1384 lines
76 KiB
Fortran
1384 lines
76 KiB
Fortran
!* $Id$
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!************************************
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!* Module: CONSTITUTIVE *
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!************************************
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MODULE constitutive_dislotwin
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!* Include other modules
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use prec, only: pReal,pInt
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implicit none
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!* Lists of states and physical parameters
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character(len=*), parameter :: constitutive_dislotwin_label = 'dislotwin'
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character(len=18), dimension(2), parameter:: constitutive_dislotwin_listBasicSlipStates = (/'rhoEdge ', &
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'rhoEdgeDip'/)
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character(len=18), dimension(1), parameter:: constitutive_dislotwin_listBasicTwinStates = (/'twinFraction'/)
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character(len=18), dimension(4), parameter:: constitutive_dislotwin_listDependentSlipStates =(/'invLambdaSlip ', &
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'invLambdaSlipTwin', &
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'meanFreePathSlip ', &
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'tauSlipThreshold '/)
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character(len=18), dimension(4), parameter:: constitutive_dislotwin_listDependentTwinStates =(/'invLambdaTwin ', &
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'meanFreePathTwin', &
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'tauTwinThreshold', &
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'twinVolume '/)
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real(pReal), parameter :: kB = 1.38e-23_pReal ! Boltzmann constant in J/Kelvin
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!* Definition of global variables
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integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_sizeDotState, & ! number of dotStates
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constitutive_dislotwin_sizeState, & ! total number of microstructural state variables
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constitutive_dislotwin_sizePostResults ! cumulative size of post results
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integer(pInt), dimension(:,:), allocatable, target :: constitutive_dislotwin_sizePostResult ! size of each post result output
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character(len=64), dimension(:,:), allocatable, target :: constitutive_dislotwin_output ! name of each post result output
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character(len=32), dimension(:), allocatable :: constitutive_dislotwin_structureName ! name of the lattice structure
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integer(pInt), dimension(:), allocatable :: constitutive_dislotwin_structure, & ! number representing the kind of lattice structure
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constitutive_dislotwin_totalNslip, & ! total number of active slip systems for each instance
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constitutive_dislotwin_totalNtwin ! total number of active twin systems for each instance
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integer(pInt), dimension(:,:), allocatable :: constitutive_dislotwin_Nslip, & ! number of active slip systems for each family and instance
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constitutive_dislotwin_Ntwin, & ! number of active twin systems for each family and instance
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constitutive_dislotwin_slipFamily, & ! lookup table relating active slip system to slip family for each instance
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constitutive_dislotwin_twinFamily, & ! lookup table relating active twin system to twin family for each instance
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constitutive_dislotwin_slipSystemLattice, & ! lookup table relating active slip system index to lattice slip system index for each instance
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constitutive_dislotwin_twinSystemLattice ! lookup table relating active twin system index to lattice twin system index for each instance
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real(pReal), dimension(:), allocatable :: constitutive_dislotwin_CoverA, & ! c/a ratio for hex type lattice
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constitutive_dislotwin_C11, & ! C11 element in elasticity matrix
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constitutive_dislotwin_C12, & ! C12 element in elasticity matrix
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constitutive_dislotwin_C13, & ! C13 element in elasticity matrix
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constitutive_dislotwin_C33, & ! C33 element in elasticity matrix
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constitutive_dislotwin_C44, & ! C44 element in elasticity matrix
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constitutive_dislotwin_Gmod, & ! shear modulus
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constitutive_dislotwin_CAtomicVolume, & ! atomic volume in Bugers vector unit
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constitutive_dislotwin_D0, & ! prefactor for self-diffusion coefficient
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constitutive_dislotwin_Qsd, & ! activation energy for dislocation climb
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constitutive_dislotwin_GrainSize, & ! grain size
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constitutive_dislotwin_p, & ! p-exponent in glide velocity
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constitutive_dislotwin_q, & ! q-exponent in glide velocity
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constitutive_dislotwin_MaxTwinFraction, & ! maximum allowed total twin volume fraction
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constitutive_dislotwin_r, & ! r-exponent in twin nucleation rate
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constitutive_dislotwin_CEdgeDipMinDistance, & !
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constitutive_dislotwin_Cmfptwin, & !
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constitutive_dislotwin_Cthresholdtwin, & !
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constitutive_dislotwin_relevantRho ! dislocation density considered relevant
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real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_Cslip_66 ! elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_66 ! twin elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_dislotwin_Cslip_3333 ! elasticity matrix for each instance
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real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_dislotwin_Ctwin_3333 ! twin elasticity matrix for each instance
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real(pReal), dimension(:,:), allocatable :: constitutive_dislotwin_rhoEdge0, & ! initial edge dislocation density per slip system for each family and instance
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constitutive_dislotwin_rhoEdgeDip0, & ! initial edge dipole density per slip system for each family and instance
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constitutive_dislotwin_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each slip family and instance
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constitutive_dislotwin_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
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constitutive_dislotwin_burgersPerTwinFamily, & ! absolute length of burgers vector [m] for each twin family and instance
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constitutive_dislotwin_burgersPerTwinSystem, & ! absolute length of burgers vector [m] for each twin system and instance
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constitutive_dislotwin_QedgePerSlipFamily, & ! activation energy for glide [J] for each slip family and instance
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constitutive_dislotwin_QedgePerSlipSystem, & ! activation energy for glide [J] for each slip system and instance
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constitutive_dislotwin_v0PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
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constitutive_dislotwin_v0PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
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constitutive_dislotwin_Ndot0PerTwinFamily, & ! twin nucleation rate [1/m³s] for each twin family and instance
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constitutive_dislotwin_Ndot0PerTwinSystem, & ! twin nucleation rate [1/m³s] for each twin system and instance
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constitutive_dislotwin_twinsizePerTwinFamily, & ! twin thickness [m] for each twin family and instance
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constitutive_dislotwin_twinsizePerTwinSystem, & ! twin thickness [m] for each twin system and instance
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constitutive_dislotwin_CLambdaSlipPerSlipFamily, & ! Adj. parameter for distance between 2 forest dislocations for each slip family and instance
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constitutive_dislotwin_CLambdaSlipPerSlipSystem, & ! Adj. parameter for distance between 2 forest dislocations for each slip system and instance
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constitutive_dislotwin_interactionSlipSlip, & ! coefficients for slip-slip interaction for each interaction type and instance
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constitutive_dislotwin_interactionSlipTwin, & ! coefficients for slip-twin interaction for each interaction type and instance
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constitutive_dislotwin_interactionTwinSlip, & ! coefficients for twin-slip interaction for each interaction type and instance
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constitutive_dislotwin_interactionTwinTwin ! coefficients for twin-twin interaction for each interaction type and instance
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real(pReal), dimension(:,:,:), allocatable :: constitutive_dislotwin_interactionMatrixSlipSlip, & ! interaction matrix of the different slip systems for each instance
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constitutive_dislotwin_interactionMatrixSlipTwin, & ! interaction matrix of slip systems with twin systems for each instance
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constitutive_dislotwin_interactionMatrixTwinSlip, & ! interaction matrix of twin systems with slip systems for each instance
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constitutive_dislotwin_interactionMatrixTwinTwin, & ! interaction matrix of the different twin systems for each instance
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constitutive_dislotwin_forestProjectionEdge ! matrix of forest projections of edge dislocations for each instance
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CONTAINS
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!****************************************
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!* - constitutive_dislotwin_init
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!* - constitutive_dislotwin_stateInit
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!* - constitutive_dislotwin_relevantState
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!* - constitutive_dislotwin_homogenizedC
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!* - constitutive_dislotwin_microstructure
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!* - constitutive_dislotwin_LpAndItsTangent
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!* - consistutive_dislotwin_dotState
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!* - constitutive_dislotwin_dotTemperature
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!* - consistutive_dislotwin_postResults
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!****************************************
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subroutine constitutive_dislotwin_init(file)
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!**************************************
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!* Module initialization *
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!**************************************
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use prec, only: pInt,pReal
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use math, only: math_Mandel3333to66,math_Voigt66to3333,math_mul3x3
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use IO
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use material
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use lattice
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!* Input variables
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integer(pInt), intent(in) :: file
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!* Local variables
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integer(pInt), parameter :: maxNchunks = 21
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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integer(pInt) section,maxNinstance,f,i,j,k,l,m,n,o,p,q,r,s,s1,s2,t1,t2,ns,nt,output,mySize,myStructure,maxTotalNslip,maxTotalNtwin
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character(len=64) tag
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character(len=1024) line
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!write(6,*)
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!write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_dislotwin_label,' init -+>>>'
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!write(6,*) '$Id$'
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!write(6,*)
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maxNinstance = count(phase_constitution == constitutive_dislotwin_label)
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if (maxNinstance == 0) return
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!* Space allocation for global variables
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allocate(constitutive_dislotwin_sizeDotState(maxNinstance))
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allocate(constitutive_dislotwin_sizeState(maxNinstance))
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allocate(constitutive_dislotwin_sizePostResults(maxNinstance))
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allocate(constitutive_dislotwin_sizePostResult(maxval(phase_Noutput),maxNinstance))
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allocate(constitutive_dislotwin_output(maxval(phase_Noutput),maxNinstance))
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constitutive_dislotwin_sizeDotState = 0_pInt
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constitutive_dislotwin_sizeState = 0_pInt
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constitutive_dislotwin_sizePostResults = 0_pInt
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constitutive_dislotwin_sizePostResult = 0_pInt
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constitutive_dislotwin_output = ''
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allocate(constitutive_dislotwin_structureName(maxNinstance))
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allocate(constitutive_dislotwin_structure(maxNinstance))
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allocate(constitutive_dislotwin_Nslip(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_Ntwin(lattice_maxNtwinFamily,maxNinstance))
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allocate(constitutive_dislotwin_slipFamily(lattice_maxNslip,maxNinstance))
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allocate(constitutive_dislotwin_twinFamily(lattice_maxNtwin,maxNinstance))
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allocate(constitutive_dislotwin_slipSystemLattice(lattice_maxNslip,maxNinstance))
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allocate(constitutive_dislotwin_twinSystemLattice(lattice_maxNtwin,maxNinstance))
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allocate(constitutive_dislotwin_totalNslip(maxNinstance))
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allocate(constitutive_dislotwin_totalNtwin(maxNinstance))
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constitutive_dislotwin_structureName = ''
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constitutive_dislotwin_structure = 0_pInt
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constitutive_dislotwin_Nslip = 0_pInt
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constitutive_dislotwin_Ntwin = 0_pInt
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constitutive_dislotwin_slipFamily = 0_pInt
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constitutive_dislotwin_twinFamily = 0_pInt
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constitutive_dislotwin_slipSystemLattice = 0.0_pReal
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constitutive_dislotwin_twinSystemLattice = 0.0_pReal
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constitutive_dislotwin_totalNslip = 0_pInt
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constitutive_dislotwin_totalNtwin = 0_pInt
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allocate(constitutive_dislotwin_CoverA(maxNinstance))
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allocate(constitutive_dislotwin_C11(maxNinstance))
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allocate(constitutive_dislotwin_C12(maxNinstance))
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allocate(constitutive_dislotwin_C13(maxNinstance))
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allocate(constitutive_dislotwin_C33(maxNinstance))
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allocate(constitutive_dislotwin_C44(maxNinstance))
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allocate(constitutive_dislotwin_Gmod(maxNinstance))
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allocate(constitutive_dislotwin_CAtomicVolume(maxNinstance))
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allocate(constitutive_dislotwin_D0(maxNinstance))
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allocate(constitutive_dislotwin_Qsd(maxNinstance))
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allocate(constitutive_dislotwin_GrainSize(maxNinstance))
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allocate(constitutive_dislotwin_p(maxNinstance))
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allocate(constitutive_dislotwin_q(maxNinstance))
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allocate(constitutive_dislotwin_MaxTwinFraction(maxNinstance))
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allocate(constitutive_dislotwin_r(maxNinstance))
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allocate(constitutive_dislotwin_CEdgeDipMinDistance(maxNinstance))
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allocate(constitutive_dislotwin_Cmfptwin(maxNinstance))
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allocate(constitutive_dislotwin_Cthresholdtwin(maxNinstance))
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allocate(constitutive_dislotwin_relevantRho(maxNinstance))
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allocate(constitutive_dislotwin_Cslip_66(6,6,maxNinstance))
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allocate(constitutive_dislotwin_Cslip_3333(3,3,3,3,maxNinstance))
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constitutive_dislotwin_CoverA = 0.0_pReal
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constitutive_dislotwin_C11 = 0.0_pReal
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constitutive_dislotwin_C12 = 0.0_pReal
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constitutive_dislotwin_C13 = 0.0_pReal
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constitutive_dislotwin_C33 = 0.0_pReal
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constitutive_dislotwin_C44 = 0.0_pReal
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constitutive_dislotwin_Gmod = 0.0_pReal
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constitutive_dislotwin_CAtomicVolume = 0.0_pReal
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constitutive_dislotwin_D0 = 0.0_pReal
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constitutive_dislotwin_Qsd = 0.0_pReal
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constitutive_dislotwin_GrainSize = 0.0_pReal
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constitutive_dislotwin_p = 0.0_pReal
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constitutive_dislotwin_q = 0.0_pReal
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constitutive_dislotwin_MaxTwinFraction = 0.0_pReal
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constitutive_dislotwin_r = 0.0_pReal
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constitutive_dislotwin_CEdgeDipMinDistance = 0.0_pReal
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constitutive_dislotwin_Cmfptwin = 0.0_pReal
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constitutive_dislotwin_Cthresholdtwin = 0.0_pReal
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constitutive_dislotwin_relevantRho = 0.0_pReal
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constitutive_dislotwin_Cslip_66 = 0.0_pReal
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constitutive_dislotwin_Cslip_3333 = 0.0_pReal
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allocate(constitutive_dislotwin_rhoEdge0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_rhoEdgeDip0(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_burgersPerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
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allocate(constitutive_dislotwin_QedgePerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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allocate(constitutive_dislotwin_Ndot0PerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
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allocate(constitutive_dislotwin_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance))
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allocate(constitutive_dislotwin_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance))
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constitutive_dislotwin_rhoEdge0 = 0.0_pReal
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constitutive_dislotwin_rhoEdgeDip0 = 0.0_pReal
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constitutive_dislotwin_burgersPerSlipFamily = 0.0_pReal
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constitutive_dislotwin_burgersPerTwinFamily = 0.0_pReal
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constitutive_dislotwin_QedgePerSlipFamily = 0.0_pReal
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constitutive_dislotwin_v0PerSlipFamily = 0.0_pReal
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constitutive_dislotwin_Ndot0PerTwinFamily = 0.0_pReal
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constitutive_dislotwin_twinsizePerTwinFamily = 0.0_pReal
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constitutive_dislotwin_CLambdaSlipPerSlipFamily = 0.0_pReal
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allocate(constitutive_dislotwin_interactionSlipSlip(lattice_maxNinteraction,maxNinstance))
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allocate(constitutive_dislotwin_interactionSlipTwin(lattice_maxNinteraction,maxNinstance))
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allocate(constitutive_dislotwin_interactionTwinSlip(lattice_maxNinteraction,maxNinstance))
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allocate(constitutive_dislotwin_interactionTwinTwin(lattice_maxNinteraction,maxNinstance))
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constitutive_dislotwin_interactionSlipSlip = 0.0_pReal
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constitutive_dislotwin_interactionSlipTwin = 0.0_pReal
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constitutive_dislotwin_interactionTwinSlip = 0.0_pReal
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constitutive_dislotwin_interactionTwinTwin = 0.0_pReal
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!* Readout data from material.config file
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rewind(file)
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line = ''
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section = 0
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do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
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read(file,'(a1024)',END=100) line
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enddo
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do ! read thru sections of phase part
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read(file,'(a1024)',END=100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
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if (IO_getTag(line,'[',']') /= '') then ! next section
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section = section + 1
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output = 0 ! reset output counter
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endif
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if (section > 0 .and. phase_constitution(section) == constitutive_dislotwin_label) then ! one of my sections
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i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
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positions = IO_stringPos(line,maxNchunks)
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tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
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select case(tag)
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case ('(output)')
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output = output + 1
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constitutive_dislotwin_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
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case ('lattice_structure')
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constitutive_dislotwin_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
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case ('covera_ratio')
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constitutive_dislotwin_CoverA(i) = IO_floatValue(line,positions,2)
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case ('c11')
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constitutive_dislotwin_C11(i) = IO_floatValue(line,positions,2)
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case ('c12')
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constitutive_dislotwin_C12(i) = IO_floatValue(line,positions,2)
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case ('c13')
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constitutive_dislotwin_C13(i) = IO_floatValue(line,positions,2)
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case ('c33')
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constitutive_dislotwin_C33(i) = IO_floatValue(line,positions,2)
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case ('c44')
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constitutive_dislotwin_C44(i) = IO_floatValue(line,positions,2)
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case ('nslip')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_Nslip(j,i) = IO_intValue(line,positions,1+j)
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case ('ntwin')
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forall (j = 1:lattice_maxNtwinFamily) &
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constitutive_dislotwin_Ntwin(j,i) = IO_intValue(line,positions,1+j)
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case ('rhoedge0')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_rhoEdge0(j,i) = IO_floatValue(line,positions,1+j)
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case ('rhoedgedip0')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_rhoEdgeDip0(j,i) = IO_floatValue(line,positions,1+j)
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case ('slipburgers')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_burgersPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('twinburgers')
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forall (j = 1:lattice_maxNtwinFamily) &
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constitutive_dislotwin_burgersPerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('qedge')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_QedgePerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('v0')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_v0PerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('ndot0')
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forall (j = 1:lattice_maxNtwinFamily) &
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constitutive_dislotwin_Ndot0PerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('twinsize')
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forall (j = 1:lattice_maxNtwinFamily) &
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constitutive_dislotwin_twinsizePerTwinFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('clambdaslip')
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forall (j = 1:lattice_maxNslipFamily) &
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constitutive_dislotwin_CLambdaSlipPerSlipFamily(j,i) = IO_floatValue(line,positions,1+j)
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case ('grainsize')
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constitutive_dislotwin_GrainSize(i) = IO_floatValue(line,positions,2)
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case ('maxtwinfraction')
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constitutive_dislotwin_MaxTwinFraction(i) = IO_floatValue(line,positions,2)
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case ('pexponent')
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constitutive_dislotwin_p(i) = IO_floatValue(line,positions,2)
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case ('qexponent')
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constitutive_dislotwin_q(i) = IO_floatValue(line,positions,2)
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case ('rexponent')
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constitutive_dislotwin_r(i) = IO_floatValue(line,positions,2)
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case ('d0')
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constitutive_dislotwin_D0(i) = IO_floatValue(line,positions,2)
|
|
case ('qsd')
|
|
constitutive_dislotwin_Qsd(i) = IO_floatValue(line,positions,2)
|
|
case ('relevantrho')
|
|
constitutive_dislotwin_relevantRho(i) = IO_floatValue(line,positions,2)
|
|
case ('cmfptwin')
|
|
constitutive_dislotwin_Cmfptwin(i) = IO_floatValue(line,positions,2)
|
|
case ('cthresholdtwin')
|
|
constitutive_dislotwin_Cthresholdtwin(i) = IO_floatValue(line,positions,2)
|
|
case ('cedgedipmindistance')
|
|
constitutive_dislotwin_CEdgeDipMinDistance(i) = IO_floatValue(line,positions,2)
|
|
case ('catomicvolume')
|
|
constitutive_dislotwin_CAtomicVolume(i) = IO_floatValue(line,positions,2)
|
|
case ('interactionslipslip')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislotwin_interactionSlipSlip(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interactionsliptwin')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislotwin_interactionSlipTwin(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interactiontwinslip')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislotwin_interactionTwinSlip(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interactiontwintwin')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislotwin_interactionTwinTwin(j,i) = IO_floatValue(line,positions,1+j)
|
|
end select
|
|
endif
|
|
enddo
|
|
|
|
100 do i = 1,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 .or. myStructure > 3) call IO_error(205)
|
|
if (sum(constitutive_dislotwin_Nslip(:,i)) <= 0_pInt) call IO_error(225)
|
|
if (sum(constitutive_dislotwin_Ntwin(:,i)) < 0_pInt) call IO_error(225) !***
|
|
do f = 1,lattice_maxNslipFamily
|
|
if (constitutive_dislotwin_Nslip(f,i) > 0_pInt) then
|
|
if (constitutive_dislotwin_rhoEdge0(f,i) < 0.0_pReal) call IO_error(220)
|
|
if (constitutive_dislotwin_rhoEdgeDip0(f,i) < 0.0_pReal) call IO_error(220)
|
|
if (constitutive_dislotwin_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221)
|
|
if (constitutive_dislotwin_v0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(226)
|
|
endif
|
|
enddo
|
|
do f = 1,lattice_maxNtwinFamily
|
|
if (constitutive_dislotwin_Nslip(f,i) > 0_pInt) then
|
|
if (constitutive_dislotwin_burgersPerTwinFamily(f,i) <= 0.0_pReal) call IO_error(221) !***
|
|
if (constitutive_dislotwin_Ndot0PerTwinFamily(f,i) < 0.0_pReal) call IO_error(226) !***
|
|
endif
|
|
enddo
|
|
! if (any(constitutive_dislotwin_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 1.0_pReal)) call IO_error(229)
|
|
if (constitutive_dislotwin_CAtomicVolume(i) <= 0.0_pReal) call IO_error(230)
|
|
if (constitutive_dislotwin_D0(i) <= 0.0_pReal) call IO_error(231)
|
|
if (constitutive_dislotwin_Qsd(i) <= 0.0_pReal) call IO_error(232)
|
|
if (constitutive_dislotwin_relevantRho(i) <= 0.0_pReal) call IO_error(233)
|
|
|
|
!* 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))
|
|
allocate(constitutive_dislotwin_burgersPerTwinSystem(maxTotalNtwin, maxNinstance))
|
|
allocate(constitutive_dislotwin_QedgePerSlipSystem(maxTotalNslip, maxNinstance))
|
|
allocate(constitutive_dislotwin_v0PerSlipSystem(maxTotalNslip, maxNinstance))
|
|
allocate(constitutive_dislotwin_Ndot0PerTwinSystem(maxTotalNtwin, maxNinstance))
|
|
allocate(constitutive_dislotwin_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance))
|
|
allocate(constitutive_dislotwin_CLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance))
|
|
constitutive_dislotwin_burgersPerSlipSystem = 0.0_pReal
|
|
constitutive_dislotwin_burgersPerTwinSystem = 0.0_pReal
|
|
constitutive_dislotwin_QedgePerSlipSystem = 0.0_pReal
|
|
constitutive_dislotwin_v0PerSlipSystem = 0.0_pReal
|
|
constitutive_dislotwin_Ndot0PerTwinSystem = 0.0_pReal
|
|
constitutive_dislotwin_twinsizePerTwinSystem = 0.0_pReal
|
|
constitutive_dislotwin_CLambdaSlipPerSlipSystem = 0.0_pReal
|
|
|
|
allocate(constitutive_dislotwin_interactionMatrixSlipSlip(maxTotalNslip,maxTotalNslip,maxNinstance))
|
|
allocate(constitutive_dislotwin_interactionMatrixSlipTwin(maxTotalNslip,maxTotalNtwin,maxNinstance))
|
|
allocate(constitutive_dislotwin_interactionMatrixTwinSlip(maxTotalNtwin,maxTotalNslip,maxNinstance))
|
|
allocate(constitutive_dislotwin_interactionMatrixTwinTwin(maxTotalNtwin,maxTotalNtwin,maxNinstance))
|
|
allocate(constitutive_dislotwin_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance))
|
|
constitutive_dislotwin_interactionMatrixSlipSlip = 0.0_pReal
|
|
constitutive_dislotwin_interactionMatrixSlipTwin = 0.0_pReal
|
|
constitutive_dislotwin_interactionMatrixTwinSlip = 0.0_pReal
|
|
constitutive_dislotwin_interactionMatrixTwinTwin = 0.0_pReal
|
|
constitutive_dislotwin_forestProjectionEdge = 0.0_pReal
|
|
|
|
allocate(constitutive_dislotwin_Ctwin_66(6,6,maxTotalNtwin,maxNinstance))
|
|
allocate(constitutive_dislotwin_Ctwin_3333(3,3,3,3,maxTotalNtwin,maxNinstance))
|
|
constitutive_dislotwin_Ctwin_66 = 0.0_pReal
|
|
constitutive_dislotwin_Ctwin_3333 = 0.0_pReal
|
|
|
|
do i = 1,maxNinstance
|
|
myStructure = constitutive_dislotwin_structure(i)
|
|
|
|
!* Inverse lookup of my slip system family
|
|
l = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily
|
|
do k = 1,constitutive_dislotwin_Nslip(f,i)
|
|
l = l + 1
|
|
constitutive_dislotwin_slipFamily(l,i) = f
|
|
constitutive_dislotwin_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1,myStructure)) + k
|
|
enddo; enddo
|
|
|
|
!* Inverse lookup of my twin system family
|
|
l = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily
|
|
do k = 1,constitutive_dislotwin_Ntwin(f,i)
|
|
l = l + 1
|
|
constitutive_dislotwin_twinFamily(l,i) = f
|
|
constitutive_dislotwin_twinSystemLattice(l,i) = sum(lattice_NtwinSystem(1:f-1,myStructure)) + k
|
|
enddo; enddo
|
|
|
|
!* Determine size of state array
|
|
ns = constitutive_dislotwin_totalNslip(i)
|
|
nt = constitutive_dislotwin_totalNtwin(i)
|
|
constitutive_dislotwin_sizeDotState(i) = &
|
|
size(constitutive_dislotwin_listBasicSlipStates)*ns+size(constitutive_dislotwin_listBasicTwinStates)*nt
|
|
constitutive_dislotwin_sizeState(i) = &
|
|
constitutive_dislotwin_sizeDotState(i)+ &
|
|
size(constitutive_dislotwin_listDependentSlipStates)*ns+size(constitutive_dislotwin_listDependentTwinStates)*nt
|
|
|
|
!* Determine size of postResults array
|
|
do o = 1,maxval(phase_Noutput)
|
|
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 default
|
|
mySize = 0_pInt
|
|
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(1:2) ! cubic(s)
|
|
forall(k=1:3)
|
|
forall(j=1:3) &
|
|
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,k+3,i) = constitutive_dislotwin_C44(i)
|
|
end forall
|
|
case(3:) ! 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,lattice_maxNtwinFamily
|
|
do k=1,constitutive_dislotwin_Ntwin(j,i)
|
|
do l=1,3 ; do m=1,3 ; do n=1,3 ; do o=1,3 ; do p=1,3 ; do q=1,3 ; do r=1,3 ; do s=1,3
|
|
constitutive_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1,i))+k,i) = &
|
|
constitutive_dislotwin_Ctwin_3333(l,m,n,o,sum(constitutive_dislotwin_Nslip(1:j-1,i))+k,i) + &
|
|
constitutive_dislotwin_Cslip_3333(p,q,r,s,i)*&
|
|
lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* &
|
|
lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* &
|
|
lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)* &
|
|
lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1,myStructure))+k,myStructure)
|
|
enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo
|
|
constitutive_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,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,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,constitutive_dislotwin_totalNslip(i)
|
|
do s2 = 1,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,constitutive_dislotwin_totalNslip(i)
|
|
do t2 = 1,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,constitutive_dislotwin_totalNtwin(i)
|
|
do s2 = 1,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,constitutive_dislotwin_totalNtwin(i)
|
|
do t2 = 1,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,constitutive_dislotwin_totalNslip(i)
|
|
do s2 = 1,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,lattice_maxNtwinFamily
|
|
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,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*ns) = rhoEdgeDip0
|
|
|
|
!* Initialize dependent slip microstructural variables
|
|
forall (s = 1:ns) &
|
|
invLambdaSlip0(s) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislotwin_forestProjectionEdge(1:ns,s,myInstance)))/ &
|
|
constitutive_dislotwin_CLambdaSlipPerSlipSystem(s,myInstance)
|
|
constitutive_dislotwin_stateInit(2*ns+nt+1:3*ns+nt) = invLambdaSlip0
|
|
|
|
forall (s = 1:ns) &
|
|
MeanFreePathSlip0(s) = &
|
|
constitutive_dislotwin_GrainSize(myInstance)/(1.0_pReal+invLambdaSlip0(s)*constitutive_dislotwin_GrainSize(myInstance))
|
|
constitutive_dislotwin_stateInit(4*ns+2*nt+1:5*ns+2*nt) = MeanFreePathSlip0
|
|
|
|
forall (s = 1:ns) &
|
|
tauSlipThreshold0(s) = &
|
|
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*ns+3*nt+1:6*ns+3*nt) = tauSlipThreshold0
|
|
|
|
!* Initialize dependent twin microstructural variables
|
|
forall (t = 1:nt) &
|
|
MeanFreePathTwin0(t) = constitutive_dislotwin_GrainSize(myInstance)
|
|
constitutive_dislotwin_stateInit(5*ns+2*nt+1:5*ns+3*nt) = MeanFreePathTwin0
|
|
|
|
forall (t = 1:nt) &
|
|
TwinVolume0(t) = &
|
|
(pi/6.0_pReal)*constitutive_dislotwin_twinsizePerTwinSystem(t,myInstance)*MeanFreePathTwin0(t)**(2.0_pReal)
|
|
constitutive_dislotwin_stateInit(6*ns+4*nt+1:6*ns+5*nt) = TwinVolume0
|
|
|
|
!write(6,*) '#STATEINIT#'
|
|
!write(6,*)
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'RhoEdge',rhoEdge0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'RhoEdgedip',rhoEdgeDip0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'invLambdaSlip',invLambdaSlip0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'MeanFreePathSlip',MeanFreePathSlip0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'tauSlipThreshold', tauSlipThreshold0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'MeanFreePathTwin', MeanFreePathTwin0
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'TwinVolume', TwinVolume0
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
pure function constitutive_dislotwin_relevantState(myInstance)
|
|
!*********************************************************************
|
|
!* relevant microstructural state *
|
|
!*********************************************************************
|
|
use prec, only: pReal, pInt
|
|
implicit none
|
|
|
|
!* Input-Output variables
|
|
integer(pInt), intent(in) :: myInstance
|
|
real(pReal), dimension(constitutive_dislotwin_sizeState(myInstance)) :: constitutive_dislotwin_relevantState
|
|
|
|
constitutive_dislotwin_relevantState = constitutive_dislotwin_relevantRho(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_constitutionInstance
|
|
implicit none
|
|
|
|
!* Input-Output variables
|
|
integer(pInt), intent(in) :: g,ip,el
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
|
|
real(pReal), dimension(6,6) :: constitutive_dislotwin_homogenizedC
|
|
!* Local variables
|
|
integer(pInt) myInstance,ns,nt,i
|
|
real(pReal) sumf
|
|
|
|
!* Shortened notation
|
|
myInstance = phase_constitutionInstance(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*ns+1):(2*ns+nt))) ! safe for nt == 0
|
|
|
|
!* Homogenized elasticity matrix
|
|
constitutive_dislotwin_homogenizedC = (1.0_pReal-sumf)*constitutive_dislotwin_Cslip_66(:,:,myInstance)
|
|
do i=1,nt
|
|
constitutive_dislotwin_homogenizedC = &
|
|
constitutive_dislotwin_homogenizedC + state(g,ip,el)%p(2*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_constitutionInstance
|
|
use lattice, only: lattice_interactionSlipTwin,lattice_interactionTwinTwin
|
|
!use debug, only: debugger
|
|
implicit none
|
|
|
|
!* Input-Output variables
|
|
integer(pInt), intent(in) :: g,ip,el
|
|
real(pReal), intent(in) :: Temperature
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: state
|
|
!* Local variables
|
|
integer(pInt) myInstance,myStructure,ns,nt,s,t,i
|
|
real(pReal) sumf,sfe
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: fOverStacksize
|
|
|
|
!* Shortened notation
|
|
myInstance = phase_constitutionInstance(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 = 0.0002_pReal*Temperature-0.0396_pReal
|
|
|
|
!* rescaled twin volume fraction for topology
|
|
forall (t = 1:nt) &
|
|
fOverStacksize(t) = &
|
|
state(g,ip,el)%p(2*ns+t)/constitutive_dislotwin_twinsizePerTwinSystem(t,myInstance)
|
|
|
|
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
|
forall (s = 1:ns) &
|
|
state(g,ip,el)%p(2*ns+nt+s) = &
|
|
sqrt(dot_product((state(g,ip,el)%p(1:ns)+state(g,ip,el)%p(ns+1:2*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
|
|
!$OMP CRITICAL (evilmatmul)
|
|
state(g,ip,el)%p((3*ns+nt+1):(4*ns+nt)) = 0.0_pReal
|
|
if (nt > 0_pInt) &
|
|
state(g,ip,el)%p((3*ns+nt+1):(4*ns+nt)) = &
|
|
matmul(constitutive_dislotwin_interactionMatrixSlipTwin(1:ns,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
|
!$OMP CRITICAL (evilmatmul)
|
|
if (nt > 0_pInt) &
|
|
state(g,ip,el)%p((4*ns+nt+1):(4*ns+2*nt)) = &
|
|
matmul(constitutive_dislotwin_interactionMatrixTwinTwin(1:nt,1:nt,myInstance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* mean free path between 2 obstacles seen by a moving dislocation
|
|
do s = 1,ns
|
|
if (nt > 0_pInt) then
|
|
state(g,ip,el)%p(4*ns+2*nt+s) = &
|
|
constitutive_dislotwin_GrainSize(myInstance)/(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*&
|
|
(state(g,ip,el)%p(2*ns+nt+s)+state(g,ip,el)%p(3*ns+nt+s)))
|
|
else
|
|
state(g,ip,el)%p(4*ns+s) = &
|
|
constitutive_dislotwin_GrainSize(myInstance)/&
|
|
(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*(state(g,ip,el)%p(2*ns+s)))
|
|
endif
|
|
enddo
|
|
|
|
!* mean free path between 2 obstacles seen by a growing twin
|
|
forall (t = 1:nt) &
|
|
state(g,ip,el)%p(5*ns+2*nt+t) = &
|
|
(constitutive_dislotwin_Cmfptwin(myInstance)*constitutive_dislotwin_GrainSize(myInstance))/&
|
|
(1.0_pReal+constitutive_dislotwin_GrainSize(myInstance)*state(g,ip,el)%p(4*ns+nt+t))
|
|
|
|
!* threshold stress for dislocation motion
|
|
forall (s = 1:ns) &
|
|
state(g,ip,el)%p(5*ns+3*nt+s) = &
|
|
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+1:2*ns)),&
|
|
constitutive_dislotwin_interactionMatrixSlipSlip(1:ns,s,myInstance)))
|
|
|
|
!* threshold stress for growing twin
|
|
forall (t = 1:nt) &
|
|
state(g,ip,el)%p(6*ns+3*nt+t) = &
|
|
constitutive_dislotwin_Cthresholdtwin(myInstance)*&
|
|
(sfe/(3.0_pReal*constitutive_dislotwin_burgersPerTwinSystem(t,myInstance))+&
|
|
(constitutive_dislotwin_burgersPerTwinSystem(t,myInstance)*constitutive_dislotwin_Gmod(myInstance))/&
|
|
state(g,ip,el)%p(5*ns+2*nt+t))
|
|
|
|
!* final twin volume after growth
|
|
forall (t = 1:nt) &
|
|
state(g,ip,el)%p(6*ns+4*nt+t) = &
|
|
(pi/6.0_pReal)*constitutive_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,x)/))') 'rhoEdge',state(g,ip,el)%p(1:ns)/1e9
|
|
! write(6,'(a,/,4(3(f10.4,x)/))') 'rhoEdgeDip',state(g,ip,el)%p(ns+1:2*ns)/1e9
|
|
! write(6,'(a,/,4(3(f10.4,x)/))') 'Fraction',state(g,ip,el)%p(2*ns+1:2*ns+nt)
|
|
!endif
|
|
|
|
|
|
return
|
|
end subroutine
|
|
|
|
|
|
subroutine constitutive_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
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
implicit none
|
|
|
|
!* Input-Output variables
|
|
integer(pInt), intent(in) :: g,ip,el
|
|
real(pReal), intent(in) :: Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: state
|
|
real(pReal), dimension(3,3), intent(out) :: Lp
|
|
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar
|
|
!* Local variables
|
|
integer(pInt) myInstance,myStructure,ns,nt,f,i,j,k,l,m,n,index_myFamily
|
|
real(pReal) sumf,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0
|
|
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
|
real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
|
gdot_slip,dgdot_dtauslip,tau_slip
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
|
gdot_twin,dgdot_dtautwin,tau_twin
|
|
|
|
!* Shortened notation
|
|
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
|
|
myStructure = constitutive_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
|
|
|
|
Lp = 0.0_pReal
|
|
dLp_dTstar3333 = 0.0_pReal
|
|
dLp_dTstar = 0.0_pReal
|
|
|
|
!* Dislocation glide part
|
|
gdot_slip = 0.0_pReal
|
|
dgdot_dtauslip = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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=1:3,l=1:3,m=1:3,n=1:3) &
|
|
dLp_dTstar3333(k,l,m,n) = &
|
|
dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*&
|
|
lattice_Sslip(k,l,index_myFamily+i,myStructure)*&
|
|
lattice_Sslip(m,n,index_myFamily+i,myStructure)
|
|
enddo
|
|
enddo
|
|
|
|
!* Mechanical twinning part
|
|
gdot_twin = 0.0_pReal
|
|
dgdot_dtautwin = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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=1:3,l=1:3,m=1:3,n=1:3) &
|
|
dLp_dTstar3333(k,l,m,n) = &
|
|
dLp_dTstar3333(k,l,m,n) + dgdot_dtautwin(j)*&
|
|
lattice_Stwin(k,l,index_myFamily+i,myStructure)*&
|
|
lattice_Stwin(m,n,index_myFamily+i,myStructure)
|
|
enddo
|
|
enddo
|
|
|
|
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
!if ((ip==1).and.(el==1)) then
|
|
! write(6,*) '#LP/TANGENT#'
|
|
! write(6,*)
|
|
! write(6,*) 'Tstar_v', Tstar_v
|
|
! write(6,*) 'tau_slip', tau_slip
|
|
! write(6,'(a10,/,4(3(e20.8,x),/))') 'state',state(1,1,1)%p
|
|
! write(6,'(a,/,3(3(f10.4,x)/))') 'Lp',Lp
|
|
! write(6,'(a,/,9(9(f10.4,x)/))') 'dLp_dTstar',dLp_dTstar
|
|
!endif
|
|
|
|
return
|
|
end subroutine
|
|
|
|
|
|
function constitutive_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_constitutionInstance
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
implicit none
|
|
|
|
!* Input-Output variables
|
|
integer(pInt), intent(in) :: g,ip,el
|
|
real(pReal), intent(in) :: Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
|
|
real(pReal), dimension(constitutive_dislotwin_sizeDotState(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
|
constitutive_dislotwin_dotState
|
|
!* Local variables
|
|
integer(pInt) MyInstance,MyStructure,ns,nt,f,i,j,k,index_myFamily
|
|
real(pReal) sumf,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
|
|
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r
|
|
real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
|
gdot_slip,tau_slip,DotRhoMultiplication,EdgeDipDistance,DotRhoEdgeEdgeAnnihilation,DotRhoEdgeDipAnnihilation,&
|
|
|
|
ClimbVelocity,DotRhoEdgeDipClimb,DotRhoDipFormation
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_constitutionInstance(material_phase(g,ip,el)))) :: gdot_twin,tau_twin
|
|
|
|
!* Shortened notation
|
|
myInstance = phase_constitutionInstance(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
|
|
|
|
constitutive_dislotwin_dotState = 0.0_pReal
|
|
|
|
!* Dislocation density evolution
|
|
gdot_slip = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,MyStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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*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))
|
|
|
|
!* 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,lattice_maxNtwinFamily ! loop over all twin families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,MyStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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*ns+j) = &
|
|
(constitutive_dislotwin_MaxTwinFraction(myInstance)-sumf)*&
|
|
state(g,ip,el)%p(6*ns+4*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,x)/))') 'tau slip',tau_slip
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'gamma slip',gdot_slip
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'RhoEdge',state(g,ip,el)%p(1:ns)
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'Threshold Slip', state(g,ip,el)%p(5*ns+3*nt+1:6*ns+3*nt)
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'Multiplication',DotRhoMultiplication
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'DipFormation',DotRhoDipFormation
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'SingleSingle',DotRhoEdgeEdgeAnnihilation
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'SingleDipole',DotRhoEdgeDipAnnihilation
|
|
!write(6,'(a,/,4(3(f30.20,x)/))') 'DipClimb',DotRhoEdgeDipClimb
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
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
|
|
|
|
|
|
pure 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
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
|
|
use lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), intent(in) :: g,ip,el
|
|
real(pReal), intent(in) :: dt,Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
|
|
integer(pInt) myInstance,myStructure,ns,nt,f,o,i,c,j,index_myFamily
|
|
real(pReal) sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,gdot_slip,dgdot_dtauslip
|
|
real(pReal), dimension(constitutive_dislotwin_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
|
constitutive_dislotwin_postResults
|
|
|
|
!* Shortened notation
|
|
myInstance = phase_constitutionInstance(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
|
|
|
|
do o = 1,phase_Noutput(material_phase(g,ip,el))
|
|
select case(constitutive_dislotwin_output(o,myInstance))
|
|
|
|
case ('edge_density')
|
|
constitutive_dislotwin_postResults(c+1:c+ns) = state(g,ip,el)%p(1:ns)
|
|
c = c + ns
|
|
case ('dipole_density')
|
|
constitutive_dislotwin_postResults(c+1:c+ns) = state(g,ip,el)%p(ns+1:2*ns)
|
|
c = c + ns
|
|
case ('shear_rate_slip')
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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*ns+3*nt+j))**constitutive_dislotwin_p(myInstance)
|
|
StressRatio_pminus1 = (abs(tau)/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
|
|
constitutive_dislotwin_postResults(c+j) = &
|
|
DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_dislotwin_q(myInstance))*sign(1.0_pReal,tau)
|
|
enddo ; enddo
|
|
c = c + ns
|
|
case ('mfp_slip')
|
|
constitutive_dislotwin_postResults(c+1:c+ns) = state(g,ip,el)%p((4*ns+2*nt+1):(5*ns+2*nt))
|
|
c = c + ns
|
|
case ('resolved_stress_slip')
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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:c+ns) = state(g,ip,el)%p((5*ns+3*nt+1):(6*ns+3*nt))
|
|
c = c + ns
|
|
case ('edge_dipole_distance')
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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 ('twin_fraction')
|
|
constitutive_dislotwin_postResults(c+1:c+nt) = state(g,ip,el)%p((2*ns+1):(2*ns+nt))
|
|
c = c + nt
|
|
case ('shear_rate_twin')
|
|
if (nt > 0_pInt) then
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all twin families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_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*ns+3*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*ns+4*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:c+nt) = state(g,ip,el)%p((5*ns+2*nt+1):(5*ns+3*nt))
|
|
c = c + nt
|
|
case ('resolved_stress_twin')
|
|
if (nt > 0_pInt) then
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,myStructure)) ! at which index starts my family
|
|
do i = 1,constitutive_dislotwin_Ntwin(f,myInstance) ! process each (active) slip system in family
|
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j = j + 1_pInt
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constitutive_dislotwin_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,myStructure))
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enddo; enddo
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endif
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c = c + nt
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case ('threshold_stress_twin')
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constitutive_dislotwin_postResults(c+1:c+nt) = state(g,ip,el)%p((6*ns+3*nt+1):(6*ns+4*nt))
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c = c + nt
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case ('stress_exponent')
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j = 0_pInt
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do f = 1,lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum(lattice_NslipSystem(1:f-1,myStructure)) ! at which index starts my family
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do i = 1,constitutive_dislotwin_Nslip(f,myInstance) ! process each (active) slip system in family
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j = j + 1_pInt
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!* Resolved shear stress on slip system
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tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,myStructure))
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!* Stress ratios
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StressRatio_p = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))**constitutive_dislotwin_p(myInstance)
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StressRatio_pminus1 = (abs(tau)/state(g,ip,el)%p(5*ns+3*nt+j))**(constitutive_dislotwin_p(myInstance)-1.0_pReal)
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!* Boltzmann ratio
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BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(f,myInstance)/(kB*Temperature)
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!* Initial shear rates
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DotGamma0 = &
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state(g,ip,el)%p(j)*constitutive_dislotwin_burgersPerSlipSystem(f,myInstance)* &
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constitutive_dislotwin_v0PerSlipSystem(f,myInstance)
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!* Shear rates due to slip
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gdot_slip = &
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DotGamma0*exp(-BoltzmannRatio*(1-StressRatio_p)**constitutive_dislotwin_q(myInstance))*sign(1.0_pReal,tau)
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!* Derivatives of shear rates
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dgdot_dtauslip = &
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((abs(gdot_slip)*BoltzmannRatio*&
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constitutive_dislotwin_p(myInstance)*constitutive_dislotwin_q(myInstance))/state(g,ip,el)%p(5*ns+3*nt+j))*&
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StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislotwin_q(myInstance)-1.0_pReal)
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!* Stress exponent
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if (gdot_slip==0.0_pReal) then
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constitutive_dislotwin_postResults(c+j) = 0.0_pReal
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else
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constitutive_dislotwin_postResults(c+j) = (tau/gdot_slip)*dgdot_dtauslip
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endif
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enddo ; enddo
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c = c + ns
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end select
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enddo
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return
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end function
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END MODULE
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