!-------------------------------------------------------------------------------------------------- !> @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 !> @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 character(len=64), dimension(:,:), allocatable, target, public :: & plastic_phenopowerlaw_output !< name of each post result output 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 type, private :: tParameters !< container type for internal constitutive parameters integer(pInt) :: & totalNslip, & totalNtwin 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) !ToDo: Better name! shear_twin !< characteristic shear for twins real(pReal), dimension(:,:), allocatable :: & 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 :: & Schmid_slip, & Schmid_twin real(pReal), dimension(:,:,:,:), allocatable :: & nonSchmid_pos, & nonSchmid_neg integer(kind(undefined_ID)), dimension(:), allocatable :: & outputID !< ID of each post result output end type type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance) type, private :: tPhenopowerlawState real(pReal), pointer, dimension(:,:) :: & s_slip, & s_twin, & accshear_slip, & accshear_twin, & whole 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 use prec, only: & dEq0 use debug, only: & debug_level, & debug_constitutive,& debug_levelBasic use math, only: & math_expand use IO, only: & IO_warning, & IO_error, & IO_timeStamp use material, only: & phase_plasticity, & phase_plasticityInstance, & phase_Noutput, & PLASTICITY_PHENOPOWERLAW_label, & PLASTICITY_PHENOPOWERLAW_ID, & material_phase, & plasticState use config, only: & MATERIAL_partPhase, & config_phase use lattice use numerics,only: & numerics_integrator implicit none integer(pInt) :: & maxNinstance, & instance,p,j,k, f,o, i,& NipcMyPhase, outputSize, & index_myFamily, index_otherFamily, & sizeState,sizeDotState, & startIndex, endIndex real(pReal), dimension(:,:), allocatable :: temp1, temp2 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)::] type(tParameters) :: prm integer(kind(undefined_ID)) :: & outputID !< ID of each post result output character(len=512) :: & extmsg = '' character(len=65536), dimension(:), allocatable :: outputs write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_PHENOPOWERLAW_label//' init -+>>>' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" 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 allocate(plastic_phenopowerlaw_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt) allocate(plastic_phenopowerlaw_output(maxval(phase_Noutput),maxNinstance)) plastic_phenopowerlaw_output = '' allocate(param(maxNinstance)) ! one container of parameters per instance allocate(state(maxNinstance)) allocate(dotState(maxNinstance)) do p = 1_pInt, size(phase_plasticityInstance) if (phase_plasticity(p) /= PLASTICITY_PHENOPOWERLAW_ID) cycle instance = phase_plasticityInstance(p) associate(prm => param(instance)) prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyIntArray) if (size(prm%Nslip) > count(lattice_NslipSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip') if (any(lattice_NslipSystem(1:size(prm%Nslip),p)-prm%Nslip < 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip') prm%totalNslip = sum(prm%Nslip) if (prm%totalNslip > 0_pInt) then prm%tau0_slip = config_phase(p)%getFloats('tau0_slip') prm%tausat_slip = config_phase(p)%getFloats('tausat_slip') prm%interaction_SlipSlip = spread(config_phase(p)%getFloats('interaction_slipslip'),2,1) prm%H_int = config_phase(p)%getFloats('h_int',& defaultVal=[(0.0_pReal,i=1_pInt,size(prm%Nslip))]) prm%nonSchmidCoeff = config_phase(p)%getFloats('nonschmid_coefficients',& defaultVal = emptyRealArray ) prm%gdot0_slip = config_phase(p)%getFloat('gdot0_slip') prm%n_slip = config_phase(p)%getFloat('n_slip') prm%a_slip = config_phase(p)%getFloat('a_slip') prm%h0_SlipSlip = config_phase(p)%getFloat('h0_slipslip') endif prm%Ntwin = config_phase(p)%getInts('ntwin', defaultVal=emptyIntArray) if (size(prm%Ntwin) > count(lattice_NtwinSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin') if (any(lattice_NtwinSystem(1:size(prm%Ntwin),p)-prm%Ntwin < 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin') prm%totalNtwin = sum(prm%Ntwin) if (prm%totalNtwin > 0_pInt) then prm%tau0_twin = config_phase(p)%getFloats('tau0_twin') prm%interaction_TwinTwin = spread(config_phase(p)%getFloats('interaction_twintwin'),2,1) prm%gdot0_twin = config_phase(p)%getFloat('gdot0_twin') prm%n_twin = config_phase(p)%getFloat('n_twin') prm%spr = config_phase(p)%getFloat('s_pr') prm%h0_TwinTwin = config_phase(p)%getFloat('h0_twintwin') endif if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then prm%interaction_SlipTwin = spread(config_phase(p)%getFloats('interaction_sliptwin'),2,1) prm%interaction_TwinSlip = spread(config_phase(p)%getFloats('interaction_twinslip'),2,1) prm%h0_TwinSlip = config_phase(p)%getFloat('h0_twinslip') endif prm%twinB = config_phase(p)%getFloat('twin_b',defaultVal=1.0_pReal) prm%twinC = config_phase(p)%getFloat('twin_c',defaultVal=0.0_pReal) prm%twinD = config_phase(p)%getFloat('twin_d',defaultVal=0.0_pReal) prm%twinE = config_phase(p)%getFloat('twin_e',defaultVal=0.0_pReal) prm%aTolResistance = config_phase(p)%getFloat('atol_resistance',defaultVal=1.0_pReal) prm%aTolShear = config_phase(p)%getFloat('atol_shear',defaultVal=1.0e-6_pReal) prm%aTolTwinfrac = config_phase(p)%getFloat('atol_twinfrac',defaultVal=1.0e-6_pReal) outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray) allocate(prm%outputID(0)) do i=1_pInt, size(outputs) outputID = undefined_ID select case(outputs(i)) case ('resistance_slip') outputID = resistance_slip_ID outputSize = prm%totalNslip case ('accumulatedshear_slip') outputID = accumulatedshear_slip_ID outputSize = prm%totalNslip case ('shearrate_slip') outputID = shearrate_slip_ID outputSize = prm%totalNslip case ('resolvedstress_slip') outputID = resolvedstress_slip_ID outputSize = prm%totalNslip case ('resistance_twin') outputID = resistance_twin_ID outputSize = prm%totalNtwin case ('accumulatedshear_twin') outputID = accumulatedshear_twin_ID outputSize = prm%totalNtwin case ('shearrate_twin') outputID = shearrate_twin_ID outputSize = prm%totalNtwin case ('resolvedstress_twin') outputID = resolvedstress_twin_ID outputSize = prm%totalNtwin 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 prm%outputID = [prm%outputID , outputID] endif end do extmsg = '' if (prm%totalNslip > 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//')') if (any(prm%tau0_slip < 0.0_pReal .and. prm%Nslip > 0_pInt)) & extmsg = trim(extmsg)//"tau0_slip " if (any(prm%tausat_slip < prm%tau0_slip .and. prm%Nslip > 0_pInt)) & extmsg = trim(extmsg)//"tausat_slip " if (prm%gdot0_slip <= 0.0_pReal) extmsg = trim(extmsg)//" gdot0_slip " 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? prm%H_int = math_expand(prm%H_int,prm%Nslip) prm%tausat_slip = math_expand(prm%tausat_slip,prm%Nslip) endif if (prm%totalNtwin > 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//')') if (any(prm%tau0_twin < 0.0_pReal .and. prm%Ntwin > 0_pInt)) & extmsg = trim(extmsg)//"tau0_twin " 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? 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 " if (extmsg /= '') call IO_error(211_pInt,ip=instance,& ext_msg=trim(extmsg)//'('//PLASTICITY_PHENOPOWERLAW_label//')') !-------------------------------------------------------------------------------------------------- ! allocate state arrays NipcMyPhase = count(material_phase == p) ! number of IPCs containing my phase sizeState = size(['tau_slip ','accshear_slip']) * prm%TotalNslip & + size(['tau_twin ','accshear_twin']) * prm%TotalNtwin & + size(['sum(gamma)', 'sum(f) ']) sizeDotState = sizeState plasticState(p)%sizeState = sizeState plasticState(p)%sizeDotState = sizeDotState plasticState(p)%sizePostResults = sum(plastic_phenopowerlaw_sizePostResult(:,instance)) plasticState(p)%nSlip = prm%totalNslip plasticState(p)%nTwin = prm%totalNtwin allocate(plasticState(p)%aTolState ( sizeState), source=0.0_pReal) allocate(plasticState(p)%state0 ( sizeState,NipcMyPhase), source=0.0_pReal) allocate(plasticState(p)%partionedState0 ( sizeState,NipcMyPhase), source=0.0_pReal) allocate(plasticState(p)%subState0 ( sizeState,NipcMyPhase), source=0.0_pReal) allocate(plasticState(p)%state ( sizeState,NipcMyPhase), source=0.0_pReal) allocate(plasticState(p)%dotState (sizeDotState,NipcMyPhase), source=0.0_pReal) allocate(plasticState(p)%deltaState (0_pInt,NipcMyPhase), source=0.0_pReal) if (any(numerics_integrator == 1_pInt)) then allocate(plasticState(p)%previousDotState (sizeDotState,NipcMyPhase),source=0.0_pReal) allocate(plasticState(p)%previousDotState2(sizeDotState,NipcMyPhase),source=0.0_pReal) endif if (any(numerics_integrator == 4_pInt)) & allocate(plasticState(p)%RK4dotState (sizeDotState,NipcMyPhase), source=0.0_pReal) if (any(numerics_integrator == 5_pInt)) & allocate(plasticState(p)%RKCK45dotState (6,sizeDotState,NipcMyPhase), source=0.0_pReal) !-------------------------------------------------------------------------------------------------- ! calculate hardening matrices allocate(temp1(prm%totalNslip,prm%totalNslip),source = 0.0_pReal) allocate(temp2(prm%totalNslip,prm%totalNtwin),source = 0.0_pReal) allocate(prm%Schmid_slip(3,3,prm%totalNslip),source = 0.0_pReal) allocate(prm%nonSchmid_pos(3,3,size(prm%nonSchmidCoeff),prm%totalNslip),source = 0.0_pReal) allocate(prm%nonSchmid_neg(3,3,size(prm%nonSchmidCoeff),prm%totalNslip),source = 0.0_pReal) i = 0_pInt 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) i = i + 1_pInt prm%Schmid_slip(1:3,1:3,i) = lattice_Sslip(1:3,1:3,1,sum(lattice_Nslipsystem(1:f-1,p))+j,p) do k = 1,size(prm%nonSchmidCoeff) prm%nonSchmid_pos(1:3,1:3,k,i) = lattice_Sslip(1:3,1:3,2*k, index_myFamily+j,p) & * prm%nonSchmidCoeff(k) prm%nonSchmid_neg(1:3,1:3,k,i) = lattice_Sslip(1:3,1:3,2*k+1,index_myFamily+j,p) & * prm%nonSchmidCoeff(k) enddo 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) temp1(index_myFamily+j,index_otherFamily+k) = & prm%interaction_SlipSlip(lattice_interactionSlipSlip( & sum(lattice_NslipSystem(1:f-1,p))+j, & sum(lattice_NslipSystem(1:o-1,p))+k, & p),1) enddo otherSlipSystems; enddo otherSlipFamilies 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) temp2(index_myFamily+j,index_otherFamily+k) = & prm%interaction_SlipTwin(lattice_interactionSlipTwin( & sum(lattice_NslipSystem(1:f-1_pInt,p))+j, & sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, & p),1) enddo twinSystems; enddo twinFamilies enddo mySlipSystems enddo mySlipFamilies prm%interaction_SlipSlip = temp1; deallocate(temp1) prm%interaction_SlipTwin = temp2; deallocate(temp2) allocate(temp1(prm%totalNtwin,prm%totalNslip),source = 0.0_pReal) allocate(temp2(prm%totalNtwin,prm%totalNtwin),source = 0.0_pReal) allocate(prm%Schmid_twin(3,3,prm%totalNtwin),source = 0.0_pReal) allocate(prm%shear_twin(prm%totalNtwin),source = 0.0_pReal) i = 0_pInt 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) i = i + 1_pInt prm%Schmid_twin(1:3,1:3,i) = lattice_Stwin(1:3,1:3,sum(lattice_NTwinsystem(1:f-1,p))+j,p) prm%shear_twin(i) = lattice_shearTwin(sum(lattice_Ntwinsystem(1:f-1,p))+j,p) 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) temp1(index_myFamily+j,index_otherFamily+k) = & prm%interaction_TwinSlip(lattice_interactionTwinSlip( & sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, & sum(lattice_NslipSystem(1:o-1_pInt,p))+k, & p),1) enddo slipSystems; enddo slipFamilies 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) temp2(index_myFamily+j,index_otherFamily+k) = & prm%interaction_TwinTwin(lattice_interactionTwinTwin( & sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, & sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, & p),1) enddo otherTwinSystems; enddo otherTwinFamilies enddo myTwinSystems enddo myTwinFamilies prm%interaction_TwinSlip = temp1; deallocate(temp1) prm%interaction_TwinTwin = temp2; deallocate(temp2) !-------------------------------------------------------------------------------------------------- ! locally defined state aliases and initialization of state0 and aTolState startIndex = 1_pInt endIndex = prm%totalNslip state (instance)%s_slip => plasticState(p)%state (startIndex:endIndex,:) state (instance)%s_slip = spread(math_expand(prm%tau0_slip, prm%Nslip), 2, NipcMyPhase) dotState(instance)%s_slip => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%state0(startIndex:endIndex,:) = & spread(math_expand(prm%tau0_slip, prm%Nslip), 2, NipcMyPhase) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolResistance startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNtwin state (instance)%s_twin => plasticState(p)%state (startIndex:endIndex,:) state (instance)%s_twin = spread(math_expand(prm%tau0_twin, prm%Ntwin), 2, NipcMyPhase) dotState(instance)%s_twin => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%state0(startIndex:endIndex,:) = & spread(math_expand(prm%tau0_twin, prm%Ntwin), 2, NipcMyPhase) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolResistance startIndex = endIndex + 1_pInt endIndex = endIndex + 1_pInt state (instance)%sumGamma => plasticState(p)%state (startIndex,:) dotState(instance)%sumGamma => plasticState(p)%dotState(startIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolShear startIndex = endIndex + 1_pInt endIndex = endIndex + 1_pInt state (instance)%sumF=>plasticState(p)%state (startIndex,:) dotState(instance)%sumF=>plasticState(p)%dotState(startIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNslip state (instance)%accshear_slip => plasticState(p)%state (startIndex:endIndex,:) dotState(instance)%accshear_slip => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolShear ! global alias plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:) startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNtwin state (instance)%accshear_twin => plasticState(p)%state (startIndex:endIndex,:) dotState(instance)%accshear_twin => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolShear dotState(instance)%whole => plasticState(p)%dotState end associate enddo end subroutine plastic_phenopowerlaw_init !-------------------------------------------------------------------------------------------------- !> @brief calculates plastic velocity gradient and its tangent !-------------------------------------------------------------------------------------------------- subroutine plastic_phenopowerlaw_LpAndItsTangent(Lp,dLp_dMstar99,Mstar_v,ipc,ip,el) use prec, only: & dNeq0 use math, only: & math_Mandel6to33, & math_Plain3333to99 use material, only: & phasememberAt, & material_phase, & phase_plasticityInstance implicit none real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(9,9), intent(out) :: & dLp_dMstar99 !< derivative of Lp with respect to the Mandel stress integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element real(pReal), dimension(6), intent(in) :: & Mstar_v !< Mandel stress integer(pInt) :: & index_myFamily, & j,k,l,m,n, & of real(pReal) :: & dgdot_dtauslip_pos,dgdot_dtauslip_neg, & dgdot_dtautwin real(pReal), dimension(3,3) :: & S !< Second-Piola Kirchhoff stress real(pReal), dimension(3,3,3,3) :: & dLp_dS !< derivative of Lp with respect to Mstar as 4th order tensor real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNslip) :: & tau_slip_pos,tau_slip_neg, & gdot_slip_pos,gdot_slip_neg real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNtwin) :: & gdot_twin,tau_twin type(tParameters) :: prm type(tPhenopowerlawState) :: stt of = phasememberAt(ipc,ip,el) associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),& stt => state(phase_plasticityInstance(material_phase(ipc,ip,el)))) Lp = 0.0_pReal dLp_dS = 0.0_pReal S = math_Mandel6to33(Mstar_v) call resolvedStress_slip(prm,S,tau_slip_pos,tau_slip_neg) call shearRates_slip(prm,stt,of,tau_slip_pos,tau_slip_neg,gdot_slip_pos,gdot_slip_neg) slipSystems: do j = 1_pInt, prm%totalNslip Lp = Lp + (1.0_pReal-stt%sumF(of))*(gdot_slip_pos(j)+gdot_slip_neg(j))*prm%Schmid_slip(1:3,1:3,j) if (dNeq0(tau_slip_pos(j))) then dgdot_dtauslip_pos = gdot_slip_pos(j)*prm%n_slip/tau_slip_pos(j) forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) & + dgdot_dtauslip_pos * prm%Schmid_slip(k,l,j) & *(prm%Schmid_slip(m,n,j) + sum(prm%nonSchmid_pos(m,n,:,j))) endif if (dNeq0(tau_slip_neg(j))) then dgdot_dtauslip_neg = gdot_slip_neg(j)*prm%n_slip/tau_slip_neg(j) forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) & + dgdot_dtauslip_neg * prm%Schmid_slip(k,l,j) & *(prm%Schmid_slip(m,n,j) + sum(prm%nonSchmid_neg(m,n,:,j))) endif enddo slipSystems call resolvedStress_twin(prm,S,tau_twin) call shearRates_twin(prm,stt,of,tau_twin,gdot_twin) twinSystems: do j = 1_pInt, prm%totalNtwin Lp = Lp + gdot_twin(j)*prm%Schmid_twin(1:3,1:3,j) if (dNeq0(gdot_twin(j))) then dgdot_dtautwin = gdot_twin(j)*prm%n_twin/tau_twin(j) forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) & + dgdot_dtautwin*prm%Schmid_twin(k,l,j)*prm%Schmid_twin(m,n,j) endif enddo twinSystems dLp_dMstar99 = math_Plain3333to99(dLp_dS) end associate end subroutine plastic_phenopowerlaw_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates the rate of change of microstructure !-------------------------------------------------------------------------------------------------- subroutine plastic_phenopowerlaw_dotState(Mstar6,ipc,ip,el) use math, only: & math_Mandel6to33 use material, only: & material_phase, & phasememberAt, & phase_plasticityInstance implicit none real(pReal), dimension(6), intent(in) :: & Mstar6 !< Mandel stress integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element !< microstructure state integer(pInt) :: & ph, & j,k, & index_myFamily, & of real(pReal) :: & c_SlipSlip,c_TwinSlip,c_TwinTwin, & ssat_offset real(pReal), dimension(3,3) :: & S !< Second-Piola Kirchhoff stress real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNslip) :: & left_SlipSlip,right_SlipSlip, & tau_slip_pos,tau_slip_neg, & gdot_slip_pos,gdot_slip_neg real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNtwin) :: & tau_twin type(tParameters) :: prm type(tPhenopowerlawState) :: dst,stt of = phasememberAt(ipc,ip,el) associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))), & stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))), & dst => dotState(phase_plasticityInstance(material_phase(ipc,ip,el)))) dst%whole(:,of) = 0.0_pReal S = math_Mandel6to33(Mstar6) !-------------------------------------------------------------------------------------------------- ! system-independent (nonlinear) prefactors to M_Xx (X influenced by x) matrices c_SlipSlip = prm%h0_slipslip * (1.0_pReal + prm%twinC*stt%sumF(of)** prm%twinB) c_TwinSlip = prm%h0_TwinSlip * stt%sumGamma(of)**prm%twinE c_TwinTwin = prm%h0_TwinTwin * stt%sumF(of)**prm%twinD !-------------------------------------------------------------------------------------------------- ! calculate left and right vectors left_SlipSlip = 1.0_pReal + prm%H_int ssat_offset = prm%spr*sqrt(stt%sumF(of)) right_SlipSlip = abs(1.0_pReal-stt%s_slip(:,of) / (prm%tausat_slip+ssat_offset)) **prm%a_slip & * sign(1.0_pReal,1.0_pReal-stt%s_slip(:,of) / (prm%tausat_slip+ssat_offset)) !-------------------------------------------------------------------------------------------------- ! shear rates call resolvedStress_slip(prm,S,tau_slip_pos,tau_slip_neg) call shearRates_slip(prm,stt,of,tau_slip_pos,tau_slip_neg,gdot_slip_pos,gdot_slip_neg) dst%accshear_slip(:,of) = abs(gdot_slip_pos+gdot_slip_neg) dst%sumGamma(of) = sum(dst%accshear_slip(:,of)) call resolvedStress_twin(prm,S,tau_twin) call shearRates_twin(prm,stt,of,tau_twin,dst%accshear_twin(:,of)) if (stt%sumF(of) < 0.98_pReal) dst%sumF(of) = sum(dst%accshear_twin(:,of)/prm%shear_twin) !-------------------------------------------------------------------------------------------------- ! hardening hardeningSlip: do j = 1_pInt, prm%totalNslip dst%s_slip(j,of) = & c_SlipSlip * left_SlipSlip(j) & * dot_product(prm%interaction_SlipSlip(j,:),right_SlipSlip*dst%accshear_slip(:,of)) & + & dot_product(prm%interaction_SlipTwin(j,:),dst%accshear_twin(:,of)) enddo hardeningSlip hardeningTwin: do j = 1_pInt, prm%totalNtwin dst%s_twin(j,of) = & c_TwinSlip & * dot_product(prm%interaction_TwinSlip(j,:),dst%accshear_slip(:,of)) & + & c_TwinTwin & * dot_product(prm%interaction_TwinTwin(j,:),dst%accshear_twin(:,of)) enddo hardeningTwin end associate end subroutine plastic_phenopowerlaw_dotState !-------------------------------------------------------------------------------------------------- !> @brief calculates shear rates on slip systems !-------------------------------------------------------------------------------------------------- subroutine shearRates_slip(prm,stt,of,tau_slip_pos,tau_slip_neg,gdot_slip_pos,gdot_slip_neg) implicit none type(tParameters), intent(in) :: & prm type(tPhenopowerlawState), intent(in) :: & stt integer(pInt), intent(in) :: & of real, dimension(prm%totalNslip), intent(in) :: & tau_slip_pos, & tau_slip_neg real, dimension(prm%totalNslip), intent(out) :: & gdot_slip_pos, & gdot_slip_neg gdot_slip_pos = 0.5_pReal*prm%gdot0_slip & * sign(abs(tau_slip_pos/stt%s_slip(:,of))**prm%n_slip, tau_slip_pos) gdot_slip_neg = 0.5_pReal*prm%gdot0_slip & * sign(abs(tau_slip_neg/stt%s_slip(:,of))**prm%n_slip, tau_slip_neg) end subroutine shearRates_slip !-------------------------------------------------------------------------------------------------- !> @brief calculates shear rates on twin systems !-------------------------------------------------------------------------------------------------- subroutine shearRates_twin(prm,stt,of,tau_twin,gdot_twin) implicit none type(tParameters), intent(in) :: & prm type(tPhenopowerlawState), intent(in) :: & stt integer(pInt), intent(in) :: & of real, dimension(prm%totalNtwin), intent(in) :: & tau_twin real, dimension(prm%totalNtwin), intent(out) :: & gdot_twin gdot_twin = merge((1.0_pReal-stt%sumF(of))*prm%gdot0_twin*(abs(tau_twin)/stt%s_twin(:,of))**prm%n_twin, & 0.0_pReal, tau_twin>0.0_pReal) end subroutine shearRates_twin !-------------------------------------------------------------------------------------------------- !> @brief calculates resolved stress on slip systems !-------------------------------------------------------------------------------------------------- subroutine resolvedStress_slip(prm,S,tau_slip_pos,tau_slip_neg) use math, only: & math_mul33xx33 implicit none type(tParameters), intent(in) :: & prm real(pReal), dimension(3,3), intent(in) :: & S real, dimension(prm%totalNslip), intent(out) :: & tau_slip_pos, & tau_slip_neg integer(pInt) :: i,j do i = 1_pInt, prm%totalNslip tau_slip_pos(i) = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,i)) tau_slip_neg(i) = tau_slip_pos(i) do j = 1,size(prm%nonSchmidCoeff) tau_slip_pos(i) = tau_slip_pos(i) + math_mul33xx33(S,prm%nonSchmid_pos(1:3,1:3,j,i)) tau_slip_neg(i) = tau_slip_neg(i) + math_mul33xx33(S,prm%nonSchmid_neg(1:3,1:3,j,i)) enddo enddo end subroutine resolvedStress_slip !-------------------------------------------------------------------------------------------------- !> @brief calculates resolved stress on twin systems !-------------------------------------------------------------------------------------------------- subroutine resolvedStress_twin(prm,S,tau_twin) use math, only: & math_mul33xx33 implicit none type(tParameters), intent(in) :: & prm real(pReal), dimension(3,3), intent(in) :: & S real, dimension(prm%totalNtwin), intent(out) :: & tau_twin integer(pInt) :: i do i = 1_pInt, prm%totalNtwin tau_twin(i) = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,i)) enddo end subroutine resolvedStress_twin !-------------------------------------------------------------------------------------------------- !> @brief return array of constitutive results !-------------------------------------------------------------------------------------------------- function plastic_phenopowerlaw_postResults(Mstar6,ipc,ip,el) result(postResults) use material, only: & material_phase, & plasticState, & phasememberAt, & phase_plasticityInstance use math, only: & math_mul33xx33, & math_Mandel6to33 implicit none real(pReal), dimension(6), intent(in) :: & Mstar6 !< Mandel stress integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element !< microstructure state real(pReal), dimension(3,3) :: & S !< Second-Piola Kirchhoff stress real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: & postResults integer(pInt) :: & of, & o,c real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNslip) :: & tau_slip_pos,tau_slip_neg, & gdot_slip_pos,gdot_slip_neg real(pReal), dimension(param(phase_plasticityInstance(material_phase(ipc,ip,el)))%totalNtwin) :: & gdot_twin,tau_twin type(tParameters) :: prm type(tPhenopowerlawState) :: stt of = phasememberAt(ipc,ip,el) associate( prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))), & stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))) ) postResults = 0.0_pReal c = 0_pInt S = math_Mandel6to33(Mstar6) outputsLoop: do o = 1_pInt,size(prm%outputID) select case(prm%outputID(o)) case (resistance_slip_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%s_slip(1:prm%totalNslip,of) c = c + prm%totalNslip case (accumulatedshear_slip_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1:prm%totalNslip,of) c = c + prm%totalNslip case (shearrate_slip_ID) call resolvedStress_slip(prm,S,tau_slip_pos,tau_slip_neg) call shearRates_slip(prm,stt,of,tau_slip_pos,tau_slip_neg,gdot_slip_pos,gdot_slip_neg) postResults(c+1_pInt:c+prm%totalNslip) = gdot_slip_pos+gdot_slip_neg c = c + prm%totalNslip case (resolvedstress_slip_ID) call resolvedStress_slip(prm,S,tau_slip_pos,tau_slip_neg) postResults(c+1_pInt:c+prm%totalNslip) = 0.5_pReal*(tau_slip_pos+tau_slip_neg) c = c + prm%totalNslip case (resistance_twin_ID) postResults(c+1_pInt:c+prm%totalNtwin) = stt%s_twin(1:prm%totalNtwin,of) c = c + prm%totalNtwin case (accumulatedshear_twin_ID) postResults(c+1_pInt:c+prm%totalNtwin) = stt%accshear_twin(1:prm%totalNtwin,of) c = c + prm%totalNtwin case (shearrate_twin_ID) call resolvedStress_twin(prm,S,tau_twin) call shearRates_twin(prm,stt,of,tau_twin,gdot_twin) postResults(c+1_pInt:c+prm%totalNtwin) = gdot_twin c = c + prm%totalNtwin case (resolvedstress_twin_ID) call resolvedStress_twin(prm,S,tau_twin) postResults(c+1_pInt:c+prm%totalNtwin) = tau_twin c = c + prm%totalNtwin case (totalvolfrac_twin_ID) postResults(c+1_pInt) = stt%sumF(of) c = c + 1_pInt case (totalshear_ID) postResults(c+1_pInt) = stt%sumGamma(of) c = c + 1_pInt end select enddo outputsLoop end associate end function plastic_phenopowerlaw_postResults end module plastic_phenopowerlaw