! Copyright 2011-13 Max-Planck-Institut für Eisenforschung GmbH
!
! This file is part of DAMASK,
! the Düsseldorf Advanced MAterial Simulation Kit.
!
! DAMASK is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! DAMASK is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
!
!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @author Alankar Alankar, Max-Planck-Institut für Eisenforschung GmbH
!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief material subroutine for titanium
!--------------------------------------------------------------------------------------------------
module constitutive_titanmod
use prec, only: &
pReal, &
pInt
implicit none
private
character(len=*), parameter, public :: &
CONSTITUTIVE_TITANMOD_label = 'titanmod'
character(len=18), dimension(3), parameter, private :: &
CONSTITUTIVE_TITANMOD_listBasicSlipStates = &
['rho_edge ', 'rho_screw ', 'shear_system']
character(len=18), dimension(1), parameter, private :: &
CONSTITUTIVE_TITANMOD_listBasicTwinStates = ['gdot_twin']
character(len=19), dimension(11), parameter, private :: &
CONSTITUTIVE_TITANMOD_listDependentSlipStates = &
['segment_edge ', 'segment_screw ', &
'resistance_edge ', 'resistance_screw ', &
'tau_slip ', &
'velocity_edge ', 'velocity_screw ', &
'gdot_slip_edge ', 'gdot_slip_screw ', &
'stressratio_edge_p ', 'stressratio_screw_p' ]
character(len=18), dimension(2), parameter, private :: &
constitutive_titanmod_listDependentTwinStates = &
['twin_fraction', 'tau_twin ']
real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
integer(pInt), dimension(:), allocatable, public, protected :: &
constitutive_titanmod_sizeState, & !< total number of microstructural state variables
constitutive_titanmod_sizeDotState, & !< number of dotStates
constitutive_titanmod_sizePostResults !< cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target, public :: &
constitutive_titanmod_sizePostResult !< size of each post result output
character(len=64), dimension(:,:), allocatable, target, public :: &
constitutive_titanmod_output !< name of each post result output
integer(pInt), dimension(:), allocatable, private :: &
constitutive_titanmod_Noutput !< number of outputs per instance of this plasticity
character(len=32), dimension(:), allocatable, public, protected :: &
constitutive_titanmod_structureName !< name of the lattice structure
integer(pInt), dimension(:), allocatable, private :: &
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, private :: &
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, private :: &
constitutive_titanmod_CoverA, & !< c/a ratio for hex type lattice
constitutive_titanmod_debyefrequency, & !< Debye frequency
constitutive_titanmod_kinkf0, & !<
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, private :: &
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_shear_system0, & !< accumulated shear on each system
constitutive_titanmod_burgersPerSlipFam, & !< absolute length of burgers vector [m] for each slip family and instance
constitutive_titanmod_burgersPerSlipSys, & !< absolute length of burgers vector [m] for each slip system and instance
constitutive_titanmod_burgersPerTwinFam, & !< absolute length of burgers vector [m] for each twin family and instance
constitutive_titanmod_burgersPerTwinSys, & !< absolute length of burgers vector [m] for each twin system and instance
constitutive_titanmod_f0_PerSlipFam, & !< activation energy for glide [J] for each slip family and instance
constitutive_titanmod_f0_PerSlipSys, & !< activation energy for glide [J] for each slip system and instance
constitutive_titanmod_twinf0_PerTwinFam, & !< activation energy for glide [J] for each twin family and instance
constitutive_titanmod_twinf0_PerTwinSys, & !< activation energy for glide [J] for each twin system and instance
constitutive_titanmod_twinshearconstant_PerTwinFam, & !< activation energy for glide [J] for each twin family and instance
constitutive_titanmod_twinshearconstant_PerTwinSys, & !< activation energy for glide [J] for each twin system and instance
constitutive_titanmod_tau0e_PerSlipFam, & !< Initial yield stress for edge dislocations per slip family
constitutive_titanmod_tau0e_PerSlipSys, & !< Initial yield stress for edge dislocations per slip system
constitutive_titanmod_tau0s_PerSlipFam, & !< Initial yield stress for screw dislocations per slip family
constitutive_titanmod_tau0s_PerSlipSys, & !< Initial yield stress for screw dislocations per slip system
constitutive_titanmod_twintau0_PerTwinFam, & !< Initial yield stress for edge dislocations per twin family
constitutive_titanmod_twintau0_PerTwinSys, & !< Initial yield stress for edge dislocations per twin system
constitutive_titanmod_capre_PerSlipFam, & !< Capture radii for edge dislocations per slip family
constitutive_titanmod_capre_PerSlipSys, & !< Capture radii for edge dislocations per slip system
constitutive_titanmod_caprs_PerSlipFam, & !< Capture radii for screw dislocations per slip family
constitutive_titanmod_caprs_PerSlipSys, & !< Capture radii for screw dislocations per slip system
constitutive_titanmod_pe_PerSlipFam, & !< p-exponent in glide velocity
constitutive_titanmod_ps_PerSlipFam, & !< p-exponent in glide velocity
constitutive_titanmod_qe_PerSlipFam, & !< q-exponent in glide velocity
constitutive_titanmod_qs_PerSlipFam, & !< q-exponent in glide velocity
constitutive_titanmod_pe_PerSlipSys, & !< p-exponent in glide velocity
constitutive_titanmod_ps_PerSlipSys, & !< p-exponent in glide velocity
constitutive_titanmod_qe_PerSlipSys, & !< q-exponent in glide velocity
constitutive_titanmod_qs_PerSlipSys, & !< q-exponent in glide velocity
constitutive_titanmod_twinp_PerTwinFam, & !< p-exponent in glide velocity
constitutive_titanmod_twinq_PerTwinFam, & !< q-exponent in glide velocity
constitutive_titanmod_twinp_PerTwinSys, & !< p-exponent in glide velocity
constitutive_titanmod_twinq_PerTwinSys, & !< p-exponent in glide velocity
constitutive_titanmod_v0e_PerSlipFam, & !< edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0e_PerSlipSys, & !< screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_v0s_PerSlipFam, & !< edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_v0s_PerSlipSys, & !< screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_twingamma0_PerTwinFam, & !< edge dislocation velocity prefactor [m/s] for each family and instance
constitutive_titanmod_twingamma0_PerTwinSys, & !< screw dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_titanmod_kinkcriticallength_PerSlipFam, & !< screw dislocation mobility prefactor for kink-pairs per slip family
constitutive_titanmod_kinkcriticallength_PerSlipSys, & !< screw dislocation mobility prefactor for kink-pairs per slip system
constitutive_titanmod_twinsizePerTwinFam, & !< twin thickness [m] for each twin family and instance
constitutive_titanmod_twinsizePerTwinSys, & !< twin thickness [m] for each twin system and instance
constitutive_titanmod_CeLambdaSlipPerSlipFam, & !< Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_CeLambdaSlipPerSlipSys, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_titanmod_CsLambdaSlipPerSlipFam, & !< Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_CsLambdaSlipPerSlipSys, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_titanmod_twinLambdaSlipPerTwinFam, & !< Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_titanmod_twinLambdaSlipPerTwinSys, & !< 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, private :: &
constitutive_titanmod_Cslip_66, & !< elasticity matrix in Mandel notation for each instance
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
real(pReal), dimension(:,:,:,:), allocatable, private :: &
constitutive_titanmod_Ctwin_66 !< twin elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
constitutive_titanmod_Cslip_3333 !< elasticity matrix for each instance
real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: &
constitutive_titanmod_Ctwin_3333 !< twin elasticity matrix for each instance
public :: &
constitutive_titanmod_microstructure, &
constitutive_titanmod_stateInit, &
constitutive_titanmod_init, &
constitutive_titanmod_LpAndItsTangent, &
constitutive_titanmod_dotState, &
constitutive_titanmod_postResults, &
constitutive_titanmod_homogenizedC, &
constitutive_titanmod_aTolState
contains
!--------------------------------------------------------------------------------------------------
!> @brief module initialization
!> @details reads in material parameters, allocates arrays, and does sanity checks
!--------------------------------------------------------------------------------------------------
subroutine constitutive_titanmod_init(myFile)
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use math, only: &
math_Mandel3333to66,&
math_Voigt66to3333,&
math_mul3x3
use IO
use material
use debug, only: &
debug_level,&
debug_constitutive,&
debug_levelBasic
use lattice
implicit none
integer(pInt), intent(in) :: myFile
integer(pInt), parameter :: MAXNCHUNKS = LATTICE_maxNinteraction + 1_pInt
integer(pInt), dimension(1_pInt+2_pInt*MAXNCHUNKS) :: positions
integer(pInt), dimension(7) :: configNchunks
integer(pInt) :: &
section = 0_pInt, &
i, j, k, l, m, n, p, q, r, &
f, o, &
s, s1, s2, &
t, t1, t2, &
ns, nt, &
Nchunks_SlipSlip, Nchunks_SlipTwin, Nchunks_TwinSlip, Nchunks_TwinTwin, &
Nchunks_SlipFamilies, Nchunks_TwinFamilies, &
mySize, structID, &
maxTotalNslip,maxTotalNtwin, maxNinstance
character(len=65536) :: &
tag = '', &
line = '' ! to start initialized
write(6,'(/,a)') ' <<<+- constitutive_'//CONSTITUTIVE_TITANMOD_label//' init -+>>>'
write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
maxNinstance = int(count(phase_plasticity == CONSTITUTIVE_TITANMOD_label),pInt)
if (maxNinstance == 0_pInt) return
if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
Nchunks_SlipFamilies = lattice_maxNslipFamily
Nchunks_TwinFamilies = lattice_maxNtwinFamily
Nchunks_SlipSlip = lattice_maxNinteraction
Nchunks_SlipTwin = lattice_maxNinteraction
Nchunks_TwinSlip = lattice_maxNinteraction
Nchunks_TwinTwin = lattice_maxNinteraction
allocate(constitutive_titanmod_sizeDotState(maxNinstance))
constitutive_titanmod_sizeDotState = 0_pInt
allocate(constitutive_titanmod_sizeState(maxNinstance))
constitutive_titanmod_sizeState = 0_pInt
allocate(constitutive_titanmod_sizePostResults(maxNinstance))
constitutive_titanmod_sizePostResults = 0_pInt
allocate(constitutive_titanmod_sizePostResult(maxval(phase_Noutput),maxNinstance))
constitutive_titanmod_sizePostResult = 0_pInt
allocate(constitutive_titanmod_output(maxval(phase_Noutput),maxNinstance))
constitutive_titanmod_output = ''
allocate(constitutive_titanmod_Noutput(maxNinstance))
constitutive_titanmod_Noutput = 0_pInt
allocate(constitutive_titanmod_structureName(maxNinstance))
constitutive_titanmod_structureName = ''
allocate(constitutive_titanmod_structure(maxNinstance))
constitutive_titanmod_structure = 0_pInt
allocate(constitutive_titanmod_Nslip(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_Nslip = 0_pInt
allocate(constitutive_titanmod_Ntwin(lattice_maxNtwinFamily,maxNinstance))
constitutive_titanmod_Ntwin = 0_pInt
allocate(constitutive_titanmod_slipFamily(lattice_maxNslip,maxNinstance))
constitutive_titanmod_slipFamily = 0_pInt
allocate(constitutive_titanmod_twinFamily(lattice_maxNtwin,maxNinstance))
constitutive_titanmod_twinFamily = 0_pInt
allocate(constitutive_titanmod_slipSystemLattice(lattice_maxNslip,maxNinstance))
constitutive_titanmod_slipSystemLattice = 0_pInt
allocate(constitutive_titanmod_twinSystemLattice(lattice_maxNtwin,maxNinstance))
constitutive_titanmod_twinSystemLattice = 0_pInt
allocate(constitutive_titanmod_totalNslip(maxNinstance))
constitutive_titanmod_totalNslip = 0_pInt
allocate(constitutive_titanmod_totalNtwin(maxNinstance))
constitutive_titanmod_totalNtwin = 0_pInt
allocate(constitutive_titanmod_CoverA(maxNinstance))
constitutive_titanmod_CoverA = 0.0_pReal
allocate(constitutive_titanmod_debyefrequency(maxNinstance))
constitutive_titanmod_debyefrequency = 0.0_pReal
allocate(constitutive_titanmod_kinkf0(maxNinstance))
constitutive_titanmod_kinkf0 = 0.0_pReal
allocate(constitutive_titanmod_Gmod(maxNinstance))
constitutive_titanmod_Gmod = 0.0_pReal
allocate(constitutive_titanmod_CAtomicVolume(maxNinstance))
constitutive_titanmod_CAtomicVolume = 0.0_pReal
allocate(constitutive_titanmod_dc(maxNinstance))
constitutive_titanmod_dc = 0.0_pReal
allocate(constitutive_titanmod_twinhpconstant(maxNinstance))
constitutive_titanmod_twinhpconstant = 0.0_pReal
allocate(constitutive_titanmod_GrainSize(maxNinstance))
constitutive_titanmod_GrainSize = 0.0_pReal
allocate(constitutive_titanmod_MaxTwinFraction(maxNinstance))
constitutive_titanmod_MaxTwinFraction = 0.0_pReal
allocate(constitutive_titanmod_r(maxNinstance))
constitutive_titanmod_r = 0.0_pReal
allocate(constitutive_titanmod_CEdgeDipMinDistance(maxNinstance))
constitutive_titanmod_CEdgeDipMinDistance = 0.0_pReal
allocate(constitutive_titanmod_Cmfptwin(maxNinstance))
constitutive_titanmod_Cmfptwin = 0.0_pReal
allocate(constitutive_titanmod_Cthresholdtwin(maxNinstance))
constitutive_titanmod_Cthresholdtwin = 0.0_pReal
allocate(constitutive_titanmod_aTolRho(maxNinstance))
constitutive_titanmod_aTolRho = 0.0_pReal
allocate(constitutive_titanmod_Cslip_66(6,6,maxNinstance))
constitutive_titanmod_Cslip_66 = 0.0_pReal
allocate(constitutive_titanmod_Cslip_3333(3,3,3,3,maxNinstance))
constitutive_titanmod_Cslip_3333 = 0.0_pReal
allocate(constitutive_titanmod_rho_edge0(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_rho_edge0 = 0.0_pReal
allocate(constitutive_titanmod_rho_screw0(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_rho_screw0 = 0.0_pReal
allocate(constitutive_titanmod_shear_system0(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_shear_system0 = 0.0_pReal
allocate(constitutive_titanmod_burgersPerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_burgersPerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_burgersPerTwinFam(lattice_maxNtwinFamily,maxNinstance))
constitutive_titanmod_burgersPerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_f0_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_f0_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_tau0e_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_tau0e_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_tau0s_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_tau0s_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_capre_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_capre_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_caprs_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_caprs_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_pe_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_pe_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_ps_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_ps_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_qe_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_qe_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_qs_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_qs_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_v0e_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_v0e_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_v0s_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_v0s_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_kinkcriticallength_PerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_kinkcriticallength_PerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_twinsizePerTwinFam(lattice_maxNtwinFamily,maxNinstance))
constitutive_titanmod_twinsizePerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_CeLambdaSlipPerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_CeLambdaSlipPerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_CsLambdaSlipPerSlipFam(lattice_maxNslipFamily,maxNinstance))
constitutive_titanmod_CsLambdaSlipPerSlipFam = 0.0_pReal
allocate(constitutive_titanmod_twinf0_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twinf0_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twinshearconstant_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twinshearconstant_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twintau0_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twintau0_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twinp_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twingamma0_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twinq_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twinLambdaSlipPerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twingamma0_PerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twinp_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_twinLambdaSlipPerTwinFam(lattice_maxNTwinFamily,maxNinstance))
constitutive_titanmod_twinq_PerTwinFam = 0.0_pReal
allocate(constitutive_titanmod_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interactionSlipSlip = 0.0_pReal
allocate(constitutive_titanmod_interaction_ee(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interaction_ee = 0.0_pReal
allocate(constitutive_titanmod_interaction_ss(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interaction_ss = 0.0_pReal
allocate(constitutive_titanmod_interaction_es(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interaction_ss = 0.0_pReal
allocate(constitutive_titanmod_interactionSlipTwin(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interactionSlipTwin = 0.0_pReal
allocate(constitutive_titanmod_interactionTwinSlip(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interactionTwinSlip = 0.0_pReal
allocate(constitutive_titanmod_interactionTwinTwin(lattice_maxNinteraction,maxNinstance))
constitutive_titanmod_interactionTwinTwin = 0.0_pReal
rewind(myFile)
do while (trim(line) /= '#EOF#' .and. IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
line = IO_read(myFile)
enddo
do while (trim(line) /= '#EOF#') ! read through sections of phase part
line = IO_read(myFile)
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_pInt ! advance section counter
cycle ! skip to next line
endif
if (section > 0_pInt ) then ! do not short-circuit here (.and. with next if-statement). It's not safe in Fortran
if (trim(phase_plasticity(section)) == CONSTITUTIVE_TITANMOD_label) then ! one of my sections
i = phase_plasticityInstance(section) ! which instance of my plasticity is present phase
positions = IO_stringPos(line,MAXNCHUNKS)
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('plasticity','elasticity')
cycle
case ('(output)')
constitutive_titanmod_Noutput(i) = constitutive_titanmod_Noutput(i) + 1_pInt
constitutive_titanmod_output(constitutive_titanmod_Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('lattice_structure')
constitutive_titanmod_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
configNchunks = lattice_configNchunks(constitutive_titanmod_structureName(i))
Nchunks_SlipFamilies = configNchunks(1)
Nchunks_TwinFamilies = configNchunks(2)
Nchunks_SlipSlip = configNchunks(3)
Nchunks_SlipTwin = configNchunks(4)
Nchunks_TwinSlip = configNchunks(5)
Nchunks_TwinTwin = configNchunks(6)
case ('covera_ratio')
constitutive_titanmod_CoverA(i) = IO_floatValue(line,positions,2_pInt)
case ('c11')
constitutive_titanmod_Cslip_66(1,1,i) = IO_floatValue(line,positions,2_pInt)
case ('c12')
constitutive_titanmod_Cslip_66(1,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c13')
constitutive_titanmod_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c22')
constitutive_titanmod_Cslip_66(2,2,i) = IO_floatValue(line,positions,2_pInt)
case ('c23')
constitutive_titanmod_Cslip_66(2,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c33')
constitutive_titanmod_Cslip_66(3,3,i) = IO_floatValue(line,positions,2_pInt)
case ('c44')
constitutive_titanmod_Cslip_66(4,4,i) = IO_floatValue(line,positions,2_pInt)
case ('c55')
constitutive_titanmod_Cslip_66(5,5,i) = IO_floatValue(line,positions,2_pInt)
case ('c66')
constitutive_titanmod_Cslip_66(1,3,i) = IO_floatValue(line,positions,2_pInt)
case ('debyefrequency')
constitutive_titanmod_debyefrequency(i) = IO_floatValue(line,positions,2_pInt)
case ('kinkf0')
constitutive_titanmod_kinkf0(i) = IO_floatValue(line,positions,2_pInt)
case ('nslip')
if (positions(1) < 1_pInt + Nchunks_SlipFamilies) &
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_Nslip(j,i) = IO_intValue(line,positions,1_pInt+j)
enddo
case ('ntwin')
if (positions(1) < 1_pInt + Nchunks_TwinFamilies) &
call IO_warning(51_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_Ntwin(j,i) = IO_intValue(line,positions,1_pInt+j)
enddo
case ('rho_edge0')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_rho_edge0(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('rho_screw0')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_rho_screw0(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('slipburgers')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_burgersPerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinburgers')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_burgersPerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('f0')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_f0_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinf0')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinf0_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('tau0e')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_tau0e_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twintau0')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twintau0_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('tau0s')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_tau0s_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('capre')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_capre_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('caprs')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_caprs_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('v0e')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_v0e_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twingamma0')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twingamma0_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('v0s')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_v0s_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('kinkcriticallength')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_kinkcriticallength_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinsize')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinsizePerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('celambdaslip')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_CeLambdaSlipPerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinlambdaslip')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinlambdaslipPerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('cslambdaslip')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_CsLambdaSlipPerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('grainsize')
constitutive_titanmod_GrainSize(i) = IO_floatValue(line,positions,2_pInt)
case ('maxtwinfraction')
constitutive_titanmod_MaxTwinFraction(i) = IO_floatValue(line,positions,2_pInt)
case ('pe')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_pe_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinp')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinp_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('ps')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_ps_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('qe')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_qe_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinq')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinq_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('qs')
do j = 1_pInt, Nchunks_SlipFamilies
constitutive_titanmod_qs_PerSlipFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('twinshearconstant')
do j = 1_pInt, Nchunks_TwinFamilies
constitutive_titanmod_twinshearconstant_PerTwinFam(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('dc')
constitutive_titanmod_dc(i) = IO_floatValue(line,positions,2_pInt)
case ('twinhpconstant')
constitutive_titanmod_twinhpconstant(i) = IO_floatValue(line,positions,2_pInt)
case ('atol_rho')
constitutive_titanmod_aTolRho(i) = IO_floatValue(line,positions,2_pInt)
case ('interactionee')
do j = 1_pInt, lattice_maxNinteraction
constitutive_titanmod_interaction_ee(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interactionss')
do j = 1_pInt, lattice_maxNinteraction
constitutive_titanmod_interaction_ss(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interactiones')
do j = 1_pInt, lattice_maxNinteraction
constitutive_titanmod_interaction_es(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_slipslip','interactionslipslip')
if (positions(1) < 1_pInt + Nchunks_SlipSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_SlipSlip
constitutive_titanmod_interactionSlipSlip(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_sliptwin','interactionsliptwin')
if (positions(1) < 1_pInt + Nchunks_SlipTwin) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_SlipTwin
constitutive_titanmod_interactionSlipTwin(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_twinslip','interactiontwinslip')
if (positions(1) < 1_pInt + Nchunks_TwinSlip) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_TwinSlip
constitutive_titanmod_interactionTwinSlip(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case ('interaction_twintwin','interactiontwintwin')
if (positions(1) < 1_pInt + Nchunks_TwinTwin) &
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
do j = 1_pInt, Nchunks_TwinTwin
constitutive_titanmod_interactionTwinTwin(j,i) = IO_floatValue(line,positions,1_pInt+j)
enddo
case default
call IO_error(210_pInt,ext_msg=trim(tag)//' ('//CONSTITUTIVE_TITANMOD_label//')')
end select
endif
endif
enddo
sanityChecks: do i = 1_pInt,maxNinstance
constitutive_titanmod_structure(i) = &
lattice_initializeStructure(constitutive_titanmod_structureName(i),constitutive_titanmod_CoverA(i))
structID = constitutive_titanmod_structure(i)
if (structID < 1_pInt) call IO_error(205_pInt,el=i)
if (sum(constitutive_titanmod_Nslip(:,i)) <= 0_pInt) call IO_error(211_pInt,el=i,ext_msg='nslip (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (sum(constitutive_titanmod_Ntwin(:,i)) < 0_pInt) call IO_error(211_pInt,el=i,ext_msg='ntwin (' &
//CONSTITUTIVE_TITANMOD_label//')')
do f = 1_pInt,lattice_maxNslipFamily
if (constitutive_titanmod_Nslip(f,i) > 0_pInt) then
if (constitutive_titanmod_rho_edge0(f,i) < 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='rho_edge0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_rho_screw0(f,i) < 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='rho_screw0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_burgersPerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='slipburgers (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_f0_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='f0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_tau0e_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='tau0e (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_tau0s_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='tau0s (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_capre_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='capre (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_caprs_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='caprs (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_v0e_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='v0e (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_v0s_PerSlipFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='v0s (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_kinkcriticallength_PerSlipFam(f,i) <= 0.0_pReal) &
call IO_error(211_pInt,el=i,ext_msg='kinkCriticalLength (' &
//CONSTITUTIVE_TITANMOD_label//')')
endif
enddo
do f = 1_pInt,lattice_maxNtwinFamily
if (constitutive_titanmod_Ntwin(f,i) > 0_pInt) then
if (constitutive_titanmod_burgersPerTwinFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='twinburgers (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_twinf0_PerTwinFam(f,i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='twinf0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_twinshearconstant_PerTwinFam(f,i) <= 0.0_pReal) &
call IO_error(211_pInt,el=i,ext_msg='twinshearconstant (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_twintau0_PerTwinFam(f,i) <= 0.0_pReal)call IO_error(211_pInt,el=i,ext_msg='twintau0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_twingamma0_PerTwinFam(f,i) <= 0.0_pReal) &
call IO_error(211_pInt,el=i,ext_msg='twingamma0 (' &
//CONSTITUTIVE_TITANMOD_label//')')
endif
enddo
if (constitutive_titanmod_dc(i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='dc (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_twinhpconstant(i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='twinhpconstant (' &
//CONSTITUTIVE_TITANMOD_label//')')
if (constitutive_titanmod_aTolRho(i) <= 0.0_pReal) call IO_error(211_pInt,el=i,ext_msg='aTolRho (' &
//CONSTITUTIVE_TITANMOD_label//')')
!--------------------------------------------------------------------------------------------------
! determine total number of active slip or twin systems
constitutive_titanmod_Nslip(:,i) = min(lattice_NslipSystem(:,structID),constitutive_titanmod_Nslip(:,i))
constitutive_titanmod_Ntwin(:,i) = min(lattice_NtwinSystem(:,structID),constitutive_titanmod_Ntwin(:,i))
constitutive_titanmod_totalNslip(i) = sum(constitutive_titanmod_Nslip(:,i))
constitutive_titanmod_totalNtwin(i) = sum(constitutive_titanmod_Ntwin(:,i))
enddo sanityChecks
!--------------------------------------------------------------------------------------------------
! allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(constitutive_titanmod_totalNslip)
maxTotalNtwin = maxval(constitutive_titanmod_totalNtwin)
allocate(constitutive_titanmod_burgersPerSlipSys(maxTotalNslip, maxNinstance))
constitutive_titanmod_burgersPerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_f0_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_f0_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_tau0e_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_tau0e_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_tau0s_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_tau0s_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_capre_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_capre_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_caprs_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_caprs_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_pe_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_pe_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_ps_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_ps_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_qe_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_qe_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_qs_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_qs_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_v0e_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_v0e_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_v0s_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_v0s_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_kinkcriticallength_PerSlipSys(maxTotalNslip,maxNinstance))
constitutive_titanmod_kinkcriticallength_PerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_CeLambdaSlipPerSlipSys(maxTotalNslip, maxNinstance))
constitutive_titanmod_CeLambdaSlipPerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_CsLambdaSlipPerSlipSys(maxTotalNslip, maxNinstance))
constitutive_titanmod_CsLambdaSlipPerSlipSys = 0.0_pReal
allocate(constitutive_titanmod_burgersPerTwinSys (maxTotalNtwin,maxNinstance))
constitutive_titanmod_burgersPerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinf0_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twinf0_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinshearconstant_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twinshearconstant_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twintau0_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twintau0_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinp_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twinp_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinq_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twinq_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twingamma0_PerTwinSys(maxTotalNTwin,maxNinstance))
constitutive_titanmod_twingamma0_PerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinsizePerTwinSys(maxTotalNtwin, maxNinstance))
constitutive_titanmod_twinsizePerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_twinLambdaSlipPerTwinSys(maxTotalNtwin, maxNinstance))
constitutive_titanmod_twinLambdaSlipPerTwinSys = 0.0_pReal
allocate(constitutive_titanmod_Ctwin_66 (6,6,maxTotalNtwin,maxNinstance))
constitutive_titanmod_Ctwin_66 = 0.0_pReal
allocate(constitutive_titanmod_Ctwin_3333 (3,3,3,3,maxTotalNtwin,maxNinstance))
constitutive_titanmod_Ctwin_3333 = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrixSlipSlip(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_interactionMatrixSlipSlip = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrix_ee(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_interactionMatrix_ee = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrix_ss(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_interactionMatrix_ss = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrix_es(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_interactionMatrix_es = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrixSlipTwin(maxTotalNslip,maxTotalNtwin,maxNinstance))
constitutive_titanmod_interactionMatrixSlipTwin = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrixTwinSlip(maxTotalNtwin,maxTotalNslip,maxNinstance))
constitutive_titanmod_interactionMatrixTwinSlip = 0.0_pReal
allocate(constitutive_titanmod_interactionMatrixTwinTwin(maxTotalNtwin,maxTotalNtwin,maxNinstance))
constitutive_titanmod_interactionMatrixTwinTwin = 0.0_pReal
allocate(constitutive_titanmod_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_forestProjectionEdge = 0.0_pReal
allocate(constitutive_titanmod_forestProjectionScrew(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_titanmod_forestProjectionScrew = 0.0_pReal
allocate(constitutive_titanmod_TwinforestProjectionEdge(maxTotalNtwin,maxTotalNtwin,maxNinstance))
constitutive_titanmod_TwinforestProjectionEdge = 0.0_pReal
allocate(constitutive_titanmod_TwinforestProjectionScrew(maxTotalNtwin,maxTotalNtwin,maxNinstance))
constitutive_titanmod_TwinforestProjectionScrew = 0.0_pReal
instancesLoop: do i = 1_pInt,maxNinstance
structID = constitutive_titanmod_structure(i)
!--------------------------------------------------------------------------------------------------
! inverse lookup of slip system family
l = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily
do s = 1_pInt,constitutive_titanmod_Nslip(f,i)
l = l + 1_pInt
constitutive_titanmod_slipFamily(l,i) = f
constitutive_titanmod_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1_pInt,structID)) + s
enddo; enddo
!--------------------------------------------------------------------------------------------------
! inverse lookup of twin system family
l = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily
do t = 1_pInt,constitutive_titanmod_Ntwin(f,i)
l = l + 1_pInt
constitutive_titanmod_twinFamily(l,i) = f
constitutive_titanmod_twinSystemLattice(l,i) = sum(lattice_NtwinSystem(1:f-1_pInt,structID)) + t
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
!--------------------------------------------------------------------------------------------------
! determine size of postResults array
outputsLoop: do o = 1_pInt,constitutive_titanmod_Noutput(i)
mySize = 0_pInt
select case(constitutive_titanmod_output(o,i))
case('rhoedge', 'rhoscrew', &
'segment_edge', 'segment_screw', &
'resistance_edge', 'resistance_screw', &
'velocity_edge', 'velocity_screw', &
'tau_slip', &
'gdot_slip_edge', 'gdot_slip_screw', &
'gdot_slip', &
'stressratio_edge_p', 'stressratio_screw_p', &
'shear_system')
mySize = constitutive_titanmod_totalNslip(i)
case('twin_fraction', &
'gdot_twin', &
'tau_twin' )
mySize = constitutive_titanmod_totalNtwin(i)
case('shear_basal', 'shear_prism', 'shear_pyra', 'shear_pyrca', & ! use only if all 4 slip families in hex are considered
'rhoedge_basal', 'rhoedge_prism', 'rhoedge_pyra', 'rhoedge_pyrca', &
'rhoscrew_basal', 'rhoscrew_prism', 'rhoscrew_pyra', 'rhoscrew_pyrca', &
'shear_total')
mySize = 1_pInt
case default
call IO_error(212_pInt,ext_msg=constitutive_titanmod_output(o,i)// &
' ('//CONSTITUTIVE_TITANMOD_label//')')
end select
outputFound: if (mySize > 0_pInt) then
constitutive_titanmod_sizePostResult(o,i) = mySize
constitutive_titanmod_sizePostResults(i) = constitutive_titanmod_sizePostResults(i) + mySize
endif outputFound
enddo outputsLoop
constitutive_titanmod_Cslip_66(1:6,1:6,i) = &
lattice_symmetrizeC66(constitutive_titanmod_structureName(i),&
constitutive_titanmod_Cslip_66(1:6,1:6,i)) ! assign elasticity tensor
constitutive_titanmod_Gmod(i) = &
0.2_pReal*(constitutive_titanmod_Cslip_66(1,1,i)-constitutive_titanmod_Cslip_66(1,2,i))&
+ 0.3_pReal*constitutive_titanmod_Cslip_66(4,4,i)
constitutive_titanmod_Cslip_66(1:6,1:6,i) = &
math_Mandel3333to66(math_Voigt66to3333(constitutive_titanmod_Cslip_66(1:6,1:6,i)))
constitutive_titanmod_Cslip_3333(1:3,1:3,1:3,1:3,i) = &
math_Voigt66to3333(constitutive_titanmod_Cslip_66(1:6,1:6,i))
!--------------------------------------------------------------------------------------------------
! construction of the twin elasticity matrices
do j=1_pInt,lattice_maxNtwinFamily
do k=1_pInt,constitutive_titanmod_Ntwin(j,i)
do l=1_pInt,3_pInt ; do m=1_pInt,3_pInt ; do n=1_pInt,3_pInt ; do o=1_pInt,3_pInt
do p=1_pInt,3_pInt ; do q=1_pInt,3_pInt ; do r=1_pInt,3_pInt ; do s=1_pInt,3_pInt
constitutive_titanmod_Ctwin_3333(l,m,n,o,sum(constitutive_titanmod_Nslip(1:j-1_pInt,i))+k,i) = &
constitutive_titanmod_Ctwin_3333(l,m,n,o,sum(constitutive_titanmod_Nslip(1:j-1_pInt,i))+k,i) + &
constitutive_titanmod_Cslip_3333(p,q,r,s,i)*&
lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1_pInt,structID))+k,structID)* &
lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1_pInt,structID))+k,structID)* &
lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1_pInt,structID))+k,structID)* &
lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1_pInt,structID))+k,structID)
enddo; enddo; enddo; enddo
enddo; enddo; enddo ; enddo
constitutive_titanmod_Ctwin_66(1:6,1:6,k,i) = &
math_Mandel3333to66(constitutive_titanmod_Ctwin_3333(1:3,1:3,1:3,1:3,k,i))
enddo; enddo
!--------------------------------------------------------------------------------------------------
! Burgers vector, dislocation velocity prefactor for each slip system
do s = 1_pInt,constitutive_titanmod_totalNslip(i)
f = constitutive_titanmod_slipFamily(s,i)
constitutive_titanmod_burgersPerSlipSys(s,i) = constitutive_titanmod_burgersPerSlipFam(f,i)
constitutive_titanmod_f0_PerSlipSys(s,i) = constitutive_titanmod_f0_PerSlipFam(f,i)
constitutive_titanmod_tau0e_PerSlipSys(s,i) = constitutive_titanmod_tau0e_PerSlipFam(f,i)
constitutive_titanmod_tau0s_PerSlipSys(s,i) = constitutive_titanmod_tau0s_PerSlipFam(f,i)
constitutive_titanmod_capre_PerSlipSys(s,i) = constitutive_titanmod_capre_PerSlipFam(f,i)
constitutive_titanmod_caprs_PerSlipSys(s,i) = constitutive_titanmod_caprs_PerSlipFam(f,i)
constitutive_titanmod_v0e_PerSlipSys(s,i) = constitutive_titanmod_v0e_PerSlipFam(f,i)
constitutive_titanmod_v0s_PerSlipSys(s,i) = constitutive_titanmod_v0s_PerSlipFam(f,i)
constitutive_titanmod_kinkcriticallength_PerSlipSys(s,i) = constitutive_titanmod_kinkcriticallength_PerSlipFam(f,i)
constitutive_titanmod_pe_PerSlipSys(s,i) = constitutive_titanmod_pe_PerSlipFam(f,i)
constitutive_titanmod_ps_PerSlipSys(s,i) = constitutive_titanmod_ps_PerSlipFam(f,i)
constitutive_titanmod_qe_PerSlipSys(s,i) = constitutive_titanmod_qe_PerSlipFam(f,i)
constitutive_titanmod_qs_PerSlipSys(s,i) = constitutive_titanmod_qs_PerSlipFam(f,i)
constitutive_titanmod_CeLambdaSlipPerSlipSys(s,i) = constitutive_titanmod_CeLambdaSlipPerSlipFam(f,i)
constitutive_titanmod_CsLambdaSlipPerSlipSys(s,i) = constitutive_titanmod_CsLambdaSlipPerSlipFam(f,i)
enddo
!--------------------------------------------------------------------------------------------------
! Burgers vector, nucleation rate prefactor and twin size for each twin system
do t = 1_pInt,constitutive_titanmod_totalNtwin(i)
f = constitutive_titanmod_twinFamily(t,i)
constitutive_titanmod_burgersPerTwinSys(t,i) = constitutive_titanmod_burgersPerTwinFam(f,i)
constitutive_titanmod_twinsizePerTwinSys(t,i) = constitutive_titanmod_twinsizePerTwinFam(f,i)
constitutive_titanmod_twinf0_PerTwinSys(t,i) = constitutive_titanmod_twinf0_PerTwinFam(f,i)
constitutive_titanmod_twinshearconstant_PerTwinSys(t,i) = constitutive_titanmod_twinshearconstant_PerTwinFam(f,i)
constitutive_titanmod_twintau0_PerTwinSys(t,i) = constitutive_titanmod_twintau0_PerTwinFam(f,i)
constitutive_titanmod_twingamma0_PerTwinSys(t,i) = constitutive_titanmod_twingamma0_PerTwinFam(f,i)
constitutive_titanmod_twinp_PerTwinSys(t,i) = constitutive_titanmod_twinp_PerTwinFam(f,i)
constitutive_titanmod_twinq_PerTwinSys(t,i) = constitutive_titanmod_twinq_PerTwinFam(f,i)
constitutive_titanmod_twinLambdaSlipPerTwinSys(t,i) = constitutive_titanmod_twinLambdaSlipPerTwinFam(f,i)
enddo
!--------------------------------------------------------------------------------------------------
! Construction of interaction matrices
do s1 = 1_pInt,constitutive_titanmod_totalNslip(i)
do s2 = 1_pInt,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), &
structID),i)
constitutive_titanmod_interactionMatrix_ee(s1,s2,i) = &
constitutive_titanmod_interaction_ee(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), &
constitutive_titanmod_slipSystemLattice(s2,i), &
structID),i)
constitutive_titanmod_interactionMatrix_ss(s1,s2,i) = &
constitutive_titanmod_interaction_ss(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), &
constitutive_titanmod_slipSystemLattice(s2,i), &
structID),i)
constitutive_titanmod_interactionMatrix_es(s1,s2,i) = &
constitutive_titanmod_interaction_es(lattice_interactionSlipSlip(constitutive_titanmod_slipSystemLattice(s1,i), &
constitutive_titanmod_slipSystemLattice(s2,i), &
structID),i)
enddo; enddo
do s1 = 1_pInt,constitutive_titanmod_totalNslip(i)
do t2 = 1_pInt,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), &
structID),i)
enddo; enddo
do t1 = 1_pInt,constitutive_titanmod_totalNtwin(i)
do s2 = 1_pInt,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), &
structID),i)
enddo; enddo
do t1 = 1_pInt,constitutive_titanmod_totalNtwin(i)
do t2 = 1_pInt,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), &
structID),i)
enddo; enddo
do s1 = 1_pInt,constitutive_titanmod_totalNslip(i)
do s2 = 1_pInt,constitutive_titanmod_totalNslip(i)
!--------------------------------------------------------------------------------------------------
! calculation of forest projections for edge dislocations
constitutive_titanmod_forestProjectionEdge(s1,s2,i) = &
abs(math_mul3x3(lattice_sn(:,constitutive_titanmod_slipSystemLattice(s1,i),structID), &
lattice_st(:,constitutive_titanmod_slipSystemLattice(s2,i),structID)))
!--------------------------------------------------------------------------------------------------
! calculation of forest projections for screw dislocations
constitutive_titanmod_forestProjectionScrew(s1,s2,i) = &
abs(math_mul3x3(lattice_sn(:,constitutive_titanmod_slipSystemLattice(s1,i),structID), &
lattice_sd(:,constitutive_titanmod_slipSystemLattice(s2,i),structID)))
enddo; enddo
!--------------------------------------------------------------------------------------------------
! calculation of forest projections for edge dislocations in twin system
do t1 = 1_pInt,constitutive_titanmod_totalNtwin(i)
do t2 = 1_pInt,constitutive_titanmod_totalNtwin(i)
constitutive_titanmod_TwinforestProjectionEdge(t1,t2,i) = &
abs(math_mul3x3(lattice_tn(:,constitutive_titanmod_twinSystemLattice(t1,i),structID), &
lattice_tt(:,constitutive_titanmod_twinSystemLattice(t2,i),structID)))
!--------------------------------------------------------------------------------------------------
! calculation of forest projections for screw dislocations in twin system
constitutive_titanmod_TwinforestProjectionScrew(t1,t2,i) = &
abs(math_mul3x3(lattice_tn(:,constitutive_titanmod_twinSystemLattice(t1,i),structID), &
lattice_td(:,constitutive_titanmod_twinSystemLattice(t2,i),structID)))
enddo; enddo
enddo instancesLoop
end subroutine constitutive_titanmod_init
!--------------------------------------------------------------------------------------------------
!> @brief sets the initial microstructural state for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
pure function constitutive_titanmod_stateInit(matID)
use lattice, only: &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily
implicit none
integer(pInt), intent(in) :: matID !< number specifying the instance of the plasticity
real(pReal), dimension(constitutive_titanmod_sizeState(matID)) :: &
constitutive_titanmod_stateInit
integer(pInt) :: &
s,s0,s1, &
t,t0,t1, &
ns,nt,f
real(pReal), dimension(constitutive_titanmod_totalNslip(matID)) :: &
rho_edge0, &
rho_screw0, &
shear_system0, &
segment_edge0, &
segment_screw0, &
resistance_edge0, &
resistance_screw0
real(pReal), dimension(constitutive_titanmod_totalNtwin(matID)) :: &
twingamma_dot0, &
resistance_twin0
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables for slip
s1 = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily
s0 = s1 + 1_pInt
s1 = s0 + constitutive_titanmod_Nslip(f,matID) - 1_pInt
do s = s0,s1
rho_edge0(s) = constitutive_titanmod_rho_edge0(f,matID)
rho_screw0(s) = constitutive_titanmod_rho_screw0(f,matID)
shear_system0(s) = 0.0_pReal
enddo
enddo
!--------------------------------------------------------------------------------------------------
! initialize basic slip state variables for twin
t1 = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily
t0 = t1 + 1_pInt
t1 = t0 + constitutive_titanmod_Ntwin(f,matID) - 1_pInt
do t = t0,t1
twingamma_dot0(t)=0.0_pReal
enddo
enddo
!--------------------------------------------------------------------------------------------------
! initialize dependent slip microstructural variables
forall (s = 1_pInt:ns)
segment_edge0(s) = constitutive_titanmod_CeLambdaSlipPerSlipSys(s,matID)/ &
sqrt(dot_product((rho_edge0),constitutive_titanmod_forestProjectionEdge(1:ns,s,matID))+ &
dot_product((rho_screw0),constitutive_titanmod_forestProjectionScrew(1:ns,s,matID)))
segment_screw0(s) = constitutive_titanmod_CsLambdaSlipPerSlipSys(s,matID)/ &
sqrt(dot_product((rho_edge0),constitutive_titanmod_forestProjectionEdge(1:ns,s,matID))+ &
dot_product((rho_screw0),constitutive_titanmod_forestProjectionScrew(1:ns,s,matID)))
resistance_edge0(s) = &
constitutive_titanmod_Gmod(matID)*constitutive_titanmod_burgersPerSlipSys(s,matID)* &
sqrt(dot_product((rho_edge0),constitutive_titanmod_interactionMatrix_ee(1:ns,s,matID))+ &
dot_product((rho_screw0),constitutive_titanmod_interactionMatrix_es(1:ns,s,matID)))
resistance_screw0(s) = &
constitutive_titanmod_Gmod(matID)*constitutive_titanmod_burgersPerSlipSys(s,matID)* &
sqrt(dot_product((rho_edge0),constitutive_titanmod_interactionMatrix_es(1:ns,s,matID))+ &
dot_product((rho_screw0), constitutive_titanmod_interactionMatrix_ss(1:ns,s,matID)))
end forall
forall (t = 1_pInt:nt) &
resistance_twin0(t) = 0.0_pReal
constitutive_titanmod_stateInit = 0.0_pReal
constitutive_titanmod_stateInit(1:ns) = rho_edge0
constitutive_titanmod_stateInit(1_pInt*ns+1_pInt:2_pInt*ns) = rho_screw0
constitutive_titanmod_stateInit(2_pInt*ns+1_pInt:3_pInt*ns) = shear_system0
constitutive_titanmod_stateInit(3_pInt*ns+1_pInt:3_pInt*ns+nt) = twingamma_dot0
constitutive_titanmod_stateInit(3_pInt*ns+nt+1_pInt:4_pInt*ns+nt) = segment_edge0
constitutive_titanmod_stateInit(4_pInt*ns+nt+1_pInt:5_pInt*ns+nt) = segment_screw0
constitutive_titanmod_stateInit(5_pInt*ns+nt+1_pInt:6_pInt*ns+nt) = resistance_edge0
constitutive_titanmod_stateInit(6_pInt*ns+nt+1_pInt:7_pInt*ns+nt) = resistance_screw0
constitutive_titanmod_stateInit(7_pInt*ns+nt+1_pInt:7_pInt*ns+2_pInt*nt)=resistance_twin0
end function constitutive_titanmod_stateInit
!--------------------------------------------------------------------------------------------------
!> @brief sets the relevant state values for a given instance of this plasticity
!--------------------------------------------------------------------------------------------------
pure function constitutive_titanmod_aTolState(matID)
implicit none
integer(pInt), intent(in) :: matID !< number specifying the instance of the plasticity
real(pReal), dimension(constitutive_titanmod_sizeState(matID)) :: &
constitutive_titanmod_aTolState
constitutive_titanmod_aTolState = constitutive_titanmod_aTolRho(matID)
endfunction constitutive_titanmod_aTolState
!--------------------------------------------------------------------------------------------------
!> @brief returns the homogenized elasticity matrix
!--------------------------------------------------------------------------------------------------
pure function constitutive_titanmod_homogenizedC(state,ipc,ip,el)
use prec, only: &
p_vec
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
real(pReal), dimension(6,6) :: &
constitutive_titanmod_homogenizedC
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
volumefraction_PerTwinSys
integer(pInt) :: &
matID, &
ns, nt, &
i
real(pReal) :: &
sumf
!--------------------------------------------------------------------------------------------------
! shortened notation
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
!--------------------------------------------------------------------------------------------------
! total twin volume fraction
do i=1_pInt,nt
volumefraction_PerTwinSys(i)=state(ipc,ip,el)%p(3_pInt*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSys(i,matID)
enddo
sumf = sum(abs(volumefraction_PerTwinSys(1:nt))) ! safe for nt == 0
!--------------------------------------------------------------------------------------------------
! homogenized elasticity matrix
constitutive_titanmod_homogenizedC = (1.0_pReal-sumf)*constitutive_titanmod_Cslip_66(:,:,matID)
do i=1_pInt,nt
constitutive_titanmod_homogenizedC = &
constitutive_titanmod_homogenizedC + volumefraction_PerTwinSys(i)*constitutive_titanmod_Ctwin_66(:,:,i,matID)
enddo
end function constitutive_titanmod_homogenizedC
!--------------------------------------------------------------------------------------------------
!> @brief calculates derived quantities from state
!--------------------------------------------------------------------------------------------------
subroutine constitutive_titanmod_microstructure(temperature,state,ipc,ip,el)
use prec, only: &
p_vec
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase,&
phase_plasticityInstance
implicit none
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
real(pReal), intent(in) :: &
temperature !< temperature at IP
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state !< microstructure state
integer(pInt) :: &
matID, structID, &
ns, nt, s, t, &
i
real(pReal) :: &
sumf, &
sfe ! stacking fault energy
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
volumefraction_PerTwinSys
!--------------------------------------------------------------------------------------------------
!Shortened notation
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
structID = constitutive_titanmod_structure(matID)
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
!--------------------------------------------------------------------------------------------------
! Need to update this list
!* State: 1 : ns rho_edge
!* State: ns+1 : 2*ns rho_screw
!* State: 2*ns+1 : 3*ns shear_system
!* State: 3*ns+1 : 3*ns+nt gamma_twin
!* State: 3*ns+nt+1 : 4*ns+nt segment_edge
!* State: 4*ns+nt+1 : 5*ns+nt segment_screw
!* State: 5*ns+nt+1 : 6*ns+nt resistance_edge
!* State: 6*ns+nt+1 : 7*ns+nt resistance_screw
!* State: 7*ns+nt+1 : 7*ns+2*nt resistance_twin
!* State: 7*ns+2*nt+1 : 8*ns+2*nt velocity_edge
!* State: 8*ns+2*nt+1 : 9*ns+2*nt velocity_screw
!* State: 9*ns+2*nt+1 : 10*ns+2*nt tau_slip
!* State: 10*ns+2*nt+1 : 11*ns+2*nt gdot_slip_edge
!* State: 11*ns+2*nt+1 : 12*ns+2*nt gdot_slip_screw
!* State: 12*ns+2*nt+1 : 13*ns+2*nt StressRatio_edge_p
!* State: 13*ns+2*nt+1 : 14*ns+2*nt StressRatio_screw_p
!--------------------------------------------------------------------------------------------------
! total twin volume fraction
do i=1_pInt,nt
volumefraction_PerTwinSys(i)=state(ipc,ip,el)%p(3_pInt*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSys(i,matID)
enddo
sumf = sum(abs(volumefraction_PerTwinSys(1:nt))) ! safe for nt == 0
sfe = 0.0002_pReal*Temperature-0.0396_pReal
!--------------------------------------------------------------------------------------------------
! average segment length for edge dislocations in matrix
forall (s = 1_pInt:ns) &
state(ipc,ip,el)%p(3_pInt*ns+nt+s) = constitutive_titanmod_CeLambdaSlipPerSlipSys(s,matID)/ &
sqrt(dot_product(state(ipc,ip,el)%p(1:ns), &
constitutive_titanmod_forestProjectionEdge(1:ns,s,matID))+ &
dot_product(state(ipc,ip,el)%p(ns+1_pInt:2_pInt*ns), &
constitutive_titanmod_forestProjectionScrew(1:ns,s,matID)))
!--------------------------------------------------------------------------------------------------
! average segment length for screw dislocations in matrix
forall (s = 1_pInt:ns) &
state(ipc,ip,el)%p(4_pInt*ns+nt+s) = constitutive_titanmod_CsLambdaSlipPerSlipSys(s,matID)/ &
sqrt(dot_product(state(ipc,ip,el)%p(1:ns), &
constitutive_titanmod_forestProjectionEdge(1:ns,s,matID))+ &
dot_product(state(ipc,ip,el)%p(ns+1_pInt:2_pInt*ns), &
constitutive_titanmod_forestProjectionScrew(1:ns,s,matID)))
!--------------------------------------------------------------------------------------------------
! threshold stress or slip resistance for edge dislocation motion
forall (s = 1_pInt:ns) &
state(ipc,ip,el)%p(5_pInt*ns+nt+s) = &
constitutive_titanmod_Gmod(matID)*constitutive_titanmod_burgersPerSlipSys(s,matID)*&
sqrt(dot_product((state(ipc,ip,el)%p(1:ns)),&
constitutive_titanmod_interactionMatrix_ee(1:ns,s,matID))+ &
dot_product((state(ipc,ip,el)%p(ns+1_pInt:2_pInt*ns)),&
constitutive_titanmod_interactionMatrix_es(1:ns,s,matID)))
!--------------------------------------------------------------------------------------------------
! threshold stress or slip resistance for screw dislocation motion
forall (s = 1_pInt:ns) &
state(ipc,ip,el)%p(6_pInt*ns+nt+s) = &
constitutive_titanmod_Gmod(matID)*constitutive_titanmod_burgersPerSlipSys(s,matID)*&
sqrt(dot_product((state(ipc,ip,el)%p(1:ns)),&
constitutive_titanmod_interactionMatrix_es(1:ns,s,matID))+ &
dot_product((state(ipc,ip,el)%p(ns+1_pInt:2_pInt*ns)),&
constitutive_titanmod_interactionMatrix_ss(1:ns,s,matID)))
!--------------------------------------------------------------------------------------------------
! threshold stress or slip resistance for dislocation motion in twin
forall (t = 1_pInt:nt) &
state(ipc,ip,el)%p(7_pInt*ns+nt+t) = &
constitutive_titanmod_Gmod(matID)*constitutive_titanmod_burgersPerTwinSys(t,matID)*&
(dot_product((abs(state(ipc,ip,el)%p(2_pInt*ns+1_pInt:2_pInt*ns+nt))),&
constitutive_titanmod_interactionMatrixTwinTwin(1:nt,t,matID)))
end subroutine constitutive_titanmod_microstructure
!--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent
!--------------------------------------------------------------------------------------------------
subroutine constitutive_titanmod_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,&
temperature,state,ipc,ip,el)
use prec, only: &
p_vec
use math, only: &
math_Plain3333to99, &
math_Mandel6to33
use lattice, only: &
lattice_Sslip, &
lattice_Sslip_v, &
lattice_Stwin, &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
real(pReal), dimension(3,3), intent(out) :: &
Lp !< plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: &
dLp_dTstar99 !< derivative of Lp with respect to 2nd Piola Kirchhoff stress
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at IP
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state !< microstructure state
integer(pInt) :: &
index_myFamily, matID,structID, &
ns,nt, &
f,i,j,k,l,m,n
real(pReal) :: sumf, &
StressRatio_edge_p, minusStressRatio_edge_p, StressRatio_edge_pminus1, BoltzmannRatioedge, &
StressRatio_screw_p, minusStressRatio_screw_p, StressRatio_screw_pminus1, BoltzmannRatioscrew, &
twinStressRatio_p, twinminusStressRatio_p, twinStressRatio_pminus1, BoltzmannRatiotwin, &
twinDotGamma0, bottomstress_edge, bottomstress_screw, screwvelocity_prefactor
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
real(pReal), dimension(constitutive_titanmod_totalNslip(phase_plasticityInstance(material_phase(ipc,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_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_twin,dgdot_dtautwin,tau_twin, volumefraction_PerTwinSys
!--------------------------------------------------------------------------------------------------
! shortened notation
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
structID = constitutive_titanmod_structure(matID)
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
do i=1_pInt,nt
volumefraction_PerTwinSys(i)=state(ipc,ip,el)%p(3_pInt*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSys(i,matID)
enddo
sumf = sum(abs(volumefraction_PerTwinSys(1:nt))) ! safe for nt == 0
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar99 = 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
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,structID)) ! at which index starts my family
do i = 1_pInt,constitutive_titanmod_Nslip(f,matID) ! 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(:,1,index_myFamily+i,structID))
if(structID==3_pInt) then ! only for prismatic and pyr <a> systems in hex
screwvelocity_prefactor=constitutive_titanmod_debyefrequency(matID)* &
state(ipc,ip,el)%p(4_pInt*ns+nt+j)*(constitutive_titanmod_burgersPerSlipSys(j,matID)/ &
constitutive_titanmod_kinkcriticallength_PerSlipSys(j,matID))**2
!* Stress ratio for screw ! No slip resistance for screw dislocations, only Peierls stress
bottomstress_screw=constitutive_titanmod_tau0s_PerSlipSys(j,matID)
StressRatio_screw_p = ((abs(tau_slip(j)))/ &
( bottomstress_screw) &
)**constitutive_titanmod_ps_PerSlipSys(j,matID)
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
bottomstress_screw=constitutive_titanmod_tau0s_PerSlipSys(j,matID)
StressRatio_screw_pminus1 = ((abs(tau_slip(j)))/ &
( bottomstress_screw) &
)**(constitutive_titanmod_ps_PerSlipSys(j,matID)-1.0_pReal)
!* Boltzmann ratio for screw
BoltzmannRatioscrew = constitutive_titanmod_kinkf0(matID)/(kB*Temperature)
else ! if the structure is not hex or the slip family is basal
screwvelocity_prefactor=constitutive_titanmod_v0s_PerSlipSys(j,matID)
bottomstress_screw=constitutive_titanmod_tau0s_PerSlipSys(j,matID)+state(ipc,ip,el)%p(6*ns+nt+j)
StressRatio_screw_p = ((abs(tau_slip(j)))/( bottomstress_screw ))**constitutive_titanmod_ps_PerSlipSys(j,matID)
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_screw_pminus1 = ((abs(tau_slip(j)))/( bottomstress_screw))** &
(constitutive_titanmod_ps_PerSlipSys(j,matID)-1.0_pReal)
!* Boltzmann ratio for screw
BoltzmannRatioscrew = constitutive_titanmod_f0_PerSlipSys(j,matID)/(kB*Temperature)
endif
!* Stress ratio for edge
bottomstress_edge=constitutive_titanmod_tau0e_PerSlipSys(j,matID)+state(ipc,ip,el)%p(5*ns+nt+j)
StressRatio_edge_p = ((abs(tau_slip(j)))/ &
( bottomstress_edge) &
)**constitutive_titanmod_pe_PerSlipSys(j,matID)
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
StressRatio_edge_pminus1 = ((abs(tau_slip(j)))/( bottomstress_edge))** &
(constitutive_titanmod_pe_PerSlipSys(j,matID)-1.0_pReal)
!* Boltzmann ratio for edge. For screws it is defined above
BoltzmannRatioedge = constitutive_titanmod_f0_PerSlipSys(j,matID)/(kB*Temperature)
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_PerSlipSys(j,matID))
edge_velocity(j) =constitutive_titanmod_v0e_PerSlipSys(j,matID)*exp(-BoltzmannRatioedge* &
(minusStressRatio_edge_p)** &
constitutive_titanmod_qe_PerSlipSys(j,matID))
!* Shear rates due to edge slip
gdot_slip_edge(j) = constitutive_titanmod_burgersPerSlipSys(j,matID)*(state(ipc,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_burgersPerSlipSys(j,matID)*(state(ipc,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(ipc,ip,el)%p(7*ns+2*nt+j)=edge_velocity(j)
state(ipc,ip,el)%p(8*ns+2*nt+j)=screw_velocity(j)
state(ipc,ip,el)%p(9*ns+2*nt+j)=tau_slip(j)
state(ipc,ip,el)%p(10*ns+2*nt+j)=gdot_slip_edge(j)
state(ipc,ip,el)%p(11*ns+2*nt+j)=gdot_slip_screw(j)
state(ipc,ip,el)%p(12*ns+2*nt+j)=StressRatio_edge_p
state(ipc,ip,el)%p(13*ns+2*nt+j)=StressRatio_screw_p
!* Derivatives of shear rates
dgdot_dtauslip(j) = constitutive_titanmod_burgersPerSlipSys(j,matID)*(( &
( &
( &
( &
(edge_velocity(j)*state(ipc,ip,el)%p(j))) * &
BoltzmannRatioedge*&
constitutive_titanmod_pe_PerSlipSys(j,matID)* &
constitutive_titanmod_qe_PerSlipSys(j,matID) &
)/ &
bottomstress_edge &
)*&
StressRatio_edge_pminus1*(minusStressRatio_edge_p)** &
(constitutive_titanmod_qe_PerSlipSys(j,matID)-1.0_pReal) &
) + &
( &
( &
( &
(state(ipc,ip,el)%p(ns+j) * screw_velocity(j)) * &
BoltzmannRatioscrew* &
constitutive_titanmod_ps_PerSlipSys(j,matID)* &
constitutive_titanmod_qs_PerSlipSys(j,matID) &
)/ &
bottomstress_screw &
)*&
StressRatio_screw_pminus1*(minusStressRatio_screw_p)**(constitutive_titanmod_qs_PerSlipSys(j,matID)-1.0_pReal) &
) &
) !* sign(1.0_pReal,tau_slip(j))
!*************************************************
!sumf=0.0_pReal
!* Plastic velocity gradient for dislocation glide
Lp = Lp + (1.0_pReal - sumf)*gdot_slip(j)*lattice_Sslip(1:3,1:3,1,index_myFamily+i,structID)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*&
lattice_Sslip(k,l,1,index_myFamily+i,structID)*&
lattice_Sslip(m,n,1,index_myFamily+i,structID)
enddo
enddo slipFamiliesLoop
!* Mechanical twinning part
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
j = 0_pInt
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,structID)) ! at which index starts my family
do i = 1_pInt,constitutive_titanmod_Ntwin(f,matID) ! 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,structID))
!**************************************************************************************
!* Stress ratios
! StressRatio_r = (state(ipc,ip,el)%p(6*ns+3*nt+j)/tau_twin(j))**constitutive_titanmod_r(matID)
!* 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(matID)-sumf)*lattice_shearTwin(index_myFamily+i,structID)*&
! state(ipc,ip,el)%p(6*ns+4*nt+j)*constitutive_titanmod_Ndot0PerTwinSys(f,matID)*exp(-StressRatio_r)
! dgdot_dtautwin(j) = ((gdot_twin(j)*constitutive_titanmod_r(matID))/tau_twin(j))*StressRatio_r
! endif
!**************************************************************************************
!* Stress ratio for edge
twinStressRatio_p = ((abs(tau_twin(j)))/ &
( constitutive_titanmod_twintau0_PerTwinSys(j,matID)+state(ipc,ip,el)%p(7*ns+nt+j)) &
)**constitutive_titanmod_twinp_PerTwinSys(j,matID)
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_PerTwinSys(j,matID)+state(ipc,ip,el)%p(7*ns+nt+j)) &
)**(constitutive_titanmod_twinp_PerTwinSys(j,matID)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatiotwin = constitutive_titanmod_twinf0_PerTwinSys(j,matID)/(kB*Temperature)
!* Initial twin shear rates
TwinDotGamma0 = &
constitutive_titanmod_twingamma0_PerTwinSys(j,matID)
!* Shear rates due to twin
gdot_twin(j) =sign(1.0_pReal,tau_twin(j))*constitutive_titanmod_twingamma0_PerTwinSys(j,matID)* &
exp(-BoltzmannRatiotwin*(twinminusStressRatio_p)**constitutive_titanmod_twinq_PerTwinSys(j,matID))
!* Derivatives of shear rates in twin
dgdot_dtautwin(j) = ( &
( &
( &
(abs(gdot_twin(j))) * &
BoltzmannRatiotwin*&
constitutive_titanmod_twinp_PerTwinSys(j,matID)* &
constitutive_titanmod_twinq_PerTwinSys(j,matID) &
)/ &
constitutive_titanmod_twintau0_PerTwinSys(j,matID) &
)*&
twinStressRatio_pminus1*(twinminusStressRatio_p)** &
(constitutive_titanmod_twinq_PerTwinSys(j,matID)-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,structID)
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,structID)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = &
dLp_dTstar3333(k,l,m,n) + dgdot_dtautwin(j)*&
lattice_Stwin(k,l,index_myFamily+i,structID)*&
lattice_Stwin(m,n,index_myFamily+i,structID)
enddo
enddo twinFamiliesLoop
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
end subroutine constitutive_titanmod_LpAndItsTangent
!--------------------------------------------------------------------------------------------------
!> @brief calculates the rate of change of microstructure
!--------------------------------------------------------------------------------------------------
function constitutive_titanmod_dotState(Tstar_v,temperature,state,ipc,ip,el)
use prec, only: &
p_vec
use lattice, only: &
lattice_Stwin_v, &
lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_NslipSystem, &
lattice_NtwinSystem
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
real(pReal), dimension(6), intent(in):: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature !< temperature at integration point
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
real(pReal), dimension(constitutive_titanmod_sizeDotState(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
constitutive_titanmod_dotState
integer(pInt) :: &
index_myFamily, matID,structID, &
ns,nt,&
f,i,j
real(pReal) :: &
sumf,BoltzmannRatio, &
twinStressRatio_p,twinminusStressRatio_p
real(pReal), dimension(constitutive_titanmod_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
DotRhoEdgeGeneration, &
DotRhoEdgeAnnihilation, &
DotRhoScrewGeneration, &
DotRhoScrewAnnihilation
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
gdot_twin, &
tau_twin, &
volumefraction_PerTwinSys
!--------------------------------------------------------------------------------------------------
! shortened notation
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
structID = constitutive_titanmod_structure(matID)
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
do i=1_pInt,nt
volumefraction_PerTwinSys(i)=state(ipc,ip,el)%p(3_pInt*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSys(i,matID)
enddo
sumf = sum(abs(volumefraction_PerTwinSys(1_pInt:nt))) ! safe for nt == 0
constitutive_titanmod_dotState = 0.0_pReal
j = 0_pInt
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,structID)) ! at which index starts my family
do i = 1_pInt,constitutive_titanmod_Nslip(f,matID) ! process each (active) slip system in family
j = j+1_pInt
DotRhoEdgeGeneration(j) = & ! multiplication of edge dislocations
state(ipc,ip,el)%p(ns+j)*state(ipc,ip,el)%p(8*ns+2*nt+j)/state(ipc,ip,el)%p(4*ns+nt+j)
DotRhoScrewGeneration(j) = & ! multiplication of screw dislocations
state(ipc,ip,el)%p(j)*state(ipc,ip,el)%p(7*ns+2*nt+j)/state(ipc,ip,el)%p(3*ns+nt+j)
DotRhoEdgeAnnihilation(j) = -((state(ipc,ip,el)%p(j))**2)* & ! annihilation of edge dislocations
constitutive_titanmod_capre_PerSlipSys(j,matID)*state(ipc,ip,el)%p(7*ns+2*nt+j)*0.5_pReal
DotRhoScrewAnnihilation(j) = -((state(ipc,ip,el)%p(ns+j))**2)* & ! annihilation of screw dislocations
constitutive_titanmod_caprs_PerSlipSys(j,matID)*state(ipc,ip,el)%p(8*ns+2*nt+j)*0.5_pReal
constitutive_titanmod_dotState(j) = & ! edge dislocation density rate of change
DotRhoEdgeGeneration(j)+DotRhoEdgeAnnihilation(j)
constitutive_titanmod_dotState(ns+j) = & ! screw dislocation density rate of change
DotRhoScrewGeneration(j)+DotRhoScrewAnnihilation(j)
constitutive_titanmod_dotState(2*ns+j) = & ! sum of shear due to edge and screw
state(ipc,ip,el)%p(10*ns+2*nt+j)+state(ipc,ip,el)%p(11*ns+2*nt+j)
enddo
enddo slipFamiliesLoop
!* Twin fraction evolution
j = 0_pInt
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,structID)) ! at which index starts my family
do i = 1_pInt,constitutive_titanmod_Ntwin(f,matID) ! 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,structID))
!* Stress ratio for edge
twinStressRatio_p = ((abs(tau_twin(j)))/ &
( constitutive_titanmod_twintau0_PerTwinSys(j,matID)+state(ipc,ip,el)%p(7*ns+nt+j)) &
)**(constitutive_titanmod_twinp_PerTwinSys(j,matID))
if((1.0_pReal-twinStressRatio_p)>0.001_pReal) then
twinminusStressRatio_p=1.0_pReal-twinStressRatio_p
else
twinminusStressRatio_p=0.001_pReal
endif
BoltzmannRatio = constitutive_titanmod_twinf0_PerTwinSys(j,matID)/(kB*Temperature)
gdot_twin(j) =constitutive_titanmod_twingamma0_PerTwinSys(j,matID)*exp(-BoltzmannRatio* &
(twinminusStressRatio_p)** &
constitutive_titanmod_twinq_PerTwinSys(j,matID))*sign(1.0_pReal,tau_twin(j))
constitutive_titanmod_dotState(3*ns+j)=gdot_twin(j)
enddo
enddo twinFamiliesLoop
end function constitutive_titanmod_dotState
!--------------------------------------------------------------------------------------------------
!> @brief return array of constitutive results
!--------------------------------------------------------------------------------------------------
pure function constitutive_titanmod_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
use prec, only: &
p_vec
use mesh, only: &
mesh_NcpElems, &
mesh_maxNips
use material, only: &
homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance, &
phase_Noutput
implicit none
real(pReal), dimension(6), intent(in) :: &
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
real(pReal), intent(in) :: &
temperature, & !< temperature at integration point
dt
integer(pInt), intent(in) :: &
ipc, & !< component-ID of integration point
ip, & !< integration point
el !< element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state !< microstructure state
integer(pInt) :: &
matID, structID,&
ns,nt,&
o,i,c
real(pReal) :: sumf
real(pReal), dimension(constitutive_titanmod_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
constitutive_titanmod_postResults
real(pReal), dimension(constitutive_titanmod_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
volumefraction_PerTwinSys
!--------------------------------------------------------------------------------------------------
! shortened notation
matID = phase_plasticityInstance(material_phase(ipc,ip,el))
structID = constitutive_titanmod_structure(matID)
ns = constitutive_titanmod_totalNslip(matID)
nt = constitutive_titanmod_totalNtwin(matID)
do i=1_pInt,nt
volumefraction_PerTwinSys(i)=state(ipc,ip,el)%p(3_pInt*ns+i)/ &
constitutive_titanmod_twinshearconstant_PerTwinSys(i,matID)
enddo
sumf = sum(abs(volumefraction_PerTwinSys(1:nt))) ! safe for nt == 0
!--------------------------------------------------------------------------------------------------
! required output
c = 0_pInt
constitutive_titanmod_postResults = 0.0_pReal
do o = 1_pInt,phase_Noutput(material_phase(ipc,ip,el))
select case(constitutive_titanmod_output(o,matID))
case ('rhoedge')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(1_pInt:ns)
c = c + ns
case ('rhoscrew')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(ns+1_pInt:2_pInt*ns)
c = c + ns
case ('segment_edge')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(3_pInt*ns+nt+1_pInt:4_pInt*ns+nt)
c = c + ns
case ('segment_screw')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(4_pInt*ns+nt+1_pInt:5_pInt*ns+nt)
c = c + ns
case ('resistance_edge')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(5_pInt*ns+nt+1_pInt:6_pInt*ns+nt)
c = c + ns
case ('resistance_screw')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(6_pInt*ns+nt+1_pInt:7_pInt*ns+nt)
c = c + ns
case ('velocity_edge')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(7*ns+2*nt+1:8*ns+2*nt)
c = c + ns
case ('velocity_screw')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = state(ipc,ip,el)%p(8*ns+2*nt+1:9*ns+2*nt)
c = c + ns
case ('tau_slip')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(9*ns+2*nt+1:10*ns+2*nt))
c = c + ns
case ('gdot_slip_edge')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(10*ns+2*nt+1:11*ns+2*nt))
c = c + ns
case ('gdot_slip_screw')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(11*ns+2*nt+1:12*ns+2*nt))
c = c + ns
case ('gdot_slip')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(10*ns+2*nt+1:11*ns+2*nt)) + &
abs(state(ipc,ip,el)%p(11*ns+2*nt+1:12*ns+2*nt))
c = c + ns
case ('stressratio_edge_p')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(12*ns+2*nt+1:13*ns+2*nt))
c = c + ns
case ('stressratio_screw_p')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(13*ns+2*nt+1:14*ns+2*nt))
c = c + ns
case ('shear_system')
constitutive_titanmod_postResults(c+1_pInt:c+ns) = abs(state(ipc,ip,el)%p(2*ns+1:3*ns))
c = c + ns
case ('shear_basal')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(abs(state(ipc,ip,el)%p(2*ns+1:2*ns+3)))
c = c + 1_pInt
case ('shear_prism')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(abs(state(ipc,ip,el)%p(2*ns+4:2*ns+6)))
c = c + 1_pInt
case ('shear_pyra')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(abs(state(ipc,ip,el)%p(2*ns+7:2*ns+12)))
c = c + 1_pInt
case ('shear_pyrca')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(abs(state(ipc,ip,el)%p(2*ns+13:2*ns+24)))
c = c + 1_pInt
case ('rhoedge_basal')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(1:3))
c = c + 1_pInt
case ('rhoedge_prism')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(4:6))
c = c + 1_pInt
case ('rhoedge_pyra')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(7:12))
c = c + 1_pInt
case ('rhoedge_pyrca')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(13:24))
c = c + 1_pInt
case ('rhoscrew_basal')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(ns+1:ns+3))
c = c + 1_pInt
case ('rhoscrew_prism')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(ns+4:ns+6))
c = c + 1_pInt
case ('rhoscrew_pyra')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(ns+7:ns+12))
c = c + 1_pInt
case ('rhoscrew_pyrca')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(state(ipc,ip,el)%p(ns+13:ns+24))
c = c + 1_pInt
case ('shear_total')
constitutive_titanmod_postResults(c+1_pInt:c+1_pInt) = sum(abs(state(ipc,ip,el)%p(2*ns+1:3*ns)))
c = c + 1_pInt
case ('twin_fraction')
constitutive_titanmod_postResults(c+1_pInt:c+nt) = abs(volumefraction_PerTwinSys(1:nt))
c = c + nt
end select
enddo
end function constitutive_titanmod_postResults
end module constitutive_titanmod