537 lines
24 KiB
Fortran
537 lines
24 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @author David Cereceda, Lawrence Livermore National Laboratory
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief crystal plasticity model for bcc metals, especially Tungsten
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!--------------------------------------------------------------------------------------------------
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submodule(phase:plastic) dislotungsten
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type :: tParameters
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real(pREAL) :: &
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D = 1.0_pREAL, & !< grain size
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D_0 = 1.0_pREAL, & !< prefactor for self-diffusion coefficient
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Q_cl = 1.0_pREAL !< activation energy for dislocation climb
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real(pREAL), allocatable, dimension(:) :: &
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b_sl, & !< magnitude of Burgers vector [m]
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d_caron, & !< distance of spontaneous annhihilation
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i_sl, & !< Adj. parameter for distance between 2 forest dislocations
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f_at, & !< factor to calculate atomic volume
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tau_Peierls, & !< Peierls stress
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!* mobility law parameters
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Q_s, & !< activation energy for glide [J]
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p, & !< p-exponent in glide velocity
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q, & !< q-exponent in glide velocity
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B, & !< friction coefficient
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h, & !< height of the kink pair
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w, & !< width of the kink pair
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omega !< attempt frequency for kink pair nucleation
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real(pREAL), allocatable, dimension(:,:) :: &
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h_sl_sl, & !< slip resistance from slip activity
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forestProjection
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real(pREAL), allocatable, dimension(:,:,:) :: &
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P_sl, &
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P_nS_pos, &
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P_nS_neg
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integer :: &
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sum_N_sl !< total number of active slip system
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character(len=:), allocatable :: &
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isotropic_bound
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character(len=pSTRLEN), allocatable, dimension(:) :: &
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output
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logical :: &
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dipoleFormation !< flag indicating consideration of dipole formation
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character(len=:), allocatable, dimension(:) :: &
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systems_sl
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end type tParameters !< container type for internal constitutive parameters
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type :: tIndexDotState
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integer, dimension(2) :: &
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rho_mob, &
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rho_dip, &
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gamma_sl
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end type tIndexDotState
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type :: tDislotungstenState
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real(pREAL), dimension(:,:), pointer :: &
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rho_mob, &
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rho_dip, &
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gamma_sl
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end type tDislotungstenState
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type :: tDislotungstenDependentState
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real(pREAL), dimension(:,:), allocatable :: &
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Lambda_sl, &
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tau_pass
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end type tDislotungstenDependentState
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!--------------------------------------------------------------------------------------------------
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! containers for parameters and state
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type(tParameters), allocatable, dimension(:) :: param
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type(tIndexDotState), allocatable, dimension(:) :: indexDotState
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type(tDisloTungstenState), allocatable, dimension(:) :: state
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type(tDisloTungstenDependentState), allocatable, dimension(:) :: dependentState
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Perform module initialization.
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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module function plastic_dislotungsten_init() result(myPlasticity)
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logical, dimension(:), allocatable :: myPlasticity
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integer :: &
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ph, i, &
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Nmembers, &
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sizeState, sizeDotState, &
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startIndex, endIndex
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integer, dimension(:), allocatable :: &
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N_sl
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real(pREAL),dimension(:), allocatable :: &
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f_edge, & !< edge character fraction of total dislocation density
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rho_mob_0, & !< initial dislocation density
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rho_dip_0 !< initial dipole density
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real(pREAL), dimension(:,:), allocatable :: &
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a_nS !< non-Schmid coefficients
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character(len=:), allocatable :: &
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refs, &
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extmsg
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type(tDict), pointer :: &
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phases, &
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phase, &
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mech, &
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pl
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myPlasticity = plastic_active('dislotungsten')
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if (count(myPlasticity) == 0) return
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print'(/,1x,a)', '<<<+- phase:mechanical:plastic:dislotungsten init -+>>>'
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print'(/,1x,a)', 'D. Cereceda et al., International Journal of Plasticity 78:242–256, 2016'
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print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2015.09.002'
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print'(/,1x,a,1x,i0)', '# phases:',count(myPlasticity); flush(IO_STDOUT)
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phases => config_material%get_dict('phase')
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allocate(param(phases%length))
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allocate(indexDotState(phases%length))
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allocate(state(phases%length))
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allocate(dependentState(phases%length))
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extmsg = ''
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do ph = 1, phases%length
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if (.not. myPlasticity(ph)) cycle
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associate(prm => param(ph), &
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stt => state(ph), dst => dependentState(ph), &
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idx_dot => indexDotState(ph))
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phase => phases%get_dict(ph)
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mech => phase%get_dict('mechanical')
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pl => mech%get_dict('plastic')
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print'(/,1x,a,1x,i0,a)', 'phase',ph,': '//phases%key(ph)
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refs = config_listReferences(pl,indent=3)
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if (len(refs) > 0) print'(/,1x,a)', refs
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#if defined (__GFORTRAN__)
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prm%output = output_as1dStr(pl)
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#else
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prm%output = pl%get_as1dStr('output',defaultVal=emptyStrArray)
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#endif
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prm%isotropic_bound = pl%get_asStr('isotropic_bound',defaultVal='isostrain')
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(abs(N_sl))
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slipActive: if (prm%sum_N_sl > 0) then
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prm%systems_sl = crystal_labels_slip(N_sl,phase_lattice(ph))
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prm%P_sl = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
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if (phase_lattice(ph) == 'cI') then
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allocate(a_nS(3,size(pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray))))
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a_nS(1,:) = pl%get_as1dReal('a_nonSchmid_110',defaultVal=emptyRealArray)
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prm%P_nS_pos = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=+1)
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prm%P_nS_neg = crystal_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph),nonSchmidCoefficients=a_nS,sense=-1)
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deallocate(a_nS)
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else
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prm%P_nS_pos = +prm%P_sl
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prm%P_nS_neg = -prm%P_sl
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end if
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prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal=.false.)
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prm%D = pl%get_asReal('D')
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prm%D_0 = pl%get_asReal('D_0')
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prm%Q_cl = pl%get_asReal('Q_cl')
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f_edge = math_expand(pl%get_as1dReal('f_edge', requiredSize=size(N_sl), &
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defaultVal=[(0.5_pREAL, i=1,size(N_sl))]),N_sl)
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rho_mob_0 = math_expand(pl%get_as1dReal('rho_mob_0', requiredSize=size(N_sl)),N_sl)
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rho_dip_0 = math_expand(pl%get_as1dReal('rho_dip_0', requiredSize=size(N_sl)),N_sl)
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prm%b_sl = math_expand(pl%get_as1dReal('b_sl', requiredSize=size(N_sl)),N_sl)
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prm%Q_s = math_expand(pl%get_as1dReal('Q_s', requiredSize=size(N_sl)),N_sl)
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prm%i_sl = math_expand(pl%get_as1dReal('i_sl', requiredSize=size(N_sl)),N_sl)
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prm%tau_Peierls = math_expand(pl%get_as1dReal('tau_Peierls', requiredSize=size(N_sl)),N_sl)
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prm%p = math_expand(pl%get_as1dReal('p_sl', requiredSize=size(N_sl)),N_sl)
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prm%q = math_expand(pl%get_as1dReal('q_sl', requiredSize=size(N_sl)),N_sl)
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prm%h = math_expand(pl%get_as1dReal('h', requiredSize=size(N_sl)),N_sl)
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prm%w = math_expand(pl%get_as1dReal('w', requiredSize=size(N_sl)),N_sl)
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prm%omega = math_expand(pl%get_as1dReal('omega', requiredSize=size(N_sl)),N_sl)
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prm%B = math_expand(pl%get_as1dReal('B', requiredSize=size(N_sl)),N_sl)
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prm%d_caron = prm%b_sl * pl%get_asReal('D_a')
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prm%f_at = prm%b_sl**3*pl%get_asReal('f_at')
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prm%h_sl_sl = crystal_interaction_SlipBySlip(N_sl,pl%get_as1dReal('h_sl-sl'), &
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phase_lattice(ph))
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prm%forestProjection = spread( f_edge,1,prm%sum_N_sl) &
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* crystal_forestProjection_edge (N_sl,phase_lattice(ph),phase_cOverA(ph)) &
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+ spread(1.0_pREAL-f_edge,1,prm%sum_N_sl) &
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* crystal_forestProjection_screw(N_sl,phase_lattice(ph),phase_cOverA(ph))
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! sanity checks
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if ( prm%D_0 < 0.0_pREAL) extmsg = trim(extmsg)//' D_0'
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if ( prm%Q_cl <= 0.0_pREAL) extmsg = trim(extmsg)//' Q_cl'
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if (any(rho_mob_0 < 0.0_pREAL)) extmsg = trim(extmsg)//' rho_mob_0'
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if (any(rho_dip_0 < 0.0_pREAL)) extmsg = trim(extmsg)//' rho_dip_0'
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if (any(prm%b_sl <= 0.0_pREAL)) extmsg = trim(extmsg)//' b_sl'
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if (any(prm%Q_s <= 0.0_pREAL)) extmsg = trim(extmsg)//' Q_s'
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if (any(prm%tau_Peierls < 0.0_pREAL)) extmsg = trim(extmsg)//' tau_Peierls'
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if (any(prm%B < 0.0_pREAL)) extmsg = trim(extmsg)//' B'
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if (any(prm%d_caron < 0.0_pREAL)) extmsg = trim(extmsg)//' d_caron(D_a,b_sl)'
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if (any(prm%f_at <= 0.0_pREAL)) extmsg = trim(extmsg)//' f_at or b_sl'
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else slipActive
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rho_mob_0 = emptyRealArray
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rho_dip_0 = emptyRealArray
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allocate(prm%b_sl, &
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prm%d_caron, &
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prm%i_sl, &
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prm%f_at, &
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prm%tau_Peierls, &
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prm%Q_s, &
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prm%p, &
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prm%q, &
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prm%B, &
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prm%h, &
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prm%w, &
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prm%omega, &
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source = emptyRealArray)
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allocate(prm%forestProjection(0,0))
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allocate(prm%h_sl_sl (0,0))
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end if slipActive
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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Nmembers = count(material_ID_phase == ph)
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sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl
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sizeState = sizeDotState
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call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,0)
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deallocate(plasticState(ph)%dotState) ! ToDo: remove dotState completely
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!--------------------------------------------------------------------------------------------------
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! state aliases and initialization
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startIndex = 1
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endIndex = prm%sum_N_sl
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idx_dot%rho_mob = [startIndex,endIndex]
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stt%rho_mob => plasticState(ph)%state(startIndex:endIndex,:)
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stt%rho_mob = spread(rho_mob_0,2,Nmembers)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_rho',defaultVal=1.0_pREAL)
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if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pREAL)) extmsg = trim(extmsg)//' atol_rho'
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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idx_dot%rho_dip = [startIndex,endIndex]
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stt%rho_dip => plasticState(ph)%state(startIndex:endIndex,:)
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stt%rho_dip = spread(rho_dip_0,2,Nmembers)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_rho',defaultVal=1.0_pREAL)
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startIndex = endIndex + 1
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endIndex = endIndex + prm%sum_N_sl
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idx_dot%gamma_sl = [startIndex,endIndex]
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stt%gamma_sl => plasticState(ph)%state(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asReal('atol_gamma',defaultVal=1.0e-6_pREAL)
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if (any(plasticState(ph)%atol(startIndex:endIndex) < 0.0_pREAL)) extmsg = trim(extmsg)//' atol_gamma'
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allocate(dst%Lambda_sl(prm%sum_N_sl,Nmembers), source=0.0_pREAL)
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allocate(dst%tau_pass (prm%sum_N_sl,Nmembers), source=0.0_pREAL)
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end associate
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!--------------------------------------------------------------------------------------------------
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! exit if any parameter is out of range
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if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg))
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end do
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end function plastic_dislotungsten_init
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate plastic velocity gradient and its tangent.
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!--------------------------------------------------------------------------------------------------
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pure module subroutine dislotungsten_LpAndItsTangent(Lp,dLp_dMp, &
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Mp,ph,en)
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real(pREAL), dimension(3,3), intent(out) :: &
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Lp !< plastic velocity gradient
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real(pREAL), dimension(3,3,3,3), intent(out) :: &
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dLp_dMp !< derivative of Lp with respect to the Mandel stress
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real(pREAL), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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integer :: &
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i,k,l,m,n
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real(pREAL) :: &
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T !< temperature
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma, ddot_gamma_dtau
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real(pREAL), dimension(3,3,param(ph)%sum_N_sl) :: &
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P_nS
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T = thermal_T(ph,en)
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Lp = 0.0_pREAL
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dLp_dMp = 0.0_pREAL
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associate(prm => param(ph))
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call kinetics(Mp,T,ph,en, dot_gamma,ddot_gamma_dtau)
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P_nS = merge(prm%P_nS_pos,prm%P_nS_neg, spread(spread(dot_gamma,1,3),2,3)>0.0_pREAL) ! faster than 'merge' in loop
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do i = 1, prm%sum_N_sl
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Lp = Lp + dot_gamma(i)*prm%P_sl(1:3,1:3,i)
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forall (k=1:3,l=1:3,m=1:3,n=1:3) &
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dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
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+ ddot_gamma_dtau(i) * prm%P_sl(k,l,i) * P_nS(m,n,i)
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end do
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end associate
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end subroutine dislotungsten_LpAndItsTangent
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate the rate of change of microstructure.
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!--------------------------------------------------------------------------------------------------
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module function dislotungsten_dotState(Mp,ph,en) result(dotState)
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real(pREAL), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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integer, intent(in) :: &
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ph, &
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en
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real(pREAL), dimension(plasticState(ph)%sizeDotState) :: &
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dotState
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real(pREAL), dimension(param(ph)%sum_N_sl) :: &
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tau_eff, &
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v_cl, &
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dot_rho_dip_formation, &
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dot_rho_dip_climb, &
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d_hat
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real(pREAL) :: &
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mu, nu, T
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph), &
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dot_rho_mob => dotState(indexDotState(ph)%rho_mob(1):indexDotState(ph)%rho_mob(2)), &
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dot_rho_dip => dotState(indexDotState(ph)%rho_dip(1):indexDotState(ph)%rho_dip(2)), &
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dot_gamma => dotState(indexDotState(ph)%gamma_sl(1):indexDotState(ph)%gamma_sl(2)))
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mu = elastic_mu(ph,en,prm%isotropic_bound)
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nu = elastic_nu(ph,en,prm%isotropic_bound)
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T = thermal_T(ph,en)
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call kinetics(Mp,T,ph,en,&
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dot_gamma, tau = tau_eff)
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dot_gamma = abs(dot_gamma)
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where(dEq0(dot_gamma))
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d_hat = dst%Lambda_sl(:,en) ! upper limit
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dot_rho_dip_formation = 0.0_pREAL
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else where
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d_hat = mu*prm%b_sl/(8.0_pREAL*PI*(1.0_pREAL-nu)*tau_eff)
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d_hat = math_clip(d_hat, right = dst%Lambda_sl(:,en)) ! upper limit
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d_hat = math_clip(d_hat, left = prm%d_caron) ! lower limit
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dot_rho_dip_formation = merge(dot_gamma * 2.0_pREAL*(d_hat-prm%d_caron)/prm%b_sl * stt%rho_mob(:,en), &
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0.0_pREAL, &
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prm%dipoleformation)
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end where
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where(dEq0(d_hat-prm%d_caron))
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dot_rho_dip_climb = 0.0_pREAL
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else where
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v_cl = (3.0_pREAL*mu*prm%D_0*exp(-prm%Q_cl/(K_B*T))*prm%f_at/(2.0_pREAL*PI*K_B*T)) &
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* (1.0_pREAL/(d_hat+prm%d_caron))
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dot_rho_dip_climb = (4.0_pREAL*v_cl*stt%rho_dip(:,en))/(d_hat-prm%d_caron) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot_rho_mob = dot_gamma / (prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_mob(:,en) ! spontaneous annihilation of 2 edges
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dot_rho_dip = dot_rho_dip_formation &
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- dot_rho_dip_climb &
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- dot_gamma * 2.0_pREAL*prm%d_caron/prm%b_sl * stt%rho_dip(:,en) ! spontaneous annihilation of an edge with a dipole
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end associate
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end function dislotungsten_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief Calculate derived quantities from state.
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!--------------------------------------------------------------------------------------------------
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module subroutine dislotungsten_dependentState(ph,en)
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integer, intent(in) :: &
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ph, &
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en
|
||
|
||
real(pREAL), dimension(param(ph)%sum_N_sl) :: &
|
||
Lambda_sl_inv
|
||
|
||
|
||
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
|
||
|
||
dst%tau_pass(:,en) = elastic_mu(ph,en,prm%isotropic_bound)*prm%b_sl &
|
||
* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
|
||
|
||
Lambda_sl_inv = 1.0_pREAL/prm%D &
|
||
+ sqrt(matmul(prm%forestProjection,stt%rho_mob(:,en)+stt%rho_dip(:,en)))/prm%i_sl
|
||
dst%Lambda_sl(:,en) = Lambda_sl_inv**(-1.0_pREAL)
|
||
|
||
end associate
|
||
|
||
end subroutine dislotungsten_dependentState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Write results to HDF5 output file.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_dislotungsten_result(ph,group)
|
||
|
||
integer, intent(in) :: ph
|
||
character(len=*), intent(in) :: group
|
||
|
||
integer :: ou
|
||
|
||
|
||
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
|
||
|
||
do ou = 1,size(prm%output)
|
||
|
||
select case(trim(prm%output(ou)))
|
||
|
||
case('rho_mob')
|
||
call result_writeDataset(stt%rho_mob,group,trim(prm%output(ou)), &
|
||
'mobile dislocation density','1/m²',prm%systems_sl)
|
||
case('rho_dip')
|
||
call result_writeDataset(stt%rho_dip,group,trim(prm%output(ou)), &
|
||
'dislocation dipole density','1/m²',prm%systems_sl)
|
||
case('gamma_sl')
|
||
call result_writeDataset(stt%gamma_sl,group,trim(prm%output(ou)), &
|
||
'plastic shear','1',prm%systems_sl)
|
||
case('Lambda_sl')
|
||
call result_writeDataset(dst%Lambda_sl,group,trim(prm%output(ou)), &
|
||
'mean free path for slip','m',prm%systems_sl)
|
||
case('tau_pass')
|
||
call result_writeDataset(dst%tau_pass,group,trim(prm%output(ou)), &
|
||
'threshold stress for slip','Pa',prm%systems_sl)
|
||
end select
|
||
|
||
end do
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotungsten_result
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @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: Contrary to common convention, here the result (i.e. intent(out)) variables have to be put
|
||
! at the end since some of them are optional.
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics(Mp,T,ph,en, &
|
||
dot_gamma,ddot_gamma_dtau,tau)
|
||
|
||
real(pREAL), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pREAL), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
en
|
||
|
||
real(pREAL), dimension(param(ph)%sum_N_sl), intent(out) :: &
|
||
dot_gamma
|
||
real(pREAL), dimension(param(ph)%sum_N_sl), optional, intent(out) :: &
|
||
ddot_gamma_dtau, &
|
||
tau
|
||
|
||
real(pREAL), dimension(param(ph)%sum_N_sl) :: &
|
||
StressRatio, &
|
||
StressRatio_p,StressRatio_pminus1, &
|
||
tau_pos, tau_neg, tau_eff, &
|
||
t_n,t_k, dtk,dtn
|
||
integer :: i
|
||
|
||
|
||
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
|
||
|
||
tau_pos = [(math_tensordot(Mp,prm%P_nS_pos(1:3,1:3,i)),i=1,prm%sum_N_sl)]
|
||
tau_neg = [(math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,i)),i=1,prm%sum_N_sl)]
|
||
tau_eff = math_clip(max(tau_pos,tau_neg) - dst%tau_pass(:,en),left = 0.0_pREAL)
|
||
|
||
if (present(tau)) tau = tau_eff
|
||
|
||
associate(BoltzmannRatio => prm%Q_s/(K_B*T), &
|
||
b_rho => stt%rho_mob(:,en) * prm%b_sl, &
|
||
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
|
||
|
||
|
||
where(tau_eff > tol_math_check)
|
||
StressRatio = tau_eff/prm%tau_Peierls
|
||
StressRatio_p = StressRatio** prm%p
|
||
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pREAL)
|
||
|
||
t_n = prm%b_sl*exp(BoltzmannRatio*(1.0_pREAL-StressRatio_p) ** prm%q) &
|
||
/ (prm%omega*effectiveLength)
|
||
t_k = effectiveLength * prm%B /(2.0_pREAL*prm%b_sl*tau_eff) ! corrected eq. (14)
|
||
|
||
dot_gamma = b_rho * prm%h/(t_n + t_k) * merge(+1.0_pREAL,-1.0_pREAL, tau_pos>tau_neg)
|
||
else where
|
||
dot_gamma = 0.0_pREAL
|
||
end where
|
||
|
||
if (present(ddot_gamma_dtau)) then
|
||
where(tau_eff > tol_math_check)
|
||
dtn = -1.0_pREAL * t_n * BoltzmannRatio * prm%p * prm%q * (1.0_pREAL-StressRatio_p)**(prm%q - 1.0_pREAL) &
|
||
* StressRatio_pminus1 / prm%tau_Peierls
|
||
dtk = -1.0_pREAL * t_k / tau_eff
|
||
|
||
ddot_gamma_dtau = -1.0_pREAL * dot_gamma * (dtn + dtk) / (t_n + t_k)
|
||
else where
|
||
ddot_gamma_dtau = 0.0_pREAL
|
||
end where
|
||
end if
|
||
|
||
end associate
|
||
end associate
|
||
|
||
end subroutine kinetics
|
||
|
||
end submodule dislotungsten
|