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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 crystal definitions including Schmid matrices for slip, twin, trans,
! and cleavage as well as interaction among the various systems.
!--------------------------------------------------------------------------------------------------
module crystal
use prec
use misc
use IO
use config
use math
use rotations
implicit none(type,external)
private
!--------------------------------------------------------------------------------------------------
! cF: face centered cubic (fcc)
integer, dimension(*), parameter :: &
CF_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for cF
integer, dimension(*), parameter :: &
CF_NTWINSYSTEM = [12] !< # of twin systems per family for cF
integer, dimension(*), parameter :: &
CF_NTRANSSYSTEM = [12] !< # of transformation systems per family for cF
integer, dimension(*), parameter :: &
CF_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for cF
integer, parameter :: &
CF_NSLIP = sum(CF_NSLIPSYSTEM), & !< total # of slip systems for cF
CF_NTWIN = sum(CF_NTWINSYSTEM), & !< total # of twin systems for cF
CF_NTRANS = sum(CF_NTRANSSYSTEM), & !< total # of transformation systems for cF
CF_NCLEAVAGE = sum(CF_NCLEAVAGESYSTEM) !< total # of cleavage systems for cF
real(pREAL), dimension(3+3,CF_NSLIP), parameter :: &
CF_SYSTEMSLIP = reshape(real([&
! <110>{111} systems (Thompson tetrahedron labeling according to Fig. 3 of 10.1016/S1572-4859(05)80003-8)
0, 1,-1, 1, 1, 1, & ! AC(d)
-1, 0, 1, 1, 1, 1, & ! CB(d)
1,-1, 0, 1, 1, 1, & ! BA(d)
0,-1,-1, -1,-1, 1, & ! BD(c)
1, 0, 1, -1,-1, 1, & ! DA(c)
-1, 1, 0, -1,-1, 1, & ! AB(c)
0,-1, 1, 1,-1,-1, & ! CA(b)
-1, 0,-1, 1,-1,-1, & ! AD(b)
1, 1, 0, 1,-1,-1, & ! DC(b)
0, 1, 1, -1, 1,-1, & ! DB(a)
1, 0,-1, -1, 1,-1, & ! BC(a)
-1,-1, 0, -1, 1,-1, & ! CD(a)
! <110>{110}/non-octahedral systems
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(CF_SYSTEMSLIP)) !< cF slip systems
real(pREAL), dimension(3+3,CF_NTWIN), parameter :: &
CF_SYSTEMTWIN = reshape(real( [&
! <112>{111} systems
-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(CF_SYSTEMTWIN)) !< cF twin systems
integer, dimension(2,CF_NTWIN), parameter, public :: &
crystal_CF_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(crystal_CF_TWINNUCLEATIONSLIPPAIR))
real(pREAL), dimension(3+3,CF_NCLEAVAGE), parameter :: &
CF_SYSTEMCLEAVAGE = reshape(real([&
! <001>{001} systems
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1 &
],pREAL),shape(CF_SYSTEMCLEAVAGE)) !< cF cleavage systems
!--------------------------------------------------------------------------------------------------
! cI: body centered cubic (bcc)
integer, dimension(*), parameter :: &
CI_NSLIPSYSTEM = [12, 12, 24] !< # of slip systems per family for cI
integer, dimension(*), parameter :: &
CI_NTWINSYSTEM = [12] !< # of twin systems per family for cI
integer, dimension(*), parameter :: &
CI_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for cI
integer, parameter :: &
CI_NSLIP = sum(CI_NSLIPSYSTEM), & !< total # of slip systems for cI
CI_NTWIN = sum(CI_NTWINSYSTEM), & !< total # of twin systems for cI
CI_NCLEAVAGE = sum(CI_NCLEAVAGESYSTEM) !< total # of cleavage systems for cI
real(pREAL), dimension(3+3,CI_NSLIP), parameter :: &
CI_SYSTEMSLIP = reshape(real([&
! <111>{110} systems
! Sign convention follows Table 1 of 10.1016/j.ijplas.2020.102733
! to allow for universal calculation of non-glide plane normal n1 = Rot(-m,60°) @ n
! The choice matters since Rot(-m,60°) @ n ≠ Rot(m,60°) @ -n ..!
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, &
! <111>{112} systems
-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, &
! Slip system <111>{123}
1, 1,-1, 1, 2, 3, &
1,-1, 1, -1, 2, 3, &
-1, 1, 1, 1,-2, 3, &
1, 1, 1, 1, 2,-3, &
1,-1, 1, 1, 3, 2, &
1, 1,-1, -1, 3, 2, &
1, 1, 1, 1,-3, 2, &
-1, 1, 1, 1, 3,-2, &
1, 1,-1, 2, 1, 3, &
1,-1, 1, -2, 1, 3, &
-1, 1, 1, 2,-1, 3, &
1, 1, 1, 2, 1,-3, &
1,-1, 1, 2, 3, 1, &
1, 1,-1, -2, 3, 1, &
1, 1, 1, 2,-3, 1, &
-1, 1, 1, 2, 3,-1, &
-1, 1, 1, 3, 1, 2, &
1, 1, 1, -3, 1, 2, &
1, 1,-1, 3,-1, 2, &
1,-1, 1, 3, 1,-2, &
-1, 1, 1, 3, 2, 1, &
1, 1, 1, -3, 2, 1, &
1, 1,-1, 3,-2, 1, &
1,-1, 1, 3, 2,-1 &
],pREAL),shape(CI_SYSTEMSLIP)) !< cI slip systems
real(pREAL), dimension(3+3,CI_NTWIN), parameter :: &
CI_SYSTEMTWIN = reshape(real([&
! <111>{112} systems
-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(CI_SYSTEMTWIN)) !< cI twin systems
real(pREAL), dimension(3+3,CI_NCLEAVAGE), parameter :: &
CI_SYSTEMCLEAVAGE = reshape(real([&
! <001>{001} systems
0, 1, 0, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
1, 0, 0, 0, 0, 1 &
],pREAL),shape(CI_SYSTEMCLEAVAGE)) !< cI cleavage systems
!--------------------------------------------------------------------------------------------------
! hP: hexagonal [close packed] (hex, hcp)
integer, dimension(*), parameter :: &
HP_NSLIPSYSTEM = [3, 3, 6, 12, 6] !< # of slip systems per family for hP
integer, dimension(*), parameter :: &
HP_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hP
integer, parameter :: &
HP_NSLIP = sum(HP_NSLIPSYSTEM), & !< total # of slip systems for hP
HP_NTWIN = sum(HP_NTWINSYSTEM) !< total # of twin systems for hP
real(pREAL), dimension(4+4,HP_NSLIP), parameter :: &
HP_SYSTEMSLIP = reshape(real([&
! <-1-1.0>{00.1}/basal systems (independent of c/a-ratio)
2, -1, -1, 0, 0, 0, 0, 1, &
-1, 2, -1, 0, 0, 0, 0, 1, &
-1, -1, 2, 0, 0, 0, 0, 1, &
! <-1-1.0>{1-1.0}/prismatic systems (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, &
! <-1-1.0>{-11.1}/1. order pyramidal <a> systems (direction independent of 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, &
! <11.3>{-10.1}/1. order pyramidal <c+a> systems (direction independent of 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, &
! <11.3>{-1-1.2}/2. order pyramidal <c+a> systems
-1, -1, 2, 3, 1, 1, -2, 2, &
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(HP_SYSTEMSLIP)) !< hP slip systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
real(pREAL), dimension(4+4,HP_NTWIN), parameter :: &
HP_SYSTEMTWIN = reshape(real([&
! <-10.1>{10.2} systems, shear = (3-(c/a)^2)/(sqrt(3) c/a)
! tension in Co, Mg, Zr, Ti, and Be; compression in Cd and Zn
-1, 0, 1, 1, 1, 0, -1, 2, & !
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, &
! <11.6>{-1-1.1} systems, shear = 1/(c/a)
! tension in Co, Re, and Zr
-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, 1, -2, 6, -1, -1, 2, 1, &
-1, 2, -1, 6, 1, -2, 1, 1, &
-2, 1, 1, 6, 2, -1, -1, 1, &
! <10.-2>{10.1} systems, shear = (4(c/a)^2-9)/(4 sqrt(3) c/a)
! compression in Mg
1, 0, -1, -2, 1, 0, -1, 1, &
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, &
! <11.-3>{11.2} systems, shear = 2((c/a)^2-2)/(3 c/a)
! compression in Ti and Zr
1, 1, -2, -3, 1, 1, -2, 2, &
-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(HP_SYSTEMTWIN)) !< hP twin systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
!--------------------------------------------------------------------------------------------------
! tI: body centered tetragonal (bct)
integer, dimension(*), parameter :: &
TI_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for tI
integer, parameter :: &
TI_NSLIP = sum(TI_NSLIPSYSTEM) !< total # of slip systems for tI
real(pREAL), dimension(3+3,TI_NSLIP), parameter :: &
TI_SYSTEMSLIP = reshape(real([&
! {100)<001] systems
0, 0, 1, 1, 0, 0, &
0, 0, 1, 0, 1, 0, &
! {110)<001] systems
0, 0, 1, 1, 1, 0, &
0, 0, 1, -1, 1, 0, &
! {100)<010] systems
0, 1, 0, 1, 0, 0, &
1, 0, 0, 0, 1, 0, &
! {110)<1-11]/2 systems
1,-1, 1, 1, 1, 0, &
1,-1,-1, 1, 1, 0, &
-1,-1,-1, -1, 1, 0, &
-1,-1, 1, -1, 1, 0, &
! {110)<1-10] systems
1, -1, 0, 1, 1, 0, &
1, 1, 0, 1,-1, 0, &
! {100)<011] systems
0, 1, 1, 1, 0, 0, &
0,-1, 1, 1, 0, 0, &
-1, 0, 1, 0, 1, 0, &
1, 0, 1, 0, 1, 0, &
! {001)<010] systems
0, 1, 0, 0, 0, 1, &
1, 0, 0, 0, 0, 1, &
! {001)<110] systems
1, 1, 0, 0, 0, 1, &
-1, 1, 0, 0, 0, 1, &
! {011)<01-1] systems
0, 1,-1, 0, 1, 1, &
0,-1,-1, 0,-1, 1, &
-1, 0,-1, -1, 0, 1, &
1, 0,-1, 1, 0, 1, &
! {011)<1-11]/2 systems
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, &
! {011)<100] systems
1, 0, 0, 0, 1, 1, &
1, 0, 0, 0, 1,-1, &
0, 1, 0, 1, 0, 1, &
0, 1, 0, 1, 0,-1, &
! {211)<01-1] systems
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, &
! {211)<-111]/2 systems
-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(TI_SYSTEMSLIP)) !< tI slip systems for c/a = 0.5456 (Sn), sorted by Bieler 2009 (https://doi.org/10.1007/s11664-009-0909-x)
interface crystal_forestProjection_edge
module procedure slipProjection_transverse
end interface crystal_forestProjection_edge
interface crystal_forestProjection_screw
module procedure slipProjection_direction
end interface crystal_forestProjection_screw
public :: &
crystal_init, &
crystal_selfTest, &
crystal_isotropic_nu, &
crystal_isotropic_mu, &
crystal_symmetrize_33, &
crystal_symmetrize_C66, &
crystal_SchmidMatrix_slip, &
crystal_SchmidMatrix_twin, &
crystal_SchmidMatrix_trans, &
crystal_SchmidMatrix_cleavage, &
crystal_interaction_SlipBySlip, &
crystal_interaction_TwinByTwin, &
crystal_interaction_TransByTrans, &
crystal_interaction_SlipByTwin, &
crystal_interaction_SlipByTrans, &
crystal_interaction_TwinBySlip, &
crystal_characteristicShear_Twin, &
crystal_C66_twin, &
crystal_C66_trans, &
crystal_forestProjection_edge, &
crystal_forestProjection_screw, &
crystal_slip_normal, &
crystal_slip_direction, &
crystal_slip_transverse, &
crystal_labels_slip, &
crystal_labels_twin
contains
!--------------------------------------------------------------------------------------------------
!> @brief Run self test.
!--------------------------------------------------------------------------------------------------
subroutine crystal_init()
print'(/,1x,a)', '<<<+- crystal init -+>>>'; flush(IO_STDOUT)
call crystal_selfTest()
end subroutine crystal_init
!--------------------------------------------------------------------------------------------------
!> @brief Characteristic shear for twinning
!--------------------------------------------------------------------------------------------------
function crystal_characteristicShear_Twin(Ntwin,lattice,CoverA) result(characteristicShear)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), intent(in) :: cOverA !< c/a ratio
real(pREAL), dimension(sum(Ntwin)) :: characteristicShear
integer :: &
f, & !< index of my family
s, e
select case(lattice)
case('cF','cI') ! 10.1016/0079-6425(94)00007-7, Table 1
characteristicShear = 0.5_pREAL*sqrt(2.0_pREAL)
case('hP') ! 10.1016/0079-6425(94)00007-7, Table 3
if (cOverA < 1.0_pREAL .or. cOverA > 2.0_pREAL) &
call IO_error(131,ext_msg='crystal_characteristicShear_Twin')
myFamilies: do f = 1,size(Ntwin,1)
s = sum(Ntwin(:f-1)) + 1
e = sum(Ntwin(:f))
select case(f)
case (1) ! <-10.1>{10.2}
characteristicShear(s:e) = (3.0_pREAL-cOverA**2)/sqrt(3.0_pREAL)/CoverA
case (2) ! <11.6>{-1-1.1}
characteristicShear(s:e) = 1.0_pREAL/cOverA
case (3) ! <10.-2>{10.1}
characteristicShear(s:e) = (4.0_pREAL*cOverA**2-9.0_pREAL)/sqrt(48.0_pREAL)/cOverA
case (4) ! <11.-3>{11.2}
characteristicShear(s:e) = 2.0_pREAL*(cOverA**2-2.0_pREAL)/3.0_pREAL/cOverA
end select
end do myFamilies
case default
call IO_error(137,ext_msg='crystal_characteristicShear_Twin: '//trim(lattice))
end select
end function crystal_characteristicShear_Twin
!--------------------------------------------------------------------------------------------------
!> @brief Rotated elasticity matrices for twinning in 6x6-matrix notation
!--------------------------------------------------------------------------------------------------
function crystal_C66_twin(Ntwin,C66,lattice,CoverA)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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)) :: crystal_C66_twin
real(pREAL), dimension(3,3,sum(Ntwin)):: coordinateSystem
type(tRotation) :: R
integer :: i
select case(lattice)
case('cF')
coordinateSystem = buildCoordinateSystem(Ntwin,CF_NTWINSYSTEM,CF_SYSTEMTWIN,&
lattice,0.0_pREAL)
case('cI')
coordinateSystem = buildCoordinateSystem(Ntwin,CI_NTWINSYSTEM,CI_SYSTEMTWIN,&
lattice,0.0_pREAL)
case('hP')
coordinateSystem = buildCoordinateSystem(Ntwin,HP_NTWINSYSTEM,HP_SYSTEMTWIN,&
lattice,cOverA)
case default
call IO_error(137,ext_msg='crystal_C66_twin: '//trim(lattice))
end select
do i = 1, sum(Ntwin)
call R%fromAxisAngle([coordinateSystem(1:3,2,i),PI]) ! mirror on habit (twin shear) plane
crystal_C66_twin(1:6,1:6,i) = R%rotStiffness(C66)
end do
end function crystal_C66_twin
!--------------------------------------------------------------------------------------------------
!> @brief Rotated elasticity matrices for transformation in 6x6-matrix notation
!--------------------------------------------------------------------------------------------------
function crystal_C66_trans(Ntrans,C_parent66,crystal_target, &
cOverA_trans,a_cF,a_cI)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=*), intent(in) :: crystal_target !< Bravais lattice (Pearson symbol)
real(pREAL), dimension(6,6), intent(in) :: C_parent66
real(pREAL), optional, intent(in) :: cOverA_trans, a_cF, a_cI
real(pREAL), dimension(6,6,sum(Ntrans)) :: crystal_C66_trans
real(pREAL), dimension(6,6) :: C_bar66, C_target_unrotated66
real(pREAL), dimension(3,3,sum(Ntrans)) :: Q,S
type(tRotation) :: R
integer :: i
!--------------------------------------------------------------------------------------------------
! elasticity matrix of the target phase in cube orientation
if (crystal_target == 'hP' .and. present(cOverA_trans)) then
! https://doi.org/10.1063/1.1663858 eq. (16), eq. (18), eq. (19)
! https://doi.org/10.1016/j.actamat.2016.07.032 eq. (47), eq. (48)
if (cOverA_trans < 1.0_pREAL .or. cOverA_trans > 2.0_pREAL) &
call IO_error(131,ext_msg='crystal_C66_trans: '//trim(crystal_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/C_bar66(4,4)
C_target_unrotated66(1,2) = C_bar66(1,2) + C_bar66(1,4)**2/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/(0.5_pREAL*(C_bar66(1,1) - C_bar66(1,2)))
C_target_unrotated66 = crystal_symmetrize_C66(C_target_unrotated66,'hP')
elseif (crystal_target == 'cI' .and. present(a_cF) .and. present(a_cI)) then
if (a_cI <= 0.0_pREAL .or. a_cF <= 0.0_pREAL) &
call IO_error(134,ext_msg='crystal_C66_trans: '//trim(crystal_target))
C_target_unrotated66 = C_parent66
else
call IO_error(137,ext_msg='crystal_C66_trans : '//trim(crystal_target))
end if
do i = 1,6
if (abs(C_target_unrotated66(i,i))<tol_math_check) &
call IO_error(135,'matrix diagonal in transformation',label1='entry',ID1=i)
end do
call buildTransformationSystem(Q,S,Ntrans,cOverA_trans,a_cF,a_cI)
do i = 1,sum(Ntrans)
call R%fromMatrix(Q(1:3,1:3,i))
crystal_C66_trans(1:6,1:6,i) = R%rotStiffness(C_target_unrotated66)
end do
end function crystal_C66_trans
!--------------------------------------------------------------------------------------------------
!> @brief Slip-slip interaction matrix
!> @details only active slip systems are considered
!> @details https://doi.org/10.1016/j.actamat.2016.12.040 (cF: Tab S4-1, cI: Tab S5-1)
!> @details https://doi.org/10.1016/j.ijplas.2014.06.010 (hP: Tab 3b)
!--------------------------------------------------------------------------------------------------
function crystal_interaction_SlipBySlip(Nslip,interactionValues,lattice) 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) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), dimension(sum(Nslip),sum(Nslip)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NSLIP,CF_NSLIP), parameter :: &
CF_INTERACTIONSLIPSLIP = reshape( [&
1, 2, 2, 4, 7, 5, 3, 5, 5, 4, 6, 7, 10,11,10,11,12,13, & ! -----> acting (forest)
2, 1, 2, 7, 4, 5, 6, 4, 7, 5, 3, 5, 10,11,12,13,10,11, & ! |
2, 2, 1, 5, 5, 3, 6, 7, 4, 7, 6, 4, 12,13,10,11,10,11, & ! |
4, 7, 6, 1, 2, 2, 4, 6, 7, 3, 5, 5, 10,11,11,10,13,12, & ! v
7, 4, 6, 2, 1, 2, 5, 3, 5, 6, 4, 7, 10,11,13,12,11,10, & ! reacting (primary)
5, 5, 3, 2, 2, 1, 7, 6, 4, 6, 7, 4, 12,13,11,10,11,10, &
3, 5, 5, 4, 6, 7, 1, 2, 2, 4, 7, 6, 11,10,11,10,12,13, &
6, 4, 7, 5, 3, 5, 2, 1, 2, 7, 4, 6, 11,10,13,12,10,11, &
6, 7, 4, 7, 6, 4, 2, 2, 1, 5, 5, 3, 13,12,11,10,10,11, &
4, 6, 7, 3, 5, 5, 4, 7, 6, 1, 2, 2, 11,10,10,11,13,12, &
5, 3, 5, 6, 4, 7, 7, 4, 6, 2, 1, 2, 11,10,12,13,11,10, &
7, 6, 4, 6, 7, 4, 5, 5, 3, 2, 2, 1, 13,12,10,11,11,10, &
10,10,12,10,10,12,11,11,13,11,11,13, 1, 8, 9, 9, 9, 9, &
11,11,13,11,11,13,10,10,12,10,10,12, 8, 1, 9, 9, 9, 9, &
10,12,10,11,13,11,11,13,11,10,12,10, 9, 9, 1, 8, 9, 9, &
11,13,11,10,12,10,10,12,10,11,13,11, 9, 9, 8, 1, 9, 9, &
12,10,10,13,11,11,12,10,10,13,11,11, 9, 9, 9, 9, 1, 8, &
13,11,11,12,10,10,13,11,11,12,10,10, 9, 9, 9, 9, 8, 1 &
],shape(CF_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for cF / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
!< 1: self interaction --> alpha 0
!< 2: coplanar interaction --> alpha copla
!< 3: collinear interaction --> alpha coli
!< 4: Hirth locks --> alpha 1
!< 5: glissile junctions I --> alpha 2
!< 6: glissile junctions II --> alpha 2*
!< 7: Lomer locks --> alpha 3
!< 8: crossing (similar to Hirth locks in <110>{111} for two {110} planes)
!< 9: similar to Lomer locks in <110>{111} for two {110} planes
!<10: similar to Lomer locks in <110>{111} btw one {110} and one {111} plane
!<11: similar to glissile junctions in <110>{111} btw one {110} and one {111} plane
!<12: crossing btw one {110} and one {111} plane
!<13: collinear btw one {110} and one {111} plane
integer, dimension(CI_NSLIP,CI_NSLIP), parameter :: &
CI_INTERACTIONSLIPSLIP = reshape( [&
1, 3, 6, 6, 7, 5, 4, 2, 4, 2, 7, 5, 18,18,11, 8, 9,13,17,14,13, 9,17,14, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &! -----> acting (forest)
3, 1, 6, 6, 4, 2, 7, 5, 7, 5, 4, 2, 18,18, 8,11,13, 9,14,17, 9,13,14,17, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &! |
6, 6, 1, 3, 5, 7, 2, 4, 5, 7, 2, 4, 11, 8,18,18,17,14, 9,13,17,14,13, 9, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &! |
6, 6, 3, 1, 2, 4, 5, 7, 2, 4, 5, 7, 8,11,18,18,14,17,13, 9,14,17, 9,13, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &! v
7, 5, 4, 2, 1, 3, 6, 6, 2, 4, 7, 5, 9,17,13,14,18,11,18, 8,13,17, 9,14, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &! reacting (primary)
4, 2, 7, 5, 3, 1, 6, 6, 5, 7, 4, 2, 13,14, 9,17,18, 8,18,11, 9,14,13,17, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &
5, 7, 2, 4, 6, 6, 1, 3, 7, 5, 2, 4, 17, 9,14,13,11,18, 8,18,17,13,14, 9, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &
2, 4, 5, 7, 6, 6, 3, 1, 4, 2, 5, 7, 14,13,17, 9, 8,18,11,18,14, 9,17,13, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &
5, 7, 4, 2, 2, 4, 7, 5, 1, 3, 6, 6, 9,17,14,13,13,17,14, 9,18,11, 8,18, 28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,25,25,28,28,28,25,28,28,28, &
2, 4, 7, 5, 5, 7, 4, 2, 3, 1, 6, 6, 13,14,17, 9, 9,14,17,13,18, 8,11,18, 28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,28,28,28,28,25,28,28,28,25, &
7, 5, 2, 4, 7, 5, 2, 4, 6, 6, 1, 3, 17, 9,13,14,17,13, 9,14,11,18,18, 8, 28,28,28,25,28,28,25,28,28,28,28,25,28,28,25,28,28,25,28,28,28,25,28,28, &
4, 2, 5, 7, 4, 2, 5, 7, 6, 6, 3, 1, 14,13, 9,17,14, 9,13,17, 8,18,18,11, 25,28,28,28,28,25,28,28,25,28,28,28,28,25,28,28,28,28,25,28,28,28,25,28, &
19,19,10, 8, 9,12,16,15, 9,12,16,15, 1,20,24,24,23,22,21, 2,23,22, 2,21, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
19,19, 8,10,16,15, 9,12,16,15, 9,12, 20, 1,24,24,22,23, 2,21,22,23,21, 2, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
10, 8,19,19,12, 9,15,16,15,16,12, 9, 24,24, 1,20,21, 2,23,22, 2,21,23,22, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
8,10,19,19,15,16,12, 9,12, 9,15,16, 24,24,20, 1, 2,21,22,23,21, 2,22,23, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
9,12,16,15,19,19,10, 8,12, 9,16,15, 23,21,22, 2, 1,24,20,24,23, 2,22,21, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
12, 9,15,16,10, 8,19,19,16,15,12, 9, 21,23, 2,21,24, 1,24,20, 2,23,21,22, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
16,15, 9,12,19,19, 8,10,15,16, 9,12, 22, 2,23,22,20,24, 1,24,22,21,23, 2, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
15,16,12, 9, 8,10,19,19, 9,12,15,16, 2,22,21,23,24,20,24, 1,21,22, 2,23, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
12, 9,16,15,12, 9,16,15,19,19,10, 8, 23,21, 2,22,23, 2,21,22, 1,24,24,20, 26,28,28,28,28,26,28,28,26,28,28,28,28,26,28,28,28,28,26,28,28,28,26,28, &
9,12,15,16,16,15,12, 9,10, 8,19,19, 21,23,22, 2, 2,23,22,21,24, 1,20,24, 28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,28,28,26,28,28,28,26, &
16,15,12, 9, 9,12,15,16, 8,10,19,19, 2,22,23,21,21,22,23, 2,24,20, 1,24, 28,28,26,28,28,28,28,26,28,28,26,28,28,28,28,26,26,28,28,28,26,28,28,28, &
15,16, 9,12,15,16, 9,12,19,19, 8,10, 22, 2,21,23,22,21, 2,23,20,24,24, 1, 28,28,28,26,28,28,26,28,28,28,28,26,28,28,26,28,28,26,28,28,28,26,28,28, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28, 1,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,27,27,28,28,28,27,28,28,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28, 1,28,28,27,28,28,28,28,27,28,28,27,28,28,27,28,28,28,27,28,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28, 1,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28, 1,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28, 1,28,28,28,28,27,28,28,27,28,28,27,28,28,28,27,28,28, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28, 1,28,28,27,28,28,28,28,27,27,28,28,28,27,28,28,28, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28, 1,28,28,28,28,27,28,28,28,28,27,28,28,28,27,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28, 1,28,28,27,28,28,28,28,28,28,27,28,28,28,27, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28, 1,28,28,28,28,27,27,28,28,28,27,28,28,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28, 1,28,28,27,28,28,27,28,28,28,27,28,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28, 1,28,28,28,28,28,28,27,28,28,28,27, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28, 1,28,28,28,28,27,28,28,28,27,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28, 1,28,28,27,28,28,28,27,28,28, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28, 1,27,28,28,28,27,28,28,28, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,27, 1,28,28,28,27,28,28,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28,27,28,28, 1,28,28,28,27,28,28, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28, 1,28,28,28,27,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28, 1,28,28,28,27, &
28,28,28,25,25,28,28,28,25,28,28,28, 26,28,28,28,28,28,28,26,28,28,26,28, 28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,27,27,28,28,28, 1,28,28,28, &
28,28,25,28,28,28,25,28,28,28,25,28, 28,26,28,28,28,28,26,28,28,28,28,26, 28,28,28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,27,28,28,28, 1,28,28, &
28,25,28,28,28,25,28,28,28,28,28,25, 28,28,26,28,28,26,28,28,26,28,28,28, 27,28,28,28,28,27,28,28,27,28,28,28,28,27,28,28,28,28,27,28,28,28, 1,28, &
25,28,28,28,28,28,28,25,28,25,28,28, 28,28,28,26,26,28,28,28,28,26,28,28, 28,27,28,28,27,28,28,28,28,27,28,28,27,28,28,28,28,28,28,27,28,28,28, 1 &
],shape(CI_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for cI / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
!< 1: self interaction --> alpha 0
!< 2: collinear interaction --> alpha 1
!< 3: coplanar interaction --> alpha 2
!< 4-7: other coefficients
!< 8: {110}-{112} collinear and perpendicular planes --> alpha 6
!< 9: {110}-{112} collinear --> alpha 7
!< 10-24: other coefficients
!< 25: {110}-{123} collinear
!< 26: {112}-{123} collinear
!< 27: {123}-{123} collinear
!< 28: other interaction
integer, dimension(HP_NSLIP,HP_NSLIP), parameter :: &
HP_INTERACTIONSLIPSLIP = reshape( [&
! basal prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
1, 2, 2, 3, 4, 4, 9,10, 9, 9,10, 9, 20,21,22,22,21,20,20,21,22,22,21,20, 47,47,48,47,47,48, & ! -----> acting (forest)
2, 1, 2, 4, 3, 4, 10, 9, 9,10, 9, 9, 22,22,21,20,20,21,22,22,21,20,20,21, 47,48,47,47,48,47, & ! | basal
2, 2, 1, 4, 4, 3, 9, 9,10, 9, 9,10, 21,20,20,21,22,22,21,20,20,21,22,22, 48,47,47,48,47,47, & ! |
! v
7, 8, 8, 5, 6, 6, 11,12,11,11,12,11, 23,24,25,25,24,23,23,24,25,25,24,23, 49,49,50,49,49,50, & ! reacting (primary)
8, 7, 8, 6, 5, 6, 12,11,11,12,11,11, 25,25,24,23,23,24,25,25,24,23,23,24, 49,50,49,49,50,49, & ! prism
8, 8, 7, 6, 6, 5, 11,11,12,11,11,12, 24,23,23,24,25,25,24,23,23,24,25,25, 50,49,49,50,49,49, &
18,19,18, 16,17,16, 13,14,14,15,14,14, 26,26,27,28,28,27,29,29,27,28,28,27, 51,52,51,51,52,51, &
19,18,18, 17,16,16, 14,13,14,14,15,14, 28,27,26,26,27,28,28,27,29,29,27,28, 51,51,52,51,51,52, &
18,18,19, 16,16,17, 14,14,13,14,14,15, 27,28,28,27,26,26,27,28,28,27,29,29, 52,51,51,52,51,51, &
18,19,18, 16,17,16, 15,14,14,13,14,14, 29,29,27,28,28,27,26,26,27,28,28,27, 51,52,51,51,52,51, & ! 1. pyr<a>
19,18,18, 17,16,16, 14,15,14,14,13,14, 28,27,29,29,27,28,28,27,26,26,27,28, 51,51,52,51,51,52, &
18,18,19, 16,16,17, 14,14,15,14,14,13, 27,28,28,27,29,29,27,28,28,27,26,26, 52,51,51,52,51,51, &
44,45,46, 41,42,43, 37,38,39,40,38,39, 30,31,32,32,32,33,34,35,32,32,32,36, 53,54,55,53,54,56, &
46,45,44, 43,42,41, 37,39,38,40,39,38, 31,30,36,32,32,32,35,34,33,32,32,32, 56,54,53,55,54,53, &
45,46,44, 42,43,41, 39,37,38,39,40,38, 32,36,30,31,32,32,32,33,34,35,32,32, 56,53,54,55,53,54, &
45,44,46, 42,41,43, 38,37,39,38,40,39, 32,32,31,30,36,32,32,32,35,34,33,32, 53,56,54,53,55,54, &
46,44,45, 43,41,42, 38,39,37,38,39,40, 32,32,32,36,30,31,32,32,32,33,34,35, 54,56,53,54,55,53, &
44,46,45, 41,43,42, 39,38,37,39,38,40, 33,32,32,32,31,30,36,32,32,32,35,34, 54,53,56,54,53,55, &
44,45,46, 41,42,43, 40,38,39,37,38,39, 34,35,32,32,32,36,30,31,32,32,32,33, 53,54,56,53,54,55, & ! 1. pyr<c+a>
46,45,44, 43,42,41, 40,39,38,37,39,38, 35,34,33,32,32,32,31,30,36,32,32,32, 55,54,53,56,54,53, &
45,46,44, 42,43,41, 39,40,38,39,37,38, 32,33,34,35,32,32,32,36,30,31,32,32, 55,53,54,56,53,54, &
45,44,46, 42,41,43, 38,40,39,38,37,39, 32,32,35,34,33,32,32,32,31,30,36,32, 53,55,54,53,56,54, &
46,44,45, 43,41,42, 38,39,40,38,39,37, 32,32,32,33,34,35,32,32,32,36,30,31, 54,55,53,54,56,53, &
44,46,45, 41,43,42, 39,38,40,39,38,37, 36,32,32,32,35,34,33,32,32,32,31,30, 54,53,55,54,53,56, &
68,68,69, 66,66,67, 64,64,65,64,65,65, 60,61,61,60,62,62,60,63,63,60,62,62, 57,58,58,59,58,58, &
68,69,68, 66,67,66, 65,64,64,65,64,64, 62,62,60,61,61,60,62,62,60,63,63,60, 58,57,58,58,59,58, &
69,68,68, 67,66,66, 64,65,64,64,65,64, 63,60,62,62,60,61,61,60,62,62,60,63, 58,58,57,58,58,59, &
68,68,69, 66,66,67, 64,64,65,64,64,65, 60,63,63,60,62,62,60,61,61,60,62,62, 59,58,58,57,58,58, & ! 2. pyr<c+a>
68,69,68, 66,67,66, 65,64,64,65,64,64, 62,62,60,63,63,60,62,62,60,61,61,60, 58,59,58,58,57,58, &
69,68,68, 67,66,66, 64,65,64,64,65,64, 61,60,62,62,60,63,63,60,62,62,60,61, 58,58,59,58,58,57 &
],shape(HP_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for hP (onion peel naming scheme)
!< 10.1016/j.ijplas.2014.06.010 table 3
!< 10.1080/14786435.2012.699689 table 2 and 3
!< index & label & description
!< 1 & S1 & basal self-interaction
!< 2 & 1 & basal/basal coplanar
!< 3 & 3 & basal/prismatic collinear
!< 4 & 4 & basal/prismatic non-collinear
!< 5 & S2 & prismatic self-interaction
!< 6 & 2 & prismatic/prismatic
!< 7 & 5 & prismatic/basal collinear
!< 8 & 6 & prismatic/basal non-collinear
!< 9 & - & basal/pyramidal <a> non-collinear
!< 10 & - & basal/pyramidal <a> collinear
!< 11 & - & prismatic/pyramidal <a> non-collinear
!< 12 & - & prismatic/pyramidal <a> collinear
!< 13 & - & pyramidal <a> self-interaction
!< 14 & - & pyramidal <a> non-collinear
!< 15 & - & pyramidal <a> collinear
!< 16 & - & pyramidal <a>/prismatic non-collinear
!< 17 & - & pyramidal <a>/prismatic collinear
!< 18 & - & pyramidal <a>/basal non-collinear
!< 19 & - & pyramidal <a>/basal collinear
!< 20 & - & basal/1. order pyramidal <c+a> semi-collinear
!< 21 & - & basal/1. order pyramidal <c+a>
!< 22 & - & basal/1. order pyramidal <c+a>
!< 23 & - & prismatic/1. order pyramidal <c+a> semi-collinear
!< 24 & - & prismatic/1. order pyramidal <c+a>
!< 25 & - & prismatic/1. order pyramidal <c+a> semi-coplanar?
!< 26 & - & pyramidal <a>/1. order pyramidal <c+a> coplanar
!< 27 & - & pyramidal <a>/1. order pyramidal <c+a>
!< 28 & - & pyramidal <a>/1. order pyramidal <c+a> semi-collinear
!< 29 & - & pyramidal <a>/1. order pyramidal <c+a> semi-coplanar
!< 30 & - & 1. order pyramidal <c+a> self-interaction
!< 31 & - & 1. order pyramidal <c+a> coplanar
!< 32 & - & 1. order pyramidal <c+a>
!< 33 & - & 1. order pyramidal <c+a>
!< 34 & - & 1. order pyramidal <c+a> semi-coplanar
!< 35 & - & 1. order pyramidal <c+a> semi-coplanar
!< 36 & - & 1. order pyramidal <c+a> collinear
!< 37 & - & 1. order pyramidal <c+a>/pyramidal <a> coplanar
!< 38 & - & 1. order pyramidal <c+a>/pyramidal <a> semi-collinear
!< 39 & - & 1. order pyramidal <c+a>/pyramidal <a>
!< 40 & - & 1. order pyramidal <c+a>/pyramidal <a> semi-coplanar
!< 41 & - & 1. order pyramidal <c+a>/prismatic semi-collinear
!< 42 & - & 1. order pyramidal <c+a>/prismatic semi-coplanar
!< 43 & - & 1. order pyramidal <c+a>/prismatic
!< 44 & - & 1. order pyramidal <c+a>/basal semi-collinear
!< 45 & - & 1. order pyramidal <c+a>/basal
!< 46 & - & 1. order pyramidal <c+a>/basal
!< 47 & 8 & basal/2. order pyramidal <c+a> non-collinear
!< 48 & 7 & basal/2. order pyramidal <c+a> semi-collinear
!< 49 & 10 & prismatic/2. order pyramidal <c+a>
!< 50 & 9 & prismatic/2. order pyramidal <c+a> semi-collinear
!< 51 & - & pyramidal <a>/2. order pyramidal <c+a>
!< 52 & - & pyramidal <a>/2. order pyramidal <c+a> semi collinear
!< 53 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 54 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 55 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a>
!< 56 & - & 1. order pyramidal <c+a>/2. order pyramidal <c+a> collinear
!< 57 & S3 & 2. order pyramidal <c+a> self-interaction
!< 58 & 16 & 2. order pyramidal <c+a> non-collinear
!< 59 & 15 & 2. order pyramidal <c+a> semi-collinear
!< 60 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 61 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a> collinear
!< 62 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 63 & - & 2. order pyramidal <c+a>/1. order pyramidal <c+a>
!< 64 & - & 2. order pyramidal <c+a>/pyramidal <a> non-collinear
!< 65 & - & 2. order pyramidal <c+a>/pyramidal <a> semi-collinear
!< 66 & 14 & 2. order pyramidal <c+a>/prismatic non-collinear
!< 67 & 13 & 2. order pyramidal <c+a>/prismatic semi-collinear
!< 68 & 12 & 2. order pyramidal <c+a>/basal non-collinear
!< 69 & 11 & 2. order pyramidal <c+a>/basal semi-collinear
integer, dimension(TI_NSLIP,TI_NSLIP), parameter :: &
TI_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(TI_INTERACTIONSLIPSLIP))
select case(lattice)
case('cF')
interactionTypes = CF_INTERACTIONSLIPSLIP
NslipMax = CF_NSLIPSYSTEM
case('cI')
interactionTypes = CI_INTERACTIONSLIPSLIP
NslipMax = CI_NSLIPSYSTEM
case('hP')
interactionTypes = HP_INTERACTIONSLIPSLIP
NslipMax = HP_NSLIPSYSTEM
case('tI')
interactionTypes = TI_INTERACTIONSLIPSLIP
NslipMax = TI_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='crystal_interaction_SlipBySlip: '//trim(lattice))
end select
interactionMatrix = buildInteraction(Nslip,Nslip,NslipMax,NslipMax,interactionValues,interactionTypes)
end function crystal_interaction_SlipBySlip
!--------------------------------------------------------------------------------------------------
!> @brief Twin-twin interaction matrix
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_interaction_TwinByTwin(Ntwin,interactionValues,lattice) 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) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), dimension(sum(Ntwin),sum(Ntwin)) :: interactionMatrix
integer, dimension(:), allocatable :: NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NTWIN,CF_NTWIN), parameter :: &
CF_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(CF_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for cF
integer, dimension(CI_NTWIN,CI_NTWIN), parameter :: &
CI_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(CI_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for cI
!< 1: self interaction
!< 2: collinear interaction
!< 3: other interaction
integer, dimension(HP_NTWIN,HP_NTWIN), parameter :: &
HP_INTERACTIONTWINTWIN = reshape( [&
! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
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 <-10.1>{10.2}
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, & ! <11.6>{-1-1.1}
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, & ! <10.-2>{10.1}
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, & ! <11.-3>{11.2}
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(HP_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hP
select case(lattice)
case('cF')
interactionTypes = CF_INTERACTIONTWINTWIN
NtwinMax = CF_NTWINSYSTEM
case('cI')
interactionTypes = CI_INTERACTIONTWINTWIN
NtwinMax = CI_NTWINSYSTEM
case('hP')
interactionTypes = HP_INTERACTIONTWINTWIN
NtwinMax = HP_NTWINSYSTEM
case default
call IO_error(137,ext_msg='crystal_interaction_TwinByTwin: '//trim(lattice))
end select
interactionMatrix = buildInteraction(Ntwin,Ntwin,NtwinMax,NtwinMax,interactionValues,interactionTypes)
end function crystal_interaction_TwinByTwin
!--------------------------------------------------------------------------------------------------
!> @brief Trans-trans interaction matrix
!> details only active trans systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_interaction_TransByTrans(Ntrans,interactionValues,lattice) 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) :: lattice !<Bravais lattice (Pearson symbol) (parent crystal)
real(pREAL), dimension(sum(Ntrans),sum(Ntrans)) :: interactionMatrix
integer, dimension(:), allocatable :: NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NTRANS,CF_NTRANS), parameter :: &
CF_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(CF_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for cF
if (lattice == 'cF') then
interactionTypes = CF_INTERACTIONTRANSTRANS
NtransMax = CF_NTRANSSYSTEM
else
call IO_error(137,ext_msg='crystal_interaction_TransByTrans: '//trim(lattice))
end if
interactionMatrix = buildInteraction(Ntrans,Ntrans,NtransMax,NtransMax,interactionValues,interactionTypes)
end function crystal_interaction_TransByTrans
!--------------------------------------------------------------------------------------------------
!> @brief Slip-twin interaction matrix
!> details only active slip and twin systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) 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) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), dimension(sum(Nslip),sum(Ntwin)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax, &
NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NTWIN,CF_NSLIP), parameter :: &
CF_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(CF_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for cF
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
integer, dimension(CI_NTWIN,CI_NSLIP), parameter :: &
CI_INTERACTIONSLIPTWIN = reshape( [&
3,3,3,2,2,3,3,3,3,2,3,3, & ! -----> twin (acting)
3,3,2,3,3,2,3,3,2,3,3,3, & ! |
3,2,3,3,3,3,2,3,3,3,3,2, & ! |
2,3,3,3,3,3,3,2,3,3,2,3, & ! v
2,3,3,3,3,3,3,2,3,3,2,3, & ! slip (reacting)
3,3,2,3,3,2,3,3,2,3,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,3,2,2,3,3,3,3,2,3,3, &
2,3,3,3,3,3,3,2,3,3,2,3, &
3,3,3,2,2,3,3,3,3,2,3,3, &
3,2,3,3,3,3,2,3,3,3,3,2, &
3,3,2,3,3,2,3,3,2,3,3,3, &
1,3,3,3,3,3,3,2,3,3,2,3, &
3,1,3,3,3,3,2,3,3,3,3,2, &
3,3,1,3,3,2,3,3,2,3,3,3, &
3,3,3,1,2,3,3,3,3,2,3,3, &
3,3,3,2,1,3,3,3,3,2,3,3, &
3,3,2,3,3,1,3,3,2,3,3,3, &
3,2,3,3,3,3,1,3,3,3,3,2, &
2,3,3,3,3,3,3,1,3,3,2,3, &
3,3,2,3,3,2,3,3,1,3,3,3, &
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4 &
],shape(CI_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for cI
!< 1: coplanar interaction
!< 2: screw trace between slip system and twin habit plane (easy cross slip)
!< 3: other interaction
!< 4: other interaction with slip family {123}
integer, dimension(HP_NTWIN,HP_NSLIP), parameter :: &
HP_INTERACTIONSLIPTWIN = reshape( [&
! <-10.1>{10.2} <11.6>{-1-1.1} <10.-2>{10.1} <11.-3>{11.2}
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, & ! | basal
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, & ! prism
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, &
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, & ! 1. pyr<a>
9, 9, 9, 9, 9, 9, 10,10,10,10,10,10, 11,11,11,11,11,11, 12,12,12,12,12,12, &
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, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, & ! 1. pyr<c+a>
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
13,13,13,13,13,13, 14,14,14,14,14,14, 15,15,15,15,15,15, 16,16,16,16,16,16, &
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, & ! 2. pyr<c+a>
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 &
],shape(HP_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hP
select case(lattice)
case('cF')
interactionTypes = CF_INTERACTIONSLIPTWIN
NslipMax = CF_NSLIPSYSTEM
NtwinMax = CF_NTWINSYSTEM
case('cI')
interactionTypes = CI_INTERACTIONSLIPTWIN
NslipMax = CI_NSLIPSYSTEM
NtwinMax = CI_NTWINSYSTEM
case('hP')
interactionTypes = HP_INTERACTIONSLIPTWIN
NslipMax = HP_NSLIPSYSTEM
NtwinMax = HP_NTWINSYSTEM
case default
call IO_error(137,ext_msg='crystal_interaction_SlipByTwin: '//trim(lattice))
end select
interactionMatrix = buildInteraction(Nslip,Ntwin,NslipMax,NtwinMax,interactionValues,interactionTypes)
end function crystal_interaction_SlipByTwin
!--------------------------------------------------------------------------------------------------
!> @brief Slip-trans interaction matrix
!> details only active slip and trans systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice) 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) :: lattice !< Bravais lattice (Pearson symbol) (parent crystal)
real(pREAL), dimension(sum(Nslip),sum(Ntrans)) :: interactionMatrix
integer, dimension(:), allocatable :: NslipMax, &
NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NTRANS,CF_NSLIP), parameter :: &
CF_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(CF_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for cF
select case(lattice)
case('cF')
interactionTypes = CF_INTERACTIONSLIPTRANS
NslipMax = CF_NSLIPSYSTEM
NtransMax = CF_NTRANSSYSTEM
case default
call IO_error(137,ext_msg='crystal_interaction_SlipByTrans: '//trim(lattice))
end select
interactionMatrix = buildInteraction(Nslip,Ntrans,NslipMax,NtransMax,interactionValues,interactionTypes)
end function crystal_interaction_SlipByTrans
!--------------------------------------------------------------------------------------------------
!> @brief Twin-slip interaction matrix
!> details only active twin and slip systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) 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) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), dimension(sum(Ntwin),sum(Nslip)) :: interactionMatrix
integer, dimension(:), allocatable :: NtwinMax, &
NslipMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(CF_NSLIP,CF_NTWIN), parameter :: &
CF_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for cF
integer, dimension(CI_NSLIP,CI_NTWIN), parameter :: &
CI_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for cI
integer, dimension(HP_NSLIP,HP_NTWIN), parameter :: &
HP_INTERACTIONTWINSLIP = reshape( [&
! basal prism 1. pyr<a> 1. pyr<c+a> 2. pyr<c+a>
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! ----> slip (acting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! |
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! v <-10.1>{10.2}
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, & ! twin (reacting)
1, 1, 1, 5, 5, 5, 9, 9, 9, 9, 9, 9, 13,13,13,13,13,13,13,13,13,13,13,13, 17,17,17,17,17,17, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, & ! <11.6>{-1-1.1}
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
2, 2, 2, 6, 6, 6, 10,10,10,10,10,10, 14,14,14,14,14,14,14,14,14,14,14,14, 18,18,18,18,18,18, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, & ! <10.-2>{10.1}
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
3, 3, 3, 7, 7, 7, 11,11,11,11,11,11, 15,15,15,15,15,15,15,15,15,15,15,15, 19,19,19,19,19,19, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, & ! <11.-3>{11.2}
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20, &
4, 4, 4, 8, 8, 8, 12,12,12,12,12,12, 16,16,16,16,16,16,16,16,16,16,16,16, 20,20,20,20,20,20 &
],shape(HP_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hP
select case(lattice)
case('cF')
interactionTypes = CF_INTERACTIONTWINSLIP
NtwinMax = CF_NTWINSYSTEM
NslipMax = CF_NSLIPSYSTEM
case('cI')
interactionTypes = CI_INTERACTIONTWINSLIP
NtwinMax = CI_NTWINSYSTEM
NslipMax = CI_NSLIPSYSTEM
case('hP')
interactionTypes = HP_INTERACTIONTWINSLIP
NtwinMax = HP_NTWINSYSTEM
NslipMax = HP_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='crystal_interaction_TwinBySlip: '//trim(lattice))
end select
interactionMatrix = buildInteraction(Ntwin,Nslip,NtwinMax,NslipMax,interactionValues,interactionTypes)
end function crystal_interaction_TwinBySlip
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for slip
!> details only active slip systems are considered
! Non-schmid projections for cI with up to 6 coefficients
! https://doi.org/10.1016/j.actamat.2012.03.053, eq. (17)
! https://doi.org/10.1016/j.actamat.2008.07.037, table 1
!--------------------------------------------------------------------------------------------------
function crystal_SchmidMatrix_slip(Nslip,lattice,cOverA,nonSchmidCoefficients,sense) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
real(pREAL), intent(in) :: cOverA
real(pREAL), dimension(:,:), optional, intent(in) :: nonSchmidCoefficients !< non-Schmid coefficients for projections
integer, optional, intent(in) :: sense !< sense (-1,+1)
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, dimension(:), allocatable :: slipFamily
real(pREAL), dimension(3) :: direction, normal, np
real(pREAL), dimension(6) :: coeff !< local nonSchmid coefficient variable
type(tRotation) :: R
integer :: i
select case(lattice)
case('cF')
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='crystal_SchmidMatrix_slip: '//trim(lattice))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(lattice))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(lattice))
slipFamily = math_expand([(i, i=1,size(Nslip))],Nslip)
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,lattice,cOverA)
if (present(sense)) then
if (abs(sense) /= 1) error stop 'neither +1 nor -1 sense in crystal_SchmidMatrix_slip'
coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip)) * real(sense,pREAL)
end if
do i = 1,sum(Nslip)
direction = coordinateSystem(1:3,1,i)
normal = coordinateSystem(1:3,2,i)
SchmidMatrix(1:3,1:3,i) = math_outer(direction,normal)
if (abs(math_trace33(SchmidMatrix(1:3,1:3,i))) > tol_math_check) &
error stop 'dilatational Schmid matrix for slip'
if (present(nonSchmidCoefficients)) then
select case(lattice)
case('cI')
coeff(:) = 0.0_pREAL
select case(slipFamily(i))
case(1)
coeff(:size(nonSchmidCoefficients(1,:))) = nonSchmidCoefficients(1,:)
call R%fromAxisAngle([direction,60.0_pREAL],degrees=.true.,P=1)
np = R%rotate(normal)
SchmidMatrix(1:3,1:3,i) = SchmidMatrix(1:3,1:3,i) &
+ coeff(1) * math_outer(direction, np) &
+ coeff(2) * math_outer(math_cross(normal, direction), normal) &
+ coeff(3) * math_outer(math_cross(np, direction), np) &
+ coeff(4) * math_outer(normal, normal) &
+ coeff(5) * math_outer(math_cross(normal, direction), &
math_cross(normal, direction)) &
+ coeff(6) * math_outer(direction, direction)
end select
end select
end if
end do
end function crystal_SchmidMatrix_slip
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for twinning
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_SchmidMatrix_twin(Ntwin,lattice,cOverA) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ntwin !< number of active twin systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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(lattice)
case('cF')
NtwinMax = CF_NTWINSYSTEM
twinSystems = CF_SYSTEMTWIN
case('cI')
NtwinMax = CI_NTWINSYSTEM
twinSystems = CI_SYSTEMTWIN
case('hP')
NtwinMax = HP_NTWINSYSTEM
twinSystems = HP_SYSTEMTWIN
case default
allocate(NtwinMax(0))
call IO_error(137,ext_msg='crystal_SchmidMatrix_twin: '//trim(lattice))
end select
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
call IO_error(145,ext_msg='Ntwin '//trim(lattice))
if (any(Ntwin < 0)) &
call IO_error(144,ext_msg='Ntwin '//trim(lattice))
coordinateSystem = buildCoordinateSystem(Ntwin,NtwinMax,twinSystems,lattice,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) &
error stop 'dilatational Schmid matrix for twin'
end do
end function crystal_SchmidMatrix_twin
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for transformation
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_SchmidMatrix_trans(Ntrans,crystal_target,cOverA,a_cF,a_cI) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=*), intent(in) :: crystal_target !< Bravais lattice (Pearson symbol)
real(pREAL), optional, intent(in) :: cOverA, a_cI, a_cF
real(pREAL), dimension(3,3,sum(Ntrans)) :: SchmidMatrix
real(pREAL), dimension(3,3,sum(Ntrans)) :: devNull
if (crystal_target == 'hP' .and. present(cOverA)) then
if (cOverA < 1.0_pREAL .or. cOverA > 2.0_pREAL) &
call IO_error(131,ext_msg='crystal_SchmidMatrix_trans: '//trim(crystal_target))
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA=cOverA)
else if (crystal_target == 'cI' .and. present(a_cF) .and. present(a_cI)) then
if (a_cI <= 0.0_pREAL .or. a_cF <= 0.0_pREAL) &
call IO_error(134,ext_msg='crystal_SchmidMatrix_trans: '//trim(crystal_target))
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,a_cF=a_cF,a_cI=a_cI)
else
call IO_error(131,ext_msg='crystal_SchmidMatrix_trans: '//trim(crystal_target))
end if
end function crystal_SchmidMatrix_trans
!--------------------------------------------------------------------------------------------------
!> @brief Schmid matrix for cleavage
!> details only active cleavage systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_SchmidMatrix_cleavage(Ncleavage,lattice,cOverA) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ncleavage !< number of active cleavage systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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(lattice)
case('cF')
NcleavageMax = CF_NCLEAVAGESYSTEM
cleavageSystems = CF_SYSTEMCLEAVAGE
case('cI')
NcleavageMax = CI_NCLEAVAGESYSTEM
cleavageSystems = CI_SYSTEMCLEAVAGE
case default
allocate(NcleavageMax(0))
call IO_error(137,ext_msg='crystal_SchmidMatrix_cleavage: '//trim(lattice))
end select
if (any(NcleavageMax(1:size(Ncleavage)) - Ncleavage < 0)) &
call IO_error(145,ext_msg='Ncleavage '//trim(lattice))
if (any(Ncleavage < 0)) &
call IO_error(144,ext_msg='Ncleavage '//trim(lattice))
coordinateSystem = buildCoordinateSystem(Ncleavage,NcleavageMax,cleavageSystems,lattice,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))
end do
end function crystal_SchmidMatrix_cleavage
!--------------------------------------------------------------------------------------------------
!> @brief Slip direction of slip systems (|| b)
!--------------------------------------------------------------------------------------------------
function crystal_slip_direction(Nslip,lattice,cOverA) result(d)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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,lattice,cOverA)
d = coordinateSystem(1:3,1,1:sum(Nslip))
end function crystal_slip_direction
!--------------------------------------------------------------------------------------------------
!> @brief Normal direction of slip systems (|| n)
!--------------------------------------------------------------------------------------------------
function crystal_slip_normal(Nslip,lattice,cOverA) result(n)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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,lattice,cOverA)
n = coordinateSystem(1:3,2,1:sum(Nslip))
end function crystal_slip_normal
!--------------------------------------------------------------------------------------------------
!> @brief Transverse direction of slip systems (|| t = b x n)
!--------------------------------------------------------------------------------------------------
function crystal_slip_transverse(Nslip,lattice,cOverA) result(t)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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,lattice,cOverA)
t = coordinateSystem(1:3,3,1:sum(Nslip))
end function crystal_slip_transverse
!--------------------------------------------------------------------------------------------------
!> @brief Labels of slip systems
!> details only active slip systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_labels_slip(Nslip,lattice) result(labels)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
character(len=:), dimension(:), allocatable :: labels
real(pREAL), dimension(:,:), allocatable :: slipSystems
integer, dimension(:), allocatable :: NslipMax
select case(lattice)
case('cF')
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
call IO_error(137,ext_msg='crystal_labels_slip: '//trim(lattice))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(lattice))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(lattice))
labels = getLabels(Nslip,NslipMax,slipSystems)
end function crystal_labels_slip
!--------------------------------------------------------------------------------------------------
!> @brief Return 3x3 tensor with symmetry according to given Bravais lattice
!--------------------------------------------------------------------------------------------------
pure function crystal_symmetrize_33(T,lattice) result(T_sym)
real(pREAL), dimension(3,3) :: T_sym
real(pREAL), dimension(3,3), intent(in) :: T
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
T_sym = 0.0_pREAL
select case(lattice)
case('cF','cI')
T_sym(1,1) = T(1,1)
T_sym(2,2) = T(1,1)
T_sym(3,3) = T(1,1)
case('hP','tI')
T_sym(1,1) = T(1,1)
T_sym(2,2) = T(1,1)
T_sym(3,3) = T(3,3)
end select
end function crystal_symmetrize_33
!--------------------------------------------------------------------------------------------------
!> @brief Return stiffness matrix in 6x6 notation with symmetry according to given Bravais lattice
!> @details J. A. Rayne and B. S. Chandrasekhar Phys. Rev. 120, 1658 Erratum Phys. Rev. 122, 1962
!--------------------------------------------------------------------------------------------------
pure function crystal_symmetrize_C66(C66,lattice) result(C66_sym)
real(pREAL), dimension(6,6) :: C66_sym
real(pREAL), dimension(6,6), intent(in) :: C66
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
integer :: i,j
C66_sym = 0.0_pREAL
select case(lattice)
case ('cF','cI')
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1); C66_sym(3,3) = C66(1,1)
C66_sym(1,2) = C66(1,2); C66_sym(1,3) = C66(1,2); C66_sym(2,3) = C66(1,2)
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4); C66_sym(6,6) = C66(4,4) ! isotropic C_44 = (C_11-C_12)/2
case ('hP')
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1)
C66_sym(3,3) = C66(3,3)
C66_sym(1,2) = C66(1,2)
C66_sym(1,3) = C66(1,3); C66_sym(2,3) = C66(1,3)
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4)
C66_sym(6,6) = 0.5_pREAL*(C66(1,1)-C66(1,2))
case ('tI')
C66_sym(1,1) = C66(1,1); C66_sym(2,2) = C66(1,1)
C66_sym(3,3) = C66(3,3)
C66_sym(1,2) = C66(1,2)
C66_sym(1,3) = C66(1,3); C66_sym(2,3) = C66(1,3)
C66_sym(4,4) = C66(4,4); C66_sym(5,5) = C66(4,4)
C66_sym(6,6) = C66(6,6)
end select
do i = 1, 6
do j = i+1, 6
C66_sym(j,i) = C66_sym(i,j)
end do
end do
end function crystal_symmetrize_C66
!--------------------------------------------------------------------------------------------------
!> @brief Labels for twin systems
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function crystal_labels_twin(Ntwin,lattice) result(labels)
integer, dimension(:), intent(in) :: Ntwin !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
character(len=:), dimension(:), allocatable :: labels
real(pREAL), dimension(:,:), allocatable :: twinSystems
integer, dimension(:), allocatable :: NtwinMax
select case(lattice)
case('cF')
NtwinMax = CF_NTWINSYSTEM
twinSystems = CF_SYSTEMTWIN
case('cI')
NtwinMax = CI_NTWINSYSTEM
twinSystems = CI_SYSTEMTWIN
case('hP')
NtwinMax = HP_NTWINSYSTEM
twinSystems = HP_SYSTEMTWIN
case default
call IO_error(137,ext_msg='crystal_labels_twin: '//trim(lattice))
end select
if (any(NtwinMax(1:size(Ntwin)) - Ntwin < 0)) &
call IO_error(145,ext_msg='Ntwin '//trim(lattice))
if (any(Ntwin < 0)) &
call IO_error(144,ext_msg='Ntwin '//trim(lattice))
labels = getLabels(Ntwin,NtwinMax,twinSystems)
end function crystal_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,lattice,cOverA) result(projection)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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 = crystal_slip_normal (Nslip,lattice,cOverA)
t = crystal_slip_transverse(Nslip,lattice,cOverA)
do i=1, sum(Nslip); do j=1, sum(Nslip)
projection(i,j) = abs(math_inner(n(:,i),t(:,j)))
end do; end do
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,lattice,cOverA) result(projection)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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 = crystal_slip_normal (Nslip,lattice,cOverA)
d = crystal_slip_direction(Nslip,lattice,cOverA)
do i=1, sum(Nslip); do j=1, sum(Nslip)
projection(i,j) = abs(math_inner(n(:,i),d(:,j)))
end do; end do
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,lattice,cOverA) result(coordinateSystem)
integer, dimension(:), intent(in) :: Nslip !< number of active slip systems per family
character(len=*), intent(in) :: lattice !< Bravais lattice (Pearson symbol)
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(lattice)
case('cF')
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(lattice))
end select
if (any(NslipMax(1:size(Nslip)) - Nslip < 0)) &
call IO_error(145,ext_msg='Nslip '//trim(lattice))
if (any(Nslip < 0)) &
call IO_error(144,ext_msg='Nslip '//trim(lattice))
coordinateSystem = buildCoordinateSystem(Nslip,NslipMax,slipSystems,lattice,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))
end do; end do
end do; end do
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,lattice,cOverA) result(coordinateSystem)
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) :: &
lattice !< Bravais lattice (Pearson symbol)
real(pREAL), intent(in) :: &
cOverA
real(pREAL), dimension(3,3,sum(active)) :: &
coordinateSystem
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 (lattice == 'tI' .and. cOverA > 2.0_pREAL) &
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(lattice))
if (lattice == 'hP' .and. (cOverA < 1.0_pREAL .or. cOverA > 2.0_pREAL)) &
call IO_error(131,ext_msg='buildCoordinateSystem:'//trim(lattice))
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(lattice)
case ('cF','cI')
direction = system(1:3,p)
normal = system(4:6,p)
case ('tI')
direction = [ system(1,p), system(2,p), system(3,p)*cOverA ]
normal = [ system(4,p), system(5,p), system(6,p)/cOverA ]
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(lattice))
end select
coordinateSystem(1:3,1,a) = direction/norm2(direction)
coordinateSystem(1:3,2,a) = normal /norm2(normal)
coordinateSystem(1:3,3,a) = math_cross(direction/norm2(direction),&
normal /norm2(normal))
end do activeSystems
end do activeFamilies
end function buildCoordinateSystem
!--------------------------------------------------------------------------------------------------
!> @brief Helper function to define transformation systems
! Needed to calculate Schmid matrix and rotated stiffness matrices.
! @details: use c/a for cF -> hP transformation
! use a_cX for cF -> cI transformation
!--------------------------------------------------------------------------------------------------
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_cF,a_cI)
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), optional, intent(in) :: &
cOverA, & !< c/a for target hP lattice
a_cF, & !< lattice parameter a for cF target lattice
a_cI !< lattice parameter a for cI parent lattice
type(tRotation) :: &
R, & !< Pitsch rotation
B !< Rotation of cF 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,CF_NTRANS), parameter :: &
CFTOHP_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(CFTOHP_SYSTEMTRANS))
real(pREAL), dimension(4,cF_Ntrans), parameter :: &
CFTOCI_SYSTEMTRANS = real(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(CFTOCI_SYSTEMTRANS)),pREAL)
integer, dimension(9,cF_Ntrans), parameter :: &
CFTOCI_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(CFTOCI_BAINVARIANT))
real(pREAL), dimension(4,cF_Ntrans), parameter :: &
CFTOCI_BAINROT = real(reshape([&
1.0, 0.0, 0.0, 45.0, & ! Rotate cF 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(CFTOCI_BAINROT)),pREAL)
if (present(a_cI) .and. present(a_cF)) then
do i = 1,sum(Ntrans)
call R%fromAxisAngle(CFTOCI_SYSTEMTRANS(:,i),degrees=.true.,P=1)
call B%fromAxisAngle(CFTOCI_BAINROT(:,i), degrees=.true.,P=1)
x = real(CFTOCI_BAINVARIANT(1:3,i),pREAL)
y = real(CFTOCI_BAINVARIANT(4:6,i),pREAL)
z = real(CFTOCI_BAINVARIANT(7:9,i),pREAL)
U = (a_cI/a_cF) * (math_outer(x,x) + (math_outer(y,y)+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
end do
else if (present(cOverA)) then
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 = CFTOHP_SYSTEMTRANS(1:3,i)/norm2(CFTOHP_SYSTEMTRANS(1:3,i))
z = CFTOHP_SYSTEMTRANS(4:6,i)/norm2(CFTOHP_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
end do
else
call IO_error(132,ext_msg='buildTransformationSystem')
end if
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
end do 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
end do normal
label(i:i) = ')'
labels(a) = label
end do activeSystems
end do activeFamilies
end function getlabels
!--------------------------------------------------------------------------------------------------
!> @brief Equivalent Poisson's ratio (ν)
!> @details https://doi.org/10.1143/JPSJ.20.635
!--------------------------------------------------------------------------------------------------
pure function crystal_isotropic_nu(C,assumption,lattice) result(nu)
real(pREAL), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=*), intent(in) :: assumption !< Assumption (isostrain = 'Voigt', isostress = 'Reuss')
character(len=*), optional, intent(in) :: lattice
real(pREAL) :: nu
real(pREAL) :: K, mu
logical :: error
real(pREAL), dimension(6,6) :: S
if (assumption == 'isostrain') then
K = sum(C(1:3,1:3)) / 9.0_pREAL
elseif (assumption == 'isostress') then
call math_invert(S,error,C)
if (error) error stop 'matrix inversion failed'
K = 1.0_pREAL / sum(S(1:3,1:3))
else
error stop 'invalid assumption'
end if
mu = crystal_isotropic_mu(C,assumption,lattice)
nu = (1.5_pREAL*K-mu)/(3.0_pREAL*K+mu)
end function crystal_isotropic_nu
!--------------------------------------------------------------------------------------------------
!> @brief Equivalent shear modulus (μ)
!> @details https://doi.org/10.1143/JPSJ.20.635
!> @details Nonlinear Mechanics of Crystals 10.1007/978-94-007-0350-6, pp 563
!--------------------------------------------------------------------------------------------------
pure function crystal_isotropic_mu(C,assumption,lattice) result(mu)
real(pREAL), dimension(6,6), intent(in) :: C !< Stiffness tensor (Voigt notation)
character(len=*), intent(in) :: assumption !< Assumption (isostrain = 'Voigt', isostress = 'Reuss')
character(len=*), optional, intent(in) :: lattice
real(pREAL) :: mu
logical :: error
real(pREAL), dimension(6,6) :: S
if (assumption == 'isostrain') then
select case(misc_optional(lattice,''))
case('cF','cI')
mu = ( C(1,1) - C(1,2) + C(4,4)*3.0_pREAL) / 5.0_pREAL
case default
mu = ( C(1,1)+C(2,2)+C(3,3) &
- C(1,2)-C(2,3)-C(1,3) &
+(C(4,4)+C(5,5)+C(6,6)) * 3.0_pREAL &
) / 15.0_pREAL
end select
elseif (assumption == 'isostress') then
select case(misc_optional(lattice,''))
case('cF','cI')
mu = 5.0_pREAL &
/ (4.0_pREAL/(C(1,1)-C(1,2)) + 3.0_pREAL/C(4,4))
case default
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)-S(1,2)-S(2,3)-S(1,3)) + 3.0_pREAL*(S(4,4)+S(5,5)+S(6,6)))
end select
else
error stop 'invalid assumption'
end if
end function crystal_isotropic_mu
!--------------------------------------------------------------------------------------------------
!> @brief Check correctness of some crystal functions.
!--------------------------------------------------------------------------------------------------
subroutine crystal_selfTest()
real(pREAL), dimension(:,:,:), allocatable :: CoSy
real(pREAL), dimension(:,:), allocatable :: system
real(pREAL), dimension(6,6) :: C, C_cF, C_cI, C_hP, C_tI
real(pREAL), dimension(3,3) :: T, T_cF, T_cI, T_hP, T_tI
real(pREAL), dimension(2) :: r
real(pREAL) :: lambda
integer :: i
call random_number(r)
system = reshape([1.0_pREAL+r(1),0.0_pREAL,0.0_pREAL, 0.0_pREAL,1.0_pREAL+r(2),0.0_pREAL],[6,1])
CoSy = buildCoordinateSystem([1],[1],system,'cF',0.0_pREAL)
if (any(dNeq(CoSy(1:3,1:3,1),math_I3))) error stop 'buildCoordinateSystem'
if (any(dNeq(buildCoordinateSystem(TI_NSLIPSYSTEM,TI_NSLIPSYSTEM,TI_SYSTEMSLIP,'cI',0.0_pReal), &
buildCoordinateSystem(TI_NSLIPSYSTEM,TI_NSLIPSYSTEM,TI_SYSTEMSLIP,'tI',1.0_pReal)))) &
error stop 'cI/tI coordinate system'
if (all(dEq( buildCoordinateSystem(TI_NSLIPSYSTEM,TI_NSLIPSYSTEM,TI_SYSTEMSLIP,'tI',1.1_pReal + r(1)*0.9_pReal), &
buildCoordinateSystem(TI_NSLIPSYSTEM,TI_NSLIPSYSTEM,TI_SYSTEMSLIP,'tI',1.0_pReal)))) &
error stop 'tI coordinate system'
do i = 1, 10
call random_number(C)
C_cF = crystal_symmetrize_C66(C,'cI')
C_cI = crystal_symmetrize_C66(C,'cF')
C_hP = crystal_symmetrize_C66(C,'hP')
C_tI = crystal_symmetrize_C66(C,'tI')
if (any(dNeq(C_cI,transpose(C_cF)))) error stop 'SymmetryC66/cI-cF'
if (any(dNeq(C_cF,transpose(C_cI)))) error stop 'SymmetryC66/cF-cI'
if (any(dNeq(C_hP,transpose(C_hP)))) error stop 'SymmetryC66/hP'
if (any(dNeq(C_tI,transpose(C_tI)))) error stop 'SymmetryC66/tI'
if (any(dNeq(C(1,1),[C_cF(1,1),C_cF(2,2),C_cF(3,3)]))) error stop 'SymmetryC_11-22-33/c'
if (any(dNeq(C(1,2),[C_cF(1,2),C_cF(1,3),C_cF(2,3)]))) error stop 'SymmetryC_12-13-23/c'
if (any(dNeq(C(4,4),[C_cF(4,4),C_cF(5,5),C_cF(6,6)]))) error stop 'SymmetryC_44-55-66/c'
if (any(dNeq(C(1,1),[C_hP(1,1),C_hP(2,2)]))) error stop 'SymmetryC_11-22/hP'
if (any(dNeq(C(1,3),[C_hP(1,3),C_hP(2,3)]))) error stop 'SymmetryC_13-23/hP'
if (any(dNeq(C(4,4),[C_hP(4,4),C_hP(5,5)]))) error stop 'SymmetryC_44-55/hP'
if (any(dNeq(C(1,1),[C_tI(1,1),C_tI(2,2)]))) error stop 'SymmetryC_11-22/tI'
if (any(dNeq(C(1,3),[C_tI(1,3),C_tI(2,3)]))) error stop 'SymmetryC_13-23/tI'
if (any(dNeq(C(4,4),[C_tI(4,4),C_tI(5,5)]))) error stop 'SymmetryC_44-55/tI'
call random_number(T)
T_cF = crystal_symmetrize_33(T,'cI')
T_cI = crystal_symmetrize_33(T,'cF')
T_hP = crystal_symmetrize_33(T,'hP')
T_tI = crystal_symmetrize_33(T,'tI')
if (any(dNeq0(T_cF) .and. math_I3<1.0_pREAL)) error stop 'Symmetry33/c'
if (any(dNeq0(T_hP) .and. math_I3<1.0_pREAL)) error stop 'Symmetry33/hP'
if (any(dNeq0(T_tI) .and. math_I3<1.0_pREAL)) error stop 'Symmetry33/tI'
if (any(dNeq(T(1,1),[T_cI(1,1),T_cI(2,2),T_cI(3,3)]))) error stop 'Symmetry33_11-22-33/c'
if (any(dNeq(T(1,1),[T_hP(1,1),T_hP(2,2)]))) error stop 'Symmetry33_11-22/hP'
if (any(dNeq(T(1,1),[T_tI(1,1),T_tI(2,2)]))) error stop 'Symmetry33_11-22/tI'
end do
call random_number(C)
C(1,1) = C(1,1) + C(1,2) + 0.1_pREAL
C(1,3) = C(1,2)
C(3,3) = C(1,1)
C(4,4) = 0.5_pREAL * (C(1,1) - C(1,2))
C(6,6) = C(4,4)
C_cI = crystal_symmetrize_C66(C,'cI')
if (dNeq(C_cI(4,4),crystal_isotropic_mu(C_cI,'isostrain','cI'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostrain/cI'
if (dNeq(C_cI(4,4),crystal_isotropic_mu(C_cI,'isostress','cI'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostress/cI'
lambda = C_cI(1,2)
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_cI,'isostrain','cI')), &
crystal_isotropic_nu(C_cI,'isostrain','cI'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostrain/cI'
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_cI,'isostress','cI')), &
crystal_isotropic_nu(C_cI,'isostress','cI'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostress/cI'
C_hP = crystal_symmetrize_C66(C,'hP')
if (dNeq(C(4,4),crystal_isotropic_mu(C_hP,'isostrain','hP'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostrain/hP'
if (dNeq(C(4,4),crystal_isotropic_mu(C_hP,'isostress','hP'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostress/hP'
lambda = C_hP(1,2)
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_hP,'isostrain','hP')), &
crystal_isotropic_nu(C_hP,'isostrain','hP'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostrain/hP'
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_hP,'isostress','hP')), &
crystal_isotropic_nu(C_hP,'isostress','hP'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostress/hP'
C_tI = crystal_symmetrize_C66(C,'tI')
if (dNeq(C(6,6),crystal_isotropic_mu(C_tI,'isostrain','tI'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostrain/tI'
if (dNeq(C(6,6),crystal_isotropic_mu(C_tI,'isostress','tI'),1.0e-12_pREAL)) error stop 'isotropic_mu/isostress/tI'
lambda = C_tI(1,2)
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_tI,'isostrain','tI')), &
crystal_isotropic_nu(C_tI,'isostrain','tI'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostrain/tI'
if (dNeq(lambda*0.5_pREAL/(lambda+crystal_isotropic_mu(C_tI,'isostress','tI')), &
crystal_isotropic_nu(C_tI,'isostress','tI'),1.0e-12_pREAL)) error stop 'isotropic_nu/isostress/tI'
call random_number(C)
C = crystal_symmetrize_C66(C+math_eye(6),'cI')
if (dNeq(crystal_isotropic_mu(C,'isostrain','cI'), crystal_isotropic_mu(C,'isostrain','hP'), 1.0e-12_pREAL)) &
error stop 'isotropic_mu/isostrain/cI-hP'
if (dNeq(crystal_isotropic_nu(C,'isostrain','cF'), crystal_isotropic_nu(C,'isostrain','cI'), 1.0e-12_pREAL)) &
error stop 'isotropic_nu/isostrain/cF-tI'
if (dNeq(crystal_isotropic_mu(C,'isostress','cI'), crystal_isotropic_mu(C,'isostress'), 1.0e-12_pREAL)) &
error stop 'isotropic_mu/isostress/cI-hP'
if (dNeq(crystal_isotropic_nu(C,'isostress','cF'), crystal_isotropic_nu(C,'isostress'), 1.0e-12_pREAL)) &
error stop 'isotropic_nu/isostress/cF-tI'
end subroutine crystal_selfTest
end module crystal
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