DAMASK_EICMD/src/constitutive_plastic_dislot...

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!--------------------------------------------------------------------------------------------------
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH
!> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine incoprorating dislocation and twinning physics
!> @details to be done
!--------------------------------------------------------------------------------------------------
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submodule(constitutive) plastic_dislotwin
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real(pReal), parameter :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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type :: tParameters
real(pReal) :: &
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mu = 1.0_pReal, & !< equivalent shear modulus
nu = 1.0_pReal, & !< equivalent shear Poisson's ratio
D0 = 1.0_pReal, & !< prefactor for self-diffusion coefficient
Qsd = 1.0_pReal, & !< activation energy for dislocation climb
omega = 1.0_pReal, & !< frequency factor for dislocation climb
D = 1.0_pReal, & !< grain size
p_sb = 1.0_pReal, & !< p-exponent in shear band velocity
q_sb = 1.0_pReal, & !< q-exponent in shear band velocity
CEdgeDipMinDistance = 1.0_pReal, & !<
i_tw = 1.0_pReal, & !<
tau_0 = 1.0_pReal, & !< strength due to elements in solid solution
L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors
L_tr = 1.0_pReal, & !< Length of trans nuclei in Burgers vectors
xc_twin = 1.0_pReal, & !< critical distance for formation of twin nucleus
xc_trans = 1.0_pReal, & !< critical distance for formation of trans nucleus
V_cs = 1.0_pReal, & !< cross slip volume
sbResistance = 1.0_pReal, & !< value for shearband resistance
sbVelocity = 1.0_pReal, & !< value for shearband velocity_0
E_sb = 1.0_pReal, & !< activation energy for shear bands
SFE_0K = 1.0_pReal, & !< stacking fault energy at zero K
dSFE_dT = 1.0_pReal, & !< temperature dependence of stacking fault energy
gamma_fcc_hex = 1.0_pReal, & !< Free energy difference between austensite and martensite
i_tr = 1.0_pReal, & !<
h = 1.0_pReal !< Stack height of hex nucleus
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real(pReal), allocatable, dimension(:) :: &
b_sl, & !< absolute length of burgers vector [m] for each slip system
b_tw, & !< absolute length of burgers vector [m] for each twin system
b_tr, & !< absolute length of burgers vector [m] for each transformation system
Delta_F,& !< activation energy for glide [J] for each slip system
v0, & !< dislocation velocity prefactor [m/s] for each slip system
dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system
dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system
t_tw, & !< twin thickness [m] for each twin system
CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
t_tr, & !< martensite lamellar thickness [m] for each trans system and instance
p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
r, & !< r-exponent in twin nucleation rate
s, & !< s-exponent in trans nucleation rate
gamma_char, & !< characteristic shear for twins
B !< drag coefficient
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real(pReal), allocatable, dimension(:,:) :: &
h_sl_sl, & !<
h_sl_tw, & !<
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h_tw_tw, & !<
h_sl_tr, & !<
h_tr_tr, & !<
n0_sl, & !< slip system normal
forestProjection, &
C66
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real(pReal), allocatable, dimension(:,:,:) :: &
P_sl, &
P_tw, &
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P_tr, &
C66_tw, &
C66_tr
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integer :: &
sum_N_sl, & !< total number of active slip system
sum_N_tw, & !< total number of active twin system
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sum_N_tr !< total number of active transformation system
integer, allocatable, dimension(:,:) :: &
fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
character(len=pStringLen), allocatable, dimension(:) :: &
output
logical :: &
ExtendedDislocations, & !< consider split into partials for climb calculation
fccTwinTransNucleation, & !< twinning and transformation models are for fcc
dipoleFormation !< flag indicating consideration of dipole formation
end type !< container type for internal constitutive parameters
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type :: tDislotwinState
real(pReal), dimension(:,:), pointer :: &
rho_mob, &
rho_dip, &
gamma_sl, &
f_tw, &
f_tr
end type tDislotwinState
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type :: tDislotwinMicrostructure
real(pReal), dimension(:,:), allocatable :: &
Lambda_sl, & !< mean free path between 2 obstacles seen by a moving dislocation
Lambda_tw, & !< mean free path between 2 obstacles seen by a growing twin
Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite
tau_pass, &
tau_hat_tw, &
tau_hat_tr, &
V_tw, & !< volume of a new twin
V_tr, & !< volume of a new martensite disc
tau_r_tw, & !< stress to bring partials close together (twin)
tau_r_tr !< stress to bring partials close together (trans)
end type tDislotwinMicrostructure
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!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:) :: param
type(tDislotwinState), allocatable, dimension(:) :: &
dotState, &
state
type(tDislotwinMicrostructure), allocatable, dimension(:) :: dependentState
contains
!--------------------------------------------------------------------------------------------------
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!> @brief Perform module initialization.
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_init
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integer :: &
Ninstance, &
p, i, &
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NipcMyPhase, &
sizeState, sizeDotState, &
startIndex, endIndex
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integer, dimension(:), allocatable :: &
N_sl, N_tw, N_tr
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real(pReal), allocatable, dimension(:) :: &
rho_mob_0, & !< initial unipolar dislocation density per slip system
rho_dip_0 !< initial dipole dislocation density per slip system
character(len=pStringLen) :: &
extmsg = ''
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_LABEL//' init -+>>>'; flush(6)
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write(6,'(/,a)') ' Ma and Roters, Acta Materialia 52(12):36033612, 2004'
write(6,'(a)') ' https://doi.org/10.1016/j.actamat.2004.04.012'
write(6,'(/,a)') ' Roters et al., Computational Materials Science 39:9195, 2007'
write(6,'(a)') ' https://doi.org/10.1016/j.commatsci.2006.04.014'
write(6,'(/,a)') ' Wong et al., Acta Materialia 118:140151, 2016'
write(6,'(a,/)') ' https://doi.org/10.1016/j.actamat.2016.07.032'
Ninstance = count(phase_plasticity == PLASTICITY_DISLOTWIN_ID)
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
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allocate(param(Ninstance))
allocate(state(Ninstance))
allocate(dotState(Ninstance))
allocate(dependentState(Ninstance))
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do p = 1, size(phase_plasticity)
if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
associate(prm => param(phase_plasticityInstance(p)), &
dot => dotState(phase_plasticityInstance(p)), &
stt => state(phase_plasticityInstance(p)), &
dst => dependentState(phase_plasticityInstance(p)), &
config => config_phase(p))
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prm%output = config%getStrings('(output)', defaultVal=emptyStringArray)
! This data is read in already in lattice
prm%mu = lattice_mu(p)
prm%nu = lattice_nu(p)
prm%C66 = lattice_C66(1:6,1:6,p)
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!--------------------------------------------------------------------------------------------------
! slip related parameters
N_sl = config%getInts('nslip',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(abs(N_sl))
slipActive: if (prm%sum_N_sl > 0) then
prm%P_sl = lattice_SchmidMatrix_slip(N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,config%getFloats('interaction_slipslip'), &
config%getString('lattice_structure'))
prm%forestProjection = lattice_forestProjection_edge(N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%forestProjection = transpose(prm%forestProjection)
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prm%n0_sl = lattice_slip_normal(N_sl,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == lattice_FCC_ID) &
.and. (N_sl(1) == 12)
if(prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_FCC_TWINNUCLEATIONSLIPPAIR
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rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(N_sl))
rho_dip_0 = config%getFloats('rhoedgedip0',requiredSize=size(N_sl))
prm%v0 = config%getFloats('v0', requiredSize=size(N_sl))
prm%b_sl = config%getFloats('slipburgers',requiredSize=size(N_sl))
prm%Delta_F = config%getFloats('qedge', requiredSize=size(N_sl))
prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(N_sl))
prm%p = config%getFloats('p_slip', requiredSize=size(N_sl))
prm%q = config%getFloats('q_slip', requiredSize=size(N_sl))
prm%B = config%getFloats('b', requiredSize=size(N_sl), &
defaultVal=[(0.0_pReal, i=1,size(N_sl))])
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prm%tau_0 = config%getFloat('solidsolutionstrength')
prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
prm%D0 = config%getFloat('d0')
prm%Qsd = config%getFloat('qsd')
prm%ExtendedDislocations = config%keyExists('/extend_dislocations/')
if (prm%ExtendedDislocations) then
prm%SFE_0K = config%getFloat('sfe_0k')
prm%dSFE_dT = config%getFloat('dsfe_dt')
endif
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prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
! multiplication factor according to crystal structure (nearest neighbors bcc vs fcc/hex)
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! details: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
prm%omega = config%getFloat('omega', defaultVal = 1000.0_pReal) &
* merge(12.0_pReal,8.0_pReal,any(lattice_structure(p) == [lattice_FCC_ID,lattice_HEX_ID]))
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! expand: family => system
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rho_mob_0 = math_expand(rho_mob_0, N_sl)
rho_dip_0 = math_expand(rho_dip_0, N_sl)
prm%v0 = math_expand(prm%v0, N_sl)
prm%b_sl = math_expand(prm%b_sl, N_sl)
prm%Delta_F = math_expand(prm%Delta_F, N_sl)
prm%CLambdaSlip = math_expand(prm%CLambdaSlip, N_sl)
prm%p = math_expand(prm%p, N_sl)
prm%q = math_expand(prm%q, N_sl)
prm%B = math_expand(prm%B, N_sl)
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! sanity checks
if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' D0'
if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' Qsd'
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if (any(rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0'
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
if (any(prm%Delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' Delta_F'
if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//' CLambdaSlip'
if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B'
if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//' p'
if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//' q'
else slipActive
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rho_mob_0 = emptyRealArray; rho_dip_0 = emptyRealArray
allocate(prm%b_sl,prm%Delta_F,prm%v0,prm%CLambdaSlip,prm%p,prm%q,prm%B,source=emptyRealArray)
allocate(prm%forestProjection(0,0),prm%h_sl_sl(0,0))
endif slipActive
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!--------------------------------------------------------------------------------------------------
! twin related parameters
N_tw = config%getInts('ntwin', defaultVal=emptyIntArray)
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prm%sum_N_tw = sum(abs(N_tw))
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twinActive: if (prm%sum_N_tw > 0) then
prm%P_tw = lattice_SchmidMatrix_twin(N_tw,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%h_tw_tw = lattice_interaction_TwinByTwin(N_tw,&
config%getFloats('interaction_twintwin'), &
config%getString('lattice_structure'))
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prm%b_tw = config%getFloats('twinburgers', requiredSize=size(N_tw))
prm%t_tw = config%getFloats('twinsize', requiredSize=size(N_tw))
prm%r = config%getFloats('r_twin', requiredSize=size(N_tw))
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prm%xc_twin = config%getFloat('xc_twin')
prm%L_tw = config%getFloat('l0_twin')
prm%i_tw = config%getFloat('cmfptwin')
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prm%gamma_char= lattice_characteristicShear_Twin(N_tw,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%C66_tw = lattice_C66_twin(N_tw,prm%C66,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
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if (.not. prm%fccTwinTransNucleation) then
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prm%dot_N_0_tw = config%getFloats('ndot0_twin')
prm%dot_N_0_tw = math_expand(prm%dot_N_0_tw,N_tw)
endif
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! expand: family => system
prm%b_tw = math_expand(prm%b_tw,N_tw)
prm%t_tw = math_expand(prm%t_tw,N_tw)
prm%r = math_expand(prm%r,N_tw)
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! sanity checks
if ( prm%xc_twin < 0.0_pReal) extmsg = trim(extmsg)//' xc_twin'
if ( prm%L_tw < 0.0_pReal) extmsg = trim(extmsg)//' L_tw'
if ( prm%i_tw < 0.0_pReal) extmsg = trim(extmsg)//' i_tw'
if (any(prm%b_tw < 0.0_pReal)) extmsg = trim(extmsg)//' b_tw'
if (any(prm%t_tw < 0.0_pReal)) extmsg = trim(extmsg)//' t_tw'
if (any(prm%r < 0.0_pReal)) extmsg = trim(extmsg)//' r'
if (.not. prm%fccTwinTransNucleation) then
if (any(prm%dot_N_0_tw < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tw'
endif
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else twinActive
allocate(prm%gamma_char,prm%b_tw,prm%dot_N_0_tw,prm%t_tw,prm%r,source=emptyRealArray)
allocate(prm%h_tw_tw(0,0))
endif twinActive
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!--------------------------------------------------------------------------------------------------
! transformation related parameters
N_tr = config%getInts('ntrans', defaultVal=emptyIntArray)
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prm%sum_N_tr = sum(abs(N_tr))
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transActive: if (prm%sum_N_tr > 0) then
prm%b_tr = config%getFloats('transburgers')
prm%b_tr = math_expand(prm%b_tr,N_tr)
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prm%h = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%i_tr = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%gamma_fcc_hex = config%getFloat('deltag')
prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%L_tr = config%getFloat('l0_trans')
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prm%h_tr_tr = lattice_interaction_TransByTrans(N_tr,config%getFloats('interaction_transtrans'), &
config%getString('lattice_structure'))
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prm%C66_tr = lattice_C66_trans(N_tr,prm%C66,config%getString('trans_lattice_structure'), &
0.0_pReal, &
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
config%getFloat('a_fcc', defaultVal=0.0_pReal))
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prm%P_tr = lattice_SchmidMatrix_trans(N_tr,config%getString('trans_lattice_structure'), &
0.0_pReal, &
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
config%getFloat('a_fcc', defaultVal=0.0_pReal))
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if (lattice_structure(p) /= lattice_FCC_ID) then
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prm%dot_N_0_tr = config%getFloats('ndot0_trans')
prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,N_tr)
endif
prm%t_tr = config%getFloats('lamellarsize')
prm%t_tr = math_expand(prm%t_tr,N_tr)
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
prm%s = math_expand(prm%s,N_tr)
! sanity checks
if ( prm%xc_trans < 0.0_pReal) extmsg = trim(extmsg)//' xc_trans'
if ( prm%L_tr < 0.0_pReal) extmsg = trim(extmsg)//' L_tr'
if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr'
if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr'
if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' s'
if (lattice_structure(p) /= lattice_FCC_ID) then
if (any(prm%dot_N_0_tr < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tr'
endif
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else transActive
allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyRealArray)
allocate(prm%h_tr_tr(0,0))
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endif transActive
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!--------------------------------------------------------------------------------------------------
! shearband related parameters
prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
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if (prm%sbVelocity > 0.0_pReal) then
prm%sbResistance = config%getFloat('shearbandresistance')
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prm%E_sb = config%getFloat('qedgepersbsystem')
prm%p_sb = config%getFloat('p_shearband')
prm%q_sb = config%getFloat('q_shearband')
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! sanity checks
if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' shearbandresistance'
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if (prm%E_sb < 0.0_pReal) extmsg = trim(extmsg)//' qedgepersbsystem'
if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_shearband'
if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_shearband'
endif
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!--------------------------------------------------------------------------------------------------
! parameters required for several mechanisms and their interactions
if(prm%sum_N_sl + prm%sum_N_tw + prm%sum_N_tw > 0) &
prm%D = config%getFloat('grainsize')
twinOrSlipActive: if (prm%sum_N_tw + prm%sum_N_tr > 0) then
prm%SFE_0K = config%getFloat('sfe_0k')
prm%dSFE_dT = config%getFloat('dsfe_dt')
prm%V_cs = config%getFloat('vcrossslip')
endif twinOrSlipActive
slipAndTwinActive: if (prm%sum_N_sl * prm%sum_N_tw > 0) then
prm%h_sl_tw = lattice_interaction_SlipByTwin(N_sl,N_tw,&
config%getFloats('interaction_sliptwin'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. size(N_tw) /= 1) extmsg = trim(extmsg)//' interaction_sliptwin'
endif slipAndTwinActive
slipAndTransActive: if (prm%sum_N_sl * prm%sum_N_tr > 0) then
prm%h_sl_tr = lattice_interaction_SlipByTrans(N_sl,N_tr,&
config%getFloats('interaction_sliptrans'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. size(N_tr) /= 1) extmsg = trim(extmsg)//' interaction_sliptrans'
endif slipAndTransActive
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!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl &
+ size(['f_tw']) * prm%sum_N_tw &
+ size(['f_tr']) * prm%sum_N_tr
sizeState = sizeDotState
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call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0)
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!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and atol
startIndex = 1
endIndex = prm%sum_N_sl
stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:)
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stt%rho_mob= spread(rho_mob_0,2,NipcMyPhase)
dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('atol_rho',defaultVal=1.0_pReal)
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_rho'
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startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:)
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stt%rho_dip= spread(rho_dip_0,2,NipcMyPhase)
dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('atol_rho',defaultVal=1.0_pReal)
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startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_sl
stt%gamma_sl=>plasticState(p)%state(startIndex:endIndex,:)
dot%gamma_sl=>plasticState(p)%dotState(startIndex:endIndex,:)
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plasticState(p)%atol(startIndex:endIndex) = 1.0e-2_pReal
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
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startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_tw
stt%f_tw=>plasticState(p)%state(startIndex:endIndex,:)
dot%f_tw=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('f_twin',defaultVal=1.0e-7_pReal)
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_twin'
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startIndex = endIndex + 1
endIndex = endIndex + prm%sum_N_tr
stt%f_tr=>plasticState(p)%state(startIndex:endIndex,:)
dot%f_tr=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%atol(startIndex:endIndex) = config%getFloat('f_trans',defaultVal=1.0e-6_pReal)
if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_trans'
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allocate(dst%Lambda_sl (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_pass (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal)
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allocate(dst%Lambda_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_hat_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_r_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
allocate(dst%V_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal)
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allocate(dst%Lambda_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_hat_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_r_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
allocate(dst%V_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
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plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
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end associate
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!--------------------------------------------------------------------------------------------------
! exit if any parameter is out of range
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOTWIN_LABEL//')')
enddo
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end subroutine plastic_dislotwin_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Return the homogenized elasticity matrix.
!--------------------------------------------------------------------------------------------------
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module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
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real(pReal), dimension(6,6) :: &
homogenizedC
integer, intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
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integer :: i, &
of
real(pReal) :: f_unrotated
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of = material_phasememberAt(ipc,ip,el)
associate(prm => param(phase_plasticityInstance(material_phaseAt(ipc,el))),&
stt => state(phase_plasticityInstance(material_phaseAT(ipc,el))))
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f_unrotated = 1.0_pReal &
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
- sum(stt%f_tr(1:prm%sum_N_tr,of))
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homogenizedC = f_unrotated * prm%C66
do i=1,prm%sum_N_tw
homogenizedC = homogenizedC &
+ stt%f_tw(i,of)*prm%C66_tw(1:6,1:6,i)
enddo
do i=1,prm%sum_N_tr
homogenizedC = homogenizedC &
+ stt%f_tr(i,of)*prm%C66_tr(1:6,1:6,i)
enddo
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end associate
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end function plastic_dislotwin_homogenizedC
!--------------------------------------------------------------------------------------------------
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!> @brief Calculate plastic velocity gradient and its tangent.
!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
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real(pReal), dimension(3,3), intent(out) :: Lp
real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
real(pReal), dimension(3,3), intent(in) :: Mp
integer, intent(in) :: instance,of
real(pReal), intent(in) :: T
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integer :: i,k,l,m,n
real(pReal) :: &
f_unrotated,StressRatio_p,&
BoltzmannRatio, &
ddot_gamma_dtau, &
tau
real(pReal), dimension(param(instance)%sum_N_sl) :: &
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dot_gamma_sl,ddot_gamma_dtau_slip
real(pReal), dimension(param(instance)%sum_N_tw) :: &
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dot_gamma_twin,ddot_gamma_dtau_twin
real(pReal), dimension(param(instance)%sum_N_tr) :: &
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dot_gamma_tr,ddot_gamma_dtau_trans
real(pReal):: dot_gamma_sb
real(pReal), dimension(3,3) :: eigVectors, P_sb
real(pReal), dimension(3) :: eigValues
real(pReal), dimension(3,6), parameter :: &
sb_sComposition = &
reshape(real([&
1, 0, 1, &
1, 0,-1, &
1, 1, 0, &
1,-1, 0, &
0, 1, 1, &
0, 1,-1 &
],pReal),[ 3,6]), &
sb_mComposition = &
reshape(real([&
1, 0,-1, &
1, 0,+1, &
1,-1, 0, &
1, 1, 0, &
0, 1,-1, &
0, 1, 1 &
],pReal),[ 3,6])
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associate(prm => param(instance), stt => state(instance))
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f_unrotated = 1.0_pReal &
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
- sum(stt%f_tr(1:prm%sum_N_tr,of))
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Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
call kinetics_slip(Mp,T,instance,of,dot_gamma_sl,ddot_gamma_dtau_slip)
slipContribution: do i = 1, prm%sum_N_sl
Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau_slip(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i)
enddo slipContribution
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!ToDo: Why do this before shear banding?
Lp = Lp * f_unrotated
dLp_dMp = dLp_dMp * f_unrotated
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shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
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BoltzmannRatio = prm%E_sb/(kB*T)
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call math_eigh33(Mp,eigValues,eigVectors) ! is Mp symmetric by design?
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do i = 1,6
P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),&
matmul(eigVectors,sb_mComposition(1:3,i)))
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tau = math_tensordot(Mp,P_sb)
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significantShearBandStress: if (abs(tau) > tol_math_check) then
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%p_sb
dot_gamma_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1-StressRatio_p)**prm%q_sb), tau)
ddot_gamma_dtau = abs(dot_gamma_sb)*BoltzmannRatio* prm%p_sb*prm%q_sb/ prm%sbResistance &
* (abs(tau)/prm%sbResistance)**(prm%p_sb-1.0_pReal) &
* (1.0_pReal-StressRatio_p)**(prm%q_sb-1.0_pReal)
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Lp = Lp + dot_gamma_sb * P_sb
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau * P_sb(k,l) * P_sb(m,n)
endif significantShearBandStress
enddo
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endif shearBandingContribution
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call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin,ddot_gamma_dtau_twin)
twinContibution: do i = 1, prm%sum_N_tw
Lp = Lp + dot_gamma_twin(i)*prm%P_tw(1:3,1:3,i) * f_unrotated
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau_twin(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i) * f_unrotated
enddo twinContibution
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call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr,ddot_gamma_dtau_trans)
transContibution: do i = 1, prm%sum_N_tr
Lp = Lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i) * f_unrotated
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ ddot_gamma_dtau_trans(i)* prm%P_tr(k,l,i)*prm%P_tr(m,n,i) * f_unrotated
enddo transContibution
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end associate
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end subroutine plastic_dislotwin_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
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!> @brief Calculate the rate of change of microstructure.
!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_dotState(Mp,T,instance,of)
real(pReal), dimension(3,3), intent(in):: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature at integration point
integer, intent(in) :: &
instance, &
of
integer :: i
real(pReal) :: &
f_unrotated, &
rho_dip_distance, &
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v_cl, & !< climb velocity
Gamma, & !< stacking fault energy
tau, &
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sigma_cl, & !< climb stress
b_d !< ratio of burgers vector to stacking fault width
real(pReal), dimension(param(instance)%sum_N_sl) :: &
dot_rho_dip_formation, &
dot_rho_dip_climb, &
rho_dip_distance_min, &
dot_gamma_sl
real(pReal), dimension(param(instance)%sum_N_tw) :: &
dot_gamma_twin
real(pReal), dimension(param(instance)%sum_N_tr) :: &
dot_gamma_tr
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associate(prm => param(instance), stt => state(instance), &
dot => dotState(instance), dst => dependentState(instance))
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f_unrotated = 1.0_pReal &
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
- sum(stt%f_tr(1:prm%sum_N_tr,of))
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call kinetics_slip(Mp,T,instance,of,dot_gamma_sl)
dot%gamma_sl(:,of) = abs(dot_gamma_sl)
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rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl
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slipState: do i = 1, prm%sum_N_sl
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tau = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
significantSlipStress: if (dEq0(tau)) then
dot_rho_dip_formation(i) = 0.0_pReal
dot_rho_dip_climb(i) = 0.0_pReal
else significantSlipStress
rho_dip_distance = 3.0_pReal*prm%mu*prm%b_sl(i)/(16.0_pReal*PI*abs(tau))
rho_dip_distance = math_clip(rho_dip_distance, right = dst%Lambda_sl(i,of))
rho_dip_distance = math_clip(rho_dip_distance, left = rho_dip_distance_min(i))
if (prm%dipoleFormation) then
dot_rho_dip_formation(i) = 2.0_pReal*(rho_dip_distance-rho_dip_distance_min(i))/prm%b_sl(i) &
* stt%rho_mob(i,of)*abs(dot_gamma_sl(i))
else
dot_rho_dip_formation(i) = 0.0_pReal
endif
if (dEq(rho_dip_distance,rho_dip_distance_min(i))) then
dot_rho_dip_climb(i) = 0.0_pReal
else
!@details: Refer: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981
sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i)))
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if (prm%ExtendedDislocations) then
Gamma = prm%SFE_0K + prm%dSFE_dT * T
b_d = 24.0_pReal*PI*(1.0_pReal - prm%nu)/(2.0_pReal + prm%nu)* Gamma/(prm%mu*prm%b_sl(i))
else
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b_d = 1.0_pReal
endif
v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Qsd/(kB*T)) &
* (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal)
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dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,of) &
/ (rho_dip_distance-rho_dip_distance_min(i))
endif
endif significantSlipStress
enddo slipState
dot%rho_mob(:,of) = abs(dot_gamma_sl)/(prm%b_sl*dst%Lambda_sl(:,of)) &
- dot_rho_dip_formation &
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_mob(:,of)*abs(dot_gamma_sl)
dot%rho_dip(:,of) = dot_rho_dip_formation &
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_dip(:,of)*abs(dot_gamma_sl) &
- dot_rho_dip_climb
call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin)
dot%f_tw(:,of) = f_unrotated*dot_gamma_twin/prm%gamma_char
call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr)
dot%f_tr(:,of) = f_unrotated*dot_gamma_tr
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end associate
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end subroutine plastic_dislotwin_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate derived quantities from state.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_dependentState(T,instance,of)
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integer, intent(in) :: &
instance, &
of
real(pReal), intent(in) :: &
T
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real(pReal) :: &
sumf_twin,Gamma,sumf_trans
real(pReal), dimension(param(instance)%sum_N_sl) :: &
inv_lambda_sl_sl, & !< 1/mean free distance between 2 forest dislocations seen by a moving dislocation
inv_lambda_sl_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
inv_lambda_sl_tr !< 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
real(pReal), dimension(param(instance)%sum_N_tw) :: &
inv_lambda_tw_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
f_over_t_tw
real(pReal), dimension(param(instance)%sum_N_tr) :: &
inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite
f_over_t_tr
real(pReal), dimension(:), allocatable :: &
x0
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associate(prm => param(instance),&
stt => state(instance),&
dst => dependentState(instance))
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sumf_twin = sum(stt%f_tw(1:prm%sum_N_tw,of))
sumf_trans = sum(stt%f_tr(1:prm%sum_N_tr,of))
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Gamma = prm%SFE_0K + prm%dSFE_dT * T
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!* rescaled volume fraction for topology
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f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,of)/prm%t_tw ! this is per system ...
f_over_t_tr = sumf_trans/prm%t_tr ! but this not
! ToDo ...Physically correct, but naming could be adjusted
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inv_lambda_sl_sl = sqrt(matmul(prm%forestProjection, &
stt%rho_mob(:,of)+stt%rho_dip(:,of)))/prm%CLambdaSlip
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if (prm%sum_N_tw > 0 .and. prm%sum_N_sl > 0) &
inv_lambda_sl_tw = matmul(prm%h_sl_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
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inv_lambda_tw_tw = matmul(prm%h_tw_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
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if (prm%sum_N_tr > 0 .and. prm%sum_N_sl > 0) &
inv_lambda_sl_tr = matmul(prm%h_sl_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
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inv_lambda_tr_tr = matmul(prm%h_tr_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
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if ((prm%sum_N_tw > 0) .or. (prm%sum_N_tr > 0)) then ! ToDo: better logic needed here
dst%Lambda_sl(:,of) = prm%D &
/ (1.0_pReal+prm%D*(inv_lambda_sl_sl + inv_lambda_sl_tw + inv_lambda_sl_tr))
else
dst%Lambda_sl(:,of) = prm%D &
/ (1.0_pReal+prm%D*inv_lambda_sl_sl) !!!!!! correct?
endif
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dst%Lambda_tw(:,of) = prm%i_tw*prm%D/(1.0_pReal+prm%D*inv_lambda_tw_tw)
dst%Lambda_tr(:,of) = prm%i_tr*prm%D/(1.0_pReal+prm%D*inv_lambda_tr_tr)
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!* threshold stress for dislocation motion
dst%tau_pass(:,of) = prm%mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
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!* threshold stress for growing twin/martensite
if(prm%sum_N_tw == prm%sum_N_sl) &
dst%tau_hat_tw(:,of) = Gamma/(3.0_pReal*prm%b_tw) &
+ 3.0_pReal*prm%b_tw*prm%mu/(prm%L_tw*prm%b_sl) ! slip burgers here correct?
if(prm%sum_N_tr == prm%sum_N_sl) &
dst%tau_hat_tr(:,of) = Gamma/(3.0_pReal*prm%b_tr) &
+ 3.0_pReal*prm%b_tr*prm%mu/(prm%L_tr*prm%b_sl) & ! slip burgers here correct?
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+ prm%h*prm%gamma_fcc_hex/ (3.0_pReal*prm%b_tr)
dst%V_tw(:,of) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,of)**2.0_pReal
dst%V_tr(:,of) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,of)**2.0_pReal
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x0 = prm%mu*prm%b_tw**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip and is the same for twin and trans
dst%tau_r_tw(:,of) = prm%mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
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x0 = prm%mu*prm%b_tr**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip
dst%tau_r_tr(:,of) = prm%mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
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end associate
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end subroutine plastic_dislotwin_dependentState
!--------------------------------------------------------------------------------------------------
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!> @brief Write results to HDF5 output file.
!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotwin_results(instance,group)
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integer, intent(in) :: instance
character(len=*), intent(in) :: group
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integer :: o
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
outputsLoop: do o = 1,size(prm%output)
select case(trim(prm%output(o)))
case('rho_mob')
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_mob,'rho_mob',&
'mobile dislocation density','1/m²')
case('rho_dip')
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip,'rho_dip',&
'dislocation dipole density''1/m²')
case('gamma_sl')
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma_sl,'gamma_sl',&
'plastic shear','1')
case('lambda_sl')
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
'mean free path for slip','m')
case('tau_pass')
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%tau_pass,'tau_pass',&
'passing stress for slip','Pa')
case('f_tw')
if(prm%sum_N_tw>0) call results_writeDataset(group,stt%f_tw,'f_tw',&
'twinned volume fraction','m³/m³')
case('lambda_tw')
if(prm%sum_N_tw>0) call results_writeDataset(group,dst%Lambda_tw,'Lambda_tw',&
'mean free path for twinning','m')
case('tau_hat_tw')
if(prm%sum_N_tw>0) call results_writeDataset(group,dst%tau_hat_tw,'tau_hat_tw',&
'threshold stress for twinning','Pa')
case('f_tr')
if(prm%sum_N_tr>0) call results_writeDataset(group,stt%f_tr,'f_tr',&
'martensite volume fraction','m³/m³')
end select
enddo outputsLoop
end associate
end subroutine plastic_dislotwin_results
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved
! stress, and the resolved stress.
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!> @details Derivatives and resolved stress are calculated only optionally.
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_slip(Mp,T,instance,of, &
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dot_gamma_sl,ddot_gamma_dtau_slip,tau_slip)
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
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real(pReal), dimension(param(instance)%sum_N_sl), intent(out) :: &
dot_gamma_sl
real(pReal), dimension(param(instance)%sum_N_sl), optional, intent(out) :: &
ddot_gamma_dtau_slip, &
tau_slip
real(pReal), dimension(param(instance)%sum_N_sl) :: &
ddot_gamma_dtau
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real(pReal), dimension(param(instance)%sum_N_sl) :: &
tau, &
stressRatio, &
StressRatio_p, &
BoltzmannRatio, &
v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned)
v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned)
dV_wait_inverse_dTau, &
dV_run_inverse_dTau, &
dV_dTau, &
tau_eff !< effective resolved stress
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integer :: i
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_sl
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tau(i) = math_tensordot(Mp,prm%P_sl(1:3,1:3,i))
enddo
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tau_eff = abs(tau)-dst%tau_pass(:,of)
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significantStress: where(tau_eff > tol_math_check)
stressRatio = tau_eff/prm%tau_0
StressRatio_p = stressRatio** prm%p
BoltzmannRatio = prm%Delta_F/(kB*T)
v_wait_inverse = prm%v0**(-1.0_pReal) * exp(BoltzmannRatio*(1.0_pReal-StressRatio_p)** prm%q)
v_run_inverse = prm%B/(tau_eff*prm%b_sl)
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dot_gamma_sl = sign(stt%rho_mob(:,of)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau)
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dV_wait_inverse_dTau = -1.0_pReal * v_wait_inverse * prm%p * prm%q * BoltzmannRatio &
* (stressRatio**(prm%p-1.0_pReal)) &
* (1.0_pReal-StressRatio_p)**(prm%q-1.0_pReal) &
/ prm%tau_0
dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff
dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
/ (v_wait_inverse+v_run_inverse)**2.0_pReal
ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,of)*prm%b_sl
else where significantStress
dot_gamma_sl = 0.0_pReal
ddot_gamma_dtau = 0.0_pReal
end where significantStress
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end associate
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if(present(ddot_gamma_dtau_slip)) ddot_gamma_dtau_slip = ddot_gamma_dtau
if(present(tau_slip)) tau_slip = tau
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end subroutine kinetics_slip
!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved
! stress.
!> @details Derivatives are calculated only optionally.
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end.
!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_twin(Mp,T,dot_gamma_sl,instance,of,&
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dot_gamma_twin,ddot_gamma_dtau_twin)
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
dot_gamma_sl
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real(pReal), dimension(param(instance)%sum_N_tw), intent(out) :: &
dot_gamma_twin
real(pReal), dimension(param(instance)%sum_N_tw), optional, intent(out) :: &
ddot_gamma_dtau_twin
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real, dimension(param(instance)%sum_N_tw) :: &
tau, &
Ndot0, &
stressRatio_r, &
ddot_gamma_dtau
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integer :: i,s1,s2
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_tw
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tau(i) = math_tensordot(Mp,prm%P_tw(1:3,1:3,i))
isFCC: if (prm%fccTwinTransNucleation) then
s1=prm%fcc_twinNucleationSlipPair(1,i)
s2=prm%fcc_twinNucleationSlipPair(2,i)
if (tau(i) < dst%tau_r_tw(i,of)) then ! ToDo: correct?
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
(prm%L_tw*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tw(i,of)-tau(i)))) ! P_ncs
else
Ndot0=0.0_pReal
end if
else isFCC
Ndot0=prm%dot_N_0_tw(i)
endif isFCC
enddo
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significantStress: where(tau > tol_math_check)
StressRatio_r = (dst%tau_hat_tw(:,of)/tau)**prm%r
dot_gamma_twin = prm%gamma_char * dst%V_tw(:,of) * Ndot0*exp(-StressRatio_r)
ddot_gamma_dtau = (dot_gamma_twin*prm%r/tau)*StressRatio_r
else where significantStress
dot_gamma_twin = 0.0_pReal
ddot_gamma_dtau = 0.0_pReal
end where significantStress
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end associate
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if(present(ddot_gamma_dtau_twin)) ddot_gamma_dtau_twin = ddot_gamma_dtau
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end subroutine kinetics_twin
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate shear rates on transformation systems and their derivatives with respect to
! resolved stress.
!> @details Derivatives are calculated only optionally.
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
! have the optional arguments at the end.
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics_trans(Mp,T,dot_gamma_sl,instance,of,&
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dot_gamma_tr,ddot_gamma_dtau_trans)
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
T !< temperature
integer, intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
dot_gamma_sl
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real(pReal), dimension(param(instance)%sum_N_tr), intent(out) :: &
dot_gamma_tr
real(pReal), dimension(param(instance)%sum_N_tr), optional, intent(out) :: &
ddot_gamma_dtau_trans
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real, dimension(param(instance)%sum_N_tr) :: &
tau, &
Ndot0, &
stressRatio_s, &
ddot_gamma_dtau
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integer :: i,s1,s2
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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do i = 1, prm%sum_N_tr
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tau(i) = math_tensordot(Mp,prm%P_tr(1:3,1:3,i))
isFCC: if (prm%fccTwinTransNucleation) then
s1=prm%fcc_twinNucleationSlipPair(1,i)
s2=prm%fcc_twinNucleationSlipPair(2,i)
if (tau(i) < dst%tau_r_tr(i,of)) then ! ToDo: correct?
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
(prm%L_tr*prm%b_sl(i))*&
(1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tr(i,of)-tau(i)))) ! P_ncs
else
Ndot0=0.0_pReal
end if
else isFCC
Ndot0=prm%dot_N_0_tr(i)
endif isFCC
enddo
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significantStress: where(tau > tol_math_check)
StressRatio_s = (dst%tau_hat_tr(:,of)/tau)**prm%s
dot_gamma_tr = dst%V_tr(:,of) * Ndot0*exp(-StressRatio_s)
ddot_gamma_dtau = (dot_gamma_tr*prm%s/tau)*StressRatio_s
else where significantStress
dot_gamma_tr = 0.0_pReal
ddot_gamma_dtau = 0.0_pReal
end where significantStress
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end associate
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if(present(ddot_gamma_dtau_trans)) ddot_gamma_dtau_trans = ddot_gamma_dtau
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end subroutine kinetics_trans
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end submodule plastic_dislotwin