!-------------------------------------------------------------------------------------------------- !> @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 isotropic plasticity !> @details Isotropic Plasticity which resembles the phenopowerlaw plasticity without !! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an !! untextured polycrystal !-------------------------------------------------------------------------------------------------- module plastic_isotropic use prec, only: & pReal, & pInt implicit none private integer(pInt), dimension(:,:), allocatable, target, public :: & plastic_isotropic_sizePostResult !< size of each post result output character(len=64), dimension(:,:), allocatable, target, public :: & plastic_isotropic_output !< name of each post result output enum, bind(c) enumerator :: & undefined_ID, & flowstress_ID, & strainrate_ID end enum type, private :: tParameters real(pReal) :: & fTaylor, & !< Taylor factor tau0, & !< initial critical stress gdot0, & !< reference strain rate n, & !< stress exponent h0, & h0_slopeLnRate, & tausat, & !< maximum critical stress a, & tausat_SinhFitA, & tausat_SinhFitB, & tausat_SinhFitC, & tausat_SinhFitD, & aTolFlowstress, & aTolShear integer(pInt) :: & of_debug = 0_pInt integer(kind(undefined_ID)), allocatable, dimension(:) :: & outputID logical :: & dilatation end type tParameters type, private :: tIsotropicState real(pReal), pointer, dimension(:) :: & flowstress, & accumulatedShear end type tIsotropicState !-------------------------------------------------------------------------------------------------- ! containers for parameters and state type(tParameters), allocatable, dimension(:), private :: param type(tIsotropicState), allocatable, dimension(:), private :: & dotState, & state public :: & plastic_isotropic_init, & plastic_isotropic_LpAndItsTangent, & plastic_isotropic_LiAndItsTangent, & plastic_isotropic_dotState, & plastic_isotropic_postResults contains !-------------------------------------------------------------------------------------------------- !> @brief module initialization !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- subroutine plastic_isotropic_init use prec, only: & pStringLen use debug, only: & #ifdef DEBUG debug_e, & debug_i, & debug_g, & debug_levelExtensive, & #endif debug_level, & debug_constitutive, & debug_levelBasic use IO, only: & IO_error use material, only: & #ifdef DEBUG phasememberAt, & #endif phase_plasticity, & phase_plasticityInstance, & phase_Noutput, & material_allocatePlasticState, & PLASTICITY_ISOTROPIC_label, & PLASTICITY_ISOTROPIC_ID, & material_phase, & plasticState use config, only: & config_phase use lattice implicit none integer(pInt) :: & Ninstance, & p, i, & NipcMyPhase, & sizeState, sizeDotState character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::] integer(kind(undefined_ID)) :: & outputID character(len=pStringLen) :: & extmsg = '' character(len=65536), dimension(:), allocatable :: & outputs write(6,'(/,a)') ' <<<+- plastic_'//PLASTICITY_ISOTROPIC_label//' init -+>>>' write(6,'(/,a)') ' Maiti and Eisenlohr, Scripta Materialia, 145:37-40, 2018' write(6,'(/,a)') ' https://doi.org/10.1016/j.scriptamat.2017.09.047' Ninstance = count(phase_plasticity == PLASTICITY_ISOTROPIC_ID) if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) & write(6,'(a16,1x,i5,/)') '# instances:',Ninstance allocate(plastic_isotropic_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt) allocate(plastic_isotropic_output(maxval(phase_Noutput),Ninstance)) plastic_isotropic_output = '' allocate(param(Ninstance)) allocate(state(Ninstance)) allocate(dotState(Ninstance)) do p = 1_pInt, size(phase_plasticity) if (phase_plasticity(p) /= PLASTICITY_ISOTROPIC_ID) cycle associate(prm => param(phase_plasticityInstance(p)), & dot => dotState(phase_plasticityInstance(p)), & stt => state(phase_plasticityInstance(p)), & config => config_phase(p)) #ifdef DEBUG if (p==material_phase(debug_g,debug_i,debug_e)) then prm%of_debug = phasememberAt(debug_g,debug_i,debug_e) endif #endif prm%tau0 = config%getFloat('tau0') prm%tausat = config%getFloat('tausat') prm%gdot0 = config%getFloat('gdot0') prm%n = config%getFloat('n') prm%h0 = config%getFloat('h0') prm%fTaylor = config%getFloat('m') prm%h0_slopeLnRate = config%getFloat('h0_slopelnrate', defaultVal=0.0_pReal) prm%tausat_SinhFitA = config%getFloat('tausat_sinhfita',defaultVal=0.0_pReal) prm%tausat_SinhFitB = config%getFloat('tausat_sinhfitb',defaultVal=0.0_pReal) prm%tausat_SinhFitC = config%getFloat('tausat_sinhfitc',defaultVal=0.0_pReal) prm%tausat_SinhFitD = config%getFloat('tausat_sinhfitd',defaultVal=0.0_pReal) prm%a = config%getFloat('a') prm%aTolFlowStress = config%getFloat('atol_flowstress',defaultVal=1.0_pReal) prm%aTolShear = config%getFloat('atol_shear', defaultVal=1.0e-6_pReal) prm%dilatation = config%keyExists('/dilatation/') !-------------------------------------------------------------------------------------------------- ! sanity checks extmsg = '' if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//' aTolShear' if (prm%tau0 < 0.0_pReal) extmsg = trim(extmsg)//' tau0' if (prm%gdot0 <= 0.0_pReal) extmsg = trim(extmsg)//' gdot0' if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' n' if (prm%tausat <= prm%tau0) extmsg = trim(extmsg)//' tausat' if (prm%a <= 0.0_pReal) extmsg = trim(extmsg)//' a' if (prm%fTaylor <= 0.0_pReal) extmsg = trim(extmsg)//' m' if (prm%aTolFlowstress <= 0.0_pReal) extmsg = trim(extmsg)//' atol_flowstress' if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//' atol_shear' !-------------------------------------------------------------------------------------------------- ! exit if any parameter is out of range if (extmsg /= '') & call IO_error(211_pInt,ext_msg=trim(extmsg)//'('//PLASTICITY_ISOTROPIC_label//')') !-------------------------------------------------------------------------------------------------- ! output pararameters outputs = config%getStrings('(output)',defaultVal=emptyStringArray) allocate(prm%outputID(0)) do i=1_pInt, size(outputs) outputID = undefined_ID select case(outputs(i)) case ('flowstress') outputID = flowstress_ID case ('strainrate') outputID = strainrate_ID end select if (outputID /= undefined_ID) then plastic_isotropic_output(i,phase_plasticityInstance(p)) = outputs(i) plastic_isotropic_sizePostResult(i,phase_plasticityInstance(p)) = 1_pInt prm%outputID = [prm%outputID, outputID] endif enddo !-------------------------------------------------------------------------------------------------- ! allocate state arrays NipcMyPhase = count(material_phase == p) sizeDotState = size(['flowstress ','accumulated_shear']) sizeState = sizeDotState call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, & 1_pInt,0_pInt,0_pInt) plasticState(p)%sizePostResults = sum(plastic_isotropic_sizePostResult(:,phase_plasticityInstance(p))) !-------------------------------------------------------------------------------------------------- ! locally defined state aliases and initialization of state0 and aTolState stt%flowstress => plasticState(p)%state (1,:) stt%flowstress = prm%tau0 dot%flowstress => plasticState(p)%dotState(1,:) plasticState(p)%aTolState(1) = prm%aTolFlowstress stt%accumulatedShear => plasticState(p)%state (2,:) dot%accumulatedShear => plasticState(p)%dotState(2,:) plasticState(p)%aTolState(2) = prm%aTolShear ! global alias plasticState(p)%slipRate => plasticState(p)%dotState(2:2,:) plasticState(p)%accumulatedSlip => plasticState(p)%state (2:2,:) plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally end associate enddo end subroutine plastic_isotropic_init !-------------------------------------------------------------------------------------------------- !> @brief calculates plastic velocity gradient and its tangent !-------------------------------------------------------------------------------------------------- subroutine plastic_isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of) #ifdef DEBUG use debug, only: & debug_level, & debug_constitutive,& debug_levelExtensive, & debug_levelSelective #endif use math, only: & math_deviatoric33, & math_mul33xx33 implicit none real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer(pInt), intent(in) :: & instance, & of real(pReal), dimension(3,3) :: & Mp_dev !< deviatoric part of the Mandel stress real(pReal) :: & gamma_dot, & !< strainrate norm_Mp_dev, & !< norm of the deviatoric part of the Mandel stress squarenorm_Mp_dev !< square of the norm of the deviatoric part of the Mandel stress integer(pInt) :: & k, l, m, n associate(prm => param(instance), stt => state(instance)) Mp_dev = math_deviatoric33(Mp) squarenorm_Mp_dev = math_mul33xx33(Mp_dev,Mp_dev) norm_Mp_dev = sqrt(squarenorm_Mp_dev) if (norm_Mp_dev > 0.0_pReal) then gamma_dot = prm%gdot0 * (sqrt(1.5_pReal) * norm_Mp_dev/(prm%fTaylor*stt%flowstress(of))) **prm%n Lp = Mp_dev/norm_Mp_dev * gamma_dot/prm%fTaylor #ifdef DEBUG if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt & .and. (of == prm%of_debug .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then write(6,'(/,a,/,3(12x,3(f12.4,1x)/))') '<< CONST isotropic >> Tstar (dev) / MPa', & transpose(Mp_dev)*1.0e-6_pReal write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> norm Tstar / MPa', norm_Mp_dev*1.0e-6_pReal write(6,'(/,a,/,f12.5)') '<< CONST isotropic >> gdot', gamma_dot end if #endif forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & dLp_dMp(k,l,m,n) = (prm%n-1.0_pReal) * Mp_dev(k,l)*Mp_dev(m,n) / squarenorm_Mp_dev forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt) & dLp_dMp(k,l,k,l) = dLp_dMp(k,l,k,l) + 1.0_pReal forall (k=1_pInt:3_pInt,m=1_pInt:3_pInt) & dLp_dMp(k,k,m,m) = dLp_dMp(k,k,m,m) - 1.0_pReal/3.0_pReal dLp_dMp = gamma_dot / prm%fTaylor * dLp_dMp / norm_Mp_dev else Lp = 0.0_pReal dLp_dMp = 0.0_pReal end if end associate end subroutine plastic_isotropic_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates plastic velocity gradient and its tangent ! ToDo: Rename Tstar to Mi? !-------------------------------------------------------------------------------------------------- subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dTstar,Tstar,instance,of) use math, only: & math_spherical33, & math_mul33xx33 implicit none real(pReal), dimension(3,3), intent(out) :: & Li !< inleastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLi_dTstar !< derivative of Li with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Tstar !< Mandel stress ToDo: Mi? integer(pInt), intent(in) :: & instance, & of real(pReal), dimension(3,3) :: & Tstar_sph !< sphiatoric part of the Mandel stress real(pReal) :: & gamma_dot, & !< strainrate norm_Tstar_sph, & !< euclidean norm of Tstar_sph squarenorm_Tstar_sph !< square of the euclidean norm of Tstar_sph integer(pInt) :: & k, l, m, n associate(prm => param(instance), stt => state(instance)) Tstar_sph = math_spherical33(Tstar) squarenorm_Tstar_sph = math_mul33xx33(Tstar_sph,Tstar_sph) norm_Tstar_sph = sqrt(squarenorm_Tstar_sph) if (prm%dilatation .and. norm_Tstar_sph > 0.0_pReal) then ! no stress or J2 plastitiy --> Li and its derivative are zero gamma_dot = prm%gdot0 * (sqrt(1.5_pReal) * norm_Tstar_sph /(prm%fTaylor*stt%flowstress(of))) **prm%n Li = Tstar_sph/norm_Tstar_sph * gamma_dot/prm%fTaylor forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & dLi_dTstar(k,l,m,n) = (prm%n-1.0_pReal) * Tstar_sph(k,l)*Tstar_sph(m,n) / squarenorm_Tstar_sph forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt) & dLi_dTstar(k,l,k,l) = dLi_dTstar(k,l,k,l) + 1.0_pReal dLi_dTstar = gamma_dot / prm%fTaylor * dLi_dTstar / norm_Tstar_sph else Li = 0.0_pReal dLi_dTstar = 0.0_pReal endif end associate end subroutine plastic_isotropic_LiAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates the rate of change of microstructure !-------------------------------------------------------------------------------------------------- subroutine plastic_isotropic_dotState(Mp,instance,of) use prec, only: & dEq0 use math, only: & math_mul33xx33, & math_deviatoric33 implicit none real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer(pInt), intent(in) :: & instance, & of real(pReal) :: & gamma_dot, & !< strainrate hardening, & !< hardening coefficient saturation, & !< saturation flowstress norm_Mp !< norm of the (deviatoric) Mandel stress associate(prm => param(instance), stt => state(instance), dot => dotState(instance)) if (prm%dilatation) then norm_Mp = sqrt(math_mul33xx33(Mp,Mp)) else norm_Mp = sqrt(math_mul33xx33(math_deviatoric33(Mp),math_deviatoric33(Mp))) endif gamma_dot = prm%gdot0 * (sqrt(1.5_pReal) * norm_Mp /(prm%fTaylor*stt%flowstress(of))) **prm%n if (abs(gamma_dot) > 1e-12_pReal) then if (dEq0(prm%tausat_SinhFitA)) then saturation = prm%tausat else saturation = prm%tausat & + asinh( (gamma_dot / prm%tausat_SinhFitA)**(1.0_pReal / prm%tausat_SinhFitD) & )**(1.0_pReal / prm%tausat_SinhFitC) & / prm%tausat_SinhFitB * (gamma_dot / prm%gdot0)**(1.0_pReal / prm%n) endif hardening = ( prm%h0 + prm%h0_slopeLnRate * log(gamma_dot) ) & * abs( 1.0_pReal - stt%flowstress(of)/saturation )**prm%a & * sign(1.0_pReal, 1.0_pReal - stt%flowstress(of)/saturation) else hardening = 0.0_pReal endif dot%flowstress (of) = hardening * gamma_dot dot%accumulatedShear(of) = gamma_dot end associate end subroutine plastic_isotropic_dotState !-------------------------------------------------------------------------------------------------- !> @brief return array of constitutive results !-------------------------------------------------------------------------------------------------- function plastic_isotropic_postResults(Mp,instance,of) result(postResults) use math, only: & math_mul33xx33, & math_deviatoric33 implicit none real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer(pInt), intent(in) :: & instance, & of real(pReal), dimension(sum(plastic_isotropic_sizePostResult(:,instance))) :: & postResults real(pReal) :: & norm_Mp !< norm of the Mandel stress integer(pInt) :: & o,c associate(prm => param(instance), stt => state(instance)) if (prm%dilatation) then norm_Mp = sqrt(math_mul33xx33(Mp,Mp)) else norm_Mp = sqrt(math_mul33xx33(math_deviatoric33(Mp),math_deviatoric33(Mp))) endif c = 0_pInt outputsLoop: do o = 1_pInt,size(prm%outputID) select case(prm%outputID(o)) case (flowstress_ID) postResults(c+1_pInt) = stt%flowstress(of) c = c + 1_pInt case (strainrate_ID) postResults(c+1_pInt) = prm%gdot0 & * (sqrt(1.5_pReal) * norm_Mp /(prm%fTaylor * stt%flowstress(of)))**prm%n c = c + 1_pInt end select enddo outputsLoop end associate end function plastic_isotropic_postResults end module plastic_isotropic