!> @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 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 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, & 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, & offset_slip, index_myFamily, index_otherFamily, & sizeState,sizeDotState, & startIndex, endIndex 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), pointer :: 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) then instance = phase_plasticityInstance(p) prm => param(instance) prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyIntArray) !if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg) if (sum(prm%Nslip) > 0_pInt) then prm%tau0_slip = config_phase(p)%getFloats('tau0_slip') prm%tausat_slip = config_phase(p)%getFloats('tausat_slip') prm%interaction_SlipSlip = config_phase(p)%getFloats('interaction_slipslip') 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 > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg) if (sum(prm%Ntwin) > 0_pInt) then prm%tau0_twin = config_phase(p)%getFloats('tau0_twin') prm%interaction_TwinTwin = config_phase(p)%getFloats('interaction_twintwin') 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%twinB = config_phase(p)%getFloat('twin_b') prm%twinC = config_phase(p)%getFloat('twin_c') prm%twinD = config_phase(p)%getFloat('twin_d') prm%twinE = config_phase(p)%getFloat('twin_e') prm%h0_TwinTwin = config_phase(p)%getFloat('h0_twintwin') endif if (sum(prm%Nslip) > 0_pInt .and. sum(prm%Ntwin) > 0_pInt) then prm%interaction_SlipTwin = config_phase(p)%getFloats('interaction_sliptwin') prm%interaction_TwinSlip = config_phase(p)%getFloats('interaction_twinslip') prm%h0_TwinSlip = config_phase(p)%getFloat('h0_twinslip') endif 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) 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 = sum(prm%Nslip) case ('accumulatedshear_slip') outputID = accumulatedshear_slip_ID outputSize = sum(prm%Nslip) case ('shearrate_slip') outputID = shearrate_slip_ID outputSize = sum(prm%Nslip) case ('resolvedstress_slip') outputID = resolvedstress_slip_ID outputSize = sum(prm%Nslip) case ('resistance_twin') outputID = resistance_twin_ID outputSize = sum(prm%Ntwin) case ('accumulatedshear_twin') outputID = accumulatedshear_twin_ID outputSize = sum(prm%Ntwin) case ('shearrate_twin') outputID = shearrate_twin_ID outputSize = sum(prm%Ntwin) case ('resolvedstress_twin') outputID = resolvedstress_twin_ID 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 prm%outputID = [prm%outputID , outputID] endif end do extmsg = '' 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//')') 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? endif 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//')') 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']) * sum(prm%nslip) & + size(['tau_twin ','accshear_twin']) * sum(prm%ntwin) & + 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 = sum(prm%Nslip) plasticState(p)%nTwin = sum(prm%Ntwin) 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 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,p))+j, & sum(lattice_NslipSystem(1:o-1,p))+k, & p)) 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) prm%matrix_SlipTwin(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)) enddo twinSystems; enddo twinFamilies enddo mySlipSystems enddo mySlipFamilies 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,p))+j, & sum(lattice_NslipSystem(1:o-1_pInt,p))+k, & p)) 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) prm%matrix_TwinTwin(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)) enddo otherTwinSystems; enddo otherTwinFamilies enddo myTwinSystems enddo myTwinFamilies !-------------------------------------------------------------------------------------------------- ! locally defined state aliases and initialization of state0 and aTolState startIndex = 1_pInt endIndex = plasticState(p)%nSlip state (instance)%s_slip=>plasticState(p)%state (startIndex:endIndex,:) 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 + plasticState(p)%nTwin state (instance)%s_twin=>plasticState(p)%state (startIndex:endIndex,:) 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 + plasticState(p)%nSlip 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 + plasticState(p)%nTwin 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 offset_slip = plasticState(p)%nSlip+plasticState(p)%nTwin+2_pInt plasticState(p)%slipRate => & plasticState(p)%dotState(offset_slip+1:offset_slip+plasticState(p)%nSlip,1:NipcMyPhase) plasticState(p)%accumulatedSlip => & plasticState(p)%state(offset_slip+1:offset_slip+plasticState(p)%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) 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, & 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) :: & 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 of = phasememberAt(ipc,ip,el) ph = phaseAt(ipc,ip,el) instance = phase_plasticityInstance(ph) Lp = 0.0_pReal dLp_dTstar3333 = 0.0_pReal 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 ! 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) 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 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 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 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 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 of = phasememberAt(ipc,ip,el) ph = phaseAt(ipc,ip,el) instance = phase_plasticityInstance(ph) nSlip= sum(param(instance)%nslip) nTwin= sum(param(instance)%nTwin) plasticState(ph)%dotState(:,of) = 0.0_pReal !-------------------------------------------------------------------------------------------------- ! 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 !-------------------------------------------------------------------------------------------------- ! 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 & *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 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 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 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 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, & 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 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 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