545 lines
25 KiB
Fortran
545 lines
25 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=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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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 :: 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(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, &
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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'(/,1x,a)', '<<<+- phase:mechanical:plastic:dislotungsten init -+>>>'
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print'(/,a,i0)', ' # phases: ',count(myPlasticity); flush(IO_STDOUT)
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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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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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!--------------------------------------------------------------------------------------------------
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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 = lattice_labels_slip(N_sl,phase_lattice(ph))
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prm%P_sl = lattice_SchmidMatrix_slip(N_sl,phase_lattice(ph),phase_cOverA(ph))
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if (phase_lattice(ph) == 'cI') then
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a = pl%get_as1dFloat('a_nonSchmid',defaultVal = emptyRealArray)
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prm%P_nS_pos = lattice_nonSchmidMatrix(N_sl,a,+1)
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prm%P_nS_neg = lattice_nonSchmidMatrix(N_sl,a,-1)
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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%h_sl_sl = lattice_interaction_SlipBySlip(N_sl,pl%get_as1dFloat('h_sl-sl'), &
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phase_lattice(ph))
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prm%forestProjection = lattice_forestProjection_edge(N_sl,phase_lattice(ph),&
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phase_cOverA(ph))
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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%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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prm%q = pl%get_as1dFloat('q_sl', requiredSize=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
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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%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_caron = pl%get_asFloat('D_a') * prm%b_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%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; rho_dip_0 = emptyRealArray
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allocate(prm%b_sl,prm%d_caron,prm%i_sl,prm%f_at,prm%tau_Peierls, &
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prm%Q_s,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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end if 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%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)//'(dislotungsten)')
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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_pos,dot_gamma_neg, &
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ddot_gamma_dtau_pos,ddot_gamma_dtau_neg
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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_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%P_nS_pos(m,n,i) &
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+ ddot_gamma_dtau_neg(i) * prm%P_sl(k,l,i) * prm%P_nS_neg(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 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), dimension(param(ph)%sum_N_sl) :: &
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dot_gamma_pos, dot_gamma_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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d_hat
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real(pReal) :: &
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mu
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associate(prm => param(ph), stt => state(ph), dot => dotState(ph), dst => dependentState(ph))
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mu = elastic_mu(ph,en)
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call kinetics(Mp,T,ph,en,&
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dot_gamma_pos,dot_gamma_neg, &
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tau_pos_out = tau_pos,tau_neg_out = tau_neg)
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dot%gamma_sl(:,en) = abs(dot_gamma_pos+dot_gamma_neg)
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where(dEq0((tau_pos+tau_neg)*0.5_pReal))
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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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d_hat = math_clip(3.0_pReal*mu*prm%b_sl/(16.0_pReal*PI*abs(tau_pos+tau_neg)*0.5_pReal), &
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prm%d_caron, & ! lower limit
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dst%Lambda_sl(:,en)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pReal*(d_hat-prm%d_caron)*stt%rho_mob(:,en)*dot%gamma_sl(:,en)/prm%b_sl, &
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0.0_pReal, &
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prm%dipoleformation)
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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(:,en) = 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_caron)/prm%b_sl*stt%rho_mob(:,en)*dot%gamma_sl(:,en) ! Spontaneous annihilation of 2 edges
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dot%rho_dip(:,en) = dot_rho_dip_formation &
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- (2.0_pReal*prm%d_caron)/prm%b_sl*stt%rho_dip(:,en)*dot%gamma_sl(:,en) & ! Spontaneous annihilation of an edge with a dipole
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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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Lambda_sl_inv
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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dst%tau_pass(:,en) = elastic_mu(ph,en)*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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Lambda_sl_inv = 1.0_pReal/prm%D &
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+ sqrt(matmul(prm%forestProjection,stt%rho_mob(:,en)+stt%rho_dip(:,en)))/prm%i_sl
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dst%Lambda_sl(:,en) = Lambda_sl_inv**(-1.0_pReal)
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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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integer, intent(in) :: ph
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character(len=*), intent(in) :: group
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integer :: ou
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associate(prm => param(ph), stt => state(ph), dst => dependentState(ph))
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do ou = 1,size(prm%output)
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select case(trim(prm%output(ou)))
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case('rho_mob')
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call results_writeDataset(stt%rho_mob,group,trim(prm%output(ou)), &
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'mobile dislocation density','1/m²',prm%systems_sl)
|
||
case('rho_dip')
|
||
call results_writeDataset(stt%rho_dip,group,trim(prm%output(ou)), &
|
||
'dislocation dipole density','1/m²',prm%systems_sl)
|
||
case('gamma_sl')
|
||
call results_writeDataset(stt%gamma_sl,group,trim(prm%output(ou)), &
|
||
'plastic shear','1',prm%systems_sl)
|
||
case('Lambda_sl')
|
||
call results_writeDataset(dst%Lambda_sl,group,trim(prm%output(ou)), &
|
||
'mean free path for slip','m',prm%systems_sl)
|
||
case('tau_pass')
|
||
call results_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_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, &
|
||
tau_pos, tau_neg, tau_eff, &
|
||
t_n, t_k, dtk,dtn
|
||
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%P_nS_pos(1:3,1:3,j))
|
||
tau_neg(j) = math_tensordot(Mp,prm%P_nS_neg(1:3,1:3,j))
|
||
end do
|
||
|
||
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/(K_B*T), &
|
||
b_rho_half => stt%rho_mob(:,en) * prm%b_sl * 0.5_pReal, &
|
||
effectiveLength => dst%Lambda_sl(:,en) - prm%w)
|
||
|
||
tau_eff = abs(tau_pos)-dst%tau_pass(:,en)
|
||
|
||
significantPositiveTau: 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_pos = b_rho_half * sign(prm%h/(t_n + t_k),tau_pos)
|
||
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%tau_pass(:,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_pminus1 / prm%tau_Peierls
|
||
dtk = -1.0_pReal * t_k / tau_pos
|
||
|
||
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
|
||
|
||
ddot_gamma_dtau_pos = b_rho_half * dvel
|
||
else where significantPositiveTau2
|
||
ddot_gamma_dtau_pos = 0.0_pReal
|
||
end where significantPositiveTau2
|
||
end if
|
||
|
||
tau_eff = abs(tau_neg)-dst%tau_pass(:,en)
|
||
|
||
significantNegativeTau: 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_neg = b_rho_half * sign(prm%h/(t_n + t_k),tau_neg)
|
||
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%tau_pass(:,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_pminus1 / prm%tau_Peierls
|
||
dtk = -1.0_pReal * t_k / tau_neg
|
||
|
||
dvel = -1.0_pReal * prm%h * (dtk + dtn) / (t_n + t_k)**2
|
||
|
||
ddot_gamma_dtau_neg = b_rho_half * dvel
|
||
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
|