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DAMASK_EICMD/src/plastic_disloUCLA.f90

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!--------------------------------------------------------------------------------------------------
!> @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 plastic_disloUCLA
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:), allocatable, public, protected :: &
plastic_disloUCLA_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
plastic_disloUCLA_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_disloUCLA_output !< name of each post result output
real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
integer(pInt), dimension(:), allocatable, target, public :: &
plastic_disloUCLA_Noutput !< number of outputs per instance of this plasticity
integer(pInt), dimension(:), allocatable, private :: &
plastic_disloUCLA_totalNslip !< total number of active slip systems for each instance
integer(pInt), dimension(:,:), allocatable, private :: &
plastic_disloUCLA_Nslip !< number of active slip systems for each family and instance
real(pReal), dimension(:), allocatable, private :: &
plastic_disloUCLA_CAtomicVolume, & !< atomic volume in Bugers vector unit
plastic_disloUCLA_D0, & !< prefactor for self-diffusion coefficient
plastic_disloUCLA_Qsd, & !< activation energy for dislocation climb
plastic_disloUCLA_GrainSize, & !< grain size
plastic_disloUCLA_CEdgeDipMinDistance, & !<
plastic_disloUCLA_SolidSolutionStrength, & !< Strength due to elements in solid solution
plastic_disloUCLA_dipoleFormationFactor, & !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
plastic_disloUCLA_aTolRho !< absolute tolerance for integration of dislocation density
real(pReal), dimension(:,:), allocatable, private :: &
plastic_disloUCLA_rhoEdge0, & !< initial edge dislocation density per slip system for each family and instance
plastic_disloUCLA_rhoEdgeDip0, & !< initial edge dipole density per slip system for each family and instance
plastic_disloUCLA_burgersPerSlipFamily, & !< absolute length of burgers vector [m] for each slip family and instance
plastic_disloUCLA_burgersPerSlipSystem, & !< absolute length of burgers vector [m] for each slip system and instance
plastic_disloUCLA_QedgePerSlipFamily, & !< activation energy for glide [J] for each slip family and instance
plastic_disloUCLA_QedgePerSlipSystem, & !< activation energy for glide [J] for each slip system and instance
plastic_disloUCLA_v0PerSlipFamily, & !< dislocation velocity prefactor [m/s] for each family and instance
plastic_disloUCLA_v0PerSlipSystem, & !< dislocation velocity prefactor [m/s] for each slip system and instance
plastic_disloUCLA_tau_peierlsPerSlipFamily, & !< Peierls stress [Pa] for each family and instance
plastic_disloUCLA_CLambdaSlipPerSlipFamily, & !< Adj. parameter for distance between 2 forest dislocations for each slip family and instance
plastic_disloUCLA_CLambdaSlipPerSlipSystem, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
plastic_disloUCLA_interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type and instance
plastic_disloUCLA_pPerSlipFamily, & !< p-exponent in glide velocity
plastic_disloUCLA_qPerSlipFamily, & !< q-exponent in glide velocity
!* mobility law parameters
plastic_disloUCLA_kinkheight, & !< height of the kink pair
plastic_disloUCLA_omega, & !< attempt frequency for kink pair nucleation
plastic_disloUCLA_kinkwidth, & !< width of the kink pair
plastic_disloUCLA_dislolength, & !< dislocation length (lamda)
plastic_disloUCLA_friction, & !< friction coeff. B (kMC)
!*
plastic_disloUCLA_nonSchmidCoeff !< non-Schmid coefficients (bcc)
real(pReal), dimension(:,:,:), allocatable, private :: &
plastic_disloUCLA_interactionMatrix_SlipSlip, & !< interaction matrix of the different slip systems for each instance
plastic_disloUCLA_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
end enum
integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: &
plastic_disloUCLA_outputID !< ID of each post result output
type, private :: tDisloUCLAState
real(pReal), pointer, dimension(:,:) :: &
rhoEdge, &
rhoEdgeDip, &
accshear_slip, &
invLambdaSlip, &
mfp_slip, &
threshold_stress_slip
end type
type(tDisloUCLAState ), allocatable, dimension(:), private :: &
state, &
state0, &
dotState
public :: &
plastic_disloUCLA_init, &
plastic_disloUCLA_microstructure, &
plastic_disloUCLA_LpAndItsTangent, &
plastic_disloUCLA_dotState, &
plastic_disloUCLA_postResults
private :: &
plastic_disloUCLA_stateInit, &
plastic_disloUCLA_aTolState
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_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 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: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
PLASTICITY_DISLOUCLA_label, &
PLASTICITY_DISLOUCLA_ID, &
material_phase, &
plasticState, &
MATERIAL_partPhase
use lattice
use numerics,only: &
numerics_integrator
implicit none
integer(pInt), intent(in) :: fileUnit
integer(pInt), allocatable, dimension(:) :: chunkPos
integer(pInt) :: maxNinstance,mySize=0_pInt,phase,maxTotalNslip,&
f,instance,j,k,o,ns, &
Nchunks_SlipSlip = 0_pInt, &
Nchunks_SlipFamilies = 0_pInt,Nchunks_nonSchmid = 0_pInt, &
offset_slip, index_myFamily, index_otherFamily, &
startIndex, endIndex
integer(pInt) :: sizeState, sizeDotState, sizeDeltaState
integer(pInt) :: NofMyPhase
character(len=65536) :: &
tag = '', &
line = ''
real(pReal), dimension(:), allocatable :: tempPerSlip
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOUCLA_label//' init -+>>>'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_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(plastic_disloUCLA_sizePostResults(maxNinstance), source=0_pInt)
allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
allocate(plastic_disloUCLA_output(maxval(phase_Noutput),maxNinstance))
plastic_disloUCLA_output = ''
allocate(plastic_disloUCLA_outputID(maxval(phase_Noutput),maxNinstance), source=undefined_ID)
allocate(plastic_disloUCLA_Noutput(maxNinstance), source=0_pInt)
allocate(plastic_disloUCLA_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
allocate(plastic_disloUCLA_totalNslip(maxNinstance), source=0_pInt)
allocate(plastic_disloUCLA_CAtomicVolume(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_D0(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_Qsd(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_GrainSize(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_CEdgeDipMinDistance(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_SolidSolutionStrength(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_aTolRho(maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_dipoleFormationFactor(maxNinstance), source=1.0_pReal) !should be on by default
allocate(plastic_disloUCLA_rhoEdge0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_rhoEdgeDip0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
allocate(plastic_disloUCLA_kinkheight(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_omega(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_kinkwidth(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_dislolength(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_friction(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_QedgePerSlipFamily(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_tau_peierlsPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(plastic_disloUCLA_pPerSlipFamily(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_qPerSlipFamily(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
allocate(plastic_disloUCLA_interaction_SlipSlip(lattice_maxNinteraction,maxNinstance),source=0.0_pReal)
allocate(plastic_disloUCLA_nonSchmidCoeff(lattice_maxNnonSchmid,maxNinstance), source=0.0_pReal)
rewind(fileUnit)
phase = 0_pInt
do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= MATERIAL_partPhase) ! wind forward to <phase>
line = IO_read(fileUnit)
enddo
parsingFile: do while (trim(line) /= IO_EOF) ! read through sections of phase part
line = IO_read(fileUnit)
if (IO_isBlank(line)) cycle ! skip empty lines
if (IO_getTag(line,'<','>') /= '') then ! stop at next part
line = IO_read(fileUnit, .true.) ! reset IO_read
exit
endif
if (IO_getTag(line,'[',']') /= '') then ! next phase section
phase = phase + 1_pInt ! advance phase section counter
if (phase_plasticity(phase) == PLASTICITY_DISLOUCLA_ID) then
Nchunks_SlipFamilies = count(lattice_NslipSystem(:,phase) > 0_pInt)
Nchunks_SlipSlip = maxval(lattice_interactionSlipSlip(:,:,phase))
Nchunks_nonSchmid = lattice_NnonSchmid(phase)
if(allocated(tempPerSlip)) deallocate(tempPerSlip)
allocate(tempPerSlip(Nchunks_SlipFamilies))
endif
cycle ! skip to next line
endif
if (phase > 0_pInt ) then; if (phase_plasticity(phase) == PLASTICITY_DISLOUCLA_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
chunkPos = IO_stringPos(line)
tag = IO_lc(IO_stringValue(line,chunkPos,1_pInt)) ! extract key
select case(tag)
case ('(output)')
select case(IO_lc(IO_stringValue(line,chunkPos,2_pInt)))
case ('edge_density')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = edge_density_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('dipole_density')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = dipole_density_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('shear_rate_slip','shearrate_slip')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = shear_rate_slip_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('accumulated_shear_slip')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = accumulated_shear_slip_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('mfp_slip')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = mfp_slip_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('resolved_stress_slip')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = resolved_stress_slip_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('threshold_stress_slip')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = threshold_stress_slip_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('edge_dipole_distance')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = edge_dipole_distance_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('stress_exponent')
plastic_disloUCLA_Noutput(instance) = plastic_disloUCLA_Noutput(instance) + 1_pInt
plastic_disloUCLA_outputID(plastic_disloUCLA_Noutput(instance),instance) = stress_exponent_ID
plastic_disloUCLA_output(plastic_disloUCLA_Noutput(instance),instance) = &
IO_lc(IO_stringValue(line,chunkPos,2_pInt))
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on number of slip system families
case ('nslip')
if (chunkPos(1) < Nchunks_SlipFamilies + 1_pInt) &
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOUCLA_label//')')
if (chunkPos(1) > Nchunks_SlipFamilies + 1_pInt) &
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOUCLA_label//')')
Nchunks_SlipFamilies = chunkPos(1) - 1_pInt
do j = 1_pInt, Nchunks_SlipFamilies
plastic_disloUCLA_Nslip(j,instance) = IO_intValue(line,chunkPos,1_pInt+j)
enddo
case ('rhoedge0','rhoedgedip0','slipburgers','qedge','v0','clambdaslip','tau_peierls','p_slip','q_slip',&
'kink_height','omega','kink_width','dislolength','friction_coeff')
do j = 1_pInt, Nchunks_SlipFamilies
tempPerSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
select case(tag)
case ('rhoedge0')
plastic_disloUCLA_rhoEdge0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('rhoedgedip0')
plastic_disloUCLA_rhoEdgeDip0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('slipburgers')
plastic_disloUCLA_burgersPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('qedge')
plastic_disloUCLA_QedgePerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('v0')
plastic_disloUCLA_v0PerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('clambdaslip')
plastic_disloUCLA_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_DISLOUCLA_label//')')
plastic_disloUCLA_tau_peierlsPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('p_slip')
plastic_disloUCLA_pPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('q_slip')
plastic_disloUCLA_qPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('kink_height')
plastic_disloUCLA_kinkheight(1:Nchunks_SlipFamilies,instance) = &
tempPerSlip(1:Nchunks_SlipFamilies)
case ('omega')
plastic_disloUCLA_omega(1:Nchunks_SlipFamilies,instance) = &
tempPerSlip(1:Nchunks_SlipFamilies)
case ('kink_width')
plastic_disloUCLA_kinkwidth(1:Nchunks_SlipFamilies,instance) = &
tempPerSlip(1:Nchunks_SlipFamilies)
case ('dislolength')
plastic_disloUCLA_dislolength(1:Nchunks_SlipFamilies,instance) = &
tempPerSlip(1:Nchunks_SlipFamilies)
case ('friction_coeff')
plastic_disloUCLA_friction(1:Nchunks_SlipFamilies,instance) = &
tempPerSlip(1:Nchunks_SlipFamilies)
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on number of interactions
case ('interaction_slipslip','interactionslipslip')
if (chunkPos(1) < 1_pInt + Nchunks_SlipSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOUCLA_label//')')
do j = 1_pInt, Nchunks_SlipSlip
plastic_disloUCLA_interaction_SlipSlip(j,instance) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
case ('nonschmid_coefficients')
if (chunkPos(1) < 1_pInt + Nchunks_nonSchmid) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOUCLA_label//')')
do j = 1_pInt,Nchunks_nonSchmid
plastic_disloUCLA_nonSchmidCoeff(j,instance) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
!--------------------------------------------------------------------------------------------------
! parameters independent of number of slip systems
case ('grainsize')
plastic_disloUCLA_GrainSize(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('d0')
plastic_disloUCLA_D0(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('qsd')
plastic_disloUCLA_Qsd(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('atol_rho')
plastic_disloUCLA_aTolRho(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('solidsolutionstrength')
plastic_disloUCLA_SolidSolutionStrength(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('cedgedipmindistance')
plastic_disloUCLA_CEdgeDipMinDistance(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('catomicvolume')
plastic_disloUCLA_CAtomicVolume(instance) = IO_floatValue(line,chunkPos,2_pInt)
case ('dipoleformationfactor')
plastic_disloUCLA_dipoleFormationFactor(instance) = IO_floatValue(line,chunkPos,2_pInt)
end select
endif; endif
enddo parsingFile
sanityChecks: do phase = 1_pInt, size(phase_plasticity)
myPhase: if (phase_plasticity(phase) == PLASTICITY_disloUCLA_ID) then
instance = phase_plasticityInstance(phase)
if (sum(plastic_disloUCLA_Nslip(:,instance)) < 0_pInt) &
call IO_error(211_pInt,el=instance,ext_msg='Nslip ('//PLASTICITY_DISLOUCLA_label//')')
do f = 1_pInt,lattice_maxNslipFamily
if (plastic_disloUCLA_Nslip(f,instance) > 0_pInt) then
if (plastic_disloUCLA_rhoEdge0(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_rhoEdgeDip0(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_v0PerSlipFamily(f,instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOUCLA_label//')')
endif
enddo
if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_D0(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOUCLA_label//')')
if (plastic_disloUCLA_Qsd(instance) <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOUCLA_label//')')
! if (plastic_disloUCLA_aTolRho(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOUCLA_label//')')
!--------------------------------------------------------------------------------------------------
! Determine total number of active slip systems
plastic_disloUCLA_Nslip(:,instance) = min(lattice_NslipSystem(:,phase),plastic_disloUCLA_Nslip(:,instance))
plastic_disloUCLA_totalNslip(instance) = sum(plastic_disloUCLA_Nslip(:,instance))
endif myPhase
enddo sanityChecks
!--------------------------------------------------------------------------------------------------
! allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(plastic_disloUCLA_totalNslip)
allocate(plastic_disloUCLA_burgersPerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_QedgePerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_v0PerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_CLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance),source=0.0_pReal)
allocate(plastic_disloUCLA_interactionMatrix_SlipSlip(maxval(plastic_disloUCLA_totalNslip),& ! slip resistance from slip activity
maxval(plastic_disloUCLA_totalNslip),&
maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance), &
source=0.0_pReal)
allocate(state(maxNinstance))
allocate(state0(maxNinstance))
allocate(dotState(maxNinstance))
initializeInstances: do phase = 1_pInt, size(phase_plasticity)
myPhase2: if (phase_plasticity(phase) == PLASTICITY_disloUCLA_ID) then
NofMyPhase=count(material_phase==phase)
instance = phase_plasticityInstance(phase)
ns = plastic_disloUCLA_totalNslip(instance)
!--------------------------------------------------------------------------------------------------
! Determine size of postResults array
outputs: do o = 1_pInt,plastic_disloUCLA_Noutput(instance)
select case(plastic_disloUCLA_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
end select
if (mySize > 0_pInt) then ! any meaningful output found
plastic_disloUCLA_sizePostResult(o,instance) = mySize
plastic_disloUCLA_sizePostResults(instance) = plastic_disloUCLA_sizePostResults(instance) + mySize
endif
enddo outputs
!--------------------------------------------------------------------------------------------------
! allocate state arrays
sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * ns
sizeDeltaState = 0_pInt
sizeState = sizeDotState &
+ int(size(['invLambdaSlip ',&
'meanFreePathSlip ','tauSlipThreshold ']),pInt) * ns
plasticState(phase)%sizeState = sizeState
plasticState(phase)%sizeDotState = sizeDotState
plasticState(phase)%sizeDeltaState = sizeDeltaState
plasticState(phase)%sizePostResults = plastic_disloUCLA_sizePostResults(instance)
plasticState(phase)%nSlip = plastic_disloucla_totalNslip(instance)
plasticState(phase)%nTwin = 0_pInt
plasticState(phase)%nTrans= 0_pInt
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)%dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%deltaState (sizeDeltaState,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)
offset_slip = 2_pInt*plasticState(phase)%nSlip
plasticState(phase)%slipRate => &
plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase)
plasticState(phase)%accumulatedSlip => &
plasticState(phase)%state (offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase)
!* Process slip related parameters ------------------------------------------------
mySlipFamilies: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(plastic_disloUCLA_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
mySlipSystems: do j = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
!* Burgers vector,
! dislocation velocity prefactor,
! mean free path prefactor,
! and minimum dipole distance
plastic_disloUCLA_burgersPerSlipSystem(index_myFamily+j,instance) = &
plastic_disloUCLA_burgersPerSlipFamily(f,instance)
plastic_disloUCLA_QedgePerSlipSystem(index_myFamily+j,instance) = &
plastic_disloUCLA_QedgePerSlipFamily(f,instance)
plastic_disloUCLA_v0PerSlipSystem(index_myFamily+j,instance) = &
plastic_disloUCLA_v0PerSlipFamily(f,instance)
plastic_disloUCLA_CLambdaSlipPerSlipSystem(index_myFamily+j,instance) = &
plastic_disloUCLA_CLambdaSlipPerSlipFamily(f,instance)
!* Calculation of forest projections for edge dislocations
!* Interaction matrices
otherSlipFamilies: do o = 1_pInt,lattice_maxNslipFamily
index_otherFamily = sum(plastic_disloUCLA_Nslip(1:o-1_pInt,instance))
otherSlipSystems: do k = 1_pInt,plastic_disloUCLA_Nslip(o,instance)
plastic_disloUCLA_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)))
plastic_disloUCLA_interactionMatrix_SlipSlip(index_myFamily+j,index_otherFamily+k,instance) = &
plastic_disloUCLA_interaction_SlipSlip(lattice_interactionSlipSlip( &
sum(lattice_NslipSystem(1:f-1,phase))+j, &
sum(lattice_NslipSystem(1:o-1,phase))+k, &
phase), instance )
enddo otherSlipSystems; enddo otherSlipFamilies
enddo mySlipSystems
enddo mySlipFamilies
startIndex=1_pInt
endIndex=ns
state(instance)%rhoEdge=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%rhoEdge=>plasticState(phase)%state0(startIndex:endIndex,:)
dotState(instance)%rhoEdge=>plasticState(phase)%dotState(startIndex:endIndex,:)
startIndex=endIndex+1_pInt
endIndex=endIndex+ns
state(instance)%rhoEdgeDip=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%rhoEdgeDip=>plasticState(phase)%state0(startIndex:endIndex,:)
dotState(instance)%rhoEdgeDip=>plasticState(phase)%dotState(startIndex:endIndex,:)
startIndex=endIndex+1_pInt
endIndex=endIndex+ns
state(instance)%accshear_slip=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%accshear_slip=>plasticState(phase)%state0(startIndex:endIndex,:)
dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
startIndex=endIndex+1_pInt
endIndex=endIndex+ns
state(instance)%invLambdaSlip=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%invLambdaSlip=>plasticState(phase)%state0(startIndex:endIndex,:)
startIndex=endIndex+1_pInt
endIndex=endIndex+ns
state(instance)%mfp_slip=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%mfp_slip=>plasticState(phase)%state0(startIndex:endIndex,:)
startIndex=endIndex+1_pInt
endIndex=endIndex+ns
state(instance)%threshold_stress_slip=>plasticState(phase)%state(startIndex:endIndex,:)
state0(instance)%threshold_stress_slip=>plasticState(phase)%state0(startIndex:endIndex,:)
call plastic_disloUCLA_stateInit(phase,instance)
call plastic_disloUCLA_aTolState(phase,instance)
endif myPhase2
enddo initializeInstances
end subroutine plastic_disloUCLA_init
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_stateInit(ph,instance)
use math, only: &
pi
use lattice, only: &
lattice_maxNslipFamily, &
lattice_mu
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,f,ns, index_myFamily
real(pReal), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
rhoEdge0, &
rhoEdgeDip0, &
invLambdaSlip0, &
MeanFreePathSlip0, &
tauSlipThreshold0
tempState = 0.0_pReal
ns = plastic_disloUCLA_totalNslip(instance)
!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables
do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(plastic_disloUCLA_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
rhoEdge0(index_myFamily+1_pInt: &
index_myFamily+plastic_disloUCLA_Nslip(f,instance)) = &
plastic_disloUCLA_rhoEdge0(f,instance)
rhoEdgeDip0(index_myFamily+1_pInt: &
index_myFamily+plastic_disloUCLA_Nslip(f,instance)) = &
plastic_disloUCLA_rhoEdgeDip0(f,instance)
enddo
tempState(1_pInt:ns) = rhoEdge0
tempState(ns+1_pInt:2_pInt*ns) = rhoEdgeDip0
!--------------------------------------------------------------------------------------------------
! initialize dependent slip microstructural variables
forall (i = 1_pInt:ns) &
invLambdaSlip0(i) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),plastic_disloUCLA_forestProjectionEdge(1:ns,i,instance)))/ &
plastic_disloUCLA_CLambdaSlipPerSlipSystem(i,instance)
tempState(3_pInt*ns+1:4_pInt*ns) = invLambdaSlip0
forall (i = 1_pInt:ns) &
MeanFreePathSlip0(i) = &
plastic_disloUCLA_GrainSize(instance)/(1.0_pReal+invLambdaSlip0(i)*plastic_disloUCLA_GrainSize(instance))
tempState(4_pInt*ns+1:5_pInt*ns) = MeanFreePathSlip0
forall (i = 1_pInt:ns) &
tauSlipThreshold0(i) = &
lattice_mu(ph)*plastic_disloUCLA_burgersPerSlipSystem(i,instance) * &
sqrt(dot_product((rhoEdge0+rhoEdgeDip0),plastic_disloUCLA_interactionMatrix_SlipSlip(i,1:ns,instance)))
tempState(5_pInt*ns+1:6_pInt*ns) = tauSlipThreshold0
plasticState(ph)%state0 = spread(tempState,2,size(plasticState(ph)%state(1,:)))
end subroutine plastic_disloUCLA_stateInit
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_aTolState(ph,instance)
use material, only: &
plasticState
implicit none
integer(pInt), intent(in) :: &
ph, &
instance ! number specifying the current instance of the plasticity
! Tolerance state for dislocation densities
plasticState(ph)%aTolState(1_pInt:2_pInt*plastic_disloUCLA_totalNslip(instance)) = &
plastic_disloUCLA_aTolRho(instance)
! Tolerance state for accumulated shear due to slip
plasticState(ph)%aTolState(2_pInt*plastic_disloUCLA_totalNslip(instance)+1_pInt: &
3_pInt*plastic_disloUCLA_totalNslip(instance))=1e6_pReal
end subroutine plastic_disloUCLA_aTolState
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_microstructure(temperature,ipc,ip,el)
use math, only: &
pi
use material, only: &
phase_plasticityInstance, &
phaseAt, phasememberAt
use lattice, only: &
lattice_mu
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,s, &
ph, &
of
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = plastic_disloUCLA_totalNslip(instance)
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
forall (s = 1_pInt:ns) &
state(instance)%invLambdaSlip(s,of) = &
sqrt(dot_product((state(instance)%rhoEdge(1_pInt:ns,of)+state(instance)%rhoEdgeDip(1_pInt:ns,of)),&
plastic_disloUCLA_forestProjectionEdge(1:ns,s,instance)))/ &
plastic_disloUCLA_CLambdaSlipPerSlipSystem(s,instance)
!* mean free path between 2 obstacles seen by a moving dislocation
do s = 1_pInt,ns
state(instance)%mfp_slip(s,of) = &
plastic_disloUCLA_GrainSize(instance)/&
(1.0_pReal+plastic_disloUCLA_GrainSize(instance)*(state(instance)%invLambdaSlip(s,of)))
enddo
!* threshold stress for dislocation motion
forall (s = 1_pInt:ns) &
state(instance)%threshold_stress_slip(s,of) = &
lattice_mu(ph)*plastic_disloUCLA_burgersPerSlipSystem(s,instance)*&
sqrt(dot_product((state(instance)%rhoEdge(1_pInt:ns,of)+state(instance)%rhoEdgeDip(1_pInt:ns,of)),&
plastic_disloUCLA_interactionMatrix_SlipSlip(s,1:ns,instance)))
end subroutine plastic_disloUCLA_microstructure
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
tol_math_check
use math, only: &
math_Plain3333to99, &
math_Mandel6to33, &
math_Mandel33to6, &
math_symmetric33, &
math_mul33x3
use material, only: &
material_phase, &
phase_plasticityInstance, &
phaseAt, phasememberAt
use lattice, only: &
lattice_Sslip, &
lattice_Sslip_v, &
lattice_maxNslipFamily,&
lattice_NslipSystem, &
lattice_NnonSchmid
implicit none
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
real(pReal), dimension(3,3), intent(out) :: Lp
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99
integer(pInt) :: instance,ph,of,ns,f,i,j,k,l,m,n,index_myFamily
real(pReal) :: StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0, &
tau_slip_pos,tau_slip_neg,vel_slip,dvel_slip,&
dgdot_dtauslip_pos,dgdot_dtauslip_neg,stressRatio
real(pReal), dimension(3,3,2) :: &
nonSchmid_tensor
real(pReal), dimension(3,3,3,3) :: &
dLp_dTstar3333
real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip_pos,gdot_slip_neg
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = plastic_disloUCLA_totalNslip(instance)
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! Dislocation glide part
gdot_slip_pos = 0.0_pReal
gdot_slip_neg = 0.0_pReal
dgdot_dtauslip_pos = 0.0_pReal
dgdot_dtauslip_neg = 0.0_pReal
j = 0_pInt
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j+1_pInt
!* Boltzmann ratio
BoltzmannRatio = plastic_disloUCLA_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(instance)%rhoEdge(j,of)*plastic_disloUCLA_burgersPerSlipSystem(j,instance)*&
plastic_disloUCLA_v0PerSlipSystem(j,instance)
!* Resolved shear stress on slip system
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_slip_neg = tau_slip_pos
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)
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
tau_slip_pos = tau_slip_pos + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k, index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
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) + plastic_disloUCLA_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) + plastic_disloUCLA_nonSchmidCoeff(k,instance)*&
lattice_Sslip(1:3,1:3,2*k+1,index_myFamily+i,ph)
enddo nonSchmidSystems
significantPostitiveStress: if((abs(tau_slip_pos)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
!* Stress ratio
stressRatio = ((abs(tau_slip_pos)-state(instance)%threshold_stress_slip(j,of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
stressRatio_pminus1 = stressRatio**(plastic_disloUCLA_pPerSlipFamily(f,instance)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_pos &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_pos(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_pos)
!* Derivatives of shear rates
dvel_slip = &
2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
+ tau_slip_pos &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) ) &!deltaf(f)
) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
) &
- (tau_slip_pos &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) )& !deltaf(f)
) &
) &
/ ( &
( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)**2.0_pReal &
)
dgdot_dtauslip_pos = DotGamma0 * dvel_slip
endif significantPostitiveStress
significantNegativeStress: if((abs(tau_slip_neg)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
!* Stress ratio
stressRatio = ((abs(tau_slip_neg)-state(instance)%threshold_stress_slip(j,of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
stressRatio_pminus1 = stressRatio**(plastic_disloUCLA_pPerSlipFamily(f,instance)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_neg &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_neg(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_neg)
!* Derivatives of shear rates
dvel_slip = &
2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
+ tau_slip_neg &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) ) &!deltaf(f)
) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
) &
- (tau_slip_neg &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) )& !deltaf(f)
) &
) &
/ ( &
( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)**2.0_pReal &
)
dgdot_dtauslip_neg = DotGamma0 * dvel_slip
endif significantNegativeStress
!* Plastic velocity gradient for dislocation glide
Lp = Lp + (gdot_slip_pos(j)+gdot_slip_neg(j))*0.5_pReal*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + (dgdot_dtauslip_pos*nonSchmid_tensor(m,n,1)+&
dgdot_dtauslip_neg*nonSchmid_tensor(m,n,2))*0.5_pReal*&
lattice_Sslip(k,l,1,index_myFamily+i,ph)
enddo slipSystems
enddo slipFamilies
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
end subroutine plastic_disloUCLA_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_disloUCLA_dotState(Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
tol_math_check, &
dEq0
use math, only: &
pi
use material, only: &
material_phase, &
phase_plasticityInstance, &
plasticState, &
phaseAt, phasememberAt
use lattice, only: &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_NnonSchmid, &
lattice_mu
implicit none
real(pReal), dimension(6), intent(in):: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
integer(pInt) :: instance,ns,f,i,j,k,index_myFamily, &
ph, &
of
real(pReal) :: &
stressRatio_p,&
BoltzmannRatio,&
DotGamma0,&
stressRatio, &
EdgeDipMinDistance,&
AtomicVolume,&
VacancyDiffusion,&
tau_slip_pos,&
tau_slip_neg,&
DotRhoMultiplication,&
EdgeDipDistance, &
DotRhoEdgeDipAnnihilation, &
DotRhoEdgeEdgeAnnihilation, &
ClimbVelocity, &
DotRhoEdgeDipClimb, &
DotRhoDipFormation, &
vel_slip, &
gdot_slip
real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip_pos, gdot_slip_neg
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = plastic_disloUCLA_totalNslip(instance)
plasticState(ph)%dotState(:,of) = 0.0_pReal
!* Dislocation density evolution
gdot_slip_pos = 0.0_pReal
gdot_slip_neg = 0.0_pReal
j = 0_pInt
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j+1_pInt
!* Boltzmann ratio
BoltzmannRatio = plastic_disloUCLA_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(instance)%rhoEdge(j,of)*plastic_disloUCLA_burgersPerSlipSystem(j,instance)*&
plastic_disloUCLA_v0PerSlipSystem(j,instance)
!* Resolved shear stress on slip system
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_slip_neg = tau_slip_pos
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
tau_slip_pos = tau_slip_pos + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k, index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
enddo nonSchmidSystems
significantPositiveStress: if((abs(tau_slip_pos)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
!* Stress ratios
stressRatio = ((abs(tau_slip_pos)-state(instance)%threshold_stress_slip(j,of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
!* Shear rates due to slip
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_pos &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_pos(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_pos)
endif significantPositiveStress
significantNegativeStress: if((abs(tau_slip_neg)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
!* Stress ratios
stressRatio = ((abs(tau_slip_neg)-state(instance)%threshold_stress_slip(j,of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_neg &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_neg(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_neg)
endif significantNegativeStress
gdot_slip = (gdot_slip_pos(j)+gdot_slip_neg(j))*0.5_pReal
!* Multiplication
DotRhoMultiplication = abs(gdot_slip)/&
(plastic_disloUCLA_burgersPerSlipSystem(j,instance)* &
state(instance)%mfp_slip(j,of))
!* Dipole formation
EdgeDipMinDistance = &
plastic_disloUCLA_CEdgeDipMinDistance(instance)*plastic_disloUCLA_burgersPerSlipSystem(j,instance)
if (dEq0(tau_slip_pos)) then
DotRhoDipFormation = 0.0_pReal
else
EdgeDipDistance = &
(3.0_pReal*lattice_mu(ph)*plastic_disloUCLA_burgersPerSlipSystem(j,instance))/&
(16.0_pReal*pi*abs(tau_slip_pos))
if (EdgeDipDistance>state(instance)%mfp_slip(j,of)) EdgeDipDistance=state(instance)%mfp_slip(j,of)
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
DotRhoDipFormation = &
((2.0_pReal*EdgeDipDistance)/plastic_disloUCLA_burgersPerSlipSystem(j,instance))*&
state(instance)%rhoEdge(j,of)*abs(gdot_slip)*plastic_disloUCLA_dipoleFormationFactor(instance)
endif
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation = &
((2.0_pReal*EdgeDipMinDistance)/plastic_disloUCLA_burgersPerSlipSystem(j,instance))*&
state(instance)%rhoEdge(j,of)*abs(gdot_slip)
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation = &
((2.0_pReal*EdgeDipMinDistance)/plastic_disloUCLA_burgersPerSlipSystem(j,instance))*&
state(instance)%rhoEdgeDip(j,of)*abs(gdot_slip)
!* Dislocation dipole climb
AtomicVolume = &
plastic_disloUCLA_CAtomicVolume(instance)*plastic_disloUCLA_burgersPerSlipSystem(j,instance)**(3.0_pReal)
VacancyDiffusion = &
plastic_disloUCLA_D0(instance)*exp(-plastic_disloUCLA_Qsd(instance)/(kB*Temperature))
if (dEq0(tau_slip_pos)) then
DotRhoEdgeDipClimb = 0.0_pReal
else
ClimbVelocity = &
((3.0_pReal*lattice_mu(ph)*VacancyDiffusion*AtomicVolume)/(2.0_pReal*pi*kB*Temperature))*&
(1/(EdgeDipDistance+EdgeDipMinDistance))
DotRhoEdgeDipClimb = &
(4.0_pReal*ClimbVelocity*state(instance)%rhoEdgeDip(j,of))/(EdgeDipDistance-EdgeDipMinDistance)
endif
!* Edge dislocation density rate of change
dotState(instance)%rhoEdge(j,of) = &
DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
!* Edge dislocation dipole density rate of change
dotState(instance)%rhoEdgeDip(j,of) = &
DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
!* Dotstate for accumulated shear due to slip
dotState(instance)%accshear_slip(j,of) = gdot_slip
enddo slipSystems
enddo slipFamilies
end subroutine plastic_disloUCLA_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_disloUCLA_postResults(Tstar_v,Temperature,ipc,ip,el)
use prec, only: &
tol_math_check, &
dEq
use math, only: &
pi
use material, only: &
material_phase, &
phase_plasticityInstance,&
!plasticState, &
phaseAt, phasememberAt
use lattice, only: &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_NnonSchmid, &
lattice_mu
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(plastic_disloUCLA_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
plastic_disloUCLA_postResults
integer(pInt) :: &
instance,&
ns,&
f,o,i,c,j,k,index_myFamily,&
ph, &
of
real(pReal) :: StressRatio_p,StressRatio_pminus1,&
BoltzmannRatio,DotGamma0,stressRatio,&
dvel_slip, vel_slip
real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
ns = plastic_disloUCLA_totalNslip(instance)
!* Required output
c = 0_pInt
plastic_disloUCLA_postResults = 0.0_pReal
do o = 1_pInt,plastic_disloUCLA_Noutput(instance)
select case(plastic_disloUCLA_outputID(o,instance))
case (edge_density_ID)
plastic_disloUCLA_postResults(c+1_pInt:c+ns) = state(instance)%rhoEdge(1_pInt:ns,of)
c = c + ns
case (dipole_density_ID)
plastic_disloUCLA_postResults(c+1_pInt:c+ns) = state(instance)%rhoEdgeDip(1_pInt:ns,of)
c = c + ns
case (shear_rate_slip_ID,stress_exponent_ID)
gdot_slip_pos = 0.0_pReal
gdot_slip_neg = 0.0_pReal
dgdot_dtauslip_pos = 0.0_pReal
dgdot_dtauslip_neg = 0.0_pReal
j = 0_pInt
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j + 1_pInt
!* Boltzmann ratio
BoltzmannRatio = plastic_disloUCLA_QedgePerSlipSystem(j,instance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(instance)%rhoEdge(j,of)*plastic_disloUCLA_burgersPerSlipSystem(j,instance)*&
plastic_disloUCLA_v0PerSlipSystem(j,instance)
!* Resolved shear stress on slip system
tau_slip_pos(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
tau_slip_neg(j) = tau_slip_pos(j)
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
tau_slip_pos = tau_slip_pos + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg + plastic_disloUCLA_nonSchmidCoeff(k,instance)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
enddo nonSchmidSystems
significantPositiveTau: if((abs(tau_slip_pos(j))-state(instance)%threshold_stress_slip(j, of)) > tol_math_check) then
!* Stress ratio
stressRatio = ((abs(tau_slip_pos(j))-state(instance)%threshold_stress_slip(j, of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
stressRatio_pminus1 = stressRatio**(plastic_disloUCLA_pPerSlipFamily(f,instance)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_pos(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_pos(j))
!* Derivatives of shear rates
dvel_slip = &
2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
+ tau_slip_pos(j) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) ) &!deltaf(f)
) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
) &
- (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) )& !deltaf(f)
) &
) &
/ ( &
( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_pos(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)**2.0_pReal &
)
dgdot_dtauslip_pos(j) = DotGamma0 * dvel_slip
endif significantPositiveTau
significantNegativeTau: if((abs(tau_slip_neg(j))-state(instance)%threshold_stress_slip(j, of)) > tol_math_check) then
!* Stress ratios
stressRatio = ((abs(tau_slip_neg(j))-state(instance)%threshold_stress_slip(j, of))/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** plastic_disloUCLA_pPerSlipFamily(f,instance)
stressRatio_pminus1 = stressRatio**(plastic_disloUCLA_pPerSlipFamily(f,instance)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
/ ( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)
gdot_slip_neg(j) = DotGamma0 &
* vel_slip &
* sign(1.0_pReal,tau_slip_neg(j))
!* Derivatives of shear rates
dvel_slip = &
2.0_pReal*plastic_disloUCLA_burgersPerSlipFamily(f,instance) &
* plastic_disloUCLA_kinkheight(f,instance) * plastic_disloUCLA_omega(f,instance) &
* ( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) ) &
* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
+ tau_slip_neg(j) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) ) &!deltaf(f)
) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
) &
- (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) ) &
* (2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)))& !deltaf(i)
*BoltzmannRatio*plastic_disloUCLA_pPerSlipFamily(f,instance)&
*plastic_disloUCLA_qPerSlipFamily(f,instance)/&
(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(plastic_disloUCLA_qPerSlipFamily(f,instance)-1.0_pReal) )& !deltaf(f)
) &
) &
/ ( &
( &
2.0_pReal*(plastic_disloUCLA_burgersPerSlipFamily(f,instance)**2.0_pReal)*tau_slip_neg(j) &
+ plastic_disloUCLA_omega(f,instance) * plastic_disloUCLA_friction(f,instance) &
*(( state(instance)%mfp_slip(j,of) - plastic_disloUCLA_kinkwidth(f,instance) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** plastic_disloUCLA_qPerSlipFamily(f,instance)) &
)**2.0_pReal &
)
dgdot_dtauslip_neg(j) = DotGamma0 * dvel_slip
endif significantNegativeTau
enddo slipSystems
enddo slipFamilies
if (plastic_disloUCLA_outputID(o,instance) == shear_rate_slip_ID) then
plastic_disloUCLA_postResults(c+1:c+ns) = (gdot_slip_pos + gdot_slip_neg)*0.5_pReal
c = c + ns
elseif(plastic_disloUCLA_outputID(o,instance) == stress_exponent_ID) then
do j = 1_pInt, ns
if (dEq(gdot_slip_pos(j)+gdot_slip_neg(j),0.0_pReal)) then
plastic_disloUCLA_postResults(c+j) = 0.0_pReal
else
plastic_disloUCLA_postResults(c+j) = (tau_slip_pos(j)+tau_slip_neg(j))/&
(gdot_slip_pos(j)+gdot_slip_neg(j))*&
(dgdot_dtauslip_pos(j)+dgdot_dtauslip_neg(j))* 0.5_pReal
endif
enddo
c = c + ns
endif
case (accumulated_shear_slip_ID)
plastic_disloUCLA_postResults(c+1_pInt:c+ns) = &
state(instance)%accshear_slip(1_pInt:ns, of)
c = c + ns
case (mfp_slip_ID)
plastic_disloUCLA_postResults(c+1_pInt:c+ns) =&
state(instance)%mfp_slip(1_pInt:ns, of)
c = c + ns
case (resolved_stress_slip_ID)
j = 0_pInt
slipFamilies1: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems1: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j + 1_pInt
plastic_disloUCLA_postResults(c+j) =&
dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
enddo slipSystems1; enddo slipFamilies1
c = c + ns
case (threshold_stress_slip_ID)
plastic_disloUCLA_postResults(c+1_pInt:c+ns) = &
state(instance)%threshold_stress_slip(1_pInt:ns,of)
c = c + ns
case (edge_dipole_distance_ID)
j = 0_pInt
slipFamilies2: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems2: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j + 1_pInt
plastic_disloUCLA_postResults(c+j) = &
(3.0_pReal*lattice_mu(ph)*plastic_disloUCLA_burgersPerSlipSystem(j,instance))/&
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))))
plastic_disloUCLA_postResults(c+j)=min(plastic_disloUCLA_postResults(c+j),&
state(instance)%mfp_slip(j,of))
enddo slipSystems2; enddo slipFamilies2
c = c + ns
end select
enddo
end function plastic_disloUCLA_postResults
end module plastic_disloUCLA
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