pReal)
|
||
|
||
do i = 1,sum(Ntrans)
|
||
x = LATTICE_FCCTOHEX_SYSTEMTRANS(1:3,i)/norm2(LATTICE_FCCTOHEX_SYSTEMTRANS(1:3,i))
|
||
z = LATTICE_FCCTOHEX_SYSTEMTRANS(4:6,i)/norm2(LATTICE_FCCTOHEX_SYSTEMTRANS(4:6,i))
|
||
y = -math_cross(x,z)
|
||
Q(1:3,1,i) = x
|
||
Q(1:3,2,i) = y
|
||
Q(1:3,3,i) = z
|
||
S(1:3,1:3,i) = matmul(Q(1:3,1:3,i), matmul(matmul(sd,ss), transpose(Q(1:3,1:3,i)))) - MATH_I3 ! ToDo: This is of interest for the Schmid matrix only
|
||
enddo
|
||
else
|
||
call IO_error(132,ext_msg='buildTransformationSystem')
|
||
endif
|
||
|
||
end subroutine buildTransformationSystem
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief select active systems as strings
|
||
!--------------------------------------------------------------------------------------------------
|
||
function getlabels(active,potential,system,structure) result(labels)
|
||
|
||
integer, dimension(:), intent(in) :: &
|
||
active, &
|
||
potential
|
||
real(pReal), dimension(:,:), intent(in) :: &
|
||
system
|
||
character(len=*), intent(in) :: structure !< lattice structure
|
||
|
||
character(len=:), dimension(:), allocatable :: labels
|
||
character(len=:), allocatable :: label
|
||
|
||
integer :: i,j
|
||
integer :: &
|
||
a, & !< index of active system
|
||
p, & !< index in potential system matrix
|
||
f, & !< index of my family
|
||
s !< index of my system in current family
|
||
|
||
i = 2*size(system,1) + (size(system,1) - 2) + 4 ! 2 letters per index + spaces + brackets
|
||
allocate(character(len=i) :: labels(sum(active)), label)
|
||
|
||
a = 0
|
||
activeFamilies: do f = 1,size(active,1)
|
||
activeSystems: do s = 1,active(f)
|
||
a = a + 1
|
||
p = sum(potential(1:f-1))+s
|
||
|
||
i = 1
|
||
label(i:i) = merge('[','<',structure(1:3) /= 'bct')
|
||
direction: do j = 1, size(system,1)/2
|
||
write(label(i+1:i+2),"(I2.1)") int(system(j,p))
|
||
label(i+3:i+3) = ' '
|
||
i = i + 3
|
||
enddo direction
|
||
label(i:i) = ']'
|
||
i = i +1
|
||
label(i:i) = merge('(','{',structure(1:3) /= 'bct')
|
||
normal: do j = size(system,1)/2+1, size(system,1)
|
||
write(label(i+1:i+2),"(I2.1)") int(system(j,p))
|
||
label(i+3:i+3) = ' '
|
||
i = i + 3
|
||
enddo normal
|
||
label(i:i) = ')'
|
||
|
||
labels(s) = label
|
||
|
||
enddo activeSystems
|
||
enddo activeFamilies
|
||
|
||
end function getlabels
|
||
|
||
|
||
end module lattice
|