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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
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integer ( pInt ) , dimension ( : ) , allocatable , target , public :: &
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constitutive_dislokmc_Noutput !< number of outputs per instance of this plasticity
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integer ( pInt ) , dimension ( : ) , allocatable , public , protected :: &
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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_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_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
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constitutive_dislokmc_rPerTwinFamily , & !< r-exponent in twin nucleation rate
constitutive_dislokmc_nonSchmidCoeff !< non-Schmid coefficients (bcc)
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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
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 , &
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threshold_stress_twin_ID
!resolved_stress_shearband_ID, &
!shear_rate_shearband_ID, &
!sb_eigenvalues_ID, &
!sb_eigenvectors_ID
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end enum
integer ( kind ( undefined_ID ) ) , dimension ( : , : ) , allocatable , private :: &
constitutive_dislokmc_outputID !< ID of each post result output
public :: &
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constitutive_dislokmc_init , &
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constitutive_dislokmc_homogenizedC , &
constitutive_dislokmc_microstructure , &
constitutive_dislokmc_LpAndItsTangent , &
constitutive_dislokmc_dotState , &
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constitutive_dislokmc_getAccumulatedSlip , &
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constitutive_dislokmc_getSlipRate , &
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constitutive_dislokmc_postResults
private :: &
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constitutive_dislokmc_stateInit , &
constitutive_dislokmc_aTolState
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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 : &
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worldrank , &
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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 , &
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Nchunks_SlipFamilies , Nchunks_TwinFamilies , Nchunks_nonSchmid , &
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index_myFamily , index_otherFamily
integer ( pInt ) :: sizeState , sizeDotState
integer ( pInt ) :: NofMyPhase
character ( len = 65536 ) :: &
tag = '' , &
line = ''
real ( pReal ) , dimension ( : ) , allocatable :: tempPerSlip , tempPerTwin
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mainProcess : if ( worldrank == 0 ) then
write ( 6 , '(/,a)' ) ' <<<+- constitutive_' / / PLASTICITY_DISLOKMC_label / / ' init -+>>>'
write ( 6 , '(a)' ) ' $Id$'
write ( 6 , '(a15,a)' ) ' Current time: ' , IO_timeStamp ( )
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#include "compilation_info.f90"
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endif mainProcess
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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_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_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 )
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allocate ( constitutive_dislokmc_nonSchmidCoeff ( lattice_maxNnonSchmid , maxNinstance ) , &
source = 0.0_pReal )
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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 ) )
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Nchunks_nonSchmid = lattice_NnonSchmid ( phase )
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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 ) )
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
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!--------------------------------------------------------------------------------------------------
! 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
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case ( 'nonschmid_coefficients' )
if ( positions ( 1 ) < 1_pInt + Nchunks_nonSchmid ) &
call IO_warning ( 52_pInt , ext_msg = trim ( tag ) / / ' (' / / PLASTICITY_DISLOKMC_label / / ')' )
do j = 1_pInt , Nchunks_nonSchmid
constitutive_dislokmc_nonSchmidCoeff ( j , instance ) = IO_floatValue ( line , positions , 1_pInt + j )
enddo
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!--------------------------------------------------------------------------------------------------
! parameters independent of number of slip/twin systems
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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 ( '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 )
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_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 / / ')' )
!--------------------------------------------------------------------------------------------------
! 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 )
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myPhase2 : if ( phase_plasticity ( phase ) == PLASTICITY_dislokmc_ID ) then
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NofMyPhase = count ( material_phase == phase )
instance = phase_plasticityInstance ( phase )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
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!--------------------------------------------------------------------------------------------------
! 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
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
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sizeDotState = int ( size ( CONSTITUTIVE_DISLOKMC_listBasicSlipStates ) , pInt ) * ns &
+ int ( size ( CONSTITUTIVE_DISLOKMC_listBasicTwinStates ) , pInt ) * nt
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sizeState = sizeDotState &
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+ int ( size ( CONSTITUTIVE_DISLOKMC_listDependentSlipStates ) , pInt ) * ns &
+ int ( size ( CONSTITUTIVE_DISLOKMC_listDependentTwinStates ) , pInt ) * nt
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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
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end subroutine constitutive_dislokmc_init
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!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislokmc_stateInit ( ph , instance )
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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
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real ( pReal ) , dimension ( constitutive_dislokmc_totalNslip ( instance ) ) :: &
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rhoEdge0 , &
rhoEdgeDip0 , &
invLambdaSlip0 , &
MeanFreePathSlip0 , &
tauSlipThreshold0
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real ( pReal ) , dimension ( constitutive_dislokmc_totalNtwin ( instance ) ) :: &
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MeanFreePathTwin0 , TwinVolume0
tempState = 0.0_pReal
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
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!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables
do f = 1_pInt , lattice_maxNslipFamily
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index_myFamily = sum ( constitutive_dislokmc_Nslip ( 1 : f - 1_pInt , instance ) ) ! index in truncated slip system list
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rhoEdge0 ( index_myFamily + 1_pInt : &
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index_myFamily + constitutive_dislokmc_Nslip ( f , instance ) ) = &
constitutive_dislokmc_rhoEdge0 ( f , instance )
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rhoEdgeDip0 ( index_myFamily + 1_pInt : &
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index_myFamily + constitutive_dislokmc_Nslip ( f , instance ) ) = &
constitutive_dislokmc_rhoEdgeDip0 ( f , instance )
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enddo
tempState ( 1_pInt : ns ) = rhoEdge0
tempState ( ns + 1_pInt : 2_pInt * ns ) = rhoEdgeDip0
!--------------------------------------------------------------------------------------------------
! initialize dependent slip microstructural variables
forall ( i = 1_pInt : ns ) &
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invLambdaSlip0 ( i ) = sqrt ( dot_product ( ( rhoEdge0 + rhoEdgeDip0 ) , constitutive_dislokmc_forestProjectionEdge ( 1 : ns , i , instance ) ) ) / &
constitutive_dislokmc_CLambdaSlipPerSlipSystem ( i , instance )
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tempState ( 3_pInt * ns + 2_pInt * nt + 1 : 4_pInt * ns + 2_pInt * nt ) = invLambdaSlip0
forall ( i = 1_pInt : ns ) &
MeanFreePathSlip0 ( i ) = &
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constitutive_dislokmc_GrainSize ( instance ) / ( 1.0_pReal + invLambdaSlip0 ( i ) * constitutive_dislokmc_GrainSize ( instance ) )
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tempState ( 5_pInt * ns + 3_pInt * nt + 1 : 6_pInt * ns + 3_pInt * nt ) = MeanFreePathSlip0
forall ( i = 1_pInt : ns ) &
tauSlipThreshold0 ( i ) = &
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lattice_mu ( ph ) * constitutive_dislokmc_burgersPerSlipSystem ( i , instance ) * &
sqrt ( dot_product ( ( rhoEdge0 + rhoEdgeDip0 ) , constitutive_dislokmc_interactionMatrix_SlipSlip ( i , 1 : ns , instance ) ) )
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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 ) &
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MeanFreePathTwin0 ( j ) = constitutive_dislokmc_GrainSize ( instance )
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tempState ( 6_pInt * ns + 3_pInt * nt + 1_pInt : 6_pInt * ns + 4_pInt * nt ) = MeanFreePathTwin0
forall ( j = 1_pInt : nt ) &
TwinVolume0 ( j ) = &
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( pi / 4.0_pReal ) * constitutive_dislokmc_twinsizePerTwinSystem ( j , instance ) * MeanFreePathTwin0 ( j ) ** ( 2.0_pReal )
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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 , : ) ) )
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end subroutine constitutive_dislokmc_stateInit
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!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislokmc_aTolState ( ph , instance )
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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
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plasticState ( ph ) % aTolState ( 1_pInt : 2_pInt * constitutive_dislokmc_totalNslip ( instance ) ) = &
constitutive_dislokmc_aTolRho ( instance )
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! Tolerance state for accumulated shear due to slip
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plasticState ( ph ) % aTolState ( 2_pInt * constitutive_dislokmc_totalNslip ( instance ) + 1_pInt : &
3_pInt * constitutive_dislokmc_totalNslip ( instance ) ) = 1e6_pReal
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! Tolerance state for twin volume fraction
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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 )
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! Tolerance state for accumulated shear due to twin
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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
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end subroutine constitutive_dislokmc_aTolState
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!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
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function constitutive_dislokmc_homogenizedC ( ipc , ip , el )
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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 ) :: &
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constitutive_dislokmc_homogenizedC
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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 )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
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!* 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
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constitutive_dislokmc_homogenizedC = ( 1.0_pReal - sumf ) * lattice_C66 ( 1 : 6 , 1 : 6 , ph )
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do i = 1_pInt , nt
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constitutive_dislokmc_homogenizedC = constitutive_dislokmc_homogenizedC &
+ plasticState ( ph ) % state ( 3_pInt * ns + i , of ) * constitutive_dislokmc_Ctwin66 ( 1 : 6 , 1 : 6 , i , instance )
enddo
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end function constitutive_dislokmc_homogenizedC
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!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislokmc_microstructure ( temperature , ipc , ip , el )
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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
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real ( pReal ) , dimension ( constitutive_dislokmc_totalNtwin ( phase_plasticityInstance ( material_phase ( ipc , ip , el ) ) ) ) :: fOverStacksize
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!* Shortened notation
of = mappingConstitutive ( 1 , ipc , ip , el )
ph = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( ph )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
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!* 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
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sfe = constitutive_dislokmc_SFE_0K ( instance ) + &
constitutive_dislokmc_dSFE_dT ( instance ) * Temperature
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!* rescaled twin volume fraction for topology
forall ( t = 1_pInt : nt ) &
fOverStacksize ( t ) = &
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plasticState ( ph ) % state ( 3_pInt * ns + t , of ) / constitutive_dislokmc_twinsizePerTwinSystem ( t , instance )
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!* 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 ) ) , &
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constitutive_dislokmc_forestProjectionEdge ( 1 : ns , s , instance ) ) ) / &
constitutive_dislokmc_CLambdaSlipPerSlipSystem ( s , instance )
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!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
!$OMP CRITICAL (evilmatmul)
plasticState ( ph ) % state ( ( 4_pInt * ns + 2_pInt * nt + 1_pInt ) : ( 5_pInt * ns + 2_pInt * nt ) , of ) = 0.0_pReal
if ( nt > 0_pInt . and . ns > 0_pInt ) &
plasticState ( ph ) % state ( ( 4_pInt * ns + 2_pInt * nt + 1 ) : ( 5_pInt * ns + 2_pInt * nt ) , of ) = &
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matmul ( constitutive_dislokmc_interactionMatrix_SlipTwin ( 1 : ns , 1 : nt , instance ) , fOverStacksize ( 1 : nt ) ) / ( 1.0_pReal - sumf )
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!$OMP END CRITICAL (evilmatmul)
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!$OMP CRITICAL (evilmatmul)
if ( nt > 0_pInt ) &
plasticState ( ph ) % state ( ( 5_pInt * ns + 2_pInt * nt + 1_pInt ) : ( 5_pInt * ns + 3_pInt * nt ) , of ) = &
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matmul ( constitutive_dislokmc_interactionMatrix_TwinTwin ( 1 : nt , 1 : nt , instance ) , fOverStacksize ( 1 : nt ) ) / ( 1.0_pReal - sumf )
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!$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 ) = &
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constitutive_dislokmc_GrainSize ( instance ) / ( 1.0_pReal + constitutive_dislokmc_GrainSize ( instance ) * &
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( 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 ) = &
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constitutive_dislokmc_GrainSize ( instance ) / &
( 1.0_pReal + constitutive_dislokmc_GrainSize ( instance ) * ( plasticState ( ph ) % state ( 3_pInt * ns + s , of ) ) )
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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 ) = &
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( 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 ) )
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!* threshold stress for dislocation motion
forall ( s = 1_pInt : ns ) &
plasticState ( ph ) % state ( 6_pInt * ns + 4_pInt * nt + s , of ) = &
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lattice_mu ( ph ) * constitutive_dislokmc_burgersPerSlipSystem ( s , instance ) * &
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sqrt ( dot_product ( ( plasticState ( ph ) % state ( 1 : ns , of ) + plasticState ( ph ) % state ( ns + 1_pInt : 2_pInt * ns , of ) ) , &
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constitutive_dislokmc_interactionMatrix_SlipSlip ( s , 1 : ns , instance ) ) )
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!* threshold stress for growing twin
forall ( t = 1_pInt : nt ) &
plasticState ( ph ) % state ( 7_pInt * ns + 4_pInt * nt + t , of ) = &
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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 ) ) )
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!* final twin volume after growth
forall ( t = 1_pInt : nt ) &
plasticState ( ph ) % state ( 7_pInt * ns + 5_pInt * nt + t , of ) = &
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( pi / 4.0_pReal ) * constitutive_dislokmc_twinsizePerTwinSystem ( t , instance ) * plasticState ( ph ) % state ( 6 * ns + 3 * nt + t , of ) ** ( 2.0_pReal )
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!* equilibrium seperation of partial dislocations
do t = 1_pInt , nt
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x0 = lattice_mu ( ph ) * constitutive_dislokmc_burgersPerTwinSystem ( t , instance ) ** ( 2.0_pReal ) / &
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( sfe * 8.0_pReal * pi ) * ( 2.0_pReal + lattice_nu ( ph ) ) / ( 1.0_pReal - lattice_nu ( ph ) )
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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??
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enddo
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end subroutine constitutive_dislokmc_microstructure
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!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislokmc_LpAndItsTangent ( Lp , dLp_dTstar , Tstar_v , Temperature , slipDamage , ipc , ip , el )
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use prec , only : &
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 , &
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phase_plasticityInstance , &
plasticState , &
mappingConstitutive
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use lattice , only : &
lattice_Sslip , &
lattice_Sslip_v , &
lattice_Stwin , &
lattice_Stwin_v , &
lattice_maxNslipFamily , &
lattice_maxNtwinFamily , &
lattice_NslipSystem , &
lattice_NtwinSystem , &
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lattice_NnonSchmid , &
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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
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real ( pReal ) , &
dimension ( constitutive_dislokmc_totalNslip ( phase_plasticityInstance ( material_phase ( ipc , ip , el ) ) ) ) , &
intent ( in ) :: &
slipDamage
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real ( pReal ) , dimension ( 3 , 3 ) , intent ( out ) :: Lp
real ( pReal ) , dimension ( 9 , 9 ) , intent ( out ) :: dLp_dTstar
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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 , &
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StressRatio_u , StressRatio_uminus1 , tau_slip_pos , tau_slip_neg , vel_slip , dvel_slip , &
dgdot_dtauslip_pos , dgdot_dtauslip_neg , dgdot_dtautwin , tau_twin , gdot_twin
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real ( pReal ) , dimension ( 3 , 3 , 2 ) :: &
nonSchmid_tensor
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: &
dLp_dTstar3333
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real ( pReal ) , dimension ( constitutive_dislokmc_totalNslip ( phase_plasticityInstance ( material_phase ( ipc , ip , el ) ) ) ) :: &
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gdot_slip_pos , gdot_slip_neg
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!* Shortened notation
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of = mappingConstitutive ( 1 , ipc , ip , el )
ph = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( ph )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
!* Total twin volume fraction
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sumf = sum ( plasticState ( ph ) % state ( ( 3_pInt * ns + 1_pInt ) : ( 3_pInt * ns + nt ) , of ) ) ! safe for nt == 0
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Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar = 0.0_pReal
!* Dislocation glide part
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gdot_slip_pos = 0.0_pReal
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gdot_slip_neg = 0.0_pReal
dgdot_dtauslip_pos = 0.0_pReal
dgdot_dtauslip_neg = 0.0_pReal
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j = 0_pInt
slipFamiliesLoop : do f = 1_pInt , lattice_maxNslipFamily
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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slipSystemsLoop : do i = 1_pInt , constitutive_dislokmc_Nslip ( f , instance )
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j = j + 1_pInt
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!--------------------------------------------------------------------------------------------------
! Calculation of Lp
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tau_slip_pos = dot_product ( Tstar_v , lattice_Sslip_v ( 1 : 6 , 1 , index_myFamily + i , ph ) )
tau_slip_neg = tau_slip_pos
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nonSchmid_tensor ( 1 : 3 , 1 : 3 , 1 ) = lattice_Sslip ( 1 : 3 , 1 : 3 , 1 , index_myFamily + i , ph )
nonSchmid_tensor ( 1 : 3 , 1 : 3 , 2 ) = nonSchmid_tensor ( 1 : 3 , 1 : 3 , 1 )
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nonSchmidSystems : do k = 1 , lattice_NnonSchmid ( ph )
tau_slip_pos = tau_slip_pos + constitutive_dislokmc_nonSchmidCoeff ( k , instance ) * &
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dot_product ( Tstar_v , lattice_Sslip_v ( 1 : 6 , 2 * k , index_myFamily + i , ph ) )
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tau_slip_neg = tau_slip_neg + constitutive_dislokmc_nonSchmidCoeff ( k , instance ) * &
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dot_product ( Tstar_v , lattice_Sslip_v ( 1 : 6 , 2 * k + 1 , index_myFamily + i , ph ) )
nonSchmid_tensor ( 1 : 3 , 1 : 3 , 1 ) = nonSchmid_tensor ( 1 : 3 , 1 : 3 , 1 ) + constitutive_dislokmc_nonSchmidCoeff ( k , instance ) * &
lattice_Sslip ( 1 : 3 , 1 : 3 , 2 * k , index_myFamily + i , ph )
nonSchmid_tensor ( 1 : 3 , 1 : 3 , 2 ) = nonSchmid_tensor ( 1 : 3 , 1 : 3 , 2 ) + constitutive_dislokmc_nonSchmidCoeff ( k , instance ) * &
lattice_Sslip ( 1 : 3 , 1 : 3 , 2 * k + 1 , index_myFamily + i , ph )
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enddo nonSchmidSystems
BoltzmannRatio = constitutive_dislokmc_QedgePerSlipSystem ( j , instance ) / ( kB * Temperature )
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DotGamma0 = &
plasticState ( ph ) % state ( j , of ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
constitutive_dislokmc_v0PerSlipSystem ( j , instance )
significantPostitiveSlip : if ( ( abs ( tau_slip_pos ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) > tol_math_check ) then
!* Stress ratios
StressRatio_p = ( ( abs ( tau_slip_pos ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** constitutive_dislokmc_pPerSlipFamily ( f , instance )
StressRatio_pminus1 = ( ( abs ( tau_slip_pos ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** ( constitutive_dislokmc_pPerSlipFamily ( f , instance ) - 1.0_pReal )
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StressRatio_u = ( ( abs ( tau_slip_pos ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** constitutive_dislokmc_uPerSlipFamily ( f , instance )
StressRatio_uminus1 = ( ( abs ( tau_slip_pos ) - 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 )
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!* Shear rates due to slip
vel_slip = 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 ) ) )
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gdot_slip_pos ( j ) = ( 1.0_pReal - sumf ) * DotGamma0 &
* StressRatio_u * vel_slip &
* sign ( 1.0_pReal , tau_slip_pos )
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!* Derivatives of shear rates
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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 ) ) ) )
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dgdot_dtauslip_pos = ( 1.0_pReal - sumf ) * DotGamma0 * &
( constitutive_dislokmc_uPerSlipFamily ( f , instance ) * StressRatio_uminus1 &
/ ( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) &
* vel_slip &
+ StressRatio_u * dvel_slip )
endif significantPostitiveSlip
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!* Plastic velocity gradient for dislocation glide
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Lp = Lp + ( gdot_slip_pos ( j ) ) * lattice_Sslip ( 1 : 3 , 1 : 3 , 1 , index_myFamily + i , ph )
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!* 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 ) = &
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dLp_dTstar3333 ( k , l , m , n ) + ( dgdot_dtauslip_pos ) * &
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lattice_Sslip ( k , l , 1 , index_myFamily + i , ph ) * &
lattice_Sslip ( m , n , 1 , index_myFamily + i , ph )
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enddo slipSystemsLoop
enddo slipFamiliesLoop
!* Mechanical twinning part
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
j = 0_pInt
twinFamiliesLoop : do f = 1_pInt , lattice_maxNtwinFamily
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index_myFamily = sum ( lattice_NtwinSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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twinSystemsLoop : do i = 1_pInt , constitutive_dislokmc_Ntwin ( f , instance )
j = j + 1_pInt
!* Calculation of Lp
!* Resolved shear stress on twin system
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tau_twin = dot_product ( Tstar_v , lattice_Stwin_v ( : , index_myFamily + i , ph ) )
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!* Stress ratios
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if ( tau_twin > tol_math_check ) then
StressRatio_r = ( plasticState ( ph ) % state ( 7 * ns + 4 * nt + j , of ) / tau_twin ) ** constitutive_dislokmc_rPerTwinFamily ( f , instance )
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!* Shear rates and their derivatives due to twin
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select case ( lattice_structure ( ph ) )
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case ( LATTICE_fcc_ID )
s1 = lattice_fcc_twinNucleationSlipPair ( 1 , index_myFamily + i )
s2 = lattice_fcc_twinNucleationSlipPair ( 2 , index_myFamily + i )
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if ( tau_twin < constitutive_dislokmc_tau_r ( j , instance ) ) then
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Ndot0 = ( abs ( gdot_slip_pos ( s1 ) ) * ( plasticState ( ph ) % state ( s2 , of ) + plasticState ( ph ) % state ( ns + s2 , of ) ) + &
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abs ( gdot_slip_pos ( s2 ) ) * ( plasticState ( ph ) % state ( s1 , of ) + plasticState ( ph ) % state ( ns + s1 , of ) ) ) / &
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( constitutive_dislokmc_L0 ( instance ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) * &
( 1.0_pReal - exp ( - constitutive_dislokmc_VcrossSlip ( instance ) / ( kB * Temperature ) * &
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( constitutive_dislokmc_tau_r ( j , instance ) - tau_twin ) ) )
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else
Ndot0 = 0.0_pReal
end if
case default
Ndot0 = constitutive_dislokmc_Ndot0PerTwinSystem ( j , instance )
end select
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gdot_twin = &
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( constitutive_dislokmc_MaxTwinFraction ( instance ) - sumf ) * lattice_shearTwin ( index_myFamily + i , ph ) * &
plasticState ( ph ) % state ( 7 * ns + 5 * nt + j , of ) * Ndot0 * exp ( - StressRatio_r )
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dgdot_dtautwin = ( ( gdot_twin * constitutive_dislokmc_rPerTwinFamily ( f , instance ) ) / tau_twin ) * StressRatio_r
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endif
!* Plastic velocity gradient for mechanical twinning
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Lp = Lp + gdot_twin * lattice_Stwin ( 1 : 3 , 1 : 3 , index_myFamily + i , ph )
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!* 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 ) = &
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dLp_dTstar3333 ( k , l , m , n ) + dgdot_dtautwin * &
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lattice_Stwin ( k , l , index_myFamily + i , ph ) * &
lattice_Stwin ( m , n , index_myFamily + i , ph )
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enddo twinSystemsLoop
enddo twinFamiliesLoop
dLp_dTstar = math_Plain3333to99 ( dLp_dTstar3333 )
end subroutine constitutive_dislokmc_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislokmc_dotState ( Tstar_v , Temperature , ipc , ip , el )
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use prec , only : &
tol_math_check
use math , only : &
pi
use mesh , only : &
mesh_NcpElems , &
mesh_maxNips
use material , only : &
homogenization_maxNgrains , &
material_phase , &
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phase_plasticityInstance , &
plasticState , &
mappingConstitutive
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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
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integer ( pInt ) :: instance , ns , nt , f , i , j , index_myFamily , s1 , s2 , &
ph , &
of
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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 ) ) ) ) :: &
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gdot_slip_pos , tau_slip_pos , DotRhoMultiplication , EdgeDipDistance , DotRhoEdgeEdgeAnnihilation , DotRhoEdgeDipAnnihilation , &
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ClimbVelocity , DotRhoEdgeDipClimb , DotRhoDipFormation
real ( pReal ) , dimension ( constitutive_dislokmc_totalNtwin ( phase_plasticityInstance ( material_phase ( ipc , ip , el ) ) ) ) :: &
tau_twin
!* Shortened notation
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of = mappingConstitutive ( 1 , ipc , ip , el )
ph = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( ph )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
!* Total twin volume fraction
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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
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!* Dislocation density evolution
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gdot_slip_pos = 0.0_pReal
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j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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tau_slip_pos ( j ) = dot_product ( Tstar_v , lattice_Sslip_v ( : , 1 , index_myFamily + i , ph ) )
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if ( ( abs ( tau_slip_pos ( j ) ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) > tol_math_check ) then
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!* Stress ratios
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StressRatio_p = ( ( abs ( tau_slip_pos ( j ) ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** constitutive_dislokmc_pPerSlipFamily ( f , instance )
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StressRatio_pminus1 = ( ( abs ( tau_slip_pos ( j ) ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** ( constitutive_dislokmc_pPerSlipFamily ( f , instance ) - 1.0_pReal )
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StressRatio_u = ( ( abs ( tau_slip_pos ( j ) ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** constitutive_dislokmc_uPerSlipFamily ( f , instance )
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StressRatio_uminus1 = ( ( abs ( tau_slip_pos ( j ) ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( 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 = &
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plasticState ( ph ) % state ( j , of ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
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constitutive_dislokmc_v0PerSlipSystem ( j , instance )
!* Shear rates due to slip
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gdot_slip_pos ( j ) = DotGamma0 * exp ( - BoltzmannRatio * ( 1.0_pReal - StressRatio_p ) ** &
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constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) * sign ( 1.0_pReal , tau_slip_pos ( j ) ) &
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* ( 1.0_pReal - constitutive_dislokmc_sPerSlipFamily ( f , instance ) &
* exp ( - BoltzmannRatio * ( 1.0_pReal - StressRatio_p ) ** constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) ) &
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* StressRatio_u
endif
!* Multiplication
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DotRhoMultiplication ( j ) = abs ( gdot_slip_pos ( j ) ) / &
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( constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
plasticState ( ph ) % state ( 5 * ns + 3 * nt + j , of ) )
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!* Dipole formation
EdgeDipMinDistance = &
constitutive_dislokmc_CEdgeDipMinDistance ( instance ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance )
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if ( tau_slip_pos ( j ) == 0.0_pReal ) then
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DotRhoDipFormation ( j ) = 0.0_pReal
else
EdgeDipDistance ( j ) = &
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( 3.0_pReal * lattice_mu ( ph ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) / &
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( 1 6.0_pReal * pi * abs ( tau_slip_pos ( j ) ) )
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if ( EdgeDipDistance ( j ) > plasticState ( ph ) % state ( 5 * ns + 3 * nt + j , of ) ) EdgeDipDistance ( j ) = plasticState ( ph ) % state ( 5 * ns + 3 * nt + j , of )
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if ( EdgeDipDistance ( j ) < EdgeDipMinDistance ) EdgeDipDistance ( j ) = EdgeDipMinDistance
DotRhoDipFormation ( j ) = &
( ( 2.0_pReal * EdgeDipDistance ( j ) ) / constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) * &
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plasticState ( ph ) % state ( j , of ) * abs ( gdot_slip_pos ( j ) ) * constitutive_dislokmc_dipoleFormationFactor ( instance )
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endif
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation ( j ) = &
( ( 2.0_pReal * EdgeDipMinDistance ) / constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) * &
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plasticState ( ph ) % state ( j , of ) * abs ( gdot_slip_pos ( j ) )
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!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation ( j ) = &
( ( 2.0_pReal * EdgeDipMinDistance ) / constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) * &
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plasticState ( ph ) % state ( ns + j , of ) * abs ( gdot_slip_pos ( j ) )
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!* 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 ) )
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if ( tau_slip_pos ( j ) == 0.0_pReal ) then
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DotRhoEdgeDipClimb ( j ) = 0.0_pReal
else
ClimbVelocity ( j ) = &
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( ( 3.0_pReal * lattice_mu ( ph ) * VacancyDiffusion * AtomicVolume ) / ( 2.0_pReal * pi * kB * Temperature ) ) * &
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( 1 / ( EdgeDipDistance ( j ) + EdgeDipMinDistance ) )
DotRhoEdgeDipClimb ( j ) = &
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( 4.0_pReal * ClimbVelocity ( j ) * plasticState ( ph ) % state ( ns + j , of ) ) / ( EdgeDipDistance ( j ) - EdgeDipMinDistance )
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endif
!* Edge dislocation density rate of change
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plasticState ( ph ) % dotState ( j , of ) = &
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DotRhoMultiplication ( j ) - DotRhoDipFormation ( j ) - DotRhoEdgeEdgeAnnihilation ( j )
!* Edge dislocation dipole density rate of change
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plasticState ( ph ) % dotState ( ns + j , of ) = &
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DotRhoDipFormation ( j ) - DotRhoEdgeDipAnnihilation ( j ) - DotRhoEdgeDipClimb ( j )
!* Dotstate for accumulated shear due to slip
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plasticState ( ph ) % dotState ( 2_pInt * ns + j , of ) = gdot_slip_pos ( j )
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enddo
enddo
!* Twin volume fraction evolution
j = 0_pInt
do f = 1_pInt , lattice_maxNtwinFamily ! loop over all twin families
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index_myFamily = sum ( lattice_NtwinSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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tau_twin ( j ) = dot_product ( Tstar_v , lattice_Stwin_v ( : , index_myFamily + i , ph ) )
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!* Stress ratios
if ( tau_twin ( j ) > tol_math_check ) then
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StressRatio_r = ( plasticState ( ph ) % state ( 7 * ns + 4 * nt + j , of ) / tau_twin ( j ) ) ** constitutive_dislokmc_rPerTwinFamily ( f , instance )
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!* Shear rates and their derivatives due to twin
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select case ( lattice_structure ( ph ) )
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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
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Ndot0 = ( abs ( gdot_slip_pos ( s1 ) ) * ( plasticState ( ph ) % state ( s2 , of ) + plasticState ( ph ) % state ( ns + s2 , of ) ) + &
abs ( gdot_slip_pos ( s2 ) ) * ( plasticState ( ph ) % state ( s1 , of ) + plasticState ( ph ) % state ( ns + s1 , of ) ) ) / &
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( 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
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plasticState ( ph ) % dotState ( 3_pInt * ns + j , of ) = &
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( constitutive_dislokmc_MaxTwinFraction ( instance ) - sumf ) * &
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plasticState ( ph ) % state ( 7_pInt * ns + 5_pInt * nt + j , of ) * Ndot0 * exp ( - StressRatio_r )
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!* Dotstate for accumulated shear due to twin
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plasticState ( ph ) % dotState ( 3_pInt * ns + nt + j , of ) = plasticState ( ph ) % dotState ( 3_pInt * ns + j , of ) * &
lattice_sheartwin ( index_myfamily + i , ph )
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endif
enddo
enddo
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end subroutine constitutive_dislokmc_dotState
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!--------------------------------------------------------------------------------------------------
!> @brief returns accumulated slip
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_getAccumulatedSlip ( nSlip , accumulatedSlip , ipc , ip , el )
use lattice , only : &
lattice_maxNslipFamily
use material , only : &
mappingConstitutive , &
plasticState , &
phase_plasticityInstance
implicit none
real ( pReal ) , dimension ( : ) , allocatable :: &
accumulatedSlip
integer ( pInt ) :: &
nSlip
integer ( pInt ) , intent ( in ) :: &
ipc , & !< grain number
ip , & !< integration point number
el !< element number
integer ( pInt ) :: &
offset , &
phase , &
instance , &
offset_accshear_slip , &
f , j , i
offset = mappingConstitutive ( 1 , ipc , ip , el )
phase = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( phase )
nSlip = constitutive_dislokmc_totalNslip ( instance )
allocate ( accumulatedSlip ( nSlip ) )
offset_accshear_slip = 2_pInt * nSlip
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
do i = 1_pInt , constitutive_dislokmc_Nslip ( f , instance ) ! process each (active) slip system in family
j = j + 1_pInt
accumulatedSlip ( j ) = plasticState ( phase ) % state ( offset_accshear_slip + j , offset )
enddo
enddo
end subroutine constitutive_dislokmc_getAccumulatedSlip
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!--------------------------------------------------------------------------------------------------
!> @brief returns accumulated slip
!--------------------------------------------------------------------------------------------------
subroutine constitutive_dislokmc_getSlipRate ( nSlip , slipRate , ipc , ip , el )
use lattice , only : &
lattice_maxNslipFamily
use material , only : &
mappingConstitutive , &
plasticState , &
phase_plasticityInstance
implicit none
real ( pReal ) , dimension ( : ) , allocatable :: &
slipRate
integer ( pInt ) :: &
nSlip
integer ( pInt ) , intent ( in ) :: &
ipc , & !< grain number
ip , & !< integration point number
el !< element number
integer ( pInt ) :: &
offset , &
phase , &
instance , &
offset_accshear_slip , &
f , j , i
offset = mappingConstitutive ( 1 , ipc , ip , el )
phase = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( phase )
nSlip = constitutive_dislokmc_totalNslip ( instance )
allocate ( slipRate ( nSlip ) )
offset_accshear_slip = 2_pInt * nSlip
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
do i = 1_pInt , constitutive_dislokmc_Nslip ( f , instance ) ! process each (active) slip system in family
j = j + 1_pInt
slipRate ( j ) = plasticState ( phase ) % dotState ( offset_accshear_slip + j , offset )
enddo
enddo
end subroutine constitutive_dislokmc_getSlipRate
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!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
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function constitutive_dislokmc_postResults ( Tstar_v , Temperature , ipc , ip , el )
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use prec , only : &
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 , &
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phase_Noutput , &
plasticState , &
mappingConstitutive
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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 ) :: &
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instance , &
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ns , nt , &
f , o , i , c , j , index_myFamily , &
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s1 , s2 , &
ph , &
of
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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 ) ) ) ) :: &
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gdot_slip_pos , vel_slip
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real ( pReal ) , dimension ( 3 , 3 ) :: eigVectors
real ( pReal ) , dimension ( 3 ) :: eigValues
logical :: error
!* Shortened notation
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of = mappingConstitutive ( 1 , ipc , ip , el )
ph = mappingConstitutive ( 2 , ipc , ip , el )
instance = phase_plasticityInstance ( ph )
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ns = constitutive_dislokmc_totalNslip ( instance )
nt = constitutive_dislokmc_totalNtwin ( instance )
!* Total twin volume fraction
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sumf = sum ( plasticState ( ph ) % state ( ( 3_pInt * ns + 1_pInt ) : ( 3_pInt * ns + nt ) , of ) ) ! safe for nt == 0
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!* 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 )
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do o = 1_pInt , constitutive_dislokmc_Noutput ( instance )
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select case ( constitutive_dislokmc_outputID ( o , instance ) )
case ( edge_density_ID )
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constitutive_dislokmc_postResults ( c + 1_pInt : c + ns ) = plasticState ( ph ) % state ( 1_pInt : ns , of )
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c = c + ns
case ( dipole_density_ID )
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constitutive_dislokmc_postResults ( c + 1_pInt : c + ns ) = plasticState ( ph ) % state ( ns + 1_pInt : 2_pInt * ns , of )
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c = c + ns
case ( shear_rate_slip_ID )
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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tau = dot_product ( Tstar_v , lattice_Sslip_v ( : , 1 , index_myFamily + i , ph ) )
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!* Stress ratios
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if ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) > tol_math_check ) then
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!* Stress ratios
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StressRatio_p = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** constitutive_dislokmc_pPerSlipFamily ( f , instance )
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StressRatio_pminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** ( constitutive_dislokmc_pPerSlipFamily ( f , instance ) - 1.0_pReal )
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StressRatio_u = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** constitutive_dislokmc_uPerSlipFamily ( f , instance )
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StressRatio_uminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( 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 = &
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plasticState ( ph ) % state ( j , of ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
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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 ) &
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* ( 1.0_pReal - constitutive_dislokmc_sPerSlipFamily ( f , instance ) &
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* 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 ) = &
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plasticState ( ph ) % state ( ( 2_pInt * ns + 1_pInt ) : ( 3_pInt * ns ) , of )
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c = c + ns
case ( mfp_slip_ID )
constitutive_dislokmc_postResults ( c + 1_pInt : c + ns ) = &
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plasticState ( ph ) % state ( ( 5_pInt * ns + 3_pInt * nt + 1_pInt ) : ( 6_pInt * ns + 3_pInt * nt ) , of )
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c = c + ns
case ( resolved_stress_slip_ID )
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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 ) = &
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dot_product ( Tstar_v , lattice_Sslip_v ( : , 1 , index_myFamily + i , ph ) )
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enddo ; enddo
c = c + ns
case ( threshold_stress_slip_ID )
constitutive_dislokmc_postResults ( c + 1_pInt : c + ns ) = &
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plasticState ( ph ) % state ( ( 6_pInt * ns + 4_pInt * nt + 1_pInt ) : ( 7_pInt * ns + 4_pInt * nt ) , of )
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c = c + ns
case ( edge_dipole_distance_ID )
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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 ) = &
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( 3.0_pReal * lattice_mu ( ph ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) ) / &
( 1 6.0_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 ) )
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enddo ; enddo
c = c + ns
case ( twin_fraction_ID )
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constitutive_dislokmc_postResults ( c + 1_pInt : c + nt ) = plasticState ( ph ) % state ( ( 3_pInt * ns + 1_pInt ) : ( 3_pInt * ns + nt ) , of )
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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
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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tau = dot_product ( Tstar_v , lattice_Sslip_v ( : , 1 , index_myFamily + i , ph ) )
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!* Stress ratios
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if ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) > tol_math_check ) then
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!* Stress ratios
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StressRatio_p = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** constitutive_dislokmc_pPerSlipFamily ( f , instance )
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StressRatio_pminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** ( constitutive_dislokmc_pPerSlipFamily ( f , instance ) - 1.0_pReal )
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StressRatio_u = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** constitutive_dislokmc_uPerSlipFamily ( f , instance )
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StressRatio_uminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( 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 = &
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plasticState ( ph ) % state ( j , of ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
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constitutive_dislokmc_v0PerSlipSystem ( j , instance )
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!* Shear rates due to slip
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gdot_slip_pos ( j ) = DotGamma0 * exp ( - BoltzmannRatio * ( 1_pInt - StressRatio_p ) ** &
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constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) * sign ( 1.0_pReal , tau ) &
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* ( 1.0_pReal - constitutive_dislokmc_sPerSlipFamily ( f , instance ) &
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* exp ( - BoltzmannRatio * ( 1_pInt - StressRatio_p ) ** constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) ) &
* StressRatio_u
else
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gdot_slip_pos ( j ) = 0.0_pReal
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endif
enddo ; enddo
j = 0_pInt
do f = 1_pInt , lattice_maxNtwinFamily ! loop over all twin families
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index_myFamily = sum ( lattice_NtwinSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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tau = dot_product ( Tstar_v , lattice_Stwin_v ( : , index_myFamily + i , ph ) )
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!* Stress ratios
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StressRatio_r = ( plasticState ( ph ) % state ( 7_pInt * ns + 4_pInt * nt + j , of ) / &
tau ) ** constitutive_dislokmc_rPerTwinFamily ( f , instance )
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!* Shear rates due to twin
if ( tau > 0.0_pReal ) then
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select case ( lattice_structure ( ph ) )
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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
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Ndot0 = ( abs ( gdot_slip_pos ( s1 ) ) * ( plasticState ( ph ) % state ( s2 , of ) + plasticState ( ph ) % state ( ns + s2 , of ) ) + &
abs ( gdot_slip_pos ( s2 ) ) * ( plasticState ( ph ) % state ( s1 , of ) + plasticState ( ph ) % state ( ns + s1 , of ) ) ) / &
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( 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 ) = &
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( 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 )
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endif
enddo ; enddo
endif
c = c + nt
case ( accumulated_shear_twin_ID )
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constitutive_dislokmc_postResults ( c + 1_pInt : c + nt ) = plasticState ( ph ) % &
state ( ( 3_pInt * ns + nt + 1_pInt ) : ( 3_pInt * ns + 2_pInt * nt ) , of )
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c = c + nt
case ( mfp_twin_ID )
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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 )
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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
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index_myFamily = sum ( lattice_NtwinSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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do i = 1_pInt , constitutive_dislokmc_Ntwin ( f , instance ) ! process each (active) slip system in family
j = j + 1_pInt
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constitutive_dislokmc_postResults ( c + j ) = dot_product ( Tstar_v , lattice_Stwin_v ( : , index_myFamily + i , ph ) )
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enddo ; enddo
endif
c = c + nt
case ( threshold_stress_twin_ID )
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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 )
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c = c + nt
case ( stress_exponent_ID )
j = 0_pInt
do f = 1_pInt , lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum ( lattice_NslipSystem ( 1 : f - 1_pInt , ph ) ) ! at which index starts my family
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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
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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
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!* Stress ratios
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StressRatio_p = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** constitutive_dislokmc_pPerSlipFamily ( f , instance )
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StressRatio_pminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
( constitutive_dislokmc_SolidSolutionStrength ( instance ) + &
constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
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** ( constitutive_dislokmc_pPerSlipFamily ( f , instance ) - 1.0_pReal )
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StressRatio_u = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( constitutive_dislokmc_SolidSolutionStrength ( instance ) + constitutive_dislokmc_tau_peierlsPerSlipFamily ( f , instance ) ) ) &
** constitutive_dislokmc_uPerSlipFamily ( f , instance )
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StressRatio_uminus1 = ( ( abs ( tau ) - plasticState ( ph ) % state ( 6 * ns + 4 * nt + j , of ) ) / &
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( 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 = &
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plasticState ( ph ) % state ( j , of ) * constitutive_dislokmc_burgersPerSlipSystem ( j , instance ) * &
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constitutive_dislokmc_v0PerSlipSystem ( j , instance )
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!* Shear rates due to slip
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vel_slip ( j ) = exp ( - BoltzmannRatio * ( 1 - StressRatio_p ) ** constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) &
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* ( 1.0_pReal - constitutive_dislokmc_sPerSlipFamily ( f , instance ) &
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* exp ( - BoltzmannRatio * ( 1 - StressRatio_p ) ** constitutive_dislokmc_qPerSlipFamily ( f , instance ) ) )
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gdot_slip_pos ( j ) = ( 1.0_pReal - sumf ) * DotGamma0 &
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* 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
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gdot_slip_pos ( j ) = 0.0_pReal
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dgdot_dtauslip = 0.0_pReal
endif
!* Stress exponent
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if ( gdot_slip_pos ( j ) == 0.0_pReal ) then
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constitutive_dislokmc_postResults ( c + j ) = 0.0_pReal
else
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constitutive_dislokmc_postResults ( c + j ) = ( tau / gdot_slip_pos ( j ) ) * dgdot_dtauslip
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endif
enddo ; enddo
c = c + ns
end select
enddo
end function constitutive_dislokmc_postResults
end module constitutive_dislokmc
