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DAMASK_EICMD/src/plastic_kinematichardening.f90

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fixed backstress rate of change based on its own slip system evolution and its sense
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!--------------------------------------------------------------------------------------------------
first shot at kinematic hardening constitutive law
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
fixed backstress rate of change based on its own slip system evolution and its sense
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!> @author Zhuowen Zhao, Michigan State University
change tag to all lowercase; make pheno hardeing only depend on its own system
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!> @brief Introducing Voce-type kinematic hardening rule into crystal plasticity
first shot at kinematic hardening constitutive law
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!! formulation using a power law fitting
!--------------------------------------------------------------------------------------------------
module plastic_kinehardening
use prec, only: &
pReal,&
pInt
implicit none
private
integer(pInt), dimension(:), allocatable, public, protected :: &
plastic_kinehardening_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
plastic_kinehardening_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_kinehardening_output !< name of each post result output
integer(pInt), dimension(:), allocatable, target, public :: &
plastic_kinehardening_Noutput !< number of outputs per instance
integer(pInt), dimension(:), allocatable, public, protected :: &
plastic_kinehardening_totalNslip !< no. of slip system used in simulation
integer(pInt), dimension(:,:), allocatable, private :: &
plastic_kinehardening_Nslip !< active number of slip systems per family (input parameter, per family)
enum, bind(c)
enumerator :: undefined_ID, &
crss_ID, & !< critical resolved stress
crss_back_ID, & !< critical resolved back stress
sense_ID, & !< sense of acting shear stress (-1 or +1)
chi0_ID, & !< backstress at last switch of stress sense (positive?)
gamma0_ID, & !< accumulated shear at last switch of stress sense (at current switch?)
accshear_ID, &
sumGamma_ID, &
shearrate_ID, &
resolvedstress_ID
end enum
type, private :: tParameters !< container type for internal constitutive parameters
integer(kind(undefined_ID)), dimension(:), allocatable, private :: &
outputID !< ID of each post result output
real(pReal) :: &
fixed backstress rate of change based on its own slip system evolution and its sense
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! F0, &
! mu, &
! mu0, &
! tau_hat0, &
! p1, &
! q1, &
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gdot0, & !< reference shear strain rate for slip (input parameter)
n_slip, & !< stress exponent for slip (input parameter)
aTolResistance, &
aTolShear
real(pReal), dimension(:), allocatable, private :: &
renamed "tau0" to "crss0"
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crss0, & !< initial critical shear stress for slip (input parameter, per family)
first shot at kinematic hardening constitutive law
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theta0, & !< initial hardening rate of forward stress for each slip
theta1, & !< asymptotic hardening rate of forward stress for each slip >
theta0_b, & !< initial hardening rate of back stress for each slip >
theta1_b, & !< asymptotic hardening rate of back stress for each slip >
tau1, &
tau1_b, &
interaction_slipslip, & !< latent hardening matrix
nonSchmidCoeff
real(pReal), dimension(:,:), allocatable, private :: &
hardeningMatrix_SlipSlip
end type
type, private :: tKinehardeningState
real(pReal), pointer, dimension(:,:) :: & !< vectors along NipcMyInstance
crss, & !< critical resolved stress
crss_back, & !< critical resolved back stress
sense, & !< sense of acting shear stress (-1 or +1)
chi0, & !< backstress at last switch of stress sense
gamma0, & !< accumulated shear at last switch of stress sense
accshear !< accumulated (absolute) shear
real(pReal), pointer, dimension(:) :: & !< scalars along NipcMyInstance
sumGamma !< accumulated shear across all systems
end type
type(tParameters), dimension(:), allocatable, private :: &
param !< containers of constitutive parameters (len Ninstance)
type(tKinehardeningState), allocatable, dimension(:), private :: &
dotState, &
deltaState, &
state, &
state0
public :: &
plastic_kinehardening_init, &
plastic_kinehardening_LpAndItsTangent, &
plastic_kinehardening_dotState, &
plastic_kinehardening_deltaState, &
plastic_kinehardening_postResults
private :: &
plastic_kinehardening_shearRates
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_kinehardening_init(fileUnit)
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use prec, only: &
dEq0
use debug, only: &
debug_level, &
debug_constitutive,&
debug_levelBasic
use math, only: &
math_Mandel3333to66, &
math_Voigt66to3333, &
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: &
PLASTICITY_kinehardening_label, &
PLASTICITY_kinehardening_ID, &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
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) :: &
o, j, k, f, &
output_ID, &
phase, &
instance, &
maxNinstance, &
NipcMyPhase, &
Nchunks_SlipSlip = 0_pInt, Nchunks_SlipFamilies = 0_pInt, &
Nchunks_nonSchmid = 0_pInt, &
offset_slip, index_myFamily, index_otherFamily, &
startIndex, endIndex, &
mySize, nSlip, nSlipFamilies, &
sizeDotState, &
sizeState, &
sizeDeltaState
real(pReal), dimension(:), allocatable :: tempPerSlip
character(len=65536) :: &
tag = '', &
line = '', &
extmsg = ''
character(len=64) :: &
outputtag = ''
write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_KINEHARDENING_label//' init -+>>>'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == PLASTICITY_KINEHARDENING_ID),pInt)
if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a,1x,i5,/)') '# instances:',maxNinstance
allocate(plastic_kinehardening_sizePostResults(maxNinstance), source=0_pInt)
allocate(plastic_kinehardening_sizePostResult(maxval(phase_Noutput),maxNinstance), &
source=0_pInt)
allocate(plastic_kinehardening_output(maxval(phase_Noutput),maxNinstance))
plastic_kinehardening_output = ''
allocate(plastic_kinehardening_Noutput(maxNinstance), source=0_pInt)
allocate(plastic_kinehardening_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
allocate(plastic_kinehardening_totalNslip(maxNinstance), source=0_pInt)
allocate(param(maxNinstance)) ! one container of parameters per instance
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
phase = phase + 1_pInt ! advance phase section counter
if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then
instance = phase_plasticityInstance(phase) ! count instances of my constitutive law
Nchunks_SlipFamilies = count(lattice_NslipSystem(:,phase) > 0_pInt) ! maximum number of slip families according to lattice type of current phase
Nchunks_SlipSlip = maxval(lattice_interactionSlipSlip(:,:,phase))
Nchunks_nonSchmid = lattice_NnonSchmid(phase)
assign outputID type to undifined
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allocate(param(instance)%outputID(phase_Noutput(phase)), source=undefined_ID) ! allocate space for IDs of every requested output
added "plastic_kinematichardeing.f90" to commercialFEM_fileList Changed outputID type
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allocate(param(instance)%crss0 (Nchunks_SlipFamilies), source=0.0_pReal)
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allocate(param(instance)%tau1 (Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%tau1_b (Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%theta0 (Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%theta1 (Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%theta0_b(Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%theta1_b(Nchunks_SlipFamilies), source=0.0_pReal)
allocate(param(instance)%interaction_slipslip(Nchunks_SlipSlip), source=0.0_pReal)
allocate(param(instance)%nonSchmidCoeff(Nchunks_nonSchmid), source=0.0_pReal)
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_KINEHARDENING_ID) then ! one of my phases. Do not short-circuit here (.and. between if-statements), 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)')
outputtag = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
output_ID = undefined_ID
select case(outputtag)
case ('resistance')
output_ID = crss_ID
case ('backstress')
output_ID = crss_back_ID
case ('sense')
output_ID = sense_ID
case ('chi0')
output_ID = chi0_ID
case ('gamma0')
output_ID = gamma0_ID
case ('accumulatedshear')
output_ID = accshear_ID
case ('totalshear')
output_ID = sumGamma_ID
case ('shearrate')
output_ID = shearrate_ID
case ('resolvedstress')
output_ID = resolvedstress_ID
end select
if (output_ID /= undefined_ID) then
plastic_kinehardening_Noutput(instance) = plastic_kinehardening_Noutput(instance) + 1_pInt
plastic_kinehardening_output(plastic_kinehardening_Noutput(instance),instance) = outputtag
param(instance)%outputID (plastic_kinehardening_Noutput(instance)) = output_ID
endif
!--------------------------------------------------------------------------------------------------
! parameters depending on number of slip families
case ('nslip')
if (chunkPos(1) < Nchunks_SlipFamilies + 1_pInt) &
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
if (chunkPos(1) > Nchunks_SlipFamilies + 1_pInt) &
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
Nchunks_SlipFamilies = chunkPos(1) - 1_pInt ! user specified number of (possibly) active slip families (e.g. 6 0 6 --> 3)
do j = 1_pInt, Nchunks_SlipFamilies
plastic_kinehardening_Nslip(j,instance) = IO_intValue(line,chunkPos,1_pInt+j)
enddo
renamed "tau0" to "crss0"
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case ('crss0','tau1','tau1_b','theta0','theta1','theta0_b','theta1_b')
first shot at kinematic hardening constitutive law
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tempPerSlip = 0.0_pReal
do j = 1_pInt, Nchunks_SlipFamilies
if (plastic_kinehardening_Nslip(j,instance) > 0_pInt) &
tempPerSlip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
select case(tag)
renamed "tau0" to "crss0"
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case ('crss0')
param(instance)%crss0(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
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case ('tau1')
param(instance)%tau1(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('tau1_b')
param(instance)%tau1_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('theta0')
param(instance)%theta0(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('theta1')
param(instance)%theta1(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('theta0_b')
param(instance)%theta0_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
case ('theta1_b')
param(instance)%theta1_b(1:Nchunks_SlipFamilies) = tempPerSlip(1:Nchunks_SlipFamilies)
end select
!--------------------------------------------------------------------------------------------------
! parameters depending on number of interactions
case ('interaction_slipslip')
if (chunkPos(1) < 1_pInt + Nchunks_SlipSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
do j = 1_pInt, Nchunks_SlipSlip
param(instance)%interaction_slipslip(j) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
change tag to all lowercase; make pheno hardeing only depend on its own system
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case ('nonschmidcoeff')
first shot at kinematic hardening constitutive law
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if (chunkPos(1) < 1_pInt + Nchunks_nonSchmid) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_KINEHARDENING_label//')')
do j = 1_pInt,Nchunks_nonSchmid
param(instance)%nonSchmidCoeff(j) = IO_floatValue(line,chunkPos,1_pInt+j)
enddo
!--------------------------------------------------------------------------------------------------
fixed backstress rate of change based on its own slip system evolution and its sense
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! parameters independent of number of slip families
! case ('F0')
! param(instance)%F0 = IO_floatValue(line,chunkPos,2_pInt)
!
! case ('mu')
! param(instance)%mu = IO_floatValue(line,chunkPos,2_pInt)
!
! case ('mu0')
! param(instance)%mu0 = IO_floatValue(line,chunkPos,2_pInt)
!
! case ('tau_hat0')
! param(instance)%tau_hat0 = IO_floatValue(line,chunkPos,2_pInt)
!
! case ('p1')
! param(instance)%p1 = IO_floatValue(line,chunkPos,2_pInt)
!
! case ('q1')
! param(instance)%q1 = IO_floatValue(line,chunkPos,2_pInt)
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case ('gdot0')
param(instance)%gdot0 = IO_floatValue(line,chunkPos,2_pInt)
case ('n_slip')
param(instance)%n_slip = IO_floatValue(line,chunkPos,2_pInt)
change tag to all lowercase; make pheno hardeing only depend on its own system
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case ('atol_resistance')
first shot at kinematic hardening constitutive law
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param(instance)%aTolResistance = IO_floatValue(line,chunkPos,2_pInt)
change tag to all lowercase; make pheno hardeing only depend on its own system
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case ('atol_shear')
first shot at kinematic hardening constitutive law
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param(instance)%aTolShear = IO_floatValue(line,chunkPos,2_pInt)
case default
end select
endif; endif
enddo parsingFile
!--------------------------------------------------------------------------------------------------
! allocation of variables whose size depends on the total number of active slip systems
allocate(state(maxNinstance))
allocate(state0(maxNinstance))
allocate(dotState(maxNinstance))
allocate(deltaState(maxNinstance))
initializeInstances: do phase = 1_pInt, size(phase_plasticity) ! loop through all phases in material.config
myPhase2: if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then ! only consider my phase
NipcMyPhase = count(material_phase == phase) ! number of IPCs containing my phase
instance = phase_plasticityInstance(phase) ! which instance of my phase
plastic_kinehardening_Nslip(1:lattice_maxNslipFamily,instance) = &
min(lattice_NslipSystem(1:lattice_maxNslipFamily,phase),& ! limit active slip systems per family to min of available and requested
plastic_kinehardening_Nslip(1:lattice_maxNslipFamily,instance))
plastic_kinehardening_totalNslip(instance) = sum(plastic_kinehardening_Nslip(:,instance)) ! how many slip systems altogether
nSlipFamilies = count(plastic_kinehardening_Nslip(:,instance) > 0_pInt)
nSlip = plastic_kinehardening_totalNslip(instance) ! total number of active slip systems
!--------------------------------------------------------------------------------------------------
! sanity checks
if (any(plastic_kinehardening_Nslip(1:nSlipFamilies,instance) > 0_pInt &
renamed "tau0" to "crss0"
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.and. param(instance)%crss0(1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' crss0'
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if (any(plastic_kinehardening_Nslip(1:nSlipFamilies,instance) > 0_pInt &
.and. param(instance)%tau1(1:nSlipFamilies) <= 0.0_pReal)) extmsg = trim(extmsg)//' tau1'
if (any(plastic_kinehardening_Nslip(1:nSlipFamilies,instance) > 0_pInt &
.and. param(instance)%tau1_b(1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' tau1_b'
if (param(instance)%gdot0 <= 0.0_pReal) extmsg = trim(extmsg)//' gdot0'
if (param(instance)%n_slip <= 0.0_pReal) extmsg = trim(extmsg)//' n_slip'
if (param(instance)%aTolResistance <= 0.0_pReal) param(instance)%aTolResistance = 1.0_pReal ! default absolute tolerance 1 Pa
if (param(instance)%aTolShear <= 0.0_pReal) param(instance)%aTolShear = 1.0e-6_pReal ! default absolute tolerance 1e-6
if (extmsg /= '') then
extmsg = trim(extmsg)//' ('//PLASTICITY_KINEHARDENING_label//')' ! prepare error message identifier
call IO_error(211_pInt,ip=instance,ext_msg=extmsg)
endif
!--------------------------------------------------------------------------------------------------
! Determine size of postResults array
outputsLoop: do o = 1_pInt,plastic_kinehardening_Noutput(instance)
select case(param(instance)%outputID(o))
case(crss_ID, & !< critical resolved stress
crss_back_ID, & !< critical resolved back stress
sense_ID, & !< sense of acting shear stress (-1 or +1)
chi0_ID, & !< backstress at last switch of stress sense
gamma0_ID, & !< accumulated shear at last switch of stress sense
accshear_ID, &
shearrate_ID, &
resolvedstress_ID)
mySize = nSlip
case(sumGamma_ID)
mySize = 1_pInt
case default
end select
outputFound: if (mySize > 0_pInt) then
plastic_kinehardening_sizePostResult(o,instance) = mySize
plastic_kinehardening_sizePostResults(instance) = plastic_kinehardening_sizePostResults(instance) + mySize
endif outputFound
enddo outputsLoop
!--------------------------------------------------------------------------------------------------
! allocate state arrays
sizeDotState = nSlip & !< crss
+ nSlip & !< crss_back
+ nSlip & !< accumulated (absolute) shear
+ 1_pInt !< sum(gamma)
sizeDeltaState = nSlip & !< sense of acting shear stress (-1 or +1)
+ nSlip & !< backstress at last switch of stress sense
+ nSlip !< accumulated shear at last switch of stress sense
sizeState = sizeDotState + sizeDeltaState
plasticState(phase)%sizeState = sizeState
plasticState(phase)%sizeDotState = sizeDotState
plasticState(phase)%sizeDeltaState = sizeDeltaState
renamed "tau0" to "crss0"
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plasticState(phase)%offsetDeltaState = sizeDotState
first shot at kinematic hardening constitutive law
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plasticState(phase)%sizePostResults = plastic_kinehardening_sizePostResults(instance)
plasticState(phase)%nSlip = nSlip
allocate(plasticState(phase)%state0 ( sizeState,NipcMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%partionedState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%subState0 ( sizeState,NipcMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%state ( sizeState,NipcMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%aTolState (sizeDotState), source=0.0_pReal)
allocate(plasticState(phase)%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
allocate(plasticState(phase)%deltaState (sizeDeltaState,NipcMyPhase), source=0.0_pReal) ! allocate space for deltaState
if (any(numerics_integrator == 1_pInt)) then
allocate(plasticState(phase)%previousDotState (sizeDotState,NipcMyPhase),source=0.0_pReal)
allocate(plasticState(phase)%previousDotState2(sizeDotState,NipcMyPhase),source=0.0_pReal)
endif
if (any(numerics_integrator == 4_pInt)) &
allocate(plasticState(phase)%RK4dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
if (any(numerics_integrator == 5_pInt)) &
allocate(plasticState(phase)%RKCK45dotState (6,sizeDotState,NipcMyPhase), source=0.0_pReal)
offset_slip = plasticState(phase)%nSlip+plasticState(phase)%nTwin+2_pInt
plasticState(phase)%slipRate => &
plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
plasticState(phase)%accumulatedSlip => &
fixed backstress rate of change based on its own slip system evolution and its sense
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plasticState(phase)%state(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
first shot at kinematic hardening constitutive law
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fixed backstress rate of change based on its own slip system evolution and its sense
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allocate(param(instance)%hardeningMatrix_SlipSlip(nSlip,nSlip), source=0.0_pReal)
first shot at kinematic hardening constitutive law
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do f = 1_pInt,lattice_maxNslipFamily ! >>> interaction slip -- X
index_myFamily = sum(plastic_kinehardening_Nslip(1:f-1_pInt,instance))
do j = 1_pInt,plastic_kinehardening_Nslip(f,instance) ! loop over (active) systems in my family (slip)
do o = 1_pInt,lattice_maxNslipFamily
index_otherFamily = sum(plastic_kinehardening_Nslip(1:o-1_pInt,instance))
do k = 1_pInt,plastic_kinehardening_Nslip(o,instance) ! loop over (active) systems in other family (slip)
param(instance)%hardeningMatrix_SlipSlip(index_myFamily+j,index_otherFamily+k) = &
param(instance)%interaction_SlipSlip(lattice_interactionSlipSlip( &
sum(lattice_NslipSystem(1:f-1,phase))+j, &
sum(lattice_NslipSystem(1:o-1,phase))+k, &
phase))
enddo; enddo
enddo; enddo
!----------------------------------------------------------------------------------------------
!locally define dotState alias
endindex = 0_pInt
o = endIndex ! offset of dotstate index relative to state index
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%crss => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%crss => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
dotState(instance)%crss => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
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state0(instance)%crss = spread(math_expand(param(instance)%crss0,&
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plastic_kinehardening_Nslip(:,instance)), &
2, NipcMyPhase)
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolResistance
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%crss_back => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%crss_back => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
dotState(instance)%crss_back => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
state0(instance)%crss_back = 0.0_pReal
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolResistance
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%accshear => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%accshear => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
dotState(instance)%accshear => plasticState(phase)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
state0(instance)%accshear = 0.0_pReal
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolShear
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + 1_pInt
state (instance)%sumGamma => plasticState(phase)%state (startIndex ,1:NipcMyPhase)
state0 (instance)%sumGamma => plasticState(phase)%state0 (startIndex ,1:NipcMyPhase)
dotState(instance)%sumGamma => plasticState(phase)%dotState (startIndex-o ,1:NipcMyPhase)
state0(instance)%sumGamma = 0.0_pReal
plasticState(phase)%aTolState(startIndex-o:endIndex-o) = param(instance)%aTolShear
!----------------------------------------------------------------------------------------------
!locally define deltaState alias
o = endIndex
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%sense => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%sense => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
deltaState(instance)%sense => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
state0(instance)%sense = 0.0_pReal
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%chi0 => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%chi0 => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
deltaState(instance)%chi0 => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
state0(instance)%chi0 = 0.0_pReal
! .............................................
startIndex = endIndex + 1_pInt
endIndex = endIndex + nSlip
state (instance)%gamma0 => plasticState(phase)%state (startIndex :endIndex ,1:NipcMyPhase)
state0 (instance)%gamma0 => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
deltaState(instance)%gamma0 => plasticState(phase)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
state0(instance)%gamma0 = 0.0_pReal
endif myPhase2
enddo initializeInstances
end subroutine plastic_kinehardening_init
!--------------------------------------------------------------------------------------------------
!> @brief calculation of shear rates (\dot \gamma)
!--------------------------------------------------------------------------------------------------
subroutine plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
Tstar_v,ph,instance,of)
use lattice, only: &
lattice_NslipSystem, &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NnonSchmid
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
integer(pInt), intent(in) :: &
ph, & !< phase ID
instance, & !< instance of that phase
of !< index of phaseMember
real(pReal), dimension(plastic_kinehardening_totalNslip(instance)), intent(out) :: &
gdot_pos, & !< shear rates from positive line segments
gdot_neg, & !< shear rates from negative line segments
tau_pos, & !< shear stress on positive line segments
tau_neg !< shear stress on negative line segments
integer(pInt) :: &
index_myFamily, &
f,i,j,k
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_kinehardening_Nslip(f,instance)
j = j + 1_pInt
tau_pos(j) = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_neg(j) = tau_pos(j)
nonSchmidSystems: do k = 1,lattice_NnonSchmid(ph)
tau_pos(j) = tau_pos(j) + param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+0,index_myFamily+i,ph))
tau_neg(j) = tau_neg(j) + param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
enddo nonSchmidSystems
enddo slipSystems
enddo slipFamilies
gdot_pos = 0.5_pReal * param(instance)%gdot0 * &
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(abs(tau_pos-state(instance)%sense(:,of)*state(instance)%crss_back(:,of))/ &
state(instance)%crss(:,of))**param(instance)%n_slip &
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*sign(1.0_pReal,tau_pos)
gdot_neg = 0.5_pReal * param(instance)%gdot0 * &
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(abs(tau_neg-state(instance)%sense(:,of)*state(instance)%crss_back(:,of))/ &
state(instance)%crss(:,of))**param(instance)%n_slip &
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*sign(1.0_pReal,tau_neg)
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! gdot_pos = 0.5_pReal * param(instance)%gdot0 * &
! exp(-param(instance)%F0/(1.38e-23*298.15)* &
! (1-((abs(tau_pos-state(instance)%crss_back(:,of)) &
! -state(instance)%crss(:,of)*param(instance)%mu/param(instance)%mu) / &
! !----------------------------------------------------------------------------
! param(instance)%tau_hat0*param(instance)%mu/param(instance)%mu &
! )**param(instance)%p1 &
! )**param(instance)%q1 &
! )*sign(1.0_pReal,(tau_pos-state(instance)%crss_back(:,of)))
!
!
!
! gdot_neg = 0.5_pReal * param(instance)%gdot0 * &
! exp(-param(instance)%F0/(1.38e-23*298.15)* &
! (1-((abs(tau_neg-state(instance)%crss_back(:,of)) &
! -state(instance)%crss(:,of)*param(instance)%mu/param(instance)%mu) / &
! !----------------------------------------------------------------------------
! param(instance)%tau_hat0*param(instance)%mu/param(instance)%mu &
! )**param(instance)%p1 &
! )**param(instance)%q1 &
! )*sign(1.0_pReal,(tau_neg-state(instance)%crss_back(:,of)))
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end subroutine plastic_kinehardening_shearRates
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_kinehardening_LpAndItsTangent(Lp,dLp_dTstar99, &
Tstar_v,ipc,ip,el)
use prec, only: &
dNeq0
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use debug, only: &
debug_level, &
debug_constitutive, &
debug_levelExtensive, &
debug_levelSelective, &
debug_e, &
debug_i, &
debug_g
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use math, only: &
math_Plain3333to99, &
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math_Mandel6to33, &
math_transpose33
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use lattice, only: &
lattice_Sslip, & !< schmid matrix
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_NnonSchmid
use material, only: &
phaseAt, phasememberAt, &
phase_plasticityInstance
implicit none
real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: &
dLp_dTstar99 !< derivative of Lp with respect to 2nd Piola Kirchhoff stress
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
integer(pInt) :: &
instance, &
index_myFamily, &
f,i,j,k,l,m,n, &
of, &
ph
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(phaseAt(ipc,ip,el)))) :: &
gdot_pos,gdot_neg, &
tau_pos,tau_neg
real(pReal) :: &
dgdot_dtau_pos,dgdot_dtau_neg
real(pReal), dimension(3,3,3,3) :: &
dLp_dTstar3333 !< derivative of Lp with respect to Tstar as 4th order tensor
real(pReal), dimension(3,3,2) :: &
nonSchmid_tensor
ph = phaseAt(ipc,ip,el) !< figures phase for each material point
of = phasememberAt(ipc,ip,el) !< index of the positions of each constituent of material point, phasememberAt is a function in material that helps figure them out
instance = phase_plasticityInstance(ph)
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar99 = 0.0_pReal
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
Tstar_v,ph,instance,of)
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j = 0_pInt ! reading and marking the starting index for each slip family
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_kinehardening_Nslip(f,instance)
j = j + 1_pInt
! build nonSchmid tensor
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)
do k = 1,lattice_NnonSchmid(ph)
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nonSchmid_tensor(1:3,1:3,1) = &
nonSchmid_tensor(1:3,1:3,1) + param(instance)%nonSchmidCoeff(k) * &
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) + param(instance)%nonSchmidCoeff(k) * &
lattice_Sslip(1:3,1:3,2*k+1,index_myFamily+i,ph)
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enddo
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Lp = Lp + (gdot_pos(j)+gdot_neg(j))*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph) ! sum of all gdot*SchmidTensor gives Lp
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! Calculation of the tangent of Lp ! sensitivity of Lp
if (dNeq0(gdot_pos(j))) then
dgdot_dtau_pos = gdot_pos(j)*param(instance)%n_slip/(tau_pos(j)-state(instance)%crss_back(j,of))
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
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dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtau_pos*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
nonSchmid_tensor(m,n,1)
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endif
if (dNeq0(gdot_neg(j))) then
dgdot_dtau_neg = gdot_neg(j)*param(instance)%n_slip/(tau_neg(j)-state(instance)%crss_back(j,of))
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
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dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtau_neg*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
nonSchmid_tensor(m,n,2)
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endif
enddo slipSystems
enddo slipFamilies
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dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
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end subroutine plastic_kinehardening_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates (instantaneous) incremental change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_kinehardening_deltaState(Tstar_v,ipc,ip,el)
use prec, only: &
dNeq
renamed "tau0" to "crss0"
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use debug, only: &
debug_level, &
debug_constitutive, &
debug_levelExtensive, &
delete extra variable
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debug_levelSelective, &
debug_e, &
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debug_i, &
debug_g
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use material, only: &
phaseAt, &
phasememberAt, &
phase_plasticityInstance
implicit none
real(pReal), dimension(6), intent(in):: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), dimension(6) :: &
Tstar_dev_v !< deviatoric 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(phaseAt(ipc,ip,el)))) :: &
gdot_pos,gdot_neg, &
tau_pos,tau_neg, &
sense
integer(pInt) :: &
ph, &
instance, & !< instance of my instance (unique number of my constitutive model)
of, &
j !< shortcut notation for offset position in state array
ph = phaseAt(ipc,ip,el)
of = phasememberAt(ipc,ip,el) ! phasememberAt should be tackled by material and be renamed to material_phasemember
instance = phase_plasticityInstance(ph)
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
Tstar_v,ph,instance,of)
sense = sign(1.0_pReal,gdot_pos+gdot_neg) ! current sense of shear direction
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#ifdef DEBUG
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
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.and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
renamed "tau0" to "crss0"
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.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
delete extra variable
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write(6,'(a)') '======= kinehardening delta state ======='
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endif
#endif
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!--------------------------------------------------------------------------------------------------
! switch in sense of shear?
do j = 1,plastic_kinehardening_totalNslip(instance)
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#ifdef DEBUG
if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
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.and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
renamed "tau0" to "crss0"
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.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
delete extra variable
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write(6,'(i2,1x,f7.4,1x,f7.4)') j,sense(j),state(instance)%sense(j,of)
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endif
#endif
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if (dNeq(sense(j),state(instance)%sense(j,of),0.1_pReal)) then
deltaState(instance)%sense (j,of) = sense(j) - state(instance)%sense(j,of) ! switch sense
deltaState(instance)%chi0 (j,of) = abs(state(instance)%crss_back(j,of)) - state(instance)%chi0(j,of) ! remember current backstress magnitude
deltaState(instance)%gamma0(j,of) = state(instance)%accshear(j,of) - state(instance)%gamma0(j,of) ! remember current accumulated shear
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else
deltaState(instance)%sense (j,of) = 0.0_pReal ! no change
deltaState(instance)%chi0 (j,of) = 0.0_pReal
deltaState(instance)%gamma0(j,of) = 0.0_pReal
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endif
enddo
end subroutine plastic_kinehardening_deltaState
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_kinehardening_dotState(Tstar_v,ipc,ip,el)
use lattice, only: &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_NnonSchmid
use material, only: &
material_phase, &
phaseAt, phasememberAt, &
plasticState, &
phase_plasticityInstance
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation, vector form
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element !< microstructure state
integer(pInt) :: &
instance,ph, &
f,i,j,k, &
renamed "tau0" to "crss0"
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index_myFamily,index_otherFamily, &
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nSlip, &
offset_accshear, &
of
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_pos,gdot_neg, &
tau_pos,tau_neg
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
nSlip = plastic_kinehardening_totalNslip(instance)
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dotState(instance)%sumGamma(of) = 0.0_pReal
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call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
Tstar_v,ph,instance,of)
j = 0_pInt
slipFamilies: do f = 1_pInt,lattice_maxNslipFamily
slipSystems: do i = 1_pInt,plastic_kinehardening_Nslip(f,instance)
j = j+1_pInt
dotState(instance)%crss(j,of) = & ! evolution of slip resistance j
dot_product(param(instance)%hardeningMatrix_SlipSlip(j,1:nSlip),abs(gdot_pos+gdot_neg)) * &
( param(instance)%theta1(f) + &
(param(instance)%theta0(f) - param(instance)%theta1(f) &
+ param(instance)%theta0(f)*param(instance)%theta1(f)*state(instance)%sumGamma(of)/param(instance)%tau1(f)) &
*exp(-state(instance)%sumGamma(of)*param(instance)%theta0(f)/param(instance)%tau1(f)) & ! V term depending on the harding law
)
dotState(instance)%crss_back(j,of) = & ! evolution of back stress resistance j
fixed backstress rate of change based on its own slip system evolution and its sense
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state(instance)%sense(j,of)*abs(gdot_pos(j)+gdot_neg(j)) * &
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( param(instance)%theta1_b(f) + &
(param(instance)%theta0_b(f) - param(instance)%theta1_b(f) &
+ param(instance)%theta0_b(f)*param(instance)%theta1_b(f)/(param(instance)%tau1_b(f)+state(instance)%chi0(j,of)) &
*(state(instance)%accshear(j,of)-state(instance)%gamma0(j,of))) &
*exp(-(state(instance)%accshear(j,of)-state(instance)%gamma0(j,of)) &
*param(instance)%theta0_b(f)/(param(instance)%tau1_b(f)+state(instance)%chi0(j,of))) &
) ! V term depending on the harding law for back stress
dotState(instance)%accshear(j,of) = abs(gdot_pos(j)+gdot_neg(j))
dotState(instance)%sumGamma(of) = dotState(instance)%sumGamma(of) + dotState(instance)%accshear(j,of)
enddo slipSystems
enddo slipFamilies
end subroutine plastic_kinehardening_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_kinehardening_postResults(Tstar_v,ipc,ip,el)
use material, only: &
material_phase, &
plasticState, &
phaseAt, phasememberAt, &
phase_plasticityInstance
use lattice, only: &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_NnonSchmid
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element !< microstructure state
real(pReal), dimension(plastic_kinehardening_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
plastic_kinehardening_postResults
integer(pInt) :: &
instance,ph, of, &
nSlip,&
o,f,i,c,j,k, &
renamed "tau0" to "crss0"
2017-11-07 04:41:02 +05:30
index_myFamily
first shot at kinematic hardening constitutive law
2017-09-30 04:06:28 +05:30
real(pReal), dimension(plastic_kinehardening_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_pos,gdot_neg, &
tau_pos,tau_neg
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
nSlip = plastic_kinehardening_totalNslip(instance)
plastic_kinehardening_postResults = 0.0_pReal
c = 0_pInt
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
Tstar_v,ph,instance,of)
outputsLoop: do o = 1_pInt,plastic_kinehardening_Noutput(instance)
select case(param(instance)%outputID(o))
case (crss_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%crss(:,of)
c = c + nSlip
case(crss_back_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%crss_back(:,of)
c = c + nSlip
case (sense_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%sense(:,of)
c = c + nSlip
case (chi0_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%chi0(:,of)
c = c + nSlip
case (gamma0_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%gamma0(:,of)
c = c + nSlip
case (accshear_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = state(instance)%accshear(:,of)
c = c + nSlip
case (sumGamma_ID)
plastic_kinehardening_postResults(c+1_pInt) = state(instance)%sumGamma(of)
c = c + 1_pInt
case (shearrate_ID)
plastic_kinehardening_postResults(c+1_pInt:c+nSlip) = gdot_pos+gdot_neg
c = c + nSlip
case (resolvedstress_ID)
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_kinehardening_Nslip(f,instance)
j = j + 1_pInt
plastic_kinehardening_postResults(c+j) = &
dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
enddo slipSystems
enddo slipFamilies
c = c + nSlip
end select
enddo outputsLoop
end function plastic_kinehardening_postResults
end module plastic_kinehardening