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DAMASK_EICMD/code/constitutive_dislotwin.f90

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! Copyright 2011 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/>.
!
!##############################################################
!* $Id$
!************************************
!* Module: CONSTITUTIVE *
!************************************
MODULE constitutive_dislotwin
!* Include other modules
use prec, only: pReal,pInt
implicit none
!* Lists of states and physical parameters
character(len=*), parameter :: constitutive_dislotwin_label = 'dislotwin'
character(len=18), dimension(2), parameter:: constitutive_dislotwin_listBasicSlipStates = (/'rhoEdge ', &
'rhoEdgeDip'/)
character(len=18), dimension(1), parameter:: constitutive_dislotwin_listBasicTwinStates = (/'twinFraction'/)
character(len=18), dimension(4), parameter:: constitutive_dislotwin_listDependentSlipStates =(/'invLambdaSlip ', &
'invLambdaSlipTwin', &
'meanFreePathSlip ', &
'tauSlipThreshold '/)
character(len=18), dimension(4), parameter:: constitutive_dislotwin_listDependentTwinStates =(/'invLambdaTwin ', &
'meanFreePathTwin', &
'tauTwinThreshold', &
'twinVolume '/)
real(pReal), parameter :: kB = 1.38e-23_pReal ! Boltzmann constant in J/Kelvin
!* Definition of global variables
integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_sizeDotState, & ! number of dotStates
constitutive_dislotwin_sizeState, & ! total number of microstructural state variables
constitutive_dislotwin_sizePostResults ! cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target :: constitutive_dislotwin_sizePostResult ! size of each post result output
character(len=64), dimension(:,:), allocatable, target :: constitutive_dislotwin_output ! name of each post result output
integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_Noutput ! number of outputs per instance of this plasticity
character(len=32), dimension(:), allocatable :: constitutive_dislotwin_structureName ! name of the lattice structure
integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_structure, & ! number representing the kind of lattice structure
constitutive_dislotwin_totalNslip, & ! total number of active slip systems for each instance
constitutive_dislotwin_totalNtwin ! total number of active twin systems for each instance
integer(pInt), dimension(:,:), allocatable :: constitutive_dislotwin_Nslip, & ! number of active slip systems for each family and instance
constitutive_dislotwin_Ntwin, & ! number of active twin systems for each family and instance
constitutive_dislotwin_slipFamily, & ! lookup table relating active slip system to slip family for each instance
constitutive_dislotwin_twinFamily, & ! lookup table relating active twin system to twin family for each instance
constitutive_dislotwin_slipSystemLattice, & ! lookup table relating active slip system index to lattice slip system index for each instance
constitutive_dislotwin_twinSystemLattice ! lookup table relating active twin system index to lattice twin system index for each instance
real(pReal), dimension(:), allocatable :: constitutive_dislotwin_CoverA, & ! c/a ratio for hex type lattice
constitutive_dislotwin_C11, & ! C11 element in elasticity matrix
constitutive_dislotwin_C12, & ! C12 element in elasticity matrix
constitutive_dislotwin_C13, & ! C13 element in elasticity matrix
constitutive_dislotwin_C33, & ! C33 element in elasticity matrix
constitutive_dislotwin_C44, & ! C44 element in elasticity matrix
constitutive_dislotwin_Gmod, & ! shear modulus
constitutive_dislotwin_CAtomicVolume, & ! atomic volume in Bugers vector unit
constitutive_dislotwin_D0, & ! prefactor for self-diffusion coefficient
constitutive_dislotwin_Qsd, & ! activation energy for dislocation climb
constitutive_dislotwin_GrainSize, & ! grain size
constitutive_dislotwin_p, & ! p-exponent in glide velocity
constitutive_dislotwin_q, & ! q-exponent in glide velocity
constitutive_dislotwin_MaxTwinFraction, & ! maximum allowed total twin volume fraction
constitutive_dislotwin_r, & ! r-exponent in twin nucleation rate
constitutive_dislotwin_CEdgeDipMinDistance, & !
constitutive_dislotwin_Cmfptwin, & !
constitutive_dislotwin_Cthresholdtwin, & !
constitutive_dislotwin_SolidSolutionStrength, & ! Strength due to elements in solid solution
constitutive_dislotwin_L0, & ! Length of twin nuclei in Burgers vectors
constitutive_dislotwin_sbResistance, & ! FIXED (for now) value for shearband resistance (might become an internal state variable at some point)
constitutive_dislotwin_sbVelocity, & ! FIXED (for now) value for shearband velocity_0
constitutive_dislotwin_sbQedge, & ! FIXED (for now) value for shearband systems Qedge
constitutive_dislotwin_SFE_0K, & ! stacking fault energy at zero K
constitutive_dislotwin_dSFE_dT, & ! temperature dependance of stacking fault energy
constitutive_dislotwin_aTolRho ! absolute tolerance for integration of dislocation density
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_Cslip_66 ! elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_66 ! twin elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_dislotwin_Cslip_3333 ! elasticity matrix for each instance
real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_3333 ! twin elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable :: constitutive_dislotwin_rhoEdge0, & ! initial edge dislocation density per slip system for each family and instance
constitutive_dislotwin_rhoEdgeDip0, & ! initial edge dipole density per slip system for each family and instance
constitutive_dislotwin_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each slip family and instance
constitutive_dislotwin_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
constitutive_dislotwin_burgersPerTwinFamily, & ! absolute length of burgers vector [m] for each twin family and instance
constitutive_dislotwin_burgersPerTwinSystem, & ! absolute length of burgers vector [m] for each twin system and instance
constitutive_dislotwin_QedgePerSlipFamily, & ! activation energy for glide [J] for each slip family and instance
constitutive_dislotwin_QedgePerSlipSystem, & ! activation energy for glide [J] for each slip system and instance
constitutive_dislotwin_v0PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_dislotwin_v0PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_dislotwin_Ndot0PerTwinFamily, & ! twin nucleation rate [1/m³s] for each twin family and instance
constitutive_dislotwin_Ndot0PerTwinSystem, & ! twin nucleation rate [1/m³s] for each twin system and instance
constitutive_dislotwin_twinsizePerTwinFamily, & ! twin thickness [m] for each twin family and instance
constitutive_dislotwin_twinsizePerTwinSystem, & ! twin thickness [m] for each twin system and instance
constitutive_dislotwin_CLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance
constitutive_dislotwin_CLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance
constitutive_dislotwin_interactionSlipSlip, & ! coefficients for slip-slip interaction for each interaction type and instance
constitutive_dislotwin_interactionSlipTwin, & ! coefficients for slip-twin interaction for each interaction type and instance
constitutive_dislotwin_interactionTwinSlip, & ! coefficients for twin-slip interaction for each interaction type and instance
constitutive_dislotwin_interactionTwinTwin ! coefficients for twin-twin interaction for each interaction type and instance
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_interactionMatrixSlipSlip, & ! interaction matrix of the different slip systems for each instance
constitutive_dislotwin_interactionMatrixSlipTwin, & ! interaction matrix of slip systems with twin systems for each instance
constitutive_dislotwin_interactionMatrixTwinSlip, & ! interaction matrix of twin systems with slip systems for each instance
constitutive_dislotwin_interactionMatrixTwinTwin, & ! interaction matrix of the different twin systems for each instance
constitutive_dislotwin_forestProjectionEdge ! matrix of forest projections of edge dislocations for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_dislotwin_sbSv
CONTAINS
!****************************************
!* - constitutive_dislotwin_init
!* - constitutive_dislotwin_stateInit
!* - constitutive_dislotwin_relevantState
!* - constitutive_dislotwin_homogenizedC
!* - constitutive_dislotwin_microstructure
!* - constitutive_dislotwin_LpAndItsTangent
!* - constitutive_dislotwin_dotState
!* - constitutive_dislotwin_deltaState
!* - constitutive_dislotwin_dotTemperature
!* - constitutive_dislotwin_postResults
!****************************************
subroutine constitutive_dislotwin_init(file)
!**************************************
!* Module initialization *
!**************************************
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
use prec, only: pInt,pReal
use math, only: math_Mandel3333to66,math_Voigt66to3333,math_mul3x3
use mesh, only: mesh_maxNips, mesh_NcpElems
use IO
use material
use lattice
!* Input variables
integer(pInt), intent(in) :: file
!* Local variables
integer(pInt), parameter :: maxNchunks = 21_pInt
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) :: section, maxNinstance,mySize,myStructure,maxTotalNslip,maxTotalNtwin,&
f,i,j,k,l,m,n,o,p,q,r,s,s1,s2,t1,t2,ns,nt
character(len=64) tag
character(len=1024) line
!$OMP CRITICAL (write2out)
write(6,*)
write(6,*) '<<<+- constitutive_',trim(constitutive_dislotwin_label),' init -+>>>'
write(6,*) '$Id$'
#include "compilation_info.f90"
!$OMP END CRITICAL (write2out)
maxNinstance = int(count(phase_plasticity == constitutive_dislotwin_label),pInt)
if (maxNinstance == 0_pInt) return
!* Space allocation for global variables
allocate(constitutive_dislotwin_sizeDotState(maxNinstance))
constitutive_dislotwin_sizeDotState = 0_pInt
allocate(constitutive_dislotwin_sizeState(maxNinstance))
constitutive_dislotwin_sizeState = 0_pInt
allocate(constitutive_dislotwin_sizePostResults(maxNinstance))
constitutive_dislotwin_sizePostResults = 0_pInt
allocate(constitutive_dislotwin_sizePostResult(maxval(phase_Noutput),maxNinstance))
constitutive_dislotwin_sizePostResult = 0_pInt
allocate(constitutive_dislotwin_output(maxval(phase_Noutput),maxNinstance))
constitutive_dislotwin_output = ''
allocate(constitutive_dislotwin_Noutput(maxNinstance))
constitutive_dislotwin_Noutput = 0_pInt
allocate(constitutive_dislotwin_structureName(maxNinstance))
constitutive_dislotwin_structureName = ''
allocate(constitutive_dislotwin_structure(maxNinstance))
constitutive_dislotwin_structure = 0_pInt
allocate(constitutive_dislotwin_Nslip(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_Nslip = 0_pInt
allocate(constitutive_dislotwin_Ntwin(lattice_maxNtwinFamily,maxNinstance))
constitutive_dislotwin_Ntwin = 0_pInt
allocate(constitutive_dislotwin_slipFamily(lattice_maxNslip,maxNinstance))
constitutive_dislotwin_slipFamily = 0_pInt
allocate(constitutive_dislotwin_twinFamily(lattice_maxNtwin,maxNinstance))
constitutive_dislotwin_twinFamily = 0_pInt
allocate(constitutive_dislotwin_slipSystemLattice(lattice_maxNslip,maxNinstance))
constitutive_dislotwin_slipSystemLattice = 0_pInt
allocate(constitutive_dislotwin_twinSystemLattice(lattice_maxNtwin,maxNinstance))
constitutive_dislotwin_twinSystemLattice = 0_pInt
allocate(constitutive_dislotwin_totalNslip(maxNinstance))
constitutive_dislotwin_totalNslip = 0_pInt
allocate(constitutive_dislotwin_totalNtwin(maxNinstance))
constitutive_dislotwin_totalNtwin = 0_pInt
allocate(constitutive_dislotwin_CoverA(maxNinstance))
constitutive_dislotwin_CoverA = 0.0_pReal
allocate(constitutive_dislotwin_C11(maxNinstance))
constitutive_dislotwin_C11 = 0.0_pReal
allocate(constitutive_dislotwin_C12(maxNinstance))
constitutive_dislotwin_C12 = 0.0_pReal
allocate(constitutive_dislotwin_C13(maxNinstance))
constitutive_dislotwin_C13 = 0.0_pReal
allocate(constitutive_dislotwin_C33(maxNinstance))
constitutive_dislotwin_C33 = 0.0_pReal
allocate(constitutive_dislotwin_C44(maxNinstance))
constitutive_dislotwin_C44 = 0.0_pReal
allocate(constitutive_dislotwin_Gmod(maxNinstance))
constitutive_dislotwin_Gmod = 0.0_pReal
allocate(constitutive_dislotwin_CAtomicVolume(maxNinstance))
constitutive_dislotwin_CAtomicVolume = 0.0_pReal
allocate(constitutive_dislotwin_D0(maxNinstance))
constitutive_dislotwin_D0 = 0.0_pReal
allocate(constitutive_dislotwin_Qsd(maxNinstance))
constitutive_dislotwin_Qsd = 0.0_pReal
allocate(constitutive_dislotwin_GrainSize(maxNinstance))
constitutive_dislotwin_GrainSize = 0.0_pReal
allocate(constitutive_dislotwin_p(maxNinstance))
constitutive_dislotwin_p = 0.0_pReal
allocate(constitutive_dislotwin_q(maxNinstance))
constitutive_dislotwin_q = 0.0_pReal
allocate(constitutive_dislotwin_MaxTwinFraction(maxNinstance))
constitutive_dislotwin_MaxTwinFraction = 0.0_pReal
allocate(constitutive_dislotwin_r(maxNinstance))
constitutive_dislotwin_r = 0.0_pReal
allocate(constitutive_dislotwin_CEdgeDipMinDistance(maxNinstance))
constitutive_dislotwin_CEdgeDipMinDistance = 0.0_pReal
allocate(constitutive_dislotwin_Cmfptwin(maxNinstance))
constitutive_dislotwin_Cmfptwin = 0.0_pReal
allocate(constitutive_dislotwin_Cthresholdtwin(maxNinstance))
constitutive_dislotwin_Cthresholdtwin = 0.0_pReal
allocate(constitutive_dislotwin_SolidSolutionStrength(maxNinstance))
constitutive_dislotwin_SolidSolutionStrength = 0.0_pReal
allocate(constitutive_dislotwin_L0(maxNinstance))
constitutive_dislotwin_L0 = 0.0_pReal
allocate(constitutive_dislotwin_aTolRho(maxNinstance))
constitutive_dislotwin_aTolRho = 0.0_pReal
allocate(constitutive_dislotwin_Cslip_66(6,6,maxNinstance))
constitutive_dislotwin_Cslip_66 = 0.0_pReal
allocate(constitutive_dislotwin_Cslip_3333(3,3,3,3,maxNinstance))
constitutive_dislotwin_Cslip_3333 = 0.0_pReal
allocate(constitutive_dislotwin_sbResistance(maxNinstance))
constitutive_dislotwin_sbResistance = 0.0_pReal
allocate(constitutive_dislotwin_sbVelocity(maxNinstance))
constitutive_dislotwin_sbVelocity = 0.0_pReal
allocate(constitutive_dislotwin_sbQedge(maxNinstance))
constitutive_dislotwin_sbQedge = 0.0_pReal
allocate(constitutive_dislotwin_SFE_0K(maxNinstance))
constitutive_dislotwin_SFE_0K = 0.0_pReal
allocate(constitutive_dislotwin_dSFE_dT(maxNinstance))
constitutive_dislotwin_dSFE_dT = 0.0_pReal
allocate(constitutive_dislotwin_rhoEdge0(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_rhoEdge0 = 0.0_pReal
allocate(constitutive_dislotwin_rhoEdgeDip0(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_rhoEdgeDip0 = 0.0_pReal
allocate(constitutive_dislotwin_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_burgersPerSlipFamily = 0.0_pReal
allocate(constitutive_dislotwin_burgersPerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
constitutive_dislotwin_burgersPerTwinFamily = 0.0_pReal
allocate(constitutive_dislotwin_QedgePerSlipFamily(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_QedgePerSlipFamily = 0.0_pReal
allocate(constitutive_dislotwin_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_v0PerSlipFamily = 0.0_pReal
allocate(constitutive_dislotwin_Ndot0PerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
constitutive_dislotwin_Ndot0PerTwinFamily = 0.0_pReal
allocate(constitutive_dislotwin_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
constitutive_dislotwin_twinsizePerTwinFamily = 0.0_pReal
allocate(constitutive_dislotwin_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
constitutive_dislotwin_CLambdaSlipPerSlipFamily = 0.0_pReal
allocate(constitutive_dislotwin_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
constitutive_dislotwin_interactionSlipSlip = 0.0_pReal
allocate(constitutive_dislotwin_interactionSlipTwin(lattice_maxNinteraction,maxNinstance))
constitutive_dislotwin_interactionSlipTwin = 0.0_pReal
allocate(constitutive_dislotwin_interactionTwinSlip(lattice_maxNinteraction,maxNinstance))
constitutive_dislotwin_interactionTwinSlip = 0.0_pReal
allocate(constitutive_dislotwin_interactionTwinTwin(lattice_maxNinteraction,maxNinstance))
constitutive_dislotwin_interactionTwinTwin = 0.0_pReal
allocate(constitutive_dislotwin_sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems))
constitutive_dislotwin_sbSv = 0.0_pReal
!* Readout data from material.config file
rewind(file)
line = ''
section = 0_pInt
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_pInt ! advance section counter
cycle
endif
if (section > 0_pInt .and. phase_plasticity(section) == constitutive_dislotwin_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_dislotwin_Noutput(i) = constitutive_dislotwin_Noutput(i) + 1_pInt
constitutive_dislotwin_output(constitutive_dislotwin_Noutput(i),i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('lattice_structure')
constitutive_dislotwin_structureName(i) = IO_lc(IO_stringValue(line,positions,2_pInt))
case ('covera_ratio')
constitutive_dislotwin_CoverA(i) = IO_floatValue(line,positions,2_pInt)
case ('c11')
constitutive_dislotwin_C11(i) = IO_floatValue(line,positions,2_pInt)
case ('c12')
constitutive_dislotwin_C12(i) = IO_floatValue(line,positions,2_pInt)
case ('c13')
constitutive_dislotwin_C13(i) = IO_floatValue(line,positions,2_pInt)
case ('c33')
constitutive_dislotwin_C33(i) = IO_floatValue(line,positions,2_pInt)
case ('c44')
constitutive_dislotwin_C44(i) = IO_floatValue(line,positions,2_pInt)
case ('nslip')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_Nslip(j,i) = IO_intValue(line,positions,1_pInt+j)
case ('ntwin')
forall (j = 1_pInt:lattice_maxNtwinFamily) &
constitutive_dislotwin_Ntwin(j,i) = IO_intValue(line,positions,1_pInt+j)
case ('rhoedge0')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_rhoEdge0(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('rhoedgedip0')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_rhoEdgeDip0(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('slipburgers')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('twinburgers')
forall (j = 1_pInt:lattice_maxNtwinFamily) &
constitutive_dislotwin_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('qedge')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_QedgePerSlipFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('v0')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_v0PerSlipFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('ndot0')
forall (j = 1_pInt:lattice_maxNtwinFamily) &
constitutive_dislotwin_Ndot0PerTwinFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('twinsize')
forall (j = 1_pInt:lattice_maxNtwinFamily) &
constitutive_dislotwin_twinsizePerTwinFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('clambdaslip')
forall (j = 1_pInt:lattice_maxNslipFamily) &
constitutive_dislotwin_CLambdaSlipPerSlipFamily(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('grainsize')
constitutive_dislotwin_GrainSize(i) = IO_floatValue(line,positions,2_pInt)
case ('maxtwinfraction')
constitutive_dislotwin_MaxTwinFraction(i) = IO_floatValue(line,positions,2_pInt)
case ('pexponent')
constitutive_dislotwin_p(i) = IO_floatValue(line,positions,2_pInt)
case ('qexponent')
constitutive_dislotwin_q(i) = IO_floatValue(line,positions,2_pInt)
case ('rexponent')
constitutive_dislotwin_r(i) = IO_floatValue(line,positions,2_pInt)
case ('d0')
constitutive_dislotwin_D0(i) = IO_floatValue(line,positions,2_pInt)
case ('qsd')
constitutive_dislotwin_Qsd(i) = IO_floatValue(line,positions,2_pInt)
case ('atol_rho')
constitutive_dislotwin_aTolRho(i) = IO_floatValue(line,positions,2_pInt)
case ('cmfptwin')
constitutive_dislotwin_Cmfptwin(i) = IO_floatValue(line,positions,2_pInt)
case ('cthresholdtwin')
constitutive_dislotwin_Cthresholdtwin(i) = IO_floatValue(line,positions,2_pInt)
case ('solidsolutionstrength')
constitutive_dislotwin_SolidSolutionStrength(i) = IO_floatValue(line,positions,2_pInt)
case ('l0')
constitutive_dislotwin_L0(i) = IO_floatValue(line,positions,2_pInt)
case ('cedgedipmindistance')
constitutive_dislotwin_CEdgeDipMinDistance(i) = IO_floatValue(line,positions,2_pInt)
case ('catomicvolume')
constitutive_dislotwin_CAtomicVolume(i) = IO_floatValue(line,positions,2_pInt)
case ('interactionslipslip')
forall (j = 1_pInt:lattice_maxNinteraction) &
constitutive_dislotwin_interactionSlipSlip(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('interactionsliptwin')
forall (j = 1_pInt:lattice_maxNinteraction) &
constitutive_dislotwin_interactionSlipTwin(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('interactiontwinslip')
forall (j = 1_pInt:lattice_maxNinteraction) &
constitutive_dislotwin_interactionTwinSlip(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('interactiontwintwin')
forall (j = 1_pInt:lattice_maxNinteraction) &
constitutive_dislotwin_interactionTwinTwin(j,i) = IO_floatValue(line,positions,1_pInt+j)
case ('sfe_0k')
constitutive_dislotwin_SFE_0K(i) = IO_floatValue(line,positions,2_pInt)
case ('dsfe_dt')
constitutive_dislotwin_dSFE_dT(i) = IO_floatValue(line,positions,2_pInt)
case ('shearbandresistance')
constitutive_dislotwin_sbResistance(i) = IO_floatValue(line,positions,2_pInt)
case ('shearbandvelocity')
constitutive_dislotwin_sbVelocity(i) = IO_floatValue(line,positions,2_pInt)
case ('qedgepersbsystem')
constitutive_dislotwin_sbQedge(i) = IO_floatValue(line,positions,2_pInt)
case default
call IO_error(240_pInt,ext_msg=tag)
end select
endif
enddo
100 do i = 1_pInt,maxNinstance
constitutive_dislotwin_structure(i) = &
lattice_initializeStructure(constitutive_dislotwin_structureName(i),constitutive_dislotwin_CoverA(i))
myStructure = constitutive_dislotwin_structure(i)
!* Sanity checks
if (myStructure < 1_pInt .or. myStructure > 3_pInt) call IO_error(205_pInt,e=i)
if (sum(constitutive_dislotwin_Nslip(:,i)) <= 0_pInt) call IO_error(241_pInt,e=i,ext_msg='nslip')
if (sum(constitutive_dislotwin_Ntwin(:,i)) < 0_pInt) call IO_error(241_pInt,e=i,ext_msg='ntwin')
do f = 1_pInt,lattice_maxNslipFamily
if (constitutive_dislotwin_Nslip(f,i) > 0_pInt) then
if (constitutive_dislotwin_rhoEdge0(f,i) < 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='rhoEdge0')
if (constitutive_dislotwin_rhoEdgeDip0(f,i) < 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='rhoEdgeDip0')
if (constitutive_dislotwin_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='slipburgers')
if (constitutive_dislotwin_v0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='v0')
endif
enddo
do f = 1_pInt,lattice_maxNtwinFamily
if (constitutive_dislotwin_Ntwin(f,i) > 0_pInt) then
if (constitutive_dislotwin_burgersPerTwinFamily(f,i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='twinburgers')
if (constitutive_dislotwin_Ndot0PerTwinFamily(f,i) < 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='ndot0')
endif
enddo
if (constitutive_dislotwin_CAtomicVolume(i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='cAtomicVolume')
if (constitutive_dislotwin_D0(i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='D0')
if (constitutive_dislotwin_Qsd(i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='Qsd')
if (constitutive_dislotwin_aTolRho(i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='aTolRho')
if (constitutive_dislotwin_sbResistance(i) <= 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='sbResistance')
if (constitutive_dislotwin_sbVelocity(i) < 0.0_pReal) call IO_error(241_pInt,e=i,ext_msg='sbVelocity')
if (constitutive_dislotwin_SFE_0K(i) == 0.0_pReal .AND. &
constitutive_dislotwin_dSFE_dT(i) == 0.0_pReal) call IO_error(243_pInt,e=i)
!* Determine total number of active slip or twin systems
constitutive_dislotwin_Nslip(:,i) = min(lattice_NslipSystem(:,myStructure),constitutive_dislotwin_Nslip(:,i))
constitutive_dislotwin_Ntwin(:,i) = min(lattice_NtwinSystem(:,myStructure),constitutive_dislotwin_Ntwin(:,i))
constitutive_dislotwin_totalNslip(i) = sum(constitutive_dislotwin_Nslip(:,i))
constitutive_dislotwin_totalNtwin(i) = sum(constitutive_dislotwin_Ntwin(:,i))
enddo
!* Allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(constitutive_dislotwin_totalNslip)
maxTotalNtwin = maxval(constitutive_dislotwin_totalNtwin)
allocate(constitutive_dislotwin_burgersPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_dislotwin_burgersPerSlipSystem = 0.0_pReal
allocate(constitutive_dislotwin_burgersPerTwinSystem(maxTotalNtwin, maxNinstance))
constitutive_dislotwin_burgersPerTwinSystem= 0.0_pReal
allocate(constitutive_dislotwin_QedgePerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_dislotwin_QedgePerSlipSystem = 0.0_pReal
allocate(constitutive_dislotwin_v0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_dislotwin_v0PerSlipSystem = 0.0_pReal
allocate(constitutive_dislotwin_Ndot0PerTwinSystem(maxTotalNtwin, maxNinstance))
constitutive_dislotwin_Ndot0PerTwinSystem = 0.0_pReal
allocate(constitutive_dislotwin_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance))
constitutive_dislotwin_twinsizePerTwinSystem = 0.0_pReal
allocate(constitutive_dislotwin_CLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_dislotwin_CLambdaSlipPerSlipSystem = 0.0_pReal
allocate(constitutive_dislotwin_interactionMatrixSlipSlip(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_dislotwin_interactionMatrixSlipSlip = 0.0_pReal
allocate(constitutive_dislotwin_interactionMatrixSlipTwin(maxTotalNslip,maxTotalNtwin,maxNinstance))
constitutive_dislotwin_interactionMatrixSlipTwin = 0.0_pReal
allocate(constitutive_dislotwin_interactionMatrixTwinSlip(maxTotalNtwin,maxTotalNslip,maxNinstance))
constitutive_dislotwin_interactionMatrixTwinSlip = 0.0_pReal
allocate(constitutive_dislotwin_interactionMatrixTwinTwin(maxTotalNtwin,maxTotalNtwin,maxNinstance))
constitutive_dislotwin_interactionMatrixTwinTwin = 0.0_pReal
allocate(constitutive_dislotwin_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance))
constitutive_dislotwin_forestProjectionEdge = 0.0_pReal
allocate(constitutive_dislotwin_Ctwin_66(6,6,maxTotalNtwin,maxNinstance))
constitutive_dislotwin_Ctwin_66 = 0.0_pReal
allocate(constitutive_dislotwin_Ctwin_3333(3,3,3,3,maxTotalNtwin,maxNinstance))
constitutive_dislotwin_Ctwin_3333 = 0.0_pReal
do i = 1_pInt,maxNinstance
myStructure = constitutive_dislotwin_structure(i)
!* Inverse lookup of my slip system family
l = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily
do k = 1_pInt,constitutive_dislotwin_Nslip(f,i)
l = l + 1_pInt
constitutive_dislotwin_slipFamily(l,i) = f
constitutive_dislotwin_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) + k
enddo; enddo
!* Inverse lookup of my twin system family
l = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily
do k = 1_pInt,constitutive_dislotwin_Ntwin(f,i)
l = l + 1_pInt
constitutive_dislotwin_twinFamily(l,i) = f
constitutive_dislotwin_twinSystemLattice(l,i) = sum(lattice_NtwinSystem(1:f-1_pInt,myStructure)) + k
enddo; enddo
!* Determine size of state array
ns = constitutive_dislotwin_totalNslip(i)
nt = constitutive_dislotwin_totalNtwin(i)
constitutive_dislotwin_sizeDotState(i) =int(size(constitutive_dislotwin_listBasicSlipStates),pInt)*ns&
+int(size(constitutive_dislotwin_listBasicTwinStates),pInt)*nt
constitutive_dislotwin_sizeState(i) = constitutive_dislotwin_sizeDotState(i)&
+ int(size(constitutive_dislotwin_listDependentSlipStates),pInt)*ns&
+ int(size(constitutive_dislotwin_listDependentTwinStates),pInt)*nt
!* Determine size of postResults array
do o = 1_pInt,constitutive_dislotwin_Noutput(i)
select case(constitutive_dislotwin_output(o,i))
case('edge_density', &
'dipole_density', &
'shear_rate_slip', &
'mfp_slip', &
'resolved_stress_slip', &
'threshold_stress_slip', &
'edge_dipole_distance', &
'stress_exponent' &
)
mySize = constitutive_dislotwin_totalNslip(i)
case('twin_fraction', &
'shear_rate_twin', &
'mfp_twin', &
'resolved_stress_twin', &
'threshold_stress_twin' &
)
mySize = constitutive_dislotwin_totalNtwin(i)
case('resolved_stress_shearband', &
'shear_rate_shearband' &
)
mySize = 6_pInt
case('schmid_factor_shearband')
mySize = 6_pInt
case('sb_eigenvalues')
mySize = 3_pInt
case('sb_eigenvectors')
mySize = 9_pInt
case default
call IO_error(242_pInt,ext_msg=constitutive_dislotwin_output(o,i))
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_dislotwin_sizePostResult(o,i) = mySize
constitutive_dislotwin_sizePostResults(i) = constitutive_dislotwin_sizePostResults(i) + mySize
endif
enddo
!* Elasticity matrix and shear modulus according to material.config
select case (myStructure)
case(1_pInt:2_pInt) ! cubic(s)
forall(k=1_pInt:3_pInt)
forall(j=1_pInt:3_pInt) &
constitutive_dislotwin_Cslip_66(k,j,i) = constitutive_dislotwin_C12(i)
constitutive_dislotwin_Cslip_66(k,k,i) = constitutive_dislotwin_C11(i)
constitutive_dislotwin_Cslip_66(k+3_pInt,k+3_pInt,i) = constitutive_dislotwin_C44(i)
end forall
case(3_pInt:) ! all hex
constitutive_dislotwin_Cslip_66(1,1,i) = constitutive_dislotwin_C11(i)
constitutive_dislotwin_Cslip_66(2,2,i) = constitutive_dislotwin_C11(i)
constitutive_dislotwin_Cslip_66(3,3,i) = constitutive_dislotwin_C33(i)
constitutive_dislotwin_Cslip_66(1,2,i) = constitutive_dislotwin_C12(i)
constitutive_dislotwin_Cslip_66(2,1,i) = constitutive_dislotwin_C12(i)
constitutive_dislotwin_Cslip_66(1,3,i) = constitutive_dislotwin_C13(i)
constitutive_dislotwin_Cslip_66(3,1,i) = constitutive_dislotwin_C13(i)
constitutive_dislotwin_Cslip_66(2,3,i) = constitutive_dislotwin_C13(i)
constitutive_dislotwin_Cslip_66(3,2,i) = constitutive_dislotwin_C13(i)
constitutive_dislotwin_Cslip_66(4,4,i) = constitutive_dislotwin_C44(i)
constitutive_dislotwin_Cslip_66(5,5,i) = constitutive_dislotwin_C44(i)
constitutive_dislotwin_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_dislotwin_C11(i)-constitutive_dislotwin_C12(i))
end select
constitutive_dislotwin_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_dislotwin_Cslip_66(:,:,i)))
constitutive_dislotwin_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_dislotwin_Cslip_66(:,:,i))
constitutive_dislotwin_Gmod(i) = &
0.2_pReal*(constitutive_dislotwin_C11(i)-constitutive_dislotwin_C12(i))+0.3_pReal*constitutive_dislotwin_C44(i)
!* Construction of the twin elasticity matrices
do j=1_pInt,lattice_maxNtwinFamily
do k=1_pInt,constitutive_dislotwin_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_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1_pInt,i))+k,i) = &
constitutive_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1_pInt,i))+k,i) + &
constitutive_dislotwin_Cslip_3333(p,q,r,s,i)*&
lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1_pInt,myStructure))+k,myStructure)* &
lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1_pInt,myStructure))+k,myStructure)* &
lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1_pInt,myStructure))+k,myStructure)* &
lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1_pInt,myStructure))+k,myStructure)
enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo
constitutive_dislotwin_Ctwin_66(:,:,k,i) = math_Mandel3333to66(constitutive_dislotwin_Ctwin_3333(:,:,:,:,k,i))
enddo
enddo
!* Burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system
do s = 1_pInt,constitutive_dislotwin_totalNslip(i)
f = constitutive_dislotwin_slipFamily(s,i)
constitutive_dislotwin_burgersPerSlipSystem(s,i) = constitutive_dislotwin_burgersPerSlipFamily(f,i)
constitutive_dislotwin_QedgePerSlipSystem(s,i) = constitutive_dislotwin_QedgePerSlipFamily(f,i)
constitutive_dislotwin_v0PerSlipSystem(s,i) = constitutive_dislotwin_v0PerSlipFamily(f,i)
constitutive_dislotwin_CLambdaSlipPerSlipSystem(s,i) = constitutive_dislotwin_CLambdaSlipPerSlipFamily(f,i)
enddo
!* Burgers vector, nucleation rate prefactor and twin size for each twin system
do s = 1_pInt,constitutive_dislotwin_totalNtwin(i)
f = constitutive_dislotwin_twinFamily(s,i)
constitutive_dislotwin_burgersPerTwinSystem(s,i) = constitutive_dislotwin_burgersPerTwinFamily(f,i)
constitutive_dislotwin_Ndot0PerTwinSystem(s,i) = constitutive_dislotwin_Ndot0PerTwinFamily(f,i)
constitutive_dislotwin_twinsizePerTwinSystem(s,i) = constitutive_dislotwin_twinsizePerTwinFamily(f,i)
enddo
!* Construction of interaction matrices
do s1 = 1_pInt,constitutive_dislotwin_totalNslip(i)
do s2 = 1_pInt,constitutive_dislotwin_totalNslip(i)
constitutive_dislotwin_interactionMatrixSlipSlip(s1,s2,i) = &
constitutive_dislotwin_interactionSlipSlip(lattice_interactionSlipSlip(constitutive_dislotwin_slipSystemLattice(s1,i), &
constitutive_dislotwin_slipSystemLattice(s2,i), &
myStructure),i)
enddo; enddo
do s1 = 1_pInt,constitutive_dislotwin_totalNslip(i)
do t2 = 1_pInt,constitutive_dislotwin_totalNtwin(i)
constitutive_dislotwin_interactionMatrixSlipTwin(s1,t2,i) = &
constitutive_dislotwin_interactionSlipTwin(&
lattice_interactionSlipTwin(constitutive_dislotwin_slipSystemLattice(s1,i), &
constitutive_dislotwin_twinSystemLattice(t2,i),myStructure),i)
enddo; enddo
do t1 = 1_pInt,constitutive_dislotwin_totalNtwin(i)
do s2 = 1_pInt,constitutive_dislotwin_totalNslip(i)
constitutive_dislotwin_interactionMatrixTwinSlip(t1,s2,i) = &
constitutive_dislotwin_interactionTwinSlip(lattice_interactionTwinSlip(&
constitutive_dislotwin_twinSystemLattice(t1,i), &
constitutive_dislotwin_slipSystemLattice(s2,i), myStructure),i)
enddo; enddo
do t1 = 1_pInt,constitutive_dislotwin_totalNtwin(i)
do t2 = 1_pInt,constitutive_dislotwin_totalNtwin(i)
constitutive_dislotwin_interactionMatrixTwinTwin(t1,t2,i) = &
constitutive_dislotwin_interactionTwinTwin(&
lattice_interactionTwinTwin(constitutive_dislotwin_twinSystemLattice(t1,i), &
constitutive_dislotwin_twinSystemLattice(t2,i), myStructure),i)
enddo; enddo
!* Calculation of forest projections for edge dislocations
do s1 = 1_pInt,constitutive_dislotwin_totalNslip(i)
do s2 = 1_pInt,constitutive_dislotwin_totalNslip(i)
constitutive_dislotwin_forestProjectionEdge(s1,s2,i) = &
abs(math_mul3x3(lattice_sn(:,constitutive_dislotwin_slipSystemLattice(s1,i),myStructure), &
lattice_st(:,constitutive_dislotwin_slipSystemLattice(s2,i),myStructure)))
enddo; enddo
enddo
return
end subroutine
function constitutive_dislotwin_stateInit(myInstance)
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
use prec, only: pReal,pInt
use math, only: pi
use lattice, only: lattice_maxNslipFamily
implicit none
!* Input-Output variables
integer(pInt) :: myInstance
real(pReal), dimension(constitutive_dislotwin_sizeState(myInstance)) :: constitutive_dislotwin_stateInit
!* Local variables
integer(pInt) s0,s1,s,t,f,ns,nt
real(pReal), dimension(constitutive_dislotwin_totalNslip(myInstance)) :: rhoEdge0, &
rhoEdgeDip0, &
invLambdaSlip0, &
MeanFreePathSlip0, &
tauSlipThreshold0
real(pReal), dimension(constitutive_dislotwin_totalNtwin(myInstance)) :: MeanFreePathTwin0,TwinVolume0
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
constitutive_dislotwin_stateInit = 0.0_pReal
!* Initialize basic slip state variables
s1 = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily
s0 = s1 + 1_pInt
s1 = s0 + constitutive_dislotwin_Nslip(f,myInstance) - 1_pInt
do s = s0,s1
rhoEdge0(s) = constitutive_dislotwin_rhoEdge0(f,myInstance)
rhoEdgeDip0(s) = constitutive_dislotwin_rhoEdgeDip0(f,myInstance)
enddo
enddo
constitutive_dislotwin_stateInit(1:ns) = rhoEdge0
constitutive_dislotwin_stateInit(ns+1:2_pInt*ns) = rhoEdgeDip0
!* Initialize dependent slip microstructural variables
forall (s = 1_pInt:ns) &
invLambdaSlip0(s) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislotwin_forestProjectionEdge(1:ns,s,myInstance)))/ &
constitutive_dislotwin_CLambdaSlipPerSlipSystem(s,myInstance)
constitutive_dislotwin_stateInit(2_pInt*ns+nt+1_pInt:3_pInt*ns+nt) = invLambdaSlip0
forall (s = 1_pInt:ns) &
MeanFreePathSlip0(s) = &
constitutive_dislotwin_GrainSize(myInstance)/(1.0_pReal+invLambdaSlip0(s)*constitutive_dislotwin_GrainSize(myInstance))
constitutive_dislotwin_stateInit(4_pInt*ns+2_pInt*nt+1:5_pInt*ns+2_pInt*nt) = MeanFreePathSlip0
forall (s = 1_pInt:ns) &
tauSlipThreshold0(s) = constitutive_dislotwin_SolidSolutionStrength(myInstance)+ &
constitutive_dislotwin_Gmod(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(s,myInstance)* &
sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislotwin_interactionMatrixSlipSlip(1:ns,s,myInstance)))
constitutive_dislotwin_stateInit(5_pInt*ns+3_pInt*nt+1:6_pInt*ns+3_pInt*nt) = tauSlipThreshold0
!* Initialize dependent twin microstructural variables
forall (t = 1_pInt:nt) &
MeanFreePathTwin0(t) = constitutive_dislotwin_GrainSize(myInstance)
constitutive_dislotwin_stateInit(5_pInt*ns+2_pInt*nt+1_pInt:5_pInt*ns+3_pInt*nt) = MeanFreePathTwin0
forall (t = 1_pInt:nt) &
TwinVolume0(t) = &
(pi/6.0_pReal)*constitutive_dislotwin_twinsizePerTwinSystem(t,myInstance)*MeanFreePathTwin0(t)**(2.0_pReal)
constitutive_dislotwin_stateInit(6_pInt*ns+4_pInt*nt+1_pInt:6_pInt*ns+5_pInt*nt) = TwinVolume0
!write(6,*) '#STATEINIT#'
!write(6,*)
!write(6,'(a,/,4(3(f30.20,1x)/))') 'RhoEdge',rhoEdge0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'RhoEdgedip',rhoEdgeDip0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'invLambdaSlip',invLambdaSlip0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'MeanFreePathSlip',MeanFreePathSlip0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'tauSlipThreshold', tauSlipThreshold0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'MeanFreePathTwin', MeanFreePathTwin0
!write(6,'(a,/,4(3(f30.20,1x)/))') 'TwinVolume', TwinVolume0
return
end function
pure function constitutive_dislotwin_aTolState(myInstance)
!*********************************************************************
!* absolute state tolerance *
!*********************************************************************
use prec, only: pReal, pInt
implicit none
!* Input-Output variables
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(constitutive_dislotwin_sizeState(myInstance)) :: constitutive_dislotwin_aTolState
constitutive_dislotwin_aTolState = constitutive_dislotwin_aTolRho(myInstance)
return
endfunction
pure function constitutive_dislotwin_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_plasticityInstance
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_dislotwin_homogenizedC
!* Local variables
integer(pInt) myInstance,ns,nt,i
real(pReal) sumf
!* Shortened notation
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
!* Total twin volume fraction
sumf = sum(state(g,ip,el)%p((2_pInt*ns+1_pInt):(2_pInt*ns+nt))) ! safe for nt == 0
!* Homogenized elasticity matrix
constitutive_dislotwin_homogenizedC = (1.0_pReal-sumf)*constitutive_dislotwin_Cslip_66(:,:,myInstance)
do i=1_pInt,nt
constitutive_dislotwin_homogenizedC = &
constitutive_dislotwin_homogenizedC + state(g,ip,el)%p(2_pInt*ns+i)*constitutive_dislotwin_Ctwin_66(:,:,i,myInstance)
enddo
return
end function
subroutine constitutive_dislotwin_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_plasticityInstance
!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
real(pReal) sumf,sfe
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(g,ip,el)))) :: fOverStacksize
!* Shortened notation
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_dislotwin_structure(myInstance)
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
!* State: 1 : ns rho_edge
!* State: ns+1 : 2*ns rho_dipole
!* State: 2*ns+1 : 2*ns+nt f
!* State: 2*ns+nt+1 : 3*ns+nt 1/lambda_slip
!* State: 3*ns+nt+1 : 4*ns+nt 1/lambda_sliptwin
!* State: 4*ns+nt+1 : 4*ns+2*nt 1/lambda_twin
!* State: 4*ns+2*nt+1 : 5*ns+2*nt mfp_slip
!* State: 5*ns+2*nt+1 : 5*ns+3*nt mfp_twin
!* State: 5*ns+3*nt+1 : 6*ns+3*nt threshold_stress_slip
!* State: 6*ns+3*nt+1 : 6*ns+4*nt threshold_stress_twin
!* State: 6*ns+4*nt+1 : 6*ns+5*nt twin volume
!* Total twin volume fraction
sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0
!* Stacking fault energy
sfe = constitutive_dislotwin_SFE_0K(myInstance) + &
constitutive_dislotwin_dSFE_dT(myInstance) * Temperature
!* rescaled twin volume fraction for topology
forall (t = 1_pInt:nt) &
fOverStacksize(t) = &
state(g,ip,el)%p(2_pInt*ns+t)/constitutive_dislotwin_twinsizePerTwinSystem(t,myInstance)
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
forall (s = 1_pInt:ns) &
state(g,ip,el)%p(2_pInt*ns+nt+s) = &
sqrt(dot_product((state(g,ip,el)%p(1:ns)+state(g,ip,el)%p(ns+1_pInt:2_pInt*ns)),&
constitutive_dislotwin_forestProjectionEdge(1:ns,s,myInstance)))/ &
constitutive_dislotwin_CLambdaSlipPerSlipSystem(s,myInstance)
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
!$OMP CRITICAL (evilmatmul)
state(g,ip,el)%p((3_pInt*ns+nt+1_pInt):(4_pInt*ns+nt)) = 0.0_pReal
if (nt > 0_pInt) &
state(g,ip,el)%p((3_pInt*ns+nt+1):(4_pInt*ns+nt)) = &
matmul(constitutive_dislotwin_interactionMatrixSlipTwin(1:ns,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
!$OMP END CRITICAL (evilmatmul)
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!$OMP CRITICAL (evilmatmul)
if (nt > 0_pInt) &
state(g,ip,el)%p((4_pInt*ns+nt+1_pInt):(4_pInt*ns+2_pInt*nt)) = &
matmul(constitutive_dislotwin_interactionMatrixTwinTwin(1:nt,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
!$OMP END CRITICAL (evilmatmul)
!* mean free path between 2 obstacles seen by a moving dislocation
do s = 1_pInt,ns
if (nt > 0_pInt) then
state(g,ip,el)%p(4_pInt*ns+2_pInt*nt+s) = &
constitutive_dislotwin_GrainSize(myInstance)/(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*&
(state(g,ip,el)%p(2_pInt*ns+nt+s)+state(g,ip,el)%p(3_pInt*ns+nt+s)))
else
state(g,ip,el)%p(4_pInt*ns+s) = &
constitutive_dislotwin_GrainSize(myInstance)/&
(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*(state(g,ip,el)%p(2_pInt*ns+s)))
endif
enddo
!* mean free path between 2 obstacles seen by a growing twin
forall (t = 1_pInt:nt) &
state(g,ip,el)%p(5_pInt*ns+2_pInt*nt+t) = &
(constitutive_dislotwin_Cmfptwin(myInstance)*constitutive_dislotwin_GrainSize(myInstance))/&
(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*state(g,ip,el)%p(4_pInt*ns+nt+t))
!* threshold stress for dislocation motion
forall (s = 1_pInt:ns) &
state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+s) = constitutive_dislotwin_SolidSolutionStrength(myInstance)+ &
constitutive_dislotwin_Gmod(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(s,myInstance)*&
sqrt(dot_product((state(g,ip,el)%p(1:ns)+state(g,ip,el)%p(ns+1_pInt:2_pInt*ns)),&
constitutive_dislotwin_interactionMatrixSlipSlip(1:ns,s,myInstance)))
!* threshold stress for growing twin
forall (t = 1_pInt:nt) &
state(g,ip,el)%p(6_pInt*ns+3_pInt*nt+t) = &
constitutive_dislotwin_Cthresholdtwin(myInstance)*&
(sfe/(3.0_pReal*constitutive_dislotwin_burgersPerTwinSystem(t,myInstance))+&
3.0_pReal*constitutive_dislotwin_burgersPerTwinSystem(t,myInstance)*constitutive_dislotwin_Gmod(myInstance)/&
(constitutive_dislotwin_L0(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(t,myInstance)))
!* final twin volume after growth
forall (t = 1_pInt:nt) &
state(g,ip,el)%p(6_pInt*ns+4_pInt*nt+t) = &
(pi/6.0_pReal)*constitutive_dislotwin_twinsizePerTwinSystem(t,myInstance)*state(g,ip,el)%p(5*ns+2*nt+t)**(2.0_pReal)
!if ((ip==1).and.(el==1)) then
! write(6,*) '#MICROSTRUCTURE#'
! write(6,*)
! write(6,'(a,/,4(3(f10.4,1x)/))') 'rhoEdge',state(g,ip,el)%p(1:ns)/1e9
! write(6,'(a,/,4(3(f10.4,1x)/))') 'rhoEdgeDip',state(g,ip,el)%p(ns+1:2*ns)/1e9
! write(6,'(a,/,4(3(f10.4,1x)/))') 'Fraction',state(g,ip,el)%p(2*ns+1:2*ns+nt)
!endif
return
end subroutine
subroutine constitutive_dislotwin_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, math_Mandel6to33, math_Mandel33to6, &
math_spectralDecompositionSym33, math_tensorproduct, math_symmetric33,math_mul33x3
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase,phase_plasticityInstance
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_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
gdot_slip,dgdot_dtauslip,tau_slip
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
gdot_twin,dgdot_dtautwin,tau_twin
real(pReal), dimension(6) :: gdot_sb,dgdot_dtausb,tau_sb
real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix
real(pReal), dimension(3) :: eigValues, sb_s, sb_m
real(pReal), dimension(3,6), parameter :: &
sb_sComposition = &
reshape(real([&
1, 0, 1, &
1, 0,-1, &
1, 1, 0, &
1,-1, 0, &
0, 1, 1, &
0, 1,-1 &
],pReal),[ 3,6]), &
sb_mComposition = &
reshape(real([&
1, 0,-1, &
1, 0,+1, &
1,-1, 0, &
1, 1, 0, &
0, 1,-1, &
0, 1, 1 &
],pReal),[ 3,6])
logical error
!* Shortened notation
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_dislotwin_structure(myInstance)
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
!* Total twin volume fraction
sumf = sum(state(g,ip,el)%p((2_pInt*ns+1_pInt):(2_pInt*ns+nt))) ! safe for nt == 0
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar = 0.0_pReal
!* Dislocation glide part
gdot_slip = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j+1_pInt
!* Calculation of Lp
!* Resolved shear stress on slip system
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_p = (abs(tau_slip(j))/state(g,ip,el)%p(5*ns+3*nt+j))**constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau_slip(j))/state(g,ip,el)%p(5*ns+3*nt+j))**(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(f,myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)*&
constitutive_dislotwin_v0PerSlipSystem(f,myInstance)
!* Shear rates due to slip
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_dislotwin_q(myInstance))*&
sign(1.0_pReal,tau_slip(j))
!* Derivatives of shear rates
dgdot_dtauslip(j) = &
((abs(gdot_slip(j))*BoltzmannRatio*&
constitutive_dislotwin_p(myInstance)*constitutive_dislotwin_q(myInstance))/state(g,ip,el)%p(5*ns+3*nt+j))*&
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislotwin_q(myInstance)-1.0_pReal)
!* Plastic velocity gradient for dislocation glide
Lp = Lp + (1.0_pReal - sumf)*gdot_slip(j)*lattice_Sslip(:,:,index_myFamily+i,myStructure)
!* Calculation of the tangent of Lp
forall (k=1_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,index_myFamily+i,myStructure)*&
lattice_Sslip(m,n,index_myFamily+i,myStructure)
enddo
enddo
!* Shear banding (shearband) part
if(constitutive_dislotwin_sbVelocity(myInstance) /= 0.0_pReal) then
gdot_sb = 0.0_pReal
dgdot_dtausb = 0.0_pReal
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
do j = 1_pInt,6_pInt
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j))
sb_m = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_mComposition(1:3,j))
sb_Smatrix = math_tensorproduct(sb_s,sb_m)
constitutive_dislotwin_sbSv(1:6,j,g,ip,el) = math_Mandel33to6(math_symmetric33(sb_Smatrix))
!* Calculation of Lp
!* Resolved shear stress on shear banding system
tau_sb(j) = dot_product(Tstar_v,constitutive_dislotwin_sbSv(1:6,j,g,ip,el))
! if (debug_selectiveDebugger .and. g==debug_g .and. ip==debug_i .and. el==debug_e) then
! write(6,'(a,3(i3,1x),a,i1,a,e10.3)') '### TAU SHEARBAND at g ip el ',g,ip,el,' on family ',j,' : ',tau
! endif
!* Stress ratios
StressRatio_p = (abs(tau_sb(j))/constitutive_dislotwin_sbResistance(myInstance))**constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau_sb(j))/constitutive_dislotwin_sbResistance(myInstance))&
**(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_sbQedge(myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = constitutive_dislotwin_sbVelocity(myInstance)
!* Shear rates due to shearband
gdot_sb(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislotwin_q(myInstance))*&
sign(1.0_pReal,tau_sb(j))
!* Derivatives of shear rates
dgdot_dtausb(j) = &
((abs(gdot_sb(j))*BoltzmannRatio*&
constitutive_dislotwin_p(myInstance)*constitutive_dislotwin_q(myInstance))/constitutive_dislotwin_sbResistance(myInstance))*&
StressRatio_pminus1*(1_pInt-StressRatio_p)**(constitutive_dislotwin_q(myInstance)-1.0_pReal)
!* Plastic velocity gradient for shear banding
Lp = Lp + gdot_sb(j)*sb_Smatrix
!* 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_dtausb(j)*&
sb_Smatrix(k,l)*&
sb_Smatrix(m,n)
enddo
end if
!* Mechanical twinning part
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all slip families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_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_dislotwin_r(myInstance)
!* Shear rates and their derivatives due to twin
if ( tau_twin(j) > 0.0_pReal ) then
gdot_twin(j) = &
(constitutive_dislotwin_MaxTwinFraction(myInstance)-sumf)*lattice_shearTwin(index_myFamily+i,myStructure)*&
state(g,ip,el)%p(6*ns+4*nt+j)*constitutive_dislotwin_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r)
dgdot_dtautwin(j) = ((gdot_twin(j)*constitutive_dislotwin_r(myInstance))/tau_twin(j))*StressRatio_r
endif
!* Plastic velocity gradient for mechanical twinning
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,myStructure)
!* Calculation of the tangent of Lp
forall (k=1_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,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(e20.8,1x),/))') 'state',state(1,1,1)%p
! write(6,'(a,/,3(3(f10.4,1x)/))') 'Lp',Lp
! write(6,'(a,/,9(9(f10.4,1x)/))') 'dLp_dTstar',dLp_dTstar
!endif
return
end subroutine
function constitutive_dislotwin_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_plasticityInstance
use lattice, only: lattice_Sslip_v, lattice_Stwin_v, &
lattice_maxNslipFamily,lattice_maxNtwinFamily, &
lattice_NslipSystem,lattice_NtwinSystem
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_dislotwin_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_dislotwin_dotState
!* Local variables
integer(pInt) MyInstance,MyStructure,ns,nt,f,i,j,index_myFamily
real(pReal) sumf,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r
real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
gdot_slip,tau_slip,DotRhoMultiplication,EdgeDipDistance,DotRhoEdgeEdgeAnnihilation,DotRhoEdgeDipAnnihilation,&
ClimbVelocity,DotRhoEdgeDipClimb,DotRhoDipFormation
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tau_twin
!* Shortened notation
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
MyStructure = constitutive_dislotwin_structure(myInstance)
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
!* Total twin volume fraction
sumf = sum(state(g,ip,el)%p((2_pInt*ns+1_pInt):(2_pInt*ns+nt))) ! safe for nt == 0
constitutive_dislotwin_dotState = 0.0_pReal
!* Dislocation density evolution
gdot_slip = 0.0_pReal
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,MyStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j+1_pInt
!* Resolved shear stress on slip system
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_p = (abs(tau_slip(j))/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau_slip(j))/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(f,myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)*&
constitutive_dislotwin_v0PerSlipSystem(f,myInstance)
!* Shear rates due to slip
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislotwin_q(myInstance))*&
sign(1.0_pReal,tau_slip(j))
!* Multiplication
DotRhoMultiplication(j) = abs(gdot_slip(j))/&
(constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)*state(g,ip,el)%p(4*ns+2*nt+j))
!* Dipole formation
EdgeDipMinDistance = &
constitutive_dislotwin_CEdgeDipMinDistance(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)
if (tau_slip(j) == 0.0_pReal) then
DotRhoDipFormation(j) = 0.0_pReal
else
EdgeDipDistance(j) = &
(3.0_pReal*constitutive_dislotwin_Gmod(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance))/&
(16.0_pReal*pi*abs(tau_slip(j)))
if (EdgeDipDistance(j)>state(g,ip,el)%p(4*ns+2*nt+j)) EdgeDipDistance(j)=state(g,ip,el)%p(4*ns+2*nt+j)
if (EdgeDipDistance(j)<EdgeDipMinDistance) EdgeDipDistance(j)=EdgeDipMinDistance
DotRhoDipFormation(j) = &
((2.0_pReal*EdgeDipDistance(j))/constitutive_dislotwin_burgersPerSlipSystem(f,myInstance))*&
state(g,ip,el)%p(j)*abs(gdot_slip(j))
endif
!* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation(j) = &
((2.0_pReal*EdgeDipMinDistance)/constitutive_dislotwin_burgersPerSlipSystem(f,myInstance))*&
state(g,ip,el)%p(j)*abs(gdot_slip(j))
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation(j) = &
((2.0_pReal*EdgeDipMinDistance)/constitutive_dislotwin_burgersPerSlipSystem(f,myInstance))*&
state(g,ip,el)%p(ns+j)*abs(gdot_slip(j))
!* Dislocation dipole climb
AtomicVolume = &
constitutive_dislotwin_CAtomicVolume(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)**(3.0_pReal)
VacancyDiffusion = &
constitutive_dislotwin_D0(myInstance)*exp(-constitutive_dislotwin_Qsd(myInstance)/(kB*Temperature))
if (tau_slip(j) == 0.0_pReal) then
DotRhoEdgeDipClimb(j) = 0.0_pReal
else
ClimbVelocity(j) = &
((3.0_pReal*constitutive_dislotwin_Gmod(myInstance)*VacancyDiffusion*AtomicVolume)/(2.0_pReal*pi*kB*Temperature))*&
(1/(EdgeDipDistance(j)+EdgeDipMinDistance))
DotRhoEdgeDipClimb(j) = &
(4.0_pReal*ClimbVelocity(j)*state(g,ip,el)%p(ns+j))/(EdgeDipDistance(j)-EdgeDipMinDistance)
endif
!* Edge dislocation density rate of change
constitutive_dislotwin_dotState(j) = &
DotRhoMultiplication(j)-DotRhoDipFormation(j)-DotRhoEdgeEdgeAnnihilation(j)
!* Edge dislocation dipole density rate of change
constitutive_dislotwin_dotState(ns+j) = &
DotRhoDipFormation(j)-DotRhoEdgeDipAnnihilation(j)-DotRhoEdgeDipClimb(j)
enddo
enddo
!* Twin volume fraction evolution
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,MyStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Ntwin(f,myInstance) ! process each (active) twin system in family
j = j+1_pInt
!* Resolved shear stress on twin system
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_r = (state(g,ip,el)%p(6*ns+3*nt+j)/tau_twin(j))**constitutive_dislotwin_r(myInstance)
!* Shear rates and their derivatives due to twin
if ( tau_twin(j) > 0.0_pReal ) then
constitutive_dislotwin_dotState(2_pInt*ns+j) = &
(constitutive_dislotwin_MaxTwinFraction(myInstance)-sumf)*&
state(g,ip,el)%p(6_pInt*ns+4_pInt*nt+j)*constitutive_dislotwin_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r)
endif
enddo
enddo
!write(6,*) '#DOTSTATE#'
!write(6,*)
!write(6,'(a,/,4(3(f30.20,1x)/))') 'tau slip',tau_slip
!write(6,'(a,/,4(3(f30.20,1x)/))') 'gamma slip',gdot_slip
!write(6,'(a,/,4(3(f30.20,1x)/))') 'RhoEdge',state(g,ip,el)%p(1:ns)
!write(6,'(a,/,4(3(f30.20,1x)/))') 'Threshold Slip', state(g,ip,el)%p(5*ns+3*nt+1:6*ns+3*nt)
!write(6,'(a,/,4(3(f30.20,1x)/))') 'Multiplication',DotRhoMultiplication
!write(6,'(a,/,4(3(f30.20,1x)/))') 'DipFormation',DotRhoDipFormation
!write(6,'(a,/,4(3(f30.20,1x)/))') 'SingleSingle',DotRhoEdgeEdgeAnnihilation
!write(6,'(a,/,4(3(f30.20,1x)/))') 'SingleDipole',DotRhoEdgeDipAnnihilation
!write(6,'(a,/,4(3(f30.20,1x)/))') 'DipClimb',DotRhoEdgeDipClimb
return
end function
!*********************************************************************
!* (instantaneous) incremental change of microstructure *
!*********************************************************************
function constitutive_dislotwin_deltaState(Tstar_v, Temperature, state, g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_plasticityInstance
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! current microstructural state
!*** output variables
real(pReal), dimension(constitutive_dislotwin_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_dislotwin_deltaState ! change of state variables / microstructure
!*** local variables
constitutive_dislotwin_deltaState = 0.0_pReal
endfunction
pure function constitutive_dislotwin_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_dislotwin_dotTemperature
constitutive_dislotwin_dotTemperature = 0.0_pReal
return
end function
function constitutive_dislotwin_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,math_Mandel6to33, math_spectralDecompositionSym33
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase,phase_plasticityInstance,phase_Noutput
use lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
lattice_NslipSystem,lattice_NtwinSystem
implicit none
!* Definition of variables
integer(pInt), intent(in) :: g,ip,el
real(pReal), intent(in) :: dt,Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
integer(pInt) myInstance,myStructure,ns,nt,f,o,i,c,j,index_myFamily
real(pReal) sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,gdot_slip,dgdot_dtauslip
real(pReal), dimension(3,3) :: eigVectors
real(pReal), dimension (3) :: eigValues
logical error
real(pReal), dimension(constitutive_dislotwin_sizePostResults(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
constitutive_dislotwin_postResults
!* Shortened notation
myInstance = phase_plasticityInstance(material_phase(g,ip,el))
myStructure = constitutive_dislotwin_structure(myInstance)
ns = constitutive_dislotwin_totalNslip(myInstance)
nt = constitutive_dislotwin_totalNtwin(myInstance)
!* Total twin volume fraction
sumf = sum(state(g,ip,el)%p((2*ns+1):(2*ns+nt))) ! safe for nt == 0
!* Required output
c = 0_pInt
constitutive_dislotwin_postResults = 0.0_pReal
!* Spectral decomposition of stress
call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
do o = 1_pInt,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_dislotwin_output(o,myInstance))
case ('edge_density')
constitutive_dislotwin_postResults(c+1_pInt:c+ns) = state(g,ip,el)%p(1:ns)
c = c + ns
case ('dipole_density')
constitutive_dislotwin_postResults(c+1_pInt:c+ns) = state(g,ip,el)%p(ns+1:2_pInt*ns)
c = c + ns
case ('shear_rate_slip')
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_p = (abs(tau)/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau)/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(f,myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)* &
constitutive_dislotwin_v0PerSlipSystem(f,myInstance)
!* Shear rates due to slip
constitutive_dislotwin_postResults(c+j) = &
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
constitutive_dislotwin_q(myInstance))*sign(1.0_pReal,tau)
enddo ; enddo
c = c + ns
case ('mfp_slip')
constitutive_dislotwin_postResults(c+1_pInt:c+ns) =&
state(g,ip,el)%p((4_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+2_pInt*nt))
c = c + ns
case ('resolved_stress_slip')
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislotwin_postResults(c+j) =&
dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
enddo; enddo
c = c + ns
case ('threshold_stress_slip')
constitutive_dislotwin_postResults(c+1_pInt:c+ns) = &
state(g,ip,el)%p((5_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+3_pInt*nt))
c = c + ns
case ('edge_dipole_distance')
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislotwin_postResults(c+j) = &
(3.0_pReal*constitutive_dislotwin_Gmod(myInstance)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance))/&
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))))
constitutive_dislotwin_postResults(c+j) = min(constitutive_dislotwin_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j))
! constitutive_dislotwin_postResults(c+j) = max(constitutive_dislotwin_postResults(c+j),state(g,ip,el)%p(4*ns+2*nt+j))
enddo; enddo
c = c + ns
case ('resolved_stress_shearband')
do j = 1_pInt,6_pInt ! loop over all shearband families
constitutive_dislotwin_postResults(c+j) = dot_product(Tstar_v, constitutive_dislotwin_sbSv(1:6,j,g,ip,el))
enddo
c = c + 6_pInt
case ('schmid_factor_shearband')
constitutive_dislotwin_postResults(c+1_pInt:c+6_pInt) = constitutive_dislotwin_sbSv(1:6,j,g,ip,el)
c = c + 6_pInt
case ('shear_rate_shearband')
do j = 1_pInt,6_pInt ! loop over all shearband families
!* Resolved shear stress on shearband system
tau = dot_product(Tstar_v,constitutive_dislotwin_sbSv(1:6,j,g,ip,el))
!* Stress ratios
StressRatio_p = (abs(tau)/constitutive_dislotwin_sbResistance(myInstance))**constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau)/constitutive_dislotwin_sbResistance(myInstance))&
**(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_sbQedge(myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = constitutive_dislotwin_sbVelocity(myInstance)
!* Shear rates due to slip
constitutive_dislotwin_postResults(c+j) = &
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislotwin_q(myInstance))*sign(1.0_pReal,tau)
enddo
c = c + 6_pInt
case ('twin_fraction')
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state(g,ip,el)%p((2_pInt*ns+1_pInt):(2_pInt*ns+nt))
c = c + nt
case ('shear_rate_twin')
if (nt > 0_pInt) then
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1,constitutive_dislotwin_Ntwin(f,myInstance) ! process each (active) twin system in family
j = j + 1_pInt
!* Resolved shear stress on twin system
tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_r = (state(g,ip,el)%p(6_pInt*ns+3_pInt*nt+j)/tau)**constitutive_dislotwin_r(myInstance)
!* Shear rates and their derivatives due to twin
if ( tau > 0.0_pReal ) then
constitutive_dislotwin_postResults(c+j) = &
(constitutive_dislotwin_MaxTwinFraction(myInstance)-sumf)*&
state(g,ip,el)%p(6_pInt*ns+4_pInt*nt+j)*constitutive_dislotwin_Ndot0PerTwinSystem(f,myInstance)*exp(-StressRatio_r)
endif
enddo ; enddo
endif
c = c + nt
case ('mfp_twin')
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state(g,ip,el)%p((5_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+3_pInt*nt))
c = c + nt
case ('resolved_stress_twin')
if (nt > 0_pInt) then
j = 0_pInt
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all slip families
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Ntwin(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
constitutive_dislotwin_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure))
enddo; enddo
endif
c = c + nt
case ('threshold_stress_twin')
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state(g,ip,el)%p((6_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+4_pInt*nt))
c = c + nt
case ('stress_exponent')
j = 0_pInt
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,myStructure)) ! at which index starts my family
do i = 1_pInt,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
j = j + 1_pInt
!* Resolved shear stress on slip system
tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
!* Stress ratios
StressRatio_p = (abs(tau)/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
constitutive_dislotwin_p(myInstance)
StressRatio_pminus1 = (abs(tau)/state(g,ip,el)%p(5_pInt*ns+3_pInt*nt+j))**&
(constitutive_dislotwin_p(myInstance)-1.0_pReal)
!* Boltzmann ratio
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(f,myInstance)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = &
state(g,ip,el)%p(j)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)* &
constitutive_dislotwin_v0PerSlipSystem(f,myInstance)
!* Shear rates due to slip
gdot_slip = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
constitutive_dislotwin_q(myInstance))*sign(1.0_pReal,tau)
!* Derivatives of shear rates
dgdot_dtauslip = &
((abs(gdot_slip)*BoltzmannRatio*&
constitutive_dislotwin_p(myInstance)*constitutive_dislotwin_q(myInstance))/state(g,ip,el)%p(5*ns+3*nt+j))*&
StressRatio_pminus1*(1_pInt-StressRatio_p)**(constitutive_dislotwin_q(myInstance)-1.0_pReal)
!* Stress exponent
if (gdot_slip==0.0_pReal) then
constitutive_dislotwin_postResults(c+j) = 0.0_pReal
else
constitutive_dislotwin_postResults(c+j) = (tau/gdot_slip)*dgdot_dtauslip
endif
enddo ; enddo
c = c + ns
case ('sb_eigenvalues')
forall (j = 1_pInt:3_pInt) &
constitutive_dislotwin_postResults(c+j) = eigValues(j)
c = c + 3_pInt
case ('sb_eigenvectors')
constitutive_dislotwin_postResults(c+1_pInt:c+9_pInt) = reshape(eigVectors,(/9/))
c = c + 9_pInt
end select
enddo
return
end function
END MODULE
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