!* $Id: constitutive_titanmod.f90 519 2010-03-24 08:17:27Z MPIE\f.roters $ !************************************ !* Module: CONSTITUTIVE * !************************************ MODULE constitutive_titanmod !* Include other modules use prec, only: pReal,pInt implicit none !* Lists of states and physical parameters character(len=*), parameter :: constitutive_titanmod_label = 'titanmod' character(len=18), dimension(2), parameter:: constitutive_titanmod_listBasicSlipStates = (/'rho_edge ', & 'rho_screw'/) character(len=18), dimension(1), parameter:: constitutive_titanmod_listBasicTwinStates = (/'twinFraction'/) character(len=18), dimension(5), parameter:: constitutive_titanmod_listDependentSlipStates =(/'invLambdaSlipe', & 'invLambdaSlips', & 'etauSlipThreshold', & 'stauSlipThreshold', & 'invLambdaSlipTwin'/) character(len=18), dimension(4), parameter:: constitutive_titanmod_listDependentTwinStates =(/'invLambdaTwin ', & 'meanFreePathTwin', & 'tauTwinThreshold', & 'twinVolume '/) real(pReal), parameter :: kB = 1.38e-23_pReal ! Boltzmann constant in J/Kelvin !* Definition of global variables integer(pInt), dimension(:), allocatable :: constitutive_titanmod_sizeDotState, & ! number of dotStates constitutive_titanmod_sizeState, & ! total number of microstructural state variables constitutive_titanmod_sizePostResults ! cumulative size of post results integer(pInt), dimension(:,:), allocatable, target :: constitutive_titanmod_sizePostResult ! size of each post result output character(len=64), dimension(:,:), allocatable, target :: constitutive_titanmod_output ! name of each post result output character(len=32), dimension(:), allocatable :: constitutive_titanmod_structureName ! name of the lattice structure integer(pInt), dimension(:), allocatable :: constitutive_titanmod_structure, & ! number representing the kind of lattice structure constitutive_titanmod_totalNslip, & ! total number of active slip systems for each instance constitutive_titanmod_totalNtwin ! total number of active twin systems for each instance integer(pInt), dimension(:,:), allocatable :: constitutive_titanmod_Nslip, & ! number of active slip systems for each family and instance constitutive_titanmod_Ntwin, & ! number of active twin systems for each family and instance constitutive_titanmod_slipFamily, & ! lookup table relating active slip system to slip family for each instance constitutive_titanmod_twinFamily, & ! lookup table relating active twin system to twin family for each instance constitutive_titanmod_slipSystemLattice, & ! lookup table relating active slip system index to lattice slip system index for each instance constitutive_titanmod_twinSystemLattice ! lookup table relating active twin system index to lattice twin system index for each instance real(pReal), dimension(:), allocatable :: constitutive_titanmod_CoverA, & ! c/a ratio for hex type lattice constitutive_titanmod_C11, & ! C11 element in elasticity matrix constitutive_titanmod_C12, & ! C12 element in elasticity matrix constitutive_titanmod_C13, & ! C13 element in elasticity matrix constitutive_titanmod_C33, & ! C33 element in elasticity matrix constitutive_titanmod_C44, & ! C44 element in elasticity matrix constitutive_titanmod_Gmod, & ! shear modulus constitutive_titanmod_CAtomicVolume, & ! atomic volume in Bugers vector unit constitutive_titanmod_D0, & ! prefactor for self-diffusion coefficient constitutive_titanmod_Qsd, & ! activation energy for dislocation climb constitutive_titanmod_GrainSize, & ! grain size - Not being used constitutive_titanmod_MaxTwinFraction, & ! maximum allowed total twin volume fraction constitutive_titanmod_r, & ! r-exponent in twin nucleation rate constitutive_titanmod_CEdgeDipMinDistance, & ! Not being used constitutive_titanmod_Cmfptwin, & ! Not being used constitutive_titanmod_Cthresholdtwin, & ! Not being used constitutive_titanmod_relevantRho ! dislocation density considered relevant real(pReal), dimension(:,:,:), allocatable :: constitutive_titanmod_Cslip_66 ! elasticity matrix in Mandel notation for each instance real(pReal), dimension(:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_66 ! twin elasticity matrix in Mandel notation for each instance real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_titanmod_Cslip_3333 ! elasticity matrix for each instance real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_titanmod_Ctwin_3333 ! twin elasticity matrix for each instance real(pReal), dimension(:,:), allocatable :: constitutive_titanmod_rho_edge0, & ! initial edge dislocation density per slip system for each family and instance constitutive_titanmod_rho_screw0, & ! initial screw dislocation density per slip system for each family and instance constitutive_titanmod_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each slip family and instance constitutive_titanmod_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance constitutive_titanmod_burgersPerTwinFamily, & ! absolute length of burgers vector [m] for each twin family and instance constitutive_titanmod_burgersPerTwinSystem, & ! absolute length of burgers vector [m] for each twin system and instance constitutive_titanmod_f0_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance constitutive_titanmod_f0_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance constitutive_titanmod_tau0e_PerSlipFamily, & ! Initial yield stress edge dislocations per slip family constitutive_titanmod_tau0e_PerSlipSystem, & ! Initial yield stress edge dislocations per slip system constitutive_titanmod_tau0s_PerSlipFamily, & ! Initial yield stress screw dislocations per slip family constitutive_titanmod_tau0s_PerSlipSystem, & ! Initial yield stress screw dislocations per slip system constitutive_titanmod_capre_PerSlipFamily, & ! Capture radii for edge dislocations per slip family constitutive_titanmod_capre_PerSlipSystem, & ! Capture radii for edge dislocations per slip system constitutive_titanmod_caprs_PerSlipFamily, & ! Capture radii for screw dislocations per slip family constitutive_titanmod_caprs_PerSlipSystem, & ! Capture radii for screw dislocations per slip system constitutive_titanmod_pe_PerSlipFamily, & ! p-exponent in glide velocity constitutive_titanmod_ps_PerSlipFamily, & ! p-exponent in glide velocity constitutive_titanmod_qe_PerSlipFamily, & ! q-exponent in glide velocity constitutive_titanmod_qs_PerSlipFamily, & ! q-exponent in glide velocity constitutive_titanmod_pe_PerSlipSystem, & ! p-exponent in glide velocity constitutive_titanmod_ps_PerSlipSystem, & ! p-exponent in glide velocity constitutive_titanmod_qe_PerSlipSystem, & ! q-exponent in glide velocity constitutive_titanmod_qs_PerSlipSystem, & ! q-exponent in glide velocity constitutive_titanmod_v0e_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance constitutive_titanmod_v0e_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance constitutive_titanmod_v0s_PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance constitutive_titanmod_v0s_PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance constitutive_titanmod_Ndot0PerTwinFamily, & ! twin nucleation rate [1/m³s] for each twin family and instance constitutive_titanmod_Ndot0PerTwinSystem, & ! twin nucleation rate [1/m³s] for each twin system and instance constitutive_titanmod_twinsizePerTwinFamily, & ! twin thickness [m] for each twin family and instance constitutive_titanmod_twinsizePerTwinSystem, & ! twin thickness [m] for each twin system and instance constitutive_titanmod_CeLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance constitutive_titanmod_CeLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance constitutive_titanmod_CsLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance constitutive_titanmod_CsLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance constitutive_titanmod_interactionSlipSlip, & ! coefficients for slip-slip interaction for each interaction type and instance constitutive_titanmod_interactionSlipTwin, & ! coefficients for slip-twin interaction for each interaction type and instance constitutive_titanmod_interactionTwinSlip, & ! coefficients for twin-slip interaction for each interaction type and instance constitutive_titanmod_interactionTwinTwin ! coefficients for twin-twin interaction for each interaction type and instance real(pReal), dimension(:,:,:), allocatable :: constitutive_titanmod_interactionMatrixSlipSlip, & ! interaction matrix of the different slip systems for each instance constitutive_titanmod_interactionMatrixSlipTwin, & ! interaction matrix of slip systems with twin systems for each instance constitutive_titanmod_interactionMatrixTwinSlip, & ! interaction matrix of twin systems with slip systems for each instance constitutive_titanmod_interactionMatrixTwinTwin, & ! interaction matrix of the different twin systems for each instance constitutive_titanmod_forestProjectionEdge ! matrix of forest projections of edge dislocations for each instance CONTAINS !**************************************** !* - constitutive_titanmod_init !* - constitutive_titanmod_stateInit !* - constitutive_titanmod_relevantState !* - constitutive_titanmod_homogenizedC !* - constitutive_titanmod_microstructure !* - constitutive_titanmod_LpAndItsTangent !* - consistutive_titanmod_dotState !* - constitutive_titanmod_dotTemperature !* - consistutive_titanmod_postResults !**************************************** subroutine constitutive_titanmod_init(file) !************************************** !* Module initialization * !************************************** use prec, only: pInt,pReal use math, only: math_Mandel3333to66,math_Voigt66to3333,math_mul3x3 use IO use material use lattice !* 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,f,i,j,k,l,m,n,o,p,q,r,s,s1,s2,t1,t2,ns,nt,output,mySize,myStructure,maxTotalNslip,maxTotalNtwin character(len=64) tag character(len=1024) line !write(6,*) !write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_titanmod_label,' init -+>>>' !write(6,*) '$Id: constitutive_titanmod.f90 519 2010-03-24 08:17:27Z MPIE\f.roters $' !write(6,*) maxNinstance = count(phase_constitution == constitutive_titanmod_label) if (maxNinstance == 0) return !* Space allocation for global variables allocate(constitutive_titanmod_sizeDotState(maxNinstance)) allocate(constitutive_titanmod_sizeState(maxNinstance)) allocate(constitutive_titanmod_sizePostResults(maxNinstance)) allocate(constitutive_titanmod_sizePostResult(maxval(phase_Noutput),maxNinstance)) allocate(constitutive_titanmod_output(maxval(phase_Noutput),maxNinstance)) constitutive_titanmod_sizeDotState = 0_pInt constitutive_titanmod_sizeState = 0_pInt constitutive_titanmod_sizePostResults = 0_pInt constitutive_titanmod_sizePostResult = 0_pInt constitutive_titanmod_output = '' allocate(constitutive_titanmod_structureName(maxNinstance)) allocate(constitutive_titanmod_structure(maxNinstance)) allocate(constitutive_titanmod_Nslip(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_Ntwin(lattice_maxNtwinFamily,maxNinstance)) allocate(constitutive_titanmod_slipFamily(lattice_maxNslip,maxNinstance)) allocate(constitutive_titanmod_twinFamily(lattice_maxNtwin,maxNinstance)) allocate(constitutive_titanmod_slipSystemLattice(lattice_maxNslip,maxNinstance)) allocate(constitutive_titanmod_twinSystemLattice(lattice_maxNtwin,maxNinstance)) allocate(constitutive_titanmod_totalNslip(maxNinstance)) allocate(constitutive_titanmod_totalNtwin(maxNinstance)) constitutive_titanmod_structureName = '' constitutive_titanmod_structure = 0_pInt constitutive_titanmod_Nslip = 0_pInt constitutive_titanmod_Ntwin = 0_pInt constitutive_titanmod_slipFamily = 0_pInt constitutive_titanmod_twinFamily = 0_pInt constitutive_titanmod_slipSystemLattice = 0.0_pReal constitutive_titanmod_twinSystemLattice = 0.0_pReal constitutive_titanmod_totalNslip = 0_pInt constitutive_titanmod_totalNtwin = 0_pInt allocate(constitutive_titanmod_CoverA(maxNinstance)) allocate(constitutive_titanmod_C11(maxNinstance)) allocate(constitutive_titanmod_C12(maxNinstance)) allocate(constitutive_titanmod_C13(maxNinstance)) allocate(constitutive_titanmod_C33(maxNinstance)) allocate(constitutive_titanmod_C44(maxNinstance)) allocate(constitutive_titanmod_Gmod(maxNinstance)) allocate(constitutive_titanmod_CAtomicVolume(maxNinstance)) allocate(constitutive_titanmod_D0(maxNinstance)) allocate(constitutive_titanmod_Qsd(maxNinstance)) allocate(constitutive_titanmod_GrainSize(maxNinstance)) allocate(constitutive_titanmod_MaxTwinFraction(maxNinstance)) allocate(constitutive_titanmod_r(maxNinstance)) allocate(constitutive_titanmod_CEdgeDipMinDistance(maxNinstance)) allocate(constitutive_titanmod_Cmfptwin(maxNinstance)) allocate(constitutive_titanmod_Cthresholdtwin(maxNinstance)) allocate(constitutive_titanmod_relevantRho(maxNinstance)) allocate(constitutive_titanmod_Cslip_66(6,6,maxNinstance)) allocate(constitutive_titanmod_Cslip_3333(3,3,3,3,maxNinstance)) constitutive_titanmod_CoverA = 0.0_pReal constitutive_titanmod_C11 = 0.0_pReal constitutive_titanmod_C12 = 0.0_pReal constitutive_titanmod_C13 = 0.0_pReal constitutive_titanmod_C33 = 0.0_pReal constitutive_titanmod_C44 = 0.0_pReal constitutive_titanmod_Gmod = 0.0_pReal constitutive_titanmod_CAtomicVolume = 0.0_pReal constitutive_titanmod_D0 = 0.0_pReal constitutive_titanmod_Qsd = 0.0_pReal constitutive_titanmod_GrainSize = 0.0_pReal constitutive_titanmod_MaxTwinFraction = 0.0_pReal constitutive_titanmod_r = 0.0_pReal constitutive_titanmod_CEdgeDipMinDistance = 0.0_pReal constitutive_titanmod_Cmfptwin = 0.0_pReal constitutive_titanmod_Cthresholdtwin = 0.0_pReal constitutive_titanmod_relevantRho = 0.0_pReal constitutive_titanmod_Cslip_66 = 0.0_pReal constitutive_titanmod_Cslip_3333 = 0.0_pReal allocate(constitutive_titanmod_rho_edge0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_rho_screw0(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_burgersPerTwinFamily(lattice_maxNtwinFamily,maxNinstance)) allocate(constitutive_titanmod_f0_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_tau0e_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_tau0s_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_capre_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_caprs_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_pe_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_ps_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_qe_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_qs_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_v0e_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_v0s_PerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_Ndot0PerTwinFamily(lattice_maxNtwinFamily,maxNinstance)) allocate(constitutive_titanmod_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance)) allocate(constitutive_titanmod_CeLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance)) allocate(constitutive_titanmod_CsLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance)) constitutive_titanmod_rho_edge0 = 0.0_pReal constitutive_titanmod_rho_screw0 = 0.0_pReal constitutive_titanmod_burgersPerSlipFamily = 0.0_pReal constitutive_titanmod_burgersPerTwinFamily = 0.0_pReal constitutive_titanmod_f0_PerSlipFamily = 0.0_pReal constitutive_titanmod_tau0e_PerSlipFamily = 0.0_pReal constitutive_titanmod_tau0s_PerSlipFamily = 0.0_pReal constitutive_titanmod_capre_PerSlipFamily = 0.0_pReal constitutive_titanmod_caprs_PerSlipFamily = 0.0_pReal constitutive_titanmod_v0e_PerSlipFamily = 0.0_pReal constitutive_titanmod_v0s_PerSlipFamily = 0.0_pReal constitutive_titanmod_Ndot0PerTwinFamily = 0.0_pReal constitutive_titanmod_twinsizePerTwinFamily = 0.0_pReal constitutive_titanmod_CeLambdaSlipPerSlipFamily = 0.0_pReal constitutive_titanmod_CsLambdaSlipPerSlipFamily = 0.0_pReal constitutive_titanmod_pe_PerSlipFamily = 0.0_pReal constitutive_titanmod_ps_PerSlipFamily = 0.0_pReal constitutive_titanmod_qe_PerSlipFamily = 0.0_pReal constitutive_titanmod_qs_PerSlipFamily = 0.0_pReal allocate(constitutive_titanmod_interactionSlipSlip(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionSlipTwin(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionTwinSlip(lattice_maxNinteraction,maxNinstance)) allocate(constitutive_titanmod_interactionTwinTwin(lattice_maxNinteraction,maxNinstance)) constitutive_titanmod_interactionSlipSlip = 0.0_pReal constitutive_titanmod_interactionSlipTwin = 0.0_pReal constitutive_titanmod_interactionTwinSlip = 0.0_pReal constitutive_titanmod_interactionTwinTwin = 0.0_pReal !* Readout data from material.config file rewind(file) line = '' section = 0 write(6,*) 'Reading material parameters from material config file' 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_titanmod_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_titanmod_output(output,i) = IO_lc(IO_stringValue(line,positions,2)) write(6,*) tag case ('lattice_structure') constitutive_titanmod_structureName(i) = IO_lc(IO_stringValue(line,positions,2)) write(6,*) tag case ('covera_ratio') constitutive_titanmod_CoverA(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('c11') constitutive_titanmod_C11(i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_C11(i) case ('c12') constitutive_titanmod_C12(i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_C12(i) case ('c13') constitutive_titanmod_C13(i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_C13(i) case ('c33') constitutive_titanmod_C33(i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_C33(i) case ('c44') constitutive_titanmod_C44(i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_C44(i) case ('nslip') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_Nslip(j,i) = IO_intValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_Nslip(1,i),constitutive_titanmod_Nslip(2,i),constitutive_titanmod_Nslip(3,i), & constitutive_titanmod_Nslip(4,i) case ('ntwin') forall (j = 1:lattice_maxNtwinFamily) & constitutive_titanmod_Ntwin(j,i) = IO_intValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_Ntwin(1,i),constitutive_titanmod_Ntwin(2,i),constitutive_titanmod_Ntwin(3,i), & constitutive_titanmod_Ntwin(4,i) case ('rho_edge0') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_rho_edge0(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_rho_edge0(1,i),constitutive_titanmod_rho_edge0(2,i), & constitutive_titanmod_rho_edge0(3,i), constitutive_titanmod_rho_edge0(4,i) case ('rho_screw0') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_rho_screw0(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_rho_screw0(1,i),constitutive_titanmod_rho_screw0(2,i), & constitutive_titanmod_rho_screw0(3,i), constitutive_titanmod_rho_screw0(4,i) case ('slipburgers') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_burgersPerSlipFamily(1,i),constitutive_titanmod_burgersPerSlipFamily(2,i), & constitutive_titanmod_burgersPerSlipFamily(3,i), constitutive_titanmod_burgersPerSlipFamily(4,i) case ('twinburgers') forall (j = 1:lattice_maxNtwinFamily) & constitutive_titanmod_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('f0') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_f0_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_f0_PerSlipFamily(1,i),constitutive_titanmod_f0_PerSlipFamily(2,i), & constitutive_titanmod_f0_PerSlipFamily(3,i), constitutive_titanmod_f0_PerSlipFamily(4,i) case ('tau0e') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_tau0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_tau0e_PerSlipFamily(1,i),constitutive_titanmod_tau0e_PerSlipFamily(2,i), & constitutive_titanmod_tau0e_PerSlipFamily(3,i), constitutive_titanmod_tau0e_PerSlipFamily(4,i) case ('tau0s') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_tau0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_tau0s_PerSlipFamily(1,i),constitutive_titanmod_tau0s_PerSlipFamily(2,i), & constitutive_titanmod_tau0s_PerSlipFamily(3,i), constitutive_titanmod_tau0s_PerSlipFamily(4,i) case ('capre') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_capre_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_capre_PerSlipFamily(1,i),constitutive_titanmod_capre_PerSlipFamily(2,i), & constitutive_titanmod_capre_PerSlipFamily(3,i), constitutive_titanmod_capre_PerSlipFamily(4,i) case ('caprs') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_caprs_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_caprs_PerSlipFamily(1,i),constitutive_titanmod_caprs_PerSlipFamily(2,i), & constitutive_titanmod_caprs_PerSlipFamily(3,i), constitutive_titanmod_caprs_PerSlipFamily(4,i) case ('v0e') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_v0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_v0e_PerSlipFamily(1,i),constitutive_titanmod_v0e_PerSlipFamily(2,i), & constitutive_titanmod_v0e_PerSlipFamily(3,i), constitutive_titanmod_v0e_PerSlipFamily(4,i) case ('v0s') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_v0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag,constitutive_titanmod_v0s_PerSlipFamily(1,i),constitutive_titanmod_v0s_PerSlipFamily(2,i), & constitutive_titanmod_v0s_PerSlipFamily(3,i), constitutive_titanmod_v0s_PerSlipFamily(4,i) case ('ndot0') forall (j = 1:lattice_maxNtwinFamily) & constitutive_titanmod_Ndot0PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('twinsize') forall (j = 1:lattice_maxNtwinFamily) & constitutive_titanmod_twinsizePerTwinFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('celambdaslip') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_CeLambdaSlipPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('cslambdaslip') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_CsLambdaSlipPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('grainsize') constitutive_titanmod_GrainSize(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('maxtwinfraction') constitutive_titanmod_MaxTwinFraction(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('pe') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_pe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_pe_PerSlipFamily(1,i),constitutive_titanmod_pe_PerSlipFamily(2,i), & constitutive_titanmod_pe_PerSlipFamily(3,i), constitutive_titanmod_pe_PerSlipFamily(4,i),i case ('ps') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_ps_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_ps_PerSlipFamily(1,i),constitutive_titanmod_ps_PerSlipFamily(2,i), & constitutive_titanmod_ps_PerSlipFamily(3,i), constitutive_titanmod_ps_PerSlipFamily(4,i),i case ('qe') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_qe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_qe_PerSlipFamily(1,i),constitutive_titanmod_qe_PerSlipFamily(2,i), & constitutive_titanmod_qe_PerSlipFamily(3,i), constitutive_titanmod_qe_PerSlipFamily(4,i),i case ('qs') forall (j = 1:lattice_maxNslipFamily) & constitutive_titanmod_qs_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) write(6,*) tag,constitutive_titanmod_qs_PerSlipFamily(1,i),constitutive_titanmod_qs_PerSlipFamily(2,i), & constitutive_titanmod_qs_PerSlipFamily(3,i), constitutive_titanmod_qs_PerSlipFamily(4,i),i case ('rexponent') constitutive_titanmod_r(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('d0') constitutive_titanmod_D0(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('qsd') constitutive_titanmod_Qsd(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('relevantrho') constitutive_titanmod_relevantRho(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('cmfptwin') constitutive_titanmod_Cmfptwin(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('cthresholdtwin') constitutive_titanmod_Cthresholdtwin(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('cedgedipmindistance') constitutive_titanmod_CEdgeDipMinDistance(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('catomicvolume') constitutive_titanmod_CAtomicVolume(i) = IO_floatValue(line,positions,2) write(6,*) tag case ('interactionslipslip') forall (j = 1:lattice_maxNinteraction) & constitutive_titanmod_interactionSlipSlip(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('interactionsliptwin') forall (j = 1:lattice_maxNinteraction) & constitutive_titanmod_interactionSlipTwin(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('interactiontwinslip') forall (j = 1:lattice_maxNinteraction) & constitutive_titanmod_interactionTwinSlip(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag case ('interactiontwintwin') forall (j = 1:lattice_maxNinteraction) & constitutive_titanmod_interactionTwinTwin(j,i) = IO_floatValue(line,positions,1+j) write(6,*) tag end select endif enddo write(6,*) 'Material Property reading done' 100 do i = 1,maxNinstance constitutive_titanmod_structure(i) = & lattice_initializeStructure(constitutive_titanmod_structureName(i),constitutive_titanmod_CoverA(i)) myStructure = constitutive_titanmod_structure(i) !* Sanity checks if (myStructure < 1 .or. myStructure > 3) call IO_error(205) if (sum(constitutive_titanmod_Nslip(:,i)) <= 0_pInt) call IO_error(225) if (sum(constitutive_titanmod_Ntwin(:,i)) < 0_pInt) call IO_error(225) !*** do f = 1,lattice_maxNslipFamily if (constitutive_titanmod_Nslip(f,i) > 0_pInt) then if (constitutive_titanmod_rho_edge0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_titanmod_rho_screw0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_titanmod_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221) if (constitutive_titanmod_f0_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228) if (constitutive_titanmod_tau0e_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(229) if (constitutive_titanmod_tau0s_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(233) if (constitutive_titanmod_capre_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(234) if (constitutive_titanmod_caprs_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(235) if (constitutive_titanmod_v0e_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(226) if (constitutive_titanmod_v0s_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(227) endif enddo do f = 1,lattice_maxNtwinFamily if (constitutive_titanmod_Nslip(f,i) > 0_pInt) then if (constitutive_titanmod_burgersPerTwinFamily(f,i) <= 0.0_pReal) call IO_error(221) !*** if (constitutive_titanmod_Ndot0PerTwinFamily(f,i) < 0.0_pReal) call IO_error(226) !*** endif enddo ! if (any(constitutive_titanmod_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 1.0_pReal)) call IO_error(229) if (constitutive_titanmod_CAtomicVolume(i) <= 0.0_pReal) call IO_error(230) if (constitutive_titanmod_D0(i) <= 0.0_pReal) call IO_error(231) if (constitutive_titanmod_Qsd(i) <= 0.0_pReal) call IO_error(232) if (constitutive_titanmod_relevantRho(i) <= 0.0_pReal) call IO_error(233) !* Determine total number of active slip or twin systems constitutive_titanmod_Nslip(:,i) = min(lattice_NslipSystem(:,myStructure),constitutive_titanmod_Nslip(:,i)) constitutive_titanmod_Ntwin(:,i) = min(lattice_NtwinSystem(:,myStructure),constitutive_titanmod_Ntwin(:,i)) constitutive_titanmod_totalNslip(i) = sum(constitutive_titanmod_Nslip(:,i)) constitutive_titanmod_totalNtwin(i) = sum(constitutive_titanmod_Ntwin(:,i)) write(6,*) 'Sanity Checks done !' enddo !* Allocation of variables whose size depends on the total number of active slip systems maxTotalNslip = maxval(constitutive_titanmod_totalNslip) maxTotalNtwin = maxval(constitutive_titanmod_totalNtwin) write(6,*) 'maxTotalNslip',maxTotalNslip write(6,*) 'maxTotalNtwin',maxTotalNtwin allocate(constitutive_titanmod_burgersPerSlipSystem(maxTotalNslip, maxNinstance)) allocate(constitutive_titanmod_burgersPerTwinSystem(maxTotalNtwin, maxNinstance)) allocate(constitutive_titanmod_f0_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_tau0e_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_tau0s_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_capre_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_caprs_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_pe_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_ps_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_qe_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_qs_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_v0e_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_v0s_PerSlipSystem(maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_Ndot0PerTwinSystem(maxTotalNtwin, maxNinstance)) allocate(constitutive_titanmod_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance)) allocate(constitutive_titanmod_CeLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance)) allocate(constitutive_titanmod_CsLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance)) constitutive_titanmod_burgersPerSlipSystem = 0.0_pReal constitutive_titanmod_burgersPerTwinSystem = 0.0_pReal constitutive_titanmod_f0_PerSlipSystem = 0.0_pReal constitutive_titanmod_tau0e_PerSlipSystem = 0.0_pReal constitutive_titanmod_tau0s_PerSlipSystem = 0.0_pReal constitutive_titanmod_capre_PerSlipSystem = 0.0_pReal constitutive_titanmod_caprs_PerSlipSystem = 0.0_pReal constitutive_titanmod_v0e_PerSlipSystem = 0.0_pReal constitutive_titanmod_v0s_PerSlipSystem = 0.0_pReal constitutive_titanmod_pe_PerSlipSystem = 0.0_pReal constitutive_titanmod_ps_PerSlipSystem = 0.0_pReal constitutive_titanmod_qe_PerSlipSystem = 0.0_pReal constitutive_titanmod_qs_PerSlipSystem = 0.0_pReal constitutive_titanmod_Ndot0PerTwinSystem = 0.0_pReal constitutive_titanmod_twinsizePerTwinSystem = 0.0_pReal constitutive_titanmod_CeLambdaSlipPerSlipSystem = 0.0_pReal constitutive_titanmod_CsLambdaSlipPerSlipSystem = 0.0_pReal allocate(constitutive_titanmod_interactionMatrixSlipSlip(maxTotalNslip,maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_interactionMatrixSlipTwin(maxTotalNslip,maxTotalNtwin,maxNinstance)) allocate(constitutive_titanmod_interactionMatrixTwinSlip(maxTotalNtwin,maxTotalNslip,maxNinstance)) allocate(constitutive_titanmod_interactionMatrixTwinTwin(maxTotalNtwin,maxTotalNtwin,maxNinstance)) allocate(constitutive_titanmod_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance)) constitutive_titanmod_interactionMatrixSlipSlip = 0.0_pReal constitutive_titanmod_interactionMatrixSlipTwin = 0.0_pReal constitutive_titanmod_interactionMatrixTwinSlip = 0.0_pReal constitutive_titanmod_interactionMatrixTwinTwin = 0.0_pReal constitutive_titanmod_forestProjectionEdge = 0.0_pReal allocate(constitutive_titanmod_Ctwin_66(6,6,maxTotalNtwin,maxNinstance)) allocate(constitutive_titanmod_Ctwin_3333(3,3,3,3,maxTotalNtwin,maxNinstance)) constitutive_titanmod_Ctwin_66 = 0.0_pReal constitutive_titanmod_Ctwin_3333 = 0.0_pReal write(6,*) 'Allocated slip system variables' do i = 1,maxNinstance myStructure = constitutive_titanmod_structure(i) !* Inverse lookup of my slip system family l = 0_pInt do f = 1,lattice_maxNslipFamily do k = 1,constitutive_titanmod_Nslip(f,i) l = l + 1 constitutive_titanmod_slipFamily(l,i) = f constitutive_titanmod_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1,myStructure)) + k enddo; enddo !* Inverse lookup of my twin system family l = 0_pInt do f = 1,lattice_maxNtwinFamily do k = 1,constitutive_titanmod_Ntwin(f,i) l = l + 1 constitutive_titanmod_twinFamily(l,i) = f constitutive_titanmod_twinSystemLattice(l,i) = sum(lattice_NtwinSystem(1:f-1,myStructure)) + k enddo; enddo !* Determine size of state array ns = constitutive_titanmod_totalNslip(i) nt = constitutive_titanmod_totalNtwin(i) constitutive_titanmod_sizeDotState(i) = & size(constitutive_titanmod_listBasicSlipStates)*ns+size(constitutive_titanmod_listBasicTwinStates)*nt constitutive_titanmod_sizeState(i) = & constitutive_titanmod_sizeDotState(i)+ & size(constitutive_titanmod_listDependentSlipStates)*ns+size(constitutive_titanmod_listDependentTwinStates)*nt write(6,*) 'Determined size of state and dot state' !* Determine size of postResults array do o = 1,maxval(phase_Noutput) select case(constitutive_titanmod_output(o,i)) case('rhoedge', & 'rhoscrew', & 'shear_rate_slip', & 'mfp_slip', & 'resolved_stress_slip', & 'threshold_stress_slip' & ) mySize = constitutive_titanmod_totalNslip(i) case('twin_fraction', & 'shear_rate_twin', & 'mfp_twin', & 'resolved_stress_twin', & 'threshold_stress_twin' & ) mySize = constitutive_titanmod_totalNtwin(i) case default mySize = 0_pInt end select if (mySize > 0_pInt) then ! any meaningful output found constitutive_titanmod_sizePostResult(o,i) = mySize constitutive_titanmod_sizePostResults(i) = constitutive_titanmod_sizePostResults(i) + mySize endif enddo write(6,*) 'Determining elasticity matrix' !* 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_titanmod_Cslip_66(k,j,i) = constitutive_titanmod_C12(i) constitutive_titanmod_Cslip_66(k,k,i) = constitutive_titanmod_C11(i) constitutive_titanmod_Cslip_66(k+3,k+3,i) = constitutive_titanmod_C44(i) end forall case(3:) ! all hex constitutive_titanmod_Cslip_66(1,1,i) = constitutive_titanmod_C11(i) constitutive_titanmod_Cslip_66(2,2,i) = constitutive_titanmod_C11(i) constitutive_titanmod_Cslip_66(3,3,i) = constitutive_titanmod_C33(i) constitutive_titanmod_Cslip_66(1,2,i) = constitutive_titanmod_C12(i) constitutive_titanmod_Cslip_66(2,1,i) = constitutive_titanmod_C12(i) constitutive_titanmod_Cslip_66(1,3,i) = constitutive_titanmod_C13(i) constitutive_titanmod_Cslip_66(3,1,i) = constitutive_titanmod_C13(i) constitutive_titanmod_Cslip_66(2,3,i) = constitutive_titanmod_C13(i) constitutive_titanmod_Cslip_66(3,2,i) = constitutive_titanmod_C13(i) constitutive_titanmod_Cslip_66(4,4,i) = constitutive_titanmod_C44(i) constitutive_titanmod_Cslip_66(5,5,i) = constitutive_titanmod_C44(i) constitutive_titanmod_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_titanmod_C11(i)-constitutive_titanmod_C12(i)) end select constitutive_titanmod_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_titanmod_Cslip_66(:,:,i))) constitutive_titanmod_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_titanmod_Cslip_66(:,:,i)) constitutive_titanmod_Gmod(i) = & 0.2_pReal*(constitutive_titanmod_C11(i)-constitutive_titanmod_C12(i))+0.3_pReal*constitutive_titanmod_C44(i) !* Construction of the twin elasticity matrices do j=1,lattice_maxNtwinFamily do k=1,constitutive_titanmod_Ntwin(j,i) do l=1,3 ; do m=1,3 ; do n=1,3 ; do o=1,3 ; do p=1,3 ; do q=1,3 ; do r=1,3 ; do s=1,3 constitutive_titanmod_Ctwin_3333(l,m,n,o,sum(constitutive_titanmod_Nslip(1:j-1,i))+k,i) = & constitutive_titanmod_Ctwin_3333(l,m,n,o,sum(constitutive_titanmod_Nslip(1:j-1,i))+k,i) + & constitutive_titanmod_Cslip_3333(p,q,r,s,i)*& lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* & lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* & lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* & lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure) enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo constitutive_titanmod_Ctwin_66(:,:,k,i) = math_Mandel3333to66(constitutive_titanmod_Ctwin_3333(:,:,:,:,k,i)) enddo enddo !* Burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system do s = 1,constitutive_titanmod_totalNslip(i) f = constitutive_titanmod_slipFamily(s,i) constitutive_titanmod_burgersPerSlipSystem(s,i) = constitutive_titanmod_burgersPerSlipFamily(f,i) constitutive_titanmod_f0_PerSlipSystem(s,i) = constitutive_titanmod_f0_PerSlipFamily(f,i) constitutive_titanmod_tau0e_PerSlipSystem(s,i) = constitutive_titanmod_tau0e_PerSlipFamily(f,i) constitutive_titanmod_tau0s_PerSlipSystem(s,i) = constitutive_titanmod_tau0s_PerSlipFamily(f,i) constitutive_titanmod_capre_PerSlipSystem(s,i) = constitutive_titanmod_capre_PerSlipFamily(f,i) constitutive_titanmod_caprs_PerSlipSystem(s,i) = constitutive_titanmod_caprs_PerSlipFamily(f,i) constitutive_titanmod_v0e_PerSlipSystem(s,i) = constitutive_titanmod_v0e_PerSlipFamily(f,i) constitutive_titanmod_v0s_PerSlipSystem(s,i) = constitutive_titanmod_v0s_PerSlipFamily(f,i) constitutive_titanmod_pe_PerSlipSystem(s,i) = constitutive_titanmod_pe_PerSlipFamily(f,i) constitutive_titanmod_ps_PerSlipSystem(s,i) = constitutive_titanmod_ps_PerSlipFamily(f,i) constitutive_titanmod_qe_PerSlipSystem(s,i) = constitutive_titanmod_qe_PerSlipFamily(f,i) constitutive_titanmod_qs_PerSlipSystem(s,i) = constitutive_titanmod_qs_PerSlipFamily(f,i) constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,i) = constitutive_titanmod_CeLambdaSlipPerSlipFamily(f,i) constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,i) = constitutive_titanmod_CsLambdaSlipPerSlipFamily(f,i) enddo !* Burgers vector, nucleation rate prefactor and twin size for each twin system do s = 1,constitutive_titanmod_totalNtwin(i) f = constitutive_titanmod_twinFamily(s,i) constitutive_titanmod_burgersPerTwinSystem(s,i) = constitutive_titanmod_burgersPerTwinFamily(f,i) constitutive_titanmod_Ndot0PerTwinSystem(s,i) = constitutive_titanmod_Ndot0PerTwinFamily(f,i) constitutive_titanmod_twinsizePerTwinSystem(s,i) = constitutive_titanmod_twinsizePerTwinFamily(f,i) enddo !* Construction of interaction matrices do s1 = 1,constitutive_titanmod_totalNslip(i) do s2 = 1,constitutive_titanmod_totalNslip(i) constitutive_titanmod_interactionMatrixSlipSlip(s1,s2,i) = & constitutive_titanmod_interactionSlipSlip(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), & constitutive_titanmod_slipSystemLattice(s2,i), & myStructure),i) enddo; enddo do s1 = 1,constitutive_titanmod_totalNslip(i) do t2 = 1,constitutive_titanmod_totalNtwin(i) constitutive_titanmod_interactionMatrixSlipTwin(s1,t2,i) = & constitutive_titanmod_interactionSlipTwin(lattice_interactionSlipTwin(constitutive_titanmod_slipSystemLattice(s1,i), & constitutive_titanmod_twinSystemLattice(t2,i), & myStructure),i) enddo; enddo do t1 = 1,constitutive_titanmod_totalNtwin(i) do s2 = 1,constitutive_titanmod_totalNslip(i) constitutive_titanmod_interactionMatrixTwinSlip(t1,s2,i) = & constitutive_titanmod_interactionTwinSlip(lattice_interactionTwinSlip(constitutive_titanmod_twinSystemLattice(t1,i), & constitutive_titanmod_slipSystemLattice(s2,i), & myStructure),i) enddo; enddo do t1 = 1,constitutive_titanmod_totalNtwin(i) do t2 = 1,constitutive_titanmod_totalNtwin(i) constitutive_titanmod_interactionMatrixTwinTwin(t1,t2,i) = & constitutive_titanmod_interactionTwinTwin(lattice_interactionTwinTwin(constitutive_titanmod_twinSystemLattice(t1,i), & constitutive_titanmod_twinSystemLattice(t2,i), & myStructure),i) enddo; enddo !* Calculation of forest projections for edge dislocations do s1 = 1,constitutive_titanmod_totalNslip(i) do s2 = 1,constitutive_titanmod_totalNslip(i) constitutive_titanmod_forestProjectionEdge(s1,s2,i) = & abs(math_mul3x3(lattice_sn(:,constitutive_titanmod_slipSystemLattice(s1,i),myStructure), & lattice_st(:,constitutive_titanmod_slipSystemLattice(s2,i),myStructure))) enddo; enddo enddo write(6,*) 'Init All done' return end subroutine function constitutive_titanmod_stateInit(myInstance) !********************************************************************* !* initial microstructural state * !********************************************************************* use prec, only: pReal,pInt use math, only: pi use lattice, only: lattice_maxNslipFamily,lattice_maxNtwinFamily implicit none !* Input-Output variables integer(pInt) :: myInstance real(pReal), dimension(constitutive_titanmod_sizeState(myInstance)) :: constitutive_titanmod_stateInit !* Local variables integer(pInt) s0,s1,s,t,f,ns,nt real(pReal), dimension(constitutive_titanmod_totalNslip(myInstance)) :: rho_edge0, & rho_screw0, & invLambdaSlip0e, & invLambdaSlip0s, & etauSlipThreshold0, & stauSlipThreshold0 real(pReal), dimension(constitutive_titanmod_totalNtwin(myInstance)) :: MeanFreePathTwin0,TwinVolume0 ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) constitutive_titanmod_stateInit = 0.0_pReal !* Initialize basic slip state variables s1 = 0_pInt do f = 1,lattice_maxNslipFamily s0 = s1 + 1_pInt s1 = s0 + constitutive_titanmod_Nslip(f,myInstance) - 1_pInt do s = s0,s1 rho_edge0(s) = constitutive_titanmod_rho_edge0(f,myInstance) rho_screw0(s) = constitutive_titanmod_rho_screw0(f,myInstance) enddo enddo constitutive_titanmod_stateInit(1:ns) = rho_edge0 constitutive_titanmod_stateInit(ns+1:2*ns) = rho_screw0 !* Initialize dependent slip microstructural variables forall (s = 1:ns) & invLambdaSlip0e(s) = sqrt(sum(rho_edge0(1:ns))+sum(rho_screw0(1:ns)))/ & constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,myInstance) constitutive_titanmod_stateInit(2*ns+nt+1:3*ns+nt) = invLambdaSlip0e forall (s = 1:ns) & invLambdaSlip0s(s) = sqrt(sum(rho_edge0(1:ns))+sum(rho_screw0(1:ns)))/ & constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance) constitutive_titanmod_stateInit(4*ns+2*nt+1:5*ns+2*nt) = invLambdaSlip0s forall (s = 1:ns) & etauSlipThreshold0(s) = & constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)* & sqrt(dot_product((rho_edge0+rho_screw0),constitutive_titanmod_interactionMatrixSlipSlip(1:ns,s,myInstance))) constitutive_titanmod_stateInit(5*ns+3*nt+1:6*ns+3*nt) = etauSlipThreshold0 forall (s = 1:ns) & stauSlipThreshold0(s) = & constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)* & sqrt(dot_product((rho_edge0+rho_screw0),constitutive_titanmod_interactionMatrixSlipSlip(1:ns,s,myInstance))) constitutive_titanmod_stateInit(6*ns+3*nt+1:7*ns+3*nt) = stauSlipThreshold0 !* Initialize dependent twin microstructural variables forall (t = 1:nt) & MeanFreePathTwin0(t) = constitutive_titanmod_GrainSize(myInstance) constitutive_titanmod_stateInit(5*ns+2*nt+1:5*ns+3*nt) = MeanFreePathTwin0 forall (t = 1:nt) & TwinVolume0(t) = & (pi/6.0_pReal)*constitutive_titanmod_twinsizePerTwinSystem(t,myInstance)*MeanFreePathTwin0(t)**(2.0_pReal) constitutive_titanmod_stateInit(6*ns+4*nt+1:6*ns+5*nt) = TwinVolume0 !write(6,*) '#STATEINIT#' !write(6,*) !write(6,'(a,/,4(3(f30.20,x)/))') 'rho_edge',rho_edge0 !write(6,'(a,/,4(3(f30.20,x)/))') 'rho_screw',rho_screw0 !write(6,'(a,/,4(3(f30.20,x)/))') 'invLambdaSlipe',invLambdaSlip0e !write(6,'(a,/,4(3(f30.20,x)/))') 'invLambdaSlips',invLambdaSlip0s !write(6,'(a,/,4(3(f30.20,x)/))') 'tauSlipThreshold', tauSlipThreshold0 !write(6,'(a,/,4(3(f30.20,x)/))') 'MeanFreePathTwin', MeanFreePathTwin0 !write(6,'(a,/,4(3(f30.20,x)/))') 'TwinVolume', TwinVolume0 return end function pure function constitutive_titanmod_relevantState(myInstance) !********************************************************************* !* relevant microstructural state * !********************************************************************* use prec, only: pReal, pInt implicit none !* Input-Output variables integer(pInt), intent(in) :: myInstance real(pReal), dimension(constitutive_titanmod_sizeState(myInstance)) :: constitutive_titanmod_relevantState constitutive_titanmod_relevantState = constitutive_titanmod_relevantRho(myInstance) return endfunction pure function constitutive_titanmod_homogenizedC(state,g,ip,el) !********************************************************************* !* calculates homogenized elacticity matrix * !* - state : microstructure quantities * !* - g : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* 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-Output variables integer(pInt), intent(in) :: g,ip,el type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state real(pReal), dimension(6,6) :: constitutive_titanmod_homogenizedC !* Local variables integer(pInt) myInstance,ns,nt,i real(pReal) sumf !* Shortened notation myInstance = phase_constitutionInstance(material_phase(g,ip,el)) ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) !* Total twin volume fraction sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0 !* Homogenized elasticity matrix constitutive_titanmod_homogenizedC = (1.0_pReal-sumf)*constitutive_titanmod_Cslip_66(:,:,myInstance) do i=1,nt constitutive_titanmod_homogenizedC = & constitutive_titanmod_homogenizedC + state(g,ip,el)%p(2*ns+i)*constitutive_titanmod_Ctwin_66(:,:,i,myInstance) enddo return end function subroutine constitutive_titanmod_microstructure(Temperature,state,g,ip,el) !********************************************************************* !* calculates quantities characterizing the microstructure * !* - Temperature : temperature * !* - state : microstructure quantities * !* - ipc : component-ID of current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: pi use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance use lattice, only: lattice_interactionSlipTwin,lattice_interactionTwinTwin !use debug, only: debugger implicit none !* Input-Output variables integer(pInt), intent(in) :: g,ip,el real(pReal), intent(in) :: Temperature type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: state !* Local variables integer(pInt) myInstance,myStructure,ns,nt,s,t,i real(pReal) sumf,sfe real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: fOverStacksize !* Shortened notation myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_titanmod_structure(myInstance) ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) !* State: 1 : ns rho_edge !* State: ns+1 : 2*ns rho_screw !* State: 2*ns+1 : 2*ns+nt f !* State: 2*ns+nt+1 : 3*ns+nt 1/lambda_slip !* State: 3*ns+nt+1 : 4*ns+nt 1/lambda_sliptwin !* State: 4*ns+nt+1 : 4*ns+2*nt 1/lambda_twin !* State: 4*ns+2*nt+1 : 5*ns+2*nt mfp_slip !* State: 5*ns+2*nt+1 : 5*ns+3*nt mfp_twin !* State: 5*ns+3*nt+1 : 6*ns+3*nt threshold_stress_slip !* State: 6*ns+3*nt+1 : 6*ns+4*nt threshold_stress_twin !* State: 6*ns+4*nt+1 : 6*ns+5*nt twin volume !* Total twin volume fraction sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0 !* Stacking fault energy sfe = 0.0002_pReal*Temperature-0.0396_pReal !* rescaled twin volume fraction for topology forall (t = 1:nt) & fOverStacksize(t) = & state(g,ip,el)%p(2*ns+t)/constitutive_titanmod_twinsizePerTwinSystem(t,myInstance) !* 1/mean free distance between 2 forest dislocations seen by a moving dislocation forall (s = 1:ns) & state(g,ip,el)%p(2*ns+nt+s) = & sqrt(state(g,ip,el)%p(s)+state(g,ip,el)%p(ns+s))/ & constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,myInstance) !* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation !$OMP CRITICAL (evilmatmul) state(g,ip,el)%p((3*ns+nt+1):(4*ns+nt)) = 0.0_pReal if (nt > 0_pInt) & state(g,ip,el)%p((3*ns+nt+1):(4*ns+nt)) = & matmul(constitutive_titanmod_interactionMatrixSlipTwin(1:ns,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf) !$OMP END CRITICAL (evilmatmul) !* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin !$OMP CRITICAL (evilmatmul) if (nt > 0_pInt) & state(g,ip,el)%p((4*ns+nt+1):(4*ns+2*nt)) = & matmul(constitutive_titanmod_interactionMatrixTwinTwin(1:nt,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf) !$OMP END CRITICAL (evilmatmul) !* mean free path between 2 obstacles seen by a moving dislocation do s = 1,ns if (nt > 0_pInt) then state(g,ip,el)%p(4*ns+2*nt+s) = & constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance) / & sqrt(sum(state(g,ip,el)%p(1:2*ns))) else state(g,ip,el)%p(4*ns+s) = & constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance) / & sqrt(sum(state(g,ip,el)%p(1:2*ns))) ! (1.0_pReal+constitutive_titanmod_GrainSize(myInstance)*(state(g,ip,el)%p(2*ns+s))) endif enddo !* mean free path between 2 obstacles seen by a growing twin forall (t = 1:nt) & state(g,ip,el)%p(5*ns+2*nt+t) = & (constitutive_titanmod_Cmfptwin(myInstance)*constitutive_titanmod_GrainSize(myInstance))/& (1.0_pReal+constitutive_titanmod_GrainSize(myInstance)*state(g,ip,el)%p(4*ns+nt+t)) !* threshold stress for edge dislocation motion forall (s = 1:ns) & state(g,ip,el)%p(5*ns+3*nt+s) = & constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)*& sqrt(dot_product((state(g,ip,el)%p(1:ns)+state(g,ip,el)%p(ns+1:2*ns)),& constitutive_titanmod_interactionMatrixSlipSlip(1:ns,s,myInstance))) !* threshold stress for screw dislocation motion forall (s = 1:ns) & state(g,ip,el)%p(6*ns+3*nt+s) = & constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)*& sqrt(dot_product((state(g,ip,el)%p(1:ns)+state(g,ip,el)%p(ns+1:2*ns)),& constitutive_titanmod_interactionMatrixSlipSlip(1:ns,s,myInstance))) !* threshold stress for growing twin forall (t = 1:nt) & state(g,ip,el)%p(6*ns+3*nt+t) = & constitutive_titanmod_Cthresholdtwin(myInstance)*& (sfe/(3.0_pReal*constitutive_titanmod_burgersPerTwinSystem(t,myInstance))+& 3.0_pReal*constitutive_titanmod_burgersPerTwinSystem(t,myInstance)*constitutive_titanmod_Gmod(myInstance)/& state(g,ip,el)%p(5*ns+2*nt+t)) !* final twin volume after growth forall (t = 1:nt) & state(g,ip,el)%p(6*ns+4*nt+t) = & (pi/6.0_pReal)*constitutive_titanmod_twinsizePerTwinSystem(t,myInstance)*state(g,ip,el)%p(5*ns+2*nt+t)**(2.0_pReal) !if ((ip==1).and.(el==1)) then ! write(6,*) '#MICROSTRUCTURE#' ! write(6,*) ! write(6,'(a,/,4(3(f10.4,x)/))') 'rho_edge',state(g,ip,el)%p(1:ns)/1e9 ! write(6,'(a,/,4(3(f10.4,x)/))') 'rho_screw',state(g,ip,el)%p(ns+1:2*ns)/1e9 ! write(6,'(a,/,4(3(f10.4,x)/))') 'Fraction',state(g,ip,el)%p(2*ns+1:2*ns+nt) !endif return end subroutine subroutine constitutive_titanmod_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,g,ip,el) !********************************************************************* !* calculates plastic velocity gradient and its tangent * !* INPUT: * !* - Temperature : temperature * !* - state : microstructure quantities * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - Lp : plastic velocity gradient * !* - dLp_dTstar : derivative of Lp (4th-rank tensor) * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: math_Plain3333to99 use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Input-Output variables integer(pInt), intent(in) :: g,ip,el real(pReal), intent(in) :: Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: state real(pReal), dimension(3,3), intent(out) :: Lp real(pReal), dimension(9,9), intent(out) :: dLp_dTstar !* Local variables integer(pInt) myInstance,myStructure,ns,nt,f,i,j,k,l,m,n,index_myFamily real(pReal) sumf,StressRatio_edge_p,StressRatio_edge_pminus1,StressRatio_screw_p,StressRatio_screw_pminus1, & StressRatio_r,BoltzmannRatio,DotGamma0 real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(constitutive_titanmod_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & gdot_slip,dgdot_dtauslip,tau_slip real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: & gdot_twin,dgdot_dtautwin,tau_twin !* Shortened notation myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_titanmod_structure(myInstance) ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) !* Total twin volume fraction sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0 Lp = 0.0_pReal dLp_dTstar3333 = 0.0_pReal dLp_dTstar = 0.0_pReal !* Dislocation glide part gdot_slip = 0.0_pReal dgdot_dtauslip = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family j = j+1_pInt !* Calculation of Lp !* Resolved shear stress on slip system tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) !************************************************* !* Stress ratio for edge if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))>0.0_pReal) then StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance) else StressRatio_edge_p=0.0_pReal endif !* Stress ratio for screw if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))>0.0_pReal) then StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ & constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance) else StressRatio_screw_p=0.0_pReal endif !* Stress ratio for edge p minus1 if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))>0.0_pReal) then StressRatio_edge_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1) else StressRatio_edge_pminus1=0.0_pReal endif !* Stress ratio for screw p minus1 if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))>0.0_pReal) then StressRatio_screw_pminus1 = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ & constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1) else StressRatio_screw_pminus1=0.0_pReal endif !* Boltzmann ratio BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature) !* Initial shear rates DotGamma0 = & constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*2.0_pReal*(state(g,ip,el)%p(j)*& + constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)+state(g,ip,el)%p(ns+j)* & constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)) !* Shear rates due to slip gdot_slip(j) = constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*2.0_pReal*(state(g,ip,el)%p(j)* & constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** & constitutive_titanmod_qe_PerSlipSystem(j,myInstance))+state(g,ip,el)%p(ns+j)* & constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_screw_p)** & constitutive_titanmod_qs_PerSlipSystem(j,myInstance)))* sign(1.0_pReal,tau_slip(j)) !* Derivatives of shear rates dgdot_dtauslip(j) = & 2.0_pReal* & ( & ( & ( & ( & abs(gdot_slip(j)) & *BoltzmannRatio*& constitutive_titanmod_pe_PerSlipSystem(j,myInstance)* & constitutive_titanmod_qe_PerSlipSystem(j,myInstance) & )/ & constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance) & )*& StressRatio_edge_pminus1*(1-StressRatio_edge_p)** & (constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal) & ) + & ( & ( & (abs(gdot_slip(j))*BoltzmannRatio*& constitutive_titanmod_ps_PerSlipSystem(j,myInstance)* & constitutive_titanmod_qs_PerSlipSystem(j,myInstance) & )/ & constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance) & )*& StressRatio_screw_pminus1*(1-StressRatio_screw_p)**(constitutive_titanmod_qs_PerSlipSystem(j,myInstance)-1.0_pReal) & ) & ) !************************************************* !* Plastic velocity gradient for dislocation glide Lp = Lp + (1.0_pReal - sumf)*gdot_slip(j)*lattice_Sslip(:,:,index_myFamily+i,myStructure) !* Calculation of the tangent of Lp forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dTstar3333(k,l,m,n) = & dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*& lattice_Sslip(k,l,index_myFamily+i,myStructure)*& lattice_Sslip(m,n,index_myFamily+i,myStructure) enddo enddo !* Mechanical twinning part gdot_twin = 0.0_pReal dgdot_dtautwin = 0.0_pReal j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all slip families index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Ntwin(f,myInstance) ! process each (active) slip system in family j = j+1_pInt !* Calculation of Lp !* Resolved shear stress on twin system tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure)) !* Stress ratios StressRatio_r = (state(g,ip,el)%p(6*ns+3*nt+j)/tau_twin(j))**constitutive_titanmod_r(myInstance) !* Shear rates and their derivatives due to twin if ( tau_twin(j) > 0.0_pReal ) then gdot_twin(j) = & (constitutive_titanmod_MaxTwinFraction(myInstance)-sumf)*lattice_shearTwin(index_myFamily+i,myStructure)*& state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r) dgdot_dtautwin(j) = ((gdot_twin(j)*constitutive_titanmod_r(myInstance))/tau_twin(j))*StressRatio_r endif !* Plastic velocity gradient for mechanical twinning Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,myStructure) !* Calculation of the tangent of Lp forall (k=1:3,l=1:3,m=1:3,n=1:3) & dLp_dTstar3333(k,l,m,n) = & dLp_dTstar3333(k,l,m,n) + dgdot_dtautwin(j)*& lattice_Stwin(k,l,index_myFamily+i,myStructure)*& lattice_Stwin(m,n,index_myFamily+i,myStructure) enddo enddo dLp_dTstar = math_Plain3333to99(dLp_dTstar3333) !if ((ip==1).and.(el==1)) then ! write(6,*) '#LP/TANGENT#' ! write(6,*) ! write(6,*) 'Tstar_v', Tstar_v ! write(6,*) 'tau_slip', tau_slip ! write(6,'(a10,/,4(3(e20.8,x),/))') 'state',state(1,1,1)%p ! write(6,'(a,/,3(3(f10.4,x)/))') 'Lp',Lp ! write(6,'(a,/,9(9(f10.4,x)/))') 'dLp_dTstar',dLp_dTstar !endif return end subroutine function constitutive_titanmod_dotState(Tstar_v,Temperature,state,g,ip,el) !********************************************************************* !* rate of change of microstructure * !* INPUT: * !* - Temperature : temperature * !* - state : microstructure quantities * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_dotState : evolution of state variable * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: pi use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Input-Output variables integer(pInt), intent(in) :: g,ip,el real(pReal), intent(in) :: Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state real(pReal), dimension(constitutive_titanmod_sizeDotState(phase_constitutionInstance(material_phase(g,ip,el)))) :: & constitutive_titanmod_dotState !* Local variables integer(pInt) MyInstance,MyStructure,ns,nt,f,i,j,k,index_myFamily,s real(pReal) sumf,StressRatio_edge_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,& EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,StressRatio_screw_p real(pReal), dimension(constitutive_titanmod_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & gdot_slip,tau_slip,DotRhoEdgeGeneration,EdgeDipDistance,DotRhoEdgeAnnihilation,DotRhoScrewAnnihilation,& ClimbVelocity,DotRhoScrewGeneration, edge_segment, screw_segment,edge_velocity,screw_velocity real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: gdot_twin,tau_twin !* Shortened notation myInstance = phase_constitutionInstance(material_phase(g,ip,el)) MyStructure = constitutive_titanmod_structure(myInstance) ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) !* Total twin volume fraction sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0 constitutive_titanmod_dotState = 0.0_pReal !* average segment length for edge dislocations forall (s = 1:ns) & edge_segment(s) = & (constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,myInstance))/(sum(state(g,ip,el)%p(1:2*ns) & ))**0.5_pReal !* average segment length for screw dislocations forall (s = 1:ns) & screw_segment(s) = & (constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance))/(sum(state(g,ip,el)%p(1:2*ns) & ))**0.5_pReal j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family j = j+1_pInt ! Resolved shear stress tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) !* Stress ratio for edge if((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j)) > 0.0_pReal) then StressRatio_edge_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance))** constitutive_titanmod_pe_PerSlipSystem(j,myInstance) else StressRatio_edge_p=0.0_pReal endif !* Stress ratio for screw if((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j)) > 0.0_pReal) then StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(6*ns+3*nt+j))/ & constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_ps_PerSlipSystem(j,myInstance) else StressRatio_screw_p=0.0_pReal endif !* Boltzmann ratio BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature) ! if (tau_slip(j) == 0.0_pReal) then ! edge_velocity(j) = 0.0_pReal ! screw_velocity(j) = 0.0_pReal ! else edge_velocity(j) =constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** & constitutive_titanmod_qe_PerSlipSystem(j,myInstance)) screw_velocity(j) =constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_screw_p)** & constitutive_titanmod_qs_PerSlipSystem(j,myInstance)) ! endif ! write(6,*) 'edge_segment(j) ',edge_segment(j) ! write(6,*) 'screw_segment(j) ',screw_segment(j) ! write(6,*) 'tau_slip(j) ',tau_slip(j) ! write(6,*) 'Temperature ',Temperature ! write(6,*) 'kB ',kB ! write(6,*) 'constitutive_titanmod_f0_PerSlipSystem(j,myInstance) ',constitutive_titanmod_f0_PerSlipSystem(j,myInstance) ! write(6,*) 'StressRatio_edge_p',StressRatio_edge_p,j ! write(6,*) 'StressRatio_screw_p',StressRatio_screw_p,j ! write(6,*) 'edge_velocity(j)',edge_velocity(j),j ! write(6,*) 'screw_velocity(j)',screw_velocity(j),j !* Multiplication of edge dislocations DotRhoEdgeGeneration(j) = 4.0_pReal*(state(g,ip,el)%p(ns+j)*screw_velocity(j)/screw_segment(j)) !* Multiplication of screw dislocations DotRhoScrewGeneration(j) = 4.0_pReal*(state(g,ip,el)%p(j)*edge_velocity(j)/edge_segment(j)) !* Annihilation of edge dislocations DotRhoEdgeAnnihilation(j) = -4.0_pReal*((state(g,ip,el)%p(j))**2)* & constitutive_titanmod_capre_PerSlipSystem(j,myInstance)*edge_velocity(j) !* Annihilation of screw dislocations DotRhoScrewAnnihilation(j) = -4.0_pReal*((state(g,ip,el)%p(ns+j))**2)* & constitutive_titanmod_caprs_PerSlipSystem(j,myInstance)*screw_velocity(j) !* Edge dislocation density rate of change constitutive_titanmod_dotState(j) = & DotRhoEdgeGeneration(j)+DotRhoEdgeAnnihilation(j) !* Screw dislocation density rate of change constitutive_titanmod_dotState(ns+j) = & DotRhoScrewGeneration(j)+DotRhoScrewAnnihilation(j) ! write(6,*) 'DotRhoEdgeGeneration(j)',DotRhoEdgeGeneration(j) ! write(6,*) 'DotRhoScrewGeneration(j)',DotRhoScrewGeneration(j) ! write(6,*) 'DotRhoEdgeAnnihilation(j)',DotRhoEdgeAnnihilation(j) ! write(6,*) 'DotRhoScrewAnnihilation(j)',DotRhoScrewAnnihilation(j) enddo enddo !* Twin volume fraction evolution j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all twin families index_myFamily = sum(lattice_NtwinSystem(1:f-1,MyStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Ntwin(f,myInstance) ! process each (active) twin system in family j = j+1_pInt !* Resolved shear stress on twin system tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure)) !* Stress ratios StressRatio_r = (state(g,ip,el)%p(6*ns+3*nt+j)/tau_twin(j))**constitutive_titanmod_r(myInstance) !* Shear rates and their derivatives due to twin if ( tau_twin(j) > 0.0_pReal ) then constitutive_titanmod_dotState(2*ns+j) = & (constitutive_titanmod_MaxTwinFraction(myInstance)-sumf)*& state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r) endif enddo enddo !write(6,*) '#DOTSTATE#' !write(6,*) !write(6,'(a,/,4(3(f30.20,x)/))') 'tau slip',tau_slip !write(6,'(a,/,4(3(f30.20,x)/))') 'gamma slip',gdot_slip !write(6,'(a,/,4(3(f30.20,x)/))') 'rho_edge',state(g,ip,el)%p(1:ns) !write(6,'(a,/,4(3(f30.20,x)/))') 'Threshold Slip Edge', state(g,ip,el)%p(5*ns+3*nt+1:6*ns+3*nt) !write(6,'(a,/,4(3(f30.20,x)/))') 'Threshold Slip Screw', state(g,ip,el)%p(6*ns+3*nt+1:7*ns+3*nt) !write(6,'(a,/,4(3(f30.20,x)/))') 'EdgeGeneration',DotRhoEdgeGeneration !write(6,'(a,/,4(3(f30.20,x)/))') 'ScrewGeneration',DotRhoScrewGeneration !write(6,'(a,/,4(3(f30.20,x)/))') 'EdgeAnnihilation',DotRhoEdgeAnnihilation !write(6,'(a,/,4(3(f30.20,x)/))') 'ScrewAnnihilation',DotRhoScrewAnnihilation !write(6,'(a,/,4(3(f30.20,x)/))') 'DipClimb',DotRhoEdgeDipClimb return end function pure function constitutive_titanmod_dotTemperature(Tstar_v,Temperature,state,g,ip,el) !********************************************************************* !* rate of change of microstructure * !* INPUT: * !* - Temperature : temperature * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !* OUTPUT: * !* - constitutive_dotTemperature : evolution of Temperature * !********************************************************************* use prec, only: pReal,pInt,p_vec use mesh, only: mesh_NcpElems,mesh_maxNips use material, only: homogenization_maxNgrains implicit none !* Input-Output variables integer(pInt), intent(in) :: g,ip,el real(pReal), intent(in) :: Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state real(pReal) constitutive_titanmod_dotTemperature constitutive_titanmod_dotTemperature = 0.0_pReal return end function pure function constitutive_titanmod_postResults(Tstar_v,Temperature,dt,state,g,ip,el) !********************************************************************* !* return array of constitutive results * !* INPUT: * !* - Temperature : temperature * !* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) * !* - dt : current time increment * !* - ipc : component-ID at current integration point * !* - ip : current integration point * !* - el : current element * !********************************************************************* use prec, only: pReal,pInt,p_vec use math, only: pi 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_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, & lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin implicit none !* Definition of variables integer(pInt), intent(in) :: g,ip,el real(pReal), intent(in) :: dt,Temperature real(pReal), dimension(6), intent(in) :: Tstar_v type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state integer(pInt) myInstance,myStructure,ns,nt,f,o,i,c,j,index_myFamily real(pReal) sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,gdot_slip,dgdot_dtauslip real(pReal), dimension(constitutive_titanmod_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: & constitutive_titanmod_postResults !* Shortened notation myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myStructure = constitutive_titanmod_structure(myInstance) ns = constitutive_titanmod_totalNslip(myInstance) nt = constitutive_titanmod_totalNtwin(myInstance) !* Total twin volume fraction sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0 !* Required output c = 0_pInt constitutive_titanmod_postResults = 0.0_pReal do o = 1,phase_Noutput(material_phase(g,ip,el)) select case(constitutive_titanmod_output(o,myInstance)) case ('rhoedge') constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns) c = c + ns case ('rhoscrew') constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p(ns+1:2*ns) c = c + ns case ('shear_rate_slip') j = 0_pInt do f = 1,lattice_maxNslipFamily ! loop over all slip families index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Nslip(f,myInstance) ! process each (active) slip system in family j = j + 1_pInt !* Resolved shear stress on slip system tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) !* Stress ratios StressRatio_p = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))**constitutive_titanmod_pe_PerSlipSystem(j,myInstance) StressRatio_pminus1 = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1.0_pReal) !* Boltzmann ratio BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature) !* Initial shear rates DotGamma0 = & state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(f,myInstance)* & constitutive_titanmod_v0e_PerSlipSystem(f,myInstance) !* Shear rates due to slip constitutive_titanmod_postResults(c+j) = & DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* & sign(1.0_pReal,tau) enddo ; enddo ! invLambdaSlipe', & ! 'invLambdaSlips', & ! 'etauSlipThreshold', & ! 'stauSlipThreshold', & ! 'invLambdaSlipTwin c = c + ns case ('edgesegment') constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((4*ns+2*nt+1):(5*ns+2*nt)) c = c + ns case ('screwsegment') j = 0_pInt do f = 1,lattice_maxNslipFamily index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) do i = 1,constitutive_titanmod_Nslip(f,myInstance) j = j + 1_pInt constitutive_titanmod_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) enddo; enddo c = c + ns case ('edgeresistance') constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((5*ns+3*nt+1):(6*ns+3*nt)) c = c + ns case ('screwresistance') constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+3*nt)) c = c + ns case ('twin_fraction') constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((2*ns+1):(2*ns+nt)) c = c + nt case ('shear_rate_twin') if (nt > 0_pInt) then j = 0_pInt do f = 1,lattice_maxNtwinFamily index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) do i = 1,constitutive_titanmod_Ntwin(f,myInstance) j = j + 1_pInt !* Resolved shear stress on twin system tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure)) !* Stress ratios StressRatio_r = (state(g,ip,el)%p(6*ns+3*nt+j)/tau)**constitutive_titanmod_r(myInstance) !* Shear rates and their derivatives due to twin if ( tau > 0.0_pReal ) then constitutive_titanmod_postResults(c+j) = & (constitutive_titanmod_MaxTwinFraction(myInstance)-sumf)*& state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r) endif enddo ; enddo endif c = c + nt case ('mfp_twin') constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((5*ns+2*nt+1):(5*ns+3*nt)) c = c + nt case ('resolved_stress_twin') if (nt > 0_pInt) then j = 0_pInt do f = 1,lattice_maxNtwinFamily ! loop over all slip families index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family do i = 1,constitutive_titanmod_Ntwin(f,myInstance) ! process each (active) slip system in family j = j + 1_pInt constitutive_titanmod_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure)) enddo; enddo endif c = c + nt case ('threshold_stress_twin') constitutive_titanmod_postResults(c+1:c+nt) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+4*nt)) c = c + nt end select enddo return end function END MODULE