DAMASK_EICMD/src/plastic_phenopowerlaw.f90

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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief material subroutine for phenomenological crystal plasticity formulation using a powerlaw
!! fitting
!--------------------------------------------------------------------------------------------------
module plastic_phenopowerlaw
use prec, only: &
pReal,&
pInt
implicit none
private
integer(pInt), dimension(:,:), allocatable, target, public :: &
plastic_phenopowerlaw_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
plastic_phenopowerlaw_output !< name of each post result output
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enum, bind(c)
enumerator :: &
undefined_ID, &
resistance_slip_ID, &
accumulatedshear_slip_ID, &
shearrate_slip_ID, &
resolvedstress_slip_ID, &
totalshear_ID, &
resistance_twin_ID, &
accumulatedshear_twin_ID, &
shearrate_twin_ID, &
resolvedstress_twin_ID, &
totalvolfrac_twin_ID
end enum
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type, private :: tParameters !< container type for internal constitutive parameters
real(pReal) :: &
gdot0_slip, & !< reference shear strain rate for slip
gdot0_twin, & !< reference shear strain rate for twin
n_slip, & !< stress exponent for slip
n_twin, & !< stress exponent for twin
spr, & !< push-up factor for slip saturation due to twinning
twinB, &
twinC, &
twinD, &
twinE, &
h0_SlipSlip, & !< reference hardening slip - slip
h0_TwinSlip, & !< reference hardening twin - slip
h0_TwinTwin, & !< reference hardening twin - twin
a_slip, &
aTolResistance, & ! default absolute tolerance 1 Pa
aTolShear, & ! default absolute tolerance 1e-6
aTolTwinfrac ! default absolute tolerance 1e-6
integer(pInt), dimension(:), allocatable :: &
Nslip, & !< active number of slip systems per family
Ntwin !< active number of twin systems per family
real(pReal), dimension(:), allocatable :: &
tau0_slip, & !< initial critical shear stress for slip
tau0_twin, & !< initial critical shear stress for twin
tausat_slip, & !< maximum critical shear stress for slip
nonSchmidCoeff, &
H_int, & !< per family hardening activity (optional)
interaction_SlipSlip, & !< slip resistance from slip activity
interaction_SlipTwin, & !< slip resistance from twin activity
interaction_TwinSlip, & !< twin resistance from slip activity
interaction_TwinTwin !< twin resistance from twin activity
real(pReal), dimension(:,:), allocatable :: &
matrix_SlipSlip, & !< slip resistance from slip activity
matrix_SlipTwin, & !< slip resistance from twin activity
matrix_TwinSlip, & !< twin resistance from slip activity
matrix_TwinTwin !< twin resistance from twin activity
integer(kind(undefined_ID)), dimension(:), allocatable :: &
outputID !< ID of each post result output
end type
type(tParameters), dimension(:), allocatable, target, private :: param !< containers of constitutive parameters (len Ninstance)
type, private :: tPhenopowerlawState
real(pReal), pointer, dimension(:,:) :: &
s_slip, &
s_twin, &
accshear_slip, &
accshear_twin
real(pReal), pointer, dimension(:) :: &
sumGamma, &
sumF
end type
type(tPhenopowerlawState), allocatable, dimension(:), private :: &
dotState, &
state
public :: &
plastic_phenopowerlaw_init, &
plastic_phenopowerlaw_LpAndItsTangent, &
plastic_phenopowerlaw_dotState, &
plastic_phenopowerlaw_postResults
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_init
#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
use, intrinsic :: iso_fortran_env, only: &
compiler_version, &
compiler_options
#endif
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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_warning, &
IO_error, &
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IO_timeStamp
use material, only: &
phase_plasticity, &
phase_plasticityInstance, &
phase_Noutput, &
PLASTICITY_PHENOPOWERLAW_label, &
PLASTICITY_PHENOPOWERLAW_ID, &
material_phase, &
plasticState
use config, only: &
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MATERIAL_partPhase, &
phaseConfig
use lattice
use numerics,only: &
numerics_integrator
implicit none
integer(pInt) :: &
maxNinstance, &
instance,phase,j,k, f,o, i,&
NipcMyPhase, outputSize, &
offset_slip, index_myFamily, index_otherFamily, &
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sizeState,sizeDotState, &
startIndex, endIndex
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integer(pInt), dimension(0), parameter :: emptyInt = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyReal = [real(pReal)::]
character(len=65536), dimension(0), parameter :: emptyString = [character(len=65536)::]
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type(tParameters), pointer :: prm
integer(kind(undefined_ID)) :: &
outputID !< ID of each post result output
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character(len=512) :: &
extmsg = ''
character(len=65536), dimension(:), allocatable :: outputs
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_PHENOPOWERLAW_label//' init -+>>>'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
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maxNinstance = int(count(phase_plasticity == PLASTICITY_PHENOPOWERLAW_ID),pInt)
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
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allocate(plastic_phenopowerlaw_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
allocate(plastic_phenopowerlaw_output(maxval(phase_Noutput),maxNinstance))
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plastic_phenopowerlaw_output = ''
allocate(param(maxNinstance)) ! one container of parameters per instance
allocate(state(maxNinstance))
allocate(dotState(maxNinstance))
do phase = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(phase) == PLASTICITY_PHENOPOWERLAW_ID) then
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instance = phase_plasticityInstance(phase)
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prm => param(instance)
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prm%Nslip = phaseConfig(phase)%getInts('nslip',defaultVal=emptyInt)
!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
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if (sum(prm%Nslip) > 0_pInt) then
prm%tau0_slip = phaseConfig(phase)%getFloats('tau0_slip')
prm%tausat_slip = phaseConfig(phase)%getFloats('tausat_slip')
prm%interaction_SlipSlip = phaseConfig(phase)%getFloats('interaction_slipslip')
prm%H_int = phaseConfig(phase)%getFloats('h_int',&
defaultVal=[(0.0_pReal,i=1_pInt,size(prm%Nslip))])
prm%nonSchmidCoeff = phaseConfig(phase)%getFloats('nonschmid_coefficients',&
defaultVal = emptyReal )
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prm%gdot0_slip = phaseConfig(phase)%getFloat('gdot0_slip')
prm%n_slip = phaseConfig(phase)%getFloat('n_slip')
prm%a_slip = phaseConfig(phase)%getFloat('a_slip')
prm%h0_SlipSlip = phaseConfig(phase)%getFloat('h0_slipslip')
endif
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prm%Ntwin = phaseConfig(phase)%getInts('ntwin', defaultVal=emptyInt)
!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
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if (sum(prm%Ntwin) > 0_pInt) then
prm%tau0_twin = phaseConfig(phase)%getFloats('tau0_twin')
prm%interaction_TwinTwin = phaseConfig(phase)%getFloats('interaction_twintwin')
prm%gdot0_twin = phaseConfig(phase)%getFloat('gdot0_twin')
prm%n_twin = phaseConfig(phase)%getFloat('n_twin')
prm%spr = phaseConfig(phase)%getFloat('s_pr')
prm%twinB = phaseConfig(phase)%getFloat('twin_b')
prm%twinC = phaseConfig(phase)%getFloat('twin_c')
prm%twinD = phaseConfig(phase)%getFloat('twin_d')
prm%twinE = phaseConfig(phase)%getFloat('twin_e')
prm%h0_TwinTwin = phaseConfig(phase)%getFloat('h0_twintwin')
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endif
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if (sum(prm%Nslip) > 0_pInt .and. sum(prm%Ntwin) > 0_pInt) then
prm%interaction_SlipTwin = phaseConfig(phase)%getFloats('interaction_sliptwin')
prm%interaction_TwinSlip = phaseConfig(phase)%getFloats('interaction_twinslip')
prm%h0_TwinSlip = phaseConfig(phase)%getFloat('h0_twinslip')
endif
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allocate(prm%matrix_SlipSlip(sum(prm%Nslip),sum(prm%Nslip)),source =0.0_pReal)
allocate(prm%matrix_SlipTwin(sum(prm%Nslip),sum(prm%Ntwin)),source =0.0_pReal)
allocate(prm%matrix_TwinSlip(sum(prm%Ntwin),sum(prm%Nslip)),source =0.0_pReal)
allocate(prm%matrix_TwinTwin(sum(prm%Ntwin),sum(prm%Ntwin)),source =0.0_pReal)
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prm%aTolResistance = phaseConfig(phase)%getFloat('atol_resistance',defaultVal=1.0_pReal)
prm%aTolShear = phaseConfig(phase)%getFloat('atol_shear',defaultVal=1.0e-6_pReal)
prm%aTolTwinfrac = phaseConfig(phase)%getFloat('atol_twinfrac',defaultVal=1.0e-6_pReal)
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outputs = phaseConfig(phase)%getStrings('(output)',defaultVal=emptyString)
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allocate(prm%outputID(0))
do i=1_pInt, size(outputs)
outputID = undefined_ID
select case(outputs(i))
case ('resistance_slip')
outputID = resistance_slip_ID
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outputSize = sum(prm%Nslip)
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case ('accumulatedshear_slip')
outputID = accumulatedshear_slip_ID
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outputSize = sum(prm%Nslip)
case ('shearrate_slip')
outputID = shearrate_slip_ID
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outputSize = sum(prm%Nslip)
case ('resolvedstress_slip')
outputID = resolvedstress_slip_ID
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outputSize = sum(prm%Nslip)
case ('resistance_twin')
outputID = resistance_twin_ID
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outputSize = sum(prm%Ntwin)
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case ('accumulatedshear_twin')
outputID = accumulatedshear_twin_ID
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outputSize = sum(prm%Ntwin)
case ('shearrate_twin')
outputID = shearrate_twin_ID
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outputSize = sum(prm%Ntwin)
case ('resolvedstress_twin')
outputID = resolvedstress_twin_ID
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outputSize = sum(prm%Ntwin)
case ('totalvolfrac_twin')
outputID = totalvolfrac_twin_ID
outputSize = 1_pInt
case ('totalshear')
outputID = totalshear_ID
outputSize = 1_pInt
end select
if (outputID /= undefined_ID) then
plastic_phenopowerlaw_output(i,instance) = outputs(i)
plastic_phenopowerlaw_sizePostResult(i,instance) = outputSize
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prm%outputID = [prm%outputID , outputID]
endif
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end do
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extmsg = ''
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if (sum(prm%Nslip) > 0_pInt) then
if (size(prm%tau0_slip) /= size(prm%Nslip)) call IO_error(211_pInt,ip=instance, &
ext_msg='shape(tau0_slip) ('//PLASTICITY_PHENOPOWERLAW_label//')')
if (size(prm%tausat_slip) /= size(prm%Nslip)) call IO_error(211_pInt,ip=instance, &
ext_msg='shape(tausat_slip) ('//PLASTICITY_PHENOPOWERLAW_label//')')
if (size(prm%H_int) /= size(prm%Nslip)) call IO_error(211_pInt,ip=instance, &
ext_msg='shape(H_int) ('//PLASTICITY_PHENOPOWERLAW_label//')')
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if (any(prm%tau0_slip < 0.0_pReal .and. prm%Nslip > 0_pInt)) &
extmsg = trim(extmsg)//"tau0_slip "
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if (any(prm%tausat_slip < prm%tau0_slip .and. prm%Nslip > 0_pInt)) &
extmsg = trim(extmsg)//"tausat_slip "
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if (prm%gdot0_slip <= 0.0_pReal) extmsg = trim(extmsg)//" gdot0_slip "
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if (dEq0(prm%a_slip)) extmsg = trim(extmsg)//" a_slip " ! ToDo: negative values ok?
if (dEq0(prm%n_slip)) extmsg = trim(extmsg)//" n_slip " ! ToDo: negative values ok?
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endif
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if (sum(prm%Ntwin) > 0_pInt) then
if (size(prm%tau0_twin) /= size(prm%ntwin)) call IO_error(211_pInt,ip=instance,&
ext_msg='shape(tau0_twin) ('//PLASTICITY_PHENOPOWERLAW_label//')')
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if (any(prm%tau0_twin < 0.0_pReal .and. prm%Ntwin > 0_pInt)) &
extmsg = trim(extmsg)//"tau0_twin "
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if (prm%gdot0_twin <= 0.0_pReal) extmsg = trim(extmsg)//"gdot0_twin "
if (dEq0(prm%n_twin)) extmsg = trim(extmsg)//"n_twin " ! ToDo: negative values ok?
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endif
if (prm%aTolResistance <= 0.0_pReal) extmsg = trim(extmsg)//"aTolresistance "
if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//"aTolShear "
if (prm%aTolTwinfrac <= 0.0_pReal) extmsg = trim(extmsg)//"atoltwinfrac "
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if (extmsg /= '') call IO_error(211_pInt,ip=instance,&
ext_msg=trim(extmsg)//'('//PLASTICITY_PHENOPOWERLAW_label//')')
!--------------------------------------------------------------------------------------------------
! allocate state arrays
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NipcMyPhase = count(material_phase == phase) ! number of IPCs containing my phase
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sizeState = size(['tau_slip ','accshear_slip']) * sum(prm%nslip) &
+ size(['tau_twin ','accshear_twin']) * sum(prm%ntwin) &
+ size(['sum(gamma)', 'sum(f) '])
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sizeDotState = sizeState
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plasticState(phase)%sizeState = sizeState
plasticState(phase)%sizeDotState = sizeDotState
plasticState(phase)%sizePostResults = sum(plastic_phenopowerlaw_sizePostResult(:,instance))
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plasticState(phase)%nSlip = sum(prm%Nslip)
plasticState(phase)%nTwin = sum(prm%Ntwin)
allocate(plasticState(phase)%aTolState ( sizeState), source=0.0_pReal)
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)
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allocate(plasticState(phase)%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal)
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allocate(plasticState(phase)%deltaState (0_pInt,NipcMyPhase), source=0.0_pReal)
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)
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!--------------------------------------------------------------------------------------------------
! calculate hardening matrices
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mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1) ! >>> interaction slip -- X
index_myFamily = sum(prm%Nslip(1:f-1_pInt))
mySlipSystems: do j = 1_pInt,prm%Nslip(f)
otherSlipFamilies: do o = 1_pInt,size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
otherSlipSystems: do k = 1_pInt,prm%Nslip(o)
prm%matrix_SlipSlip(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_SlipSlip(lattice_interactionSlipSlip( &
sum(lattice_NslipSystem(1:f-1,phase))+j, &
sum(lattice_NslipSystem(1:o-1,phase))+k, &
phase))
enddo otherSlipSystems; enddo otherSlipFamilies
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twinFamilies: do o = 1_pInt,size(prm%Ntwin,1)
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
twinSystems: do k = 1_pInt,prm%Ntwin(o)
prm%matrix_SlipTwin(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_SlipTwin(lattice_interactionSlipTwin( &
sum(lattice_NslipSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
phase))
enddo twinSystems; enddo twinFamilies
enddo mySlipSystems
enddo mySlipFamilies
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myTwinFamilies: do f = 1_pInt,size(prm%Ntwin,1) ! >>> interaction twin -- X
index_myFamily = sum(prm%Ntwin(1:f-1_pInt))
myTwinSystems: do j = 1_pInt,prm%Ntwin(f)
slipFamilies: do o = 1_pInt,size(prm%Nslip,1)
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
slipSystems: do k = 1_pInt,prm%Nslip(o)
prm%matrix_TwinSlip(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TwinSlip(lattice_interactionTwinSlip( &
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NslipSystem(1:o-1_pInt,phase))+k, &
phase))
enddo slipSystems; enddo slipFamilies
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otherTwinFamilies: do o = 1_pInt,size(prm%Ntwin,1)
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
otherTwinSystems: do k = 1_pInt,prm%Ntwin(o)
prm%matrix_TwinTwin(index_myFamily+j,index_otherFamily+k) = &
prm%interaction_TwinTwin(lattice_interactionTwinTwin( &
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
phase))
enddo otherTwinSystems; enddo otherTwinFamilies
enddo myTwinSystems
enddo myTwinFamilies
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!--------------------------------------------------------------------------------------------------
! locally defined state aliases and initialization of state0 and aTolState
startIndex = 1_pInt
endIndex = plasticState(phase)%nSlip
state (instance)%s_slip=>plasticState(phase)%state (startIndex:endIndex,:)
dotState(instance)%s_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(phase)%state0(startIndex:endIndex,:) = &
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spread(math_expand(prm%tau0_slip, prm%Nslip), 2, NipcMyPhase)
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plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolResistance
startIndex = endIndex + 1_pInt
endIndex = endIndex + plasticState(phase)%nTwin
state (instance)%s_twin=>plasticState(phase)%state (startIndex:endIndex,:)
dotState(instance)%s_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(phase)%state0(startIndex:endIndex,:) = &
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spread(math_expand(prm%tau0_twin, prm%Ntwin), 2, NipcMyPhase)
plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolResistance
startIndex = endIndex + 1_pInt
endIndex = endIndex + 1_pInt
state (instance)%sumGamma=>plasticState(phase)%state (startIndex,:)
dotState(instance)%sumGamma=>plasticState(phase)%dotState(startIndex,:)
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plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
startIndex = endIndex + 1_pInt
endIndex = endIndex + 1_pInt
state (instance)%sumF=>plasticState(phase)%state (startIndex,:)
dotState(instance)%sumF=>plasticState(phase)%dotState(startIndex,:)
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plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
startIndex = endIndex + 1_pInt
endIndex = endIndex + plasticState(phase)%nSlip
state (instance)%accshear_slip=>plasticState(phase)%state (startIndex:endIndex,:)
dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
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plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
! global alias
plasticState(phase)%slipRate =>plasticState(phase)%dotState(startIndex:endIndex,:)
plasticState(phase)%accumulatedSlip =>plasticState(phase)%state(startIndex:endIndex,:)
startIndex = endIndex + 1_pInt
endIndex = endIndex + plasticState(phase)%nTwin
state (instance)%accshear_twin=>plasticState(phase)%state (startIndex:endIndex,:)
dotState(instance)%accshear_twin=>plasticState(phase)%dotState(startIndex:endIndex,:)
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plasticState(phase)%aTolState(startIndex:endIndex) = prm%aTolShear
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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 => &
plasticState(phase)%state(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
endif
enddo
end subroutine plastic_phenopowerlaw_init
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,ipc,ip,el)
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use prec, only: &
dNeq0
use math, only: &
math_Plain3333to99, &
math_Mandel6to33
use lattice, only: &
lattice_Sslip, &
lattice_Sslip_v, &
lattice_Stwin, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
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lattice_NtwinSystem
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) :: &
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instance, &
index_myFamily, &
f,i,j,k,l,m,n, &
of, &
ph
real(pReal) :: &
tau_slip_pos,tau_slip_neg, &
gdot_slip_pos,gdot_slip_neg, &
dgdot_dtauslip_pos,dgdot_dtauslip_neg, &
gdot_twin,dgdot_dtautwin,tau_twin
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
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of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
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dLp_dTstar99 = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! Slip part
j = 0_pInt
slipFamilies: do f = 1_pInt,size(param(instance)%Nslip,1)
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems: do i = 1_pInt,param(instance)%Nslip(f)
j = j+1_pInt
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! Calculation of Lp
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_slip_neg = tau_slip_pos
nonSchmid_tensor(1:3,1:3,1) = lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
nonSchmid_tensor(1:3,1:3,2) = nonSchmid_tensor(1:3,1:3,1)
do k = 1,size(param(instance)%nonSchmidCoeff)
tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg + param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
nonSchmid_tensor(1:3,1:3,1) = nonSchmid_tensor(1:3,1:3,1) + 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)
enddo
gdot_slip_pos = 0.5_pReal*param(instance)%gdot0_slip* &
((abs(tau_slip_pos)/(state(instance)%s_slip(j,of))) &
**param(instance)%n_slip)*sign(1.0_pReal,tau_slip_pos)
gdot_slip_neg = 0.5_pReal*param(instance)%gdot0_slip* &
((abs(tau_slip_neg)/(state(instance)%s_slip(j,of))) &
**param(instance)%n_slip)*sign(1.0_pReal,tau_slip_neg)
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Lp = Lp + (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
(gdot_slip_pos+gdot_slip_neg)*lattice_Sslip(1:3,1:3,1,index_myFamily+i,ph)
! Calculation of the tangent of Lp
if (dNeq0(gdot_slip_pos)) then
dgdot_dtauslip_pos = gdot_slip_pos*param(instance)%n_slip/tau_slip_pos
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
dgdot_dtauslip_pos*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
nonSchmid_tensor(m,n,1)
endif
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if (dNeq0(gdot_slip_neg)) then
dgdot_dtauslip_neg = gdot_slip_neg*param(instance)%n_slip/tau_slip_neg
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
dgdot_dtauslip_neg*lattice_Sslip(k,l,1,index_myFamily+i,ph)* &
nonSchmid_tensor(m,n,2)
endif
enddo slipSystems
enddo slipFamilies
!--------------------------------------------------------------------------------------------------
! Twinning part
j = 0_pInt
twinFamilies: do f = 1_pInt,size(param(instance)%Ntwin,1)
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystems: do i = 1_pInt,param(instance)%Ntwin(f)
j = j+1_pInt
! Calculation of Lp
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tau_twin = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
gdot_twin = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
param(instance)%gdot0_twin*&
(abs(tau_twin)/state(instance)%s_twin(j,of))**&
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
Lp = Lp + gdot_twin*lattice_Stwin(1:3,1:3,index_myFamily+i,ph)
! Calculation of the tangent of Lp
if (dNeq0(gdot_twin)) then
dgdot_dtautwin = gdot_twin*param(instance)%n_twin/tau_twin
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
dgdot_dtautwin*lattice_Stwin(k,l,index_myFamily+i,ph)* &
lattice_Stwin(m,n,index_myFamily+i,ph)
endif
enddo twinSystems
enddo twinFamilies
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dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
end subroutine plastic_phenopowerlaw_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
subroutine plastic_phenopowerlaw_dotState(Tstar_v,ipc,ip,el)
use lattice, only: &
lattice_Sslip_v, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_shearTwin
use material, only: &
material_phase, &
phaseAt, phasememberAt, &
plasticState, &
phase_plasticityInstance
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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
integer(pInt) :: &
instance,ph, &
f,i,j,k, &
index_myFamily, nslip,ntwin,&
of
real(pReal) :: &
c_SlipSlip,c_TwinSlip,c_TwinTwin, &
ssat_offset, &
tau_slip_pos,tau_slip_neg,tau_twin
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
gdot_slip,left_SlipSlip,left_SlipTwin,right_SlipSlip,right_TwinSlip
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: &
gdot_twin,left_TwinSlip,left_TwinTwin,right_SlipTwin,right_TwinTwin
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of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
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nSlip= sum(param(instance)%nslip)
nTwin= sum(param(instance)%nTwin)
plasticState(ph)%dotState(:,of) = 0.0_pReal
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!--------------------------------------------------------------------------------------------------
! system-independent (nonlinear) prefactors to M_Xx (X influenced by x) matrices
c_SlipSlip = param(instance)%h0_slipslip*&
(1.0_pReal + param(instance)%twinC*state(instance)%sumF(of)**&
param(instance)%twinB)
c_TwinSlip = param(instance)%h0_TwinSlip*&
state(instance)%sumGamma(of)**param(instance)%twinE
c_TwinTwin = param(instance)%h0_TwinTwin*&
state(instance)%sumF(of)**param(instance)%twinD
!--------------------------------------------------------------------------------------------------
! calculate left and right vectors and calculate dot gammas
ssat_offset = param(instance)%spr*sqrt(state(instance)%sumF(of))
j = 0_pInt
slipFamilies1: do f =1_pInt,size(param(instance)%Nslip,1)
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
j = j+1_pInt
left_SlipSlip(j) = 1.0_pReal + param(instance)%H_int(f) ! modified no system-dependent left part
left_SlipTwin(j) = 1.0_pReal ! no system-dependent left part
right_SlipSlip(j) = abs(1.0_pReal-state(instance)%s_slip(j,of) / &
(param(instance)%tausat_slip(f)+ssat_offset)) &
**param(instance)%a_slip&
*sign(1.0_pReal,1.0_pReal-state(instance)%s_slip(j,of) / &
(param(instance)%tausat_slip(f)+ssat_offset))
right_TwinSlip(j) = 1.0_pReal ! no system-dependent part
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!--------------------------------------------------------------------------------------------------
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! Calculation of dot gamma
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_slip_neg = tau_slip_pos
nonSchmidSystems: do k = 1,size(param(instance)%nonSchmidCoeff)
tau_slip_pos = tau_slip_pos + param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k, index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
enddo nonSchmidSystems
gdot_slip(j) = param(instance)%gdot0_slip*0.5_pReal* &
((abs(tau_slip_pos)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
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*sign(1.0_pReal,tau_slip_pos) &
+(abs(tau_slip_neg)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
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*sign(1.0_pReal,tau_slip_neg))
enddo slipSystems1
enddo slipFamilies1
j = 0_pInt
twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
j = j+1_pInt
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left_TwinSlip(j) = 1.0_pReal ! no system-dependent left part
left_TwinTwin(j) = 1.0_pReal ! no system-dependent left part
right_SlipTwin(j) = 1.0_pReal ! no system-dependent right part
right_TwinTwin(j) = 1.0_pReal ! no system-dependent right part
!--------------------------------------------------------------------------------------------------
! Calculation of dot vol frac
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tau_twin = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
gdot_twin(j) = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
param(instance)%gdot0_twin*&
(abs(tau_twin)/state(instance)%s_twin(j,of))**&
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau_twin))
enddo twinSystems1
enddo twinFamilies1
!--------------------------------------------------------------------------------------------------
! calculate the overall hardening based on above
j = 0_pInt
slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
j = j+1_pInt
dotState(instance)%s_slip(j,of) = & ! evolution of slip resistance j
c_SlipSlip * left_SlipSlip(j) * &
dot_product(param(instance)%matrix_SlipSlip(j,1:nslip), &
right_SlipSlip*abs(gdot_slip)) + & ! dot gamma_slip modulated by right-side slip factor
dot_product(param(instance)%matrix_SlipTwin(j,1:ntwin), &
right_SlipTwin*gdot_twin) ! dot gamma_twin modulated by right-side twin factor
dotState(instance)%sumGamma(of) = dotState(instance)%sumGamma(of) + &
abs(gdot_slip(j))
dotState(instance)%accshear_slip(j,of) = abs(gdot_slip(j))
enddo slipSystems2
enddo slipFamilies2
j = 0_pInt
twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
j = j+1_pInt
dotState(instance)%s_twin(j,of) = & ! evolution of twin resistance j
c_TwinSlip * left_TwinSlip(j) * &
dot_product(param(instance)%matrix_TwinSlip(j,1:nslip), &
right_TwinSlip*abs(gdot_slip)) + & ! dot gamma_slip modulated by right-side slip factor
c_TwinTwin * left_TwinTwin(j) * &
dot_product(param(instance)%matrix_TwinTwin(j,1:ntwin), &
right_TwinTwin*gdot_twin) ! dot gamma_twin modulated by right-side twin factor
if (state(instance)%sumF(of) < 0.98_pReal) & ! ensure twin volume fractions stays below 1.0
dotState(instance)%sumF(of) = dotState(instance)%sumF(of) + &
gdot_twin(j)/lattice_shearTwin(index_myFamily+i,ph)
dotState(instance)%accshear_twin(j,of) = abs(gdot_twin(j))
enddo twinSystems2
enddo twinFamilies2
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end subroutine plastic_phenopowerlaw_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
function plastic_phenopowerlaw_postResults(Tstar_v,ipc,ip,el)
use material, only: &
material_phase, &
plasticState, &
phaseAt, phasememberAt, &
phase_plasticityInstance
use lattice, only: &
lattice_Sslip_v, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
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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(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: &
plastic_phenopowerlaw_postResults
integer(pInt) :: &
instance,ph, of, &
nSlip,nTwin, &
o,f,i,c,j,k, &
index_myFamily
real(pReal) :: &
tau_slip_pos,tau_slip_neg,tau
of = phasememberAt(ipc,ip,el)
ph = phaseAt(ipc,ip,el)
instance = phase_plasticityInstance(ph)
nSlip= sum(param(instance)%nslip)
nTwin= sum(param(instance)%nTwin)
plastic_phenopowerlaw_postResults = 0.0_pReal
c = 0_pInt
outputsLoop: do o = 1_pInt,size(param(instance)%outputID)
select case(param(instance)%outputID(o))
case (resistance_slip_ID)
plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = state(instance)%s_slip(1:nSlip,of)
c = c + nSlip
case (accumulatedshear_slip_ID)
plastic_phenopowerlaw_postResults(c+1_pInt:c+nSlip) = state(instance)%accshear_slip(1:nSlip,of)
c = c + nSlip
case (shearrate_slip_ID)
j = 0_pInt
slipFamilies1: do f = 1_pInt,size(param(instance)%Nslip,1)
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems1: do i = 1_pInt,param(instance)%Nslip(f)
j = j + 1_pInt
tau_slip_pos = dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
tau_slip_neg = tau_slip_pos
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do k = 1,lattice_NnonSchmid(ph)
tau_slip_pos = tau_slip_pos +param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k,index_myFamily+i,ph))
tau_slip_neg = tau_slip_neg +param(instance)%nonSchmidCoeff(k)* &
dot_product(Tstar_v,lattice_Sslip_v(1:6,2*k+1,index_myFamily+i,ph))
enddo
plastic_phenopowerlaw_postResults(c+j) = param(instance)%gdot0_slip*0.5_pReal* &
((abs(tau_slip_pos)/state(instance)%s_slip(j,of))**param(instance)%n_slip &
*sign(1.0_pReal,tau_slip_pos) &
+(abs(tau_slip_neg)/(state(instance)%s_slip(j,of)))**param(instance)%n_slip &
*sign(1.0_pReal,tau_slip_neg))
enddo slipSystems1
enddo slipFamilies1
c = c + nSlip
case (resolvedstress_slip_ID)
j = 0_pInt
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slipFamilies2: do f = 1_pInt,size(param(instance)%Nslip,1)
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
slipSystems2: do i = 1_pInt,param(instance)%Nslip(f)
j = j + 1_pInt
plastic_phenopowerlaw_postResults(c+j) = &
dot_product(Tstar_v,lattice_Sslip_v(1:6,1,index_myFamily+i,ph))
enddo slipSystems2
enddo slipFamilies2
c = c + nSlip
case (totalshear_ID)
plastic_phenopowerlaw_postResults(c+1_pInt) = &
state(instance)%sumGamma(of)
c = c + 1_pInt
case (resistance_twin_ID)
plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
state(instance)%s_twin(1:nTwin,of)
c = c + nTwin
case (accumulatedshear_twin_ID)
plastic_phenopowerlaw_postResults(c+1_pInt:c+nTwin) = &
state(instance)%accshear_twin(1:nTwin,of)
c = c + nTwin
case (shearrate_twin_ID)
j = 0_pInt
twinFamilies1: do f = 1_pInt,size(param(instance)%Ntwin,1)
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystems1: do i = 1_pInt,param(instance)%Ntwin(f)
j = j + 1_pInt
tau = dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
plastic_phenopowerlaw_postResults(c+j) = (1.0_pReal-state(instance)%sumF(of))*& ! 1-F
param(instance)%gdot0_twin*&
(abs(tau)/state(instance)%s_twin(j,of))**&
param(instance)%n_twin*max(0.0_pReal,sign(1.0_pReal,tau))
enddo twinSystems1
enddo twinFamilies1
c = c + nTwin
case (resolvedstress_twin_ID)
j = 0_pInt
twinFamilies2: do f = 1_pInt,size(param(instance)%Ntwin,1)
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
twinSystems2: do i = 1_pInt,param(instance)%Ntwin(f)
j = j + 1_pInt
plastic_phenopowerlaw_postResults(c+j) = &
dot_product(Tstar_v,lattice_Stwin_v(1:6,index_myFamily+i,ph))
enddo twinSystems2
enddo twinFamilies2
c = c + nTwin
case (totalvolfrac_twin_ID)
plastic_phenopowerlaw_postResults(c+1_pInt) = state(instance)%sumF(of)
c = c + 1_pInt
end select
enddo outputsLoop
end function plastic_phenopowerlaw_postResults
end module plastic_phenopowerlaw