2061 lines
99 KiB
Fortran
2061 lines
99 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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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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real(pReal), dimension(:,:,:,:), allocatable, private :: &
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Ctwin66,& !< twin elasticity matrix in Mandel notation for each instance
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Ctrans66 !< trans elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:), allocatable, private :: &
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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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real(pReal), dimension(:,:,:), allocatable, private :: &
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forestProjectionEdge, & !< matrix of forest projections of edge dislocations for each instance
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projectionMatrix_Trans !< matrix for projection of slip system shear on fault band (twin) systems for each instance
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real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
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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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stress_trans_fraction_ID, &
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strain_trans_fraction_ID, &
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trans_fraction_ID
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end enum
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type,private :: tParameters
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integer(kind(undefined_ID)), dimension(:), allocatable, private :: &
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outputID !< ID of each post result output
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real(pReal) :: &
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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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dipoleFormationFactor, & !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
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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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integer(pInt), private :: &
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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, private :: &
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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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real(pReal), dimension(:), allocatable, private :: &
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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 systems
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burgers_twin, & !< absolute length of burgers vector [m] for each slip systems
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burgers_trans, & !< absolute length of burgers vector [m] for each twin family and instance
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Qedge,& !< activation energy for glide [J] for each slip system and instance
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v0, & !dislocation velocity prefactor [m/s] for each slip system and instance
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tau_peierlsPerSlipFamily,& !< Peierls stress [Pa] for each family and instance
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Ndot0_twin, & !< twin nucleation rate [1/m³s] for each twin system and instance
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Ndot0_trans, & !< trans nucleation rate [1/m³s] for each trans system and instance
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twinsize, & !< twin thickness [m] for each twin system and instance
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CLambdaSlipPerSlipSystem, & !< Adj. parameter for distance between 2 forest dislocations for each slip system and instance
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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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real(pReal), dimension(:,:), allocatable, private :: &
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interaction_SlipSlip, & !< coefficients for slip-slip interaction for each interaction type and instance
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interaction_SlipTwin, & !< coefficients for slip-twin interaction for each interaction type and instance
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interaction_TwinSlip, & !< coefficients for twin-slip interaction for each interaction type and instance
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interaction_TwinTwin, & !< coefficients for twin-twin interaction for each interaction type and instance
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interaction_SlipTrans, & !< coefficients for slip-trans interaction for each interaction type and instance
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interaction_TransSlip, & !< coefficients for trans-slip interaction for each interaction type and instance
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interaction_TransTrans !< coefficients for trans-trans interaction for each interaction type and instance
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end type
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type(tParameters), dimension(:), allocatable, private,target :: 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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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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end type
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type(tDislotwinState), allocatable, dimension(:), private :: &
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state, &
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dotState
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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(fileUnit)
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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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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_Mandel3333to66, &
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math_Voigt66to3333, &
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math_mul3x3, &
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math_expand,&
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pi
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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_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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use numerics,only: &
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numerics_integrator
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implicit none
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integer(pInt), intent(in) :: fileUnit
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integer(pInt) :: maxNinstance,&
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f,instance,j,i,k,l,m,n,o,p,q,r,s,p1, &
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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, sizeDeltaState
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integer(pInt) :: NofMyPhase
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integer(kind(undefined_ID)) outputID
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real(pReal), dimension(:,:,:,:,:), allocatable :: &
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Ctwin3333, & !< twin elasticity matrix for each instance
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Ctrans3333 !< trans elasticity matrix for each instance
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real(pReal), allocatable, dimension(:) :: &
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invLambdaSlip0,&
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MeanFreePathSlip0,&
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MeanFreePathTrans0,&
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MeanFreePathTwin0,&
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tauSlipThreshold0,&
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TwinVolume0,&
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MartensiteVolume0
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real(pReal), allocatable, dimension(:,:) :: temp1,temp2,temp3
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character(len=65536) :: &
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tag = ''
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character(len=65536), dimension(:), allocatable :: outputs
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integer(pInt), dimension(0), parameter :: emptyInt = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyReal = [real(pReal)::]
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character(len=65536), dimension(0), parameter :: emptyString = [character(len=65536)::]
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type(tParameters),pointer :: prm
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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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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(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
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allocate(plastic_dislotwin_output(maxval(phase_Noutput),maxNinstance))
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plastic_dislotwin_output = ''
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allocate(param(maxNinstance))
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allocate(sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), source=0.0_pReal)
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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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instance = phase_plasticityInstance(p)
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prm => param(instance)
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prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyInt)
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if (size(prm%Nslip) > count(lattice_NslipSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
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if (any(lattice_NslipSystem(1:size(prm%Nslip),p)-prm%Nslip < 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
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if (any(prm%Nslip < 0_pInt)) call IO_error(150_pInt,ext_msg='Nslip')
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prm%totalNslip = sum(prm%Nslip)
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if (prm%totalNslip > 0_pInt) then
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prm%rho0 = config_phase(p)%getFloats('rhoedge0')
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prm%rhoDip0 = config_phase(p)%getFloats('rhoedgedip0')
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prm%burgers_slip = config_phase(p)%getFloats('slipburgers')
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if (size(prm%burgers_slip) /= size(prm%Nslip)) call IO_error(150_pInt,ext_msg='slipburgers')
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prm%burgers_slip = math_expand(prm%burgers_slip,prm%Nslip)
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prm%Qedge = config_phase(p)%getFloats('qedge')
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prm%Qedge = math_expand(prm%Qedge,prm%Nslip)
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prm%v0 = config_phase(p)%getFloats('v0')
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prm%v0 = math_expand(prm%v0,prm%Nslip)
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prm%interaction_SlipSlip = spread(config_phase(p)%getFloats('interaction_slipslip'),2,1)
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prm%CEdgeDipMinDistance = config_phase(p)%getFloat('cedgedipmindistance')
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prm%CLambdaSlipPerSlipSystem = config_phase(p)%getFloats('clambdaslip')
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prm%CLambdaSlipPerSlipSystem= math_expand(prm%CLambdaSlipPerSlipSystem,prm%Nslip)
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prm%tau_peierlsPerSlipFamily = config_phase(p)%getFloats('tau_peierls',defaultVal=[0.0_pReal])
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prm%p = config_phase(p)%getFloats('p_slip')
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prm%q = config_phase(p)%getFloats('q_slip')
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endif
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prm%Ntwin = config_phase(p)%getInts('ntwin', defaultVal=emptyInt)
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if (size(prm%Ntwin) > count(lattice_NtwinSystem(:,p) > 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
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if (any(lattice_NtwinSystem(1:size(prm%Ntwin),p)-prm%Ntwin < 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
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if (any(prm%Ntwin < 0_pInt)) call IO_error(150_pInt,ext_msg='Ntwin')
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prm%totalNtwin = sum(prm%Ntwin)
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if (prm%totalNtwin > 0_pInt) then
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prm%burgers_twin = config_phase(p)%getFloats('twinburgers')
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prm%burgers_twin = math_expand(prm%burgers_twin,prm%Ntwin)
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prm%xc_twin = config_phase(p)%getFloat('xc_twin')
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prm%Cthresholdtwin = config_phase(p)%getFloat('cthresholdtwin', defaultVal=0.0_pReal)
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prm%Cmfptwin = config_phase(p)%getFloat('cmfptwin', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%interaction_TwinTwin = spread(config_phase(p)%getFloats('interaction_twintwin'),2,1)
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if (lattice_structure(p) /= LATTICE_fcc_ID) then
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prm%Ndot0_twin = config_phase(p)%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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prm%twinsize = config_phase(p)%getFloats('twinsize')
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prm%twinsize= math_expand(prm%twinsize,prm%Ntwin)
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prm%r = config_phase(p)%getFloats('r_twin')
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prm%r = math_expand(prm%r,prm%Ntwin)
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prm%L0_twin = config_phase(p)%getFloat('l0_twin')
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endif
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prm%Ntrans = config_phase(p)%getInts('ntrans', defaultVal=emptyInt)
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prm%totalNtrans = sum(prm%Ntrans)
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!if (size > Nchunks_SlipFamilies + 1_pInt) call IO_error(150_pInt,ext_msg=extmsg)
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if (prm%totalNtrans > 0_pInt) then
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prm%burgers_trans = config_phase(p)%getFloats('transburgers')
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prm%burgers_trans = math_expand(prm%burgers_trans,prm%Ntrans)
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prm%Cthresholdtrans = config_phase(p)%getFloat('cthresholdtrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%transStackHeight = config_phase(p)%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%Cmfptrans = config_phase(p)%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%deltaG = config_phase(p)%getFloat('deltag')
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prm%xc_trans = config_phase(p)%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%L0_trans = config_phase(p)%getFloat('l0_trans')
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prm%interaction_TransTrans = spread(config_phase(p)%getFloats('interaction_transtrans'),2,1)
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if (lattice_structure(p) /= LATTICE_fcc_ID) then
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prm%Ndot0_trans = config_phase(p)%getFloats('ndot0_trans')
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prm%Ndot0_trans = math_expand(prm%Ndot0_trans,prm%Ntrans)
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endif
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prm%lamellarsizePerTransSystem = config_phase(p)%getFloats('lamellarsize')
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prm%lamellarsizePerTransSystem = math_expand(prm%lamellarsizePerTransSystem,prm%Ntrans)
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prm%s = config_phase(p)%getFloats('s_trans',defaultVal=[0.0_pReal])
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endif
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if (sum(prm%Ntwin) > 0_pInt .or. sum(prm%Ntrans) > 0_pInt) then
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prm%SFE_0K = config_phase(p)%getFloat('sfe_0k')
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prm%dSFE_dT = config_phase(p)%getFloat('dsfe_dt')
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prm%VcrossSlip = config_phase(p)%getFloat('vcrossslip')
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endif
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if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then
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prm%interaction_SlipTwin = spread(config_phase(p)%getFloats('interaction_sliptwin'),2,1)
|
||
prm%interaction_TwinSlip = spread(config_phase(p)%getFloats('interaction_twinslip'),2,1)
|
||
endif
|
||
|
||
if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then
|
||
prm%interaction_TransSlip = spread(config_phase(p)%getFloats('interaction_transslip'),2,1)
|
||
prm%interaction_SlipTrans = spread(config_phase(p)%getFloats('interaction_sliptrans'),2,1)
|
||
endif
|
||
|
||
|
||
prm%aTolRho = config_phase(p)%getFloat('atol_rho')
|
||
prm%aTolTwinFrac = config_phase(p)%getFloat('atol_twinfrac')
|
||
prm%aTolTransFrac = config_phase(p)%getFloat('atol_transfrac')
|
||
|
||
prm%CAtomicVolume = config_phase(p)%getFloat('catomicvolume')
|
||
prm%GrainSize = config_phase(p)%getFloat('grainsize')
|
||
prm%MaxTwinFraction = config_phase(p)%getFloat('maxtwinfraction') ! ToDo: only used in postResults
|
||
|
||
prm%D0 = config_phase(p)%getFloat('d0')
|
||
prm%Qsd = config_phase(p)%getFloat('qsd')
|
||
prm%SolidSolutionStrength = config_phase(p)%getFloat('solidsolutionstrength')
|
||
prm%dipoleFormationFactor= config_phase(p)%getFloat('dipoleformationfactor', defaultVal=1.0_pReal) ! ToDo: How to handle that???
|
||
|
||
prm%sbResistance = config_phase(p)%getFloat('shearbandresistance',defaultVal=0.0_pReal)
|
||
prm%sbVelocity = config_phase(p)%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
|
||
prm%sbQedge = config_phase(p)%getFloat('qedgepersbsystem')
|
||
prm%pShearBand = config_phase(p)%getFloat('p_shearband')
|
||
prm%qShearBand = config_phase(p)%getFloat('q_shearband')
|
||
|
||
outputs = config_phase(p)%getStrings('(output)', defaultVal=emptyString)
|
||
allocate(prm%outputID(0))
|
||
do i= 1_pInt, size(outputs)
|
||
outputID = undefined_ID
|
||
select case(outputs(i))
|
||
|
||
case ('edge_density')
|
||
outputID = edge_density_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('dipole_density')
|
||
outputID = dipole_density_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('shear_rate_slip','shearrate_slip')
|
||
outputID = shear_rate_slip_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('accumulated_shear_slip')
|
||
outputID = accumulated_shear_slip_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('mfp_slip')
|
||
outputID = mfp_slip_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('resolved_stress_slip')
|
||
outputID = resolved_stress_slip_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('threshold_stress_slip')
|
||
outputID= threshold_stress_slip_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('edge_dipole_distance')
|
||
outputID = edge_dipole_distance_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('stress_exponent')
|
||
outputID = stress_exponent_ID
|
||
outputSize = sum(prm%Nslip)
|
||
|
||
case ('twin_fraction')
|
||
outputID = twin_fraction_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
case ('shear_rate_twin','shearrate_twin')
|
||
outputID= shear_rate_twin_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
case ('accumulated_shear_twin')
|
||
outputID = accumulated_shear_twin_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
case ('mfp_twin')
|
||
outputID = mfp_twin_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
case ('resolved_stress_twin')
|
||
outputID = resolved_stress_twin_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
case ('threshold_stress_twin')
|
||
outputID = threshold_stress_twin_ID
|
||
outputSize = sum(prm%Ntwin)
|
||
|
||
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 ('sb_eigenvalues')
|
||
outputID = sb_eigenvalues_ID
|
||
outputSize = 3_pInt
|
||
|
||
case ('sb_eigenvectors')
|
||
outputID = sb_eigenvectors_ID
|
||
outputSize = 3_pInt
|
||
|
||
case ('stress_trans_fraction')
|
||
outputID = stress_trans_fraction_ID
|
||
outputSize = sum(prm%Ntrans)
|
||
|
||
case ('strain_trans_fraction')
|
||
outputID = strain_trans_fraction_ID
|
||
outputSize = sum(prm%Ntrans)
|
||
|
||
case ('trans_fraction','total_trans_fraction')
|
||
outputID = trans_fraction_ID
|
||
outputSize = sum(prm%Ntrans)
|
||
|
||
end select
|
||
|
||
if (outputID /= undefined_ID) then
|
||
plastic_dislotwin_output(i,instance) = outputs(i)
|
||
plastic_dislotwin_sizePostResult(i,instance) = outputSize
|
||
prm%outputID = [prm%outputID , outputID]
|
||
endif
|
||
|
||
enddo
|
||
enddo
|
||
|
||
|
||
sanityChecks: do p = 1_pInt, size(phase_plasticity)
|
||
if (phase_plasticity(p) /= PLASTICITY_dislotwin_ID) cycle
|
||
instance = phase_plasticityInstance(p)
|
||
prm => param(instance)
|
||
do f = 1_pInt,lattice_maxNslipFamily
|
||
! if (rhoEdge0(f,instance) < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOTWIN_label//')')
|
||
! if (rhoEdgeDip0(f,instance) < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOTWIN_label//')')
|
||
! if (burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOTWIN_label//')')
|
||
!if (v0PerSlipFamily(f,instance) <= 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOTWIN_label//')')
|
||
!if (prm%tau_peierlsPerSlipFamily(f) < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOTWIN_label//')')
|
||
enddo
|
||
do f = 1_pInt,lattice_maxNtwinFamily
|
||
! if (burgersPerTwinFamily(f,instance) <= 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='twinburgers ('//PLASTICITY_DISLOTWIN_label//')')
|
||
!if (Ndot0PerTwinFamily(f,instance) < 0.0_pReal) &
|
||
! call IO_error(211_pInt,el=instance,ext_msg='ndot0_twin ('//PLASTICITY_DISLOTWIN_label//')')
|
||
enddo
|
||
if (prm%CAtomicVolume <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%D0 <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%Qsd <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,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=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolRho <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolTwinFrac <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,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=instance,ext_msg='SFE0K ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTolTransFrac <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='aTolTransFrac ('//PLASTICITY_DISLOTWIN_label//')')
|
||
endif
|
||
if (prm%sbResistance < 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='sbResistance ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%sbVelocity < 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='sbVelocity ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%sbVelocity > 0.0_pReal .and. &
|
||
prm%pShearBand <= 0.0_pReal) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='pShearBand ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (dNeq0(prm%dipoleFormationFactor) .and. &
|
||
dNeq(prm%dipoleFormationFactor, 1.0_pReal)) &
|
||
call IO_error(211_pInt,el=instance,ext_msg='dipoleFormationFactor ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%sbVelocity > 0.0_pReal .and. &
|
||
prm%qShearBand <= 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
|
||
enddo sanityChecks
|
||
|
||
! ToDo: this should be stored somewhere else. Works only for the whole instance!!
|
||
allocate(tau_r_twin(prm%totalNtwin, maxNinstance), source=0.0_pReal)
|
||
allocate(tau_r_trans(prm%totalNtrans, maxNinstance), source=0.0_pReal)
|
||
|
||
allocate(forestProjectionEdge(prm%totalNslip,prm%totalNslip,maxNinstance), source=0.0_pReal)
|
||
allocate(projectionMatrix_Trans(prm%totalNtrans,prm%totalNslip,maxNinstance), source=0.0_pReal)
|
||
|
||
allocate(Ctwin66(6,6,prm%totalNtwin,maxNinstance), source=0.0_pReal)
|
||
allocate(Ctrans66(6,6,prm%totalNtrans,maxNinstance), source=0.0_pReal)
|
||
|
||
allocate(Ctwin3333(3,3,3,3,prm%totalNtwin), source=0.0_pReal)
|
||
allocate(Ctrans3333(3,3,3,3,prm%totalNtrans), source=0.0_pReal)
|
||
|
||
allocate(state(maxNinstance))
|
||
allocate(dotState(maxNinstance))
|
||
|
||
initializeInstances: do p = 1_pInt, size(phase_plasticity)
|
||
if (phase_plasticity(p) /= PLASTICITY_dislotwin_ID) cycle
|
||
NofMyPhase=count(material_phase==p)
|
||
instance = phase_plasticityInstance(p)
|
||
prm => param(instance)
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
|
||
sizeDotState = int(size(['rho ','rhoDip ','accshearslip']),pInt) * prm%totalNslip &
|
||
+ int(size(['twinFraction','accsheartwin']),pInt) * prm%totalNtwin &
|
||
+ int(size(['stressTransFraction','strainTransFraction']),pInt) * prm%totalNtrans
|
||
sizeDeltaState = 0_pInt
|
||
sizeState = sizeDotState &
|
||
+ int(size(['invLambdaSlip ','invLambdaSlipTwin ','invLambdaSlipTrans',&
|
||
'meanFreePathSlip ','tauSlipThreshold ']),pInt) * prm%totalNslip &
|
||
+ int(size(['invLambdaTwin ','meanFreePathTwin','tauTwinThreshold',&
|
||
'twinVolume ']),pInt) * prm%totalNtwin &
|
||
+ int(size(['invLambdaTrans ','meanFreePathTrans','tauTransThreshold', &
|
||
'martensiteVolume ']),pInt) * prm%totalNtrans
|
||
|
||
plasticState(p)%sizeState = sizeState
|
||
plasticState(p)%sizeDotState = sizeDotState
|
||
plasticState(p)%sizeDeltaState = sizeDeltaState
|
||
plasticState(p)%sizePostResults = sum(plastic_dislotwin_sizePostResult(:,instance))
|
||
plasticState(p)%nSlip = prm%totalNslip
|
||
plasticState(p)%nTwin = prm%totalNtwin
|
||
plasticState(p)%nTrans= prm%totalNtrans
|
||
allocate(plasticState(p)%aTolState (sizeState), source=0.0_pReal)
|
||
allocate(plasticState(p)%state0 (sizeState,NofMyPhase), source=0.0_pReal)
|
||
allocate(plasticState(p)%partionedState0 (sizeState,NofMyPhase), source=0.0_pReal)
|
||
allocate(plasticState(p)%subState0 (sizeState,NofMyPhase), source=0.0_pReal)
|
||
allocate(plasticState(p)%state (sizeState,NofMyPhase), source=0.0_pReal)
|
||
|
||
allocate(plasticState(p)%dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
|
||
allocate(plasticState(p)%deltaState (sizeDeltaState,NofMyPhase), source=0.0_pReal)
|
||
if (any(numerics_integrator == 1_pInt)) then
|
||
allocate(plasticState(p)%previousDotState (sizeDotState,NofMyPhase), source=0.0_pReal)
|
||
allocate(plasticState(p)%previousDotState2 (sizeDotState,NofMyPhase), source=0.0_pReal)
|
||
endif
|
||
if (any(numerics_integrator == 4_pInt)) &
|
||
allocate(plasticState(p)%RK4dotState (sizeDotState,NofMyPhase), source=0.0_pReal)
|
||
if (any(numerics_integrator == 5_pInt)) &
|
||
allocate(plasticState(p)%RKCK45dotState (6,sizeDotState,NofMyPhase),source=0.0_pReal)
|
||
offset_slip = 2_pInt*plasticState(p)%nslip
|
||
plasticState(p)%slipRate => &
|
||
plasticState(p)%dotState(offset_slip+1:offset_slip+plasticState(p)%nslip,1:NofMyPhase)
|
||
plasticState(p)%accumulatedSlip => &
|
||
plasticState(p)%state (offset_slip+1:offset_slip+plasticState(p)%nslip,1:NofMyPhase)
|
||
|
||
allocate(temp1(prm%totalNslip,prm%totalNslip), source =0.0_pReal)
|
||
allocate(temp2(prm%totalNslip,prm%totalNtwin), source =0.0_pReal)
|
||
allocate(temp3(prm%totalNslip,prm%totalNtrans),source =0.0_pReal)
|
||
|
||
mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1)
|
||
index_myFamily = sum(prm%Nslip(1:f-1_pInt))
|
||
|
||
slipSystemsLoop: do j = 1_pInt,prm%Nslip(f)
|
||
do o = 1_pInt, size(prm%Nslip,1)
|
||
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
|
||
forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = &
|
||
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,p))+j,p), &
|
||
lattice_st(:,sum(lattice_NslipSystem(1:o-1,p))+k,p)))
|
||
temp1(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_SlipSlip(lattice_interactionSlipSlip( &
|
||
sum(lattice_NslipSystem(1:f-1,p))+j, &
|
||
sum(lattice_NslipSystem(1:o-1,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
do o = 1_pInt,size(prm%Ntwin,1)
|
||
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Ntwin(o) ! loop over (active) systems in other family (twin)
|
||
temp2(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_SlipTwin(lattice_interactionSlipTwin( &
|
||
sum(lattice_NslipSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
do o = 1_pInt,size(prm%Ntrans,1)
|
||
index_otherFamily = sum(prm%Ntrans(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Ntrans(o) ! loop over (active) systems in other family (trans)
|
||
temp3(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_SlipTrans(lattice_interactionSlipTrans( &
|
||
sum(lattice_NslipSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NtransSystem(1:o-1_pInt,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
enddo slipSystemsLoop
|
||
enddo mySlipFamilies
|
||
prm%interaction_SlipSlip = temp1; deallocate(temp1)
|
||
prm%interaction_SlipTwin = temp2; deallocate(temp2)
|
||
prm%interaction_SlipTrans = temp3; deallocate(temp3)
|
||
|
||
|
||
allocate(temp1(prm%totalNtwin,prm%totalNslip), source =0.0_pReal)
|
||
allocate(temp2(prm%totalNtwin,prm%totalNtwin), source =0.0_pReal)
|
||
|
||
Ctwin3333 = 0.0_pReal
|
||
|
||
twinFamiliesLoop: do f = 1_pInt, size(prm%Ntwin,1)
|
||
index_myFamily = sum(prm%Ntwin(1:f-1_pInt)) ! index in truncated twin system list
|
||
twinSystemsLoop: do j = 1_pInt,prm%Ntwin(f)
|
||
|
||
! nucleation rate prefactor,
|
||
! and twin size
|
||
!* Rotate twin elasticity matrices
|
||
index_otherFamily = sum(lattice_NtwinSystem(1:f-1_pInt,p)) ! 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 p1 = 1_pInt,3_pInt; do q = 1_pInt,3_pInt; do r = 1_pInt,3_pInt; do s = 1_pInt,3_pInt
|
||
Ctwin3333(l,m,n,o,index_myFamily+j) = &
|
||
Ctwin3333(l,m,n,o,index_myFamily+j) + &
|
||
lattice_C3333(p1,q,r,s,p) * &
|
||
lattice_Qtwin(l,p1,index_otherFamily+j,p) * &
|
||
lattice_Qtwin(m,q,index_otherFamily+j,p) * &
|
||
lattice_Qtwin(n,r,index_otherFamily+j,p) * &
|
||
lattice_Qtwin(o,s,index_otherFamily+j,p)
|
||
enddo; enddo; enddo; enddo
|
||
enddo; enddo; enddo; enddo
|
||
Ctwin66(1:6,1:6,index_myFamily+j,instance) = &
|
||
math_Mandel3333to66(Ctwin3333(1:3,1:3,1:3,1:3,index_myFamily+j))
|
||
|
||
!* Interaction matrices
|
||
do o = 1_pInt,size(prm%Nslip,1)
|
||
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
|
||
temp1(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_TwinSlip(lattice_interactionTwinSlip( &
|
||
sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NslipSystem(1:o-1_pInt,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
do o = 1_pInt,size(prm%Ntwin,1)
|
||
index_otherFamily = sum(prm%Ntwin(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Ntwin(o) ! loop over (active) systems in other family (twin)
|
||
temp2(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_TwinTwin(lattice_interactionTwinTwin( &
|
||
sum(lattice_NtwinSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NtwinSystem(1:o-1_pInt,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
enddo twinSystemsLoop
|
||
enddo twinFamiliesLoop
|
||
prm%interaction_TwinSlip = temp1; deallocate(temp1)
|
||
prm%interaction_TwinTwin = temp2; deallocate(temp2)
|
||
|
||
|
||
allocate(temp1(prm%totalNtrans,prm%totalNslip), source =0.0_pReal)
|
||
allocate(temp2(prm%totalNtrans,prm%totalNtrans), source =0.0_pReal)
|
||
|
||
|
||
transFamiliesLoop: do f = 1_pInt,size(prm%Ntrans,1)
|
||
index_myFamily = sum(prm%Ntrans(1:f-1_pInt)) ! index in truncated trans system list
|
||
transSystemsLoop: do j = 1_pInt,prm%Ntrans(f)
|
||
|
||
Ctrans3333 = 0.0_pReal
|
||
index_otherFamily = sum(lattice_NtransSystem(1:f-1_pInt,p)) ! index in full lattice trans 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 p1 = 1_pInt,3_pInt; do q = 1_pInt,3_pInt; do r = 1_pInt,3_pInt; do s = 1_pInt,3_pInt
|
||
Ctrans3333(l,m,n,o,index_myFamily+j) = &
|
||
Ctrans3333(l,m,n,o,index_myFamily+j) + &
|
||
lattice_trans_C3333(p1,q,r,s,p) * &
|
||
lattice_Qtrans(l,p1,index_otherFamily+j,p) * &
|
||
lattice_Qtrans(m,q,index_otherFamily+j,p) * &
|
||
lattice_Qtrans(n,r,index_otherFamily+j,p) * &
|
||
lattice_Qtrans(o,s,index_otherFamily+j,p)
|
||
enddo; enddo; enddo; enddo
|
||
enddo; enddo; enddo; enddo
|
||
Ctrans66(1:6,1:6,index_myFamily+j,instance) = &
|
||
math_Mandel3333to66(Ctrans3333(1:3,1:3,1:3,1:3,index_myFamily+j))
|
||
|
||
!* Interaction matrices
|
||
do o = 1_pInt,size(prm%Nslip,1)
|
||
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (slip)
|
||
temp1(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_TransSlip(lattice_interactionTransSlip( &
|
||
sum(lattice_NtransSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NslipSystem(1:o-1_pInt,p))+k, &
|
||
p) ,1 )
|
||
enddo; enddo
|
||
|
||
do o = 1_pInt,size(prm%Ntrans,1)
|
||
index_otherFamily = sum(prm%Ntrans(1:o-1_pInt))
|
||
do k = 1_pInt,prm%Ntrans(o) ! loop over (active) systems in other family (trans)
|
||
temp2(index_myFamily+j,index_otherFamily+k) = &
|
||
prm%interaction_TransTrans(lattice_interactionTransTrans( &
|
||
sum(lattice_NtransSystem(1:f-1_pInt,p))+j, &
|
||
sum(lattice_NtransSystem(1:o-1_pInt,p))+k, &
|
||
p),1 )
|
||
enddo; enddo
|
||
|
||
!* Projection matrices for shear from slip systems to fault-band (twin) systems for strain-induced martensite nucleation
|
||
! select case(trans_lattice_structure(p))
|
||
! case (LATTICE_bcc_ID)
|
||
! do o = 1_pInt,sum(prm%Ntrans,1)
|
||
! index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
|
||
! do k = 1_pInt,prm%Nslip(o) ! loop over (active) systems in other family (trans)
|
||
! temp3(index_myFamily+j,index_otherFamily+k) = &
|
||
! lattice_projectionTrans( sum(lattice_NtransSystem(1:f-1,p))+j, &
|
||
! sum(lattice_NslipSystem(1:o-1,p))+k, p)
|
||
! enddo; enddo
|
||
! end select
|
||
|
||
enddo transSystemsLoop
|
||
enddo transFamiliesLoop
|
||
|
||
|
||
prm%interaction_TransSlip = temp1; deallocate(temp1)
|
||
prm%interaction_TransTrans = temp2; deallocate(temp2)
|
||
|
||
startIndex=1_pInt
|
||
endIndex=prm%totalNslip
|
||
state(instance)%rhoEdge=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%rhoEdge=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(prm%rho0,prm%Nslip),2,NofMyPhase)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%rhoEdgeDip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%rhoEdgeDip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(prm%rhoDip0,prm%Nslip),2,NofMyPhase)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%accshear_slip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%accshear_slip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%twinFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%twinFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTwinFrac
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%accshear_twin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%accshear_twin=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%stressTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%stressTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%strainTransFraction=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dotState(instance)%strainTransFraction=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolTransFrac
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%invLambdaSlip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
invLambdaSlip0 = spread(0.0_pReal,1,prm%totalNslip)
|
||
forall (i = 1_pInt:prm%totalNslip) &
|
||
invLambdaSlip0(i) = sqrt(dot_product(math_expand(prm%rho0,prm%Nslip)+ &
|
||
math_expand(prm%rhoDip0,prm%Nslip),forestProjectionEdge(1:prm%totalNslip,i,instance)))/ &
|
||
prm%CLambdaSlipPerSlipSystem(i)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(invLambdaSlip0,prm%Nslip),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%invLambdaSlipTwin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%invLambdaTwin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%invLambdaSlipTrans=>plasticState(p)%state(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%invLambdaTrans=>plasticState(p)%state(startIndex:endIndex,:)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = 0.0_pReal
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%mfp_slip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
MeanFreePathSlip0 = prm%GrainSize/(1.0_pReal+invLambdaSlip0*prm%GrainSize)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(MeanFreePathSlip0,prm%Nslip),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%mfp_twin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
MeanFreePathTwin0 = spread(prm%GrainSize,1,prm%totalNtwin)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(MeanFreePathTwin0,prm%Ntwin),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%mfp_trans=>plasticState(p)%state(startIndex:endIndex,:)
|
||
MeanFreePathTrans0 = spread(prm%GrainSize,1,prm%totalNtrans)
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(MeanFreePathTrans0,prm%Ntrans),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNslip
|
||
state(instance)%threshold_stress_slip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
tauSlipThreshold0 = spread(0.0_pReal,1,prm%totalNslip)
|
||
forall (i = 1_pInt:prm%totalNslip) tauSlipThreshold0(i) = &
|
||
lattice_mu(p)*prm%burgers_slip(i) * &
|
||
sqrt(dot_product(math_expand(prm%rho0 + prm%rhoDip0,prm%Nslip),&
|
||
prm%interaction_SlipSlip(i,1:prm%totalNslip)))
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(tauSlipThreshold0,prm%Nslip),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%threshold_stress_twin=>plasticState(p)%state(startIndex:endIndex,:)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%threshold_stress_trans=>plasticState(p)%state(startIndex:endIndex,:)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtwin
|
||
state(instance)%twinVolume=>plasticState(p)%state(startIndex:endIndex,:)
|
||
TwinVolume0= spread(0.0_pReal,1,prm%totalNtwin)
|
||
forall (i = 1_pInt:prm%totalNtwin) TwinVolume0(i) = &
|
||
(PI/4.0_pReal)*prm%twinsize(i)*MeanFreePathTwin0(i)**2.0_pReal
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(TwinVolume0,prm%Ntwin),2, NofMyPhase)
|
||
|
||
startIndex=endIndex+1
|
||
endIndex=endIndex+prm%totalNtrans
|
||
state(instance)%martensiteVolume=>plasticState(p)%state(startIndex:endIndex,:)
|
||
MartensiteVolume0= spread(0.0_pReal,1,prm%totalNtrans)
|
||
forall (i = 1_pInt:prm%totalNtrans) MartensiteVolume0(i) = &
|
||
(PI/4.0_pReal)*prm%lamellarsizePerTransSystem(i)*MeanFreePathTrans0(i)**2.0_pReal
|
||
plasticState(p)%state0(startIndex:endIndex,:) = &
|
||
spread(math_expand(MartensiteVolume0,prm%Ntrans),2, NofMyPhase)
|
||
|
||
enddo initializeInstances
|
||
end subroutine plastic_dislotwin_init
|
||
|
||
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief returns the homogenized elasticity matrix
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_homogenizedC(ipc,ip,el)
|
||
use material, only: &
|
||
phase_plasticityInstance, &
|
||
phaseAt, phasememberAt
|
||
use lattice, only: &
|
||
lattice_C66
|
||
|
||
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
|
||
type(tParameters) :: prm
|
||
type(tDislotwinState) :: ste
|
||
|
||
integer(pInt) :: instance,i, &
|
||
ph, &
|
||
of
|
||
real(pReal) :: sumf, sumftr
|
||
|
||
!* Shortened notation
|
||
of = phasememberAt(ipc,ip,el)
|
||
ph = phaseAt(ipc,ip,el)
|
||
instance = phase_plasticityInstance(ph)
|
||
associate( prm => param(instance), ste =>state(instance))
|
||
|
||
|
||
!* Total twin volume fraction
|
||
sumf = sum(ste%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
|
||
|
||
!* Total transformed volume fraction
|
||
sumftr = sum(ste%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
|
||
sum(ste%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
|
||
!* Homogenized elasticity matrix
|
||
plastic_dislotwin_homogenizedC = (1.0_pReal-sumf-sumftr)*lattice_C66(1:6,1:6,ph)
|
||
do i=1_pInt,prm%totalNtwin
|
||
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
|
||
+ ste%twinFraction(i,of)*Ctwin66(1:6,1:6,i,instance)
|
||
enddo
|
||
do i=1_pInt,prm%totalNtrans
|
||
plastic_dislotwin_homogenizedC = plastic_dislotwin_homogenizedC &
|
||
+ (ste%stressTransFraction(i,of) + ste%strainTransFraction(i,of))*&
|
||
Ctrans66(1:6,1:6,i,instance)
|
||
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, &
|
||
plasticState, &
|
||
phaseAt, phasememberAt
|
||
use lattice, only: &
|
||
lattice_mu, &
|
||
lattice_nu
|
||
|
||
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) :: &
|
||
instance, &
|
||
s, &
|
||
ph, &
|
||
of
|
||
real(pReal) :: &
|
||
sumf,sfe,sumftr
|
||
real(pReal), dimension(:), allocatable :: &
|
||
x0
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: fOverStacksize
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntrans) :: ftransOverLamellarSize
|
||
|
||
type(tParameters):: prm
|
||
type(tDislotwinState) :: ste
|
||
|
||
|
||
!* Shortened notation
|
||
of = phasememberAt(ipc,ip,el)
|
||
ph = phaseAt(ipc,ip,el)
|
||
instance = phase_plasticityInstance(ph)
|
||
|
||
associate(prm => param(instance), ste => state(instance))
|
||
!* Total twin volume fraction
|
||
sumf = sum(ste%twinFraction(1:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
|
||
sumftr = sum(ste%stressTransFraction(1:prm%totalNtrans,of)) + &
|
||
sum(ste%strainTransFraction(1:prm%totalNtrans,of))
|
||
|
||
!* Stacking fault energy
|
||
sfe = prm%SFE_0K + prm%dSFE_dT * Temperature
|
||
|
||
!* rescaled volume fraction for topology
|
||
fOverStacksize = ste%twinFraction(1_pInt:prm%totalNtwin,of)/prm%twinsize
|
||
ftransOverLamellarSize = sumftr /prm%lamellarsizePerTransSystem
|
||
|
||
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
||
forall (s = 1_pInt:prm%totalNslip) &
|
||
ste%invLambdaSlip(s,of) = &
|
||
sqrt(dot_product((ste%rhoEdge(1_pInt:prm%totalNslip,of)+ste%rhoEdgeDip(1_pInt:prm%totalNslip,of)),&
|
||
forestProjectionEdge(1:prm%totalNslip,s,instance)))/prm%CLambdaSlipPerSlipSystem(s)
|
||
|
||
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
||
!$OMP CRITICAL (evilmatmul)
|
||
if (prm%totalNtwin > 0_pInt .and. prm%totalNslip > 0_pInt) &
|
||
ste%invLambdaSlipTwin(1_pInt:prm%totalNslip,of) = &
|
||
matmul(prm%interaction_SlipTwin,fOverStacksize)/(1.0_pReal-sumf)
|
||
|
||
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
||
|
||
!ToDo: needed? if (prm%totalNtwin > 0_pInt) &
|
||
ste%invLambdaTwin(1_pInt:prm%totalNtwin,of) = &
|
||
matmul(prm%interaction_TwinTwin,fOverStacksize)/(1.0_pReal-sumf)
|
||
|
||
|
||
!* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
|
||
if (prm%totalNtrans > 0_pInt .and. prm%totalNslip > 0_pInt) &
|
||
ste%invLambdaSlipTrans(1_pInt:prm%totalNslip,of) = &
|
||
matmul(prm%interaction_SlipTrans,ftransOverLamellarSize)/(1.0_pReal-sumftr)
|
||
|
||
!* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
|
||
!ToDo: needed? if (prm%totalNtrans > 0_pInt) &
|
||
|
||
ste%invLambdaTrans(1_pInt:prm%totalNtrans,of) = &
|
||
matmul(prm%interaction_TransTrans,ftransOverLamellarSize)/(1.0_pReal-sumftr)
|
||
!$OMP END CRITICAL (evilmatmul)
|
||
|
||
!* mean free path between 2 obstacles seen by a moving dislocation
|
||
do s = 1_pInt,prm%totalNslip
|
||
if ((prm%totalNtwin > 0_pInt) .or. (prm%totalNtrans > 0_pInt)) then ! ToDo: This is two simplified
|
||
ste%mfp_slip(s,of) = &
|
||
prm%GrainSize/(1.0_pReal+prm%GrainSize*&
|
||
(ste%invLambdaSlip(s,of) + ste%invLambdaSlipTwin(s,of) + ste%invLambdaSlipTrans(s,of)))
|
||
else
|
||
ste%mfp_slip(s,of) = &
|
||
prm%GrainSize/&
|
||
(1.0_pReal+prm%GrainSize*(ste%invLambdaSlip(s,of))) !!!!!! correct?
|
||
endif
|
||
enddo
|
||
|
||
!* mean free path between 2 obstacles seen by a growing twin/martensite
|
||
ste%mfp_twin(:,of) = prm%Cmfptwin*prm%GrainSize/ (1.0_pReal+prm%GrainSize*ste%invLambdaTwin(:,of))
|
||
ste%mfp_trans(:,of) = prm%Cmfptrans*prm%GrainSize/(1.0_pReal+prm%GrainSize*ste%invLambdaTrans(:,of))
|
||
|
||
!* threshold stress for dislocation motion
|
||
forall (s = 1_pInt:prm%totalNslip) ste%threshold_stress_slip(s,of) = &
|
||
lattice_mu(ph)*prm%burgers_slip(s)*&
|
||
sqrt(dot_product(ste%rhoEdge(1_pInt:prm%totalNslip,of)+ste%rhoEdgeDip(1_pInt:prm%totalNslip,of),&
|
||
prm%interaction_SlipSlip(s,1:prm%totalNslip)))
|
||
|
||
!* threshold stress for growing twin/martensite
|
||
ste%threshold_stress_twin(:,of) = prm%Cthresholdtwin* &
|
||
(sfe/(3.0_pReal*prm%burgers_twin)+ 3.0_pReal*prm%burgers_twin*lattice_mu(ph)/ &
|
||
(prm%L0_twin*prm%burgers_slip)) ! slip burgers here correct?
|
||
ste%threshold_stress_trans(:,of) = prm%Cthresholdtrans* &
|
||
(sfe/(3.0_pReal*prm%burgers_trans) + 3.0_pReal*prm%burgers_trans*lattice_mu(ph)/&
|
||
(prm%L0_trans*prm%burgers_slip) + prm%transStackHeight*prm%deltaG/ (3.0_pReal*prm%burgers_trans) )
|
||
|
||
! final volume after growth
|
||
ste%twinVolume(:,of) = (PI/4.0_pReal)*prm%twinsize*ste%mfp_twin(:,of)**2.0_pReal
|
||
ste%martensiteVolume(:,of) = (PI/4.0_pReal)*prm%lamellarsizePerTransSystem*ste%mfp_trans(:,of)**2.0_pReal
|
||
|
||
!* equilibrium separation of partial dislocations (twin)
|
||
x0 = lattice_mu(ph)*prm%burgers_twin**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+lattice_nu(ph))/(1.0_pReal-lattice_nu(ph))
|
||
tau_r_twin(:,instance)= lattice_mu(ph)*prm%burgers_twin/(2.0_pReal*PI)*&
|
||
(1/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
|
||
|
||
!* equilibrium separation of partial dislocations (trans)
|
||
x0 = lattice_mu(ph)*prm%burgers_trans**2.0_pReal/(sfe*8.0_pReal*PI)*(2.0_pReal+lattice_nu(ph))/(1.0_pReal-lattice_nu(ph))
|
||
tau_r_trans(:,instance)= lattice_mu(ph)*prm%burgers_trans/(2.0_pReal*PI)*&
|
||
(1/(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_dTstar99,Tstar_v,Temperature,ipc,ip,el)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_Plain3333to99, &
|
||
math_Mandel6to33, &
|
||
math_Mandel33to6, &
|
||
math_eigenValuesVectorsSym, &
|
||
math_tensorproduct33, &
|
||
math_symmetric33, &
|
||
math_mul33x3
|
||
use material, only: &
|
||
material_phase, &
|
||
plasticState, &
|
||
phase_plasticityInstance, &
|
||
phaseAt, phasememberAt
|
||
use lattice, only: &
|
||
lattice_Sslip, &
|
||
lattice_Sslip_v, &
|
||
lattice_Stwin, &
|
||
lattice_Stwin_v, &
|
||
lattice_Strans, &
|
||
lattice_Strans_v, &
|
||
lattice_maxNslipFamily,&
|
||
lattice_maxNtwinFamily, &
|
||
lattice_maxNtransFamily, &
|
||
lattice_NslipSystem, &
|
||
lattice_NtwinSystem, &
|
||
lattice_NtransSystem, &
|
||
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
|
||
real(pReal), dimension(3,3), intent(out) :: Lp
|
||
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99
|
||
|
||
integer(pInt) :: instance,ph,of,f,i,j,k,l,m,n,index_myFamily,s1,s2
|
||
real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0_twin,stressRatio, &
|
||
Ndot0_trans,StressRatio_s
|
||
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
|
||
gdot_slip,dgdot_dtauslip,tau_slip
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: &
|
||
gdot_twin,dgdot_dtautwin,tau_twin
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntrans) :: &
|
||
gdot_trans,dgdot_dtautrans,tau_trans
|
||
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
|
||
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])
|
||
|
||
type(tParameters) :: prm
|
||
|
||
!* Shortened notation
|
||
of = phasememberAt(ipc,ip,el)
|
||
ph = phaseAt(ipc,ip,el)
|
||
instance = phase_plasticityInstance(ph)
|
||
|
||
|
||
Lp = 0.0_pReal
|
||
dLp_dTstar3333 = 0.0_pReal
|
||
|
||
|
||
associate(prm => param(instance))
|
||
!--------------------------------------------------------------------------------------------------
|
||
! Dislocation glide part
|
||
gdot_slip = 0.0_pReal
|
||
dgdot_dtauslip = 0.0_pReal
|
||
j = 0_pInt
|
||
slipFamiliesLoop: do f = 1_pInt,size(prm%Nslip,1)
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
slipSystemsLoop: do i = 1_pInt,prm%Nslip(f)
|
||
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,ph))
|
||
|
||
if((abs(tau_slip(j))-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
!* Stress ratios
|
||
stressRatio =((abs(tau_slip(j))- state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+prm%tau_peierlsPerSlipFamily(f)))
|
||
StressRatio_p = stressRatio** prm%p(f)
|
||
StressRatio_pminus1 = stressRatio**(prm%p(f)-1.0_pReal)
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = &
|
||
state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)*&
|
||
prm%v0(j)
|
||
|
||
!* Shear rates due to slip
|
||
gdot_slip(j) = DotGamma0 &
|
||
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(f)) &
|
||
* sign(1.0_pReal,tau_slip(j))
|
||
|
||
!* Derivatives of shear rates
|
||
dgdot_dtauslip(j) = &
|
||
abs(gdot_slip(j))*BoltzmannRatio*prm%p(f)&
|
||
*prm%q(f)/&
|
||
(prm%SolidSolutionStrength+prm%tau_peierlsPerSlipFamily(f))*&
|
||
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(f)-1.0_pReal)
|
||
endif
|
||
|
||
!* Plastic velocity gradient for dislocation glide
|
||
Lp = Lp + gdot_slip(j)*lattice_Sslip(:,:,1,index_myFamily+i,ph)
|
||
|
||
!* 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,ph)*&
|
||
lattice_Sslip(m,n,1,index_myFamily+i,ph)
|
||
enddo slipSystemsLoop
|
||
enddo slipFamiliesLoop
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! correct Lp and dLp_dTstar3333 for twinned and transformed fraction
|
||
!* Total twin volume fraction
|
||
sumf = sum(state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
|
||
|
||
!* Total transformed volume fraction
|
||
sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
|
||
sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
Lp = Lp * (1.0_pReal - sumf - sumftr)
|
||
dLp_dTstar3333 = dLp_dTstar3333 * (1.0_pReal - sumf - sumftr)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! Shear banding (shearband) part
|
||
if(dNeq0(prm%sbVelocity) .and. dNeq0(prm%sbResistance)) then
|
||
gdot_sb = 0.0_pReal
|
||
dgdot_dtausb = 0.0_pReal
|
||
call math_eigenValuesVectorsSym(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_tensorproduct33(sb_s,sb_m)
|
||
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,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))/prm%sbResistance)&
|
||
**prm%pShearBand
|
||
StressRatio_pminus1 = (abs(tau_sb(j))/prm%sbResistance)&
|
||
**(prm%pShearBand-1.0_pReal)
|
||
endif
|
||
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = prm%sbVelocity
|
||
|
||
!* Shear rates due to shearband
|
||
gdot_sb(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%qShearBand)*sign(1.0_pReal,tau_sb(j))
|
||
|
||
!* Derivatives of shear rates
|
||
dgdot_dtausb(j) = &
|
||
((abs(gdot_sb(j))*BoltzmannRatio*&
|
||
prm%pShearBand*prm%qShearBand)/&
|
||
prm%sbResistance)*&
|
||
StressRatio_pminus1*(1_pInt-StressRatio_p)**(prm%qShearBand-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,size(prm%Ntwin,1)
|
||
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
twinSystemsLoop: do i = 1_pInt,prm%Ntwin(f)
|
||
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,ph))
|
||
|
||
!* Stress ratios
|
||
if (tau_twin(j) > tol_math_check) then
|
||
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/tau_twin(j))**prm%r(f)
|
||
!* Shear rates and their derivatives due to twin
|
||
select case(lattice_structure(ph))
|
||
case (LATTICE_fcc_ID)
|
||
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
||
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
||
if (tau_twin(j) < tau_r_twin(j,instance)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(ph)%rhoEdgeDip(s2,of))+& !!!!! correct?
|
||
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin*prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(tau_r_twin(j,instance)-tau_twin(j))))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
case default
|
||
Ndot0_twin=prm%Ndot0_twin(j)
|
||
end select
|
||
gdot_twin(j) = &
|
||
(1.0_pReal-sumf-sumftr)*lattice_shearTwin(index_myFamily+i,ph)*&
|
||
state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
|
||
dgdot_dtautwin(j) = ((gdot_twin(j)*prm%r(j))/tau_twin(j))*StressRatio_r
|
||
endif
|
||
|
||
!* Plastic velocity gradient for mechanical twinning
|
||
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,ph)
|
||
!* 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,ph)*&
|
||
lattice_Stwin(m,n,index_myFamily+i,ph)
|
||
enddo twinSystemsLoop
|
||
enddo twinFamiliesLoop
|
||
|
||
!* Phase transformation part
|
||
gdot_trans = 0.0_pReal
|
||
dgdot_dtautrans = 0.0_pReal
|
||
j = 0_pInt
|
||
transFamiliesLoop: do f = 1_pInt,size(prm%Ntrans,1)
|
||
index_myFamily = sum(lattice_NtransSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
transSystemsLoop: do i = 1_pInt,prm%Ntrans(f)
|
||
j = j+1_pInt
|
||
|
||
!* Resolved shear stress on transformation system
|
||
tau_trans(j) = dot_product(Tstar_v,lattice_Strans_v(:,index_myFamily+i,ph))
|
||
|
||
!* Stress ratios
|
||
if (tau_trans(j) > tol_math_check) then
|
||
StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/tau_trans(j))**prm%s(f)
|
||
!* Shear rates and their derivatives due to transformation
|
||
select case(lattice_structure(ph))
|
||
case (LATTICE_fcc_ID)
|
||
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
||
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
||
if (tau_trans(j) < tau_r_trans(j,instance)) then
|
||
Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+& !!!!! correct?
|
||
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_trans*prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(tau_r_trans(j,instance)-tau_trans(j))))
|
||
else
|
||
Ndot0_trans=0.0_pReal
|
||
end if
|
||
case default
|
||
Ndot0_trans=prm%Ndot0_trans(j)
|
||
end select
|
||
gdot_trans(j) = &
|
||
(1.0_pReal-sumf-sumftr)*&
|
||
state(instance)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
|
||
dgdot_dtautrans(j) = ((gdot_trans(j)*prm%s(f))/tau_trans(j))*StressRatio_s
|
||
endif
|
||
|
||
!* Plastic velocity gradient for phase transformation
|
||
Lp = Lp + gdot_trans(j)*lattice_Strans(:,:,index_myFamily+i,ph)
|
||
|
||
!* 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_dtautrans(j)*&
|
||
lattice_Strans(k,l,index_myFamily+i,ph)*&
|
||
lattice_Strans(m,n,index_myFamily+i,ph)
|
||
|
||
enddo transSystemsLoop
|
||
enddo transFamiliesLoop
|
||
end associate
|
||
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
|
||
|
||
end subroutine plastic_dislotwin_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
pi
|
||
use material, only: &
|
||
material_phase, &
|
||
phase_plasticityInstance, &
|
||
plasticState, &
|
||
phaseAt, phasememberAt
|
||
use lattice, only: &
|
||
lattice_Sslip_v, &
|
||
lattice_Stwin_v, &
|
||
lattice_Strans_v, &
|
||
lattice_maxNslipFamily, &
|
||
lattice_maxNtwinFamily, &
|
||
lattice_maxNtransFamily, &
|
||
lattice_NslipSystem, &
|
||
lattice_NtwinSystem, &
|
||
lattice_NtransSystem, &
|
||
lattice_sheartwin, &
|
||
lattice_mu, &
|
||
lattice_structure, &
|
||
lattice_fcc_twinNucleationSlipPair, &
|
||
lattice_fccTobcc_transNucleationTwinPair, &
|
||
lattice_fccTobcc_shearCritTrans, &
|
||
LATTICE_fcc_ID
|
||
|
||
implicit none
|
||
real(pReal), dimension(6), intent(in):: &
|
||
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
||
real(pReal), intent(in) :: &
|
||
temperature !< temperature at integration point
|
||
integer(pInt), intent(in) :: &
|
||
ipc, & !< component-ID of integration point
|
||
ip, & !< integration point
|
||
el !< element
|
||
|
||
integer(pInt) :: instance,f,i,j,index_myFamily,s1,s2, &
|
||
ph, &
|
||
of
|
||
real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
|
||
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,&
|
||
Ndot0_trans,StressRatio_s,EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, &
|
||
DotRhoDipFormation,DotRhoMultiplication,DotRhoEdgeEdgeAnnihilation
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
|
||
gdot_slip,tau_slip
|
||
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: &
|
||
tau_twin
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntrans) :: &
|
||
tau_trans
|
||
|
||
type(tParameters) :: prm
|
||
|
||
!* Shortened notation
|
||
of = phasememberAt(ipc,ip,el)
|
||
ph = phaseAt(ipc,ip,el)
|
||
instance = phase_plasticityInstance(ph)
|
||
|
||
associate(prm => param(instance))
|
||
!* Total twin volume fraction
|
||
sumf = sum(state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
|
||
plasticState(ph)%dotState(:,of) = 0.0_pReal
|
||
|
||
!* Total transformed volume fraction
|
||
sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
|
||
sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of))
|
||
|
||
!* Dislocation density evolution
|
||
gdot_slip = 0.0_pReal
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1)
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! process each (active) slip system in family
|
||
j = j+1_pInt
|
||
|
||
!* Resolved shear stress on slip system
|
||
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
|
||
|
||
if((abs(tau_slip(j))-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
!* Stress ratios
|
||
stressRatio =((abs(tau_slip(j))- state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+prm%tau_peierlsPerSlipFamily(f)))
|
||
StressRatio_p = stressRatio** prm%p(f)
|
||
StressRatio_pminus1 = stressRatio**(prm%p(f)-1.0_pReal)
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = plasticState(ph)%state(j, of)*prm%burgers_slip(j)*prm%v0(j)
|
||
|
||
!* Shear rates due to slip
|
||
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)** &
|
||
prm%q(f))*sign(1.0_pReal,tau_slip(j))
|
||
endif
|
||
!* Multiplication
|
||
DotRhoMultiplication = abs(gdot_slip(j))/(prm%burgers_slip(j)*state(instance)%mfp_slip(j,of))
|
||
|
||
!* Dipole formation
|
||
EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip(j)
|
||
if (dEq0(tau_slip(j))) then
|
||
DotRhoDipFormation = 0.0_pReal
|
||
else
|
||
EdgeDipDistance = &
|
||
(3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j))/&
|
||
(16.0_pReal*pi*abs(tau_slip(j)))
|
||
if (EdgeDipDistance>state(instance)%mfp_slip(j,of)) EdgeDipDistance=state(instance)%mfp_slip(j,of)
|
||
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
|
||
DotRhoDipFormation = &
|
||
((2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance))/prm%burgers_slip(j))*&
|
||
state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))*prm%dipoleFormationFactor
|
||
endif
|
||
|
||
!* Spontaneous annihilation of 2 single edge dislocations
|
||
DotRhoEdgeEdgeAnnihilation = &
|
||
((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j))*&
|
||
state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))
|
||
|
||
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
|
||
DotRhoEdgeDipAnnihilation = &
|
||
((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j))*&
|
||
state(instance)%rhoEdgeDip(j,of)*abs(gdot_slip(j))
|
||
|
||
!* Dislocation dipole climb
|
||
AtomicVolume = &
|
||
prm%CAtomicVolume*prm%burgers_slip(j)**(3.0_pReal)
|
||
VacancyDiffusion = &
|
||
prm%D0*exp(-prm%Qsd/(kB*Temperature))
|
||
if (dEq0(tau_slip(j))) then
|
||
DotRhoEdgeDipClimb = 0.0_pReal
|
||
else
|
||
if (dEq0(EdgeDipDistance-EdgeDipMinDistance)) then
|
||
DotRhoEdgeDipClimb = 0.0_pReal
|
||
else
|
||
ClimbVelocity = 3.0_pReal*lattice_mu(ph)*VacancyDiffusion*AtomicVolume/ &
|
||
(2.0_pReal*pi*kB*Temperature*(EdgeDipDistance+EdgeDipMinDistance))
|
||
DotRhoEdgeDipClimb = 4.0_pReal*ClimbVelocity*state(instance)%rhoEdgeDip(j,of)/ &
|
||
(EdgeDipDistance-EdgeDipMinDistance)
|
||
endif
|
||
endif
|
||
!* Edge dislocation density rate of change
|
||
dotState(instance)%rhoEdge(j,of) = DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
|
||
|
||
!* Edge dislocation dipole density rate of change
|
||
dotState(instance)%rhoEdgeDip(j,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
|
||
|
||
!* Dotstate for accumulated shear due to slip
|
||
dotState(instance)%accshear_slip(j,of) = abs(gdot_slip(j))
|
||
|
||
enddo
|
||
enddo
|
||
|
||
!* Twin volume fraction evolution
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Ntwin,1)
|
||
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Ntwin(f) ! process each (active) twin system in family
|
||
j = j+1_pInt
|
||
|
||
!* Resolved shear stress on twin system
|
||
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
|
||
!* Stress ratios
|
||
if (tau_twin(j) > tol_math_check) then
|
||
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/&
|
||
tau_twin(j))**prm%r(j)
|
||
!* Shear rates and their derivatives due to twin
|
||
select case(lattice_structure(ph))
|
||
case (LATTICE_fcc_ID)
|
||
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
||
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
||
if (tau_twin(j) < tau_r_twin(j,instance)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin*prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(tau_r_twin(j,instance)-tau_twin(j))))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
case default
|
||
Ndot0_twin=prm%Ndot0_twin(j)
|
||
end select
|
||
dotState(instance)%twinFraction(j,of) = &
|
||
(1.0_pReal-sumf-sumftr)*&
|
||
state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
|
||
!* Dotstate for accumulated shear due to twin
|
||
dotState(instance)%accshear_twin(j,of) = dotState(instance)%twinFraction(j,of) * &
|
||
lattice_sheartwin(index_myfamily+i,ph)
|
||
endif
|
||
enddo
|
||
enddo
|
||
|
||
!* Transformation volume fraction evolution
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Ntrans,1)
|
||
index_myFamily = sum(lattice_NtransSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Ntrans(f) ! process each (active) trans system in family
|
||
j = j+1_pInt
|
||
|
||
!* Resolved shear stress on transformation system
|
||
tau_trans(j) = dot_product(Tstar_v,lattice_Strans_v(:,index_myFamily+i,ph))
|
||
|
||
!* Stress ratios
|
||
if (tau_trans(j) > tol_math_check) then
|
||
StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/&
|
||
tau_trans(j))**prm%s(f)
|
||
!* Shear rates and their derivatives due to transformation
|
||
select case(lattice_structure(ph))
|
||
case (LATTICE_fcc_ID)
|
||
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
||
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
||
if (tau_trans(j) < tau_r_trans(j,instance)) then
|
||
Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_trans*prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(tau_r_trans(j,instance)-tau_trans(j))))
|
||
else
|
||
Ndot0_trans=0.0_pReal
|
||
end if
|
||
case default
|
||
Ndot0_trans=prm%Ndot0_trans(j)
|
||
end select
|
||
dotState(instance)%strainTransFraction(j,of) = &
|
||
(1.0_pReal-sumf-sumftr)*&
|
||
state(instance)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
|
||
!* Dotstate for accumulated shear due to transformation
|
||
!dotState(instance)%accshear_trans(j,of) = dotState(instance)%strainTransFraction(j,of) * &
|
||
! lattice_sheartrans(index_myfamily+i,ph)
|
||
endif
|
||
|
||
enddo
|
||
enddo
|
||
end associate
|
||
end subroutine plastic_dislotwin_dotState
|
||
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief return array of constitutive results
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
pi, &
|
||
math_Mandel6to33, &
|
||
math_eigenValuesSym33, &
|
||
math_eigenValuesVectorsSym33
|
||
use material, only: &
|
||
material_phase, &
|
||
plasticState, &
|
||
phase_plasticityInstance,&
|
||
phaseAt, phasememberAt
|
||
use lattice, only: &
|
||
lattice_Sslip_v, &
|
||
lattice_Stwin_v, &
|
||
lattice_NslipSystem, &
|
||
lattice_NtwinSystem, &
|
||
lattice_shearTwin, &
|
||
lattice_mu, &
|
||
lattice_structure, &
|
||
lattice_fcc_twinNucleationSlipPair, &
|
||
LATTICE_fcc_ID
|
||
|
||
implicit none
|
||
real(pReal), dimension(6), intent(in) :: &
|
||
Tstar_v !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
||
real(pReal), intent(in) :: &
|
||
temperature !< temperature at integration point
|
||
integer(pInt), intent(in) :: &
|
||
ipc, & !< component-ID of integration point
|
||
ip, & !< integration point
|
||
el !< element
|
||
|
||
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%sizePostResults) :: &
|
||
plastic_dislotwin_postResults
|
||
integer(pInt) :: &
|
||
instance,&
|
||
f,o,i,c,j,index_myFamily,&
|
||
s1,s2, &
|
||
ph, &
|
||
of
|
||
real(pReal) :: sumf,tau,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,StressRatio_r,Ndot0_twin,dgdot_dtauslip, &
|
||
stressRatio
|
||
real(preal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
|
||
gdot_slip
|
||
real(pReal), dimension(3,3) :: eigVectors
|
||
real(pReal), dimension (3) :: eigValues
|
||
|
||
type(tParameters) :: prm
|
||
|
||
!* Shortened notation
|
||
of = phasememberAt(ipc,ip,el)
|
||
ph = phaseAt(ipc,ip,el)
|
||
instance = phase_plasticityInstance(ph)
|
||
|
||
|
||
associate(prm => param(instance))
|
||
!* Total twin volume fraction
|
||
sumf = sum(state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
|
||
|
||
!* Required output
|
||
c = 0_pInt
|
||
plastic_dislotwin_postResults = 0.0_pReal
|
||
do o = 1_pInt,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
|
||
case (edge_density_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNslip) = state(instance)%rhoEdge(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (dipole_density_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNslip) = state(instance)%rhoEdgeDip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (shear_rate_slip_ID)
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1) ! loop over all slip families
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! process each (active) slip system in family
|
||
j = j + 1_pInt ! could be taken from state by now!
|
||
|
||
!* Resolved shear stress on slip system
|
||
tau = dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
|
||
!* Stress ratios
|
||
if((abs(tau)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
!* Stress ratios
|
||
stressRatio = ((abs(tau)-state(ph)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f)))
|
||
StressRatio_p = stressRatio** prm%p(f)
|
||
StressRatio_pminus1 = stressRatio**(prm%p(f)-1.0_pReal)
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = &
|
||
state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* &
|
||
prm%v0(j)
|
||
|
||
!* Shear rates due to slip
|
||
plastic_dislotwin_postResults(c+j) = &
|
||
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%q(f))*sign(1.0_pReal,tau)
|
||
else
|
||
plastic_dislotwin_postResults(c+j) = 0.0_pReal
|
||
endif
|
||
|
||
enddo ; enddo
|
||
c = c + prm%totalNslip
|
||
case (accumulated_shear_slip_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNslip) = &
|
||
state(instance)%accshear_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (mfp_slip_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNslip) =&
|
||
state(instance)%mfp_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (resolved_stress_slip_ID)
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1) ! loop over all slip families
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! process each (active) slip system in family
|
||
j = j + 1_pInt
|
||
plastic_dislotwin_postResults(c+j) =&
|
||
dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))
|
||
enddo; enddo
|
||
c = c + prm%totalNslip
|
||
case (threshold_stress_slip_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNslip) = &
|
||
state(instance)%threshold_stress_slip(1_pInt:prm%totalNslip,of)
|
||
c = c + prm%totalNslip
|
||
case (edge_dipole_distance_ID)
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1) ! loop over all slip families
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! process each (active) slip system in family
|
||
j = j + 1_pInt
|
||
plastic_dislotwin_postResults(c+j) = &
|
||
(3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j))/&
|
||
(16.0_pReal*pi*abs(dot_product(Tstar_v,lattice_Sslip_v(:,1,index_myFamily+i,ph))))
|
||
plastic_dislotwin_postResults(c+j)=min(plastic_dislotwin_postResults(c+j),&
|
||
state(instance)%mfp_slip(j,of))
|
||
! plastic_dislotwin_postResults(c+j)=max(plastic_dislotwin_postResults(c+j),&
|
||
! plasticState(ph)%state(4*ns+2*nt+2*nr+j, of))
|
||
enddo; enddo
|
||
c = c + prm%totalNslip
|
||
case (resolved_stress_shearband_ID)
|
||
do j = 1_pInt,6_pInt ! loop over all shearband families
|
||
plastic_dislotwin_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
|
||
!* Resolved shear stress on shearband system
|
||
tau = dot_product(Tstar_v,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)/prm%sbResistance)**&
|
||
prm%pShearBand
|
||
StressRatio_pminus1 = (abs(tau)/prm%sbResistance)**&
|
||
(prm%pShearBand-1.0_pReal)
|
||
endif
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%sbQedge/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = prm%sbVelocity
|
||
! Shear rate due to shear band
|
||
plastic_dislotwin_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)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtwin) = state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (shear_rate_twin_ID)
|
||
if (prm%totalNtwin > 0_pInt) then
|
||
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1)
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! 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,ph))
|
||
!* Stress ratios
|
||
if((abs(tau)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
!* Stress ratios
|
||
StressRatio_p = ((abs(tau)-state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f)))&
|
||
**prm%p(f)
|
||
StressRatio_pminus1 = ((abs(tau)-state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f)))&
|
||
**(prm%p(f)-1.0_pReal)
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = &
|
||
state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* &
|
||
prm%v0(j)
|
||
|
||
!* Shear rates due to slip
|
||
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%q(f))*sign(1.0_pReal,tau)
|
||
else
|
||
gdot_slip(j) = 0.0_pReal
|
||
endif
|
||
enddo;enddo
|
||
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Ntwin,1)
|
||
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1,prm%Ntwin(f) ! process each (active) twin system in family
|
||
j = j + 1_pInt
|
||
|
||
tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
|
||
|
||
|
||
!* Shear rates due to twin
|
||
if ( tau > 0.0_pReal ) then
|
||
select case(lattice_structure(ph))
|
||
case (LATTICE_fcc_ID)
|
||
s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
|
||
s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
|
||
if (tau < tau_r_twin(j,instance)) then
|
||
Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+&
|
||
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
|
||
(prm%L0_twin*&
|
||
prm%burgers_slip(j))*&
|
||
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
|
||
(tau_r_twin(j,instance)-tau)))
|
||
else
|
||
Ndot0_twin=0.0_pReal
|
||
end if
|
||
case default
|
||
Ndot0_twin=prm%Ndot0_twin(j)
|
||
end select
|
||
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/tau) &
|
||
**prm%r(j)
|
||
plastic_dislotwin_postResults(c+j) = &
|
||
(prm%MaxTwinFraction-sumf)*lattice_shearTwin(index_myFamily+i,ph)*&
|
||
state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
|
||
endif
|
||
|
||
enddo ; enddo
|
||
endif
|
||
c = c + prm%totalNtwin
|
||
case (accumulated_shear_twin_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtwin) = state(instance)%accshear_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (mfp_twin_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtwin) = state(instance)%mfp_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (resolved_stress_twin_ID)
|
||
if (prm%totalNtwin > 0_pInt) then
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Ntwin,1)
|
||
index_myFamily = sum(lattice_NtwinSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Ntwin(f) ! process each (active) slip system in family
|
||
j = j + 1_pInt
|
||
plastic_dislotwin_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,ph))
|
||
enddo; enddo
|
||
endif
|
||
c = c + prm%totalNtwin
|
||
case (threshold_stress_twin_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtwin) = state(instance)%threshold_stress_twin(1_pInt:prm%totalNtwin,of)
|
||
c = c + prm%totalNtwin
|
||
case (stress_exponent_ID)
|
||
j = 0_pInt
|
||
do f = 1_pInt,size(prm%Nslip,1)
|
||
index_myFamily = sum(lattice_NslipSystem(1:f-1_pInt,ph)) ! at which index starts my family
|
||
do i = 1_pInt,prm%Nslip(f) ! 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,ph))
|
||
if((abs(tau)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
|
||
!* Stress ratios
|
||
StressRatio_p = ((abs(tau)-state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f)))&
|
||
**prm%p(f)
|
||
StressRatio_pminus1 = ((abs(tau)-state(instance)%threshold_stress_slip(j,of))/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f)))&
|
||
**(prm%p(f)-1.0_pReal)
|
||
!* Boltzmann ratio
|
||
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
|
||
!* Initial shear rates
|
||
DotGamma0 = &
|
||
state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* &
|
||
prm%v0(j)
|
||
|
||
!* Shear rates due to slip
|
||
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
|
||
prm%q(f))*sign(1.0_pReal,tau)
|
||
|
||
!* Derivatives of shear rates
|
||
dgdot_dtauslip = &
|
||
abs(gdot_slip(j))*BoltzmannRatio*prm%p(f)&
|
||
*prm%q(f)/&
|
||
(prm%SolidSolutionStrength+&
|
||
prm%tau_peierlsPerSlipFamily(f))*&
|
||
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(f)-1.0_pReal)
|
||
|
||
else
|
||
gdot_slip(j) = 0.0_pReal
|
||
dgdot_dtauslip = 0.0_pReal
|
||
endif
|
||
|
||
!* Stress exponent
|
||
plastic_dislotwin_postResults(c+j) = &
|
||
merge(0.0_pReal,(tau/gdot_slip(j))*dgdot_dtauslip,dEq0(gdot_slip(j)))
|
||
enddo ; enddo
|
||
c = c + prm%totalNslip
|
||
case (sb_eigenvalues_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+3_pInt) = math_eigenvaluesSym33(math_Mandel6to33(Tstar_v))
|
||
c = c + 3_pInt
|
||
case (sb_eigenvectors_ID)
|
||
call math_eigenValuesVectorsSym33(math_Mandel6to33(Tstar_v),eigValues,eigVectors)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+9_pInt) = reshape(eigVectors,[9])
|
||
c = c + 9_pInt
|
||
case (stress_trans_fraction_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtrans) = &
|
||
state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)
|
||
c = c + prm%totalNtrans
|
||
case (strain_trans_fraction_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtrans) = &
|
||
state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of)
|
||
c = c + prm%totalNtrans
|
||
case (trans_fraction_ID)
|
||
plastic_dislotwin_postResults(c+1_pInt:c+prm%totalNtrans) = &
|
||
state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of) + &
|
||
state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of)
|
||
c = c + prm%totalNtrans
|
||
end select
|
||
enddo
|
||
end associate
|
||
end function plastic_dislotwin_postResults
|
||
|
||
end module plastic_dislotwin
|