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DAMASK_EICMD/code/constitutive_dislokmc.f90

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!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author David Cereceda, Lawrence Livermore National Laboratory
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine incoprorating dislocation and twinning physics
!> @details to be done
!--------------------------------------------------------------------------------------------------
module constitutive_dislokmc
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:), allocatable, public, protected :: &
constitutive_dislokmc_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
constitutive_dislokmc_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
constitutive_dislokmc_output !< name of each post result output
character(len=12), dimension(3), parameter, private :: &
CONSTITUTIVE_DISLOKMC_listBasicSlipStates = &
['rhoEdge ', 'rhoEdgeDip ', 'accshearslip']
character(len=12), dimension(2), parameter, private :: &
CONSTITUTIVE_DISLOKMC_listBasicTwinStates = &
['twinFraction', 'accsheartwin']
character(len=17), dimension(4), parameter, private :: &
CONSTITUTIVE_DISLOKMC_listDependentSlipStates = &
['invLambdaSlip ', 'invLambdaSlipTwin', 'meanFreePathSlip ', 'tauSlipThreshold ']
character(len=16), dimension(4), parameter, private :: &
CONSTITUTIVE_DISLOKMC_listDependentTwinStates = &
['invLambdaTwin ', 'meanFreePathTwin', 'tauTwinThreshold', 'twinVolume ']
real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
integer(pInt), dimension(:), allocatable, private :: &
constitutive_dislokmc_Noutput !< number of outputs per instance of this plasticity
integer(pInt), dimension(:), allocatable, private :: &
constitutive_dislokmc_totalNslip, & !< total number of active slip systems for each instance
constitutive_dislokmc_totalNtwin !< total number of active twin systems for each instance
integer(pInt), dimension(:,:), allocatable, private :: &
constitutive_dislokmc_Nslip, & !< number of active slip systems for each family and instance
constitutive_dislokmc_Ntwin !< number of active twin systems for each family and instance
real(pReal), dimension(:), allocatable, private :: &
constitutive_dislokmc_CAtomicVolume, & !< atomic volume in Bugers vector unit
constitutive_dislokmc_D0, & !< prefactor for self-diffusion coefficient
constitutive_dislokmc_Qsd, & !< activation energy for dislocation climb
constitutive_dislokmc_GrainSize, & !< grain size
constitutive_dislokmc_pShearBand, & !< p-exponent in shearband velocity
constitutive_dislokmc_qShearBand, & !< q-exponent in shearband velocity
constitutive_dislokmc_MaxTwinFraction, & !< maximum allowed total twin volume fraction
constitutive_dislokmc_CEdgeDipMinDistance, & !<
constitutive_dislokmc_Cmfptwin, & !<
constitutive_dislokmc_Cthresholdtwin, & !<
constitutive_dislokmc_SolidSolutionStrength, & !< Strength due to elements in solid solution
constitutive_dislokmc_L0, & !< Length of twin nuclei in Burgers vectors
constitutive_dislokmc_xc, & !< critical distance for formation of twin nucleus
constitutive_dislokmc_VcrossSlip, & !< cross slip volume
constitutive_dislokmc_sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
constitutive_dislokmc_sbVelocity, & !< value for shearband velocity_0
constitutive_dislokmc_sbQedge, & !< value for shearband systems Qedge
constitutive_dislokmc_SFE_0K, & !< stacking fault energy at zero K
constitutive_dislokmc_dSFE_dT, & !< temperature dependance of stacking fault energy
constitutive_dislokmc_dipoleFormationFactor, & !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
constitutive_dislokmc_aTolRho, & !< absolute tolerance for integration of dislocation density
constitutive_dislokmc_aTolTwinFrac !< absolute tolerance for integration of twin volume fraction
real(pReal), dimension(:,:,:,:), allocatable, private :: &
constitutive_dislokmc_Ctwin66 !< twin elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: &
constitutive_dislokmc_Ctwin3333 !< twin elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable, private :: &
constitutive_dislokmc_rhoEdge0, & !< initial edge dislocation density per slip system for each family and instance
constitutive_dislokmc_rhoEdgeDip0, & !< initial edge dipole density per slip system for each family and instance
constitutive_dislokmc_burgersPerSlipFamily, & !< absolute length of burgers vector [m] for each slip family and instance
constitutive_dislokmc_burgersPerSlipSystem, & !< absolute length of burgers vector [m] for each slip system and instance
constitutive_dislokmc_burgersPerTwinFamily, & !< absolute length of burgers vector [m] for each twin family and instance
constitutive_dislokmc_burgersPerTwinSystem, & !< absolute length of burgers vector [m] for each twin system and instance
constitutive_dislokmc_QedgePerSlipFamily, & !< activation energy for glide [J] for each slip family and instance
constitutive_dislokmc_QedgePerSlipSystem, & !< activation energy for glide [J] for each slip system and instance
constitutive_dislokmc_v0PerSlipFamily, & !< dislocation velocity prefactor [m/s] for each family and instance
constitutive_dislokmc_v0PerSlipSystem, & !< dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_dislokmc_tau_peierlsPerSlipFamily, & !< Peierls stress [Pa] for each family and instance
constitutive_dislokmc_Ndot0PerTwinFamily, & !< twin nucleation rate [1/m³s] for each twin family and instance
constitutive_dislokmc_Ndot0PerTwinSystem, & !< twin nucleation rate [1/m³s] for each twin system and instance
constitutive_dislokmc_tau_r, & !< stress to bring partial close together for each twin system and instance
constitutive_dislokmc_twinsizePerTwinFamily, & !< twin thickness [m] for each twin family and instance
constitutive_dislokmc_twinsizePerTwinSystem, & !< twin thickness [m] for each twin system and instance
constitutive_dislokmc_CLambdaSlipPerSlipFamily, & !< Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_dislokmc_CLambdaSlipPerSlipSystem, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_dislokmc_interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type and instance
constitutive_dislokmc_interaction_SlipTwin, & !< coefficients for slip-twin interaction for each interaction type and instance
constitutive_dislokmc_interaction_TwinSlip, & !< coefficients for twin-slip interaction for each interaction type and instance
constitutive_dislokmc_interaction_TwinTwin, & !< coefficients for twin-twin interaction for each interaction type and instance
constitutive_dislokmc_pPerSlipFamily, & !< p-exponent in glide velocity
constitutive_dislokmc_qPerSlipFamily, & !< q-exponent in glide velocity
constitutive_dislokmc_uPerSlipFamily, & !< u-exponent in glide velocity
constitutive_dislokmc_vPerSlipFamily, & !< v-exponent in glide velocity
constitutive_dislokmc_sPerSlipFamily, & !< self-hardening in glide velocity
constitutive_dislokmc_rPerTwinFamily !< r-exponent in twin nucleation rate
real(pReal), dimension(:,:,:), allocatable, private :: &
constitutive_dislokmc_interactionMatrix_SlipSlip, & !< interaction matrix of the different slip systems for each instance
constitutive_dislokmc_interactionMatrix_SlipTwin, & !< interaction matrix of slip systems with twin systems for each instance
constitutive_dislokmc_interactionMatrix_TwinSlip, & !< interaction matrix of twin systems with slip systems for each instance
constitutive_dislokmc_interactionMatrix_TwinTwin, & !< interaction matrix of the different twin systems for each instance
constitutive_dislokmc_forestProjectionEdge !< matrix of forest projections of edge dislocations for each instance
real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
constitutive_dislokmc_sbSv
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, &
stress_exponent_ID, &
twin_fraction_ID, &
shear_rate_twin_ID, &
accumulated_shear_twin_ID, &
mfp_twin_ID, &
resolved_stress_twin_ID, &
threshold_stress_twin_ID, &
resolved_stress_shearband_ID, &
shear_rate_shearband_ID, &
sb_eigenvalues_ID, &
sb_eigenvectors_ID
end enum
integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: &
constitutive_dislokmc_outputID !< ID of each post result output
public :: &
constitutive_dislokmc_init, &
constitutive_dislokmc_homogenizedC, &
constitutive_dislokmc_microstructure, &
constitutive_dislokmc_LpAndItsTangent, &
constitutive_dislokmc_dotState, &
constitutive_dislokmc_postResults
private :: &
constitutive_dislokmc_stateInit, &
constitutive_dislokmc_aTolState
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_init(fileUnit)
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333, &
math_mul3x3
use mesh, only: &
mesh_maxNips, &
mesh_NcpElems
use IO, only: &
IO_read, &
IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_intValue, &
IO_warning, &
IO_error, &
IO_timeStamp, &
IO_EOF
use material, only: &
homogenization_maxNgrains, &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
PLASTICITY_DISLOKMC_label, &
PLASTICITY_DISLOKMC_ID, &
material_phase, &
plasticState, &
MATERIAL_partPhase
use lattice
use numerics,only: &
numerics_integrator
implicit none
integer(pInt), intent(in) :: fileUnit
integer(pInt), parameter :: MAXNCHUNKS = LATTICE_maxNinteraction + 1_pInt
integer(pInt), dimension(1+2*MAXNCHUNKS) :: positions
integer(pInt) :: maxNinstance,mySize=0_pInt,phase,maxTotalNslip,maxTotalNtwin,&
f,instance,j,k,l,m,n,o,p,q,r,s,ns,nt, &
Nchunks_SlipSlip, Nchunks_SlipTwin, Nchunks_TwinSlip, Nchunks_TwinTwin, &
Nchunks_SlipFamilies, Nchunks_TwinFamilies, &
index_myFamily, index_otherFamily
integer(pInt) :: sizeState, sizeDotState
integer(pInt) :: NofMyPhase
character(len=65536) :: &
tag = '', &
line = ''
real(pReal), dimension(:), allocatable :: tempPerSlip, tempPerTwin
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOKMC_label//' init -+>>>'
write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOKMC_ID),pInt)
if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
allocate(constitutive_dislokmc_sizePostResults(maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
allocate(constitutive_dislokmc_output(maxval(phase_Noutput),maxNinstance))
constitutive_dislokmc_output = ''
allocate(constitutive_dislokmc_outputID(maxval(phase_Noutput),maxNinstance), source=undefined_ID)
allocate(constitutive_dislokmc_Noutput(maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_Ntwin(lattice_maxNtwinFamily,maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_totalNslip(maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_totalNtwin(maxNinstance), source=0_pInt)
allocate(constitutive_dislokmc_CAtomicVolume(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_D0(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_Qsd(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_GrainSize(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_pShearBand(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_qShearBand(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_MaxTwinFraction(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_CEdgeDipMinDistance(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_Cmfptwin(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_Cthresholdtwin(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_SolidSolutionStrength(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_L0(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_xc(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_VcrossSlip(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_aTolRho(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_aTolTwinFrac(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_sbResistance(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_sbVelocity(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_sbQedge(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_SFE_0K(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_dSFE_dT(maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_dipoleFormationFactor(maxNinstance), source=1.0_pReal) !should be on by default
allocate(constitutive_dislokmc_rhoEdge0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_rhoEdgeDip0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_burgersPerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_QedgePerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_tau_peierlsPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_pPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_qPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_uPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_vPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_sPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_Ndot0PerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_rPerTwinFamily(lattice_maxNtwinFamily,maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_interaction_SlipSlip(lattice_maxNinteraction,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_interaction_SlipTwin(lattice_maxNinteraction,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_interaction_TwinSlip(lattice_maxNinteraction,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_interaction_TwinTwin(lattice_maxNinteraction,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), &
source=0.0_pReal)
rewind(fileUnit)
phase = 0_pInt
do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= MATERIAL_partPhase) ! wind forward to <phase>
line = IO_read(fileUnit)
enddo
parsingFile: do while (trim(line) /= IO_EOF) ! read through sections of phase part
line = IO_read(fileUnit)
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') then ! stop at next part
line = IO_read(fileUnit, .true.) ! reset IO_read
exit
endif
if (IO_getTag(line,'[',']') /= '') then ! next phase section
phase = phase + 1_pInt ! advance phase section counter
if (phase_plasticity(phase) == PLASTICITY_DISLOKMC_ID) then
Nchunks_SlipFamilies = count(lattice_NslipSystem(:,phase) > 0_pInt)
Nchunks_TwinFamilies = count(lattice_NtwinSystem(:,phase) > 0_pInt)
Nchunks_SlipSlip = maxval(lattice_interactionSlipSlip(:,:,phase))
Nchunks_SlipTwin = maxval(lattice_interactionSlipTwin(:,:,phase))
Nchunks_TwinSlip = maxval(lattice_interactionTwinSlip(:,:,phase))
Nchunks_TwinTwin = maxval(lattice_interactionTwinTwin(:,:,phase))
if(allocated(tempPerSlip)) deallocate(tempPerSlip)
if(allocated(tempPerTwin)) deallocate(tempPerTwin)
allocate(tempPerSlip(Nchunks_SlipFamilies))
allocate(tempPerTwin(Nchunks_TwinFamilies))
endif
cycle ! skip to next line
endif
if (phase > 0_pInt ) then; if (phase_plasticity(phase) == PLASTICITY_DISLOKMC_ID) then ! do not short-circuit here (.and. with next if statemen). It's not safe in Fortran
instance = phase_plasticityInstance(phase) ! which instance of my plasticity is present phase
positions = IO_stringPos(line,MAXNCHUNKS)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('(output)')
select case(IO_lc(IO_stringValue(line,positions,2_pInt)))
case ('edge_density')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = edge_density_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('dipole_density')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = dipole_density_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('shear_rate_slip')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = shear_rate_slip_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('accumulated_shear_slip')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = accumulated_shear_slip_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('mfp_slip')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = mfp_slip_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('resolved_stress_slip')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = resolved_stress_slip_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('edge_dipole_distance')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = edge_dipole_distance_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('stress_exponent')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = stress_exponent_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('twin_fraction')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = twin_fraction_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('shear_rate_twin')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = shear_rate_twin_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('accumulated_shear_twin')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = accumulated_shear_twin_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('mfp_twin')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = mfp_twin_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('resolved_stress_twin')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = resolved_stress_twin_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('threshold_stress_twin')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = threshold_stress_twin_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('resolved_stress_shearband')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = resolved_stress_shearband_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('shear_rate_shearband')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = shear_rate_shearband_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('sb_eigenvalues')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = sb_eigenvalues_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
case ('sb_eigenvectors')
constitutive_dislokmc_Noutput(instance) = constitutive_dislokmc_Noutput(instance) + 1_pInt
constitutive_dislokmc_outputID(constitutive_dislokmc_Noutput(instance),instance) = sb_eigenvectors_ID
constitutive_dislokmc_output(constitutive_dislokmc_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,positions,2_pInt))
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on number of slip system families
case ('nslip')
if (positions(1) < Nchunks_SlipFamilies + 1_pInt) &
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
if (positions(1) > Nchunks_SlipFamilies + 1_pInt) &
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
Nchunks_SlipFamilies = positions(1) - 1_pInt
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_dislokmc_Nslip(j,instance) = IO_intValue(line,positions,1_pInt+j)
enddo
case ('rhoedge0','rhoedgedip0','slipburgers','qedge','v0','clambdaslip','tau_peierls','p_slip','q_slip',&
'u_slip','v_slip','s_slip')
do j = 1_pInt, Nchunks_SlipFamilies
tempPerSlip(j) = IO_floatValue(line,positions,1_pInt+j)
enddo
select case(tag)
case ('rhoedge0')
constitutive_dislokmc_rhoEdge0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('rhoedgedip0')
constitutive_dislokmc_rhoEdgeDip0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('slipburgers')
constitutive_dislokmc_burgersPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('qedge')
constitutive_dislokmc_QedgePerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('v0')
constitutive_dislokmc_v0PerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('clambdaslip')
constitutive_dislokmc_CLambdaSlipPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('tau_peierls')
if (lattice_structure(phase) /= LATTICE_bcc_ID) &
call IO_warning(42_pInt,ext_msg=trim(tag)//' for non-bcc ('//PLASTICITY_DISLOKMC_label//')')
constitutive_dislokmc_tau_peierlsPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('p_slip')
constitutive_dislokmc_pPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('q_slip')
constitutive_dislokmc_qPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('u_slip')
constitutive_dislokmc_uPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('v_slip')
constitutive_dislokmc_vPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('s_slip')
constitutive_dislokmc_sPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on slip number of twin families
case ('ntwin')
if (positions(1) < Nchunks_TwinFamilies + 1_pInt) &
call IO_warning(51_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
if (positions(1) > Nchunks_TwinFamilies + 1_pInt) &
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
Nchunks_TwinFamilies = positions(1) - 1_pInt
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_dislokmc_Ntwin(j,instance) = IO_intValue(line,positions,1_pInt+j)
enddo
case ('ndot0','twinsize','twinburgers','r_twin')
do j = 1_pInt, Nchunks_TwinFamilies
tempPerTwin(j) = IO_floatValue(line,positions,1_pInt+j)
enddo
select case(tag)
case ('ndot0')
if (lattice_structure(phase) == LATTICE_fcc_ID) &
call IO_warning(42_pInt,ext_msg=trim(tag)//' for fcc ('//PLASTICITY_DISLOKMC_label//')')
constitutive_dislokmc_Ndot0PerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
case ('twinsize')
constitutive_dislokmc_twinsizePerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
case ('twinburgers')
constitutive_dislokmc_burgersPerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
case ('r_twin')
constitutive_dislokmc_rPerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on number of interactions
case ('interaction_slipslip','interactionslipslip')
if (positions(1) < 1_pInt + Nchunks_SlipSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
do j = 1_pInt, Nchunks_SlipSlip
constitutive_dislokmc_interaction_SlipSlip(j,instance) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_sliptwin','interactionsliptwin')
if (positions(1) < 1_pInt + Nchunks_SlipTwin) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
do j = 1_pInt, Nchunks_SlipTwin
constitutive_dislokmc_interaction_SlipTwin(j,instance) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_twinslip','interactiontwinslip')
if (positions(1) < 1_pInt + Nchunks_TwinSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
do j = 1_pInt, Nchunks_TwinSlip
constitutive_dislokmc_interaction_TwinSlip(j,instance) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_twintwin','interactiontwintwin')
if (positions(1) < 1_pInt + Nchunks_TwinTwin) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOKMC_label//')')
do j = 1_pInt, Nchunks_TwinTwin
constitutive_dislokmc_interaction_TwinTwin(j,instance) = IO_floatValue(line,positions,1_pInt+j)
enddo
!--------------------------------------------------------------------------------------------------
! parameters independent of number of slip/twin systems
case ('grainsize')
constitutive_dislokmc_GrainSize(instance) = IO_floatValue(line,positions,2_pInt)
case ('maxtwinfraction')
constitutive_dislokmc_MaxTwinFraction(instance) = IO_floatValue(line,positions,2_pInt)
case ('p_shearband')
constitutive_dislokmc_pShearBand(instance) = IO_floatValue(line,positions,2_pInt)
case ('q_shearband')
constitutive_dislokmc_qShearBand(instance) = IO_floatValue(line,positions,2_pInt)
case ('d0')
constitutive_dislokmc_D0(instance) = IO_floatValue(line,positions,2_pInt)
case ('qsd')
constitutive_dislokmc_Qsd(instance) = IO_floatValue(line,positions,2_pInt)
case ('atol_rho')
constitutive_dislokmc_aTolRho(instance) = IO_floatValue(line,positions,2_pInt)
case ('atol_twinfrac')
constitutive_dislokmc_aTolTwinFrac(instance) = IO_floatValue(line,positions,2_pInt)
case ('cmfptwin')
constitutive_dislokmc_Cmfptwin(instance) = IO_floatValue(line,positions,2_pInt)
case ('cthresholdtwin')
constitutive_dislokmc_Cthresholdtwin(instance) = IO_floatValue(line,positions,2_pInt)
case ('solidsolutionstrength')
constitutive_dislokmc_SolidSolutionStrength(instance) = IO_floatValue(line,positions,2_pInt)
case ('l0')
constitutive_dislokmc_L0(instance) = IO_floatValue(line,positions,2_pInt)
case ('xc')
constitutive_dislokmc_xc(instance) = IO_floatValue(line,positions,2_pInt)
case ('vcrossslip')
constitutive_dislokmc_VcrossSlip(instance) = IO_floatValue(line,positions,2_pInt)
case ('cedgedipmindistance')
constitutive_dislokmc_CEdgeDipMinDistance(instance) = IO_floatValue(line,positions,2_pInt)
case ('catomicvolume')
constitutive_dislokmc_CAtomicVolume(instance) = IO_floatValue(line,positions,2_pInt)
case ('sfe_0k')
constitutive_dislokmc_SFE_0K(instance) = IO_floatValue(line,positions,2_pInt)
case ('dsfe_dt')
constitutive_dislokmc_dSFE_dT(instance) = IO_floatValue(line,positions,2_pInt)
case ('dipoleformationfactor')
constitutive_dislokmc_dipoleFormationFactor(instance) = IO_floatValue(line,positions,2_pInt)
case ('shearbandresistance')
constitutive_dislokmc_sbResistance(instance) = IO_floatValue(line,positions,2_pInt)
case ('shearbandvelocity')
constitutive_dislokmc_sbVelocity(instance) = IO_floatValue(line,positions,2_pInt)
case ('qedgepersbsystem')
constitutive_dislokmc_sbQedge(instance) = IO_floatValue(line,positions,2_pInt)
end select
endif; endif
enddo parsingFile
sanityChecks: do phase = 1_pInt, size(phase_plasticity)
myPhase: if (phase_plasticity(phase) == PLASTICITY_dislokmc_ID) then
instance = phase_plasticityInstance(phase)
if (sum(constitutive_dislokmc_Nslip(:,instance)) < 0_pInt) &
call IO_error(211_pInt,el=instance,ext_msg='Nslip ('//PLASTICITY_DISLOKMC_label//')')
if (sum(constitutive_dislokmc_Ntwin(:,instance)) < 0_pInt) &
call IO_error(211_pInt,el=instance,ext_msg='Ntwin ('//PLASTICITY_DISLOKMC_label//')')
do f = 1_pInt,lattice_maxNslipFamily
if (constitutive_dislokmc_Nslip(f,instance) > 0_pInt) then
if (constitutive_dislokmc_rhoEdge0(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_rhoEdgeDip0(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_v0PerSlipFamily(f,instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOKMC_label//')')
endif
enddo
do f = 1_pInt,lattice_maxNtwinFamily
if (constitutive_dislokmc_Ntwin(f,instance) > 0_pInt) then
if (constitutive_dislokmc_burgersPerTwinFamily(f,instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='twinburgers ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_Ndot0PerTwinFamily(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='ndot0 ('//PLASTICITY_DISLOKMC_label//')')
endif
enddo
if (constitutive_dislokmc_CAtomicVolume(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_D0(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_Qsd(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOKMC_label//')')
if (sum(constitutive_dislokmc_Ntwin(:,instance)) > 0_pInt) then
if (constitutive_dislokmc_SFE_0K(instance) == 0.0_pReal .and. &
constitutive_dislokmc_dSFE_dT(instance) == 0.0_pReal .and. &
lattice_structure(phase) == LATTICE_fcc_ID) &
call IO_error(211_pInt,el=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_aTolRho(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_aTolTwinFrac(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOKMC_label//')')
endif
if (constitutive_dislokmc_sbResistance(instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='sbResistance ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_sbVelocity(instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='sbVelocity ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_sbVelocity(instance) > 0.0_pReal .and. &
constitutive_dislokmc_pShearBand(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='pShearBand ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_dipoleFormationFactor(instance) /= 0.0_pReal .and. &
constitutive_dislokmc_dipoleFormationFactor(instance) /= 1.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='dipoleFormationFactor ('//PLASTICITY_DISLOKMC_label//')')
if (constitutive_dislokmc_sbVelocity(instance) > 0.0_pReal .and. &
constitutive_dislokmc_qShearBand(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='qShearBand ('//PLASTICITY_DISLOKMC_label//')')
!--------------------------------------------------------------------------------------------------
! Determine total number of active slip or twin systems
constitutive_dislokmc_Nslip(:,instance) = min(lattice_NslipSystem(:,phase),constitutive_dislokmc_Nslip(:,instance))
constitutive_dislokmc_Ntwin(:,instance) = min(lattice_NtwinSystem(:,phase),constitutive_dislokmc_Ntwin(:,instance))
constitutive_dislokmc_totalNslip(instance) = sum(constitutive_dislokmc_Nslip(:,instance))
constitutive_dislokmc_totalNtwin(instance) = sum(constitutive_dislokmc_Ntwin(:,instance))
endif myPhase
enddo sanityChecks
!--------------------------------------------------------------------------------------------------
! allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(constitutive_dislokmc_totalNslip)
maxTotalNtwin = maxval(constitutive_dislokmc_totalNtwin)
allocate(constitutive_dislokmc_burgersPerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_burgersPerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_QedgePerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_v0PerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_Ndot0PerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_tau_r(maxTotalNtwin, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_CLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance),source=0.0_pReal)
allocate(constitutive_dislokmc_interactionMatrix_SlipSlip(maxval(constitutive_dislokmc_totalNslip),& ! slip resistance from slip activity
maxval(constitutive_dislokmc_totalNslip),&
maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_interactionMatrix_SlipTwin(maxval(constitutive_dislokmc_totalNslip),& ! slip resistance from twin activity
maxval(constitutive_dislokmc_totalNtwin),&
maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_interactionMatrix_TwinSlip(maxval(constitutive_dislokmc_totalNtwin),& ! twin resistance from slip activity
maxval(constitutive_dislokmc_totalNslip),&
maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_interactionMatrix_TwinTwin(maxval(constitutive_dislokmc_totalNtwin),& ! twin resistance from twin activity
maxval(constitutive_dislokmc_totalNtwin),&
maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance), &
source=0.0_pReal)
allocate(constitutive_dislokmc_Ctwin66(6,6,maxTotalNtwin,maxNinstance), source=0.0_pReal)
allocate(constitutive_dislokmc_Ctwin3333(3,3,3,3,maxTotalNtwin,maxNinstance), source=0.0_pReal)
initializeInstances: do phase = 1_pInt, size(phase_plasticity)
myPhase2: if (phase_plasticity(phase) == PLASTICITY_dislokmc_ID) then
NofMyPhase=count(material_phase==phase)
instance = phase_plasticityInstance(phase)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!--------------------------------------------------------------------------------------------------
! Determine size of postResults array
outputsLoop: do o = 1_pInt,constitutive_dislokmc_Noutput(instance)
select case(constitutive_dislokmc_outputID(o,instance))
case(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, &
stress_exponent_ID &
)
mySize = ns
case(twin_fraction_ID, &
shear_rate_twin_ID, &
accumulated_shear_twin_ID, &
mfp_twin_ID, &
resolved_stress_twin_ID, &
threshold_stress_twin_ID &
)
mySize = nt
case(resolved_stress_shearband_ID, &
shear_rate_shearband_ID &
)
mySize = 6_pInt
case(sb_eigenvalues_ID)
mySize = 3_pInt
case(sb_eigenvectors_ID)
mySize = 9_pInt
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_dislokmc_sizePostResult(o,instance) = mySize
constitutive_dislokmc_sizePostResults(instance) = constitutive_dislokmc_sizePostResults(instance) + mySize
endif
enddo outputsLoop
!--------------------------------------------------------------------------------------------------
! allocate state arrays
sizeDotState = int(size(CONSTITUTIVE_DISLOKMC_listBasicSlipStates),pInt) * ns &
+ int(size(CONSTITUTIVE_DISLOKMC_listBasicTwinStates),pInt) * nt
sizeState = sizeDotState &
+ int(size(CONSTITUTIVE_DISLOKMC_listDependentSlipStates),pInt) * ns &
+ int(size(CONSTITUTIVE_DISLOKMC_listDependentTwinStates),pInt) * nt
plasticState(phase)%sizeState = sizeState
plasticState(phase)%sizeDotState = sizeDotState
allocate(plasticState(phase)%aTolState (sizeState), source=0.0_pReal)
allocate(plasticState(phase)%state0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%partionedState0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%subState0 (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%state (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%state_backup (sizeState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%deltaState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%dotState_backup (sizeDotState,NofMyPhase), source=0.0_pReal)
if (any(numerics_integrator == 1_pInt)) then
allocate(plasticState(phase)%previousDotState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%previousDotState2 (sizeDotState,NofMyPhase), source=0.0_pReal)
endif
if (any(numerics_integrator == 4_pInt)) &
allocate(plasticState(phase)%RK4dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
if (any(numerics_integrator == 5_pInt)) &
allocate(plasticState(phase)%RKCK45dotState (6,sizeDotState,NofMyPhase),source=0.0_pReal)
!* Process slip related parameters ------------------------------------------------
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(constitutive_dislokmc_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
slipSystemsLoop: do j = 1_pInt,constitutive_dislokmc_Nslip(f,instance)
!* Burgers vector,
! dislocation velocity prefactor,
! mean free path prefactor,
! and minimum dipole distance
constitutive_dislokmc_burgersPerSlipSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_burgersPerSlipFamily(f,instance)
constitutive_dislokmc_QedgePerSlipSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_QedgePerSlipFamily(f,instance)
constitutive_dislokmc_v0PerSlipSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_v0PerSlipFamily(f,instance)
constitutive_dislokmc_CLambdaSlipPerSlipSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_CLambdaSlipPerSlipFamily(f,instance)
!* Calculation of forest projections for edge dislocations
!* Interaction matrices
do o = 1_pInt,lattice_maxNslipFamily
index_otherFamily = sum(constitutive_dislokmc_Nslip(1:o-1_pInt,instance))
do k = 1_pInt,constitutive_dislokmc_Nslip(o,instance) ! loop over (active) systems in other family (slip)
constitutive_dislokmc_forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = &
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,phase))+j,phase), &
lattice_st(:,sum(lattice_NslipSystem(1:o-1,phase))+k,phase)))
constitutive_dislokmc_interactionMatrix_SlipSlip(index_myFamily+j,index_otherFamily+k,instance) = &
constitutive_dislokmc_interaction_SlipSlip(lattice_interactionSlipSlip( &
sum(lattice_NslipSystem(1:f-1,phase))+j, &
sum(lattice_NslipSystem(1:o-1,phase))+k, &
phase), instance )
enddo; enddo
do o = 1_pInt,lattice_maxNtwinFamily
index_otherFamily = sum(constitutive_dislokmc_Ntwin(1:o-1_pInt,instance))
do k = 1_pInt,constitutive_dislokmc_Ntwin(o,instance) ! loop over (active) systems in other family (twin)
constitutive_dislokmc_interactionMatrix_SlipTwin(index_myFamily+j,index_otherFamily+k,instance) = &
constitutive_dislokmc_interaction_SlipTwin(lattice_interactionSlipTwin( &
sum(lattice_NslipSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
phase), instance )
enddo; enddo
enddo slipSystemsLoop
enddo slipFamiliesLoop
!* Process twin related parameters ------------------------------------------------
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
index_myFamily = sum(constitutive_dislokmc_Ntwin(1:f-1_pInt,instance)) ! index in truncated twin system list
twinSystemsLoop: do j = 1_pInt,constitutive_dislokmc_Ntwin(f,instance)
!* Burgers vector,
! nucleation rate prefactor,
! and twin size
constitutive_dislokmc_burgersPerTwinSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_burgersPerTwinFamily(f,instance)
constitutive_dislokmc_Ndot0PerTwinSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_Ndot0PerTwinFamily(f,instance)
constitutive_dislokmc_twinsizePerTwinSystem(index_myFamily+j,instance) = &
constitutive_dislokmc_twinsizePerTwinFamily(f,instance)
!* Rotate twin elasticity matrices
index_otherFamily = sum(lattice_NtwinSystem(1:f-1_pInt,phase)) ! index in full lattice twin list
do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt; do o = 1_pInt,3_pInt
do p = 1_pInt,3_pInt; do q = 1_pInt,3_pInt; do r = 1_pInt,3_pInt; do s = 1_pInt,3_pInt
constitutive_dislokmc_Ctwin3333(l,m,n,o,index_myFamily+j,instance) = &
constitutive_dislokmc_Ctwin3333(l,m,n,o,index_myFamily+j,instance) + &
lattice_C3333(p,q,r,s,instance) * &
lattice_Qtwin(l,p,index_otherFamily+j,phase) * &
lattice_Qtwin(m,q,index_otherFamily+j,phase) * &
lattice_Qtwin(n,r,index_otherFamily+j,phase) * &
lattice_Qtwin(o,s,index_otherFamily+j,phase)
enddo; enddo; enddo; enddo
enddo; enddo; enddo; enddo
constitutive_dislokmc_Ctwin66(1:6,1:6,index_myFamily+j,instance) = &
math_Mandel3333to66(constitutive_dislokmc_Ctwin3333(1:3,1:3,1:3,1:3,index_myFamily+j,instance))
!* Interaction matrices
do o = 1_pInt,lattice_maxNslipFamily
index_otherFamily = sum(constitutive_dislokmc_Nslip(1:o-1_pInt,instance))
do k = 1_pInt,constitutive_dislokmc_Nslip(o,instance) ! loop over (active) systems in other family (slip)
constitutive_dislokmc_interactionMatrix_TwinSlip(index_myFamily+j,index_otherFamily+k,instance) = &
constitutive_dislokmc_interaction_TwinSlip(lattice_interactionTwinSlip( &
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NslipSystem(1:o-1_pInt,phase))+k, &
phase), instance )
enddo; enddo
do o = 1_pInt,lattice_maxNtwinFamily
index_otherFamily = sum(constitutive_dislokmc_Ntwin(1:o-1_pInt,instance))
do k = 1_pInt,constitutive_dislokmc_Ntwin(o,instance) ! loop over (active) systems in other family (twin)
constitutive_dislokmc_interactionMatrix_TwinTwin(index_myFamily+j,index_otherFamily+k,instance) = &
constitutive_dislokmc_interaction_TwinTwin(lattice_interactionTwinTwin( &
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
phase), instance )
enddo; enddo
enddo twinSystemsLoop
enddo twinFamiliesLoop
call constitutive_dislokmc_stateInit(phase,instance)
call constitutive_dislokmc_aTolState(phase,instance)
endif myPhase2
enddo initializeInstances
end subroutine constitutive_dislokmc_init
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_stateInit(ph,instance)
use math, only: &
pi
use lattice, only: &
lattice_maxNslipFamily, &
lattice_structure, &
lattice_mu, &
lattice_bcc_ID
use material, only: &
plasticState
implicit none
integer(pInt), intent(in) :: &
instance, & !< number specifying the instance of the plasticity
ph
real(pReal), dimension(plasticState(ph)%sizeState) :: tempState
integer(pInt) :: i,j,f,ns,nt, index_myFamily
real(pReal), dimension(constitutive_dislokmc_totalNslip(instance)) :: &
rhoEdge0, &
rhoEdgeDip0, &
invLambdaSlip0, &
MeanFreePathSlip0, &
tauSlipThreshold0
real(pReal), dimension(constitutive_dislokmc_totalNtwin(instance)) :: &
MeanFreePathTwin0,TwinVolume0
tempState = 0.0_pReal
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables
do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(constitutive_dislokmc_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
rhoEdge0(index_myFamily+1_pInt: &
index_myFamily+constitutive_dislokmc_Nslip(f,instance)) = &
constitutive_dislokmc_rhoEdge0(f,instance)
rhoEdgeDip0(index_myFamily+1_pInt: &
index_myFamily+constitutive_dislokmc_Nslip(f,instance)) = &
constitutive_dislokmc_rhoEdgeDip0(f,instance)
enddo
tempState(1_pInt:ns) = rhoEdge0
tempState(ns+1_pInt:2_pInt*ns) = rhoEdgeDip0
!--------------------------------------------------------------------------------------------------
! initialize dependent slip microstructural variables
forall (i = 1_pInt:ns) &
invLambdaSlip0(i) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislokmc_forestProjectionEdge(1:ns,i,instance)))/ &
constitutive_dislokmc_CLambdaSlipPerSlipSystem(i,instance)
tempState(3_pInt*ns+2_pInt*nt+1:4_pInt*ns+2_pInt*nt) = invLambdaSlip0
forall (i = 1_pInt:ns) &
MeanFreePathSlip0(i) = &
constitutive_dislokmc_GrainSize(instance)/(1.0_pReal+invLambdaSlip0(i)*constitutive_dislokmc_GrainSize(instance))
tempState(5_pInt*ns+3_pInt*nt+1:6_pInt*ns+3_pInt*nt) = MeanFreePathSlip0
forall (i = 1_pInt:ns) &
tauSlipThreshold0(i) = &
lattice_mu(ph)*constitutive_dislokmc_burgersPerSlipSystem(i,instance) * &
sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislokmc_interactionMatrix_SlipSlip(i,1:ns,instance)))
tempState(6_pInt*ns+4_pInt*nt+1:7_pInt*ns+4_pInt*nt) = tauSlipThreshold0
!--------------------------------------------------------------------------------------------------
! initialize dependent twin microstructural variables
forall (j = 1_pInt:nt) &
MeanFreePathTwin0(j) = constitutive_dislokmc_GrainSize(instance)
tempState(6_pInt*ns+3_pInt*nt+1_pInt:6_pInt*ns+4_pInt*nt) = MeanFreePathTwin0
forall (j = 1_pInt:nt) &
TwinVolume0(j) = &
(pi/4.0_pReal)*constitutive_dislokmc_twinsizePerTwinSystem(j,instance)*MeanFreePathTwin0(j)**(2.0_pReal)
tempState(7_pInt*ns+5_pInt*nt+1_pInt:7_pInt*ns+6_pInt*nt) = TwinVolume0
plasticState(ph)%state0 = spread(tempState,2,size(plasticState(ph)%state(1,:)))
end subroutine constitutive_dislokmc_stateInit
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_aTolState(ph,instance)
use material, only: &
plasticState
implicit none
integer(pInt), intent(in) :: &
ph, &
instance ! number specifying the current instance of the plasticity
! Tolerance state for dislocation densities
plasticState(ph)%aTolState(1_pInt:2_pInt*constitutive_dislokmc_totalNslip(instance)) = &
constitutive_dislokmc_aTolRho(instance)
! Tolerance state for accumulated shear due to slip
plasticState(ph)%aTolState(2_pInt*constitutive_dislokmc_totalNslip(instance)+1_pInt: &
3_pInt*constitutive_dislokmc_totalNslip(instance))=1e6_pReal
! Tolerance state for twin volume fraction
plasticState(ph)%aTolState(3_pInt*constitutive_dislokmc_totalNslip(instance)+1_pInt: &
3_pInt*constitutive_dislokmc_totalNslip(instance)+&
constitutive_dislokmc_totalNtwin(instance)) = &
constitutive_dislokmc_aTolTwinFrac(instance)
! Tolerance state for accumulated shear due to twin
plasticState(ph)%aTolState(3_pInt*constitutive_dislokmc_totalNslip(instance)+ &
constitutive_dislokmc_totalNtwin(instance)+1_pInt: &
3_pInt*constitutive_dislokmc_totalNslip(instance)+ &
2_pInt*constitutive_dislokmc_totalNtwin(instance)) = 1e6_pReal
end subroutine constitutive_dislokmc_aTolState
!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
function constitutive_dislokmc_homogenizedC(ipc,ip,el)
use prec, only: &
p_vec
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
plasticState, &
mappingConstitutive
use lattice, only: &
lattice_C66
implicit none
real(pReal), dimension(6,6) :: &
constitutive_dislokmc_homogenizedC
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
integer(pInt) :: instance,ns,nt,i, &
ph, &
of
real(pReal) :: sumf
!* Shortened notation
of = mappingConstitutive(1,ipc,ip,el)
ph = mappingConstitutive(2,ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!* Total twin volume fraction
sumf = sum(plasticState(ph)%state((3_pInt*ns+1_pInt):(3_pInt*ns+nt),of)) ! safe for nt == 0
!* Homogenized elasticity matrix
constitutive_dislokmc_homogenizedC = (1.0_pReal-sumf)*lattice_C66(1:6,1:6,ph)
do i=1_pInt,nt
constitutive_dislokmc_homogenizedC = constitutive_dislokmc_homogenizedC &
+ plasticState(ph)%state(3_pInt*ns+i, of)*constitutive_dislokmc_Ctwin66(1:6,1:6,i,instance)
enddo
end function constitutive_dislokmc_homogenizedC
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_microstructure(temperature,ipc,ip,el)
use prec, only: &
p_vec
use math, only: &
pi
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
plasticState, &
mappingConstitutive
use lattice, only: &
lattice_structure, &
lattice_mu, &
lattice_nu, &
lattice_bcc_ID, &
lattice_maxNslipFamily
implicit none
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in) :: &
temperature !< temperature at IP
integer(pInt) :: &
instance, &
ns,nt,s,t, &
ph, &
of
real(pReal) :: &
sumf,sfe,x0
real(pReal), dimension(constitutive_dislokmc_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: fOverStacksize
!* Shortened notation
of = mappingConstitutive(1,ipc,ip,el)
ph = mappingConstitutive(2,ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!* State: 1 : ns rho_edge
!* State: ns+1 : 2*ns rho_dipole
!* State: 2*ns+1 : 3*ns accumulated shear due to slip
!* State: 3*ns+1 : 3*ns+nt f
!* State: 3*ns+nt+1 : 3*ns+2*nt accumulated shear due to twin
!* State: 3*ns+2*nt+1 : 4*ns+2*nt 1/lambda_slip
!* State: 4*ns+2*nt+1 : 5*ns+2*nt 1/lambda_sliptwin
!* State: 5*ns+2*nt+1 : 5*ns+3*nt 1/lambda_twin
!* State: 5*ns+3*nt+1 : 6*ns+3*nt mfp_slip
!* State: 6*ns+3*nt+1 : 6*ns+4*nt mfp_twin
!* State: 6*ns+4*nt+1 : 7*ns+4*nt threshold_stress_slip
!* State: 7*ns+4*nt+1 : 7*ns+5*nt threshold_stress_twin
!* State: 7*ns+5*nt+1 : 7*ns+6*nt twin volume
!* Total twin volume fraction
sumf = sum(plasticState(ph)%state((3*ns+1):(3*ns+nt), of)) ! safe for nt == 0
!* Stacking fault energy
sfe = constitutive_dislokmc_SFE_0K(instance) + &
constitutive_dislokmc_dSFE_dT(instance) * Temperature
!* rescaled twin volume fraction for topology
forall (t = 1_pInt:nt) &
fOverStacksize(t) = &
plasticState(ph)%state(3_pInt*ns+t, of)/constitutive_dislokmc_twinsizePerTwinSystem(t,instance)
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
forall (s = 1_pInt:ns) &
plasticState(ph)%state(3_pInt*ns+2_pInt*nt+s, of) = &
sqrt(dot_product((plasticState(ph)%state(1:ns,of)+plasticState(ph)%state(ns+1_pInt:2_pInt*ns,of)),&
constitutive_dislokmc_forestProjectionEdge(1:ns,s,instance)))/ &
constitutive_dislokmc_CLambdaSlipPerSlipSystem(s,instance)
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
!$OMP CRITICAL (evilmatmul)
plasticState(ph)%state((4_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+2_pInt*nt), of) = 0.0_pReal
if (nt > 0_pInt .and. ns > 0_pInt) &
plasticState(ph)%state((4_pInt*ns+2_pInt*nt+1):(5_pInt*ns+2_pInt*nt), of) = &
matmul(constitutive_dislokmc_interactionMatrix_SlipTwin(1:ns,1:nt,instance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
!$OMP END CRITICAL (evilmatmul)
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!$OMP CRITICAL (evilmatmul)
if (nt > 0_pInt) &
plasticState(ph)%state((5_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+3_pInt*nt), of) = &
matmul(constitutive_dislokmc_interactionMatrix_TwinTwin(1:nt,1:nt,instance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
!$OMP END CRITICAL (evilmatmul)
!* mean free path between 2 obstacles seen by a moving dislocation
do s = 1_pInt,ns
if (nt > 0_pInt) then
plasticState(ph)%state(5_pInt*ns+3_pInt*nt+s, of) = &
constitutive_dislokmc_GrainSize(instance)/(1.0_pReal+constitutive_dislokmc_GrainSize(instance)*&
(plasticState(ph)%state(3_pInt*ns+2_pInt*nt+s, of)+plasticState(ph)%state(4_pInt*ns+2_pInt*nt+s, of)))
else
plasticState(ph)%state(5_pInt*ns+s, of) = &
constitutive_dislokmc_GrainSize(instance)/&
(1.0_pReal+constitutive_dislokmc_GrainSize(instance)*(plasticState(ph)%state(3_pInt*ns+s, of)))
endif
enddo
!* mean free path between 2 obstacles seen by a growing twin
forall (t = 1_pInt:nt) &
plasticState(ph)%state(6_pInt*ns+3_pInt*nt+t, of) = &
(constitutive_dislokmc_Cmfptwin(instance)*constitutive_dislokmc_GrainSize(instance))/&
(1.0_pReal+constitutive_dislokmc_GrainSize(instance)*plasticState(ph)%state(5_pInt*ns+2_pInt*nt+t, of))
!* threshold stress for dislocation motion
forall (s = 1_pInt:ns) &
plasticState(ph)%state(6_pInt*ns+4_pInt*nt+s, of) = &
lattice_mu(ph)*constitutive_dislokmc_burgersPerSlipSystem(s,instance)*&
sqrt(dot_product((plasticState(ph)%state(1:ns, of)+plasticState(ph)%state(ns+1_pInt:2_pInt*ns, of)),&
constitutive_dislokmc_interactionMatrix_SlipSlip(s,1:ns,instance)))
!* threshold stress for growing twin
forall (t = 1_pInt:nt) &
plasticState(ph)%state(7_pInt*ns+4_pInt*nt+t, of) = &
constitutive_dislokmc_Cthresholdtwin(instance)*&
(sfe/(3.0_pReal*constitutive_dislokmc_burgersPerTwinSystem(t,instance))+&
3.0_pReal*constitutive_dislokmc_burgersPerTwinSystem(t,instance)*lattice_mu(ph)/&
(constitutive_dislokmc_L0(instance)*constitutive_dislokmc_burgersPerSlipSystem(t,instance)))
!* final twin volume after growth
forall (t = 1_pInt:nt) &
plasticState(ph)%state(7_pInt*ns+5_pInt*nt+t, of) = &
(pi/4.0_pReal)*constitutive_dislokmc_twinsizePerTwinSystem(t,instance)*plasticState(ph)%state(6*ns+3*nt+t, of)**(2.0_pReal)
!* equilibrium seperation of partial dislocations
do t = 1_pInt,nt
x0 = lattice_mu(ph)*constitutive_dislokmc_burgersPerTwinSystem(t,instance)**(2.0_pReal)/&
(sfe*8.0_pReal*pi)*(2.0_pReal+lattice_nu(ph))/(1.0_pReal-lattice_nu(ph))
constitutive_dislokmc_tau_r(t,instance)= &
lattice_mu(ph)*constitutive_dislokmc_burgersPerTwinSystem(t,instance)/(2.0_pReal*pi)*&
(1/(x0+constitutive_dislokmc_xc(instance))+cos(pi/3.0_pReal)/x0) !!! used where??
enddo
end subroutine constitutive_dislokmc_microstructure
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
p_vec, &
tol_math_check
use math, only: &
math_Plain3333to99, &
math_Mandel6to33, &
math_Mandel33to6, &
math_spectralDecompositionSym33, &
math_tensorproduct, &
math_symmetric33, &
math_mul33x3
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
plasticState, &
mappingConstitutive
use lattice, only: &
lattice_Sslip, &
lattice_Sslip_v, &
lattice_Stwin, &
lattice_Stwin_v, &
lattice_maxNslipFamily,&
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_shearTwin, &
lattice_structure, &
lattice_fcc_twinNucleationSlipPair, &
LATTICE_fcc_ID
implicit none
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
real(pReal), dimension(3,3), intent(out) :: Lp
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar
integer(pInt) :: instance,ph,of,ns,nt,f,i,j,k,l,m,n,index_myFamily,s1,s2
real(pReal) :: sumf,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0, &
StressRatio_u,StressRatio_uminus1
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
real(pReal), dimension(constitutive_dislokmc_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip,dgdot_dtauslip,tau_slip,vel_slip,dvel_slip
real(pReal), dimension(constitutive_dislokmc_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_twin,dgdot_dtautwin,tau_twin
real(pReal), dimension(6) :: gdot_sb,dgdot_dtausb,tau_sb
real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix
real(pReal), dimension(3) :: eigValues, sb_s, sb_m
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])
logical error
!* Shortened notation
of = mappingConstitutive(1,ipc,ip,el)
ph = mappingConstitutive(2,ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!* Total twin volume fraction
sumf = sum(plasticState(ph)%state((3_pInt*ns+1_pInt):(3_pInt*ns+nt), of)) ! safe for nt == 0
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar = 0.0_pReal
!* Dislocation glide part
gdot_slip = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
j = 0_pInt
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystemsLoop: do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance)
j = j+1_pInt
!* Calculation of Lp
!* Resolved shear stress on slip system
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
if((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of)) > tol_math_check) then
!* Stress ratios
StressRatio_p = ((abs(tau_slip(j))- plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_pPerSlipFamily(f,instance)
StressRatio_pminus1 = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_pPerSlipFamily(f,instance)-1.0_pReal)
StressRatio_u = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_uPerSlipFamily(f,instance)
StressRatio_uminus1 = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_uPerSlipFamily(f,instance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
plasticState(ph)%state(j, of)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)*&
constitutive_dislokmc_v0PerSlipSystem(j,instance)
!* Shear rates due to slip
vel_slip(j) = exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)) &
* (1.0_pReal-constitutive_dislokmc_sPerSlipFamily(f,instance) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)))
gdot_slip(j) = (1.0_pReal - sumf) * DotGamma0 &
* StressRatio_u * vel_slip(j) &
* sign(1.0_pReal,tau_slip(j))
!* Derivatives of shear rates
dvel_slip(j) = &
(abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)))&
*BoltzmannRatio*constitutive_dislokmc_pPerSlipFamily(f,instance)&
*constitutive_dislokmc_qPerSlipFamily(f,instance)/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislokmc_qPerSlipFamily(f,instance)-1.0_pReal) )&
*(1.0_pReal - 2.0_pReal*constitutive_dislokmc_sPerSlipFamily(f,instance)&
*abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance))))
dgdot_dtauslip(j) = &
(1.0_pReal - sumf) * DotGamma0 * &
( constitutive_dislokmc_uPerSlipFamily(f,instance)*StressRatio_uminus1 &
/(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance))&
* vel_slip(j) &
+ StressRatio_u * dvel_slip(j) )
endif
!* Plastic velocity gradient for dislocation glide
Lp = Lp + gdot_slip(j)*lattice_Sslip(:,:,1,index_myFamily+i,ph)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*&
lattice_Sslip(k,l,1,index_myFamily+i,ph)*&
lattice_Sslip(m,n,1,index_myFamily+i,ph)
enddo slipSystemsLoop
enddo slipFamiliesLoop
!* Shear banding (shearband) part
if(constitutive_dislokmc_sbVelocity(instance) /= 0.0_pReal .and. &
constitutive_dislokmc_sbResistance(instance) /= 0.0_pReal) then
gdot_sb = 0.0_pReal
dgdot_dtausb = 0.0_pReal
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
do j = 1_pInt,6_pInt
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j))
sb_m = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_mComposition(1:3,j))
sb_Smatrix = math_tensorproduct(sb_s,sb_m)
constitutive_dislokmc_sbSv(1:6,j,ipc,ip,el) = math_Mandel33to6(math_symmetric33(sb_Smatrix))
!* Calculation of Lp
!* Resolved shear stress on shear banding system
tau_sb(j) = dot_product(Tstar_v,constitutive_dislokmc_sbSv(1:6,j,ipc,ip,el))
!* Stress ratios
if (abs(tau_sb(j)) < tol_math_check) then
StressRatio_p = 0.0_pReal
StressRatio_pminus1 = 0.0_pReal
else
StressRatio_p = (abs(tau_sb(j))/constitutive_dislokmc_sbResistance(instance))&
**constitutive_dislokmc_pShearBand(instance)
StressRatio_pminus1 = (abs(tau_sb(j))/constitutive_dislokmc_sbResistance(instance))&
**(constitutive_dislokmc_pShearBand(instance)-1.0_pReal)
endif
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_sbQedge(instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = constitutive_dislokmc_sbVelocity(instance)
!* Shear rates due to shearband
gdot_sb(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
constitutive_dislokmc_qShearBand(instance))*sign(1.0_pReal,tau_sb(j))
!* Derivatives of shear rates
dgdot_dtausb(j) = &
((abs(gdot_sb(j))*BoltzmannRatio*&
constitutive_dislokmc_pShearBand(instance)*constitutive_dislokmc_qShearBand(instance))/&
constitutive_dislokmc_sbResistance(instance))*&
StressRatio_pminus1*(1_pInt-StressRatio_p)**(constitutive_dislokmc_qShearBand(instance)-1.0_pReal)
!* Plastic velocity gradient for shear banding
Lp = Lp + gdot_sb(j)*sb_Smatrix
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtausb(j)*&
sb_Smatrix(k,l)*&
sb_Smatrix(m,n)
enddo
end if
!* Mechanical twinning part
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
j = 0_pInt
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystemsLoop: do i = 1_pInt,constitutive_dislokmc_Ntwin(f,instance)
j = j+1_pInt
!* Calculation of Lp
!* Resolved shear stress on twin system
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
!* Stress ratios
if (tau_twin(j) > tol_math_check) then
StressRatio_r = (plasticState(ph)%state(7*ns+4*nt+j, of)/tau_twin(j))**constitutive_dislokmc_rPerTwinFamily(f,instance)
!* Shear rates and their derivatives due to twin
select case(lattice_structure(ph))
case (LATTICE_fcc_ID)
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
if (tau_twin(j) < constitutive_dislokmc_tau_r(j,instance)) then
Ndot0=(abs(gdot_slip(s1))*(plasticState(ph)%state(s2,of)+plasticState(ph)%state(ns+s2, of))+&
abs(gdot_slip(s2))*(plasticState(ph)%state(s1, of)+plasticState(ph)%state(ns+s1, of)))/&
(constitutive_dislokmc_L0(instance)*constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
(1.0_pReal-exp(-constitutive_dislokmc_VcrossSlip(instance)/(kB*Temperature)*&
(constitutive_dislokmc_tau_r(j,instance)-tau_twin(j))))
else
Ndot0=0.0_pReal
end if
case default
Ndot0=constitutive_dislokmc_Ndot0PerTwinSystem(j,instance)
end select
gdot_twin(j) = &
(constitutive_dislokmc_MaxTwinFraction(instance)-sumf)*lattice_shearTwin(index_myFamily+i,ph)*&
plasticState(ph)%state(7*ns+5*nt+j, of)*Ndot0*exp(-StressRatio_r)
dgdot_dtautwin(j) = ((gdot_twin(j)*constitutive_dislokmc_rPerTwinFamily(f,instance))/tau_twin(j))*StressRatio_r
endif
!* Plastic velocity gradient for mechanical twinning
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,ph)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtautwin(j)*&
lattice_Stwin(k,l,index_myFamily+i,ph)*&
lattice_Stwin(m,n,index_myFamily+i,ph)
enddo twinSystemsLoop
enddo twinFamiliesLoop
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
end subroutine constitutive_dislokmc_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_dotState(Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
p_vec, &
tol_math_check
use math, only: &
pi
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
plasticState, &
mappingConstitutive
use lattice, only: &
lattice_Sslip_v, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_sheartwin, &
lattice_mu, &
lattice_structure, &
lattice_fcc_twinNucleationSlipPair, &
LATTICE_fcc_ID, &
LATTICE_bcc_ID
implicit none
real(pReal), dimension(6), intent(in):: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
integer(pInt) :: instance,ns,nt,f,i,j,index_myFamily,s1,s2, &
ph, &
of
real(pReal) :: sumf,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_u,StressRatio_uminus1,&
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0
real(pReal), dimension(constitutive_dislokmc_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip,tau_slip,DotRhoMultiplication,EdgeDipDistance,DotRhoEdgeEdgeAnnihilation,DotRhoEdgeDipAnnihilation,&
ClimbVelocity,DotRhoEdgeDipClimb,DotRhoDipFormation
real(pReal), dimension(constitutive_dislokmc_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
tau_twin
!* Shortened notation
of = mappingConstitutive(1,ipc,ip,el)
ph = mappingConstitutive(2,ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!* Total twin volume fraction
sumf = sum(plasticState(ph)%state((3_pInt*ns+1_pInt):(3_pInt*ns+nt), of)) ! safe for nt == 0
plasticState(ph)%dotState(:,of) = 0.0_pReal
!* Dislocation density evolution
gdot_slip = 0.0_pReal
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j+1_pInt
!* Resolved shear stress on slip system
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
if((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of)) > tol_math_check) then
!* Stress ratios
StressRatio_p = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_pPerSlipFamily(f,instance)
StressRatio_pminus1 = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_pPerSlipFamily(f,instance)-1.0_pReal)
StressRatio_u = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_uPerSlipFamily(f,instance)
StressRatio_uminus1 = ((abs(tau_slip(j))-plasticState(ph)%state(6*ns+4*nt+j,of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_uPerSlipFamily(f,instance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
plasticState(ph)%state(j, of)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)*&
constitutive_dislokmc_v0PerSlipSystem(j,instance)
!* Shear rates due to slip
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)** &
constitutive_dislokmc_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau_slip(j)) &
* (1_pInt-constitutive_dislokmc_sPerSlipFamily(f,instance) &
* exp(-BoltzmannRatio*(1_pInt-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance))) &
* StressRatio_u
endif
!* Multiplication
DotRhoMultiplication(j) = abs(gdot_slip(j))/&
(constitutive_dislokmc_burgersPerSlipSystem(j,instance)* &
plasticState(ph)%state(5*ns+3*nt+j, of))
!* Dipole formation
EdgeDipMinDistance = &
constitutive_dislokmc_CEdgeDipMinDistance(instance)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)
if (tau_slip(j) == 0.0_pReal) then
DotRhoDipFormation(j) = 0.0_pReal
else
EdgeDipDistance(j) = &
(3.0_pReal*lattice_mu(ph)*constitutive_dislokmc_burgersPerSlipSystem(j,instance))/&
(16.0_pReal*pi*abs(tau_slip(j)))
if (EdgeDipDistance(j)>plasticState(ph)%state(5*ns+3*nt+j, of)) EdgeDipDistance(j)=plasticState(ph)%state(5*ns+3*nt+j, of)
if (EdgeDipDistance(j)<EdgeDipMinDistance) EdgeDipDistance(j)=EdgeDipMinDistance
DotRhoDipFormation(j) = &
((2.0_pReal*EdgeDipDistance(j))/constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
plasticState(ph)%state(j, of)*abs(gdot_slip(j))*constitutive_dislokmc_dipoleFormationFactor(instance)
endif
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation(j) = &
((2.0_pReal*EdgeDipMinDistance)/constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
plasticState(ph)%state(j, of)*abs(gdot_slip(j))
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation(j) = &
((2.0_pReal*EdgeDipMinDistance)/constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
plasticState(ph)%state(ns+j, of)*abs(gdot_slip(j))
!* Dislocation dipole climb
AtomicVolume = &
constitutive_dislokmc_CAtomicVolume(instance)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)**(3.0_pReal)
VacancyDiffusion = &
constitutive_dislokmc_D0(instance)*exp(-constitutive_dislokmc_Qsd(instance)/(kB*Temperature))
if (tau_slip(j) == 0.0_pReal) then
DotRhoEdgeDipClimb(j) = 0.0_pReal
else
ClimbVelocity(j) = &
((3.0_pReal*lattice_mu(ph)*VacancyDiffusion*AtomicVolume)/(2.0_pReal*pi*kB*Temperature))*&
(1/(EdgeDipDistance(j)+EdgeDipMinDistance))
DotRhoEdgeDipClimb(j) = &
(4.0_pReal*ClimbVelocity(j)*plasticState(ph)%state(ns+j, of))/(EdgeDipDistance(j)-EdgeDipMinDistance)
endif
!* Edge dislocation density rate of change
plasticState(ph)%dotState(j, of) = &
DotRhoMultiplication(j)-DotRhoDipFormation(j)-DotRhoEdgeEdgeAnnihilation(j)
!* Edge dislocation dipole density rate of change
plasticState(ph)%dotState(ns+j, of) = &
DotRhoDipFormation(j)-DotRhoEdgeDipAnnihilation(j)-DotRhoEdgeDipClimb(j)
!* Dotstate for accumulated shear due to slip
plasticState(ph)%dotState(2_pInt*ns+j, of) = gdot_slip(j)
enddo
enddo
!* Twin volume fraction evolution
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Ntwin(f,instance) ! process each (active) twin system in family
j = j+1_pInt
!* Resolved shear stress on twin system
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
!* Stress ratios
if (tau_twin(j) > tol_math_check) then
StressRatio_r = (plasticState(ph)%state(7*ns+4*nt+j, of)/tau_twin(j))**constitutive_dislokmc_rPerTwinFamily(f,instance)
!* Shear rates and their derivatives due to twin
select case(lattice_structure(ph))
case (LATTICE_fcc_ID)
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
if (tau_twin(j) < constitutive_dislokmc_tau_r(j,instance)) then
Ndot0=(abs(gdot_slip(s1))*(plasticState(ph)%state(s2, of)+plasticState(ph)%state(ns+s2, of))+&
abs(gdot_slip(s2))*(plasticState(ph)%state(s1, of)+plasticState(ph)%state(ns+s1, of)))/&
(constitutive_dislokmc_L0(instance)*constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
(1.0_pReal-exp(-constitutive_dislokmc_VcrossSlip(instance)/(kB*Temperature)*&
(constitutive_dislokmc_tau_r(j,instance)-tau_twin(j))))
else
Ndot0=0.0_pReal
end if
case default
Ndot0=constitutive_dislokmc_Ndot0PerTwinSystem(j,instance)
end select
plasticState(ph)%dotState(3_pInt*ns+j, of) = &
(constitutive_dislokmc_MaxTwinFraction(instance)-sumf)*&
plasticState(ph)%state(7_pInt*ns+5_pInt*nt+j, of)*Ndot0*exp(-StressRatio_r)
!* Dotstate for accumulated shear due to twin
plasticState(ph)%dotState(3_pInt*ns+nt+j, of) = plasticState(ph)%dotState(3_pInt*ns+j, of) * &
lattice_sheartwin(index_myfamily+i,ph)
endif
enddo
enddo
end subroutine constitutive_dislokmc_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function constitutive_dislokmc_postResults(Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
p_vec, &
tol_math_check
use math, only: &
pi, &
math_Mandel6to33, &
math_spectralDecompositionSym33
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains,&
material_phase, &
phase_plasticityInstance,&
phase_Noutput, &
plasticState, &
mappingConstitutive
use lattice, only: &
lattice_Sslip_v, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_shearTwin, &
lattice_mu, &
lattice_structure, &
lattice_fcc_twinNucleationSlipPair, &
LATTICE_fcc_ID
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), dimension(constitutive_dislokmc_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
constitutive_dislokmc_postResults
integer(pInt) :: &
instance,phase,&
ns,nt,&
f,o,i,c,j,index_myFamily,&
s1,s2, &
ph, &
of
real(pReal) :: sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,Ndot0,dgdot_dtauslip
real(pReal) :: dvel_slip
real(pReal) :: StressRatio_u,StressRatio_uminus1
real(preal), dimension(constitutive_dislokmc_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip, vel_slip
real(pReal), dimension(3,3) :: eigVectors
real(pReal), dimension (3) :: eigValues
logical :: error
!* Shortened notation
of = mappingConstitutive(1,ipc,ip,el)
ph = mappingConstitutive(2,ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = constitutive_dislokmc_totalNslip(instance)
nt = constitutive_dislokmc_totalNtwin(instance)
!* Total twin volume fraction
sumf = sum(plasticState(ph)%state((3_pInt*ns+1_pInt):(3_pInt*ns+nt), of)) ! safe for nt == 0
!* Required output
c = 0_pInt
constitutive_dislokmc_postResults = 0.0_pReal
!* Spectral decomposition of stress
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
do o = 1_pInt,constitutive_dislokmc_Noutput(instance)
select case(constitutive_dislokmc_outputID(o,instance))
case (edge_density_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+ns) = plasticState(ph)%state(1_pInt:ns, of)
c = c + ns
case (dipole_density_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+ns) = plasticState(ph)%state(ns+1_pInt:2_pInt*ns, of)
c = c + ns
case (shear_rate_slip_ID)
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
!* Stress ratios
if((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of)) > tol_math_check) then
!* Stress ratios
StressRatio_p = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_pPerSlipFamily(f,instance)
StressRatio_pminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_pPerSlipFamily(f,instance)-1.0_pReal)
StressRatio_u = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_uPerSlipFamily(f,instance)
StressRatio_uminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_uPerSlipFamily(f,instance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
plasticState(ph)%state(j, of)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)* &
constitutive_dislokmc_v0PerSlipSystem(j,instance)
!* Shear rates due to slip
constitutive_dislokmc_postResults(c+j) = &
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
constitutive_dislokmc_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau) &
* (1.0_pReal-constitutive_dislokmc_sPerSlipFamily(f,instance) &
* exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislokmc_qPerSlipFamily(f,instance)))
else
constitutive_dislokmc_postResults(c+j) = 0.0_pReal
endif
enddo ; enddo
c = c + ns
case (accumulated_shear_slip_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+ns) = &
plasticState(ph)%state((2_pInt*ns+1_pInt):(3_pInt*ns), of)
c = c + ns
case (mfp_slip_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+ns) =&
plasticState(ph)%state((5_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+3_pInt*nt), of)
c = c + ns
case (resolved_stress_slip_ID)
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislokmc_postResults(c+j) =&
dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
enddo; enddo
c = c + ns
case (threshold_stress_slip_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+ns) = &
plasticState(ph)%state((6_pInt*ns+4_pInt*nt+1_pInt):(7_pInt*ns+4_pInt*nt), of)
c = c + ns
case (edge_dipole_distance_ID)
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislokmc_postResults(c+j) = &
(3.0_pReal*lattice_mu(ph)*constitutive_dislokmc_burgersPerSlipSystem(j,instance))/&
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))))
constitutive_dislokmc_postResults(c+j)=min(constitutive_dislokmc_postResults(c+j),&
plasticState(ph)%state(5*ns+3*nt+j, of))
enddo; enddo
c = c + ns
case (resolved_stress_shearband_ID)
do j = 1_pInt,6_pInt ! loop over all shearband families
constitutive_dislokmc_postResults(c+j) = dot_product(Tstar_v, &
constitutive_dislokmc_sbSv(1:6,j,ipc,ip,el))
enddo
c = c + 6_pInt
case (shear_rate_shearband_ID)
do j = 1_pInt,6_pInt ! loop over all shearbands
!* Resolved shear stress on shearband system
tau = dot_product(Tstar_v,constitutive_dislokmc_sbSv(1:6,j,ipc,ip,el))
!* Stress ratios
if (abs(tau) < tol_math_check) then
StressRatio_p = 0.0_pReal
StressRatio_pminus1 = 0.0_pReal
else
StressRatio_p = (abs(tau)/constitutive_dislokmc_sbResistance(instance))**&
constitutive_dislokmc_pShearBand(instance)
StressRatio_pminus1 = (abs(tau)/constitutive_dislokmc_sbResistance(instance))**&
(constitutive_dislokmc_pShearBand(instance)-1.0_pReal)
endif
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_sbQedge(instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = constitutive_dislokmc_sbVelocity(instance)
! Shear rate due to shear band
constitutive_dislokmc_postResults(c+j) = &
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislokmc_qShearBand(instance))*&
sign(1.0_pReal,tau)
enddo
c = c + 6_pInt
case (twin_fraction_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+nt) = plasticState(ph)%state((3_pInt*ns+1_pInt):(3_pInt*ns+nt), of)
c = c + nt
case (shear_rate_twin_ID)
if (nt > 0_pInt) then
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
!* Stress ratios
if((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of)) > tol_math_check) then
!* Stress ratios
StressRatio_p = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_pPerSlipFamily(f,instance)
StressRatio_pminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_pPerSlipFamily(f,instance)-1.0_pReal)
StressRatio_u = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_uPerSlipFamily(f,instance)
StressRatio_uminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_uPerSlipFamily(f,instance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
plasticState(ph)%state(j, of)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)* &
constitutive_dislokmc_v0PerSlipSystem(j,instance)
!* Shear rates due to slip
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
constitutive_dislokmc_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau) &
* (1.0_pReal-constitutive_dislokmc_sPerSlipFamily(f,instance) &
* exp(-BoltzmannRatio*(1_pInt-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)) ) &
* StressRatio_u
else
gdot_slip(j) = 0.0_pReal
endif
enddo;enddo
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1,constitutive_dislokmc_Ntwin(f,instance) ! process each (active) twin system in family
j = j + 1_pInt
!* Resolved shear stress on twin system
tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
!* Stress ratios
StressRatio_r = (plasticState(ph)%state(7_pInt*ns+4_pInt*nt+j, of)/ &
tau)**constitutive_dislokmc_rPerTwinFamily(f,instance)
!* Shear rates due to twin
if ( tau > 0.0_pReal ) then
select case(lattice_structure(ph))
case (LATTICE_fcc_ID)
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
if (tau < constitutive_dislokmc_tau_r(j,instance)) then
Ndot0=(abs(gdot_slip(s1))*(plasticState(ph)%state(s2, of)+plasticState(ph)%state(ns+s2, of))+&
abs(gdot_slip(s2))*(plasticState(ph)%state(s1, of)+plasticState(ph)%state(ns+s1, of)))/&
(constitutive_dislokmc_L0(instance)*&
constitutive_dislokmc_burgersPerSlipSystem(j,instance))*&
(1.0_pReal-exp(-constitutive_dislokmc_VcrossSlip(instance)/(kB*Temperature)*&
(constitutive_dislokmc_tau_r(j,instance)-tau)))
else
Ndot0=0.0_pReal
end if
case default
Ndot0=constitutive_dislokmc_Ndot0PerTwinSystem(j,instance)
end select
constitutive_dislokmc_postResults(c+j) = &
(constitutive_dislokmc_MaxTwinFraction(instance)-sumf)*lattice_shearTwin(index_myFamily+i,ph)*&
plasticState(ph)%state(7_pInt*ns+5_pInt*nt+j, of)*Ndot0*exp(-StressRatio_r)
endif
enddo ; enddo
endif
c = c + nt
case (accumulated_shear_twin_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+nt) = plasticState(ph)% &
state((3_pInt*ns+nt+1_pInt) :(3_pInt*ns+2_pInt*nt), of)
c = c + nt
case (mfp_twin_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+nt) = plasticState(ph)% &
state((6_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+4_pInt*nt), of)
c = c + nt
case (resolved_stress_twin_ID)
if (nt > 0_pInt) then
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all slip families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Ntwin(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislokmc_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
enddo; enddo
endif
c = c + nt
case (threshold_stress_twin_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+nt) = plasticState(ph)% &
state((7_pInt*ns+4_pInt*nt+1_pInt):(7_pInt*ns+5_pInt*nt), of)
c = c + nt
case (stress_exponent_ID)
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
do i = 1_pInt,constitutive_dislokmc_Nslip(f,instance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
if((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of)) > tol_math_check) then
!* Stress ratios
StressRatio_p = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_pPerSlipFamily(f,instance)
StressRatio_pminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j, of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+&
constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_pPerSlipFamily(f,instance)-1.0_pReal)
StressRatio_u = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j,of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**constitutive_dislokmc_uPerSlipFamily(f,instance)
StressRatio_uminus1 = ((abs(tau)-plasticState(ph)%state(6*ns+4*nt+j,of))/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance)))&
**(constitutive_dislokmc_uPerSlipFamily(f,instance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
plasticState(ph)%state(j, of)*constitutive_dislokmc_burgersPerSlipSystem(j,instance)* &
constitutive_dislokmc_v0PerSlipSystem(j,instance)
!* Shear rates due to slip
vel_slip(j) = exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)) &
* (1.0_pReal-constitutive_dislokmc_sPerSlipFamily(f,instance) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)))
gdot_slip(j) = (1.0_pReal - sumf) * DotGamma0 &
* StressRatio_u * vel_slip(j) &
* sign(1.0_pReal,tau)
!* Derivatives of shear rates
dvel_slip = &
(abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance)))&
*BoltzmannRatio*constitutive_dislokmc_pPerSlipFamily(f,instance)&
*constitutive_dislokmc_qPerSlipFamily(f,instance)/&
(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislokmc_qPerSlipFamily(f,instance)-1.0_pReal) )&
*(1.0_pReal - 2.0_pReal*constitutive_dislokmc_sPerSlipFamily(f,instance)&
*abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislokmc_qPerSlipFamily(f,instance))))
dgdot_dtauslip = &
(1.0_pReal - sumf) * DotGamma0 * &
( constitutive_dislokmc_uPerSlipFamily(f,instance)*StressRatio_uminus1 &
/(constitutive_dislokmc_SolidSolutionStrength(instance)+constitutive_dislokmc_tau_peierlsPerSlipFamily(f,instance))&
* vel_slip(j) &
+ StressRatio_u * dvel_slip )
else
gdot_slip(j) = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
endif
!* Stress exponent
if (gdot_slip(j)==0.0_pReal) then
constitutive_dislokmc_postResults(c+j) = 0.0_pReal
else
constitutive_dislokmc_postResults(c+j) = (tau/gdot_slip(j))*dgdot_dtauslip
endif
enddo ; enddo
c = c + ns
case (sb_eigenvalues_ID)
forall (j = 1_pInt:3_pInt) &
constitutive_dislokmc_postResults(c+j) = eigValues(j)
c = c + 3_pInt
case (sb_eigenvectors_ID)
constitutive_dislokmc_postResults(c+1_pInt:c+9_pInt) = reshape(eigVectors,[9])
c = c + 9_pInt
end select
enddo
end function constitutive_dislokmc_postResults
end module constitutive_dislokmc
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