1836 lines
103 KiB
Fortran
1836 lines
103 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Christoph Kords, Max-Planck-Institut für Eisenforschung GmbH
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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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!> @brief material subroutine for plasticity including dislocation flux
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!--------------------------------------------------------------------------------------------------
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submodule(phase:plastic) nonlocal
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use geometry_plastic_nonlocal, only: &
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nIPneighbors => geometry_plastic_nonlocal_nIPneighbors, &
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IPneighborhood => geometry_plastic_nonlocal_IPneighborhood, &
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IPvolume => geometry_plastic_nonlocal_IPvolume0, &
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IParea => geometry_plastic_nonlocal_IParea0, &
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IPareaNormal => geometry_plastic_nonlocal_IPareaNormal0, &
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geometry_plastic_nonlocal_disable
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type :: tGeometry
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real(pReal), dimension(:), allocatable :: V_0
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end type tGeometry
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type(tGeometry), dimension(:), allocatable :: geom
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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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! storage order of dislocation types
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integer, dimension(*), parameter :: &
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sgl = [1,2,3,4,5,6,7,8] !< signed (single)
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integer, dimension(*), parameter :: &
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edg = [1,2,5,6,9], & !< edge
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scr = [3,4,7,8,10] !< screw
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integer, dimension(*), parameter :: &
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mob = [1,2,3,4], & !< mobile
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imm = [5,6,7,8] !< immobile (blocked)
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integer, dimension(*), parameter :: &
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dip = [9,10], & !< dipole
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imm_edg = imm(1:2), & !< immobile edge
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imm_scr = imm(3:4) !< immobile screw
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integer, parameter :: &
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mob_edg_pos = 1, & !< mobile edge positive
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mob_edg_neg = 2, & !< mobile edge negative
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mob_scr_pos = 3, & !< mobile screw positive
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mob_scr_neg = 4 !< mobile screw positive
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! BEGIN DEPRECATED
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integer, dimension(:,:,:), allocatable :: &
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iRhoU, & !< state indices for unblocked density
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iV, & !< state indices for dislocation velocities
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iD !< state indices for stable dipole height
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!END DEPRECATED
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real(pReal), dimension(:,:,:,:,:,:), allocatable :: &
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compatibility !< slip system compatibility between me and my neighbors
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type :: tInitialParameters !< container type for internal constitutive parameters
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real(pReal) :: &
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sigma_rho_u, & !< standard deviation of scatter in initial dislocation density
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random_rho_u, &
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random_rho_u_binning
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real(pReal), dimension(:), allocatable :: &
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rho_u_ed_pos_0, & !< initial edge_pos dislocation density
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rho_u_ed_neg_0, & !< initial edge_neg dislocation density
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rho_u_sc_pos_0, & !< initial screw_pos dislocation density
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rho_u_sc_neg_0, & !< initial screw_neg dislocation density
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rho_d_ed_0, & !< initial edge dipole dislocation density
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rho_d_sc_0 !< initial screw dipole dislocation density
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integer, dimension(:), allocatable :: &
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N_sl
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end type tInitialParameters
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type :: tParameters !< container type for internal constitutive parameters
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real(pReal) :: &
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V_at, & !< atomic volume
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D_0, & !< prefactor for self-diffusion coefficient
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Q_cl, & !< activation enthalpy for diffusion
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atol_rho, & !< absolute tolerance for dislocation density in state integration
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rho_significant, & !< density considered significant
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rho_min, & !< number of dislocations considered significant
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w, & !< width of a doubkle kink in multiples of the Burgers vector length b
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Q_sol, & !< activation energy for solid solution in J
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f_sol, & !< solid solution obstacle size in multiples of the Burgers vector length
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c_sol, & !< concentration of solid solution in atomic parts
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p, & !< parameter for kinetic law (Kocks,Argon,Ashby)
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q, & !< parameter for kinetic law (Kocks,Argon,Ashby)
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eta, & !< viscosity for dislocation glide in Pa s
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nu_a, & !< attack frequency in Hz
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chi_surface, & !< transmissivity at free surface
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chi_GB, & !< transmissivity at grain boundary (identified by different texture)
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f_c, & !< safety factor for CFL flux condition
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f_ed_mult, & !< factor that determines how much edge dislocations contribute to multiplication (0...1)
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f_F, &
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f_ed, &
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mu, &
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nu
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real(pReal), dimension(:), allocatable :: &
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d_ed, & !< minimum stable edge dipole height
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d_sc, & !< minimum stable screw dipole height
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tau_Peierls_ed, &
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tau_Peierls_sc, &
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i_sl, & !< mean free path prefactor for each
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b_sl !< absolute length of Burgers vector [m]
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real(pReal), dimension(:,:), allocatable :: &
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slip_normal, &
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slip_direction, &
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slip_transverse, &
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minDipoleHeight, & ! edge and screw
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peierlsstress, & ! edge and screw
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h_sl_sl ,& !< coefficients for slip-slip interaction
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forestProjection_Edge, & !< matrix of forest projections of edge dislocations
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forestProjection_Screw !< matrix of forest projections of screw dislocations
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real(pReal), dimension(:,:,:), allocatable :: &
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Schmid, & !< Schmid contribution
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nonSchmid_pos, &
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nonSchmid_neg !< combined projection of Schmid and non-Schmid contributions to the resolved shear stress (only for screws)
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integer :: &
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sum_N_sl
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integer, dimension(:), allocatable :: &
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colinearSystem !< colinear system to the active slip system (only valid for fcc!)
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character(len=pStringLen), dimension(:), allocatable :: &
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output
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logical :: &
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shortRangeStressCorrection, & !< use of short range stress correction by excess density gradient term
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nonSchmidActive = .false.
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end type tParameters
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type :: tNonlocalMicrostructure
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real(pReal), allocatable, dimension(:,:) :: &
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tau_pass, &
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tau_Back
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end type tNonlocalMicrostructure
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type :: tNonlocalState
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real(pReal), pointer, dimension(:,:) :: &
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rho, & ! < all dislocations
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rhoSgl, &
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rhoSglMobile, & ! iRhoU
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rho_sgl_mob_edg_pos, &
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rho_sgl_mob_edg_neg, &
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rho_sgl_mob_scr_pos, &
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rho_sgl_mob_scr_neg, &
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rhoSglImmobile, &
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rho_sgl_imm_edg_pos, &
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rho_sgl_imm_edg_neg, &
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rho_sgl_imm_scr_pos, &
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rho_sgl_imm_scr_neg, &
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rhoDip, &
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rho_dip_edg, &
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rho_dip_scr, &
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rho_forest, &
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gamma, &
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v, &
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v_edg_pos, &
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v_edg_neg, &
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v_scr_pos, &
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v_scr_neg
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end type tNonlocalState
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type(tNonlocalState), allocatable, dimension(:) :: &
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deltaState, &
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dotState, &
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state, &
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state0
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type(tParameters), dimension(:), allocatable :: param !< containers of constitutive parameters
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type(tNonlocalMicrostructure), dimension(:), allocatable :: microstructure
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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_nonlocal_init() result(myPlasticity)
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logical, dimension(:), allocatable :: myPlasticity
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integer :: &
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Ninstances, &
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ph, &
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Nmembers, &
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sizeState, sizeDotState, sizeDependentState, sizeDeltaState, &
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s1, s2, &
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s, t, l
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real(pReal), dimension(:), allocatable :: &
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a
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character(len=pStringLen) :: &
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extmsg = ''
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type(tInitialParameters) :: &
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ini
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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('nonlocal')
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Ninstances = count(myPlasticity)
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if(Ninstances == 0) then
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call geometry_plastic_nonlocal_disable
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return
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endif
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print'(/,a)', ' <<<+- phase:mechanical:plastic:nonlocal init -+>>>'
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print'(a,i0)', ' # phases: ',Ninstances; flush(IO_STDOUT)
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print*, 'C. Reuber et al., Acta Materialia 71:333–348, 2014'
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print*, 'https://doi.org/10.1016/j.actamat.2014.03.012'//IO_EOL
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print*, 'C. Kords, Dissertation RWTH Aachen, 2014'
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print*, 'http://publications.rwth-aachen.de/record/229993'
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phases => config_material%get('phase')
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allocate(geom(phases%length))
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allocate(param(phases%length))
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allocate(state(phases%length))
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allocate(state0(phases%length))
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allocate(dotState(phases%length))
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allocate(deltaState(phases%length))
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allocate(microstructure(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), &
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st0 => state0(ph), del => deltaState(ph), dst => microstructure(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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phase_localPlasticity(ph) = .not. pl%contains('nonlocal')
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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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prm%atol_rho = pl%get_asFloat('atol_rho',defaultVal=1.0e4_pReal)
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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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prm%nu = lattice_nu(ph)
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ini%N_sl = pl%get_as1dInt('N_sl',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(abs(ini%N_sl))
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slipActive: if (prm%sum_N_sl > 0) then
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prm%Schmid = lattice_SchmidMatrix_slip(ini%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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if(size(a) > 0) prm%nonSchmidActive = .true.
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prm%nonSchmid_pos = lattice_nonSchmidMatrix(ini%N_sl,a,+1)
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prm%nonSchmid_neg = lattice_nonSchmidMatrix(ini%N_sl,a,-1)
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else
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prm%nonSchmid_pos = prm%Schmid
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prm%nonSchmid_neg = prm%Schmid
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endif
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prm%h_sl_sl = lattice_interaction_SlipBySlip(ini%N_sl, &
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pl%get_as1dFloat('h_sl_sl'), &
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phase%get_asString('lattice'))
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prm%forestProjection_edge = lattice_forestProjection_edge (ini%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_screw = lattice_forestProjection_screw(ini%N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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prm%slip_direction = lattice_slip_direction (ini%N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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prm%slip_transverse = lattice_slip_transverse(ini%N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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prm%slip_normal = lattice_slip_normal (ini%N_sl,phase%get_asString('lattice'),&
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phase%get_asFloat('c/a',defaultVal=0.0_pReal))
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! collinear systems (only for octahedral slip systems in fcc)
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allocate(prm%colinearSystem(prm%sum_N_sl), source = -1)
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do s1 = 1, prm%sum_N_sl
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do s2 = 1, prm%sum_N_sl
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if (all(dEq0 (math_cross(prm%slip_direction(1:3,s1),prm%slip_direction(1:3,s2)))) .and. &
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any(dNeq0(math_cross(prm%slip_normal (1:3,s1),prm%slip_normal (1:3,s2))))) &
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prm%colinearSystem(s1) = s2
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enddo
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enddo
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ini%rho_u_ed_pos_0 = pl%get_as1dFloat('rho_u_ed_pos_0', requiredSize=size(ini%N_sl))
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ini%rho_u_ed_neg_0 = pl%get_as1dFloat('rho_u_ed_neg_0', requiredSize=size(ini%N_sl))
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ini%rho_u_sc_pos_0 = pl%get_as1dFloat('rho_u_sc_pos_0', requiredSize=size(ini%N_sl))
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ini%rho_u_sc_neg_0 = pl%get_as1dFloat('rho_u_sc_neg_0', requiredSize=size(ini%N_sl))
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ini%rho_d_ed_0 = pl%get_as1dFloat('rho_d_ed_0', requiredSize=size(ini%N_sl))
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ini%rho_d_sc_0 = pl%get_as1dFloat('rho_d_sc_0', requiredSize=size(ini%N_sl))
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prm%i_sl = pl%get_as1dFloat('i_sl', requiredSize=size(ini%N_sl))
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prm%b_sl = pl%get_as1dFloat('b_sl', requiredSize=size(ini%N_sl))
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prm%i_sl = math_expand(prm%i_sl,ini%N_sl)
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prm%b_sl = math_expand(prm%b_sl,ini%N_sl)
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prm%d_ed = pl%get_as1dFloat('d_ed', requiredSize=size(ini%N_sl))
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prm%d_sc = pl%get_as1dFloat('d_sc', requiredSize=size(ini%N_sl))
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prm%d_ed = math_expand(prm%d_ed,ini%N_sl)
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prm%d_sc = math_expand(prm%d_sc,ini%N_sl)
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allocate(prm%minDipoleHeight(prm%sum_N_sl,2))
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prm%minDipoleHeight(:,1) = prm%d_ed
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prm%minDipoleHeight(:,2) = prm%d_sc
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prm%tau_Peierls_ed = pl%get_as1dFloat('tau_Peierls_ed', requiredSize=size(ini%N_sl))
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prm%tau_Peierls_sc = pl%get_as1dFloat('tau_Peierls_sc', requiredSize=size(ini%N_sl))
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prm%tau_Peierls_ed = math_expand(prm%tau_Peierls_ed,ini%N_sl)
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prm%tau_Peierls_sc = math_expand(prm%tau_Peierls_sc,ini%N_sl)
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allocate(prm%peierlsstress(prm%sum_N_sl,2))
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prm%peierlsstress(:,1) = prm%tau_Peierls_ed
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prm%peierlsstress(:,2) = prm%tau_Peierls_sc
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prm%rho_significant = pl%get_asFloat('rho_significant')
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prm%rho_min = pl%get_asFloat('rho_min', 0.0_pReal)
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prm%f_c = pl%get_asFloat('f_c',defaultVal=2.0_pReal)
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prm%V_at = pl%get_asFloat('V_at')
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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_F = pl%get_asFloat('f_F')
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prm%f_ed = pl%get_asFloat('f_ed') !,'edgejogs'
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prm%w = pl%get_asFloat('w')
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prm%Q_sol = pl%get_asFloat('Q_sol')
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prm%f_sol = pl%get_asFloat('f_sol')
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prm%c_sol = pl%get_asFloat('c_sol')
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prm%p = pl%get_asFloat('p_sl')
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prm%q = pl%get_asFloat('q_sl')
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prm%eta = pl%get_asFloat('eta')
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prm%nu_a = pl%get_asFloat('nu_a')
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! ToDo: discuss logic
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ini%sigma_rho_u = pl%get_asFloat('sigma_rho_u')
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ini%random_rho_u = pl%get_asFloat('random_rho_u',defaultVal= 0.0_pReal)
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if (pl%contains('random_rho_u')) &
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ini%random_rho_u_binning = pl%get_asFloat('random_rho_u_binning',defaultVal=0.0_pReal) !ToDo: useful default?
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! if (rhoSglRandom(instance) < 0.0_pReal) &
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! if (rhoSglRandomBinning(instance) <= 0.0_pReal) &
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prm%chi_surface = pl%get_asFloat('chi_surface',defaultVal=1.0_pReal)
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prm%chi_GB = pl%get_asFloat('chi_GB', defaultVal=-1.0_pReal)
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prm%f_ed_mult = pl%get_asFloat('f_ed_mult')
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prm%shortRangeStressCorrection = pl%get_asBool('short_range_stress_correction', defaultVal = .false.)
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!--------------------------------------------------------------------------------------------------
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! sanity checks
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if (any(prm%b_sl < 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
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if (any(prm%i_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' i_sl'
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if (any(ini%rho_u_ed_pos_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_u_ed_pos_0'
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if (any(ini%rho_u_ed_neg_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_u_ed_neg_0'
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if (any(ini%rho_u_sc_pos_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_u_sc_pos_0'
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if (any(ini%rho_u_sc_neg_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_u_sc_neg_0'
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if (any(ini%rho_d_ed_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_d_ed_0'
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if (any(ini%rho_d_sc_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_d_sc_0'
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if (any(prm%peierlsstress < 0.0_pReal)) extmsg = trim(extmsg)//' tau_peierls'
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if (any(prm%minDipoleHeight < 0.0_pReal)) extmsg = trim(extmsg)//' d_ed or d_sc'
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if (prm%eta <= 0.0_pReal) extmsg = trim(extmsg)//' eta'
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if (prm%Q_cl <= 0.0_pReal) extmsg = trim(extmsg)//' Q_cl'
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if (prm%nu_a <= 0.0_pReal) extmsg = trim(extmsg)//' nu_a'
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if (prm%w <= 0.0_pReal) extmsg = trim(extmsg)//' w'
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if (prm%D_0 < 0.0_pReal) extmsg = trim(extmsg)//' D_0'
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if (prm%V_at <= 0.0_pReal) extmsg = trim(extmsg)//' V_at' ! ToDo: in dislotungsten, the atomic volume is given as a factor
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if (prm%rho_min < 0.0_pReal) extmsg = trim(extmsg)//' rho_min'
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if (prm%rho_significant < 0.0_pReal) extmsg = trim(extmsg)//' rho_significant'
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if (prm%atol_rho < 0.0_pReal) extmsg = trim(extmsg)//' atol_rho'
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if (prm%f_c < 0.0_pReal) extmsg = trim(extmsg)//' f_c'
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if (prm%p <= 0.0_pReal .or. prm%p > 1.0_pReal) extmsg = trim(extmsg)//' p_sl'
|
||
if (prm%q < 1.0_pReal .or. prm%q > 2.0_pReal) extmsg = trim(extmsg)//' q_sl'
|
||
|
||
if (prm%f_F < 0.0_pReal .or. prm%f_F > 1.0_pReal) &
|
||
extmsg = trim(extmsg)//' f_F'
|
||
if (prm%f_ed < 0.0_pReal .or. prm%f_ed > 1.0_pReal) &
|
||
extmsg = trim(extmsg)//' f_ed'
|
||
|
||
if (prm%Q_sol <= 0.0_pReal) extmsg = trim(extmsg)//' Q_sol'
|
||
if (prm%f_sol <= 0.0_pReal) extmsg = trim(extmsg)//' f_sol'
|
||
if (prm%c_sol <= 0.0_pReal) extmsg = trim(extmsg)//' c_sol'
|
||
|
||
if (prm%chi_GB > 1.0_pReal) extmsg = trim(extmsg)//' chi_GB'
|
||
if (prm%chi_surface < 0.0_pReal .or. prm%chi_surface > 1.0_pReal) &
|
||
extmsg = trim(extmsg)//' chi_surface'
|
||
|
||
if (prm%f_ed_mult < 0.0_pReal .or. prm%f_ed_mult > 1.0_pReal) &
|
||
extmsg = trim(extmsg)//' f_ed_mult'
|
||
|
||
endif slipActive
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
Nmembers = count(material_phaseAt2 == ph)
|
||
sizeDotState = size([ 'rhoSglEdgePosMobile ','rhoSglEdgeNegMobile ', &
|
||
'rhoSglScrewPosMobile ','rhoSglScrewNegMobile ', &
|
||
'rhoSglEdgePosImmobile ','rhoSglEdgeNegImmobile ', &
|
||
'rhoSglScrewPosImmobile','rhoSglScrewNegImmobile', &
|
||
'rhoDipEdge ','rhoDipScrew ', &
|
||
'gamma ' ]) * prm%sum_N_sl !< "basic" microstructural state variables that are independent from other state variables
|
||
sizeDependentState = size([ 'rhoForest ']) * prm%sum_N_sl !< microstructural state variables that depend on other state variables
|
||
sizeState = sizeDotState + sizeDependentState &
|
||
+ size([ 'velocityEdgePos ','velocityEdgeNeg ', &
|
||
'velocityScrewPos ','velocityScrewNeg ', &
|
||
'maxDipoleHeightEdge ','maxDipoleHeightScrew' ]) * prm%sum_N_sl !< other dependent state variables that are not updated by microstructure
|
||
sizeDeltaState = sizeDotState
|
||
|
||
call phase_allocateState(plasticState(ph),Nmembers,sizeState,sizeDotState,sizeDeltaState)
|
||
|
||
allocate(geom(ph)%V_0(Nmembers))
|
||
call storeGeometry(ph)
|
||
|
||
plasticState(ph)%nonlocal = pl%get_asBool('nonlocal')
|
||
if(plasticState(ph)%nonlocal .and. .not. allocated(IPneighborhood)) &
|
||
call IO_error(212,ext_msg='IPneighborhood does not exist')
|
||
|
||
|
||
plasticState(ph)%offsetDeltaState = 0 ! ToDo: state structure does not follow convention
|
||
|
||
st0%rho => plasticState(ph)%state0 (0*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
stt%rho => plasticState(ph)%state (0*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
dot%rho => plasticState(ph)%dotState (0*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
del%rho => plasticState(ph)%deltaState (0*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
plasticState(ph)%atol(1:10*prm%sum_N_sl) = prm%atol_rho
|
||
|
||
stt%rhoSgl => plasticState(ph)%state (0*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
dot%rhoSgl => plasticState(ph)%dotState (0*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
del%rhoSgl => plasticState(ph)%deltaState (0*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
|
||
stt%rhoSglMobile => plasticState(ph)%state (0*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
dot%rhoSglMobile => plasticState(ph)%dotState (0*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
del%rhoSglMobile => plasticState(ph)%deltaState (0*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_mob_edg_pos => plasticState(ph)%state (0*prm%sum_N_sl+1: 1*prm%sum_N_sl,:)
|
||
dot%rho_sgl_mob_edg_pos => plasticState(ph)%dotState (0*prm%sum_N_sl+1: 1*prm%sum_N_sl,:)
|
||
del%rho_sgl_mob_edg_pos => plasticState(ph)%deltaState (0*prm%sum_N_sl+1: 1*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_mob_edg_neg => plasticState(ph)%state (1*prm%sum_N_sl+1: 2*prm%sum_N_sl,:)
|
||
dot%rho_sgl_mob_edg_neg => plasticState(ph)%dotState (1*prm%sum_N_sl+1: 2*prm%sum_N_sl,:)
|
||
del%rho_sgl_mob_edg_neg => plasticState(ph)%deltaState (1*prm%sum_N_sl+1: 2*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_mob_scr_pos => plasticState(ph)%state (2*prm%sum_N_sl+1: 3*prm%sum_N_sl,:)
|
||
dot%rho_sgl_mob_scr_pos => plasticState(ph)%dotState (2*prm%sum_N_sl+1: 3*prm%sum_N_sl,:)
|
||
del%rho_sgl_mob_scr_pos => plasticState(ph)%deltaState (2*prm%sum_N_sl+1: 3*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_mob_scr_neg => plasticState(ph)%state (3*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
dot%rho_sgl_mob_scr_neg => plasticState(ph)%dotState (3*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
del%rho_sgl_mob_scr_neg => plasticState(ph)%deltaState (3*prm%sum_N_sl+1: 4*prm%sum_N_sl,:)
|
||
|
||
stt%rhoSglImmobile => plasticState(ph)%state (4*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
dot%rhoSglImmobile => plasticState(ph)%dotState (4*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
del%rhoSglImmobile => plasticState(ph)%deltaState (4*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_imm_edg_pos => plasticState(ph)%state (4*prm%sum_N_sl+1: 5*prm%sum_N_sl,:)
|
||
dot%rho_sgl_imm_edg_pos => plasticState(ph)%dotState (4*prm%sum_N_sl+1: 5*prm%sum_N_sl,:)
|
||
del%rho_sgl_imm_edg_pos => plasticState(ph)%deltaState (4*prm%sum_N_sl+1: 5*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_imm_edg_neg => plasticState(ph)%state (5*prm%sum_N_sl+1: 6*prm%sum_N_sl,:)
|
||
dot%rho_sgl_imm_edg_neg => plasticState(ph)%dotState (5*prm%sum_N_sl+1: 6*prm%sum_N_sl,:)
|
||
del%rho_sgl_imm_edg_neg => plasticState(ph)%deltaState (5*prm%sum_N_sl+1: 6*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_imm_scr_pos => plasticState(ph)%state (6*prm%sum_N_sl+1: 7*prm%sum_N_sl,:)
|
||
dot%rho_sgl_imm_scr_pos => plasticState(ph)%dotState (6*prm%sum_N_sl+1: 7*prm%sum_N_sl,:)
|
||
del%rho_sgl_imm_scr_pos => plasticState(ph)%deltaState (6*prm%sum_N_sl+1: 7*prm%sum_N_sl,:)
|
||
|
||
stt%rho_sgl_imm_scr_neg => plasticState(ph)%state (7*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
dot%rho_sgl_imm_scr_neg => plasticState(ph)%dotState (7*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
del%rho_sgl_imm_scr_neg => plasticState(ph)%deltaState (7*prm%sum_N_sl+1: 8*prm%sum_N_sl,:)
|
||
|
||
stt%rhoDip => plasticState(ph)%state (8*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
dot%rhoDip => plasticState(ph)%dotState (8*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
del%rhoDip => plasticState(ph)%deltaState (8*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
|
||
stt%rho_dip_edg => plasticState(ph)%state (8*prm%sum_N_sl+1: 9*prm%sum_N_sl,:)
|
||
dot%rho_dip_edg => plasticState(ph)%dotState (8*prm%sum_N_sl+1: 9*prm%sum_N_sl,:)
|
||
del%rho_dip_edg => plasticState(ph)%deltaState (8*prm%sum_N_sl+1: 9*prm%sum_N_sl,:)
|
||
|
||
stt%rho_dip_scr => plasticState(ph)%state (9*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
dot%rho_dip_scr => plasticState(ph)%dotState (9*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
del%rho_dip_scr => plasticState(ph)%deltaState (9*prm%sum_N_sl+1:10*prm%sum_N_sl,:)
|
||
|
||
stt%gamma => plasticState(ph)%state (10*prm%sum_N_sl + 1:11*prm%sum_N_sl,1:Nmembers)
|
||
dot%gamma => plasticState(ph)%dotState (10*prm%sum_N_sl + 1:11*prm%sum_N_sl,1:Nmembers)
|
||
del%gamma => plasticState(ph)%deltaState (10*prm%sum_N_sl + 1:11*prm%sum_N_sl,1:Nmembers)
|
||
plasticState(ph)%atol(10*prm%sum_N_sl+1:11*prm%sum_N_sl ) = pl%get_asFloat('atol_gamma', defaultVal = 1.0e-2_pReal)
|
||
if(any(plasticState(ph)%atol(10*prm%sum_N_sl+1:11*prm%sum_N_sl) < 0.0_pReal)) &
|
||
extmsg = trim(extmsg)//' atol_gamma'
|
||
plasticState(ph)%slipRate => plasticState(ph)%dotState (10*prm%sum_N_sl + 1:11*prm%sum_N_sl,1:Nmembers)
|
||
|
||
stt%rho_forest => plasticState(ph)%state (11*prm%sum_N_sl + 1:12*prm%sum_N_sl,1:Nmembers)
|
||
stt%v => plasticState(ph)%state (12*prm%sum_N_sl + 1:16*prm%sum_N_sl,1:Nmembers)
|
||
stt%v_edg_pos => plasticState(ph)%state (12*prm%sum_N_sl + 1:13*prm%sum_N_sl,1:Nmembers)
|
||
stt%v_edg_neg => plasticState(ph)%state (13*prm%sum_N_sl + 1:14*prm%sum_N_sl,1:Nmembers)
|
||
stt%v_scr_pos => plasticState(ph)%state (14*prm%sum_N_sl + 1:15*prm%sum_N_sl,1:Nmembers)
|
||
stt%v_scr_neg => plasticState(ph)%state (15*prm%sum_N_sl + 1:16*prm%sum_N_sl,1:Nmembers)
|
||
|
||
allocate(dst%tau_pass(prm%sum_N_sl,Nmembers),source=0.0_pReal)
|
||
allocate(dst%tau_back(prm%sum_N_sl,Nmembers),source=0.0_pReal)
|
||
end associate
|
||
|
||
if (Nmembers > 0) call stateInit(ini,ph,Nmembers)
|
||
plasticState(ph)%state0 = plasticState(ph)%state
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! exit if any parameter is out of range
|
||
if (extmsg /= '') call IO_error(211,ext_msg=trim(extmsg)//'(nonlocal)')
|
||
|
||
enddo
|
||
|
||
allocate(compatibility(2,maxval(param%sum_N_sl),maxval(param%sum_N_sl),nIPneighbors,&
|
||
discretization_nIPs,discretization_Nelems), source=0.0_pReal)
|
||
|
||
! BEGIN DEPRECATED----------------------------------------------------------------------------------
|
||
allocate(iRhoU(maxval(param%sum_N_sl),4,phases%length), source=0)
|
||
allocate(iV(maxval(param%sum_N_sl),4,phases%length), source=0)
|
||
allocate(iD(maxval(param%sum_N_sl),2,phases%length), source=0)
|
||
|
||
do ph = 1, phases%length
|
||
|
||
if(.not. myPlasticity(ph)) cycle
|
||
|
||
phase => phases%get(ph)
|
||
Nmembers = count(material_phaseAt2 == ph)
|
||
l = 0
|
||
do t = 1,4
|
||
do s = 1,param(ph)%sum_N_sl
|
||
l = l + 1
|
||
iRhoU(s,t,ph) = l
|
||
enddo
|
||
enddo
|
||
l = l + (4+2+1+1)*param(ph)%sum_N_sl ! immobile(4), dipole(2), shear, forest
|
||
do t = 1,4
|
||
do s = 1,param(ph)%sum_N_sl
|
||
l = l + 1
|
||
iV(s,t,ph) = l
|
||
enddo
|
||
enddo
|
||
do t = 1,2
|
||
do s = 1,param(ph)%sum_N_sl
|
||
l = l + 1
|
||
iD(s,t,ph) = l
|
||
enddo
|
||
enddo
|
||
if (iD(param(ph)%sum_N_sl,2,ph) /= plasticState(ph)%sizeState) &
|
||
error stop 'state indices not properly set (nonlocal)'
|
||
enddo
|
||
|
||
end function plastic_nonlocal_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates quantities characterizing the microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine nonlocal_dependentState(ph, me, ip, el)
|
||
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
me, &
|
||
ip, &
|
||
el
|
||
|
||
integer :: &
|
||
no, & !< neighbor offset
|
||
neighbor_el, & ! element number of neighboring material point
|
||
neighbor_ip, & ! integration point of neighboring material point
|
||
c, & ! index of dilsocation character (edge, screw)
|
||
s, & ! slip system index
|
||
dir, &
|
||
n
|
||
real(pReal) :: &
|
||
FVsize, &
|
||
nRealNeighbors ! number of really existing neighbors
|
||
integer, dimension(2) :: &
|
||
neighbors
|
||
real(pReal), dimension(2) :: &
|
||
rhoExcessGradient, &
|
||
rhoExcessGradient_over_rho, &
|
||
rhoTotal
|
||
real(pReal), dimension(3) :: &
|
||
rhoExcessDifferences, &
|
||
normal_latticeConf
|
||
real(pReal), dimension(3,3) :: &
|
||
invFe, & !< inverse of elastic deformation gradient
|
||
invFp, & !< inverse of plastic deformation gradient
|
||
connections, &
|
||
invConnections
|
||
real(pReal), dimension(3,nIPneighbors) :: &
|
||
connection_latticeConf
|
||
real(pReal), dimension(2,param(ph)%sum_N_sl) :: &
|
||
rhoExcess
|
||
real(pReal), dimension(param(ph)%sum_N_sl) :: &
|
||
rho_edg_delta, &
|
||
rho_scr_delta
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
rho, &
|
||
rho0, &
|
||
rho_neighbor0
|
||
real(pReal), dimension(param(ph)%sum_N_sl,param(ph)%sum_N_sl) :: &
|
||
myInteractionMatrix ! corrected slip interaction matrix
|
||
real(pReal), dimension(param(ph)%sum_N_sl,nIPneighbors) :: &
|
||
rho_edg_delta_neighbor, &
|
||
rho_scr_delta_neighbor
|
||
real(pReal), dimension(2,maxval(param%sum_N_sl),nIPneighbors) :: &
|
||
neighbor_rhoExcess, & ! excess density at neighboring material point
|
||
neighbor_rhoTotal ! total density at neighboring material point
|
||
real(pReal), dimension(3,param(ph)%sum_N_sl,2) :: &
|
||
m ! direction of dislocation motion
|
||
|
||
associate(prm => param(ph),dst => microstructure(ph), stt => state(ph))
|
||
|
||
rho = getRho(ph,me)
|
||
|
||
stt%rho_forest(:,me) = matmul(prm%forestProjection_Edge, sum(abs(rho(:,edg)),2)) &
|
||
+ matmul(prm%forestProjection_Screw,sum(abs(rho(:,scr)),2))
|
||
|
||
|
||
! coefficients are corrected for the line tension effect
|
||
! (see Kubin,Devincre,Hoc; 2008; Modeling dislocation storage rates and mean free paths in face-centered cubic crystals)
|
||
if (any(lattice_structure(material_phaseAt(1,el)) == [LATTICE_bcc_ID,LATTICE_fcc_ID])) then
|
||
myInteractionMatrix = prm%h_sl_sl &
|
||
* spread(( 1.0_pReal - prm%f_F &
|
||
+ prm%f_F &
|
||
* log(0.35_pReal * prm%b_sl * sqrt(max(stt%rho_forest(:,me),prm%rho_significant))) &
|
||
/ log(0.35_pReal * prm%b_sl * 1e6_pReal))** 2.0_pReal,2,prm%sum_N_sl)
|
||
else
|
||
myInteractionMatrix = prm%h_sl_sl
|
||
endif
|
||
|
||
dst%tau_pass(:,me) = prm%mu * prm%b_sl &
|
||
* sqrt(matmul(myInteractionMatrix,sum(abs(rho),2)))
|
||
|
||
!*** calculate the dislocation stress of the neighboring excess dislocation densities
|
||
!*** zero for material points of local plasticity
|
||
|
||
!#################################################################################################
|
||
! ToDo: MD: this is most likely only correct for F_i = I
|
||
!#################################################################################################
|
||
|
||
rho0 = getRho0(ph,me)
|
||
if (.not. phase_localPlasticity(material_phaseAt(1,el)) .and. prm%shortRangeStressCorrection) then
|
||
invFp = math_inv33(phase_mechanical_Fp(ph)%data(1:3,1:3,me))
|
||
invFe = math_inv33(phase_mechanical_Fe(ph)%data(1:3,1:3,me))
|
||
|
||
rho_edg_delta = rho0(:,mob_edg_pos) - rho0(:,mob_edg_neg)
|
||
rho_scr_delta = rho0(:,mob_scr_pos) - rho0(:,mob_scr_neg)
|
||
|
||
rhoExcess(1,:) = rho_edg_delta
|
||
rhoExcess(2,:) = rho_scr_delta
|
||
|
||
FVsize = geom(ph)%V_0(me) ** (1.0_pReal/3.0_pReal)
|
||
|
||
!* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities
|
||
|
||
nRealNeighbors = 0.0_pReal
|
||
neighbor_rhoTotal = 0.0_pReal
|
||
do n = 1,nIPneighbors
|
||
neighbor_el = IPneighborhood(1,n,ip,el)
|
||
neighbor_ip = IPneighborhood(2,n,ip,el)
|
||
no = material_phasememberAt(1,neighbor_ip,neighbor_el)
|
||
if (neighbor_el > 0 .and. neighbor_ip > 0) then
|
||
if (material_phaseAt(1,neighbor_el) == ph) then
|
||
|
||
nRealNeighbors = nRealNeighbors + 1.0_pReal
|
||
rho_neighbor0 = getRho0(ph,no)
|
||
|
||
rho_edg_delta_neighbor(:,n) = rho_neighbor0(:,mob_edg_pos) - rho_neighbor0(:,mob_edg_neg)
|
||
rho_scr_delta_neighbor(:,n) = rho_neighbor0(:,mob_scr_pos) - rho_neighbor0(:,mob_scr_neg)
|
||
|
||
neighbor_rhoTotal(1,:,n) = sum(abs(rho_neighbor0(:,edg)),2)
|
||
neighbor_rhoTotal(2,:,n) = sum(abs(rho_neighbor0(:,scr)),2)
|
||
|
||
connection_latticeConf(1:3,n) = matmul(invFe, discretization_IPcoords(1:3,neighbor_el+neighbor_ip-1) &
|
||
- discretization_IPcoords(1:3,el+neighbor_ip-1))
|
||
normal_latticeConf = matmul(transpose(invFp), IPareaNormal(1:3,n,ip,el))
|
||
if (math_inner(normal_latticeConf,connection_latticeConf(1:3,n)) < 0.0_pReal) & ! neighboring connection points in opposite direction to face normal: must be periodic image
|
||
connection_latticeConf(1:3,n) = normal_latticeConf * IPvolume(ip,el)/IParea(n,ip,el) ! instead take the surface normal scaled with the diameter of the cell
|
||
else
|
||
! local neighbor or different lattice structure or different constitution instance -> use central values instead
|
||
connection_latticeConf(1:3,n) = 0.0_pReal
|
||
rho_edg_delta_neighbor(:,n) = rho_edg_delta
|
||
rho_scr_delta_neighbor(:,n) = rho_scr_delta
|
||
endif
|
||
else
|
||
! free surface -> use central values instead
|
||
connection_latticeConf(1:3,n) = 0.0_pReal
|
||
rho_edg_delta_neighbor(:,n) = rho_edg_delta
|
||
rho_scr_delta_neighbor(:,n) = rho_scr_delta
|
||
endif
|
||
enddo
|
||
|
||
neighbor_rhoExcess(1,:,:) = rho_edg_delta_neighbor
|
||
neighbor_rhoExcess(2,:,:) = rho_scr_delta_neighbor
|
||
|
||
!* loop through the slip systems and calculate the dislocation gradient by
|
||
!* 1. interpolation of the excess density in the neighorhood
|
||
!* 2. interpolation of the dead dislocation density in the central volume
|
||
m(1:3,:,1) = prm%slip_direction
|
||
m(1:3,:,2) = -prm%slip_transverse
|
||
|
||
do s = 1,prm%sum_N_sl
|
||
|
||
! gradient from interpolation of neighboring excess density ...
|
||
do c = 1,2
|
||
do dir = 1,3
|
||
neighbors(1) = 2 * dir - 1
|
||
neighbors(2) = 2 * dir
|
||
connections(dir,1:3) = connection_latticeConf(1:3,neighbors(1)) &
|
||
- connection_latticeConf(1:3,neighbors(2))
|
||
rhoExcessDifferences(dir) = neighbor_rhoExcess(c,s,neighbors(1)) &
|
||
- neighbor_rhoExcess(c,s,neighbors(2))
|
||
enddo
|
||
invConnections = math_inv33(connections)
|
||
if (all(dEq0(invConnections))) call IO_error(-1,ext_msg='back stress calculation: inversion error')
|
||
|
||
rhoExcessGradient(c) = math_inner(m(1:3,s,c), matmul(invConnections,rhoExcessDifferences))
|
||
enddo
|
||
|
||
! ... plus gradient from deads ...
|
||
rhoExcessGradient(1) = rhoExcessGradient(1) + sum(rho(s,imm_edg)) / FVsize
|
||
rhoExcessGradient(2) = rhoExcessGradient(2) + sum(rho(s,imm_scr)) / FVsize
|
||
|
||
! ... normalized with the total density ...
|
||
rhoTotal(1) = (sum(abs(rho(s,edg))) + sum(neighbor_rhoTotal(1,s,:))) / (1.0_pReal + nRealNeighbors)
|
||
rhoTotal(2) = (sum(abs(rho(s,scr))) + sum(neighbor_rhoTotal(2,s,:))) / (1.0_pReal + nRealNeighbors)
|
||
|
||
rhoExcessGradient_over_rho = 0.0_pReal
|
||
where(rhoTotal > 0.0_pReal) rhoExcessGradient_over_rho = rhoExcessGradient / rhoTotal
|
||
|
||
! ... gives the local stress correction when multiplied with a factor
|
||
dst%tau_back(s,me) = - prm%mu * prm%b_sl(s) / (2.0_pReal * PI) &
|
||
* ( rhoExcessGradient_over_rho(1) / (1.0_pReal - prm%nu) &
|
||
+ rhoExcessGradient_over_rho(2))
|
||
enddo
|
||
endif
|
||
|
||
#ifdef DEBUG
|
||
if (debugConstitutive%extensive &
|
||
.and. ((debugConstitutive%element == el .and. debugConstitutive%ip == ip)&
|
||
.or. .not. debugConstitutive%selective)) then
|
||
print'(/,a,i8,1x,i2,1x,i1,/)', '<< CONST >> nonlocal_microstructure at el ip ',el,ip
|
||
print'(a,/,12x,12(e10.3,1x))', '<< CONST >> rhoForest', stt%rho_forest(:,me)
|
||
print'(a,/,12x,12(f10.5,1x))', '<< CONST >> tauThreshold / MPa', dst%tau_pass(:,me)*1e-6
|
||
print'(a,/,12x,12(f10.5,1x),/)', '<< CONST >> tauBack / MPa', dst%tau_back(:,me)*1e-6
|
||
endif
|
||
#endif
|
||
|
||
end associate
|
||
|
||
end subroutine nonlocal_dependentState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates plastic velocity gradient and its tangent
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine nonlocal_LpAndItsTangent(Lp,dLp_dMp, &
|
||
Mp,Temperature,ph,me)
|
||
real(pReal), dimension(3,3), intent(out) :: &
|
||
Lp !< plastic velocity gradient
|
||
real(pReal), dimension(3,3,3,3), intent(out) :: &
|
||
dLp_dMp
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
me
|
||
real(pReal), intent(in) :: &
|
||
Temperature !< temperature
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp
|
||
!< derivative of Lp with respect to Mp
|
||
integer :: &
|
||
ns, & !< short notation for the total number of active slip systems
|
||
i, &
|
||
j, &
|
||
k, &
|
||
l, &
|
||
t, & !< dislocation type
|
||
s !< index of my current slip system
|
||
real(pReal), dimension(param(ph)%sum_N_sl,8) :: &
|
||
rhoSgl !< single dislocation densities (including blocked)
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
rho
|
||
real(pReal), dimension(param(ph)%sum_N_sl,4) :: &
|
||
v, & !< velocity
|
||
tauNS, & !< resolved shear stress including non Schmid and backstress terms
|
||
dv_dtau, & !< velocity derivative with respect to the shear stress
|
||
dv_dtauNS !< velocity derivative with respect to the shear stress
|
||
real(pReal), dimension(param(ph)%sum_N_sl) :: &
|
||
tau, & !< resolved shear stress including backstress terms
|
||
gdotTotal !< shear rate
|
||
|
||
associate(prm => param(ph),dst=>microstructure(ph),&
|
||
stt=>state(ph))
|
||
ns = prm%sum_N_sl
|
||
|
||
!*** shortcut to state variables
|
||
rho = getRho(ph,me)
|
||
rhoSgl = rho(:,sgl)
|
||
|
||
do s = 1,ns
|
||
tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s))
|
||
tauNS(s,1) = tau(s)
|
||
tauNS(s,2) = tau(s)
|
||
if (tau(s) > 0.0_pReal) then
|
||
tauNS(s,3) = math_tensordot(Mp, +prm%nonSchmid_pos(1:3,1:3,s))
|
||
tauNS(s,4) = math_tensordot(Mp, -prm%nonSchmid_neg(1:3,1:3,s))
|
||
else
|
||
tauNS(s,3) = math_tensordot(Mp, +prm%nonSchmid_neg(1:3,1:3,s))
|
||
tauNS(s,4) = math_tensordot(Mp, -prm%nonSchmid_pos(1:3,1:3,s))
|
||
endif
|
||
enddo
|
||
tauNS = tauNS + spread(dst%tau_back(:,me),2,4)
|
||
tau = tau + dst%tau_back(:,me)
|
||
|
||
! edges
|
||
call kinetics(v(:,1), dv_dtau(:,1), dv_dtauNS(:,1), &
|
||
tau, tauNS(:,1), dst%tau_pass(:,me),1,Temperature, ph)
|
||
v(:,2) = v(:,1)
|
||
dv_dtau(:,2) = dv_dtau(:,1)
|
||
dv_dtauNS(:,2) = dv_dtauNS(:,1)
|
||
|
||
!screws
|
||
if (prm%nonSchmidActive) then
|
||
do t = 3,4
|
||
call kinetics(v(:,t), dv_dtau(:,t), dv_dtauNS(:,t), &
|
||
tau, tauNS(:,t), dst%tau_pass(:,me),2,Temperature, ph)
|
||
enddo
|
||
else
|
||
v(:,3:4) = spread(v(:,1),2,2)
|
||
dv_dtau(:,3:4) = spread(dv_dtau(:,1),2,2)
|
||
dv_dtauNS(:,3:4) = spread(dv_dtauNS(:,1),2,2)
|
||
endif
|
||
|
||
stt%v(:,me) = pack(v,.true.)
|
||
|
||
!*** Bauschinger effect
|
||
forall (s = 1:ns, t = 5:8, rhoSgl(s,t) * v(s,t-4) < 0.0_pReal) &
|
||
rhoSgl(s,t-4) = rhoSgl(s,t-4) + abs(rhoSgl(s,t))
|
||
|
||
gdotTotal = sum(rhoSgl(:,1:4) * v, 2) * prm%b_sl
|
||
|
||
Lp = 0.0_pReal
|
||
dLp_dMp = 0.0_pReal
|
||
do s = 1,ns
|
||
Lp = Lp + gdotTotal(s) * prm%Schmid(1:3,1:3,s)
|
||
forall (i=1:3,j=1:3,k=1:3,l=1:3) &
|
||
dLp_dMp(i,j,k,l) = dLp_dMp(i,j,k,l) &
|
||
+ prm%Schmid(i,j,s) * prm%Schmid(k,l,s) &
|
||
* sum(rhoSgl(s,1:4) * dv_dtau(s,1:4)) * prm%b_sl(s) &
|
||
+ prm%Schmid(i,j,s) &
|
||
* (+ prm%nonSchmid_pos(k,l,s) * rhoSgl(s,3) * dv_dtauNS(s,3) &
|
||
- prm%nonSchmid_neg(k,l,s) * rhoSgl(s,4) * dv_dtauNS(s,4)) * prm%b_sl(s)
|
||
enddo
|
||
|
||
end associate
|
||
|
||
end subroutine nonlocal_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief (instantaneous) incremental change of microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_nonlocal_deltaState(Mp,ph,me)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< MandelStress
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
me
|
||
|
||
integer :: &
|
||
ns, & ! short notation for the total number of active slip systems
|
||
c, & ! character of dislocation
|
||
t, & ! type of dislocation
|
||
s ! index of my current slip system
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
deltaRhoRemobilization, & ! density increment by remobilization
|
||
deltaRhoDipole2SingleStress ! density increment by dipole dissociation (by stress change)
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
rho ! current dislocation densities
|
||
real(pReal), dimension(param(ph)%sum_N_sl,4) :: &
|
||
v ! dislocation glide velocity
|
||
real(pReal), dimension(param(ph)%sum_N_sl) :: &
|
||
tau ! current resolved shear stress
|
||
real(pReal), dimension(param(ph)%sum_N_sl,2) :: &
|
||
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
|
||
dUpper, & ! current maximum stable dipole distance for edges and screws
|
||
dUpperOld, & ! old maximum stable dipole distance for edges and screws
|
||
deltaDUpper ! change in maximum stable dipole distance for edges and screws
|
||
|
||
associate(prm => param(ph),dst => microstructure(ph),del => deltaState(ph))
|
||
ns = prm%sum_N_sl
|
||
|
||
!*** shortcut to state variables
|
||
forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),me)
|
||
forall (s = 1:ns, c = 1:2) dUpperOld(s,c) = plasticState(ph)%state(iD(s,c,ph),me)
|
||
|
||
rho = getRho(ph,me)
|
||
rhoDip = rho(:,dip)
|
||
|
||
!****************************************************************************
|
||
!*** dislocation remobilization (bauschinger effect)
|
||
where(rho(:,imm) * v < 0.0_pReal)
|
||
deltaRhoRemobilization(:,mob) = abs(rho(:,imm))
|
||
deltaRhoRemobilization(:,imm) = - rho(:,imm)
|
||
rho(:,mob) = rho(:,mob) + abs(rho(:,imm))
|
||
rho(:,imm) = 0.0_pReal
|
||
elsewhere
|
||
deltaRhoRemobilization(:,mob) = 0.0_pReal
|
||
deltaRhoRemobilization(:,imm) = 0.0_pReal
|
||
endwhere
|
||
deltaRhoRemobilization(:,dip) = 0.0_pReal
|
||
|
||
!****************************************************************************
|
||
!*** calculate dipole formation and dissociation by stress change
|
||
|
||
!*** calculate limits for stable dipole height
|
||
do s = 1,prm%sum_N_sl
|
||
tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) +dst%tau_back(s,me)
|
||
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
|
||
enddo
|
||
|
||
dUpper(:,1) = prm%mu * prm%b_sl/(8.0_pReal * PI * (1.0_pReal - prm%nu) * abs(tau))
|
||
dUpper(:,2) = prm%mu * prm%b_sl/(4.0_pReal * PI * abs(tau))
|
||
|
||
where(dNeq0(sqrt(sum(abs(rho(:,edg)),2)))) &
|
||
dUpper(:,1) = min(1.0_pReal/sqrt(sum(abs(rho(:,edg)),2)),dUpper(:,1))
|
||
where(dNeq0(sqrt(sum(abs(rho(:,scr)),2)))) &
|
||
dUpper(:,2) = min(1.0_pReal/sqrt(sum(abs(rho(:,scr)),2)),dUpper(:,2))
|
||
|
||
dUpper = max(dUpper,prm%minDipoleHeight)
|
||
deltaDUpper = dUpper - dUpperOld
|
||
|
||
|
||
!*** dissociation by stress increase
|
||
deltaRhoDipole2SingleStress = 0.0_pReal
|
||
forall (c=1:2, s=1:ns, deltaDUpper(s,c) < 0.0_pReal .and. &
|
||
dNeq0(dUpperOld(s,c) - prm%minDipoleHeight(s,c))) &
|
||
deltaRhoDipole2SingleStress(s,8+c) = rhoDip(s,c) * deltaDUpper(s,c) &
|
||
/ (dUpperOld(s,c) - prm%minDipoleHeight(s,c))
|
||
|
||
forall (t=1:4) deltaRhoDipole2SingleStress(:,t) = -0.5_pReal * deltaRhoDipole2SingleStress(:,(t-1)/2+9)
|
||
forall (s = 1:ns, c = 1:2) plasticState(ph)%state(iD(s,c,ph),me) = dUpper(s,c)
|
||
|
||
plasticState(ph)%deltaState(:,me) = 0.0_pReal
|
||
del%rho(:,me) = reshape(deltaRhoRemobilization + deltaRhoDipole2SingleStress, [10*ns])
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_nonlocal_deltaState
|
||
|
||
|
||
!---------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!---------------------------------------------------------------------------------------------------
|
||
module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
|
||
ph,me,ip,el)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< MandelStress
|
||
real(pReal), intent(in) :: &
|
||
Temperature, & !< temperature
|
||
timestep !< substepped crystallite time increment
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
me, &
|
||
ip, & !< current integration point
|
||
el !< current element number
|
||
|
||
integer :: &
|
||
ns, & !< short notation for the total number of active slip systems
|
||
c, & !< character of dislocation
|
||
t, & !< type of dislocation
|
||
s !< index of my current slip system
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
rho, &
|
||
rho0, & !< dislocation density at beginning of time step
|
||
rhoDot, & !< density evolution
|
||
rhoDotMultiplication, & !< density evolution by multiplication
|
||
rhoDotSingle2DipoleGlide, & !< density evolution by dipole formation (by glide)
|
||
rhoDotAthermalAnnihilation, & !< density evolution by athermal annihilation
|
||
rhoDotThermalAnnihilation !< density evolution by thermal annihilation
|
||
real(pReal), dimension(param(ph)%sum_N_sl,8) :: &
|
||
rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
|
||
my_rhoSgl0 !< single dislocation densities of central ip (positive/negative screw and edge without dipoles)
|
||
real(pReal), dimension(param(ph)%sum_N_sl,4) :: &
|
||
v, & !< current dislocation glide velocity
|
||
v0, &
|
||
gdot !< shear rates
|
||
real(pReal), dimension(param(ph)%sum_N_sl) :: &
|
||
tau, & !< current resolved shear stress
|
||
vClimb !< climb velocity of edge dipoles
|
||
real(pReal), dimension(param(ph)%sum_N_sl,2) :: &
|
||
rhoDip, & !< current dipole dislocation densities (screw and edge dipoles)
|
||
dLower, & !< minimum stable dipole distance for edges and screws
|
||
dUpper !< current maximum stable dipole distance for edges and screws
|
||
real(pReal) :: &
|
||
selfDiffusion !< self diffusion
|
||
|
||
if (timestep <= 0.0_pReal) then
|
||
plasticState(ph)%dotState = 0.0_pReal
|
||
return
|
||
endif
|
||
|
||
associate(prm => param(ph), &
|
||
dst => microstructure(ph), &
|
||
dot => dotState(ph), &
|
||
stt => state(ph))
|
||
ns = prm%sum_N_sl
|
||
|
||
tau = 0.0_pReal
|
||
gdot = 0.0_pReal
|
||
|
||
rho = getRho(ph,me)
|
||
rhoSgl = rho(:,sgl)
|
||
rhoDip = rho(:,dip)
|
||
rho0 = getRho0(ph,me)
|
||
my_rhoSgl0 = rho0(:,sgl)
|
||
|
||
forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),me)
|
||
gdot = rhoSgl(:,1:4) * v * spread(prm%b_sl,2,4)
|
||
|
||
#ifdef DEBUG
|
||
if (debugConstitutive%basic &
|
||
.and. ((debugConstitutive%element == el .and. debugConstitutive%ip == ip) &
|
||
.or. .not. debugConstitutive%selective)) then
|
||
print'(a,/,10(12x,12(e12.5,1x),/))', '<< CONST >> rho / 1/m^2', rhoSgl, rhoDip
|
||
print'(a,/,4(12x,12(e12.5,1x),/))', '<< CONST >> gdot / 1/s',gdot
|
||
endif
|
||
#endif
|
||
|
||
!****************************************************************************
|
||
!*** limits for stable dipole height
|
||
do s = 1,ns
|
||
tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) + dst%tau_back(s,me)
|
||
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
|
||
enddo
|
||
|
||
dLower = prm%minDipoleHeight
|
||
dUpper(:,1) = prm%mu * prm%b_sl/(8.0_pReal * PI * (1.0_pReal - prm%nu) * abs(tau))
|
||
dUpper(:,2) = prm%mu * prm%b_sl/(4.0_pReal * PI * abs(tau))
|
||
|
||
where(dNeq0(sqrt(sum(abs(rho(:,edg)),2)))) &
|
||
dUpper(:,1) = min(1.0_pReal/sqrt(sum(abs(rho(:,edg)),2)),dUpper(:,1))
|
||
where(dNeq0(sqrt(sum(abs(rho(:,scr)),2)))) &
|
||
dUpper(:,2) = min(1.0_pReal/sqrt(sum(abs(rho(:,scr)),2)),dUpper(:,2))
|
||
|
||
dUpper = max(dUpper,dLower)
|
||
|
||
!****************************************************************************
|
||
!*** dislocation multiplication
|
||
rhoDotMultiplication = 0.0_pReal
|
||
isBCC: if (lattice_structure(ph) == LATTICE_bcc_ID) then
|
||
forall (s = 1:ns, sum(abs(v(s,1:4))) > 0.0_pReal)
|
||
rhoDotMultiplication(s,1:2) = sum(abs(gdot(s,3:4))) / prm%b_sl(s) & ! assuming double-cross-slip of screws to be decisive for multiplication
|
||
* sqrt(stt%rho_forest(s,me)) / prm%i_sl(s) ! & ! mean free path
|
||
! * 2.0_pReal * sum(abs(v(s,3:4))) / sum(abs(v(s,1:4))) ! ratio of screw to overall velocity determines edge generation
|
||
rhoDotMultiplication(s,3:4) = sum(abs(gdot(s,3:4))) /prm%b_sl(s) & ! assuming double-cross-slip of screws to be decisive for multiplication
|
||
* sqrt(stt%rho_forest(s,me)) / prm%i_sl(s) ! & ! mean free path
|
||
! * 2.0_pReal * sum(abs(v(s,1:2))) / sum(abs(v(s,1:4))) ! ratio of edge to overall velocity determines screw generation
|
||
endforall
|
||
|
||
else isBCC
|
||
rhoDotMultiplication(:,1:4) = spread( &
|
||
(sum(abs(gdot(:,1:2)),2) * prm%f_ed_mult + sum(abs(gdot(:,3:4)),2)) &
|
||
* sqrt(stt%rho_forest(:,me)) / prm%i_sl / prm%b_sl, 2, 4)
|
||
endif isBCC
|
||
|
||
forall (s = 1:ns, t = 1:4) v0(s,t) = plasticState(ph)%state0(iV(s,t,ph),me)
|
||
|
||
|
||
!****************************************************************************
|
||
!*** calculate dipole formation and annihilation
|
||
|
||
!*** formation by glide
|
||
do c = 1,2
|
||
rhoDotSingle2DipoleGlide(:,2*c-1) = -2.0_pReal * dUpper(:,c) / prm%b_sl &
|
||
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
|
||
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
|
||
+ abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) ! positive mobile --> negative immobile
|
||
|
||
rhoDotSingle2DipoleGlide(:,2*c) = -2.0_pReal * dUpper(:,c) / prm%b_sl &
|
||
* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
|
||
+ rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! positive mobile --> negative mobile
|
||
+ abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile --> positive immobile
|
||
|
||
rhoDotSingle2DipoleGlide(:,2*c+3) = -2.0_pReal * dUpper(:,c) / prm%b_sl &
|
||
* rhoSgl(:,2*c+3) * abs(gdot(:,2*c)) ! negative mobile --> positive immobile
|
||
|
||
rhoDotSingle2DipoleGlide(:,2*c+4) = -2.0_pReal * dUpper(:,c) / prm%b_sl &
|
||
* rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! positive mobile --> negative immobile
|
||
|
||
rhoDotSingle2DipoleGlide(:,c+8) = abs(rhoDotSingle2DipoleGlide(:,2*c+3)) &
|
||
+ abs(rhoDotSingle2DipoleGlide(:,2*c+4)) &
|
||
- rhoDotSingle2DipoleGlide(:,2*c-1) &
|
||
- rhoDotSingle2DipoleGlide(:,2*c)
|
||
enddo
|
||
|
||
|
||
!*** athermal annihilation
|
||
rhoDotAthermalAnnihilation = 0.0_pReal
|
||
forall (c=1:2) &
|
||
rhoDotAthermalAnnihilation(:,c+8) = -2.0_pReal * dLower(:,c) / prm%b_sl &
|
||
* ( 2.0_pReal * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1))) & ! was single hitting single
|
||
+ 2.0_pReal * (abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
|
||
+ rhoDip(:,c) * (abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)))) ! single knocks dipole constituent
|
||
|
||
! annihilated screw dipoles leave edge jogs behind on the colinear system
|
||
if (lattice_structure(ph) == LATTICE_fcc_ID) &
|
||
forall (s = 1:ns, prm%colinearSystem(s) > 0) &
|
||
rhoDotAthermalAnnihilation(prm%colinearSystem(s),1:2) = - rhoDotAthermalAnnihilation(s,10) &
|
||
* 0.25_pReal * sqrt(stt%rho_forest(s,me)) * (dUpper(s,2) + dLower(s,2)) * prm%f_ed
|
||
|
||
|
||
!*** thermally activated annihilation me edge dipoles by climb
|
||
rhoDotThermalAnnihilation = 0.0_pReal
|
||
selfDiffusion = prm%D_0 * exp(-prm%Q_cl / (kB * Temperature))
|
||
vClimb = prm%V_at * selfDiffusion * prm%mu &
|
||
/ ( kB * Temperature * PI * (1.0_pReal-prm%nu) * (dUpper(:,1) + dLower(:,1)))
|
||
forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) &
|
||
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
|
||
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
|
||
- rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
|
||
|
||
rhoDot = rhoDotFlux(timestep, ph,me,ip,el) &
|
||
+ rhoDotMultiplication &
|
||
+ rhoDotSingle2DipoleGlide &
|
||
+ rhoDotAthermalAnnihilation &
|
||
+ rhoDotThermalAnnihilation
|
||
|
||
|
||
if ( any(rho(:,mob) + rhoDot(:,1:4) * timestep < -prm%atol_rho) &
|
||
.or. any(rho(:,dip) + rhoDot(:,9:10) * timestep < -prm%atol_rho)) then
|
||
#ifdef DEBUG
|
||
if (debugConstitutive%extensive) then
|
||
print'(a,i5,a,i2)', '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
|
||
print'(a)', '<< CONST >> enforcing cutback !!!'
|
||
endif
|
||
#endif
|
||
plasticState(ph)%dotState = IEEE_value(1.0_pReal,IEEE_quiet_NaN)
|
||
else
|
||
dot%rho(:,me) = pack(rhoDot,.true.)
|
||
dot%gamma(:,me) = sum(gdot,2)
|
||
endif
|
||
|
||
end associate
|
||
|
||
end subroutine nonlocal_dotState
|
||
|
||
|
||
!---------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!---------------------------------------------------------------------------------------------------
|
||
function rhoDotFlux(timestep,ph,me,ip,el)
|
||
|
||
real(pReal), intent(in) :: &
|
||
timestep !< substepped crystallite time increment
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
me, &
|
||
ip, & !< current integration point
|
||
el !< current element number
|
||
|
||
integer :: &
|
||
neighbor_ph, & !< phase of my neighbor's plasticity
|
||
ns, & !< short notation for the total number of active slip systems
|
||
c, & !< character of dislocation
|
||
n, & !< index of my current neighbor
|
||
neighbor_el, & !< element number of my neighbor
|
||
neighbor_ip, & !< integration point of my neighbor
|
||
neighbor_n, & !< neighbor index pointing to me when looking from my neighbor
|
||
opposite_neighbor, & !< index of my opposite neighbor
|
||
opposite_ip, & !< ip of my opposite neighbor
|
||
opposite_el, & !< element index of my opposite neighbor
|
||
opposite_n, & !< neighbor index pointing to me when looking from my opposite neighbor
|
||
t, & !< type of dislocation
|
||
no,& !< neighbor offset shortcut
|
||
np,& !< neighbor phase shortcut
|
||
topp, & !< type of dislocation with opposite sign to t
|
||
s !< index of my current slip system
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: &
|
||
rho, &
|
||
rho0, & !< dislocation density at beginning of time step
|
||
rhoDotFlux !< density evolution by flux
|
||
real(pReal), dimension(param(ph)%sum_N_sl,8) :: &
|
||
rhoSgl, & !< current single dislocation densities (positive/negative screw and edge without dipoles)
|
||
neighbor_rhoSgl0, & !< current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
|
||
my_rhoSgl0 !< single dislocation densities of central ip (positive/negative screw and edge without dipoles)
|
||
real(pReal), dimension(param(ph)%sum_N_sl,4) :: &
|
||
v, & !< current dislocation glide velocity
|
||
v0, &
|
||
neighbor_v0, & !< dislocation glide velocity of enighboring ip
|
||
gdot !< shear rates
|
||
real(pReal), dimension(3,param(ph)%sum_N_sl,4) :: &
|
||
m !< direction of dislocation motion
|
||
real(pReal), dimension(3,3) :: &
|
||
my_F, & !< my total deformation gradient
|
||
neighbor_F, & !< total deformation gradient of my neighbor
|
||
my_Fe, & !< my elastic deformation gradient
|
||
neighbor_Fe, & !< elastic deformation gradient of my neighbor
|
||
Favg !< average total deformation gradient of me and my neighbor
|
||
real(pReal), dimension(3) :: &
|
||
normal_neighbor2me, & !< interface normal pointing from my neighbor to me in neighbor's lattice configuration
|
||
normal_neighbor2me_defConf, & !< interface normal pointing from my neighbor to me in shared deformed configuration
|
||
normal_me2neighbor, & !< interface normal pointing from me to my neighbor in my lattice configuration
|
||
normal_me2neighbor_defConf !< interface normal pointing from me to my neighbor in shared deformed configuration
|
||
real(pReal) :: &
|
||
area, & !< area of the current interface
|
||
transmissivity, & !< overall transmissivity of dislocation flux to neighboring material point
|
||
lineLength !< dislocation line length leaving the current interface
|
||
|
||
|
||
associate(prm => param(ph), &
|
||
dst => microstructure(ph), &
|
||
dot => dotState(ph), &
|
||
stt => state(ph))
|
||
ns = prm%sum_N_sl
|
||
|
||
gdot = 0.0_pReal
|
||
|
||
rho = getRho(ph,me)
|
||
rhoSgl = rho(:,sgl)
|
||
rho0 = getRho0(ph,me)
|
||
my_rhoSgl0 = rho0(:,sgl)
|
||
|
||
forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),me) !ToDo: MD: I think we should use state0 here
|
||
gdot = rhoSgl(:,1:4) * v * spread(prm%b_sl,2,4)
|
||
|
||
|
||
forall (s = 1:ns, t = 1:4) v0(s,t) = plasticState(ph)%state0(iV(s,t,ph),me)
|
||
|
||
!****************************************************************************
|
||
!*** calculate dislocation fluxes (only for nonlocal plasticity)
|
||
rhoDotFlux = 0.0_pReal
|
||
if (.not. phase_localPlasticity(material_phaseAt(1,el))) then
|
||
|
||
!*** check CFL (Courant-Friedrichs-Lewy) condition for flux
|
||
if (any( abs(gdot) > 0.0_pReal & ! any active slip system ...
|
||
.and. prm%f_c * abs(v0) * timestep &
|
||
> IPvolume(ip,el) / maxval(IParea(:,ip,el)))) then ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
|
||
#ifdef DEBUG
|
||
if (debugConstitutive%extensive) then
|
||
print'(a,i5,a,i2)', '<< CONST >> CFL condition not fullfilled at el ',el,' ip ',ip
|
||
print'(a,e10.3,a,e10.3)', '<< CONST >> velocity is at ', &
|
||
maxval(abs(v0), abs(gdot) > 0.0_pReal &
|
||
.and. prm%f_c * abs(v0) * timestep &
|
||
> IPvolume(ip,el) / maxval(IParea(:,ip,el))), &
|
||
' at a timestep of ',timestep
|
||
print*, '<< CONST >> enforcing cutback !!!'
|
||
endif
|
||
#endif
|
||
rhoDotFlux = IEEE_value(1.0_pReal,IEEE_quiet_NaN) ! enforce cutback
|
||
return
|
||
endif
|
||
|
||
|
||
!*** be aware of the definition of slip_transverse = slip_direction x slip_normal !!!
|
||
!*** opposite sign to our t vector in the (s,t,n) triplet !!!
|
||
|
||
m(1:3,:,1) = prm%slip_direction
|
||
m(1:3,:,2) = -prm%slip_direction
|
||
m(1:3,:,3) = -prm%slip_transverse
|
||
m(1:3,:,4) = prm%slip_transverse
|
||
|
||
my_F = phase_mechanical_F(ph)%data(1:3,1:3,me)
|
||
my_Fe = matmul(my_F, math_inv33(phase_mechanical_Fp(ph)%data(1:3,1:3,me)))
|
||
|
||
neighbors: do n = 1,nIPneighbors
|
||
|
||
neighbor_el = IPneighborhood(1,n,ip,el)
|
||
neighbor_ip = IPneighborhood(2,n,ip,el)
|
||
neighbor_n = IPneighborhood(3,n,ip,el)
|
||
np = material_phaseAt(1,neighbor_el)
|
||
no = material_phasememberAt(1,neighbor_ip,neighbor_el)
|
||
|
||
opposite_neighbor = n + mod(n,2) - mod(n+1,2)
|
||
opposite_el = IPneighborhood(1,opposite_neighbor,ip,el)
|
||
opposite_ip = IPneighborhood(2,opposite_neighbor,ip,el)
|
||
opposite_n = IPneighborhood(3,opposite_neighbor,ip,el)
|
||
|
||
if (neighbor_n > 0) then ! if neighbor exists, average deformation gradient
|
||
neighbor_ph = material_phaseAt(1,neighbor_el)
|
||
neighbor_F = phase_mechanical_F(np)%data(1:3,1:3,no)
|
||
neighbor_Fe = matmul(neighbor_F, math_inv33(phase_mechanical_Fp(np)%data(1:3,1:3,no)))
|
||
Favg = 0.5_pReal * (my_F + neighbor_F)
|
||
else ! if no neighbor, take my value as average
|
||
Favg = my_F
|
||
endif
|
||
|
||
neighbor_v0 = 0.0_pReal ! needed for check of sign change in flux density below
|
||
|
||
!* FLUX FROM MY NEIGHBOR TO ME
|
||
!* This is only considered, if I have a neighbor of nonlocal plasticity
|
||
!* (also nonlocal constitutive law with local properties) that is at least a little bit
|
||
!* compatible.
|
||
!* If it's not at all compatible, no flux is arriving, because everything is dammed in front of
|
||
!* my neighbor's interface.
|
||
!* The entering flux from my neighbor will be distributed on my slip systems according to the
|
||
!* compatibility
|
||
if (neighbor_n > 0) then
|
||
if (phase_plasticity(material_phaseAt(1,neighbor_el)) == PLASTICITY_NONLOCAL_ID .and. &
|
||
any(compatibility(:,:,:,n,ip,el) > 0.0_pReal)) then
|
||
|
||
forall (s = 1:ns, t = 1:4)
|
||
neighbor_v0(s,t) = plasticState(np)%state0(iV (s,t,neighbor_ph),no)
|
||
neighbor_rhoSgl0(s,t) = max(plasticState(np)%state0(iRhoU(s,t,neighbor_ph),no),0.0_pReal)
|
||
endforall
|
||
|
||
where (neighbor_rhoSgl0 * IPvolume(neighbor_ip,neighbor_el) ** 0.667_pReal < prm%rho_min &
|
||
.or. neighbor_rhoSgl0 < prm%rho_significant) &
|
||
neighbor_rhoSgl0 = 0.0_pReal
|
||
normal_neighbor2me_defConf = math_det33(Favg) * matmul(math_inv33(transpose(Favg)), &
|
||
IPareaNormal(1:3,neighbor_n,neighbor_ip,neighbor_el)) ! normal of the interface in (average) deformed configuration (pointing neighbor => me)
|
||
normal_neighbor2me = matmul(transpose(neighbor_Fe), normal_neighbor2me_defConf) &
|
||
/ math_det33(neighbor_Fe) ! interface normal in the lattice configuration of my neighbor
|
||
area = IParea(neighbor_n,neighbor_ip,neighbor_el) * norm2(normal_neighbor2me)
|
||
normal_neighbor2me = normal_neighbor2me / norm2(normal_neighbor2me) ! normalize the surface normal to unit length
|
||
do s = 1,ns
|
||
do t = 1,4
|
||
c = (t + 1) / 2
|
||
topp = t + mod(t,2) - mod(t+1,2)
|
||
if (neighbor_v0(s,t) * math_inner(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal & ! flux from my neighbor to me == entering flux for me
|
||
.and. v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal ) then ! ... only if no sign change in flux density
|
||
lineLength = neighbor_rhoSgl0(s,t) * neighbor_v0(s,t) &
|
||
* math_inner(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
|
||
where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) &
|
||
rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) &
|
||
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to equally signed mobile dislocation type
|
||
where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) &
|
||
rhoDotFlux(:,topp) = rhoDotFlux(:,topp) &
|
||
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to opposite signed mobile dislocation type
|
||
|
||
endif
|
||
enddo
|
||
enddo
|
||
endif; endif
|
||
|
||
|
||
!* FLUX FROM ME TO MY NEIGHBOR
|
||
!* This is not considered, if my opposite neighbor has a different constitutive law than nonlocal (still considered for nonlocal law with local properties).
|
||
!* Then, we assume, that the opposite(!) neighbor sends an equal amount of dislocations to me.
|
||
!* So the net flux in the direction of my neighbor is equal to zero:
|
||
!* leaving flux to neighbor == entering flux from opposite neighbor
|
||
!* In case of reduced transmissivity, part of the leaving flux is stored as dead dislocation density.
|
||
!* That means for an interface of zero transmissivity the leaving flux is fully converted to dead dislocations.
|
||
if (opposite_n > 0) then
|
||
if (phase_plasticity(material_phaseAt(1,opposite_el)) == PLASTICITY_NONLOCAL_ID) then
|
||
|
||
normal_me2neighbor_defConf = math_det33(Favg) &
|
||
* matmul(math_inv33(transpose(Favg)),IPareaNormal(1:3,n,ip,el)) ! normal of the interface in (average) deformed configuration (pointing me => neighbor)
|
||
normal_me2neighbor = matmul(transpose(my_Fe), normal_me2neighbor_defConf) &
|
||
/ math_det33(my_Fe) ! interface normal in my lattice configuration
|
||
area = IParea(n,ip,el) * norm2(normal_me2neighbor)
|
||
normal_me2neighbor = normal_me2neighbor / norm2(normal_me2neighbor) ! normalize the surface normal to unit length
|
||
do s = 1,ns
|
||
do t = 1,4
|
||
c = (t + 1) / 2
|
||
if (v0(s,t) * math_inner(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from me to my neighbor == leaving flux for me (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
|
||
if (v0(s,t) * neighbor_v0(s,t) >= 0.0_pReal) then ! no sign change in flux density
|
||
transmissivity = sum(compatibility(c,:,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor
|
||
else ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
|
||
transmissivity = 0.0_pReal
|
||
endif
|
||
lineLength = my_rhoSgl0(s,t) * v0(s,t) &
|
||
* math_inner(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of mobiles that wants to leave through this interface
|
||
rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / IPvolume(ip,el) ! subtract dislocation flux from current type
|
||
rhoDotFlux(s,t+4) = rhoDotFlux(s,t+4) &
|
||
+ lineLength / IPvolume(ip,el) * (1.0_pReal - transmissivity) &
|
||
* sign(1.0_pReal, v0(s,t)) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
|
||
endif
|
||
enddo
|
||
enddo
|
||
endif; endif
|
||
|
||
enddo neighbors
|
||
endif
|
||
|
||
end associate
|
||
|
||
end function rhoDotFlux
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Compatibility update
|
||
!> @detail Compatibility is defined as normalized product of signed cosine of the angle between the slip
|
||
! plane normals and signed cosine of the angle between the slip directions. Only the largest values
|
||
! that sum up to a total of 1 are considered, all others are set to zero.
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_nonlocal_updateCompatibility(orientation,ph,i,e)
|
||
|
||
type(rotation), dimension(1,discretization_nIPs,discretization_Nelems), intent(in) :: &
|
||
orientation ! crystal orientation
|
||
integer, intent(in) :: &
|
||
ph, &
|
||
i, &
|
||
e
|
||
|
||
integer :: &
|
||
n, & ! neighbor index
|
||
me, &
|
||
neighbor_e, & ! element index of my neighbor
|
||
neighbor_i, & ! integration point index of my neighbor
|
||
neighbor_me, &
|
||
neighbor_phase, &
|
||
ns, & ! number of active slip systems
|
||
s1, & ! slip system index (me)
|
||
s2 ! slip system index (my neighbor)
|
||
real(pReal), dimension(2,param(ph)%sum_N_sl,param(ph)%sum_N_sl,nIPneighbors) :: &
|
||
my_compatibility ! my_compatibility for current element and ip
|
||
real(pReal) :: &
|
||
my_compatibilitySum, &
|
||
thresholdValue, &
|
||
nThresholdValues
|
||
logical, dimension(param(ph)%sum_N_sl) :: &
|
||
belowThreshold
|
||
type(rotation) :: mis
|
||
|
||
associate(prm => param(ph))
|
||
ns = prm%sum_N_sl
|
||
|
||
me = material_phaseMemberAt(1,i,e)
|
||
!*** start out fully compatible
|
||
my_compatibility = 0.0_pReal
|
||
forall(s1 = 1:ns) my_compatibility(:,s1,s1,:) = 1.0_pReal
|
||
|
||
neighbors: do n = 1,nIPneighbors
|
||
neighbor_e = IPneighborhood(1,n,i,e)
|
||
neighbor_i = IPneighborhood(2,n,i,e)
|
||
neighbor_me = material_phaseMemberAt(1,neighbor_i,neighbor_e)
|
||
neighbor_phase = material_phaseAt(1,neighbor_e)
|
||
|
||
if (neighbor_e <= 0 .or. neighbor_i <= 0) then
|
||
!* FREE SURFACE
|
||
!* Set surface transmissivity to the value specified in the material.config
|
||
forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_surface)
|
||
elseif (neighbor_phase /= ph) then
|
||
!* PHASE BOUNDARY
|
||
!* If we encounter a different nonlocal phase at the neighbor,
|
||
!* we consider this to be a real "physical" phase boundary, so completely incompatible.
|
||
!* If one of the two phases has a local plasticity law,
|
||
!* we do not consider this to be a phase boundary, so completely compatible.
|
||
if (.not. phase_localPlasticity(neighbor_phase) .and. .not. phase_localPlasticity(ph)) &
|
||
forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = 0.0_pReal
|
||
elseif (prm%chi_GB >= 0.0_pReal) then
|
||
!* GRAIN BOUNDARY !
|
||
!* fixed transmissivity for adjacent ips with different texture (only if explicitly given in material.config)
|
||
if (any(dNeq(material_orientation0(1,ph,me)%asQuaternion(), &
|
||
material_orientation0(1,neighbor_phase,neighbor_me)%asQuaternion())) .and. &
|
||
(.not. phase_localPlasticity(neighbor_phase))) &
|
||
forall(s1 = 1:ns) my_compatibility(:,s1,s1,n) = sqrt(prm%chi_GB)
|
||
else
|
||
!* GRAIN BOUNDARY ?
|
||
!* Compatibility defined by relative orientation of slip systems:
|
||
!* The my_compatibility value is defined as the product of the slip normal projection and the slip direction projection.
|
||
!* Its sign is always positive for screws, for edges it has the same sign as the slip normal projection.
|
||
!* Since the sum for each slip system can easily exceed one (which would result in a transmissivity larger than one),
|
||
!* only values above or equal to a certain threshold value are considered. This threshold value is chosen, such that
|
||
!* the number of compatible slip systems is minimized with the sum of the original compatibility values exceeding one.
|
||
!* Finally the smallest compatibility value is decreased until the sum is exactly equal to one.
|
||
!* All values below the threshold are set to zero.
|
||
mis = orientation(1,i,e)%misorientation(orientation(1,neighbor_i,neighbor_e))
|
||
mySlipSystems: do s1 = 1,ns
|
||
neighborSlipSystems: do s2 = 1,ns
|
||
my_compatibility(1,s2,s1,n) = math_inner(prm%slip_normal(1:3,s1), &
|
||
mis%rotate(prm%slip_normal(1:3,s2))) &
|
||
* abs(math_inner(prm%slip_direction(1:3,s1), &
|
||
mis%rotate(prm%slip_direction(1:3,s2))))
|
||
my_compatibility(2,s2,s1,n) = abs(math_inner(prm%slip_normal(1:3,s1), &
|
||
mis%rotate(prm%slip_normal(1:3,s2)))) &
|
||
* abs(math_inner(prm%slip_direction(1:3,s1), &
|
||
mis%rotate(prm%slip_direction(1:3,s2))))
|
||
enddo neighborSlipSystems
|
||
|
||
my_compatibilitySum = 0.0_pReal
|
||
belowThreshold = .true.
|
||
do while (my_compatibilitySum < 1.0_pReal .and. any(belowThreshold))
|
||
thresholdValue = maxval(my_compatibility(2,:,s1,n), belowThreshold) ! screws always positive
|
||
nThresholdValues = real(count(my_compatibility(2,:,s1,n) >= thresholdValue),pReal)
|
||
where (my_compatibility(2,:,s1,n) >= thresholdValue) belowThreshold = .false.
|
||
if (my_compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
|
||
where (abs(my_compatibility(:,:,s1,n)) >= thresholdValue) &
|
||
my_compatibility(:,:,s1,n) = sign((1.0_pReal - my_compatibilitySum)/nThresholdValues,&
|
||
my_compatibility(:,:,s1,n))
|
||
my_compatibilitySum = my_compatibilitySum + nThresholdValues * thresholdValue
|
||
enddo
|
||
|
||
where(belowThreshold) my_compatibility(1,:,s1,n) = 0.0_pReal
|
||
where(belowThreshold) my_compatibility(2,:,s1,n) = 0.0_pReal
|
||
|
||
enddo mySlipSystems
|
||
endif
|
||
|
||
enddo neighbors
|
||
|
||
compatibility(:,:,:,:,i,e) = my_compatibility
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_nonlocal_updateCompatibility
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief writes results to HDF5 output file
|
||
!--------------------------------------------------------------------------------------------------
|
||
module subroutine plastic_nonlocal_results(ph,group)
|
||
|
||
integer, intent(in) :: ph
|
||
character(len=*),intent(in) :: group
|
||
|
||
integer :: o
|
||
|
||
associate(prm => param(ph),dst => microstructure(ph),stt=>state(ph))
|
||
outputsLoop: do o = 1,size(prm%output)
|
||
select case(trim(prm%output(o)))
|
||
case('rho_u_ed_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_mob_edg_pos, trim(prm%output(o)), &
|
||
'positive mobile edge density','1/m²')
|
||
case('rho_b_ed_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_imm_edg_pos, trim(prm%output(o)), &
|
||
'positive immobile edge density','1/m²')
|
||
case('rho_u_ed_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_mob_edg_neg, trim(prm%output(o)), &
|
||
'negative mobile edge density','1/m²')
|
||
case('rho_b_ed_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_imm_edg_neg, trim(prm%output(o)), &
|
||
'negative immobile edge density','1/m²')
|
||
case('rho_d_ed')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip_edg, trim(prm%output(o)), &
|
||
'edge dipole density','1/m²')
|
||
case('rho_u_sc_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_mob_scr_pos, trim(prm%output(o)), &
|
||
'positive mobile screw density','1/m²')
|
||
case('rho_b_sc_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_imm_scr_pos, trim(prm%output(o)), &
|
||
'positive immobile screw density','1/m²')
|
||
case('rho_u_sc_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_mob_scr_neg, trim(prm%output(o)), &
|
||
'negative mobile screw density','1/m²')
|
||
case('rho_b_sc_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_sgl_imm_scr_neg, trim(prm%output(o)), &
|
||
'negative immobile screw density','1/m²')
|
||
case('rho_d_sc')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_dip_scr, trim(prm%output(o)), &
|
||
'screw dipole density','1/m²')
|
||
case('rho_f')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%rho_forest, trim(prm%output(o)), &
|
||
'forest density','1/m²')
|
||
case('v_ed_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%v_edg_pos, trim(prm%output(o)), &
|
||
'positive edge velocity','m/s')
|
||
case('v_ed_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%v_edg_neg, trim(prm%output(o)), &
|
||
'negative edge velocity','m/s')
|
||
case('v_sc_pos')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%v_scr_pos, trim(prm%output(o)), &
|
||
'positive srew velocity','m/s')
|
||
case('v_sc_neg')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%v_scr_neg, trim(prm%output(o)), &
|
||
'negative screw velocity','m/s')
|
||
case('gamma')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,stt%gamma, trim(prm%output(o)), &
|
||
'plastic shear','1')
|
||
case('tau_pass')
|
||
if(prm%sum_N_sl>0) call results_writeDataset(group,dst%tau_pass, trim(prm%output(o)), &
|
||
'passing stress for slip','Pa')
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
|
||
end subroutine plastic_nonlocal_results
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief populates the initial dislocation density
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine stateInit(ini,phase,Nmembers)
|
||
|
||
type(tInitialParameters) :: &
|
||
ini
|
||
integer,intent(in) :: &
|
||
phase, &
|
||
Nmembers
|
||
integer :: &
|
||
i, &
|
||
e, &
|
||
f, &
|
||
from, &
|
||
upto, &
|
||
s, &
|
||
phasemember
|
||
real(pReal), dimension(2) :: &
|
||
noise, &
|
||
rnd
|
||
real(pReal) :: &
|
||
meanDensity, &
|
||
totalVolume, &
|
||
densityBinning, &
|
||
minimumIpVolume
|
||
real(pReal), dimension(Nmembers) :: &
|
||
volume
|
||
|
||
|
||
associate(stt => state(phase))
|
||
|
||
if (ini%random_rho_u > 0.0_pReal) then ! randomly distribute dislocation segments on random slip system and of random type in the volume
|
||
do e = 1,discretization_Nelems
|
||
do i = 1,discretization_nIPs
|
||
if (material_phaseAt(1,e) == phase) volume(material_phasememberAt(1,i,e)) = IPvolume(i,e)
|
||
enddo
|
||
enddo
|
||
totalVolume = sum(volume)
|
||
minimumIPVolume = minval(volume)
|
||
densityBinning = ini%random_rho_u_binning / minimumIpVolume ** (2.0_pReal / 3.0_pReal)
|
||
|
||
! fill random material points with dislocation segments until the desired overall density is reached
|
||
meanDensity = 0.0_pReal
|
||
do while(meanDensity < ini%random_rho_u)
|
||
call random_number(rnd)
|
||
phasemember = nint(rnd(1)*real(Nmembers,pReal) + 0.5_pReal)
|
||
s = nint(rnd(2)*real(sum(ini%N_sl),pReal)*4.0_pReal + 0.5_pReal)
|
||
meanDensity = meanDensity + densityBinning * volume(phasemember) / totalVolume
|
||
stt%rhoSglMobile(s,phasemember) = densityBinning
|
||
enddo
|
||
else ! homogeneous distribution with noise
|
||
do e = 1, Nmembers
|
||
do f = 1,size(ini%N_sl,1)
|
||
from = 1 + sum(ini%N_sl(1:f-1))
|
||
upto = sum(ini%N_sl(1:f))
|
||
do s = from,upto
|
||
noise = [math_sampleGaussVar(0.0_pReal, ini%sigma_rho_u), &
|
||
math_sampleGaussVar(0.0_pReal, ini%sigma_rho_u)]
|
||
stt%rho_sgl_mob_edg_pos(s,e) = ini%rho_u_ed_pos_0(f) + noise(1)
|
||
stt%rho_sgl_mob_edg_neg(s,e) = ini%rho_u_ed_neg_0(f) + noise(1)
|
||
stt%rho_sgl_mob_scr_pos(s,e) = ini%rho_u_sc_pos_0(f) + noise(2)
|
||
stt%rho_sgl_mob_scr_neg(s,e) = ini%rho_u_sc_neg_0(f) + noise(2)
|
||
enddo
|
||
stt%rho_dip_edg(from:upto,e) = ini%rho_d_ed_0(f)
|
||
stt%rho_dip_scr(from:upto,e) = ini%rho_d_sc_0(f)
|
||
enddo
|
||
enddo
|
||
endif
|
||
|
||
end associate
|
||
|
||
end subroutine stateInit
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates kinetics
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Temperature, ph)
|
||
|
||
integer, intent(in) :: &
|
||
c, & !< dislocation character (1:edge, 2:screw)
|
||
ph
|
||
real(pReal), intent(in) :: &
|
||
Temperature !< temperature
|
||
real(pReal), dimension(param(ph)%sum_N_sl), intent(in) :: &
|
||
tau, & !< resolved external shear stress (without non Schmid effects)
|
||
tauNS, & !< resolved external shear stress (including non Schmid effects)
|
||
tauThreshold !< threshold shear stress
|
||
real(pReal), dimension(param(ph)%sum_N_sl), intent(out) :: &
|
||
v, & !< velocity
|
||
dv_dtau, & !< velocity derivative with respect to resolved shear stress (without non Schmid contributions)
|
||
dv_dtauNS !< velocity derivative with respect to resolved shear stress (including non Schmid contributions)
|
||
|
||
integer :: &
|
||
s !< index of my current slip system
|
||
real(pReal) :: &
|
||
tauRel_P, &
|
||
tauRel_S, &
|
||
tauEff, & !< effective shear stress
|
||
tPeierls, & !< waiting time in front of a peierls barriers
|
||
tSolidSolution, & !< waiting time in front of a solid solution obstacle
|
||
vViscous, & !< viscous glide velocity
|
||
dtPeierls_dtau, & !< derivative with respect to resolved shear stress
|
||
dtSolidSolution_dtau, & !< derivative with respect to resolved shear stress
|
||
meanfreepath_S, & !< mean free travel distance for dislocations between two solid solution obstacles
|
||
meanfreepath_P, & !< mean free travel distance for dislocations between two Peierls barriers
|
||
jumpWidth_P, & !< depth of activated area
|
||
jumpWidth_S, & !< depth of activated area
|
||
activationLength_P, & !< length of activated dislocation line
|
||
activationLength_S, & !< length of activated dislocation line
|
||
activationVolume_P, & !< volume that needs to be activated to overcome barrier
|
||
activationVolume_S, & !< volume that needs to be activated to overcome barrier
|
||
activationEnergy_P, & !< energy that is needed to overcome barrier
|
||
activationEnergy_S, & !< energy that is needed to overcome barrier
|
||
criticalStress_P, & !< maximum obstacle strength
|
||
criticalStress_S, & !< maximum obstacle strength
|
||
mobility !< dislocation mobility
|
||
|
||
associate(prm => param(ph))
|
||
v = 0.0_pReal
|
||
dv_dtau = 0.0_pReal
|
||
dv_dtauNS = 0.0_pReal
|
||
|
||
do s = 1,prm%sum_N_sl
|
||
if (abs(tau(s)) > tauThreshold(s)) then
|
||
|
||
!* Peierls contribution
|
||
!* Effective stress includes non Schmid constributions
|
||
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
|
||
tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) ! ensure that the effective stress is positive
|
||
meanfreepath_P = prm%b_sl(s)
|
||
jumpWidth_P = prm%b_sl(s)
|
||
activationLength_P = prm%w *prm%b_sl(s)
|
||
activationVolume_P = activationLength_P * jumpWidth_P * prm%b_sl(s)
|
||
criticalStress_P = prm%peierlsStress(s,c)
|
||
activationEnergy_P = criticalStress_P * activationVolume_P
|
||
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) ! ensure that the activation probability cannot become greater than one
|
||
tPeierls = 1.0_pReal / prm%nu_a &
|
||
* exp(activationEnergy_P / (kB * Temperature) &
|
||
* (1.0_pReal - tauRel_P**prm%p)**prm%q)
|
||
if (tauEff < criticalStress_P) then
|
||
dtPeierls_dtau = tPeierls * prm%p * prm%q * activationVolume_P / (kB * Temperature) &
|
||
* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal)
|
||
else
|
||
dtPeierls_dtau = 0.0_pReal
|
||
endif
|
||
|
||
!* Contribution from solid solution strengthening
|
||
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
|
||
tauEff = abs(tau(s)) - tauThreshold(s)
|
||
meanfreepath_S = prm%b_sl(s) / sqrt(prm%c_sol)
|
||
jumpWidth_S = prm%f_sol * prm%b_sl(s)
|
||
activationLength_S = prm%b_sl(s) / sqrt(prm%c_sol)
|
||
activationVolume_S = activationLength_S * jumpWidth_S * prm%b_sl(s)
|
||
activationEnergy_S = prm%Q_sol
|
||
criticalStress_S = activationEnergy_S / activationVolume_S
|
||
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) ! ensure that the activation probability cannot become greater than one
|
||
tSolidSolution = 1.0_pReal / prm%nu_a &
|
||
* exp(activationEnergy_S / (kB * Temperature)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
|
||
if (tauEff < criticalStress_S) then
|
||
dtSolidSolution_dtau = tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * Temperature) &
|
||
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal)
|
||
else
|
||
dtSolidSolution_dtau = 0.0_pReal
|
||
endif
|
||
|
||
!* viscous glide velocity
|
||
tauEff = abs(tau(s)) - tauThreshold(s)
|
||
mobility = prm%b_sl(s) / prm%eta
|
||
vViscous = mobility * tauEff
|
||
|
||
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
|
||
!* free flight at glide velocity in between.
|
||
!* adopt sign from resolved stress
|
||
v(s) = sign(1.0_pReal,tau(s)) &
|
||
/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
|
||
dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / meanfreepath_S + mobility /vViscous**2.0_pReal)
|
||
dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / meanfreepath_P
|
||
endif
|
||
enddo
|
||
|
||
end associate
|
||
|
||
end subroutine kinetics
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief returns copy of current dislocation densities from state
|
||
!> @details raw values is rectified
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function getRho(ph,me)
|
||
|
||
integer, intent(in) :: ph, me
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: getRho
|
||
|
||
|
||
associate(prm => param(ph))
|
||
|
||
getRho = reshape(state(ph)%rho(:,me),[prm%sum_N_sl,10])
|
||
|
||
! ensure positive densities (not for imm, they have a sign)
|
||
getRho(:,mob) = max(getRho(:,mob),0.0_pReal)
|
||
getRho(:,dip) = max(getRho(:,dip),0.0_pReal)
|
||
|
||
where(abs(getRho) < max(prm%rho_min/geom(ph)%V_0(me)**(2.0_pReal/3.0_pReal),prm%rho_significant)) &
|
||
getRho = 0.0_pReal
|
||
|
||
end associate
|
||
|
||
end function getRho
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief returns copy of current dislocation densities from state
|
||
!> @details raw values is rectified
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function getRho0(ph,me)
|
||
|
||
integer, intent(in) :: ph, me
|
||
real(pReal), dimension(param(ph)%sum_N_sl,10) :: getRho0
|
||
|
||
|
||
associate(prm => param(ph))
|
||
|
||
getRho0 = reshape(state0(ph)%rho(:,me),[prm%sum_N_sl,10])
|
||
|
||
! ensure positive densities (not for imm, they have a sign)
|
||
getRho0(:,mob) = max(getRho0(:,mob),0.0_pReal)
|
||
getRho0(:,dip) = max(getRho0(:,dip),0.0_pReal)
|
||
|
||
where (abs(getRho0) < max(prm%rho_min/geom(ph)%V_0(me)**(2.0_pReal/3.0_pReal),prm%rho_significant)) &
|
||
getRho0 = 0.0_pReal
|
||
|
||
end associate
|
||
|
||
end function getRho0
|
||
|
||
|
||
subroutine storeGeometry(ph)
|
||
|
||
integer, intent(in) :: ph
|
||
|
||
integer :: ce, co
|
||
real(pReal), dimension(:), allocatable :: V
|
||
|
||
|
||
V = reshape(IPvolume,[product(shape(IPvolume))])
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||
do ce = 1, size(material_homogenizationMemberAt2,1)
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||
do co = 1, homogenization_maxNconstituents
|
||
if (material_phaseAt2(co,ce) == ph) geom(ph)%V_0(material_phaseMemberAt2(co,ce)) = V(ce)
|
||
enddo
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||
enddo
|
||
|
||
end subroutine
|
||
|
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end submodule nonlocal
|