!* $Id$ !************************************ !* 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=16), dimension(6), parameter :: constitutive_nonlocal_listBasicStates = (/'rhoEdgePos ', & 'rhoEdgeNeg ', & 'rhoScrewPos ', & 'rhoScrewNeg ', & 'rhoEdgeDip ', & 'rhoScrewDip ' /) ! list of "basic" microstructural state variables that are independent from other state variables character(len=16), dimension(3), parameter :: constitutive_nonlocal_listDependentStates = (/'rhoForest ', & 'tauSlipThreshold', & 'Tdislocation_v ' /) ! list of microstructural state variables that depend on other state variables 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 constitutive_nonlocal_sizeState, & ! total number of microstructural 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 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_Q0, & ! activation energy for dislocation glide constitutive_nonlocal_atomicVolume, & ! atomic volume constitutive_nonlocal_D0, & ! prefactor for self-diffusion coefficient constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion constitutive_nonlocal_relevantRho ! dislocation density considered relevant 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_rhoEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance constitutive_nonlocal_rhoScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance constitutive_nonlocal_rhoEdgeDip0, & ! initial edge dipole dislocation density per slip system for each family and instance constitutive_nonlocal_rhoScrewDip0, & ! initial screw dipole dislocation density per slip system for each family and instance constitutive_nonlocal_v0PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance constitutive_nonlocal_v0PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance constitutive_nonlocal_lambda0PerSlipSystem, & ! 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_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance constitutive_nonlocal_dLowerEdgePerSlipFamily, & ! minimum stable edge dipole height for each family and instance constitutive_nonlocal_dLowerEdgePerSlipSystem, & ! minimum stable edge dipole height for each slip system and instance constitutive_nonlocal_dLowerScrewPerSlipFamily, & ! minimum stable screw dipole height for each family and instance constitutive_nonlocal_dLowerScrewPerSlipSystem, & ! minimum stable screw dipole height 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_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 CONTAINS !**************************************** !* - constitutive_init !* - constitutive_stateInit !* - constitutive_homogenizedC !* - constitutive_microstructure !* - constitutive_LpAndItsTangent !* - constitutive_dotState !* - constitutive_dotTemperature !* - constitutive_postResults !**************************************** !************************************** !* Module initialization * !************************************** subroutine constitutive_nonlocal_init(file) use prec, only: pInt, pReal use math, only: math_Mandel3333to66, & math_Voigt66to3333, & math_mul3x3 use IO, only: IO_lc, & IO_getTag, & IO_isBlank, & IO_stringPos, & IO_stringValue, & IO_floatValue, & IO_intValue, & IO_error use material, only: phase_constitution, & phase_constitutionInstance, & phase_Noutput use lattice, only: lattice_maxNslipFamily, & lattice_maxNtwinFamily, & lattice_maxNslip, & lattice_maxNtwin, & 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) :: file !*** local variables integer(pInt), parameter :: maxNchunks = 21 integer(pInt), dimension(1+2*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 output, & mySize character(len=64) tag character(len=1024) line write(6,*) write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_nonlocal_label,' init -+>>>' write(6,*) '$Id$' write(6,*) maxNinstance = count(phase_constitution == constitutive_nonlocal_label) if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law !*** space allocation for global variables allocate(constitutive_nonlocal_sizeDotState(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)) constitutive_nonlocal_sizeDotState = 0_pInt constitutive_nonlocal_sizeState = 0_pInt constitutive_nonlocal_sizePostResults = 0_pInt constitutive_nonlocal_sizePostResult = 0_pInt constitutive_nonlocal_output = '' 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_Q0(maxNinstance)) allocate(constitutive_nonlocal_atomicVolume(maxNinstance)) allocate(constitutive_nonlocal_D0(maxNinstance)) allocate(constitutive_nonlocal_Qsd(maxNinstance)) allocate(constitutive_nonlocal_relevantRho(maxNinstance)) allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance)) allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,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_Q0 = 0.0_pReal constitutive_nonlocal_atomicVolume = 0.0_pReal constitutive_nonlocal_D0 = 0.0_pReal constitutive_nonlocal_Qsd = 0.0_pReal constitutive_nonlocal_relevantRho = 0.0_pReal constitutive_nonlocal_nu = 0.0_pReal constitutive_nonlocal_Cslip_66 = 0.0_pReal constitutive_nonlocal_Cslip_3333 = 0.0_pReal allocate(constitutive_nonlocal_rhoEdgePos0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_rhoEdgeNeg0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_rhoScrewPos0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_rhoScrewNeg0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_rhoEdgeDip0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_rhoScrewDip0(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_v0PerSlipFamily(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction, maxNinstance)) allocate(constitutive_nonlocal_dLowerEdgePerSlipFamily(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_dLowerScrewPerSlipFamily(lattice_maxNslipFamily, maxNinstance)) constitutive_nonlocal_rhoEdgePos0 = 0.0_pReal constitutive_nonlocal_rhoEdgeNeg0 = 0.0_pReal constitutive_nonlocal_rhoScrewPos0 = 0.0_pReal constitutive_nonlocal_rhoScrewNeg0 = 0.0_pReal constitutive_nonlocal_rhoEdgeDip0 = 0.0_pReal constitutive_nonlocal_rhoScrewDip0 = 0.0_pReal constitutive_nonlocal_v0PerSlipFamily = 0.0_pReal constitutive_nonlocal_burgersPerSlipFamily = 0.0_pReal constitutive_nonlocal_lambda0PerSlipFamily = 0.0_pReal constitutive_nonlocal_interactionSlipSlip = 0.0_pReal constitutive_nonlocal_dLowerEdgePerSlipFamily = 0.0_pReal constitutive_nonlocal_dLowerScrewPerSlipFamily = 0.0_pReal !*** readout data from material.config file rewind(file) line = '' section = 0 do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to read(file,'(a1024)',END=100) line enddo do ! read thru sections of phase part read(file,'(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 output = 0 ! reset output counter endif if (section > 0 .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)) ! extract key select case(tag) case ('(output)') output = output + 1 constitutive_nonlocal_output(output,i) = IO_lc(IO_stringValue(line,positions,2)) case ('lattice_structure') constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2)) case ('covera_ratio') constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2) case ('c11') constitutive_nonlocal_C11(i) = IO_floatValue(line,positions,2) case ('c12') constitutive_nonlocal_C12(i) = IO_floatValue(line,positions,2) case ('c13') constitutive_nonlocal_C13(i) = IO_floatValue(line,positions,2) case ('c33') constitutive_nonlocal_C33(i) = IO_floatValue(line,positions,2) case ('c44') constitutive_nonlocal_C44(i) = IO_floatValue(line,positions,2) case ('nslip') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1+f) case ('rhoedgepos0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgePos0(f,i) = IO_floatValue(line,positions,1+f) case ('rhoedgeneg0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeNeg0(f,i) = IO_floatValue(line,positions,1+f) case ('rhoscrewpos0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewPos0(f,i) = IO_floatValue(line,positions,1+f) case ('rhoscrewneg0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewNeg0(f,i) = IO_floatValue(line,positions,1+f) case ('rhoedgedip0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeDip0(f,i) = IO_floatValue(line,positions,1+f) case ('rhoscrewdip0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewDip0(f,i) = IO_floatValue(line,positions,1+f) case ('v0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_v0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case ('lambda0') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case ('burgers') forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case('ddipminedge') forall (f = 1:lattice_maxNslipFamily) & constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case('ddipminscrew') forall (f = 1:lattice_maxNslipFamily) & constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case('q0') constitutive_nonlocal_Q0(i) = IO_floatValue(line,positions,2) case('atomicvolume') constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2) case('d0') constitutive_nonlocal_D0(i) = IO_floatValue(line,positions,2) case('qsd') constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2) case('relevantrho') constitutive_nonlocal_relevantRho(i) = IO_floatValue(line,positions,2) case ('interaction_slipslip') forall (it = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1+it) end select endif enddo 100 do i = 1,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 .or. myStructure > 3) call IO_error(205) if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0_pInt) call IO_error(225) do o = 1,maxval(phase_Noutput) if(len(constitutive_nonlocal_output(o,i)) > 64) call IO_error(666) enddo do f = 1,lattice_maxNslipFamily if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then if (constitutive_nonlocal_rhoEdgePos0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoEdgeNeg0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoScrewPos0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoScrewNeg0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoEdgeDip0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoScrewDip0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221) if (constitutive_nonlocal_v0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(226) if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(227) if (constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228) if (constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228) endif enddo if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) & call IO_error(229) if (constitutive_nonlocal_Q0(i) <= 0.0_pReal) call IO_error(-1) if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(230) if (constitutive_nonlocal_D0(i) <= 0.0_pReal) call IO_error(231) if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(232) if (constitutive_nonlocal_relevantRho(i) <= 0.0_pReal) call IO_error(233) !*** determine total number of active slip systems constitutive_nonlocal_Nslip(:,i) = min( lattice_NslipSystem(:, myStructure), constitutive_nonlocal_Nslip(:,i) ) ! we can't use more slip systems per family than specified in lattice constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(:,i)) enddo !*** allocation of variables whose size depends on the total number of active slip systems maxTotalNslip = maxval(constitutive_nonlocal_totalNslip) allocate(constitutive_nonlocal_burgersPerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_burgersPerSlipSystem = 0.0_pReal allocate(constitutive_nonlocal_v0PerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_v0PerSlipSystem = 0.0_pReal allocate(constitutive_nonlocal_lambda0PerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_lambda0PerSlipSystem = 0.0_pReal allocate(constitutive_nonlocal_dLowerEdgePerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_dLowerEdgePerSlipSystem = 0.0_pReal allocate(constitutive_nonlocal_dLowerScrewPerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_dLowerScrewPerSlipSystem = 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 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,lattice_maxNslipFamily do s = 1,constitutive_nonlocal_Nslip(f,i) l = l + 1 constitutive_nonlocal_slipFamily(l,i) = f constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1, myStructure)) + s enddo; enddo !*** determine size of state array ns = constitutive_nonlocal_totalNslip(i) constitutive_nonlocal_sizeState(i) = size(constitutive_nonlocal_listBasicStates) * ns & + ( size(constitutive_nonlocal_listDependentStates) - 1_pInt ) * ns + 6_pInt constitutive_nonlocal_sizeDotState(i) = size(constitutive_nonlocal_listBasicStates) * ns !*** determine size of postResults array do o = 1,maxval(phase_Noutput) select case(constitutive_nonlocal_output(o,i)) case( 'rho', & 'delta', & 'rho_edge', & 'rho_edge_pos', & 'rho_edge_neg', & 'rho_screw', & 'rho_screw_pos', & 'rho_screw_neg', & 'excess_rho', & 'excess_rho_edge', & 'excess_rho_screw', & 'rho_forest', & 'rho_dip', & 'delta_dip', & 'rho_edge_dip', & 'rho_screw_dip', & 'shearrate', & 'resolvedstress', & 'resistance', & 'rho_dot', & 'rho_dot_dip', & 'rho_dot_gen', & 'rho_dot_sgl2dip', & 'rho_dot_dip2sgl', & 'rho_dot_ann_ath', & 'rho_dot_ann_the', & 'rho_dot_flux', & 'rho_dot_flux_ep', & 'rho_dot_flux_en', & 'rho_dot_flux_sp', & 'rho_dot_flux_sn', & 'rho_dot_flux_n1_ep', & 'rho_dot_flux_n1_en', & 'rho_dot_flux_n1_sp', & 'rho_dot_flux_n1_sn', & 'rho_dot_flux_n2_ep', & 'rho_dot_flux_n2_en', & 'rho_dot_flux_n2_sp', & 'rho_dot_flux_n2_sn', & 'rho_dot_flux_n3_ep', & 'rho_dot_flux_n3_en', & 'rho_dot_flux_n3_sp', & 'rho_dot_flux_n3_sn', & 'rho_dot_flux_n4_ep', & 'rho_dot_flux_n4_en', & 'rho_dot_flux_n4_sp', & 'rho_dot_flux_n4_sn', & 'rho_dot_flux_n5_ep', & 'rho_dot_flux_n5_en', & 'rho_dot_flux_n5_sp', & 'rho_dot_flux_n5_sn', & 'rho_dot_flux_n6_ep', & 'rho_dot_flux_n6_en', & 'rho_dot_flux_n6_sp', & 'rho_dot_flux_n6_sn', & 'd_upper_edge', & 'd_upper_screw', & 'd_upper_dot_edge', & 'd_upper_dot_screw' ) mySize = constitutive_nonlocal_totalNslip(i) case default mySize = 0_pInt 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(1:2) ! cubic(s) forall(k=1:3) forall(j=1:3) 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,k+3,i) = constitutive_nonlocal_C44(i) end forall case(3:) ! 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(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i))) constitutive_nonlocal_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i)) constitutive_nonlocal_Gmod(i) = constitutive_nonlocal_C44(i) constitutive_nonlocal_nu(i) = 0.5_pReal * constitutive_nonlocal_C12(i) & / (constitutive_nonlocal_C12(i) + constitutive_nonlocal_C44(i)) do s1 = 1,ns f = constitutive_nonlocal_slipFamily(s1,i) !*** burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system constitutive_nonlocal_burgersPerSlipSystem(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i) constitutive_nonlocal_v0PerSlipSystem(s1,i) = constitutive_nonlocal_v0PerSlipFamily(f,i) constitutive_nonlocal_lambda0PerSlipSystem(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i) constitutive_nonlocal_dLowerEdgePerSlipSystem(s1,i) = constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) constitutive_nonlocal_dLowerScrewPerSlipSystem(s1,i) = constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) do s2 = 1,ns !*** calculation of forest projections for edge and screw dislocations. s2 acts as forest to s1 constitutive_nonlocal_forestProjectionEdge(s1, s2, i) & = abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), & lattice_st(:, 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(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), & lattice_sd(:, 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; enddo enddo endsubroutine !********************************************************************* !* initial microstructural state (just the "basic" states) * !********************************************************************* pure function constitutive_nonlocal_stateInit(myInstance) use prec, only: pReal, & pInt use lattice, only: lattice_maxNslipFamily 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)) :: & rhoEdgePos, & ! positive edge dislocation density rhoEdgeNeg, & ! negative edge dislocation density rhoScrewPos, & ! positive screw dislocation density rhoScrewNeg, & ! negative screw dislocation density rhoEdgeDip, & ! edge dipole dislocation density rhoScrewDip, & ! screw dipole dislocation density rhoForest, & ! forest dislocation density tauSlipThreshold ! threshold shear stress for slip integer(pInt) ns, & ! short notation for total number of active slip systems f, & ! index of lattice family from, & upto, & s ! index of slip system constitutive_nonlocal_stateInit = 0.0_pReal ns = constitutive_nonlocal_totalNslip(myInstance) !*** set the basic state variables do f = 1,lattice_maxNslipFamily from = 1+sum(constitutive_nonlocal_Nslip(1:f-1,myInstance)) upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance)) rhoEdgePos(from:upto) = constitutive_nonlocal_rhoEdgePos0(f, myInstance) rhoEdgeNeg(from:upto) = constitutive_nonlocal_rhoEdgeNeg0(f, myInstance) rhoScrewPos(from:upto) = constitutive_nonlocal_rhoScrewPos0(f, myInstance) rhoScrewNeg(from:upto) = constitutive_nonlocal_rhoScrewNeg0(f, myInstance) rhoEdgeDip(from:upto) = constitutive_nonlocal_rhoEdgeDip0(f, myInstance) rhoScrewDip(from:upto) = constitutive_nonlocal_rhoScrewDip0(f, myInstance) enddo !*** calculate the dependent state variables ! forest dislocation density forall (s = 1:ns) & rhoForest(s) & = dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip), constitutive_nonlocal_forestProjectionEdge(s, 1:ns, myInstance) ) & + dot_product( (rhoScrewPos + rhoScrewNeg + rhoScrewDip), constitutive_nonlocal_forestProjectionScrew(s, 1:ns, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations ! threshold shear stress for dislocation slip forall (s = 1:ns) & tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) & * constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) & * sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg + rhoEdgeDip + rhoScrewDip), & constitutive_nonlocal_interactionMatrixSlipSlip(s, 1:ns, myInstance) ) ) !*** put everything together and in right order constitutive_nonlocal_stateInit( 1: ns) = rhoEdgePos constitutive_nonlocal_stateInit( ns+1:2*ns) = rhoEdgeNeg constitutive_nonlocal_stateInit(2*ns+1:3*ns) = rhoScrewPos constitutive_nonlocal_stateInit(3*ns+1:4*ns) = rhoScrewNeg constitutive_nonlocal_stateInit(4*ns+1:5*ns) = rhoEdgeDip constitutive_nonlocal_stateInit(5*ns+1:6*ns) = rhoScrewDip constitutive_nonlocal_stateInit(6*ns+1:7*ns) = rhoForest constitutive_nonlocal_stateInit(7*ns+1:8*ns) = tauSlipThreshold endfunction !********************************************************************* !* relevant microstructural state * !********************************************************************* pure function constitutive_nonlocal_relevantState(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_relevantState ! relevant state values for the current instance of this constitution !*** local variables constitutive_nonlocal_relevantState = constitutive_nonlocal_relevantRho(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(:,:,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 math, only: math_Plain3333to99, & math_Mandel33to6, & math_Mandel6to33, & math_mul33x33, & math_mul3x3, & math_mul33x3, & math_inv3x3, & math_det3x3, & pi use debug, only: debugger use mesh, only: mesh_NcpElems, & mesh_maxNips, & mesh_element, & FE_NipNeighbors, & mesh_ipNeighborhood, & mesh_ipVolume, & mesh_ipCenterOfGravity use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance use lattice, only: lattice_Sslip, & lattice_Sslip_v, & lattice_maxNslipFamily, & lattice_NslipSystem, & lattice_maxNslip, & lattice_sd, & lattice_sn, & 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,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & Fe, & ! elastic deformation gradient Fp ! plastic 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) myInstance, & ! current instance of this constitution myStructure, & ! current lattice structure ns, & ! short notation for the total number of active slip systems neighboring_el, & ! element number of my neighbor neighboring_ip, & ! integration point of my neighbor n, & ! index of my current neighbor s, & ! index of my current slip system sLattice ! index of my current slip system according to lattice order real(pReal) gb, & ! short notation for G*b/2/pi x, & ! coordinate in direction of lvec y, & ! coordinate in direction of bvec z, & ! coordinate in direction of nvec detFe, & ! determinant of elastic deformation gradient neighboring_detFe ! determinant of my neighboring elastic deformation gradient real(pReal), dimension(3) :: connectingVector ! vector connecting the centers of gravity of me and my neigbor real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(3,3) :: lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system with e1=bxn, e2=b, e3=n neighboringSlip2myLattice, &! mapping from my neighbors slip coordinate system to my lattice coordinate system sigma, & ! Tdislocation resulting from the excess dislocation density of a single slip system and a single neighbor calculated in the coordinate system of the slip system F, & ! total deformation gradient neighboring_F, & ! total deformation gradient of my neighbor Favg, & ! average total deformation gradient of me and my neighbor invFe, & ! inverse of elastic deformation gradient neighboring_invFe ! inverse of my neighboring elastic deformation gradient real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & rhoEdgePos, & ! positive edge dislocation density rhoEdgeNeg, & ! negative edge dislocation density rhoScrewPos, & ! positive screw dislocation density rhoScrewNeg, & ! negative screw dislocation density rhoEdgeDip, & ! edge dipole dislocation density rhoScrewDip, & ! screw dipole dislocation density rhoForest, & ! forest dislocation density tauSlipThreshold, & ! threshold shear stress neighboring_rhoEdgePos, & ! positive edge dislocation density of my neighbor neighboring_rhoEdgeNeg, & ! negative edge dislocation density of my neighbor neighboring_rhoScrewPos, & ! positive screw dislocation density of my neighbor neighboring_rhoScrewNeg, & ! negative screw dislocation density of my neighbor neighboring_rhoEdgeExcess, &! edge excess dislocation density of my neighbor neighboring_rhoScrewExcess,&! screw excess dislocation density of my neighbor neighboring_Nedge, & ! total number of edge excess dislocations in my neighbor neighboring_Nscrew myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance) !********************************************************************** !*** get basic states rhoEdgePos = state(g,ip,el)%p( 1: ns) rhoEdgeNeg = state(g,ip,el)%p( ns+1:2*ns) rhoScrewPos = state(g,ip,el)%p(2*ns+1:3*ns) rhoScrewNeg = state(g,ip,el)%p(3*ns+1:4*ns) rhoEdgeDip = state(g,ip,el)%p(4*ns+1:5*ns) rhoScrewDip = state(g,ip,el)%p(5*ns+1:6*ns) !********************************************************************** !*** calculate dependent states !*** calculate the forest dislocation density forall (s = 1:ns) & rhoForest(s) & = dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) & + dot_product( (rhoScrewPos + rhoScrewNeg + rhoScrewDip), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations ! if (debugger) write(6,'(a30,3(i3,x),/,12(e10.3,x),/)') 'forest dislocation density at ',g,ip,el, rhoForest !*** calculate the threshold shear stress for dislocation slip forall (s = 1:ns) & tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) & * constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) & * sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip + rhoScrewPos + rhoScrewNeg + rhoScrewDip), & constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) ) ! if (debugger) write(6,'(a26,3(i3,x),/,12(f10.5,x),/)') 'tauSlipThreshold / MPa at ',g,ip,el, tauSlipThreshold/1e6 !*** calculate the dislocation stress of the neighboring excess dislocation densities Tdislocation_v = 0.0_pReal F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el)) detFe = math_det3x3(Fe) invFe = math_inv3x3(Fe) ! loop through my neighbors (if existent!) do n = 1,FE_NipNeighbors(mesh_element(2,el)) neighboring_el = mesh_ipNeighborhood(1,n,ip,el) neighboring_ip = mesh_ipNeighborhood(2,n,ip,el) if ( neighboring_el == 0 .or. neighboring_ip == 0 ) cycle ! deformation gradients needed for mapping between configurations neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el)) Favg = 0.5_pReal * (F + neighboring_F) neighboring_detFe = math_det3x3(Fe(:,:,g,neighboring_ip,neighboring_el)) neighboring_invFe = math_inv3x3(Fe(:,:,g,neighboring_ip,neighboring_el)) ! calculate connection vector between me and my neighbor in its lattice configuration connectingVector = math_mul33x3(neighboring_invFe, math_mul33x3(Favg, & (mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el)) ) ) ! neighboring dislocation densities neighboring_rhoEdgePos = state(1, neighboring_ip, neighboring_el)%p( 1: ns) neighboring_rhoEdgeNeg = state(1, neighboring_ip, neighboring_el)%p( ns+1:2*ns) neighboring_rhoScrewPos = state(1, neighboring_ip, neighboring_el)%p(2*ns+1:3*ns) neighboring_rhoScrewNeg = state(1, neighboring_ip, neighboring_el)%p(3*ns+1:4*ns) neighboring_rhoEdgeExcess = neighboring_rhoEdgePos - neighboring_rhoEdgeNeg neighboring_rhoScrewExcess = neighboring_rhoScrewPos - neighboring_rhoScrewNeg neighboring_Nedge = neighboring_rhoEdgeExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal) neighboring_Nscrew = neighboring_rhoScrewExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal) ! loop over slip systems and get their slip directions, slip normals, and sd x sn do s = 1,ns lattice2slip = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) ) ! coordinate transformation of connecting vector from the lattice coordinate system to the slip coordinate system x = math_mul3x3(lattice2slip(1,:), -connectingVector) y = math_mul3x3(lattice2slip(2,:), -connectingVector) z = math_mul3x3(lattice2slip(3,:), -connectingVector) ! calculate the back stress in the slip coordinate system for this slip system gb = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) / (2.0_pReal*pi) sigma(2,2) = - gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) & * z * (3.0_pReal*y**2.0_pReal + z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal sigma(3,3) = gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) & * z * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal sigma(1,1) = constitutive_nonlocal_nu(myInstance) * (sigma(2,2) + sigma(3,3)) sigma(1,2) = gb * neighboring_Nscrew(s) * z / (x**2.0_pReal + z**2.0_pReal) sigma(2,3) = gb * ( neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) & * y * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal & - neighboring_Nscrew(s) * x / (x**2.0_pReal + z**2.0_pReal) ) sigma(2,1) = sigma(1,2) sigma(3,2) = sigma(2,3) sigma(1,3) = 0.0_pReal sigma(3,1) = 0.0_pReal ! coordinate transformation from the slip coordinate system to the lattice coordinate system neighboringSlip2myLattice = math_mul33x33(invFe,math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el),transpose(lattice2slip))) Tdislocation_v = Tdislocation_v + math_Mandel33to6( detFe / neighboring_detFe & * math_mul33x33(neighboringSlip2myLattice, math_mul33x33(sigma, transpose(neighboringSlip2myLattice))) ) enddo enddo !********************************************************************** !*** set dependent states state(g,ip,el)%p(6*ns+1:7*ns) = rhoForest state(g,ip,el)%p(7*ns+1:8*ns) = tauSlipThreshold state(g,ip,el)%p(8*ns+1:8*ns+6) = Tdislocation_v 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, & math_Mandel6to33 use debug, only: debugger 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 type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & state ! microstructural state real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation !*** 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 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(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress 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) :: & rho ! dislocation densities real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & rhoForest, & ! forest dislocation density tauSlipThreshold, & ! threshold shear stress tauSlip, & ! resolved shear stress gdotSlip, & ! shear rate dgdot_dtauSlip, & ! derivative of the shear rate with respect to the shear stress v ! dislocation velocity !*** initialize local variables v = 0.0_pReal tauSlip = 0.0_pReal gdotSlip = 0.0_pReal 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 (t = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns) rhoForest = state(g,ip,el)%p(6*ns+1:7*ns) tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns) Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6) !*** calculation of resolved stress forall (s =1:ns) & tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, & lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure) ) !*** Calculation of gdot and its tangent v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) & * exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) & * sign(1.0_pReal,tauSlip) gdotSlip = sum(rho,2) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v dgdot_dtauSlip = abs(gdotSlip) * constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature * tauSlipThreshold ) !*** Calculation of Lp and its tangent do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) Lp = Lp + gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure) forall (i=1:3,j=1:3,k=1:3,l=1:3) & dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) + dgdot_dtauSlip(s) * lattice_Sslip(i,j, sLattice,myStructure) & * lattice_Sslip(k,l, sLattice,myStructure) enddo dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333) if (debugger) then !$OMP CRITICAL (write2out) write(6,*) '::: LpandItsTangent',g,ip,el write(6,*) write(6,'(a,/,3(3(f12.3,x)/))') 'Tdislocation / MPa', math_Mandel6to33(Tdislocation_v/1e6) write(6,'(a,/,3(3(f12.3,x)/))') 'Tstar / MPa', math_Mandel6to33(Tstar_v/1e6) write(6,'(a,/,12(f12.5,x),/)') 'tauSlip / MPa', tauSlip/1e6_pReal ! write(6,'(a,/,12(f12.5,x),/)') 'tauSlipThreshold / MPa', tauSlipThreshold/1e6_pReal ! write(6,'(a,/,12(f12.5,x),/)') 'v', v ! write(6,'(a,/,12(f12.5,x),/)') 'gdot total /1e-3',gdotSlip*1e3_pReal ! write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp ! call flush(6) !$OMPEND CRITICAL (write2out) endif endsubroutine !********************************************************************* !* rate of change of microstructure * !********************************************************************* subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, previousTstar_v, Fe, Fp, Temperature, misorientation, dt_previous, & state, previousState, timestep, g,ip,el) use prec, only: pReal, & pInt, & p_vec use debug, only: debugger use math, only: math_norm3, & math_mul6x6, & math_mul3x3, & math_mul33x3, & math_mul33x33, & math_inv3x3, & math_det3x3, & math_Mandel6to33, & pi use mesh, only: mesh_NcpElems, & mesh_maxNips, & mesh_maxNipNeighbors, & mesh_element, & FE_NipNeighbors, & mesh_ipNeighborhood, & mesh_ipVolume, & mesh_ipArea, & mesh_ipAreaNormal use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance use lattice, only: lattice_Sslip, & lattice_Sslip_v, & lattice_sd, & lattice_sn, & lattice_st, & lattice_maxNslipFamily, & lattice_NslipSystem 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 dt_previous ! time increment between previous and current state real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: & misorientation ! crystal misorientation between me and my neighbor (axis, angle pair) real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & Fe, & ! elastic deformation gradient Fp ! plastic deformation gradient type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & state, & ! current microstructural state previousState ! previous microstructural state !*** input/output variables type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), 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 neighboring_el, & ! element number of my neighbor neighboring_ip, & ! integration point of my neighbor c, & ! character of dislocation n, & ! index of my current neighbor 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))),4) :: & rho, & ! current dislocation densities (positive/negative screw and edge without dipoles) previousRho, & ! previous dislocation densities (positive/negative screw and edge without dipoles) totalRhoDot, & ! total rate of change of dislocation densities thisRhoDot, & ! rate of change of dislocation densities for this mechanism gdot, & ! shear rates lineLength ! dislocation line length leaving the current interface real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & rhoForest, & ! forest dislocation density tauSlipThreshold, & ! threshold shear stress tauSlip, & ! current resolved shear stress previousTauSlip, & ! previous resolved shear stress v, & ! dislocation velocity invLambda, & ! inverse of mean free path for dislocations 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) previousRhoDip, & ! previous dipole dislocation densities (screw and edge dipoles) totalRhoDipDot, & ! total rate of change of dipole dislocation densities thisRhoDipDot, & ! rate of change of dipole dislocation densities for this mechanism dLower, & ! minimum stable dipole distance for edges and screws dUpper, & ! current maximum stable dipole distance for edges and screws previousDUpper, & ! previous maximum stable dipole distance for edges and screws dUpperDot ! rate of change of the 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) :: F, & ! total deformation gradient neighboring_F, & ! total deformation gradient of my neighbor Favg ! average total deformation gradient of me and my neighbor real(pReal), dimension(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress previousTdislocation_v ! previous dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress real(pReal), dimension(3) :: surfaceNormal, & ! surface normal in lattice configuration surfaceNormal_currentconf ! surface normal in current configuration real(pReal) area, & ! area of the current interface detFe, & ! determinant of elastic defornmation gradient D ! self diffusion myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance) tauSlip = 0.0_pReal previousTauSlip = 0.0_pReal v = 0.0_pReal gdot = 0.0_pReal dLower = 0.0_pReal dUpper = 0.0_pReal previousDUpper = 0.0_pReal dUpperDot = 0.0_pReal totalRhoDot = 0.0_pReal thisRhoDot = 0.0_pReal totalRhoDipDot = 0.0_pReal thisRhoDipDot = 0.0_pReal !*** shortcut to state variables forall (t = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns) forall (t = 1:4) previousRho(:,t) = previousState(g,ip,el)%p((t-1)*ns+1:t*ns) forall (c = 1:2) rhoDip(:,c) = state(g,ip,el)%p((3+c)*ns+1:(4+c)*ns) forall (c = 1:2) previousRhoDip(:,c) = previousState(g,ip,el)%p((3+c)*ns+1:(4+c)*ns) rhoForest = state(g,ip,el)%p(6*ns+1:7*ns) tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns) Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6) previousTdislocation_v = previousState(g,ip,el)%p(8*ns+1:8*ns+6) !**************************************************************************** !*** Calculate shear rate do s = 1,ns ! loop over slip systems sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) ) previousTauSlip(s) = math_mul6x6( previousTstar_v + previousTdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) ) enddo v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) & * exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) & * sign(1.0_pReal,tauSlip) forall (t = 1:4) & gdot(:,t) = rho(:,t) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v if (debugger) then !$OMP CRITICAL (write2out) write(6,*) '::: constitutive_nonlocal_dotState at ',g,ip,el write(6,*) write(6,'(a,/,3(3(f12.6,x)/))') 'Tdislocation / MPa', math_Mandel6to33(Tdislocation_v/1e6) write(6,'(a,/,3(3(f12.6,x)/))') 'Tstar / MPa', math_Mandel6to33(Tstar_v/1e6) write(6,'(a,/,12(f12.5,x),/)') 'tauSlip / MPa', tauSlip / 1e6_pReal write(6,'(a,/,12(f12.5,x),/)') 'tauSlipThreshold / MPa', tauSlipThreshold / 1e6_pReal write(6,'(a,/,12(e12.5,x),/)') 'v', v write(6,'(a,/,4(12(e12.5,x),/))') 'gdot / 1e-3', gdot*1e3_pReal ! write(6,'(a,/,(12(f12.5,x),/))') 'gdot total/ 1e-3', sum(gdot,2)*1e3_pReal ! call flush(6) !$OMPEND CRITICAL (write2out) endif !**************************************************************************** !*** calculate limits for stable dipole height and its rate of change dLower(:,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(:,myInstance) dLower(:,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(:,myInstance) dUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(tauSlip) ), & 1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) ) dUpper(:,1) = dUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) previousDUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(previousTauSlip) ), & 1.0_pReal / sqrt( sum(previousRho,2) + sum(previousRhoDip,2) ) ) previousDUpper(:,1) = previousDUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) if (dt_previous > 0.0_pReal) dUpperDot = (dUpper - previousDUpper) / dt_previous if (debugger) then !$OMP CRITICAL (write2out) ! write(6,'(a,/,2(12(f12.5,x),/))') 'dUpper / micron', dUpper*1e6_pReal ! write(6,'(a,/,2(12(f12.5,x),/))') 'dUpperDot / micron/s', dUpperDot * 1e6_pReal ! call flush(6) !$OMPEND CRITICAL (write2out) endif !**************************************************************************** !*** calculate dislocation multiplication thisRhoDot(:,1:2) = spread(0.5_pReal * sum(abs(gdot(:,3:4)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) & / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2) thisRhoDot(:,3:4) = spread(0.5_pReal * sum(abs(gdot(:,1:2)),2) * sqrt(rhoForest) & / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) & / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2) thisRhoDipDot = 0.0_pReal ! dipoles don't multiplicate totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', thisRhoDot * timestep !$OMPEND CRITICAL (write2out) endif !**************************************************************************** !*** calculate dislocation fluxes thisRhoDot = 0.0_pReal thisRhoDipDot = 0.0_pReal m(:,:,1) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,2) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,3) = lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,4) = -lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el)) detFe = math_det3x3(Fe(:,:,g,ip,el)) do n = 1,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 neighbor exists, total deformation gradient is averaged over me and my neighbor if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el)) Favg = 0.5_pReal * (F + neighboring_F) else Favg = F endif ! calculate the normal of the interface in current and lattice configuration surfaceNormal_currentconf = math_det3x3(Favg) * math_mul33x3(math_inv3x3(transpose(Favg)), mesh_ipAreaNormal(:,n,ip,el)) surfaceNormal = math_mul33x3(transpose(Fe(:,:,g,ip,el)), surfaceNormal_currentconf) / detFe ! calculate the area of the interface area = mesh_ipArea(n,ip,el) * math_norm3(surfaceNormal) ! normalize the surface normal to unit length surfaceNormal = surfaceNormal / math_norm3(surfaceNormal) lineLength = 0.0_pReal do s = 1,ns ! loop over slip systems do t = 1,4 ! loop over dislocation types if ( sign(1.0_pReal,math_mul3x3(m(:,s,t),surfaceNormal)) == sign(1.0_pReal,gdot(s,t)) ) then lineLength(s,t) = gdot(s,t) / constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) & * math_mul3x3(m(:,s,t), surfaceNormal) * area & * constitutive_nonlocal_transmissivity(misorientation(4,n), misorientation(1:3,n)) ! dislocation line length that leaves this interface per second; weighted by a transmissivity factor thisRhoDot(s,t) = thisRhoDot(s,t) - lineLength(s,t) / mesh_ipVolume(ip,el) ! subtract dislocation density rate (= line length over volume) that leaves through an interface from my dotState ... if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then !$OMP CRITICAL (dotStateLock) !$OMP FLUSH (dotState) dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) = dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) & + lineLength(s,t) / mesh_ipVolume(neighboring_ip,neighboring_el) ! ... and add it to the neighboring dotState (if neighbor exists) !$OMP FLUSH (dotState) !$OMPEND CRITICAL (dotStateLock) endif endif enddo enddo enddo totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation flux', thisRhoDot * timestep !$OMPEND CRITICAL (write2out) endif !**************************************************************************** !*** calculate dipole formation and annihilation !*** formation by glide forall (c=1:2) & thisRhoDipDot(:,c) = 4.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) ) forall (t=1:4) & thisRhoDot(:,t) = -0.5_pReal * thisRhoDipDot(:,(t-1)/2+1) totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,6(12(e12.5,x),/))') 'dipole formation by glide', thisRhoDot * timestep, thisRhoDipDot * timestep !$OMPEND CRITICAL (write2out) endif !*** athermal annihilation forall (c=1:2) & thisRhoDipDot(:,c) = - 4.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) & ! was single hitting single + 0.5_pReal * rhoDip(:,c) * (abs(gdot(:,2*c-1))+abs(gdot(:,2*c))) ) ! single knocks dipole constituent thisRhoDot = 0.0_pReal ! singles themselves don't annihilate totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', thisRhoDipDot * timestep !$OMPEND CRITICAL (write2out) endif !*** thermally activated annihilation of dipoles D = constitutive_nonlocal_D0(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) + dLower(:,1) ) thisRhoDipDot(:,1) = - 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) ) ! edge climb thisRhoDipDot(:,2) = 0.0_pReal !!! cross slipping still has to be implemented !!! thisRhoDot = 0.0_pReal totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', thisRhoDipDot * timestep !$OMPEND CRITICAL (write2out) endif !*** formation/dissociation by stress change = alteration in dUpper thisRhoDipDot = 0.0_pReal ! forall (c=1:2, s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! stress decrease => dipole formation ! thisRhoDipDot(s,c) = 8.0_pReal * rho(s,2*c-1) * rho(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c) forall (c=1:2, s=1:ns, dUpperDot(s,c) < 0.0_pReal) & ! increased stress => dipole dissociation thisRhoDipDot(s,c) = rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c)) forall (t=1:4) & thisRhoDot(:,t) = -0.5_pReal * thisRhoDipDot(:,(t-1)/2+1) totalRhoDot = totalRhoDot + thisRhoDot totalRhoDipDot = totalRhoDipDot + thisRhoDipDot if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,6(12(e12.5,x),/))') 'dipole stability by stress change', thisRhoDot * timestep, thisRhoDipDot * timestep !$OMPEND CRITICAL (write2out) endif !**************************************************************************** !*** assign the rates of dislocation densities to my dotState dotState(1,ip,el)%p(1:4*ns) = dotState(1,ip,el)%p(1:4*ns) + reshape(totalRhoDot,(/4*ns/)) dotState(1,ip,el)%p(4*ns+1:6*ns) = dotState(1,ip,el)%p(4*ns+1:6*ns) + reshape(totalRhoDipDot,(/2*ns/)) if (debugger) then !$OMP CRITICAL (write2out) write(6,'(a,/,4(12(e12.5,x),/))') 'deltaRho:', totalRhoDot * timestep write(6,'(a,/,2(12(e12.5,x),/))') 'deltaRhoDip:', totalRhoDipDot * timestep !$OMPEND CRITICAL (write2out) endif endsubroutine !********************************************************************* !* transmissivity of IP interface * !********************************************************************* function constitutive_nonlocal_transmissivity(misorientationAngle, misorientationAxis) use prec, only: pReal, & pInt implicit none !* input variables real(pReal), dimension(3), intent(in) :: misorientationAxis ! misorientation axis real(pReal), intent(in) :: misorientationAngle ! misorientation angle !* output variables real(pReal) constitutive_nonlocal_transmissivity ! transmissivity of an IP interface for dislocations !* local variables ! transmissivity depends on misorientation angle if (misorientationAngle < 3.0_pReal) then constitutive_nonlocal_transmissivity = 1.0_pReal elseif (misorientationAngle < 10.0_pReal) then constitutive_nonlocal_transmissivity = 0.5_pReal else constitutive_nonlocal_transmissivity = 0.1_pReal endif endfunction !********************************************************************* !* 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 !********************************************************************* !* return array of constitutive results * !********************************************************************* function constitutive_nonlocal_postResults(Tstar_v, previousTstar_v, Fe, Fp, Temperature, misorientation, dt, dt_previous, & state, previousState, dotState, g,ip,el) use prec, only: pReal, & pInt, & p_vec use math, only: math_norm3, & math_mul6x6, & math_mul3x3, & math_mul33x3, & math_mul33x33, & math_inv3x3, & math_det3x3, & math_Mandel6to33, & pi use mesh, only: mesh_NcpElems, & mesh_maxNips, & mesh_maxNipNeighbors, & mesh_element, & FE_NipNeighbors, & mesh_ipNeighborhood, & mesh_ipVolume, & mesh_ipArea, & mesh_ipAreaNormal use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance, & phase_Noutput use lattice, only: lattice_Sslip, & lattice_Sslip_v, & lattice_sd, & lattice_sn, & lattice_st, & lattice_maxNslipFamily, & lattice_NslipSystem 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 dt_previous ! time increment between previous and current state real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: & misorientation ! crystal misorientation between me and my neighbor (axis, angle pair) real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & Fe, & ! elastic deformation gradient Fp ! plastic deformation gradient type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & state, & ! current microstructural state previousState, & ! previous microstructural state 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 neighboring_el, & ! element number of my neighbor neighboring_ip, & ! integration point of my neighbor c, & ! character of dislocation cs, & ! constitutive result index n, & ! index of my current neighbor 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))),6,4) :: & fluxes ! outgoing fluxes per slipsystem, neighbor and dislocation type real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: & rho, & ! current dislocation densities (positive/negative screw and edge without dipoles) previousRho, & ! previous dislocation densities (positive/negative screw and edge without dipoles) rhoDot, & ! evolution rate of dislocation densities (positive/negative screw and edge without dipoles) gdot, & ! shear rates lineLength ! dislocation line length leaving the current interface real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & rhoForest, & ! forest dislocation density tauSlipThreshold, & ! threshold shear stress tauSlip, & ! current resolved shear stress previousTauSlip, & ! previous resolved shear stress v, & ! dislocation velocity invLambda, & ! inverse of mean free path for dislocations 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) previousRhoDip, & ! previous dipole dislocation densities (screw and edge dipoles) rhoDipDot, & ! 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 previousDUpper, & ! previous maximum stable dipole distance for edges and screws dUpperDot ! rate of change of the 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) :: F, & ! total deformation gradient neighboring_F, & ! total deformation gradient of my neighbor Favg ! average total deformation gradient of me and my neighbor real(pReal), dimension(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress previousTdislocation_v ! previous dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress real(pReal), dimension(3) :: surfaceNormal, & ! surface normal in lattice configuration surfaceNormal_currentconf ! surface normal in current configuration real(pReal) area, & ! area of the current interface detFe, & ! determinant of elastic defornmation gradient D ! self diffusion 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 = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns) forall (t = 1:4) previousRho(:,t) = previousState(g,ip,el)%p((t-1)*ns+1:t*ns) forall (c = 1:2) rhoDip(:,c) = state(g,ip,el)%p((3+c)*ns+1:(4+c)*ns) forall (c = 1:2) previousRhoDip(:,c) = previousState(g,ip,el)%p((3+c)*ns+1:(4+c)*ns) rhoForest = state(g,ip,el)%p(6*ns+1:7*ns) tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns) Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6) previousTdislocation_v = previousState(g,ip,el)%p(8*ns+1:8*ns+6) forall (t = 1:4) rhoDot(:,t) = dotState(g,ip,el)%p((t-1)*ns+1:t*ns) forall (c = 1:2) rhoDipDot(:,c) = dotState(g,ip,el)%p((3+c)*ns+1:(4+c)*ns) ! Calculate shear rate do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) ) previousTauSlip(s) = math_mul6x6( previousTstar_v + previousTdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) ) enddo v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) & * exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) & * sign(1.0_pReal,tauSlip) forall (t = 1:4) & gdot(:,t) = rho(:,t) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v ! calculate limits for stable dipole height and its rate of change dLower(:,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(:,myInstance) dLower(:,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(:,myInstance) dUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(tauSlip) ), & 1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) ) dUpper(:,1) = dUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) previousDUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(previousTauSlip) ), & 1.0_pReal / sqrt( sum(previousRho,2) + sum(previousRhoDip,2) ) ) previousDUpper(:,1) = previousDUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) if (dt_previous > 0.0_pReal) then dUpperDot = (dUpper - previousDUpper) / dt_previous else dUpperDot = 0.0_pReal endif ! calculate fluxes m(:,:,1) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,2) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,3) = lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,4) = -lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el)) detFe = math_det3x3(Fe(:,:,g,ip,el)) fluxes = 0.0_pReal do n = 1,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 neighbor exists, total deformation gradient is averaged over me and my neighbor if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el)) Favg = 0.5_pReal * (F + neighboring_F) else Favg = F endif ! calculate the normal of the interface in current and lattice configuration surfaceNormal_currentconf = math_det3x3(Favg) * math_mul33x3(math_inv3x3(transpose(Favg)), mesh_ipAreaNormal(:,n,ip,el)) surfaceNormal = math_mul33x3(transpose(Fe(:,:,g,ip,el)), surfaceNormal_currentconf) / detFe ! normalize the surface normal to unit length surfaceNormal = surfaceNormal / math_norm3(surfaceNormal) ! calculate the area of the interface area = mesh_ipArea(n,ip,el) * math_norm3(surfaceNormal) do s = 1,ns ! loop over slip systems do t = 1,4 ! loop over dislocation types if ( sign(1.0_pReal,math_mul3x3(m(:,s,t),surfaceNormal)) == sign(1.0_pReal,gdot(s,t)) ) & fluxes(s,n,t) = gdot(s,t) / constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) & * math_mul3x3(m(:,s,t), surfaceNormal) * area & * constitutive_nonlocal_transmissivity(misorientation(4,n), misorientation(1:3,n)) & / mesh_ipVolume(ip,el) enddo enddo enddo do o = 1,phase_Noutput(material_phase(g,ip,el)) select case(constitutive_nonlocal_output(o,myInstance)) case ('rho') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rho,2) cs = cs + ns case ('delta') constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt( sum(rho,2) ) cs = cs + ns case ('rho_edge') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) + rho(:,2) cs = cs + ns case ('rho_edge_pos') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) cs = cs + ns case ('rho_edge_neg') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,2) cs = cs + ns case ('rho_screw') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,3) + rho(:,4) cs = cs + ns case ('rho_screw_pos') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,3) cs = cs + ns case ('rho_screw_neg') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,4) cs = cs + ns case ('excess_rho') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) - rho(:,2) + rho(:,3) - rho(:,4) cs = cs + ns case ('excess_rho_edge') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) - rho(:,2) cs = cs + ns case ('excess_rho_screw') constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,3) - rho(:,4) cs = cs + ns case ('rho_forest') constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoForest cs = cs + ns case ('rho_dip') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDip,2) cs = cs + ns case ('delta_dip') constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt( sum(rhoDip,2) ) cs = cs + ns case ('rho_edge_dip') constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(:,1) cs = cs + ns case ('rho_screw_dip') constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(:,2) cs = cs + ns case ('shearrate') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(gdot),2) cs = cs + ns case ('resolvedstress') do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) constitutive_nonlocal_postResults(cs+s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) ) enddo cs = cs + ns case ('resistance') constitutive_nonlocal_postResults(cs+1:cs+ns) = tauSlipThreshold cs = cs + ns case ('rho_dot') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDot,2) cs = cs + ns case ('rho_dot_dip') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDipDot,2) cs = cs + ns case ('rho_dot_gen') invLambda = sqrt(rhoForest) / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) constitutive_nonlocal_postResults(cs+1:cs+ns) = & sum(abs(gdot),2) * invLambda / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) cs = cs + ns case ('rho_dot_sgl2dip') do c=1,2 ! dipole formation by glide constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + & 4.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) ) enddo ! do c=1,2 ! forall (s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! dipole formation by stress decrease ! constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) + & ! 8.0_pReal * rho(s,2*c-1) * rho(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c) ! enddo cs = cs + ns case ('rho_dot_dip2sgl') do c=1,2 forall (s=1:ns, dUpperDot(s,c) < 0.0_pReal) & constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) - & rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c)) enddo cs = cs + ns case ('rho_dot_ann_ath') do c=1,2 constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + & 4.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) & + 0.5_pReal * rhoDip(:,c) * (abs(gdot(:,2*c-1))+abs(gdot(:,2*c))) ) enddo cs = cs + ns case ('rho_dot_ann_the') D = constitutive_nonlocal_D0(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) + dLower(:,1) ) constitutive_nonlocal_postResults(cs+1:cs+ns) = 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) ) ! !!! cross-slip of screws missing !!! cs = cs + ns case ('rho_dot_flux_n1_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,1,1) cs = cs + ns case ('rho_dot_flux_n1_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,1,2) cs = cs + ns case ('rho_dot_flux_n1_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,1,3) cs = cs + ns case ('rho_dot_flux_n1_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,1,4) cs = cs + ns case ('rho_dot_flux_n2_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,2,1) cs = cs + ns case ('rho_dot_flux_n2_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,2,2) cs = cs + ns case ('rho_dot_flux_n2_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,2,3) cs = cs + ns case ('rho_dot_flux_n2_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,2,4) cs = cs + ns case ('rho_dot_flux_n3_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,3,1) cs = cs + ns case ('rho_dot_flux_n3_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,3,2) cs = cs + ns case ('rho_dot_flux_n3_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,3,3) cs = cs + ns case ('rho_dot_flux_n3_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,3,4) cs = cs + ns case ('rho_dot_flux_n4_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,4,1) cs = cs + ns case ('rho_dot_flux_n4_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,4,2) cs = cs + ns case ('rho_dot_flux_n4_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,4,3) cs = cs + ns case ('rho_dot_flux_n4_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,4,4) cs = cs + ns case ('rho_dot_flux_n5_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,5,1) cs = cs + ns case ('rho_dot_flux_n5_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,5,2) cs = cs + ns case ('rho_dot_flux_n5_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,5,3) cs = cs + ns case ('rho_dot_flux_n5_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,5,4) cs = cs + ns case ('rho_dot_flux_n6_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,6,1) cs = cs + ns case ('rho_dot_flux_n6_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,6,2) cs = cs + ns case ('rho_dot_flux_n6_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,6,3) cs = cs + ns case ('rho_dot_flux_n6_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = fluxes(:,6,4) cs = cs + ns case ('rho_dot_flux_ep') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(fluxes(:,:,1), 2) cs = cs + ns case ('rho_dot_flux_en') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(fluxes(:,:,2), 2) cs = cs + ns case ('rho_dot_flux_sp') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(fluxes(:,:,3), 2) cs = cs + ns case ('rho_dot_flux_sn') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(fluxes(:,:,4), 2) cs = cs + ns case ('rho_dot_flux') constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(fluxes(:,:,1), 2) + sum(fluxes(:,:,2), 2) & + sum(fluxes(:,:,3), 2) + sum(fluxes(:,:,4), 2) cs = cs + ns case ('d_upper_edge') constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(:,1) cs = cs + ns case ('d_upper_screw') constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(:,2) cs = cs + ns case ('d_upper_dot_edge') constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(:,1) cs = cs + ns case ('d_upper_dot_screw') constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(:,2) cs = cs + ns end select enddo endfunction END MODULE