!* $Id$ !************************************ !* 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_atomicVolume, & ! atomic volume constitutive_nonlocal_D0, & ! prefactor for self-diffusion coefficient constitutive_nonlocal_Qsd, & ! activation energy for dislocation climb 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_dDipMinEdgePerSlipFamily, & ! minimum stable edge dipole height for each family and instance constitutive_nonlocal_dDipMinEdgePerSlipSystem, & ! minimum stable edge dipole height for each slip system and instance constitutive_nonlocal_dDipMinScrewPerSlipFamily, & ! minimum stable screw dipole height for each family and instance constitutive_nonlocal_dDipMinScrewPerSlipSystem, & ! 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_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_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_dDipMinEdgePerSlipFamily(lattice_maxNslipFamily, maxNinstance)) allocate(constitutive_nonlocal_dDipMinScrewPerSlipFamily(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_dDipMinEdgePerSlipFamily = 0.0_pReal constitutive_nonlocal_dDipMinScrewPerSlipFamily = 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_dDipMinEdgePerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) case('ddipminscrew') forall (f = 1:lattice_maxNslipFamily) & constitutive_nonlocal_dDipMinScrewPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f) 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 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_dDipMinEdgePerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228) if (constitutive_nonlocal_dDipMinScrewPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228) endif enddo if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 1.0_pReal)) & call IO_error(229) 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_dDipMinEdgePerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_dDipMinEdgePerSlipSystem = 0.0_pReal allocate(constitutive_nonlocal_dDipMinScrewPerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_nonlocal_dDipMinScrewPerSlipSystem = 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', & 'rho_edge', & 'rho_screw', & 'excess_rho', & 'excess_rho_edge', & 'excess_rho_screw', & 'rho_forest', & 'rho_dip', & 'rho_edge_dip', & 'rho_screw_dip', & 'shearrate', & 'resolvedstress', & 'resistance') 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) = constitutive_nonlocal_C12(i) / constitutive_nonlocal_C11(i) !*** burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system do s = 1,constitutive_nonlocal_totalNslip(i) f = constitutive_nonlocal_slipFamily(s,i) constitutive_nonlocal_burgersPerSlipSystem(s,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i) constitutive_nonlocal_v0PerSlipSystem(s,i) = constitutive_nonlocal_v0PerSlipFamily(f,i) constitutive_nonlocal_lambda0PerSlipSystem(s,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i) constitutive_nonlocal_dDipMinEdgePerSlipSystem(s,i) = constitutive_nonlocal_dDipMinEdgePerSlipFamily(f,i) constitutive_nonlocal_dDipMinScrewPerSlipSystem(s,i) = constitutive_nonlocal_dDipMinScrewPerSlipFamily(f,i) enddo !*** calculation of forest projections for edge and screw dislocations do s1 = 1,constitutive_nonlocal_totalNslip(i) do s2 = 1,constitutive_nonlocal_totalNslip(i) 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 (b x n) onto the slip normal of the respective splip 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 enddo; enddo !*** calculation of interaction matrices do s1 = 1,constitutive_nonlocal_totalNslip(i) do s2 = 1,constitutive_nonlocal_totalNslip(i) 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 s0, & s1, & s ! index of slip system constitutive_nonlocal_stateInit = 0.0_pReal ns = constitutive_nonlocal_totalNslip(myInstance) !*** set the basic state variables s1 = 0_pInt do f = 1,lattice_maxNslipFamily s0 = s1 + 1_pInt s1 = s0 + constitutive_nonlocal_Nslip(f,myInstance) - 1_pInt do s = s0,s1 rhoEdgePos(s) = constitutive_nonlocal_rhoEdgePos0(f, myInstance) rhoEdgeNeg(s) = constitutive_nonlocal_rhoEdgeNeg0(f, myInstance) rhoScrewPos(s) = constitutive_nonlocal_rhoScrewPos0(f, myInstance) rhoScrewNeg(s) = constitutive_nonlocal_rhoScrewNeg0(f, myInstance) rhoEdgeDip(s) = constitutive_nonlocal_rhoEdgeDip0(f, myInstance) rhoScrewDip(s) = constitutive_nonlocal_rhoScrewDip0(f, myInstance) enddo enddo !*** calculate the dependent state variables ! 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 ! 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), & constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, 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(Temperature, Fp, state, 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, & 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) :: & 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 as specified by lattice 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 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) :: transform, & ! orthogonal transformation matrix from slip coordinate system with e1=bxn, e2=b, e3=n to 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 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,'(a23,3(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 + rhoScrewPos + rhoScrewNeg), & 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 ! 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 ! calculate the connecting vector between me and my neighbor and his excess dislocation density connectingVector = math_mul33x3( Fp(:,:,g,neighboring_ip,neighboring_el), & (mesh_ipCenterOfGravity(:,ip,el) - mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el)) ) 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 transform = 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 p from the lattice coordinate system to the slip coordinate system x = math_mul3x3(connectingVector, transform(:,1)) y = math_mul3x3(connectingVector, transform(:,2)) z = math_mul3x3(connectingVector, transform(:,3)) ! 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**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**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 Tdislocation_v = Tdislocation_v + math_Mandel33to6( math_mul33x33(transform, math_mul33x33(sigma, transpose(transform)) ) ) ! if (debugger) write(6,'(a15,3(i3,x),/,3(3(f12.3,x)/))') 'sigma / MPa at ',g,ip,el, sigma/1e6 ! if (debugger) write(6,'(a15,3(i3,x),/,3(3(f12.3,x)/))') 'Tdislocation / MPa at ',g,ip,el, math_Mandel6to33(Tdislocation_v/1e6) 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 as specified by lattice 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) ! if (debugger) write(6,'(a20,3(i3,x),/,3(3(f12.3,x)/))') 'Tdislocation / MPa at ', g,ip,el, math_Mandel6to33(Tdislocation_v/1e6) ! if (debugger) write(6,'(a15,3(i3,x),/,3(3(f12.3,x)/))') 'Tstar / MPa at ',g,ip,el, math_Mandel6to33(Tstar_v/1e6) !*** 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( - ( tauSlipThreshold - abs(tauSlip) ) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance)**2.0_pReal & / ( kB * Temperature * sqrt(rhoForest) ) ) & * sign(1.0_pReal,tauSlip) gdotSlip = sum(rho,2) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v dgdot_dtauSlip = gdotSlip * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance)**2.0_pReal & / ( kB * Temperature * sqrt(rhoForest) ) !*** Calculation of Lp and its tangent do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) Lp = Lp + gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure) ! if (debugger) write(6,'(a4,i2,a3,/,3(3(f15.7)/))') 'dLp(',s,'): ',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 ! !$OMP CRITICAL (write2out) ! write(6,*) '::: LpandItsTangent',g,ip,el ! write(6,*) ! write(6,'(a,/,12(f12.5,x))') 'gdot/1e-3',gdotSlip*1e3_pReal ! write(6,*) ! write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp ! write(6,*) ! !$OMPEND CRITICAL (write2out) ! endif endsubroutine !********************************************************************* !* rate of change of microstructure * !********************************************************************* subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, subTstar0_v, Fp, invFp, Temperature, subdt, state, subState0, 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_transpose3x3, & pi use mesh, only: mesh_NcpElems, & mesh_maxNips, & 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 subdt ! substepped crystallite time increment real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation subTstar0_v ! 2nd Piola-Kirchhoff stress in Mandel notation at start of crystallite increment real(pReal), dimension(3,3), intent(in) :: Fp, & ! plastic deformation gradient invFp ! inverse of plastic deformation gradient type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & state, & ! current microstructural state subState0 ! microstructural state at start of crystallite increment !*** 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 real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: & rho, & ! dislocation densities (positive/negative screw and edge without dipoles) rhoDot, & ! rate of change of dislocation densities 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 subTauSlip0, & ! resolved shear stress at start of crystallite increment 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, & ! dipole dislocation densities (screw and edge dipoles) rhoDipDot, & ! rate of change of dipole dislocation densities rhoDotTransfer, & ! dislocation density rate that is transferred from single dislocation to dipole dislocation dDipMin, & ! minimum stable dipole distance for edges and screws dDipMax, & ! current maximum stable dipole distance for edges and screws dDipMax0, & ! maximum stable dipole distance for edges and screws at start of crystallite increment dDipMaxDot ! 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(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress subTdislocation0_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress at start of crystallite increment real(pReal), dimension(3) :: surfaceNormal ! surface normal of the current interface real(pReal) norm_surfaceNormal, & ! euclidic norm of the surface normal area, & ! area of the current interface 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 subTauSlip0 = 0.0_pReal v = 0.0_pReal gdot = 0.0_pReal dDipMin = 0.0_pReal dDipMax = 0.0_pReal dDipMax0 = 0.0_pReal dDipMaxDot = 0.0_pReal rhoDot = 0.0_pReal rhoDipDot = 0.0_pReal rhoDotTransfer = 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 (c = 1:2) rhoDip(:,c) = state(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) subTdislocation0_v = subState0(g,ip,el)%p(8*ns+1:8*ns+6) !**************************************************************************** !*** Calculate shear rate do s = 1,ns ! loop over slip systems tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, & lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure) ) subTauSlip0(s) = math_mul6x6( subTstar0_v + subTdislocation0_v, & lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure) ) enddo v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) & * exp( - ( tauSlipThreshold - abs(tauSlip) ) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance)**2.0_pReal & / ( kB * Temperature * sqrt(rhoForest) ) ) & * sign(1.0_pReal,tauSlip) forall (t = 1:4) & gdot(:,t) = rho(:,t) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v !**************************************************************************** !*** calculate dislocation multiplication invLambda = sqrt(rhoForest) / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) rhoDot = rhoDot + spread(0.25_pReal * sum(abs(gdot),2) * invLambda / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 4) if (debugger) then write(6,*) '::: constitutive_nonlocal_dotState at ',g,ip,el write(6,*) 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(e10.3,x),/)') 'v', v write(6,'(a,/,4(12(f12.5,x),/))') 'gdot / 1e-3', gdot*1e3_pReal write(6,'(a,/,(12(f12.5,x),/))') 'gdot total/ 1e-3', sum(gdot,2)*1e3_pReal write(6,'(a,/,6(12(e12.5,x),/))') 'dislocation multiplication', & spread(0.25_pReal * sum(abs(gdot),2) * invLambda / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 4)*subdt, & 0.0_pReal*rhoDotTransfer endif !**************************************************************************** !*** calculate dislocation 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) 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) ! calculate the area and the surface normal of the interface surfaceNormal = math_mul33x3(math_transpose3x3(invFp), mesh_ipAreaNormal(:,n,ip,el)) norm_surfaceNormal = math_norm3(surfaceNormal) surfaceNormal = surfaceNormal / norm_surfaceNormal area = mesh_ipArea(n,ip,el) / norm_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 ! dislocation line length that leaves this interface per second rhoDot(s,t) = rhoDot(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 locking for this neighbor missing !***************************************************************************************************** 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) endif endif enddo enddo enddo if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'dislocation flux', lineLength/mesh_ipVolume(ip,el)*subdt, 0.0_pReal*rhoDotTransfer !**************************************************************************** !*** calculate dipole formation and annihilation !*** limits for stable dipole height and its tate of change dDipMin(:,1) = constitutive_nonlocal_dDipMinEdgePerSlipSystem(:,myInstance) dDipMin(:,2) = constitutive_nonlocal_dDipMinScrewPerSlipSystem(:,myInstance) dDipMax(:,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(tauSlip) ) dDipMax(:,1) = dDipMax(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) dDipMax0(:,2) = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & / ( 8.0_pReal * pi * abs(subTauSlip0) ) dDipMax0(:,1) = dDipMax0(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) ) dDipMaxDot(:,1) = (dDipMax(:,1) - dDipMax0(:,1)) / subdt dDipMaxDot(:,2) = (dDipMax(:,2) - dDipMax0(:,2)) / subdt ! if (debugger) write(6,'(a,/,2(12(e12.5,x),/))') 'dDipMax:',dDipMax ! if (debugger) write(6,'(a,/,2(12(e12.5,x),/))') 'dDipMaxDot:',dDipMaxDot !*** formation by glide forall (c=1:2) & rhoDotTransfer(:,c) = 2.0_pReal * dDipMax(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) ) if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'dipole formation by glide', & -rhoDotTransfer*subdt,-rhoDotTransfer*subdt,2.0_pReal*rhoDotTransfer*subdt rhoDot(:,(/1,3/)) = rhoDot(:,(/1,3/)) - rhoDotTransfer ! subtract from positive single dislocation density of this character rhoDot(:,(/2,4/)) = rhoDot(:,(/2,4/)) - rhoDotTransfer ! subtract from negative single dislocation density of this character rhoDipDot = rhoDipDot + 2.0_pReal * rhoDotTransfer ! add twice to dipole dislocation density of this character !*** athermal annihilation forall (c=1:2) & rhoDotTransfer(:,c) = - 2.0_pReal * dDipMin(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & * ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) ) if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'athermal dipole annihilation', & 0.0_pReal*rhoDotTransfer,0.0_pReal*rhoDotTransfer,2.0_pReal*rhoDotTransfer*subdt rhoDipDot = rhoDipDot + 2.0_pReal * rhoDotTransfer ! add twice to dipole dislocation density of this character !*** thermally activated annihilation 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 / ( dDipMax(:,1) + dDipMin(:,1) ) rhoDipDot(:,1) = rhoDipDot(:,1) - 4.0_pReal * rho(:,1) * vClimb / ( dDipMax(:,1) - dDipMin(:,1) ) if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'thermally activated dipole annihilation', & 0.0_pReal*rhoDotTransfer, 0.0_pReal*rhoDotTransfer, - 4.0_pReal * rho(:,1) * vClimb / ( dDipMax(:,1) - dDipMin(:,1) )*subdt, & 0.0_pReal*vClimb ! !*** formation by stress decrease = increase in dDipMax ! forall (s=1:ns, dDipMaxDot(s,1) > 0.0_pReal) & ! rhoDotTransfer(s,:) = 4.0_pReal * rho(s,(/1,3/)) * rho(s,(/2,4/)) * dDipMax0(s,:) * dDipMaxDot(s,:) ! if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'dipole formation by stress decrease',& ! -rhoDotTransfer*subdt,-rhoDotTransfer*subdt,2.0_pReal*rhoDotTransfer*subdt ! rhoDot(:,(/1,3/)) = rhoDot(:,(/1,3/)) - rhoDotTransfer ! subtract from positive single dislocation density of this character ! rhoDot(:,(/2,4/)) = rhoDot(:,(/2,4/)) - rhoDotTransfer ! subtract from negative single dislocation density of this character ! rhoDipDot = rhoDipDot + 2.0_pReal * rhoDotTransfer ! add twice to dipole dislocation density of this character ! !*** dipole dissociation by increased stress = decrease in dDipMax ! forall (s=1:ns, dDipMaxDot(s,1) < 0.0_pReal) & ! rhoDotTransfer(s,:) = 0.5_pReal * rhoDip(s,:) * dDipMaxDot(s,:) / (dDipMax0(s,:) - dDipMin(s,:)) ! if (debugger) write(6,'(a,/,6(12(e12.5,x),/))') 'dipole formation by stress decrease',& ! -rhoDotTransfer*subdt,-rhoDotTransfer*subdt,2.0_pReal*rhoDotTransfer*subdt ! rhoDot(:,(/1,3/)) = rhoDot(:,(/1,3/)) - rhoDotTransfer ! subtract from positive single dislocation density of this character ! rhoDot(:,(/2,4/)) = rhoDot(:,(/2,4/)) - rhoDotTransfer ! subtract from negative single dislocation density of this character ! rhoDipDot = rhoDipDot + 2.0_pReal * rhoDotTransfer ! add twice to dipole dislocation density of this character !**************************************************************************** !*** assign the rates of dislocation densities to my dotState dotState(1,ip,el)%p(1:4*ns) = reshape(rhoDot,(/4*ns/)) dotState(1,ip,el)%p(4*ns+1:6*ns) = reshape(rhoDipDot,(/2*ns/)) if (debugger) write(6,'(a,/,4(12(e12.5,x),/))') 'deltaRho:',rhoDot*subdt if (debugger) write(6,'(a,/,2(12(e12.5,x),/))') 'deltaRhoDip:',rhoDipDot*subdt 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 !********************************************************************* !* return array of constitutive results * !********************************************************************* pure function constitutive_nonlocal_postResults(Tstar_v, Temperature, dt, state, g, ip, el) use prec, only: pReal, & pInt, & p_vec use math, only: math_mul6x6 use mesh, only: mesh_NcpElems, & mesh_maxNips use material, only: homogenization_maxNgrains, & material_phase, & phase_constitutionInstance, & phase_Noutput use lattice, only: lattice_Sslip_v, & 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) :: dt, & ! time increment 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), 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 o, & ! index of current output s, & ! index of current slip system sLattice, & ! index of current slip system as specified by lattice c real(pReal) tau, & ! resolved shear stress on current slip system v ! dislocation velocity on current slip system myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_nonlocal_structure(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance) c = 0_pInt constitutive_nonlocal_postResults = 0.0_pReal do o = 1,phase_Noutput(material_phase(g,ip,el)) select case(constitutive_nonlocal_output(o,myInstance)) case ('rho') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) + state(g,ip,el)%p(ns+1:2*ns) & + state(g,ip,el)%p(2*ns+1:3*ns) + state(g,ip,el)%p(3*ns+1:4*ns) c = c + ns case ('rho_edge') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) + state(g,ip,el)%p(ns+1:2*ns) c = c + ns case ('rho_screw') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(2*ns+1:3*ns) + state(g,ip,el)%p(3*ns+1:4*ns) c = c + ns case ('excess_rho') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) - state(g,ip,el)%p(ns+1:2*ns) & + state(g,ip,el)%p(2*ns+1:3*ns) - state(g,ip,el)%p(3*ns+1:4*ns) c = c + ns case ('excess_rho_edge') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) - state(g,ip,el)%p(ns+1:2*ns) c = c + ns case ('excess_rho_screw') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(2*ns+1:3*ns) - state(g,ip,el)%p(3*ns+1:4*ns) c = c + ns case ('rho_forest') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(6*ns+1:7*ns) c = c + ns case ('rho_dip') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(4*ns+1:5*ns) + state(g,ip,el)%p(5*ns+1:6*ns) c = c + ns case ('rho_edge_dip') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(4*ns+1:5*ns) c = c + ns case ('rho_screw_dip') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(5*ns+1:6*ns) c = c + ns case ('shearrate') do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) tau = math_mul6x6( Tstar_v + state(g,ip,el)%p(8*ns+1:8*ns+6), lattice_Sslip_v(:,sLattice,myStructure) ) if (state(g,ip,el)%p(4*ns+s) > 0.0_pReal) then v = constitutive_nonlocal_v0PerSlipSystem(s,myInstance) & * exp( - ( state(g,ip,el)%p(7*ns+s) - abs(tau) ) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance)**2.0_pReal & / ( kB * Temperature * sqrt(state(g,ip,el)%p(4*ns+s)) ) ) & * sign(1.0_pReal,tau) else v = 0.0_pReal endif constitutive_nonlocal_postResults(c+s) = ( state(g,ip,el)%p(s) + state(g,ip,el)%p(ns+s) & + state(g,ip,el)%p(2*ns+s) + state(g,ip,el)%p(3*ns+s) ) & * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) * v enddo c = c + ns case ('resolvedstress') do s = 1,ns sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance) constitutive_nonlocal_postResults(c+s) = math_mul6x6( Tstar_v + state(g,ip,el)%p(8*ns+1:8*ns+6), & lattice_Sslip_v(:,sLattice,myStructure) ) enddo c = c + ns case ('resistance') constitutive_nonlocal_postResults(c+1:c+ns) = state(g,ip,el)%p(7*ns+1:8*ns) c = c + ns end select enddo endfunction END MODULE