!-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @author David Cereceda, Lawrence Livermore National Laboratory !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @brief crystal plasticity model for bcc metals, especially Tungsten !-------------------------------------------------------------------------------------------------- module plastic_disloUCLA use prec, only: & pReal, & pInt implicit none private integer(pInt), dimension(:,:), allocatable, target, public :: & plastic_disloUCLA_sizePostResult !< size of each post result output character(len=64), dimension(:,:), allocatable, target, public :: & plastic_disloUCLA_output !< name of each post result output real(pReal), parameter, private :: & kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin enum, bind(c) enumerator :: & undefined_ID, & rho_ID, & rhoDip_ID, & shearrate_ID, & accumulatedshear_ID, & mfp_ID, & thresholdstress_ID end enum type, private :: tParameters real(pReal) :: & aTolRho, & grainSize, & SolidSolutionStrength, & !< Strength due to elements in solid solution mu, & D0, & !< prefactor for self-diffusion coefficient Qsd !< activation energy for dislocation climb real(pReal), allocatable, dimension(:) :: & rho0, & !< initial edge dislocation density rhoDip0, & !< initial edge dipole density burgers, & !< absolute length of burgers vector [m] nonSchmidCoeff, & minDipDistance, & CLambda, & !< Adj. parameter for distance between 2 forest dislocations atomicVolume, & tau_Peierls, & tau0, & !* mobility law parameters H0kp, & !< activation energy for glide [J] v0, & !< dislocation velocity prefactor [m/s] p, & !< p-exponent in glide velocity q, & !< q-exponent in glide velocity B, & !< friction coefficient kink_height, & !< height of the kink pair w, & !< width of the kink pair omega !< attempt frequency for kink pair nucleation real(pReal), allocatable, dimension(:,:) :: & interaction_SlipSlip, & !< slip resistance from slip activity forestProjectionEdge real(pReal), allocatable, dimension(:,:,:) :: & Schmid, & nonSchmid_pos, & nonSchmid_neg integer(pInt) :: & totalNslip !< total number of active slip system integer(pInt), allocatable, dimension(:) :: & Nslip !< number of active slip systems for each family integer(kind(undefined_ID)), allocatable, dimension(:) :: & outputID !< ID of each post result output logical :: & dipoleFormation !< flag indicating consideration of dipole formation end type !< container type for internal constitutive parameters type, private :: tDisloUCLAState real(pReal), pointer, dimension(:,:) :: & rhoEdge, & rhoEdgeDip, & accshear end type tDisloUCLAState type, private :: tDisloUCLAdependentState real(pReal), allocatable, dimension(:,:) :: & mfp, & dislocationSpacing, & threshold_stress end type tDisloUCLAdependentState !-------------------------------------------------------------------------------------------------- ! containers for parameters and state type(tParameters), allocatable, dimension(:), private :: param type(tDisloUCLAState), allocatable, dimension(:), private :: & dotState, & state type(tDisloUCLAdependentState), allocatable, dimension(:), private :: dependentState public :: & plastic_disloUCLA_init, & plastic_disloUCLA_dependentState, & plastic_disloUCLA_LpAndItsTangent, & plastic_disloUCLA_dotState, & plastic_disloUCLA_postResults private :: & kinetics contains !-------------------------------------------------------------------------------------------------- !> @brief module initialization !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- subroutine plastic_disloUCLA_init() #if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800 use, intrinsic :: iso_fortran_env, only: & compiler_version, & compiler_options #endif use prec, only: & pStringLen use debug, only: & debug_level,& debug_constitutive,& debug_levelBasic use math, only: & math_expand use IO, only: & IO_error, & IO_timeStamp use material, only: & phase_plasticity, & phase_plasticityInstance, & phase_Noutput, & material_allocatePlasticState, & PLASTICITY_DISLOUCLA_label, & PLASTICITY_DISLOUCLA_ID, & material_phase, & plasticState use config, only: & MATERIAL_partPhase, & config_phase use lattice implicit none integer(pInt) :: & Ninstance, & p, i, & NipcMyPhase, & 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)::] integer(kind(undefined_ID)) :: & outputID character(len=pStringLen) :: & extmsg = '' character(len=65536), dimension(:), allocatable :: & outputs write(6,'(/,a)') ' <<<+- plastic_'//PLASTICITY_DISLOUCLA_label//' init -+>>>' write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78, 2016, 242-256' write(6,'(/,a)') ' http://dx.doi.org/10.1016/j.ijplas.2015.09.002' write(6,'(a15,a)') ' Current time: ',IO_timeStamp() #include "compilation_info.f90" Ninstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt) if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) & write(6,'(a16,1x,i5,/)') '# instances:',Ninstance allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt) allocate(plastic_disloUCLA_output(maxval(phase_Noutput),Ninstance)) plastic_disloUCLA_output = '' allocate(param(Ninstance)) allocate(state(Ninstance)) allocate(dotState(Ninstance)) allocate(dependentState(Ninstance)) do p = 1_pInt, size(phase_plasticity) if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle associate(prm => param(phase_plasticityInstance(p)), & dot => dotState(phase_plasticityInstance(p)), & stt => state(phase_plasticityInstance(p)), & dst => dependentState(phase_plasticityInstance(p)), & config => config_phase(p)) !-------------------------------------------------------------------------------------------------- ! optional parameters that need to be defined prm%mu = lattice_mu(p) prm%aTolRho = config%getFloat('atol_rho') ! sanity checks if (prm%aTolRho <= 0.0_pReal) extmsg = trim(extmsg)//' atol_rho' !-------------------------------------------------------------------------------------------------- ! slip related parameters prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray) prm%totalNslip = sum(prm%Nslip) slipActive: if (prm%totalNslip > 0_pInt) then prm%Schmid = lattice_SchmidMatrix_slip(prm%Nslip,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) if(trim(config%getString('lattice_structure')) == 'bcc') then prm%nonSchmidCoeff = config%getFloats('nonschmid_coefficients',& defaultVal = emptyRealArray) prm%nonSchmid_pos = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,+1_pInt) prm%nonSchmid_neg = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,-1_pInt) else prm%nonSchmid_pos = prm%Schmid prm%nonSchmid_neg = prm%Schmid endif prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, & config%getFloats('interaction_slipslip'), & config%getString('lattice_structure')) prm%forestProjectionEdge = lattice_forestProjection(prm%Nslip,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) prm%rho0 = config%getFloats('rhoedge0', requiredSize=size(prm%Nslip)) prm%rhoDip0 = config%getFloats('rhoedgedip0', requiredSize=size(prm%Nslip)) prm%v0 = config%getFloats('v0', requiredSize=size(prm%Nslip)) prm%burgers = config%getFloats('slipburgers', requiredSize=size(prm%Nslip)) prm%H0kp = config%getFloats('qedge', requiredSize=size(prm%Nslip)) prm%clambda = config%getFloats('clambdaslip', requiredSize=size(prm%Nslip)) prm%tau_Peierls = config%getFloats('tau_peierls', requiredSize=size(prm%Nslip)) ! ToDo: Deprecated prm%p = config%getFloats('p_slip', requiredSize=size(prm%Nslip), & defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))]) prm%q = config%getFloats('q_slip', requiredSize=size(prm%Nslip), & defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))]) prm%kink_height = config%getFloats('kink_height', requiredSize=size(prm%Nslip)) prm%w = config%getFloats('kink_width', requiredSize=size(prm%Nslip)) prm%omega = config%getFloats('omega', requiredSize=size(prm%Nslip)) prm%B = config%getFloats('friction_coeff', requiredSize=size(prm%Nslip)) prm%SolidSolutionStrength = config%getFloat('solidsolutionstrength') ! ToDo: Deprecated prm%grainSize = config%getFloat('grainsize') prm%D0 = config%getFloat('d0') prm%Qsd = config%getFloat('qsd') prm%atomicVolume = config%getFloat('catomicvolume') * prm%burgers**3.0_pReal prm%minDipDistance = config%getFloat('cedgedipmindistance') * prm%burgers prm%dipoleformation = config%getFloat('dipoleformationfactor') > 0.0_pReal !should be on by default, ToDo: change to /key/-type key ! expand: family => system prm%rho0 = math_expand(prm%rho0, prm%Nslip) prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip) prm%q = math_expand(prm%q, prm%Nslip) prm%p = math_expand(prm%p, prm%Nslip) prm%H0kp = math_expand(prm%H0kp, prm%Nslip) prm%burgers = math_expand(prm%burgers, prm%Nslip) prm%kink_height = math_expand(prm%kink_height, prm%Nslip) prm%w = math_expand(prm%w, prm%Nslip) prm%omega = math_expand(prm%omega, prm%Nslip) prm%tau_Peierls = math_expand(prm%tau_Peierls, prm%Nslip) prm%v0 = math_expand(prm%v0, prm%Nslip) prm%B = math_expand(prm%B, prm%Nslip) prm%clambda = math_expand(prm%clambda, prm%Nslip) prm%atomicVolume = math_expand(prm%atomicVolume, prm%Nslip) prm%minDipDistance = math_expand(prm%minDipDistance, prm%Nslip) prm%tau0 = prm%tau_peierls + prm%SolidSolutionStrength ! sanity checks if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' d0' if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' qsd' if (any(prm%rho0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedge0' if (any(prm%rhoDip0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedgedip0' if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0' if (any(prm%burgers <= 0.0_pReal)) extmsg = trim(extmsg)//' slipburgers' if (any(prm%H0kp <= 0.0_pReal)) extmsg = trim(extmsg)//' qedge' if (any(prm%tau_peierls < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls' if (any(prm%minDipDistance <= 0.0_pReal)) extmsg = trim(extmsg)//' cedgedipmindistance or slipburgers' if (any(prm%atomicVolume <= 0.0_pReal)) extmsg = trim(extmsg)//' catomicvolume or slipburgers' else slipActive allocate(prm%rho0(0)) allocate(prm%rhoDip0(0)) endif slipActive !-------------------------------------------------------------------------------------------------- ! exit if any parameter is out of range if (extmsg /= '') & call IO_error(211_pInt,ext_msg=trim(extmsg)//'('//PLASTICITY_DISLOUCLA_label//')') !-------------------------------------------------------------------------------------------------- ! output pararameters outputs = config%getStrings('(output)',defaultVal=emptyStringArray) allocate(prm%outputID(0)) do i=1_pInt, size(outputs) outputID = undefined_ID select case(trim(outputs(i))) case ('edge_density') outputID = merge(rho_ID,undefined_ID,prm%totalNslip>0_pInt) case ('dipole_density') outputID = merge(rhoDip_ID,undefined_ID,prm%totalNslip>0_pInt) case ('shear_rate','shearrate','shear_rate_slip','shearrate_slip') outputID = merge(shearrate_ID,undefined_ID,prm%totalNslip>0_pInt) case ('accumulated_shear','accumulatedshear','accumulated_shear_slip') outputID = merge(accumulatedshear_ID,undefined_ID,prm%totalNslip>0_pInt) case ('mfp','mfp_slip') outputID = merge(mfp_ID,undefined_ID,prm%totalNslip>0_pInt) case ('threshold_stress','threshold_stress_slip') outputID = merge(thresholdstress_ID,undefined_ID,prm%totalNslip>0_pInt) end select if (outputID /= undefined_ID) then plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i) plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = prm%totalNslip prm%outputID = [prm%outputID, outputID] endif enddo !-------------------------------------------------------------------------------------------------- ! allocate state arrays NipcMyPhase = count(material_phase == p) sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * prm%totalNslip sizeState = sizeDotState call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, & prm%totalNslip,0_pInt,0_pInt) plasticState(p)%sizePostResults = sum(plastic_disloUCLA_sizePostResult(:,phase_plasticityInstance(p))) !-------------------------------------------------------------------------------------------------- ! locally defined state aliases and initialization of state0 and aTolState startIndex = 1_pInt endIndex = prm%totalNslip stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:) stt%rhoEdge= spread(prm%rho0,2,NipcMyPhase) dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNslip stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:) stt%rhoEdgeDip= spread(prm%rhoDip0,2,NipcMyPhase) dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNslip stt%accshear=>plasticState(p)%state(startIndex:endIndex,:) dot%accshear=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal !ToDo: better make optional parameter ! global alias plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:) allocate(dst%mfp(prm%totalNslip,NipcMyPhase), source=0.0_pReal) allocate(dst%dislocationSpacing(prm%totalNslip,NipcMyPhase),source=0.0_pReal) allocate(dst%threshold_stress(prm%totalNslip,NipcMyPhase), source=0.0_pReal) plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally end associate enddo end subroutine plastic_disloUCLA_init !-------------------------------------------------------------------------------------------------- !> @brief calculates plastic velocity gradient and its tangent !-------------------------------------------------------------------------------------------------- pure subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of) 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 real(pReal), intent(in) :: & temperature !< temperature integer(pInt), intent(in) :: & instance, & of integer(pInt) :: & i,k,l,m,n real(pReal), dimension(param(instance)%totalNslip) :: & gdot_pos,gdot_neg, & dgdot_dtau_pos,dgdot_dtau_neg Lp = 0.0_pReal dLp_dMp = 0.0_pReal associate(prm => param(instance)) call kinetics(Mp,Temperature,instance,of,gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg) do i = 1_pInt, prm%totalNslip Lp = Lp + (gdot_pos(i)+gdot_neg(i))*prm%Schmid(1:3,1:3,i) 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) = dLp_dMp(k,l,m,n) & + dgdot_dtau_pos(i) * prm%Schmid(k,l,i) * prm%nonSchmid_pos(m,n,i) & + dgdot_dtau_neg(i) * prm%Schmid(k,l,i) * prm%nonSchmid_neg(m,n,i) enddo end associate end subroutine plastic_disloUCLA_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates the rate of change of microstructure !-------------------------------------------------------------------------------------------------- subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of) use prec, only: & tol_math_check, & dEq0 use math, only: & PI, & math_clip implicit none real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & temperature !< temperature integer(pInt), intent(in) :: & instance, & of real(pReal) :: & VacancyDiffusion real(pReal), dimension(param(instance)%totalNslip) :: & gdot_pos, gdot_neg,& tau_pos,& tau_neg, & DotRhoDipFormation, ClimbVelocity, EdgeDipDistance, & DotRhoEdgeDipClimb associate(prm => param(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance)) call kinetics(Mp,Temperature,instance,of,& gdot_pos,gdot_neg, & tau_pos1 = tau_pos,tau_neg1 = tau_neg) dot%accshear(:,of) = (gdot_pos+gdot_neg) ! ToDo: needs to be abs VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature)) where(dEq0(tau_pos)) ! ToDo: use avg of pos and neg DotRhoDipFormation = 0.0_pReal DotRhoEdgeDipClimb = 0.0_pReal else where EdgeDipDistance = math_clip((3.0_pReal*prm%mu*prm%burgers)/(16.0_pReal*PI*abs(tau_pos)), & prm%minDipDistance, & ! lower limit dst%mfp(:,of)) ! upper limit DotRhoDipFormation = merge(((2.0_pReal*EdgeDipDistance)/prm%burgers)* stt%rhoEdge(:,of)*abs(dot%accshear(:,of)), & ! ToDo: ignore region of spontaneous annihilation 0.0_pReal, & prm%dipoleformation) ClimbVelocity = (3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume/(2.0_pReal*pi*kB*Temperature)) & * (1.0_pReal/(EdgeDipDistance+prm%minDipDistance)) DotRhoEdgeDipClimb = (4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(:,of))/(EdgeDipDistance-prm%minDipDistance) ! ToDo: Discuss with Franz: Stress dependency? end where dot%rhoEdge(:,of) = abs(dot%accshear(:,of))/(prm%burgers*dst%mfp(:,of)) & ! multiplication - DotRhoDipFormation & - (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdge(:,of)*abs(dot%accshear(:,of)) !* Spontaneous annihilation of 2 single edge dislocations dot%rhoEdgeDip(:,of) = DotRhoDipFormation & - (2.0_pReal*prm%minDipDistance)/prm%burgers*stt%rhoEdgeDip(:,of)*abs(dot%accshear(:,of)) & !* Spontaneous annihilation of a single edge dislocation with a dipole constituent - DotRhoEdgeDipClimb end associate end subroutine plastic_disloUCLA_dotState !-------------------------------------------------------------------------------------------------- !> @brief calculates derived quantities from state !-------------------------------------------------------------------------------------------------- subroutine plastic_disloUCLA_dependentState(instance,of) implicit none integer(pInt), intent(in) :: & instance, & of integer(pInt) :: & i associate(prm => param(instance), stt => state(instance),dst => dependentState(instance)) forall (i = 1_pInt:prm%totalNslip) dst%dislocationSpacing(i,of) = sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), & prm%forestProjectionEdge(:,i))) dst%threshold_stress(i,of) = prm%mu*prm%burgers(i) & * sqrt(dot_product(stt%rhoEdge(:,of)+stt%rhoEdgeDip(:,of), & prm%interaction_SlipSlip(i,:))) end forall dst%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*dst%dislocationSpacing(:,of)/prm%Clambda) dst%dislocationSpacing(:,of) = dst%mfp(:,of) ! ToDo: Hack to recover wrong behavior for the moment end associate end subroutine plastic_disloUCLA_dependentState !-------------------------------------------------------------------------------------------------- !> @brief return array of constitutive results !-------------------------------------------------------------------------------------------------- function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postResults) use prec, only: & dEq, dNeq0 use math, only: & PI, & math_mul33xx33 implicit none real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & temperature !< temperature integer(pInt), intent(in) :: & instance, & of real(pReal), dimension(sum(plastic_disloUCLA_sizePostResult(:,instance))) :: & postResults integer(pInt) :: & o,c,i real(pReal), dimension(param(instance)%totalNslip) :: & gdot_pos,gdot_neg c = 0_pInt associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) outputsLoop: do o = 1_pInt,size(prm%outputID) select case(prm%outputID(o)) case (rho_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of) case (rhoDip_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of) case (shearrate_ID) call kinetics(Mp,Temperature,instance,of,gdot_pos,gdot_neg) postResults(c+1:c+prm%totalNslip) = gdot_pos + gdot_neg case (accumulatedshear_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear(1_pInt:prm%totalNslip, of) case (mfp_ID) postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp(1_pInt:prm%totalNslip, of) case (thresholdstress_ID) postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress(1_pInt:prm%totalNslip,of) end select c = c + prm%totalNslip enddo outputsLoop end associate end function plastic_disloUCLA_postResults !-------------------------------------------------------------------------------------------------- !> @brief Shear rates on slip systems, their derivatives with respect to resolved stress and the ! resolved stresss !> @details Derivatives and resolved stress are calculated only optionally. ! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to ! have the optional arguments at the end !-------------------------------------------------------------------------------------------------- pure subroutine kinetics(Mp,Temperature,instance,of, & gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg,tau_pos1,tau_neg1) use prec, only: & tol_math_check, & dEq, dNeq0 use math, only: & PI, & math_mul33xx33 implicit none real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & temperature !< temperature integer(pInt), intent(in) :: & instance, & of real(pReal), intent(out), dimension(param(instance)%totalNslip) :: & gdot_pos, & gdot_neg real(pReal), intent(out), optional, dimension(param(instance)%totalNslip) :: & dgdot_dtau_pos, & dgdot_dtau_neg, & tau_pos1, & tau_neg1 real(pReal), dimension(param(instance)%totalNslip) :: & StressRatio, & StressRatio_p,StressRatio_pminus1, & dvel, vel, & tau_pos,tau_neg, & needsGoodName ! ToDo: @Karo: any idea? integer(pInt) :: j associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) do j = 1_pInt, prm%totalNslip tau_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j)) tau_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j)) enddo if (present(tau_pos1)) tau_pos1 = tau_pos if (present(tau_neg1)) tau_neg1 = tau_neg associate(BoltzmannRatio => prm%H0kp/(kB*Temperature), & DotGamma0 => stt%rhoEdge(:,of)*prm%burgers*prm%v0, & effectiveLength => dst%mfp(:,of) - prm%w) significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check) StressRatio = (abs(tau_pos)-dst%threshold_stress(:,of))/prm%tau0 StressRatio_p = StressRatio** prm%p StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal) needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q) vel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega & * effectiveLength * tau_pos * needsGoodName & / ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_pos & + prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName & ) gdot_pos = DotGamma0 * sign(vel,tau_pos) * 0.5_pReal else where significantPositiveTau gdot_pos = 0.0_pReal end where significantPositiveTau if (present(dgdot_dtau_pos)) then significantPositiveTau2: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check) dvel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength & * ( & (needsGoodName + tau_pos * abs(needsGoodName)*BoltzmannRatio*prm%p & * prm%q/prm%tau0 & * StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) & ) & * ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_pos & + prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName & ) & - tau_pos * needsGoodName * (2.0_pReal*prm%burgers**2.0_pReal & + prm%omega * prm%B *effectiveLength **2.0_pReal& * (abs(needsGoodName)*BoltzmannRatio*prm%p *prm%q/prm%tau0 & *StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) )& ) & ) & /(2.0_pReal*prm%burgers**2.0_pReal*tau_pos & + prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal dgdot_dtau_pos = DotGamma0 * dvel* 0.5_pReal else where significantPositiveTau2 dgdot_dtau_pos = 0.0_pReal end where significantPositiveTau2 endif significantNegativeTau: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check) StressRatio = (abs(tau_neg)-dst%threshold_stress(:,of))/prm%tau0 StressRatio_p = StressRatio** prm%p StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal) needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q) vel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega & * effectiveLength * tau_neg * needsGoodName & / ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_neg & + prm%omega * prm%B * effectiveLength**2.0_pReal* needsGoodName & ) gdot_neg = DotGamma0 * sign(vel,tau_neg) * 0.5_pReal else where significantNegativeTau gdot_neg = 0.0_pReal end where significantNegativeTau if (present(dgdot_dtau_neg)) then significantNegativeTau2: where(abs(tau_neg)-dst%threshold_stress(:,of) > tol_math_check) dvel = 2.0_pReal*prm%burgers * prm%kink_height * prm%omega* effectiveLength & * ( & (needsGoodName + tau_neg * abs(needsGoodName)*BoltzmannRatio*prm%p & * prm%q/prm%tau0 & * StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) & ) & * ( 2.0_pReal*(prm%burgers**2.0_pReal)*tau_neg & + prm%omega * prm%B* effectiveLength **2.0_pReal* needsGoodName & ) & - tau_neg * needsGoodName * (2.0_pReal*prm%burgers**2.0_pReal & + prm%omega * prm%B *effectiveLength **2.0_pReal& * (abs(needsGoodName)*BoltzmannRatio*prm%p *prm%q/prm%tau0 & *StressRatio_pminus1*(1-StressRatio_p)**(prm%q-1.0_pReal) )& ) & ) & /(2.0_pReal*prm%burgers**2.0_pReal*tau_neg & + prm%omega * prm%B* effectiveLength**2.0_pReal* needsGoodName )**2.0_pReal dgdot_dtau_neg = DotGamma0 * dvel * 0.5_pReal else where significantNegativeTau2 dgdot_dtau_neg = 0.0_pReal end where significantNegativeTau2 end if end associate end associate end subroutine kinetics end module plastic_disloUCLA