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Update crystal structure name

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Martin Diehl 2022-02-21 09:00:00 +00:00 committed by Franz Roters
parent 9ba0a4bd86
commit f6bcabd328
2 changed files with 235 additions and 233 deletions
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src/lattice.f90
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@ -17,27 +17,28 @@ module lattice
private
!--------------------------------------------------------------------------------------------------
! face centered cubic (cF)
integer, dimension(*), parameter :: &
FCC_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for fcc
! cF: face centered cubic (fcc)
integer, dimension(*), parameter :: &
FCC_NTWINSYSTEM = [12] !< # of twin systems per family for fcc
CF_NSLIPSYSTEM = [12, 6] !< # of slip systems per family for cF
integer, dimension(*), parameter :: &
FCC_NTRANSSYSTEM = [12] !< # of transformation systems per family for fcc
CF_NTWINSYSTEM = [12] !< # of twin systems per family for cF
integer, dimension(*), parameter :: &
FCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for fcc
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 :: &
FCC_NSLIP = sum(FCC_NSLIPSYSTEM), & !< total # of slip systems for fcc
FCC_NTWIN = sum(FCC_NTWINSYSTEM), & !< total # of twin systems for fcc
FCC_NTRANS = sum(FCC_NTRANSSYSTEM), & !< total # of transformation systems for fcc
FCC_NCLEAVAGE = sum(FCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for fcc
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,FCC_NSLIP), parameter :: &
FCC_SYSTEMSLIP = reshape(real([&
real(pReal), dimension(3+3,CF_NSLIP), parameter :: &
CF_SYSTEMSLIP = reshape(real([&
! <110>{111} systems
0, 1,-1, 1, 1, 1, & ! B2
-1, 0, 1, 1, 1, 1, & ! B4
@ -58,10 +59,10 @@ module lattice
1, 0,-1, 1, 0, 1, &
0, 1, 1, 0, 1,-1, &
0, 1,-1, 0, 1, 1 &
],pReal),shape(FCC_SYSTEMSLIP)) !< fcc slip systems
],pReal),shape(CF_SYSTEMSLIP)) !< cF slip systems
real(pReal), dimension(3+3,FCC_NTWIN), parameter :: &
FCC_SYSTEMTWIN = reshape(real( [&
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, &
@ -75,10 +76,10 @@ module lattice
2, 1,-1, -1, 1,-1, &
-1,-2,-1, -1, 1,-1, &
-1, 1, 2, -1, 1,-1 &
],pReal),shape(FCC_SYSTEMTWIN)) !< fcc twin systems
],pReal),shape(CF_SYSTEMTWIN)) !< cF twin systems
integer, dimension(2,FCC_NTWIN), parameter, public :: &
lattice_FCC_TWINNUCLEATIONSLIPPAIR = reshape( [&
integer, dimension(2,CF_NTWIN), parameter, public :: &
lattice_CF_TWINNUCLEATIONSLIPPAIR = reshape( [&
2,3, &
1,3, &
1,2, &
@ -91,34 +92,35 @@ module lattice
11,12, &
10,12, &
10,11 &
],shape(lattice_FCC_TWINNUCLEATIONSLIPPAIR))
],shape(lattice_CF_TWINNUCLEATIONSLIPPAIR))
real(pReal), dimension(3+3,FCC_NCLEAVAGE), parameter :: &
FCC_SYSTEMCLEAVAGE = reshape(real([&
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(FCC_SYSTEMCLEAVAGE)) !< fcc cleavage systems
],pReal),shape(CF_SYSTEMCLEAVAGE)) !< cF cleavage systems
!--------------------------------------------------------------------------------------------------
! body centered cubic (cI)
integer, dimension(*), parameter :: &
BCC_NSLIPSYSTEM = [12, 12, 24] !< # of slip systems per family for bcc
! cI: body centered cubic (bcc)
integer, dimension(*), parameter :: &
BCC_NTWINSYSTEM = [12] !< # of twin systems per family for bcc
CI_NSLIPSYSTEM = [12, 12, 24] !< # of slip systems per family for cI
integer, dimension(*), parameter :: &
BCC_NCLEAVAGESYSTEM = [3] !< # of cleavage systems per family for bcc
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 :: &
BCC_NSLIP = sum(BCC_NSLIPSYSTEM), & !< total # of slip systems for bcc
BCC_NTWIN = sum(BCC_NTWINSYSTEM), & !< total # of twin systems for bcc
BCC_NCLEAVAGE = sum(BCC_NCLEAVAGESYSTEM) !< total # of cleavage systems for bcc
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,BCC_NSLIP), parameter :: &
BCC_SYSTEMSLIP = reshape(real([&
real(pReal), dimension(3+3,CI_NSLIP), parameter :: &
CI_SYSTEMSLIP = reshape(real([&
! <111>{110} systems
1,-1, 1, 0, 1, 1, & ! D1
-1,-1, 1, 0, 1, 1, & ! C1
@ -170,10 +172,10 @@ module lattice
1, 1, 1, -3, 2, 1, &
1, 1,-1, 3,-2, 1, &
1,-1, 1, 3, 2,-1 &
],pReal),shape(BCC_SYSTEMSLIP)) !< bcc slip systems
],pReal),shape(CI_SYSTEMSLIP)) !< cI slip systems
real(pReal), dimension(3+3,BCC_NTWIN), parameter :: &
BCC_SYSTEMTWIN = reshape(real([&
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, &
@ -187,30 +189,31 @@ module lattice
1,-1, 1, -1, 1, 2, &
-1, 1, 1, 1,-1, 2, &
1, 1, 1, 1, 1,-2 &
],pReal),shape(BCC_SYSTEMTWIN)) !< bcc twin systems
],pReal),shape(CI_SYSTEMTWIN)) !< cI twin systems
real(pReal), dimension(3+3,BCC_NCLEAVAGE), parameter :: &
BCC_SYSTEMCLEAVAGE = reshape(real([&
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(BCC_SYSTEMCLEAVAGE)) !< bcc cleavage systems
],pReal),shape(CI_SYSTEMCLEAVAGE)) !< cI cleavage systems
!--------------------------------------------------------------------------------------------------
! hexagonal (hP)
integer, dimension(*), parameter :: &
HEX_NSLIPSYSTEM = [3, 3, 6, 12, 6] !< # of slip systems per family for hex
! hP: hexagonal [close packed] (hex, hcp)
integer, dimension(*), parameter :: &
HEX_NTWINSYSTEM = [6, 6, 6, 6] !< # of slip systems per family for hex
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 :: &
HEX_NSLIP = sum(HEX_NSLIPSYSTEM), & !< total # of slip systems for hex
HEX_NTWIN = sum(HEX_NTWINSYSTEM) !< total # of twin systems for hex
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,HEX_NSLIP), parameter :: &
HEX_SYSTEMSLIP = reshape(real([&
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, &
@ -246,10 +249,10 @@ module lattice
1, 1, -2, 3, -1, -1, 2, 2, &
-1, 2, -1, 3, 1, -2, 1, 2, &
-2, 1, 1, 3, 2, -1, -1, 2 &
],pReal),shape(HEX_SYSTEMSLIP)) !< hex slip systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
],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,HEX_NTWIN), parameter :: &
HEX_SYSTEMTWIN = reshape(real([&
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, & !
@ -282,18 +285,19 @@ module lattice
-1, -1, 2, -3, -1, -1, 2, 2, &
1, -2, 1, -3, 1, -2, 1, 2, &
2, -1, -1, -3, 2, -1, -1, 2 &
],pReal),shape(HEX_SYSTEMTWIN)) !< hex twin systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
],pReal),shape(HP_SYSTEMTWIN)) !< hP twin systems, sorted by P. Eisenlohr CCW around <c> starting next to a_1 axis
!--------------------------------------------------------------------------------------------------
! body centered tetragonal (tI)
! tI: body centered tetragonal (bct)
integer, dimension(*), parameter :: &
BCT_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for bct
TI_NSLIPSYSTEM = [2, 2, 2, 4, 2, 4, 2, 2, 4, 8, 4, 8, 8 ] !< # of slip systems per family for tI
integer, parameter :: &
BCT_NSLIP = sum(BCT_NSLIPSYSTEM) !< total # of slip systems for bct
TI_NSLIP = sum(TI_NSLIPSYSTEM) !< total # of slip systems for tI
real(pReal), dimension(3+3,BCT_NSLIP), parameter :: &
BCT_SYSTEMSLIP = reshape(real([&
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, &
@ -359,7 +363,7 @@ module lattice
1,-1, 1, -2,-1, 1, &
-1, 1, 1, -1,-2, 1, &
1, 1, 1, 1,-2, 1 &
],pReal),shape(BCT_SYSTEMSLIP)) !< bct slip systems for c/a = 0.5456 (Sn), sorted by Bieler 2009 (https://doi.org/10.1007/s11664-009-0909-x)
],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 lattice_forestProjection_edge
@ -428,8 +432,8 @@ function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(character
f, & !< index of my family
s !< index of my system in current family
integer, dimension(HEX_NTWIN), parameter :: &
HEX_SHEARTWIN = reshape( [&
integer, dimension(HP_NTWIN), parameter :: &
HP_SHEARTWIN = reshape( [&
1, & ! <-10.1>{10.2}
1, &
1, &
@ -454,7 +458,7 @@ function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(character
4, &
4, &
4 &
],[HEX_NTWIN]) ! indicator to formulas below
],[HP_NTWIN]) !< indicator to formulas below
a = 0
myFamilies: do f = 1,size(Ntwin,1)
@ -466,8 +470,8 @@ function lattice_characteristicShear_Twin(Ntwin,lattice,CoverA) result(character
case('hP')
if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) &
call IO_error(131,ext_msg='lattice_characteristicShear_Twin')
p = sum(HEX_NTWINSYSTEM(1:f-1))+s
select case(HEX_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
p = sum(HP_NTWINSYSTEM(1:f-1))+s
select case(HP_SHEARTWIN(p)) ! from Christian & Mahajan 1995 p.29
case (1) ! <-10.1>{10.2}
characteristicShear(a) = (3.0_pReal-cOverA**2)/sqrt(3.0_pReal)/CoverA
case (2) ! <11.6>{-1-1.1}
@ -504,13 +508,13 @@ function lattice_C66_twin(Ntwin,C66,lattice,CoverA)
select case(lattice)
case('cF')
coordinateSystem = buildCoordinateSystem(Ntwin,FCC_NSLIPSYSTEM,FCC_SYSTEMTWIN,&
coordinateSystem = buildCoordinateSystem(Ntwin,CF_NSLIPSYSTEM,CF_SYSTEMTWIN,&
lattice,0.0_pReal)
case('cI')
coordinateSystem = buildCoordinateSystem(Ntwin,BCC_NSLIPSYSTEM,BCC_SYSTEMTWIN,&
coordinateSystem = buildCoordinateSystem(Ntwin,CI_NSLIPSYSTEM,CI_SYSTEMTWIN,&
lattice,0.0_pReal)
case('hP')
coordinateSystem = buildCoordinateSystem(Ntwin,HEX_NSLIPSYSTEM,HEX_SYSTEMTWIN,&
coordinateSystem = buildCoordinateSystem(Ntwin,HP_NSLIPSYSTEM,HP_SYSTEMTWIN,&
lattice,cOverA)
case default
call IO_error(137,ext_msg='lattice_C66_twin: '//trim(lattice))
@ -528,12 +532,12 @@ end function lattice_C66_twin
!> @brief Rotated elasticity matrices for transformation in 6x6-matrix notation
!--------------------------------------------------------------------------------------------------
function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
cOverA_trans,a_fcc,a_bcc)
cOverA_trans,a_cF,a_cI)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=2), intent(in) :: lattice_target !< Bravais lattice (Pearson symbol)
real(pReal), dimension(6,6), intent(in) :: C_parent66
real(pReal), optional, intent(in) :: cOverA_trans, a_fcc, a_bcc
real(pReal), optional, intent(in) :: cOverA_trans, a_cF, a_cI
real(pReal), dimension(6,6,sum(Ntrans)) :: lattice_C66_trans
real(pReal), dimension(6,6) :: C_bar66, C_target_unrotated66
@ -562,8 +566,8 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
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 = lattice_symmetrize_C66(C_target_unrotated66,'hP')
elseif (lattice_target == 'cI' .and. present(a_fcc) .and. present(a_bcc)) then
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
elseif (lattice_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='lattice_C66_trans: '//trim(lattice_target))
C_target_unrotated66 = C_parent66
else
@ -575,7 +579,7 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
call IO_error(135,el=i,ext_msg='matrix diagonal "el"ement in transformation')
enddo
call buildTransformationSystem(Q,S,Ntrans,cOverA_trans,a_fcc,a_bcc)
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))
@ -586,7 +590,7 @@ function lattice_C66_trans(Ntrans,C_parent66,lattice_target, &
!--------------------------------------------------------------------------------------------------
!> @brief Non-schmid projections for bcc with up to 6 coefficients
!> @brief 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
!--------------------------------------------------------------------------------------------------
@ -605,7 +609,7 @@ function lattice_nonSchmidMatrix(Nslip,nonSchmidCoefficients,sense) result(nonSc
if (abs(sense) /= 1) error stop 'Sense in lattice_nonSchmidMatrix'
coordinateSystem = buildCoordinateSystem(Nslip,BCC_NSLIPSYSTEM,BCC_SYSTEMSLIP,'cI',0.0_pReal)
coordinateSystem = buildCoordinateSystem(Nslip,CI_NSLIPSYSTEM,CI_SYSTEMSLIP,'cI',0.0_pReal)
coordinateSystem(1:3,1,1:sum(Nslip)) = coordinateSystem(1:3,1,1:sum(Nslip))*real(sense,pReal) ! convert unidirectional coordinate system
nonSchmidMatrix = lattice_SchmidMatrix_slip(Nslip,'cI',0.0_pReal) ! Schmid contribution
@ -636,8 +640,8 @@ end function lattice_nonSchmidMatrix
!--------------------------------------------------------------------------------------------------
!> @brief Slip-slip interaction matrix
!> @details only active slip systems are considered
!> @details https://doi.org/10.1016/j.actamat.2016.12.040 (fcc: Tab S4-1, bcc: Tab S5-1)
!> @details https://doi.org/10.1016/j.ijplas.2014.06.010 (hex: Tab 3b)
!> @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 lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(interactionMatrix)
@ -650,8 +654,8 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NSLIP,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPSLIP = reshape( [&
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, & ! |
@ -671,7 +675,7 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
11,13,11,10,12,10,10,12,10,11,13,11, 9, 9, 8, 1, 9, 9, &
12,10,10,13,11,11,12,10,10,13,11,11, 9, 9, 9, 9, 1, 8, &
13,11,11,12,10,10,13,11,11,12,10,10, 9, 9, 9, 9, 8, 1 &
],shape(FCC_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for fcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
],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
@ -686,8 +690,8 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
!<12: crossing btw one {110} and one {111} plane
!<13: collinear btw one {110} and one {111} plane
integer, dimension(BCC_NSLIP,BCC_NSLIP), parameter :: &
BCC_INTERACTIONSLIPSLIP = reshape( [&
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, &! |
@ -738,7 +742,7 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
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(BCC_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for bcc / Madec 2017 (https://doi.org/10.1016/j.actamat.2016.12.040)
],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
@ -751,8 +755,8 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
!< 27: {123}-{123} collinear
!< 28: other interaction
integer, dimension(HEX_NSLIP,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPSLIP = reshape( [&
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
@ -788,7 +792,7 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
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(HEX_INTERACTIONSLIPSLIP)) !< Slip-slip interaction types for hex (onion peel naming scheme)
],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
@ -862,8 +866,8 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
!< 68 & 12 & 2. order pyramidal <c+a>/basal non-collinear
!< 69 & 11 & 2. order pyramidal <c+a>/basal semi-collinear
integer, dimension(BCT_NSLIP,BCT_NSLIP), parameter :: &
BCT_INTERACTIONSLIPSLIP = reshape( [&
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, & ! |
! |
@ -928,22 +932,22 @@ function lattice_interaction_SlipBySlip(Nslip,interactionValues,lattice) result(
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,169,170,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,169,170, &
182,182, 181,181, 180,180, 179,179,179,179, 178,178, 177,177,177,177, 176,176, 175,175, 174,174,174,174, 173,173,173,173,173,173,173,173, 172, 172, 172, 172, 171,171,171,171,171,171,171,171, 169,170,170,170,170,170,170,169 &
],shape(BCT_INTERACTIONSLIPSLIP))
],shape(TI_INTERACTIONSLIPSLIP))
select case(lattice)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPSLIP
NslipMax = FCC_NSLIPSYSTEM
interactionTypes = CF_INTERACTIONSLIPSLIP
NslipMax = CF_NSLIPSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONSLIPSLIP
NslipMax = BCC_NSLIPSYSTEM
interactionTypes = CI_INTERACTIONSLIPSLIP
NslipMax = CI_NSLIPSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONSLIPSLIP
NslipMax = HEX_NSLIPSYSTEM
interactionTypes = HP_INTERACTIONSLIPSLIP
NslipMax = HP_NSLIPSYSTEM
case('tI')
interactionTypes = BCT_INTERACTIONSLIPSLIP
NslipMax = BCT_NSLIPSYSTEM
interactionTypes = TI_INTERACTIONSLIPSLIP
NslipMax = TI_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipBySlip: '//trim(lattice))
end select
@ -967,8 +971,8 @@ function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(
integer, dimension(:), allocatable :: NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTWIN,FCC_NTWIN), parameter :: &
FCC_INTERACTIONTWINTWIN = reshape( [&
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, & ! |
@ -981,10 +985,10 @@ function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1 &
],shape(FCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for fcc
],shape(CF_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for cF
integer, dimension(BCC_NTWIN,BCC_NTWIN), parameter :: &
BCC_INTERACTIONTWINTWIN = reshape( [&
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, & ! |
@ -997,12 +1001,12 @@ function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(
3,3,3,2,2,3,3,3,3,1,3,3, &
2,3,3,3,3,3,3,2,3,3,1,3, &
3,2,3,3,3,3,2,3,3,3,3,1 &
],shape(BCC_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for bcc
],shape(CI_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for cI
!< 1: self interaction
!< 2: collinear interaction
!< 3: other interaction
integer, dimension(HEX_NTWIN,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINTWIN = reshape( [&
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, & ! |
@ -1031,18 +1035,18 @@ function lattice_interaction_TwinByTwin(Ntwin,interactionValues,lattice) result(
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(HEX_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hex
],shape(HP_INTERACTIONTWINTWIN)) !< Twin-twin interaction types for hP
select case(lattice)
case('cF')
interactionTypes = FCC_INTERACTIONTWINTWIN
NtwinMax = FCC_NTWINSYSTEM
interactionTypes = CF_INTERACTIONTWINTWIN
NtwinMax = CF_NTWINSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONTWINTWIN
NtwinMax = BCC_NTWINSYSTEM
interactionTypes = CI_INTERACTIONTWINTWIN
NtwinMax = CI_NTWINSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONTWINTWIN
NtwinMax = HEX_NTWINSYSTEM
interactionTypes = HP_INTERACTIONTWINTWIN
NtwinMax = HP_NTWINSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_TwinByTwin: '//trim(lattice))
end select
@ -1066,8 +1070,8 @@ function lattice_interaction_TransByTrans(Ntrans,interactionValues,lattice) resu
integer, dimension(:), allocatable :: NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTRANS,FCC_NTRANS), parameter :: &
FCC_INTERACTIONTRANSTRANS = reshape( [&
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, & ! |
@ -1080,11 +1084,11 @@ function lattice_interaction_TransByTrans(Ntrans,interactionValues,lattice) resu
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1, &
2,2,2,2,2,2,2,2,2,1,1,1 &
],shape(FCC_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for fcc
],shape(CF_INTERACTIONTRANSTRANS)) !< Trans-trans interaction types for cF
if (lattice == 'cF') then
interactionTypes = FCC_INTERACTIONTRANSTRANS
NtransMax = FCC_NTRANSSYSTEM
interactionTypes = CF_INTERACTIONTRANSTRANS
NtransMax = CF_NTRANSSYSTEM
else
call IO_error(137,ext_msg='lattice_interaction_TransByTrans: '//trim(lattice))
end if
@ -1110,8 +1114,8 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
NtwinMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTWIN,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPTWIN = reshape( [&
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, & ! |
@ -1131,12 +1135,12 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4 &
],shape(FCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for fcc
],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(BCC_NTWIN,BCC_NSLIP), parameter :: &
BCC_INTERACTIONSLIPTWIN = reshape( [&
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, & ! |
@ -1187,14 +1191,14 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
4,4,4,4,4,4,4,4,4,4,4,4, &
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(BCC_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for bcc
],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(HEX_NTWIN,HEX_NSLIP), parameter :: &
HEX_INTERACTIONSLIPTWIN = reshape( [&
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
@ -1230,21 +1234,21 @@ function lattice_interaction_SlipByTwin(Nslip,Ntwin,interactionValues,lattice) r
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(HEX_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hex
],shape(HP_INTERACTIONSLIPTWIN)) !< Slip-twin interaction types for hP
select case(lattice)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPTWIN
NslipMax = FCC_NSLIPSYSTEM
NtwinMax = FCC_NTWINSYSTEM
interactionTypes = CF_INTERACTIONSLIPTWIN
NslipMax = CF_NSLIPSYSTEM
NtwinMax = CF_NTWINSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONSLIPTWIN
NslipMax = BCC_NSLIPSYSTEM
NtwinMax = BCC_NTWINSYSTEM
interactionTypes = CI_INTERACTIONSLIPTWIN
NslipMax = CI_NSLIPSYSTEM
NtwinMax = CI_NTWINSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONSLIPTWIN
NslipMax = HEX_NSLIPSYSTEM
NtwinMax = HEX_NTWINSYSTEM
interactionTypes = HP_INTERACTIONSLIPTWIN
NslipMax = HP_NSLIPSYSTEM
NtwinMax = HP_NTWINSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipByTwin: '//trim(lattice))
end select
@ -1270,8 +1274,8 @@ function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice)
NtransMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NTRANS,FCC_NSLIP), parameter :: &
FCC_INTERACTIONSLIPTRANS = reshape( [&
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, & ! |
@ -1291,13 +1295,13 @@ function lattice_interaction_SlipByTrans(Nslip,Ntrans,interactionValues,lattice)
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4, &
4,4,4,4,4,4,4,4,4,4,4,4 &
],shape(FCC_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for fcc
],shape(CF_INTERACTIONSLIPTRANS)) !< Slip-trans interaction types for cF
select case(lattice)
case('cF')
interactionTypes = FCC_INTERACTIONSLIPTRANS
NslipMax = FCC_NSLIPSYSTEM
NtransMax = FCC_NTRANSSYSTEM
interactionTypes = CF_INTERACTIONSLIPTRANS
NslipMax = CF_NSLIPSYSTEM
NtransMax = CF_NTRANSSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_SlipByTrans: '//trim(lattice))
end select
@ -1323,14 +1327,14 @@ function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) r
NslipMax
integer, dimension(:,:), allocatable :: interactionTypes
integer, dimension(FCC_NSLIP,FCC_NTWIN), parameter :: &
FCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for fcc
integer, dimension(CF_NSLIP,CF_NTWIN), parameter :: &
CF_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for cF
integer, dimension(BCC_NSLIP,BCC_NTWIN), parameter :: &
BCC_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for bcc
integer, dimension(CI_NSLIP,CI_NTWIN), parameter :: &
CI_INTERACTIONTWINSLIP = 1 !< Twin-slip interaction types for cI
integer, dimension(HEX_NSLIP,HEX_NTWIN), parameter :: &
HEX_INTERACTIONTWINSLIP = reshape( [&
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, & ! |
@ -1359,21 +1363,21 @@ function lattice_interaction_TwinBySlip(Ntwin,Nslip,interactionValues,lattice) r
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(HEX_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hex
],shape(HP_INTERACTIONTWINSLIP)) !< Twin-slip interaction types for hP
select case(lattice)
case('cF')
interactionTypes = FCC_INTERACTIONTWINSLIP
NtwinMax = FCC_NTWINSYSTEM
NslipMax = FCC_NSLIPSYSTEM
interactionTypes = CF_INTERACTIONTWINSLIP
NtwinMax = CF_NTWINSYSTEM
NslipMax = CF_NSLIPSYSTEM
case('cI')
interactionTypes = BCC_INTERACTIONTWINSLIP
NtwinMax = BCC_NTWINSYSTEM
NslipMax = BCC_NSLIPSYSTEM
interactionTypes = CI_INTERACTIONTWINSLIP
NtwinMax = CI_NTWINSYSTEM
NslipMax = CI_NSLIPSYSTEM
case('hP')
interactionTypes = HEX_INTERACTIONTWINSLIP
NtwinMax = HEX_NTWINSYSTEM
NslipMax = HEX_NSLIPSYSTEM
interactionTypes = HP_INTERACTIONTWINSLIP
NtwinMax = HP_NTWINSYSTEM
NslipMax = HP_NSLIPSYSTEM
case default
call IO_error(137,ext_msg='lattice_interaction_TwinBySlip: '//trim(lattice))
end select
@ -1401,17 +1405,17 @@ function lattice_SchmidMatrix_slip(Nslip,lattice,cOverA) result(SchmidMatrix)
select case(lattice)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_slip: '//trim(lattice))
@ -1451,14 +1455,14 @@ function lattice_SchmidMatrix_twin(Ntwin,lattice,cOverA) result(SchmidMatrix)
select case(lattice)
case('cF')
NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
NtwinMax = CF_NTWINSYSTEM
twinSystems = CF_SYSTEMTWIN
case('cI')
NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
NtwinMax = CI_NTWINSYSTEM
twinSystems = CI_SYSTEMTWIN
case('hP')
NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
NtwinMax = HP_NTWINSYSTEM
twinSystems = HP_SYSTEMTWIN
case default
allocate(NtwinMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_twin: '//trim(lattice))
@ -1484,11 +1488,11 @@ end function lattice_SchmidMatrix_twin
!> @brief Schmid matrix for transformation
!> details only active twin systems are considered
!--------------------------------------------------------------------------------------------------
function lattice_SchmidMatrix_trans(Ntrans,lattice_target,cOverA,a_fcc,a_bcc) result(SchmidMatrix)
function lattice_SchmidMatrix_trans(Ntrans,lattice_target,cOverA,a_cF,a_cI) result(SchmidMatrix)
integer, dimension(:), intent(in) :: Ntrans !< number of active twin systems per family
character(len=2), intent(in) :: lattice_target !< Bravais lattice (Pearson symbol)
real(pReal), optional, intent(in) :: cOverA, a_bcc, a_fcc
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
@ -1498,10 +1502,10 @@ function lattice_SchmidMatrix_trans(Ntrans,lattice_target,cOverA,a_fcc,a_bcc) re
if (cOverA < 1.0_pReal .or. cOverA > 2.0_pReal) &
call IO_error(131,ext_msg='lattice_SchmidMatrix_trans: '//trim(lattice_target))
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,cOverA=cOverA)
else if (lattice_target == 'cI' .and. present(a_fcc) .and. present(a_bcc)) then
if (a_bcc <= 0.0_pReal .or. a_fcc <= 0.0_pReal) &
else if (lattice_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='lattice_SchmidMatrix_trans: '//trim(lattice_target))
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,a_fcc=a_fcc,a_bcc=a_bcc)
call buildTransformationSystem(devNull,SchmidMatrix,Ntrans,a_cF=a_cF,a_cI=a_cI)
else
call IO_error(131,ext_msg='lattice_SchmidMatrix_trans: '//trim(lattice_target))
end if
@ -1527,11 +1531,11 @@ function lattice_SchmidMatrix_cleavage(Ncleavage,lattice,cOverA) result(SchmidMa
select case(lattice)
case('cF')
NcleavageMax = FCC_NCLEAVAGESYSTEM
cleavageSystems = FCC_SYSTEMCLEAVAGE
NcleavageMax = CF_NCLEAVAGESYSTEM
cleavageSystems = CF_SYSTEMCLEAVAGE
case('cI')
NcleavageMax = BCC_NCLEAVAGESYSTEM
cleavageSystems = BCC_SYSTEMCLEAVAGE
NcleavageMax = CI_NCLEAVAGESYSTEM
cleavageSystems = CI_SYSTEMCLEAVAGE
case default
allocate(NcleavageMax(0))
call IO_error(137,ext_msg='lattice_SchmidMatrix_cleavage: '//trim(lattice))
@ -1623,17 +1627,17 @@ function lattice_labels_slip(Nslip,lattice) result(labels)
select case(lattice)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
call IO_error(137,ext_msg='lattice_labels_slip: '//trim(lattice))
end select
@ -1737,14 +1741,14 @@ function lattice_labels_twin(Ntwin,lattice) result(labels)
select case(lattice)
case('cF')
NtwinMax = FCC_NTWINSYSTEM
twinSystems = FCC_SYSTEMTWIN
NtwinMax = CF_NTWINSYSTEM
twinSystems = CF_SYSTEMTWIN
case('cI')
NtwinMax = BCC_NTWINSYSTEM
twinSystems = BCC_SYSTEMTWIN
NtwinMax = CI_NTWINSYSTEM
twinSystems = CI_SYSTEMTWIN
case('hP')
NtwinMax = HEX_NTWINSYSTEM
twinSystems = HEX_SYSTEMTWIN
NtwinMax = HP_NTWINSYSTEM
twinSystems = HP_SYSTEMTWIN
case default
call IO_error(137,ext_msg='lattice_labels_twin: '//trim(lattice))
end select
@ -1823,17 +1827,17 @@ function coordinateSystem_slip(Nslip,lattice,cOverA) result(coordinateSystem)
select case(lattice)
case('cF')
NslipMax = FCC_NSLIPSYSTEM
slipSystems = FCC_SYSTEMSLIP
NslipMax = CF_NSLIPSYSTEM
slipSystems = CF_SYSTEMSLIP
case('cI')
NslipMax = BCC_NSLIPSYSTEM
slipSystems = BCC_SYSTEMSLIP
NslipMax = CI_NSLIPSYSTEM
slipSystems = CI_SYSTEMSLIP
case('hP')
NslipMax = HEX_NSLIPSYSTEM
slipSystems = HEX_SYSTEMSLIP
NslipMax = HP_NSLIPSYSTEM
slipSystems = HP_SYSTEMSLIP
case('tI')
NslipMax = BCT_NSLIPSYSTEM
slipSystems = BCT_SYSTEMSLIP
NslipMax = TI_NSLIPSYSTEM
slipSystems = TI_SYSTEMSLIP
case default
allocate(NslipMax(0))
call IO_error(137,ext_msg='coordinateSystem_slip: '//trim(lattice))
@ -1962,24 +1966,24 @@ end function buildCoordinateSystem
!--------------------------------------------------------------------------------------------------
!> @brief Helper function to define transformation systems
! Needed to calculate Schmid matrix and rotated stiffness matrices.
! @details: set c/a = 0.0 for fcc -> bcc transformation
! set a_Xcc = 0.0 for fcc -> hex transformation
! @details: use c/a for cF -> cI transformation
! use a_cX for cF -> hP transformation
!--------------------------------------------------------------------------------------------------
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_cF,a_cI)
integer, dimension(:), intent(in) :: &
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 hex lattice
a_bcc, & !< lattice parameter a for bcc target lattice
a_fcc !< lattice parameter a for fcc parent lattice
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 fcc to Bain coordinate system
B !< Rotation of cF to Bain coordinate system
real(pReal), dimension(3,3) :: &
U, & !< Bain deformation
ss, sd
@ -1987,8 +1991,8 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
x, y, z
integer :: &
i
real(pReal), dimension(3+3,FCC_NTRANS), parameter :: &
FCCTOHEX_SYSTEMTRANS = reshape(real( [&
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, &
@ -2001,10 +2005,10 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
2, 1,-1, -1, 1,-1, &
-1,-2,-1, -1, 1,-1, &
-1, 1, 2, -1, 1,-1 &
],pReal),shape(FCCTOHEX_SYSTEMTRANS))
],pReal),shape(CFTOHP_SYSTEMTRANS))
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
FCCTOBCC_SYSTEMTRANS = reshape([&
real(pReal), dimension(4,cF_Ntrans), parameter :: &
CFTOCI_SYSTEMTRANS = reshape([&
0.0, 1.0, 0.0, 10.26, & ! Pitsch OR (Ma & Hartmaier 2014, Table 3)
0.0,-1.0, 0.0, 10.26, &
0.0, 0.0, 1.0, 10.26, &
@ -2017,10 +2021,10 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
-1.0, 0.0, 0.0, 10.26, &
0.0, 1.0, 0.0, 10.26, &
0.0,-1.0, 0.0, 10.26 &
],shape(FCCTOBCC_SYSTEMTRANS))
],shape(CFTOCI_SYSTEMTRANS))
integer, dimension(9,fcc_Ntrans), parameter :: &
FCCTOBCC_BAINVARIANT = reshape( [&
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, &
@ -2033,11 +2037,11 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0, &
0, 0, 1, 1, 0, 0, 0, 1, 0 &
],shape(FCCTOBCC_BAINVARIANT))
],shape(CFTOCI_BAINVARIANT))
real(pReal), dimension(4,fcc_Ntrans), parameter :: &
FCCTOBCC_BAINROT = reshape([&
1.0, 0.0, 0.0, 45.0, & ! Rotate fcc austensite to bain variant
real(pReal), dimension(4,cF_Ntrans), parameter :: &
CFTOCI_BAINROT = 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, &
@ -2049,19 +2053,17 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0, &
0.0, 0.0, 1.0, 45.0 &
],shape(FCCTOBCC_BAINROT))
],shape(CFTOCI_BAINROT))
if (present(a_bcc) .and. present(a_fcc)) then
if (present(a_cI) .and. present(a_cF)) then
do i = 1,sum(Ntrans)
call R%fromAxisAngle(FCCTOBCC_SYSTEMTRANS(:,i),degrees=.true.,P=1)
call B%fromAxisAngle(FCCTOBCC_BAINROT(:,i), degrees=.true.,P=1)
x = real(FCCTOBCC_BAINVARIANT(1:3,i),pReal)
y = real(FCCTOBCC_BAINVARIANT(4:6,i),pReal)
z = real(FCCTOBCC_BAINVARIANT(7:9,i),pReal)
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_bcc/a_fcc)*math_outer(x,x) &
+ (a_bcc/a_fcc)*math_outer(y,y) * sqrt(2.0_pReal) &
+ (a_bcc/a_fcc)*math_outer(z,z) * sqrt(2.0_pReal)
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
enddo
@ -2072,8 +2074,8 @@ subroutine buildTransformationSystem(Q,S,Ntrans,cOverA,a_fcc,a_bcc)
sd(3,3) = cOverA/sqrt(8.0_pReal/3.0_pReal)
do i = 1,sum(Ntrans)
x = FCCTOHEX_SYSTEMTRANS(1:3,i)/norm2(FCCTOHEX_SYSTEMTRANS(1:3,i))
z = FCCTOHEX_SYSTEMTRANS(4:6,i)/norm2(FCCTOHEX_SYSTEMTRANS(4:6,i))
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

2
src/phase_mechanical_plastic_dislotwin.f90
View File

@ -200,7 +200,7 @@ module function plastic_dislotwin_init() result(myPlasticity)
prm%n0_sl = lattice_slip_normal(N_sl,phase_lattice(ph),phase_cOverA(ph))
prm%fccTwinTransNucleation = phase_lattice(ph) == 'cF' .and. (N_sl(1) == 12)
if (prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_FCC_TWINNUCLEATIONSLIPPAIR
if (prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_CF_TWINNUCLEATIONSLIPPAIR
rho_mob_0 = pl%get_as1dFloat('rho_mob_0', requiredSize=size(N_sl))
rho_dip_0 = pl%get_as1dFloat('rho_dip_0', requiredSize=size(N_sl))