1330 lines
59 KiB
Fortran
1330 lines
59 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Su Leen Wong, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Nan Jia, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Franz Roters, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief material subroutine incoprorating dislocation and twinning physics
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!> @details to be done
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!--------------------------------------------------------------------------------------------------
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module plastic_dislotwin
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use prec, only: &
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pReal
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implicit none
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private
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integer, dimension(:,:), allocatable, target, public :: &
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plastic_dislotwin_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_dislotwin_output !< name of each post result output
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real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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enum, bind(c)
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enumerator :: &
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undefined_ID, &
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rho_mob_ID, &
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rho_dip_ID, &
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dot_gamma_sl_ID, &
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gamma_sl_ID, &
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Lambda_sl_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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f_tw_ID, &
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Lambda_tw_ID, &
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resolved_stress_twin_ID, &
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tau_hat_tw_ID, &
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f_tr_ID
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end enum
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type, private :: tParameters
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real(pReal) :: &
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mu, &
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nu, &
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D0, & !< prefactor for self-diffusion coefficient
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Qsd, & !< activation energy for dislocation climb
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D, & !<grain size
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p_sb, & !< p-exponent in shear band velocity
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q_sb, & !< q-exponent in shear band velocity
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CEdgeDipMinDistance, & !<
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i_tw, & !<
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tau_0, & !<strength due to elements in solid solution
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L_tw, & !< Length of twin nuclei in Burgers vectors
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L_tr, & !< 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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V_cs, & !< 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, & !< activation energy for shear bands
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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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aTol_rho, & !< absolute tolerance for integration of dislocation density
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aTol_f_tw, & !< absolute tolerance for integration of twin volume fraction
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aTol_f_tr, & !< absolute tolerance for integration of trans volume fraction
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gamma_fcc_hex, & !< Free energy difference between austensite and martensite
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i_tr, & !<
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h !< Stack height of hex nucleus
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real(pReal), dimension(:), allocatable :: &
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rho_mob_0, & !< initial unipolar dislocation density per slip system
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rho_dip_0, & !< initial dipole dislocation density per slip system
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b_sl, & !< absolute length of burgers vector [m] for each slip system
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b_tw, & !< absolute length of burgers vector [m] for each twin system
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b_tr, & !< absolute length of burgers vector [m] for each transformation system
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Delta_F,& !< activation energy for glide [J] for each slip system
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v0, & !< dislocation velocity prefactor [m/s] for each slip system
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dot_N_0_tw, & !< twin nucleation rate [1/m³s] for each twin system
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dot_N_0_tr, & !< trans nucleation rate [1/m³s] for each trans system
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t_tw, & !< twin thickness [m] for each twin system
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CLambdaSlip, & !< Adj. parameter for distance between 2 forest dislocations for each slip system
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atomicVolume, &
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t_tr, & !< 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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gamma_char, & !< characteristic shear for twins
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B !< drag coefficient
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real(pReal), dimension(:,:), allocatable :: &
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h_sl_sl, & !<
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h_sl_tw, & !<
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h_tw_tw, & !<
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h_sl_tr, & !<
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h_tr_tr !<
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integer, dimension(:,:), allocatable :: &
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fcc_twinNucleationSlipPair ! ToDo: Better name? Is also use for trans
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real(pReal), dimension(:,:), allocatable :: &
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forestProjection, &
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C66
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real(pReal), dimension(:,:,:), allocatable :: &
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P_tr, &
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P_sl, &
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P_tw, &
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C66_tw, &
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C66_tr
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integer :: &
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sum_N_sl, & !< total number of active slip system
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sum_N_tw, & !< total number of active twin system
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sum_N_tr !< total number of active transformation system
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integer, dimension(:), allocatable :: &
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N_sl, & !< number of active slip systems for each family
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N_tw, & !< number of active twin systems for each family
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N_tr !< number of active transformation systems for each family
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integer(kind(undefined_ID)), dimension(:), allocatable :: &
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outputID !< ID of each post result output
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logical :: &
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fccTwinTransNucleation, & !< twinning and transformation models are for fcc
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dipoleFormation !< flag indicating consideration of dipole formation
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end type !< container type for internal constitutive parameters
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type, private :: tDislotwinState
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real(pReal), dimension(:,:), pointer :: &
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rho_mob, &
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rho_dip, &
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gamma_sl, &
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f_tw, &
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f_tr
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end type tDislotwinState
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type, private :: tDislotwinMicrostructure
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real(pReal), dimension(:,:), allocatable :: &
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Lambda_sl, & !* mean free path between 2 obstacles seen by a moving dislocation
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Lambda_tw, & !* mean free path between 2 obstacles seen by a growing twin
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Lambda_tr, &!* mean free path between 2 obstacles seen by a growing martensite
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tau_pass, &
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tau_hat_tw, &
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tau_hat_tr, &
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f_tw, &
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f_tr, &
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tau_r_tw, & !< stress to bring partials close together (twin)
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tau_r_tr !< stress to bring partials close together (trans)
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end type tDislotwinMicrostructure
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!--------------------------------------------------------------------------------------------------
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! containers for parameters and state
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type(tParameters), allocatable, dimension(:), private :: param
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type(tDislotwinState), allocatable, dimension(:), private :: &
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dotState, &
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state
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type(tDislotwinMicrostructure), allocatable, dimension(:), private :: dependentState
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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_dependentState, &
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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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plastic_dislotwin_results
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private :: &
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kinetics_slip, &
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kinetics_twin, &
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kinetics_trans
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief module initialization
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!> @details reads in material parameters, allocates arrays, and does sanity checks
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!--------------------------------------------------------------------------------------------------
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subroutine plastic_dislotwin_init
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use prec, only: &
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pStringLen, &
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dEq0, &
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dNeq0, &
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dNeq
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use debug, only: &
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debug_level,&
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debug_constitutive,&
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debug_levelBasic
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use math, only: &
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math_expand,&
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PI
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use IO, only: &
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IO_error
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use material
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use config, only: &
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config_phase
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use lattice
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integer :: &
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Ninstance, &
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p, i, &
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NipcMyPhase, outputSize, &
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sizeState, sizeDotState, &
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startIndex, endIndex
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integer, dimension(0), parameter :: emptyIntArray = [integer::]
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real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
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character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
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integer(kind(undefined_ID)) :: &
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outputID
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character(len=pStringLen) :: &
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extmsg = ''
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character(len=65536), dimension(:), allocatable :: &
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outputs
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOTWIN_label//' init -+>>>'
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write(6,'(/,a)') ' Ma and 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)') ' 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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Ninstance = count(phase_plasticity == PLASTICITY_DISLOTWIN_ID)
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0) &
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write(6,'(a16,1x,i5,/)') '# instances:',Ninstance
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allocate(plastic_dislotwin_sizePostResult(maxval(phase_Noutput),Ninstance),source=0)
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allocate(plastic_dislotwin_output(maxval(phase_Noutput),Ninstance))
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plastic_dislotwin_output = ''
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allocate(param(Ninstance))
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allocate(state(Ninstance))
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allocate(dotState(Ninstance))
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allocate(dependentState(Ninstance))
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do p = 1, size(phase_plasticity)
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if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
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associate(prm => param(phase_plasticityInstance(p)), &
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dot => dotState(phase_plasticityInstance(p)), &
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stt => state(phase_plasticityInstance(p)), &
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dst => dependentState(phase_plasticityInstance(p)), &
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config => config_phase(p))
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prm%aTol_rho = config%getFloat('atol_rho', defaultVal=0.0_pReal)
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prm%aTol_f_tw = config%getFloat('atol_twinfrac', defaultVal=0.0_pReal)
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prm%aTol_f_tr = config%getFloat('atol_transfrac', defaultVal=0.0_pReal)
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! This data is read in already in lattice
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prm%mu = lattice_mu(p)
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prm%nu = lattice_nu(p)
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prm%C66 = lattice_C66(1:6,1:6,p)
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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prm%N_sl = config%getInts('nslip',defaultVal=emptyIntArray)
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prm%sum_N_sl = sum(prm%N_sl)
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slipActive: if (prm%sum_N_sl > 0) then
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prm%P_sl = lattice_SchmidMatrix_slip(prm%N_sl,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%h_sl_sl = lattice_interaction_SlipBySlip(prm%N_sl, &
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config%getFloats('interaction_slipslip'), &
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config%getString('lattice_structure'))
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prm%forestProjection = lattice_forestProjection (prm%N_sl,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%fccTwinTransNucleation = merge(.true., .false., lattice_structure(p) == LATTICE_FCC_ID) &
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.and. (prm%N_sl(1) == 12)
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if(prm%fccTwinTransNucleation) &
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prm%fcc_twinNucleationSlipPair = lattice_fcc_twinNucleationSlipPair
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prm%rho_mob_0 = config%getFloats('rhoedge0', requiredSize=size(prm%N_sl))
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prm%rho_dip_0 = config%getFloats('rhoedgedip0',requiredSize=size(prm%N_sl))
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prm%v0 = config%getFloats('v0', requiredSize=size(prm%N_sl))
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prm%b_sl = config%getFloats('slipburgers',requiredSize=size(prm%N_sl))
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prm%Delta_F = config%getFloats('qedge', requiredSize=size(prm%N_sl))
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prm%CLambdaSlip = config%getFloats('clambdaslip',requiredSize=size(prm%N_sl))
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prm%p = config%getFloats('p_slip', requiredSize=size(prm%N_sl))
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prm%q = config%getFloats('q_slip', requiredSize=size(prm%N_sl))
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prm%B = config%getFloats('b', requiredSize=size(prm%N_sl), &
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defaultVal=[(0.0_pReal, i=1,size(prm%N_sl))])
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prm%tau_0 = config%getFloat('solidsolutionstrength')
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prm%CEdgeDipMinDistance = config%getFloat('cedgedipmindistance')
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prm%D0 = config%getFloat('d0')
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prm%Qsd = config%getFloat('qsd')
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prm%atomicVolume = config%getFloat('catomicvolume') * prm%b_sl**3.0_pReal
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! expand: family => system
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prm%rho_mob_0 = math_expand(prm%rho_mob_0, prm%N_sl)
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prm%rho_dip_0 = math_expand(prm%rho_dip_0, prm%N_sl)
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prm%v0 = math_expand(prm%v0, prm%N_sl)
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prm%b_sl = math_expand(prm%b_sl,prm%N_sl)
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prm%Delta_F = math_expand(prm%Delta_F, prm%N_sl)
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prm%CLambdaSlip = math_expand(prm%CLambdaSlip, prm%N_sl)
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prm%p = math_expand(prm%p, prm%N_sl)
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prm%q = math_expand(prm%q, prm%N_sl)
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prm%B = math_expand(prm%B, prm%N_sl)
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prm%atomicVolume = math_expand(prm%atomicVolume,prm%N_sl)
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! sanity checks
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if ( prm%D0 <= 0.0_pReal) extmsg = trim(extmsg)//' D0'
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if ( prm%Qsd <= 0.0_pReal) extmsg = trim(extmsg)//' Qsd'
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if (any(prm%rho_mob_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_mob_0'
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if (any(prm%rho_dip_0 < 0.0_pReal)) extmsg = trim(extmsg)//' rho_dip_0'
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if (any(prm%v0 < 0.0_pReal)) extmsg = trim(extmsg)//' v0'
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if (any(prm%b_sl <= 0.0_pReal)) extmsg = trim(extmsg)//' b_sl'
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if (any(prm%Delta_F <= 0.0_pReal)) extmsg = trim(extmsg)//' Delta_F'
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if (any(prm%CLambdaSlip <= 0.0_pReal)) extmsg = trim(extmsg)//' CLambdaSlip'
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if (any(prm%B < 0.0_pReal)) extmsg = trim(extmsg)//' B'
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if (any(prm%p<=0.0_pReal .or. prm%p>1.0_pReal)) extmsg = trim(extmsg)//' p'
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if (any(prm%q< 1.0_pReal .or. prm%q>2.0_pReal)) extmsg = trim(extmsg)//' q'
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else slipActive
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allocate(prm%b_sl(0))
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endif slipActive
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!--------------------------------------------------------------------------------------------------
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! twin related parameters
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prm%N_tw = config%getInts('ntwin', defaultVal=emptyIntArray)
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prm%sum_N_tw = sum(prm%N_tw)
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if (prm%sum_N_tw > 0) then
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prm%P_tw = lattice_SchmidMatrix_twin(prm%N_tw,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%h_tw_tw = lattice_interaction_TwinByTwin(prm%N_tw,&
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config%getFloats('interaction_twintwin'), &
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config%getString('lattice_structure'))
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prm%b_tw = config%getFloats('twinburgers', requiredSize=size(prm%N_tw))
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prm%t_tw = config%getFloats('twinsize', requiredSize=size(prm%N_tw))
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prm%r = config%getFloats('r_twin', requiredSize=size(prm%N_tw))
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prm%xc_twin = config%getFloat('xc_twin')
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prm%L_tw = config%getFloat('l0_twin')
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prm%i_tw = config%getFloat('cmfptwin')
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prm%gamma_char = lattice_characteristicShear_Twin(prm%N_tw,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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prm%C66_tw = lattice_C66_twin(prm%N_tw,prm%C66,config%getString('lattice_structure'),&
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config%getFloat('c/a',defaultVal=0.0_pReal))
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if (.not. prm%fccTwinTransNucleation) then
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prm%dot_N_0_tw = config%getFloats('ndot0_twin')
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prm%dot_N_0_tw = math_expand(prm%dot_N_0_tw,prm%N_tw)
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endif
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! expand: family => system
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prm%b_tw = math_expand(prm%b_tw,prm%N_tw)
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prm%t_tw = math_expand(prm%t_tw,prm%N_tw)
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prm%r = math_expand(prm%r,prm%N_tw)
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else
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allocate(prm%t_tw(0))
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allocate(prm%b_tw(0))
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allocate(prm%r(0))
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endif
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!--------------------------------------------------------------------------------------------------
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! transformation related parameters
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prm%N_tr = config%getInts('ntrans', defaultVal=emptyIntArray)
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prm%sum_N_tr = sum(prm%N_tr)
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if (prm%sum_N_tr > 0) then
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prm%b_tr = config%getFloats('transburgers')
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prm%b_tr = math_expand(prm%b_tr,prm%N_tr)
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prm%h = config%getFloat('transstackheight', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
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prm%i_tr = config%getFloat('cmfptrans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
|
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prm%gamma_fcc_hex = config%getFloat('deltag')
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prm%xc_trans = config%getFloat('xc_trans', defaultVal=0.0_pReal) ! ToDo: How to handle that???
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prm%L_tr = config%getFloat('l0_trans')
|
||
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prm%h_tr_tr = lattice_interaction_TransByTrans(prm%N_tr,&
|
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config%getFloats('interaction_transtrans'), &
|
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config%getString('lattice_structure'))
|
||
|
||
prm%C66_tr = lattice_C66_trans(prm%N_tr,prm%C66, &
|
||
config%getString('trans_lattice_structure'), &
|
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0.0_pReal, &
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||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
||
config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
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prm%P_tr = lattice_SchmidMatrix_trans(prm%N_tr, &
|
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config%getString('trans_lattice_structure'), &
|
||
0.0_pReal, &
|
||
config%getFloat('a_bcc', defaultVal=0.0_pReal), &
|
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config%getFloat('a_fcc', defaultVal=0.0_pReal))
|
||
|
||
if (lattice_structure(p) /= LATTICE_fcc_ID) then
|
||
prm%dot_N_0_tr = config%getFloats('ndot0_trans')
|
||
prm%dot_N_0_tr = math_expand(prm%dot_N_0_tr,prm%N_tr)
|
||
endif
|
||
prm%t_tr = config%getFloats('lamellarsize')
|
||
prm%t_tr = math_expand(prm%t_tr,prm%N_tr)
|
||
prm%s = config%getFloats('s_trans',defaultVal=[0.0_pReal])
|
||
prm%s = math_expand(prm%s,prm%N_tr)
|
||
else
|
||
allocate(prm%t_tr(0))
|
||
allocate(prm%b_tr(0))
|
||
endif
|
||
|
||
if (sum(prm%N_tw) > 0 .or. prm%sum_N_tr > 0) then
|
||
prm%SFE_0K = config%getFloat('sfe_0k')
|
||
prm%dSFE_dT = config%getFloat('dsfe_dt')
|
||
prm%V_cs = config%getFloat('vcrossslip')
|
||
endif
|
||
|
||
if (prm%sum_N_sl > 0 .and. prm%sum_N_tw > 0) then
|
||
prm%h_sl_tw = lattice_interaction_SlipByTwin(prm%N_sl,prm%N_tw,&
|
||
config%getFloats('interaction_sliptwin'), &
|
||
config%getString('lattice_structure'))
|
||
if (prm%fccTwinTransNucleation .and. prm%sum_N_tw > 12) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if N_tw is [6,6]
|
||
endif
|
||
|
||
if (prm%sum_N_sl > 0 .and. prm%sum_N_tr > 0) then
|
||
prm%h_sl_tr = lattice_interaction_SlipByTrans(prm%N_sl,prm%N_tr,&
|
||
config%getFloats('interaction_sliptrans'), &
|
||
config%getString('lattice_structure'))
|
||
if (prm%fccTwinTransNucleation .and. prm%sum_N_tr > 12) write(6,*) 'mist' ! ToDo: implement better test. The model will fail also if N_tr is [6,6]
|
||
endif
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! shearband related parameters
|
||
prm%sbVelocity = config%getFloat('shearbandvelocity',defaultVal=0.0_pReal)
|
||
if (prm%sbVelocity > 0.0_pReal) then
|
||
prm%sbResistance = config%getFloat('shearbandresistance')
|
||
prm%sbQedge = config%getFloat('qedgepersbsystem')
|
||
prm%p_sb = config%getFloat('p_shearband')
|
||
prm%q_sb = config%getFloat('q_shearband')
|
||
|
||
! sanity checks
|
||
if (prm%sbResistance < 0.0_pReal) extmsg = trim(extmsg)//' shearbandresistance'
|
||
if (prm%sbQedge < 0.0_pReal) extmsg = trim(extmsg)//' qedgepersbsystem'
|
||
if (prm%p_sb <= 0.0_pReal) extmsg = trim(extmsg)//' p_shearband'
|
||
if (prm%q_sb <= 0.0_pReal) extmsg = trim(extmsg)//' q_shearband'
|
||
endif
|
||
|
||
|
||
|
||
prm%D = config%getFloat('grainsize')
|
||
|
||
if (config%keyExists('dipoleformationfactor')) call IO_error(1,ext_msg='use /nodipoleformation/')
|
||
prm%dipoleformation = .not. config%keyExists('/nodipoleformation/')
|
||
|
||
|
||
!if (Ndot0PerTwinFamily(f,p) < 0.0_pReal) &
|
||
! call IO_error(211,el=p,ext_msg='dot_N_0_tw ('//PLASTICITY_DISLOTWIN_label//')')
|
||
|
||
if (any(prm%atomicVolume <= 0.0_pReal)) &
|
||
call IO_error(211,el=p,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%sum_N_tw > 0) then
|
||
if (prm%aTol_rho <= 0.0_pReal) &
|
||
call IO_error(211,el=p,ext_msg='aTol_rho ('//PLASTICITY_DISLOTWIN_label//')')
|
||
if (prm%aTol_f_tw <= 0.0_pReal) &
|
||
call IO_error(211,el=p,ext_msg='aTol_f_tw ('//PLASTICITY_DISLOTWIN_label//')')
|
||
endif
|
||
if (prm%sum_N_tr > 0) then
|
||
if (prm%aTol_f_tr <= 0.0_pReal) &
|
||
call IO_error(211,el=p,ext_msg='aTol_f_tr ('//PLASTICITY_DISLOTWIN_label//')')
|
||
endif
|
||
|
||
outputs = config%getStrings('(output)', defaultVal=emptyStringArray)
|
||
allocate(prm%outputID(0))
|
||
do i= 1, size(outputs)
|
||
outputID = undefined_ID
|
||
select case(outputs(i))
|
||
case ('edge_density')
|
||
outputID = merge(rho_mob_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('dipole_density')
|
||
outputID = merge(rho_dip_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('shear_rate_slip','shearrate_slip')
|
||
outputID = merge(dot_gamma_sl_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('accumulated_shear_slip')
|
||
outputID = merge(gamma_sl_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('mfp_slip')
|
||
outputID = merge(Lambda_sl_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('resolved_stress_slip')
|
||
outputID = merge(resolved_stress_slip_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
case ('threshold_stress_slip')
|
||
outputID= merge(threshold_stress_slip_ID,undefined_ID,prm%sum_N_sl > 0)
|
||
outputSize = prm%sum_N_sl
|
||
|
||
case ('twin_fraction')
|
||
outputID = merge(f_tw_ID,undefined_ID,prm%sum_N_tw >0)
|
||
outputSize = prm%sum_N_tw
|
||
case ('mfp_twin')
|
||
outputID = merge(Lambda_tw_ID,undefined_ID,prm%sum_N_tw >0)
|
||
outputSize = prm%sum_N_tw
|
||
case ('resolved_stress_twin')
|
||
outputID = merge(resolved_stress_twin_ID,undefined_ID,prm%sum_N_tw >0)
|
||
outputSize = prm%sum_N_tw
|
||
case ('threshold_stress_twin')
|
||
outputID = merge(tau_hat_tw_ID,undefined_ID,prm%sum_N_tw >0)
|
||
outputSize = prm%sum_N_tw
|
||
|
||
case ('strain_trans_fraction')
|
||
outputID = f_tr_ID
|
||
outputSize = prm%sum_N_tr
|
||
|
||
end select
|
||
|
||
if (outputID /= undefined_ID) then
|
||
plastic_dislotwin_output(i,phase_plasticityInstance(p)) = outputs(i)
|
||
plastic_dislotwin_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
|
||
prm%outputID = [prm%outputID, outputID]
|
||
endif
|
||
|
||
enddo
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! allocate state arrays
|
||
NipcMyPhase = count(material_phase == p)
|
||
sizeDotState = size(['rho_mob ','rho_dip ','gamma_sl']) * prm%sum_N_sl &
|
||
+ size(['f_tw']) * prm%sum_N_tw &
|
||
+ size(['f_tr']) * prm%sum_N_tr
|
||
sizeState = sizeDotState
|
||
|
||
call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,0, &
|
||
prm%sum_N_sl,prm%sum_N_tw,prm%sum_N_tr)
|
||
plasticState(p)%sizePostResults = sum(plastic_dislotwin_sizePostResult(:,phase_plasticityInstance(p)))
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! locally defined state aliases and initialization of state0 and aTolState
|
||
startIndex = 1
|
||
endIndex = prm%sum_N_sl
|
||
stt%rho_mob=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rho_mob= spread(prm%rho_mob_0,2,NipcMyPhase)
|
||
dot%rho_mob=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_sl
|
||
stt%rho_dip=>plasticState(p)%state(startIndex:endIndex,:)
|
||
stt%rho_dip= spread(prm%rho_dip_0,2,NipcMyPhase)
|
||
dot%rho_dip=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_rho
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_sl
|
||
stt%gamma_sl=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%gamma_sl=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = 1.0e6_pReal !ToDo: better make optional parameter
|
||
! global alias
|
||
plasticState(p)%slipRate => plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%accumulatedSlip => plasticState(p)%state(startIndex:endIndex,:)
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_tw
|
||
stt%f_tw=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%f_tw=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_f_tw
|
||
|
||
startIndex = endIndex + 1
|
||
endIndex = endIndex + prm%sum_N_tr
|
||
stt%f_tr=>plasticState(p)%state(startIndex:endIndex,:)
|
||
dot%f_tr=>plasticState(p)%dotState(startIndex:endIndex,:)
|
||
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTol_f_tr
|
||
|
||
allocate(dst%Lambda_sl (prm%sum_N_sl, NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_pass (prm%sum_N_sl, NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(dst%Lambda_tw (prm%sum_N_tw, NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_hat_tw (prm%sum_N_tw, NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_r_tw (prm%sum_N_tw, NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%f_tw (prm%sum_N_tw, NipcMyPhase),source=0.0_pReal)
|
||
|
||
allocate(dst%Lambda_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_hat_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%tau_r_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
allocate(dst%f_tr (prm%sum_N_tr,NipcMyPhase),source=0.0_pReal)
|
||
|
||
|
||
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
|
||
|
||
end associate
|
||
|
||
enddo
|
||
|
||
end subroutine plastic_dislotwin_init
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief returns the homogenized elasticity matrix
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_homogenizedC(ipc,ip,el) result(homogenizedC)
|
||
use material, only: &
|
||
material_phase, &
|
||
phase_plasticityInstance, &
|
||
phasememberAt
|
||
|
||
real(pReal), dimension(6,6) :: &
|
||
homogenizedC
|
||
integer, intent(in) :: &
|
||
ipc, & !< component-ID of integration point
|
||
ip, & !< integration point
|
||
el !< element
|
||
|
||
integer :: i, &
|
||
of
|
||
real(pReal) :: f_unrotated
|
||
|
||
of = phasememberAt(ipc,ip,el)
|
||
associate(prm => param(phase_plasticityInstance(material_phase(ipc,ip,el))),&
|
||
stt => state(phase_plasticityInstance(material_phase(ipc,ip,el))))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
homogenizedC = f_unrotated * prm%C66
|
||
do i=1,prm%sum_N_tw
|
||
homogenizedC = homogenizedC &
|
||
+ stt%f_tw(i,of)*prm%C66_tw(1:6,1:6,i)
|
||
enddo
|
||
do i=1,prm%sum_N_tr
|
||
homogenizedC = homogenizedC &
|
||
+ stt%f_tr(i,of)*prm%C66_tr(1:6,1:6,i)
|
||
enddo
|
||
|
||
end associate
|
||
|
||
end function plastic_dislotwin_homogenizedC
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates plastic velocity gradient and its tangent
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dMp,Mp,T,instance,of)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_eigenValuesVectorsSym, &
|
||
math_outer, &
|
||
math_symmetric33, &
|
||
math_mul33xx33
|
||
|
||
real(pReal), dimension(3,3), intent(out) :: Lp
|
||
real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
|
||
real(pReal), dimension(3,3), intent(in) :: Mp
|
||
integer, intent(in) :: instance,of
|
||
real(pReal), intent(in) :: T
|
||
|
||
integer :: i,k,l,m,n
|
||
real(pReal) :: f_unrotated,StressRatio_p,&
|
||
BoltzmannRatio, &
|
||
ddot_gamma_dtau, &
|
||
tau
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
dot_gamma_sl,ddot_gamma_dtau_slip
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
dot_gamma_twin,ddot_gamma_dtau_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
dot_gamma_tr,ddot_gamma_dtau_trans
|
||
real(pReal):: dot_gamma_sb
|
||
real(pReal), dimension(3,3) :: eigVectors, P_sb
|
||
real(pReal), dimension(3) :: eigValues
|
||
logical :: error
|
||
real(pReal), dimension(3,6), parameter :: &
|
||
sb_sComposition = &
|
||
reshape(real([&
|
||
1, 0, 1, &
|
||
1, 0,-1, &
|
||
1, 1, 0, &
|
||
1,-1, 0, &
|
||
0, 1, 1, &
|
||
0, 1,-1 &
|
||
],pReal),[ 3,6]), &
|
||
sb_mComposition = &
|
||
reshape(real([&
|
||
1, 0,-1, &
|
||
1, 0,+1, &
|
||
1,-1, 0, &
|
||
1, 1, 0, &
|
||
0, 1,-1, &
|
||
0, 1, 1 &
|
||
],pReal),[ 3,6])
|
||
|
||
associate(prm => param(instance), stt => state(instance))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
Lp = 0.0_pReal
|
||
dLp_dMp = 0.0_pReal
|
||
|
||
call kinetics_slip(Mp,T,instance,of,dot_gamma_sl,ddot_gamma_dtau_slip)
|
||
slipContribution: do i = 1, prm%sum_N_sl
|
||
Lp = Lp + dot_gamma_sl(i)*prm%P_sl(1:3,1:3,i)
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_slip(i) * prm%P_sl(k,l,i) * prm%P_sl(m,n,i)
|
||
enddo slipContribution
|
||
|
||
!ToDo: Why do this before shear banding?
|
||
Lp = Lp * f_unrotated
|
||
dLp_dMp = dLp_dMp * f_unrotated
|
||
|
||
shearBandingContribution: if(dNeq0(prm%sbVelocity)) then
|
||
|
||
BoltzmannRatio = prm%sbQedge/(kB*T)
|
||
call math_eigenValuesVectorsSym(Mp,eigValues,eigVectors,error)
|
||
|
||
do i = 1,6
|
||
P_sb = 0.5_pReal * math_outer(matmul(eigVectors,sb_sComposition(1:3,i)),&
|
||
matmul(eigVectors,sb_mComposition(1:3,i)))
|
||
tau = math_mul33xx33(Mp,P_sb)
|
||
|
||
significantShearBandStress: if (abs(tau) > tol_math_check) then
|
||
StressRatio_p = (abs(tau)/prm%sbResistance)**prm%p_sb
|
||
dot_gamma_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1-StressRatio_p)**prm%q_sb), tau)
|
||
ddot_gamma_dtau = abs(dot_gamma_sb)*BoltzmannRatio* prm%p_sb*prm%q_sb/ prm%sbResistance &
|
||
* (abs(tau)/prm%sbResistance)**(prm%p_sb-1.0_pReal) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%q_sb-1.0_pReal)
|
||
|
||
Lp = Lp + dot_gamma_sb * P_sb
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau * P_sb(k,l) * P_sb(m,n)
|
||
endif significantShearBandStress
|
||
enddo
|
||
|
||
endif shearBandingContribution
|
||
|
||
call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin,ddot_gamma_dtau_twin)
|
||
twinContibution: do i = 1, prm%sum_N_tw
|
||
Lp = Lp + dot_gamma_twin(i)*prm%P_tw(1:3,1:3,i) * f_unrotated
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_twin(i)* prm%P_tw(k,l,i)*prm%P_tw(m,n,i) * f_unrotated
|
||
enddo twinContibution
|
||
|
||
call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr,ddot_gamma_dtau_trans)
|
||
transContibution: do i = 1, prm%sum_N_tr
|
||
Lp = Lp + dot_gamma_tr(i)*prm%P_tr(1:3,1:3,i) * f_unrotated
|
||
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
||
+ ddot_gamma_dtau_trans(i)* prm%P_tr(k,l,i)*prm%P_tr(m,n,i) * f_unrotated
|
||
enddo transContibution
|
||
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_LpAndItsTangent
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates the rate of change of microstructure
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_dotState(Mp,T,instance,of)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
math_clip, &
|
||
math_mul33xx33, &
|
||
PI
|
||
|
||
real(pReal), dimension(3,3), intent(in):: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature at integration point
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
integer :: i
|
||
real(pReal) :: f_unrotated,&
|
||
VacancyDiffusion,&
|
||
rho_dip_distance, ClimbVelocity, &
|
||
tau
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
dot_rho_dip_formation, &
|
||
dot_rho_dip_climb, &
|
||
rho_dip_distance_min, &
|
||
dot_gamma_sl
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
dot_gamma_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
dot_gamma_tr
|
||
|
||
associate(prm => param(instance), stt => state(instance), &
|
||
dot => dotstate(instance), dst => dependentState(instance))
|
||
|
||
f_unrotated = 1.0_pReal &
|
||
- sum(stt%f_tw(1:prm%sum_N_tw,of)) &
|
||
- sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*T))
|
||
|
||
call kinetics_slip(Mp,T,instance,of,dot_gamma_sl)
|
||
dot%gamma_sl(:,of) = abs(dot_gamma_sl)
|
||
|
||
rho_dip_distance_min = prm%CEdgeDipMinDistance*prm%b_sl
|
||
|
||
slipState: do i = 1, prm%sum_N_sl
|
||
tau = math_mul33xx33(Mp,prm%P_sl(1:3,1:3,i))
|
||
|
||
significantSlipStress: if (dEq0(tau)) then
|
||
dot_rho_dip_formation(i) = 0.0_pReal
|
||
dot_rho_dip_climb(i) = 0.0_pReal
|
||
else significantSlipStress
|
||
rho_dip_distance = 3.0_pReal*prm%mu*prm%b_sl(i)/(16.0_pReal*PI*abs(tau))
|
||
rho_dip_distance = math_clip(rho_dip_distance, right = dst%Lambda_sl(i,of))
|
||
rho_dip_distance = math_clip(rho_dip_distance, left = rho_dip_distance_min(i))
|
||
|
||
if (prm%dipoleFormation) then
|
||
dot_rho_dip_formation(i) = 2.0_pReal*(rho_dip_distance-rho_dip_distance_min(i))/prm%b_sl(i) &
|
||
* stt%rho_mob(i,of)*abs(dot_gamma_sl(i))
|
||
else
|
||
dot_rho_dip_formation(i) = 0.0_pReal
|
||
endif
|
||
|
||
if (dEq0(rho_dip_distance-rho_dip_distance_min(i))) then
|
||
dot_rho_dip_climb(i) = 0.0_pReal
|
||
else
|
||
ClimbVelocity = 3.0_pReal*prm%mu*VacancyDiffusion*prm%atomicVolume(i) &
|
||
/ (2.0_pReal*PI*kB*T*(rho_dip_distance+rho_dip_distance_min(i)))
|
||
dot_rho_dip_climb(i) = 4.0_pReal*ClimbVelocity*stt%rho_dip(i,of) &
|
||
/ (rho_dip_distance-rho_dip_distance_min(i))
|
||
endif
|
||
endif significantSlipStress
|
||
enddo slipState
|
||
|
||
dot%rho_mob(:,of) = abs(dot_gamma_sl)/(prm%b_sl*dst%Lambda_sl(:,of)) &
|
||
- dot_rho_dip_formation &
|
||
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_mob(:,of)*abs(dot_gamma_sl)
|
||
|
||
dot%rho_dip(:,of) = dot_rho_dip_formation &
|
||
- 2.0_pReal*rho_dip_distance_min/prm%b_sl * stt%rho_dip(:,of)*abs(dot_gamma_sl) &
|
||
- dot_rho_dip_climb
|
||
|
||
|
||
call kinetics_twin(Mp,T,dot_gamma_sl,instance,of,dot_gamma_twin)
|
||
dot%f_tw(:,of) = f_unrotated*dot_gamma_twin/prm%gamma_char
|
||
|
||
call kinetics_trans(Mp,T,dot_gamma_sl,instance,of,dot_gamma_tr)
|
||
dot%f_tw(:,of) = f_unrotated*dot_gamma_tr
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_dotState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates derived quantities from state
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_dependentState(T,instance,of)
|
||
use math, only: &
|
||
PI
|
||
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), intent(in) :: &
|
||
T
|
||
|
||
integer :: &
|
||
i
|
||
real(pReal) :: &
|
||
sumf_twin,SFE,sumf_trans
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
inv_lambda_sl_sl, & !* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
||
inv_lambda_sl_tw, & !* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
||
inv_lambda_sl_tr !* 1/mean free distance between 2 martensite lamellar from different systems seen by a moving dislocation
|
||
real(pReal), dimension(param(instance)%sum_N_tw) :: &
|
||
inv_lambda_tw_tw !* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
||
real(pReal), dimension(param(instance)%sum_N_tr) :: &
|
||
inv_lambda_tr_tr !* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
|
||
|
||
real(pReal), dimension(:), allocatable :: &
|
||
x0, &
|
||
f_over_t_tw, &
|
||
f_over_t_tr
|
||
|
||
|
||
associate(prm => param(instance),&
|
||
stt => state(instance),&
|
||
dst => dependentState(instance))
|
||
|
||
sumf_twin = sum(stt%f_tw(1:prm%sum_N_tw,of))
|
||
sumf_trans = sum(stt%f_tr(1:prm%sum_N_tr,of))
|
||
|
||
SFE = prm%SFE_0K + prm%dSFE_dT * T
|
||
|
||
!* rescaled volume fraction for topology
|
||
f_over_t_tw = stt%f_tw(1:prm%sum_N_tw,of)/prm%t_tw !ToDo: this is per system
|
||
f_over_t_tr = sumf_trans/prm%t_tr !ToDo: But this not ...
|
||
!Todo: Physically ok, but naming could be adjusted
|
||
|
||
|
||
forall (i = 1:prm%sum_N_sl) &
|
||
inv_lambda_sl_sl(i) = &
|
||
sqrt(dot_product((stt%rho_mob(1:prm%sum_N_sl,of)+stt%rho_dip(1:prm%sum_N_sl,of)),&
|
||
prm%forestProjection(1:prm%sum_N_sl,i)))/prm%CLambdaSlip(i) ! change order and use matmul
|
||
|
||
|
||
if (prm%sum_N_tw > 0 .and. prm%sum_N_sl > 0) &
|
||
inv_lambda_sl_tw = matmul(prm%h_sl_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
|
||
|
||
|
||
|
||
!ToDo: needed? if (prm%sum_N_tw > 0) &
|
||
inv_lambda_tw_tw = matmul(prm%h_tw_tw,f_over_t_tw)/(1.0_pReal-sumf_twin)
|
||
|
||
|
||
|
||
if (prm%sum_N_tr > 0 .and. prm%sum_N_sl > 0) &
|
||
inv_lambda_sl_tr = matmul(prm%h_sl_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
|
||
|
||
|
||
!ToDo: needed? if (prm%sum_N_tr > 0) &
|
||
inv_lambda_tr_tr = matmul(prm%h_tr_tr,f_over_t_tr)/(1.0_pReal-sumf_trans)
|
||
|
||
|
||
|
||
if ((prm%sum_N_tw > 0) .or. (prm%sum_N_tr > 0)) then ! ToDo: Change order
|
||
dst%Lambda_sl(:,of) = &
|
||
prm%D/(1.0_pReal+prm%D*&
|
||
(inv_lambda_sl_sl + inv_lambda_sl_tw + inv_lambda_sl_tr))
|
||
else
|
||
dst%Lambda_sl(:,of) = prm%D &
|
||
/ (1.0_pReal+prm%D*inv_lambda_sl_sl) !!!!!! correct?
|
||
endif
|
||
|
||
|
||
dst%Lambda_tw(:,of) = prm%i_tw*prm%D/(1.0_pReal+prm%D*inv_lambda_tw_tw)
|
||
dst%Lambda_tr(:,of) = prm%i_tr*prm%D/(1.0_pReal+prm%D*inv_lambda_tr_tr)
|
||
|
||
!* threshold stress for dislocation motion
|
||
dst%tau_pass(:,of) = prm%mu*prm%b_sl* sqrt(matmul(prm%h_sl_sl,stt%rho_mob(:,of)+stt%rho_dip(:,of)))
|
||
|
||
!* threshold stress for growing twin/martensite
|
||
if(prm%sum_N_tw == prm%sum_N_sl) &
|
||
dst%tau_hat_tw(:,of) = &
|
||
(SFE/(3.0_pReal*prm%b_tw)+ 3.0_pReal*prm%b_tw*prm%mu/(prm%L_tw*prm%b_sl)) ! slip burgers here correct?
|
||
if(prm%sum_N_tr == prm%sum_N_sl) &
|
||
dst%tau_hat_tr(:,of) = &
|
||
(SFE/(3.0_pReal*prm%b_tr) + 3.0_pReal*prm%b_tr*prm%mu/&
|
||
(prm%L_tr*prm%b_sl) + prm%h*prm%gamma_fcc_hex/ (3.0_pReal*prm%b_tr) )
|
||
|
||
|
||
dst%f_tw(:,of) = (PI/4.0_pReal)*prm%t_tw*dst%Lambda_tw(:,of)**2.0_pReal
|
||
dst%f_tr(:,of) = (PI/4.0_pReal)*prm%t_tr*dst%Lambda_tr(:,of)**2.0_pReal
|
||
|
||
|
||
x0 = prm%mu*prm%b_tw**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip and is the same for twin and trans
|
||
dst%tau_r_tw(:,of) = prm%mu*prm%b_tw/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_twin)+cos(pi/3.0_pReal)/x0)
|
||
|
||
x0 = prm%mu*prm%b_tr**2.0_pReal/(SFE*8.0_pReal*PI)*(2.0_pReal+prm%nu)/(1.0_pReal-prm%nu) ! ToDo: In the paper, this is the burgers vector for slip
|
||
dst%tau_r_tr(:,of) = prm%mu*prm%b_tr/(2.0_pReal*PI)*(1.0_pReal/(x0+prm%xc_trans)+cos(pi/3.0_pReal)/x0)
|
||
|
||
end associate
|
||
|
||
end subroutine plastic_dislotwin_dependentState
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief return array of constitutive results
|
||
!--------------------------------------------------------------------------------------------------
|
||
function plastic_dislotwin_postResults(Mp,T,instance,of) result(postResults)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dEq0
|
||
use math, only: &
|
||
PI, &
|
||
math_mul33xx33
|
||
|
||
real(pReal), dimension(3,3),intent(in) :: &
|
||
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature at integration point
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(sum(plastic_dislotwin_sizePostResult(:,instance))) :: &
|
||
postResults
|
||
|
||
integer :: &
|
||
o,c,j
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
c = 0
|
||
|
||
do o = 1,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
|
||
case (rho_mob_ID)
|
||
postResults(c+1:c+prm%sum_N_sl) = stt%rho_mob(1:prm%sum_N_sl,of)
|
||
c = c + prm%sum_N_sl
|
||
case (rho_dip_ID)
|
||
postResults(c+1:c+prm%sum_N_sl) = stt%rho_dip(1:prm%sum_N_sl,of)
|
||
c = c + prm%sum_N_sl
|
||
case (dot_gamma_sl_ID)
|
||
call kinetics_slip(Mp,T,instance,of,postResults(c+1:c+prm%sum_N_sl))
|
||
c = c + prm%sum_N_sl
|
||
case (gamma_sl_ID)
|
||
postResults(c+1:c+prm%sum_N_sl) = stt%gamma_sl(1:prm%sum_N_sl,of)
|
||
c = c + prm%sum_N_sl
|
||
case (Lambda_sl_ID)
|
||
postResults(c+1:c+prm%sum_N_sl) = dst%Lambda_sl(1:prm%sum_N_sl,of)
|
||
c = c + prm%sum_N_sl
|
||
case (resolved_stress_slip_ID)
|
||
do j = 1, prm%sum_N_sl
|
||
postResults(c+j) = math_mul33xx33(Mp,prm%P_sl(1:3,1:3,j))
|
||
enddo
|
||
c = c + prm%sum_N_sl
|
||
case (threshold_stress_slip_ID)
|
||
postResults(c+1:c+prm%sum_N_sl) = dst%tau_pass(1:prm%sum_N_sl,of)
|
||
c = c + prm%sum_N_sl
|
||
|
||
case (f_tw_ID)
|
||
postResults(c+1:c+prm%sum_N_tw) = stt%f_tw(1:prm%sum_N_tw,of)
|
||
c = c + prm%sum_N_tw
|
||
case (Lambda_tw_ID)
|
||
postResults(c+1:c+prm%sum_N_tw) = dst%Lambda_tw(1:prm%sum_N_tw,of)
|
||
c = c + prm%sum_N_tw
|
||
case (resolved_stress_twin_ID)
|
||
do j = 1, prm%sum_N_tw
|
||
postResults(c+j) = math_mul33xx33(Mp,prm%P_tw(1:3,1:3,j))
|
||
enddo
|
||
c = c + prm%sum_N_tw
|
||
case (tau_hat_tw_ID)
|
||
postResults(c+1:c+prm%sum_N_tw) = dst%tau_hat_tw(1:prm%sum_N_tw,of)
|
||
c = c + prm%sum_N_tw
|
||
|
||
case (f_tr_ID)
|
||
postResults(c+1:c+prm%sum_N_tr) = stt%f_tr(1:prm%sum_N_tr,of)
|
||
c = c + prm%sum_N_tr
|
||
end select
|
||
enddo
|
||
|
||
end associate
|
||
|
||
end function plastic_dislotwin_postResults
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief writes results to HDF5 output file
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine plastic_dislotwin_results(instance,group)
|
||
#if defined(PETSc) || defined(DAMASK_HDF5)
|
||
use results, only: &
|
||
results_writeDataset
|
||
|
||
integer, intent(in) :: instance
|
||
character(len=*) :: group
|
||
integer :: o
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
outputsLoop: do o = 1,size(prm%outputID)
|
||
select case(prm%outputID(o))
|
||
|
||
case (rho_mob_ID)
|
||
call results_writeDataset(group,stt%rho_mob,'rho_mob',&
|
||
'mobile dislocation density','1/m²')
|
||
case (rho_dip_ID)
|
||
call results_writeDataset(group,stt%rho_dip,'rho_dip',&
|
||
'dislocation dipole density''1/m²')
|
||
case (dot_gamma_sl_ID)
|
||
call results_writeDataset(group,stt%gamma_sl,'dot_gamma_sl',&
|
||
'plastic shear','1')
|
||
case (Lambda_sl_ID)
|
||
call results_writeDataset(group,dst%Lambda_sl,'Lambda_sl',&
|
||
'mean free path for slip','m')
|
||
case (threshold_stress_slip_ID)
|
||
call results_writeDataset(group,dst%tau_pass,'tau_pass',&
|
||
'passing stress for slip','Pa')
|
||
|
||
case (f_tw_ID)
|
||
call results_writeDataset(group,stt%f_tw,'f_tw',&
|
||
'twinned volume fraction','m³/m³')
|
||
case (Lambda_tw_ID)
|
||
call results_writeDataset(group,dst%Lambda_tw,'Lambda_tw',&
|
||
'mean free path for twinning','m')
|
||
case (tau_hat_tw_ID)
|
||
call results_writeDataset(group,dst%tau_hat_tw,'tau_hat_tw',&
|
||
'threshold stress for twinning','Pa')
|
||
|
||
case (f_tr_ID)
|
||
call results_writeDataset(group,stt%f_tr,'f_tr',&
|
||
'martensite volume fraction','m³/m³')
|
||
|
||
end select
|
||
enddo outputsLoop
|
||
end associate
|
||
|
||
#else
|
||
integer, intent(in) :: instance
|
||
character(len=*) :: group
|
||
#endif
|
||
|
||
end subroutine plastic_dislotwin_results
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief Shear rates on slip systems, their derivatives with respect to resolved stress and the
|
||
! resolved stresss
|
||
!> @details Derivatives and resolved stress are calculated only optionally.
|
||
! NOTE: Against the common convention, the result (i.e. intent(out)) variables are the last to
|
||
! have the optional arguments at the end
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_slip(Mp,T,instance,of, &
|
||
dot_gamma_sl,ddot_gamma_dtau_slip,tau_slip)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(out) :: &
|
||
dot_gamma_sl
|
||
real(pReal), dimension(param(instance)%sum_N_sl), optional, intent(out) :: &
|
||
ddot_gamma_dtau_slip, &
|
||
tau_slip
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
ddot_gamma_dtau
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_sl) :: &
|
||
tau, &
|
||
stressRatio, &
|
||
StressRatio_p, &
|
||
BoltzmannRatio, &
|
||
v_wait_inverse, & !< inverse of the effective velocity of a dislocation waiting at obstacles (unsigned)
|
||
v_run_inverse, & !< inverse of the velocity of a free moving dislocation (unsigned)
|
||
dV_wait_inverse_dTau, &
|
||
dV_run_inverse_dTau, &
|
||
dV_dTau, &
|
||
tau_eff !< effective resolved stress
|
||
integer :: i
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_sl
|
||
tau(i) = math_mul33xx33(Mp,prm%P_sl(1:3,1:3,i))
|
||
enddo
|
||
|
||
tau_eff = abs(tau)-dst%tau_pass(:,of)
|
||
|
||
significantStress: where(tau_eff > tol_math_check)
|
||
stressRatio = tau_eff/prm%tau_0
|
||
StressRatio_p = stressRatio** prm%p
|
||
BoltzmannRatio = prm%Delta_F/(kB*T)
|
||
v_wait_inverse = prm%v0**(-1.0_pReal) * exp(BoltzmannRatio*(1.0_pReal-StressRatio_p)** prm%q)
|
||
v_run_inverse = prm%B/(tau_eff*prm%b_sl)
|
||
|
||
dot_gamma_sl = sign(stt%rho_mob(:,of)*prm%b_sl/(v_wait_inverse+v_run_inverse),tau)
|
||
|
||
dV_wait_inverse_dTau = -1.0_pReal * v_wait_inverse * prm%p * prm%q * BoltzmannRatio &
|
||
* (stressRatio**(prm%p-1.0_pReal)) &
|
||
* (1.0_pReal-StressRatio_p)**(prm%q-1.0_pReal) &
|
||
/ prm%tau_0
|
||
dV_run_inverse_dTau = -1.0_pReal * v_run_inverse/tau_eff
|
||
dV_dTau = -1.0_pReal * (dV_wait_inverse_dTau+dV_run_inverse_dTau) &
|
||
/ (v_wait_inverse+v_run_inverse)**2.0_pReal
|
||
ddot_gamma_dtau = dV_dTau*stt%rho_mob(:,of)*prm%b_sl
|
||
else where significantStress
|
||
dot_gamma_sl = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_slip)) ddot_gamma_dtau_slip = ddot_gamma_dtau
|
||
if(present(tau_slip)) tau_slip = tau
|
||
|
||
end subroutine kinetics_slip
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates shear rates on twin systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_twin(Mp,T,dot_gamma_sl,instance,of,&
|
||
dot_gamma_twin,ddot_gamma_dtau_twin)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
|
||
dot_gamma_sl
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_tw), intent(out) :: &
|
||
dot_gamma_twin
|
||
real(pReal), dimension(param(instance)%sum_N_tw), optional, intent(out) :: &
|
||
ddot_gamma_dtau_twin
|
||
|
||
real, dimension(param(instance)%sum_N_tw) :: &
|
||
tau, &
|
||
Ndot0, &
|
||
stressRatio_r, &
|
||
ddot_gamma_dtau
|
||
|
||
integer :: i,s1,s2
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_tw
|
||
tau(i) = math_mul33xx33(Mp,prm%P_tw(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < dst%tau_r_tw(i,of)) then
|
||
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
|
||
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
|
||
(prm%L_tw*prm%b_sl(i))*&
|
||
(1.0_pReal-exp(-prm%V_cs/(kB*T)*&
|
||
(dst%tau_r_tw(i,of)-tau)))
|
||
else
|
||
Ndot0=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0=prm%dot_N_0_tw(i)
|
||
endif isFCC
|
||
enddo
|
||
|
||
significantStress: where(tau > tol_math_check)
|
||
StressRatio_r = (dst%tau_hat_tw(:,of)/tau)**prm%r
|
||
dot_gamma_twin = prm%gamma_char * dst%f_tw(:,of) * Ndot0*exp(-StressRatio_r)
|
||
ddot_gamma_dtau = (dot_gamma_twin*prm%r/tau)*StressRatio_r
|
||
else where significantStress
|
||
dot_gamma_twin = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_twin)) ddot_gamma_dtau_twin = ddot_gamma_dtau
|
||
|
||
end subroutine kinetics_twin
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates shear rates on twin systems
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure subroutine kinetics_trans(Mp,T,dot_gamma_sl,instance,of,&
|
||
dot_gamma_tr,ddot_gamma_dtau_trans)
|
||
use prec, only: &
|
||
tol_math_check, &
|
||
dNeq0
|
||
use math, only: &
|
||
math_mul33xx33
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: &
|
||
Mp !< Mandel stress
|
||
real(pReal), intent(in) :: &
|
||
T !< temperature
|
||
integer, intent(in) :: &
|
||
instance, &
|
||
of
|
||
real(pReal), dimension(param(instance)%sum_N_sl), intent(in) :: &
|
||
dot_gamma_sl
|
||
|
||
real(pReal), dimension(param(instance)%sum_N_tr), intent(out) :: &
|
||
dot_gamma_tr
|
||
real(pReal), dimension(param(instance)%sum_N_tr), optional, intent(out) :: &
|
||
ddot_gamma_dtau_trans
|
||
|
||
real, dimension(param(instance)%sum_N_tr) :: &
|
||
tau, &
|
||
Ndot0, &
|
||
stressRatio_s, &
|
||
ddot_gamma_dtau
|
||
|
||
integer :: i,s1,s2
|
||
|
||
associate(prm => param(instance), stt => state(instance), dst => dependentState(instance))
|
||
|
||
do i = 1, prm%sum_N_tr
|
||
tau(i) = math_mul33xx33(Mp,prm%P_tr(1:3,1:3,i))
|
||
isFCC: if (prm%fccTwinTransNucleation) then
|
||
s1=prm%fcc_twinNucleationSlipPair(1,i)
|
||
s2=prm%fcc_twinNucleationSlipPair(2,i)
|
||
if (tau(i) < dst%tau_r_tr(i,of)) then
|
||
Ndot0=(abs(dot_gamma_sl(s1))*(stt%rho_mob(s2,of)+stt%rho_dip(s2,of))+&
|
||
abs(dot_gamma_sl(s2))*(stt%rho_mob(s1,of)+stt%rho_dip(s1,of)))/& ! ToDo: MD: it would be more consistent to use shearrates from state
|
||
(prm%L_tr*prm%b_sl(i))*&
|
||
(1.0_pReal-exp(-prm%V_cs/(kB*T)*&
|
||
(dst%tau_r_tr(i,of)-tau)))
|
||
else
|
||
Ndot0=0.0_pReal
|
||
end if
|
||
else isFCC
|
||
Ndot0=prm%dot_N_0_tr(i)
|
||
endif isFCC
|
||
enddo
|
||
|
||
significantStress: where(tau > tol_math_check)
|
||
StressRatio_s = (dst%tau_hat_tr(:,of)/tau)**prm%s
|
||
dot_gamma_tr = dst%f_tr(:,of) * Ndot0*exp(-StressRatio_s)
|
||
ddot_gamma_dtau = (dot_gamma_tr*prm%r/tau)*StressRatio_s
|
||
else where significantStress
|
||
dot_gamma_tr = 0.0_pReal
|
||
ddot_gamma_dtau = 0.0_pReal
|
||
end where significantStress
|
||
|
||
end associate
|
||
|
||
if(present(ddot_gamma_dtau_trans)) ddot_gamma_dtau_trans = ddot_gamma_dtau
|
||
|
||
end subroutine kinetics_trans
|
||
|
||
end module plastic_dislotwin
|