! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH ! ! This file is part of DAMASK, ! the Düsseldorf Advanced MAterial Simulation Kit. ! ! DAMASK is free software: you can redistribute it and/or modify ! it under the terms of the GNU General Public License as published by ! the Free Software Foundation, either version 3 of the License, or ! (at your option) any later version. ! ! DAMASK is distributed in the hope that it will be useful, ! but WITHOUT ANY WARRANTY; without even the implied warranty of ! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ! GNU General Public License for more details. ! ! You should have received a copy of the GNU General Public License ! along with DAMASK. If not, see . ! !############################################################## !* $Id$ !************************************ !* Module: CONSTITUTIVE_NONLOCAL * !************************************ !* contains: * !* - constitutive equations * !* - parameters definition * !************************************ MODULE constitutive_nonlocal !* Include other modules use prec, only: pReal,pInt implicit none !* Definition of parameters character (len=*), parameter :: constitutive_nonlocal_label = 'nonlocal' character(len=22), dimension(10), parameter :: constitutive_nonlocal_listBasicStates = (/'rhoSglEdgePosMobile ', & 'rhoSglEdgeNegMobile ', & 'rhoSglScrewPosMobile ', & 'rhoSglScrewNegMobile ', & 'rhoSglEdgePosImmobile ', & 'rhoSglEdgeNegImmobile ', & 'rhoSglScrewPosImmobile', & 'rhoSglScrewNegImmobile', & 'rhoDipEdge ', & 'rhoDipScrew ' /) ! list of "basic" microstructural state variables that are independent from other state variables character(len=16), dimension(3), parameter :: constitutive_nonlocal_listDependentStates = (/'rhoForest ', & 'tauThreshold ', & 'tauBack ' /) ! list of microstructural state variables that depend on other state variables character(len=16), dimension(4), parameter :: constitutive_nonlocal_listOtherStates = (/'velocityEdgePos ', & 'velocityEdgeNeg ', & 'velocityScrewPos', & 'velocityScrewNeg' /) ! list of other dependent state variables that are not updated by microstructure real(pReal), parameter :: kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin !* Definition of global variables integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_sizeDotState, & ! number of dotStates = number of basic state variables constitutive_nonlocal_sizeDependentState, & ! number of dependent state variables constitutive_nonlocal_sizeState, & ! total number of state variables constitutive_nonlocal_sizePostResults ! cumulative size of post results integer(pInt), dimension(:,:), allocatable, target :: constitutive_nonlocal_sizePostResult ! size of each post result output character(len=64), dimension(:,:), allocatable, target :: constitutive_nonlocal_output ! name of each post result output integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_Noutput ! number of outputs per instance of this constitution character(len=32), dimension(:), allocatable :: constitutive_nonlocal_structureName ! name of the lattice structure integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_structure, & ! number representing the kind of lattice structure constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance integer(pInt), dimension(:,:), allocatable :: constitutive_nonlocal_Nslip, & ! number of active slip systems for each family and instance constitutive_nonlocal_slipFamily, & ! lookup table relating active slip system to slip family for each instance constitutive_nonlocal_slipSystemLattice ! lookup table relating active slip system index to lattice slip system index for each instance real(pReal), dimension(:), allocatable :: constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice constitutive_nonlocal_C11, & ! C11 element in elasticity matrix constitutive_nonlocal_C12, & ! C12 element in elasticity matrix constitutive_nonlocal_C13, & ! C13 element in elasticity matrix constitutive_nonlocal_C33, & ! C33 element in elasticity matrix constitutive_nonlocal_C44, & ! C44 element in elasticity matrix constitutive_nonlocal_Gmod, & ! shear modulus constitutive_nonlocal_nu, & ! poisson's ratio constitutive_nonlocal_atomicVolume, & ! atomic volume constitutive_nonlocal_Dsd0, & ! prefactor for self-diffusion coefficient constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion constitutive_nonlocal_aTolRho, & ! absolute tolerance for dislocation density in state integration constitutive_nonlocal_R, & ! cutoff radius for dislocation stress constitutive_nonlocal_doublekinkwidth, & ! width of a doubkle kink in multiples of the burgers vector length b constitutive_nonlocal_solidSolutionEnergy, & ! activation energy for solid solution in J constitutive_nonlocal_solidSolutionSize, & ! solid solution obstacle size in multiples of the burgers vector length constitutive_nonlocal_solidSolutionConcentration, & ! concentration of solid solution in atomic parts constitutive_nonlocal_p, & ! parameter for kinetic law (Kocks,Argon,Ashby) constitutive_nonlocal_q, & ! parameter for kinetic law (Kocks,Argon,Ashby) constitutive_nonlocal_viscosity, & ! viscosity for dislocation glide in Pa s constitutive_nonlocal_fattack, & ! attack frequency in Hz constitutive_nonlocal_rhoSglScatter, & ! standard deviation of scatter in initial dislocation density constitutive_nonlocal_surfaceTransmissivity ! transmissivity at free surface real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_rhoSglEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoSglScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoDipEdge0, & ! initial edge dipole dislocation density per slip system for each family and instance constitutive_nonlocal_rhoDipScrew0, & ! initial screw dipole dislocation density per slip system for each family and instance constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance constitutive_nonlocal_lambda0, & ! mean free path prefactor for each slip system and instance constitutive_nonlocal_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each family and instance constitutive_nonlocal_burgers, & ! absolute length of burgers vector [m] for each slip system and instance constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_minimumDipoleHeightPerSlipFamily, & ! minimum stable edge/screw dipole height for each family and instance constitutive_nonlocal_minimumDipoleHeight, & ! minimum stable edge/screw dipole height for each slip system and instance constitutive_nonlocal_peierlsStressPerSlipFamily, & ! Peierls stress (edge and screw) constitutive_nonlocal_peierlsStress ! Peierls stress (edge and screw) real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_rhoDotFlux ! dislocation convection term real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_nonlocal_compatibility ! slip system compatibility between me and my neighbors real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each instance constitutive_nonlocal_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance real(pReal), dimension(:,:,:,:), allocatable :: constitutive_nonlocal_lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!) constitutive_nonlocal_accumulatedShear ! accumulated shear per slip system up to the start of the FE increment CONTAINS !**************************************** !* - constitutive_nonlocal_init !* - constitutive_nonlocal_stateInit !* - constitutive_nonlocal_aTolState !* - constitutive_nonlocal_homogenizedC !* - constitutive_nonlocal_microstructure !* - constitutive_nonlocal_kinetics !* - constitutive_nonlocal_LpAndItsTangent !* - constitutive_nonlocal_dotState !* - constitutive_nonlocal_dotTemperature !* - constitutive_nonlocal_updateCompatibility !* - constitutive_nonlocal_postResults !**************************************** !************************************** !* Module initialization * !************************************** subroutine constitutive_nonlocal_init(myFile) use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment) use prec, only: pInt, pReal use math, only: math_Mandel3333to66, & math_Voigt66to3333, & math_mul3x3, & math_transpose33 use IO, only: IO_lc, & IO_getTag, & IO_isBlank, & IO_stringPos, & IO_stringValue, & IO_floatValue, & IO_intValue, & IO_error use debug, only: debug_verbosity use mesh, only: mesh_NcpElems, & mesh_maxNips, & FE_maxNipNeighbors use material, only: homogenization_maxNgrains, & phase_constitution, & phase_constitutionInstance, & phase_Noutput use lattice, only: lattice_maxNslipFamily, & lattice_maxNslip, & lattice_maxNinteraction, & lattice_NslipSystem, & lattice_NtwinSystem, & lattice_initializeStructure, & lattice_Qtwin, & lattice_sd, & lattice_sn, & lattice_st, & lattice_interactionSlipSlip !*** output variables !*** input variables integer(pInt), intent(in) :: myFile !*** local variables integer(pInt), parameter :: maxNchunks = 21_pInt integer(pInt), & dimension(1_pInt+2_pInt*maxNchunks) :: positions integer(pInt) section, & maxNinstance, & maxTotalNslip, & myStructure, & f, & ! index of my slip family i, & ! index of my instance of this constitution j, & k, & l, & ns, & ! short notation for total number of active slip systems for the current instance o, & ! index of my output s, & ! index of my slip system s1, & ! index of my slip system s2, & ! index of my slip system it, & ! index of my interaction type mySize character(len=64) tag character(len=1024) line !$OMP CRITICAL (write2out) write(6,*) write(6,*) '<<<+- constitutive_',trim(constitutive_nonlocal_label),' init -+>>>' write(6,*) '$Id$' #include "compilation_info.f90" !$OMP END CRITICAL (write2out) maxNinstance = int(count(phase_constitution == constitutive_nonlocal_label),pInt) if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law if (debug_verbosity > 0) then !$OMP CRITICAL (write2out) write(6,'(a16,1x,i5)') '# instances:',maxNinstance !$OMP END CRITICAL (write2out) endif !*** space allocation for global variables allocate(constitutive_nonlocal_sizeDotState(maxNinstance)) allocate(constitutive_nonlocal_sizeDependentState(maxNinstance)) allocate(constitutive_nonlocal_sizeState(maxNinstance)) allocate(constitutive_nonlocal_sizePostResults(maxNinstance)) allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance)) allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance)) allocate(constitutive_nonlocal_Noutput(maxNinstance)) constitutive_nonlocal_sizeDotState = 0_pInt constitutive_nonlocal_sizeDependentState = 0_pInt constitutive_nonlocal_sizeState = 0_pInt constitutive_nonlocal_sizePostResults = 0_pInt constitutive_nonlocal_sizePostResult = 0_pInt constitutive_nonlocal_output = '' constitutive_nonlocal_Noutput = 0_pInt allocate(constitutive_nonlocal_structureName(maxNinstance)) allocate(constitutive_nonlocal_structure(maxNinstance)) allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance)) allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance)) allocate(constitutive_nonlocal_totalNslip(maxNinstance)) constitutive_nonlocal_structureName = '' constitutive_nonlocal_structure = 0_pInt constitutive_nonlocal_Nslip = 0_pInt constitutive_nonlocal_slipFamily = 0_pInt constitutive_nonlocal_slipSystemLattice = 0_pInt constitutive_nonlocal_totalNslip = 0_pInt allocate(constitutive_nonlocal_CoverA(maxNinstance)) allocate(constitutive_nonlocal_C11(maxNinstance)) allocate(constitutive_nonlocal_C12(maxNinstance)) allocate(constitutive_nonlocal_C13(maxNinstance)) allocate(constitutive_nonlocal_C33(maxNinstance)) allocate(constitutive_nonlocal_C44(maxNinstance)) allocate(constitutive_nonlocal_Gmod(maxNinstance)) allocate(constitutive_nonlocal_nu(maxNinstance)) allocate(constitutive_nonlocal_atomicVolume(maxNinstance)) allocate(constitutive_nonlocal_Dsd0(maxNinstance)) allocate(constitutive_nonlocal_Qsd(maxNinstance)) allocate(constitutive_nonlocal_aTolRho(maxNinstance)) allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance)) allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance)) allocate(constitutive_nonlocal_R(maxNinstance)) allocate(constitutive_nonlocal_doublekinkwidth(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionEnergy(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionSize(maxNinstance)) allocate(constitutive_nonlocal_solidSolutionConcentration(maxNinstance)) allocate(constitutive_nonlocal_p(maxNinstance)) allocate(constitutive_nonlocal_q(maxNinstance)) allocate(constitutive_nonlocal_viscosity(maxNinstance)) allocate(constitutive_nonlocal_fattack(maxNinstance)) allocate(constitutive_nonlocal_rhoSglScatter(maxNinstance)) allocate(constitutive_nonlocal_surfaceTransmissivity(maxNinstance)) constitutive_nonlocal_CoverA = 0.0_pReal constitutive_nonlocal_C11 = 0.0_pReal constitutive_nonlocal_C12 = 0.0_pReal constitutive_nonlocal_C13 = 0.0_pReal constitutive_nonlocal_C33 = 0.0_pReal constitutive_nonlocal_C44 = 0.0_pReal constitutive_nonlocal_Gmod = 0.0_pReal constitutive_nonlocal_atomicVolume = 0.0_pReal constitutive_nonlocal_Dsd0 = 0.0_pReal constitutive_nonlocal_Qsd = 0.0_pReal constitutive_nonlocal_aTolRho = 0.0_pReal constitutive_nonlocal_nu = 0.0_pReal constitutive_nonlocal_Cslip_66 = 0.0_pReal constitutive_nonlocal_Cslip_3333 = 0.0_pReal constitutive_nonlocal_R = -1.0_pReal constitutive_nonlocal_doublekinkwidth = 0.0_pReal constitutive_nonlocal_solidSolutionEnergy = 0.0_pReal constitutive_nonlocal_solidSolutionSize = 0.0_pReal constitutive_nonlocal_solidSolutionConcentration = 0.0_pReal constitutive_nonlocal_p = 1.0_pReal constitutive_nonlocal_q = 1.0_pReal constitutive_nonlocal_viscosity = 0.0_pReal constitutive_nonlocal_fattack = 0.0_pReal constitutive_nonlocal_rhoSglScatter = 0.0_pReal constitutive_nonlocal_surfaceTransmissivity = 1.0_pReal allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglScrewPos0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoSglScrewNeg0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoDipEdge0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_rhoDipScrew0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction,maxNinstance)) 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 = 0.0_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 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_constitution(section) == constitutive_nonlocal_label) then ! one of my sections i = phase_constitutionInstance(section) ! which instance of my constitution is present phase positions = IO_stringPos(line,maxNchunks) tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key select case(tag) case('constitution','/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_C11(i) = IO_floatValue(line,positions,2_pInt) case ('c12') constitutive_nonlocal_C12(i) = IO_floatValue(line,positions,2_pInt) case ('c13') constitutive_nonlocal_C13(i) = IO_floatValue(line,positions,2_pInt) case ('c33') constitutive_nonlocal_C33(i) = IO_floatValue(line,positions,2_pInt) case ('c44') constitutive_nonlocal_C44(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') constitutive_nonlocal_aTolRho(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('peierlsstressedge') forall (f = 1_pInt:lattice_maxNslipFamily) & constitutive_nonlocal_peierlsStressPerSlipFamily(f,1_pInt,i) = IO_floatValue(line,positions,1_pInt+f) case('peierlsstressscrew') 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('rhosglscatter') constitutive_nonlocal_rhoSglScatter(i) = IO_floatValue(line,positions,2_pInt) case('surfacetransmissivity') constitutive_nonlocal_surfaceTransmissivity(i) = IO_floatValue(line,positions,2_pInt) case default call IO_error(250_pInt,ext_msg=tag) 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 .or. myStructure > 3_pInt) call IO_error(205_pInt) if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0_pInt) call IO_error(251_pInt,ext_msg='Nslip') 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(251_pInt,ext_msg='rhoSglEdgePos0') if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoSglEdgeNeg0') if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoSglScrewPos0') if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoSglScrewNeg0') if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoDipEdge0') if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoDipScrew0') if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='burgers') if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='lambda0') if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,1,i) <= 0.0_pReal) & call IO_error(251_pInt,ext_msg='minimumDipoleHeightEdge') if (constitutive_nonlocal_minimumDipoleHeightPerSlipFamily(f,2,i) <= 0.0_pReal) & call IO_error(251_pInt,ext_msg='minimumDipoleHeightScrew') if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,1,i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='peierlsStressEdge') if (constitutive_nonlocal_peierlsStressPerSlipFamily(f,2,i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='peierlsStressScrew') endif enddo if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) & call IO_error(251_pInt,ext_msg='interaction_SlipSlip') if (constitutive_nonlocal_R(i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='r') if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='atomicVolume') if (constitutive_nonlocal_Dsd0(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='selfDiffusionPrefactor') if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='selfDiffusionEnergy') if (constitutive_nonlocal_aTolRho(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='aTol_rho') if (constitutive_nonlocal_doublekinkwidth(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='doublekinkwidth') if (constitutive_nonlocal_solidSolutionEnergy(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='solidSolutionEnergy') if (constitutive_nonlocal_solidSolutionSize(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='solidSolutionSize') if (constitutive_nonlocal_solidSolutionConcentration(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='solidSolutionConcentration') if (constitutive_nonlocal_p(i) <= 0.0_pReal .or. constitutive_nonlocal_p(i) > 1.0_pReal) call IO_error(251_pInt,ext_msg='p') if (constitutive_nonlocal_q(i) < 1.0_pReal .or. constitutive_nonlocal_q(i) > 2.0_pReal) call IO_error(251_pInt,ext_msg='q') if (constitutive_nonlocal_viscosity(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='viscosity') if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(251_pInt,ext_msg='attackFrequency') if (constitutive_nonlocal_rhoSglScatter(i) < 0.0_pReal) call IO_error(251_pInt,ext_msg='rhoSglScatter') if (constitutive_nonlocal_surfaceTransmissivity(i) < 0.0_pReal & .or. constitutive_nonlocal_surfaceTransmissivity(i) > 1.0_pReal) call IO_error(251_pInt,ext_msg='surfaceTransmissivity') !*** 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 = 0.0_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_rhoDotFlux(maxTotalNslip, 10, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) constitutive_nonlocal_rhoDotFlux = 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 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_ann_ath', & 'rho_dot_ann_the', & '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' ) mySize = constitutive_nonlocal_totalNslip(i) case('dislocationstress') mySize = 6_pInt case default call IO_error(252_pInt,ext_msg=constitutive_nonlocal_output(o,i)) 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 select case (myStructure) case(1_pInt:2_pInt) ! cubic(s) forall(k=1_pInt:3_pInt) forall(j=1_pInt:3_pInt) constitutive_nonlocal_Cslip_66(k,j,i) = constitutive_nonlocal_C12(i) constitutive_nonlocal_Cslip_66(k,k,i) = constitutive_nonlocal_C11(i) constitutive_nonlocal_Cslip_66(k+3_pInt,k+3_pInt,i) = constitutive_nonlocal_C44(i) end forall case(3_pInt:) ! all hex constitutive_nonlocal_Cslip_66(1,1,i) = constitutive_nonlocal_C11(i) constitutive_nonlocal_Cslip_66(2,2,i) = constitutive_nonlocal_C11(i) constitutive_nonlocal_Cslip_66(3,3,i) = constitutive_nonlocal_C33(i) constitutive_nonlocal_Cslip_66(1,2,i) = constitutive_nonlocal_C12(i) constitutive_nonlocal_Cslip_66(2,1,i) = constitutive_nonlocal_C12(i) constitutive_nonlocal_Cslip_66(1,3,i) = constitutive_nonlocal_C13(i) constitutive_nonlocal_Cslip_66(3,1,i) = constitutive_nonlocal_C13(i) constitutive_nonlocal_Cslip_66(2,3,i) = constitutive_nonlocal_C13(i) constitutive_nonlocal_Cslip_66(3,2,i) = constitutive_nonlocal_C13(i) constitutive_nonlocal_Cslip_66(4,4,i) = constitutive_nonlocal_C44(i) constitutive_nonlocal_Cslip_66(5,5,i) = constitutive_nonlocal_C44(i) constitutive_nonlocal_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_nonlocal_C11(i)- constitutive_nonlocal_C12(i)) end select 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)) constitutive_nonlocal_Gmod(i) = 0.2_pReal * ( constitutive_nonlocal_C11(i) - constitutive_nonlocal_C12(i) & + 3.0_pReal*constitutive_nonlocal_C44(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_C11(i) + 4.0_pReal*constitutive_nonlocal_C12(i) & - 2.0_pReal*constitutive_nonlocal_C44(i) ) & / ( 4.0_pReal*constitutive_nonlocal_C11(i) + 6.0_pReal*constitutive_nonlocal_C12(i) & + 2.0_pReal*constitutive_nonlocal_C44(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) 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) * !********************************************************************* function constitutive_nonlocal_stateInit(myInstance) use prec, only: pReal, & pInt use lattice, only: lattice_maxNslipFamily use math, only: math_sampleGaussVar implicit none !*** input variables integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution !*** output variables real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: & constitutive_nonlocal_stateInit !*** local variables real(pReal), dimension(constitutive_nonlocal_totalNslip(myInstance)) :: & rhoSglEdgePos, & ! positive edge dislocation density rhoSglEdgeNeg, & ! negative edge dislocation density rhoSglScrewPos, & ! positive screw dislocation density rhoSglScrewNeg, & ! negative screw dislocation density rhoSglEdgePosUsed, & ! used positive edge dislocation density rhoSglEdgeNegUsed, & ! used negative edge dislocation density rhoSglScrewPosUsed, & ! used positive screw dislocation density rhoSglScrewNegUsed, & ! used negative screw dislocation density rhoDipEdge, & ! edge dipole dislocation density rhoDipScrew ! screw dipole dislocation density integer(pInt) ns, & ! short notation for total number of active slip systems f, & ! index of lattice family from, & upto, & s, & ! index of slip system i real(pReal), dimension(2) :: noise constitutive_nonlocal_stateInit = 0.0_pReal ns = constitutive_nonlocal_totalNslip(myInstance) !*** set the basic state variables 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 rhoSglEdgePosUsed(from:upto) = 0.0_pReal rhoSglEdgeNegUsed(from:upto) = 0.0_pReal rhoSglScrewPosUsed(from:upto) = 0.0_pReal rhoSglScrewNegUsed(from:upto) = 0.0_pReal rhoDipEdge(from:upto) = constitutive_nonlocal_rhoDipEdge0(f, myInstance) rhoDipScrew(from:upto) = constitutive_nonlocal_rhoDipScrew0(f, myInstance) enddo !*** put everything together and in right order constitutive_nonlocal_stateInit( 1: ns) = rhoSglEdgePos constitutive_nonlocal_stateInit( ns+1: 2*ns) = rhoSglEdgeNeg constitutive_nonlocal_stateInit( 2*ns+1: 3*ns) = rhoSglScrewPos constitutive_nonlocal_stateInit( 3*ns+1: 4*ns) = rhoSglScrewNeg constitutive_nonlocal_stateInit( 4*ns+1: 5*ns) = rhoSglEdgePosUsed constitutive_nonlocal_stateInit( 5*ns+1: 6*ns) = rhoSglEdgeNegUsed constitutive_nonlocal_stateInit( 6*ns+1: 7*ns) = rhoSglScrewPosUsed constitutive_nonlocal_stateInit( 7*ns+1: 8*ns) = rhoSglScrewNegUsed constitutive_nonlocal_stateInit( 8*ns+1: 9*ns) = rhoDipEdge constitutive_nonlocal_stateInit( 9*ns+1:10*ns) = rhoDipScrew endfunction !********************************************************************* !* 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 constitution !*** output variables real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: & constitutive_nonlocal_aTolState ! absolute state tolerance for the current instance of this constitution !*** 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_constitutionInstance 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 constitution myInstance = phase_constitutionInstance(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_verbosity, & debug_selectiveDebugger, & debug_g, & debug_i, & debug_e use mesh, only: mesh_NcpElems, & mesh_maxNips, & mesh_element, & FE_NipNeighbors, & FE_maxNipNeighbors, & mesh_ipNeighborhood, & mesh_ipCenterOfGravity, & mesh_ipVolume, & mesh_ipAreaNormal use material, only: homogenization_maxNgrains, & material_phase, & phase_localConstitution, & phase_constitutionInstance use lattice, only: lattice_sd, & lattice_st 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 constitution neighboring_instance, & ! instance of this constitution 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, & side, & n integer(pInt), dimension(2) :: neighbor real(pReal) nu, & ! poisson's ratio mu, & b, & detFe, & detFp, & FVsize, & rhoExcessGradient real(pReal), dimension(2) :: rhoExcessGradient_over_rho, & gradient, & gradientDeads, & gradientInter, & gradientDistance, & gradientDistanceDeads, & gradientDistanceInter, & rhoExcessAtSampledPoint real(pReal), dimension(3) :: ipCoords, & neighboring_ipCoords real(pReal), dimension(FE_maxNipNeighbors) :: & distance ! length of connection vector real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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(3,2) :: rhoExcessDifferences, & sampledPoint real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient invFp ! inverse of plastic deformation gradient real(pReal), dimension(3,FE_maxNipNeighbors) :: & connection_latticeConf, & areaNormal_latticeConf real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & rhoExcess real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: & rhoDip ! dipole dislocation density (edge, screw) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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(3,3,2) :: connections 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_constitutionInstance(material_phase(g,ip,el))),2) :: & m ! direction of dislocation motion logical inversionError phase = material_phase(g,ip,el) instance = phase_constitutionInstance(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 !*** 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 tauThreshold(s) = constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) & * sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), & constitutive_nonlocal_interactionMatrixSlipSlip(s,1:ns,instance))) end forall !*** calculate the dislocation stress of the neighboring excess dislocation densities !*** zero for material points of local constitution tauBack = 0.0_pReal if (.not. phase_localConstitution(phase)) then call math_invert33(Fe, invFe, detFe, inversionError) call math_invert33(Fp, invFp, detFp, inversionError) ipCoords = mesh_ipCenterOfGravity(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(mesh_element(2,el)) neighboring_el = mesh_ipNeighborhood(1,n,ip,el) neighboring_ip = mesh_ipNeighborhood(2,n,ip,el) areaNormal_latticeConf(1:3,n) = detFp * math_mul33x3(math_transpose33(invFp), mesh_ipAreaNormal(1:3,n,ip,el)) ! calculate the normal of the interface in lattice configuration areaNormal_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) / math_norm3(areaNormal_latticeConf(1:3,n)) ! normalize the surface normal to unit length if (neighboring_el > 0 .and. neighboring_ip > 0) then neighboring_phase = material_phase(g,neighboring_ip,neighboring_el) neighboring_instance = phase_constitutionInstance(neighboring_phase) neighboring_latticeStruct = constitutive_nonlocal_structure(neighboring_instance) neighboring_ns = constitutive_nonlocal_totalNslip(neighboring_instance) neighboring_ipCoords = mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) if (.not. phase_localConstitution(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 connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize 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 connection_latticeConf(1:3,n) = math_mul33x3(invFe, neighboring_ipCoords - ipCoords) neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess endif else ! free surface connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess endif distance(n) = math_norm3(connection_latticeConf(1:3,n)) enddo !* loop through the slip systems !* calculate the dislocation gradient in both directions of m with two different methods: !* 1. gradient between central excess density and dead dislocations in central ip !* 2. interpolate gradient from excess density in three neighboring ips !* take the heigher gradient in both directions and do a weighted sum with weights according to the distance 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 rhoExcessGradient_over_rho = 0.0_pReal do c = 1_pInt,2_pInt if (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c) < 1.0_pReal) then cycle ! no siginificant density endif !* gradient from dead dislocations gradientDeads = 0.0_pReal if (rhoSgl(s,2_pInt*c+3_pInt) > 0.0_pReal) then ! positive deads gradientDeads(1) = + 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on positive side else gradientDeads(2) = - 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on negative side endif if (rhoSgl(s,2_pInt*c+4_pInt) > 0.0_pReal) then ! negative deads gradientDeads(2) = gradientDeads(2) + 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on negative side else gradientDeads(1) = gradientDeads(1) - 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on positive side endif gradientDistanceDeads(1:2) = 0.5_pReal * FVsize !* gradient from interpolation gradientInter = 0.0_pReal rhoExcessDifferences = 0.0_pReal connections = 0.0_pReal gradientDistanceInter = 0.0_pReal do dir = 1_pInt,3_pInt if (math_mul3x3(areaNormal_latticeConf(1:3,2_pInt*dir-1_pInt),m(1:3,s,c)) > 0.0_pReal) then ! on positive side neighbor(1) = 2_pInt * dir - 1_pInt neighbor(2) = 2_pInt * dir else ! on negative side neighbor(1) = 2_pInt * dir neighbor(2) = 2_pInt * dir - 1_pInt endif do side = 1_pInt,2_pInt n = neighbor(side) rhoExcessDifferences(dir,side) = neighboring_rhoExcess(c,s,n) - rhoExcess(c,s) connections(dir,1:3,side) = connection_latticeConf(1:3,n) gradientDistanceInter(side) = gradientDistanceInter(side) & + (math_mul3x3(connection_latticeConf(1:3,n),m(1:3,s,c))) ** 2.0_pReal / distance(n) enddo enddo sampledPoint(1:3,1) = + gradientDistanceInter(1) * m(1:3,s,c) sampledPoint(1:3,2) = - gradientDistanceInter(2) * m(1:3,s,c) do side = 1_pInt,2_pInt rhoExcessAtSampledPoint(side) = math_mul3x3(math_mul33x3(math_inv33(connections(1:3,1:3,side)), & rhoExcessDifferences(1:3,side)), & sampledPoint(1:3,side)) & + rhoExcess(c,s) enddo gradientInter(1) = (rhoExcessAtSampledPoint(1) - rhoExcess(c,s)) / gradientDistanceInter(1) gradientInter(2) = (rhoExcess(c,s) - rhoExcessAtSampledPoint(2)) / gradientDistanceInter(2) !* take maximum of both gradients and mix contributions from both sides according to weighted distances do dir = 1_pInt,2_pInt if (abs(gradientDeads(dir)) > abs(gradientInter(dir))) then gradient(dir) = gradientDeads(dir) gradientDistance(dir) = gradientDistanceDeads(dir) else gradient(dir) = gradientInter(dir) gradientDistance(dir) = gradientDistanceInter(dir) endif enddo rhoExcessGradient = (gradient(1) * gradientDistance(2) + gradient(2) * gradientDistance(1)) & / (gradientDistance(1) + gradientDistance(2)) !* excess gradient over density: in case of vanishing central total density we take the distance squared instead!!! rhoExcessGradient_over_rho(c) = rhoExcessGradient / (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c)) enddo 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 (debug_verbosity > 6_pInt .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) .or. .not. debug_selectiveDebugger)) 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 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_verbosity, & debug_selectiveDebugger, & debug_g, & debug_i, & debug_e use mesh, only: mesh_NcpElems, & mesh_maxNips use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance use lattice, only: lattice_Sslip, & lattice_Sslip_v implicit none !*** input variables integer(pInt), intent(in) :: g, & ! current grain number ip, & ! current integration point el, & ! current element number c ! dislocation character (1:edge, 2:screw) real(pReal), intent(in) :: Temperature ! temperature real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))), & intent(in) :: tau ! resolved external shear stress (for bcc this already contains non Schmid effects) type(p_vec), intent(in) :: state ! microstructural state !*** input/output variables !*** output variables real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))), & intent(out) :: v ! velocity real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))), & intent(out), optional :: dv_dtau ! velocity derivative with respect to resolved shear stress !*** local variables integer(pInt) instance, & ! current instance of this constitution ns, & ! short notation for the total number of active slip systems s ! index of my current slip system real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & tauThreshold ! threshold shear stress real(pReal) tauRel_P, & tauRel_S, & tPeierls, & ! waiting time in front of a peierls barriers tSolidSolution, & ! waiting time in front of a solid solution obstacle vViscous, & ! viscous glide velocity dtPeierls_dtau, & ! derivative with respect to resolved shear stress dtSolidSolution_dtau, & ! derivative with respect to resolved shear stress p, & ! shortcut to Kocks,Argon,Ashby parameter p q, & ! shortcut to Kocks,Argon,Ashby parameter q meanfreepath_S, & ! mean free travel distance for dislocations between two solid solution obstacles meanfreepath_P, & ! mean free travel distance for dislocations between two Peierls barriers jumpWidth_P, & ! depth of activated area jumpWidth_S, & ! depth of activated area activationLength_P, & ! length of activated dislocation line activationLength_S, & ! length of activated dislocation line activationVolume_P, & ! volume that needs to be activated to overcome barrier activationVolume_S, & ! volume that needs to be activated to overcome barrier activationEnergy_P, & ! energy that is needed to overcome barrier activationEnergy_S, & ! energy that is needed to overcome barrier criticalStress_P, & ! maximum obstacle strength criticalStress_S, & ! maximum obstacle strength mobility ! dislocation mobility instance = phase_constitutionInstance(material_phase(g,ip,el)) ns = constitutive_nonlocal_totalNslip(instance) tauThreshold = state%p(11_pInt*ns+1:12_pInt*ns) p = constitutive_nonlocal_p(instance) q = constitutive_nonlocal_q(instance) v = 0.0_pReal if (present(dv_dtau)) dv_dtau = 0.0_pReal if (Temperature > 0.0_pReal) then do s = 1_pInt,ns if (abs(tau(s)) > tauThreshold(s)) then !* Peierls contribution !* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity meanfreepath_P = constitutive_nonlocal_burgers(s,instance) jumpWidth_P = constitutive_nonlocal_burgers(s,instance) activationLength_P = constitutive_nonlocal_doublekinkwidth(instance) * constitutive_nonlocal_burgers(s,instance) activationVolume_P = activationLength_P * jumpWidth_P * constitutive_nonlocal_burgers(s,instance) criticalStress_P = constitutive_nonlocal_peierlsStress(s,c,instance) activationEnergy_P = criticalStress_P * activationVolume_P tauRel_P = (abs(tau(s)) - tauThreshold(s)) / criticalStress_P tPeierls = 1.0_pReal / constitutive_nonlocal_fattack(instance) & * exp(activationEnergy_P / (kB * Temperature) * (1.0_pReal - tauRel_P**p)**q) if (present(dv_dtau)) then dtPeierls_dtau = tPeierls * p * q * activationVolume_P / (kB * Temperature) & * (1.0_pReal - tauRel_P**p)**(q-1.0_pReal) * tauRel_P**(p-1.0_pReal) endif !* Contribution from solid solution strengthening !* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity meanfreepath_S = constitutive_nonlocal_burgers(s,instance) / sqrt(constitutive_nonlocal_solidSolutionConcentration(instance)) jumpWidth_S = constitutive_nonlocal_solidSolutionSize(instance) * constitutive_nonlocal_burgers(s,instance) activationLength_S = constitutive_nonlocal_burgers(s,instance) & / sqrt(constitutive_nonlocal_solidSolutionConcentration(instance)) activationVolume_S = activationLength_S * jumpWidth_S * constitutive_nonlocal_burgers(s,instance) activationEnergy_S = constitutive_nonlocal_solidSolutionEnergy(instance) criticalStress_S = activationEnergy_S / activationVolume_S tauRel_S = (abs(tau(s)) - tauThreshold(s)) / criticalStress_S tSolidSolution = 1.0_pReal / constitutive_nonlocal_fattack(instance) & * exp(activationEnergy_S / (kB * Temperature) * (1.0_pReal - tauRel_S**p)**q) if (present(dv_dtau)) then dtSolidSolution_dtau = tSolidSolution * p * q * activationVolume_S / (kB * Temperature) & * (1.0_pReal - tauRel_S**p)**(q-1.0_pReal) * tauRel_S**(p-1.0_pReal) endif !* viscous glide velocity mobility = constitutive_nonlocal_burgers(s,instance) / constitutive_nonlocal_viscosity(instance) vViscous = mobility * abs(tau(s)) !* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of !* free flight at glide velocity in between. Backward jumps at low stresses are considered only at peierls barriers, !* since those have the smallest activation volume, thus are decisive. v(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) & * (1.0_pReal - exp(-(abs(tau(s)) - tauThreshold(s)) * activationVolume_P / (kB * Temperature))) v(s) = sign(v(s),tau(s)) if (present(dv_dtau)) then dv_dtau(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) & * (abs(v(s)) * (dtPeierls_dtau + dtSolidSolution_dtau + 1.0_pReal / (mobility * tau(s) * tau(s))) & + activationVolume_P / (kB * Temperature) * exp(-(abs(tau(s)) - tauThreshold(s)) * activationVolume_P & / (kB * Temperature))) endif endif enddo endif #ifndef _OPENMP if (debug_verbosity > 6 .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) .or. .not. debug_selectiveDebugger)) then write(6,*) write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g write(6,*) write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3 endif #endif endsubroutine !********************************************************************* !* calculates plastic velocity gradient and its tangent * !********************************************************************* subroutine constitutive_nonlocal_LpAndItsTangent(Lp, dLp_dTstar99, Tstar_v, Temperature, state, g, ip, el) use prec, only: pReal, & pInt, & p_vec use math, only: math_Plain3333to99, & math_mul6x6 use debug, only: debug_verbosity, & debug_selectiveDebugger, & debug_g, & debug_i, & debug_e use mesh, only: mesh_NcpElems, & mesh_maxNips use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance use lattice, only: lattice_Sslip, & lattice_Sslip_v 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 ! 2nd Piola-Kirchhoff stress in Mandel notation !*** input/output variables type(p_vec), intent(inout) :: state ! microstructural state !*** output variables real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99 ! derivative of Lp with respect to Tstar (9x9 matrix) !*** local variables integer(pInt) myInstance, & ! current instance of this constitution myStructure, & ! current lattice structure ns, & ! short notation for the total number of active slip systems c, & i, & j, & k, & l, & t, & ! dislocation type s, & ! index of my current slip system sLattice ! index of my current slip system according to lattice order real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix) real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: & rhoSgl, & ! single dislocation densities (including used) v, & ! velocity dv_dtau ! velocity derivative with respect to the shear stress real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & tau, & ! resolved shear stress including non Schmid and backstress terms gdotTotal, & ! shear rate dgdotTotal_dtau, & ! derivative of the shear rate with respect to the shear stress tauBack ! back stress from dislocation gradients on same slip system !*** initialize local variables Lp = 0.0_pReal dLp_dTstar3333 = 0.0_pReal myInstance = phase_constitutionInstance(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%p((t-1_pInt)*ns+s), 0.0_pReal) tauBack = state%p(12_pInt*ns+1:13_pInt*ns) !*** get effective resolved shear stress do s = 1_pInt,ns 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 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) 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, state%p((t-1)*ns+s) * v(s,t-4_pInt) < 0.0_pReal) & rhoSgl(s,t-4_pInt) = rhoSgl(s,t-4_pInt) + abs(state%p((t-1_pInt)*ns+s)) !*** Calculation of gdot and its tangent gdotTotal = sum(rhoSgl * v, 2) * constitutive_nonlocal_burgers(1:ns,myInstance) dgdotTotal_dtau = sum(rhoSgl * dv_dtau, 2) * constitutive_nonlocal_burgers(1:ns,myInstance) !*** 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 (debug_verbosity > 6_pInt .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) .or. .not. debug_selectiveDebugger)) 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 !********************************************************************* !* rate of change of microstructure * !********************************************************************* subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, Fe, Fp, Temperature, state, timestep, orientation, g,ip,el) use prec, only: pReal, & pInt, & p_vec, & DAMASK_NaN use numerics, only: numerics_integrationMode use IO, only: IO_error use debug, only: debug_verbosity, & debug_selectiveDebugger, & 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_maxNipNeighbors, & mesh_element, & FE_NipNeighbors, & mesh_ipNeighborhood, & mesh_ipVolume, & mesh_ipArea, & mesh_ipAreaNormal, & mesh_ipCenterOfGravity use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance, & phase_localConstitution, & phase_constitution use lattice, only: lattice_Sslip, & lattice_Sslip_v, & lattice_sd, & lattice_sn, & lattice_st, & lattice_NslipSystem use FEsolving, only:theInc, & FEsolving_execElem, & FEsolving_execIP 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(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & Fe, & ! elastic deformation gradient Fp ! plastic deformation gradient real(pReal), dimension(4,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & orientation ! crystal lattice orientation type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & state ! current microstructural state !*** input/output variables type(p_vec), intent(inout) :: dotState ! evolution of state variables / microstructure !*** output variables !*** local variables integer(pInt) myInstance, & ! current instance of this constitution 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_n, & ! index of my opposite neighbor opposite_ip, & ! ip of my opposite neighbor opposite_el, & ! element index of 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 real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),10) :: & rhoDot, & ! density evolution rhoDotRemobilization, & ! density evolution by remobilization 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_constitutionInstance(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_constitutionInstance(material_phase(g,ip,el))),4) :: & v, & ! dislocation glide velocity fluxdensity, & ! flux density at central material point neighboring_fluxdensity, & ! flux density at neighboring material point gdot ! shear rates real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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 real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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 real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(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 logical considerEnteringFlux, & considerLeavingFlux #ifndef _OPENMP if (debug_verbosity > 6_pInt .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) & .or. .not. debug_selectiveDebugger)) 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 select case(mesh_element(2,el)) case (1_pInt,6_pInt,7_pInt,8_pInt,9_pInt) ! all fine case default call IO_error(253_pInt,el,ip,g) end select myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance) tau = 0.0_pReal gdot = 0.0_pReal dLower = 0.0_pReal dUpper = 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) !*** sanity check for timestep if (timestep <= 0.0_pReal) then ! if illegal timestep... dotState%p = 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) forall (s = 1_pInt:ns, t = 1_pInt:4_pInt, rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) & ! contribution of used rho for changing sign of v gdot(s,t) = gdot(s,t) + abs(rhoSgl(s,t+4)) * constitutive_nonlocal_burgers(s,myInstance) * v(s,t) #ifndef _OPENMP if (debug_verbosity > 6_pInt .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) & .or. .not. debug_selectiveDebugger)) 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 !**************************************************************************** !*** check CFL (Courant-Friedrichs-Lewy) condition for flux if (any(abs(gdot) > 0.0_pReal .and. 2.0_pReal * abs(v) * timestep > mesh_ipVolume(ip,el) / maxval(mesh_ipArea(:,ip,el)))) then ! safety factor 2.0 (we use the reference volume and are for simplicity here) #ifndef _OPENMP if (debug_verbosity > 6_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)),' at a timestep of ',timestep write(6,'(a)') '<< CONST >> enforcing cutback !!!' endif #endif dotState%p = DAMASK_NaN return 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) enddo dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance) dUpper(1:ns,2) = min( 1.0_pReal / sqrt( sum(abs(rhoSgl),2)+sum(rhoDip,2) ), & constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) & / ( 8.0_pReal * pi * abs(tau) ) ) dUpper(1:ns,1) = dUpper(1:ns,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) !**************************************************************************** !*** dislocation remobilization (bauschinger effect) rhoDotRemobilization = 0.0_pReal if (timestep > 0.0_pReal) then do t = 1_pInt,4_pInt do s = 1_pInt,ns if (rhoSgl(s,t+4_pInt) * v(s,t) < 0.0_pReal) then rhoDotRemobilization(s,t) = abs(rhoSgl(s,t+4_pInt)) / timestep rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4_pInt)) rhoDotRemobilization(s,t+4_pInt) = - rhoSgl(s,t+4_pInt) / timestep rhoSgl(s,t+4_pInt) = 0.0_pReal endif enddo enddo endif !**************************************************************************** !*** calculate dislocation multiplication rhoDotMultiplication = 0.0_pReal where (rhoSgl(1:ns,3:4) > 0.0_pReal) & rhoDotMultiplication(1:ns,1:2) = spread(0.5_pReal * sum(abs(gdot(1:ns,3:4)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0(1:ns,myInstance) & / constitutive_nonlocal_burgers(1:ns,myInstance), 2, 2) where (rhoSgl(1:ns,1:2) > 0.0_pReal) & rhoDotMultiplication(1:ns,3:4) = spread(0.5_pReal * sum(abs(gdot(1:ns,1:2)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0(1:ns,myInstance) & / constitutive_nonlocal_burgers(1:ns,myInstance), 2, 2) !**************************************************************************** !*** calculate dislocation fluxes (only for nonlocal constitution) rhoDotFlux = 0.0_pReal if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only for nonlocal constitution !*** take care 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)) fluxdensity = rhoSgl(1:ns,1:4) * v do n = 1_pInt,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors neighboring_el = mesh_ipNeighborhood(1,n,ip,el) neighboring_ip = mesh_ipNeighborhood(2,n,ip,el) if (neighboring_el > 0_pInt .and. neighboring_ip > 0_pInt) then ! if neighbor exists ... do neighboring_n = 1_pInt,FE_NipNeighbors(mesh_element(2,neighboring_el)) ! find neighboring index that points from my neighbor to myself if ( el == mesh_ipNeighborhood(1,neighboring_n,neighboring_ip,neighboring_el) & .and. ip == mesh_ipNeighborhood(2,neighboring_n,neighboring_ip,neighboring_el)) then ! possible candidate if (math_mul3x3(mesh_ipAreaNormal(1:3,n,ip,el),& mesh_ipAreaNormal(1:3,neighboring_n,neighboring_ip,neighboring_el)) < 0.0_pReal) then ! area normals have opposite orientation (we have to check that because of special case for single element with two ips and periodicity. In this case the neighbor is identical in two different directions.) exit endif endif enddo endif opposite_n = n + mod(n,2_pInt) - mod(n+1_pInt,2_pInt) opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el) opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el) if (neighboring_el > 0_pInt .and. neighboring_ip > 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 constitution (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_fluxdensity = 0.0_pReal ! needed for check of sign change in flux density below if (neighboring_el > 0_pInt .or. neighboring_ip > 0_pInt) then if (phase_constitution(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 forall (t = 1_pInt:4_pInt) & neighboring_fluxdensity(1:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1)*ns+1:t*ns) & * state(g,neighboring_ip,neighboring_el)%p((12+t)*ns+1:(13+t)*ns) 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_fluxdensity(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. fluxdensity(s,t) * neighboring_fluxdensity(s,t) >= 0.0_pReal ) then ! ... only if no sign change in flux density lineLength = neighboring_fluxdensity(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:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility... rhoDotFlux(1:ns,t) = rhoDotFlux(1:ns,t) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed dislocation type * constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal where (constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility... rhoDotFlux(1:ns,topp) = rhoDotFlux(1:ns,topp) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed dislocation type * constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal 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_el > 0_pInt .and. opposite_ip > 0_pInt) then if (phase_constitution(material_phase(1,opposite_ip,opposite_el)) /= constitutive_nonlocal_label) & considerLeavingFlux = .false. endif if (considerLeavingFlux) then 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 (fluxdensity(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) lineLength = fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length that wants to leave through this interface if (fluxdensity(s,t) * neighboring_fluxdensity(s,t) >= 0.0_pReal) then ! no sign change in flux density transmissivity = sum(constitutive_nonlocal_compatibility(c,1: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 rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract dislocation flux from current mobile type rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) & * sign(1.0_pReal, fluxdensity(s,t)) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point endif enddo enddo endif enddo ! neighbor loop endif if (numerics_integrationMode == 1_pInt) then constitutive_nonlocal_rhoDotFlux(1:ns,1:10,g,ip,el) = rhoDotFlux(1:ns,1:10) ! save flux calculation for output (if in central integration mode) 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 !*** thermally activated annihilation of dipoles 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) ) rhoDotThermalAnnihilation(1:ns,9) = - 4.0_pReal * rhoDip(1:ns,1) * vClimb / (dUpper(1:ns,1) - dLower(1:ns,1)) ! edge climb rhoDotThermalAnnihilation(1:ns,10) = 0.0_pReal !!! cross slipping still has to be implemented !!! !**************************************************************************** !*** 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 & + rhoDotRemobilization & + rhoDotSingle2DipoleGlide & + rhoDotAthermalAnnihilation & + rhoDotThermalAnnihilation if ( any(rhoSgl(1:ns,1:4) + rhoDot(1:ns,1:4) * timestep < - constitutive_nonlocal_aTolRho(myInstance)) & .or. any(rhoDip(1:ns,1:2) + rhoDot(1:ns,9:10) * timestep < - constitutive_nonlocal_aTolRho(myInstance))) then #ifndef _OPENMP if (debug_verbosity > 6_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 dotState%p = DAMASK_NaN return else dotState%p(1:10_pInt*ns) = dotState%p(1:10_pInt*ns) + reshape(rhoDot,(/10_pInt*ns/)) endif #ifndef _OPENMP if (debug_verbosity > 6_pInt .and. ((debug_e == el .and. debug_i == ip .and. debug_g == g) .or. .not. debug_selectiveDebugger)) then write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation remobilization', rhoDotRemobilization(1:ns,1:8) * timestep 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,/,2(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', & rhoDotAthermalAnnihilation(1:ns,1:2) * 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(f12.7,1x),/))') '<< CONST >> relative density change', & rhoDot(1:ns,1:8) * timestep / (abs(rhoSgl)+1.0e-10), & rhoDot(1:ns,9:10) * timestep / (rhoDip+1.0e-10) write(6,*) endif #endif endsubroutine !********************************************************************* !* 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, & phase_constitution, & phase_localConstitution, & phase_constitutionInstance, & homogenization_maxNgrains use mesh, only: mesh_element, & mesh_ipNeighborhood, & FE_NipNeighbors, & mesh_maxNips, & mesh_NcpElems use lattice, only: lattice_sn, & lattice_sd, & lattice_st 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_structure, & ! lattice structure my_instance, & ! instance of constitution 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_constitutionInstance(material_phase(1,i,e))),& constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(1,i,e))),& FE_NipNeighbors(mesh_element(2,e))) :: & compatibility ! compatibility for current element and ip real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(1,i,e)))) :: & slipNormal, & slipDirection real(pReal) compatibilitySum, & thresholdValue, & nThresholdValues logical, dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(1,i,e)))) :: & belowThreshold Nneighbors = FE_NipNeighbors(mesh_element(2,e)) my_phase = material_phase(1,i,e) my_instance = phase_constitutionInstance(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 the neighboring "cpfem" phase has a local constitution, !* 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_localConstitution(neighboring_phase)) then forall(s1 = 1_pInt:ns) & compatibility(1:2,s1,s1,n) = 0.0_pReal ! = sqrt(0.0) endif cycle endif !* GRAIN BOUNDARY ? !* 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. 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 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, & FE_Nips, & mesh_ipCenterOfGravity, & mesh_ipVolume, & mesh_periodicSurface use material, only: homogenization_maxNgrains, & material_phase, & phase_localConstitution, & phase_constitutionInstance 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 constitution neighboring_instance, & ! instance of this constitution 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, & ipCoords, & neighboring_ipCoords 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 Tdislo, & ! dislocation stress as 2nd Piola-Kirchhoff stress at my 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_constitutionInstance(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_constitutionInstance(material_phase(g,ip,el)))) :: & rhoForest, & ! forest dislocation density tauThreshold ! threshold shear stress logical inversionError phase = material_phase(g,ip,el) instance = phase_constitutionInstance(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 constitution constitutive_nonlocal_dislocationstress = 0.0_pReal if (.not. phase_localConstitution(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 ipCoords = mesh_ipCenterOfGravity(1:3,ip,el) periodicImages = 0_pInt do dir = 1_pInt,3_pInt if (mesh_periodicSurface(dir)) then periodicImages(1,dir) = floor((ipCoords(dir) - constitutive_nonlocal_R(instance) - minCoord(dir)) / meshSize(dir), pInt) periodicImages(2,dir) = ceiling((ipCoords(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(mesh_element(2,neighboring_el)) neighboring_phase = material_phase(g,neighboring_ip,neighboring_el) if (phase_localConstitution(neighboring_phase)) then cycle endif neighboring_instance = phase_constitutionInstance(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_ipCoords = mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) & + (/real(deltaX,pReal), real(deltaY,pReal), real(deltaZ,pReal)/) * meshSize connection = neighboring_ipCoords - ipCoords 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_aTolRho(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_aTolRho(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_aTolRho(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_aTolRho(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_element use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance, & phase_Noutput use lattice, only: lattice_Sslip, & 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_constitutionInstance(material_phase(g,ip,el)))) :: & constitutive_nonlocal_postResults !*** local variables integer(pInt) myInstance, & ! current instance of this constitution 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_constitutionInstance(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_constitutionInstance(material_phase(g,ip,el))),4) :: & gdot, & ! shear rates v ! velocities real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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 vClimb ! climb velocity of edge dipoles real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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_constitutionInstance(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) D ! self diffusion real(pReal), dimension(3,3) :: sigma myInstance = phase_constitutionInstance(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 (t = 1_pInt:8_pInt) rhoSgl(1:ns,t) = state(g,ip,el)%p((t-1_pInt)*ns+1_pInt:t*ns) forall (c = 1_pInt:2_pInt) rhoDip(1:ns,c) = state(g,ip,el)%p((7_pInt+c)*ns+1_pInt:(8_pInt+c)*ns) 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) !* 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) enddo dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance) dUpper(1:ns,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) & / (8.0_pReal * pi * abs(tau)), & 1.0_pReal / sqrt(sum(abs(rhoSgl),2)+sum(rhoDip,2)) ) dUpper(1:ns,1) = dUpper(1:ns,2) / (1.0_pReal - constitutive_nonlocal_nu(myInstance)) !*** 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) = rhoSgl(1:ns,1) cs = cs + ns case ('rho_sgl_edge_pos_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,5) 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) = rhoSgl(1:ns,2) cs = cs + ns case ('rho_sgl_edge_neg_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,6) cs = cs + ns case ('rho_dip_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDip(1:ns,1) 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) = rhoSgl(1:ns,3) cs = cs + ns case ('rho_sgl_screw_pos_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,7) 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) = rhoSgl(1:ns,4) cs = cs + ns case ('rho_sgl_screw_neg_immobile') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoSgl(1:ns,8) cs = cs + ns case ('rho_dip_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = rhoDip(1:ns,2) 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) = sum(abs(gdot),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0(1:ns,myInstance) & / constitutive_nonlocal_burgers(1:ns,myInstance) cs = cs + ns case ('rho_dot_gen_edge') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(gdot(1:ns,3:4)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0(1:ns,myInstance) & / constitutive_nonlocal_burgers(1:ns,myInstance) cs = cs + ns case ('rho_dot_gen_screw') constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(abs(gdot(1:ns,1:2)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0(1:ns,myInstance) & / constitutive_nonlocal_burgers(1:ns,myInstance) cs = cs + ns case ('rho_dot_sgl2dip') do c=1_pInt,2_pInt ! dipole formation by glide constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + & 2.0_pReal * dUpper(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) & * ( 2.0_pReal * ( rhoSgl(1:ns,2_pInt*c-1_pInt) * abs(gdot(1:ns,2*c)) & + rhoSgl(1:ns,2_pInt*c) * abs(gdot(1:ns,2_pInt*c-1_pInt))) & ! was single hitting single + 2.0_pReal * ( abs(rhoSgl(1:ns,2_pInt*c+3_pInt)) * abs(gdot(1:ns,2_pInt*c)) & + abs(rhoSgl(1:ns,2_pInt*c+4_pInt)) * abs(gdot(1:ns,2_pInt*c-1_pInt)))) ! was single hitting immobile/used single enddo cs = cs + ns case ('rho_dot_ann_ath') do c=1_pInt,2_pInt constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + & 2.0_pReal * dLower(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) & * ( 2.0_pReal * ( rhoSgl(1:ns,2_pInt*c-1_pInt) * abs(gdot(1:ns,2_pInt*c)) & + rhoSgl(1:ns,2_pInt*c) * abs(gdot(1:ns,2_pInt*c-1_pInt))) & ! was single hitting single + 2.0_pReal * ( abs(rhoSgl(1:ns,2_pInt*c+3_pInt)) * abs(gdot(1:ns,2_pInt*c)) & + abs(rhoSgl(1:ns,2_pInt*c+4_pInt)) * abs(gdot(1:ns,2_pInt*c-1_pInt))) & ! was single hitting immobile/used single + rhoDip(1:ns,c) * (abs(gdot(1:ns,2_pInt*c-1_pInt)) + abs(gdot(1:ns,2_pInt*c)))) ! single knocks dipole constituent enddo cs = cs + ns case ('rho_dot_ann_the') 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)) constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = 4.0_pReal * rhoDip(1:ns,1) * vClimb / (dUpper(1:ns,1) - dLower(1:ns,1)) ! !!! cross-slip of screws missing !!! 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 constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_accumulatedShear(1:ns,g,ip,el) cs = cs + ns end select enddo endfunction END MODULE