!-------------------------------------------------------------------------------------------------- !> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @brief material subroutine for isotropic plasticity !> @details Isotropic Plasticity which resembles the phenopowerlaw plasticity without !! resolving the stress on the slip systems. Will give the response of phenopowerlaw for an !! untextured polycrystal !-------------------------------------------------------------------------------------------------- submodule(phase:plastic) isotropic type :: tParameters real(pReal) :: & M, & !< Taylor factor dot_gamma_0, & !< reference strain rate n, & !< stress exponent h_0, & h, & !< hardening pre-factor h_ln, & xi_inf, & !< maximum critical stress a, & c_1, & c_4, & c_3, & c_2 logical :: & dilatation character(len=pStringLen), allocatable, dimension(:) :: & output end type tParameters type :: tIsotropicState real(pReal), pointer, dimension(:) :: & xi end type tIsotropicState !-------------------------------------------------------------------------------------------------- ! containers for parameters and state type(tParameters), allocatable, dimension(:) :: param type(tIsotropicState), allocatable, dimension(:) :: & dotState, & state contains !-------------------------------------------------------------------------------------------------- !> @brief Perform module initialization. !> @details reads in material parameters, allocates arrays, and does sanity checks !-------------------------------------------------------------------------------------------------- module function plastic_isotropic_init() result(myPlasticity) logical, dimension(:), allocatable :: myPlasticity integer :: & ph, & Nmembers, & sizeState, sizeDotState real(pReal) :: & xi_0 !< initial critical stress character(len=pStringLen) :: & extmsg = '' class(tNode), pointer :: & phases, & phase, & mech, & pl myPlasticity = plastic_active('isotropic') if(count(myPlasticity) == 0) return print'(/,a)', ' <<<+- phase:mechanical:plastic:isotropic init -+>>>' print'(a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT) print*, 'T. Maiti and P. Eisenlohr, Scripta Materialia 145:37–40, 2018' print*, 'https://doi.org/10.1016/j.scriptamat.2017.09.047' phases => config_material%get('phase') allocate(param(phases%length)) allocate(state(phases%length)) allocate(dotState(phases%length)) do ph = 1, phases%length if(.not. myPlasticity(ph)) cycle associate(prm => param(ph), dot => dotState(ph), stt => state(ph)) phase => phases%get(ph) mech => phase%get('mechanical') pl => mech%get('plastic') #if defined (__GFORTRAN__) prm%output = output_as1dString(pl) #else prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray) #endif xi_0 = pl%get_asFloat('xi_0') prm%xi_inf = pl%get_asFloat('xi_inf') prm%dot_gamma_0 = pl%get_asFloat('dot_gamma_0') prm%n = pl%get_asFloat('n') prm%h_0 = pl%get_asFloat('h_0') prm%h = pl%get_asFloat('h', defaultVal=3.0_pReal) ! match for fcc random polycrystal prm%M = pl%get_asFloat('M') prm%h_ln = pl%get_asFloat('h_ln', defaultVal=0.0_pReal) prm%c_1 = pl%get_asFloat('c_1', defaultVal=0.0_pReal) prm%c_4 = pl%get_asFloat('c_4', defaultVal=0.0_pReal) prm%c_3 = pl%get_asFloat('c_3', defaultVal=0.0_pReal) prm%c_2 = pl%get_asFloat('c_2', defaultVal=0.0_pReal) prm%a = pl%get_asFloat('a') prm%dilatation = pl%get_AsBool('dilatation',defaultVal = .false.) !-------------------------------------------------------------------------------------------------- ! sanity checks if (xi_0 < 0.0_pReal) extmsg = trim(extmsg)//' xi_0' if (prm%dot_gamma_0 <= 0.0_pReal) extmsg = trim(extmsg)//' dot_gamma_0' if (prm%n <= 0.0_pReal) extmsg = trim(extmsg)//' n' if (prm%a <= 0.0_pReal) extmsg = trim(extmsg)//' a' if (prm%M <= 0.0_pReal) extmsg = trim(extmsg)//' M' !-------------------------------------------------------------------------------------------------- ! allocate state arrays Nmembers = count(material_phaseID == ph) sizeDotState = size(['xi']) sizeState = sizeDotState call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,0) !-------------------------------------------------------------------------------------------------- ! state aliases and initialization stt%xi => plasticState(ph)%state (1,:) stt%xi = xi_0 dot%xi => plasticState(ph)%dotState(1,:) plasticState(ph)%atol(1) = pl%get_asFloat('atol_xi',defaultVal=1.0_pReal) if (plasticState(ph)%atol(1) < 0.0_pReal) extmsg = trim(extmsg)//' atol_xi' end associate !-------------------------------------------------------------------------------------------------- ! exit if any parameter is out of range if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(isotropic)') enddo end function plastic_isotropic_init !-------------------------------------------------------------------------------------------------- !> @brief Calculate plastic velocity gradient and its tangent. !-------------------------------------------------------------------------------------------------- module subroutine isotropic_LpAndItsTangent(Lp,dLp_dMp,Mp,ph,en) real(pReal), dimension(3,3), intent(out) :: & Lp !< plastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLp_dMp !< derivative of Lp with respect to the Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & ph, & en real(pReal), dimension(3,3) :: & Mp_dev !< deviatoric part of the Mandel stress real(pReal) :: & dot_gamma, & !< strainrate norm_Mp_dev, & !< norm of the deviatoric part of the Mandel stress squarenorm_Mp_dev !< square of the norm of the deviatoric part of the Mandel stress integer :: & k, l, m, n associate(prm => param(ph), stt => state(ph)) Mp_dev = math_deviatoric33(Mp) squarenorm_Mp_dev = math_tensordot(Mp_dev,Mp_dev) norm_Mp_dev = sqrt(squarenorm_Mp_dev) if (norm_Mp_dev > 0.0_pReal) then dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp_dev/(prm%M*stt%xi(en))) **prm%n Lp = dot_gamma * Mp_dev/norm_Mp_dev forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dMp(k,l,m,n) = (prm%n-1.0_pReal) * Mp_dev(k,l)*Mp_dev(m,n) / squarenorm_Mp_dev forall (k=1:3,l=1:3) & dLp_dMp(k,l,k,l) = dLp_dMp(k,l,k,l) + 1.0_pReal forall (k=1:3,m=1:3) & dLp_dMp(k,k,m,m) = dLp_dMp(k,k,m,m) - 1.0_pReal/3.0_pReal dLp_dMp = dot_gamma * dLp_dMp / norm_Mp_dev else Lp = 0.0_pReal dLp_dMp = 0.0_pReal end if end associate end subroutine isotropic_LpAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief Calculate inelastic velocity gradient and its tangent. !-------------------------------------------------------------------------------------------------- module subroutine plastic_isotropic_LiAndItsTangent(Li,dLi_dMi,Mi,ph,en) real(pReal), dimension(3,3), intent(out) :: & Li !< inleastic velocity gradient real(pReal), dimension(3,3,3,3), intent(out) :: & dLi_dMi !< derivative of Li with respect to Mandel stress real(pReal), dimension(3,3), intent(in) :: & Mi !< Mandel stress integer, intent(in) :: & ph, & en real(pReal) :: & tr !< trace of spherical part of Mandel stress (= 3 x pressure) integer :: & k, l, m, n associate(prm => param(ph), stt => state(ph)) tr=math_trace33(math_spherical33(Mi)) if (prm%dilatation .and. abs(tr) > 0.0_pReal) then ! no stress or J2 plasticity --> Li and its derivative are zero Li = math_I3 & * prm%dot_gamma_0 * (3.0_pReal*prm%M*stt%xi(en))**(-prm%n) & * tr * abs(tr)**(prm%n-1.0_pReal) forall (k=1:3,l=1:3,m=1:3,n=1:3) dLi_dMi(k,l,m,n) = prm%n / tr * Li(k,l) * math_I3(m,n) else Li = 0.0_pReal dLi_dMi = 0.0_pReal endif end associate end subroutine plastic_isotropic_LiAndItsTangent !-------------------------------------------------------------------------------------------------- !> @brief Calculate the rate of change of microstructure. !-------------------------------------------------------------------------------------------------- module subroutine isotropic_dotState(Mp,ph,en) real(pReal), dimension(3,3), intent(in) :: & Mp !< Mandel stress integer, intent(in) :: & ph, & en real(pReal) :: & dot_gamma, & !< strainrate xi_inf_star, & !< saturation xi norm_Mp !< norm of the (deviatoric) Mandel stress associate(prm => param(ph), stt => state(ph), & dot => dotState(ph)) if (prm%dilatation) then norm_Mp = sqrt(math_tensordot(Mp,Mp)) else norm_Mp = sqrt(math_tensordot(math_deviatoric33(Mp),math_deviatoric33(Mp))) endif dot_gamma = prm%dot_gamma_0 * (sqrt(1.5_pReal) * norm_Mp /(prm%M*stt%xi(en))) **prm%n if (dot_gamma > 1e-12_pReal) then if (dEq0(prm%c_1)) then xi_inf_star = prm%xi_inf else xi_inf_star = prm%xi_inf & + asinh( (dot_gamma / prm%c_1)**(1.0_pReal / prm%c_2))**(1.0_pReal / prm%c_3) & / prm%c_4 * (dot_gamma / prm%dot_gamma_0)**(1.0_pReal / prm%n) endif dot%xi(en) = dot_gamma & * ( prm%h_0 + prm%h_ln * log(dot_gamma) ) & * sign(abs(1.0_pReal - stt%xi(en)/xi_inf_star)**prm%a *prm%h, 1.0_pReal-stt%xi(en)/xi_inf_star) else dot%xi(en) = 0.0_pReal endif end associate end subroutine isotropic_dotState !-------------------------------------------------------------------------------------------------- !> @brief Write results to HDF5 output file. !-------------------------------------------------------------------------------------------------- module subroutine plastic_isotropic_results(ph,group) integer, intent(in) :: ph character(len=*), intent(in) :: group integer :: o associate(prm => param(ph), stt => state(ph)) outputsLoop: do o = 1,size(prm%output) select case(trim(prm%output(o))) case ('xi') call results_writeDataset(stt%xi,group,trim(prm%output(o)), & 'resistance against plastic flow','Pa') end select enddo outputsLoop end associate end subroutine plastic_isotropic_results end submodule isotropic