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
!--------------------------------------------------------------------------------------------------
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module plastic_disloUCLA
use prec, only: &
pReal, &
pInt
implicit none
private
integer(pInt), dimension(:), allocatable, public, protected :: &
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plastic_disloUCLA_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
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plastic_disloUCLA_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_disloUCLA_output !< name of each post result output
real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
integer(pInt), dimension(:), allocatable, target, public :: &
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plastic_disloUCLA_Noutput !< number of outputs per instance of this plasticity
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integer(pInt), dimension(:), allocatable, private :: &
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plastic_disloUCLA_totalNslip !< total number of active slip systems for each instance
integer(pInt), dimension(:,:), allocatable, private :: &
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plastic_disloUCLA_Nslip !< number of active slip systems for each family and instance
real(pReal), dimension(:), allocatable, private :: &
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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
real(pReal), dimension(:,:), allocatable, private :: &
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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_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
!* mobility law parameters
plastic_disloUCLA_friction !< friction coeff. B (kMC)
real(pReal), dimension(:,:,:), allocatable, private :: &
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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, &
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rho_ID, &
rhoDip_ID, &
shearrate_ID, &
accumulatedshear_ID, &
mfp_ID, &
resolvedstress_ID, &
thresholdstress_ID, &
dipoledistance_ID, &
stressexponent_ID
end enum
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type, private :: tParameters
real(pReal) :: &
aTolRho
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real(pReal), allocatable, dimension(:) :: &
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rho0, & !< initial edge dislocation density per slip system for each family and instance
rhoDip0, & !< initial edge dipole density per slip system for each family and instance
burgers, & !< absolute length of burgers vector [m] for each slip system and instance
H0kp, & !< activation energy for glide [J] for each slip system and instance
v0, & !< dislocation velocity prefactor [m/s] for each family and instance
CLambda, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
p, & !< p-exponent in glide velocity
q, & !< q-exponent in glide velocity
!* mobility law parameters
kink_height, & !< height of the kink pair
kink_width, & !< width of the kink pair
omega, & !< attempt frequency for kink pair nucleation
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viscosity, & !< friction coeff. B (kMC)
!*
tauPeierls, &
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nonSchmidCoeff
real(pReal), allocatable, dimension(:,:) :: &
interaction_SlipSlip !< slip resistance from slip activity
real(pReal), allocatable, dimension(:,:,:) :: &
Schmid_slip, &
Schmid_twin, &
nonSchmid_pos, &
nonSchmid_neg
integer(pInt) :: &
totalNslip !< total number of active slip system
integer(pInt), allocatable, dimension(:) :: &
Nslip !< number of active slip systems for each family
integer(kind(undefined_ID)), allocatable, dimension(:) :: &
outputID !< ID of each post result output
end type !< container type for internal constitutive parameters
type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance)
integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: &
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plastic_disloUCLA_outputID !< ID of each post result output
type, private :: tDisloUCLAState
real(pReal), pointer, dimension(:,:) :: &
rhoEdge, &
rhoEdgeDip, &
accshear_slip, &
invLambdaSlip, &
mfp_slip, &
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threshold_stress_slip
end type
type(tDisloUCLAState ), allocatable, dimension(:), private :: &
state, &
state0, &
dotState
public :: &
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plastic_disloUCLA_init, &
plastic_disloUCLA_microstructure, &
plastic_disloUCLA_LpAndItsTangent, &
plastic_disloUCLA_dotState, &
plastic_disloUCLA_postResults
private :: &
plastic_disloUCLA_stateInit
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_init(fileUnit)
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333, &
math_mul3x3, &
math_expand
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, &
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PLASTICITY_DISLOUCLA_label, &
PLASTICITY_DISLOUCLA_ID, &
material_phase, &
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plasticState, &
material_allocatePlasticState
use config, only: &
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MATERIAL_partPhase, &
config_phase
use lattice
implicit none
integer(pInt), intent(in) :: fileUnit
integer(pInt), allocatable, dimension(:) :: chunkPos
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integer(pInt) :: maxNinstance,mySize=0_pInt,phase,maxTotalNslip,&
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f,instance,j,k,o,ns, i, &
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Nchunks_SlipSlip = 0_pInt, outputSize, &
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Nchunks_SlipFamilies = 0_pInt,Nchunks_nonSchmid = 0_pInt, &
offset_slip, index_myFamily, index_otherFamily, &
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startIndex, endIndex, p
integer(pInt) :: sizeState, sizeDotState, sizeDeltaState
integer(pInt) :: NofMyPhase
character(len=65536) :: &
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structure = '',&
tag = '', &
line = ''
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real(pReal), dimension(:), allocatable :: tempPerSlip
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character(len=65536), dimension(:), allocatable :: outputs
integer(kind(undefined_ID)) :: outputID
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integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOUCLA_label//' init -+>>>'
write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78, 2016, 242-256'
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write(6,'(/,a)') ' http://dx.doi.org/10.1016/j.ijplas.2015.09.002'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
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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
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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_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)
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allocate(plastic_disloUCLA_friction(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
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allocate(plastic_disloUCLA_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
allocate(plastic_disloUCLA_tau_peierlsPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
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allocate(plastic_disloUCLA_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
source=0.0_pReal)
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allocate(plastic_disloUCLA_interaction_SlipSlip(lattice_maxNinteraction,maxNinstance),source=0.0_pReal)
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allocate(param(maxNinstance))
allocate(state(maxNinstance))
allocate(state0(maxNinstance))
allocate(dotState(maxNinstance))
do p = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle
associate(prm => param(phase_plasticityInstance(p)), &
dot => dotState(phase_plasticityInstance(p)), &
stt => state(phase_plasticityInstance(p)))
structure = config_phase(p)%getString('lattice_structure')
prm%aTolRho = config_phase(p)%getFloat('atol_rho')
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!--------------------------------------------------------------------------------------------------
! slip related parameters
prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyIntArray)
prm%totalNslip = sum(prm%Nslip)
slipActive: if (prm%totalNslip > 0_pInt) then
prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,structure(1:3),&
config_phase(p)%getFloat('c/a',defaultVal=0.0_pReal))
if(structure=='bcc') then
prm%nonSchmidCoeff = config_phase(p)%getFloats('nonschmid_coefficients',&
defaultVal = emptyRealArray)
prm%nonSchmid_pos = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,+1_pInt)
prm%nonSchmid_neg = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,-1_pInt)
else
prm%nonSchmid_pos = prm%Schmid_slip
prm%nonSchmid_neg = prm%Schmid_slip
endif
prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, &
config_phase(p)%getFloats('interaction_slipslip'), &
structure(1:3))
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!prm%rho0 = config_phase(p)%getFloats('rho0')
!prm%rhoDip0 = config_phase(p)%getFloats('dipole_rho0')
prm%burgers = config_phase(p)%getFloats('slipburgers')
prm%H0kp = config_phase(p)%getFloats('qedge')
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!prm%v0 = config_phase(p)%getFloats('v0')
!prm%clambda = config_phase(p)%getFloats('clambda')
!prm%tauPeierls = config_phase(p)%getFloats('peierls_stress')
prm%p = config_phase(p)%getFloats('p_slip',defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%q = config_phase(p)%getFloats('q_slip',defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%kink_height = config_phase(p)%getFloats('kink_height')
prm%kink_width = config_phase(p)%getFloats('kink_width')
prm%omega = config_phase(p)%getFloats('omega')
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!prm%viscosity = config_phase(p)%getFloats('viscosity')
! expand: family => system
prm%q = math_expand(prm%q, prm%Nslip)
prm%p = math_expand(prm%p, prm%Nslip)
prm%H0kp = math_expand(prm%H0kp, prm%Nslip)
prm%burgers = math_expand(prm%burgers, prm%Nslip)
prm%kink_height = math_expand(prm%kink_height, prm%Nslip)
prm%kink_width = math_expand(prm%kink_width, prm%Nslip)
prm%omega = math_expand(prm%omega, prm%Nslip)
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endif slipActive
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!--------------------------------------------------------------------------------------------------
! phase outputs
#if defined(__GFORTRAN__)
outputs = ['GfortranBug86277']
outputs = config_phase(p)%getStrings('(output)',defaultVal=outputs)
if (outputs(1) == 'GfortranBug86277') outputs = emptyStringArray
#else
outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray)
#endif
allocate(prm%outputID(0))
do i = 1_pInt, size(outputs)
outputID = undefined_ID
outputSize = prm%totalNslip
select case(trim(outputs(i)))
case ('edge_density')
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outputID = merge(rho_ID,undefined_ID,prm%totalNslip>0_pInt)
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case ('dipole_density')
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outputID = merge(rhoDip_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('shear_rate','shearrate','shear_rate_slip','shearrate_slip')
outputID = merge(shearrate_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('accumulated_shear','accumulatedshear','accumulated_shear_slip')
outputID = merge(accumulatedshear_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('mfp','mfp_slip')
outputID = merge(mfp_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('resolved_stress','resolved_stress_slip')
outputID = merge(resolvedstress_ID,undefined_ID,prm%totalNslip>0_pInt)
case ('threshold_stress','threshold_stress_slip')
outputID = merge(thresholdstress_ID,undefined_ID,prm%totalNslip>0_pInt)
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case ('edge_dipole_distance')
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outputID = merge(dipoleDistance_ID,undefined_ID,prm%totalNslip>0_pInt)
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case ('stress_exponent')
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outputID = merge(stressexponent_ID,undefined_ID,prm%totalNslip>0_pInt)
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end select
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if (outputID /= undefined_ID) then
plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i)
plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
prm%outputID = [prm%outputID, outputID]
plastic_disloUCLA_outputID(i,phase_plasticityInstance(p)) = outputID
plastic_disloUCLA_sizePostResults(phase_plasticityInstance(p)) = &
plastic_disloUCLA_sizePostResults(phase_plasticityInstance(p)) + outputSize
plastic_disloUCLA_Noutput(phase_plasticityInstance(p)) = plastic_disloUCLA_Noutput(phase_plasticityInstance(p)) + 1_pInt
endif
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enddo
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end associate
enddo
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
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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
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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)
!--------------------------------------------------------------------------------------------------
! parameters depending on number of slip system families
case ('nslip')
if (chunkPos(1) < Nchunks_SlipFamilies + 1_pInt) &
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call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOUCLA_label//')')
if (chunkPos(1) > Nchunks_SlipFamilies + 1_pInt) &
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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',&
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'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')
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plastic_disloUCLA_rhoEdge0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('rhoedgedip0')
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plastic_disloUCLA_rhoEdgeDip0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('v0')
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plastic_disloUCLA_v0PerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('clambdaslip')
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plastic_disloUCLA_CLambdaSlipPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('tau_peierls')
if (lattice_structure(phase) /= LATTICE_bcc_ID) &
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call IO_warning(42_pInt,ext_msg=trim(tag)//' for non-bcc ('//PLASTICITY_DISLOUCLA_label//')')
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plastic_disloUCLA_tau_peierlsPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('friction_coeff')
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plastic_disloUCLA_friction(1:Nchunks_SlipFamilies,instance) = &
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tempPerSlip(1:Nchunks_SlipFamilies)
end select
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!--------------------------------------------------------------------------------------------------
! parameters depending on number of interactions
case ('interaction_slipslip','interactionslipslip')
if (chunkPos(1) < 1_pInt + Nchunks_SlipSlip) &
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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
!--------------------------------------------------------------------------------------------------
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! 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 ('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)
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myPhase: if (phase_plasticity(phase) == PLASTICITY_disloUCLA_ID) then
instance = phase_plasticityInstance(phase)
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if (sum(plastic_disloUCLA_Nslip(:,instance)) < 0_pInt) &
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call IO_error(211_pInt,el=instance,ext_msg='Nslip ('//PLASTICITY_DISLOUCLA_label//')')
do f = 1_pInt,lattice_maxNslipFamily
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if (plastic_disloUCLA_Nslip(f,instance) > 0_pInt) then
if (plastic_disloUCLA_rhoEdge0(f,instance) < 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOUCLA_label//')')
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if (plastic_disloUCLA_rhoEdgeDip0(f,instance) < 0.0_pReal) &
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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//')')
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if (plastic_disloUCLA_v0PerSlipFamily(f,instance) <= 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOUCLA_label//')')
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if (plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOUCLA_label//')')
endif
enddo
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if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')')
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if (plastic_disloUCLA_D0(instance) <= 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOUCLA_label//')')
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if (plastic_disloUCLA_Qsd(instance) <= 0.0_pReal) &
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call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOUCLA_label//')')
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! if (plastic_disloUCLA_aTolRho(instance) <= 0.0_pReal) &
! call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOUCLA_label//')')
!--------------------------------------------------------------------------------------------------
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! Determine total number of active slip systems
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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
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maxTotalNslip = maxval(plastic_disloUCLA_totalNslip)
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)
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allocate(plastic_disloUCLA_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance), &
source=0.0_pReal)
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initializeInstances: do phase = 1_pInt, size(phase_plasticity)
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myPhase2: if (phase_plasticity(phase) == PLASTICITY_disloUCLA_ID) then
p = phase
NofMyPhase=count(material_phase==phase)
instance = phase_plasticityInstance(phase)
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ns = plastic_disloUCLA_totalNslip(instance)
associate(prm => param(instance), stt=>state(instance))
!--------------------------------------------------------------------------------------------------
! allocate state arrays
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sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * ns
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sizeDeltaState = 0_pInt
sizeState = sizeDotState &
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+ int(size(['invLambdaSlip ',&
'meanFreePathSlip ','tauSlipThreshold ']),pInt) * ns
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call material_allocatePlasticState(phase,NofMyPhase,sizeState,sizeDotState,0_pInt, &
ns,0_pInt,0_pInt)
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plasticState(phase)%sizePostResults = plastic_disloUCLA_sizePostResults(instance)
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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
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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)
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plastic_disloUCLA_v0PerSlipSystem(index_myFamily+j,instance) = &
plastic_disloUCLA_v0PerSlipFamily(f,instance)
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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
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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)))
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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
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enddo mySlipSystems
enddo mySlipFamilies
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startIndex=1_pInt
endIndex=ns
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stt%rhoEdge=>plasticState(phase)%state(startIndex:endIndex,:)
dotState(instance)%rhoEdge=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
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startIndex=endIndex+1_pInt
endIndex=endIndex+ns
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stt%rhoEdgeDip=>plasticState(phase)%state(startIndex:endIndex,:)
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dotState(instance)%rhoEdgeDip=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
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startIndex=endIndex+1_pInt
endIndex=endIndex+ns
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stt%accshear_slip=>plasticState(phase)%state(startIndex:endIndex,:)
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dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(p)%aTolState(startIndex:endIndex) = 1e6_pReal
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startIndex=endIndex+1_pInt
endIndex=endIndex+ns
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stt%invLambdaSlip=>plasticState(phase)%state(startIndex:endIndex,:)
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startIndex=endIndex+1_pInt
endIndex=endIndex+ns
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stt%mfp_slip=>plasticState(phase)%state(startIndex:endIndex,:)
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startIndex=endIndex+1_pInt
endIndex=endIndex+ns
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stt%threshold_stress_slip=>plasticState(phase)%state(startIndex:endIndex,:)
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call plastic_disloUCLA_stateInit(phase,instance)
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
end associate
endif myPhase2
enddo initializeInstances
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end subroutine plastic_disloUCLA_init
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
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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
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integer(pInt) :: i,f,ns, index_myFamily
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real(pReal), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
rhoEdge0, &
rhoEdgeDip0, &
invLambdaSlip0, &
MeanFreePathSlip0, &
tauSlipThreshold0
tempState = 0.0_pReal
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ns = plastic_disloUCLA_totalNslip(instance)
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associate(prm => param(instance))
!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables
do f = 1_pInt,lattice_maxNslipFamily
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index_myFamily = sum(plastic_disloUCLA_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
rhoEdge0(index_myFamily+1_pInt: &
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index_myFamily+plastic_disloUCLA_Nslip(f,instance)) = &
plastic_disloUCLA_rhoEdge0(f,instance)
rhoEdgeDip0(index_myFamily+1_pInt: &
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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) &
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invLambdaSlip0(i) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),plastic_disloUCLA_forestProjectionEdge(1:ns,i,instance)))/ &
plastic_disloUCLA_CLambdaSlipPerSlipSystem(i,instance)
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tempState(3_pInt*ns+1:4_pInt*ns) = invLambdaSlip0
forall (i = 1_pInt:ns) &
MeanFreePathSlip0(i) = &
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plastic_disloUCLA_GrainSize(instance)/(1.0_pReal+invLambdaSlip0(i)*plastic_disloUCLA_GrainSize(instance))
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tempState(4_pInt*ns+1:5_pInt*ns) = MeanFreePathSlip0
forall (i = 1_pInt:ns) &
tauSlipThreshold0(i) = &
lattice_mu(ph)*prm%burgers(i) * &
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sqrt(dot_product((rhoEdge0+rhoEdgeDip0),plastic_disloUCLA_interactionMatrix_SlipSlip(i,1:ns,instance)))
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tempState(5_pInt*ns+1:6_pInt*ns) = tauSlipThreshold0
plasticState(ph)%state = spread(tempState,2,size(plasticState(ph)%state(1,:)))
end associate
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end subroutine plastic_disloUCLA_stateInit
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_microstructure(temperature,ipc,ip,el)
use math, only: &
pi
use material, only: &
phase_plasticityInstance, &
phaseAt, phasememberAt
use lattice, only: &
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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, &
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ns,s, &
ph, &
of
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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ns = plastic_disloUCLA_totalNslip(instance)
associate(prm => param(instance), stt => state(instance))
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
forall (s = 1_pInt:ns) &
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stt%invLambdaSlip(s,of) = &
sqrt(dot_product((stt%rhoEdge(1_pInt:ns,of)+stt%rhoEdgeDip(1_pInt:ns,of)),&
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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
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stt%mfp_slip(s,of) = &
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plastic_disloUCLA_GrainSize(instance)/&
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(1.0_pReal+plastic_disloUCLA_GrainSize(instance)*(stt%invLambdaSlip(s,of)))
enddo
!* threshold stress for dislocation motion
forall (s = 1_pInt:ns) &
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stt%threshold_stress_slip(s,of) = &
lattice_mu(ph)*prm%burgers(s)*&
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sqrt(dot_product((stt%rhoEdge(1_pInt:ns,of)+stt%rhoEdgeDip(1_pInt:ns,of)),&
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plastic_disloUCLA_interactionMatrix_SlipSlip(s,1:ns,instance)))
end associate
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end subroutine plastic_disloUCLA_microstructure
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,ipc,ip,el)
use material, only: &
material_phase, &
phase_plasticityInstance, &
phaseAt, phasememberAt
implicit none
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: Temperature
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real(pReal), dimension(3,3), intent(in) :: Mp
real(pReal), dimension(3,3), intent(out) :: Lp
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real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
integer(pInt) :: instance,ph,of,i,k,l,m,n
2018-11-28 00:19:04 +05:30
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real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip_pos,gdot_slip_neg,tau_slip_pos,tau_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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associate(prm => param(instance))
Lp = 0.0_pReal
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dLp_dMp = 0.0_pReal
call kinetics(Mp,Temperature,ph,instance,of, &
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gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
slipSystems: do i = 1_pInt, prm%totalNslip
Lp = Lp + (gdot_slip_pos(i)+gdot_slip_neg(i))*prm%Schmid_slip(1:3,1:3,i)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
+ dgdot_dtauslip_pos(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_pos(m,n,i) &
+ dgdot_dtauslip_neg(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_neg(m,n,i)
enddo slipSystems
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end associate
Lp = 0.5_pReal * Lp
dLp_dMp = 0.5_pReal * dLp_dMp
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end subroutine plastic_disloUCLA_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
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subroutine plastic_disloUCLA_dotState(Mp,Temperature,ipc,ip,el)
use prec, only: &
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tol_math_check, &
dEq0
use math, only: &
pi
use material, only: &
material_phase, &
phase_plasticityInstance, &
plasticState, &
phaseAt, phasememberAt
use lattice, only: &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
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lattice_mu
implicit none
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real(pReal), dimension(3,3), intent(in):: &
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
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integer(pInt) :: instance,ns,f,i,j,index_myFamily, &
ph, &
of
real(pReal) :: &
EdgeDipMinDistance,&
AtomicVolume,&
VacancyDiffusion,&
DotRhoMultiplication,&
EdgeDipDistance, &
DotRhoEdgeDipAnnihilation, &
DotRhoEdgeEdgeAnnihilation, &
ClimbVelocity, &
DotRhoEdgeDipClimb, &
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DotRhoDipFormation
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real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip_pos, gdot_slip_neg,&
tau_slip_pos,&
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tau_slip_neg, &
dgdot_dtauslip_neg,dgdot_dtauslip_pos
!* Shortened notation
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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ns = plastic_disloUCLA_totalNslip(instance)
plasticState(ph)%dotState(:,of) = 0.0_pReal
associate(prm => param(instance), stt => state(instance))
!* Dislocation density evolution
call kinetics(Mp,Temperature,ph,instance,of, &
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gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
dotState(instance)%accshear_slip(:,of) = (gdot_slip_pos+gdot_slip_neg)*0.5_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
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slipSystems: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j+1_pInt
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!* Multiplication
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DotRhoMultiplication = abs(dotState(instance)%accshear_slip(j,of))/&
(prm%burgers(j)* &
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stt%mfp_slip(j,of))
!* Dipole formation
EdgeDipMinDistance = &
plastic_disloUCLA_CEdgeDipMinDistance(instance)*prm%burgers(j)
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if (dEq0(tau_slip_pos(j))) then
DotRhoDipFormation = 0.0_pReal
else
EdgeDipDistance = &
(3.0_pReal*lattice_mu(ph)*prm%burgers(j))/&
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(16.0_pReal*pi*abs(tau_slip_pos(j)))
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if (EdgeDipDistance>stt%mfp_slip(j,of)) EdgeDipDistance=stt%mfp_slip(j,of)
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
DotRhoDipFormation = &
((2.0_pReal*EdgeDipDistance)/prm%burgers(j))*&
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stt%rhoEdge(j,of)*abs(dotState(instance)%accshear_slip(j,of))*plastic_disloUCLA_dipoleFormationFactor(instance)
endif
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation = &
((2.0_pReal*EdgeDipMinDistance)/prm%burgers(j))*&
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stt%rhoEdge(j,of)*abs(dotState(instance)%accshear_slip(j,of))
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation = &
((2.0_pReal*EdgeDipMinDistance)/prm%burgers(j))*&
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stt%rhoEdgeDip(j,of)*abs(dotState(instance)%accshear_slip(j,of))
!* Dislocation dipole climb
AtomicVolume = &
plastic_disloUCLA_CAtomicVolume(instance)*prm%burgers(j)**(3.0_pReal)
VacancyDiffusion = &
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plastic_disloUCLA_D0(instance)*exp(-plastic_disloUCLA_Qsd(instance)/(kB*Temperature))
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if (dEq0(tau_slip_pos(j))) 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 = &
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(4.0_pReal*ClimbVelocity*stt%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
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enddo slipSystems
enddo slipFamilies
end associate
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end subroutine plastic_disloUCLA_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_disloUCLA_postResults(Mp,Temperature,ipc,ip,el) result(postResults)
use prec, only: &
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tol_math_check, &
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dEq, dNeq0
use math, only: &
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pi, &
math_mul33xx33
use material, only: &
material_phase, &
phase_plasticityInstance,&
!plasticState, &
phaseAt, phasememberAt
use lattice, only: &
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lattice_Sslip, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
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lattice_mu
implicit none
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
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real(pReal), dimension(plastic_disloUCLA_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
postResults
integer(pInt) :: &
instance,&
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ns,&
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f,o,i,c,j,index_myFamily,&
ph, &
of
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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)
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ns = plastic_disloUCLA_totalNslip(instance)
!* Required output
c = 0_pInt
postResults = 0.0_pReal
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associate (prm => param(instance),stt =>state(instance))
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do o = 1_pInt,plastic_disloUCLA_Noutput(instance)
select case(plastic_disloUCLA_outputID(o,instance))
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case (rho_ID)
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postResults(c+1_pInt:c+ns) = stt%rhoEdge(1_pInt:ns,of)
c = c + ns
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case (rhoDip_ID)
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postResults(c+1_pInt:c+ns) = stt%rhoEdgeDip(1_pInt:ns,of)
c = c + ns
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case (shearrate_ID,stressexponent_ID)
call kinetics(Mp,Temperature,ph,instance,of, &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
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if (plastic_disloUCLA_outputID(o,instance) == shearrate_ID) then
postResults(c+1:c+ns) = (gdot_slip_pos + gdot_slip_neg)*0.5_pReal
c = c + ns
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elseif(plastic_disloUCLA_outputID(o,instance) == stressexponent_ID) then
do j = 1_pInt, ns
if (dEq(gdot_slip_pos(j)+gdot_slip_neg(j),0.0_pReal)) then
postResults(c+j) = 0.0_pReal
else
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
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case (accumulatedshear_ID)
postResults(c+1_pInt:c+ns) = &
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stt%accshear_slip(1_pInt:ns, of)
c = c + ns
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case (mfp_ID)
postResults(c+1_pInt:c+ns) =&
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stt%mfp_slip(1_pInt:ns, of)
c = c + ns
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case (resolvedstress_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
postResults(c+j) =&
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math_mul33xx33(Mp,lattice_Sslip(:,:,1,index_myFamily+i,ph))
enddo slipSystems1; enddo slipFamilies1
c = c + ns
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case (thresholdstress_ID)
postResults(c+1_pInt:c+ns) = &
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stt%threshold_stress_slip(1_pInt:ns,of)
c = c + ns
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case (dipoleDistance_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
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if (dNeq0(abs(math_mul33xx33(Mp,lattice_Sslip(:,:,1,index_myFamily+i,ph))))) then
postResults(c+j) = &
(3.0_pReal*lattice_mu(ph)*prm%burgers(j))/&
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(16.0_pReal*pi*abs(math_mul33xx33(Mp,lattice_Sslip(:,:,1,index_myFamily+i,ph))))
else
postResults(c+j) = huge(1.0_pReal)
endif
postResults(c+j)=min(postResults(c+j),&
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stt%mfp_slip(j,of))
enddo slipSystems2; enddo slipFamilies2
c = c + ns
end select
enddo
end associate
end function plastic_disloUCLA_postResults
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
subroutine kinetics(Mp,Temperature,ph,instance,of, &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
use prec, only: &
tol_math_check, &
dEq, dNeq0
use math, only: &
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pi, &
math_mul33xx33
use material, only: &
material_phase, &
phase_plasticityInstance,&
!plasticState, &
phaseAt, phasememberAt
use lattice, only: &
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lattice_Sslip, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
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lattice_NnonSchmid
implicit none
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real(pReal), dimension(3,3), intent(in) :: &
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ph, instance,of
integer(pInt) :: &
ns,&
f,i,j,k,index_myFamily
real(pReal) :: StressRatio_p,StressRatio_pminus1,&
BoltzmannRatio,DotGamma0,stressRatio,&
dvel_slip, vel_slip
real(pReal), intent(out), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
associate(prm => param(instance), stt => state(instance))
!* Shortened notation
ns = plastic_disloUCLA_totalNslip(instance)
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
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slipSystems: do i = 1_pInt,plastic_disloUCLA_Nslip(f,instance)
j = j + 1_pInt
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!* Boltzmann ratio
BoltzmannRatio = prm%H0kp(j)/(kB*Temperature)
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!* Initial shear rates
DotGamma0 = &
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stt%rhoEdge(j,of)*prm%burgers(j)*&
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plastic_disloUCLA_v0PerSlipSystem(j,instance)
!* Resolved shear stress on slip system
tau_slip_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j))
tau_slip_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
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significantPositiveTau: if((abs(tau_slip_pos(j))-stt%threshold_stress_slip(j, of)) > tol_math_check) then
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!* Stress ratio
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stressRatio = ((abs(tau_slip_pos(j))-stt%threshold_stress_slip(j, of))/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** prm%p(j)
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
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!* Shear rates due to slip
vel_slip = 2.0_pReal*prm%burgers(j) &
* prm%kink_height(j) * prm%omega(j) &
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* ( stt%mfp_slip(j,of) - prm%kink_width(j) ) &
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* (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
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/ ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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)
gdot_slip_pos(j) = DotGamma0 &
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* vel_slip &
* sign(1.0_pReal,tau_slip_pos(j))
!* Derivatives of shear rates
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dvel_slip = &
2.0_pReal*prm%burgers(j) &
* prm%kink_height(j) * prm%omega(j) &
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* ( stt%mfp_slip(j,of) - prm%kink_width(j) ) &
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* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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+ tau_slip_pos(j) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& !deltaf(i)
*BoltzmannRatio*prm%p(j)&
*prm%q(j)/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) &!deltaf(f)
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) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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) &
- (tau_slip_pos(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& !deltaf(i)
*BoltzmannRatio*prm%p(j)&
*prm%q(j)/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )& !deltaf(f)
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) &
) &
/ ( &
( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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)**2.0_pReal &
)
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dgdot_dtauslip_pos(j) = DotGamma0 * dvel_slip
endif significantPositiveTau
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significantNegativeTau: if((abs(tau_slip_neg(j))-stt%threshold_stress_slip(j, of)) > tol_math_check) then
!* Stress ratios
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stressRatio = ((abs(tau_slip_neg(j))-stt%threshold_stress_slip(j, of))/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+&
plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance)))
stressRatio_p = stressRatio** prm%p(j)
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
!* Shear rates due to slip
vel_slip = 2.0_pReal*prm%burgers(j) &
* prm%kink_height(j) * prm%omega(j) &
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* ( stt%mfp_slip(j,of) - prm%kink_width(j) ) &
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* (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
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/ ( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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)
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gdot_slip_neg(j) = DotGamma0 &
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* vel_slip &
* sign(1.0_pReal,tau_slip_neg(j))
!* Derivatives of shear rates
dvel_slip = &
2.0_pReal*prm%burgers(j) &
* prm%kink_height(j) * prm%omega(j) &
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* ( stt%mfp_slip(j,of) - prm%kink_width(j) ) &
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* ( &
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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+ tau_slip_neg(j) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& !deltaf(i)
*BoltzmannRatio*prm%p(j)&
*prm%q(j)/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) &!deltaf(f)
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) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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) &
- (tau_slip_neg(j) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))& !deltaf(i)
*BoltzmannRatio*prm%p(j)&
*prm%q(j)/&
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(plastic_disloUCLA_SolidSolutionStrength(instance)+plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance))*&
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )& !deltaf(f)
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) &
) &
/ ( &
( &
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
+ prm%omega(j) * plastic_disloUCLA_friction(f,instance) &
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*(( stt%mfp_slip(j,of) - prm%kink_width(j) )**2.0_pReal) &
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
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)**2.0_pReal &
)
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dgdot_dtauslip_neg(j) = DotGamma0 * dvel_slip
endif significantNegativeTau
enddo slipSystems
enddo slipFamilies
end associate
end subroutine kinetics
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end module plastic_disloUCLA