!-------------------------------------------------------------------------------------------------- !> @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 !-------------------------------------------------------------------------------------------------- submodule(constitutive:constitutive_plastic) plastic_dislotwin real(pReal), parameter :: & kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin type :: tParameters real(pReal) :: & mu = 1.0_pReal, & !< equivalent shear modulus nu = 1.0_pReal, & !< equivalent shear Poisson's ratio D0 = 1.0_pReal, & !< prefactor for self-diffusion coefficient Qsd = 1.0_pReal, & !< activation energy for dislocation climb omega = 1.0_pReal, & !< frequency factor for dislocation climb D = 1.0_pReal, & !< grain size p_sb = 1.0_pReal, & !< p-exponent in shear band velocity q_sb = 1.0_pReal, & !< q-exponent in shear band velocity CEdgeDipMinDistance = 1.0_pReal, & !< adjustment parameter to calculate minimum dipole distance i_tw = 1.0_pReal, & !< adjustment parameter to calculate MFP for twinning tau_0 = 1.0_pReal, & !< strength due to elements in solid solution L_tw = 1.0_pReal, & !< Length of twin nuclei in Burgers vectors L_tr = 1.0_pReal, & !< Length of trans nuclei in Burgers vectors xc_twin = 1.0_pReal, & !< critical distance for formation of twin nucleus xc_trans = 1.0_pReal, & !< critical distance for formation of trans nucleus V_cs = 1.0_pReal, & !< cross slip volume sbResistance = 1.0_pReal, & !< value for shearband resistance sbVelocity = 1.0_pReal, & !< value for shearband velocity_0 E_sb = 1.0_pReal, & !< activation energy for shear bands SFE_0K = 1.0_pReal, & !< stacking fault energy at zero K dSFE_dT = 1.0_pReal, & !< temperature dependence of stacking fault energy gamma_fcc_hex = 1.0_pReal, & !< Free energy difference between austensite and martensite i_tr = 1.0_pReal, & !< adjustment parameter to calculate MFP for transformation h = 1.0_pReal !< Stack height of hex nucleus real(pReal), allocatable, dimension(:) :: & b_sl, & !< absolute length of burgers vector [m] for each slip system b_tw, & !< absolute length of burgers vector [m] for each twin system b_tr, & !< absolute length of burgers vector [m] for each transformation system Delta_F,& !< activation energy for glide [J] for each slip system v0, & !< dislocation velocity prefactor [m/s] for each slip system dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system t_tw, & !< twin thickness [m] for each twin system CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system t_tr, & !< martensite lamellar thickness [m] for each trans system and instance p, & !< p-exponent in glide velocity q, & !< q-exponent in glide velocity r, & !< r-exponent in twin nucleation rate s, & !< s-exponent in trans nucleation rate gamma_char, & !< characteristic shear for twins B !< drag coefficient real(pReal), allocatable, dimension(:,:) :: & h_sl_sl, & !< components of slip-slip interaction matrix h_sl_tw, & !< components of slip-twin interaction matrix h_tw_tw, & !< components of twin-twin interaction matrix h_sl_tr, & !< components of slip-trans interaction matrix h_tr_tr, & !< components of trans-trans interaction matrix n0_sl, & !< slip system normal forestProjection, & C66 real(pReal), allocatable, dimension(:,:,:) :: & P_sl, & P_tw, & P_tr, & C66_tw, & C66_tr integer :: & sum_N_sl, & !< total number of active slip system sum_N_tw, & !< total number of active twin system sum_N_tr !< total number of active transformation system integer, allocatable, dimension(:,:) :: & fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans character(len=pStringLen), allocatable, dimension(:) :: & output logical :: & ExtendedDislocations, & !< consider split into partials for climb calculation fccTwinTransNucleation, & !< twinning and transformation models are for fcc dipoleFormation !< flag indicating consideration of dipole formation end type !< container type for internal constitutive parameters type :: tDislotwinState real(pReal), dimension(:,:), pointer :: & rho_mob, & rho_dip, & gamma_sl, & f_tw, & f_tr end type tDislotwinState type :: tDislotwinMicrostructure real(pReal), dimension(:,:), allocatable :: & Lambda_sl, & !< mean free path between 2 obstacles seen by a moving dislocation Lambda_tw, & !< mean free path between 2 obstacles seen by a growing twin Lambda_tr, & !< mean free path between 2 obstacles seen by a growing martensite tau_pass, & !< threshold stress for slip tau_hat_tw, & !< threshold stress for twinning tau_hat_tr, & !< threshold stress for transformation V_tw, & !< volume of a new twin V_tr, & !< volume of a new martensite disc tau_r_tw, & !< stress to bring partials close together (twin) tau_r_tr !< stress to bring partials close together (trans) end type tDislotwinMicrostructure !-------------------------------------------------------------------------------------------------- ! containers for parameters and state type(tParameters), allocatable, dimension(:) :: param type(tDislotwinState), allocatable, dimension(:) :: & dotState, & state type(tDislotwinMicrostructure), allocatable, dimension(:) :: dependentState contains !-------------------------------------------------------------------------------------------------- !> @brief Perform module initialization. !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- module function plastic_dislotwin_init() result(myPlasticity) logical, dimension(:), allocatable :: myPlasticity integer :: & Ninstance, & p, i, & NipcMyPhase, & sizeState, sizeDotState, & startIndex, endIndex integer, dimension(:), allocatable :: & N_sl, N_tw, N_tr real(pReal), allocatable, dimension(:) :: & rho_mob_0, & !< initial unipolar dislocation density per slip system rho_dip_0 !< initial dipole dislocation density per slip system character(len=pStringLen) :: & extmsg = '' class(tNode), pointer :: & phases, & phase, & pl write(6,'(/,a)') ' <<<+- constitutive_dislotwin 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' myPlasticity = plastic_active('dislotwin') Ninstance = count(myPlasticity) write(6,'(a16,1x,i5,/)') '# instances:',Ninstance; flush(6) if(Ninstance == 0) return allocate(param(Ninstance)) allocate(state(Ninstance)) allocate(dotState(Ninstance)) allocate(dependentState(Ninstance)) phases => material_root%get('phase') i = 0 do p = 1, phases%length phase => phases%get(p) if(.not. myPlasticity(p)) cycle i = i + 1 associate(prm => param(i), & dot => dotState(i), & stt => state(i), & dst => dependentState(i)) pl => phase%get('plasticity') #if defined (__GFORTRAN__) prm%output = output_asStrings(pl) #else prm%output = pl%get_asStrings('output',defaultVal=emptyStringArray) #endif ! 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 N_sl = pl%get_asInts('N_sl',defaultVal=emptyIntArray) prm%sum_N_sl = sum(abs(N_sl)) slipActive: if (prm%sum_N_sl > 0) then prm%P_sl = lattice_SchmidMatrix_slip(N_sl,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_asFloats('h_sl_sl'), & phase%get_asString('lattice')) prm%forestProjection = lattice_forestProjection_edge(N_sl,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) prm%forestProjection = transpose(prm%forestProjection) prm%n0_sl = lattice_slip_normal(N_sl,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == lattice_FCC_ID) & .and. (N_sl(1) == 12) if(prm%fccTwinTransNucleation) prm%fcc_twinNucleationSlipPair = lattice_FCC_TWINNUCLEATIONSLIPPAIR rho_mob_0 = pl%get_asFloats('rho_mob_0', requiredSize=size(N_sl)) rho_dip_0 = pl%get_asFloats('rho_dip_0', requiredSize=size(N_sl)) prm%v0 = pl%get_asFloats('v_0', requiredSize=size(N_sl)) prm%b_sl = pl%get_asFloats('b_sl', requiredSize=size(N_sl)) prm%Delta_F = pl%get_asFloats('Q_s', requiredSize=size(N_sl)) prm%CLambdaSlip = pl%get_asFloats('i_sl', requiredSize=size(N_sl)) prm%p = pl%get_asFloats('p_sl', requiredSize=size(N_sl)) prm%q = pl%get_asFloats('q_sl', requiredSize=size(N_sl)) prm%B = pl%get_asFloats('B', requiredSize=size(N_sl), & defaultVal=[(0.0_pReal, i=1,size(N_sl))]) prm%tau_0 = pl%get_asFloat('tau_0') prm%CEdgeDipMinDistance = pl%get_asFloat('D_a') prm%D0 = pl%get_asFloat('D_0') prm%Qsd = pl%get_asFloat('Q_cl') prm%ExtendedDislocations = pl%get_asBool('extend_dislocations',defaultVal = .false.) if (prm%ExtendedDislocations) then prm%SFE_0K = pl%get_asFloat('Gamma_sf_0K') prm%dSFE_dT = pl%get_asFloat('dGamma_sf_dT') endif prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation',defaultVal = .false.) ! multiplication factor according to crystal structure (nearest neighbors bcc vs fcc/hex) ! details: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981 prm%omega = pl%get_asFloat('omega', defaultVal = 1000.0_pReal) & * merge(12.0_pReal,8.0_pReal,any(lattice_structure(p) == [lattice_FCC_ID,lattice_HEX_ID])) ! expand: family => system rho_mob_0 = math_expand(rho_mob_0, N_sl) rho_dip_0 = math_expand(rho_dip_0, N_sl) prm%v0 = math_expand(prm%v0, N_sl) prm%b_sl = math_expand(prm%b_sl, N_sl) prm%Delta_F = math_expand(prm%Delta_F, N_sl) prm%CLambdaSlip = math_expand(prm%CLambdaSlip, N_sl) prm%p = math_expand(prm%p, N_sl) prm%q = math_expand(prm%q, N_sl) prm%B = math_expand(prm%B, N_sl) ! sanity checks if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' D_0' if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' Q_cl' if (any(rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0' if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0' if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v_0' if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl' if (any(prm%Delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' Q_s' if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//' i_sl' if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B' if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//' p_sl' if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//' q_sl' else slipActive rho_mob_0 = emptyRealArray; rho_dip_0 = emptyRealArray allocate(prm%b_sl,prm%Delta_F,prm%v0,prm%CLambdaSlip,prm%p,prm%q,prm%B,source=emptyRealArray) allocate(prm%forestProjection(0,0),prm%h_sl_sl(0,0)) endif slipActive !-------------------------------------------------------------------------------------------------- ! twin related parameters N_tw = pl%get_asInts('N_tw', defaultVal=emptyIntArray) prm%sum_N_tw = sum(abs(N_tw)) twinActive: if (prm%sum_N_tw > 0) then prm%P_tw = lattice_SchmidMatrix_twin(N_tw,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) prm%h_tw_tw = lattice_interaction_TwinByTwin(N_tw,& pl%get_asFloats('h_tw_tw'), & phase%get_asString('lattice')) prm%b_tw = pl%get_asFloats('b_tw', requiredSize=size(N_tw)) prm%t_tw = pl%get_asFloats('t_tw', requiredSize=size(N_tw)) prm%r = pl%get_asFloats('p_tw', requiredSize=size(N_tw)) prm%xc_twin = pl%get_asFloat('x_c_tw') prm%L_tw = pl%get_asFloat('L_tw') prm%i_tw = pl%get_asFloat('i_tw') prm%gamma_char= lattice_characteristicShear_Twin(N_tw,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) prm%C66_tw = lattice_C66_twin(N_tw,prm%C66,phase%get_asString('lattice'),& phase%get_asFloat('c/a',defaultVal=0.0_pReal)) if (.not. prm%fccTwinTransNucleation) then prm%dot_N_0_tw = pl%get_asFloats('dot_N_0_tw') prm%dot_N_0_tw = math_expand(prm%dot_N_0_tw,N_tw) endif ! expand: family => system prm%b_tw = math_expand(prm%b_tw,N_tw) prm%t_tw = math_expand(prm%t_tw,N_tw) prm%r = math_expand(prm%r,N_tw) ! sanity checks if ( prm%xc_twin < 0.0_pReal) extmsg = trim(extmsg)//' x_c_twin' if ( prm%L_tw < 0.0_pReal) extmsg = trim(extmsg)//' L_tw' if ( prm%i_tw < 0.0_pReal) extmsg = trim(extmsg)//' i_tw' if (any(prm%b_tw < 0.0_pReal)) extmsg = trim(extmsg)//' b_tw' if (any(prm%t_tw < 0.0_pReal)) extmsg = trim(extmsg)//' t_tw' if (any(prm%r < 0.0_pReal)) extmsg = trim(extmsg)//' p_tw' if (.not. prm%fccTwinTransNucleation) then if (any(prm%dot_N_0_tw < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tw' endif else twinActive allocate(prm%gamma_char,prm%b_tw,prm%dot_N_0_tw,prm%t_tw,prm%r,source=emptyRealArray) allocate(prm%h_tw_tw(0,0)) endif twinActive !-------------------------------------------------------------------------------------------------- ! transformation related parameters N_tr = pl%get_asInts('N_tr', defaultVal=emptyIntArray) prm%sum_N_tr = sum(abs(N_tr)) transActive: if (prm%sum_N_tr > 0) then prm%b_tr = pl%get_asFloats('b_tr') prm%b_tr = math_expand(prm%b_tr,N_tr) prm%h = pl%get_asFloat('h', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%i_tr = pl%get_asFloat('i_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%gamma_fcc_hex = pl%get_asFloat('delta_G') prm%xc_trans = pl%get_asFloat('x_c_tr', defaultVal=0.0_pReal) ! ToDo: How to handle that??? prm%L_tr = pl%get_asFloat('L_tr') prm%h_tr_tr = lattice_interaction_TransByTrans(N_tr,pl%get_asFloats('h_tr_tr'), & phase%get_asString('lattice')) prm%C66_tr = lattice_C66_trans(N_tr,prm%C66,pl%get_asString('trans_lattice_structure'), & 0.0_pReal, & pl%get_asFloat('a_bcc', defaultVal=0.0_pReal), & pl%get_asFloat('a_fcc', defaultVal=0.0_pReal)) prm%P_tr = lattice_SchmidMatrix_trans(N_tr,pl%get_asString('trans_lattice_structure'), & 0.0_pReal, & pl%get_asFloat('a_bcc', defaultVal=0.0_pReal), & pl%get_asFloat('a_fcc', defaultVal=0.0_pReal)) if (lattice_structure(p) /= lattice_FCC_ID) then prm%dot_N_0_tr = pl%get_asFloats('dot_N_0_tr') prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,N_tr) endif prm%t_tr = pl%get_asFloats('t_tr') prm%t_tr = math_expand(prm%t_tr,N_tr) prm%s = pl%get_asFloats('p_tr',defaultVal=[0.0_pReal]) prm%s = math_expand(prm%s,N_tr) ! sanity checks if ( prm%xc_trans < 0.0_pReal) extmsg = trim(extmsg)//' x_c_trans' if ( prm%L_tr < 0.0_pReal) extmsg = trim(extmsg)//' L_tr' if ( prm%i_tr < 0.0_pReal) extmsg = trim(extmsg)//' i_tr' if (any(prm%t_tr < 0.0_pReal)) extmsg = trim(extmsg)//' t_tr' if (any(prm%s < 0.0_pReal)) extmsg = trim(extmsg)//' p_tr' if (lattice_structure(p) /= lattice_FCC_ID) then if (any(prm%dot_N_0_tr < 0.0_pReal)) extmsg = trim(extmsg)//' dot_N_0_tr' endif else transActive allocate(prm%s,prm%b_tr,prm%t_tr,prm%dot_N_0_tr,source=emptyRealArray) allocate(prm%h_tr_tr(0,0)) endif transActive !-------------------------------------------------------------------------------------------------- ! shearband related parameters prm%sbVelocity = pl%get_asFloat('v_sb',defaultVal=0.0_pReal) if (prm%sbVelocity > 0.0_pReal) then prm%sbResistance = pl%get_asFloat('xi_sb') prm%E_sb = pl%get_asFloat('Q_sb') prm%p_sb = pl%get_asFloat('p_sb') prm%q_sb = pl%get_asFloat('q_sb') ! sanity checks if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' xi_sb' if (prm%E_sb < 0.0_pReal) extmsg = trim(extmsg)//' Q_sb' if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_sb' if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_sb' endif !-------------------------------------------------------------------------------------------------- ! parameters required for several mechanisms and their interactions if(prm%sum_N_sl + prm%sum_N_tw + prm%sum_N_tw > 0) & prm%D = pl%get_asFloat('D') twinOrSlipActive: if (prm%sum_N_tw + prm%sum_N_tr > 0) then prm%SFE_0K = pl%get_asFloat('Gamma_sf_0K') prm%dSFE_dT = pl%get_asFloat('dGamma_sf_dT') prm%V_cs = pl%get_asFloat('V_cs') endif twinOrSlipActive slipAndTwinActive: if (prm%sum_N_sl * prm%sum_N_tw > 0) then prm%h_sl_tw = lattice_interaction_SlipByTwin(N_sl,N_tw,& pl%get_asFloats('h_sl_tw'), & phase%get_asString('lattice')) if (prm%fccTwinTransNucleation .and. size(N_tw) /= 1) extmsg = trim(extmsg)//' interaction_sliptwin' endif slipAndTwinActive slipAndTransActive: if (prm%sum_N_sl * prm%sum_N_tr > 0) then prm%h_sl_tr = lattice_interaction_SlipByTrans(N_sl,N_tr,& pl%get_asFloats('h_sl_tr'), & phase%get_asString('lattice')) if (prm%fccTwinTransNucleation .and. size(N_tr) /= 1) extmsg = trim(extmsg)//' interaction_sliptrans' endif slipAndTransActive !-------------------------------------------------------------------------------------------------- ! allocate state arrays NipcMyPhase = count(material_phaseAt == p) * discretization_nIP sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl & + size(['f_tw']) * prm%sum_N_tw & + size(['f_tr']) * prm%sum_N_tr sizeState = sizeDotState call constitutive_allocateState(plasticState(p),NipcMyPhase,sizeState,sizeDotState,0) !-------------------------------------------------------------------------------------------------- ! locally defined state aliases and initialization of state0 and atol startIndex = 1 endIndex = prm%sum_N_sl stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:) stt%rho_mob= spread(rho_mob_0,2,NipcMyPhase) dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal) if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' atol_rho' startIndex = endIndex + 1 endIndex = endIndex + prm%sum_N_sl stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:) stt%rho_dip= spread(rho_dip_0,2,NipcMyPhase) dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('atol_rho',defaultVal=1.0_pReal) startIndex = endIndex + 1 endIndex = endIndex + prm%sum_N_sl stt%gamma_sl=>plasticState(p)%state(startIndex:endIndex,:) dot%gamma_sl=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%atol(startIndex:endIndex) = 1.0e-2_pReal ! global alias plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:) startIndex = endIndex + 1 endIndex = endIndex + prm%sum_N_tw stt%f_tw=>plasticState(p)%state(startIndex:endIndex,:) dot%f_tw=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('f_twin',defaultVal=1.0e-7_pReal) if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_twin' startIndex = endIndex + 1 endIndex = endIndex + prm%sum_N_tr stt%f_tr=>plasticState(p)%state(startIndex:endIndex,:) dot%f_tr=>plasticState(p)%dotState(startIndex:endIndex,:) plasticState(p)%atol(startIndex:endIndex) = pl%get_asFloat('f_trans',defaultVal=1.0e-6_pReal) if (any(plasticState(p)%atol(startIndex:endIndex) < 0.0_pReal)) extmsg = trim(extmsg)//' f_trans' allocate(dst%Lambda_sl (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_pass (prm%sum_N_sl,NipcMyPhase),source=0.0_pReal) allocate(dst%Lambda_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_hat_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_r_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal) allocate(dst%V_tw (prm%sum_N_tw,NipcMyPhase),source=0.0_pReal) allocate(dst%Lambda_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_hat_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal) allocate(dst%tau_r_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal) allocate(dst%V_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal) plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally end associate !-------------------------------------------------------------------------------------------------- ! exit if any parameter is out of range if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(dislotwin)') enddo end function plastic_dislotwin_init !-------------------------------------------------------------------------------------------------- !> @brief Return the homogenized elasticity matrix. !-------------------------------------------------------------------------------------------------- module function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC) real(pReal), dimension(6,6) :: & homogenizedC integer, intent(in) :: & ipc, & !< component-ID of integration point ip, & !< integration point el !< element integer :: i, & of real(pReal) :: f_unrotated of = material_phasememberAt(ipc,ip,el) associate(prm => param(phase_plasticityInstance(material_phaseAt(ipc,el))),& stt => state(phase_plasticityInstance(material_phaseAT(ipc,el)))) f_unrotated = 1.0_pReal & - sum(stt%f_tw(1:prm%sum_N_tw,of)) & - sum(stt%f_tr(1:prm%sum_N_tr,of)) homogenizedC = f_unrotated * prm%C66 do i=1,prm%sum_N_tw homogenizedC = homogenizedC & + stt%f_tw(i,of)*prm%C66_tw(1:6,1:6,i) enddo do i=1,prm%sum_N_tr homogenizedC = homogenizedC & + stt%f_tr(i,of)*prm%C66_tr(1:6,1:6,i) enddo end associate end function plastic_dislotwin_homogenizedC !-------------------------------------------------------------------------------------------------- !> @brief Calculate plastic velocity gradient and its tangent. !-------------------------------------------------------------------------------------------------- module subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of) 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, intent(in) :: instance,of real(pReal), intent(in) :: T integer :: i,k,l,m,n real(pReal) :: & f_unrotated,StressRatio_p,& BoltzmannRatio, & ddot_gamma_dtau, & tau real(pReal), dimension(param(instance)%sum_N_sl) :: & dot_gamma_sl,ddot_gamma_dtau_slip real(pReal), dimension(param(instance)%sum_N_tw) :: & dot_gamma_twin,ddot_gamma_dtau_twin real(pReal), dimension(param(instance)%sum_N_tr) :: & dot_gamma_tr,ddot_gamma_dtau_trans real(pReal):: dot_gamma_sb real(pReal), dimension(3,3) :: eigVectors, P_sb real(pReal), dimension(3) :: eigValues 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)) f_unrotated = 1.0_pReal & - sum(stt%f_tw(1:prm%sum_N_tw,of)) & - sum(stt%f_tr(1:prm%sum_N_tr,of)) Lp = 0.0_pReal dLp_dMp = 0.0_pReal call kinetics_slip(Mp,T,instance,of,dot_gamma_sl,ddot_gamma_dtau_slip) slipContribution: do i = 1, prm%sum_N_sl Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i) forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) & + ddot_gamma_dtau_slip(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i) enddo slipContribution call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin,ddot_gamma_dtau_twin) twinContibution: do i = 1, prm%sum_N_tw Lp = Lp + dot_gamma_twin(i)*prm%P_tw(1:3,1:3,i) forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) & + ddot_gamma_dtau_twin(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i) enddo twinContibution call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr,ddot_gamma_dtau_trans) transContibution: do i = 1, prm%sum_N_tr Lp = Lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i) forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) & + ddot_gamma_dtau_trans(i)* prm%P_tr(k,l,i)*prm%P_tr(m,n,i) enddo transContibution Lp = Lp * f_unrotated dLp_dMp = dLp_dMp * f_unrotated shearBandingContribution: if(dNeq0(prm%sbVelocity)) then BoltzmannRatio = prm%E_sb/(kB*T) call math_eigh33(eigValues,eigVectors,Mp) ! is Mp symmetric by design? do i = 1,6 P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),& matmul(eigVectors,sb_mComposition(1:3,i))) tau = math_tensordot(Mp,P_sb) significantShearBandStress: if (abs(tau) > tol_math_check) then StressRatio_p = (abs(tau)/prm%sbResistance)**prm%p_sb dot_gamma_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1-StressRatio_p)**prm%q_sb), tau) ddot_gamma_dtau = abs(dot_gamma_sb)*BoltzmannRatio* prm%p_sb*prm%q_sb/ prm%sbResistance & * (abs(tau)/prm%sbResistance)**(prm%p_sb-1.0_pReal) & * (1.0_pReal-StressRatio_p)**(prm%q_sb-1.0_pReal) Lp = Lp + dot_gamma_sb * P_sb forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) & + ddot_gamma_dtau * P_sb(k,l) * P_sb(m,n) endif significantShearBandStress enddo endif shearBandingContribution end associate end subroutine plastic_dislotwin_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief Calculate the rate of change of microstructure. !-------------------------------------------------------------------------------------------------- module subroutine plastic_dislotwin_dotState(Mp,T,instance,of) real(pReal), dimension(3,3), intent(in):: & Mp !< Mandel stress real(pReal), intent(in) :: & T !< temperature at integration point integer, intent(in) :: & instance, & of integer :: i real(pReal) :: & f_unrotated, & rho_dip_distance, & v_cl, & !< climb velocity Gamma, & !< stacking fault energy tau, & sigma_cl, & !< climb stress b_d !< ratio of burgers vector to stacking fault width real(pReal), dimension(param(instance)%sum_N_sl) :: & dot_rho_dip_formation, & dot_rho_dip_climb, & rho_dip_distance_min, & dot_gamma_sl real(pReal), dimension(param(instance)%sum_N_tw) :: & dot_gamma_twin real(pReal), dimension(param(instance)%sum_N_tr) :: & dot_gamma_tr associate(prm => param(instance), stt => state(instance), & dot => dotState(instance), dst => dependentState(instance)) f_unrotated = 1.0_pReal & - sum(stt%f_tw(1:prm%sum_N_tw,of)) & - sum(stt%f_tr(1:prm%sum_N_tr,of)) call kinetics_slip(Mp,T,instance,of,dot_gamma_sl) dot%gamma_sl(:,of) = abs(dot_gamma_sl) rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl slipState: do i = 1, prm%sum_N_sl tau = math_tensordot(Mp,prm%P_sl(1:3,1:3,i)) significantSlipStress: if (dEq0(tau)) then dot_rho_dip_formation(i) = 0.0_pReal dot_rho_dip_climb(i) = 0.0_pReal else significantSlipStress rho_dip_distance = 3.0_pReal*prm%mu*prm%b_sl(i)/(16.0_pReal*PI*abs(tau)) rho_dip_distance = math_clip(rho_dip_distance, right = dst%Lambda_sl(i,of)) rho_dip_distance = math_clip(rho_dip_distance, left = rho_dip_distance_min(i)) if (prm%dipoleFormation) then dot_rho_dip_formation(i) = 2.0_pReal*(rho_dip_distance-rho_dip_distance_min(i))/prm%b_sl(i) & * stt%rho_mob(i,of)*abs(dot_gamma_sl(i)) else dot_rho_dip_formation(i) = 0.0_pReal endif if (dEq(rho_dip_distance,rho_dip_distance_min(i))) then dot_rho_dip_climb(i) = 0.0_pReal else !@details: Refer: Argon & Moffat, Acta Metallurgica, Vol. 29, pg 293 to 299, 1981 sigma_cl = dot_product(prm%n0_sl(1:3,i),matmul(Mp,prm%n0_sl(1:3,i))) if (prm%ExtendedDislocations) then Gamma = prm%SFE_0K + prm%dSFE_dT * T b_d = 24.0_pReal*PI*(1.0_pReal - prm%nu)/(2.0_pReal + prm%nu)* Gamma/(prm%mu*prm%b_sl(i)) else b_d = 1.0_pReal endif v_cl = 2.0_pReal*prm%omega*b_d**2.0_pReal*exp(-prm%Qsd/(kB*T)) & * (exp(abs(sigma_cl)*prm%b_sl(i)**3.0_pReal/(kB*T)) - 1.0_pReal) dot_rho_dip_climb(i) = 4.0_pReal*v_cl*stt%rho_dip(i,of) & / (rho_dip_distance-rho_dip_distance_min(i)) endif endif significantSlipStress enddo slipState dot%rho_mob(:,of) = abs(dot_gamma_sl)/(prm%b_sl*dst%Lambda_sl(:,of)) & - dot_rho_dip_formation & - 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_mob(:,of)*abs(dot_gamma_sl) dot%rho_dip(:,of) = dot_rho_dip_formation & - 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_dip(:,of)*abs(dot_gamma_sl) & - dot_rho_dip_climb call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin) dot%f_tw(:,of) = f_unrotated*dot_gamma_twin/prm%gamma_char call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr) dot%f_tr(:,of) = f_unrotated*dot_gamma_tr end associate end subroutine plastic_dislotwin_dotState !-------------------------------------------------------------------------------------------------- !> @brief Calculate derived quantities from state. !-------------------------------------------------------------------------------------------------- module subroutine plastic_dislotwin_dependentState(T,instance,of) integer, intent(in) :: & instance, & of real(pReal), intent(in) :: & T real(pReal) :: & sumf_twin,Gamma,sumf_trans real(pReal), dimension(param(instance)%sum_N_sl) :: & inv_lambda_sl_sl, & !< 1/mean free distance between 2 forest dislocations seen by a moving dislocation inv_lambda_sl_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation inv_lambda_sl_tr !< 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation real(pReal), dimension(param(instance)%sum_N_tw) :: & inv_lambda_tw_tw, & !< 1/mean free distance between 2 twin stacks from different systems seen by a growing twin f_over_t_tw real(pReal), dimension(param(instance)%sum_N_tr) :: & inv_lambda_tr_tr, & !< 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite f_over_t_tr real(pReal), dimension(:), allocatable :: & x0 associate(prm => param(instance),& stt => state(instance),& dst => dependentState(instance)) sumf_twin = sum(stt%f_tw(1:prm%sum_N_tw,of)) sumf_trans = sum(stt%f_tr(1:prm%sum_N_tr,of)) Gamma = prm%SFE_0K + prm%dSFE_dT * T !* rescaled volume fraction for topology f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,of)/prm%t_tw ! this is per system ... f_over_t_tr = sumf_trans/prm%t_tr ! but this not ! ToDo ...Physically correct, but naming could be adjusted inv_lambda_sl_sl = sqrt(matmul(prm%forestProjection, & stt%rho_mob(:,of)+stt%rho_dip(:,of)))/prm%CLambdaSlip if (prm%sum_N_tw > 0 .and. prm%sum_N_sl > 0) & inv_lambda_sl_tw = matmul(prm%h_sl_tw,f_over_t_tw)/(1.0_pReal-sumf_twin) inv_lambda_tw_tw = matmul(prm%h_tw_tw,f_over_t_tw)/(1.0_pReal-sumf_twin) if (prm%sum_N_tr > 0 .and. prm%sum_N_sl > 0) & inv_lambda_sl_tr = matmul(prm%h_sl_tr,f_over_t_tr)/(1.0_pReal-sumf_trans) inv_lambda_tr_tr = matmul(prm%h_tr_tr,f_over_t_tr)/(1.0_pReal-sumf_trans) if ((prm%sum_N_tw > 0) .or. (prm%sum_N_tr > 0)) then ! ToDo: better logic needed here dst%Lambda_sl(:,of) = prm%D & / (1.0_pReal+prm%D*(inv_lambda_sl_sl + inv_lambda_sl_tw + inv_lambda_sl_tr)) else dst%Lambda_sl(:,of) = prm%D & / (1.0_pReal+prm%D*inv_lambda_sl_sl) !!!!!! correct? endif dst%Lambda_tw(:,of) = prm%i_tw*prm%D/(1.0_pReal+prm%D*inv_lambda_tw_tw) dst%Lambda_tr(:,of) = prm%i_tr*prm%D/(1.0_pReal+prm%D*inv_lambda_tr_tr) !* threshold stress for dislocation motion dst%tau_pass(:,of) = prm%mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of))) !* threshold stress for growing twin/martensite if(prm%sum_N_tw == prm%sum_N_sl) & dst%tau_hat_tw(:,of) = Gamma/(3.0_pReal*prm%b_tw) & + 3.0_pReal*prm%b_tw*prm%mu/(prm%L_tw*prm%b_sl) ! slip burgers here correct? if(prm%sum_N_tr == prm%sum_N_sl) & dst%tau_hat_tr(:,of) = Gamma/(3.0_pReal*prm%b_tr) & + 3.0_pReal*prm%b_tr*prm%mu/(prm%L_tr*prm%b_sl) & ! slip burgers here correct? + prm%h*prm%gamma_fcc_hex/ (3.0_pReal*prm%b_tr) dst%V_tw(:,of) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,of)**2.0_pReal dst%V_tr(:,of) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,of)**2.0_pReal x0 = prm%mu*prm%b_tw**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip and is the same for twin and trans dst%tau_r_tw(:,of) = prm%mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0) x0 = prm%mu*prm%b_tr**2.0_pReal/(Gamma*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip dst%tau_r_tr(:,of) = prm%mu*prm%b_tr/(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 Write results to HDF5 output file. !-------------------------------------------------------------------------------------------------- module subroutine plastic_dislotwin_results(instance,group) integer, intent(in) :: instance character(len=*), intent(in) :: group integer :: o associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) outputsLoop: do o = 1,size(prm%output) select case(trim(prm%output(o))) case('rho_mob') if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_mob,trim(prm%output(o)), & 'mobile dislocation density','1/m²') case('rho_dip') if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip,trim(prm%output(o)), & 'dislocation dipole density','1/m²') case('gamma_sl') if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma_sl,trim(prm%output(o)), & 'plastic shear','1') case('Lambda_sl') if(prm%sum_N_sl>0) call results_writeDataset(group,dst%Lambda_sl,trim(prm%output(o)), & 'mean free path for slip','m') case('tau_pass') if(prm%sum_N_sl>0) call results_writeDataset(group,dst%tau_pass,trim(prm%output(o)), & 'passing stress for slip','Pa') case('f_tw') if(prm%sum_N_tw>0) call results_writeDataset(group,stt%f_tw,trim(prm%output(o)), & 'twinned volume fraction','m³/m³') case('Lambda_tw') if(prm%sum_N_tw>0) call results_writeDataset(group,dst%Lambda_tw,trim(prm%output(o)), & 'mean free path for twinning','m') case('tau_hat_tw') if(prm%sum_N_tw>0) call results_writeDataset(group,dst%tau_hat_tw,trim(prm%output(o)), & 'threshold stress for twinning','Pa') case('f_tr') if(prm%sum_N_tr>0) call results_writeDataset(group,stt%f_tr,trim(prm%output(o)), & 'martensite volume fraction','m³/m³') end select enddo outputsLoop end associate end subroutine plastic_dislotwin_results !-------------------------------------------------------------------------------------------------- !> @brief Calculate shear rates on slip systems, their derivatives with respect to resolved ! stress, and the resolved stress. !> @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,T,instance,of, & dot_gamma_sl,ddot_gamma_dtau_slip,tau_slip) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T !< temperature integer, intent(in) :: & instance, & of real(pReal), dimension(param(instance)%sum_N_sl), intent(out) :: & dot_gamma_sl real(pReal), dimension(param(instance)%sum_N_sl), optional, intent(out) :: & ddot_gamma_dtau_slip, & tau_slip real(pReal), dimension(param(instance)%sum_N_sl) :: & ddot_gamma_dtau real(pReal), dimension(param(instance)%sum_N_sl) :: & 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 :: i associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) do i = 1, prm%sum_N_sl tau(i) = math_tensordot(Mp,prm%P_sl(1:3,1:3,i)) enddo tau_eff = abs(tau)-dst%tau_pass(:,of) significantStress: where(tau_eff > tol_math_check) stressRatio = tau_eff/prm%tau_0 StressRatio_p = stressRatio** prm%p BoltzmannRatio = prm%Delta_F/(kB*T) 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%b_sl) dot_gamma_sl = sign(stt%rho_mob(:,of)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau) dV_wait_inverse_dTau = -1.0_pReal * 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%tau_0 dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) & / (v_wait_inverse+v_run_inverse)**2.0_pReal ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,of)*prm%b_sl else where significantStress dot_gamma_sl = 0.0_pReal ddot_gamma_dtau = 0.0_pReal end where significantStress end associate if(present(ddot_gamma_dtau_slip)) ddot_gamma_dtau_slip = ddot_gamma_dtau if(present(tau_slip)) tau_slip = tau end subroutine kinetics_slip !-------------------------------------------------------------------------------------------------- !> @brief Calculate shear rates on twin systems and their derivatives with respect to resolved ! stress. !> @details Derivatives 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_twin(Mp,T,dot_gamma_sl,instance,of,& dot_gamma_twin,ddot_gamma_dtau_twin) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T !< temperature integer, intent(in) :: & instance, & of real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: & dot_gamma_sl real(pReal), dimension(param(instance)%sum_N_tw), intent(out) :: & dot_gamma_twin real(pReal), dimension(param(instance)%sum_N_tw), optional, intent(out) :: & ddot_gamma_dtau_twin real, dimension(param(instance)%sum_N_tw) :: & tau, & Ndot0, & stressRatio_r, & ddot_gamma_dtau integer :: i,s1,s2 associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) do i = 1, prm%sum_N_tw tau(i) = math_tensordot(Mp,prm%P_tw(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_tw(i,of)) then ! ToDo: correct? Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state (prm%L_tw*prm%b_sl(i))*& (1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tw(i,of)-tau(i)))) ! P_ncs else Ndot0=0.0_pReal end if else isFCC Ndot0=prm%dot_N_0_tw(i) endif isFCC enddo significantStress: where(tau > tol_math_check) StressRatio_r = (dst%tau_hat_tw(:,of)/tau)**prm%r dot_gamma_twin = prm%gamma_char * dst%V_tw(:,of) * Ndot0*exp(-StressRatio_r) ddot_gamma_dtau = (dot_gamma_twin*prm%r/tau)*StressRatio_r else where significantStress dot_gamma_twin = 0.0_pReal ddot_gamma_dtau = 0.0_pReal end where significantStress end associate if(present(ddot_gamma_dtau_twin)) ddot_gamma_dtau_twin = ddot_gamma_dtau end subroutine kinetics_twin !-------------------------------------------------------------------------------------------------- !> @brief Calculate shear rates on transformation systems and their derivatives with respect to ! resolved stress. !> @details Derivatives 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_trans(Mp,T,dot_gamma_sl,instance,of,& dot_gamma_tr,ddot_gamma_dtau_trans) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress real(pReal), intent(in) :: & T !< temperature integer, intent(in) :: & instance, & of real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: & dot_gamma_sl real(pReal), dimension(param(instance)%sum_N_tr), intent(out) :: & dot_gamma_tr real(pReal), dimension(param(instance)%sum_N_tr), optional, intent(out) :: & ddot_gamma_dtau_trans real, dimension(param(instance)%sum_N_tr) :: & tau, & Ndot0, & stressRatio_s, & ddot_gamma_dtau integer :: i,s1,s2 associate(prm => param(instance), stt => state(instance), dst => dependentState(instance)) do i = 1, prm%sum_N_tr tau(i) = math_tensordot(Mp,prm%P_tr(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_tr(i,of)) then ! ToDo: correct? Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+& abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state (prm%L_tr*prm%b_sl(i))*& (1.0_pReal-exp(-prm%V_cs/(kB*T)*(dst%tau_r_tr(i,of)-tau(i)))) ! P_ncs else Ndot0=0.0_pReal end if else isFCC Ndot0=prm%dot_N_0_tr(i) endif isFCC enddo significantStress: where(tau > tol_math_check) StressRatio_s = (dst%tau_hat_tr(:,of)/tau)**prm%s dot_gamma_tr = dst%V_tr(:,of) * Ndot0*exp(-StressRatio_s) ddot_gamma_dtau = (dot_gamma_tr*prm%s/tau)*StressRatio_s else where significantStress dot_gamma_tr = 0.0_pReal ddot_gamma_dtau = 0.0_pReal end where significantStress end associate if(present(ddot_gamma_dtau_trans)) ddot_gamma_dtau_trans = ddot_gamma_dtau end subroutine kinetics_trans end submodule plastic_dislotwin