DAMASK_EICMD/src/plastic_dislotwin.f90

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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
!--------------------------------------------------------------------------------------------------
module plastic_dislotwin
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:,:), allocatable, target, public :: &
plastic_dislotwin_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_dislotwin_output !< name of each post result output
real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
enum, bind(c)
enumerator :: &
undefined_ID, &
edge_density_ID, &
dipole_density_ID, &
shear_rate_slip_ID, &
accumulated_shear_slip_ID, &
mfp_slip_ID, &
resolved_stress_slip_ID, &
threshold_stress_slip_ID, &
edge_dipole_distance_ID, &
twin_fraction_ID, &
mfp_twin_ID, &
resolved_stress_twin_ID, &
threshold_stress_twin_ID, &
resolved_stress_shearband_ID, &
shear_rate_shearband_ID, &
strain_trans_fraction_ID
end enum
type, private :: tParameters
real(pReal) :: &
mu, &
nu, &
D0, & !< prefactor for self-diffusion coefficient
Qsd, & !< activation energy for dislocation climb
GrainSize, & !<grain size
pShearBand, & !< p-exponent in shear band velocity
qShearBand, & !< q-exponent in shear band velocity
CEdgeDipMinDistance, & !<
Cmfptwin, & !<
Cthresholdtwin, & !<
SolidSolutionStrength, & !<strength due to elements in solid solution
L0_twin, & !< Length of twin nuclei in Burgers vectors
L0_trans, & !< Length of trans nuclei in Burgers vectors
xc_twin, & !< critical distance for formation of twin nucleus
xc_trans, & !< critical distance for formation of trans nucleus
VcrossSlip, & !< cross slip volume
sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
sbVelocity, & !< value for shearband velocity_0
sbQedge, & !< value for shearband systems Qedge
SFE_0K, & !< stacking fault energy at zero K
dSFE_dT, & !< temperature dependance of stacking fault energy
aTolRho, & !< absolute tolerance for integration of dislocation density
aTolTwinFrac, & !< absolute tolerance for integration of twin volume fraction
aTolTransFrac, & !< absolute tolerance for integration of trans volume fraction
deltaG, & !< Free energy difference between austensite and martensite
Cmfptrans, & !<
Cthresholdtrans, & !<
transStackHeight !< Stack height of hex nucleus
real(pReal), dimension(:), allocatable :: &
rho0, & !< initial unipolar dislocation density per slip system
rhoDip0, & !< initial dipole dislocation density per slip system
burgers_slip, & !< absolute length of burgers vector [m] for each slip system
burgers_twin, & !< absolute length of burgers vector [m] for each slip system
burgers_trans, & !< absolute length of burgers vector [m] for each twin system
Qedge,& !< activation energy for glide [J] for each slip system
v0, & !< dislocation velocity prefactor [m/s] for each slip system
tau_peierls,& !< Peierls stress [Pa] for each slip system
Ndot0_twin, & !< twin nucleation rate [1/m³s] for each twin system
Ndot0_trans, & !< trans nucleation rate [1/m³s] for each trans system
twinsize, & !< twin thickness [m] for each twin system
CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
atomicVolume, &
lamellarsize, & !< 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
shear_twin, & !< characteristic shear for twins
B !< drag coefficient
real(pReal), dimension(:,:), allocatable :: &
interaction_SlipSlip, & !<
interaction_SlipTwin, & !<
interaction_TwinSlip, & !<
interaction_TwinTwin, & !<
interaction_SlipTrans, & !<
interaction_TransTrans !<
integer(pInt), dimension(:,:), allocatable :: &
fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
real(pReal), dimension(:,:), allocatable :: &
forestProjection, &
C66
real(pReal), dimension(:,:,:), allocatable :: &
Schmid_trans, &
Schmid_slip, &
Schmid_twin, &
C66_twin, &
C66_trans
integer(pInt) :: &
totalNslip, & !< total number of active slip system
totalNtwin, & !< total number of active twin system
totalNtrans !< total number of active transformation system
integer(pInt), dimension(:), allocatable :: &
Nslip, & !< number of active slip systems for each family
Ntwin, & !< number of active twin systems for each family
Ntrans !< number of active transformation systems for each family
integer(kind(undefined_ID)), dimension(:), allocatable :: &
outputID !< ID of each post result output
logical :: &
fccTwinTransNucleation, & !< twinning and transformation models are for fcc
dipoleFormation !< flag indicating consideration of dipole formation
end type !< container type for internal constitutive parameters
type, private :: tDislotwinState
real(pReal), pointer, dimension(:,:) :: &
rhoEdge, &
rhoEdgeDip, &
accshear_slip, &
twinFraction, &
strainTransFraction
end type tDislotwinState
type, private :: tDislotwinMicrostructure
real(pReal), allocatable, dimension(:,:) :: &
invLambdaSlip, &
invLambdaSlipTwin, &
invLambdaSlipTrans, &
invLambdaTwin, &
invLambdaTrans, &
mfp_slip, &
mfp_twin, &
mfp_trans, &
threshold_stress_slip, &
threshold_stress_twin, &
threshold_stress_trans, &
twinVolume, &
martensiteVolume, &
tau_r_twin, & !< stress to bring partials close together (twin)
tau_r_trans !< stress to bring partials close together (trans)
end type tDislotwinMicrostructure
!--------------------------------------------------------------------------------------------------
! containers for parameters and state
type(tParameters), allocatable, dimension(:), private :: param
type(tDislotwinState), allocatable, dimension(:), private :: &
dotState, &
state
type(tDislotwinMicrostructure), allocatable, dimension(:), private :: microstructure
public :: &
plastic_dislotwin_init, &
plastic_dislotwin_homogenizedC, &
plastic_dislotwin_dependentState, &
plastic_dislotwin_LpAndItsTangent, &
plastic_dislotwin_dotState, &
plastic_dislotwin_postResults, &
plastic_dislotwin_results
private :: &
kinetics_slip, &
kinetics_twin, &
kinetics_trans
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_init
use prec, only: &
pStringLen, &
dEq0, &
dNeq0, &
dNeq
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_expand,&
PI
use IO, only: &
IO_error
use material, only: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
material_allocatePlasticState, &
PLASTICITY_DISLOTWIN_label, &
PLASTICITY_DISLOTWIN_ID, &
material_phase, &
plasticState
use config, only: &
config_phase
use lattice
implicit none
integer(pInt) :: &
Ninstance, &
p, i, &
NipcMyPhase, outputSize, &
sizeState, sizeDotState, &
startIndex, endIndex
integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
integer(kind(undefined_ID)) :: &
outputID
character(len=pStringLen) :: &
extmsg = ''
character(len=65536), dimension(:), allocatable :: &
outputs
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
allocate(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt)
allocate(plastic_dislotwin_output(maxval(phase_Noutput),Ninstance))
plastic_dislotwin_output = ''
allocate(param(Ninstance))
allocate(state(Ninstance))
allocate(dotState(Ninstance))
allocate(microstructure(Ninstance))
do p = 1_pInt, 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 => microstructure(phase_plasticityInstance(p)), &
config => config_phase(p))
prm%aTolRho = config%getFloat('atol_rho', defaultVal=0.0_pReal)
prm%aTolTwinFrac = config%getFloat('atol_twinfrac', defaultVal=0.0_pReal)
prm%aTolTransFrac = config%getFloat('atol_transfrac', defaultVal=0.0_pReal)
! 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)
!--------------------------------------------------------------------------------------------------
! slip related parameters
prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray)
prm%totalNslip = sum(prm%Nslip)
slipActive: if (prm%totalNslip > 0_pInt) then
prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%interaction_SlipSlip = lattice_interaction_SlipBySlip(prm%Nslip, &
config%getFloats('interaction_slipslip'), &
config%getString('lattice_structure'))
prm%forestProjection = lattice_forestProjection (prm%Nslip,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == LATTICE_FCC_ID) &
.and. (prm%Nslip(1) == 12_pInt)
if(prm%fccTwinTransNucleation) &
prm%fcc_twinNucleationSlipPair = lattice_fcc_twinNucleationSlipPair
prm%rho0 = config%getFloats('rhoedge0', requiredSize=size(prm%Nslip)) !ToDo: rename to rho_0
prm%rhoDip0 = config%getFloats('rhoedgedip0',requiredSize=size(prm%Nslip)) !ToDo: rename to rho_dip_0
prm%v0 = config%getFloats('v0', requiredSize=size(prm%Nslip))
prm%burgers_slip = config%getFloats('slipburgers',requiredSize=size(prm%Nslip))
prm%Qedge = config%getFloats('qedge', requiredSize=size(prm%Nslip)) !ToDo: rename (ask Karo)
prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(prm%Nslip))
prm%p = config%getFloats('p_slip', requiredSize=size(prm%Nslip))
prm%q = config%getFloats('q_slip', requiredSize=size(prm%Nslip))
prm%B = config%getFloats('b', requiredSize=size(prm%Nslip), &
defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))])
prm%tau_peierls = config%getFloats('tau_peierls',requiredSize=size(prm%Nslip), &
defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))]) ! Deprecated
prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
prm%D0 = config%getFloat('d0')
prm%Qsd = config%getFloat('qsd')
prm%atomicVolume = config%getFloat('catomicvolume') * prm%burgers_slip**3.0_pReal
! expand: family => system
prm%rho0 = math_expand(prm%rho0, prm%Nslip)
prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip)
prm%v0 = math_expand(prm%v0, prm%Nslip)
prm%burgers_slip = math_expand(prm%burgers_slip,prm%Nslip)
prm%Qedge = math_expand(prm%Qedge, prm%Nslip)
prm%CLambdaSlip = math_expand(prm%CLambdaSlip, prm%Nslip)
prm%p = math_expand(prm%p, prm%Nslip)
prm%q = math_expand(prm%q, prm%Nslip)
prm%B = math_expand(prm%B, prm%Nslip)
prm%tau_peierls = math_expand(prm%tau_peierls, prm%Nslip)
prm%atomicVolume = math_expand(prm%atomicVolume,prm%Nslip)
! sanity checks
if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' D0'
if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' Qsd'
if (any(prm%rho0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho0'
if (any(prm%rhoDip0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoDip0'
if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
if (any(prm%burgers_slip <= 0.0_pReal)) extmsg = trim(extmsg)//' burgers_slip'
if (any(prm%Qedge <= 0.0_pReal)) extmsg = trim(extmsg)//' Qedge'
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%tau_peierls < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls'
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
allocate(prm%burgers_slip(0))
endif slipActive
!--------------------------------------------------------------------------------------------------
! twin related parameters
prm%Ntwin = config%getInts('ntwin', defaultVal=emptyIntArray)
prm%totalNtwin = sum(prm%Ntwin)
if (prm%totalNtwin > 0_pInt) then
prm%Schmid_twin = lattice_SchmidMatrix_twin(prm%Ntwin,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%interaction_TwinTwin = lattice_interaction_TwinByTwin(prm%Ntwin,&
config%getFloats('interaction_twintwin'), &
config%getString('lattice_structure'))
prm%burgers_twin = config%getFloats('twinburgers', requiredSize=size(prm%Ntwin))
prm%twinsize = config%getFloats('twinsize', requiredSize=size(prm%Ntwin))
prm%r = config%getFloats('r_twin', requiredSize=size(prm%Ntwin))
prm%xc_twin = config%getFloat('xc_twin')
prm%L0_twin = config%getFloat('l0_twin')
prm%Cthresholdtwin = config%getFloat('cthresholdtwin', defaultVal=0.0_pReal)
prm%Cmfptwin = config%getFloat('cmfptwin', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%shear_twin = lattice_characteristicShear_Twin(prm%Ntwin,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
prm%C66_twin = lattice_C66_twin(prm%Ntwin,prm%C66,config%getString('lattice_structure'),&
config%getFloat('c/a',defaultVal=0.0_pReal))
if (.not. prm%fccTwinTransNucleation) then
prm%Ndot0_twin = config%getFloats('ndot0_twin')
prm%Ndot0_twin = math_expand(prm%Ndot0_twin,prm%Ntwin)
endif
! expand: family => system
prm%burgers_twin = math_expand(prm%burgers_twin,prm%Ntwin)
prm%twinsize = math_expand(prm%twinsize,prm%Ntwin)
prm%r = math_expand(prm%r,prm%Ntwin)
else
allocate(prm%twinsize(0))
allocate(prm%burgers_twin(0))
allocate(prm%r(0))
endif
!--------------------------------------------------------------------------------------------------
! transformation related parameters
prm%Ntrans = config%getInts('ntrans', defaultVal=emptyIntArray)
prm%totalNtrans = sum(prm%Ntrans)
if (prm%totalNtrans > 0_pInt) then
prm%burgers_trans = config%getFloats('transburgers')
prm%burgers_trans = math_expand(prm%burgers_trans,prm%Ntrans)
prm%Cthresholdtrans = config%getFloat('cthresholdtrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%transStackHeight = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%Cmfptrans = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%deltaG = config%getFloat('deltag')
prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
prm%L0_trans = config%getFloat('l0_trans')
prm%interaction_TransTrans = lattice_interaction_TransByTrans(prm%Ntrans,&
config%getFloats('interaction_transtrans'), &
config%getString('lattice_structure'))
prm%C66_trans = lattice_C66_trans(prm%Ntrans,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))
prm%Schmid_trans = lattice_SchmidMatrix_trans(prm%Ntrans, &
config%getString('trans_lattice_structure'), &
0.0_pReal, &
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
config%getFloat('a_fcc', defaultVal=0.0_pReal))
if (lattice_structure(p) /= LATTICE_fcc_ID) then
prm%Ndot0_trans = config%getFloats('ndot0_trans')
prm%Ndot0_trans = math_expand(prm%Ndot0_trans,prm%Ntrans)
endif
prm%lamellarsize = config%getFloats('lamellarsize')
prm%lamellarsize = math_expand(prm%lamellarsize,prm%Ntrans)
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
prm%s = math_expand(prm%s,prm%Ntrans)
else
allocate(prm%lamellarsize(0))
allocate(prm%burgers_trans(0))
endif
if (sum(prm%Ntwin) > 0_pInt .or. prm%totalNtrans > 0_pInt) then
prm%SFE_0K = config%getFloat('sfe_0k')
prm%dSFE_dT = config%getFloat('dsfe_dt')
prm%VcrossSlip = config%getFloat('vcrossslip')
endif
if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then
prm%interaction_SlipTwin = lattice_interaction_SlipByTwin(prm%Nslip,prm%Ntwin,&
config%getFloats('interaction_sliptwin'), &
config%getString('lattice_structure'))
prm%interaction_TwinSlip = lattice_interaction_TwinBySlip(prm%Ntwin,prm%Nslip,&
config%getFloats('interaction_twinslip'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. prm%totalNtwin > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntwin is [6,6]
endif
if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then
prm%interaction_SlipTrans = lattice_interaction_SlipByTrans(prm%Nslip,prm%Ntrans,&
config%getFloats('interaction_sliptrans'), &
config%getString('lattice_structure'))
if (prm%fccTwinTransNucleation .and. prm%totalNtrans > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntrans is [6,6]
endif
!--------------------------------------------------------------------------------------------------
! shearband related parameters
prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
if (prm%sbVelocity > 0.0_pReal) then
prm%sbResistance = config%getFloat('shearbandresistance')
prm%sbQedge = config%getFloat('qedgepersbsystem')
prm%pShearBand = config%getFloat('p_shearband')
prm%qShearBand = config%getFloat('q_shearband')
! sanity checks
if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' shearbandresistance'
if (prm%sbQedge < 0.0_pReal) extmsg = trim(extmsg)//' qedgepersbsystem'
if (prm%pShearBand <= 0.0_pReal) extmsg = trim(extmsg)//' p_shearband'
if (prm%qShearBand <= 0.0_pReal) extmsg = trim(extmsg)//' q_shearband'
endif
prm%GrainSize = config%getFloat('grainsize')
prm%SolidSolutionStrength = config%getFloat('solidsolutionstrength') ! Deprecated
if (config%keyExists('dipoleformationfactor')) call IO_error(1,ext_msg='use /nodipoleformation/')
prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
!if (Ndot0PerTwinFamily(f,p) < 0.0_pReal) &
! call IO_error(211_pInt,el=p,ext_msg='ndot0_twin ('//PLASTICITY_DISLOTWIN_label//')')
if (any(prm%atomicVolume <= 0.0_pReal)) &
call IO_error(211_pInt,el=p,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%totalNtwin > 0_pInt) then
if (prm%aTolRho <= 0.0_pReal) &
call IO_error(211_pInt,el=p,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')')
if (prm%aTolTwinFrac <= 0.0_pReal) &
call IO_error(211_pInt,el=p,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOTWIN_label//')')
endif
if (prm%totalNtrans > 0_pInt) then
if (prm%aTolTransFrac <= 0.0_pReal) &
call IO_error(211_pInt,el=p,ext_msg='aTolTransFrac ('//PLASTICITY_DISLOTWIN_label//')')
endif
outputs = config%getStrings('(output)', defaultVal=emptyStringArray)
allocate(prm%outputID(0))
do i= 1_pInt, size(outputs)
outputID = undefined_ID
select case(outputs(i))
case ('edge_density')
outputID = merge(edge_density_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('dipole_density')
outputID = merge(dipole_density_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('shear_rate_slip','shearrate_slip')
outputID = merge(shear_rate_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('accumulated_shear_slip')
outputID = merge(accumulated_shear_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('mfp_slip')
outputID = merge(mfp_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('resolved_stress_slip')
outputID = merge(resolved_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('threshold_stress_slip')
outputID= merge(threshold_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
outputSize = prm%totalNslip
case ('twin_fraction')
outputID = merge(twin_fraction_ID,undefined_ID,prm%totalNtwin >0_pInt)
outputSize = prm%totalNtwin
case ('mfp_twin')
outputID = merge(mfp_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
outputSize = prm%totalNtwin
case ('resolved_stress_twin')
outputID = merge(resolved_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
outputSize = prm%totalNtwin
case ('threshold_stress_twin')
outputID = merge(threshold_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
outputSize = prm%totalNtwin
case ('strain_trans_fraction')
outputID = strain_trans_fraction_ID
outputSize = prm%totalNtrans
end select
if (outputID /= undefined_ID) then
plastic_dislotwin_output(i,phase_plasticityInstance(p)) = outputs(i)
plastic_dislotwin_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
prm%outputID = [prm%outputID, outputID]
endif
enddo
!--------------------------------------------------------------------------------------------------
! allocate state arrays
NipcMyPhase = count(material_phase == p)
sizeDotState = int(size(['rho ','rhoDip ','accshearslip']),pInt) * prm%totalNslip &
+ int(size(['twinFraction']),pInt) * prm%totalNtwin &
+ int(size(['strainTransFraction']),pInt) * prm%totalNtrans
sizeState = sizeDotState
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, &
prm%totalNslip,prm%totalNtwin,prm%totalNtrans)
plasticState(p)%sizePostResults = sum(plastic_dislotwin_sizePostResult(:,phase_plasticityInstance(p)))
!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1_pInt
endIndex = prm%totalNslip
stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
stt%rhoEdge= spread(prm%rho0,2,NipcMyPhase)
dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
stt%rhoEdgeDip= spread(prm%rhoDip0,2,NipcMyPhase)
dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNslip
stt%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
dot%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal !ToDo: better make optional parameter
! global alias
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:)
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNtwin
stt%twinFraction=>plasticState(p)%state(startIndex:endIndex,:)
dot%twinFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
startIndex = endIndex + 1_pInt
endIndex = endIndex + prm%totalNtrans
stt%strainTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
dot%strainTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
allocate(dst%invLambdaSlip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
allocate(dst%invLambdaSlipTwin (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
allocate(dst%invLambdaSlipTrans (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
allocate(dst%mfp_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
allocate(dst%threshold_stress_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
allocate(dst%invLambdaTwin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
allocate(dst%mfp_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
allocate(dst%threshold_stress_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_r_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
allocate(dst%twinVolume (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
allocate(dst%invLambdaTrans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
allocate(dst%mfp_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
allocate(dst%threshold_stress_trans(prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
allocate(dst%tau_r_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
allocate(dst%martensiteVolume (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
end associate
enddo
end subroutine plastic_dislotwin_init
!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
use material, only: &
material_phase, &
phase_plasticityInstance, &
phasememberAt
implicit none
real(pReal), dimension(6,6) :: &
homogenizedC
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
integer(pInt) :: i, &
of
real(pReal) :: f_unrotated
of = phasememberAt(ipc,ip,el)
associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
f_unrotated = 1.0_pReal &
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
homogenizedC = f_unrotated * prm%C66
do i=1_pInt,prm%totalNtwin
homogenizedC = homogenizedC &
+ stt%twinFraction(i,of)*prm%C66_twin(1:6,1:6,i)
enddo
do i=1_pInt,prm%totalNtrans
homogenizedC = homogenizedC &
+ stt%strainTransFraction(i,of)*prm%C66_trans(1:6,1:6,i)
enddo
end associate
end function plastic_dislotwin_homogenizedC
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of)
use prec, only: &
tol_math_check, &
dNeq0
use math, only: &
math_eigenValuesVectorsSym, &
math_outer, &
math_symmetric33, &
math_mul33xx33, &
math_mul33x3
implicit none
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(pInt), intent(in) :: instance,of
real(pReal), intent(in) :: Temperature
integer(pInt) :: i,k,l,m,n
real(pReal) :: f_unrotated,StressRatio_p,&
BoltzmannRatio, &
dgdot_dtau, &
tau
real(pReal), dimension(param(instance)%totalNslip) :: &
gdot_slip,dgdot_dtau_slip
real(pReal), dimension(param(instance)%totalNtwin) :: &
gdot_twin,dgdot_dtau_twin
real(pReal), dimension(param(instance)%totalNtrans) :: &
gdot_trans,dgdot_dtau_trans
real(pReal):: gdot_sb
real(pReal), dimension(3,3) :: eigVectors, Schmid_shearBand
real(pReal), dimension(3) :: eigValues
logical :: error
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])
associate(prm => param(instance), stt => state(instance), dst => microstructure(instance))
f_unrotated = 1.0_pReal &
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
Lp = 0.0_pReal
dLp_dMp = 0.0_pReal
call kinetics_slip(Mp,temperature,instance,of,gdot_slip,dgdot_dtau_slip)
slipContribution: do i = 1_pInt, prm%totalNslip
Lp = Lp + gdot_slip(i)*prm%Schmid_slip(1:3,1:3,i)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtau_slip(i) * prm%Schmid_slip(k,l,i) * prm%Schmid_slip(m,n,i)
enddo slipContribution
!ToDo: Why do this before shear banding?
Lp = Lp * f_unrotated
dLp_dMp = dLp_dMp * f_unrotated
shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
call math_eigenValuesVectorsSym(Mp,eigValues,eigVectors,error)
do i = 1_pInt,6_pInt
Schmid_shearBand = 0.5_pReal * math_outer(math_mul33x3(eigVectors,sb_sComposition(1:3,i)),&
math_mul33x3(eigVectors,sb_mComposition(1:3,i)))
tau = math_mul33xx33(Mp,Schmid_shearBand)
significantShearBandStress: if (abs(tau) > tol_math_check) then
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand
gdot_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand), tau)
dgdot_dtau = abs(gdot_sb)*BoltzmannRatio* prm%pShearBand*prm%qShearBand/ prm%sbResistance &
* (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal) &
* (1.0_pReal-StressRatio_p)**(prm%qShearBand-1.0_pReal)
Lp = Lp + gdot_sb * Schmid_shearBand
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtau * Schmid_shearBand(k,l) * Schmid_shearBand(m,n)
endif significantShearBandStress
enddo
endif shearBandingContribution
call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_twin,dgdot_dtau_twin)
twinContibution: do i = 1_pInt, prm%totalNtwin
Lp = Lp + gdot_twin(i)*prm%Schmid_twin(1:3,1:3,i) * f_unrotated
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtau_twin(i)* prm%Schmid_twin(k,l,i)*prm%Schmid_twin(m,n,i) * f_unrotated
enddo twinContibution
call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_trans,dgdot_dtau_trans)
transContibution: do i = 1_pInt, prm%totalNtrans
Lp = Lp + gdot_trans(i)*prm%Schmid_trans(1:3,1:3,i) * f_unrotated
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtau_trans(i)* prm%Schmid_trans(k,l,i)*prm%Schmid_trans(m,n,i) * f_unrotated
enddo transContibution
end associate
end subroutine plastic_dislotwin_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_dotState(Mp,Temperature,instance,of)
use prec, only: &
tol_math_check, &
dEq0
use math, only: &
math_clip, &
math_mul33xx33, &
PI
use material, only: &
plasticState
implicit none
real(pReal), dimension(3,3), intent(in):: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
instance, &
of
integer(pInt) :: i
real(pReal) :: f_unrotated,&
VacancyDiffusion,&
EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, &
DotRhoDipFormation,DotRhoEdgeEdgeAnnihilation, &
tau
real(pReal), dimension(plasticState(instance)%Nslip) :: &
EdgeDipMinDistance, &
DotRhoMultiplication, &
gdot_slip
real(pReal), dimension(plasticState(instance)%Ntwin) :: &
gdot_twin
real(pReal), dimension(plasticState(instance)%Ntrans) :: &
gdot_trans
associate(prm => param(instance), stt => state(instance), &
dot => dotstate(instance), dst => microstructure(instance))
f_unrotated = 1.0_pReal &
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
call kinetics_slip(Mp,temperature,instance,of,gdot_slip)
dot%accshear_slip(:,of) = abs(gdot_slip)
DotRhoMultiplication = abs(gdot_slip)/(prm%burgers_slip*dst%mfp_slip(:,of))
EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip
slipState: do i = 1_pInt, prm%totalNslip
tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i))
significantSlipStress: if (dEq0(tau)) then
DotRhoDipFormation = 0.0_pReal
DotRhoEdgeDipClimb = 0.0_pReal
else significantSlipStress
EdgeDipDistance = 3.0_pReal*prm%mu*prm%burgers_slip(i)/(16.0_pReal*PI*abs(tau))
EdgeDipDistance = math_clip(EdgeDipDistance, right = dst%mfp_slip(i,of))
EdgeDipDistance = math_clip(EdgeDipDistance, left = EdgeDipMinDistance(i))
if (prm%dipoleFormation) then
DotRhoDipFormation = 2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance(i))/prm%burgers_slip(i) &
* stt%rhoEdge(i,of)*abs(gdot_slip(i))
else
DotRhoDipFormation = 0.0_pReal
endif
if (dEq0(EdgeDipDistance-EdgeDipMinDistance(i))) then
DotRhoEdgeDipClimb = 0.0_pReal
else
ClimbVelocity = 3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume(i) &
/ (2.0_pReal*PI*kB*Temperature*(EdgeDipDistance+EdgeDipMinDistance(i)))
DotRhoEdgeDipClimb = 4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(i,of) &
/ (EdgeDipDistance-EdgeDipMinDistance(i))
endif
endif significantSlipStress
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation = 2.0_pReal*EdgeDipMinDistance(i)/prm%burgers_slip(i) &
* stt%rhoEdge(i,of)*abs(gdot_slip(i))
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation = 2.0_pReal*EdgeDipMinDistance(i)/prm%burgers_slip(i) &
* stt%rhoEdgeDip(i,of)*abs(gdot_slip(i))
dot%rhoEdge(i,of) = DotRhoMultiplication(i)-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
dot%rhoEdgeDip(i,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
enddo slipState
call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_twin)
dot%twinFraction(:,of) = f_unrotated*gdot_twin/prm%shear_twin
call kinetics_trans(Mp,temperature,gdot_slip,instance,of,gdot_trans)
dot%twinFraction(:,of) = f_unrotated*gdot_trans
end associate
end subroutine plastic_dislotwin_dotState
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_dependentState(temperature,instance,of)
use math, only: &
PI
implicit none
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), intent(in) :: &
temperature
integer(pInt) :: &
i
real(pReal) :: &
sumf_twin,SFE,sumf_trans
real(pReal), dimension(:), allocatable :: &
x0, &
fOverStacksize, &
ftransOverLamellarSize
associate(prm => param(instance),&
stt => state(instance),&
dst => microstructure(instance))
sumf_twin = sum(stt%twinFraction(1:prm%totalNtwin,of))
sumf_trans = sum(stt%strainTransFraction(1:prm%totalNtrans,of))
SFE = prm%SFE_0K + prm%dSFE_dT * Temperature
!* rescaled volume fraction for topology
fOverStacksize = stt%twinFraction(1_pInt:prm%totalNtwin,of)/prm%twinsize !ToDo: this is per system
ftransOverLamellarSize = sumf_trans/prm%lamellarsize !ToDo: But this not ...
!Todo: Physically ok, but naming could be adjusted
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
forall (i = 1_pInt:prm%totalNslip) &
dst%invLambdaSlip(i,of) = &
sqrt(dot_product((stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)),&
prm%forestProjection(1:prm%totalNslip,i)))/prm%CLambdaSlip(i)
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
if (prm%totalNtwin > 0_pInt .and. prm%totalNslip > 0_pInt) &
dst%invLambdaSlipTwin(1_pInt:prm%totalNslip,of) = &
matmul(transpose(prm%interaction_SlipTwin),fOverStacksize)/(1.0_pReal-sumf_twin) ! ToDo: Transpose need
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!ToDo: needed? if (prm%totalNtwin > 0_pInt) &
dst%invLambdaTwin(1_pInt:prm%totalNtwin,of) = matmul(prm%interaction_TwinTwin,fOverStacksize)/(1.0_pReal-sumf_twin)
!* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
if (prm%totalNtrans > 0_pInt .and. prm%totalNslip > 0_pInt) &
dst%invLambdaSlipTrans(1_pInt:prm%totalNslip,of) = & ! ToDo: does not work if Ntrans is not 12
matmul(transpose(prm%interaction_SlipTrans),ftransOverLamellarSize)/(1.0_pReal-sumf_trans) ! ToDo: Transpose needed
!* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
!ToDo: needed? if (prm%totalNtrans > 0_pInt) &
dst%invLambdaTrans(1_pInt:prm%totalNtrans,of) = matmul(prm%interaction_TransTrans,ftransOverLamellarSize)/(1.0_pReal-sumf_trans)
!* mean free path between 2 obstacles seen by a moving dislocation
do i = 1_pInt,prm%totalNslip
if ((prm%totalNtwin > 0_pInt) .or. (prm%totalNtrans > 0_pInt)) then ! ToDo: This is too simplified
dst%mfp_slip(i,of) = &
prm%GrainSize/(1.0_pReal+prm%GrainSize*&
(dst%invLambdaSlip(i,of) + dst%invLambdaSlipTwin(i,of) + dst%invLambdaSlipTrans(i,of)))
else
dst%mfp_slip(i,of) = prm%GrainSize &
/ (1.0_pReal+prm%GrainSize*dst%invLambdaSlip(i,of)) !!!!!! correct?
endif
enddo
!* mean free path between 2 obstacles seen by a growing twin/martensite
dst%mfp_twin(:,of) = prm%Cmfptwin*prm%GrainSize/ (1.0_pReal+prm%GrainSize*dst%invLambdaTwin(:,of))
dst%mfp_trans(:,of) = prm%Cmfptrans*prm%GrainSize/(1.0_pReal+prm%GrainSize*dst%invLambdaTrans(:,of))
!* threshold stress for dislocation motion
forall (i = 1_pInt:prm%totalNslip) dst%threshold_stress_slip(i,of) = &
prm%mu*prm%burgers_slip(i)*&
sqrt(dot_product(stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of),&
prm%interaction_SlipSlip(:,i)))
!* threshold stress for growing twin/martensite
if(prm%totalNtwin == prm%totalNslip) &
dst%threshold_stress_twin(:,of) = prm%Cthresholdtwin* &
(SFE/(3.0_pReal*prm%burgers_twin)+ 3.0_pReal*prm%burgers_twin*prm%mu/ &
(prm%L0_twin*prm%burgers_slip)) ! slip burgers here correct?
if(prm%totalNtrans == prm%totalNslip) &
dst%threshold_stress_trans(:,of) = prm%Cthresholdtrans* &
(SFE/(3.0_pReal*prm%burgers_trans) + 3.0_pReal*prm%burgers_trans*prm%mu/&
(prm%L0_trans*prm%burgers_slip) + prm%transStackHeight*prm%deltaG/ (3.0_pReal*prm%burgers_trans) )
dst%twinVolume(:,of) = (PI/4.0_pReal)*prm%twinsize*dst%mfp_twin(:,of)**2.0_pReal
dst%martensiteVolume(:,of) = (PI/4.0_pReal)*prm%lamellarsize*dst%mfp_trans(:,of)**2.0_pReal
x0 = prm%mu*prm%burgers_twin**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu)
dst%tau_r_twin(:,of) = prm%mu*prm%burgers_twin/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
x0 = prm%mu*prm%burgers_trans**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu)
dst%tau_r_trans(:,of) = prm%mu*prm%burgers_trans/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
end associate
end subroutine plastic_dislotwin_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_dislotwin_postResults(Mp,Temperature,instance,of) result(postResults)
use prec, only: &
tol_math_check, &
dEq0
use math, only: &
PI, &
math_mul33xx33
implicit none
real(pReal), dimension(3,3),intent(in) :: &
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), dimension(sum(plastic_dislotwin_sizePostResult(:,instance))) :: &
postResults
integer(pInt) :: &
o,c,j
associate(prm => param(instance), stt => state(instance), dst => microstructure(instance))
c = 0_pInt
do o = 1_pInt,size(prm%outputID)
select case(prm%outputID(o))
case (edge_density_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (dipole_density_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (shear_rate_slip_ID)
call kinetics_slip(Mp,temperature,instance,of,postResults(c+1:c+prm%totalNslip))
c = c + prm%totalNslip
case (accumulated_shear_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (mfp_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (resolved_stress_slip_ID)
do j = 1_pInt, prm%totalNslip
postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))
enddo
c = c + prm%totalNslip
case (threshold_stress_slip_ID)
postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress_slip(1_pInt:prm%totalNslip,of)
c = c + prm%totalNslip
case (twin_fraction_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = stt%twinFraction(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (mfp_twin_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = dst%mfp_twin(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (resolved_stress_twin_ID)
do j = 1_pInt, prm%totalNtwin
postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,j))
enddo
c = c + prm%totalNtwin
case (threshold_stress_twin_ID)
postResults(c+1_pInt:c+prm%totalNtwin) = dst%threshold_stress_twin(1_pInt:prm%totalNtwin,of)
c = c + prm%totalNtwin
case (strain_trans_fraction_ID)
postResults(c+1_pInt:c+prm%totalNtrans) = stt%strainTransFraction(1_pInt:prm%totalNtrans,of)
c = c + prm%totalNtrans
end select
enddo
end associate
end function plastic_dislotwin_postResults
!--------------------------------------------------------------------------------------------------
!> @brief writes results to HDF5 output file
!--------------------------------------------------------------------------------------------------
subroutine plastic_dislotwin_results(instance,group)
#if defined(PETSc) || defined(DAMASKHDF5)
use results
implicit none
integer, intent(in) :: instance
character(len=*) :: group
integer :: o
associate(prm => param(instance), stt => state(instance))
outputsLoop: do o = 1_pInt,size(prm%outputID)
select case(prm%outputID(o))
end select
enddo outputsLoop
end associate
#else
integer, intent(in) :: instance
character(len=*) :: group
#endif
end subroutine plastic_dislotwin_results
!--------------------------------------------------------------------------------------------------
!> @brief Shear rates on slip systems, their derivatives with respect to resolved stress and the
! resolved stresss
!> @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
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics_slip(Mp,Temperature,instance,of, &
gdot_slip,dgdot_dtau_slip,tau_slip)
use prec, only: &
tol_math_check, &
dNeq0
use math, only: &
math_mul33xx33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%totalNslip), intent(out) :: &
gdot_slip
real(pReal), dimension(param(instance)%totalNslip), optional, intent(out) :: &
dgdot_dtau_slip, &
tau_slip
real(pReal), dimension(param(instance)%totalNslip) :: &
dgdot_dtau
real(pReal), dimension(param(instance)%totalNslip) :: &
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
integer(pInt) :: i
associate(prm => param(instance), stt => state(instance), dst => microstructure(instance))
do i = 1_pInt, prm%totalNslip
tau(i) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i))
enddo
tau_eff = abs(tau)-dst%threshold_stress_slip(:,of)
significantStress: where(tau_eff > tol_math_check)
stressRatio = tau_eff/(prm%SolidSolutionStrength+prm%tau_peierls)
StressRatio_p = stressRatio** prm%p
BoltzmannRatio = prm%Qedge/(kB*Temperature)
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%burgers_slip)
gdot_slip = sign(stt%rhoEdge(:,of)*prm%burgers_slip/(v_wait_inverse+v_run_inverse),tau)
dV_wait_inverse_dTau = 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%SolidSolutionStrength+prm%tau_peierls)
dV_run_inverse_dTau = v_run_inverse/tau_eff
dV_dTau = (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
/ (v_wait_inverse+v_run_inverse)**2.0_pReal
dgdot_dtau = dV_dTau*stt%rhoEdge(:,of)*prm%burgers_slip
else where significantStress
gdot_slip = 0.0_pReal
dgdot_dtau = 0.0_pReal
end where significantStress
end associate
if(present(dgdot_dtau_slip)) dgdot_dtau_slip = dgdot_dtau
if(present(tau_slip)) tau_slip = tau
end subroutine kinetics_slip
!--------------------------------------------------------------------------------------------------
!> @brief calculates shear rates on twin systems
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics_twin(Mp,temperature,gdot_slip,instance,of,&
gdot_twin,dgdot_dtau_twin)
use prec, only: &
tol_math_check, &
dNeq0
use math, only: &
math_mul33xx33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%totalNslip), intent(in) :: &
gdot_slip
real(pReal), dimension(param(instance)%totalNtwin), intent(out) :: &
gdot_twin
real(pReal), dimension(param(instance)%totalNtwin), optional, intent(out) :: &
dgdot_dtau_twin
real, dimension(param(instance)%totalNtwin) :: &
tau, &
Ndot0, &
stressRatio_r, &
dgdot_dtau
integer(pInt) :: i,s1,s2
associate(prm => param(instance), stt => state(instance), dst => microstructure(instance))
do i = 1_pInt, prm%totalNtwin
tau(i) = math_mul33xx33(Mp,prm%Schmid_twin(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_twin(i,of)) then
Ndot0=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
(prm%L0_twin*prm%burgers_slip(i))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(dst%tau_r_twin(i,of)-tau)))
else
Ndot0=0.0_pReal
end if
else isFCC
Ndot0=prm%Ndot0_twin(i)
endif isFCC
enddo
significantStress: where(tau > tol_math_check)
StressRatio_r = (dst%threshold_stress_twin(:,of)/tau)**prm%r
gdot_twin = prm%shear_twin * dst%twinVolume(:,of) * Ndot0*exp(-StressRatio_r)
dgdot_dtau = (gdot_twin*prm%r/tau)*StressRatio_r
else where significantStress
gdot_twin = 0.0_pReal
dgdot_dtau = 0.0_pReal
end where significantStress
end associate
if(present(dgdot_dtau_twin)) dgdot_dtau_twin = dgdot_dtau
end subroutine kinetics_twin
!--------------------------------------------------------------------------------------------------
!> @brief calculates shear rates on twin systems
!--------------------------------------------------------------------------------------------------
pure subroutine kinetics_trans(Mp,temperature,gdot_slip,instance,of,&
gdot_trans,dgdot_dtau_trans)
use prec, only: &
tol_math_check, &
dNeq0
use math, only: &
math_mul33xx33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
Mp !< Mandel stress
real(pReal), intent(in) :: &
temperature !< temperature
integer(pInt), intent(in) :: &
instance, &
of
real(pReal), dimension(param(instance)%totalNslip), intent(in) :: &
gdot_slip
real(pReal), dimension(param(instance)%totalNtrans), intent(out) :: &
gdot_trans
real(pReal), dimension(param(instance)%totalNtrans), optional, intent(out) :: &
dgdot_dtau_trans
real, dimension(param(instance)%totalNtrans) :: &
tau, &
Ndot0, &
stressRatio_s, &
dgdot_dtau
integer(pInt) :: i,s1,s2
associate(prm => param(instance), stt => state(instance), dst => microstructure(instance))
do i = 1_pInt, prm%totalNtrans
tau(i) = math_mul33xx33(Mp,prm%Schmid_trans(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_trans(i,of)) then
Ndot0=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
(prm%L0_trans*prm%burgers_slip(i))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(dst%tau_r_trans(i,of)-tau)))
else
Ndot0=0.0_pReal
end if
else isFCC
Ndot0=prm%Ndot0_trans(i)
endif isFCC
enddo
significantStress: where(tau > tol_math_check)
StressRatio_s = (dst%threshold_stress_trans(:,of)/tau)**prm%s
gdot_trans = dst%martensiteVolume(:,of) * Ndot0*exp(-StressRatio_s)
dgdot_dtau = (gdot_trans*prm%r/tau)*StressRatio_s
else where significantStress
gdot_trans = 0.0_pReal
dgdot_dtau = 0.0_pReal
end where significantStress
end associate
if(present(dgdot_dtau_trans)) dgdot_dtau_trans = dgdot_dtau
end subroutine kinetics_trans
end module plastic_dislotwin