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DAMASK_EICMD/src/lattice.f90

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!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @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
!--------------------------------------------------------------------------------------------------
! face centered cubic (cF)
integer, dimension(*), parameter :: &
FCC_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for fcc
integer, dimension(*), parameter :: &
FCC_NTWINSYSTEM = [12] !< # of twin systems per family for fcc
integer, dimension(*), parameter :: &
FCC_NTRANSSYSTEM = [12] !< # of transformation systems per family for fcc
integer, dimension(*), parameter :: &
FCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for fcc
integer, parameter :: &
#ifndef __PGI
FCC_NSLIP = sum(FCC_NSLIPSYSTEM), & !< total # of slip systems for fcc
FCC_NTWIN = sum(FCC_NTWINSYSTEM), & !< total # of twin systems for fcc
FCC_NTRANS = sum(FCC_NTRANSSYSTEM), & !< total # of transformation systems for fcc
FCC_NCLEAVAGE = sum(FCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for fcc
#else
FCC_NSLIP = 18, &
FCC_NTWIN = 12, &
FCC_NTRANS = 12, &
FCC_NCLEAVAGE = 3
#endif
real(pReal), dimension(3+3,FCC_NSLIP), parameter :: &
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(FCC_SYSTEMSLIP)) !< Slip system <110>{111} directions. Sorted according to Eisenlohr & Hantcherli
real(pReal), dimension(3+3,FCC_NTWIN), parameter :: &
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(FCC_SYSTEMTWIN)) !< Twin system <112>{111} directions. Sorted according to Eisenlohr & Hantcherli
integer, dimension(2,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,FCC_NCLEAVAGE), parameter :: &
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 &
],pReal),shape(FCC_SYSTEMCLEAVAGE))
!--------------------------------------------------------------------------------------------------
! body centered cubic (cI)
integer, dimension(*), parameter :: &
BCC_NSLIPSYSTEM = [12, 12] !< # of slip systems per family for bcc
integer, dimension(*), parameter :: &
BCC_NTWINSYSTEM = [12] !< # of twin systems per family for bcc
integer, dimension(*), parameter :: &
BCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for bcc
integer, parameter :: &
#ifndef __PGI
BCC_NSLIP = sum(BCC_NSLIPSYSTEM), & !< total # of slip systems for bcc
BCC_NTWIN = sum(BCC_NTWINSYSTEM), & !< total # of twin systems for bcc
BCC_NCLEAVAGE = sum(BCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for bcc
#else
BCC_NSLIP = 24, &
BCC_NTWIN = 12, &
BCC_NCLEAVAGE = 3
#endif
real(pReal), dimension(3+3,BCC_NSLIP), parameter :: &
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(BCC_SYSTEMSLIP))
real(pReal), dimension(3+3,BCC_NTWIN), parameter :: &
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(BCC_SYSTEMTWIN))
real(pReal), dimension(3+3,BCC_NCLEAVAGE), parameter :: &
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 &
],pReal),shape(BCC_SYSTEMCLEAVAGE))
!--------------------------------------------------------------------------------------------------
! hexagonal (hP)
integer, dimension(*), parameter :: &
HEX_NSLIPSYSTEM = [3, 3, 3, 6, 12, 6] !< # of slip systems per family for hex
integer, dimension(*), parameter :: &
HEX_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hex
integer, parameter :: &
#ifndef __PGI
HEX_NSLIP = sum(HEX_NSLIPSYSTEM), & !< total # of slip systems for hex
HEX_NTWIN = sum(HEX_NTWINSYSTEM) !< total # of twin systems for hex
#else
HEX_NSLIP = 33, &
HEX_NTWIN = 24
#endif
real(pReal), dimension(4+4,HEX_NSLIP), parameter :: &
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(HEX_SYSTEMSLIP)) !< slip systems for hex, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
real(pReal), dimension(4+4,HEX_NTWIN), parameter :: &
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(HEX_SYSTEMTWIN)) !< twin systems for hex, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
!--------------------------------------------------------------------------------------------------
! body centered tetragonal (tI)
integer, dimension(*), parameter :: &
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 :: &
#ifndef __PGI
BCT_NSLIP = sum(BCT_NSLIPSYSTEM) !< total # of slip systems for bct
#else
BCT_NSLIP = 52
#endif
real(pReal), dimension(3+3,BCT_NSLIP), parameter :: &
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),shape(BCT_SYSTEMSLIP)) !< slip systems for bct sorted by Bieler
!--------------------------------------------------------------------------------------------------
! orthorhombic primitive (oP)
integer, dimension(*), parameter :: &
ORT_NCLEAVAGESYSTEM = [1, 1, 1] !< # of cleavage systems per family for ortho
integer, parameter :: &
#ifndef __PGI
ORT_NCLEAVAGE = sum(ORT_NCLEAVAGESYSTEM) !< total # of cleavage systems for ortho
#else
ORT_NCLEAVAGE = 3
#endif
real(pReal), dimension(3+3,ORT_NCLEAVAGE), parameter :: &
ORT_SYSTEMCLEAVAGE = reshape(real([&
! Cleavage direction Plane normal
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1 &
],pReal),shape(ORT_SYSTEMCLEAVAGE))
enum, bind(c); enumerator :: &
lattice_UNDEFINED_ID, &
lattice_ISO_ID, &
lattice_FCC_ID, &
lattice_BCC_ID, &
lattice_BCT_ID, &
lattice_HEX_ID, &
lattice_ORT_ID
end enum
! SHOULD NOT BE PART OF LATTICE BEGIN
real(pReal), dimension(:), allocatable, public, protected :: &
lattice_mu, lattice_nu, &
lattice_M, &
lattice_rho, &
lattice_c_p
real(pReal), dimension(:,:,:), allocatable, public, protected :: &
lattice_C66, &
lattice_K, &
lattice_D
integer(kind(lattice_UNDEFINED_ID)), dimension(:), allocatable, public, protected :: &
lattice_structure
! SHOULD NOT BE PART OF LATTICE END
interface lattice_forestProjection_edge
module procedure slipProjection_transverse
end interface lattice_forestProjection_edge
interface lattice_forestProjection_screw
module procedure slipProjection_direction
end interface lattice_forestProjection_screw
public :: &
lattice_init, &
lattice_ISO_ID, &
lattice_FCC_ID, &
lattice_BCC_ID, &
lattice_BCT_ID, &
lattice_HEX_ID, &
lattice_ORT_ID, &
lattice_equivalent_nu, &
lattice_equivalent_mu, &
lattice_applyLatticeSymmetry33, &
lattice_SchmidMatrix_slip, &
lattice_SchmidMatrix_twin, &
lattice_SchmidMatrix_trans, &
lattice_SchmidMatrix_cleavage, &
lattice_nonSchmidMatrix, &
lattice_interaction_SlipBySlip, &
lattice_interaction_TwinByTwin, &
lattice_interaction_TransByTrans, &
lattice_interaction_SlipByTwin, &
lattice_interaction_SlipByTrans, &
lattice_interaction_TwinBySlip, &
lattice_characteristicShear_Twin, &
lattice_C66_twin, &
lattice_C66_trans, &
lattice_forestProjection_edge, &
lattice_forestProjection_screw, &
lattice_slip_normal, &
lattice_slip_direction, &
lattice_slip_transverse, &
lattice_labels_slip, &
lattice_labels_twin
contains
!--------------------------------------------------------------------------------------------------
!> @brief Module initialization
!--------------------------------------------------------------------------------------------------
subroutine lattice_init
integer :: Nphases, ph,i
class(tNode), pointer :: &
phases, &
phase, &
mech, &
elasticity, &
thermal, &
damage
print'(/,a)', ' <<<+- lattice init -+>>>'; flush(IO_STDOUT)
phases => config_material%get('phase')
Nphases = phases%length
allocate(lattice_structure(Nphases),source = lattice_UNDEFINED_ID)
allocate(lattice_C66(6,6,Nphases), source=0.0_pReal)
allocate(lattice_K (3,3,Nphases), source=0.0_pReal)
allocate(lattice_D (3,3,Nphases), source=0.0_pReal)
allocate(lattice_M,&
lattice_rho,lattice_c_p, &
lattice_mu, lattice_nu,&
source=[(0.0_pReal,i=1,Nphases)])
do ph = 1, phases%length
phase => phases%get(ph)
mech => phase%get('mechanics')
elasticity => mech%get('elasticity')
lattice_C66(1,1,ph) = elasticity%get_asFloat('C_11')
lattice_C66(1,2,ph) = elasticity%get_asFloat('C_12')
lattice_C66(1,3,ph) = elasticity%get_asFloat('C_13',defaultVal=0.0_pReal)
lattice_C66(2,2,ph) = elasticity%get_asFloat('C_22',defaultVal=0.0_pReal)
lattice_C66(2,3,ph) = elasticity%get_asFloat('C_23',defaultVal=0.0_pReal)
lattice_C66(3,3,ph) = elasticity%get_asFloat('C_33',defaultVal=0.0_pReal)
lattice_C66(4,4,ph) = elasticity%get_asFloat('C_44',defaultVal=0.0_pReal)
lattice_C66(5,5,ph) = elasticity%get_asFloat('C_55',defaultVal=0.0_pReal)
lattice_C66(6,6,ph) = elasticity%get_asFloat('C_66',defaultVal=0.0_pReal)
select case(phase%get_asString('lattice'))
case('cF')
lattice_structure(ph) = lattice_FCC_ID
case('cI')
lattice_structure(ph) = lattice_BCC_ID
case('hP')
lattice_structure(ph) = lattice_HEX_ID
case('tI')
lattice_structure(ph) = lattice_BCT_ID
case('oP')
lattice_structure(ph) = lattice_ORT_ID
case('aP')
lattice_structure(ph) = lattice_ISO_ID
case default
call IO_error(130,ext_msg='lattice_init: '//phase%get_asString('lattice'))
end select
lattice_C66(1:6,1:6,ph) = applyLatticeSymmetryC66(lattice_C66(1:6,1:6,ph),phase%get_asString('lattice'))
lattice_nu(ph) = lattice_equivalent_nu(lattice_C66(1:6,1:6,ph),'voigt')
lattice_mu(ph) = lattice_equivalent_mu(lattice_C66(1:6,1:6,ph),'voigt')
lattice_C66(1:6,1:6,ph) = math_sym3333to66(math_Voigt66to3333(lattice_C66(1:6,1:6,ph))) ! Literature data is in Voigt notation
do i = 1, 6
if (abs(lattice_C66(i,i,ph))<tol_math_check) &
call IO_error(135,el=i,ip=ph,ext_msg='matrix diagonal "el"ement of phase "ip"')
enddo
lattice_rho(ph) = phase%get_asFloat('rho', defaultVal=0.0_pReal)
! SHOULD NOT BE PART OF LATTICE BEGIN
if (phase%contains('thermal')) then
thermal => phase%get('thermal')
lattice_K(1,1,ph) = thermal%get_asFloat('K_11',defaultVal=0.0_pReal)
lattice_K(2,2,ph) = thermal%get_asFloat('K_22',defaultVal=0.0_pReal)
lattice_K(3,3,ph) = thermal%get_asFloat('K_33',defaultVal=0.0_pReal)
lattice_K(1:3,1:3,ph) = lattice_applyLatticeSymmetry33(lattice_K(1:3,1:3,ph), &
phase%get_asString('lattice'))
lattice_c_p(ph) = thermal%get_asFloat('c_p', defaultVal=0.0_pReal)
endif
if (phase%contains('damage')) then
damage => phase%get('damage')
damage => damage%get(1)
lattice_D(1,1,ph) = damage%get_asFloat('D_11',defaultVal=0.0_pReal)
lattice_D(2,2,ph) = damage%get_asFloat('D_22',defaultVal=0.0_pReal)
lattice_D(3,3,ph) = damage%get_asFloat('D_33',defaultVal=0.0_pReal)
lattice_D(1:3,1:3,ph) = lattice_applyLatticeSymmetry33(lattice_D(1:3,1:3,ph), &
phase%get_asString('lattice'))
lattice_M(ph) = damage%get_asFloat('M',defaultVal=0.0_pReal)
endif
! SHOULD NOT BE PART OF LATTICE END
call selfTest
enddo
end subroutine lattice_init
!--------------------------------------------------------------------------------------------------
!> @brief Characteristic shear for twinning
!--------------------------------------------------------------------------------------------------
function lattice_characteristicShear_Twin(Ntwin,structure,CoverA) result(characteristicShear)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(sum(Ntwin)) :: characteristicShear
integer :: &
a, & !< index of active system
p, & !< index in potential system list
f, & !< index of my family
s !< index of my system in current family
integer, dimension(HEX_NTWIN), parameter :: &
HEX_SHEARTWIN = reshape( [&
1, & ! <-10.1>{10.2}
1, &
1, &
1, &
1, &
1, &
2, & ! <11.6>{-1-1.1}
2, &
2, &
2, &
2, &
2, &
3, & ! <10.-2>{10.1}
3, &
3, &
3, &
3, &
3, &
4, & ! <11.-3>{11.2}
4, &
4, &
4, &
4, &
4 &
],[HEX_NTWIN]) ! indicator to formulas below
a = 0
myFamilies: do f = 1,size(Ntwin,1)
mySystems: do s = 1,Ntwin(f)
a = a + 1
select case(structure)
case('cF','cI')
characteristicShear(a) = 0.5_pReal*sqrt(2.0_pReal)
case('hP')
if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) &
call IO_error(131,ext_msg='lattice_characteristicShear_Twin')
p = sum(HEX_NTWINSYSTEM(1:f-1))+s
select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
case (1) ! <-10.1>{10.2}
characteristicShear(a) = (3.0_pReal-cOverA**2.0_pReal)/sqrt(3.0_pReal)/CoverA
case (2) ! <11.6>{-1-1.1}
characteristicShear(a) = 1.0_pReal/cOverA
case (3) ! <10.-2>{10.1}
characteristicShear(a) = (4.0_pReal*cOverA**2.0_pReal-9.0_pReal)/sqrt(48.0_pReal)/cOverA
case (4) ! <11.-3>{11.2}
characteristicShear(a) = 2.0_pReal*(cOverA**2.0_pReal-2.0_pReal)/3.0_pReal/cOverA
end select
case default
call IO_error(137,ext_msg='lattice_characteristicShear_Twin: '//trim(structure))
end select
enddo mySystems
enddo myFamilies
end function lattice_characteristicShear_Twin
!--------------------------------------------------------------------------------------------------
!> @brief Rotated elasticity matrices for twinning in 66-vector notation
!--------------------------------------------------------------------------------------------------
function lattice_C66_twin(Ntwin,C66,structure,CoverA)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), dimension(6,6), intent(in) :: C66 !< unrotated parent stiffness matrix
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(6,6,sum(Ntwin)) :: lattice_C66_twin
real(pReal), dimension(3,3,sum(Ntwin)):: coordinateSystem
type(rotation) :: R
integer :: i
select case(structure)
case('cF')
coordinateSystem = buildCoordinateSystem(Ntwin,FCC_NSLIPSYSTEM,FCC_SYSTEMTWIN,&
structure,0.0_pReal)
case('cI')
coordinateSystem = buildCoordinateSystem(Ntwin,BCC_NSLIPSYSTEM,BCC_SYSTEMTWIN,&
structure,0.0_pReal)
case('hP')
coordinateSystem = buildCoordinateSystem(Ntwin,HEX_NSLIPSYSTEM,HEX_SYSTEMTWIN,&
structure,cOverA)
case default
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(structure))
end select
do i = 1, sum(Ntwin)
call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI],P=1) ! ToDo: Why always 180 deg?
lattice_C66_twin(1:6,1:6,i) = R%rotTensor4sym(C66)
enddo
end function lattice_C66_twin
!--------------------------------------------------------------------------------------------------
!> @brief Rotated elasticity matrices for transformation in 66-vector notation
!--------------------------------------------------------------------------------------------------
function lattice_C66_trans(Ntrans,C_parent66,structure_target, &
cOverA_trans,a_bcc,a_fcc)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=*), intent(in) :: structure_target !< lattice structure
real(pReal), dimension(6,6), intent(in) :: C_parent66
real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans
real(pReal), dimension(6,6) :: C_bar66, C_target_unrotated66
real(pReal), dimension(3,3,sum(Ntrans)) :: Q,S
type(rotation) :: R
real(pReal) :: a_bcc, a_fcc, cOverA_trans
integer :: i
!--------------------------------------------------------------------------------------------------
! elasticity matrix of the target phase in cube orientation
if (structure_target == 'hP') then
if (cOverA_trans < 1.0_pReal .or. cOverA_trans > 2.0_pReal) &
call IO_error(131,ext_msg='lattice_C66_trans: '//trim(structure_target))
C_bar66(1,1) = (C_parent66(1,1) + C_parent66(1,2) + 2.0_pReal*C_parent66(4,4))/2.0_pReal
C_bar66(1,2) = (C_parent66(1,1) + 5.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/6.0_pReal
C_bar66(3,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) + 4.0_pReal*C_parent66(4,4))/3.0_pReal
C_bar66(1,3) = (C_parent66(1,1) + 2.0_pReal*C_parent66(1,2) - 2.0_pReal*C_parent66(4,4))/3.0_pReal
C_bar66(4,4) = (C_parent66(1,1) - C_parent66(1,2) + C_parent66(4,4))/3.0_pReal
C_bar66(1,4) = (C_parent66(1,1) - C_parent66(1,2) - 2.0_pReal*C_parent66(4,4)) /(3.0_pReal*sqrt(2.0_pReal))
C_target_unrotated66 = 0.0_pReal
C_target_unrotated66(1,1) = C_bar66(1,1) - C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2.0_pReal/C_bar66(4,4)
C_target_unrotated66(1,3) = C_bar66(1,3)
C_target_unrotated66(3,3) = C_bar66(3,3)
C_target_unrotated66(4,4) = C_bar66(4,4) - C_bar66(1,4)**2.0_pReal/(0.5_pReal*(C_bar66(1,1) - C_bar66(1,2)))
C_target_unrotated66 = applyLatticeSymmetryC66(C_target_unrotated66,'hP')
elseif (structure_target == 'cI') then
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
call IO_error(134,ext_msg='lattice_C66_trans: '//trim(structure_target))
C_target_unrotated66 = C_parent66
else
call IO_error(137,ext_msg='lattice_C66_trans : '//trim(structure_target))
endif
do i = 1, 6
if (abs(C_target_unrotated66(i,i))<tol_math_check) &
call IO_error(135,el=i,ext_msg='matrix diagonal "el"ement in transformation')
enddo
call buildTransformationSystem(Q,S,Ntrans,cOverA_trans,a_fcc,a_bcc)
do i = 1, sum(Ntrans)
call R%fromMatrix(Q(1:3,1:3,i))
lattice_C66_trans(1:6,1:6,i) = R%rotTensor4sym(C_target_unrotated66)
enddo
end function lattice_C66_trans
!--------------------------------------------------------------------------------------------------
!> @brief Non-schmid projections for bcc with up to 6 coefficients
! Koester et al. 2012, Acta Materialia 60 (2012) 3894–3901, eq. (17)
! Gröger et al. 2008, Acta Materialia 56 (2008) 5412–5425, table 1
!--------------------------------------------------------------------------------------------------
function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSchmidMatrix)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
real(pReal), dimension(:), intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections
integer, intent(in) :: sense !< sense (-1,+1)
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: nonSchmidMatrix
real(pReal), dimension(1:3,1:3,sum(Nslip)) :: coordinateSystem !< coordinate system of slip system
real(pReal), dimension(3) :: direction, normal, np
type(rotation) :: R
integer :: i
if (abs(sense) /= 1) error stop 'Sense in lattice_nonSchmidMatrix'
coordinateSystem = buildCoordinateSystem(Nslip,BCC_NSLIPSYSTEM,BCC_SYSTEMSLIP,&
'cI',0.0_pReal)
coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip))*real(sense,pReal) ! convert unidirectional coordinate system
nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'cI',0.0_pReal) ! Schmid contribution
do i = 1,sum(Nslip)
direction = coordinateSystem(1:3,1,i)
normal = coordinateSystem(1:3,2,i)
call R%fromAxisAngle([direction,60.0_pReal],degrees=.true.,P=1)
np = R%rotate(normal)
if (size(nonSchmidCoefficients)>0) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(1) * math_outer(direction, np)
if (size(nonSchmidCoefficients)>1) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(2) * math_outer(math_cross(normal, direction), normal)
if (size(nonSchmidCoefficients)>2) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(3) * math_outer(math_cross(np, direction), np)
if (size(nonSchmidCoefficients)>3) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(4) * math_outer(normal, normal)
if (size(nonSchmidCoefficients)>4) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(5) * math_outer(math_cross(normal, direction), &
math_cross(normal, direction))
if (size(nonSchmidCoefficients)>5) nonSchmidMatrix(1:3,1:3,i) = nonSchmidMatrix(1:3,1:3,i) &
+ nonSchmidCoefficients(6) * math_outer(direction, direction)
enddo
end function lattice_nonSchmidMatrix
!--------------------------------------------------------------------------------------------------
!> @brief Slip-slip interaction matrix
!> details only active slip systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipBySlip(Nslip,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-slip interaction
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NSLIP,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPSLIP = reshape( [&
1, 2, 2, 4, 6, 5, 3, 5, 5, 4, 5, 6, 9,10, 9,10,11,12, & ! -----> acting
2, 1, 2, 6, 4, 5, 5, 4, 6, 5, 3, 5, 9,10,11,12, 9,10, & ! |
2, 2, 1, 5, 5, 3, 5, 6, 4, 6, 5, 4, 11,12, 9,10, 9,10, & ! |
4, 6, 5, 1, 2, 2, 4, 5, 6, 3, 5, 5, 9,10,10, 9,12,11, & ! v
6, 4, 5, 2, 1, 2, 5, 3, 5, 5, 4, 6, 9,10,12,11,10, 9, & ! reacting
5, 5, 3, 2, 2, 1, 6, 5, 4, 5, 6, 4, 11,12,10, 9,10, 9, &
3, 5, 5, 4, 5, 6, 1, 2, 2, 4, 6, 5, 10, 9,10, 9,11,12, &
5, 4, 6, 5, 3, 5, 2, 1, 2, 6, 4, 5, 10, 9,12,11, 9,10, &
5, 6, 4, 6, 5, 4, 2, 2, 1, 5, 5, 3, 12,11,10, 9, 9,10, &
4, 5, 6, 3, 5, 5, 4, 6, 5, 1, 2, 2, 10, 9, 9,10,12,11, &
5, 3, 5, 5, 4, 6, 6, 4, 5, 2, 1, 2, 10, 9,11,12,10, 9, &
6, 5, 4, 5, 6, 4, 5, 5, 3, 2, 2, 1, 12,11, 9,10,10, 9, &
9, 9,11, 9, 9,11,10,10,12,10,10,12, 1, 7, 8, 8, 8, 8, &
10,10,12,10,10,12, 9, 9,11, 9, 9,11, 7, 1, 8, 8, 8, 8, &
9,11, 9,10,12,10,10,12,10, 9,11, 9, 8, 8, 1, 7, 8, 8, &
10,12,10, 9,11, 9, 9,11, 9,10,12,10, 8, 8, 7, 1, 8, 8, &
11, 9, 9,12,10,10,11, 9, 9,12,10,10, 8, 8, 8, 8, 1, 7, &
12,10,10,11, 9, 9,12,10,10,11, 9, 9, 8, 8, 8, 8, 7, 1 &
],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for fcc
!< 1: self interaction
!< 2: coplanar interaction
!< 3: collinear interaction
!< 4: Hirth locks
!< 5: glissile junctions
!< 6: Lomer locks
!< 7: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
!< 8: similar to Lomer locks in <110>{111} for two {110} planes
!< 9: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
!<10: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
!<11: crossing btw one {110} and one {111} plane
!<12: collinear btw one {110} and one {111} plane
integer, dimension(BCC_NSLIP,BCC_NSLIP), parameter :: &
BCC_INTERACTIONSLIPSLIP = reshape( [&
1,2,6,6,5,4,4,3,4,3,5,4, 6,6,4,3,3,4,6,6,4,3,6,6, & ! -----> acting
2,1,6,6,4,3,5,4,5,4,4,3, 6,6,3,4,4,3,6,6,3,4,6,6, & ! |
6,6,1,2,4,5,3,4,4,5,3,4, 4,3,6,6,6,6,3,4,6,6,4,3, & ! |
6,6,2,1,3,4,4,5,3,4,4,5, 3,4,6,6,6,6,4,3,6,6,3,4, & ! v
5,4,4,3,1,2,6,6,3,4,5,4, 3,6,4,6,6,4,6,3,4,6,3,6, & ! reacting
4,3,5,4,2,1,6,6,4,5,4,3, 4,6,3,6,6,3,6,4,3,6,4,6, &
4,5,3,4,6,6,1,2,5,4,3,4, 6,3,6,4,4,6,3,6,6,4,6,3, &
3,4,4,5,6,6,2,1,4,3,4,5, 6,4,6,3,3,6,4,6,6,3,6,4, &
4,5,4,3,3,4,5,4,1,2,6,6, 3,6,6,4,4,6,6,3,6,4,3,6, &
3,4,5,4,4,5,4,3,2,1,6,6, 4,6,6,3,3,6,6,4,6,3,4,6, &
5,4,3,4,5,4,3,4,6,6,1,2, 6,3,4,6,6,4,3,6,4,6,6,3, &
4,3,4,5,4,3,4,5,6,6,2,1, 6,4,3,6,6,3,4,6,3,6,6,4, &
!
6,6,4,3,3,4,6,6,3,4,6,6, 1,5,6,6,5,6,6,3,5,6,3,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 5,1,6,6,6,5,3,6,6,5,6,3, &
4,3,6,6,4,3,6,6,6,6,4,3, 6,6,1,5,6,3,5,6,3,6,5,6, &
3,4,6,6,6,6,4,3,4,3,6,6, 6,6,5,1,3,6,6,5,6,3,6,5, &
3,4,6,6,6,6,4,3,4,3,6,6, 5,6,6,3,1,6,5,6,5,3,6,6, &
4,3,6,6,4,3,6,6,6,6,4,3, 6,5,3,6,6,1,6,5,3,5,6,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,5,6,5,6,1,6,6,6,5,3, &
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,6,5,6,5,6,1,6,6,3,5, &
4,3,6,6,4,3,6,6,6,6,4,3, 5,6,3,6,5,3,6,6,1,6,6,5, &
3,4,6,6,6,6,4,3,4,3,6,6, 6,5,6,3,3,5,6,6,6,1,5,6, &
6,6,4,3,3,4,6,6,3,4,6,6, 3,6,5,6,6,6,5,3,6,5,1,6, &
6,6,3,4,6,6,3,4,6,6,3,4, 6,3,6,5,6,6,3,5,5,6,6,1 &
],shape(BCC_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for bcc from Queyreau et al. Int J Plast 25 (2009) 361–377
!< 1: self interaction
!< 2: coplanar interaction
!< 3: collinear interaction
!< 4: mixed-asymmetrical junction
!< 5: mixed-symmetrical junction
!< 6: edge junction
integer, dimension(HEX_NSLIP,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPSLIP = reshape( [&
1, 2, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! -----> acting
2, 1, 2, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
2, 2, 1, 3, 3, 3, 7, 7, 7, 13,13,13,13,13,13, 21,21,21,21,21,21,21,21,21,21,21,21, 31,31,31,31,31,31, & ! |
! ! v
6, 6, 6, 4, 5, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, & ! reacting
6, 6, 6, 5, 4, 5, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
6, 6, 6, 5, 5, 4, 8, 8, 8, 14,14,14,14,14,14, 22,22,22,22,22,22,22,22,22,22,22,22, 32,32,32,32,32,32, &
!
12,12,12, 11,11,11, 9,10,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
12,12,12, 11,11,11, 10, 9,10, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
12,12,12, 11,11,11, 10,10, 9, 15,15,15,15,15,15, 23,23,23,23,23,23,23,23,23,23,23,23, 33,33,33,33,33,33, &
!
20,20,20, 19,19,19, 18,18,18, 16,17,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,16,17,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,16,17,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,16,17,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,16,17, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
20,20,20, 19,19,19, 18,18,18, 17,17,17,17,17,16, 24,24,24,24,24,24,24,24,24,24,24,24, 34,34,34,34,34,34, &
!
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 25,26,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,25,26,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,25,26,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,25,26,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,25,26,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,25,26,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,25,26,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,25,26,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,25,26,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,25,26,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,25,26, 35,35,35,35,35,35, &
30,30,30, 29,29,29, 28,28,28, 27,27,27,27,27,27, 26,26,26,26,26,26,26,26,26,26,26,25, 35,35,35,35,35,35, &
!
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 36,37,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,36,37,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,36,37,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,36,37,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,36,37, &
42,42,42, 41,41,41, 40,40,40, 39,39,39,39,39,39, 38,38,38,38,38,38,38,38,38,38,38,38, 37,37,37,37,37,36 &
],shape(HEX_INTERACTIONSLIPSLIP)) !< Slip--slip interaction types for hex (onion peel naming scheme)
integer, dimension(BCT_NSLIP,BCT_NSLIP), parameter :: &
BCT_INTERACTIONSLIPSLIP = reshape( [&
1, 2, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! -----> acting
2, 1, 3, 3, 7, 7, 13, 13, 13, 13, 21, 21, 31, 31, 31, 31, 43, 43, 57, 57, 73, 73, 73, 73, 91, 91, 91, 91, 91, 91, 91, 91, 111, 111, 111, 111, 133,133,133,133,133,133,133,133, 157,157,157,157,157,157,157,157, & ! |
! |
6, 6, 4, 5, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! v
6, 6, 5, 4, 8, 8, 14, 14, 14, 14, 22, 22, 32, 32, 32, 32, 44, 44, 58, 58, 74, 74, 74, 74, 92, 92, 92, 92, 92, 92, 92, 92, 112, 112, 112, 112, 134,134,134,134,134,134,134,134, 158,158,158,158,158,158,158,158, & ! reacting
!
12, 12, 11, 11, 9, 10, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
12, 12, 11, 11, 10, 9, 15, 15, 15, 15, 23, 23, 33, 33, 33, 33, 45, 45, 59, 59, 75, 75, 75, 75, 93, 93, 93, 93, 93, 93, 93, 93, 113, 113, 113, 113, 135,135,135,135,135,135,135,135, 159,159,159,159,159,159,159,159, &
!
20, 20, 19, 19, 18, 18, 16, 17, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 16, 17, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 17, 16, 17, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
20, 20, 19, 19, 18, 18, 17, 17, 17, 16, 24, 24, 34, 34, 34, 34, 46, 46, 60, 60, 76, 76, 76, 76, 94, 94, 94, 94, 94, 94, 94, 94, 114, 114, 114, 114, 136,136,136,136,136,136,136,136, 160,160,160,160,160,160,160,160, &
!
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 25, 26, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
30, 30, 29, 29, 28, 28, 27, 27, 27, 27, 26, 25, 35, 35, 35, 35, 47, 47, 61, 61, 77, 77, 77, 77, 95, 95, 95, 95, 95, 95, 95, 95, 115, 115, 115, 115, 137,137,137,137,137,137,137,137, 161,161,161,161,161,161,161,161, &
!
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 36, 37, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 36, 37, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 36, 37, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
42, 42, 41, 41, 40, 40, 39, 39, 39, 39, 38, 38, 37, 37, 37, 36, 48, 48, 62, 62, 78, 78, 78, 78, 96, 96, 96, 96, 96, 96, 96, 96, 116, 116, 116, 116, 138,138,138,138,138,138,138,138, 162,162,162,162,162,162,162,162, &
!
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 49, 50, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
56, 56, 55, 55, 54, 54, 53, 53, 53, 53, 52, 52, 51, 51, 51, 51, 50, 49, 63, 63, 79, 79, 79, 79, 97, 97, 97, 97, 97, 97, 97, 97, 117, 117, 117, 117, 139,139,139,139,139,139,139,139, 163,163,163,163,163,163,163,163, &
!
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 64, 65, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
72, 72, 71, 71, 70, 70, 69, 69, 69, 69, 68, 68, 67, 67, 67, 67, 66, 66, 65, 64, 80, 80, 80, 80, 98, 98, 98, 98, 98, 98, 98, 98, 118, 118, 118, 118, 140,140,140,140,140,140,140,140, 164,164,164,164,164,164,164,164, &
!
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 81, 82, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 81, 82, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 81, 82, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
90, 90, 89, 89, 88, 88, 87, 87, 87, 87, 86, 86, 85, 85, 85, 85, 84, 84, 83, 83, 82, 82, 82, 81, 99, 99, 99, 99, 99, 99, 99, 99, 119, 119, 119, 119, 141,141,141,141,141,141,141,141, 165,165,165,165,165,165,165,165, &
!
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 100,101,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,100,101,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,100,101,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,100,101,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,100,101,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,100,101,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,100,101, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
110,110, 109,109, 108,108, 107,107,107,107, 106,106, 105,105,105,105, 104,104, 103,103, 102,102,102,102, 101,101,101,101,101,101,101,100, 120, 120, 120, 120, 142,142,142,142,142,142,142,142, 166,166,166,166,166,166,166,166, &
!
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 121, 122, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 121, 122, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
132,132, 131,131, 130,130, 129,129,129,129, 128,128, 127,127,127,127, 126,126, 125,125, 124,124,124,124, 123,123,123,123,123,123,123,123, 121, 122, 122, 121, 143,143,143,143,143,143,143,143, 167,167,167,167,167,167,167,167, &
!
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 144,145,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,144,145,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,144,145,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,144,145,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,144,145,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,144,145,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,144,145, 168,168,168,168,168,168,168,168, &
156,156, 155,155, 154,154, 153,153,153,153, 152,152, 151,151,151,151, 150,150, 149,149, 148,148,148,148, 147,147,147,147,147,147,147,147, 146, 146, 146, 146, 145,145,145,145,145,145,145,144, 168,168,168,168,168,168,168,168, &
!
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,169,170,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,169,170,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,169,170,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 170,170,170,170,169,170,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 &
],shape(BCT_INTERACTIONSLIPSLIP))
select case(structure)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPSLIP
NslipMax = FCC_NSLIPSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONSLIPSLIP
NslipMax = BCC_NSLIPSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONSLIPSLIP
NslipMax = HEX_NSLIPSYSTEM
case('tI')
interactionTypes = BCT_INTERACTIONSLIPSLIP
NslipMax = BCT_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(structure))
end select
interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes)
end function lattice_interaction_SlipBySlip
!--------------------------------------------------------------------------------------------------
!> @brief Twin-twin interaction matrix
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_TwinByTwin(Ntwin,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), dimension(sum(Ntwin),sum(Ntwin)) :: interactionMatrix
integer, dimension(:), allocatable :: NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTWIN,FCC_NTWIN), parameter :: &
FCC_INTERACTIONTWINTWIN = reshape( [&
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1 &
],shape(FCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for fcc
integer, dimension(BCC_NTWIN,BCC_NTWIN), parameter :: &
BCC_INTERACTIONTWINTWIN = reshape( [&
1,3,3,3,3,3,3,2,3,3,2,3, & ! -----> acting
3,1,3,3,3,3,2,3,3,3,3,2, & ! |
3,3,1,3,3,2,3,3,2,3,3,3, & ! |
3,3,3,1,2,3,3,3,3,2,3,3, & ! v
3,3,3,2,1,3,3,3,3,2,3,3, & ! reacting
3,3,2,3,3,1,3,3,2,3,3,3, &
3,2,3,3,3,3,1,3,3,3,3,2, &
2,3,3,3,3,3,3,1,3,3,2,3, &
3,3,2,3,3,2,3,3,1,3,3,3, &
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1 &
],shape(BCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for bcc
!< 1: self interaction
!< 2: collinear interaction
!< 3: other interaction
integer, dimension(HEX_NTWIN,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINTWIN = reshape( [&
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! -----> acting
2, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! |
2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! v
2, 2, 2, 2, 1, 2, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, & ! reacting
2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 13,13,13,13,13,13, &
!
6, 6, 6, 6, 6, 6, 4, 5, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 4, 5, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 4, 5, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 4, 5, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 4, 5, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 8, 8, 8, 8, 8, 8, 14,14,14,14,14,14, &
!
12,12,12,12,12,12, 11,11,11,11,11,11, 9,10,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10, 9,10,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10, 9,10,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10, 9,10,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10, 9,10, 15,15,15,15,15,15, &
12,12,12,12,12,12, 11,11,11,11,11,11, 10,10,10,10,10, 9, 15,15,15,15,15,15, &
!
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 16,17,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,16,17,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,16,17,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,16,17,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,16,17, &
20,20,20,20,20,20, 19,19,19,19,19,19, 18,18,18,18,18,18, 17,17,17,17,17,16 &
],shape(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex
select case(structure)
case('cF')
interactionTypes = FCC_INTERACTIONTWINTWIN
NtwinMax = FCC_NTWINSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONTWINTWIN
NtwinMax = BCC_NTWINSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONTWINTWIN
NtwinMax = HEX_NTWINSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(structure))
end select
interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes)
end function lattice_interaction_TwinByTwin
!--------------------------------------------------------------------------------------------------
!> @brief Trans-trans interaction matrix
!> details only active trans systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_TransByTrans(Ntrans,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Ntrans !< number of active trans systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for trans-trans interaction
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
real(pReal), dimension(sum(Ntrans),sum(Ntrans)) :: interactionMatrix
integer, dimension(:), allocatable :: NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTRANS,FCC_NTRANS), parameter :: &
FCC_INTERACTIONTRANSTRANS = reshape( [&
1,1,1,2,2,2,2,2,2,2,2,2, & ! -----> acting
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
1,1,1,2,2,2,2,2,2,2,2,2, & ! |
2,2,2,1,1,1,2,2,2,2,2,2, & ! v
2,2,2,1,1,1,2,2,2,2,2,2, & ! reacting
2,2,2,1,1,1,2,2,2,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,1,1,1,2,2,2, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1 &
],shape(FCC_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for fcc
if(structure == 'cF') then
interactionTypes = FCC_INTERACTIONTRANSTRANS
NtransMax = FCC_NTRANSSYSTEM
else
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(structure))
end if
interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes)
end function lattice_interaction_TransByTrans
!--------------------------------------------------------------------------------------------------
!> @brief Slip-twin interaction matrix
!> details only active slip and twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
Ntwin !< number of active twin systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-twin interaction
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), dimension(sum(Nslip),sum(Ntwin)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax, &
NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTWIN,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPTWIN = reshape( [&
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> twin (acting)
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
2,2,2,1,1,1,3,3,3,3,3,3, &
2,2,2,3,3,3,1,1,1,3,3,3, &
3,3,3,2,2,2,1,1,1,3,3,3, &
3,3,3,3,3,3,1,1,1,2,2,2, &
3,3,3,2,2,2,3,3,3,1,1,1, &
2,2,2,3,3,3,3,3,3,1,1,1, &
3,3,3,3,3,3,2,2,2,1,1,1, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4 &
],shape(FCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for fcc
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
integer, dimension(BCC_NTWIN,BCC_NSLIP), parameter :: &
BCC_INTERACTIONSLIPTWIN = reshape( [&
3,3,3,2,2,3,3,3,3,2,3,3, & ! -----> twin (acting)
3,3,2,3,3,2,3,3,2,3,3,3, & ! |
3,2,3,3,3,3,2,3,3,3,3,2, & ! |
2,3,3,3,3,3,3,2,3,3,2,3, & ! v
2,3,3,3,3,3,3,2,3,3,2,3, & ! slip (reacting)
3,3,2,3,3,2,3,3,2,3,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,3,2,2,3,3,3,3,2,3,3, &
2,3,3,3,3,3,3,2,3,3,2,3, &
3,3,3,2,2,3,3,3,3,2,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,2,3,3,2,3,3,2,3,3,3, &
!
1,3,3,3,3,3,3,2,3,3,2,3, &
3,1,3,3,3,3,2,3,3,3,3,2, &
3,3,1,3,3,2,3,3,2,3,3,3, &
3,3,3,1,2,3,3,3,3,2,3,3, &
3,3,3,2,1,3,3,3,3,2,3,3, &
3,3,2,3,3,1,3,3,2,3,3,3, &
3,2,3,3,3,3,1,3,3,3,3,2, &
2,3,3,3,3,3,3,1,3,3,2,3, &
3,3,2,3,3,2,3,3,1,3,3,3, &
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1 &
],shape(BCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for bcc
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
integer, dimension(HEX_NTWIN,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPTWIN = reshape( [&
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! ----> twin (acting)
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, & ! |
! v
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, & ! slip (reacting)
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, &
!
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
!
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
!
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
17,17,17,17,17,17, 18,18,18,18,18,18, 19,19,19,19,19,19, 20,20,20,20,20,20, &
!
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24, &
21,21,21,21,21,21, 22,22,22,22,22,22, 23,23,23,23,23,23, 24,24,24,24,24,24 &
!
],shape(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex
select case(structure)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPTWIN
NslipMax = FCC_NSLIPSYSTEM
NtwinMax = FCC_NTWINSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONSLIPTWIN
NslipMax = BCC_NSLIPSYSTEM
NtwinMax = BCC_NTWINSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONSLIPTWIN
NslipMax = HEX_NSLIPSYSTEM
NtwinMax = HEX_NTWINSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(structure))
end select
interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes)
end function lattice_interaction_SlipByTwin
!--------------------------------------------------------------------------------------------------
!> @brief Slip-trans interaction matrix
!> details only active slip and trans systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Nslip, & !< number of active slip systems per family
Ntrans !< number of active trans systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for slip-trans interaction
character(len=*), intent(in) :: structure !< lattice structure (parent crystal)
real(pReal), dimension(sum(Nslip),sum(Ntrans)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax, &
NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTRANS,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPTRANS = reshape( [&
1,1,1,3,3,3,2,2,2,3,3,3, & ! -----> trans (acting)
1,1,1,3,3,3,3,3,3,2,2,2, & ! |
1,1,1,2,2,2,3,3,3,3,3,3, & ! |
3,3,3,1,1,1,3,3,3,2,2,2, & ! v
3,3,3,1,1,1,2,2,2,3,3,3, & ! slip (reacting)
2,2,2,1,1,1,3,3,3,3,3,3, &
2,2,2,3,3,3,1,1,1,3,3,3, &
3,3,3,2,2,2,1,1,1,3,3,3, &
3,3,3,3,3,3,1,1,1,2,2,2, &
3,3,3,2,2,2,3,3,3,1,1,1, &
2,2,2,3,3,3,3,3,3,1,1,1, &
3,3,3,3,3,3,2,2,2,1,1,1, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4 &
],shape(FCC_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for fcc
select case(structure)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPTRANS
NslipMax = FCC_NSLIPSYSTEM
NtransMax = FCC_NTRANSSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(structure))
end select
interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes)
end function lattice_interaction_SlipByTrans
!--------------------------------------------------------------------------------------------------
!> @brief Twin-slip interaction matrix
!> details only active twin and slip systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,structure) result(interactionMatrix)
integer, dimension(:), intent(in) :: Ntwin, & !< number of active twin systems per family
Nslip !< number of active slip systems per family
real(pReal), dimension(:), intent(in) :: interactionValues !< values for twin-twin interaction
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), dimension(sum(Ntwin),sum(Nslip)) :: interactionMatrix
integer, dimension(:), allocatable :: NtwinMax, &
NslipMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NSLIP,FCC_NTWIN), parameter :: &
FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc
integer, dimension(BCC_NSLIP,BCC_NTWIN), parameter :: &
BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc
integer, dimension(HEX_NSLIP,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINSLIP = reshape( [&
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! ----> slip (acting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! v
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, & ! twin (reacting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 13,13,13,13,13,13, 17,17,17,17,17,17,17,17,17,17,17,17, 21,21,21,21,21,21, &
!
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
2, 2, 2, 6, 6, 6, 10,10,10, 14,14,14,14,14,14, 18,18,18,18,18,18,18,18,18,18,18,18, 22,22,22,22,22,22, &
!
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
3, 3, 3, 7, 7, 7, 11,11,11, 15,15,15,15,15,15, 19,19,19,19,19,19,19,19,19,19,19,19, 23,23,23,23,23,23, &
!
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24, &
4, 4, 4, 8, 8, 8, 12,12,12, 16,16,16,16,16,16, 20,20,20,20,20,20,20,20,20,20,20,20, 24,24,24,24,24,24 &
],shape(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex
select case(structure)
case('cF')
interactionTypes = FCC_INTERACTIONTWINSLIP
NtwinMax = FCC_NTWINSYSTEM
NslipMax = FCC_NSLIPSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONTWINSLIP
NtwinMax = BCC_NTWINSYSTEM
NslipMax = BCC_NSLIPSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONTWINSLIP
NtwinMax = HEX_NTWINSYSTEM
NslipMax = HEX_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(structure))
end select
interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes)
end function lattice_interaction_TwinBySlip
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for slip
!> details only active slip systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_SchmidMatrix_slip(Nslip,structure,cOverA) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA
real(pReal), dimension(3,3,sum(Nslip)) :: SchmidMatrix
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
real(pReal), dimension(:,:), allocatable :: slipSystems
integer, dimension(:), allocatable :: NslipMax
integer :: i
select case(structure)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(structure))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(structure))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(structure))
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
do i = 1, sum(Nslip)
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for slip')
enddo
end function lattice_SchmidMatrix_slip
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for twinning
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_SchmidMatrix_twin(Ntwin,structure,cOverA) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,3,sum(Ntwin)) :: SchmidMatrix
real(pReal), dimension(3,3,sum(Ntwin)) :: coordinateSystem
real(pReal), dimension(:,:), allocatable :: twinSystems
integer, dimension(:), allocatable :: NtwinMax
integer :: i
select case(structure)
case('cF')
NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
case('cI')
NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
case('hP')
NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
case default
allocate(NtwinMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(structure))
end select
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
call IO_error(145,ext_msg='Ntwin '//trim(structure))
if (any(Ntwin < 0)) &
call IO_error(144,ext_msg='Ntwin '//trim(structure))
coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,structure,cOverA)
do i = 1, sum(Ntwin)
SchmidMatrix(1:3,1:3,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
call IO_error(0,i,ext_msg = 'dilatational Schmid matrix for twin')
enddo
end function lattice_SchmidMatrix_twin
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for twinning
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_SchmidMatrix_trans(Ntrans,structure_target,cOverA,a_bcc,a_fcc) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=*), intent(in) :: structure_target !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,3,sum(Ntrans)) :: SchmidMatrix
real(pReal), dimension(3,3,sum(Ntrans)) :: devNull
real(pReal) :: a_bcc, a_fcc
if (structure_target /= 'cI' .and. structure_target /= 'hP') &
call IO_error(137,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
if (structure_target == 'hP' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
call IO_error(131,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
if (structure_target == 'cI' .and. (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal)) &
call IO_error(134,ext_msg='lattice_SchmidMatrix_trans: '//trim(structure_target))
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA,a_fcc,a_bcc)
end function lattice_SchmidMatrix_trans
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for cleavage
!> details only active cleavage systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_SchmidMatrix_cleavage(Ncleavage,structure,cOverA) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ncleavage !< number of active cleavage systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,3,3,sum(Ncleavage)) :: SchmidMatrix
real(pReal), dimension(3,3,sum(Ncleavage)) :: coordinateSystem
real(pReal), dimension(:,:), allocatable :: cleavageSystems
integer, dimension(:), allocatable :: NcleavageMax
integer :: i
select case(structure)
case('oP')
NcleavageMax = ORT_NCLEAVAGESYSTEM
cleavageSystems = ORT_SYSTEMCLEAVAGE
case('cF')
NcleavageMax = FCC_NCLEAVAGESYSTEM
cleavageSystems = FCC_SYSTEMCLEAVAGE
case('cI')
NcleavageMax = BCC_NCLEAVAGESYSTEM
cleavageSystems = BCC_SYSTEMCLEAVAGE
case default
allocate(NcleavageMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(structure))
end select
if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0)) &
call IO_error(145,ext_msg='Ncleavage '//trim(structure))
if (any(Ncleavage < 0)) &
call IO_error(144,ext_msg='Ncleavage '//trim(structure))
coordinateSystem = buildCoordinateSystem(Ncleavage,NcleavageMax,cleavageSystems,structure,cOverA)
do i = 1, sum(Ncleavage)
SchmidMatrix(1:3,1:3,1,i) = math_outer(coordinateSystem(1:3,1,i),coordinateSystem(1:3,2,i))
SchmidMatrix(1:3,1:3,2,i) = math_outer(coordinateSystem(1:3,3,i),coordinateSystem(1:3,2,i))
SchmidMatrix(1:3,1:3,3,i) = math_outer(coordinateSystem(1:3,2,i),coordinateSystem(1:3,2,i))
enddo
end function lattice_SchmidMatrix_cleavage
!--------------------------------------------------------------------------------------------------
!> @brief Slip direction of slip systems (|| b)
!--------------------------------------------------------------------------------------------------
function lattice_slip_direction(Nslip,structure,cOverA) result(d)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,sum(Nslip)) :: d
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
d = coordinateSystem(1:3,1,1:sum(Nslip))
end function lattice_slip_direction
!--------------------------------------------------------------------------------------------------
!> @brief Normal direction of slip systems (|| n)
!--------------------------------------------------------------------------------------------------
function lattice_slip_normal(Nslip,structure,cOverA) result(n)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,sum(Nslip)) :: n
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
n = coordinateSystem(1:3,2,1:sum(Nslip))
end function lattice_slip_normal
!--------------------------------------------------------------------------------------------------
!> @brief Transverse direction of slip systems ( || t = b x n)
!--------------------------------------------------------------------------------------------------
function lattice_slip_transverse(Nslip,structure,cOverA) result(t)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,sum(Nslip)) :: t
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
coordinateSystem = coordinateSystem_slip(Nslip,structure,cOverA)
t = coordinateSystem(1:3,3,1:sum(Nslip))
end function lattice_slip_transverse
!--------------------------------------------------------------------------------------------------
!> @brief Labels for slip systems
!> details only active slip systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_labels_slip(Nslip,structure) result(labels)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
character(len=:), dimension(:), allocatable :: labels
real(pReal), dimension(:,:), allocatable :: slipSystems
integer, dimension(:), allocatable :: NslipMax
select case(structure)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
case default
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(structure))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(structure))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(structure))
labels = getLabels(Nslip,NslipMax,slipSystems)
end function lattice_labels_slip
!--------------------------------------------------------------------------------------------------
!> @brief Return 3x3 tensor with symmetry according to given crystal structure
!--------------------------------------------------------------------------------------------------
function lattice_applyLatticeSymmetry33(T,structure) result(T_sym)
real(pReal), dimension(3,3) :: T_sym
real(pReal), dimension(3,3), intent(in) :: T
character(len=*), intent(in) :: structure
integer :: k
T_sym = 0.0_pReal
select case(structure)
case('aP','cF','cI')
do k=1,3
T_sym(k,k) = T(1,1)
enddo
case('hP')
T_sym(1,1) = T(1,1)
T_sym(2,2) = T(1,1)
T_sym(3,3) = T(3,3)
case('oP','tI')
T_sym(1,1) = T(1,1)
T_sym(2,2) = T(2,2)
T_sym(3,3) = T(3,3)
case default
call IO_error(137,ext_msg='lattice_applyLatticeSymmetry33: '//trim(structure))
end select
end function lattice_applyLatticeSymmetry33
!--------------------------------------------------------------------------------------------------
!> @brief Return stiffness matrix in 6x6 notation with symmetry according to given crystal structure
!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
!--------------------------------------------------------------------------------------------------
function applyLatticeSymmetryC66(C66,structure) result(C66_sym)
real(pReal), dimension(6,6) :: C66_sym
real(pReal), dimension(6,6), intent(in) :: C66
character(len=*), intent(in) :: structure
integer :: j,k
C66_sym = 0.0_pReal
select case(structure)
case ('aP')
do k=1,3
do j=1,3
C66_sym(k,j) = C66(1,2)
enddo
C66_sym(k,k) = C66(1,1)
C66_sym(k+3,k+3) = 0.5_pReal*(C66(1,1)-C66(1,2))
enddo
case ('cF','cI')
do k=1,3
do j=1,3
C66_sym(k,j) = C66(1,2)
enddo
C66_sym(k,k) = C66(1,1)
C66_sym(k+3,k+3) = C66(4,4)
enddo
case ('hP')
C66_sym(1,1) = C66(1,1)
C66_sym(2,2) = C66(1,1)
C66_sym(3,3) = C66(3,3)
C66_sym(1,2) = C66(1,2)
C66_sym(2,1) = C66(1,2)
C66_sym(1,3) = C66(1,3)
C66_sym(3,1) = C66(1,3)
C66_sym(2,3) = C66(1,3)
C66_sym(3,2) = C66(1,3)
C66_sym(4,4) = C66(4,4)
C66_sym(5,5) = C66(4,4)
C66_sym(6,6) = 0.5_pReal*(C66(1,1)-C66(1,2))
case ('oP')
C66_sym(1,1) = C66(1,1)
C66_sym(2,2) = C66(2,2)
C66_sym(3,3) = C66(3,3)
C66_sym(1,2) = C66(1,2)
C66_sym(2,1) = C66(1,2)
C66_sym(1,3) = C66(1,3)
C66_sym(3,1) = C66(1,3)
C66_sym(2,3) = C66(2,3)
C66_sym(3,2) = C66(2,3)
C66_sym(4,4) = C66(4,4)
C66_sym(5,5) = C66(5,5)
C66_sym(6,6) = C66(6,6)
case ('tI')
C66_sym(1,1) = C66(1,1)
C66_sym(2,2) = C66(1,1)
C66_sym(3,3) = C66(3,3)
C66_sym(1,2) = C66(1,2)
C66_sym(2,1) = C66(1,2)
C66_sym(1,3) = C66(1,3)
C66_sym(3,1) = C66(1,3)
C66_sym(2,3) = C66(1,3)
C66_sym(3,2) = C66(1,3)
C66_sym(4,4) = C66(4,4)
C66_sym(5,5) = C66(4,4)
C66_sym(6,6) = C66(6,6)
case default
call IO_error(137,ext_msg='applyLatticeSymmetryC66: '//trim(structure))
end select
end function applyLatticeSymmetryC66
!--------------------------------------------------------------------------------------------------
!> @brief Labels for twin systems
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_labels_twin(Ntwin,structure) result(labels)
integer, dimension(:), intent(in) :: Ntwin !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
character(len=:), dimension(:), allocatable :: labels
real(pReal), dimension(:,:), allocatable :: twinSystems
integer, dimension(:), allocatable :: NtwinMax
select case(structure)
case('cF')
NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
case('cI')
NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
case('hP')
NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
case default
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(structure))
end select
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
call IO_error(145,ext_msg='Ntwin '//trim(structure))
if (any(Ntwin < 0)) &
call IO_error(144,ext_msg='Ntwin '//trim(structure))
labels = getLabels(Ntwin,NtwinMax,twinSystems)
end function lattice_labels_twin
!--------------------------------------------------------------------------------------------------
!> @brief Projection of the transverse direction onto the slip plane
!> @details: This projection is used to calculate forest hardening for edge dislocations
!--------------------------------------------------------------------------------------------------
function slipProjection_transverse(Nslip,structure,cOverA) result(projection)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
real(pReal), dimension(3,sum(Nslip)) :: n, t
integer :: i, j
n = lattice_slip_normal (Nslip,structure,cOverA)
t = lattice_slip_transverse(Nslip,structure,cOverA)
do i=1, sum(Nslip); do j=1, sum(Nslip)
projection(i,j) = abs(math_inner(n(:,i),t(:,j)))
enddo; enddo
end function slipProjection_transverse
!--------------------------------------------------------------------------------------------------
!> @brief Projection of the slip direction onto the slip plane
!> @details: This projection is used to calculate forest hardening for screw dislocations
!--------------------------------------------------------------------------------------------------
function slipProjection_direction(Nslip,structure,cOverA) result(projection)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(sum(Nslip),sum(Nslip)) :: projection
real(pReal), dimension(3,sum(Nslip)) :: n, d
integer :: i, j
n = lattice_slip_normal (Nslip,structure,cOverA)
d = lattice_slip_direction(Nslip,structure,cOverA)
do i=1, sum(Nslip); do j=1, sum(Nslip)
projection(i,j) = abs(math_inner(n(:,i),d(:,j)))
enddo; enddo
end function slipProjection_direction
!--------------------------------------------------------------------------------------------------
!> @brief build a local coordinate system on slip systems
!> @details Order: Direction, plane (normal), and common perpendicular
!--------------------------------------------------------------------------------------------------
function coordinateSystem_slip(Nslip,structure,cOverA) result(coordinateSystem)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: structure !< lattice structure
real(pReal), intent(in) :: cOverA !< c/a ratio
real(pReal), dimension(3,3,sum(Nslip)) :: coordinateSystem
real(pReal), dimension(:,:), allocatable :: slipSystems
integer, dimension(:), allocatable :: NslipMax
select case(structure)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(structure))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(structure))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(structure))
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,structure,cOverA)
end function coordinateSystem_slip
!--------------------------------------------------------------------------------------------------
!> @brief Populate reduced interaction matrix
!--------------------------------------------------------------------------------------------------
function buildInteraction(reacting_used,acting_used,reacting_max,acting_max,values,matrix)
integer, dimension(:), intent(in) :: &
reacting_used, & !< # of reacting systems per family as specified in material.config
acting_used, & !< # of acting systems per family as specified in material.config
reacting_max, & !< max # of reacting systems per family for given lattice
acting_max !< max # of acting systems per family for given lattice
real(pReal), dimension(:), intent(in) :: values !< interaction values
integer, dimension(:,:), intent(in) :: matrix !< interaction types
real(pReal), dimension(sum(reacting_used),sum(acting_used)) :: buildInteraction
integer :: &
acting_family_index, acting_family, acting_system, &
reacting_family_index, reacting_family, reacting_system, &
i,j,k,l
do acting_family = 1,size(acting_used,1)
acting_family_index = sum(acting_used(1:acting_family-1))
do acting_system = 1,acting_used(acting_family)
do reacting_family = 1,size(reacting_used,1)
reacting_family_index = sum(reacting_used(1:reacting_family-1))
do reacting_system = 1,reacting_used(reacting_family)
i = sum( acting_max(1: acting_family-1)) + acting_system
j = sum(reacting_max(1:reacting_family-1)) + reacting_system
k = acting_family_index + acting_system
l = reacting_family_index + reacting_system
if (matrix(i,j) > size(values)) call IO_error(138,ext_msg='buildInteraction')
buildInteraction(l,k) = values(matrix(i,j))
enddo; enddo
enddo; enddo
end function buildInteraction
!--------------------------------------------------------------------------------------------------
!> @brief Build a local coordinate system on slip, twin, trans, cleavage systems
!> @details Order: Direction, plane (normal), and common perpendicular
!--------------------------------------------------------------------------------------------------
function buildCoordinateSystem(active,potential,system,structure,cOverA)
integer, dimension(:), intent(in) :: &
active, & !< # of active systems per family
potential !< # of potential systems per family
real(pReal), dimension(:,:), intent(in) :: &
system
character(len=*), intent(in) :: &
structure !< lattice structure
real(pReal), intent(in) :: &
cOverA
real(pReal), dimension(3,3,sum(active)) :: &
buildCoordinateSystem
real(pReal), dimension(3) :: &
direction, normal
integer :: &
a, & !< index of active system
p, & !< index in potential system matrix
f, & !< index of my family
s !< index of my system in current family
if (structure == 'tI' .and. cOverA > 2.0_pReal) &
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
if (structure == 'hP' .and. (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal)) &
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(structure))
a = 0
activeFamilies: do f = 1,size(active,1)
activeSystems: do s = 1,active(f)
a = a + 1
p = sum(potential(1:f-1))+s
select case(structure)
case ('cF','cI','aP','oP','tI')
direction = system(1:3,p)
normal = system(4:6,p)
case ('hP')
direction = [ system(1,p)*1.5_pReal, &
(system(1,p)+2.0_pReal*system(2,p))*sqrt(0.75_pReal), &
system(4,p)*cOverA ] ! direction [uvtw]->[3u/2 (u+2v)*sqrt(3)/2 w*(p/a)])
normal = [ system(5,p), &
(system(5,p)+2.0_pReal*system(6,p))/sqrt(3.0_pReal), &
system(8,p)/cOverA ] ! plane (hkil)->(h (h+2k)/sqrt(3) l/(p/a))
case default
call IO_error(137,ext_msg='buildCoordinateSystem: '//trim(structure))
end select
buildCoordinateSystem(1:3,1,a) = direction/norm2(direction)
buildCoordinateSystem(1:3,2,a) = normal /norm2(normal)
buildCoordinateSystem(1:3,3,a) = math_cross(direction/norm2(direction),&
normal /norm2(normal))
enddo activeSystems
enddo activeFamilies
end function buildCoordinateSystem
!--------------------------------------------------------------------------------------------------
!> @brief Helper function to define transformation systems
! Needed to calculate Schmid matrix and rotated stiffness matrices.
! @details: set c/a = 0.0 for fcc -> bcc transformation
! set a_Xcc = 0.0 for fcc -> hex transformation
!--------------------------------------------------------------------------------------------------
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
integer, dimension(:), intent(in) :: &
Ntrans
real(pReal), dimension(3,3,sum(Ntrans)), intent(out) :: &
Q, & !< Total rotation: Q = R*B
S !< Eigendeformation tensor for phase transformation
real(pReal), intent(in) :: &
cOverA, & !< c/a for target hex structure
a_bcc, & !< lattice parameter a for target bcc structure
a_fcc !< lattice parameter a for parent fcc structure
type(rotation) :: &
R, & !< Pitsch rotation
B !< Rotation of fcc to Bain coordinate system
real(pReal), dimension(3,3) :: &
U, & !< Bain deformation
ss, sd
real(pReal), dimension(3) :: &
x, y, z
integer :: &
i
real(pReal), dimension(3+3,FCC_NTRANS), parameter :: &
FCCTOHEX_SYSTEMTRANS = reshape(real( [&
-2, 1, 1, 1, 1, 1, &
1,-2, 1, 1, 1, 1, &
1, 1,-2, 1, 1, 1, &
2,-1, 1, -1,-1, 1, &
-1, 2, 1, -1,-1, 1, &
-1,-1,-2, -1,-1, 1, &
-2,-1,-1, 1,-1,-1, &
1, 2,-1, 1,-1,-1, &
1,-1, 2, 1,-1,-1, &
2, 1,-1, -1, 1,-1, &
-1,-2,-1, -1, 1,-1, &
-1, 1, 2, -1, 1,-1 &
],pReal),shape(FCCTOHEX_SYSTEMTRANS))
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
FCCTOBCC_SYSTEMTRANS = reshape([&
0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
0.0,-1.0, 0.0, 10.26, &
0.0, 0.0, 1.0, 10.26, &
0.0, 0.0,-1.0, 10.26, &
1.0, 0.0, 0.0, 10.26, &
-1.0, 0.0, 0.0, 10.26, &
0.0, 0.0, 1.0, 10.26, &
0.0, 0.0,-1.0, 10.26, &
1.0, 0.0, 0.0, 10.26, &
-1.0, 0.0, 0.0, 10.26, &
0.0, 1.0, 0.0, 10.26, &
0.0,-1.0, 0.0, 10.26 &
],shape(FCCTOBCC_SYSTEMTRANS))
integer, dimension(9,fcc_Ntrans), parameter :: &
FCCTOBCC_BAINVARIANT = reshape( [&
1, 0, 0, 0, 1, 0, 0, 0, 1, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
1, 0, 0, 0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 1, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 1, 0, 1, 0, 0, 0, 0, 1, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0 &
],shape(FCCTOBCC_BAINVARIANT))
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
FCCTOBCC_BAINROT = reshape([&
1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
1.0, 0.0, 0.0, 45.0, &
1.0, 0.0, 0.0, 45.0, &
1.0, 0.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 1.0, 0.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0 &
],shape(FCCTOBCC_BAINROT))
if (a_bcc > 0.0_pReal .and. a_fcc > 0.0_pReal .and. dEq0(cOverA)) then ! fcc -> bcc transformation
do i = 1,sum(Ntrans)
call R%fromAxisAngle(FCCTOBCC_SYSTEMTRANS(:,i),degrees=.true.,P=1)
call B%fromAxisAngle(FCCTOBCC_BAINROT(:,i), degrees=.true.,P=1)
x = real(FCCTOBCC_BAINVARIANT(1:3,i),pReal)
y = real(FCCTOBCC_BAINVARIANT(4:6,i),pReal)
z = real(FCCTOBCC_BAINVARIANT(7:9,i),pReal)
U = (a_bcc/a_fcc)*math_outer(x,x) &
+ (a_bcc/a_fcc)*math_outer(y,y) * sqrt(2.0_pReal) &
+ (a_bcc/a_fcc)*math_outer(z,z) * sqrt(2.0_pReal)
Q(1:3,1:3,i) = matmul(R%asMatrix(),B%asMatrix())
S(1:3,1:3,i) = matmul(R%asMatrix(),U) - MATH_I3
enddo
elseif (cOverA > 0.0_pReal .and. dEq0(a_bcc)) then ! fcc -> hex transformation
ss = MATH_I3
sd = MATH_I3
ss(1,3) = sqrt(2.0_pReal)/4.0_pReal
sd(3,3) = cOverA/sqrt(8.0_pReal/3.0_pReal)
do i = 1,sum(Ntrans)
x = FCCTOHEX_SYSTEMTRANS(1:3,i)/norm2(FCCTOHEX_SYSTEMTRANS(1:3,i))
z = FCCTOHEX_SYSTEMTRANS(4:6,i)/norm2(FCCTOHEX_SYSTEMTRANS(4:6,i))
y = -math_cross(x,z)
Q(1:3,1,i) = x
Q(1:3,2,i) = y
Q(1:3,3,i) = z
S(1:3,1:3,i) = matmul(Q(1:3,1:3,i), matmul(matmul(sd,ss), transpose(Q(1:3,1:3,i)))) - MATH_I3 ! ToDo: This is of interest for the Schmid matrix only
enddo
else
call IO_error(132,ext_msg='buildTransformationSystem')
endif
end subroutine buildTransformationSystem
!--------------------------------------------------------------------------------------------------
!> @brief select active systems as strings
!--------------------------------------------------------------------------------------------------
function getlabels(active,potential,system) result(labels)
integer, dimension(:), intent(in) :: &
active, & !< # of active systems per family
potential !< # of potential systems per family
real(pReal), dimension(:,:), intent(in) :: &
system
character(len=:), dimension(:), allocatable :: labels
character(len=:), allocatable :: label
integer :: i,j
integer :: &
a, & !< index of active system
p, & !< index in potential system matrix
f, & !< index of my family
s !< index of my system in current family
i = 2*size(system,1) + (size(system,1) - 2) + 4 ! 2 letters per index + spaces + brackets
allocate(character(len=i) :: labels(sum(active)), label)
a = 0
activeFamilies: do f = 1,size(active,1)
activeSystems: do s = 1,active(f)
a = a + 1
p = sum(potential(1:f-1))+s
i = 1
label(i:i) = '['
direction: do j = 1, size(system,1)/2
write(label(i+1:i+2),'(I2.1)') int(system(j,p))
label(i+3:i+3) = ' '
i = i + 3
enddo direction
label(i:i) = ']'
i = i +1
label(i:i) = '('
normal: do j = size(system,1)/2+1, size(system,1)
write(label(i+1:i+2),'(I2.1)') int(system(j,p))
label(i+3:i+3) = ' '
i = i + 3
enddo normal
label(i:i) = ')'
labels(s) = label
enddo activeSystems
enddo activeFamilies
end function getlabels
!--------------------------------------------------------------------------------------------------
!> @brief Equivalent Poisson's ratio (ν)
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
function lattice_equivalent_nu(C,assumption) result(nu)
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=*), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
real(pReal) :: K, mu, nu
logical :: error
real(pReal), dimension(6,6) :: S
if (IO_lc(assumption) == 'voigt') then
K = (C(1,1)+C(2,2)+C(3,3) +2.0_pReal*(C(1,2)+C(2,3)+C(1,3))) &
/ 9.0_pReal
elseif(IO_lc(assumption) == 'reuss') then
call math_invert(S,error,C)
if(error) error stop 'matrix inversion failed'
K = 1.0_pReal &
/ (S(1,1)+S(2,2)+S(3,3) +2.0_pReal*(S(1,2)+S(2,3)+S(1,3)))
else
error stop 'invalid assumption'
K = 0.0_pReal
endif
mu = lattice_equivalent_mu(C,assumption)
nu = (1.5_pReal*K -mu)/(3.0_pReal*K+mu)
end function lattice_equivalent_nu
!--------------------------------------------------------------------------------------------------
!> @brief Equivalent shear modulus (μ)
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
function lattice_equivalent_mu(C,assumption) result(mu)
real(pReal), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=*), intent(in) :: assumption !< Assumption ('Voigt' = isostrain, 'Reuss' = isostress)
real(pReal) :: mu
logical :: error
real(pReal), dimension(6,6) :: S
if (IO_lc(assumption) == 'voigt') then
mu = (1.0_pReal*(C(1,1)+C(2,2)+C(3,3)) -1.0_pReal*(C(1,2)+C(2,3)+C(1,3)) +3.0_pReal*(C(4,4)+C(5,5)+C(6,6))) &
/ 15.0_pReal
elseif(IO_lc(assumption) == 'reuss') then
call math_invert(S,error,C)
if(error) error stop 'matrix inversion failed'
mu = 15.0_pReal &
/ (4.0_pReal*(S(1,1)+S(2,2)+S(3,3)) -4.0_pReal*(S(1,2)+S(2,3)+S(1,3)) +3.0_pReal*(S(4,4)+S(5,5)+S(6,6)))
else
error stop 'invalid assumption'
mu = 0.0_pReal
endif
end function lattice_equivalent_mu
!--------------------------------------------------------------------------------------------------
!> @brief Check correctness of some lattice functions.
!--------------------------------------------------------------------------------------------------
subroutine selfTest
real(pReal), dimension(:,:,:), allocatable :: CoSy
real(pReal), dimension(:,:), allocatable :: system
real(pReal), dimension(6,6) :: C
real(pReal), dimension(2) :: r
real(pReal) :: lambda
call random_number(r)
system = reshape([1.0_pReal+r(1),0.0_pReal,0.0_pReal, 0.0_pReal,1.0_pReal+r(2),0.0_pReal],[6,1])
CoSy = buildCoordinateSystem([1],[1],system,'cF',0.0_pReal)
if(any(dNeq(CoSy(1:3,1:3,1),math_I3))) error stop 'buildCoordinateSystem'
call random_number(C)
C(1,1) = C(1,1) + 1.0_pReal
C = applyLatticeSymmetryC66(C,'aP')
if(dNeq(C(6,6),lattice_equivalent_mu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_mu/voigt'
if(dNeq(C(6,6),lattice_equivalent_mu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_mu/reuss'
lambda = C(1,2)
if(dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'voigt')), &
lattice_equivalent_nu(C,'voigt'),1.0e-12_pReal)) error stop 'equivalent_nu/voigt'
if(dNeq(lambda*0.5_pReal/(lambda+lattice_equivalent_mu(C,'reuss')), &
lattice_equivalent_nu(C,'reuss'),1.0e-12_pReal)) error stop 'equivalent_nu/reuss'
end subroutine selfTest
end module lattice
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