!* $Id$
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 = (/'gdot_twin'/)
character(len=18), dimension(12), parameter:: constitutive_titanmod_listDependentSlipStates =(/'segment_edge', &
'segment_screw', &
'resistance_edge', &
'resistance_screw', &
'tau_slip', &
'gdot_slip', &
'velocity_edge', &
'velocity_screw', &
'gdot_slip_edge', &
'gdot_slip_screw', &
'stressratio_edge_p', &
'stressratio_screw_p' &
/)
character(len=18), dimension(2), parameter:: constitutive_titanmod_listDependentTwinStates =(/'twin_fraction', &
'tau_twin' &
/)
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_debyefrequency, & !Debye frequency
constitutive_titanmod_kinkf0, & !Debye frequency
constitutive_titanmod_Gmod, & ! shear modulus
constitutive_titanmod_CAtomicVolume, & ! atomic volume in Bugers vector unit
constitutive_titanmod_dc, & ! prefactor for self-diffusion coefficient
constitutive_titanmod_twinhpconstant, & ! 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_aTolRho ! absolute tolerance for integration of dislocation density
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_twinf0_PerTwinFamily, & ! activation energy for glide [J] for each twin family and instance
constitutive_titanmod_twinf0_PerTwinSystem, & ! activation energy for glide [J] for each twin system and instance
constitutive_titanmod_twinshearconstant_PerTwinFamily, & ! activation energy for glide [J] for each twin family and instance
constitutive_titanmod_twinshearconstant_PerTwinSystem, & ! activation energy for glide [J] for each twin system and instance
constitutive_titanmod_tau0e_PerSlipFamily, & ! Initial yield stress for edge dislocations per slip family
constitutive_titanmod_tau0e_PerSlipSystem, & ! Initial yield stress for edge dislocations per slip system
constitutive_titanmod_tau0s_PerSlipFamily, & ! Initial yield stress for screw dislocations per slip family
constitutive_titanmod_tau0s_PerSlipSystem, & ! Initial yield stress for screw dislocations per slip system
constitutive_titanmod_twintau0_PerTwinFamily, & ! Initial yield stress for edge dislocations per twin family
constitutive_titanmod_twintau0_PerTwinSystem, & ! Initial yield stress for edge dislocations per twin 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_twinp_PerTwinFamily, & ! p-exponent in glide velocity
constitutive_titanmod_twinq_PerTwinFamily, & ! q-exponent in glide velocity
constitutive_titanmod_twinp_PerTwinSystem, & ! p-exponent in glide velocity
constitutive_titanmod_twinq_PerTwinSystem, & ! p-exponent in glide velocity
constitutive_titanmod_v0e_PerSlipFamily, & ! edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0e_PerSlipSystem, & ! screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_v0s_PerSlipFamily, & ! edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0s_PerSlipSystem, & ! screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_twingamma0_PerTwinFamily, & ! edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_twingamma0_PerTwinSystem, & ! screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_kinkcriticallength_PerSlipFamily, & ! screw dislocation mobility prefactor for kink-pairs per slip family
constitutive_titanmod_kinkcriticallength_PerSlipSystem, & ! screw dislocation mobility prefactor for kink-pairs per slip system
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_twinLambdaSlipPerTwinFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_twinLambdaSlipPerTwinSystem, & ! 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_interaction_ee, & ! coefficients for e-e interaction for each interaction type and instance
constitutive_titanmod_interaction_ss, & ! coefficients for s-s interaction for each interaction type and instance
constitutive_titanmod_interaction_es, & ! coefficients for e-s-twin interaction for each interaction type and instance
constitutive_titanmod_interactionSlipTwin, & ! coefficients for twin-slip 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_interactionMatrix_ee, & ! interaction matrix of e-e for each instance
constitutive_titanmod_interactionMatrix_ss, & ! interaction matrix of s-s for each instance
constitutive_titanmod_interactionMatrix_es, & ! interaction matrix of e-s 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
constitutive_titanmod_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance
constitutive_titanmod_TwinforestProjectionEdge, & ! matrix of forest projections of edge dislocations in twin system for each instance
constitutive_titanmod_TwinforestProjectionScrew ! matrix of forest projections of screw dislocations in twin system 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,t,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,*) '$Id$'
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_debyefrequency(maxNinstance))
allocate(constitutive_titanmod_kinkf0(maxNinstance))
allocate(constitutive_titanmod_Gmod(maxNinstance))
allocate(constitutive_titanmod_CAtomicVolume(maxNinstance))
allocate(constitutive_titanmod_dc(maxNinstance))
allocate(constitutive_titanmod_twinhpconstant(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_aTolRho(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_debyefrequency = 0.0_pReal
constitutive_titanmod_kinkf0 = 0.0_pReal
constitutive_titanmod_Gmod = 0.0_pReal
constitutive_titanmod_CAtomicVolume = 0.0_pReal
constitutive_titanmod_dc = 0.0_pReal
constitutive_titanmod_twinhpconstant = 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_aTolRho = 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_kinkcriticallength_PerSlipFamily(lattice_maxNslipFamily,maxNinstance))
allocate(constitutive_titanmod_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
allocate(constitutive_titanmod_CeLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
allocate(constitutive_titanmod_CsLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
allocate(constitutive_titanmod_twinf0_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twinshearconstant_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twintau0_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twinp_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twinq_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twingamma0_PerTwinFamily(lattice_maxNTwinFamily,maxNinstance))
allocate(constitutive_titanmod_twinLambdaSlipPerTwinFamily(lattice_maxNTwinFamily,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_kinkcriticallength_PerSlipFamily = 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
constitutive_titanmod_twinf0_PerTwinFamily = 0.0_pReal
constitutive_titanmod_twinshearconstant_PerTwinFamily = 0.0_pReal
constitutive_titanmod_twintau0_PerTwinFamily = 0.0_pReal
constitutive_titanmod_twingamma0_PerTwinFamily = 0.0_pReal
constitutive_titanmod_twinLambdaSlipPerTwinFamily = 0.0_pReal
constitutive_titanmod_twinp_PerTwinFamily = 0.0_pReal
constitutive_titanmod_twinq_PerTwinFamily = 0.0_pReal
allocate(constitutive_titanmod_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
allocate(constitutive_titanmod_interaction_ee(lattice_maxNinteraction,maxNinstance))
allocate(constitutive_titanmod_interaction_ss(lattice_maxNinteraction,maxNinstance))
allocate(constitutive_titanmod_interaction_es(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_interaction_ee = 0.0_pReal
constitutive_titanmod_interaction_ss = 0.0_pReal
constitutive_titanmod_interaction_ss = 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,*) 'titanmod: Reading material parameters from material config file'
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
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,constitutive_titanmod_output(output,i)
case ('lattice_structure')
constitutive_titanmod_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
write(6,*) tag,constitutive_titanmod_structureName(i)
case ('covera_ratio')
constitutive_titanmod_CoverA(i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_CoverA(i)
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 ('debyefrequency')
constitutive_titanmod_debyefrequency(i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_debyefrequency(i)
case ('kinkf0')
constitutive_titanmod_kinkf0(i) = IO_floatValue(line,positions,2)
write(6,*) tag,constitutive_titanmod_kinkf0(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(1:4,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(1:4,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(1:4,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(1:4,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(1:4,i)
case ('twinburgers')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_burgersPerTwinFamily(1:4,i)
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(1:4,i)
case ('twinf0')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twinf0_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twinf0_PerTwinFamily(1:4,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(1:4,i)
case ('twintau0')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twintau0_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twintau0_PerTwinFamily(1:4,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(1:4,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(1:4,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(1:4,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(1:4,i)
case ('twingamma0')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twingamma0_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twingamma0_PerTwinFamily(1:4,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(1:4,i)
case ('kinkcriticallength')
forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_kinkcriticallength_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_kinkcriticallength_PerSlipFamily(1:4,i)
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 ('twinlambdaslip')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twinlambdaslipPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twinlambdaslipPerTwinFamily(1:4,i)
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,1+j)
write(6,*) tag,constitutive_titanmod_pe_PerSlipFamily(1:4,i)
case ('twinp')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twinp_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twinp_PerTwinFamily(1:4,i)
case ('ps')
forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_ps_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_ps_PerSlipFamily(1:4,i)
case ('qe')
forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_qe_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_qe_PerSlipFamily(1:4,i)
case ('twinq')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twinq_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twinq_PerTwinFamily(1:4,i)
case ('qs')
forall (j = 1:lattice_maxNslipFamily) &
constitutive_titanmod_qs_PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_qs_PerSlipFamily(1:4,i)
case ('twinshearconstant')
forall (j = 1:lattice_maxNtwinFamily) &
constitutive_titanmod_twinshearconstant_PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag,constitutive_titanmod_twinshearconstant_PerTwinFamily(1:4,i)
case ('dc')
constitutive_titanmod_dc(i) = IO_floatValue(line,positions,2)
write(6,*) tag
case ('twinhpconstant')
constitutive_titanmod_twinhpconstant(i) = IO_floatValue(line,positions,2)
write(6,*) tag
case ('atol_rho')
constitutive_titanmod_aTolRho(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 ('interactionee')
forall (j = 1:lattice_maxNinteraction) &
constitutive_titanmod_interaction_ee(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag
case ('interactionss')
forall (j = 1:lattice_maxNinteraction) &
constitutive_titanmod_interaction_ss(j,i) = IO_floatValue(line,positions,1+j)
write(6,*) tag
case ('interactiones')
forall (j = 1:lattice_maxNinteraction) &
constitutive_titanmod_interaction_es(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(207)
if (sum(constitutive_titanmod_Ntwin(:,i)) < 0_pInt) call IO_error(208) !***
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(209)
if (constitutive_titanmod_rho_screw0(f,i) < 0.0_pReal) call IO_error(210)
if (constitutive_titanmod_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(211)
if (constitutive_titanmod_f0_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(212)
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(226)
if (constitutive_titanmod_kinkcriticallength_PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(238)
endif
enddo
do f = 1,lattice_maxNtwinFamily
if (constitutive_titanmod_Ntwin(f,i) > 0_pInt) then
if (constitutive_titanmod_burgersPerTwinFamily(f,i) <= 0.0_pReal) call IO_error(221) !***
if (constitutive_titanmod_twinf0_PerTwinFamily(f,i) <= 0.0_pReal) call IO_error(228)
if (constitutive_titanmod_twinshearconstant_PerTwinFamily(f,i) <= 0.0_pReal) call IO_error(228)
if (constitutive_titanmod_twintau0_PerTwinFamily(f,i) <= 0.0_pReal) call IO_error(229)
if (constitutive_titanmod_twingamma0_PerTwinFamily(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_dc(i) <= 0.0_pReal) call IO_error(231)
if (constitutive_titanmod_twinhpconstant(i) <= 0.0_pReal) call IO_error(232)
if (constitutive_titanmod_aTolRho(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_kinkcriticallength_PerSlipSystem(maxTotalNslip,maxNinstance))
allocate(constitutive_titanmod_CeLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance))
allocate(constitutive_titanmod_CsLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance))
allocate(constitutive_titanmod_twinf0_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twinshearconstant_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twintau0_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twinp_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twinq_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twingamma0_PerTwinSystem(maxTotalNTwin,maxNinstance))
allocate(constitutive_titanmod_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance))
allocate(constitutive_titanmod_twinLambdaSlipPerTwinSystem(maxTotalNtwin, 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_kinkcriticallength_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_twinf0_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twinshearconstant_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twintau0_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twingamma0_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twinp_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twinq_PerTwinSystem = 0.0_pReal
constitutive_titanmod_twinsizePerTwinSystem = 0.0_pReal
constitutive_titanmod_CeLambdaSlipPerSlipSystem = 0.0_pReal
constitutive_titanmod_CsLambdaSlipPerSlipSystem = 0.0_pReal
constitutive_titanmod_twinLambdaSlipPerTwinSystem = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrixSlipSlip(maxTotalNslip,maxTotalNslip,maxNinstance))
allocate(constitutive_titanmod_interactionMatrix_ee(maxTotalNslip,maxTotalNslip,maxNinstance))
allocate(constitutive_titanmod_interactionMatrix_ss(maxTotalNslip,maxTotalNslip,maxNinstance))
allocate(constitutive_titanmod_interactionMatrix_es(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))
allocate(constitutive_titanmod_forestProjectionScrew(maxTotalNslip,maxTotalNslip,maxNinstance))
allocate(constitutive_titanmod_TwinforestProjectionEdge(maxTotalNtwin,maxTotalNtwin,maxNinstance))
allocate(constitutive_titanmod_TwinforestProjectionScrew(maxTotalNtwin,maxTotalNtwin,maxNinstance))
constitutive_titanmod_interactionMatrixSlipSlip = 0.0_pReal
constitutive_titanmod_interactionMatrix_ee = 0.0_pReal
constitutive_titanmod_interactionMatrix_ss = 0.0_pReal
constitutive_titanmod_interactionMatrix_es = 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
constitutive_titanmod_forestProjectionScrew = 0.0_pReal
constitutive_titanmod_TwinforestProjectionEdge = 0.0_pReal
constitutive_titanmod_TwinforestProjectionScrew = 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 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 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
! 'segment_edge'
! 'segment_screw'
! 'resistance_edge'
! 'resistance_screw'
! 'tau_slip'
! 'gdot_slip'
! 'velocity_edge'
! 'velocity_screw'
! 'gdot_slip_edge'
! 'gdot_slip_screw'
! 'StressRatio_edge_p'
! 'StressRatio_screw_p'
do o = 1,maxval(phase_Noutput)
select case(constitutive_titanmod_output(o,i))
case('rhoedge', &
'rhoscrew', &
'segment_edge', &
'segment_screw', &
'resistance_edge', &
'resistance_screw', &
'tau_slip', &
'gdot_slip', &
'velocity_edge', &
'velocity_screw', &
'gdot_slip_edge', &
'gdot_slip_screw', &
'stressratio_edge_p', &
'stressratio_screw_p' &
)
mySize = constitutive_titanmod_totalNslip(i)
case('twin_fraction', &
'gdot_twin', &
'tau_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 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_kinkcriticallength_PerSlipSystem(s,i) = constitutive_titanmod_kinkcriticallength_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 t = 1,constitutive_titanmod_totalNtwin(i)
f = constitutive_titanmod_twinFamily(t,i)
constitutive_titanmod_burgersPerTwinSystem(t,i) = constitutive_titanmod_burgersPerTwinFamily(f,i)
constitutive_titanmod_twinsizePerTwinSystem(t,i) = constitutive_titanmod_twinsizePerTwinFamily(f,i)
constitutive_titanmod_twinf0_PerTwinSystem(t,i) = constitutive_titanmod_twinf0_PerTwinFamily(f,i)
constitutive_titanmod_twinshearconstant_PerTwinSystem(t,i) = constitutive_titanmod_twinshearconstant_PerTwinFamily(f,i)
constitutive_titanmod_twintau0_PerTwinSystem(t,i) = constitutive_titanmod_twintau0_PerTwinFamily(f,i)
constitutive_titanmod_twingamma0_PerTwinSystem(t,i) = constitutive_titanmod_twingamma0_PerTwinFamily(f,i)
constitutive_titanmod_twinp_PerTwinSystem(t,i) = constitutive_titanmod_twinp_PerTwinFamily(f,i)
constitutive_titanmod_twinq_PerTwinSystem(t,i) = constitutive_titanmod_twinq_PerTwinFamily(f,i)
constitutive_titanmod_twinLambdaSlipPerTwinSystem(t,i) = constitutive_titanmod_twinLambdaSlipPerTwinFamily(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 s2 = 1,constitutive_titanmod_totalNslip(i)
constitutive_titanmod_interactionMatrix_ee(s1,s2,i) = &
constitutive_titanmod_interaction_ee(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), &
constitutive_titanmod_slipSystemLattice(s2,i), &
myStructure),i)
enddo; enddo
do s1 = 1,constitutive_titanmod_totalNslip(i)
do s2 = 1,constitutive_titanmod_totalNslip(i)
constitutive_titanmod_interactionMatrix_ss(s1,s2,i) = &
constitutive_titanmod_interaction_ss(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), &
constitutive_titanmod_slipSystemLattice(s2,i), &
myStructure),i)
enddo; enddo
do s1 = 1,constitutive_titanmod_totalNslip(i)
do s2 = 1,constitutive_titanmod_totalNslip(i)
constitutive_titanmod_interactionMatrix_es(s1,s2,i) = &
constitutive_titanmod_interaction_es(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
!* Calculation of forest projections for screw dislocations
do s1 = 1,constitutive_titanmod_totalNslip(i)
do s2 = 1,constitutive_titanmod_totalNslip(i)
constitutive_titanmod_forestProjectionScrew(s1,s2,i) = &
abs(math_mul3x3(lattice_sn(:,constitutive_titanmod_slipSystemLattice(s1,i),myStructure), &
lattice_sd(:,constitutive_titanmod_slipSystemLattice(s2,i),myStructure)))
enddo; enddo
!* Calculation of forest projections for edge dislocations in twin system
do t1 = 1,constitutive_titanmod_totalNtwin(i)
do t2 = 1,constitutive_titanmod_totalNtwin(i)
constitutive_titanmod_TwinforestProjectionEdge(t1,t2,i) = &
abs(math_mul3x3(lattice_tn(:,constitutive_titanmod_twinSystemLattice(t1,i),myStructure), &
lattice_tt(:,constitutive_titanmod_twinSystemLattice(t2,i),myStructure)))
enddo; enddo
!* Calculation of forest projections for screw dislocations in twin system
do t1 = 1,constitutive_titanmod_totalNtwin(i)
do t2 = 1,constitutive_titanmod_totalNtwin(i)
constitutive_titanmod_TwinforestProjectionScrew(t1,t2,i) = &
abs(math_mul3x3(lattice_tn(:,constitutive_titanmod_twinSystemLattice(t1,i),myStructure), &
lattice_td(:,constitutive_titanmod_twinSystemLattice(t2,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,ts0,ts1,tf,ts
real(pReal), dimension(constitutive_titanmod_totalNslip(myInstance)) :: rho_edge0, &
rho_screw0, &
segment_edge0, &
segment_screw0, &
resistance_edge0, &
resistance_screw0
real(pReal), dimension(constitutive_titanmod_totalNtwin(myInstance)) :: twingamma_dot0, &
resistance_twin0
ns = constitutive_titanmod_totalNslip(myInstance)
nt = constitutive_titanmod_totalNtwin(myInstance)
constitutive_titanmod_stateInit = 0.0_pReal
!* Initialize basic slip state variables
! For slip
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
!* Initialize basic slip state variables
! For twin
ts1 = 0_pInt
do tf = 1,lattice_maxNtwinFamily
ts0 = ts1 + 1_pInt
ts1 = ts0 + constitutive_titanmod_Ntwin(tf,myInstance) - 1_pInt
do ts = ts0,ts1
twingamma_dot0(ts)=0.0_pReal
enddo
enddo
constitutive_titanmod_stateInit(1:ns) = rho_edge0
constitutive_titanmod_stateInit(ns+1:2*ns) = rho_screw0
constitutive_titanmod_stateInit(2*ns+1:2*ns+nt) = twingamma_dot0
!* Initialize dependent slip microstructural variables
forall (s = 1:ns) &
segment_edge0(s) = constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,myInstance)/ &
sqrt(dot_product((rho_edge0),constitutive_titanmod_forestProjectionEdge(1:ns,s,myInstance))+ &
dot_product((rho_screw0),constitutive_titanmod_forestProjectionScrew(1:ns,s,myInstance)))
constitutive_titanmod_stateInit(2*ns+nt+1:3*ns+nt) = segment_edge0
forall (s = 1:ns) &
segment_screw0(s) = constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance)/ &
sqrt(dot_product((rho_edge0),constitutive_titanmod_forestProjectionEdge(1:ns,s,myInstance))+ &
dot_product((rho_screw0),constitutive_titanmod_forestProjectionScrew(1:ns,s,myInstance)))
constitutive_titanmod_stateInit(3*ns+nt+1:4*ns+nt) = segment_screw0
forall (s = 1:ns) &
resistance_edge0(s) = &
constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)* &
sqrt(dot_product((rho_edge0),constitutive_titanmod_interactionMatrix_ee(1:ns,s,myInstance))+dot_product((rho_screw0), &
constitutive_titanmod_interactionMatrix_es(1:ns,s,myInstance)))
constitutive_titanmod_stateInit(4*ns+nt+1:5*ns+nt) = resistance_edge0
forall (s = 1:ns) &
resistance_screw0(s) = &
constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)* &
sqrt(dot_product((rho_edge0),constitutive_titanmod_interactionMatrix_es(1:ns,s,myInstance))+dot_product((rho_screw0), &
constitutive_titanmod_interactionMatrix_ss(1:ns,s,myInstance)))
constitutive_titanmod_stateInit(5*ns+nt+1:6*ns+nt) = resistance_screw0
forall (t = 1:nt) &
resistance_twin0(t) = 0.0_pReal
constitutive_titanmod_stateInit(6*ns+nt+1:6*ns+2*nt)=resistance_twin0
return
end function
pure function constitutive_titanmod_aTolState(myInstance)
!*********************************************************************
!* absolute state tolerance *
!*********************************************************************
use prec, only: pReal, pInt
implicit none
!* Input-Output variables
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(constitutive_titanmod_sizeState(myInstance)) :: constitutive_titanmod_aTolState
constitutive_titanmod_aTolState = constitutive_titanmod_aTolRho(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
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
volumefraction_pertwinsystem
!* 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
do i=1,nt
volumefraction_pertwinsystem(i)=state(g,ip,el)%p(2*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSystem(i,myInstance)
enddo
!sumf = sum(state(g,ip,el)%p((6*ns+7*nt+1):(6*ns+8*nt))) ! safe for nt == 0
sumf = sum(abs(volumefraction_pertwinsystem(1: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(6*ns+7*nt+i)*constitutive_titanmod_Ctwin_66(:,:,i,myInstance)
constitutive_titanmod_homogenizedC + volumefraction_pertwinsystem(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, volumefraction_pertwinsystem
!* 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)
! Need to update this list
!* State: 1 : ns rho_edge
!* State: ns+1 : 2*ns rho_screw
!* State: 2*ns+1 : 2*ns+nt gamma_twin
!* 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
do i=1,nt
volumefraction_pertwinsystem(i)=state(g,ip,el)%p(2*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSystem(i,myInstance)
enddo
!sumf = sum(state(g,ip,el)%p((6*ns+7*nt+1):(6*ns+8*nt))) ! safe for nt == 0
sumf = sum(abs(volumefraction_pertwinsystem(1: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)
! average segment length for edge dislocations in matrix
forall (s = 1:ns) &
state(g,ip,el)%p(2*ns+nt+s) = constitutive_titanmod_CeLambdaSlipPerSlipSystem(s,myInstance)/ &
sqrt(dot_product(state(g,ip,el)%p(1:ns), &
constitutive_titanmod_forestProjectionEdge(1:ns,s,myInstance))+ &
dot_product(state(g,ip,el)%p(ns+1:2*ns), &
constitutive_titanmod_forestProjectionScrew(1:ns,s,myInstance)))
! average segment length for screw dislocations in matrix
forall (s = 1:ns) &
state(g,ip,el)%p(3*ns+nt+s) = constitutive_titanmod_CsLambdaSlipPerSlipSystem(s,myInstance)/ &
sqrt(dot_product(state(g,ip,el)%p(1:ns), &
constitutive_titanmod_forestProjectionEdge(1:ns,s,myInstance))+ &
dot_product(state(g,ip,el)%p(ns+1:2*ns), &
constitutive_titanmod_forestProjectionScrew(1:ns,s,myInstance)))
!* threshold stress or slip resistance for edge dislocation motion
forall (s = 1:ns) &
state(g,ip,el)%p(4*ns+nt+s) = &
constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)*&
sqrt(dot_product((state(g,ip,el)%p(1:ns)),&
constitutive_titanmod_interactionMatrix_ee(1:ns,s,myInstance))+ &
dot_product((state(g,ip,el)%p(ns+1:2*ns)),&
constitutive_titanmod_interactionMatrix_es(1:ns,s,myInstance)))
!* threshold stress or slip resistance for screw dislocation motion
forall (s = 1:ns) &
state(g,ip,el)%p(5*ns+nt+s) = &
constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerSlipSystem(s,myInstance)*&
sqrt(dot_product((state(g,ip,el)%p(1:ns)),&
constitutive_titanmod_interactionMatrix_es(1:ns,s,myInstance))+ &
dot_product((state(g,ip,el)%p(ns+1:2*ns)),&
constitutive_titanmod_interactionMatrix_ss(1:ns,s,myInstance)))
!* threshold stress or slip resistance for dislocation motion in twin
forall (t = 1:nt) &
state(g,ip,el)%p(6*ns+nt+t) = &
constitutive_titanmod_Gmod(myInstance)*constitutive_titanmod_burgersPerTwinSystem(t,myInstance)*&
(dot_product((abs(state(g,ip,el)%p(2*ns+1:2*ns+nt))),&
constitutive_titanmod_interactionMatrixTwinTwin(1:nt,t,myInstance)))
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,minusStressRatio_edge_p,StressRatio_edge_pminus1,StressRatio_screw_p, &
StressRatio_screw_pminus1, StressRatio_r,BoltzmannRatio,DotGamma0, minusStressRatio_screw_p,gdotTotal, &
screwvelocity_prefactor,twinStressRatio_p,twinminusStressRatio_p,twinStressRatio_pminus1, &
twinStressRatio_r, twinDotGamma0,BoltzmannRatioscrew
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, edge_velocity, screw_velocity,gdot_slip_edge,gdot_slip_screw
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
gdot_twin,dgdot_dtautwin,tau_twin, twinedge_velocity, twinscrew_velocity,volumefraction_pertwinsystem
!* 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)
do i=1,nt
volumefraction_pertwinsystem(i)=state(g,ip,el)%p(2*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSystem(i,myInstance)
enddo
sumf = sum(abs(volumefraction_pertwinsystem(1: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
gdot_slip_edge = 0.0_pReal
gdot_slip_screw = 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))
!*************************************************
! if(myStructure==3.and.j>3.and.j<13) then ! only for prismatic and pyr <a> systems in hex
! if(myStructure==3) then ! only for prismatic and pyr <a> systems in hex
screwvelocity_prefactor=constitutive_titanmod_debyefrequency(myInstance)* &
state(g,ip,el)%p(3*ns+nt+j)*(constitutive_titanmod_burgersPerSlipSystem(j,myInstance)/ &
constitutive_titanmod_kinkcriticallength_PerSlipSystem(j,myInstance))**2
! else
! screwvelocity_prefactor=constitutive_titanmod_v0s_PerSlipSystem(j,myInstance)
! endif
!* Stress ratio for edge
StressRatio_edge_p = ((abs(tau_slip(j)))/ &
( constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance)+state(g,ip,el)%p(4*ns+nt+j)) &
)**constitutive_titanmod_pe_PerSlipSystem(j,myInstance)
!* Stress ratio for screw ! No slip resistance for screw dislocations, only Peierls stress
StressRatio_screw_p = ((abs(tau_slip(j)))/ &
( constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance)) &
)**constitutive_titanmod_ps_PerSlipSystem(j,myInstance)
if((1.0_pReal-StressRatio_edge_p)>0.001_pReal) then
minusStressRatio_edge_p=1.0_pReal-StressRatio_edge_p
else
minusStressRatio_edge_p=0.001_pReal
endif
if((1.0_pReal-StressRatio_screw_p)>0.001_pReal) then
minusStressRatio_screw_p=1.0_pReal-StressRatio_screw_p
else
minusStressRatio_screw_p=0.001_pReal
endif
StressRatio_edge_pminus1 = ((abs(tau_slip(j)))/ &
( constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance)+state(g,ip,el)%p(4*ns+nt+j)) &
)**(constitutive_titanmod_pe_PerSlipSystem(j,myInstance)-1.0_pReal)
StressRatio_screw_pminus1 = ((abs(tau_slip(j)))/ &
( constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance)+state(g,ip,el)%p(5*ns+nt+j)) &
)**(constitutive_titanmod_ps_PerSlipSystem(j,myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_titanmod_f0_PerSlipSystem(j,myInstance)/(kB*Temperature)
!* Boltzmann ratio for screw
BoltzmannRatioscrew = constitutive_titanmod_kinkf0(myInstance)/(kB*Temperature)
edge_velocity(j) =constitutive_titanmod_v0e_PerSlipSystem(j,myInstance)*exp(-BoltzmannRatio* &
(minusStressRatio_edge_p)** &
constitutive_titanmod_qe_PerSlipSystem(j,myInstance))
screw_velocity(j) =screwvelocity_prefactor * & ! there is no v0 for screw now because it is included in the prefactor
exp(-BoltzmannRatioscrew*(minusStressRatio_screw_p)** &
constitutive_titanmod_qs_PerSlipSystem(j,myInstance))
!* Shear rates due to edge slip
gdot_slip_edge(j) = constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*(state(g,ip,el)%p(j)* &
edge_velocity(j))* sign(1.0_pReal,tau_slip(j))
!* Shear rates due to screw slip
gdot_slip_screw(j) = constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*(state(g,ip,el)%p(ns+j) * &
screw_velocity(j))* sign(1.0_pReal,tau_slip(j))
!Total shear rate
gdot_slip(j) = gdot_slip_edge(j) + gdot_slip_screw(j)
state(g,ip,el)%p(6*ns+3*nt+j)=gdot_slip(j)
state(g,ip,el)%p(7*ns+3*nt+j)=edge_velocity(j)
state(g,ip,el)%p(8*ns+3*nt+j)=screw_velocity(j)
state(g,ip,el)%p(9*ns+3*nt+j)=tau_slip(j)
state(g,ip,el)%p(10*ns+3*nt+j)=gdot_slip_edge(j)
state(g,ip,el)%p(11*ns+3*nt+j)=gdot_slip_screw(j)
state(g,ip,el)%p(12*ns+3*nt+j)=StressRatio_edge_p
state(g,ip,el)%p(13*ns+3*nt+j)=StressRatio_screw_p
!* Derivatives of shear rates
dgdot_dtauslip(j) = constitutive_titanmod_burgersPerSlipSystem(j,myInstance)*(( &
( &
( &
( &
(edge_velocity(j)*state(g,ip,el)%p(j))) * &
BoltzmannRatio*&
constitutive_titanmod_pe_PerSlipSystem(j,myInstance)* &
constitutive_titanmod_qe_PerSlipSystem(j,myInstance) &
)/ &
constitutive_titanmod_tau0e_PerSlipSystem(j,myInstance) &
)*&
StressRatio_edge_pminus1*(minusStressRatio_edge_p)** &
(constitutive_titanmod_qe_PerSlipSystem(j,myInstance)-1.0_pReal) &
) + &
( &
( &
( &
(state(g,ip,el)%p(ns+j) * screw_velocity(j)) * &
BoltzmannRatio* &
constitutive_titanmod_ps_PerSlipSystem(j,myInstance)* &
constitutive_titanmod_qs_PerSlipSystem(j,myInstance) &
)/ &
constitutive_titanmod_tau0s_PerSlipSystem(j,myInstance) &
)*&
StressRatio_screw_pminus1*(minusStressRatio_screw_p)**(constitutive_titanmod_qs_PerSlipSystem(j,myInstance)-1.0_pReal) &
) &
) !* sign(1.0_pReal,tau_slip(j))
! state(g,ip,el)%p(13*ns+3*nt+j)=dgdot_dtauslip(j)
!*************************************************
!sumf=0.0_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) = 0.0_pReal!&
! (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
!**************************************************************************************
!* Stress ratio for edge
twinStressRatio_p = ((abs(tau_twin(j)))/ &
( constitutive_titanmod_twintau0_PerTwinSystem(j,myInstance)+state(g,ip,el)%p(6*ns+nt+j)) &
)**constitutive_titanmod_twinp_PerTwinSystem(j,myInstance)
if((1.0_pReal-twinStressRatio_p)>0.001_pReal) then
twinminusStressRatio_p=1.0_pReal-twinStressRatio_p
else
twinminusStressRatio_p=0.001_pReal
endif
twinStressRatio_pminus1 = ((abs(tau_twin(j)))/ &
( constitutive_titanmod_twintau0_PerTwinSystem(j,myInstance)+state(g,ip,el)%p(6*ns+nt+j)) &
)**(constitutive_titanmod_twinp_PerTwinSystem(j,myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_titanmod_twinf0_PerTwinSystem(j,myInstance)/(kB*Temperature)
!* Initial twin shear rates
TwinDotGamma0 = &
constitutive_titanmod_twingamma0_PerTwinSystem(j,myInstance)
!* Shear rates due to twin
gdot_twin(j) =sign(1.0_pReal,tau_twin(j))*constitutive_titanmod_twingamma0_PerTwinSystem(j,myInstance)* &
exp(-BoltzmannRatio*(twinminusStressRatio_p)**constitutive_titanmod_twinq_PerTwinSystem(j,myInstance))
state(g,ip,el)%p(6*ns+2*nt+j)=gdot_twin(j)
!* Derivatives of shear rates in twin
dgdot_dtautwin(j) = ( &
( &
( &
(abs(gdot_twin(j))) * &
BoltzmannRatio*&
constitutive_titanmod_twinp_PerTwinSystem(j,myInstance)* &
constitutive_titanmod_twinq_PerTwinSystem(j,myInstance) &
)/ &
constitutive_titanmod_twintau0_PerTwinSystem(j,myInstance) &
)*&
twinStressRatio_pminus1*(twinminusStressRatio_p)** &
(constitutive_titanmod_twinq_PerTwinSystem(j,myInstance)-1.0_pReal) &
) !* sign(1.0_pReal,tau_slip(j))
!* Plastic velocity gradient for mechanical twinning
! Lp = Lp + sumf*gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,myStructure)
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,t
real(pReal) sumf,StressRatio_edge_p,minusStressRatio_edge_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,StressRatio_screw_p,minusStressRatio_screw_p, &
twinStressRatio_p,twinminusStressRatio_p,twinStressRatio_pminus1, &
twinDotGamma0
real(pReal), dimension(constitutive_titanmod_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
gdot_slip,tau_slip,DotRhoEdgeGeneration,EdgeDipDistance,DotRhoEdgeAnnihilation,DotRhoScrewAnnihilation,&
ClimbVelocity,DotRhoScrewGeneration, edge_velocity,screw_velocity
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: gdot_twin, &
tau_twin,twinedge_segment,twinscrew_segment,twinedge_velocity,twinscrew_velocity,TwinDotRhoEdgeGeneration, &
TwinDotRhoEdgeAnnihilation,TwinDotRhoScrewGeneration,TwinDotRhoScrewAnnihilation,volumefraction_pertwinsystem
!* 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)
do i=1,nt
volumefraction_pertwinsystem(i)=state(g,ip,el)%p(2*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSystem(i,myInstance)
enddo
sumf = sum(abs(volumefraction_pertwinsystem(1:nt))) ! safe for nt == 0
constitutive_titanmod_dotState = 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
!* Multiplication of edge dislocations
DotRhoEdgeGeneration(j) = (state(g,ip,el)%p(ns+j)*state(g,ip,el)%p(8*ns+3*nt+j)/state(g,ip,el)%p(3*ns+nt+j))
!* Multiplication of screw dislocations
DotRhoScrewGeneration(j) = (state(g,ip,el)%p(j)*state(g,ip,el)%p(7*ns+3*nt+j)/state(g,ip,el)%p(2*ns+nt+j))
!* Annihilation of edge dislocations
DotRhoEdgeAnnihilation(j) = -((state(g,ip,el)%p(j))**2)* &
constitutive_titanmod_capre_PerSlipSystem(j,myInstance)*state(g,ip,el)%p(7*ns+3*nt+j)/2.0_pReal
!* Annihilation of screw dislocations
DotRhoScrewAnnihilation(j) = -((state(g,ip,el)%p(ns+j))**2)* &
constitutive_titanmod_caprs_PerSlipSystem(j,myInstance)*state(g,ip,el)%p(8*ns+3*nt+j)/2.0_pReal
!* 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 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
!*************************************************************************
!This was in dislotwin - keeping it for safety
!*************************************************************************
! !* 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
!*************************************************************************
!* Resolved shear stress on twin system
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure))
!* Stress ratio for edge
twinStressRatio_p = ((abs(tau_twin(j)))/ &
( constitutive_titanmod_twintau0_PerTwinSystem(j,myInstance)+state(g,ip,el)%p(6*ns+nt+j)) &
)**(constitutive_titanmod_twinp_PerTwinSystem(j,myInstance))
if((1.0_pReal-twinStressRatio_p)>0.001_pReal) then
twinminusStressRatio_p=1.0_pReal-twinStressRatio_p
else
twinminusStressRatio_p=0.001_pReal
endif
!* Boltzmann ratio
BoltzmannRatio = constitutive_titanmod_twinf0_PerTwinSystem(j,myInstance)/(kB*Temperature)
gdot_twin(j) =constitutive_titanmod_twingamma0_PerTwinSystem(j,myInstance)*exp(-BoltzmannRatio* &
(twinminusStressRatio_p)** &
constitutive_titanmod_twinq_PerTwinSystem(j,myInstance))*sign(1.0_pReal,tau_twin(j))
constitutive_titanmod_dotState(2*ns+j)=gdot_twin(j)
enddo
enddo
!write(6,*) '#DOTSTATE#'
!write(6,*)
!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
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
real(pReal), dimension(constitutive_titanmod_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
constitutive_titanmod_postResults
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
volumefraction_pertwinsystem
!* 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)
do i=1,nt
volumefraction_pertwinsystem(i)=state(g,ip,el)%p(2*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSystem(i,myInstance)
enddo
!sumf = sum(state(g,ip,el)%p((6*ns+7*nt+1):(6*ns+8*nt))) ! safe for nt == 0
sumf = sum(abs(volumefraction_pertwinsystem(1: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 ('segment_edge')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((2*ns+nt+1):(3*ns+nt))
c = c + ns
case ('segment_screw')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((3*ns+nt+1):(4*ns+nt))
c = c + ns
case ('resistance_edge')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((4*ns+nt+1):(5*ns+nt))
c = c + ns
case ('resistance_screw')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((5*ns+nt+1):(6*ns+nt))
c = c + ns
case ('tau_slip')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((9*ns+3*nt+1):(10*ns+3*nt)))
c = c + ns
case ('gdot_slip')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((6*ns+3*nt+1):(7*ns+3*nt)))
c = c + ns
case ('velocity_edge')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((7*ns+3*nt+1):(8*ns+3*nt))
c = c + ns
case ('velocity_screw')
constitutive_titanmod_postResults(c+1:c+ns) = state(g,ip,el)%p((8*ns+3*nt+1):(9*ns+3*nt))
c = c + ns
case ('gdot_slip_edge')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((10*ns+3*nt+1):(11*ns+3*nt)))
c = c + ns
case ('gdot_slip_screw')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((11*ns+3*nt+1):(12*ns+3*nt)))
c = c + ns
case ('stressratio_edge_p')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((12*ns+3*nt+1):(13*ns+3*nt)))
c = c + ns
case ('stressratio_screw_p')
constitutive_titanmod_postResults(c+1:c+ns) = abs(state(g,ip,el)%p((13*ns+3*nt+1):(14*ns+3*nt)))
c = c + ns
case ('gdot_twin')
constitutive_titanmod_postResults(c+1:c+nt) = abs(state(g,ip,el)%p((6*ns+2*nt+1):(6*ns+3*nt)))
c = c + nt
case ('twin_fraction')
constitutive_titanmod_postResults(c+1:c+nt) = abs(volumefraction_pertwinsystem(1:nt))
c = c + nt
! 'rhoedge', &
! 'rhoscrew', &
! 'segment_edge', &
! 'segment_screw', &
! 'resistance_edge', &
! 'resistance_screw', &
! 'tau_slip', &
! 'gdot_slip', &
! 'velocity_edge', &
! 'velocity_screw', &
! 'gdot_slip_edge' &
! 'gdot_slip_screw' &
! 'StressRatio_edge_p' &
! 'StressRatio_screw_p'
end select
enddo
return
end function
END MODULE