1891 lines
107 KiB
Fortran
1891 lines
107 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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! $Id$
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!--------------------------------------------------------------------------------------------------
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief material subroutine incoprorating dislocation and twinning physics
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!> @details to be done
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!--------------------------------------------------------------------------------------------------
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module constitutive_dislotwin
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use prec, only: &
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pReal, &
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pInt
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implicit none
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private
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integer(pInt), dimension(:), allocatable, public, protected :: &
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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, public :: &
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constitutive_dislotwin_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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constitutive_dislotwin_output !< name of each post result output
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character(len=12), dimension(3), parameter, private :: &
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CONSTITUTIVE_DISLOTWIN_listBasicSlipStates = &
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['rhoEdge ', 'rhoEdgeDip ', 'accshearslip']
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character(len=12), dimension(2), parameter, private :: &
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CONSTITUTIVE_DISLOTWIN_listBasicTwinStates = &
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['twinFraction', 'accsheartwin']
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character(len=17), dimension(4), parameter, private :: &
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CONSTITUTIVE_DISLOTWIN_listDependentSlipStates = &
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['invLambdaSlip ', 'invLambdaSlipTwin', 'meanFreePathSlip ', 'tauSlipThreshold ']
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character(len=16), dimension(4), parameter, private :: &
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CONSTITUTIVE_DISLOTWIN_listDependentTwinStates = &
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['invLambdaTwin ', 'meanFreePathTwin', 'tauTwinThreshold', 'twinVolume ']
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real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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integer(pInt), dimension(:), allocatable, private :: &
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constitutive_dislotwin_Noutput !< number of outputs per instance of this plasticity
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integer(pInt), dimension(:), allocatable, private :: &
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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, private :: &
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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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real(pReal), dimension(:), allocatable, private :: &
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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_pShearBand, & !< p-exponent in shearband velocity
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constitutive_dislotwin_qShearBand, & !< q-exponent in shearband velocity
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constitutive_dislotwin_MaxTwinFraction, & !< maximum allowed total twin volume fraction
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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_SolidSolutionStrength, & !< Strength due to elements in solid solution
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constitutive_dislotwin_L0, & !< Length of twin nuclei in Burgers vectors
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constitutive_dislotwin_xc, & !< critical distance for formation of twin nucleus
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constitutive_dislotwin_VcrossSlip, & !< cross slip volume
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constitutive_dislotwin_sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
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constitutive_dislotwin_sbVelocity, & !< value for shearband velocity_0
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constitutive_dislotwin_sbQedge, & !< value for shearband systems Qedge
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constitutive_dislotwin_SFE_0K, & !< stacking fault energy at zero K
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constitutive_dislotwin_dSFE_dT, & !< temperature dependance of stacking fault energy
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constitutive_dislotwin_dipoleFormationFactor, & !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
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constitutive_dislotwin_aTolRho, & !< absolute tolerance for integration of dislocation density
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constitutive_dislotwin_aTolTwinFrac !< absolute tolerance for integration of twin volume fraction
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real(pReal), dimension(:,:,:,:), allocatable, private :: &
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constitutive_dislotwin_Ctwin66 !< twin elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:,:,:,:,:), allocatable, private :: &
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constitutive_dislotwin_Ctwin3333 !< twin elasticity matrix for each instance
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real(pReal), dimension(:,:), allocatable, private :: &
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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_tau_peierlsPerSlipFamily, & !< Peierls stress [Pa] for each family 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_tau_r, & !< stress to bring partial close together 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_interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type and instance
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constitutive_dislotwin_interaction_SlipTwin, & !< coefficients for slip-twin interaction for each interaction type and instance
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constitutive_dislotwin_interaction_TwinSlip, & !< coefficients for twin-slip interaction for each interaction type and instance
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constitutive_dislotwin_interaction_TwinTwin, & !< coefficients for twin-twin interaction for each interaction type and instance
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constitutive_dislotwin_pPerSlipFamily, & !< p-exponent in glide velocity
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constitutive_dislotwin_qPerSlipFamily, & !< q-exponent in glide velocity
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constitutive_dislotwin_rPerTwinFamily !< r-exponent in twin nucleation rate
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real(pReal), dimension(:,:,:), allocatable, private :: &
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constitutive_dislotwin_interactionMatrix_SlipSlip, & !< interaction matrix of the different slip systems for each instance
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constitutive_dislotwin_interactionMatrix_SlipTwin, & !< interaction matrix of slip systems with twin systems for each instance
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constitutive_dislotwin_interactionMatrix_TwinSlip, & !< interaction matrix of twin systems with slip systems for each instance
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constitutive_dislotwin_interactionMatrix_TwinTwin, & !< 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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real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
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constitutive_dislotwin_sbSv
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enum, bind(c)
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enumerator :: undefined_ID, &
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edge_density_ID, &
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dipole_density_ID, &
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shear_rate_slip_ID, &
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accumulated_shear_slip_ID, &
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mfp_slip_ID, &
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resolved_stress_slip_ID, &
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threshold_stress_slip_ID, &
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edge_dipole_distance_ID, &
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stress_exponent_ID, &
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twin_fraction_ID, &
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shear_rate_twin_ID, &
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accumulated_shear_twin_ID, &
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mfp_twin_ID, &
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resolved_stress_twin_ID, &
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threshold_stress_twin_ID, &
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resolved_stress_shearband_ID, &
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shear_rate_shearband_ID, &
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sb_eigenvalues_ID, &
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sb_eigenvectors_ID
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end enum
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integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: &
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constitutive_dislotwin_outputID !< ID of each post result output
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public :: &
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constitutive_dislotwin_init, &
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constitutive_dislotwin_stateInit, &
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constitutive_dislotwin_aTolState, &
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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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constitutive_dislotwin_dotState, &
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constitutive_dislotwin_postResults
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief module initialization
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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subroutine constitutive_dislotwin_init(fileUnit)
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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use debug, only: &
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debug_level,&
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debug_constitutive,&
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debug_levelBasic
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use math, only: &
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math_Mandel3333to66, &
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math_Voigt66to3333, &
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math_mul3x3
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use mesh, only: &
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mesh_maxNips, &
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mesh_NcpElems
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use IO, only: &
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IO_read, &
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IO_lc, &
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IO_getTag, &
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IO_isBlank, &
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IO_stringPos, &
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IO_stringValue, &
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IO_floatValue, &
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IO_intValue, &
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IO_warning, &
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IO_error, &
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IO_timeStamp, &
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IO_EOF
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use material, only: &
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homogenization_maxNgrains, &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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PLASTICITY_DISLOTWIN_label, &
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PLASTICITY_DISLOTWIN_ID, &
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MATERIAL_partPhase
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use lattice
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implicit none
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integer(pInt), intent(in) :: fileUnit
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integer(pInt), parameter :: MAXNCHUNKS = LATTICE_maxNinteraction + 1_pInt
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integer(pInt), dimension(1+2*MAXNCHUNKS) :: positions
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integer(pInt) :: maxNinstance,mySize=0_pInt,phase,maxTotalNslip,maxTotalNtwin,&
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f,instance,j,k,l,m,n,o,p,q,r,s,ns,nt, &
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Nchunks_SlipSlip, Nchunks_SlipTwin, Nchunks_TwinSlip, Nchunks_TwinTwin, &
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Nchunks_SlipFamilies, Nchunks_TwinFamilies, &
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index_myFamily, index_otherFamily
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character(len=65536) :: &
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tag = '', &
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line = ''
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real(pReal), dimension(:), allocatable :: tempPerSlip, tempPerTwin
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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write(6,'(a)') ' $Id$'
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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#include "compilation_info.f90"
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maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOTWIN_ID),pInt)
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if (maxNinstance == 0_pInt) return
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
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write(6,'(a16,1x,i5,/)') '# instances:',maxNinstance
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allocate(constitutive_dislotwin_sizeDotState(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_sizeState(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_sizePostResults(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
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allocate(constitutive_dislotwin_output(maxval(phase_Noutput),maxNinstance))
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constitutive_dislotwin_output = ''
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allocate(constitutive_dislotwin_outputID(maxval(phase_Noutput),maxNinstance), source=undefined_ID)
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allocate(constitutive_dislotwin_Noutput(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_Ntwin(lattice_maxNtwinFamily,maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_totalNslip(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_totalNtwin(maxNinstance), source=0_pInt)
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allocate(constitutive_dislotwin_CAtomicVolume(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_D0(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_Qsd(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_GrainSize(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_pShearBand(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_qShearBand(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_MaxTwinFraction(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_CEdgeDipMinDistance(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_Cmfptwin(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_Cthresholdtwin(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_SolidSolutionStrength(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_L0(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_xc(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_VcrossSlip(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_aTolRho(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_aTolTwinFrac(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_sbResistance(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_sbVelocity(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_sbQedge(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_SFE_0K(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_dSFE_dT(maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_dipoleFormationFactor(maxNinstance), source=1.0_pReal) !should be on by default
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allocate(constitutive_dislotwin_rhoEdge0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_rhoEdgeDip0(lattice_maxNslipFamily,maxNinstance), source=0.0_pReal)
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allocate(constitutive_dislotwin_burgersPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_burgersPerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_QedgePerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_v0PerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_tau_peierlsPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_pPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
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allocate(constitutive_dislotwin_qPerSlipFamily(lattice_maxNslipFamily,maxNinstance),source=0.0_pReal)
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allocate(constitutive_dislotwin_Ndot0PerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_twinsizePerTwinFamily(lattice_maxNtwinFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_CLambdaSlipPerSlipFamily(lattice_maxNslipFamily,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_rPerTwinFamily(lattice_maxNtwinFamily,maxNinstance),source=0.0_pReal)
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allocate(constitutive_dislotwin_interaction_SlipSlip(lattice_maxNinteraction,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_interaction_SlipTwin(lattice_maxNinteraction,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_interaction_TwinSlip(lattice_maxNinteraction,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_interaction_TwinTwin(lattice_maxNinteraction,maxNinstance), &
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source=0.0_pReal)
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allocate(constitutive_dislotwin_sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), &
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source=0.0_pReal)
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rewind(fileUnit)
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phase = 0_pInt
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do while (trim(line) /= IO_EOF .and. IO_lc(IO_getTag(line,'<','>')) /= MATERIAL_partPhase) ! wind forward to <phase>
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line = IO_read(fileUnit)
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enddo
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parsingFile: do while (trim(line) /= IO_EOF) ! read through sections of phase part
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line = IO_read(fileUnit)
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') then ! stop at next part
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line = IO_read(fileUnit, .true.) ! reset IO_read
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exit
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endif
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if (IO_getTag(line,'[',']') /= '') then ! next phase section
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phase = phase + 1_pInt ! advance phase section counter
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if (phase_plasticity(phase) == PLASTICITY_DISLOTWIN_ID) then
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Nchunks_SlipFamilies = count(lattice_NslipSystem(:,phase) > 0_pInt)
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Nchunks_TwinFamilies = count(lattice_NtwinSystem(:,phase) > 0_pInt)
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Nchunks_SlipSlip = maxval(lattice_interactionSlipSlip(:,:,phase))
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Nchunks_SlipTwin = maxval(lattice_interactionSlipTwin(:,:,phase))
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Nchunks_TwinSlip = maxval(lattice_interactionTwinSlip(:,:,phase))
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Nchunks_TwinTwin = maxval(lattice_interactionTwinTwin(:,:,phase))
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if(allocated(tempPerSlip)) deallocate(tempPerSlip)
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if(allocated(tempPerTwin)) deallocate(tempPerTwin)
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allocate(tempPerSlip(Nchunks_SlipFamilies))
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allocate(tempPerTwin(Nchunks_TwinFamilies))
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endif
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cycle ! skip to next line
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endif
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if (phase > 0_pInt ) then; if (phase_plasticity(phase) == PLASTICITY_DISLOTWIN_ID) then ! do not short-circuit here (.and. with next if statemen). It's not safe in Fortran
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instance = phase_plasticityInstance(phase) ! which instance of my plasticity is present phase
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positions = IO_stringPos(line,MAXNCHUNKS)
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tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
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select case(tag)
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case ('plasticity','elasticity','lattice_structure', & ! already known
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'covera_ratio','c/a_ratio','c/a', &
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'c11','c12','c13','c22','c23','c33','c44','c55','c66')
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cycle
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case ('(output)')
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constitutive_dislotwin_Noutput(instance) = constitutive_dislotwin_Noutput(instance) + 1_pInt
|
|
constitutive_dislotwin_output(constitutive_dislotwin_Noutput(instance),instance) = &
|
|
IO_lc(IO_stringValue(line,positions,2_pInt))
|
|
select case(IO_lc(IO_stringValue(line,positions,2_pInt)))
|
|
case ('edge_density')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = edge_density_ID
|
|
case ('dipole_density')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = dipole_density_ID
|
|
case ('shear_rate_slip')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = shear_rate_slip_ID
|
|
case ('accumulated_shear_slip')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = accumulated_shear_slip_ID
|
|
case ('mfp_slip')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = mfp_slip_ID
|
|
case ('resolved_stress_slip')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = resolved_stress_slip_ID
|
|
case ('edge_dipole_distance')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = edge_dipole_distance_ID
|
|
case ('stress_exponent')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = stress_exponent_ID
|
|
case ('twin_fraction')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = twin_fraction_ID
|
|
case ('shear_rate_twin')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = shear_rate_twin_ID
|
|
case ('accumulated_shear_twin')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = accumulated_shear_twin_ID
|
|
case ('mfp_twin')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = mfp_twin_ID
|
|
case ('resolved_stress_twin')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = resolved_stress_twin_ID
|
|
case ('threshold_stress_twin')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = threshold_stress_twin_ID
|
|
case ('resolved_stress_shearband')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = resolved_stress_shearband_ID
|
|
case ('shear_rate_shearband')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = shear_rate_shearband_ID
|
|
case ('sb_eigenvalues')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = sb_eigenvalues_ID
|
|
case ('sb_eigenvectors')
|
|
constitutive_dislotwin_outputID(constitutive_dislotwin_Noutput(instance),instance) = sb_eigenvectors_ID
|
|
case default
|
|
call IO_error(105_pInt,ext_msg=IO_stringValue(line,positions,2_pInt)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
end select
|
|
!--------------------------------------------------------------------------------------------------
|
|
! parameters depending on number of slip system families
|
|
case ('nslip')
|
|
if (positions(1) < Nchunks_SlipFamilies + 1_pInt) &
|
|
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (positions(1) > Nchunks_SlipFamilies + 1_pInt) &
|
|
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
Nchunks_SlipFamilies = positions(1) - 1_pInt
|
|
do j = 1_pInt, Nchunks_SlipFamilies
|
|
constitutive_dislotwin_Nslip(j,instance) = IO_intValue(line,positions,1_pInt+j)
|
|
enddo
|
|
case ('rhoedge0','rhoedgedip0','slipburgers','qedge','v0','clambdaslip','tau_peierls','p_slip','q_slip')
|
|
do j = 1_pInt, Nchunks_SlipFamilies
|
|
tempPerSlip(j) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
select case(tag)
|
|
case ('rhoedge0')
|
|
constitutive_dislotwin_rhoEdge0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('rhoedgedip0')
|
|
constitutive_dislotwin_rhoEdgeDip0(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('slipburgers')
|
|
constitutive_dislotwin_burgersPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('qedge')
|
|
constitutive_dislotwin_QedgePerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('v0')
|
|
constitutive_dislotwin_v0PerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('clambdaslip')
|
|
constitutive_dislotwin_CLambdaSlipPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('tau_peierls')
|
|
if (lattice_structure(phase) /= LATTICE_bcc_ID) &
|
|
call IO_warning(42_pInt,ext_msg=trim(tag)//' for non-bcc ('//PLASTICITY_DISLOTWIN_label//')')
|
|
constitutive_dislotwin_tau_peierlsPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('p_slip')
|
|
constitutive_dislotwin_pPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
case ('q_slip')
|
|
constitutive_dislotwin_qPerSlipFamily(1:Nchunks_SlipFamilies,instance) = tempPerSlip(1:Nchunks_SlipFamilies)
|
|
end select
|
|
!--------------------------------------------------------------------------------------------------
|
|
! parameters depending on slip number of twin families
|
|
case ('ntwin')
|
|
if (positions(1) < Nchunks_TwinFamilies + 1_pInt) &
|
|
call IO_warning(50_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (positions(1) > Nchunks_TwinFamilies + 1_pInt) &
|
|
call IO_error(150_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
Nchunks_TwinFamilies = positions(1) - 1_pInt
|
|
do j = 1_pInt, Nchunks_TwinFamilies
|
|
constitutive_dislotwin_Ntwin(j,instance) = IO_intValue(line,positions,1_pInt+j)
|
|
enddo
|
|
case ('ndot0','twinsize','twinburgers','r_twin')
|
|
do j = 1_pInt, Nchunks_TwinFamilies
|
|
tempPerTwin(j) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
select case(tag)
|
|
case ('ndot0')
|
|
if (lattice_structure(phase) == LATTICE_fcc_ID) &
|
|
call IO_warning(42_pInt,ext_msg=trim(tag)//' for fcc ('//PLASTICITY_DISLOTWIN_label//')')
|
|
constitutive_dislotwin_Ndot0PerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
|
|
case ('twinsize')
|
|
constitutive_dislotwin_twinsizePerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
|
|
case ('twinburgers')
|
|
constitutive_dislotwin_burgersPerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
|
|
case ('r_twin')
|
|
constitutive_dislotwin_rPerTwinFamily(1:Nchunks_TwinFamilies,instance) = tempPerTwin(1:Nchunks_TwinFamilies)
|
|
end select
|
|
!--------------------------------------------------------------------------------------------------
|
|
! parameters depending on number of interactions
|
|
case ('interaction_slipslip','interactionslipslip')
|
|
if (positions(1) < 1_pInt + Nchunks_SlipSlip) &
|
|
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
do j = 1_pInt, Nchunks_SlipSlip
|
|
constitutive_dislotwin_interaction_SlipSlip(j,instance) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
case ('interaction_sliptwin','interactionsliptwin')
|
|
if (positions(1) < 1_pInt + Nchunks_SlipTwin) &
|
|
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
do j = 1_pInt, Nchunks_SlipTwin
|
|
constitutive_dislotwin_interaction_SlipTwin(j,instance) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
case ('interaction_twinslip','interactiontwinslip')
|
|
if (positions(1) < 1_pInt + Nchunks_TwinSlip) &
|
|
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
do j = 1_pInt, Nchunks_TwinSlip
|
|
constitutive_dislotwin_interaction_TwinSlip(j,instance) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
case ('interaction_twintwin','interactiontwintwin')
|
|
if (positions(1) < 1_pInt + Nchunks_TwinTwin) &
|
|
call IO_warning(52_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
do j = 1_pInt, Nchunks_TwinTwin
|
|
constitutive_dislotwin_interaction_TwinTwin(j,instance) = IO_floatValue(line,positions,1_pInt+j)
|
|
enddo
|
|
!--------------------------------------------------------------------------------------------------
|
|
! parameters independent of number of slip/twin systems
|
|
case ('grainsize')
|
|
constitutive_dislotwin_GrainSize(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('maxtwinfraction')
|
|
constitutive_dislotwin_MaxTwinFraction(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('p_shearband')
|
|
constitutive_dislotwin_pShearBand(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('q_shearband')
|
|
constitutive_dislotwin_qShearBand(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('d0')
|
|
constitutive_dislotwin_D0(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('qsd')
|
|
constitutive_dislotwin_Qsd(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('atol_rho')
|
|
constitutive_dislotwin_aTolRho(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('atol_twinfrac')
|
|
constitutive_dislotwin_aTolTwinFrac(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('cmfptwin')
|
|
constitutive_dislotwin_Cmfptwin(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('cthresholdtwin')
|
|
constitutive_dislotwin_Cthresholdtwin(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('solidsolutionstrength')
|
|
constitutive_dislotwin_SolidSolutionStrength(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('l0')
|
|
constitutive_dislotwin_L0(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('xc')
|
|
constitutive_dislotwin_xc(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('vcrossslip')
|
|
constitutive_dislotwin_VcrossSlip(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('cedgedipmindistance')
|
|
constitutive_dislotwin_CEdgeDipMinDistance(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('catomicvolume')
|
|
constitutive_dislotwin_CAtomicVolume(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('sfe_0k')
|
|
constitutive_dislotwin_SFE_0K(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('dsfe_dt')
|
|
constitutive_dislotwin_dSFE_dT(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('dipoleformationfactor')
|
|
constitutive_dislotwin_dipoleFormationFactor(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('shearbandresistance')
|
|
constitutive_dislotwin_sbResistance(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('shearbandvelocity')
|
|
constitutive_dislotwin_sbVelocity(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case ('qedgepersbsystem')
|
|
constitutive_dislotwin_sbQedge(instance) = IO_floatValue(line,positions,2_pInt)
|
|
case default
|
|
call IO_error(210_pInt,ext_msg=trim(tag)//' ('//PLASTICITY_DISLOTWIN_label//')')
|
|
end select
|
|
endif; endif
|
|
enddo parsingFile
|
|
|
|
sanityChecks: do phase = 1_pInt, size(phase_plasticity)
|
|
myPhase: if (phase_plasticity(phase) == PLASTICITY_dislotwin_ID) then
|
|
instance = phase_plasticityInstance(phase)
|
|
if (sum(constitutive_dislotwin_Nslip(:,instance)) < 0_pInt) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='Nslip ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (sum(constitutive_dislotwin_Ntwin(:,instance)) < 0_pInt) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='Ntwin ('//PLASTICITY_DISLOTWIN_label//')')
|
|
do f = 1_pInt,lattice_maxNslipFamily
|
|
if (constitutive_dislotwin_Nslip(f,instance) > 0_pInt) then
|
|
if (constitutive_dislotwin_rhoEdge0(f,instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_rhoEdgeDip0(f,instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_v0PerSlipFamily(f,instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOTWIN_label//')')
|
|
endif
|
|
enddo
|
|
do f = 1_pInt,lattice_maxNtwinFamily
|
|
if (constitutive_dislotwin_Ntwin(f,instance) > 0_pInt) then
|
|
if (constitutive_dislotwin_burgersPerTwinFamily(f,instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='twinburgers ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_Ndot0PerTwinFamily(f,instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='ndot0 ('//PLASTICITY_DISLOTWIN_label//')')
|
|
endif
|
|
enddo
|
|
if (constitutive_dislotwin_CAtomicVolume(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_D0(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_Qsd(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (sum(constitutive_dislotwin_Ntwin(:,instance)) > 0_pInt) then
|
|
if (constitutive_dislotwin_SFE_0K(instance) == 0.0_pReal .and. &
|
|
constitutive_dislotwin_dSFE_dT(instance) == 0.0_pReal .and. &
|
|
lattice_structure(phase) == LATTICE_fcc_ID) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_aTolRho(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_aTolTwinFrac(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOTWIN_label//')')
|
|
endif
|
|
if (constitutive_dislotwin_sbResistance(instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='sbResistance ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_sbVelocity(instance) < 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='sbVelocity ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_sbVelocity(instance) > 0.0_pReal .and. &
|
|
constitutive_dislotwin_pShearBand(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='pShearBand ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_dipoleFormationFactor(instance) /= 0.0_pReal .and. &
|
|
constitutive_dislotwin_dipoleFormationFactor(instance) /= 1.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='dipoleFormationFactor ('//PLASTICITY_DISLOTWIN_label//')')
|
|
if (constitutive_dislotwin_sbVelocity(instance) > 0.0_pReal .and. &
|
|
constitutive_dislotwin_qShearBand(instance) <= 0.0_pReal) &
|
|
call IO_error(211_pInt,el=instance,ext_msg='qShearBand ('//PLASTICITY_DISLOTWIN_label//')')
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Determine total number of active slip or twin systems
|
|
constitutive_dislotwin_Nslip(:,instance) = min(lattice_NslipSystem(:,phase),constitutive_dislotwin_Nslip(:,instance))
|
|
constitutive_dislotwin_Ntwin(:,instance) = min(lattice_NtwinSystem(:,phase),constitutive_dislotwin_Ntwin(:,instance))
|
|
constitutive_dislotwin_totalNslip(instance) = sum(constitutive_dislotwin_Nslip(:,instance))
|
|
constitutive_dislotwin_totalNtwin(instance) = sum(constitutive_dislotwin_Ntwin(:,instance))
|
|
endif myPhase
|
|
enddo sanityChecks
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_burgersPerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_QedgePerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_v0PerSlipSystem(maxTotalNslip, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_Ndot0PerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_tau_r(maxTotalNtwin, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_twinsizePerTwinSystem(maxTotalNtwin, maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_CLambdaSlipPerSlipSystem(maxTotalNslip, maxNinstance),source=0.0_pReal)
|
|
|
|
allocate(constitutive_dislotwin_interactionMatrix_SlipSlip(maxval(constitutive_dislotwin_totalNslip),& ! slip resistance from slip activity
|
|
maxval(constitutive_dislotwin_totalNslip),&
|
|
maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_interactionMatrix_SlipTwin(maxval(constitutive_dislotwin_totalNslip),& ! slip resistance from twin activity
|
|
maxval(constitutive_dislotwin_totalNtwin),&
|
|
maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_interactionMatrix_TwinSlip(maxval(constitutive_dislotwin_totalNtwin),& ! twin resistance from slip activity
|
|
maxval(constitutive_dislotwin_totalNslip),&
|
|
maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_interactionMatrix_TwinTwin(maxval(constitutive_dislotwin_totalNtwin),& ! twin resistance from twin activity
|
|
maxval(constitutive_dislotwin_totalNtwin),&
|
|
maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance), &
|
|
source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_Ctwin66(6,6,maxTotalNtwin,maxNinstance), source=0.0_pReal)
|
|
allocate(constitutive_dislotwin_Ctwin3333(3,3,3,3,maxTotalNtwin,maxNinstance), source=0.0_pReal)
|
|
|
|
initializeInstances: do phase = 1_pInt, size(phase_plasticity)
|
|
if (phase_plasticity(phase) == PLASTICITY_dislotwin_ID) then
|
|
instance = phase_plasticityInstance(phase)
|
|
|
|
ns = constitutive_dislotwin_totalNslip(instance)
|
|
nt = constitutive_dislotwin_totalNtwin(instance)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Determine size of state array
|
|
constitutive_dislotwin_sizeDotState(instance) = int(size(CONSTITUTIVE_DISLOTWIN_listBasicSlipStates),pInt) * ns &
|
|
+ int(size(CONSTITUTIVE_DISLOTWIN_listBasicTwinStates),pInt) * nt
|
|
constitutive_dislotwin_sizeState(instance) = constitutive_dislotwin_sizeDotState(instance) &
|
|
+ int(size(CONSTITUTIVE_DISLOTWIN_listDependentSlipStates),pInt) * ns &
|
|
+ int(size(CONSTITUTIVE_DISLOTWIN_listDependentTwinStates),pInt) * nt
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! Determine size of postResults array
|
|
outputsLoop: do o = 1_pInt,constitutive_dislotwin_Noutput(instance)
|
|
select case(constitutive_dislotwin_outputID(o,instance))
|
|
case(edge_density_ID, &
|
|
dipole_density_ID, &
|
|
shear_rate_slip_ID, &
|
|
accumulated_shear_slip_ID, &
|
|
mfp_slip_ID, &
|
|
resolved_stress_slip_ID, &
|
|
threshold_stress_slip_ID, &
|
|
edge_dipole_distance_ID, &
|
|
stress_exponent_ID &
|
|
)
|
|
mySize = ns
|
|
case(twin_fraction_ID, &
|
|
shear_rate_twin_ID, &
|
|
accumulated_shear_twin_ID, &
|
|
mfp_twin_ID, &
|
|
resolved_stress_twin_ID, &
|
|
threshold_stress_twin_ID &
|
|
)
|
|
mySize = nt
|
|
case(resolved_stress_shearband_ID, &
|
|
shear_rate_shearband_ID &
|
|
)
|
|
mySize = 6_pInt
|
|
case(sb_eigenvalues_ID)
|
|
mySize = 3_pInt
|
|
case(sb_eigenvectors_ID)
|
|
mySize = 9_pInt
|
|
end select
|
|
|
|
if (mySize > 0_pInt) then ! any meaningful output found
|
|
constitutive_dislotwin_sizePostResult(o,instance) = mySize
|
|
constitutive_dislotwin_sizePostResults(instance) = constitutive_dislotwin_sizePostResults(instance) + mySize
|
|
endif
|
|
enddo outputsLoop
|
|
|
|
!* Process slip related parameters ------------------------------------------------
|
|
|
|
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(constitutive_dislotwin_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
|
|
slipSystemsLoop: do j = 1_pInt,constitutive_dislotwin_Nslip(f,instance)
|
|
|
|
!* Burgers vector,
|
|
! dislocation velocity prefactor,
|
|
! mean free path prefactor,
|
|
! and minimum dipole distance
|
|
|
|
constitutive_dislotwin_burgersPerSlipSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_burgersPerSlipFamily(f,instance)
|
|
|
|
constitutive_dislotwin_QedgePerSlipSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_QedgePerSlipFamily(f,instance)
|
|
|
|
constitutive_dislotwin_v0PerSlipSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_v0PerSlipFamily(f,instance)
|
|
|
|
constitutive_dislotwin_CLambdaSlipPerSlipSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_CLambdaSlipPerSlipFamily(f,instance)
|
|
|
|
!* Calculation of forest projections for edge dislocations
|
|
!* Interaction matrices
|
|
|
|
do o = 1_pInt,lattice_maxNslipFamily
|
|
index_otherFamily = sum(constitutive_dislotwin_Nslip(1:o-1_pInt,instance))
|
|
do k = 1_pInt,constitutive_dislotwin_Nslip(o,instance) ! loop over (active) systems in other family (slip)
|
|
constitutive_dislotwin_forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = &
|
|
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,phase))+j,phase), &
|
|
lattice_st(:,sum(lattice_NslipSystem(1:o-1,phase))+k,phase)))
|
|
constitutive_dislotwin_interactionMatrix_SlipSlip(index_myFamily+j,index_otherFamily+k,instance) = &
|
|
constitutive_dislotwin_interaction_SlipSlip(lattice_interactionSlipSlip( &
|
|
sum(lattice_NslipSystem(1:f-1,phase))+j, &
|
|
sum(lattice_NslipSystem(1:o-1,phase))+k, &
|
|
phase), instance )
|
|
enddo; enddo
|
|
|
|
do o = 1_pInt,lattice_maxNtwinFamily
|
|
index_otherFamily = sum(constitutive_dislotwin_Ntwin(1:o-1_pInt,instance))
|
|
do k = 1_pInt,constitutive_dislotwin_Ntwin(o,instance) ! loop over (active) systems in other family (twin)
|
|
constitutive_dislotwin_interactionMatrix_SlipTwin(index_myFamily+j,index_otherFamily+k,instance) = &
|
|
constitutive_dislotwin_interaction_SlipTwin(lattice_interactionSlipTwin( &
|
|
sum(lattice_NslipSystem(1:f-1_pInt,phase))+j, &
|
|
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
|
|
phase), instance )
|
|
enddo; enddo
|
|
|
|
enddo slipSystemsLoop
|
|
enddo slipFamiliesLoop
|
|
|
|
!* Process twin related parameters ------------------------------------------------
|
|
|
|
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
|
|
index_myFamily = sum(constitutive_dislotwin_Ntwin(1:f-1_pInt,instance)) ! index in truncated twin system list
|
|
twinSystemsLoop: do j = 1_pInt,constitutive_dislotwin_Ntwin(f,instance)
|
|
|
|
!* Burgers vector,
|
|
! nucleation rate prefactor,
|
|
! and twin size
|
|
|
|
constitutive_dislotwin_burgersPerTwinSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_burgersPerTwinFamily(f,instance)
|
|
|
|
constitutive_dislotwin_Ndot0PerTwinSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_Ndot0PerTwinFamily(f,instance)
|
|
|
|
constitutive_dislotwin_twinsizePerTwinSystem(index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_twinsizePerTwinFamily(f,instance)
|
|
|
|
!* Rotate twin elasticity matrices
|
|
|
|
index_otherFamily = sum(lattice_NtwinSystem(1:f-1_pInt,phase)) ! index in full lattice twin list
|
|
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_Ctwin3333(l,m,n,o,index_myFamily+j,instance) = &
|
|
constitutive_dislotwin_Ctwin3333(l,m,n,o,index_myFamily+j,instance) + &
|
|
lattice_C3333(p,q,r,s,instance) * &
|
|
lattice_Qtwin(l,p,index_otherFamily+j,phase) * &
|
|
lattice_Qtwin(m,q,index_otherFamily+j,phase) * &
|
|
lattice_Qtwin(n,r,index_otherFamily+j,phase) * &
|
|
lattice_Qtwin(o,s,index_otherFamily+j,phase)
|
|
enddo; enddo; enddo; enddo
|
|
enddo; enddo; enddo; enddo
|
|
constitutive_dislotwin_Ctwin66(1:6,1:6,index_myFamily+j,instance) = &
|
|
math_Mandel3333to66(constitutive_dislotwin_Ctwin3333(1:3,1:3,1:3,1:3,index_myFamily+j,instance))
|
|
|
|
!* Interaction matrices
|
|
do o = 1_pInt,lattice_maxNslipFamily
|
|
index_otherFamily = sum(constitutive_dislotwin_Nslip(1:o-1_pInt,instance))
|
|
do k = 1_pInt,constitutive_dislotwin_Nslip(o,instance) ! loop over (active) systems in other family (slip)
|
|
constitutive_dislotwin_interactionMatrix_TwinSlip(index_myFamily+j,index_otherFamily+k,instance) = &
|
|
constitutive_dislotwin_interaction_TwinSlip(lattice_interactionTwinSlip( &
|
|
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
|
|
sum(lattice_NslipSystem(1:o-1_pInt,phase))+k, &
|
|
phase), instance )
|
|
enddo; enddo
|
|
|
|
do o = 1_pInt,lattice_maxNtwinFamily
|
|
index_otherFamily = sum(constitutive_dislotwin_Ntwin(1:o-1_pInt,instance))
|
|
do k = 1_pInt,constitutive_dislotwin_Ntwin(o,instance) ! loop over (active) systems in other family (twin)
|
|
constitutive_dislotwin_interactionMatrix_TwinTwin(index_myFamily+j,index_otherFamily+k,instance) = &
|
|
constitutive_dislotwin_interaction_TwinTwin(lattice_interactionTwinTwin( &
|
|
sum(lattice_NtwinSystem(1:f-1_pInt,phase))+j, &
|
|
sum(lattice_NtwinSystem(1:o-1_pInt,phase))+k, &
|
|
phase), instance )
|
|
enddo; enddo
|
|
|
|
enddo twinSystemsLoop
|
|
enddo twinFamiliesLoop
|
|
endif
|
|
|
|
enddo initializeInstances
|
|
|
|
end subroutine constitutive_dislotwin_init
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief sets the initial microstructural state for a given instance of this plasticity
|
|
!--------------------------------------------------------------------------------------------------
|
|
function constitutive_dislotwin_stateInit(instance,phase)
|
|
use math, only: &
|
|
pi
|
|
use lattice, only: &
|
|
lattice_maxNslipFamily, &
|
|
lattice_structure, &
|
|
lattice_mu, &
|
|
lattice_bcc_ID
|
|
|
|
implicit none
|
|
integer(pInt), intent(in) :: instance !< number specifying the instance of the plasticity
|
|
integer(pInt), intent(in) :: phase !< number specifying the phase of the plasticity
|
|
real(pReal), dimension(constitutive_dislotwin_sizeState(instance)) :: &
|
|
constitutive_dislotwin_stateInit
|
|
|
|
integer(pInt) :: i,j,f,ns,nt, index_myFamily
|
|
real(pReal), dimension(constitutive_dislotwin_totalNslip(instance)) :: &
|
|
rhoEdge0, &
|
|
rhoEdgeDip0, &
|
|
invLambdaSlip0, &
|
|
MeanFreePathSlip0, &
|
|
tauSlipThreshold0
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(instance)) :: &
|
|
MeanFreePathTwin0,TwinVolume0
|
|
|
|
ns = constitutive_dislotwin_totalNslip(instance)
|
|
nt = constitutive_dislotwin_totalNtwin(instance)
|
|
constitutive_dislotwin_stateInit = 0.0_pReal
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! initialize basic slip state variables
|
|
do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(constitutive_dislotwin_Nslip(1:f-1_pInt,instance)) ! index in truncated slip system list
|
|
rhoEdge0(index_myFamily+1_pInt: &
|
|
index_myFamily+constitutive_dislotwin_Nslip(f,instance)) = &
|
|
constitutive_dislotwin_rhoEdge0(f,instance)
|
|
rhoEdgeDip0(index_myFamily+1_pInt: &
|
|
index_myFamily+constitutive_dislotwin_Nslip(f,instance)) = &
|
|
constitutive_dislotwin_rhoEdgeDip0(f,instance)
|
|
enddo
|
|
|
|
constitutive_dislotwin_stateInit(1_pInt:ns) = rhoEdge0
|
|
constitutive_dislotwin_stateInit(ns+1_pInt:2_pInt*ns) = rhoEdgeDip0
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! initialize dependent slip microstructural variables
|
|
forall (i = 1_pInt:ns) &
|
|
invLambdaSlip0(i) = sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislotwin_forestProjectionEdge(1:ns,i,instance)))/ &
|
|
constitutive_dislotwin_CLambdaSlipPerSlipSystem(i,instance)
|
|
constitutive_dislotwin_stateInit(3_pInt*ns+2_pInt*nt+1:4_pInt*ns+2_pInt*nt) = invLambdaSlip0
|
|
|
|
forall (i = 1_pInt:ns) &
|
|
MeanFreePathSlip0(i) = &
|
|
constitutive_dislotwin_GrainSize(instance)/(1.0_pReal+invLambdaSlip0(i)*constitutive_dislotwin_GrainSize(instance))
|
|
constitutive_dislotwin_stateInit(5_pInt*ns+3_pInt*nt+1:6_pInt*ns+3_pInt*nt) = MeanFreePathSlip0
|
|
|
|
forall (i = 1_pInt:ns) &
|
|
tauSlipThreshold0(i) = &
|
|
lattice_mu(phase)*constitutive_dislotwin_burgersPerSlipSystem(i,instance) * &
|
|
sqrt(dot_product((rhoEdge0+rhoEdgeDip0),constitutive_dislotwin_interactionMatrix_SlipSlip(i,1:ns,instance)))
|
|
|
|
constitutive_dislotwin_stateInit(6_pInt*ns+4_pInt*nt+1:7_pInt*ns+4_pInt*nt) = tauSlipThreshold0
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! initialize dependent twin microstructural variables
|
|
forall (j = 1_pInt:nt) &
|
|
MeanFreePathTwin0(j) = constitutive_dislotwin_GrainSize(instance)
|
|
constitutive_dislotwin_stateInit(6_pInt*ns+3_pInt*nt+1_pInt:6_pInt*ns+4_pInt*nt) = MeanFreePathTwin0
|
|
|
|
forall (j = 1_pInt:nt) &
|
|
TwinVolume0(j) = &
|
|
(pi/4.0_pReal)*constitutive_dislotwin_twinsizePerTwinSystem(j,instance)*MeanFreePathTwin0(j)**(2.0_pReal)
|
|
constitutive_dislotwin_stateInit(7_pInt*ns+5_pInt*nt+1_pInt:7_pInt*ns+6_pInt*nt) = TwinVolume0
|
|
|
|
end function constitutive_dislotwin_stateInit
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief sets the relevant state values for a given instance of this plasticity
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function constitutive_dislotwin_aTolState(instance)
|
|
|
|
implicit none
|
|
integer(pInt), intent(in) :: &
|
|
instance ! number specifying the current instance of the plasticity
|
|
real(pReal), dimension(constitutive_dislotwin_sizeState(instance)) :: &
|
|
constitutive_dislotwin_aTolState ! relevant state values for the current instance of this plasticity
|
|
|
|
! Tolerance state for dislocation densities
|
|
constitutive_dislotwin_aTolState(1_pInt:2_pInt*constitutive_dislotwin_totalNslip(instance)) = &
|
|
constitutive_dislotwin_aTolRho(instance)
|
|
|
|
! Tolerance state for accumulated shear due to slip
|
|
constitutive_dislotwin_aTolState(2_pInt*constitutive_dislotwin_totalNslip(instance)+1_pInt: &
|
|
3_pInt*constitutive_dislotwin_totalNslip(instance))=1e6_pReal
|
|
|
|
|
|
! Tolerance state for twin volume fraction
|
|
constitutive_dislotwin_aTolState(3_pInt*constitutive_dislotwin_totalNslip(instance)+1_pInt: &
|
|
3_pInt*constitutive_dislotwin_totalNslip(instance)+&
|
|
constitutive_dislotwin_totalNtwin(instance)) = &
|
|
constitutive_dislotwin_aTolTwinFrac(instance)
|
|
|
|
! Tolerance state for accumulated shear due to twin
|
|
constitutive_dislotwin_aTolState(3_pInt*constitutive_dislotwin_totalNslip(instance)+ &
|
|
constitutive_dislotwin_totalNtwin(instance)+1_pInt: &
|
|
3_pInt*constitutive_dislotwin_totalNslip(instance)+ &
|
|
2_pInt*constitutive_dislotwin_totalNtwin(instance)) = 1e6_pReal
|
|
|
|
end function constitutive_dislotwin_aTolState
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief returns the homogenized elasticity matrix
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function constitutive_dislotwin_homogenizedC(state,ipc,ip,el)
|
|
use prec, only: &
|
|
p_vec
|
|
use mesh, only: &
|
|
mesh_NcpElems, &
|
|
mesh_maxNips
|
|
use material, only: &
|
|
homogenization_maxNgrains, &
|
|
material_phase, &
|
|
phase_plasticityInstance
|
|
use lattice, only: &
|
|
lattice_C66
|
|
|
|
implicit none
|
|
real(pReal), dimension(6,6) :: &
|
|
constitutive_dislotwin_homogenizedC
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
type(p_vec), intent(in) :: &
|
|
state !< microstructure state
|
|
|
|
integer(pInt) :: instance,ns,nt,i,phase
|
|
real(pReal) :: sumf
|
|
|
|
!* Shortened notation
|
|
phase = material_phase(ipc,ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
ns = constitutive_dislotwin_totalNslip(instance)
|
|
nt = constitutive_dislotwin_totalNtwin(instance)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state%p((3_pInt*ns+1_pInt):(3_pInt*ns+nt))) ! safe for nt == 0
|
|
|
|
!* Homogenized elasticity matrix
|
|
constitutive_dislotwin_homogenizedC = (1.0_pReal-sumf)*lattice_C66(1:6,1:6,phase)
|
|
do i=1_pInt,nt
|
|
constitutive_dislotwin_homogenizedC = &
|
|
constitutive_dislotwin_homogenizedC + state%p(3_pInt*ns+i)*lattice_C66(1:6,1:6,phase)
|
|
enddo
|
|
|
|
end function constitutive_dislotwin_homogenizedC
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates derived quantities from state
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_dislotwin_microstructure(temperature,state,ipc,ip,el)
|
|
use prec, only: &
|
|
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_structure, &
|
|
lattice_mu, &
|
|
lattice_nu, &
|
|
lattice_bcc_ID, &
|
|
lattice_maxNslipFamily
|
|
|
|
|
|
implicit none
|
|
integer(pInt), intent(in) :: &
|
|
ipc, & !< component-ID of integration point
|
|
ip, & !< integration point
|
|
el !< element
|
|
real(pReal), intent(in) :: &
|
|
temperature !< temperature at IP
|
|
type(p_vec), intent(inout) :: &
|
|
state !< microstructure state
|
|
|
|
integer(pInt) :: &
|
|
instance,phase,&
|
|
ns,nt,s,t
|
|
real(pReal) :: &
|
|
sumf,sfe,x0
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: fOverStacksize
|
|
|
|
!* Shortened notation
|
|
phase = material_phase(ipc,ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
ns = constitutive_dislotwin_totalNslip(instance)
|
|
nt = constitutive_dislotwin_totalNtwin(instance)
|
|
!* State: 1 : ns rho_edge
|
|
!* State: ns+1 : 2*ns rho_dipole
|
|
!* State: 2*ns+1 : 3*ns accumulated shear due to slip
|
|
!* State: 3*ns+1 : 3*ns+nt f
|
|
!* State: 3*ns+nt+1 : 3*ns+2*nt accumulated shear due to twin
|
|
!* State: 3*ns+2*nt+1 : 4*ns+2*nt 1/lambda_slip
|
|
!* State: 4*ns+2*nt+1 : 5*ns+2*nt 1/lambda_sliptwin
|
|
!* State: 5*ns+2*nt+1 : 5*ns+3*nt 1/lambda_twin
|
|
!* State: 5*ns+3*nt+1 : 6*ns+3*nt mfp_slip
|
|
!* State: 6*ns+3*nt+1 : 6*ns+4*nt mfp_twin
|
|
!* State: 6*ns+4*nt+1 : 7*ns+4*nt threshold_stress_slip
|
|
!* State: 7*ns+4*nt+1 : 7*ns+5*nt threshold_stress_twin
|
|
!* State: 7*ns+5*nt+1 : 7*ns+6*nt twin volume
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state%p((3*ns+1):(3*ns+nt))) ! safe for nt == 0
|
|
|
|
!* Stacking fault energy
|
|
sfe = constitutive_dislotwin_SFE_0K(instance) + &
|
|
constitutive_dislotwin_dSFE_dT(instance) * Temperature
|
|
|
|
!* rescaled twin volume fraction for topology
|
|
forall (t = 1_pInt:nt) &
|
|
fOverStacksize(t) = &
|
|
state%p(3_pInt*ns+t)/constitutive_dislotwin_twinsizePerTwinSystem(t,instance)
|
|
|
|
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
|
forall (s = 1_pInt:ns) &
|
|
state%p(3_pInt*ns+2_pInt*nt+s) = &
|
|
sqrt(dot_product((state%p(1:ns)+state%p(ns+1_pInt:2_pInt*ns)),&
|
|
constitutive_dislotwin_forestProjectionEdge(1:ns,s,instance)))/ &
|
|
constitutive_dislotwin_CLambdaSlipPerSlipSystem(s,instance)
|
|
|
|
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
|
!$OMP CRITICAL (evilmatmul)
|
|
state%p((4_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+2_pInt*nt)) = 0.0_pReal
|
|
if (nt > 0_pInt .and. ns > 0_pInt) &
|
|
state%p((4_pInt*ns+2_pInt*nt+1):(5_pInt*ns+2_pInt*nt)) = &
|
|
matmul(constitutive_dislotwin_interactionMatrix_SlipTwin(1:ns,1:nt,instance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
|
!$OMP CRITICAL (evilmatmul)
|
|
if (nt > 0_pInt) &
|
|
state%p((5_pInt*ns+2_pInt*nt+1_pInt):(5_pInt*ns+3_pInt*nt)) = &
|
|
matmul(constitutive_dislotwin_interactionMatrix_TwinTwin(1:nt,1:nt,instance),fOverStacksize(1:nt))/(1.0_pReal-sumf)
|
|
!$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%p(5_pInt*ns+3_pInt*nt+s) = &
|
|
constitutive_dislotwin_GrainSize(instance)/(1.0_pReal+constitutive_dislotwin_GrainSize(instance)*&
|
|
(state%p(3_pInt*ns+2_pInt*nt+s)+state%p(4_pInt*ns+2_pInt*nt+s)))
|
|
else
|
|
state%p(5_pInt*ns+s) = &
|
|
constitutive_dislotwin_GrainSize(instance)/&
|
|
(1.0_pReal+constitutive_dislotwin_GrainSize(instance)*(state%p(3_pInt*ns+s)))
|
|
endif
|
|
enddo
|
|
|
|
!* mean free path between 2 obstacles seen by a growing twin
|
|
forall (t = 1_pInt:nt) &
|
|
state%p(6_pInt*ns+3_pInt*nt+t) = &
|
|
(constitutive_dislotwin_Cmfptwin(instance)*constitutive_dislotwin_GrainSize(instance))/&
|
|
(1.0_pReal+constitutive_dislotwin_GrainSize(instance)*state%p(5_pInt*ns+2_pInt*nt+t))
|
|
|
|
!* threshold stress for dislocation motion
|
|
forall (s = 1_pInt:ns) &
|
|
state%p(6_pInt*ns+4_pInt*nt+s) = &
|
|
lattice_mu(phase)*constitutive_dislotwin_burgersPerSlipSystem(s,instance)*&
|
|
sqrt(dot_product((state%p(1:ns)+state%p(ns+1_pInt:2_pInt*ns)),&
|
|
constitutive_dislotwin_interactionMatrix_SlipSlip(s,1:ns,instance)))
|
|
|
|
!* threshold stress for growing twin
|
|
forall (t = 1_pInt:nt) &
|
|
state%p(7_pInt*ns+4_pInt*nt+t) = &
|
|
constitutive_dislotwin_Cthresholdtwin(instance)*&
|
|
(sfe/(3.0_pReal*constitutive_dislotwin_burgersPerTwinSystem(t,instance))+&
|
|
3.0_pReal*constitutive_dislotwin_burgersPerTwinSystem(t,instance)*lattice_mu(phase)/&
|
|
(constitutive_dislotwin_L0(instance)*constitutive_dislotwin_burgersPerSlipSystem(t,instance)))
|
|
|
|
!* final twin volume after growth
|
|
forall (t = 1_pInt:nt) &
|
|
state%p(7_pInt*ns+5_pInt*nt+t) = &
|
|
(pi/4.0_pReal)*constitutive_dislotwin_twinsizePerTwinSystem(t,instance)*state%p(6*ns+3*nt+t)**(2.0_pReal)
|
|
|
|
!* equilibrium seperation of partial dislocations
|
|
do t = 1_pInt,nt
|
|
x0 = lattice_mu(phase)*constitutive_dislotwin_burgersPerTwinSystem(t,instance)**(2.0_pReal)/&
|
|
(sfe*8.0_pReal*pi)*(2.0_pReal+lattice_nu(phase))/(1.0_pReal-lattice_nu(phase))
|
|
constitutive_dislotwin_tau_r(t,instance)= &
|
|
lattice_mu(phase)*constitutive_dislotwin_burgersPerTwinSystem(t,instance)/(2.0_pReal*pi)*&
|
|
(1/(x0+constitutive_dislotwin_xc(instance))+cos(pi/3.0_pReal)/x0)
|
|
enddo
|
|
|
|
end subroutine constitutive_dislotwin_microstructure
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates plastic velocity gradient and its tangent
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine constitutive_dislotwin_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
|
|
use prec, only: &
|
|
p_vec, &
|
|
tol_math_check
|
|
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, &
|
|
lattice_structure, &
|
|
lattice_fcc_twinNucleationSlipPair, &
|
|
LATTICE_fcc_ID
|
|
|
|
implicit none
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
|
real(pReal), intent(in) :: Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), intent(inout) :: state
|
|
real(pReal), dimension(3,3), intent(out) :: Lp
|
|
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar
|
|
|
|
integer(pInt) :: instance,phase,ns,nt,f,i,j,k,l,m,n,index_myFamily,s1,s2
|
|
real(pReal) :: sumf,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0
|
|
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
|
real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_slip,dgdot_dtauslip,tau_slip
|
|
real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(ipc,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
|
|
phase = material_phase(ipc,ip,el)
|
|
instance = phase_plasticityInstance(phase)
|
|
ns = constitutive_dislotwin_totalNslip(instance)
|
|
nt = constitutive_dislotwin_totalNtwin(instance)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state%p((3_pInt*ns+1_pInt):(3_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
|
|
slipFamiliesLoop: do f = 1_pInt,lattice_maxNslipFamily
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
slipSystemsLoop: do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance)
|
|
j = j+1_pInt
|
|
|
|
!* Calculation of Lp
|
|
!* Resolved shear stress on slip system
|
|
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))
|
|
|
|
if((abs(tau_slip(j))-state%p(6*ns+4*nt+j)) > tol_math_check) then
|
|
!* Stress ratios
|
|
StressRatio_p = ((abs(tau_slip(j))-state%p(6*ns+4*nt+j))/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
|
**constitutive_dislotwin_pPerSlipFamily(f,instance)
|
|
StressRatio_pminus1 = ((abs(tau_slip(j))-state%p(6*ns+4*nt+j))/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
|
**(constitutive_dislotwin_pPerSlipFamily(f,instance)-1.0_pReal)
|
|
!* Boltzmann ratio
|
|
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(j,instance)/(kB*Temperature)
|
|
!* Initial shear rates
|
|
DotGamma0 = &
|
|
state%p(j)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)*&
|
|
constitutive_dislotwin_v0PerSlipSystem(j,instance)
|
|
|
|
!* Shear rates due to slip
|
|
gdot_slip(j) = (1.0_pReal - sumf) * DotGamma0 &
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** constitutive_dislotwin_qPerSlipFamily(f,instance)) &
|
|
* sign(1.0_pReal,tau_slip(j))
|
|
|
|
!* Derivatives of shear rates
|
|
dgdot_dtauslip(j) = &
|
|
abs(gdot_slip(j))*BoltzmannRatio*constitutive_dislotwin_pPerSlipFamily(f,instance)&
|
|
*constitutive_dislotwin_qPerSlipFamily(f,instance)/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance))*&
|
|
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislotwin_qPerSlipFamily(f,instance)-1.0_pReal)
|
|
endif
|
|
|
|
!* Plastic velocity gradient for dislocation glide
|
|
Lp = Lp + gdot_slip(j)*lattice_Sslip(:,:,1,index_myFamily+i,phase)
|
|
|
|
!* Calculation of the tangent of Lp
|
|
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
|
dLp_dTstar3333(k,l,m,n) = &
|
|
dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(j)*&
|
|
lattice_Sslip(k,l,1,index_myFamily+i,phase)*&
|
|
lattice_Sslip(m,n,1,index_myFamily+i,phase)
|
|
enddo slipSystemsLoop
|
|
enddo slipFamiliesLoop
|
|
|
|
!* Shear banding (shearband) part
|
|
if(constitutive_dislotwin_sbVelocity(instance) /= 0.0_pReal .and. &
|
|
constitutive_dislotwin_sbResistance(instance) /= 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,ipc,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,ipc,ip,el))
|
|
|
|
!* Stress ratios
|
|
if (abs(tau_sb(j)) < tol_math_check) then
|
|
StressRatio_p = 0.0_pReal
|
|
StressRatio_pminus1 = 0.0_pReal
|
|
else
|
|
StressRatio_p = (abs(tau_sb(j))/constitutive_dislotwin_sbResistance(instance))&
|
|
**constitutive_dislotwin_pShearBand(instance)
|
|
StressRatio_pminus1 = (abs(tau_sb(j))/constitutive_dislotwin_sbResistance(instance))&
|
|
**(constitutive_dislotwin_pShearBand(instance)-1.0_pReal)
|
|
endif
|
|
|
|
!* Boltzmann ratio
|
|
BoltzmannRatio = constitutive_dislotwin_sbQedge(instance)/(kB*Temperature)
|
|
!* Initial shear rates
|
|
DotGamma0 = constitutive_dislotwin_sbVelocity(instance)
|
|
|
|
!* Shear rates due to shearband
|
|
gdot_sb(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
|
constitutive_dislotwin_qShearBand(instance))*sign(1.0_pReal,tau_sb(j))
|
|
|
|
!* Derivatives of shear rates
|
|
dgdot_dtausb(j) = &
|
|
((abs(gdot_sb(j))*BoltzmannRatio*&
|
|
constitutive_dislotwin_pShearBand(instance)*constitutive_dislotwin_qShearBand(instance))/&
|
|
constitutive_dislotwin_sbResistance(instance))*&
|
|
StressRatio_pminus1*(1_pInt-StressRatio_p)**(constitutive_dislotwin_qShearBand(instance)-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
|
|
twinFamiliesLoop: do f = 1_pInt,lattice_maxNtwinFamily
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
twinSystemsLoop: do i = 1_pInt,constitutive_dislotwin_Ntwin(f,instance)
|
|
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,phase))
|
|
|
|
!* Stress ratios
|
|
if (tau_twin(j) > tol_math_check) then
|
|
StressRatio_r = (state%p(7*ns+4*nt+j)/tau_twin(j))**constitutive_dislotwin_rPerTwinFamily(f,instance)
|
|
!* Shear rates and their derivatives due to twin
|
|
select case(lattice_structure(phase))
|
|
case (LATTICE_fcc_ID)
|
|
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
|
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
|
if (tau_twin(j) < constitutive_dislotwin_tau_r(j,instance)) then
|
|
Ndot0=(abs(gdot_slip(s1))*(state%p(s2)+state%p(ns+s2))+&
|
|
abs(gdot_slip(s2))*(state%p(s1)+state%p(ns+s1)))/&
|
|
(constitutive_dislotwin_L0(instance)*constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
|
|
(1.0_pReal-exp(-constitutive_dislotwin_VcrossSlip(instance)/(kB*Temperature)*&
|
|
(constitutive_dislotwin_tau_r(j,instance)-tau_twin(j))))
|
|
else
|
|
Ndot0=0.0_pReal
|
|
end if
|
|
case default
|
|
Ndot0=constitutive_dislotwin_Ndot0PerTwinSystem(j,instance)
|
|
end select
|
|
gdot_twin(j) = &
|
|
(constitutive_dislotwin_MaxTwinFraction(instance)-sumf)*lattice_shearTwin(index_myFamily+i,phase)*&
|
|
state%p(7*ns+5*nt+j)*Ndot0*exp(-StressRatio_r)
|
|
dgdot_dtautwin(j) = ((gdot_twin(j)*constitutive_dislotwin_rPerTwinFamily(f,instance))/tau_twin(j))*StressRatio_r
|
|
endif
|
|
|
|
!* Plastic velocity gradient for mechanical twinning
|
|
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,phase)
|
|
|
|
!* 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,phase)*&
|
|
lattice_Stwin(m,n,index_myFamily+i,phase)
|
|
enddo twinSystemsLoop
|
|
enddo twinFamiliesLoop
|
|
|
|
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
end subroutine constitutive_dislotwin_LpAndItsTangent
|
|
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates the rate of change of microstructure
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!--------------------------------------------------------------------------------------------------
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pure function constitutive_dislotwin_dotState(Tstar_v,Temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec, &
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tol_math_check
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use math, only: &
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pi
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains, &
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material_phase, &
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phase_plasticityInstance
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use lattice, only: &
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lattice_Sslip_v, &
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lattice_Stwin_v, &
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lattice_maxNslipFamily, &
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lattice_maxNtwinFamily, &
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lattice_NslipSystem, &
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lattice_NtwinSystem, &
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lattice_sheartwin, &
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lattice_mu, &
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lattice_structure, &
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lattice_fcc_twinNucleationSlipPair, &
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LATTICE_fcc_ID, &
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LATTICE_bcc_ID
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implicit none
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real(pReal), dimension(6), intent(in):: &
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Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
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real(pReal), intent(in) :: &
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temperature !< temperature at integration point
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integer(pInt), intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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type(p_vec), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(constitutive_dislotwin_sizeDotState(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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constitutive_dislotwin_dotState
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integer(pInt) :: instance,phase,ns,nt,f,i,j,index_myFamily,s1,s2
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real(pReal) :: sumf,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
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EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0
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real(pReal), dimension(constitutive_dislotwin_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip,tau_slip,DotRhoMultiplication,EdgeDipDistance,DotRhoEdgeEdgeAnnihilation,DotRhoEdgeDipAnnihilation,&
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ClimbVelocity,DotRhoEdgeDipClimb,DotRhoDipFormation
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real(pReal), dimension(constitutive_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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tau_twin
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!* Shortened notation
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phase = material_phase(ipc,ip,el)
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instance = phase_plasticityInstance(phase)
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ns = constitutive_dislotwin_totalNslip(instance)
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nt = constitutive_dislotwin_totalNtwin(instance)
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!* Total twin volume fraction
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sumf = sum(state%p((3_pInt*ns+1_pInt):(3_pInt*ns+nt))) ! safe for nt == 0
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constitutive_dislotwin_dotState = 0.0_pReal
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!* Dislocation density evolution
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gdot_slip = 0.0_pReal
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j = 0_pInt
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do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
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do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! 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_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))
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if((abs(tau_slip(j))-state%p(6*ns+4*nt+j)) > tol_math_check) then
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!* Stress ratios
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StressRatio_p = ((abs(tau_slip(j))-state%p(6*ns+4*nt+j))/&
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(constitutive_dislotwin_SolidSolutionStrength(instance)+constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
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**constitutive_dislotwin_pPerSlipFamily(f,instance)
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StressRatio_pminus1 = ((abs(tau_slip(j))-state%p(6*ns+4*nt+j))/&
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(constitutive_dislotwin_SolidSolutionStrength(instance)+constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
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**(constitutive_dislotwin_pPerSlipFamily(f,instance)-1.0_pReal)
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!* Boltzmann ratio
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BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(j,instance)/(kB*Temperature)
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!* Initial shear rates
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DotGamma0 = &
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state%p(j)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)*&
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constitutive_dislotwin_v0PerSlipSystem(j,instance)
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!* Shear rates due to slip
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gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)** &
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constitutive_dislotwin_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau_slip(j))
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endif
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!* Multiplication
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DotRhoMultiplication(j) = abs(gdot_slip(j))/&
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(constitutive_dislotwin_burgersPerSlipSystem(j,instance)*state%p(5*ns+3*nt+j))
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!* Dipole formation
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EdgeDipMinDistance = &
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constitutive_dislotwin_CEdgeDipMinDistance(instance)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)
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if (tau_slip(j) == 0.0_pReal) then
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DotRhoDipFormation(j) = 0.0_pReal
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else
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EdgeDipDistance(j) = &
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(3.0_pReal*lattice_mu(phase)*constitutive_dislotwin_burgersPerSlipSystem(j,instance))/&
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(16.0_pReal*pi*abs(tau_slip(j)))
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if (EdgeDipDistance(j)>state%p(5*ns+3*nt+j)) EdgeDipDistance(j)=state%p(5*ns+3*nt+j)
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if (EdgeDipDistance(j)<EdgeDipMinDistance) EdgeDipDistance(j)=EdgeDipMinDistance
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DotRhoDipFormation(j) = &
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((2.0_pReal*EdgeDipDistance(j))/constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
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state%p(j)*abs(gdot_slip(j))*constitutive_dislotwin_dipoleFormationFactor(instance)
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endif
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!* Spontaneous annihilation of 2 single edge dislocations
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DotRhoEdgeEdgeAnnihilation(j) = &
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((2.0_pReal*EdgeDipMinDistance)/constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
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state%p(j)*abs(gdot_slip(j))
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!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
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DotRhoEdgeDipAnnihilation(j) = &
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((2.0_pReal*EdgeDipMinDistance)/constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
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state%p(ns+j)*abs(gdot_slip(j))
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!* Dislocation dipole climb
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AtomicVolume = &
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constitutive_dislotwin_CAtomicVolume(instance)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)**(3.0_pReal)
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VacancyDiffusion = &
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constitutive_dislotwin_D0(instance)*exp(-constitutive_dislotwin_Qsd(instance)/(kB*Temperature))
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if (tau_slip(j) == 0.0_pReal) then
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DotRhoEdgeDipClimb(j) = 0.0_pReal
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else
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ClimbVelocity(j) = &
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((3.0_pReal*lattice_mu(phase)*VacancyDiffusion*AtomicVolume)/(2.0_pReal*pi*kB*Temperature))*&
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(1/(EdgeDipDistance(j)+EdgeDipMinDistance))
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DotRhoEdgeDipClimb(j) = &
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(4.0_pReal*ClimbVelocity(j)*state%p(ns+j))/(EdgeDipDistance(j)-EdgeDipMinDistance)
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endif
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!* Edge dislocation density rate of change
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constitutive_dislotwin_dotState(j) = &
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DotRhoMultiplication(j)-DotRhoDipFormation(j)-DotRhoEdgeEdgeAnnihilation(j)
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!* Edge dislocation dipole density rate of change
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constitutive_dislotwin_dotState(ns+j) = &
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DotRhoDipFormation(j)-DotRhoEdgeDipAnnihilation(j)-DotRhoEdgeDipClimb(j)
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!* Dotstate for accumulated shear due to slip
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constitutive_dislotwin_dotstate(2_pInt*ns+j) = gdot_slip(j)
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enddo
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enddo
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!* Twin volume fraction evolution
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j = 0_pInt
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do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
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index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,phase)) ! at which index starts my family
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do i = 1_pInt,constitutive_dislotwin_Ntwin(f,instance) ! process each (active) twin system in family
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j = j+1_pInt
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!* Resolved shear stress on twin system
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tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,phase))
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!* Stress ratios
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if (tau_twin(j) > tol_math_check) then
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StressRatio_r = (state%p(7*ns+4*nt+j)/tau_twin(j))**constitutive_dislotwin_rPerTwinFamily(f,instance)
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!* Shear rates and their derivatives due to twin
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select case(lattice_structure(phase))
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case (LATTICE_fcc_ID)
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s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
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s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
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if (tau_twin(j) < constitutive_dislotwin_tau_r(j,instance)) then
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Ndot0=(abs(gdot_slip(s1))*(state%p(s2)+state%p(ns+s2))+&
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abs(gdot_slip(s2))*(state%p(s1)+state%p(ns+s1)))/&
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(constitutive_dislotwin_L0(instance)*constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
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(1.0_pReal-exp(-constitutive_dislotwin_VcrossSlip(instance)/(kB*Temperature)*&
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(constitutive_dislotwin_tau_r(j,instance)-tau_twin(j))))
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else
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Ndot0=0.0_pReal
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end if
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case default
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Ndot0=constitutive_dislotwin_Ndot0PerTwinSystem(j,instance)
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end select
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constitutive_dislotwin_dotState(3_pInt*ns+j) = &
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(constitutive_dislotwin_MaxTwinFraction(instance)-sumf)*&
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state%p(7_pInt*ns+5_pInt*nt+j)*Ndot0*exp(-StressRatio_r)
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!* Dotstate for accumulated shear due to twin
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constitutive_dislotwin_dotState(3_pInt*ns+nt+j) = constitutive_dislotwin_dotState(3_pInt*ns+j) * &
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lattice_sheartwin(index_myfamily+i,phase)
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endif
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enddo
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enddo
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end function constitutive_dislotwin_dotState
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!--------------------------------------------------------------------------------------------------
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!> @brief return array of constitutive results
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!--------------------------------------------------------------------------------------------------
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function constitutive_dislotwin_postResults(Tstar_v,Temperature,state,ipc,ip,el)
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use prec, only: &
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p_vec, &
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tol_math_check
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use math, only: &
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pi, &
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math_Mandel6to33, &
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math_spectralDecompositionSym33
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use mesh, only: &
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mesh_NcpElems, &
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mesh_maxNips
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use material, only: &
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homogenization_maxNgrains,&
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material_phase, &
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phase_plasticityInstance,&
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phase_Noutput
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use lattice, only: &
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lattice_Sslip_v, &
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lattice_Stwin_v, &
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lattice_maxNslipFamily, &
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lattice_maxNtwinFamily, &
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lattice_NslipSystem, &
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lattice_NtwinSystem, &
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lattice_shearTwin, &
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lattice_mu, &
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lattice_structure, &
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lattice_fcc_twinNucleationSlipPair, &
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LATTICE_fcc_ID
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implicit none
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real(pReal), dimension(6), intent(in) :: &
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Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
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real(pReal), intent(in) :: &
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temperature !< temperature at integration point
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integer(pInt), intent(in) :: &
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ipc, & !< component-ID of integration point
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ip, & !< integration point
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el !< element
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type(p_vec), intent(in) :: &
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state !< microstructure state
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real(pReal), dimension(constitutive_dislotwin_sizePostResults(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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constitutive_dislotwin_postResults
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integer(pInt) :: &
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instance,phase,&
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ns,nt,&
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f,o,i,c,j,index_myFamily,&
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s1,s2
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real(pReal) :: sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,Ndot0,dgdot_dtauslip
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real(preal), dimension(constitutive_dislotwin_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip
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real(pReal), dimension(3,3) :: eigVectors
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real(pReal), dimension (3) :: eigValues
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logical :: error
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!* Shortened notation
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phase = material_phase(ipc,ip,el)
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instance = phase_plasticityInstance(phase)
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ns = constitutive_dislotwin_totalNslip(instance)
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nt = constitutive_dislotwin_totalNtwin(instance)
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!* Total twin volume fraction
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sumf = sum(state%p((3_pInt*ns+1_pInt):(3_pInt*ns+nt))) ! safe for nt == 0
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!* Required output
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c = 0_pInt
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constitutive_dislotwin_postResults = 0.0_pReal
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!* Spectral decomposition of stress
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call math_spectralDecompositionSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors, error)
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do o = 1_pInt,phase_Noutput(material_phase(ipc,ip,el))
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select case(constitutive_dislotwin_outputID(o,instance))
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case (edge_density_ID)
|
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constitutive_dislotwin_postResults(c+1_pInt:c+ns) = state%p(1_pInt:ns)
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c = c + ns
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case (dipole_density_ID)
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constitutive_dislotwin_postResults(c+1_pInt:c+ns) = state%p(ns+1_pInt:2_pInt*ns)
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c = c + ns
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case (shear_rate_slip_ID)
|
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j = 0_pInt
|
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do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
|
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index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
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do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! process each (active) slip system in family
|
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j = j + 1_pInt
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|
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!* Resolved shear stress on slip system
|
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tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))
|
|
!* Stress ratios
|
|
if((abs(tau)-state%p(6*ns+4*nt+j)) > tol_math_check) then
|
|
!* Stress ratios
|
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StressRatio_p = ((abs(tau)-state%p(6*ns+4*nt+j))/&
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(constitutive_dislotwin_SolidSolutionStrength(instance)+&
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constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
|
**constitutive_dislotwin_pPerSlipFamily(f,instance)
|
|
StressRatio_pminus1 = ((abs(tau)-state%p(6*ns+4*nt+j))/&
|
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(constitutive_dislotwin_SolidSolutionStrength(instance)+&
|
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constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
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**(constitutive_dislotwin_pPerSlipFamily(f,instance)-1.0_pReal)
|
|
!* Boltzmann ratio
|
|
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(j,instance)/(kB*Temperature)
|
|
!* Initial shear rates
|
|
DotGamma0 = &
|
|
state%p(j)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)* &
|
|
constitutive_dislotwin_v0PerSlipSystem(j,instance)
|
|
|
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!* Shear rates due to slip
|
|
constitutive_dislotwin_postResults(c+j) = &
|
|
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
|
constitutive_dislotwin_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau)
|
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else
|
|
constitutive_dislotwin_postResults(c+j) = 0.0_pReal
|
|
endif
|
|
|
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enddo ; enddo
|
|
c = c + ns
|
|
case (accumulated_shear_slip_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+ns) = &
|
|
state%p((2_pInt*ns+1_pInt):(3_pInt*ns))
|
|
c = c + ns
|
|
case (mfp_slip_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+ns) =&
|
|
state%p((5_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+3_pInt*nt))
|
|
c = c + ns
|
|
case (resolved_stress_slip_ID)
|
|
j = 0_pInt
|
|
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
constitutive_dislotwin_postResults(c+j) =&
|
|
dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))
|
|
enddo; enddo
|
|
c = c + ns
|
|
case (threshold_stress_slip_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+ns) = &
|
|
state%p((6_pInt*ns+4_pInt*nt+1_pInt):(7_pInt*ns+4_pInt*nt))
|
|
c = c + ns
|
|
case (edge_dipole_distance_ID)
|
|
j = 0_pInt
|
|
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
constitutive_dislotwin_postResults(c+j) = &
|
|
(3.0_pReal*lattice_mu(phase)*constitutive_dislotwin_burgersPerSlipSystem(j,instance))/&
|
|
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))))
|
|
constitutive_dislotwin_postResults(c+j)=min(constitutive_dislotwin_postResults(c+j),state%p(5*ns+3*nt+j))
|
|
! constitutive_dislotwin_postResults(c+j)=max(constitutive_dislotwin_postResults(c+j),state%p(4*ns+2*nt+j))
|
|
enddo; enddo
|
|
c = c + ns
|
|
case (resolved_stress_shearband_ID)
|
|
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,ipc,ip,el))
|
|
enddo
|
|
c = c + 6_pInt
|
|
case (shear_rate_shearband_ID)
|
|
do j = 1_pInt,6_pInt ! loop over all shearbands
|
|
!* Resolved shear stress on shearband system
|
|
tau = dot_product(Tstar_v,constitutive_dislotwin_sbSv(1:6,j,ipc,ip,el))
|
|
!* Stress ratios
|
|
if (abs(tau) < tol_math_check) then
|
|
StressRatio_p = 0.0_pReal
|
|
StressRatio_pminus1 = 0.0_pReal
|
|
else
|
|
StressRatio_p = (abs(tau)/constitutive_dislotwin_sbResistance(instance))**&
|
|
constitutive_dislotwin_pShearBand(instance)
|
|
StressRatio_pminus1 = (abs(tau)/constitutive_dislotwin_sbResistance(instance))**&
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(constitutive_dislotwin_pShearBand(instance)-1.0_pReal)
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endif
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!* Boltzmann ratio
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BoltzmannRatio = constitutive_dislotwin_sbQedge(instance)/(kB*Temperature)
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!* Initial shear rates
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DotGamma0 = constitutive_dislotwin_sbVelocity(instance)
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! Shear rate due to shear band
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constitutive_dislotwin_postResults(c+j) = &
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DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**constitutive_dislotwin_qShearBand(instance))*&
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sign(1.0_pReal,tau)
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enddo
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c = c + 6_pInt
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case (twin_fraction_ID)
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constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state%p((3_pInt*ns+1_pInt):(3_pInt*ns+nt))
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c = c + nt
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case (shear_rate_twin_ID)
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if (nt > 0_pInt) then
|
|
|
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j = 0_pInt
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do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
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index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
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do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! process each (active) slip system in family
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j = j + 1_pInt
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|
|
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!* Resolved shear stress on slip system
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tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,phase))
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!* Stress ratios
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if((abs(tau)-state%p(6*ns+4*nt+j)) > tol_math_check) then
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!* Stress ratios
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StressRatio_p = ((abs(tau)-state%p(6*ns+4*nt+j))/&
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|
(constitutive_dislotwin_SolidSolutionStrength(instance)+&
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|
constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
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|
**constitutive_dislotwin_pPerSlipFamily(f,instance)
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StressRatio_pminus1 = ((abs(tau)-state%p(6*ns+4*nt+j))/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+&
|
|
constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
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|
**(constitutive_dislotwin_pPerSlipFamily(f,instance)-1.0_pReal)
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|
!* Boltzmann ratio
|
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BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(j,instance)/(kB*Temperature)
|
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!* Initial shear rates
|
|
DotGamma0 = &
|
|
state%p(j)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)* &
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|
constitutive_dislotwin_v0PerSlipSystem(j,instance)
|
|
|
|
!* Shear rates due to slip
|
|
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
|
constitutive_dislotwin_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau)
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else
|
|
gdot_slip(j) = 0.0_pReal
|
|
endif
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|
enddo;enddo
|
|
|
|
j = 0_pInt
|
|
do f = 1_pInt,lattice_maxNtwinFamily ! loop over all twin families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
do i = 1,constitutive_dislotwin_Ntwin(f,instance) ! 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,phase))
|
|
!* Stress ratios
|
|
StressRatio_r = (state%p(7_pInt*ns+4_pInt*nt+j)/tau)**constitutive_dislotwin_rPerTwinFamily(f,instance)
|
|
|
|
!* Shear rates due to twin
|
|
if ( tau > 0.0_pReal ) then
|
|
select case(lattice_structure(phase))
|
|
case (LATTICE_fcc_ID)
|
|
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
|
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
|
if (tau < constitutive_dislotwin_tau_r(j,instance)) then
|
|
Ndot0=(abs(gdot_slip(s1))*(state%p(s2)+state%p(ns+s2))+&
|
|
abs(gdot_slip(s2))*(state%p(s1)+state%p(ns+s1)))/&
|
|
(constitutive_dislotwin_L0(instance)*&
|
|
constitutive_dislotwin_burgersPerSlipSystem(j,instance))*&
|
|
(1.0_pReal-exp(-constitutive_dislotwin_VcrossSlip(instance)/(kB*Temperature)*&
|
|
(constitutive_dislotwin_tau_r(j,instance)-tau)))
|
|
else
|
|
Ndot0=0.0_pReal
|
|
end if
|
|
case default
|
|
Ndot0=constitutive_dislotwin_Ndot0PerTwinSystem(j,instance)
|
|
end select
|
|
constitutive_dislotwin_postResults(c+j) = &
|
|
(constitutive_dislotwin_MaxTwinFraction(instance)-sumf)*lattice_shearTwin(index_myFamily+i,phase)*&
|
|
state%p(7_pInt*ns+5_pInt*nt+j)*Ndot0*exp(-StressRatio_r)
|
|
endif
|
|
|
|
enddo ; enddo
|
|
endif
|
|
c = c + nt
|
|
case (accumulated_shear_twin_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state%p((3_pInt*ns+nt+1_pInt):(3_pInt*ns+2_pInt*nt))
|
|
c = c + nt
|
|
case (mfp_twin_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state%p((6_pInt*ns+3_pInt*nt+1_pInt):(6_pInt*ns+4_pInt*nt))
|
|
c = c + nt
|
|
case (resolved_stress_twin_ID)
|
|
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,phase)) ! at which index starts my family
|
|
do i = 1_pInt,constitutive_dislotwin_Ntwin(f,instance) ! 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,phase))
|
|
enddo; enddo
|
|
endif
|
|
c = c + nt
|
|
case (threshold_stress_twin_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+nt) = state%p((7_pInt*ns+4_pInt*nt+1_pInt):(7_pInt*ns+5_pInt*nt))
|
|
c = c + nt
|
|
case (stress_exponent_ID)
|
|
j = 0_pInt
|
|
do f = 1_pInt,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,phase)) ! at which index starts my family
|
|
do i = 1_pInt,constitutive_dislotwin_Nslip(f,instance) ! 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(:,1,index_myFamily+i,phase))
|
|
if((abs(tau)-state%p(6*ns+4*nt+j)) > tol_math_check) then
|
|
!* Stress ratios
|
|
StressRatio_p = ((abs(tau)-state%p(6*ns+4*nt+j))/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+&
|
|
constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
|
**constitutive_dislotwin_pPerSlipFamily(f,instance)
|
|
StressRatio_pminus1 = ((abs(tau)-state%p(6*ns+4*nt+j))/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+&
|
|
constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance)))&
|
|
**(constitutive_dislotwin_pPerSlipFamily(f,instance)-1.0_pReal)
|
|
!* Boltzmann ratio
|
|
BoltzmannRatio = constitutive_dislotwin_QedgePerSlipSystem(j,instance)/(kB*Temperature)
|
|
!* Initial shear rates
|
|
DotGamma0 = &
|
|
state%p(j)*constitutive_dislotwin_burgersPerSlipSystem(j,instance)* &
|
|
constitutive_dislotwin_v0PerSlipSystem(j,instance)
|
|
|
|
!* Shear rates due to slip
|
|
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
|
constitutive_dislotwin_qPerSlipFamily(f,instance))*sign(1.0_pReal,tau)
|
|
|
|
!* Derivatives of shear rates
|
|
dgdot_dtauslip = &
|
|
abs(gdot_slip(j))*BoltzmannRatio*constitutive_dislotwin_pPerSlipFamily(f,instance)&
|
|
*constitutive_dislotwin_qPerSlipFamily(f,instance)/&
|
|
(constitutive_dislotwin_SolidSolutionStrength(instance)+&
|
|
constitutive_dislotwin_tau_peierlsPerSlipFamily(f,instance))*&
|
|
StressRatio_pminus1*(1-StressRatio_p)**(constitutive_dislotwin_qPerSlipFamily(f,instance)-1.0_pReal)
|
|
|
|
else
|
|
gdot_slip(j) = 0.0_pReal
|
|
dgdot_dtauslip = 0.0_pReal
|
|
endif
|
|
|
|
!* Stress exponent
|
|
if (gdot_slip(j)==0.0_pReal) then
|
|
constitutive_dislotwin_postResults(c+j) = 0.0_pReal
|
|
else
|
|
constitutive_dislotwin_postResults(c+j) = (tau/gdot_slip(j))*dgdot_dtauslip
|
|
endif
|
|
enddo ; enddo
|
|
c = c + ns
|
|
case (sb_eigenvalues_ID)
|
|
forall (j = 1_pInt:3_pInt) &
|
|
constitutive_dislotwin_postResults(c+j) = eigValues(j)
|
|
c = c + 3_pInt
|
|
case (sb_eigenvectors_ID)
|
|
constitutive_dislotwin_postResults(c+1_pInt:c+9_pInt) = reshape(eigVectors,[9])
|
|
c = c + 9_pInt
|
|
end select
|
|
enddo
|
|
end function constitutive_dislotwin_postResults
|
|
|
|
end module constitutive_dislotwin
|