!-------------------------------------------------------------------------------------------------- !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH !> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @brief material subroutine incoprorating dislocation and twinning physics !> @details to be done !-------------------------------------------------------------------------------------------------- module plastic_dislotwin use prec, only: & pReal, & pInt implicit none private integer(pInt), dimension(:,:), allocatable, target, public :: & plastic_dislotwin_sizePostResult !< size of each post result output character(len=64), dimension(:,:), allocatable, target, public :: & plastic_dislotwin_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, & edge_density_ID, & dipole_density_ID, & shear_rate_slip_ID, & accumulated_shear_slip_ID, & mfp_slip_ID, & resolved_stress_slip_ID, & threshold_stress_slip_ID, & edge_dipole_distance_ID, & twin_fraction_ID, & mfp_twin_ID, & resolved_stress_twin_ID, & threshold_stress_twin_ID, & resolved_stress_shearband_ID, & shear_rate_shearband_ID, & strain_trans_fraction_ID end enum type, private :: tParameters real(pReal) :: & mu, & nu, & D0, & !< prefactor for self-diffusion coefficient Qsd, & !< activation energy for dislocation climb GrainSize, & ! @brief module initialization !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- subroutine plastic_dislotwin_init use prec, only: & pStringLen, & dEq0, & dNeq0, & dNeq use debug, only: & debug_level,& debug_constitutive,& debug_levelBasic use math, only: & math_expand,& PI use IO, only: & IO_error use material, only: & phase_plasticity, & phase_plasticityInstance, & phase_Noutput, & material_allocatePlasticState, & PLASTICITY_DISLOTWIN_label, & PLASTICITY_DISLOTWIN_ID, & material_phase, & plasticState use config, only: & config_phase use lattice implicit none integer(pInt) :: & Ninstance, & p, i, & NipcMyPhase, outputSize, & 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)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>' write(6,'(/,a)') ' Ma and Roters, Acta Materialia 52(12):3603–3612, 2004' write(6,'(a)') ' https://doi.org/10.1016/j.actamat.2004.04.012' write(6,'(/,a)') ' Roters et al., Computational Materials Science 39:91–95, 2007' write(6,'(a)') ' https://doi.org/10.1016/j.commatsci.2006.04.014' write(6,'(/,a)') ' Wong et al., Acta Materialia 118:140–151, 2016' write(6,'(a,/)') ' https://doi.org/10.1016/j.actamat.2016.07.032' Ninstance = count(phase_plasticity == PLASTICITY_DISLOTWIN_ID) if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) & write(6,'(a16,1x,i5,/)') '# instances:',Ninstance allocate(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt) allocate(plastic_dislotwin_output(maxval(phase_Noutput),Ninstance)) plastic_dislotwin_output = '' allocate(param(Ninstance)) allocate(state(Ninstance)) allocate(dotState(Ninstance)) allocate(microstructure(Ninstance)) do p = 1_pInt, size(phase_plasticity) if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle associate(prm => param(phase_plasticityInstance(p)), & dot => dotState(phase_plasticityInstance(p)), & stt => state(phase_plasticityInstance(p)), & dst => microstructure(phase_plasticityInstance(p)), & config => config_phase(p)) prm%aTolRho = config%getFloat('atol_rho', defaultVal=0.0_pReal) prm%aTolTwinFrac = config%getFloat('atol_twinfrac', defaultVal=0.0_pReal) prm%aTolTransFrac = config%getFloat('atol_transfrac', defaultVal=0.0_pReal) ! This data is read in already in lattice prm%mu = lattice_mu(p) prm%nu = lattice_nu(p) prm%C66 = lattice_C66(1:6,1:6,p) !-------------------------------------------------------------------------------------------------- ! slip related parameters prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray) prm%totalNslip = sum(prm%Nslip) slipActive: if (prm%totalNslip > 0_pInt) then prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) prm%interaction_SlipSlip = lattice_interaction_SlipBySlip(prm%Nslip, & config%getFloats('interaction_slipslip'), & config%getString('lattice_structure')) prm%forestProjection = lattice_forestProjection (prm%Nslip,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == LATTICE_FCC_ID) & .and. (prm%Nslip(1) == 12_pInt) if(prm%fccTwinTransNucleation) & prm%fcc_twinNucleationSlipPair = lattice_fcc_twinNucleationSlipPair prm%rho0 = config%getFloats('rhoedge0', requiredSize=size(prm%Nslip)) !ToDo: rename to rho_0 prm%rhoDip0 = config%getFloats('rhoedgedip0',requiredSize=size(prm%Nslip)) !ToDo: rename to rho_dip_0 prm%v0 = config%getFloats('v0', requiredSize=size(prm%Nslip)) prm%burgers_slip = config%getFloats('slipburgers',requiredSize=size(prm%Nslip)) prm%Qedge = config%getFloats('qedge', requiredSize=size(prm%Nslip)) !ToDo: rename (ask Karo) prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(prm%Nslip)) prm%p = config%getFloats('p_slip', requiredSize=size(prm%Nslip)) prm%q = config%getFloats('q_slip', requiredSize=size(prm%Nslip)) prm%B = config%getFloats('b', requiredSize=size(prm%Nslip), & defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))]) prm%tau_peierls = config%getFloats('tau_peierls',requiredSize=size(prm%Nslip), & defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))]) ! Deprecated prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance') prm%D0 = config%getFloat('d0') prm%Qsd = config%getFloat('qsd') prm%atomicVolume = config%getFloat('catomicvolume') * prm%burgers_slip**3.0_pReal ! expand: family => system prm%rho0 = math_expand(prm%rho0, prm%Nslip) prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip) prm%v0 = math_expand(prm%v0, prm%Nslip) prm%burgers_slip = math_expand(prm%burgers_slip,prm%Nslip) prm%Qedge = math_expand(prm%Qedge, prm%Nslip) prm%CLambdaSlip = math_expand(prm%CLambdaSlip, prm%Nslip) prm%p = math_expand(prm%p, prm%Nslip) prm%q = math_expand(prm%q, prm%Nslip) prm%B = math_expand(prm%B, prm%Nslip) prm%tau_peierls = math_expand(prm%tau_peierls, prm%Nslip) prm%atomicVolume = math_expand(prm%atomicVolume,prm%Nslip) ! 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)//' rho0' if (any(prm%rhoDip0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoDip0' if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0' if (any(prm%burgers_slip <= 0.0_pReal)) extmsg = trim(extmsg)//' burgers_slip' if (any(prm%Qedge <= 0.0_pReal)) extmsg = trim(extmsg)//' Qedge' if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//' CLambdaSlip' if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B' if (any(prm%tau_peierls < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls' if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//' p' if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//' q' else slipActive allocate(prm%burgers_slip(0)) endif slipActive !-------------------------------------------------------------------------------------------------- ! twin related parameters prm%Ntwin = config%getInts('ntwin', defaultVal=emptyIntArray) prm%totalNtwin = sum(prm%Ntwin) if (prm%totalNtwin > 0_pInt) then prm%Schmid_twin = lattice_SchmidMatrix_twin(prm%Ntwin,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) prm%interaction_TwinTwin = lattice_interaction_TwinByTwin(prm%Ntwin,& config%getFloats('interaction_twintwin'), & config%getString('lattice_structure')) prm%burgers_twin = config%getFloats('twinburgers', requiredSize=size(prm%Ntwin)) prm%twinsize = config%getFloats('twinsize', requiredSize=size(prm%Ntwin)) prm%r = config%getFloats('r_twin', requiredSize=size(prm%Ntwin)) prm%xc_twin = config%getFloat('xc_twin') prm%L0_twin = config%getFloat('l0_twin') prm%Cthresholdtwin = config%getFloat('cthresholdtwin', defaultVal=0.0_pReal) prm%Cmfptwin = config%getFloat('cmfptwin', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%shear_twin = lattice_characteristicShear_Twin(prm%Ntwin,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) prm%C66_twin = lattice_C66_twin(prm%Ntwin,prm%C66,config%getString('lattice_structure'),& config%getFloat('c/a',defaultVal=0.0_pReal)) if (.not. prm%fccTwinTransNucleation) then prm%Ndot0_twin = config%getFloats('ndot0_twin') prm%Ndot0_twin = math_expand(prm%Ndot0_twin,prm%Ntwin) endif ! expand: family => system prm%burgers_twin = math_expand(prm%burgers_twin,prm%Ntwin) prm%twinsize = math_expand(prm%twinsize,prm%Ntwin) prm%r = math_expand(prm%r,prm%Ntwin) else allocate(prm%twinsize(0)) allocate(prm%burgers_twin(0)) allocate(prm%r(0)) endif !-------------------------------------------------------------------------------------------------- ! transformation related parameters prm%Ntrans = config%getInts('ntrans', defaultVal=emptyIntArray) prm%totalNtrans = sum(prm%Ntrans) if (prm%totalNtrans > 0_pInt) then prm%burgers_trans = config%getFloats('transburgers') prm%burgers_trans = math_expand(prm%burgers_trans,prm%Ntrans) prm%Cthresholdtrans = config%getFloat('cthresholdtrans', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%transStackHeight = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%Cmfptrans = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%deltaG = config%getFloat('deltag') prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%L0_trans = config%getFloat('l0_trans') prm%interaction_TransTrans = lattice_interaction_TransByTrans(prm%Ntrans,& config%getFloats('interaction_transtrans'), & config%getString('lattice_structure')) prm%C66_trans = lattice_C66_trans(prm%Ntrans,prm%C66, & config%getString('trans_lattice_structure'), & 0.0_pReal, & config%getFloat('a_bcc', defaultVal=0.0_pReal), & config%getFloat('a_fcc', defaultVal=0.0_pReal)) prm%Schmid_trans = lattice_SchmidMatrix_trans(prm%Ntrans, & config%getString('trans_lattice_structure'), & 0.0_pReal, & config%getFloat('a_bcc', defaultVal=0.0_pReal), & config%getFloat('a_fcc', defaultVal=0.0_pReal)) if (lattice_structure(p) /= LATTICE_fcc_ID) then prm%Ndot0_trans = config%getFloats('ndot0_trans') prm%Ndot0_trans = math_expand(prm%Ndot0_trans,prm%Ntrans) endif prm%lamellarsize = config%getFloats('lamellarsize') prm%lamellarsize = math_expand(prm%lamellarsize,prm%Ntrans) prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal]) prm%s = math_expand(prm%s,prm%Ntrans) else allocate(prm%lamellarsize(0)) allocate(prm%burgers_trans(0)) endif if (sum(prm%Ntwin) > 0_pInt .or. prm%totalNtrans > 0_pInt) then prm%SFE_0K = config%getFloat('sfe_0k') prm%dSFE_dT = config%getFloat('dsfe_dt') prm%VcrossSlip = config%getFloat('vcrossslip') endif if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then prm%interaction_SlipTwin = lattice_interaction_SlipByTwin(prm%Nslip,prm%Ntwin,& config%getFloats('interaction_sliptwin'), & config%getString('lattice_structure')) prm%interaction_TwinSlip = lattice_interaction_TwinBySlip(prm%Ntwin,prm%Nslip,& config%getFloats('interaction_twinslip'), & config%getString('lattice_structure')) if (prm%fccTwinTransNucleation .and. prm%totalNtwin > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntwin is [6,6] endif if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then prm%interaction_SlipTrans = lattice_interaction_SlipByTrans(prm%Nslip,prm%Ntrans,& config%getFloats('interaction_sliptrans'), & config%getString('lattice_structure')) if (prm%fccTwinTransNucleation .and. prm%totalNtrans > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntrans is [6,6] endif !-------------------------------------------------------------------------------------------------- ! shearband related parameters prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal) if (prm%sbVelocity > 0.0_pReal) then prm%sbResistance = config%getFloat('shearbandresistance') prm%sbQedge = config%getFloat('qedgepersbsystem') prm%pShearBand = config%getFloat('p_shearband') prm%qShearBand = config%getFloat('q_shearband') ! sanity checks if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' shearbandresistance' if (prm%sbQedge < 0.0_pReal) extmsg = trim(extmsg)//' qedgepersbsystem' if (prm%pShearBand <= 0.0_pReal) extmsg = trim(extmsg)//' p_shearband' if (prm%qShearBand <= 0.0_pReal) extmsg = trim(extmsg)//' q_shearband' endif prm%GrainSize = config%getFloat('grainsize') prm%SolidSolutionStrength = config%getFloat('solidsolutionstrength') ! Deprecated if (config%keyExists('dipoleformationfactor')) call IO_error(1,ext_msg='use /nodipoleformation/') prm%dipoleformation = .not. config%keyExists('/nodipoleformation/') !if (Ndot0PerTwinFamily(f,p) < 0.0_pReal) & ! call IO_error(211_pInt,el=p,ext_msg='ndot0_twin ('//PLASTICITY_DISLOTWIN_label//')') if (any(prm%atomicVolume <= 0.0_pReal)) & call IO_error(211_pInt,el=p,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')') if (prm%totalNtwin > 0_pInt) then if (prm%aTolRho <= 0.0_pReal) & call IO_error(211_pInt,el=p,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')') if (prm%aTolTwinFrac <= 0.0_pReal) & call IO_error(211_pInt,el=p,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOTWIN_label//')') endif if (prm%totalNtrans > 0_pInt) then if (prm%aTolTransFrac <= 0.0_pReal) & call IO_error(211_pInt,el=p,ext_msg='aTolTransFrac ('//PLASTICITY_DISLOTWIN_label//')') endif outputs = config%getStrings('(output)', defaultVal=emptyStringArray) allocate(prm%outputID(0)) do i= 1_pInt, size(outputs) outputID = undefined_ID select case(outputs(i)) case ('edge_density') outputID = merge(edge_density_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('dipole_density') outputID = merge(dipole_density_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('shear_rate_slip','shearrate_slip') outputID = merge(shear_rate_slip_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('accumulated_shear_slip') outputID = merge(accumulated_shear_slip_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('mfp_slip') outputID = merge(mfp_slip_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('resolved_stress_slip') outputID = merge(resolved_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('threshold_stress_slip') outputID= merge(threshold_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt) outputSize = prm%totalNslip case ('twin_fraction') outputID = merge(twin_fraction_ID,undefined_ID,prm%totalNtwin >0_pInt) outputSize = prm%totalNtwin case ('mfp_twin') outputID = merge(mfp_twin_ID,undefined_ID,prm%totalNtwin >0_pInt) outputSize = prm%totalNtwin case ('resolved_stress_twin') outputID = merge(resolved_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt) outputSize = prm%totalNtwin case ('threshold_stress_twin') outputID = merge(threshold_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt) outputSize = prm%totalNtwin case ('strain_trans_fraction') outputID = strain_trans_fraction_ID outputSize = prm%totalNtrans end select if (outputID /= undefined_ID) then plastic_dislotwin_output(i,phase_plasticityInstance(p)) = outputs(i) plastic_dislotwin_sizePostResult(i,phase_plasticityInstance(p)) = outputSize prm%outputID = [prm%outputID, outputID] endif enddo !-------------------------------------------------------------------------------------------------- ! allocate state arrays NipcMyPhase = count(material_phase == p) sizeDotState = int(size(['rho ','rhoDip ','accshearslip']),pInt) * prm%totalNslip & + int(size(['twinFraction']),pInt) * prm%totalNtwin & + int(size(['strainTransFraction']),pInt) * prm%totalNtrans sizeState = sizeDotState call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, & prm%totalNslip,prm%totalNtwin,prm%totalNtrans) plasticState(p)%sizePostResults = sum(plastic_dislotwin_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_slip=>plasticState(p)%state(startIndex:endIndex,:) dot%accshear_slip=>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,:) startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNtwin stt%twinFraction=>plasticState(p)%state(startIndex:endIndex,:) dot%twinFraction=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac startIndex = endIndex + 1_pInt endIndex = endIndex + prm%totalNtrans stt%strainTransFraction=>plasticState(p)%state(startIndex:endIndex,:) dot%strainTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac allocate(dst%invLambdaSlip (prm%totalNslip, NipcMyPhase),source=0.0_pReal) allocate(dst%invLambdaSlipTwin (prm%totalNslip, NipcMyPhase),source=0.0_pReal) allocate(dst%invLambdaSlipTrans (prm%totalNslip, NipcMyPhase),source=0.0_pReal) allocate(dst%mfp_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal) allocate(dst%threshold_stress_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal) allocate(dst%invLambdaTwin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal) allocate(dst%mfp_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal) allocate(dst%threshold_stress_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal) allocate(dst%tau_r_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal) allocate(dst%twinVolume (prm%totalNtwin, NipcMyPhase),source=0.0_pReal) allocate(dst%invLambdaTrans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal) allocate(dst%mfp_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal) allocate(dst%threshold_stress_trans(prm%totalNtrans,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_r_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal) allocate(dst%martensiteVolume (prm%totalNtrans,NipcMyPhase),source=0.0_pReal) plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally end associate enddo end subroutine plastic_dislotwin_init !-------------------------------------------------------------------------------------------------- !> @brief returns the homogenized elasticity matrix !-------------------------------------------------------------------------------------------------- function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC) use material, only: & material_phase, & phase_plasticityInstance, & phasememberAt implicit none real(pReal), dimension(6,6) :: & homogenizedC integer(pInt), intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element integer(pInt) :: i, & of real(pReal) :: f_unrotated of = phasememberAt(ipc,ip,el) associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),& stt => state(phase_plasticityInstance(material_phase(ipc,ip,el)))) f_unrotated = 1.0_pReal & - sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) & - sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of)) homogenizedC = f_unrotated * prm%C66 do i=1_pInt,prm%totalNtwin homogenizedC = homogenizedC & + stt%twinFraction(i,of)*prm%C66_twin(1:6,1:6,i) enddo do i=1_pInt,prm%totalNtrans homogenizedC = homogenizedC & + stt%strainTransFraction(i,of)*prm%C66_trans(1:6,1:6,i) enddo end associate end function plastic_dislotwin_homogenizedC !-------------------------------------------------------------------------------------------------- !> @brief calculates plastic velocity gradient and its tangent !-------------------------------------------------------------------------------------------------- subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of) use prec, only: & tol_math_check, & dNeq0 use math, only: & math_eigenValuesVectorsSym, & math_outer, & math_symmetric33, & math_mul33xx33, & math_mul33x3 implicit none real(pReal), dimension(3,3), intent(out) :: Lp real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp real(pReal), dimension(3,3), intent(in) :: Mp integer(pInt), intent(in) :: instance,of real(pReal), intent(in) :: Temperature integer(pInt) :: i,k,l,m,n real(pReal) :: f_unrotated,StressRatio_p,& BoltzmannRatio, & dgdot_dtau, & tau real(pReal), dimension(param(instance)%totalNslip) :: & gdot_slip,dgdot_dtau_slip real(pReal), dimension(param(instance)%totalNtwin) :: & gdot_twin,dgdot_dtau_twin real(pReal), dimension(param(instance)%totalNtrans) :: & gdot_trans,dgdot_dtau_trans real(pReal):: gdot_sb real(pReal), dimension(3,3) :: eigVectors, Schmid_shearBand real(pReal), dimension(3) :: eigValues logical :: error real(pReal), dimension(3,6), parameter :: & sb_sComposition = & reshape(real([& 1, 0, 1, & 1, 0,-1, & 1, 1, 0, & 1,-1, 0, & 0, 1, 1, & 0, 1,-1 & ],pReal),[ 3,6]), & sb_mComposition = & reshape(real([& 1, 0,-1, & 1, 0,+1, & 1,-1, 0, & 1, 1, 0, & 0, 1,-1, & 0, 1, 1 & ],pReal),[ 3,6]) associate(prm => param(instance), stt => state(instance), dst => microstructure(instance)) f_unrotated = 1.0_pReal & - sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) & - sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of)) Lp = 0.0_pReal dLp_dMp = 0.0_pReal call kinetics_slip(Mp,temperature,instance,of,gdot_slip,dgdot_dtau_slip) slipContribution: do i = 1_pInt, prm%totalNslip Lp = Lp + gdot_slip(i)*prm%Schmid_slip(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_slip(i) * prm%Schmid_slip(k,l,i) * prm%Schmid_slip(m,n,i) enddo slipContribution !ToDo: Why do this before shear banding? Lp = Lp * f_unrotated dLp_dMp = dLp_dMp * f_unrotated shearBandingContribution: if(dNeq0(prm%sbVelocity)) then BoltzmannRatio = prm%sbQedge/(kB*Temperature) call math_eigenValuesVectorsSym(Mp,eigValues,eigVectors,error) do i = 1_pInt,6_pInt Schmid_shearBand = 0.5_pReal * math_outer(math_mul33x3(eigVectors,sb_sComposition(1:3,i)),& math_mul33x3(eigVectors,sb_mComposition(1:3,i))) tau = math_mul33xx33(Mp,Schmid_shearBand) significantShearBandStress: if (abs(tau) > tol_math_check) then StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand gdot_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand), tau) dgdot_dtau = abs(gdot_sb)*BoltzmannRatio* prm%pShearBand*prm%qShearBand/ prm%sbResistance & * (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal) & * (1.0_pReal-StressRatio_p)**(prm%qShearBand-1.0_pReal) Lp = Lp + gdot_sb * Schmid_shearBand 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 * Schmid_shearBand(k,l) * Schmid_shearBand(m,n) endif significantShearBandStress enddo endif shearBandingContribution call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_twin,dgdot_dtau_twin) twinContibution: do i = 1_pInt, prm%totalNtwin Lp = Lp + gdot_twin(i)*prm%Schmid_twin(1:3,1:3,i) * f_unrotated 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_twin(i)* prm%Schmid_twin(k,l,i)*prm%Schmid_twin(m,n,i) * f_unrotated enddo twinContibution call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_trans,dgdot_dtau_trans) transContibution: do i = 1_pInt, prm%totalNtrans Lp = Lp + gdot_trans(i)*prm%Schmid_trans(1:3,1:3,i) * f_unrotated 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_trans(i)* prm%Schmid_trans(k,l,i)*prm%Schmid_trans(m,n,i) * f_unrotated enddo transContibution end associate end subroutine plastic_dislotwin_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief calculates the rate of change of microstructure !-------------------------------------------------------------------------------------------------- subroutine plastic_dislotwin_dotState(Mp,Temperature,instance,of) use prec, only: & tol_math_check, & dEq0 use math, only: & math_clip, & math_mul33xx33, & PI use material, only: & plasticState implicit none real(pReal), dimension(3,3), intent(in):: & Mp !< Mandel stress real(pReal), intent(in) :: & temperature !< temperature at integration point integer(pInt), intent(in) :: & instance, & of integer(pInt) :: i real(pReal) :: f_unrotated,& VacancyDiffusion,& EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, & DotRhoDipFormation,DotRhoEdgeEdgeAnnihilation, & tau real(pReal), dimension(plasticState(instance)%Nslip) :: & EdgeDipMinDistance, & DotRhoMultiplication, & gdot_slip real(pReal), dimension(plasticState(instance)%Ntwin) :: & gdot_twin real(pReal), dimension(plasticState(instance)%Ntrans) :: & gdot_trans associate(prm => param(instance), stt => state(instance), & dot => dotstate(instance), dst => microstructure(instance)) f_unrotated = 1.0_pReal & - sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) & - sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of)) VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature)) call kinetics_slip(Mp,temperature,instance,of,gdot_slip) dot%accshear_slip(:,of) = abs(gdot_slip) DotRhoMultiplication = abs(gdot_slip)/(prm%burgers_slip*dst%mfp_slip(:,of)) EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip slipState: do i = 1_pInt, prm%totalNslip tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i)) significantSlipStress: if (dEq0(tau)) then DotRhoDipFormation = 0.0_pReal DotRhoEdgeDipClimb = 0.0_pReal else significantSlipStress EdgeDipDistance = 3.0_pReal*prm%mu*prm%burgers_slip(i)/(16.0_pReal*PI*abs(tau)) EdgeDipDistance = math_clip(EdgeDipDistance, right = dst%mfp_slip(i,of)) EdgeDipDistance = math_clip(EdgeDipDistance, left = EdgeDipMinDistance(i)) if (prm%dipoleFormation) then DotRhoDipFormation = 2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance(i))/prm%burgers_slip(i) & * stt%rhoEdge(i,of)*abs(gdot_slip(i)) else DotRhoDipFormation = 0.0_pReal endif if (dEq0(EdgeDipDistance-EdgeDipMinDistance(i))) then DotRhoEdgeDipClimb = 0.0_pReal else ClimbVelocity = 3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume(i) & / (2.0_pReal*PI*kB*Temperature*(EdgeDipDistance+EdgeDipMinDistance(i))) DotRhoEdgeDipClimb = 4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(i,of) & / (EdgeDipDistance-EdgeDipMinDistance(i)) endif endif significantSlipStress !* Spontaneous annihilation of 2 single edge dislocations DotRhoEdgeEdgeAnnihilation = 2.0_pReal*EdgeDipMinDistance(i)/prm%burgers_slip(i) & * stt%rhoEdge(i,of)*abs(gdot_slip(i)) !* Spontaneous annihilation of a single edge dislocation with a dipole constituent DotRhoEdgeDipAnnihilation = 2.0_pReal*EdgeDipMinDistance(i)/prm%burgers_slip(i) & * stt%rhoEdgeDip(i,of)*abs(gdot_slip(i)) dot%rhoEdge(i,of) = DotRhoMultiplication(i)-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation dot%rhoEdgeDip(i,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb enddo slipState call kinetics_twin(Mp,temperature,gdot_slip,instance,of,gdot_twin) dot%twinFraction(:,of) = f_unrotated*gdot_twin/prm%shear_twin call kinetics_trans(Mp,temperature,gdot_slip,instance,of,gdot_trans) dot%twinFraction(:,of) = f_unrotated*gdot_trans end associate end subroutine plastic_dislotwin_dotState !-------------------------------------------------------------------------------------------------- !> @brief calculates derived quantities from state !-------------------------------------------------------------------------------------------------- subroutine plastic_dislotwin_dependentState(temperature,instance,of) use math, only: & PI implicit none integer(pInt), intent(in) :: & instance, & of real(pReal), intent(in) :: & temperature integer(pInt) :: & i real(pReal) :: & sumf_twin,SFE,sumf_trans real(pReal), dimension(:), allocatable :: & x0, & fOverStacksize, & ftransOverLamellarSize associate(prm => param(instance),& stt => state(instance),& dst => microstructure(instance)) sumf_twin = sum(stt%twinFraction(1:prm%totalNtwin,of)) sumf_trans = sum(stt%strainTransFraction(1:prm%totalNtrans,of)) SFE = prm%SFE_0K + prm%dSFE_dT * Temperature !* rescaled volume fraction for topology fOverStacksize = stt%twinFraction(1_pInt:prm%totalNtwin,of)/prm%twinsize !ToDo: this is per system ftransOverLamellarSize = sumf_trans/prm%lamellarsize !ToDo: But this not ... !Todo: Physically ok, but naming could be adjusted !* 1/mean free distance between 2 forest dislocations seen by a moving dislocation forall (i = 1_pInt:prm%totalNslip) & dst%invLambdaSlip(i,of) = & sqrt(dot_product((stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)),& prm%forestProjection(1:prm%totalNslip,i)))/prm%CLambdaSlip(i) !* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation if (prm%totalNtwin > 0_pInt .and. prm%totalNslip > 0_pInt) & dst%invLambdaSlipTwin(1_pInt:prm%totalNslip,of) = & matmul(transpose(prm%interaction_SlipTwin),fOverStacksize)/(1.0_pReal-sumf_twin) ! ToDo: Transpose need !* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin !ToDo: needed? if (prm%totalNtwin > 0_pInt) & dst%invLambdaTwin(1_pInt:prm%totalNtwin,of) = matmul(prm%interaction_TwinTwin,fOverStacksize)/(1.0_pReal-sumf_twin) !* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation if (prm%totalNtrans > 0_pInt .and. prm%totalNslip > 0_pInt) & dst%invLambdaSlipTrans(1_pInt:prm%totalNslip,of) = & ! ToDo: does not work if Ntrans is not 12 matmul(transpose(prm%interaction_SlipTrans),ftransOverLamellarSize)/(1.0_pReal-sumf_trans) ! ToDo: Transpose needed !* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans) !ToDo: needed? if (prm%totalNtrans > 0_pInt) & dst%invLambdaTrans(1_pInt:prm%totalNtrans,of) = matmul(prm%interaction_TransTrans,ftransOverLamellarSize)/(1.0_pReal-sumf_trans) !* mean free path between 2 obstacles seen by a moving dislocation do i = 1_pInt,prm%totalNslip if ((prm%totalNtwin > 0_pInt) .or. (prm%totalNtrans > 0_pInt)) then ! ToDo: This is too simplified dst%mfp_slip(i,of) = & prm%GrainSize/(1.0_pReal+prm%GrainSize*& (dst%invLambdaSlip(i,of) + dst%invLambdaSlipTwin(i,of) + dst%invLambdaSlipTrans(i,of))) else dst%mfp_slip(i,of) = prm%GrainSize & / (1.0_pReal+prm%GrainSize*dst%invLambdaSlip(i,of)) !!!!!! correct? endif enddo !* mean free path between 2 obstacles seen by a growing twin/martensite dst%mfp_twin(:,of) = prm%Cmfptwin*prm%GrainSize/ (1.0_pReal+prm%GrainSize*dst%invLambdaTwin(:,of)) dst%mfp_trans(:,of) = prm%Cmfptrans*prm%GrainSize/(1.0_pReal+prm%GrainSize*dst%invLambdaTrans(:,of)) !* threshold stress for dislocation motion forall (i = 1_pInt:prm%totalNslip) dst%threshold_stress_slip(i,of) = & prm%mu*prm%burgers_slip(i)*& sqrt(dot_product(stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of),& prm%interaction_SlipSlip(:,i))) !* threshold stress for growing twin/martensite if(prm%totalNtwin == prm%totalNslip) & dst%threshold_stress_twin(:,of) = prm%Cthresholdtwin* & (SFE/(3.0_pReal*prm%burgers_twin)+ 3.0_pReal*prm%burgers_twin*prm%mu/ & (prm%L0_twin*prm%burgers_slip)) ! slip burgers here correct? if(prm%totalNtrans == prm%totalNslip) & dst%threshold_stress_trans(:,of) = prm%Cthresholdtrans* & (SFE/(3.0_pReal*prm%burgers_trans) + 3.0_pReal*prm%burgers_trans*prm%mu/& (prm%L0_trans*prm%burgers_slip) + prm%transStackHeight*prm%deltaG/ (3.0_pReal*prm%burgers_trans) ) dst%twinVolume(:,of) = (PI/4.0_pReal)*prm%twinsize*dst%mfp_twin(:,of)**2.0_pReal dst%martensiteVolume(:,of) = (PI/4.0_pReal)*prm%lamellarsize*dst%mfp_trans(:,of)**2.0_pReal x0 = prm%mu*prm%burgers_twin**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) dst%tau_r_twin(:,of) = prm%mu*prm%burgers_twin/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0) x0 = prm%mu*prm%burgers_trans**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) dst%tau_r_trans(:,of) = prm%mu*prm%burgers_trans/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0) end associate end subroutine plastic_dislotwin_dependentState !-------------------------------------------------------------------------------------------------- !> @brief return array of constitutive results !-------------------------------------------------------------------------------------------------- function plastic_dislotwin_postResults(Mp,Temperature,instance,of) result(postResults) use prec, only: & tol_math_check, & dEq0 use math, only: & PI, & math_mul33xx33 implicit none real(pReal), dimension(3,3),intent(in) :: & Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation real(pReal), intent(in) :: & temperature !< temperature at integration point integer(pInt), intent(in) :: & instance, & of real(pReal), dimension(sum(plastic_dislotwin_sizePostResult(:,instance))) :: & postResults integer(pInt) :: & o,c,j associate(prm => param(instance), stt => state(instance), dst => microstructure(instance)) c = 0_pInt do o = 1_pInt,size(prm%outputID) select case(prm%outputID(o)) case (edge_density_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of) c = c + prm%totalNslip case (dipole_density_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of) c = c + prm%totalNslip case (shear_rate_slip_ID) call kinetics_slip(Mp,temperature,instance,of,postResults(c+1:c+prm%totalNslip)) c = c + prm%totalNslip case (accumulated_shear_slip_ID) postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip,of) c = c + prm%totalNslip case (mfp_slip_ID) postResults(c+1_pInt:c+prm%totalNslip) = dst%mfp_slip(1_pInt:prm%totalNslip,of) c = c + prm%totalNslip case (resolved_stress_slip_ID) do j = 1_pInt, prm%totalNslip postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j)) enddo c = c + prm%totalNslip case (threshold_stress_slip_ID) postResults(c+1_pInt:c+prm%totalNslip) = dst%threshold_stress_slip(1_pInt:prm%totalNslip,of) c = c + prm%totalNslip case (twin_fraction_ID) postResults(c+1_pInt:c+prm%totalNtwin) = stt%twinFraction(1_pInt:prm%totalNtwin,of) c = c + prm%totalNtwin case (mfp_twin_ID) postResults(c+1_pInt:c+prm%totalNtwin) = dst%mfp_twin(1_pInt:prm%totalNtwin,of) c = c + prm%totalNtwin case (resolved_stress_twin_ID) do j = 1_pInt, prm%totalNtwin postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,j)) enddo c = c + prm%totalNtwin case (threshold_stress_twin_ID) postResults(c+1_pInt:c+prm%totalNtwin) = dst%threshold_stress_twin(1_pInt:prm%totalNtwin,of) c = c + prm%totalNtwin case (strain_trans_fraction_ID) postResults(c+1_pInt:c+prm%totalNtrans) = stt%strainTransFraction(1_pInt:prm%totalNtrans,of) c = c + prm%totalNtrans end select enddo end associate end function plastic_dislotwin_postResults !-------------------------------------------------------------------------------------------------- !> @brief writes results to HDF5 output file !-------------------------------------------------------------------------------------------------- subroutine plastic_dislotwin_results(instance,group) #if defined(PETSc) || defined(DAMASKHDF5) use results implicit none integer, intent(in) :: instance character(len=*) :: group integer :: o associate(prm => param(instance), stt => state(instance)) outputsLoop: do o = 1_pInt,size(prm%outputID) select case(prm%outputID(o)) end select enddo outputsLoop end associate #else integer, intent(in) :: instance character(len=*) :: group #endif end subroutine plastic_dislotwin_results !-------------------------------------------------------------------------------------------------- !> @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_slip(Mp,Temperature,instance,of, & gdot_slip,dgdot_dtau_slip,tau_slip) use prec, only: & tol_math_check, & dNeq0 use math, only: & 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(param(instance)%totalNslip), intent(out) :: & gdot_slip real(pReal), dimension(param(instance)%totalNslip), optional, intent(out) :: & dgdot_dtau_slip, & tau_slip real(pReal), dimension(param(instance)%totalNslip) :: & dgdot_dtau real(pReal), dimension(param(instance)%totalNslip) :: & tau, & stressRatio, & StressRatio_p, & BoltzmannRatio, & v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned) v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned) dV_wait_inverse_dTau, & dV_run_inverse_dTau, & dV_dTau, & tau_eff !< effective resolved stress integer(pInt) :: i associate(prm => param(instance), stt => state(instance), dst => microstructure(instance)) do i = 1_pInt, prm%totalNslip tau(i) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i)) enddo tau_eff = abs(tau)-dst%threshold_stress_slip(:,of) significantStress: where(tau_eff > tol_math_check) stressRatio = tau_eff/(prm%SolidSolutionStrength+prm%tau_peierls) StressRatio_p = stressRatio** prm%p BoltzmannRatio = prm%Qedge/(kB*Temperature) v_wait_inverse = prm%v0**(-1.0_pReal) * exp(BoltzmannRatio*(1.0_pReal-StressRatio_p)** prm%q) v_run_inverse = prm%B/(tau_eff*prm%burgers_slip) gdot_slip = sign(stt%rhoEdge(:,of)*prm%burgers_slip/(v_wait_inverse+v_run_inverse),tau) dV_wait_inverse_dTau = v_wait_inverse * prm%p * prm%q * BoltzmannRatio & * (stressRatio**(prm%p-1.0_pReal)) & * (1.0_pReal-StressRatio_p)**(prm%q-1.0_pReal) & / (prm%SolidSolutionStrength+prm%tau_peierls) dV_run_inverse_dTau = v_run_inverse/tau_eff dV_dTau = (dV_wait_inverse_dTau+dV_run_inverse_dTau) & / (v_wait_inverse+v_run_inverse)**2.0_pReal dgdot_dtau = dV_dTau*stt%rhoEdge(:,of)*prm%burgers_slip else where significantStress gdot_slip = 0.0_pReal dgdot_dtau = 0.0_pReal end where significantStress end associate if(present(dgdot_dtau_slip)) dgdot_dtau_slip = dgdot_dtau if(present(tau_slip)) tau_slip = tau end subroutine kinetics_slip !-------------------------------------------------------------------------------------------------- !> @brief calculates shear rates on twin systems !-------------------------------------------------------------------------------------------------- pure subroutine kinetics_twin(Mp,temperature,gdot_slip,instance,of,& gdot_twin,dgdot_dtau_twin) use prec, only: & tol_math_check, & dNeq0 use math, only: & 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(param(instance)%totalNslip), intent(in) :: & gdot_slip real(pReal), dimension(param(instance)%totalNtwin), intent(out) :: & gdot_twin real(pReal), dimension(param(instance)%totalNtwin), optional, intent(out) :: & dgdot_dtau_twin real, dimension(param(instance)%totalNtwin) :: & tau, & Ndot0, & stressRatio_r, & dgdot_dtau integer(pInt) :: i,s1,s2 associate(prm => param(instance), stt => state(instance), dst => microstructure(instance)) do i = 1_pInt, prm%totalNtwin tau(i) = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,i)) isFCC: if (prm%fccTwinTransNucleation) then s1=prm%fcc_twinNucleationSlipPair(1,i) s2=prm%fcc_twinNucleationSlipPair(2,i) if (tau(i) < dst%tau_r_twin(i,of)) then Ndot0=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+& abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state (prm%L0_twin*prm%burgers_slip(i))*& (1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (dst%tau_r_twin(i,of)-tau))) else Ndot0=0.0_pReal end if else isFCC Ndot0=prm%Ndot0_twin(i) endif isFCC enddo significantStress: where(tau > tol_math_check) StressRatio_r = (dst%threshold_stress_twin(:,of)/tau)**prm%r gdot_twin = prm%shear_twin * dst%twinVolume(:,of) * Ndot0*exp(-StressRatio_r) dgdot_dtau = (gdot_twin*prm%r/tau)*StressRatio_r else where significantStress gdot_twin = 0.0_pReal dgdot_dtau = 0.0_pReal end where significantStress end associate if(present(dgdot_dtau_twin)) dgdot_dtau_twin = dgdot_dtau end subroutine kinetics_twin !-------------------------------------------------------------------------------------------------- !> @brief calculates shear rates on twin systems !-------------------------------------------------------------------------------------------------- pure subroutine kinetics_trans(Mp,temperature,gdot_slip,instance,of,& gdot_trans,dgdot_dtau_trans) use prec, only: & tol_math_check, & dNeq0 use math, only: & 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(param(instance)%totalNslip), intent(in) :: & gdot_slip real(pReal), dimension(param(instance)%totalNtrans), intent(out) :: & gdot_trans real(pReal), dimension(param(instance)%totalNtrans), optional, intent(out) :: & dgdot_dtau_trans real, dimension(param(instance)%totalNtrans) :: & tau, & Ndot0, & stressRatio_s, & dgdot_dtau integer(pInt) :: i,s1,s2 associate(prm => param(instance), stt => state(instance), dst => microstructure(instance)) do i = 1_pInt, prm%totalNtrans tau(i) = math_mul33xx33(Mp,prm%Schmid_trans(1:3,1:3,i)) isFCC: if (prm%fccTwinTransNucleation) then s1=prm%fcc_twinNucleationSlipPair(1,i) s2=prm%fcc_twinNucleationSlipPair(2,i) if (tau(i) < dst%tau_r_trans(i,of)) then Ndot0=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+& abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state (prm%L0_trans*prm%burgers_slip(i))*& (1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (dst%tau_r_trans(i,of)-tau))) else Ndot0=0.0_pReal end if else isFCC Ndot0=prm%Ndot0_trans(i) endif isFCC enddo significantStress: where(tau > tol_math_check) StressRatio_s = (dst%threshold_stress_trans(:,of)/tau)**prm%s gdot_trans = dst%martensiteVolume(:,of) * Ndot0*exp(-StressRatio_s) dgdot_dtau = (gdot_trans*prm%r/tau)*StressRatio_s else where significantStress gdot_trans = 0.0_pReal dgdot_dtau = 0.0_pReal end where significantStress end associate if(present(dgdot_dtau_trans)) dgdot_dtau_trans = dgdot_dtau end subroutine kinetics_trans end module plastic_dislotwin