diff --git a/code/constitutive_titanmod.f90 b/code/constitutive_titanmod.f90 new file mode 100644 index 000000000..444701e62 --- /dev/null +++ b/code/constitutive_titanmod.f90 @@ -0,0 +1,1548 @@ +!* $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 + constitutive_titanmod_MaxTwinFraction, & ! maximum allowed total twin volume fraction + constitutive_titanmod_r, & ! r-exponent in twin nucleation rate + constitutive_titanmod_CEdgeDipMinDistance, & ! + constitutive_titanmod_Cmfptwin, & ! + constitutive_titanmod_Cthresholdtwin, & ! + 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 edge dipole 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, & ! activation energy for glide [J] for each slip family and instance + constitutive_titanmod_tau0e_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance + constitutive_titanmod_tau0s_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance + constitutive_titanmod_tau0s_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance + constitutive_titanmod_capre_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance + constitutive_titanmod_capre_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance + constitutive_titanmod_caprs_PerSlipFamily, & ! activation energy for glide [J] for each slip family and instance + constitutive_titanmod_caprs_PerSlipSystem, & ! activation energy for glide [J] for each slip system and instance + 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 +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 + case ('c12') + constitutive_titanmod_C12(i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('c13') + constitutive_titanmod_C13(i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('c33') + constitutive_titanmod_C33(i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('c44') + constitutive_titanmod_C44(i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('nslip') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_Nslip(j,i) = IO_intValue(line,positions,1+j) + write(6,*) tag + case ('ntwin') + forall (j = 1:lattice_maxNtwinFamily) & + constitutive_titanmod_Ntwin(j,i) = IO_intValue(line,positions,1+j) + write(6,*) tag + case ('rho_edge0') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_rho_edge0(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('rho_screw0') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_rho_screw0(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('slipburgers') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + 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 + case ('tau0e') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_tau0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('tau0s') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_tau0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('capre') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_capre_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('caprs') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_caprs_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('v0e') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_v0e_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + case ('v0s') + forall (j = 1:lattice_maxNslipFamily) & + constitutive_titanmod_v0s_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j) + write(6,*) tag + 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') + constitutive_titanmod_pe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('ps') + constitutive_titanmod_ps_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('qe') + constitutive_titanmod_qe_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) + write(6,*) tag + case ('qs') + constitutive_titanmod_qs_PerSlipFamily(j,i) = IO_floatValue(line,positions,2) + write(6,*) tag + 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 + 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) + + !* Stress ratio for screw + 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) + + !* Stress ratio for edge p minus1 + 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) + + !* Stress ratio for screw p minus1 + 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) + + !* Boltzmann ratio + BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(f,myInstance)/(kB*Temperature) + + !* Initial shear rates + DotGamma0 = & + state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*& + constitutive_titanmod_v0e_PerSlipSystem(j,myInstance) + + !* Shear rates due to slip + gdot_slip(j) = state(g,ip,el)%p(j)*constitutive_titanmod_burgersPerSlipSystem(j,myInstance)* & + constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio*(1-StressRatio_edge_p)** & + constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* sign(1.0_pReal,tau_slip(j)) + + !* Derivatives of shear rates + dgdot_dtauslip(j) = & + ((abs(gdot_slip(j))*BoltzmannRatio*& + constitutive_titanmod_pe_PerSlipSystem(j,myInstance)*constitutive_titanmod_qe_PerSlipSystem(j,myInstance))/ & + state(g,ip,el)%p(5*ns+3*nt+j))*& + StressRatio_edge_pminus1*(1-StressRatio_edge_p)**(constitutive_titanmod_qe_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 + 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) + + !* Stress ratio for screw + StressRatio_screw_p = ((abs(tau_slip(j))-state(g,ip,el)%p(5*ns+3*nt+j))/ & + constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance))**constitutive_titanmod_ps_PerSlipSystem(j,myInstance) + !* Boltzmann ratio + BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(s,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 + + !* 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) + + 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 + c = c + ns + case ('mfp_slip') + 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 ('resolved_stress_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 + constitutive_titanmod_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)) + enddo; enddo + c = c + ns + case ('threshold_stress_slip') + 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 ('edge_dipole_distance') + 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 + constitutive_titanmod_postResults(c+j) = & + (3.0_pReal*constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(f,myInstance))/& + (16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure)))) + constitutive_titanmod_postResults(c+j) = min(constitutive_titanmod_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j)) +! constitutive_titanmod_postResults(c+j) = max(constitutive_titanmod_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j)) + enddo; enddo + 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 ! 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 = 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 + case ('stress_exponent') + 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(j,myInstance) + + !* Shear rates due to slip + gdot_slip = & + DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_titanmod_qe_PerSlipSystem(j,myInstance))* & + sign(1.0_pReal,tau) + + !* Derivatives of shear rates + dgdot_dtauslip = & + ((abs(gdot_slip)*BoltzmannRatio*& + constitutive_titanmod_pe_PerSlipSystem(j,myInstance)*constitutive_titanmod_qe_PerSlipSystem(j,myInstance))/ & + state(g,ip,el)%p(5*ns+3*nt+j))*& + StressRatio_pminus1*(1-StressRatio_p)**(constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal) + + !* Stress exponent + if (gdot_slip==0.0_pReal) then + constitutive_titanmod_postResults(c+j) = 0.0_pReal + else + constitutive_titanmod_postResults(c+j) = (tau/gdot_slip)*dgdot_dtauslip + endif + enddo ; enddo + c = c + ns + + end select +enddo + +return +end function + +END MODULE