547 lines
26 KiB
Fortran
547 lines
26 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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real(pReal), parameter :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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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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mu = 1.0_pReal, & !< equivalent shear modulus
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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_a, &
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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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v_0, & !< dislocation velocity prefactor [m/s]
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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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nonSchmid_pos, &
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nonSchmid_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=pStringLen), 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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end type !< container type for internal constitutive parameters
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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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threshold_stress
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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(tDisloTungstenState), allocatable, dimension(:) :: &
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dotState, &
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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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rho_mob_0, & !< initial dislocation density
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rho_dip_0, & !< initial dipole density
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a !< non-Schmid coefficients
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character(len=pStringLen) :: &
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extmsg = ''
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class(tNode), 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'(/,a)', ' <<<+- phase:mechanical:plastic:dislotungsten init -+>>>'
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print'(a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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print*, 'D. Cereceda et al., International Journal of Plasticity 78:242–256, 2016'
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print*, 'https://doi.org/10.1016/j.ijplas.2015.09.002'
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phases => config_material%get('phase')
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allocate(param(phases%length))
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allocate(state(phases%length))
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allocate(dotState(phases%length))
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allocate(dependentState(phases%length))
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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), dot => dotState(ph), stt => state(ph), dst => dependentState(ph))
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phase => phases%get(ph)
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mech => phase%get('mechanical')
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pl => mech%get('plastic')
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#if defined (__GFORTRAN__)
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prm%output = output_as1dString(pl)
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#else
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prm%output = pl%get_as1dString('output',defaultVal=emptyStringArray)
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#endif
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! This data is read in already in lattice
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prm%mu = lattice_mu(ph)
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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%P_sl = lattice_SchmidMatrix_slip(N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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if(trim(phase%get_asString('lattice')) == 'cI') then
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a = pl%get_as1dFloat('a_nonSchmid',defaultVal = emptyRealArray)
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prm%nonSchmid_pos = lattice_nonSchmidMatrix(N_sl,a,+1)
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prm%nonSchmid_neg = lattice_nonSchmidMatrix(N_sl,a,-1)
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else
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prm%nonSchmid_pos = prm%P_sl
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prm%nonSchmid_neg = prm%P_sl
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endif
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prm%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_as1dFloat('h_sl-sl'), &
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phase%get_asString('lattice'))
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prm%forestProjection = lattice_forestProjection_edge(N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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prm%forestProjection = transpose(prm%forestProjection)
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rho_mob_0 = pl%get_as1dFloat('rho_mob_0', requiredSize=size(N_sl))
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rho_dip_0 = pl%get_as1dFloat('rho_dip_0', requiredSize=size(N_sl))
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prm%v_0 = pl%get_as1dFloat('v_0', requiredSize=size(N_sl))
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prm%b_sl = pl%get_as1dFloat('b_sl', requiredSize=size(N_sl))
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prm%Q_s = pl%get_as1dFloat('Q_s', requiredSize=size(N_sl))
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prm%i_sl = pl%get_as1dFloat('i_sl', requiredSize=size(N_sl))
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prm%tau_Peierls = pl%get_as1dFloat('tau_Peierls', requiredSize=size(N_sl))
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prm%p = pl%get_as1dFloat('p_sl', requiredSize=size(N_sl), &
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defaultVal=[(1.0_pReal,i=1,size(N_sl))])
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prm%q = pl%get_as1dFloat('q_sl', requiredSize=size(N_sl), &
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defaultVal=[(1.0_pReal,i=1,size(N_sl))])
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prm%h = pl%get_as1dFloat('h', requiredSize=size(N_sl))
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prm%w = pl%get_as1dFloat('w', requiredSize=size(N_sl))
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prm%omega = pl%get_as1dFloat('omega', requiredSize=size(N_sl))
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prm%B = pl%get_as1dFloat('B', requiredSize=size(N_sl))
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prm%D = pl%get_asFloat('D')
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prm%D_0 = pl%get_asFloat('D_0')
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prm%Q_cl = pl%get_asFloat('Q_cl')
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prm%f_at = pl%get_asFloat('f_at') * prm%b_sl**3.0_pReal
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prm%D_a = pl%get_asFloat('D_a') * prm%b_sl
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prm%dipoleformation = .not. pl%get_asBool('no_dipole_formation', defaultVal = .false.)
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! expand: family => system
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rho_mob_0 = math_expand(rho_mob_0, N_sl)
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rho_dip_0 = math_expand(rho_dip_0, N_sl)
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prm%q = math_expand(prm%q, N_sl)
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prm%p = math_expand(prm%p, N_sl)
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prm%Q_s = math_expand(prm%Q_s, N_sl)
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prm%b_sl = math_expand(prm%b_sl, N_sl)
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prm%h = math_expand(prm%h, N_sl)
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prm%w = math_expand(prm%w, N_sl)
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prm%omega = math_expand(prm%omega, N_sl)
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prm%tau_Peierls = math_expand(prm%tau_Peierls, N_sl)
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prm%v_0 = math_expand(prm%v_0, N_sl)
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prm%B = math_expand(prm%B, N_sl)
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prm%i_sl = math_expand(prm%i_sl, N_sl)
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prm%f_at = math_expand(prm%f_at, N_sl)
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prm%D_a = math_expand(prm%D_a, N_sl)
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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%v_0 < 0.0_pReal)) extmsg = trim(extmsg)//' v_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%D_a <= 0.0_pReal)) extmsg = trim(extmsg)//' D_a or 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; rho_dip_0 = emptyRealArray
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allocate(prm%b_sl,prm%D_a,prm%i_sl,prm%f_at,prm%tau_Peierls, &
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prm%Q_s,prm%v_0,prm%p,prm%q,prm%B,prm%h,prm%w,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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endif slipActive
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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Nmembers = count(material_phaseID == 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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!--------------------------------------------------------------------------------------------------
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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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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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dot%rho_mob => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('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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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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dot%rho_dip => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('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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stt%gamma_sl => plasticState(ph)%state(startIndex:endIndex,:)
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dot%gamma_sl => plasticState(ph)%dotState(startIndex:endIndex,:)
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plasticState(ph)%atol(startIndex:endIndex) = pl%get_asFloat('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%threshold_stress(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)//'(dislotungsten)')
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enddo
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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,T,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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real(pReal), intent(in) :: &
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T !< temperature
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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), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_pos,dot_gamma_neg, &
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ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
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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_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg)
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do i = 1, prm%sum_N_sl
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Lp = Lp + (dot_gamma_pos(i)+dot_gamma_neg(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_pos(i) * prm%P_sl(k,l,i) * prm%nonSchmid_pos(m,n,i) &
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+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%nonSchmid_neg(m,n,i)
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enddo
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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 subroutine dislotungsten_dotState(Mp,T,ph,en)
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real(pReal), dimension(3,3), intent(in) :: &
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Mp !< Mandel stress
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real(pReal), intent(in) :: &
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T !< temperature
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integer, intent(in) :: &
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ph, &
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en
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real(pReal) :: &
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VacancyDiffusion
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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gdot_pos, gdot_neg,&
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tau_pos,&
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tau_neg, &
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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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dip_distance
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associate(prm => param(ph), stt => state(ph),&
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dot => dotState(ph), dst => dependentState(ph))
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call kinetics(Mp,T,ph,en,&
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gdot_pos,gdot_neg, &
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tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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dot%gamma_sl(:,en) = (gdot_pos+gdot_neg) ! ToDo: needs to be abs
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VacancyDiffusion = prm%D_0*exp(-prm%Q_cl/(kB*T))
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where(dEq0(tau_pos)) ! ToDo: use avg of pos and neg
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dot_rho_dip_formation = 0.0_pReal
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dot_rho_dip_climb = 0.0_pReal
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else where
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dip_distance = math_clip(3.0_pReal*prm%mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos)), &
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prm%D_a, & ! lower limit
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dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pReal*dip_distance* stt%rho_mob(:,en)*abs(dot%gamma_sl(:,en))/prm%b_sl, & ! ToDo: ignore region of spontaneous annihilation
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0.0_pReal, &
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prm%dipoleformation)
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v_cl = (3.0_pReal*prm%mu*VacancyDiffusion*prm%f_at/(2.0_pReal*pi*kB*T)) &
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* (1.0_pReal/(dip_distance+prm%D_a))
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dot_rho_dip_climb = (4.0_pReal*v_cl*stt%rho_dip(:,en))/(dip_distance-prm%D_a) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot%rho_mob(:,en) = abs(dot%gamma_sl(:,en))/(prm%b_sl*dst%Lambda_sl(:,en)) & ! multiplication
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- dot_rho_dip_formation &
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- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_mob(:,en)*abs(dot%gamma_sl(:,en)) ! Spontaneous annihilation of 2 single edge dislocations
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dot%rho_dip(:,en) = dot_rho_dip_formation &
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- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_dip(:,en)*abs(dot%gamma_sl(:,en)) & ! Spontaneous annihilation of a single edge dislocation with a dipole constituent
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- dot_rho_dip_climb
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end associate
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end subroutine 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
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real(pReal), dimension(param(ph)%sum_N_sl) :: &
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dislocationSpacing
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associate(prm => param(ph), stt => state(ph),dst => dependentState(ph))
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dislocationSpacing = sqrt(matmul(prm%forestProjection,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
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dst%threshold_stress(:,en) = prm%mu*prm%b_sl &
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* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,en)+stt%rho_dip(:,en)))
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dst%Lambda_sl(:,en) = prm%D/(1.0_pReal+prm%D*dislocationSpacing/prm%i_sl)
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end associate
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end subroutine dislotungsten_dependentState
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!--------------------------------------------------------------------------------------------------
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!> @brief Write results to HDF5 output file.
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!--------------------------------------------------------------------------------------------------
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module subroutine plastic_dislotungsten_results(ph,group)
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||
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integer, intent(in) :: ph
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character(len=*), intent(in) :: group
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||
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integer :: o
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||
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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outputsLoop: do o = 1,size(prm%output)
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select case(trim(prm%output(o)))
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case('rho_mob')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%rho_mob,group,trim(prm%output(o)), &
|
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'mobile dislocation density','1/m²')
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||
case('rho_dip')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%rho_dip,group,trim(prm%output(o)), &
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'dislocation dipole density','1/m²')
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case('gamma_sl')
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if(prm%sum_N_sl>0) call results_writeDataset(stt%gamma_sl,group,trim(prm%output(o)), &
|
||
'plastic shear','1')
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||
case('Lambda_sl')
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||
if(prm%sum_N_sl>0) call results_writeDataset(dst%Lambda_sl,group,trim(prm%output(o)), &
|
||
'mean free path for slip','m')
|
||
case('tau_pass')
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if(prm%sum_N_sl>0) call results_writeDataset(dst%threshold_stress,group,trim(prm%output(o)), &
|
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'threshold stress for slip','Pa')
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
|
||
end subroutine plastic_dislotungsten_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(Mp,T,ph,en, &
|
||
dot_gamma_pos,dot_gamma_neg,ddot_gamma_dtau_pos,ddot_gamma_dtau_neg,tau_pos_out,tau_neg_out)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
en
|
||
|
||
real(pReal), intent(out), dimension(param(ph)%sum_N_sl) :: &
|
||
dot_gamma_pos, &
|
||
dot_gamma_neg
|
||
real(pReal), intent(out), optional, dimension(param(ph)%sum_N_sl) :: &
|
||
ddot_gamma_dtau_pos, &
|
||
ddot_gamma_dtau_neg, &
|
||
tau_pos_out, &
|
||
tau_neg_out
|
||
real(pReal), dimension(param(ph)%sum_N_sl) :: &
|
||
StressRatio, &
|
||
StressRatio_p,StressRatio_pminus1, &
|
||
dvel, vel, &
|
||
tau_pos,tau_neg, &
|
||
t_n, t_k, dtk,dtn, &
|
||
needsGoodName ! ToDo: @Karo: any idea?
|
||
integer :: j
|
||
|
||
associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
|
||
|
||
do j = 1, prm%sum_N_sl
|
||
tau_pos(j) = math_tensordot(Mp,prm%nonSchmid_pos(1:3,1:3,j))
|
||
tau_neg(j) = math_tensordot(Mp,prm%nonSchmid_neg(1:3,1:3,j))
|
||
enddo
|
||
|
||
|
||
if (present(tau_pos_out)) tau_pos_out = tau_pos
|
||
if (present(tau_neg_out)) tau_neg_out = tau_neg
|
||
|
||
associate(BoltzmannRatio => prm%Q_s/(kB*T), &
|
||
dot_gamma_0 => stt%rho_mob(:,en)*prm%b_sl*prm%v_0, &
|
||
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
|
||
|
||
significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,en) > tol_math_check)
|
||
StressRatio = (abs(tau_pos)-dst%threshold_stress(:,en))/prm%tau_Peierls
|
||
StressRatio_p = StressRatio** prm%p
|
||
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
|
||
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
|
||
|
||
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
|
||
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
|
||
|
||
vel = prm%h/(t_n + t_k)
|
||
|
||
dot_gamma_pos = dot_gamma_0 * sign(vel,tau_pos) * 0.5_pReal
|
||
else where significantPositiveTau
|
||
dot_gamma_pos = 0.0_pReal
|
||
end where significantPositiveTau
|
||
|
||
if (present(ddot_gamma_dtau_pos)) then
|
||
significantPositiveTau2: where(abs(tau_pos)-dst%threshold_stress(:,en) > 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)**(prm%p - 1.0_pReal) / prm%tau_Peierls
|
||
dtk = -1.0_pReal * t_k / tau_pos
|
||
|
||
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
|
||
|
||
ddot_gamma_dtau_pos = dot_gamma_0 * dvel* 0.5_pReal
|
||
else where significantPositiveTau2
|
||
ddot_gamma_dtau_pos = 0.0_pReal
|
||
end where significantPositiveTau2
|
||
endif
|
||
|
||
significantNegativeTau: where(abs(tau_neg)-dst%threshold_stress(:,en) > tol_math_check)
|
||
StressRatio = (abs(tau_neg)-dst%threshold_stress(:,en))/prm%tau_Peierls
|
||
StressRatio_p = StressRatio** prm%p
|
||
StressRatio_pminus1 = StressRatio**(prm%p-1.0_pReal)
|
||
needsGoodName = exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q)
|
||
|
||
t_n = prm%b_sl/(needsGoodName*prm%omega*effectiveLength)
|
||
t_k = effectiveLength * prm%B /(2.0_pReal*prm%b_sl*tau_pos)
|
||
|
||
vel = prm%h/(t_n + t_k)
|
||
|
||
dot_gamma_neg = dot_gamma_0 * sign(vel,tau_neg) * 0.5_pReal
|
||
else where significantNegativeTau
|
||
dot_gamma_neg = 0.0_pReal
|
||
end where significantNegativeTau
|
||
|
||
if (present(ddot_gamma_dtau_neg)) then
|
||
significantNegativeTau2: where(abs(tau_neg)-dst%threshold_stress(:,en) > 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)**(prm%p - 1.0_pReal) / prm%tau_Peierls
|
||
dtk = -1.0_pReal * t_k / tau_neg
|
||
|
||
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2.0_pReal
|
||
|
||
ddot_gamma_dtau_neg = dot_gamma_0 * dvel * 0.5_pReal
|
||
else where significantNegativeTau2
|
||
ddot_gamma_dtau_neg = 0.0_pReal
|
||
end where significantNegativeTau2
|
||
end if
|
||
|
||
end associate
|
||
end associate
|
||
|
||
end subroutine kinetics
|
||
|
||
end submodule dislotungsten
|