534 lines
27 KiB
Fortran
534 lines
27 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(constitutive) plastic_disloUCLA
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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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atomicVolume, &
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tau_0, &
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!* mobility law parameters
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delta_F, & !< activation energy for glide [J]
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v0, & !< 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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kink_height, & !< 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 :: tDisloUCLAState
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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 tDisloUCLAState
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type :: tDisloUCLAdependentState
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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 tDisloUCLAdependentState
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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(tDisloUCLAState), allocatable, dimension(:) :: &
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dotState, &
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state
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type(tDisloUCLAdependentState), 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 subroutine plastic_disloUCLA_init
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integer :: &
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Ninstance, &
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p, i, &
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NipcMyPhase, &
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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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write(6,'(/,a)') ' <<<+- plastic_'//PLASTICITY_DISLOUCLA_LABEL//' init -+>>>'; flush(6)
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write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78:242–256, 2016'
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write(6,'(a)') ' https://dx.doi.org/10.1016/j.ijplas.2015.09.002'
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Ninstance = count(phase_plasticity == PLASTICITY_DISLOUCLA_ID)
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
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write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
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allocate(param(Ninstance))
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allocate(state(Ninstance))
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allocate(dotState(Ninstance))
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allocate(dependentState(Ninstance))
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do p = 1, size(phase_plasticity)
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if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_ID) cycle
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associate(prm => param(phase_plasticityInstance(p)), &
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dot => dotState(phase_plasticityInstance(p)), &
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stt => state(phase_plasticityInstance(p)), &
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dst => dependentState(phase_plasticityInstance(p)), &
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config => config_phase(p))
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prm%output = config%getStrings('(output)',defaultVal=emptyStringArray)
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! This data is read in already in lattice
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prm%mu = lattice_mu(p)
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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N_sl = config%getInts('nslip',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,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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if(trim(config%getString('lattice_structure')) == 'bcc') then
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a = config%getFloats('nonschmid_coefficients',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,config%getFloats('interaction_slipslip'), &
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config%getString('lattice_structure'))
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prm%forestProjection = lattice_forestProjection_edge(N_sl,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%forestProjection = transpose(prm%forestProjection)
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rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(N_sl))
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rho_dip_0 = config%getFloats('rhoedgedip0', requiredSize=size(N_sl))
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prm%v0 = config%getFloats('v0', requiredSize=size(N_sl))
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prm%b_sl = config%getFloats('slipburgers', requiredSize=size(N_sl))
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prm%delta_F = config%getFloats('qedge', requiredSize=size(N_sl))
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prm%i_sl = config%getFloats('clambdaslip', requiredSize=size(N_sl))
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prm%tau_0 = config%getFloats('tau_peierls', requiredSize=size(N_sl))
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prm%p = config%getFloats('p_slip', requiredSize=size(N_sl), &
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defaultVal=[(1.0_pReal,i=1,size(N_sl))])
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prm%q = config%getFloats('q_slip', requiredSize=size(N_sl), &
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defaultVal=[(1.0_pReal,i=1,size(N_sl))])
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prm%kink_height = config%getFloats('kink_height', requiredSize=size(N_sl))
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prm%w = config%getFloats('kink_width', requiredSize=size(N_sl))
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prm%omega = config%getFloats('omega', requiredSize=size(N_sl))
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prm%B = config%getFloats('friction_coeff', requiredSize=size(N_sl))
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prm%D = config%getFloat('grainsize')
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prm%D_0 = config%getFloat('d0')
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prm%Q_cl = config%getFloat('qsd')
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prm%atomicVolume = config%getFloat('catomicvolume') * prm%b_sl**3.0_pReal
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prm%D_a = config%getFloat('cedgedipmindistance') * prm%b_sl
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prm%dipoleformation = config%getFloat('dipoleformationfactor') > 0.0_pReal !should be on by default, ToDo: change to /key/-type key
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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%delta_F = math_expand(prm%delta_F, N_sl)
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prm%b_sl = math_expand(prm%b_sl, N_sl)
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prm%kink_height = math_expand(prm%kink_height, 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_0 = math_expand(prm%tau_0, N_sl)
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prm%v0 = math_expand(prm%v0, 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%atomicVolume = math_expand(prm%atomicVolume, 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)//' rhoedge0'
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if (any(rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rhoedgedip0'
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if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
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if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
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if (any(prm%delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' qedge'
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if (any(prm%tau_0 < 0.0_pReal)) extmsg = trim(extmsg)//' tau_0'
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if (any(prm%D_a <= 0.0_pReal)) extmsg = trim(extmsg)//' cedgedipmindistance or b_sl'
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if (any(prm%atomicVolume <= 0.0_pReal)) extmsg = trim(extmsg)//' catomicvolume 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%atomicVolume,prm%tau_0, &
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prm%delta_F,prm%v0,prm%p,prm%q,prm%B,prm%kink_height,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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NipcMyPhase = count(material_phaseAt == p) * discretization_nIP
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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 material_allocateState(plasticState(p),NipcMyPhase,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(p)%state(startIndex:endIndex,:)
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stt%rho_mob = spread(rho_mob_0,2,NipcMyPhase)
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dot%rho_mob => plasticState(p)%dotState(startIndex:endIndex,:)
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plasticState(p)%atol(startIndex:endIndex) = config%getFloat('atol_rho',defaultVal=1.0_pReal)
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if (any(plasticState(p)%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(p)%state(startIndex:endIndex,:)
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stt%rho_dip = spread(rho_dip_0,2,NipcMyPhase)
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dot%rho_dip => plasticState(p)%dotState(startIndex:endIndex,:)
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plasticState(p)%atol(startIndex:endIndex) = config%getFloat('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(p)%state(startIndex:endIndex,:)
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dot%gamma_sl => plasticState(p)%dotState(startIndex:endIndex,:)
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plasticState(p)%atol(startIndex:endIndex) = 1.0e-2_pReal
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! global alias
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plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
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allocate(dst%Lambda_sl(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
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allocate(dst%threshold_stress(prm%sum_N_sl,NipcMyPhase), source=0.0_pReal)
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plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
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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)//'('//PLASTICITY_DISLOUCLA_LABEL//')')
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enddo
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end subroutine plastic_disloUCLA_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 plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp, &
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Mp,T,instance,of)
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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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instance, &
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of
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integer :: &
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i,k,l,m,n
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real(pReal), dimension(param(instance)%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(instance))
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call kinetics(Mp,T,instance,of,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 plastic_disloUCLA_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 plastic_disloUCLA_dotState(Mp,T,instance,of)
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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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instance, &
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of
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real(pReal) :: &
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VacancyDiffusion
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real(pReal), dimension(param(instance)%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(instance), stt => state(instance),dot => dotState(instance), dst => dependentState(instance))
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call kinetics(Mp,T,instance,of,&
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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(:,of) = (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(:,of)) ! upper limit
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dot_rho_dip_formation = merge(2.0_pReal*dip_distance* stt%rho_mob(:,of)*abs(dot%gamma_sl(:,of))/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%atomicVolume/(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(:,of))/(dip_distance-prm%D_a) ! ToDo: Discuss with Franz: Stress dependency?
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end where
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dot%rho_mob(:,of) = abs(dot%gamma_sl(:,of))/(prm%b_sl*dst%Lambda_sl(:,of)) & ! 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(:,of)*abs(dot%gamma_sl(:,of)) ! Spontaneous annihilation of 2 single edge dislocations
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dot%rho_dip(:,of) = dot_rho_dip_formation &
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- (2.0_pReal*prm%D_a)/prm%b_sl*stt%rho_dip(:,of)*abs(dot%gamma_sl(:,of)) & ! 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 plastic_disloUCLA_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 plastic_disloUCLA_dependentState(instance,of)
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integer, intent(in) :: &
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instance, &
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of
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real(pReal), dimension(param(instance)%sum_N_sl) :: &
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dislocationSpacing
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associate(prm => param(instance), stt => state(instance),dst => dependentState(instance))
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dislocationSpacing = sqrt(matmul(prm%forestProjection,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
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dst%threshold_stress(:,of) = prm%mu*prm%b_sl &
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* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
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dst%Lambda_sl(:,of) = prm%D/(1.0_pReal+prm%D*dislocationSpacing/prm%i_sl)
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end associate
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end subroutine plastic_disloUCLA_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_disloUCLA_results(instance,group)
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integer, intent(in) :: instance
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character(len=*), intent(in) :: group
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integer :: o
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associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
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outputsLoop: do o = 1,size(prm%output)
|
||
select case(trim(prm%output(o)))
|
||
case('edge_density') ! ToDo: should be rho_mob
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_mob,'rho_mob',&
|
||
'mobile dislocation density','1/m²')
|
||
case('dipole_density') ! ToDo: should be rho_dip
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip,'rho_dip',&
|
||
'dislocation dipole density''1/m²')
|
||
case('shear_rate_slip') ! should be gamma
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma_sl,'dot_gamma_sl',& ! this is not dot!!
|
||
'plastic shear','1')
|
||
case('mfp_slip') !ToDo: should be Lambda
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
|
||
'mean free path for slip','m')
|
||
case('threshold_stress_slip') !ToDo: should be tau_pass
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%threshold_stress,'tau_pass',&
|
||
'threshold stress for slip','Pa')
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
|
||
end subroutine plastic_disloUCLA_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,instance,of, &
|
||
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) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), intent(out), dimension(param(instance)%sum_N_sl) :: &
|
||
dot_gamma_pos, &
|
||
dot_gamma_neg
|
||
real(pReal), intent(out), optional, dimension(param(instance)%sum_N_sl) :: &
|
||
ddot_gamma_dtau_pos, &
|
||
ddot_gamma_dtau_neg, &
|
||
tau_pos_out, &
|
||
tau_neg_out
|
||
real(pReal), dimension(param(instance)%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(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
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%delta_F/(kB*T), &
|
||
dot_gamma_0 => stt%rho_mob(:,of)*prm%b_sl*prm%v0, &
|
||
effectiveLength => dst%Lambda_sl(:,of) - prm%w)
|
||
|
||
significantPositiveTau: where(abs(tau_pos)-dst%threshold_stress(:,of) > tol_math_check)
|
||
StressRatio = (abs(tau_pos)-dst%threshold_stress(:,of))/prm%tau_0
|
||
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%kink_height/(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(:,of) > 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_0
|
||
dtk = -1.0_pReal * t_k / tau_pos
|
||
|
||
dvel = -1.0_pReal * prm%kink_height * (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(:,of) > tol_math_check)
|
||
StressRatio = (abs(tau_neg)-dst%threshold_stress(:,of))/prm%tau_0
|
||
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%kink_height/(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(:,of) > 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_0
|
||
dtk = -1.0_pReal * t_k / tau_neg
|
||
|
||
dvel = -1.0_pReal * prm%kink_height * (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 plastic_disloUCLA
|