3619 lines
199 KiB
Fortran
3619 lines
199 KiB
Fortran
! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!##############################################################
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!* $Id$
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!************************************
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!* Module: CONSTITUTIVE_NONLOCAL *
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!************************************
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!* contains: *
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!* - constitutive equations *
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!* - parameters definition *
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!************************************
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MODULE constitutive_nonlocal
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!* Include other modules
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use prec, only: pReal,pInt
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implicit none
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private
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!* Definition of parameters
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character (len=*), parameter, public :: &
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constitutive_nonlocal_label = 'nonlocal'
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character(len=22), dimension(10), parameter, private :: &
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constitutive_nonlocal_listBasicStates = (/'rhoSglEdgePosMobile ', &
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'rhoSglEdgeNegMobile ', &
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'rhoSglScrewPosMobile ', &
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'rhoSglScrewNegMobile ', &
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'rhoSglEdgePosImmobile ', &
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'rhoSglEdgeNegImmobile ', &
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'rhoSglScrewPosImmobile', &
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'rhoSglScrewNegImmobile', &
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'rhoDipEdge ', &
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'rhoDipScrew ' /)! list of "basic" microstructural state variables that are independent from other state variables
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character(len=16), dimension(3), parameter, private :: &
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constitutive_nonlocal_listDependentStates = (/'rhoForest ', &
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'tauThreshold ', &
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'tauBack ' /) ! list of microstructural state variables that depend on other state variables
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character(len=20), dimension(6), parameter, private :: &
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constitutive_nonlocal_listOtherStates = (/'velocityEdgePos ', &
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'velocityEdgeNeg ', &
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'velocityScrewPos ', &
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'velocityScrewNeg ', &
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'maxDipoleHeightEdge ', &
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'maxDipoleHeightScrew' /) ! list of other dependent state variables that are not updated by microstructure
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real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin
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!* Definition of global variables
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integer(pInt), dimension(:), allocatable, public :: &
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constitutive_nonlocal_sizeDotState, & ! number of dotStates = number of basic state variables
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constitutive_nonlocal_sizeDependentState, & ! number of dependent state variables
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constitutive_nonlocal_sizeState, & ! total number of state variables
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constitutive_nonlocal_sizePostResults ! cumulative size of post results
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integer(pInt), dimension(:,:), allocatable, target, public :: &
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constitutive_nonlocal_sizePostResult ! size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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constitutive_nonlocal_output ! name of each post result output
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integer(pInt), dimension(:), allocatable, private :: &
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constitutive_nonlocal_Noutput ! number of outputs per instance of this plasticity
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character(len=32), dimension(:), allocatable, public :: &
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constitutive_nonlocal_structureName ! name of the lattice structure
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integer(pInt), dimension(:), allocatable, public :: &
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constitutive_nonlocal_structure ! number representing the kind of lattice structure
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integer(pInt), dimension(:), allocatable, private :: &
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constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance
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integer(pInt), dimension(:,:), allocatable, private :: &
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constitutive_nonlocal_Nslip, & ! number of active slip systems for each family and instance
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constitutive_nonlocal_slipFamily, & ! lookup table relating active slip system to slip family for each instance
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constitutive_nonlocal_slipSystemLattice, & ! lookup table relating active slip system index to lattice slip system index for each instance
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constitutive_nonlocal_colinearSystem ! colinear system to the active slip system (only valid for fcc!)
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real(pReal), dimension(:), allocatable, private :: &
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constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice
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constitutive_nonlocal_Gmod, & ! shear modulus
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constitutive_nonlocal_nu, & ! poisson's ratio
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constitutive_nonlocal_atomicVolume, & ! atomic volume
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constitutive_nonlocal_Dsd0, & ! prefactor for self-diffusion coefficient
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constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion
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constitutive_nonlocal_aTolRho, & ! absolute tolerance for dislocation density in state integration
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constitutive_nonlocal_significantRho, & ! density considered significant
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constitutive_nonlocal_significantN, & ! number of dislocations considered significant
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constitutive_nonlocal_R, & ! cutoff radius for dislocation stress
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constitutive_nonlocal_doublekinkwidth, & ! width of a doubkle kink in multiples of the burgers vector length b
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constitutive_nonlocal_solidSolutionEnergy, & ! activation energy for solid solution in J
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constitutive_nonlocal_solidSolutionSize, & ! solid solution obstacle size in multiples of the burgers vector length
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constitutive_nonlocal_solidSolutionConcentration, & ! concentration of solid solution in atomic parts
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constitutive_nonlocal_p, & ! parameter for kinetic law (Kocks,Argon,Ashby)
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constitutive_nonlocal_q, & ! parameter for kinetic law (Kocks,Argon,Ashby)
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constitutive_nonlocal_viscosity, & ! viscosity for dislocation glide in Pa s
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constitutive_nonlocal_fattack, & ! attack frequency in Hz
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constitutive_nonlocal_vmax, & ! maximum allowed velocity
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constitutive_nonlocal_rhoSglScatter, & ! standard deviation of scatter in initial dislocation density
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constitutive_nonlocal_surfaceTransmissivity, & ! transmissivity at free surface
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constitutive_nonlocal_grainboundaryTransmissivity, & ! transmissivity at grain boundary (identified by different texture)
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constitutive_nonlocal_CFLfactor, & ! safety factor for CFL flux condition
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constitutive_nonlocal_fEdgeMultiplication, & ! factor that determines how much edge dislocations contribute to multiplication (0...1)
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constitutive_nonlocal_rhoSglRandom, &
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constitutive_nonlocal_rhoSglRandomBinning, &
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constitutive_nonlocal_linetensionEffect, &
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constitutive_nonlocal_edgeJogFactor
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real(pReal), dimension(:,:), allocatable, private :: &
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constitutive_nonlocal_rhoSglEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoSglEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoSglScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoSglScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoDipEdge0, & ! initial edge dipole dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoDipScrew0, & ! initial screw dipole dislocation density per slip system for each family and instance
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constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance
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constitutive_nonlocal_lambda0, & ! mean free path prefactor for each slip system and instance
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constitutive_nonlocal_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each family and instance
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constitutive_nonlocal_burgers, & ! absolute length of burgers vector [m] for each slip system and instance
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constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
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real(pReal), dimension(:,:,:), allocatable, private :: &
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constitutive_nonlocal_Cslip_66, & ! elasticity matrix in Mandel notation for each instance
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constitutive_nonlocal_minimumDipoleHeightPerSlipFamily, & ! minimum stable edge/screw dipole height for each family and instance
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constitutive_nonlocal_minimumDipoleHeight, & ! minimum stable edge/screw dipole height for each slip system and instance
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constitutive_nonlocal_peierlsStressPerSlipFamily, & ! Peierls stress (edge and screw)
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constitutive_nonlocal_peierlsStress, & ! Peierls stress (edge and screw)
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constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each instance
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constitutive_nonlocal_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance
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constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance
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real(pReal), dimension(:,:,:,:), allocatable, private :: &
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constitutive_nonlocal_lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!)
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constitutive_nonlocal_accumulatedShear, & ! accumulated shear per slip system up to the start of the FE increment
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constitutive_nonlocal_rhoDotEdgeJogs, &
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constitutive_nonlocal_sourceProbability
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real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
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constitutive_nonlocal_Cslip_3333, & ! elasticity matrix for each instance
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constitutive_nonlocal_rhoDotFlux, & ! dislocation convection term
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constitutive_nonlocal_rhoDotMultiplication, &
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constitutive_nonlocal_rhoDotSingle2DipoleGlide, &
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constitutive_nonlocal_rhoDotAthermalAnnihilation, &
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constitutive_nonlocal_rhoDotThermalAnnihilation
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real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: &
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constitutive_nonlocal_compatibility ! slip system compatibility between me and my neighbors
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logical, dimension(:), allocatable, private :: &
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constitutive_nonlocal_shortRangeStressCorrection, & ! flag indicating the use of the short range stress correction by a excess density gradient term
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constitutive_nonlocal_deadZoneScaling, &
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constitutive_nonlocal_probabilisticMultiplication
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public :: &
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constitutive_nonlocal_init, &
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constitutive_nonlocal_stateInit, &
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constitutive_nonlocal_aTolState, &
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constitutive_nonlocal_homogenizedC, &
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constitutive_nonlocal_microstructure, &
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constitutive_nonlocal_LpAndItsTangent, &
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constitutive_nonlocal_dotState, &
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constitutive_nonlocal_deltaState, &
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constitutive_nonlocal_dotTemperature, &
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constitutive_nonlocal_updateCompatibility, &
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constitutive_nonlocal_postResults
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private :: &
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constitutive_nonlocal_kinetics
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CONTAINS
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!**************************************
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!* Module initialization *
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!**************************************
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subroutine constitutive_nonlocal_init(myFile)
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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use prec, only: pInt, pReal
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use math, only: math_Mandel3333to66, &
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math_Voigt66to3333, &
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math_mul3x3, &
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math_transpose33
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use IO, only: IO_lc, &
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IO_getTag, &
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IO_isBlank, &
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IO_stringPos, &
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IO_stringValue, &
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IO_floatValue, &
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IO_intValue, &
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IO_error
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use debug, only: debug_level, &
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debug_constitutive, &
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debug_levelBasic
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use mesh, only: mesh_NcpElems, &
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mesh_maxNips, &
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FE_maxNipNeighbors
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use material, only: homogenization_maxNgrains, &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput
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use lattice, only: lattice_maxNslipFamily, &
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lattice_maxNslip, &
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lattice_maxNinteraction, &
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lattice_NslipSystem, &
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lattice_initializeStructure, &
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lattice_symmetrizeC66, &
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lattice_sd, &
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lattice_sn, &
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lattice_st, &
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lattice_interactionSlipSlip
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!*** output variables
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!*** input variables
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integer(pInt), intent(in) :: myFile
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!*** local variables
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integer(pInt), parameter :: maxNchunks = 21_pInt
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integer(pInt), &
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dimension(1_pInt+2_pInt*maxNchunks) :: positions
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integer(pInt) section, &
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maxNinstance, &
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maxTotalNslip, &
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myStructure, &
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f, & ! index of my slip family
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i, & ! index of my instance of this plasticity
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j, &
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k, &
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l, &
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ns, & ! short notation for total number of active slip systems for the current instance
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o, & ! index of my output
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s, & ! index of my slip system
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s1, & ! index of my slip system
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s2, & ! index of my slip system
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it, & ! index of my interaction type
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mySize
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character(len=64) tag
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character(len=1024) :: line = '' ! to start initialized
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write(6,*)
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write(6,*) '<<<+- constitutive_',trim(constitutive_nonlocal_label),' init -+>>>'
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write(6,*) '$Id$'
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#include "compilation_info.f90"
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maxNinstance = int(count(phase_plasticity == constitutive_nonlocal_label),pInt)
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if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) then
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write(6,'(a16,1x,i5)') '# instances:',maxNinstance
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endif
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!*** space allocation for global variables
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allocate(constitutive_nonlocal_sizeDotState(maxNinstance))
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allocate(constitutive_nonlocal_sizeDependentState(maxNinstance))
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allocate(constitutive_nonlocal_sizeState(maxNinstance))
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allocate(constitutive_nonlocal_sizePostResults(maxNinstance))
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allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance))
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allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance))
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allocate(constitutive_nonlocal_Noutput(maxNinstance))
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constitutive_nonlocal_sizeDotState = 0_pInt
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constitutive_nonlocal_sizeDependentState = 0_pInt
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constitutive_nonlocal_sizeState = 0_pInt
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constitutive_nonlocal_sizePostResults = 0_pInt
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constitutive_nonlocal_sizePostResult = 0_pInt
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constitutive_nonlocal_output = ''
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constitutive_nonlocal_Noutput = 0_pInt
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allocate(constitutive_nonlocal_structureName(maxNinstance))
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allocate(constitutive_nonlocal_structure(maxNinstance))
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allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance))
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allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance))
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allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance))
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allocate(constitutive_nonlocal_totalNslip(maxNinstance))
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constitutive_nonlocal_structureName = ''
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constitutive_nonlocal_structure = 0_pInt
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constitutive_nonlocal_Nslip = 0_pInt
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constitutive_nonlocal_slipFamily = 0_pInt
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constitutive_nonlocal_slipSystemLattice = 0_pInt
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constitutive_nonlocal_totalNslip = 0_pInt
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allocate(constitutive_nonlocal_CoverA(maxNinstance))
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allocate(constitutive_nonlocal_Gmod(maxNinstance))
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allocate(constitutive_nonlocal_nu(maxNinstance))
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allocate(constitutive_nonlocal_atomicVolume(maxNinstance))
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allocate(constitutive_nonlocal_Dsd0(maxNinstance))
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allocate(constitutive_nonlocal_Qsd(maxNinstance))
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allocate(constitutive_nonlocal_aTolRho(maxNinstance))
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allocate(constitutive_nonlocal_significantRho(maxNinstance))
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allocate(constitutive_nonlocal_significantN(maxNinstance))
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allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance))
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allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance))
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allocate(constitutive_nonlocal_R(maxNinstance))
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allocate(constitutive_nonlocal_doublekinkwidth(maxNinstance))
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allocate(constitutive_nonlocal_solidSolutionEnergy(maxNinstance))
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allocate(constitutive_nonlocal_solidSolutionSize(maxNinstance))
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allocate(constitutive_nonlocal_solidSolutionConcentration(maxNinstance))
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allocate(constitutive_nonlocal_p(maxNinstance))
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allocate(constitutive_nonlocal_q(maxNinstance))
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allocate(constitutive_nonlocal_viscosity(maxNinstance))
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allocate(constitutive_nonlocal_fattack(maxNinstance))
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allocate(constitutive_nonlocal_vmax(maxNinstance))
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allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance))
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allocate(constitutive_nonlocal_rhoSglRandom(maxNinstance))
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allocate(constitutive_nonlocal_rhoSglRandomBinning(maxNinstance))
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allocate(constitutive_nonlocal_surfaceTransmissivity(maxNinstance))
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allocate(constitutive_nonlocal_grainboundaryTransmissivity(maxNinstance))
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allocate(constitutive_nonlocal_shortRangeStressCorrection(maxNinstance))
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allocate(constitutive_nonlocal_deadZoneScaling(maxNinstance))
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allocate(constitutive_nonlocal_probabilisticMultiplication(maxNinstance))
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allocate(constitutive_nonlocal_CFLfactor(maxNinstance))
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allocate(constitutive_nonlocal_fEdgeMultiplication(maxNinstance))
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allocate(constitutive_nonlocal_linetensionEffect(maxNinstance))
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allocate(constitutive_nonlocal_edgeJogFactor(maxNinstance))
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constitutive_nonlocal_CoverA = 0.0_pReal
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constitutive_nonlocal_Gmod = 0.0_pReal
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constitutive_nonlocal_atomicVolume = 0.0_pReal
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constitutive_nonlocal_Dsd0 = -1.0_pReal
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constitutive_nonlocal_Qsd = 0.0_pReal
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constitutive_nonlocal_aTolRho = 0.0_pReal
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constitutive_nonlocal_significantRho = 0.0_pReal
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constitutive_nonlocal_significantN = 0.0_pReal
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constitutive_nonlocal_nu = 0.0_pReal
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constitutive_nonlocal_Cslip_66 = 0.0_pReal
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constitutive_nonlocal_Cslip_3333 = 0.0_pReal
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constitutive_nonlocal_R = -1.0_pReal
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constitutive_nonlocal_doublekinkwidth = 0.0_pReal
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constitutive_nonlocal_solidSolutionEnergy = 0.0_pReal
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constitutive_nonlocal_solidSolutionSize = 0.0_pReal
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constitutive_nonlocal_solidSolutionConcentration = 0.0_pReal
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constitutive_nonlocal_p = 1.0_pReal
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constitutive_nonlocal_q = 1.0_pReal
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constitutive_nonlocal_viscosity = 0.0_pReal
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constitutive_nonlocal_fattack = 0.0_pReal
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constitutive_nonlocal_vmax = 0.0_pReal
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constitutive_nonlocal_rhoSglScatter = 0.0_pReal
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constitutive_nonlocal_rhoSglRandom = 0.0_pReal
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constitutive_nonlocal_rhoSglRandomBinning = 1.0_pReal
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constitutive_nonlocal_surfaceTransmissivity = 1.0_pReal
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constitutive_nonlocal_grainboundaryTransmissivity = -1.0_pReal
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constitutive_nonlocal_CFLfactor = 2.0_pReal
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constitutive_nonlocal_fEdgeMultiplication = 0.0_pReal
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constitutive_nonlocal_linetensionEffect = 0.0_pReal
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constitutive_nonlocal_edgeJogFactor = 1.0_pReal
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constitutive_nonlocal_shortRangeStressCorrection = .false.
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constitutive_nonlocal_deadZoneScaling = .false.
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constitutive_nonlocal_probabilisticMultiplication = .false.
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allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_rhoSglScrewPos0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_rhoSglScrewNeg0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_rhoDipEdge0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_rhoDipScrew0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
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constitutive_nonlocal_rhoSglEdgePos0 = -1.0_pReal
|
|
constitutive_nonlocal_rhoSglEdgeNeg0 = -1.0_pReal
|
|
constitutive_nonlocal_rhoSglScrewPos0 = -1.0_pReal
|
|
constitutive_nonlocal_rhoSglScrewNeg0 = -1.0_pReal
|
|
constitutive_nonlocal_rhoDipEdge0 = -1.0_pReal
|
|
constitutive_nonlocal_rhoDipScrew0 = -1.0_pReal
|
|
constitutive_nonlocal_burgersPerSlipFamily = 0.0_pReal
|
|
constitutive_nonlocal_lambda0PerSlipFamily = 0.0_pReal
|
|
constitutive_nonlocal_interactionSlipSlip = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance))
|
|
allocate(constitutive_nonlocal_peierlsStressPerSlipFamily(lattice_maxNslipFamily,2,maxNinstance))
|
|
constitutive_nonlocal_minimumDipoleHeightPerSlipFamily = -1.0_pReal
|
|
constitutive_nonlocal_peierlsStressPerSlipFamily = 0.0_pReal
|
|
|
|
!*** readout data from material.config file
|
|
|
|
rewind(myFile)
|
|
line = ''
|
|
section = 0_pInt
|
|
|
|
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
|
|
read(myFile,'(a1024)',END=100) line
|
|
enddo
|
|
|
|
do ! read thru sections of phase part
|
|
read(myFile,'(a1024)',END=100) line
|
|
if (IO_isBlank(line)) cycle ! skip empty lines
|
|
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
|
|
if (IO_getTag(line,'[',']') /= '') then ! next section
|
|
section = section + 1_pInt ! advance section counter
|
|
cycle
|
|
endif
|
|
if (section > 0_pInt .and. phase_plasticity(section) == constitutive_nonlocal_label) then ! one of my sections
|
|
i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
|
|
positions = IO_stringPos(line,maxNchunks)
|
|
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
|
|
select case(tag)
|
|
case('plasticity','elasticity','/nonlocal/')
|
|
cycle
|
|
case ('(output)')
|
|
constitutive_nonlocal_Noutput(i) = constitutive_nonlocal_Noutput(i) + 1_pInt
|
|
constitutive_nonlocal_output(constitutive_nonlocal_Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt))
|
|
case ('lattice_structure')
|
|
constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
|
|
case ('c/a_ratio','covera_ratio')
|
|
constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c11')
|
|
constitutive_nonlocal_Cslip_66(1,1,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c12')
|
|
constitutive_nonlocal_Cslip_66(1,2,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c13')
|
|
constitutive_nonlocal_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c22')
|
|
constitutive_nonlocal_Cslip_66(2,2,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c23')
|
|
constitutive_nonlocal_Cslip_66(2,3,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c33')
|
|
constitutive_nonlocal_Cslip_66(3,3,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c44')
|
|
constitutive_nonlocal_Cslip_66(4,4,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c55')
|
|
constitutive_nonlocal_Cslip_66(5,5,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('c66')
|
|
constitutive_nonlocal_Cslip_66(6,6,i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('nslip')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1_pInt+f)
|
|
case ('rhosgledgepos0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoSglEdgePos0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('rhosgledgeneg0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoSglEdgeNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('rhosglscrewpos0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoSglScrewPos0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('rhosglscrewneg0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoSglScrewNeg0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('rhodipedge0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoDipEdge0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('rhodipscrew0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_rhoDipScrew0(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('lambda0')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case ('burgers')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case('cutoffradius','r')
|
|
constitutive_nonlocal_R(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('minimumdipoleheightedge','ddipminedge')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case('minimumdipoleheightscrew','ddipminscrew')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case('atomicvolume')
|
|
constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('selfdiffusionprefactor','dsd0')
|
|
constitutive_nonlocal_Dsd0(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('selfdiffusionenergy','qsd')
|
|
constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('atol_rho','absolutetolerancerho','absolutetolerance_rho','absolutetolerancedensity','absolutetolerance_density')
|
|
constitutive_nonlocal_aTolRho(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('significantrho','significant_rho','significantdensity','significant_density')
|
|
constitutive_nonlocal_significantRho(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('significantn','significant_n','significantdislocations','significant_dislcations')
|
|
constitutive_nonlocal_significantN(i) = IO_floatValue(line,positions,2_pInt)
|
|
case ('interaction_slipslip')
|
|
forall (it = 1_pInt:lattice_maxNinteraction) &
|
|
constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1_pInt+it)
|
|
case('linetension','linetensioneffect','linetension_effect')
|
|
constitutive_nonlocal_linetensionEffect(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('edgejog','edgejogs','edgejogeffect','edgejog_effect')
|
|
constitutive_nonlocal_edgeJogFactor(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('peierlsstressedge','peierlsstress_edge')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_peierlsStressPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case('peierlsstressscrew','peierlsstress_screw')
|
|
forall (f = 1_pInt:lattice_maxNslipFamily) &
|
|
constitutive_nonlocal_peierlsStressPerSlipFamily(f,2_pInt,i) = IO_floatValue(line,positions,1_pInt+f)
|
|
case('doublekinkwidth')
|
|
constitutive_nonlocal_doublekinkwidth(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('solidsolutionenergy')
|
|
constitutive_nonlocal_solidSolutionEnergy(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('solidsolutionsize')
|
|
constitutive_nonlocal_solidSolutionSize(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('solidsolutionconcentration')
|
|
constitutive_nonlocal_solidSolutionConcentration(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('p')
|
|
constitutive_nonlocal_p(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('q')
|
|
constitutive_nonlocal_q(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('viscosity','glideviscosity')
|
|
constitutive_nonlocal_viscosity(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('attackfrequency','fattack')
|
|
constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('maximumvelocity','vmax')
|
|
constitutive_nonlocal_vmax(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('rhosglscatter')
|
|
constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('rhosglrandom')
|
|
constitutive_nonlocal_rhoSglRandom(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('rhosglrandombinning')
|
|
constitutive_nonlocal_rhoSglRandomBinning(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('surfacetransmissivity')
|
|
constitutive_nonlocal_surfaceTransmissivity(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('grainboundarytransmissivity')
|
|
constitutive_nonlocal_grainboundaryTransmissivity(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('cflfactor')
|
|
constitutive_nonlocal_CFLfactor(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('fedgemultiplication','edgemultiplicationfactor','edgemultiplication')
|
|
constitutive_nonlocal_fEdgeMultiplication(i) = IO_floatValue(line,positions,2_pInt)
|
|
case('shortrangestresscorrection')
|
|
constitutive_nonlocal_shortRangeStressCorrection(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
|
|
case('deadzonescaling','deadzone','deadscaling')
|
|
constitutive_nonlocal_deadZoneScaling(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
|
|
case('probabilisticmultiplication','randomsources','randommultiplication','discretesources')
|
|
constitutive_nonlocal_probabilisticMultiplication(i) = IO_floatValue(line,positions,2_pInt) > 0.0_pReal
|
|
case default
|
|
call IO_error(210_pInt,ext_msg=tag//' ('//constitutive_nonlocal_label//')')
|
|
end select
|
|
endif
|
|
enddo
|
|
|
|
|
|
100 do i = 1_pInt,maxNinstance
|
|
|
|
constitutive_nonlocal_structure(i) = &
|
|
lattice_initializeStructure(constitutive_nonlocal_structureName(i), constitutive_nonlocal_CoverA(i)) ! our lattice structure is defined in the material.config file by the structureName (and the c/a ratio)
|
|
myStructure = constitutive_nonlocal_structure(i)
|
|
|
|
|
|
!*** sanity checks
|
|
|
|
if (myStructure < 1_pInt) call IO_error(205_pInt,e=i)
|
|
if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0_pInt) call IO_error(211_pInt,ext_msg='Nslip (' &
|
|
//constitutive_nonlocal_label//')')
|
|
do o = 1_pInt,maxval(phase_Noutput)
|
|
if(len(constitutive_nonlocal_output(o,i)) > 64_pInt) call IO_error(666_pInt)
|
|
enddo
|
|
do f = 1_pInt,lattice_maxNslipFamily
|
|
if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then
|
|
if (constitutive_nonlocal_rhoSglEdgePos0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglEdgePos0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglEdgeNeg0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScrewPos0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScrewNeg0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoDipEdge0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoDipScrew0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='Burgers (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='lambda0 (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1,i) < 0.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='minimumDipoleHeightEdge (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,2,i) < 0.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='minimumDipoleHeightScrew (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,1,i) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='peierlsStressEdge (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,2,i) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='peierlsStressScrew (' &
|
|
//constitutive_nonlocal_label//')')
|
|
endif
|
|
enddo
|
|
if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) &
|
|
call IO_error(211_pInt,ext_msg='interaction_SlipSlip (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_linetensionEffect(i) < 0.0_pReal .or. constitutive_nonlocal_linetensionEffect(i) > 1.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='linetension (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_edgeJogFactor(i) < 0.0_pReal .or. constitutive_nonlocal_edgeJogFactor(i) > 1.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='edgejog (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_R(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='r (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='atomicVolume (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_Dsd0(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='selfDiffusionPrefactor (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='selfDiffusionEnergy (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_aTolRho(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='aTol_rho (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_significantRho(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='significantRho (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_significantN(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='significantN (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_doublekinkwidth(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='doublekinkwidth (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_solidSolutionEnergy(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='solidSolutionEnergy (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_solidSolutionSize(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='solidSolutionSize (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_solidSolutionConcentration(i) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='solidSolutionConcentration (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_p(i) <= 0.0_pReal .or. constitutive_nonlocal_p(i) > 1.0_pReal) call IO_error(211_pInt,ext_msg='p (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_q(i) < 1.0_pReal .or. constitutive_nonlocal_q(i) > 2.0_pReal) call IO_error(211_pInt,ext_msg='q (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_viscosity(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='viscosity (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='attackFrequency (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_vmax(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='maximumVelocity (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglScatter (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglRandom(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglRandom (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_rhoSglRandomBinning(i) <= 0.0_pReal) call IO_error(211_pInt,ext_msg='rhoSglRandomBinning (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_surfaceTransmissivity(i) < 0.0_pReal &
|
|
.or. constitutive_nonlocal_surfaceTransmissivity(i) > 1.0_pReal) call IO_error(211_pInt,ext_msg='surfaceTransmissivity (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_grainboundaryTransmissivity(i) > 1.0_pReal) call IO_error(211_pInt,&
|
|
ext_msg='grainboundaryTransmissivity ('//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_CFLfactor(i) < 0.0_pReal) call IO_error(211_pInt,ext_msg='CFLfactor (' &
|
|
//constitutive_nonlocal_label//')')
|
|
if (constitutive_nonlocal_fEdgeMultiplication(i) < 0.0_pReal .or. constitutive_nonlocal_fEdgeMultiplication(i) > 1.0_pReal) &
|
|
call IO_error(211_pInt,ext_msg='edgemultiplicationfactor ('&
|
|
//constitutive_nonlocal_label//')')
|
|
|
|
|
|
!*** determine total number of active slip systems
|
|
|
|
constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i) = min( lattice_NslipSystem(1:lattice_maxNslipFamily, myStructure), &
|
|
constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i) ) ! we can't use more slip systems per family than specified in lattice
|
|
constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(1:lattice_maxNslipFamily,i))
|
|
|
|
enddo
|
|
|
|
|
|
!*** allocation of variables whose size depends on the total number of active slip systems
|
|
|
|
maxTotalNslip = maxval(constitutive_nonlocal_totalNslip)
|
|
|
|
allocate(constitutive_nonlocal_burgers(maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_burgers = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_lambda0(maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_lambda0 = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_minimumDipoleHeight(maxTotalNslip,2,maxNinstance))
|
|
constitutive_nonlocal_minimumDipoleHeight = -1.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_forestProjectionEdge = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_forestProjectionScrew(maxTotalNslip, maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_forestProjectionScrew = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_interactionMatrixSlipSlip(maxTotalNslip, maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_interactionMatrixSlipSlip = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_lattice2slip(1:3, 1:3, maxTotalNslip, maxNinstance))
|
|
constitutive_nonlocal_lattice2slip = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_accumulatedShear(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
constitutive_nonlocal_accumulatedShear = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_sourceProbability(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
constitutive_nonlocal_sourceProbability = 2.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_rhoDotFlux(maxTotalNslip, 8, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
allocate(constitutive_nonlocal_rhoDotMultiplication(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
allocate(constitutive_nonlocal_rhoDotSingle2DipoleGlide(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
allocate(constitutive_nonlocal_rhoDotAthermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
allocate(constitutive_nonlocal_rhoDotThermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
allocate(constitutive_nonlocal_rhoDotEdgeJogs(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
|
|
constitutive_nonlocal_rhoDotFlux = 0.0_pReal
|
|
constitutive_nonlocal_rhoDotMultiplication = 0.0_pReal
|
|
constitutive_nonlocal_rhoDotSingle2DipoleGlide = 0.0_pReal
|
|
constitutive_nonlocal_rhoDotAthermalAnnihilation = 0.0_pReal
|
|
constitutive_nonlocal_rhoDotThermalAnnihilation = 0.0_pReal
|
|
constitutive_nonlocal_rhoDotEdgeJogs = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_compatibility(2,maxTotalNslip, maxTotalNslip, FE_maxNipNeighbors, mesh_maxNips, mesh_NcpElems))
|
|
constitutive_nonlocal_compatibility = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_peierlsStress(maxTotalNslip,2,maxNinstance))
|
|
constitutive_nonlocal_peierlsStress = 0.0_pReal
|
|
|
|
allocate(constitutive_nonlocal_colinearSystem(maxTotalNslip,maxNinstance))
|
|
constitutive_nonlocal_colinearSystem = 0_pInt
|
|
|
|
do i = 1,maxNinstance
|
|
|
|
myStructure = constitutive_nonlocal_structure(i) ! lattice structure of this instance
|
|
|
|
|
|
!*** Inverse lookup of my slip system family and the slip system in lattice
|
|
|
|
l = 0_pInt
|
|
do f = 1_pInt,lattice_maxNslipFamily
|
|
do s = 1_pInt,constitutive_nonlocal_Nslip(f,i)
|
|
l = l + 1_pInt
|
|
constitutive_nonlocal_slipFamily(l,i) = f
|
|
constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1_pInt, myStructure)) + s
|
|
enddo; enddo
|
|
|
|
|
|
!*** determine size of state array
|
|
|
|
ns = constitutive_nonlocal_totalNslip(i)
|
|
constitutive_nonlocal_sizeDotState(i) = int(size(constitutive_nonlocal_listBasicStates),pInt) * ns
|
|
constitutive_nonlocal_sizeDependentState(i) = int(size(constitutive_nonlocal_listDependentStates),pInt) * ns
|
|
constitutive_nonlocal_sizeState(i) = constitutive_nonlocal_sizeDotState(i) &
|
|
+ constitutive_nonlocal_sizeDependentState(i) &
|
|
+ int(size(constitutive_nonlocal_listOtherStates),pInt) * ns
|
|
|
|
|
|
!*** determine size of postResults array
|
|
|
|
do o = 1_pInt,constitutive_nonlocal_Noutput(i)
|
|
select case(constitutive_nonlocal_output(o,i))
|
|
case( 'rho', &
|
|
'delta', &
|
|
'rho_edge', &
|
|
'rho_screw', &
|
|
'rho_sgl', &
|
|
'delta_sgl', &
|
|
'rho_sgl_edge', &
|
|
'rho_sgl_edge_pos', &
|
|
'rho_sgl_edge_neg', &
|
|
'rho_sgl_screw', &
|
|
'rho_sgl_screw_pos', &
|
|
'rho_sgl_screw_neg', &
|
|
'rho_sgl_mobile', &
|
|
'rho_sgl_edge_mobile', &
|
|
'rho_sgl_edge_pos_mobile', &
|
|
'rho_sgl_edge_neg_mobile', &
|
|
'rho_sgl_screw_mobile', &
|
|
'rho_sgl_screw_pos_mobile', &
|
|
'rho_sgl_screw_neg_mobile', &
|
|
'rho_sgl_immobile', &
|
|
'rho_sgl_edge_immobile', &
|
|
'rho_sgl_edge_pos_immobile', &
|
|
'rho_sgl_edge_neg_immobile', &
|
|
'rho_sgl_screw_immobile', &
|
|
'rho_sgl_screw_pos_immobile', &
|
|
'rho_sgl_screw_neg_immobile', &
|
|
'rho_dip', &
|
|
'delta_dip', &
|
|
'rho_dip_edge', &
|
|
'rho_dip_screw', &
|
|
'excess_rho', &
|
|
'excess_rho_edge', &
|
|
'excess_rho_screw', &
|
|
'rho_forest', &
|
|
'shearrate', &
|
|
'resolvedstress', &
|
|
'resolvedstress_external', &
|
|
'resolvedstress_back', &
|
|
'resistance', &
|
|
'rho_dot', &
|
|
'rho_dot_sgl', &
|
|
'rho_dot_dip', &
|
|
'rho_dot_gen', &
|
|
'rho_dot_gen_edge', &
|
|
'rho_dot_gen_screw', &
|
|
'rho_dot_sgl2dip', &
|
|
'rho_dot_sgl2dip_edge', &
|
|
'rho_dot_sgl2dip_screw', &
|
|
'rho_dot_ann_ath', &
|
|
'rho_dot_ann_the', &
|
|
'rho_dot_ann_the_edge', &
|
|
'rho_dot_ann_the_screw', &
|
|
'rho_dot_edgejogs', &
|
|
'rho_dot_flux', &
|
|
'rho_dot_flux_edge', &
|
|
'rho_dot_flux_screw', &
|
|
'velocity_edge_pos', &
|
|
'velocity_edge_neg', &
|
|
'velocity_screw_pos', &
|
|
'velocity_screw_neg', &
|
|
'fluxdensity_edge_pos_x', &
|
|
'fluxdensity_edge_pos_y', &
|
|
'fluxdensity_edge_pos_z', &
|
|
'fluxdensity_edge_neg_x', &
|
|
'fluxdensity_edge_neg_y', &
|
|
'fluxdensity_edge_neg_z', &
|
|
'fluxdensity_screw_pos_x', &
|
|
'fluxdensity_screw_pos_y', &
|
|
'fluxdensity_screw_pos_z', &
|
|
'fluxdensity_screw_neg_x', &
|
|
'fluxdensity_screw_neg_y', &
|
|
'fluxdensity_screw_neg_z', &
|
|
'maximumdipoleheight_edge', &
|
|
'maximumdipoleheight_screw', &
|
|
'accumulatedshear', &
|
|
'boundarylayer' )
|
|
mySize = constitutive_nonlocal_totalNslip(i)
|
|
case('dislocationstress')
|
|
mySize = 6_pInt
|
|
case default
|
|
call IO_error(212_pInt,ext_msg=constitutive_nonlocal_output(o,i)//' ('//constitutive_nonlocal_label//')')
|
|
end select
|
|
|
|
if (mySize > 0_pInt) then ! any meaningful output found
|
|
constitutive_nonlocal_sizePostResult(o,i) = mySize
|
|
constitutive_nonlocal_sizePostResults(i) = constitutive_nonlocal_sizePostResults(i) + mySize
|
|
endif
|
|
enddo
|
|
|
|
|
|
!*** elasticity matrix and shear modulus according to material.config
|
|
|
|
constitutive_nonlocal_Cslip_66(:,:,i) = lattice_symmetrizeC66(constitutive_nonlocal_structureName(i),&
|
|
constitutive_nonlocal_Cslip_66)
|
|
constitutive_nonlocal_Gmod(i) = 0.2_pReal * ( constitutive_nonlocal_Cslip_66(1,1,i) - constitutive_nonlocal_Cslip_66(1,2,i) &
|
|
+ 3.0_pReal*constitutive_nonlocal_Cslip_66(4,4,i) ) ! (C11iso-C12iso)/2 with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
|
constitutive_nonlocal_nu(i) = ( constitutive_nonlocal_Cslip_66(1,1,i) + 4.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) &
|
|
- 2.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) ) &
|
|
/ ( 4.0_pReal*constitutive_nonlocal_Cslip_66(1,1,i) + 6.0_pReal*constitutive_nonlocal_Cslip_66(1,2,i) &
|
|
+ 2.0_pReal*constitutive_nonlocal_Cslip_66(4,4,i) )
|
|
constitutive_nonlocal_Cslip_66(1:6,1:6,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(1:6,1:6,i)))
|
|
constitutive_nonlocal_Cslip_3333(1:3,1:3,1:3,1:3,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(1:6,1:6,i))
|
|
! C12iso/(C11iso+C12iso) with C11iso=(3*C11+2*C12+4*C44)/5 and C12iso=(C11+4*C12-2*C44)/5
|
|
|
|
do s1 = 1_pInt,ns
|
|
f = constitutive_nonlocal_slipFamily(s1,i)
|
|
|
|
!*** burgers vector, mean free path prefactor and minimum dipole distance for each slip system
|
|
|
|
constitutive_nonlocal_burgers(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i)
|
|
constitutive_nonlocal_lambda0(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i)
|
|
constitutive_nonlocal_minimumDipoleHeight(s1,1:2,i) = constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1:2,i)
|
|
constitutive_nonlocal_peierlsStress(s1,1:2,i) = constitutive_nonlocal_peierlsStressPerSlipFamily(f,1:2,i)
|
|
|
|
do s2 = 1_pInt,ns
|
|
|
|
!*** calculation of forest projections for edge and screw dislocations. s2 acts as forest for s1
|
|
|
|
constitutive_nonlocal_forestProjectionEdge(s1,s2,i) &
|
|
= abs(math_mul3x3(lattice_sn(1:3,constitutive_nonlocal_slipSystemLattice(s1,i),myStructure), &
|
|
lattice_st(1:3,constitutive_nonlocal_slipSystemLattice(s2,i),myStructure))) ! forest projection of edge dislocations is the projection of (t = b x n) onto the slip normal of the respective slip plane
|
|
|
|
constitutive_nonlocal_forestProjectionScrew(s1,s2,i) &
|
|
= abs(math_mul3x3(lattice_sn(1:3,constitutive_nonlocal_slipSystemLattice(s1,i),myStructure), &
|
|
lattice_sd(1:3,constitutive_nonlocal_slipSystemLattice(s2,i),myStructure))) ! forest projection of screw dislocations is the projection of b onto the slip normal of the respective splip plane
|
|
|
|
!*** calculation of interaction matrices
|
|
|
|
constitutive_nonlocal_interactionMatrixSlipSlip(s1,s2,i) &
|
|
= constitutive_nonlocal_interactionSlipSlip(lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), &
|
|
constitutive_nonlocal_slipSystemLattice(s2,i), &
|
|
myStructure), i)
|
|
|
|
!*** colinear slip system (only makes sense for fcc like it is defined here)
|
|
|
|
if (lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), &
|
|
constitutive_nonlocal_slipSystemLattice(s2,i), &
|
|
myStructure) == 3_pInt) then
|
|
constitutive_nonlocal_colinearSystem(s1,i) = s2
|
|
endif
|
|
|
|
enddo
|
|
|
|
!*** rotation matrix from lattice configuration to slip system
|
|
|
|
constitutive_nonlocal_lattice2slip(1:3,1:3,s1,i) &
|
|
= math_transpose33( reshape([ lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
|
|
-lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
|
|
lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure)], [3,3]))
|
|
enddo
|
|
|
|
enddo
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* initial microstructural state (just the "basic" states) *
|
|
!*********************************************************************
|
|
subroutine constitutive_nonlocal_stateInit(state)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use lattice, only: lattice_maxNslipFamily
|
|
use math, only: math_sampleGaussVar
|
|
use mesh, only: mesh_ipVolume, &
|
|
mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_element, &
|
|
FE_Nips, &
|
|
FE_geomtype
|
|
use material, only: material_phase, &
|
|
phase_plasticityInstance, &
|
|
phase_plasticity
|
|
|
|
implicit none
|
|
|
|
!*** input/output variables
|
|
type(p_vec), dimension(1,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
|
|
state ! microstructural state
|
|
|
|
!*** local variables
|
|
real(pReal), dimension(:), allocatable :: &
|
|
rhoSglEdgePos, & ! positive edge dislocation density
|
|
rhoSglEdgeNeg, & ! negative edge dislocation density
|
|
rhoSglScrewPos, & ! positive screw dislocation density
|
|
rhoSglScrewNeg, & ! negative screw dislocation density
|
|
rhoDipEdge, & ! edge dipole dislocation density
|
|
rhoDipScrew ! screw dipole dislocation density
|
|
integer(pInt) el, &
|
|
ip, &
|
|
g, &
|
|
ns, & ! short notation for total number of active slip systems
|
|
f, & ! index of lattice family
|
|
from, &
|
|
upto, &
|
|
s, & ! index of slip system
|
|
t, &
|
|
i, &
|
|
myInstance, &
|
|
maxNinstance
|
|
real(pReal), dimension(2) :: noise
|
|
real(pReal), dimension(4) :: rnd
|
|
real(pReal) meanDensity, &
|
|
totalVolume, &
|
|
densityBinning, &
|
|
minimumIpVolume
|
|
|
|
|
|
maxNinstance = int(count(phase_plasticity == constitutive_nonlocal_label),pInt)
|
|
|
|
if (maxNinstance > 0_pInt) then
|
|
allocate(rhoSglEdgePos(maxval(constitutive_nonlocal_totalNslip)))
|
|
allocate(rhoSglEdgeNeg(maxval(constitutive_nonlocal_totalNslip)))
|
|
allocate(rhoSglScrewPos(maxval(constitutive_nonlocal_totalNslip)))
|
|
allocate(rhoSglScrewNeg(maxval(constitutive_nonlocal_totalNslip)))
|
|
allocate(rhoDipEdge(maxval(constitutive_nonlocal_totalNslip)))
|
|
allocate(rhoDipScrew(maxval(constitutive_nonlocal_totalNslip)))
|
|
endif
|
|
do myInstance = 1_pInt,maxNinstance
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
|
|
|
! randomly distribute dislocation segments on random slip system and of random type in the volume
|
|
if (constitutive_nonlocal_rhoSglRandom(myInstance) > 0.0_pReal) then
|
|
|
|
! ititalize all states to zero and get the total volume of the instance
|
|
|
|
minimumIpVolume = 1e99_pReal
|
|
do el = 1_pInt,mesh_NcpElems
|
|
do ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,el)))
|
|
if (constitutive_nonlocal_label == phase_plasticity(material_phase(1,ip,el)) &
|
|
.and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then
|
|
totalVolume = totalVolume + mesh_ipVolume(ip,el)
|
|
minimumIpVolume = min(minimumIpVolume, mesh_ipVolume(ip,el))
|
|
state(1,ip,el)%p = 0.0_pReal
|
|
endif
|
|
enddo
|
|
enddo
|
|
densityBinning = constitutive_nonlocal_rhoSglRandomBinning(myInstance) / minimumIpVolume ** (2.0_pReal / 3.0_pReal)
|
|
|
|
! subsequently fill random ips with dislocation segments until we reach the desired overall density
|
|
|
|
meanDensity = 0.0_pReal
|
|
do while(meanDensity < constitutive_nonlocal_rhoSglRandom(myInstance))
|
|
call random_number(rnd)
|
|
el = nint(rnd(1)*real(mesh_NcpElems,pReal)+0.5_pReal,pInt)
|
|
ip = nint(rnd(2)*real(FE_Nips(FE_geomtype(mesh_element(2,el))),pReal)+0.5_pReal,pInt)
|
|
if (constitutive_nonlocal_label == phase_plasticity(material_phase(1,ip,el)) &
|
|
.and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then
|
|
s = nint(rnd(3)*real(ns,pReal)+0.5_pReal,pInt)
|
|
t = nint(rnd(4)*4.0_pReal+0.5_pReal,pInt)
|
|
meanDensity = meanDensity + densityBinning * mesh_ipVolume(ip,el) / totalVolume
|
|
state(1,ip,el)%p((t-1)*ns+s) = state(1,ip,el)%p((t-1)*ns+s) + densityBinning
|
|
endif
|
|
enddo
|
|
|
|
! homogeneous distribution of density with some noise
|
|
else
|
|
do el = 1_pInt,mesh_NcpElems
|
|
do ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,el)))
|
|
if (constitutive_nonlocal_label == phase_plasticity(material_phase(1,ip,el)) &
|
|
.and. myInstance == phase_plasticityInstance(material_phase(1,ip,el))) then
|
|
do f = 1_pInt,lattice_maxNslipFamily
|
|
from = 1_pInt + sum(constitutive_nonlocal_Nslip(1:f-1_pInt,myInstance))
|
|
upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance))
|
|
do s = from,upto
|
|
do i = 1_pInt,2_pInt
|
|
noise(i) = math_sampleGaussVar(0.0_pReal, constitutive_nonlocal_rhoSglScatter(myInstance))
|
|
enddo
|
|
rhoSglEdgePos(s) = constitutive_nonlocal_rhoSglEdgePos0(f, myInstance) + noise(1)
|
|
rhoSglEdgeNeg(s) = constitutive_nonlocal_rhoSglEdgeNeg0(f, myInstance) + noise(1)
|
|
rhoSglScrewPos(s) = constitutive_nonlocal_rhoSglScrewPos0(f, myInstance) + noise(2)
|
|
rhoSglScrewNeg(s) = constitutive_nonlocal_rhoSglScrewNeg0(f, myInstance) + noise(2)
|
|
enddo
|
|
rhoDipEdge(from:upto) = constitutive_nonlocal_rhoDipEdge0(f, myInstance)
|
|
rhoDipScrew(from:upto) = constitutive_nonlocal_rhoDipScrew0(f, myInstance)
|
|
enddo
|
|
state(1,ip,el)%p( 1: ns) = rhoSglEdgePos(1:ns)
|
|
state(1,ip,el)%p( ns+1: 2*ns) = rhoSglEdgeNeg(1:ns)
|
|
state(1,ip,el)%p( 2*ns+1: 3*ns) = rhoSglScrewPos(1:ns)
|
|
state(1,ip,el)%p( 3*ns+1: 4*ns) = rhoSglScrewNeg(1:ns)
|
|
state(1,ip,el)%p( 4*ns+1: 5*ns) = 0.0_pReal
|
|
state(1,ip,el)%p( 5*ns+1: 6*ns) = 0.0_pReal
|
|
state(1,ip,el)%p( 6*ns+1: 7*ns) = 0.0_pReal
|
|
state(1,ip,el)%p( 7*ns+1: 8*ns) = 0.0_pReal
|
|
state(1,ip,el)%p( 8*ns+1: 9*ns) = rhoDipEdge(1:ns)
|
|
state(1,ip,el)%p( 9*ns+1:10*ns) = rhoDipScrew(1:ns)
|
|
endif
|
|
enddo
|
|
enddo
|
|
endif
|
|
enddo
|
|
|
|
if (maxNinstance > 0_pInt) then
|
|
deallocate(rhoSglEdgePos)
|
|
deallocate(rhoSglEdgeNeg)
|
|
deallocate(rhoSglScrewPos)
|
|
deallocate(rhoSglScrewNeg)
|
|
deallocate(rhoDipEdge)
|
|
deallocate(rhoDipScrew)
|
|
endif
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* absolute state tolerance *
|
|
!*********************************************************************
|
|
pure function constitutive_nonlocal_aTolState(myInstance)
|
|
|
|
use prec, only: pReal, &
|
|
pInt
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the plasticity
|
|
|
|
!*** output variables
|
|
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
|
|
constitutive_nonlocal_aTolState ! absolute state tolerance for the current instance of this plasticity
|
|
|
|
!*** local variables
|
|
|
|
constitutive_nonlocal_aTolState = constitutive_nonlocal_aTolRho(myInstance)
|
|
|
|
endfunction
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* calculates homogenized elacticity matrix *
|
|
!*********************************************************************
|
|
pure function constitutive_nonlocal_homogenizedC(state,g,ip,el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_plasticityInstance
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
|
ip, & ! current integration point
|
|
el ! current element
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! microstructural state
|
|
|
|
!*** output variables
|
|
real(pReal), dimension(6,6) :: constitutive_nonlocal_homogenizedC ! homogenized elasticity matrix
|
|
|
|
!*** local variables
|
|
integer(pInt) myInstance ! current instance of this plasticity
|
|
|
|
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
|
|
|
|
constitutive_nonlocal_homogenizedC = constitutive_nonlocal_Cslip_66(1:6,1:6,myInstance)
|
|
|
|
endfunction
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* calculates quantities characterizing the microstructure *
|
|
!*********************************************************************
|
|
subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, Fp, g, ip, el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use IO, only: IO_error
|
|
use math, only: math_Mandel33to6, &
|
|
math_mul33x33, &
|
|
math_mul33x3, &
|
|
math_mul3x3, &
|
|
math_norm3, &
|
|
math_inv33, &
|
|
math_invert33, &
|
|
math_transpose33, &
|
|
pi
|
|
use debug, only: debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelBasic, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_g, &
|
|
debug_i, &
|
|
debug_e
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_element, &
|
|
mesh_ipNeighborhood, &
|
|
mesh_ipCoordinates, &
|
|
mesh_ipVolume, &
|
|
mesh_ipAreaNormal, &
|
|
FE_NipNeighbors, &
|
|
FE_maxNipNeighbors, &
|
|
FE_geomtype
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_localPlasticity, &
|
|
phase_plasticityInstance
|
|
use lattice, only: lattice_sd, &
|
|
lattice_st, &
|
|
lattice_interactionSlipSlip
|
|
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
|
ip, & ! current integration point
|
|
el ! current element
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Fe, & ! elastic deformation gradient
|
|
Fp ! elastic deformation gradient
|
|
|
|
!*** input/output variables
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
|
|
state ! microstructural state
|
|
|
|
!*** output variables
|
|
|
|
!*** local variables
|
|
integer(pInt) neighboring_el, & ! element number of neighboring material point
|
|
neighboring_ip, & ! integration point of neighboring material point
|
|
instance, & ! my instance of this plasticity
|
|
neighboring_instance, & ! instance of this plasticity of neighboring material point
|
|
latticeStruct, & ! my lattice structure
|
|
neighboring_latticeStruct, & ! lattice structure of neighboring material point
|
|
phase, &
|
|
neighboring_phase, &
|
|
ns, & ! total number of active slip systems at my material point
|
|
neighboring_ns, & ! total number of active slip systems at neighboring material point
|
|
c, & ! index of dilsocation character (edge, screw)
|
|
s, & ! slip system index
|
|
s2, & ! slip system index
|
|
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
|
|
dir, &
|
|
n, &
|
|
interactionCoefficient
|
|
integer(pInt), dimension(2) :: neighbor
|
|
real(pReal) nu, & ! poisson's ratio
|
|
mu, &
|
|
b, &
|
|
detFe, &
|
|
detFp, &
|
|
FVsize, &
|
|
temp, &
|
|
correction, &
|
|
myRhoForest
|
|
real(pReal), dimension(2) :: rhoExcessGradient, &
|
|
rhoExcessGradient_over_rho, &
|
|
rhoTotal
|
|
real(pReal), dimension(3) :: ipCoords, &
|
|
neighboring_ipCoords, &
|
|
rhoExcessDifferences
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
rhoForest, & ! forest dislocation density
|
|
tauBack, & ! back stress from pileup on same slip system
|
|
tauThreshold ! threshold shear stress
|
|
real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient
|
|
invFp, & ! inverse of plastic deformation gradient
|
|
connections, &
|
|
invConnections
|
|
real(pReal), dimension(3,FE_maxNipNeighbors) :: &
|
|
connection_latticeConf
|
|
real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
rhoExcess
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
|
|
rhoDip ! dipole dislocation density (edge, screw)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
|
|
rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))), &
|
|
constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
myInteractionMatrix ! corrected slip interaction matrix
|
|
real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip),FE_maxNipNeighbors) :: &
|
|
neighboring_rhoExcess ! excess density at neighboring material point
|
|
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
|
|
m ! direction of dislocation motion
|
|
logical inversionError
|
|
|
|
|
|
phase = material_phase(g,ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
latticeStruct = constitutive_nonlocal_structure(instance)
|
|
ns = constitutive_nonlocal_totalNslip(instance)
|
|
|
|
|
|
|
|
!*** get basic states
|
|
|
|
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
|
rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal) ! ensure positive single mobile densities
|
|
forall (t = 5_pInt:8_pInt) &
|
|
rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
|
|
rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal) ! ensure positive dipole densities
|
|
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(instance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(instance)) &
|
|
rhoSgl = 0.0_pReal
|
|
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(instance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(instance)) &
|
|
rhoDip = 0.0_pReal
|
|
|
|
|
|
!*** calculate the forest dislocation density
|
|
!*** (= projection of screw and edge dislocations)
|
|
|
|
forall (s = 1_pInt:ns) &
|
|
rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,[1,2,5,6])),2) + rhoDip(1:ns,1)), &
|
|
constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) &
|
|
+ dot_product((sum(abs(rhoSgl(1:ns,[3,4,7,8])),2) + rhoDip(1:ns,2)), &
|
|
constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance))
|
|
|
|
|
|
|
|
!*** calculate the threshold shear stress for dislocation slip
|
|
|
|
myInteractionMatrix = 0.0_pReal
|
|
myInteractionMatrix(1:ns,1:ns) = constitutive_nonlocal_interactionMatrixSlipSlip(1:ns,1:ns,instance)
|
|
if (latticeStruct == 1_pInt) then ! in case of fcc: 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)
|
|
do s = 1_pInt,ns
|
|
myRhoForest = max(rhoForest(s),constitutive_nonlocal_significantRho(instance))
|
|
correction = ( 1.0_pReal - constitutive_nonlocal_linetensionEffect(instance) &
|
|
+ constitutive_nonlocal_linetensionEffect(instance) &
|
|
* log(0.35_pReal * constitutive_nonlocal_burgers(s,instance) * sqrt(myRhoForest)) &
|
|
/ log(0.35_pReal * constitutive_nonlocal_burgers(s,instance) * 1e6_pReal)) ** 2.0_pReal
|
|
do s2 = 1_pInt,ns
|
|
interactionCoefficient = lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s,instance), &
|
|
constitutive_nonlocal_slipSystemLattice(s2,instance), &
|
|
latticeStruct)
|
|
select case(interactionCoefficient)
|
|
case(4_pInt,5_pInt,6_pInt) ! only correct junction forming interactions (4,5,6)
|
|
myInteractionMatrix(s,s2) = correction * myInteractionMatrix(s,s2)
|
|
endselect
|
|
enddo
|
|
enddo
|
|
endif
|
|
forall (s = 1_pInt:ns) &
|
|
tauThreshold(s) = constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) &
|
|
* sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), myInteractionMatrix(s,1:ns)))
|
|
|
|
|
|
|
|
!*** calculate the dislocation stress of the neighboring excess dislocation densities
|
|
!*** zero for material points of local plasticity
|
|
|
|
tauBack = 0.0_pReal
|
|
|
|
if (.not. phase_localPlasticity(phase) .and. constitutive_nonlocal_shortRangeStressCorrection(instance)) then
|
|
call math_invert33(Fe, invFe, detFe, inversionError)
|
|
call math_invert33(Fp, invFp, detFp, inversionError)
|
|
ipCoords = mesh_ipCoordinates(1:3,ip,el)
|
|
rhoExcess(1,1:ns) = rhoSgl(1:ns,1) - rhoSgl(1:ns,2)
|
|
rhoExcess(2,1:ns) = rhoSgl(1:ns,3) - rhoSgl(1:ns,4)
|
|
FVsize = mesh_ipVolume(ip,el) ** (1.0_pReal/3.0_pReal)
|
|
nu = constitutive_nonlocal_nu(instance)
|
|
mu = constitutive_nonlocal_Gmod(instance)
|
|
|
|
!* loop through my neighborhood and get the connection vectors (in lattice frame) and the excess densities
|
|
|
|
do n = 1_pInt,FE_NipNeighbors(FE_geomtype(mesh_element(2,el)))
|
|
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
|
|
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
|
|
if (neighboring_el > 0 .and. neighboring_ip > 0) then
|
|
neighboring_phase = material_phase(g,neighboring_ip,neighboring_el)
|
|
neighboring_instance = phase_plasticityInstance(neighboring_phase)
|
|
neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance)
|
|
neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance)
|
|
neighboring_ipCoords = mesh_ipCoordinates(1:3,neighboring_ip,neighboring_el)
|
|
if (.not. phase_localPlasticity(neighboring_phase) &
|
|
.and. neighboring_latticeStruct == latticeStruct &
|
|
.and. neighboring_instance == instance) then
|
|
if (neighboring_ns == ns) then
|
|
if (neighboring_el /= el .or. neighboring_ip /= ip) then
|
|
connection_latticeConf(1:3,n) = math_mul33x3(invFe, neighboring_ipCoords - ipCoords)
|
|
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
|
|
neighboring_rhoExcess(c,s,n) = state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-2_pInt)*ns+s) & ! positive mobiles
|
|
- state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*ns+s) ! negative mobiles
|
|
else
|
|
! thats myself! probably using periodic images -> assume constant excess density
|
|
connection_latticeConf(1:3,n) = math_mul33x3(math_transpose33(invFp), mesh_ipAreaNormal(1:3,n,ip,el)) ! direction of area normal
|
|
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
|
|
endif
|
|
else
|
|
! different number of active slip systems
|
|
call IO_error(-1_pInt,ext_msg='different number of active slip systems in neighboring IPs of same crystal structure')
|
|
endif
|
|
else
|
|
! local neighbor or different lattice structure or different constitution instance -> use central values instead
|
|
connection_latticeConf(1:3,n) = 0.0_pReal
|
|
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
|
|
endif
|
|
else
|
|
! free surface -> use central values instead
|
|
connection_latticeConf(1:3,n) = 0.0_pReal
|
|
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
|
|
endif
|
|
enddo
|
|
|
|
|
|
!* 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:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
|
|
m(1:3,1:ns,2) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
|
|
|
|
do s = 1_pInt,ns
|
|
|
|
!* gradient from interpolation of neighboring excess density
|
|
|
|
do c = 1_pInt,2_pInt
|
|
do dir = 1_pInt,3_pInt
|
|
neighbor(1) = 2_pInt * dir - 1_pInt
|
|
neighbor(2) = 2_pInt * dir
|
|
connections(dir,1:3) = connection_latticeConf(1:3,neighbor(1)) - connection_latticeConf(1:3,neighbor(2))
|
|
rhoExcessDifferences(dir) = neighboring_rhoExcess(c,s,neighbor(1)) - neighboring_rhoExcess(c,s,neighbor(2))
|
|
enddo
|
|
call math_invert33(connections,invConnections,temp,inversionError)
|
|
if (inversionError) then
|
|
call IO_error(-1_pInt,ext_msg='back stress calculation: inversion error')
|
|
endif
|
|
rhoExcessGradient(c) = math_mul3x3(math_mul33x3(invConnections, rhoExcessDifferences), m(1:3,s,c))
|
|
enddo
|
|
|
|
!* plus gradient from deads
|
|
|
|
do t = 1_pInt,4_pInt
|
|
c = (t - 1_pInt) / 2_pInt + 1_pInt
|
|
rhoExcessGradient(c) = rhoExcessGradient(c) + rhoSgl(s,t+4_pInt) / FVsize
|
|
enddo
|
|
|
|
!* normalized with the total density
|
|
|
|
rhoExcessGradient_over_rho = 0.0_pReal
|
|
rhoTotal(1_pInt) = sum(abs(rhoSgl(s,[1_pInt,2_pInt,5_pInt,6_pInt]))) + rhoDip(s,1_pInt)
|
|
rhoTotal(2_pInt) = sum(abs(rhoSgl(s,[3_pInt,4_pInt,7_pInt,8_pInt]))) + rhoDip(s,2_pInt)
|
|
forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) &
|
|
rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c)
|
|
|
|
!* gives the local stress correction when multiplied with a factor
|
|
|
|
b = constitutive_nonlocal_burgers(s,instance)
|
|
tauBack(s) = - mu * b / (2.0_pReal * pi) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu) + rhoExcessGradient_over_rho(2))
|
|
|
|
enddo
|
|
endif
|
|
|
|
|
|
!*** set dependent states
|
|
|
|
state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns) = rhoForest
|
|
state(g,ip,el)%p(11_pInt*ns+1:12_pInt*ns) = tauThreshold
|
|
state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) = tauBack
|
|
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
write(6,*)
|
|
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_microstructure at el ip g',el,ip,g
|
|
write(6,*)
|
|
write(6,'(a,/,12x,12(e10.3,1x))') '<< CONST >> rhoForest', rhoForest
|
|
write(6,'(a,/,12x,12(f10.5,1x))') '<< CONST >> tauThreshold / MPa', tauThreshold/1e6
|
|
write(6,'(a,/,12x,12(f10.5,1x))') '<< CONST >> tauBack / MPa', tauBack/1e6
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* calculates kinetics *
|
|
!*********************************************************************
|
|
subroutine constitutive_nonlocal_kinetics(v, tau, c, Temperature, state, g, ip, el, dv_dtau)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use debug, only: debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelBasic, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_g, &
|
|
debug_i, &
|
|
debug_e
|
|
use material, only: material_phase, &
|
|
phase_plasticityInstance
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implicit none
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!*** input variables
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integer(pInt), intent(in) :: g, & ! current grain number
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ip, & ! current integration point
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el, & ! current element number
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c ! dislocation character (1:edge, 2:screw)
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real(pReal), intent(in) :: Temperature ! temperature
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
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intent(in) :: tau ! resolved external shear stress (for bcc this already contains non Schmid effects)
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type(p_vec), intent(in) :: state ! microstructural state
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!*** input/output variables
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!*** output variables
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
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intent(out) :: v ! velocity
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))), &
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intent(out), optional :: dv_dtau ! velocity derivative with respect to resolved shear stress
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!*** local variables
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integer(pInt) instance, & ! current instance of this plasticity
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ns, & ! short notation for the total number of active slip systems
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s ! index of my current slip system
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
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tauThreshold, & ! threshold shear stress
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tauEff ! effective shear stress
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real(pReal) tauRel_P, &
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tauRel_S, &
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tPeierls, & ! waiting time in front of a peierls barriers
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tSolidSolution, & ! waiting time in front of a solid solution obstacle
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vViscous, & ! viscous glide velocity
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dtPeierls_dtau, & ! derivative with respect to resolved shear stress
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dtSolidSolution_dtau, & ! derivative with respect to resolved shear stress
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p, & ! shortcut to Kocks,Argon,Ashby parameter p
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q, & ! shortcut to Kocks,Argon,Ashby parameter q
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meanfreepath_S, & ! mean free travel distance for dislocations between two solid solution obstacles
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meanfreepath_P, & ! mean free travel distance for dislocations between two Peierls barriers
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jumpWidth_P, & ! depth of activated area
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jumpWidth_S, & ! depth of activated area
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activationLength_P, & ! length of activated dislocation line
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activationLength_S, & ! length of activated dislocation line
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activationVolume_P, & ! volume that needs to be activated to overcome barrier
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activationVolume_S, & ! volume that needs to be activated to overcome barrier
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activationEnergy_P, & ! energy that is needed to overcome barrier
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activationEnergy_S, & ! energy that is needed to overcome barrier
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criticalStress_P, & ! maximum obstacle strength
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criticalStress_S, & ! maximum obstacle strength
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mobility ! dislocation mobility
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instance = phase_plasticityInstance(material_phase(g,ip,el))
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ns = constitutive_nonlocal_totalNslip(instance)
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tauThreshold = state%p(11_pInt*ns+1:12_pInt*ns)
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tauEff = abs(tau) - tauThreshold
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p = constitutive_nonlocal_p(instance)
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q = constitutive_nonlocal_q(instance)
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v = 0.0_pReal
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if (present(dv_dtau)) dv_dtau = 0.0_pReal
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if (Temperature > 0.0_pReal) then
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do s = 1_pInt,ns
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if (tauEff(s) > 0.0_pReal) then
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!* Peierls contribution
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!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
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meanfreepath_P = constitutive_nonlocal_burgers(s,instance)
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jumpWidth_P = constitutive_nonlocal_burgers(s,instance)
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activationLength_P = constitutive_nonlocal_doublekinkwidth(instance) * constitutive_nonlocal_burgers(s,instance)
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activationVolume_P = activationLength_P * jumpWidth_P * constitutive_nonlocal_burgers(s,instance)
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criticalStress_P = constitutive_nonlocal_peierlsStress(s,c,instance)
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activationEnergy_P = criticalStress_P * activationVolume_P
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tauRel_P = min(1.0_pReal, tauEff(s) / criticalStress_P) ! ensure that the activation probability cannot become greater than one
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tPeierls = 1.0_pReal / constitutive_nonlocal_fattack(instance) &
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* exp(activationEnergy_P / (kB * Temperature) * (1.0_pReal - tauRel_P**p)**q)
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if (present(dv_dtau)) then
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if (tauEff(s) < criticalStress_P) then
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dtPeierls_dtau = tPeierls * p * q * activationVolume_P / (kB * Temperature) &
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* (1.0_pReal - tauRel_P**p)**(q-1.0_pReal) * tauRel_P**(p-1.0_pReal)
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else
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dtPeierls_dtau = 0.0_pReal
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endif
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endif
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!* Contribution from solid solution strengthening
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!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
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meanfreepath_S = constitutive_nonlocal_burgers(s,instance) / sqrt(constitutive_nonlocal_solidSolutionConcentration(instance))
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jumpWidth_S = constitutive_nonlocal_solidSolutionSize(instance) * constitutive_nonlocal_burgers(s,instance)
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activationLength_S = constitutive_nonlocal_burgers(s,instance) &
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/ sqrt(constitutive_nonlocal_solidSolutionConcentration(instance))
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activationVolume_S = activationLength_S * jumpWidth_S * constitutive_nonlocal_burgers(s,instance)
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activationEnergy_S = constitutive_nonlocal_solidSolutionEnergy(instance)
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criticalStress_S = activationEnergy_S / activationVolume_S
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tauRel_S = min(1.0_pReal, tauEff(s) / criticalStress_S) ! ensure that the activation probability cannot become greater than one
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tSolidSolution = 1.0_pReal / constitutive_nonlocal_fattack(instance) &
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* exp(activationEnergy_S / (kB * Temperature) * (1.0_pReal - tauRel_S**p)**q)
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if (present(dv_dtau)) then
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if (tauEff(s) < criticalStress_S) then
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dtSolidSolution_dtau = tSolidSolution * p * q * activationVolume_S / (kB * Temperature) &
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* (1.0_pReal - tauRel_S**p)**(q-1.0_pReal) * tauRel_S**(p-1.0_pReal)
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else
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dtSolidSolution_dtau = 0.0_pReal
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endif
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endif
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!* viscous glide velocity
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mobility = constitutive_nonlocal_burgers(s,instance) / constitutive_nonlocal_viscosity(instance)
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vViscous = mobility * tauEff(s)
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!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
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!* free flight at glide velocity in between. Backward jumps at low stresses are considered only at peierls barriers,
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!* since those have the smallest activation volume, thus are decisive.
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v(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) &
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* (1.0_pReal - exp(-tauEff(s) * activationVolume_P / (kB * Temperature)))
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if (present(dv_dtau)) then
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dv_dtau(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) &
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* (v(s) * ( dtPeierls_dtau / meanfreepath_P + dtSolidSolution_dtau / meanfreepath_S &
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+ 1.0_pReal / (mobility * tauEff(s)*tauEff(s))) &
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+ activationVolume_P / (kB * Temperature) * exp(-tauEff(s) * activationVolume_P / (kB * Temperature)))
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endif
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!* relativistic correction
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if (present(dv_dtau)) then
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dv_dtau(s) = dv_dtau(s) * exp( -v(s) / constitutive_nonlocal_vmax(instance))
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endif
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v(s) = constitutive_nonlocal_vmax(instance) * (1.0_pReal - exp( -v(s) / constitutive_nonlocal_vmax(instance)))
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!* adopt sign from resolved stress
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v(s) = sign(v(s),tau(s))
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endif
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enddo
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endif
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#ifndef _OPENMP
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if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
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.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
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.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
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write(6,*)
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write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g
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write(6,*)
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write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal
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write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauEff / MPa', tauEff / 1e6_pReal
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write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3
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if (present(dv_dtau)) then
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write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtau', dv_dtau
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endif
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endif
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#endif
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endsubroutine
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!*********************************************************************
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!* calculates plastic velocity gradient and its tangent *
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!*********************************************************************
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subroutine constitutive_nonlocal_LpAndItsTangent(Lp, dLp_dTstar99, Tstar_v, Temperature, state, g, ip, el)
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use prec, only: pReal, &
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pInt, &
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p_vec
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use math, only: math_Plain3333to99, &
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math_mul6x6
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use debug, only: debug_level, &
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debug_constitutive, &
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debug_levelBasic, &
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debug_levelExtensive, &
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debug_levelSelective, &
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debug_g, &
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debug_i, &
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debug_e
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use material, only: homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance
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use lattice, only: lattice_Sslip, &
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lattice_Sslip_v
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use mesh, only: mesh_ipVolume
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implicit none
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!*** input variables
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integer(pInt), intent(in) :: g, & ! current grain number
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ip, & ! current integration point
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el ! current element number
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real(pReal), intent(in) :: Temperature ! temperature
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real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
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!*** input/output variables
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type(p_vec), intent(inout) :: state ! microstructural state
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!*** output variables
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real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
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real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99 ! derivative of Lp with respect to Tstar (9x9 matrix)
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|
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!*** local variables
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integer(pInt) myInstance, & ! current instance of this plasticity
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myStructure, & ! current lattice structure
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ns, & ! short notation for the total number of active slip systems
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c, &
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i, &
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j, &
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k, &
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l, &
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t, & ! dislocation type
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s, & ! index of my current slip system
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sLattice ! index of my current slip system according to lattice order
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real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix)
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
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rhoSgl ! single dislocation densities (including used)
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
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v, & ! velocity
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dv_dtau ! velocity derivative with respect to the shear stress
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
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tau, & ! resolved shear stress including non Schmid and backstress terms
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gdotTotal, & ! shear rate
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|
dgdotTotal_dtau, & ! derivative of the shear rate with respect to the shear stress
|
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tauBack, & ! back stress from dislocation gradients on same slip system
|
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deadZoneSize
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|
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|
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!*** initialize local variables
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|
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Lp = 0.0_pReal
|
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dLp_dTstar3333 = 0.0_pReal
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|
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myInstance = phase_plasticityInstance(material_phase(g,ip,el))
|
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myStructure = constitutive_nonlocal_structure(myInstance)
|
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ns = constitutive_nonlocal_totalNslip(myInstance)
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|
|
|
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!*** shortcut to state variables
|
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|
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forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
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rhoSgl(s,t) = max(state%p((t-1_pInt)*ns+s), 0.0_pReal)
|
|
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) &
|
|
rhoSgl(s,t) = state%p((t-1_pInt)*ns+s)
|
|
tauBack = state%p(12_pInt*ns+1:13_pInt*ns)
|
|
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoSgl = 0.0_pReal
|
|
|
|
|
|
!*** get effective resolved shear stress
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|
|
do s = 1_pInt,ns
|
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tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure)) &
|
|
+ tauBack(s)
|
|
enddo
|
|
|
|
|
|
!*** get dislocation velocity and its tangent and store the velocity in the state array
|
|
|
|
if (myStructure == 1_pInt) then ! for fcc all velcities are equal
|
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call constitutive_nonlocal_kinetics(v(1:ns,1), tau, 1_pInt, Temperature, state, g, ip, el, dv_dtau(1:ns,1))
|
|
do t = 1_pInt,4_pInt
|
|
v(1:ns,t) = v(1:ns,1)
|
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dv_dtau(1:ns,t) = dv_dtau(1:ns,1)
|
|
state%p((12_pInt+t)*ns+1:(13_pInt+t)*ns) = v(1:ns,1)
|
|
enddo
|
|
else ! for all other lattice structures the velcities may vary with character and sign
|
|
do t = 1_pInt,4_pInt
|
|
c = (t-1_pInt)/2_pInt+1_pInt
|
|
call constitutive_nonlocal_kinetics(v(1:ns,t), tau, c, Temperature, state, g, ip, el, dv_dtau(1:ns,t))
|
|
state%p((12+t)*ns+1:(13+t)*ns) = v(1:ns,t)
|
|
enddo
|
|
endif
|
|
|
|
|
|
!*** Bauschinger effect
|
|
|
|
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt, rhoSgl(s,t) * v(s,t-4_pInt) < 0.0_pReal) &
|
|
rhoSgl(s,t-4_pInt) = rhoSgl(s,t-4_pInt) + abs(rhoSgl(s,t))
|
|
|
|
|
|
!*** Calculation of gdot and its tangent
|
|
|
|
deadZoneSize = 0.0_pReal
|
|
if (constitutive_nonlocal_deadZoneScaling(myInstance)) then
|
|
forall(s = 1_pInt:ns, sum(abs(rhoSgl(s,1:8))) > 0.0_pReal) &
|
|
deadZoneSize(s) = maxval(abs(rhoSgl(s,5:8)) / (rhoSgl(s,1:4) + abs(rhoSgl(s,5:8))))
|
|
endif
|
|
gdotTotal = sum(rhoSgl(1:ns,1:4) * v, 2) * constitutive_nonlocal_burgers(1:ns,myInstance) * (1.0_pReal - deadZoneSize)
|
|
dgdotTotal_dtau = sum(rhoSgl(1:ns,1:4) * dv_dtau, 2) * constitutive_nonlocal_burgers(1:ns,myInstance) * (1.0_pReal - deadZoneSize)
|
|
|
|
|
|
!*** Calculation of Lp and its tangent
|
|
|
|
do s = 1_pInt,ns
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
|
Lp = Lp + gdotTotal(s) * lattice_Sslip(1:3,1:3,sLattice,myStructure)
|
|
forall (i=1_pInt:3_pInt,j=1_pInt:3_pInt,k=1_pInt:3_pInt,l=1_pInt:3_pInt) &
|
|
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) + dgdotTotal_dtau(s) * lattice_Sslip(i,j, sLattice,myStructure) &
|
|
* lattice_Sslip(k,l, sLattice,myStructure)
|
|
enddo
|
|
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
|
|
write(6,*)
|
|
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_LpandItsTangent at el ip g ',el,ip,g
|
|
write(6,*)
|
|
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> gdot total / 1e-3',gdotTotal*1e3_pReal
|
|
write(6,'(a,/,3(12x,3(f12.7,1x),/))') '<< CONST >> Lp',Lp
|
|
endif
|
|
#endif
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* incremental change of microstructure *
|
|
!*********************************************************************
|
|
subroutine constitutive_nonlocal_deltaState(deltaState, state, Tstar_v, Temperature, g,ip,el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use debug, only: debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelBasic, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_g, &
|
|
debug_i, &
|
|
debug_e
|
|
use math, only: pi, &
|
|
math_mul6x6
|
|
use lattice, only: lattice_Sslip_v
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_ipVolume
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_plasticityInstance
|
|
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain number
|
|
ip, & ! current integration point
|
|
el ! current element number
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
|
|
|
|
!*** input/output variables
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
|
|
state ! current microstructural state
|
|
|
|
!*** output variables
|
|
type(p_vec), intent(out) :: deltaState ! change of state variables / microstructure
|
|
|
|
!*** local variables
|
|
integer(pInt) myInstance, & ! current instance of this plasticity
|
|
myStructure, & ! current lattice structure
|
|
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
|
|
sLattice ! index of my current slip system according to lattice order
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
|
|
deltaRho, & ! density increment
|
|
deltaRhoRemobilization, & ! density increment by remobilization
|
|
deltaRhoDipole2SingleStress ! density increment by dipole dissociation (by stress change)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
|
|
rhoSgl ! current single dislocation densities (positive/negative screw and edge without dipoles)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
|
|
v ! dislocation glide velocity
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
tau, & ! current resolved shear stress
|
|
tauBack ! current back stress from pileups on same slip system
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),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
|
|
dUpperOld, & ! old maximum stable dipole distance for edges and screws
|
|
deltaDUpper ! change in maximum stable dipole distance for edges and screws
|
|
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
write(6,*)
|
|
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_deltaState at el ip g ',el,ip,g
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
|
|
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
|
|
|
|
|
!*** shortcut to state variables
|
|
|
|
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
|
rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal)
|
|
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) &
|
|
rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s)
|
|
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
|
|
rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal)
|
|
tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns)
|
|
forall (t = 1_pInt:4_pInt) &
|
|
v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
forall (c = 1_pInt:2_pInt) &
|
|
dUpperOld(1_pInt:ns,c) = state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns)
|
|
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoSgl = 0.0_pReal
|
|
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoDip = 0.0_pReal
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** dislocation remobilization (bauschinger effect)
|
|
|
|
deltaRhoRemobilization = 0.0_pReal
|
|
do t = 1_pInt,4_pInt
|
|
do s = 1_pInt,ns
|
|
if (rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) then
|
|
deltaRhoRemobilization(s,t) = abs(rhoSgl(s,t+4_pInt))
|
|
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4_pInt))
|
|
deltaRhoRemobilization(s,t+4_pInt) = - rhoSgl(s,t+4_pInt)
|
|
rhoSgl(s,t+4_pInt) = 0.0_pReal
|
|
endif
|
|
enddo
|
|
enddo
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** calculate dipole formation and dissociation by stress change
|
|
|
|
!*** calculate limits for stable dipole height
|
|
|
|
do s = 1_pInt,ns
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
|
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure)) + tauBack(s)
|
|
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
|
|
enddo
|
|
dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance)
|
|
dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau))
|
|
dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (4.0_pReal * pi * abs(tau))
|
|
forall (c = 1_pInt:2_pInt) &
|
|
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
|
|
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
|
|
dUpper(1:ns,c))
|
|
dUpper = max(dUpper,dLower)
|
|
deltaDUpper = dUpper - dUpperOld
|
|
|
|
|
|
!*** dissociation by stress increase
|
|
|
|
deltaRhoDipole2SingleStress = 0.0_pReal
|
|
forall (c=1_pInt:2_pInt, s=1_pInt:ns, deltaDUpper(s,c) < 0.0_pReal) &
|
|
deltaRhoDipole2SingleStress(s,8_pInt+c) = rhoDip(s,c) * deltaDUpper(s,c) / (dUpperOld(s,c) - dLower(s,c))
|
|
|
|
forall (t=1_pInt:4_pInt) &
|
|
deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal * deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt)
|
|
|
|
|
|
|
|
!*** store new maximum dipole height in state
|
|
|
|
forall (c = 1_pInt:2_pInt) &
|
|
state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns) = dUpper(1_pInt:ns,c)
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** assign the changes in the dislocation densities to deltaState
|
|
|
|
deltaRho = 0.0_pReal
|
|
deltaRho = deltaRhoRemobilization &
|
|
+ deltaRhoDipole2SingleStress
|
|
|
|
deltaState%p = reshape(deltaRho,(/10_pInt*ns/))
|
|
|
|
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
|
|
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation remobilization', deltaRhoRemobilization(1:ns,1:8)
|
|
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole dissociation by stress increase', deltaRhoDipole2SingleStress
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* rate of change of microstructure *
|
|
!*********************************************************************
|
|
function constitutive_nonlocal_dotState(Tstar_v, Fe, Fp, Temperature, state, state0, timestep, subfrac, g,ip,el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec, &
|
|
DAMASK_NaN
|
|
use numerics, only: numerics_integrationMode, &
|
|
numerics_timeSyncing
|
|
use IO, only: IO_error
|
|
use debug, only: debug_level, &
|
|
debug_constitutive, &
|
|
debug_levelBasic, &
|
|
debug_levelExtensive, &
|
|
debug_levelSelective, &
|
|
debug_g, &
|
|
debug_i, &
|
|
debug_e
|
|
use math, only: math_norm3, &
|
|
math_mul6x6, &
|
|
math_mul3x3, &
|
|
math_mul33x3, &
|
|
math_mul33x33, &
|
|
math_inv33, &
|
|
math_det33, &
|
|
math_transpose33, &
|
|
pi
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_element, &
|
|
mesh_maxNipNeighbors, &
|
|
mesh_ipNeighborhood, &
|
|
mesh_ipVolume, &
|
|
mesh_ipArea, &
|
|
mesh_ipAreaNormal, &
|
|
FE_NipNeighbors, &
|
|
FE_geomtype
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_plasticityInstance, &
|
|
phase_localPlasticity, &
|
|
phase_plasticity
|
|
use lattice, only: lattice_Sslip_v, &
|
|
lattice_sd, &
|
|
lattice_st
|
|
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain number
|
|
ip, & ! current integration point
|
|
el ! current element number
|
|
real(pReal), intent(in) :: Temperature, & ! temperature
|
|
timestep ! substepped crystallite time increment
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
|
|
real(pReal), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
subfrac ! fraction of timestep at the beginning of the substepped crystallite time increment
|
|
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
Fe, & ! elastic deformation gradient
|
|
Fp ! plastic deformation gradient
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
state, & ! current microstructural state
|
|
state0 ! microstructural state at beginning of crystallite increment
|
|
|
|
!*** input/output variables
|
|
|
|
!*** output variables
|
|
real(pReal), dimension(constitutive_nonlocal_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
constitutive_nonlocal_dotState ! evolution of state variables / microstructure
|
|
|
|
!*** local variables
|
|
integer(pInt) myInstance, & ! current instance of this plasticity
|
|
myStructure, & ! current lattice structure
|
|
ns, & ! short notation for the total number of active slip systems
|
|
c, & ! character of dislocation
|
|
n, & ! index of my current neighbor
|
|
neighboring_el, & ! element number of my neighbor
|
|
neighboring_ip, & ! integration point of my neighbor
|
|
neighboring_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
|
|
topp, & ! type of dislocation with opposite sign to t
|
|
s, & ! index of my current slip system
|
|
sLattice, & ! index of my current slip system according to lattice order
|
|
deads
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
|
|
rhoDot, & ! density evolution
|
|
rhoDotMultiplication, & ! density evolution by multiplication
|
|
rhoDotFlux, & ! density evolution by flux
|
|
rhoDotSingle2DipoleGlide, & ! density evolution by dipole formation (by glide)
|
|
rhoDotAthermalAnnihilation, & ! density evolution by athermal annihilation
|
|
rhoDotThermalAnnihilation ! density evolution by thermal annihilation
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
|
|
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
|
|
rhoSglOriginal, &
|
|
rhoSgl0, & ! single dislocation densities at start of cryst inc (positive/negative screw and edge without dipoles)
|
|
rhoSglMe, & ! single dislocation densities of central ip (positive/negative screw and edge without dipoles)
|
|
neighboring_rhoSgl ! current single dislocation densities of neighboring ip (positive/negative screw and edge without dipoles)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
|
|
v, & ! current dislocation glide velocity
|
|
v0, & ! dislocation glide velocity at start of cryst inc
|
|
vMe, & ! dislocation glide velocity of central ip
|
|
neighboring_v, & ! dislocation glide velocity of enighboring ip
|
|
gdot ! shear rates
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
rhoForest, & ! forest dislocation density
|
|
tauThreshold, & ! threshold shear stress
|
|
tau, & ! current resolved shear stress
|
|
tauBack, & ! current back stress from pileups on same slip system
|
|
vClimb, & ! climb velocity of edge dipoles
|
|
nSources
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
|
|
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
|
|
rhoDipOriginal, &
|
|
dLower, & ! minimum stable dipole distance for edges and screws
|
|
dUpper ! current maximum stable dipole distance for edges and screws
|
|
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
|
|
m ! direction of dislocation motion
|
|
real(pReal), dimension(3,3) :: my_F, & ! my total deformation gradient
|
|
neighboring_F, & ! total deformation gradient of my neighbor
|
|
my_Fe, & ! my elastic deformation gradient
|
|
neighboring_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
|
|
D, & ! self diffusion
|
|
rnd, &
|
|
meshlength
|
|
logical considerEnteringFlux, &
|
|
considerLeavingFlux
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
write(6,*)
|
|
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_dotState at el ip g ',el,ip,g
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
|
|
|
|
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
|
|
|
tau = 0.0_pReal
|
|
gdot = 0.0_pReal
|
|
|
|
|
|
!*** shortcut to state variables
|
|
|
|
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
|
rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal)
|
|
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) &
|
|
rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s)
|
|
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
|
|
rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal)
|
|
rhoForest = state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns)
|
|
tauThreshold = state(g,ip,el)%p(11_pInt*ns+1_pInt:12_pInt*ns)
|
|
tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns)
|
|
forall (t = 1_pInt:4_pInt) &
|
|
v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
rhoSglOriginal = rhoSgl
|
|
rhoDipOriginal = rhoDip
|
|
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoSgl = 0.0_pReal
|
|
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoDip = 0.0_pReal
|
|
|
|
|
|
!*** sanity check for timestep
|
|
|
|
if (timestep <= 0.0_pReal) then ! if illegal timestep...
|
|
constitutive_nonlocal_dotState = 0.0_pReal ! ...return without doing anything (-> zero dotState)
|
|
return
|
|
endif
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** Calculate shear rate
|
|
|
|
forall (t = 1_pInt:4_pInt) &
|
|
gdot(1_pInt:ns,t) = rhoSgl(1_pInt:ns,t) * constitutive_nonlocal_burgers(1:ns,myInstance) * v(1:ns,t)
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
|
|
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> rho / 1/m^2', rhoSgl, rhoDip
|
|
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> gdot / 1/s',gdot
|
|
endif
|
|
#endif
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** calculate limits for stable dipole height
|
|
|
|
do s = 1_pInt,ns ! loop over slip systems
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
|
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure)) + tauBack(s)
|
|
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
|
|
enddo
|
|
|
|
dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance)
|
|
dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau))
|
|
dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (4.0_pReal * pi * abs(tau))
|
|
forall (c = 1_pInt:2_pInt) &
|
|
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
|
|
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
|
|
dUpper(1:ns,c))
|
|
dUpper = max(dUpper,dLower)
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** calculate dislocation multiplication
|
|
|
|
rhoDotMultiplication = 0.0_pReal
|
|
if (constitutive_nonlocal_probabilisticMultiplication(myInstance)) then
|
|
meshlength = mesh_ipVolume(ip,el)**0.333_pReal
|
|
where(sum(rhoSgl(1:ns,1:4),2) > 0.0_pReal)
|
|
nSources = (sum(rhoSgl(1:ns,1:2),2) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(rhoSgl(1:ns,3:4),2)) &
|
|
/ sum(rhoSgl(1:ns,1:4),2) * meshlength / constitutive_nonlocal_lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns))
|
|
elsewhere
|
|
nSources = meshlength / constitutive_nonlocal_lambda0(1:ns,myInstance) * sqrt(rhoForest(1:ns))
|
|
endwhere
|
|
do s = 1_pInt,ns
|
|
if (nSources(s) < 1.0_pReal) then
|
|
if (constitutive_nonlocal_sourceProbability(s,g,ip,el) > 1.0_pReal) then
|
|
call random_number(rnd)
|
|
constitutive_nonlocal_sourceProbability(s,g,ip,el) = rnd
|
|
!$OMP FLUSH(constitutive_nonlocal_sourceProbability)
|
|
endif
|
|
if (constitutive_nonlocal_sourceProbability(s,g,ip,el) > 1.0_pReal - nSources(s)) then
|
|
rhoDotMultiplication(s,1:4) = sum(rhoSglOriginal(s,1:4) * abs(v(s,1:4))) / meshlength
|
|
endif
|
|
else
|
|
constitutive_nonlocal_sourceProbability(s,g,ip,el) = 2.0_pReal
|
|
rhoDotMultiplication(s,1:4) = &
|
|
(sum(abs(gdot(s,1:2))) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(abs(gdot(s,3:4)))) &
|
|
/ constitutive_nonlocal_burgers(s,myInstance) * sqrt(rhoForest(s)) / constitutive_nonlocal_lambda0(s,myInstance)
|
|
endif
|
|
enddo
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
|
|
write(6,'(a,/,4(12x,12(f12.5,1x),/))') '<< CONST >> sources', nSources
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
else
|
|
rhoDotMultiplication(1:ns,1:4) = spread( &
|
|
(sum(abs(gdot(1:ns,1:2)),2) * constitutive_nonlocal_fEdgeMultiplication(myInstance) + sum(abs(gdot(1:ns,3:4)),2)) &
|
|
* sqrt(rhoForest(1:ns)) / constitutive_nonlocal_lambda0(1:ns,myInstance) / constitutive_nonlocal_burgers(1:ns,myInstance), 2, 4)
|
|
endif
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** calculate dislocation fluxes (only for nonlocal plasticity)
|
|
|
|
rhoDotFlux = 0.0_pReal
|
|
|
|
if (.not. phase_localPlasticity(material_phase(g,ip,el))) then ! only for nonlocal plasticity
|
|
|
|
|
|
!*** check CFL (Courant-Friedrichs-Lewy) condition for flux
|
|
|
|
if (any( abs(gdot) > 0.0_pReal & ! any active slip system ...
|
|
.and. constitutive_nonlocal_CFLfactor(myInstance) * abs(v) * timestep &
|
|
> mesh_ipVolume(ip,el) / maxval(mesh_ipArea(:,ip,el)))) then ! ...with velocity above critical value (we use the reference volume and area for simplicity here)
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt) then
|
|
write(6,'(a,i5,a,i2)') '<< CONST >> CFL condition not fullfilled at el ',el,' ip ',ip
|
|
write(6,'(a,e10.3,a,e10.3)') '<< CONST >> velocity is at ', &
|
|
maxval(abs(v), abs(gdot) > 0.0_pReal .and. constitutive_nonlocal_CFLfactor(myInstance) * abs(v) * timestep &
|
|
> mesh_ipVolume(ip,el) / maxval(mesh_ipArea(:,ip,el))), &
|
|
' at a timestep of ',timestep
|
|
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
|
|
endif
|
|
#endif
|
|
constitutive_nonlocal_dotState = DAMASK_NaN ! -> return NaN and, hence, enforce cutback
|
|
return
|
|
endif
|
|
|
|
|
|
if (numerics_timeSyncing) then
|
|
forall (t = 1_pInt:4_pInt) &
|
|
v0(1_pInt:ns,t) = state0(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
forall (t = 1_pInt:8_pInt) &
|
|
rhoSgl0(1_pInt:ns,t) = state0(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
where (abs(rhoSgl0) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl0) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoSgl0 = 0.0_pReal
|
|
endif
|
|
|
|
|
|
!*** be aware of the definition of lattice_st = lattice_sd x lattice_sn !!!
|
|
!*** opposite sign to our p vector in the (s,p,n) triplet !!!
|
|
|
|
m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
|
|
m(1:3,1:ns,2) = -lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
|
|
m(1:3,1:ns,3) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
|
|
m(1:3,1:ns,4) = lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
|
|
|
|
my_Fe = Fe(1:3,1:3,g,ip,el)
|
|
my_F = math_mul33x33(my_Fe, Fp(1:3,1:3,g,ip,el))
|
|
|
|
do n = 1_pInt,FE_NipNeighbors(FE_geomtype(mesh_element(2,el))) ! loop through my neighbors
|
|
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
|
|
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
|
|
neighboring_n = mesh_ipNeighborhood(3,n,ip,el)
|
|
|
|
opposite_neighbor = n + mod(n,2_pInt) - mod(n+1_pInt,2_pInt)
|
|
opposite_el = mesh_ipNeighborhood(1,opposite_neighbor,ip,el)
|
|
opposite_ip = mesh_ipNeighborhood(2,opposite_neighbor,ip,el)
|
|
opposite_n = mesh_ipNeighborhood(3,opposite_neighbor,ip,el)
|
|
|
|
if (neighboring_n > 0_pInt) then ! if neighbor exists, average deformation gradient
|
|
neighboring_Fe = Fe(1:3,1:3,g,neighboring_ip,neighboring_el)
|
|
neighboring_F = math_mul33x33(neighboring_Fe, Fp(1:3,1:3,g,neighboring_ip,neighboring_el))
|
|
Favg = 0.5_pReal * (my_F + neighboring_F)
|
|
else ! if no neighbor, take my value as average
|
|
Favg = my_F
|
|
endif
|
|
|
|
|
|
!* 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
|
|
|
|
considerEnteringFlux = .false.
|
|
neighboring_v = 0.0_pReal ! needed for check of sign change in flux density below
|
|
neighboring_rhoSgl = 0.0_pReal
|
|
if (neighboring_n > 0_pInt) then
|
|
if (phase_plasticity(material_phase(1,neighboring_ip,neighboring_el)) == constitutive_nonlocal_label &
|
|
.and. any(constitutive_nonlocal_compatibility(:,:,:,n,ip,el) > 0.0_pReal)) &
|
|
considerEnteringFlux = .true.
|
|
endif
|
|
|
|
if (considerEnteringFlux) then
|
|
if(numerics_timeSyncing .and. (subfrac(g,neighboring_ip,neighboring_el) /= subfrac(g,ip,el))) then ! for timesyncing: in case of a timestep at the interface we have to use "state0" to make sure that fluxes n both sides are equal
|
|
forall (t = 1_pInt:4_pInt) &
|
|
neighboring_v(1_pInt:ns,t) = state0(g,neighboring_ip,neighboring_el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
forall (t = 1_pInt:8_pInt) &
|
|
neighboring_rhoSgl(1_pInt:ns,t) = state0(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
else
|
|
forall (t = 1_pInt:4_pInt) &
|
|
neighboring_v(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
forall (t = 1_pInt:8_pInt) &
|
|
neighboring_rhoSgl(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
endif
|
|
where (abs(neighboring_rhoSgl) * mesh_ipVolume(neighboring_ip,neighboring_el) ** 0.667_pReal &
|
|
< constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(neighboring_rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
neighboring_rhoSgl = 0.0_pReal
|
|
normal_neighbor2me_defConf = math_det33(Favg) &
|
|
* math_mul33x3(math_inv33(transpose(Favg)), mesh_ipAreaNormal(1:3,neighboring_n,neighboring_ip,neighboring_el)) ! calculate the normal of the interface in (average) deformed configuration (now pointing from my neighbor to me!!!)
|
|
normal_neighbor2me = math_mul33x3(transpose(neighboring_Fe), normal_neighbor2me_defConf) / math_det33(neighboring_Fe) ! interface normal in the lattice configuration of my neighbor
|
|
area = mesh_ipArea(neighboring_n,neighboring_ip,neighboring_el) * math_norm3(normal_neighbor2me)
|
|
normal_neighbor2me = normal_neighbor2me / math_norm3(normal_neighbor2me) ! normalize the surface normal to unit length
|
|
do s = 1_pInt,ns
|
|
do t = 1_pInt,4_pInt
|
|
c = (t + 1_pInt) / 2
|
|
topp = t + mod(t,2_pInt) - mod(t+1_pInt,2_pInt)
|
|
if (neighboring_v(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal & ! flux from my neighbor to me == entering flux for me
|
|
.and. v(s,t) * neighboring_v(s,t) >= 0.0_pReal ) then ! ... only if no sign change in flux density
|
|
do deads = 0_pInt,4_pInt,4_pInt
|
|
lineLength = abs(neighboring_rhoSgl(s,t+deads)) * neighboring_v(s,t) &
|
|
* math_mul3x3(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
|
|
where (constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility...
|
|
rhoDotFlux(1_pInt:ns,t) = rhoDotFlux(1_pInt:ns,t) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed mobile dislocation type
|
|
* constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
|
|
where (constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility...
|
|
rhoDotFlux(1_pInt:ns,topp) = rhoDotFlux(1_pInt:ns,topp) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed mobile dislocation type
|
|
* constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
|
|
enddo
|
|
endif
|
|
enddo
|
|
enddo
|
|
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 lcal 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.
|
|
|
|
considerLeavingFlux = .true.
|
|
if (opposite_n > 0_pInt) then
|
|
if (phase_plasticity(material_phase(1,opposite_ip,opposite_el)) /= constitutive_nonlocal_label) &
|
|
considerLeavingFlux = .false.
|
|
endif
|
|
|
|
if (considerLeavingFlux) then
|
|
|
|
!* timeSyncing mode: If the central ip has zero subfraction, always use "state0". This is needed in case of
|
|
!* a synchronization step for the central ip, because then "state" contains the values at the end of the
|
|
!* previously converged full time step. Also, if either me or my neighbor has zero subfraction, we have to
|
|
!* use "state0" to make sure that fluxes on both sides of the (potential) timestep are equal.
|
|
rhoSglMe = rhoSgl
|
|
vMe = v
|
|
if(numerics_timeSyncing) then
|
|
if (subfrac(g,ip,el) == 0.0_pReal) then
|
|
rhoSglMe = rhoSgl0
|
|
vMe = v0
|
|
elseif (neighboring_n > 0_pInt) then
|
|
if (subfrac(g,neighboring_ip,neighboring_el) == 0.0_pReal) then
|
|
rhoSglMe = rhoSgl0
|
|
vMe = v0
|
|
endif
|
|
endif
|
|
endif
|
|
|
|
normal_me2neighbor_defConf = math_det33(Favg) * math_mul33x3(math_inv33(math_transpose33(Favg)), &
|
|
mesh_ipAreaNormal(1:3,n,ip,el)) ! calculate the normal of the interface in (average) deformed configuration (pointing from me to my neighbor!!!)
|
|
normal_me2neighbor = math_mul33x3(math_transpose33(my_Fe), normal_me2neighbor_defConf) / math_det33(my_Fe) ! interface normal in my lattice configuration
|
|
area = mesh_ipArea(n,ip,el) * math_norm3(normal_me2neighbor)
|
|
normal_me2neighbor = normal_me2neighbor / math_norm3(normal_me2neighbor) ! normalize the surface normal to unit length
|
|
do s = 1_pInt,ns
|
|
do t = 1_pInt,4_pInt
|
|
c = (t + 1_pInt) / 2_pInt
|
|
if (vMe(s,t) * math_mul3x3(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 (vMe(s,t) * neighboring_v(s,t) >= 0.0_pReal) then ! no sign change in flux density
|
|
transmissivity = sum(constitutive_nonlocal_compatibility(c,1_pInt:ns,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 = rhoSglMe(s,t) * vMe(s,t) * math_mul3x3(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 / mesh_ipVolume(ip,el) ! subtract dislocation flux from current type
|
|
rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) &
|
|
* sign(1.0_pReal, vMe(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
|
|
lineLength = rhoSglMe(s,t+4_pInt) * vMe(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of deads that wants to leave through this interface
|
|
rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) - lineLength / mesh_ipVolume(ip,el) * transmissivity ! dead dislocations leaving through this interface
|
|
endif
|
|
enddo
|
|
enddo
|
|
endif
|
|
|
|
enddo ! neighbor loop
|
|
endif
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** calculate dipole formation and annihilation
|
|
|
|
!*** formation by glide
|
|
|
|
do c = 1_pInt,2_pInt
|
|
|
|
rhoDotSingle2DipoleGlide(1:ns,2*c-1) = -2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
* (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile
|
|
+ rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile
|
|
+ abs(rhoSgl(1:ns,2*c+4)) * abs(gdot(1:ns,2*c-1))) ! positive mobile --> negative immobile
|
|
|
|
rhoDotSingle2DipoleGlide(1:ns,2*c) = -2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
* (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) & ! negative mobile --> positive mobile
|
|
+ rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1)) & ! positive mobile --> negative mobile
|
|
+ abs(rhoSgl(1:ns,2*c+3)) * abs(gdot(1:ns,2*c))) ! negative mobile --> positive immobile
|
|
|
|
rhoDotSingle2DipoleGlide(1:ns,2*c+3) = -2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
* rhoSgl(1:ns,2*c+3) * abs(gdot(1:ns,2*c)) ! negative mobile --> positive immobile
|
|
|
|
rhoDotSingle2DipoleGlide(1:ns,2*c+4) = -2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
* rhoSgl(1:ns,2*c+4) * abs(gdot(1:ns,2*c-1)) ! positive mobile --> negative immobile
|
|
|
|
rhoDotSingle2DipoleGlide(1:ns,c+8) = - rhoDotSingle2DipoleGlide(1:ns,2*c-1) - rhoDotSingle2DipoleGlide(1:ns,2*c) &
|
|
+ abs(rhoDotSingle2DipoleGlide(1:ns,2*c+3)) + abs(rhoDotSingle2DipoleGlide(1:ns,2*c+4))
|
|
enddo
|
|
|
|
|
|
!*** athermal annihilation
|
|
|
|
rhoDotAthermalAnnihilation = 0.0_pReal
|
|
|
|
forall (c=1_pInt:2_pInt) &
|
|
rhoDotAthermalAnnihilation(1:ns,c+8_pInt) = -2.0_pReal * dLower(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
* ( 2.0_pReal * (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) + rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1))) & ! was single hitting single
|
|
+ 2.0_pReal * (abs(rhoSgl(1:ns,2*c+3)) * abs(gdot(1:ns,2*c)) + abs(rhoSgl(1:ns,2*c+4)) * abs(gdot(1:ns,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
|
|
+ rhoDip(1:ns,c) * (abs(gdot(1:ns,2*c-1)) + abs(gdot(1:ns,2*c)))) ! single knocks dipole constituent
|
|
! annihilated screw dipoles leave edge jogs behind on the colinear system
|
|
if (myStructure == 1_pInt) then ! only fcc
|
|
forall (s = 1:ns, constitutive_nonlocal_colinearSystem(s,myInstance) > 0_pInt) &
|
|
rhoDotAthermalAnnihilation(constitutive_nonlocal_colinearSystem(s,myInstance),1:2) = -rhoDotAthermalAnnihilation(s,10) &
|
|
* 0.25_pReal * sqrt(rhoForest(s)) * (dUpper(s,2) + dLower(s,2)) &
|
|
* constitutive_nonlocal_edgeJogFactor(myInstance)
|
|
endif
|
|
|
|
|
|
!*** thermally activated annihilation of edge dipoles by climb
|
|
|
|
rhoDotThermalAnnihilation = 0.0_pReal
|
|
D = constitutive_nonlocal_Dsd0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
|
|
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) &
|
|
* constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &
|
|
* 2.0_pReal / ( dUpper(1:ns,1) + dLower(1:ns,1) )
|
|
forall (s = 1_pInt: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
|
|
|
|
|
|
|
|
!****************************************************************************
|
|
!*** assign the rates of dislocation densities to my dotState
|
|
!*** if evolution rates lead to negative densities, a cutback is enforced
|
|
|
|
rhoDot = 0.0_pReal
|
|
rhoDot = rhoDotFlux &
|
|
+ rhoDotMultiplication &
|
|
+ rhoDotSingle2DipoleGlide &
|
|
+ rhoDotAthermalAnnihilation &
|
|
+ rhoDotThermalAnnihilation
|
|
|
|
if (numerics_integrationMode == 1_pInt) then ! save rates for output if in central integration mode
|
|
constitutive_nonlocal_rhoDotFlux(1:ns,1:8,g,ip,el) = rhoDotFlux(1:ns,1:8)
|
|
constitutive_nonlocal_rhoDotMultiplication(1:ns,1:2,g,ip,el) = rhoDotMultiplication(1:ns,[1,3])
|
|
constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1:2,g,ip,el) = rhoDotSingle2DipoleGlide(1:ns,9:10)
|
|
constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotAthermalAnnihilation(1:ns,9:10)
|
|
constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotThermalAnnihilation(1:ns,9:10)
|
|
constitutive_nonlocal_rhoDotEdgeJogs(1:ns,g,ip,el) = 2.0_pReal * rhoDotThermalAnnihilation(1:ns,1)
|
|
endif
|
|
|
|
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt &
|
|
.and. ((debug_e == el .and. debug_i == ip .and. debug_g == g)&
|
|
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
|
|
write(6,'(a,/,4(12x,12(e12.5,1x),/))') '<< CONST >> dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep
|
|
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation flux', rhoDotFlux(1:ns,1:8) * timestep
|
|
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
|
|
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
|
|
rhoDotAthermalAnnihilation * timestep
|
|
write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
|
|
rhoDotThermalAnnihilation(1:ns,9:10) * timestep
|
|
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', rhoDot * timestep
|
|
write(6,'(a,/,10(12x,12(f12.5,1x),/))') '<< CONST >> relative density change', &
|
|
rhoDot(1:ns,1:8) * timestep / (abs(rhoSglOriginal)+1.0e-10), &
|
|
rhoDot(1:ns,9:10) * timestep / (rhoDipOriginal+1.0e-10)
|
|
write(6,*)
|
|
endif
|
|
#endif
|
|
|
|
|
|
if ( any(rhoSglOriginal(1:ns,1:4) + rhoDot(1:ns,1:4) * timestep < -constitutive_nonlocal_aTolRho(myInstance)) &
|
|
.or. any(rhoDipOriginal(1:ns,1:2) + rhoDot(1:ns,9:10) * timestep < -constitutive_nonlocal_aTolRho(myInstance))) then
|
|
#ifndef _OPENMP
|
|
if (iand(debug_level(debug_constitutive),debug_levelExtensive) /= 0_pInt) then
|
|
write(6,'(a,i5,a,i2)') '<< CONST >> evolution rate leads to negative density at el ',el,' ip ',ip
|
|
write(6,'(a)') '<< CONST >> enforcing cutback !!!'
|
|
endif
|
|
#endif
|
|
constitutive_nonlocal_dotState = DAMASK_NaN
|
|
return
|
|
else
|
|
constitutive_nonlocal_dotState(1:10_pInt*ns) = reshape(rhoDot,(/10_pInt*ns/))
|
|
endif
|
|
|
|
endfunction
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* COMPATIBILITY UPDATE *
|
|
!* 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. *
|
|
!*********************************************************************
|
|
subroutine constitutive_nonlocal_updateCompatibility(orientation,i,e)
|
|
|
|
use prec, only: pReal, &
|
|
pInt
|
|
use math, only: math_QuaternionDisorientation, &
|
|
math_mul3x3, &
|
|
math_qRot
|
|
use material, only: material_phase, &
|
|
material_texture, &
|
|
phase_localPlasticity, &
|
|
phase_plasticityInstance, &
|
|
homogenization_maxNgrains
|
|
use mesh, only: mesh_element, &
|
|
mesh_ipNeighborhood, &
|
|
mesh_maxNips, &
|
|
mesh_NcpElems, &
|
|
FE_NipNeighbors, &
|
|
FE_geomtype
|
|
use lattice, only: lattice_sn, &
|
|
lattice_sd
|
|
|
|
implicit none
|
|
|
|
!* input variables
|
|
integer(pInt), intent(in) :: i, & ! ip index
|
|
e ! element index
|
|
real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
orientation ! crystal orientation in quaternions
|
|
|
|
!* output variables
|
|
|
|
!* local variables
|
|
integer(pInt) Nneighbors, & ! number of neighbors
|
|
n, & ! neighbor index
|
|
neighboring_e, & ! element index of my neighbor
|
|
neighboring_i, & ! integration point index of my neighbor
|
|
my_phase, &
|
|
neighboring_phase, &
|
|
my_texture, &
|
|
neighboring_texture, &
|
|
my_structure, & ! lattice structure
|
|
my_instance, & ! instance of plasticity
|
|
ns, & ! number of active slip systems
|
|
s1, & ! slip system index (me)
|
|
s2 ! slip system index (my neighbor)
|
|
real(pReal), dimension(4) :: absoluteMisorientation ! absolute misorientation (without symmetry) between me and my neighbor
|
|
real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e))),&
|
|
constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e))),&
|
|
FE_NipNeighbors(FE_geomtype(mesh_element(2,e)))) :: &
|
|
compatibility ! compatibility for current element and ip
|
|
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: &
|
|
slipNormal, &
|
|
slipDirection
|
|
real(pReal) compatibilitySum, &
|
|
thresholdValue, &
|
|
nThresholdValues
|
|
logical, dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(1,i,e)))) :: &
|
|
belowThreshold
|
|
|
|
|
|
Nneighbors = FE_NipNeighbors(FE_geomtype(mesh_element(2,e)))
|
|
my_phase = material_phase(1,i,e)
|
|
my_texture = material_texture(1,i,e)
|
|
my_instance = phase_plasticityInstance(my_phase)
|
|
my_structure = constitutive_nonlocal_structure(my_instance)
|
|
ns = constitutive_nonlocal_totalNslip(my_instance)
|
|
slipNormal(1:3,1:ns) = lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,my_instance), my_structure)
|
|
slipDirection(1:3,1:ns) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,my_instance), my_structure)
|
|
|
|
|
|
!*** start out fully compatible
|
|
|
|
compatibility = 0.0_pReal
|
|
forall(s1 = 1_pInt:ns) &
|
|
compatibility(1:2,s1,s1,1:Nneighbors) = 1.0_pReal
|
|
|
|
|
|
!*** Loop thrugh neighbors and check whether there is any compatibility.
|
|
|
|
do n = 1_pInt,Nneighbors
|
|
neighboring_e = mesh_ipNeighborhood(1,n,i,e)
|
|
neighboring_i = mesh_ipNeighborhood(2,n,i,e)
|
|
|
|
|
|
!* FREE SURFACE
|
|
!* Set surface transmissivity to the value specified in the material.config
|
|
|
|
if (neighboring_e <= 0_pInt .or. neighboring_i <= 0_pInt) then
|
|
forall(s1 = 1_pInt:ns) &
|
|
compatibility(1:2,s1,s1,n) = sqrt(constitutive_nonlocal_surfaceTransmissivity(my_instance))
|
|
cycle
|
|
endif
|
|
|
|
|
|
!* PHASE BOUNDARY
|
|
!* If we encounter a different nonlocal "cpfem" phase at the neighbor,
|
|
!* we consider this to be a real "physical" phase boundary, so completely incompatible.
|
|
!* If one of the two "CPFEM" phases has a local plasticity law,
|
|
!* we do not consider this to be a phase boundary, so completely compatible.
|
|
|
|
neighboring_phase = material_phase(1,neighboring_i,neighboring_e)
|
|
if (neighboring_phase /= my_phase) then
|
|
if (.not. phase_localPlasticity(neighboring_phase) .and. .not. phase_localPlasticity(my_phase)) then
|
|
forall(s1 = 1_pInt:ns) &
|
|
compatibility(1:2,s1,s1,n) = 0.0_pReal ! = sqrt(0.0)
|
|
endif
|
|
cycle
|
|
endif
|
|
|
|
|
|
!* GRAIN BOUNDARY !
|
|
!* fixed transmissivity for adjacent ips with different texture (only if explicitly given in material.config)
|
|
|
|
if (constitutive_nonlocal_grainboundaryTransmissivity(my_instance) >= 0.0_pReal) then
|
|
neighboring_texture = material_texture(1,neighboring_i,neighboring_e)
|
|
if (neighboring_texture /= my_texture) then
|
|
if (.not. phase_localPlasticity(neighboring_phase)) then
|
|
forall(s1 = 1_pInt:ns) &
|
|
compatibility(1:2,s1,s1,n) = sqrt(constitutive_nonlocal_grainboundaryTransmissivity(my_instance))
|
|
endif
|
|
cycle
|
|
endif
|
|
|
|
!* GRAIN BOUNDARY ?
|
|
!* Compatibility defined by relative orientation of slip systems:
|
|
!* The 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.
|
|
else
|
|
absoluteMisorientation = math_QuaternionDisorientation(orientation(1:4,1,i,e), &
|
|
orientation(1:4,1,neighboring_i,neighboring_e), &
|
|
0_pInt) ! no symmetry
|
|
do s1 = 1_pInt,ns ! my slip systems
|
|
do s2 = 1_pInt,ns ! my neighbor's slip systems
|
|
compatibility(1,s2,s1,n) = math_mul3x3(slipNormal(1:3,s1), math_qRot(absoluteMisorientation, slipNormal(1:3,s2))) &
|
|
* abs(math_mul3x3(slipDirection(1:3,s1), math_qRot(absoluteMisorientation, slipDirection(1:3,s2))))
|
|
compatibility(2,s2,s1,n) = abs(math_mul3x3(slipNormal(1:3,s1), math_qRot(absoluteMisorientation, slipNormal(1:3,s2)))) &
|
|
* abs(math_mul3x3(slipDirection(1:3,s1), math_qRot(absoluteMisorientation, slipDirection(1:3,s2))))
|
|
enddo
|
|
|
|
compatibilitySum = 0.0_pReal
|
|
belowThreshold = .true.
|
|
do while (compatibilitySum < 1.0_pReal .and. any(belowThreshold(1:ns)))
|
|
thresholdValue = maxval(compatibility(2,1:ns,s1,n), belowThreshold(1:ns)) ! screws always positive
|
|
nThresholdValues = real(count(compatibility(2,1:ns,s1,n) == thresholdValue),pReal)
|
|
where (compatibility(2,1:ns,s1,n) >= thresholdValue) &
|
|
belowThreshold(1:ns) = .false.
|
|
if (compatibilitySum + thresholdValue * nThresholdValues > 1.0_pReal) &
|
|
where (abs(compatibility(1:2,1:ns,s1,n)) == thresholdValue) &
|
|
compatibility(1:2,1:ns,s1,n) = sign((1.0_pReal - compatibilitySum) / nThresholdValues, compatibility(1:2,1:ns,s1,n))
|
|
compatibilitySum = compatibilitySum + nThresholdValues * thresholdValue
|
|
enddo
|
|
where (belowThreshold(1:ns)) compatibility(1,1:ns,s1,n) = 0.0_pReal
|
|
where (belowThreshold(1:ns)) compatibility(2,1:ns,s1,n) = 0.0_pReal
|
|
enddo ! my slip systems cycle
|
|
endif
|
|
|
|
enddo ! neighbor cycle
|
|
|
|
constitutive_nonlocal_compatibility(1:2,1:ns,1:ns,1:Nneighbors,i,e) = compatibility
|
|
|
|
endsubroutine
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* rate of change of temperature *
|
|
!*********************************************************************
|
|
pure function constitutive_nonlocal_dotTemperature(Tstar_v,Temperature,state,g,ip,el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips
|
|
use material, only: homogenization_maxNgrains
|
|
implicit none
|
|
|
|
!* input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
|
ip, & ! current integration point
|
|
el ! current element
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
state ! microstructural state
|
|
|
|
!* output variables
|
|
real(pReal) constitutive_nonlocal_dotTemperature ! evolution of Temperature
|
|
|
|
!* local variables
|
|
|
|
constitutive_nonlocal_dotTemperature = 0.0_pReal
|
|
|
|
endfunction
|
|
|
|
|
|
|
|
|
|
!*********************************************************************
|
|
!* calculates quantities characterizing the microstructure *
|
|
!*********************************************************************
|
|
function constitutive_nonlocal_dislocationstress(state, Fe, g, ip, el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use math, only: math_mul33x33, &
|
|
math_mul33x3, &
|
|
math_invert33, &
|
|
math_transpose33, &
|
|
pi
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_element, &
|
|
mesh_node0, &
|
|
mesh_cellCenterCoordinates, &
|
|
mesh_ipVolume, &
|
|
mesh_periodicSurface, &
|
|
FE_Nips, &
|
|
FE_geomtype
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_localPlasticity, &
|
|
phase_plasticityInstance
|
|
|
|
implicit none
|
|
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
|
ip, & ! current integration point
|
|
el ! current element
|
|
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
Fe ! elastic deformation gradient
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
state ! microstructural state
|
|
|
|
!*** input/output variables
|
|
|
|
!*** output variables
|
|
real(pReal), dimension(3,3) :: constitutive_nonlocal_dislocationstress
|
|
|
|
!*** local variables
|
|
integer(pInt) neighboring_el, & ! element number of neighboring material point
|
|
neighboring_ip, & ! integration point of neighboring material point
|
|
instance, & ! my instance of this plasticity
|
|
neighboring_instance, & ! instance of this plasticity of neighboring material point
|
|
latticeStruct, & ! my lattice structure
|
|
neighboring_latticeStruct, & ! lattice structure of neighboring material point
|
|
phase, &
|
|
neighboring_phase, &
|
|
ns, & ! total number of active slip systems at my material point
|
|
neighboring_ns, & ! total number of active slip systems at neighboring material point
|
|
c, & ! index of dilsocation character (edge, screw)
|
|
s, & ! slip system index
|
|
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
|
|
dir, &
|
|
deltaX, deltaY, deltaZ, &
|
|
side, &
|
|
j
|
|
integer(pInt), dimension(2,3) :: periodicImages
|
|
real(pReal) nu, & ! poisson's ratio
|
|
x, y, z, & ! coordinates of connection vector in neighboring lattice frame
|
|
xsquare, ysquare, zsquare, & ! squares of respective coordinates
|
|
distance, & ! length of connection vector
|
|
segmentLength, & ! segment length of dislocations
|
|
lambda, &
|
|
R, Rsquare, Rcube, &
|
|
denominator, &
|
|
flipSign, &
|
|
neighboring_ipVolumeSideLength, &
|
|
detFe
|
|
real(pReal), dimension(3) :: connection, & ! connection vector between me and my neighbor in the deformed configuration
|
|
connection_neighboringLattice, & ! connection vector between me and my neighbor in the lattice configuration of my neighbor
|
|
connection_neighboringSlip, & ! connection vector between me and my neighbor in the slip system frame of my neighbor
|
|
maxCoord, minCoord, &
|
|
meshSize, &
|
|
coords, & ! x,y,z coordinates of cell center of ip volume
|
|
neighboring_coords ! x,y,z coordinates of cell center of neighboring ip volume
|
|
real(pReal), dimension(3,3) :: sigma, & ! dislocation stress for one slip system in neighboring material point's slip system frame
|
|
Tdislo_neighboringLattice, & ! dislocation stress as 2nd Piola-Kirchhoff stress at neighboring material point
|
|
invFe, & ! inverse of my elastic deformation gradient
|
|
neighboring_invFe, &
|
|
neighboringLattice2myLattice ! mapping from neighboring MPs lattice configuration to my lattice configuration
|
|
real(pReal), dimension(2,2,maxval(constitutive_nonlocal_totalNslip)) :: &
|
|
neighboring_rhoExcess ! excess density at neighboring material point (edge/screw,mobile/dead,slipsystem)
|
|
real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip)) :: &
|
|
rhoExcessDead
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
|
|
rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
|
|
logical inversionError
|
|
|
|
phase = material_phase(g,ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
latticeStruct = constitutive_nonlocal_structure(instance)
|
|
ns = constitutive_nonlocal_totalNslip(instance)
|
|
|
|
|
|
|
|
!*** get basic states
|
|
|
|
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
|
rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal) ! ensure positive single mobile densities
|
|
forall (t = 5_pInt:8_pInt) &
|
|
rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
|
|
|
|
|
|
!*** calculate the dislocation stress of the neighboring excess dislocation densities
|
|
!*** zero for material points of local plasticity
|
|
|
|
constitutive_nonlocal_dislocationstress = 0.0_pReal
|
|
|
|
if (.not. phase_localPlasticity(phase)) then
|
|
call math_invert33(Fe(1:3,1:3,g,ip,el), invFe, detFe, inversionError)
|
|
! if (inversionError) then
|
|
! return
|
|
! endif
|
|
|
|
!* in case of periodic surfaces we have to find out how many periodic images in each direction we need
|
|
|
|
do dir = 1_pInt,3_pInt
|
|
maxCoord(dir) = maxval(mesh_node0(dir,:))
|
|
minCoord(dir) = minval(mesh_node0(dir,:))
|
|
enddo
|
|
meshSize = maxCoord - minCoord
|
|
coords = mesh_cellCenterCoordinates(ip,el)
|
|
periodicImages = 0_pInt
|
|
do dir = 1_pInt,3_pInt
|
|
if (mesh_periodicSurface(dir)) then
|
|
periodicImages(1,dir) = floor((coords(dir) - constitutive_nonlocal_R(instance) - minCoord(dir)) / meshSize(dir), pInt)
|
|
periodicImages(2,dir) = ceiling((coords(dir) + constitutive_nonlocal_R(instance) - maxCoord(dir)) / meshSize(dir), pInt)
|
|
endif
|
|
enddo
|
|
|
|
|
|
!* loop through all material points (also through their periodic images if present),
|
|
!* but only consider nonlocal neighbors within a certain cutoff radius R
|
|
|
|
do neighboring_el = 1_pInt,mesh_NcpElems
|
|
ipLoop: do neighboring_ip = 1_pInt,FE_Nips(FE_geomtype(mesh_element(2,neighboring_el)))
|
|
neighboring_phase = material_phase(g,neighboring_ip,neighboring_el)
|
|
if (phase_localPlasticity(neighboring_phase)) then
|
|
cycle
|
|
endif
|
|
neighboring_instance = phase_plasticityInstance(neighboring_phase)
|
|
neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance)
|
|
neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance)
|
|
call math_invert33(Fe(1:3,1:3,1,neighboring_ip,neighboring_el), neighboring_invFe, detFe, inversionError)
|
|
! if (inversionError) then
|
|
! return
|
|
! endif
|
|
neighboring_ipVolumeSideLength = mesh_ipVolume(neighboring_ip,neighboring_el) ** (1.0_pReal/3.0_pReal) ! reference volume used here
|
|
forall (s = 1_pInt:neighboring_ns, c = 1_pInt:2_pInt) &
|
|
neighboring_rhoExcess(c,1,s) = state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-2_pInt)*neighboring_ns+s) & ! positive mobiles
|
|
- state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*neighboring_ns+s) ! negative mobiles
|
|
forall (s = 1_pInt:neighboring_ns, c = 1_pInt:2_pInt) &
|
|
neighboring_rhoExcess(c,2,s) = abs(state(g,neighboring_ip,neighboring_el)%p((2_pInt*c+2_pInt)*neighboring_ns+s)) & ! positive deads
|
|
- abs(state(g,neighboring_ip,neighboring_el)%p((2_pInt*c+3_pInt)*neighboring_ns+s)) ! negative deads
|
|
nu = constitutive_nonlocal_nu(neighboring_instance)
|
|
Tdislo_neighboringLattice = 0.0_pReal
|
|
do deltaX = periodicImages(1,1),periodicImages(2,1)
|
|
do deltaY = periodicImages(1,2),periodicImages(2,2)
|
|
do deltaZ = periodicImages(1,3),periodicImages(2,3)
|
|
|
|
|
|
!* regular case
|
|
|
|
if (neighboring_el /= el .or. neighboring_ip /= ip &
|
|
.or. deltaX /= 0_pInt .or. deltaY /= 0_pInt .or. deltaZ /= 0_pInt) then
|
|
|
|
neighboring_coords = mesh_cellCenterCoordinates(neighboring_ip,neighboring_el) &
|
|
+ (/real(deltaX,pReal), real(deltaY,pReal), real(deltaZ,pReal)/) * meshSize
|
|
connection = neighboring_coords - coords
|
|
distance = sqrt(sum(connection * connection))
|
|
if (distance > constitutive_nonlocal_R(instance)) then
|
|
cycle
|
|
endif
|
|
|
|
|
|
!* the segment length is the minimum of the third root of the control volume and the ip distance
|
|
!* this ensures, that the central MP never sits on a neighboring dislocation segment
|
|
|
|
connection_neighboringLattice = math_mul33x3(neighboring_invFe, connection)
|
|
segmentLength = min(neighboring_ipVolumeSideLength, distance)
|
|
|
|
|
|
!* loop through all slip systems of the neighboring material point
|
|
!* and add up the stress contributions from egde and screw excess on these slip systems (if significant)
|
|
|
|
do s = 1_pInt,neighboring_ns
|
|
if (all(abs(neighboring_rhoExcess(:,:,s)) < constitutive_nonlocal_significantRho(instance))) then
|
|
cycle ! not significant
|
|
endif
|
|
|
|
|
|
!* map the connection vector from the lattice into the slip system frame
|
|
|
|
connection_neighboringSlip = math_mul33x3(constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_instance), &
|
|
connection_neighboringLattice)
|
|
|
|
|
|
!* edge contribution to stress
|
|
sigma = 0.0_pReal
|
|
|
|
x = connection_neighboringSlip(1)
|
|
y = connection_neighboringSlip(2)
|
|
z = connection_neighboringSlip(3)
|
|
xsquare = x * x
|
|
ysquare = y * y
|
|
zsquare = z * z
|
|
|
|
do j = 1_pInt,2_pInt
|
|
if (abs(neighboring_rhoExcess(1,j,s)) < constitutive_nonlocal_significantRho(instance)) then
|
|
cycle
|
|
elseif (j > 1_pInt) then
|
|
x = connection_neighboringSlip(1) + sign(0.5_pReal * segmentLength, &
|
|
state(g,neighboring_ip,neighboring_el)%p(4*neighboring_ns+s) &
|
|
- state(g,neighboring_ip,neighboring_el)%p(5*neighboring_ns+s))
|
|
xsquare = x * x
|
|
endif
|
|
|
|
flipSign = sign(1.0_pReal, -y)
|
|
do side = 1_pInt,-1_pInt,-2_pInt
|
|
lambda = real(side,pReal) * 0.5_pReal * segmentLength - y
|
|
R = sqrt(xsquare + zsquare + lambda * lambda)
|
|
Rsquare = R * R
|
|
Rcube = Rsquare * R
|
|
denominator = R * (R + flipSign * lambda)
|
|
if (denominator == 0.0_pReal) then
|
|
exit ipLoop
|
|
endif
|
|
|
|
sigma(1,1) = sigma(1,1) - real(side,pReal) * flipSign * z / denominator &
|
|
* (1.0_pReal + xsquare / Rsquare + xsquare / denominator) &
|
|
* neighboring_rhoExcess(1,j,s)
|
|
sigma(2,2) = sigma(2,2) - real(side,pReal) * (flipSign * 2.0_pReal * nu * z / denominator + z * lambda / Rcube)&
|
|
* neighboring_rhoExcess(1,j,s)
|
|
sigma(3,3) = sigma(3,3) + real(side,pReal) * flipSign * z / denominator &
|
|
* (1.0_pReal - zsquare / Rsquare - zsquare / denominator) &
|
|
* neighboring_rhoExcess(1,j,s)
|
|
sigma(1,2) = sigma(1,2) + real(side,pReal) * x * z / Rcube * neighboring_rhoExcess(1,j,s)
|
|
sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * x / denominator &
|
|
* (1.0_pReal - zsquare / Rsquare - zsquare / denominator) &
|
|
* neighboring_rhoExcess(1,j,s)
|
|
sigma(2,3) = sigma(2,3) - real(side,pReal) * (nu / R - zsquare / Rcube) * neighboring_rhoExcess(1,j,s)
|
|
enddo
|
|
enddo
|
|
|
|
!* screw contribution to stress
|
|
|
|
x = connection_neighboringSlip(1) ! have to restore this value, because position might have been adapted for edge deads before
|
|
do j = 1_pInt,2_pInt
|
|
if (abs(neighboring_rhoExcess(2,j,s)) < constitutive_nonlocal_significantRho(instance)) then
|
|
cycle
|
|
elseif (j > 1_pInt) then
|
|
y = connection_neighboringSlip(2) + sign(0.5_pReal * segmentLength, &
|
|
state(g,neighboring_ip,neighboring_el)%p(6_pInt*neighboring_ns+s) &
|
|
- state(g,neighboring_ip,neighboring_el)%p(7_pInt*neighboring_ns+s))
|
|
ysquare = y * y
|
|
endif
|
|
|
|
flipSign = sign(1.0_pReal, x)
|
|
do side = 1_pInt,-1_pInt,-2_pInt
|
|
lambda = x + real(side,pReal) * 0.5_pReal * segmentLength
|
|
R = sqrt(ysquare + zsquare + lambda * lambda)
|
|
Rsquare = R * R
|
|
Rcube = Rsquare * R
|
|
denominator = R * (R + flipSign * lambda)
|
|
if (denominator == 0.0_pReal) then
|
|
exit ipLoop
|
|
endif
|
|
|
|
sigma(1,2) = sigma(1,2) - real(side,pReal) * flipSign * z * (1.0_pReal - nu) / denominator &
|
|
* neighboring_rhoExcess(2,j,s)
|
|
sigma(1,3) = sigma(1,3) + real(side,pReal) * flipSign * y * (1.0_pReal - nu) / denominator &
|
|
* neighboring_rhoExcess(2,j,s)
|
|
enddo
|
|
enddo
|
|
|
|
if (all(abs(sigma) < 1.0e-10_pReal)) then ! SIGMA IS NOT A REAL STRESS, THATS WHY WE NEED A REALLY SMALL VALUE HERE
|
|
cycle
|
|
endif
|
|
|
|
!* copy symmetric parts
|
|
|
|
sigma(2,1) = sigma(1,2)
|
|
sigma(3,1) = sigma(1,3)
|
|
sigma(3,2) = sigma(2,3)
|
|
|
|
|
|
!* scale stresses and map them into the neighboring material point's lattice configuration
|
|
|
|
sigma = sigma * constitutive_nonlocal_Gmod(neighboring_instance) &
|
|
* constitutive_nonlocal_burgers(s,neighboring_instance) &
|
|
/ (4.0_pReal * pi * (1.0_pReal - nu)) &
|
|
* mesh_ipVolume(neighboring_ip,neighboring_el) / segmentLength ! reference volume is used here (according to the segment length calculation)
|
|
Tdislo_neighboringLattice = Tdislo_neighboringLattice &
|
|
+ math_mul33x33(math_transpose33(constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_instance)), &
|
|
math_mul33x33(sigma, constitutive_nonlocal_lattice2slip(1:3,1:3,s,neighboring_instance)))
|
|
|
|
enddo ! slip system loop
|
|
|
|
|
|
!* special case of central ip volume
|
|
!* only consider dead dislocations
|
|
!* we assume that they all sit at a distance equal to half the third root of V
|
|
!* in direction of the according slip direction
|
|
|
|
else
|
|
|
|
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
|
|
rhoExcessDead(c,s) = state(g,ip,el)%p((2_pInt*c+2_pInt)*ns+s) & ! positive deads (here we use symmetry: if this has negative sign it is treated as negative density at positive position instead of positive density at negative position)
|
|
+ state(g,ip,el)%p((2_pInt*c+3_pInt)*ns+s) ! negative deads (here we use symmetry: if this has negative sign it is treated as positive density at positive position instead of negative density at negative position)
|
|
|
|
do s = 1_pInt,ns
|
|
if (all(abs(rhoExcessDead(:,s)) < constitutive_nonlocal_significantRho(instance))) then
|
|
cycle ! not significant
|
|
endif
|
|
sigma = 0.0_pReal ! all components except for sigma13 are zero
|
|
sigma(1,3) = - (rhoExcessDead(1,s) + rhoExcessDead(2,s) * (1.0_pReal - nu)) * neighboring_ipVolumeSideLength &
|
|
* constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) &
|
|
/ (sqrt(2.0_pReal) * pi * (1.0_pReal - nu))
|
|
sigma(3,1) = sigma(1,3)
|
|
|
|
Tdislo_neighboringLattice = Tdislo_neighboringLattice &
|
|
+ math_mul33x33(math_transpose33(constitutive_nonlocal_lattice2slip(1:3,1:3,s,instance)), &
|
|
math_mul33x33(sigma, constitutive_nonlocal_lattice2slip(1:3,1:3,s,instance)))
|
|
|
|
enddo ! slip system loop
|
|
|
|
endif
|
|
|
|
enddo ! deltaZ loop
|
|
enddo ! deltaY loop
|
|
enddo ! deltaX loop
|
|
|
|
|
|
!* map the stress from the neighboring MP's lattice configuration into the deformed configuration
|
|
!* and back into my lattice configuration
|
|
|
|
neighboringLattice2myLattice = math_mul33x33(invFe, Fe(1:3,1:3,1,neighboring_ip,neighboring_el))
|
|
constitutive_nonlocal_dislocationstress = constitutive_nonlocal_dislocationstress &
|
|
+ math_mul33x33(neighboringLattice2myLattice, &
|
|
math_mul33x33(Tdislo_neighboringLattice, &
|
|
math_transpose33(neighboringLattice2myLattice)))
|
|
|
|
enddo ipLoop
|
|
enddo ! element loop
|
|
|
|
endif
|
|
|
|
endfunction
|
|
|
|
|
|
!*********************************************************************
|
|
!* return array of constitutive results *
|
|
!*********************************************************************
|
|
function constitutive_nonlocal_postResults(Tstar_v, Fe, Temperature, dt, state, dotState, g,ip,el)
|
|
|
|
use prec, only: pReal, &
|
|
pInt, &
|
|
p_vec
|
|
use math, only: math_mul6x6, &
|
|
math_mul33x3, &
|
|
math_mul33x33, &
|
|
pi
|
|
use mesh, only: mesh_NcpElems, &
|
|
mesh_maxNips, &
|
|
mesh_ipVolume
|
|
use material, only: homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_plasticityInstance, &
|
|
phase_Noutput
|
|
use lattice, only: lattice_Sslip_v, &
|
|
lattice_sd, &
|
|
lattice_st
|
|
|
|
implicit none
|
|
|
|
!*** input variables
|
|
integer(pInt), intent(in) :: g, & ! current grain number
|
|
ip, & ! current integration point
|
|
el ! current element number
|
|
real(pReal), intent(in) :: Temperature, & ! temperature
|
|
dt ! time increment
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
|
|
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
Fe ! elastic deformation gradient
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
|
state ! current microstructural state
|
|
type(p_vec), intent(in) :: dotState ! evolution rate of microstructural state
|
|
|
|
!*** output variables
|
|
real(pReal), dimension(constitutive_nonlocal_sizePostResults(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
constitutive_nonlocal_postResults
|
|
|
|
!*** local variables
|
|
integer(pInt) myInstance, & ! current instance of this plasticity
|
|
myStructure, & ! current lattice structure
|
|
ns, & ! short notation for the total number of active slip systems
|
|
c, & ! character of dislocation
|
|
cs, & ! constitutive result index
|
|
o, & ! index of current output
|
|
t, & ! type of dislocation
|
|
s, & ! index of my current slip system
|
|
sLattice ! index of my current slip system according to lattice order
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
|
|
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
|
|
rhoDotSgl ! evolution rate of single dislocation densities (positive/negative screw and edge without dipoles)
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
|
|
gdot, & ! shear rates
|
|
v ! velocities
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
|
|
rhoForest, & ! forest dislocation density
|
|
tauThreshold, & ! threshold shear stress
|
|
tau, & ! current resolved shear stress
|
|
tauBack ! back stress from pileups on same slip system
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
|
|
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
|
|
rhoDotDip, & ! evolution rate of 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), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
|
|
m, & ! direction of dislocation motion for edge and screw (unit vector)
|
|
m_currentconf ! direction of dislocation motion for edge and screw (unit vector) in current configuration
|
|
real(pReal), dimension(3,3) :: sigma
|
|
|
|
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
|
|
|
cs = 0_pInt
|
|
constitutive_nonlocal_postResults = 0.0_pReal
|
|
|
|
|
|
!* short hand notations for state variables
|
|
|
|
forall (s = 1_pInt:ns, t = 1_pInt:4_pInt) &
|
|
rhoSgl(s,t) = max(state(g,ip,el)%p((t-1_pInt)*ns+s), 0.0_pReal)
|
|
forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) &
|
|
rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s)
|
|
forall (c = 1_pInt:2_pInt) &
|
|
rhoDip(1:ns,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+1_pInt:(8_pInt+c)*ns), 0.0_pReal)
|
|
rhoForest = state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns)
|
|
tauThreshold = state(g,ip,el)%p(11_pInt*ns+1:12_pInt*ns)
|
|
tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns)
|
|
forall (t = 1_pInt:8_pInt) rhoDotSgl(1:ns,t) = dotState%p((t-1_pInt)*ns+1_pInt:t*ns)
|
|
forall (c = 1_pInt:2_pInt) rhoDotDip(1:ns,c) = dotState%p((7_pInt+c)*ns+1_pInt:(8_pInt+c)*ns)
|
|
forall (t = 1_pInt:4_pInt) v(1:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
|
|
where (abs(rhoSgl) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoSgl = 0.0_pReal
|
|
where (abs(rhoDip) * mesh_ipVolume(ip,el) ** 0.667_pReal < constitutive_nonlocal_significantN(myInstance) &
|
|
.or. abs(rhoSgl) < constitutive_nonlocal_significantRho(myInstance)) &
|
|
rhoDip = 0.0_pReal
|
|
|
|
|
|
|
|
!* Calculate shear rate
|
|
|
|
do t = 1_pInt,4_pInt
|
|
do s = 1_pInt,ns
|
|
if (rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) then
|
|
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4_pInt)) ! remobilization of immobile singles for changing sign of v (bauschinger effect)
|
|
rhoSgl(s,t+4_pInt) = 0.0_pReal ! remobilization of immobile singles for changing sign of v (bauschinger effect)
|
|
endif
|
|
enddo
|
|
enddo
|
|
|
|
forall (t = 1_pInt:4_pInt) &
|
|
gdot(1:ns,t) = rhoSgl(1:ns,t) * constitutive_nonlocal_burgers(1:ns,myInstance) * v(1:ns,t)
|
|
|
|
|
|
!* calculate limits for stable dipole height
|
|
|
|
do s = 1_pInt,ns
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
|
tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure)) + tauBack(s)
|
|
if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
|
|
enddo
|
|
|
|
dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance)
|
|
dUpper(1:ns,1) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (8.0_pReal * pi * (1.0_pReal - constitutive_nonlocal_nu(myInstance)) * abs(tau))
|
|
dUpper(1:ns,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
|
|
/ (4.0_pReal * pi * abs(tau))
|
|
forall (c = 1_pInt:2_pInt) &
|
|
dUpper(1:ns,c) = min(1.0_pReal / sqrt(rhoSgl(1:ns,2*c-1) + rhoSgl(1:ns,2*c) &
|
|
+ abs(rhoSgl(1:ns,2*c+3)) + abs(rhoSgl(1:ns,2*c+4)) + rhoDip(1:ns,c)), &
|
|
dUpper(1:ns,c))
|
|
dUpper = max(dUpper,dLower)
|
|
|
|
|
|
!*** dislocation motion
|
|
|
|
m(1:3,1:ns,1) = lattice_sd(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure)
|
|
m(1:3,1:ns,2) = -lattice_st(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure)
|
|
forall (c = 1_pInt:2_pInt, s = 1_pInt:ns) &
|
|
m_currentconf(1:3,s,c) = math_mul33x3(Fe, m(1:3,s,c))
|
|
|
|
|
|
do o = 1_pInt,phase_Noutput(material_phase(g,ip,el))
|
|
select case(constitutive_nonlocal_output(o,myInstance))
|
|
|
|
case ('rho')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl),2) + sum(rhoDip,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,1:4)),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,5:8),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dip')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDip,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,1:2),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,5:6),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_pos')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_pos_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(1:ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_pos_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(4*ns+1:5*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_neg')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6))
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_neg_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(ns+1:2*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_edge_neg_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(5*ns+1:6*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dip_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(8*ns+1:9*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,3:4),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoSgl(1:ns,7:8),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_pos')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_pos_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(2*ns+1:3*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_pos_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(6*ns+1:7*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_neg')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8))
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_neg_mobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(3*ns+1:4*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_sgl_screw_neg_immobile')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(7*ns+1:8*ns)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dip_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = state(g,ip,el)%p(9*ns+1:10*ns)
|
|
cs = cs + ns
|
|
|
|
case ('excess_rho')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))) &
|
|
- (rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6))) &
|
|
+ (rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))) &
|
|
- (rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8)))
|
|
cs = cs + ns
|
|
|
|
case ('excess_rho_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,1) + abs(rhoSgl(1:ns,5))) &
|
|
- (rhoSgl(1:ns,2) + abs(rhoSgl(1:ns,6)))
|
|
cs = cs + ns
|
|
|
|
case ('excess_rho_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = (rhoSgl(1:ns,3) + abs(rhoSgl(1:ns,7))) &
|
|
- (rhoSgl(1:ns,4) + abs(rhoSgl(1:ns,8)))
|
|
cs = cs + ns
|
|
|
|
case ('rho_forest')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoForest
|
|
cs = cs + ns
|
|
|
|
case ('delta')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2) + sum(rhoDip,2))
|
|
cs = cs + ns
|
|
|
|
case ('delta_sgl')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(abs(rhoSgl),2))
|
|
cs = cs + ns
|
|
|
|
case ('delta_dip')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 1.0_pReal / sqrt(sum(rhoDip,2))
|
|
cs = cs + ns
|
|
|
|
case ('shearrate')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(gdot,2)
|
|
cs = cs + ns
|
|
|
|
case ('resolvedstress')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tau
|
|
cs = cs + ns
|
|
|
|
case ('resolvedstress_back')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tauBack
|
|
cs = cs + ns
|
|
|
|
case ('resolvedstress_external')
|
|
do s = 1_pInt,ns
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
|
constitutive_nonlocal_postResults(cs+s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure))
|
|
enddo
|
|
cs = cs + ns
|
|
|
|
case ('resistance')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = tauThreshold
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotSgl,2) + sum(rhoDotDip,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_sgl')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotSgl,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_dip')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(rhoDotDip,2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_gen')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotMultiplication(1:ns,1,g,ip,el) &
|
|
+ constitutive_nonlocal_rhoDotMultiplication(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_gen_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotMultiplication(1:ns,1,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_gen_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotMultiplication(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_sgl2dip')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1,g,ip,el) &
|
|
+ constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_sgl2dip_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_sgl2dip_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_ann_ath')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1,g,ip,el) &
|
|
+ constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_ann_the')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1,g,ip,el) &
|
|
+ constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_ann_the_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_ann_the_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_edgejogs')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotEdgeJogs(1:ns,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_flux')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,1:4,g,ip,el),2) &
|
|
+ sum(abs(constitutive_nonlocal_rhoDotFlux(1:ns,5:8,g,ip,el)),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_flux_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,1:2,g,ip,el),2) &
|
|
+ sum(abs(constitutive_nonlocal_rhoDotFlux(1:ns,5:6,g,ip,el)),2)
|
|
cs = cs + ns
|
|
|
|
case ('rho_dot_flux_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,3:4,g,ip,el),2) &
|
|
+ sum(abs(constitutive_nonlocal_rhoDotFlux(1:ns,7:8,g,ip,el)),2)
|
|
cs = cs + ns
|
|
|
|
case ('velocity_edge_pos')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('velocity_edge_neg')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('velocity_screw_pos')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,3)
|
|
cs = cs + ns
|
|
|
|
case ('velocity_screw_neg')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = v(1:ns,4)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_pos_x')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(1,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_pos_y')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(2,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_pos_z')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,1) * v(1:ns,1) * m_currentconf(3,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_neg_x')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(1,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_neg_y')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(2,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_edge_neg_z')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,2) * v(1:ns,2) * m_currentconf(3,1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_pos_x')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(1,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_pos_y')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(2,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_pos_z')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,3) * v(1:ns,3) * m_currentconf(3,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_neg_x')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(1,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_neg_y')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(2,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('fluxdensity_screw_neg_z')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = - rhoSgl(1:ns,4) * v(1:ns,4) * m_currentconf(3,1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case ('maximumdipoleheight_edge')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = dUpper(1:ns,1)
|
|
cs = cs + ns
|
|
|
|
case ('maximumdipoleheight_screw')
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = dUpper(1:ns,2)
|
|
cs = cs + ns
|
|
|
|
case('dislocationstress')
|
|
sigma = constitutive_nonlocal_dislocationstress(state, Fe, g, ip, el)
|
|
constitutive_nonlocal_postResults(cs+1_pInt) = sigma(1,1)
|
|
constitutive_nonlocal_postResults(cs+2_pInt) = sigma(2,2)
|
|
constitutive_nonlocal_postResults(cs+3_pInt) = sigma(3,3)
|
|
constitutive_nonlocal_postResults(cs+4_pInt) = sigma(1,2)
|
|
constitutive_nonlocal_postResults(cs+5_pInt) = sigma(2,3)
|
|
constitutive_nonlocal_postResults(cs+6_pInt) = sigma(3,1)
|
|
cs = cs + 6_pInt
|
|
|
|
case('accumulatedshear')
|
|
constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el) = constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el) + sum(gdot,2)*dt
|
|
!$OMP FLUSH(constitutive_nonlocal_accumulatedShear)
|
|
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el)
|
|
cs = cs + ns
|
|
|
|
case('boundarylayer')
|
|
do s = 1_pInt,ns
|
|
if (sum(abs(rhoSgl(s,1:8))) > 0.0_pReal) then
|
|
constitutive_nonlocal_postResults(cs+s) = maxval(abs(rhoSgl(s,5:8))/(rhoSgl(s,1:4)+abs(rhoSgl(s,5:8))))
|
|
else
|
|
constitutive_nonlocal_postResults(cs+s) = 0.0_pReal
|
|
endif
|
|
enddo
|
|
cs = cs + ns
|
|
|
|
end select
|
|
enddo
|
|
|
|
endfunction
|
|
|
|
END MODULE
|