1600 lines
76 KiB
Fortran
1600 lines
76 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH
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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 plastic_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, target, public :: &
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plastic_dislotwin_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_dislotwin_output !< name of each post result output
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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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enum, bind(c)
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enumerator :: &
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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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stress_trans_fraction_ID, &
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strain_trans_fraction_ID
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end enum
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type, private :: tParameters
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real(pReal) :: &
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mu, &
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nu, &
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CAtomicVolume, & !< atomic volume in Bugers vector unit
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D0, & !< prefactor for self-diffusion coefficient
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Qsd, & !< activation energy for dislocation climb
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GrainSize, & !<grain size
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pShearBand, & !< p-exponent in shear band velocity
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qShearBand, & !< q-exponent in shear band velocity
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MaxTwinFraction, & !<max allowed total twin volume fraction
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CEdgeDipMinDistance, & !<
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Cmfptwin, & !<
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Cthresholdtwin, & !<
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SolidSolutionStrength, & !<strength due to elements in solid solution
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L0_twin, & !< Length of twin nuclei in Burgers vectors
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L0_trans, & !< Length of trans nuclei in Burgers vectors
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xc_twin, & !< critical distance for formation of twin nucleus
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xc_trans, & !< critical distance for formation of trans nucleus
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VcrossSlip, & !< cross slip volume
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sbResistance, & !< value for shearband resistance (might become an internal state variable at some point)
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sbVelocity, & !< value for shearband velocity_0
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sbQedge, & !< value for shearband systems Qedge
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SFE_0K, & !< stacking fault energy at zero K
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dSFE_dT, & !< temperature dependance of stacking fault energy
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aTolRho, & !< absolute tolerance for integration of dislocation density
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aTolTwinFrac, & !< absolute tolerance for integration of twin volume fraction
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aTolTransFrac, & !< absolute tolerance for integration of trans volume fraction
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deltaG, & !< Free energy difference between austensite and martensite
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Cmfptrans, & !<
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Cthresholdtrans, & !<
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transStackHeight !< Stack height of hex nucleus
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real(pReal), dimension(:), allocatable :: &
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rho0, & !< initial unipolar dislocation density per slip system
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rhoDip0, & !< initial dipole dislocation density per slip system
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burgers_slip, & !< absolute length of burgers vector [m] for each slip system
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burgers_twin, & !< absolute length of burgers vector [m] for each slip system
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burgers_trans, & !< absolute length of burgers vector [m] for each twin system
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Qedge,& !< activation energy for glide [J] for each slip system
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v0, & !< dislocation velocity prefactor [m/s] for each slip system
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tau_peierls,& !< Peierls stress [Pa] for each slip system
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Ndot0_twin, & !< twin nucleation rate [1/m³s] for each twin system
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Ndot0_trans, & !< trans nucleation rate [1/m³s] for each trans system
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twinsize, & !< twin thickness [m] for each twin system
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CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
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lamellarsizePerTransSystem, & !< martensite lamellar thickness [m] for each trans system and instance
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p, & !< p-exponent in glide velocity
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q, & !< q-exponent in glide velocity
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r, & !< r-exponent in twin nucleation rate
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s, & !< s-exponent in trans nucleation rate
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shear_twin, & !< characteristic shear for twins
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B !< drag coefficient
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real(pReal), dimension(:,:), allocatable :: &
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interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type
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interaction_SlipTwin, & !< coefficients for slip-twin interaction for each interaction type
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interaction_TwinSlip, & !< coefficients for twin-slip interaction for each interaction type
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interaction_TwinTwin, & !< coefficients for twin-twin interaction for each interaction type
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interaction_SlipTrans, & !< coefficients for slip-trans interaction for each interaction type
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interaction_TransTrans !< coefficients for trans-trans interaction for each interaction type
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integer(pInt), dimension(:,:), allocatable :: &
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fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
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real(pReal), dimension(:,:), allocatable :: &
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forestProjection, &
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C66
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real(pReal), dimension(:,:,:), allocatable :: &
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Schmid_trans, &
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Schmid_slip, &
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Schmid_twin, &
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C66_twin, &
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C66_trans
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logical :: &
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dipoleFormation !< flag indicating consideration of dipole formation
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integer(kind(undefined_ID)), dimension(:), allocatable :: &
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outputID !< ID of each post result output
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logical :: &
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fccTwinTransNucleation !< twinning and transformation models are for fcc
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integer(pInt) :: &
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totalNslip, & !< number of active slip systems for each family and instance
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totalNtwin, & !< number of active twin systems for each family and instance
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totalNtrans !< number of active transformation systems for each family and instance
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integer(pInt), dimension(:), allocatable :: &
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Nslip, & !< number of active slip systems for each family and instance
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Ntwin, & !< number of active twin systems for each family and instance
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Ntrans !< number of active transformation systems for each family and instance
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end type
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type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance)
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type, private :: tDislotwinState
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real(pReal), pointer, dimension(:,:) :: &
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rhoEdge, &
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rhoEdgeDip, &
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accshear_slip, &
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twinFraction, &
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accshear_twin, &
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stressTransFraction, &
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strainTransFraction, &
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whole
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end type tDislotwinState
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type, private :: tDislotwinMicrostructure
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real(pReal), allocatable, dimension(:,:) :: &
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invLambdaSlip, &
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invLambdaSlipTwin, &
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invLambdaTwin, &
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invLambdaSlipTrans, &
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invLambdaTrans, &
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mfp_slip, &
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mfp_twin, &
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mfp_trans, &
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threshold_stress_slip, &
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threshold_stress_twin, &
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threshold_stress_trans, &
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twinVolume, &
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martensiteVolume, &
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tau_r_twin, & !< stress to bring partial close together for each twin system and instance
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tau_r_trans !< stress to bring partial close together for each trans system and instance
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end type tDislotwinMicrostructure
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type(tDislotwinState), allocatable, dimension(:), private :: &
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state, &
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dotState
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type(tDislotwinMicrostructure), allocatable, dimension(:), private :: &
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microstructure
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public :: &
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plastic_dislotwin_init, &
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plastic_dislotwin_homogenizedC, &
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plastic_dislotwin_microstructure, &
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plastic_dislotwin_LpAndItsTangent, &
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plastic_dislotwin_dotState, &
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plastic_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 plastic_dislotwin_init
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#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
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use, intrinsic :: iso_fortran_env, only: &
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compiler_version, &
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compiler_options
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#endif
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use prec, only: &
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pStringLen, &
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dEq0, &
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dNeq0, &
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dNeq
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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_rotate_forward3333, &
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math_Mandel3333to66, &
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math_mul3x3, &
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math_expand,&
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PI
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use IO, only: &
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IO_warning, &
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IO_error, &
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IO_timeStamp
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use material, only: &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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material_allocatePlasticState, &
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PLASTICITY_DISLOTWIN_label, &
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PLASTICITY_DISLOTWIN_ID, &
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material_phase, &
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plasticState
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use config, only: &
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MATERIAL_partPhase, &
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config_phase
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use lattice
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implicit none
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integer(pInt) :: Ninstance,&
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f,j,i,k,o,p, &
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offset_slip, index_myFamily, index_otherFamily, &
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startIndex, endIndex, outputSize
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integer(pInt) :: sizeState, sizeDotState
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integer(pInt) :: NipcMyPhase
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integer(pInt), dimension(1,200), parameter :: lattice_ntranssystem = 12 ! HACK!!
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integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
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character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
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integer(kind(undefined_ID)) :: &
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outputID !< ID of each post result output
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character(len=pStringLen) :: &
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structure = '',&
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extmsg = ''
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character(len=65536), dimension(:), allocatable :: &
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outputs
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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write(6,'(/,a)') ' A. Ma and F. Roters, Acta Materialia, 52(12):3603–3612, 2004'
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write(6,'(a)') ' https://doi.org/10.1016/j.actamat.2004.04.012'
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write(6,'(/,a)') ' F.Roters et al., Computational Materials Science, 39:91–95, 2007'
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write(6,'(a)') ' https://doi.org/10.1016/j.commatsci.2006.04.014'
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write(6,'(/,a)') ' Wong et al., Acta Materialia, 118:140–151, 2016'
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write(6,'(a,/)') ' https://doi.org/10.1016/j.actamat.2016.07.032'
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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#include "compilation_info.f90"
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Ninstance = int(count(phase_plasticity == PLASTICITY_DISLOTWIN_ID),pInt)
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if (Ninstance == 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:',Ninstance
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allocate(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),Ninstance),source=0_pInt)
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allocate(plastic_dislotwin_output(maxval(phase_Noutput),Ninstance))
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plastic_dislotwin_output = ''
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allocate(param(Ninstance))
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allocate(state(Ninstance))
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allocate(dotState(Ninstance))
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allocate(microstructure(Ninstance))
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do p = 1_pInt, size(phase_plasticityInstance)
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if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
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associate(prm => param(phase_plasticityInstance(p)), &
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dot => dotState(phase_plasticityInstance(p)), &
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stt => state(phase_plasticityInstance(p)), &
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mse => microstructure(phase_plasticityInstance(p)), &
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config => config_phase(p))
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! This data is read in already in lattice
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prm%mu = lattice_mu(p)
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prm%nu = lattice_nu(p)
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prm%C66 = lattice_C66(1:6,1:6,p)
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structure = config%getString('lattice_structure')
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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prm%Nslip = config%getInts('nslip',defaultVal=emptyIntArray)
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prm%totalNslip = sum(prm%Nslip)
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slipActive: if (prm%totalNslip > 0_pInt) then
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prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == LATTICE_FCC_ID) &
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.and. (prm%Nslip(1) == 12_pInt)
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if(prm%fccTwinTransNucleation) &
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prm%fcc_twinNucleationSlipPair = lattice_fcc_twinNucleationSlipPair
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prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,structure(1:3),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%forestProjection = lattice_forestProjection (prm%Nslip,structure(1:3),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, &
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config%getFloats('interaction_slipslip'), &
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structure(1:3))
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prm%rho0 = config%getFloats('rhoedge0', requiredShape=shape(prm%Nslip)) !ToDo: rename to rho_0
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prm%rhoDip0 = config%getFloats('rhoedgedip0',requiredShape=shape(prm%Nslip)) !ToDo: rename to rho_dip_0
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prm%v0 = config%getFloats('v0', requiredShape=shape(prm%Nslip))
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prm%burgers_slip = config%getFloats('slipburgers',requiredShape=shape(prm%Nslip))
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prm%Qedge = config%getFloats('qedge', requiredShape=shape(prm%Nslip)) !ToDo: rename (ask Karo)
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prm%CLambdaSlip = config%getFloats('clambdaslip',requiredShape=shape(prm%Nslip))
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prm%p = config%getFloats('p_slip', requiredShape=shape(prm%Nslip))
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prm%q = config%getFloats('q_slip', requiredShape=shape(prm%Nslip))
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prm%B = config%getFloats('b', requiredShape=shape(prm%Nslip), &
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defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))])
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prm%tau_peierls = config%getFloats('tau_peierls',requiredShape=shape(prm%Nslip), &
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defaultVal=[(0.0_pReal, i=1,size(prm%Nslip))]) ! Deprecated
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prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
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! expand: family => system
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prm%rho0 = math_expand(prm%rho0, prm%Nslip)
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prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip)
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prm%v0 = math_expand(prm%v0, prm%Nslip)
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prm%burgers_slip = math_expand(prm%burgers_slip,prm%Nslip)
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prm%Qedge = math_expand(prm%Qedge, prm%Nslip)
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prm%CLambdaSlip = math_expand(prm%CLambdaSlip, prm%Nslip)
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prm%p = math_expand(prm%p, prm%Nslip)
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prm%q = math_expand(prm%q, prm%Nslip)
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prm%B = math_expand(prm%B, prm%Nslip)
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prm%tau_peierls = math_expand(prm%tau_peierls, prm%Nslip)
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! sanity checks
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if (any(prm%rho0 < 0.0_pReal)) extmsg = trim(extmsg)//'rho0 '
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if (any(prm%rhoDip0 < 0.0_pReal)) extmsg = trim(extmsg)//'rhoDip0 '
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if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//'v0 '
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if (any(prm%burgers_slip <= 0.0_pReal)) extmsg = trim(extmsg)//'burgers_slip '
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if (any(prm%Qedge <= 0.0_pReal)) extmsg = trim(extmsg)//'Qedge '
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if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//'CLambdaSlip '
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if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//'B '
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if (any(prm%tau_peierls < 0.0_pReal)) extmsg = trim(extmsg)//'tau_peierls '
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if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//'p '
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if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//'q '
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else slipActive
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allocate(prm%burgers_slip(0))
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endif slipActive
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!--------------------------------------------------------------------------------------------------
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! twin related parameters
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prm%Ntwin = config%getInts('ntwin', defaultVal=emptyIntArray)
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prm%totalNtwin = sum(prm%Ntwin)
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if (prm%totalNtwin > 0_pInt) then
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prm%Schmid_twin = lattice_SchmidMatrix_twin(prm%Ntwin,structure(1:3),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%interaction_TwinTwin = lattice_interaction_TwinTwin(prm%Ntwin,&
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config%getFloats('interaction_twintwin'), &
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structure(1:3))
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prm%burgers_twin = config%getFloats('twinburgers')
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prm%twinsize = config%getFloats('twinsize')
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prm%r = config%getFloats('r_twin')
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prm%xc_twin = config%getFloat('xc_twin')
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prm%L0_twin = config%getFloat('l0_twin')
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prm%MaxTwinFraction = config%getFloat('maxtwinfraction') ! ToDo: only used in postResults
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prm%Cthresholdtwin = config%getFloat('cthresholdtwin', defaultVal=0.0_pReal)
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prm%Cmfptwin = config%getFloat('cmfptwin', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%shear_twin = lattice_characteristicShear_Twin(prm%Ntwin,structure(1:3),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%C66_twin = lattice_C66_twin(prm%Ntwin,prm%C66,structure(1:3),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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if (.not. prm%fccTwinTransNucleation) then
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prm%Ndot0_twin = config%getFloats('ndot0_twin')
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prm%Ndot0_twin = math_expand(prm%Ndot0_twin,prm%Ntwin)
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endif
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! expand: family => system
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prm%burgers_twin = math_expand(prm%burgers_twin,prm%Ntwin)
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prm%twinsize = math_expand(prm%twinsize,prm%Ntwin)
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prm%r = math_expand(prm%r,prm%Ntwin)
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else
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allocate(prm%twinsize(0))
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allocate(prm%burgers_twin(0))
|
||
allocate(prm%r(0))
|
||
endif
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! transformation related parameters
|
||
prm%Ntrans = config%getInts('ntrans', defaultVal=emptyIntArray)
|
||
prm%totalNtrans = sum(prm%Ntrans)
|
||
if (prm%totalNtrans > 0_pInt) then
|
||
prm%burgers_trans = config%getFloats('transburgers')
|
||
prm%burgers_trans = math_expand(prm%burgers_trans,prm%Ntrans)
|
||
|
||
prm%Cthresholdtrans = config%getFloat('cthresholdtrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%transStackHeight = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%Cmfptrans = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%deltaG = config%getFloat('deltag')
|
||
prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
||
prm%L0_trans = config%getFloat('l0_trans')
|
||
|
||
prm%interaction_TransTrans = lattice_interaction_TransTrans(prm%Ntrans,&
|
||
config%getFloats('interaction_transtrans'), &
|
||
structure(1:3))
|
||
|
||
prm%C66_trans = lattice_C66_trans(prm%Ntrans,prm%C66, &
|
||
config%getString('trans_lattice_structure'), &
|
||
0.0_pReal, &
|
||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
||
config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
||
prm%Schmid_trans = lattice_SchmidMatrix_trans(prm%Ntrans, &
|
||
config%getString('trans_lattice_structure'), &
|
||
0.0_pReal, &
|
||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
||
config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
||
if (lattice_structure(p) /= LATTICE_fcc_ID) then
|
||
prm%Ndot0_trans = config%getFloats('ndot0_trans')
|
||
prm%Ndot0_trans = math_expand(prm%Ndot0_trans,prm%Ntrans)
|
||
endif
|
||
prm%lamellarsizePerTransSystem = config%getFloats('lamellarsize')
|
||
prm%lamellarsizePerTransSystem = math_expand(prm%lamellarsizePerTransSystem,prm%Ntrans)
|
||
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
|
||
prm%s = math_expand(prm%s,prm%Ntrans)
|
||
else
|
||
allocate(prm%lamellarsizePerTransSystem(0))
|
||
allocate(prm%burgers_trans(0))
|
||
endif
|
||
|
||
if (sum(prm%Ntwin) > 0_pInt .or. prm%totalNtrans > 0_pInt) then
|
||
prm%SFE_0K = config%getFloat('sfe_0k')
|
||
prm%dSFE_dT = config%getFloat('dsfe_dt')
|
||
prm%VcrossSlip = config%getFloat('vcrossslip')
|
||
endif
|
||
|
||
if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then
|
||
prm%interaction_SlipTwin = lattice_interaction_SlipTwin(prm%Nslip,prm%Ntwin,&
|
||
config%getFloats('interaction_sliptwin'), &
|
||
structure(1:3))
|
||
prm%interaction_TwinSlip = lattice_interaction_TwinSlip(prm%Ntwin,prm%Nslip,&
|
||
config%getFloats('interaction_twinslip'), &
|
||
structure(1:3))
|
||
if (prm%fccTwinTransNucleation .and. prm%totalNtwin > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntwin is [6,6]
|
||
endif
|
||
|
||
if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then
|
||
prm%interaction_SlipTrans = lattice_interaction_SlipTrans(prm%Nslip,prm%Ntrans,&
|
||
config%getFloats('interaction_sliptrans'), &
|
||
structure(1:3))
|
||
if (prm%fccTwinTransNucleation .and. prm%totalNtrans > 12_pInt) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if ntrans is [6,6]
|
||
endif
|
||
|
||
|
||
prm%aTolRho = config%getFloat('atol_rho', defaultVal=0.0_pReal)
|
||
prm%aTolTwinFrac = config%getFloat('atol_twinfrac', defaultVal=0.0_pReal)
|
||
prm%aTolTransFrac = config%getFloat('atol_transfrac', defaultVal=0.0_pReal)
|
||
|
||
prm%CAtomicVolume = config%getFloat('catomicvolume')
|
||
prm%GrainSize = config%getFloat('grainsize')
|
||
|
||
|
||
prm%D0 = config%getFloat('d0')
|
||
prm%Qsd = config%getFloat('qsd')
|
||
prm%SolidSolutionStrength = config%getFloat('solidsolutionstrength') ! Deprecated
|
||
if (config%keyExists('dipoleformationfactor')) call IO_error(1,ext_msg='use /nodipoleformation/')
|
||
prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
|
||
prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
|
||
if (prm%sbVelocity > 0.0_pReal) then
|
||
prm%sbResistance = config%getFloat('shearbandresistance')
|
||
prm%sbQedge = config%getFloat('qedgepersbsystem')
|
||
prm%pShearBand = config%getFloat('p_shearband')
|
||
prm%qShearBand = config%getFloat('q_shearband')
|
||
endif
|
||
|
||
!if (Ndot0PerTwinFamily(f,p) < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=p,ext_msg='ndot0_twin ('//PLASTICITY_DISLOTWIN_label//')')
|
||
|
||
if (prm%CAtomicVolume <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%D0 <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='D0 ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%Qsd <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='Qsd ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%totalNtwin > 0_pInt) then
|
||
if (dEq0(prm%SFE_0K) .and. &
|
||
dEq0(prm%dSFE_dT) .and. &
|
||
lattice_structure(p) == LATTICE_fcc_ID) &
|
||
call IO_error(211_pInt,el=p,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolRho <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolTwinFrac <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='aTolTwinFrac ('//PLASTICITY_DISLOTWIN_label//')')
|
||
endif
|
||
if (prm%totalNtrans > 0_pInt) then
|
||
if (dEq0(prm%SFE_0K) .and. &
|
||
dEq0(prm%dSFE_dT) .and. &
|
||
lattice_structure(p) == LATTICE_fcc_ID) &
|
||
call IO_error(211_pInt,el=p,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolTransFrac <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='aTolTransFrac ('//PLASTICITY_DISLOTWIN_label//')')
|
||
endif
|
||
!if (prm%sbResistance < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=p,ext_msg='sbResistance ('//PLASTICITY_DISLOTWIN_label//')')
|
||
!if (prm%sbVelocity < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=p,ext_msg='sbVelocity ('//PLASTICITY_DISLOTWIN_label//')')
|
||
!if (prm%sbVelocity > 0.0_pReal .and. &
|
||
! prm%pShearBand <= 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=p,ext_msg='pShearBand ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%sbVelocity > 0.0_pReal .and. &
|
||
prm%qShearBand <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=p,ext_msg='qShearBand ('//PLASTICITY_DISLOTWIN_label//')')
|
||
|
||
outputs = config%getStrings('(output)', defaultVal=emptyStringArray)
|
||
allocate(prm%outputID(0))
|
||
do i= 1_pInt, size(outputs)
|
||
outputID = undefined_ID
|
||
select case(outputs(i))
|
||
case ('edge_density')
|
||
outputID = merge(edge_density_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('dipole_density')
|
||
outputID = merge(dipole_density_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('shear_rate_slip','shearrate_slip')
|
||
outputID = merge(shear_rate_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('accumulated_shear_slip')
|
||
outputID = merge(accumulated_shear_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('mfp_slip')
|
||
outputID = merge(mfp_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('resolved_stress_slip')
|
||
outputID = merge(resolved_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('threshold_stress_slip')
|
||
outputID= merge(threshold_stress_slip_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('edge_dipole_distance')
|
||
outputID = merge(edge_dipole_distance_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
case ('stress_exponent')
|
||
outputID = merge(stress_exponent_ID,undefined_ID,prm%totalNslip > 0_pInt)
|
||
outputSize = prm%totalNslip
|
||
|
||
case ('twin_fraction')
|
||
outputID = merge(twin_fraction_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
case ('shear_rate_twin','shearrate_twin')
|
||
outputID = merge(shear_rate_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
case ('accumulated_shear_twin')
|
||
outputID = merge(accumulated_shear_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
case ('mfp_twin')
|
||
outputID = merge(mfp_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
case ('resolved_stress_twin')
|
||
outputID = merge(resolved_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
case ('threshold_stress_twin')
|
||
outputID = merge(threshold_stress_twin_ID,undefined_ID,prm%totalNtwin >0_pInt)
|
||
outputSize = prm%totalNtwin
|
||
|
||
case ('resolved_stress_shearband')
|
||
outputID = resolved_stress_shearband_ID
|
||
outputSize = 6_pInt
|
||
case ('shear_rate_shearband','shearrate_shearband')
|
||
outputID = shear_rate_shearband_ID
|
||
outputSize = 6_pInt
|
||
|
||
case ('stress_trans_fraction')
|
||
outputID = stress_trans_fraction_ID
|
||
outputSize = prm%totalNtrans
|
||
case ('strain_trans_fraction')
|
||
outputID = strain_trans_fraction_ID
|
||
outputSize = prm%totalNtrans
|
||
|
||
end select
|
||
|
||
if (outputID /= undefined_ID) then
|
||
plastic_dislotwin_output(i,phase_plasticityInstance(p)) = outputs(i)
|
||
plastic_dislotwin_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
|
||
prm%outputID = [prm%outputID, outputID]
|
||
endif
|
||
enddo
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
NipcMyPhase=count(material_phase==p)
|
||
sizeDotState = int(size(['rho ','rhoDip ','accshearslip']),pInt) * prm%totalNslip &
|
||
+ int(size(['twinFraction','accsheartwin']),pInt) * prm%totalNtwin &
|
||
+ int(size(['stressTransFraction','strainTransFraction']),pInt) * prm%totalNtrans
|
||
sizeState = sizeDotState
|
||
|
||
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0_pInt, &
|
||
prm%totalNslip,prm%totalNtwin,prm%totalNtrans)
|
||
plasticState(p)%sizePostResults = sum(plastic_dislotwin_sizePostResult(:,phase_plasticityInstance(p)))
|
||
|
||
! ToDo: do later on
|
||
offset_slip = 2_pInt*plasticState(p)%nslip
|
||
plasticState(p)%slipRate => &
|
||
plasticState(p)%dotState(offset_slip+1:offset_slip+plasticState(p)%nslip,1:NipcMyPhase)
|
||
plasticState(p)%accumulatedSlip => &
|
||
plasticState(p)%state (offset_slip+1:offset_slip+plasticState(p)%nslip,1:NipcMyPhase)
|
||
|
||
|
||
startIndex=1_pInt
|
||
endIndex=prm%totalNslip
|
||
stt%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rhoEdge= spread(prm%rho0,2,NipcMyPhase)
|
||
dot%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
stt%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rhoEdgeDip= spread(prm%rhoDip0,2,NipcMyPhase)
|
||
dot%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
stt%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
stt%twinFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%twinFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
stt%accshear_twin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%accshear_twin=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
stt%stressTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%stressTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
stt%strainTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%strainTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
|
||
|
||
plasticState(p)%state0 = plasticState(p)%state
|
||
dot%whole => plasticState(p)%dotState
|
||
|
||
allocate(mse%invLambdaSlip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%invLambdaSlipTwin (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%invLambdaSlipTrans (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%mfp_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%threshold_stress_slip (prm%totalNslip, NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(mse%invLambdaTwin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%mfp_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%threshold_stress_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%tau_r_twin (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%twinVolume (prm%totalNtwin, NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(mse%invLambdaTrans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%mfp_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%threshold_stress_trans(prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%tau_r_trans (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
|
||
allocate(mse%martensiteVolume (prm%totalNtrans,NipcMyPhase),source=0.0_pReal)
|
||
|
||
end associate
|
||
enddo
|
||
|
||
end subroutine plastic_dislotwin_init
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief returns the homogenized elasticity matrix
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_homogenizedC(ipc,ip,el)
|
||
use material, only: &
|
||
material_phase, &
|
||
phase_plasticityInstance, &
|
||
phasememberAt
|
||
|
||
implicit none
|
||
real(pReal), dimension(6,6) :: &
|
||
plastic_dislotwin_homogenizedC
|
||
integer(pInt), intent(in) :: &
|
||
ipc, & !< component-ID of integration point
|
||
ip, & !< integration point
|
||
el !< element
|
||
|
||
integer(pInt) :: i, &
|
||
of
|
||
real(pReal) :: f_unrotated
|
||
|
||
of = phasememberAt(ipc,ip,el)
|
||
associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
|
||
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
|
||
- sum(stt%stressTransFraction(1_pInt:prm%totalNtrans,of)) &
|
||
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
|
||
plastic_dislotwin_homogenizedC = f_unrotated * prm%C66
|
||
do i=1_pInt,prm%totalNtwin
|
||
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
|
||
+ stt%twinFraction(i,of)*prm%C66_twin(1:6,1:6,i)
|
||
enddo
|
||
do i=1_pInt,prm%totalNtrans
|
||
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
|
||
+(stt%stressTransFraction(i,of)+stt%strainTransFraction(i,of))*&
|
||
prm%C66_trans(1:6,1:6,i)
|
||
enddo
|
||
end associate
|
||
end function plastic_dislotwin_homogenizedC
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates derived quantities from state
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_microstructure(temperature,ipc,ip,el)
|
||
use math, only: &
|
||
PI
|
||
use material, only: &
|
||
material_phase, &
|
||
phase_plasticityInstance, &
|
||
phasememberAt
|
||
|
||
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
|
||
|
||
integer(pInt) :: &
|
||
i, &
|
||
of
|
||
real(pReal) :: &
|
||
sumf_twin,SFE,sumf_trans
|
||
real(pReal), dimension(:), allocatable :: &
|
||
x0, &
|
||
fOverStacksize, &
|
||
ftransOverLamellarSize
|
||
|
||
of = phasememberAt(ipc,ip,el)
|
||
|
||
associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
|
||
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))),&
|
||
mse => microstructure(phase_plasticityInstance(material_phase(ipc,ip,el))))
|
||
|
||
sumf_twin = sum(stt%twinFraction(1:prm%totalNtwin,of))
|
||
sumf_trans = sum(stt%stressTransFraction(1:prm%totalNtrans,of)) &
|
||
+ sum(stt%strainTransFraction(1:prm%totalNtrans,of))
|
||
|
||
sfe = prm%SFE_0K + prm%dSFE_dT * Temperature
|
||
|
||
!* rescaled volume fraction for topology
|
||
fOverStacksize = stt%twinFraction(1_pInt:prm%totalNtwin,of)/prm%twinsize !ToDo: this is per system
|
||
ftransOverLamellarSize = sumf_trans/prm%lamellarsizePerTransSystem !ToDo: But this not ...
|
||
!Todo: Physically ok, but naming could be adjusted
|
||
|
||
|
||
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
||
forall (i = 1_pInt:prm%totalNslip) &
|
||
mse%invLambdaSlip(i,of) = &
|
||
sqrt(dot_product((stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)),&
|
||
prm%forestProjection(1:prm%totalNslip,i)))/prm%CLambdaSlip(i)
|
||
|
||
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
||
!$OMP CRITICAL (evilmatmul)
|
||
if (prm%totalNtwin > 0_pInt .and. prm%totalNslip > 0_pInt) &
|
||
mse%invLambdaSlipTwin(1_pInt:prm%totalNslip,of) = &
|
||
matmul(prm%interaction_SlipTwin,fOverStacksize)/(1.0_pReal-sumf_twin)
|
||
|
||
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
||
|
||
!ToDo: needed? if (prm%totalNtwin > 0_pInt) &
|
||
mse%invLambdaTwin(1_pInt:prm%totalNtwin,of) = &
|
||
matmul(prm%interaction_TwinTwin,fOverStacksize)/(1.0_pReal-sumf_twin)
|
||
|
||
|
||
!* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
|
||
if (prm%totalNtrans > 0_pInt .and. prm%totalNslip > 0_pInt) &
|
||
mse%invLambdaSlipTrans(1_pInt:prm%totalNslip,of) = & ! ToDo: does not work if Ntrans is not 12
|
||
matmul(prm%interaction_SlipTrans,ftransOverLamellarSize)/(1.0_pReal-sumf_trans)
|
||
|
||
!* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
|
||
!ToDo: needed? if (prm%totalNtrans > 0_pInt) &
|
||
|
||
mse%invLambdaTrans(1_pInt:prm%totalNtrans,of) = &
|
||
matmul(prm%interaction_TransTrans,ftransOverLamellarSize)/(1.0_pReal-sumf_trans)
|
||
!$OMP END CRITICAL (evilmatmul)
|
||
|
||
!* mean free path between 2 obstacles seen by a moving dislocation
|
||
do i = 1_pInt,prm%totalNslip
|
||
if ((prm%totalNtwin > 0_pInt) .or. (prm%totalNtrans > 0_pInt)) then ! ToDo: This is too simplified
|
||
mse%mfp_slip(i,of) = &
|
||
prm%GrainSize/(1.0_pReal+prm%GrainSize*&
|
||
(mse%invLambdaSlip(i,of) + mse%invLambdaSlipTwin(i,of) + mse%invLambdaSlipTrans(i,of)))
|
||
else
|
||
mse%mfp_slip(i,of) = &
|
||
prm%GrainSize/&
|
||
(1.0_pReal+prm%GrainSize*(mse%invLambdaSlip(i,of))) !!!!!! correct?
|
||
endif
|
||
enddo
|
||
|
||
!* mean free path between 2 obstacles seen by a growing twin/martensite
|
||
mse%mfp_twin(:,of) = prm%Cmfptwin*prm%GrainSize/ (1.0_pReal+prm%GrainSize*mse%invLambdaTwin(:,of))
|
||
mse%mfp_trans(:,of) = prm%Cmfptrans*prm%GrainSize/(1.0_pReal+prm%GrainSize*mse%invLambdaTrans(:,of))
|
||
|
||
!* threshold stress for dislocation motion
|
||
forall (i = 1_pInt:prm%totalNslip) mse%threshold_stress_slip(i,of) = &
|
||
prm%mu*prm%burgers_slip(i)*&
|
||
sqrt(dot_product(stt%rhoEdge(1_pInt:prm%totalNslip,of)+stt%rhoEdgeDip(1_pInt:prm%totalNslip,of),&
|
||
prm%interaction_SlipSlip(i,1:prm%totalNslip)))
|
||
|
||
!* threshold stress for growing twin/martensite
|
||
if(prm%totalNtwin == prm%totalNslip) &
|
||
mse%threshold_stress_twin(:,of) = prm%Cthresholdtwin* &
|
||
(sfe/(3.0_pReal*prm%burgers_twin)+ 3.0_pReal*prm%burgers_twin*prm%mu/ &
|
||
(prm%L0_twin*prm%burgers_slip)) ! slip burgers here correct?
|
||
if(prm%totalNtrans == prm%totalNslip) &
|
||
mse%threshold_stress_trans(:,of) = prm%Cthresholdtrans* &
|
||
(sfe/(3.0_pReal*prm%burgers_trans) + 3.0_pReal*prm%burgers_trans*prm%mu/&
|
||
(prm%L0_trans*prm%burgers_slip) + prm%transStackHeight*prm%deltaG/ (3.0_pReal*prm%burgers_trans) )
|
||
|
||
! final volume after growth
|
||
mse%twinVolume(:,of) = (PI/4.0_pReal)*prm%twinsize*mse%mfp_twin(:,of)**2.0_pReal
|
||
mse%martensiteVolume(:,of) = (PI/4.0_pReal)*prm%lamellarsizePerTransSystem*mse%mfp_trans(:,of)**2.0_pReal
|
||
|
||
!* equilibrium separation of partial dislocations (twin)
|
||
x0 = prm%mu*prm%burgers_twin**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu)
|
||
mse%tau_r_twin(:,of) = prm%mu*prm%burgers_twin/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
|
||
|
||
!* equilibrium separation of partial dislocations (trans)
|
||
x0 = prm%mu*prm%burgers_trans**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu)
|
||
mse%tau_r_trans(:,of) = prm%mu*prm%burgers_trans/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
|
||
|
||
end associate
|
||
end subroutine plastic_dislotwin_microstructure
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates plastic velocity gradient and its tangent
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,instance,of)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_eigenValuesVectorsSym, &
|
||
math_tensorproduct33, &
|
||
math_symmetric33, &
|
||
math_mul33xx33, &
|
||
math_mul33x3
|
||
|
||
implicit none
|
||
real(pReal), dimension(3,3), intent(out) :: Lp
|
||
real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
|
||
real(pReal), dimension(3,3), intent(in) :: Mp
|
||
integer(pInt), intent(in) :: instance,of
|
||
real(pReal), intent(in) :: Temperature
|
||
|
||
integer(pInt) :: i,k,l,m,n,s1,s2
|
||
real(pReal) :: f_unrotated,StressRatio_p,&
|
||
StressRatio_r,BoltzmannRatio,Ndot0_twin,stressRatio, &
|
||
Ndot0_trans,StressRatio_s, &
|
||
dgdot_dtau, &
|
||
tau
|
||
real(pReal), dimension(param(instance)%totalNslip) :: &
|
||
gdot_slip,dgdot_dtau_slip
|
||
real(pReal), dimension(param(instance)%totalNtwin) :: &
|
||
gdot_twin,dgdot_dtau_twin
|
||
real(pReal):: gdot_sb,gdot_trans
|
||
real(pReal), dimension(3,3) :: eigVectors, Schmid_shearBand
|
||
real(pReal), dimension(3) :: eigValues, sb_s, sb_m
|
||
logical :: error
|
||
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])
|
||
|
||
associate(prm => param(instance), stt => state(instance), mse => microstructure(instance))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
|
||
- sum(stt%stressTransFraction(1_pInt:prm%totalNtrans,of)) &
|
||
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
|
||
Lp = 0.0_pReal
|
||
dLp_dMp = 0.0_pReal
|
||
|
||
call kinetics_slip(prm,stt,mse,of,Mp,temperature,gdot_slip,dgdot_dtau_slip)
|
||
slipContribution: do i = 1_pInt, prm%totalNslip
|
||
Lp = Lp + gdot_slip(i)*prm%Schmid_slip(1:3,1:3,i)
|
||
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ dgdot_dtau_slip(i) * prm%Schmid_slip(k,l,i) * prm%Schmid_slip(m,n,i)
|
||
enddo slipContribution
|
||
|
||
!ToDo: Why do this before shear banding?
|
||
Lp = Lp * f_unrotated
|
||
dLp_dMp = dLp_dMp * f_unrotated
|
||
|
||
shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
|
||
|
||
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
|
||
call math_eigenValuesVectorsSym(Mp,eigValues,eigVectors,error)
|
||
|
||
do i = 1_pInt,6_pInt
|
||
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,i))
|
||
sb_m = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_mComposition(1:3,i))
|
||
Schmid_shearBand = math_tensorproduct33(sb_s,sb_m)
|
||
tau = math_mul33xx33(Mp,Schmid_shearBand)
|
||
|
||
significantShearBandStress: if (abs(tau) > tol_math_check) then
|
||
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand
|
||
gdot_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand), tau)
|
||
dgdot_dtau = ((abs(gdot_sb)*BoltzmannRatio* prm%pShearBand*prm%qShearBand)/ prm%sbResistance) &
|
||
* (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%qShearBand-1.0_pReal)
|
||
|
||
Lp = Lp + gdot_sb * Schmid_shearBand
|
||
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ dgdot_dtau * Schmid_shearBand(k,l) * Schmid_shearBand(m,n)
|
||
endif significantShearBandStress
|
||
enddo
|
||
|
||
endif shearBandingContribution
|
||
|
||
call kinetics_twin(prm,stt,mse,of,Mp,temperature,gdot_slip,gdot_twin,dgdot_dtau_twin)
|
||
gdot_twin = f_unrotated * gdot_twin
|
||
dgdot_dtau_twin = f_unrotated * dgdot_dtau_twin
|
||
twinContibution: do i = 1_pInt, prm%totalNtwin
|
||
Lp = Lp + gdot_twin(i)*prm%Schmid_twin(1:3,1:3,i)
|
||
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ dgdot_dtau_twin(i)* prm%Schmid_twin(k,l,i)*prm%Schmid_twin(m,n,i)
|
||
enddo twinContibution
|
||
|
||
transConstribution: do i = 1_pInt, prm%totalNtrans
|
||
|
||
tau = math_mul33xx33(Mp,prm%Schmid_trans(1:3,1:3,i))
|
||
|
||
significantTransStress: if (tau > tol_math_check) then
|
||
StressRatio_s = (mse%threshold_stress_trans(i,of)/tau)**prm%s(i)
|
||
|
||
isFCCtrans: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau < mse%tau_r_trans(i,of)) then
|
||
Ndot0_trans=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+& !!!!! correct?
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_trans*prm%burgers_slip(i))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*(mse%tau_r_trans(i,of)-tau)))
|
||
else
|
||
Ndot0_trans=0.0_pReal
|
||
end if
|
||
else isFCCtrans
|
||
Ndot0_trans=prm%Ndot0_trans(i)
|
||
endif isFCCtrans
|
||
|
||
gdot_trans = mse%martensiteVolume(i,of) * Ndot0_trans*exp(-StressRatio_s)
|
||
gdot_trans = f_unrotated * gdot_trans
|
||
dgdot_dtau = ((gdot_trans*prm%s(i))/tau)*StressRatio_s
|
||
Lp = Lp + gdot_trans*prm%Schmid_trans(1:3,1:3,i)
|
||
|
||
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ dgdot_dtau * prm%Schmid_trans(k,l,i)* prm%Schmid_trans(m,n,i)
|
||
endif significantTransStress
|
||
|
||
enddo transConstribution
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_dotState(Mp,Temperature,instance,of)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
math_mul33xx33, &
|
||
math_Mandel6to33, &
|
||
pi
|
||
use material, only: &
|
||
plasticState
|
||
|
||
implicit none
|
||
real(pReal), dimension(3,3), intent(in):: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
temperature !< temperature at integration point
|
||
integer(pInt), intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
integer(pInt) :: i,s1,s2
|
||
real(pReal) :: f_unrotated,StressRatio_p,BoltzmannRatio,&
|
||
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,&
|
||
Ndot0_trans,StressRatio_s,EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, &
|
||
DotRhoDipFormation,DotRhoMultiplication,DotRhoEdgeEdgeAnnihilation, &
|
||
tau
|
||
real(pReal), dimension(plasticState(instance)%Nslip) :: &
|
||
gdot_slip
|
||
|
||
associate(prm => param(instance), stt => state(instance), &
|
||
dot => dotstate(instance), mse => microstructure(instance))
|
||
|
||
dot%whole(:,of) = 0.0_pReal
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%twinFraction(1_pInt:prm%totalNtwin,of)) &
|
||
- sum(stt%stressTransFraction(1_pInt:prm%totalNtrans,of)) &
|
||
- sum(stt%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
|
||
call kinetics_slip(prm,stt,mse,of,Mp,temperature,gdot_slip)
|
||
slipState: do i = 1_pInt, prm%totalNslip
|
||
tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i))
|
||
|
||
DotRhoMultiplication = abs(gdot_slip(i))/(prm%burgers_slip(i)*mse%mfp_slip(i,of))
|
||
EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip(i)
|
||
|
||
significantSlipStress2: if (dEq0(tau)) then
|
||
DotRhoDipFormation = 0.0_pReal
|
||
else significantSlipStress2
|
||
EdgeDipDistance = (3.0_pReal*prm%mu*prm%burgers_slip(i))/(16.0_pReal*PI*abs(tau))
|
||
if (EdgeDipDistance>mse%mfp_slip(i,of)) EdgeDipDistance = mse%mfp_slip(i,of)
|
||
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance = EdgeDipMinDistance
|
||
if (prm%dipoleFormation) then
|
||
DotRhoDipFormation = ((2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance))/prm%burgers_slip(i)) &
|
||
* stt%rhoEdge(i,of)*abs(gdot_slip(i))
|
||
else
|
||
DotRhoDipFormation = 0.0_pReal
|
||
endif
|
||
endif significantSlipStress2
|
||
|
||
!* Spontaneous annihilation of 2 single edge dislocations
|
||
DotRhoEdgeEdgeAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(i))*&
|
||
stt%rhoEdge(i,of)*abs(gdot_slip(i))
|
||
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
|
||
DotRhoEdgeDipAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(i)) &
|
||
* stt%rhoEdgeDip(i,of)*abs(gdot_slip(i))
|
||
|
||
!* Dislocation dipole climb
|
||
AtomicVolume = prm%CAtomicVolume*prm%burgers_slip(i)**(3.0_pReal) ! no need to calculate this over and over again
|
||
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
|
||
|
||
if (dEq0(tau)) then
|
||
DotRhoEdgeDipClimb = 0.0_pReal
|
||
else
|
||
if (dEq0(EdgeDipDistance-EdgeDipMinDistance)) then
|
||
DotRhoEdgeDipClimb = 0.0_pReal
|
||
else
|
||
ClimbVelocity = 3.0_pReal*prm%mu*VacancyDiffusion*AtomicVolume/ &
|
||
(2.0_pReal*pi*kB*Temperature*(EdgeDipDistance+EdgeDipMinDistance))
|
||
DotRhoEdgeDipClimb = 4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(i,of)/ &
|
||
(EdgeDipDistance-EdgeDipMinDistance)
|
||
endif
|
||
endif
|
||
dot%rhoEdge(i,of) = DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
|
||
dot%rhoEdgeDip(i,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
|
||
dot%accshear_slip(i,of) = abs(gdot_slip(i))
|
||
enddo slipState
|
||
|
||
twinState: do i = 1_pInt, prm%totalNtwin
|
||
|
||
tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i))
|
||
|
||
significantTwinStress: if (tau > tol_math_check) then
|
||
StressRatio_r = (mse%threshold_stress_twin(i,of)/tau)**prm%r(i)
|
||
isFCCtwin: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau < mse%tau_r_twin(i,of)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin*prm%burgers_slip(i))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(mse%tau_r_twin(i,of)-tau)))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
else isFCCtwin
|
||
Ndot0_twin=prm%Ndot0_twin(i)
|
||
endif isFCCtwin
|
||
dot%twinFraction(i,of) = f_unrotated * mse%twinVolume(i,of)*Ndot0_twin*exp(-StressRatio_r)
|
||
dot%accshear_twin(i,of) = dot%twinFraction(i,of) * prm%shear_twin(i)
|
||
endif significantTwinStress
|
||
|
||
enddo twinState
|
||
|
||
transState: do i = 1_pInt, prm%totalNtrans
|
||
|
||
tau = math_mul33xx33(Mp,prm%Schmid_trans(1:3,1:3,i))
|
||
|
||
significantTransStress: if (tau > tol_math_check) then
|
||
StressRatio_s = (mse%threshold_stress_trans(i,of)/tau)**prm%s(i)
|
||
isFCCtrans: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau < mse%tau_r_trans(i,of)) then
|
||
Ndot0_trans=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_trans*prm%burgers_slip(i))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(mse%tau_r_trans(i,of)-tau)))
|
||
else
|
||
Ndot0_trans=0.0_pReal
|
||
end if
|
||
else isFCCtrans
|
||
Ndot0_trans=prm%Ndot0_trans(i)
|
||
endif isFCCtrans
|
||
dot%strainTransFraction(i,of) = f_unrotated * &
|
||
mse%martensiteVolume(i,of)*Ndot0_trans*exp(-StressRatio_s)
|
||
!* Dotstate for accumulated shear due to transformation
|
||
!dot%accshear_trans(i,of) = dot%strainTransFraction(i,of) * &
|
||
! lattice_sheartrans(index_myfamily+i,ph)
|
||
endif significantTransStress
|
||
|
||
enddo transState
|
||
|
||
end associate
|
||
end subroutine plastic_dislotwin_dotState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates shear rates on slip systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_slip(prm,stt,mse,of,Mp,temperature,gdot_slip,dgdot_dtau_slip)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
implicit none
|
||
type(tParameters), intent(in) :: &
|
||
prm
|
||
type(tDislotwinState), intent(in) :: &
|
||
stt
|
||
integer(pInt), intent(in) :: &
|
||
of
|
||
type(tDislotwinMicrostructure), intent(in) :: &
|
||
mse
|
||
real(pReal), dimension(prm%totalNslip), intent(out) :: &
|
||
gdot_slip
|
||
real(pReal), dimension(prm%totalNslip), optional, intent(out) :: &
|
||
dgdot_dtau_slip
|
||
real(pReal), dimension(prm%totalNslip) :: &
|
||
dgdot_dtau
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp
|
||
real(pReal), intent(in) :: &
|
||
temperature
|
||
|
||
real, dimension(prm%totalNslip) :: &
|
||
tau, &
|
||
stressRatio, &
|
||
StressRatio_p, &
|
||
BoltzmannRatio, &
|
||
v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned)
|
||
v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned)
|
||
dV_wait_inverse_dTau, &
|
||
dV_run_inverse_dTau, &
|
||
dV_dTau, &
|
||
tau_eff !< effective resolved stress
|
||
integer(pInt) :: i
|
||
|
||
do i = 1_pInt, prm%totalNslip
|
||
tau(i) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,i))
|
||
enddo
|
||
|
||
tau_eff = abs(tau)-mse%threshold_stress_slip(:,of)
|
||
|
||
significantStress: where(tau_eff > tol_math_check)
|
||
stressRatio = tau_eff/(prm%SolidSolutionStrength+prm%tau_peierls)
|
||
StressRatio_p = stressRatio** prm%p
|
||
BoltzmannRatio = prm%Qedge/(kB*Temperature)
|
||
v_wait_inverse = prm%v0**(-1.0_pReal) * exp(BoltzmannRatio*(1.0_pReal-StressRatio_p)** prm%q)
|
||
v_run_inverse = prm%B/(tau_eff*prm%burgers_slip)
|
||
|
||
gdot_slip = sign(stt%rhoEdge(:,of)*prm%burgers_slip/(v_wait_inverse+v_run_inverse),tau)
|
||
|
||
dV_wait_inverse_dTau = v_wait_inverse * prm%p * prm%q * BoltzmannRatio &
|
||
* (stressRatio**(prm%p-1.0_pReal)) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%q-1.0_pReal) &
|
||
/ (prm%SolidSolutionStrength+prm%tau_peierls)
|
||
dV_run_inverse_dTau = v_run_inverse/tau_eff
|
||
dV_dTau = (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
|
||
/ (v_wait_inverse+v_run_inverse)**2.0_pReal
|
||
dgdot_dtau = dV_dTau*stt%rhoEdge(:,of)*prm%burgers_slip
|
||
else where significantStress
|
||
gdot_slip = 0.0_pReal
|
||
dgdot_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
if(present(dgdot_dtau_slip)) dgdot_dtau_slip = dgdot_dtau
|
||
|
||
end subroutine kinetics_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates shear rates on twin systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_twin(prm,stt,mse,of,Mp,temperature,gdot_slip,gdot_twin,dgdot_dtau_twin)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
implicit none
|
||
type(tParameters), intent(in) :: &
|
||
prm
|
||
type(tDislotwinState), intent(in) :: &
|
||
stt
|
||
integer(pInt), intent(in) :: &
|
||
of
|
||
type(tDislotwinMicrostructure), intent(in) :: &
|
||
mse
|
||
real(pReal), dimension(prm%totalNslip), intent(out) :: &
|
||
gdot_slip
|
||
real(pReal), dimension(prm%totalNtwin), intent(out) :: &
|
||
gdot_twin
|
||
real(pReal), dimension(prm%totalNtwin), optional, intent(out) :: &
|
||
dgdot_dtau_twin
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp
|
||
real(pReal), intent(in) :: &
|
||
temperature
|
||
|
||
real, dimension(prm%totalNtwin) :: &
|
||
tau, &
|
||
Ndot0_twin, &
|
||
stressRatio_r, &
|
||
dgdot_dtau
|
||
|
||
integer(pInt) :: i,s1,s2
|
||
|
||
do i = 1_pInt, prm%totalNtwin
|
||
tau(i) = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < mse%tau_r_twin(i,of)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin*prm%burgers_slip(i))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(mse%tau_r_twin(i,of)-tau)))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0_twin=prm%Ndot0_twin(i)
|
||
endif isFCC
|
||
enddo
|
||
|
||
|
||
significantStress: where(tau > tol_math_check)
|
||
StressRatio_r = (mse%threshold_stress_twin(:,of)/tau)**prm%r
|
||
gdot_twin = prm%shear_twin * mse%twinVolume(:,of) * Ndot0_twin*exp(-StressRatio_r)
|
||
dgdot_dtau = ((gdot_twin*prm%r)/tau)*StressRatio_r
|
||
else where significantStress
|
||
gdot_twin = 0.0_pReal
|
||
dgdot_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
if(present(dgdot_dtau_twin)) dgdot_dtau_twin = dgdot_dtau
|
||
|
||
end subroutine kinetics_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates shear rates on transformation systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_trans(prm,stt,mse,of,Mp,temperature,gdot_slip,gdot_trans,dgdot_dtau_trans)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
implicit none
|
||
type(tParameters), intent(in) :: &
|
||
prm
|
||
type(tDislotwinState), intent(in) :: &
|
||
stt
|
||
integer(pInt), intent(in) :: &
|
||
of
|
||
type(tDislotwinMicrostructure), intent(in) :: &
|
||
mse
|
||
real(pReal), dimension(prm%totalNslip), intent(out) :: &
|
||
gdot_slip
|
||
real(pReal), dimension(prm%totalNtrans), intent(out) :: &
|
||
gdot_trans
|
||
real(pReal), dimension(prm%totalNtrans), optional, intent(out) :: &
|
||
dgdot_dtau_trans
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp
|
||
real(pReal), intent(in) :: &
|
||
temperature
|
||
|
||
real, dimension(prm%totalNtrans) :: &
|
||
tau, &
|
||
Ndot0_trans, &
|
||
stressRatio_r, &
|
||
dgdot_dtau
|
||
|
||
integer(pInt) :: i,s1,s2
|
||
|
||
do i = 1_pInt, prm%totalNtrans
|
||
tau(i) = math_mul33xx33(Mp,prm%Schmid_trans(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < mse%tau_r_trans(i,of)) then
|
||
Ndot0_trans=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_trans*prm%burgers_slip(i))*& ! burgers_slip correct?
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(mse%tau_r_trans(i,of)-tau)))
|
||
else
|
||
Ndot0_trans=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0_trans=prm%Ndot0_trans(i)
|
||
endif isFCC
|
||
enddo
|
||
!
|
||
!
|
||
! endif isFCCtrans
|
||
! dot%strainTransFraction(i,of) = f_unrotated * &
|
||
! mse%martensiteVolume(i,of)*Ndot0_trans*exp(-StressRatio_s)
|
||
! !* Dotstate for accumulated shear due to transformation
|
||
! !dot%accshear_trans(i,of) = dot%strainTransFraction(i,of) * &
|
||
! ! lattice_sheartrans(index_myfamily+i,ph)
|
||
! endif significantTransStress
|
||
!
|
||
! enddo transState
|
||
!
|
||
!
|
||
! significantStress: where(tau > tol_math_check)
|
||
! StressRatio_r = (mse%threshold_stress_twin(:,of)/tau)**prm%r
|
||
! gdot_twin = prm%shear_twin * mse%twinVolume(:,of) * Ndot0_twin*exp(-StressRatio_r)
|
||
! dgdot_dtau = ((gdot_twin*prm%r)/tau)*StressRatio_r
|
||
! else where significantStress
|
||
! gdot_twin = 0.0_pReal
|
||
! dgdot_dtau = 0.0_pReal
|
||
! end where significantStress
|
||
!
|
||
! if(present(dgdot_dtau_twin)) dgdot_dtau_twin = dgdot_dtau
|
||
!
|
||
end subroutine kinetics_trans
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief return array of constitutive results
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_postResults(Mp,Temperature,instance,of) result(postResults)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
PI, &
|
||
math_mul33xx33, &
|
||
math_Mandel6to33
|
||
|
||
implicit none
|
||
real(pReal), dimension(3,3),intent(in) :: &
|
||
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
||
real(pReal), intent(in) :: &
|
||
temperature !< temperature at integration point
|
||
integer(pInt), intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(sum(plastic_dislotwin_sizePostResult(:,instance))) :: &
|
||
postResults
|
||
|
||
integer(pInt) :: &
|
||
o,c,j,&
|
||
s1,s2
|
||
real(pReal) :: sumf_twin,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,Ndot0_twin,dgdot_dtauslip, &
|
||
stressRatio
|
||
real(pReal), dimension(param(instance)%totalNslip) :: &
|
||
gdot_slip
|
||
|
||
type(tParameters) :: prm
|
||
type(tDislotwinState) :: stt
|
||
type(tDislotwinMicrostructure) :: mse
|
||
|
||
|
||
associate(prm => param(instance), stt => state(instance), mse => microstructure(instance))
|
||
|
||
sumf_twin = sum(stt%twinFraction(1_pInt:prm%totalNtwin,of))
|
||
|
||
c = 0_pInt
|
||
postResults = 0.0_pReal
|
||
do o = 1_pInt,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
|
||
case (edge_density_ID)
|
||
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (dipole_density_ID)
|
||
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (shear_rate_slip_ID)
|
||
call kinetics_slip(prm,stt,mse,of,Mp,temperature,postResults(c+1:c+prm%totalNslip))
|
||
c = c + prm%totalNslip
|
||
case (accumulated_shear_slip_ID)
|
||
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (mfp_slip_ID)
|
||
postResults(c+1_pInt:c+prm%totalNslip) = mse%mfp_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (resolved_stress_slip_ID)
|
||
do j = 1_pInt, prm%totalNslip
|
||
postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))
|
||
enddo
|
||
c = c + prm%totalNslip
|
||
case (threshold_stress_slip_ID)
|
||
postResults(c+1_pInt:c+prm%totalNslip) = mse%threshold_stress_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (edge_dipole_distance_ID)
|
||
do j = 1_pInt, prm%totalNslip
|
||
postResults(c+j) = (3.0_pReal*prm%mu*prm%burgers_slip(j)) &
|
||
/ (16.0_pReal*PI*abs(math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))))
|
||
postResults(c+j)=min(postResults(c+j),mse%mfp_slip(j,of))
|
||
! postResults(c+j)=max(postResults(c+j),&
|
||
! plasticState(ph)%state(4*ns+2*nt+2*nr+j, of))
|
||
enddo
|
||
c = c + prm%totalNslip
|
||
! case (resolved_stress_shearband_ID)
|
||
! do j = 1_pInt,6_pInt ! loop over all shearband families
|
||
! postResults(c+j) = dot_product(Tstar_v,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
|
||
! tau = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el))
|
||
! if (abs(tau) < tol_math_check) then
|
||
! StressRatio_p = 0.0_pReal
|
||
! StressRatio_pminus1 = 0.0_pReal
|
||
! else
|
||
! StressRatio_p = (abs(tau)/prm%sbResistance)**prm%pShearBand
|
||
! StressRatio_pminus1 = (abs(tau)/prm%sbResistance)**(prm%pShearBand-1.0_pReal)
|
||
! endif
|
||
! BoltzmannRatio = prm%sbQedge/(kB*Temperature)
|
||
! DotGamma0 = prm%sbVelocity
|
||
! postResults(c+j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand)*&
|
||
! sign(1.0_pReal,tau)
|
||
! enddo
|
||
! c = c + 6_pInt
|
||
case (twin_fraction_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtwin) = stt%twinFraction(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (shear_rate_twin_ID)
|
||
do j = 1_pInt, prm%totalNslip
|
||
tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))
|
||
if((abs(tau)-mse%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
StressRatio_p = ((abs(tau)-mse%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierls(j)))&
|
||
**prm%p(j)
|
||
StressRatio_pminus1 = ((abs(tau)-mse%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierls(j)))&
|
||
**(prm%p(j)-1.0_pReal)
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
|
||
|
||
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%q(j))*sign(1.0_pReal,tau)
|
||
else
|
||
gdot_slip(j) = 0.0_pReal
|
||
endif
|
||
enddo
|
||
|
||
do j = 1_pInt, prm%totalNtwin
|
||
tau = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,j))
|
||
|
||
if ( tau > 0.0_pReal ) then
|
||
isFCCtwin: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,j)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,j)
|
||
if (tau < mse%tau_r_twin(j,of)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(stt%rhoEdge(s2,of)+stt%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(stt%rhoEdge(s1,of)+stt%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin* prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)* (mse%tau_r_twin(j,of)-tau)))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
else isFCCtwin
|
||
Ndot0_twin=prm%Ndot0_twin(j)
|
||
endif isFCCtwin
|
||
StressRatio_r = (mse%threshold_stress_twin(j,of)/tau) **prm%r(j)
|
||
postResults(c+j) = (prm%MaxTwinFraction-sumf_twin)*prm%shear_twin(j) &
|
||
* mse%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
|
||
endif
|
||
enddo
|
||
c = c + prm%totalNtwin
|
||
case (accumulated_shear_twin_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtwin) = stt%accshear_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (mfp_twin_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtwin) = mse%mfp_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (resolved_stress_twin_ID)
|
||
do j = 1_pInt, prm%totalNtwin
|
||
postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_twin(1:3,1:3,j))
|
||
enddo
|
||
c = c + prm%totalNtwin
|
||
case (threshold_stress_twin_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtwin) = mse%threshold_stress_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (stress_exponent_ID)
|
||
do j = 1_pInt, prm%totalNslip
|
||
tau = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))
|
||
if((abs(tau)-mse%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
StressRatio_p = ((abs(tau)-mse%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierls(j)))&
|
||
**prm%p(j)
|
||
StressRatio_pminus1 = ((abs(tau)-mse%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierls(j)))&
|
||
**(prm%p(j)-1.0_pReal)
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
|
||
|
||
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%q(j))*sign(1.0_pReal,tau)
|
||
|
||
dgdot_dtauslip = abs(gdot_slip(j))*BoltzmannRatio*prm%p(j) *prm%q(j)/&
|
||
(prm%SolidSolutionStrength+ prm%tau_peierls(j))*&
|
||
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal)
|
||
else
|
||
gdot_slip(j) = 0.0_pReal
|
||
dgdot_dtauslip = 0.0_pReal
|
||
endif
|
||
postResults(c+j) = merge(0.0_pReal,(tau/gdot_slip(j))*dgdot_dtauslip,dEq0(gdot_slip(j)))
|
||
enddo
|
||
c = c + prm%totalNslip
|
||
case (stress_trans_fraction_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtrans) = stt%stressTransFraction(1_pInt:prm%totalNtrans,of)
|
||
c = c + prm%totalNtrans
|
||
case (strain_trans_fraction_ID)
|
||
postResults(c+1_pInt:c+prm%totalNtrans) = stt%strainTransFraction(1_pInt:prm%totalNtrans,of)
|
||
c = c + prm%totalNtrans
|
||
end select
|
||
enddo
|
||
end associate
|
||
end function plastic_dislotwin_postResults
|
||
|
||
end module plastic_dislotwin
|