2015-04-21 20:46:13 +05:30
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!--------------------------------------------------------------------------------------------------
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2014-11-06 00:41:09 +05:30
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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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!> @author David Cereceda, Lawrence Livermore National Laboratory
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!> @author Martin Diehl, 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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2015-01-21 20:44:00 +05:30
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module plastic_disloUCLA
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2014-11-06 00:41:09 +05:30
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use prec, only: &
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pReal, &
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pInt
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implicit none
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private
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integer(pInt), dimension(:), allocatable, public, protected :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_sizePostResults !< cumulative size of post results
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2014-11-06 00:41:09 +05:30
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integer(pInt), dimension(:,:), allocatable, target, public :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_sizePostResult !< size of each post result output
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2014-11-06 00:41:09 +05:30
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character(len=64), dimension(:,:), allocatable, target, public :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_output !< name of each post result output
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2014-11-06 00:41:09 +05:30
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real(pReal), parameter, private :: &
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2016-04-25 02:06:35 +05:30
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kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
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2014-11-06 00:41:09 +05:30
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integer(pInt), dimension(:), allocatable, target, public :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_Noutput !< number of outputs per instance of this plasticity
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2014-11-06 00:41:09 +05:30
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2016-01-16 12:36:34 +05:30
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integer(pInt), dimension(:), allocatable, private :: &
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2016-04-25 02:06:35 +05:30
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plastic_disloUCLA_totalNslip !< total number of active slip systems for each instance
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2014-11-06 00:41:09 +05:30
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integer(pInt), dimension(:,:), allocatable, private :: &
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2016-04-25 02:06:35 +05:30
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plastic_disloUCLA_Nslip !< number of active slip systems for each family and instance
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2014-11-06 00:41:09 +05:30
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real(pReal), dimension(:), allocatable, private :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_CAtomicVolume, & !< atomic volume in Bugers vector unit
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plastic_disloUCLA_D0, & !< prefactor for self-diffusion coefficient
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plastic_disloUCLA_Qsd, & !< activation energy for dislocation climb
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plastic_disloUCLA_CEdgeDipMinDistance, & !<
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2018-11-29 03:32:46 +05:30
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plastic_disloUCLA_dipoleFormationFactor !< scaling factor for dipole formation: 0: off, 1: on. other values not useful
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2014-11-06 00:41:09 +05:30
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2018-11-29 03:32:46 +05:30
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2014-11-06 00:41:09 +05:30
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real(pReal), dimension(:,:,:), allocatable, private :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_forestProjectionEdge !< matrix of forest projections of edge dislocations for each instance
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2014-11-06 00:41:09 +05:30
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enum, bind(c)
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enumerator :: undefined_ID, &
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2018-11-28 10:29:03 +05:30
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rho_ID, &
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rhoDip_ID, &
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shearrate_ID, &
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accumulatedshear_ID, &
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mfp_ID, &
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resolvedstress_ID, &
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thresholdstress_ID, &
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dipoledistance_ID, &
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stressexponent_ID
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2014-11-06 00:41:09 +05:30
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end enum
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type, private :: tParameters
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real(pReal) :: &
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2018-11-29 13:14:31 +05:30
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aTolRho, &
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2018-11-29 15:01:02 +05:30
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grainSize, &
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2018-11-30 12:55:23 +05:30
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SolidSolutionStrength, & !< Strength due to elements in solid solution
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mu
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2018-11-28 00:30:45 +05:30
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real(pReal), allocatable, dimension(:) :: &
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2018-11-29 15:07:06 +05:30
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B, & !< friction coeff. B (kMC)
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2018-11-28 10:29:03 +05:30
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rho0, & !< initial edge dislocation density per slip system for each family and instance
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rhoDip0, & !< initial edge dipole density per slip system for each family and instance
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burgers, & !< absolute length of burgers vector [m] for each slip system and instance
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H0kp, & !< activation energy for glide [J] for each slip system and instance
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v0, & !< dislocation velocity prefactor [m/s] for each family and instance
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CLambda, & !< Adj. parameter for distance between 2 forest dislocations for each slip 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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!* mobility law parameters
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2018-11-29 03:32:46 +05:30
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kink_height, & !< height of the kink pair
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kink_width, & !< width of the kink pair
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omega, & !< attempt frequency for kink pair nucleation
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2018-11-28 10:29:03 +05:30
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viscosity, & !< friction coeff. B (kMC)
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!*
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2018-11-29 13:14:31 +05:30
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tau_Peierls, &
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2018-11-28 00:30:45 +05:30
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nonSchmidCoeff
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real(pReal), allocatable, dimension(:,:) :: &
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interaction_SlipSlip !< slip resistance from slip activity
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real(pReal), allocatable, dimension(:,:,:) :: &
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Schmid_slip, &
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Schmid_twin, &
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nonSchmid_pos, &
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nonSchmid_neg
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integer(pInt) :: &
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totalNslip !< total number of active slip system
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integer(pInt), allocatable, dimension(:) :: &
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Nslip !< number of active slip systems for each family
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integer(kind(undefined_ID)), allocatable, dimension(:) :: &
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outputID !< ID of each post result output
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end type !< container type for internal constitutive parameters
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type(tParameters), dimension(:), allocatable, private :: param !< containers of constitutive parameters (len Ninstance)
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2014-11-06 00:41:09 +05:30
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integer(kind(undefined_ID)), dimension(:,:), allocatable, private :: &
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2016-01-16 12:36:34 +05:30
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plastic_disloUCLA_outputID !< ID of each post result output
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2016-01-15 20:56:24 +05:30
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type, private :: tDisloUCLAState
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real(pReal), pointer, dimension(:,:) :: &
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rhoEdge, &
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rhoEdgeDip, &
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2018-11-30 14:34:41 +05:30
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accshear_slip, &
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whole
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2016-01-15 20:56:24 +05:30
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end type
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2018-11-29 12:44:20 +05:30
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type, private :: tDisloUCLAMicrostructure
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real(pReal), allocatable, dimension(:,:) :: &
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mfp, &
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threshold_stress
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end type tDisloUCLAMicrostructure
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2016-01-15 20:56:24 +05:30
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type(tDisloUCLAState ), allocatable, dimension(:), private :: &
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state, &
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dotState
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2018-11-29 12:44:20 +05:30
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type(tDisloUCLAMicrostructure), allocatable, dimension(:), private :: &
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microstructure
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2016-01-15 20:56:24 +05:30
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2014-11-06 00:41:09 +05:30
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public :: &
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2015-01-21 20:44:00 +05:30
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plastic_disloUCLA_init, &
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plastic_disloUCLA_microstructure, &
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plastic_disloUCLA_LpAndItsTangent, &
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plastic_disloUCLA_dotState, &
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plastic_disloUCLA_postResults
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2014-11-06 00:41:09 +05:30
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private :: &
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2018-11-29 13:51:58 +05:30
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kinetics
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2018-11-28 21:42:06 +05:30
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2014-11-06 00:41:09 +05:30
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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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2015-01-21 20:44:00 +05:30
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subroutine plastic_disloUCLA_init(fileUnit)
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2018-02-02 17:06:09 +05:30
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#if defined(__GFORTRAN__) || __INTEL_COMPILER >= 1800
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2017-10-05 20:05:34 +05:30
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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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2014-11-06 00:41:09 +05:30
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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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2018-11-29 03:32:46 +05:30
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math_mul3x3, &
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math_expand
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2014-11-06 00:41:09 +05:30
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use IO, only: &
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IO_error, &
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2018-11-30 13:06:56 +05:30
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IO_timeStamp
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2014-11-06 00:41:09 +05:30
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use material, only: &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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2015-01-15 16:26:15 +05:30
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PLASTICITY_DISLOUCLA_label, &
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PLASTICITY_DISLOUCLA_ID, &
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2018-06-10 21:31:52 +05:30
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material_phase, &
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2018-11-27 23:58:00 +05:30
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plasticState, &
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material_allocatePlasticState
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2018-06-14 10:09:49 +05:30
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use config, only: &
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2018-11-28 00:30:45 +05:30
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MATERIAL_partPhase, &
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config_phase
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2014-11-06 00:41:09 +05:30
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use lattice
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implicit none
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integer(pInt), intent(in) :: fileUnit
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2018-11-29 13:51:58 +05:30
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integer(pInt) :: maxNinstance,phase,maxTotalNslip,&
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2018-11-28 10:29:03 +05:30
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f,instance,j,k,o,ns, i, &
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2018-11-30 13:06:56 +05:30
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outputSize, &
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2016-01-15 20:56:24 +05:30
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offset_slip, index_myFamily, index_otherFamily, &
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2018-11-28 00:30:45 +05:30
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startIndex, endIndex, p
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2018-11-29 15:01:02 +05:30
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integer(pInt) :: sizeState, sizeDotState
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2014-11-06 00:41:09 +05:30
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integer(pInt) :: NofMyPhase
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character(len=65536) :: &
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2018-11-28 00:30:45 +05:30
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structure = '',&
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2014-11-06 00:41:09 +05:30
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tag = '', &
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line = ''
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2016-04-25 02:06:35 +05:30
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real(pReal), dimension(:), allocatable :: tempPerSlip
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2018-11-28 10:29:03 +05:30
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character(len=65536), dimension(:), allocatable :: outputs
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integer(kind(undefined_ID)) :: outputID
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2018-11-28 00:30:45 +05:30
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integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
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character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
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2014-11-06 00:41:09 +05:30
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2016-07-25 23:42:00 +05:30
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_DISLOUCLA_label//' init -+>>>'
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2018-04-22 13:37:49 +05:30
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write(6,'(/,a)') ' Cereceda et al., International Journal of Plasticity 78, 2016, 242-256'
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2018-04-09 18:34:37 +05:30
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write(6,'(/,a)') ' http://dx.doi.org/10.1016/j.ijplas.2015.09.002'
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2016-07-25 23:42:00 +05:30
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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2014-11-06 00:41:09 +05:30
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#include "compilation_info.f90"
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2015-01-15 16:26:15 +05:30
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maxNinstance = int(count(phase_plasticity == PLASTICITY_DISLOUCLA_ID),pInt)
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2014-11-06 00:41:09 +05:30
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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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2015-01-21 20:44:00 +05:30
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allocate(plastic_disloUCLA_sizePostResults(maxNinstance), source=0_pInt)
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allocate(plastic_disloUCLA_sizePostResult(maxval(phase_Noutput),maxNinstance),source=0_pInt)
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allocate(plastic_disloUCLA_output(maxval(phase_Noutput),maxNinstance))
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plastic_disloUCLA_output = ''
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allocate(plastic_disloUCLA_outputID(maxval(phase_Noutput),maxNinstance), source=undefined_ID)
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allocate(plastic_disloUCLA_Noutput(maxNinstance), source=0_pInt)
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allocate(plastic_disloUCLA_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
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allocate(plastic_disloUCLA_totalNslip(maxNinstance), source=0_pInt)
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allocate(plastic_disloUCLA_CAtomicVolume(maxNinstance), source=0.0_pReal)
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allocate(plastic_disloUCLA_D0(maxNinstance), source=0.0_pReal)
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allocate(plastic_disloUCLA_Qsd(maxNinstance), source=0.0_pReal)
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allocate(plastic_disloUCLA_CEdgeDipMinDistance(maxNinstance), source=0.0_pReal)
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allocate(plastic_disloUCLA_dipoleFormationFactor(maxNinstance), source=1.0_pReal) !should be on by default
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2014-11-06 00:41:09 +05:30
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2018-11-28 00:30:45 +05:30
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allocate(param(maxNinstance))
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allocate(state(maxNinstance))
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allocate(dotState(maxNinstance))
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2018-11-29 12:44:20 +05:30
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allocate(microstructure(maxNinstance))
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2018-11-28 00:30:45 +05:30
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do p = 1_pInt, size(phase_plasticityInstance)
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if (phase_plasticity(p) /= PLASTICITY_DISLOUCLA_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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structure = config_phase(p)%getString('lattice_structure')
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2018-11-30 12:55:23 +05:30
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prm%mu = lattice_mu(p)
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2018-11-28 00:30:45 +05:30
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2018-11-29 03:32:46 +05:30
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prm%aTolRho = config_phase(p)%getFloat('atol_rho')
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2018-11-28 00:30:45 +05:30
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!--------------------------------------------------------------------------------------------------
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! slip related parameters
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prm%Nslip = config_phase(p)%getInts('nslip',defaultVal=emptyIntArray)
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prm%totalNslip = sum(prm%Nslip)
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slipActive: if (prm%totalNslip > 0_pInt) then
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prm%Schmid_slip = lattice_SchmidMatrix_slip(prm%Nslip,structure(1:3),&
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config_phase(p)%getFloat('c/a',defaultVal=0.0_pReal))
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if(structure=='bcc') then
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prm%nonSchmidCoeff = config_phase(p)%getFloats('nonschmid_coefficients',&
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defaultVal = emptyRealArray)
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prm%nonSchmid_pos = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,+1_pInt)
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prm%nonSchmid_neg = lattice_nonSchmidMatrix(prm%Nslip,prm%nonSchmidCoeff,-1_pInt)
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else
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prm%nonSchmid_pos = prm%Schmid_slip
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prm%nonSchmid_neg = prm%Schmid_slip
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endif
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prm%interaction_SlipSlip = lattice_interaction_SlipSlip(prm%Nslip, &
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config_phase(p)%getFloats('interaction_slipslip'), &
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structure(1:3))
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2018-11-29 12:44:20 +05:30
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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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2018-11-29 03:32:46 +05:30
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prm%burgers = config_phase(p)%getFloats('slipburgers')
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prm%H0kp = config_phase(p)%getFloats('qedge')
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2018-11-29 15:01:02 +05:30
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prm%v0 = config_phase(p)%getFloats('v0')
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2018-11-30 11:57:23 +05:30
|
|
|
prm%clambda = config_phase(p)%getFloats('clambdaslip')
|
2018-11-29 13:14:31 +05:30
|
|
|
prm%tau_Peierls = config_phase(p)%getFloats('tau_peierls')
|
2018-11-29 03:32:46 +05:30
|
|
|
prm%p = config_phase(p)%getFloats('p_slip',defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
|
|
|
|
prm%q = config_phase(p)%getFloats('q_slip',defaultVal=[(1.0_pReal,i=1_pInt,size(prm%Nslip))])
|
|
|
|
prm%kink_height = config_phase(p)%getFloats('kink_height')
|
|
|
|
prm%kink_width = config_phase(p)%getFloats('kink_width')
|
|
|
|
prm%omega = config_phase(p)%getFloats('omega')
|
2018-11-29 15:07:06 +05:30
|
|
|
|
|
|
|
prm%B = config_phase(p)%getFloats('friction_coeff')
|
2018-11-28 10:29:03 +05:30
|
|
|
!prm%viscosity = config_phase(p)%getFloats('viscosity')
|
2018-11-29 03:32:46 +05:30
|
|
|
|
|
|
|
|
2018-11-29 15:01:02 +05:30
|
|
|
prm%SolidSolutionStrength = config_phase(p)%getFloat('solidsolutionstrength')
|
|
|
|
|
2018-11-29 13:14:31 +05:30
|
|
|
prm%grainSize = config_phase(p)%getFloat('grainsize')
|
|
|
|
|
2018-11-29 15:01:02 +05:30
|
|
|
plastic_disloUCLA_D0(phase_plasticityInstance(p)) = config_phase(p)%getFloat('qsd')
|
|
|
|
plastic_disloUCLA_Qsd(phase_plasticityInstance(p)) = config_phase(p)%getFloat('qsd')
|
|
|
|
plastic_disloUCLA_CEdgeDipMinDistance(phase_plasticityInstance(p)) = config_phase(p)%getFloat('cedgedipmindistance')
|
|
|
|
plastic_disloUCLA_CAtomicVolume(phase_plasticityInstance(p)) = config_phase(p)%getFloat('catomicvolume')
|
|
|
|
plastic_disloUCLA_dipoleFormationFactor(phase_plasticityInstance(p)) = config_phase(p)%getFloat('dipoleformationfactor')
|
2018-11-29 13:14:31 +05:30
|
|
|
|
2018-11-29 03:32:46 +05:30
|
|
|
! expand: family => system
|
2018-11-29 12:44:20 +05:30
|
|
|
prm%rho0 = math_expand(prm%rho0, prm%Nslip)
|
|
|
|
prm%rhoDip0 = math_expand(prm%rhoDip0, prm%Nslip)
|
2018-11-29 03:32:46 +05:30
|
|
|
prm%q = math_expand(prm%q, prm%Nslip)
|
|
|
|
prm%p = math_expand(prm%p, prm%Nslip)
|
|
|
|
prm%H0kp = math_expand(prm%H0kp, prm%Nslip)
|
|
|
|
prm%burgers = math_expand(prm%burgers, prm%Nslip)
|
|
|
|
prm%kink_height = math_expand(prm%kink_height, prm%Nslip)
|
|
|
|
prm%kink_width = math_expand(prm%kink_width, prm%Nslip)
|
|
|
|
prm%omega = math_expand(prm%omega, prm%Nslip)
|
2018-11-29 13:14:31 +05:30
|
|
|
prm%tau_Peierls = math_expand(prm%tau_Peierls, prm%Nslip)
|
2018-11-29 15:01:02 +05:30
|
|
|
prm%v0 = math_expand(prm%v0, prm%Nslip)
|
2018-11-29 15:07:06 +05:30
|
|
|
prm%B = math_expand(prm%B, prm%Nslip)
|
2018-11-30 11:57:23 +05:30
|
|
|
prm%clambda = math_expand(prm%clambda, prm%Nslip)
|
|
|
|
|
|
|
|
instance = phase_plasticityInstance(p)
|
2018-11-30 12:55:23 +05:30
|
|
|
plastic_disloUCLA_totalNslip(instance) = prm%totalNslip
|
2018-11-30 11:57:23 +05:30
|
|
|
if (plastic_disloUCLA_CAtomicVolume(instance) <= 0.0_pReal) &
|
|
|
|
call IO_error(211_pInt,el=instance,ext_msg='cAtomicVolume ('//PLASTICITY_DISLOUCLA_label//')')
|
|
|
|
if (plastic_disloUCLA_D0(instance) <= 0.0_pReal) &
|
|
|
|
call IO_error(211_pInt,el=instance,ext_msg='D0 ('//PLASTICITY_DISLOUCLA_label//')')
|
|
|
|
if (plastic_disloUCLA_Qsd(instance) <= 0.0_pReal) &
|
|
|
|
call IO_error(211_pInt,el=instance,ext_msg='Qsd ('//PLASTICITY_DISLOUCLA_label//')')
|
|
|
|
! if (plastic_disloUCLA_aTolRho(instance) <= 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='aTolRho ('//PLASTICITY_DISLOUCLA_label//')')
|
|
|
|
|
|
|
|
else slipActive
|
|
|
|
allocate(prm%rho0(0))
|
|
|
|
allocate(prm%rhoDip0(0))
|
|
|
|
|
2018-11-28 00:30:45 +05:30
|
|
|
endif slipActive
|
2018-11-28 10:29:03 +05:30
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
! phase outputs
|
|
|
|
|
|
|
|
#if defined(__GFORTRAN__)
|
|
|
|
outputs = ['GfortranBug86277']
|
|
|
|
outputs = config_phase(p)%getStrings('(output)',defaultVal=outputs)
|
|
|
|
if (outputs(1) == 'GfortranBug86277') outputs = emptyStringArray
|
|
|
|
#else
|
|
|
|
outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray)
|
|
|
|
#endif
|
|
|
|
allocate(prm%outputID(0))
|
|
|
|
|
|
|
|
do i = 1_pInt, size(outputs)
|
|
|
|
outputID = undefined_ID
|
|
|
|
outputSize = prm%totalNslip
|
|
|
|
select case(trim(outputs(i)))
|
|
|
|
case ('edge_density')
|
2018-11-28 21:15:45 +05:30
|
|
|
outputID = merge(rho_ID,undefined_ID,prm%totalNslip>0_pInt)
|
2018-11-28 10:29:03 +05:30
|
|
|
case ('dipole_density')
|
2018-11-28 21:15:45 +05:30
|
|
|
outputID = merge(rhoDip_ID,undefined_ID,prm%totalNslip>0_pInt)
|
|
|
|
case ('shear_rate','shearrate','shear_rate_slip','shearrate_slip')
|
|
|
|
outputID = merge(shearrate_ID,undefined_ID,prm%totalNslip>0_pInt)
|
|
|
|
case ('accumulated_shear','accumulatedshear','accumulated_shear_slip')
|
|
|
|
outputID = merge(accumulatedshear_ID,undefined_ID,prm%totalNslip>0_pInt)
|
|
|
|
case ('mfp','mfp_slip')
|
|
|
|
outputID = merge(mfp_ID,undefined_ID,prm%totalNslip>0_pInt)
|
|
|
|
case ('resolved_stress','resolved_stress_slip')
|
|
|
|
outputID = merge(resolvedstress_ID,undefined_ID,prm%totalNslip>0_pInt)
|
|
|
|
case ('threshold_stress','threshold_stress_slip')
|
|
|
|
outputID = merge(thresholdstress_ID,undefined_ID,prm%totalNslip>0_pInt)
|
2018-11-28 10:29:03 +05:30
|
|
|
case ('edge_dipole_distance')
|
2018-11-28 21:15:45 +05:30
|
|
|
outputID = merge(dipoleDistance_ID,undefined_ID,prm%totalNslip>0_pInt)
|
2018-11-28 10:29:03 +05:30
|
|
|
case ('stress_exponent')
|
2018-11-28 21:15:45 +05:30
|
|
|
outputID = merge(stressexponent_ID,undefined_ID,prm%totalNslip>0_pInt)
|
2018-11-28 10:29:03 +05:30
|
|
|
end select
|
2018-11-28 21:15:45 +05:30
|
|
|
|
|
|
|
if (outputID /= undefined_ID) then
|
|
|
|
plastic_disloUCLA_output(i,phase_plasticityInstance(p)) = outputs(i)
|
|
|
|
plastic_disloUCLA_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
|
|
|
|
prm%outputID = [prm%outputID, outputID]
|
|
|
|
plastic_disloUCLA_outputID(i,phase_plasticityInstance(p)) = outputID
|
|
|
|
plastic_disloUCLA_sizePostResults(phase_plasticityInstance(p)) = &
|
|
|
|
plastic_disloUCLA_sizePostResults(phase_plasticityInstance(p)) + outputSize
|
|
|
|
plastic_disloUCLA_Noutput(phase_plasticityInstance(p)) = plastic_disloUCLA_Noutput(phase_plasticityInstance(p)) + 1_pInt
|
|
|
|
endif
|
|
|
|
|
2018-11-28 10:29:03 +05:30
|
|
|
enddo
|
2018-11-28 00:30:45 +05:30
|
|
|
end associate
|
|
|
|
enddo
|
2018-11-28 21:42:06 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-30 13:06:56 +05:30
|
|
|
|
2018-11-29 12:44:20 +05:30
|
|
|
!if (plastic_disloUCLA_rhoEdge0(f,instance) < 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdge0 ('//PLASTICITY_DISLOUCLA_label//')')
|
|
|
|
!if (plastic_disloUCLA_rhoEdgeDip0(f,instance) < 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='rhoEdgeDip0 ('//PLASTICITY_DISLOUCLA_label//')')
|
2018-11-29 03:32:46 +05:30
|
|
|
!if (plastic_disloUCLA_burgersPerSlipFamily(f,instance) <= 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='slipBurgers ('//PLASTICITY_DISLOUCLA_label//')')
|
2018-11-29 15:01:02 +05:30
|
|
|
!if (plastic_disloUCLA_v0PerSlipFamily(f,instance) <= 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='v0 ('//PLASTICITY_DISLOUCLA_label//')')
|
2018-11-29 13:14:31 +05:30
|
|
|
!if (plastic_disloUCLA_tau_peierlsPerSlipFamily(f,instance) < 0.0_pReal) &
|
|
|
|
! call IO_error(211_pInt,el=instance,ext_msg='tau_peierls ('//PLASTICITY_DISLOUCLA_label//')')
|
2018-11-30 13:06:56 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
! allocation of variables whose size depends on the total number of active slip systems
|
2015-01-21 20:44:00 +05:30
|
|
|
maxTotalNslip = maxval(plastic_disloUCLA_totalNslip)
|
|
|
|
|
|
|
|
allocate(plastic_disloUCLA_forestProjectionEdge(maxTotalNslip,maxTotalNslip,maxNinstance), &
|
2014-11-06 00:41:09 +05:30
|
|
|
source=0.0_pReal)
|
2018-11-28 00:30:45 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
initializeInstances: do phase = 1_pInt, size(phase_plasticity)
|
2016-04-25 02:06:35 +05:30
|
|
|
myPhase2: if (phase_plasticity(phase) == PLASTICITY_disloUCLA_ID) then
|
2018-11-28 21:42:06 +05:30
|
|
|
p = phase
|
2014-11-06 00:41:09 +05:30
|
|
|
NofMyPhase=count(material_phase==phase)
|
|
|
|
instance = phase_plasticityInstance(phase)
|
2015-01-21 20:44:00 +05:30
|
|
|
ns = plastic_disloUCLA_totalNslip(instance)
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-29 12:44:20 +05:30
|
|
|
associate(prm => param(instance), stt=>state(instance),mse => microstructure(phase_plasticityInstance(p)))
|
2014-11-06 00:41:09 +05:30
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
! allocate state arrays
|
2016-01-16 12:36:34 +05:30
|
|
|
|
2016-04-25 02:06:35 +05:30
|
|
|
sizeDotState = int(size(['rhoEdge ','rhoEdgeDip ','accshearslip']),pInt) * ns
|
2018-11-29 13:26:57 +05:30
|
|
|
sizeState = sizeDotState
|
2016-01-16 12:36:34 +05:30
|
|
|
|
2018-11-27 23:58:00 +05:30
|
|
|
call material_allocatePlasticState(phase,NofMyPhase,sizeState,sizeDotState,0_pInt, &
|
|
|
|
ns,0_pInt,0_pInt)
|
|
|
|
|
2018-11-28 21:15:45 +05:30
|
|
|
plasticState(phase)%sizePostResults = plastic_disloUCLA_sizePostResults(instance)
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2015-01-23 18:38:25 +05:30
|
|
|
offset_slip = 2_pInt*plasticState(phase)%nSlip
|
|
|
|
plasticState(phase)%slipRate => &
|
|
|
|
plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase)
|
|
|
|
plasticState(phase)%accumulatedSlip => &
|
|
|
|
plasticState(phase)%state (offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NofMyPhase)
|
2014-11-06 00:41:09 +05:30
|
|
|
!* Process slip related parameters ------------------------------------------------
|
|
|
|
|
2018-11-29 15:07:06 +05:30
|
|
|
mySlipFamilies: do f = 1_pInt,size(prm%Nslip,1)
|
2018-11-30 12:55:23 +05:30
|
|
|
index_myFamily = sum(prm%Nslip(1:f-1_pInt)) ! index in truncated slip system list
|
|
|
|
mySlipSystems: do j = 1_pInt,prm%Nslip(f)
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* Calculation of forest projections for edge dislocations
|
2018-11-29 15:07:06 +05:30
|
|
|
otherSlipFamilies: do o = 1_pInt,size(prm%Nslip,1)
|
2018-11-30 12:55:23 +05:30
|
|
|
index_otherFamily = sum(prm%Nslip(1:o-1_pInt))
|
|
|
|
otherSlipSystems: do k = 1_pInt,prm%Nslip(o)
|
2015-01-21 20:44:00 +05:30
|
|
|
plastic_disloUCLA_forestProjectionEdge(index_myFamily+j,index_otherFamily+k,instance) = &
|
2014-11-06 00:41:09 +05:30
|
|
|
abs(math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:f-1,phase))+j,phase), &
|
|
|
|
lattice_st(:,sum(lattice_NslipSystem(1:o-1,phase))+k,phase)))
|
|
|
|
enddo otherSlipSystems; enddo otherSlipFamilies
|
2016-04-25 02:06:35 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
enddo mySlipSystems
|
|
|
|
enddo mySlipFamilies
|
|
|
|
|
2016-04-25 02:06:35 +05:30
|
|
|
startIndex=1_pInt
|
|
|
|
endIndex=ns
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%rhoEdge=>plasticState(phase)%state(startIndex:endIndex,:)
|
2018-11-29 13:26:57 +05:30
|
|
|
stt%rhoEdge= spread(prm%rho0,2,NofMyPhase)
|
2018-11-28 21:42:06 +05:30
|
|
|
dotState(instance)%rhoEdge=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
2018-11-29 03:32:46 +05:30
|
|
|
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
2016-04-25 02:06:35 +05:30
|
|
|
|
|
|
|
startIndex=endIndex+1_pInt
|
|
|
|
endIndex=endIndex+ns
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%rhoEdgeDip=>plasticState(phase)%state(startIndex:endIndex,:)
|
2018-11-29 13:26:57 +05:30
|
|
|
stt%rhoEdgeDip= spread(prm%rhoDip0,2,NofMyPhase)
|
2016-04-25 02:06:35 +05:30
|
|
|
dotState(instance)%rhoEdgeDip=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
2018-11-29 03:32:46 +05:30
|
|
|
plasticState(p)%aTolState(startIndex:endIndex) = prm%aTolRho
|
2016-04-25 02:06:35 +05:30
|
|
|
|
|
|
|
startIndex=endIndex+1_pInt
|
|
|
|
endIndex=endIndex+ns
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%accshear_slip=>plasticState(phase)%state(startIndex:endIndex,:)
|
2016-04-25 02:06:35 +05:30
|
|
|
dotState(instance)%accshear_slip=>plasticState(phase)%dotState(startIndex:endIndex,:)
|
2018-11-28 21:42:06 +05:30
|
|
|
plasticState(p)%aTolState(startIndex:endIndex) = 1e6_pReal
|
2016-04-25 02:06:35 +05:30
|
|
|
|
2018-11-30 14:34:41 +05:30
|
|
|
dotState(instance)%whole => plasticState(phase)%dotState
|
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-29 12:44:20 +05:30
|
|
|
allocate(mse%mfp(prm%totalNslip,NofMyPhase),source=0.0_pReal)
|
|
|
|
allocate(mse%threshold_stress(prm%totalNslip,NofMyPhase),source=0.0_pReal)
|
|
|
|
|
2018-11-28 21:42:06 +05:30
|
|
|
|
|
|
|
plasticState(p)%state0 = plasticState(p)%state ! ToDo: this could be done centrally
|
2018-11-29 03:32:46 +05:30
|
|
|
end associate
|
2014-11-06 00:41:09 +05:30
|
|
|
endif myPhase2
|
2018-11-29 03:32:46 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
enddo initializeInstances
|
|
|
|
|
2015-01-21 20:44:00 +05:30
|
|
|
end subroutine plastic_disloUCLA_init
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
!> @brief calculates derived quantities from state
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
2015-01-21 20:44:00 +05:30
|
|
|
subroutine plastic_disloUCLA_microstructure(temperature,ipc,ip,el)
|
2014-11-06 00:41:09 +05:30
|
|
|
use math, only: &
|
|
|
|
pi
|
|
|
|
use material, only: &
|
|
|
|
phase_plasticityInstance, &
|
2018-11-29 13:02:15 +05:30
|
|
|
phaseAt, phasememberAt, &
|
|
|
|
material_phase
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
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, &
|
2016-04-25 02:06:35 +05:30
|
|
|
ns,s, &
|
2014-11-06 00:41:09 +05:30
|
|
|
of
|
2018-11-29 13:02:15 +05:30
|
|
|
real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
|
|
|
invLambdaSlip
|
2014-11-06 00:41:09 +05:30
|
|
|
!* Shortened notation
|
2016-01-15 05:49:44 +05:30
|
|
|
of = phasememberAt(ipc,ip,el)
|
2018-11-30 12:16:26 +05:30
|
|
|
instance = phase_plasticityInstance(phaseAt(ipc,ip,el))
|
2015-01-21 20:44:00 +05:30
|
|
|
ns = plastic_disloUCLA_totalNslip(instance)
|
2018-11-29 13:14:31 +05:30
|
|
|
|
|
|
|
|
2018-11-29 13:26:57 +05:30
|
|
|
associate(prm => param(instance), stt => state(instance),mse => microstructure(instance))
|
2014-11-06 00:41:09 +05:30
|
|
|
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
|
|
|
forall (s = 1_pInt:ns) &
|
2018-11-29 13:02:15 +05:30
|
|
|
invLambdaSlip(s) = &
|
2018-11-29 11:57:35 +05:30
|
|
|
sqrt(dot_product((stt%rhoEdge(1_pInt:ns,of)+stt%rhoEdgeDip(1_pInt:ns,of)),&
|
2015-01-21 20:44:00 +05:30
|
|
|
plastic_disloUCLA_forestProjectionEdge(1:ns,s,instance)))/ &
|
2018-11-30 11:57:23 +05:30
|
|
|
prm%Clambda(s)
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* mean free path between 2 obstacles seen by a moving dislocation
|
2018-11-29 15:01:02 +05:30
|
|
|
|
|
|
|
mse%mfp(:,of) = prm%grainSize/(1.0_pReal+prm%grainSize*invLambdaSlip)
|
2018-11-29 13:26:57 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
!* threshold stress for dislocation motion
|
|
|
|
forall (s = 1_pInt:ns) &
|
2018-11-29 13:26:57 +05:30
|
|
|
mse%threshold_stress(s,of) = &
|
2018-11-30 12:55:23 +05:30
|
|
|
prm%mu*prm%burgers(s)*&
|
2018-11-29 15:01:02 +05:30
|
|
|
sqrt(dot_product(stt%rhoEdge(1_pInt:ns,of)+stt%rhoEdgeDip(1_pInt:ns,of),&
|
|
|
|
prm%interaction_SlipSlip(s,1:ns)))
|
2018-11-29 03:32:46 +05:30
|
|
|
end associate
|
2018-11-29 13:14:31 +05:30
|
|
|
|
|
|
|
|
2015-01-21 20:44:00 +05:30
|
|
|
end subroutine plastic_disloUCLA_microstructure
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
!> @brief calculates plastic velocity gradient and its tangent
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
2018-11-28 11:14:32 +05:30
|
|
|
subroutine plastic_disloUCLA_LpAndItsTangent(Lp,dLp_dMp,Mp,Temperature,ipc,ip,el)
|
2014-11-06 00:41:09 +05:30
|
|
|
use material, only: &
|
|
|
|
material_phase, &
|
|
|
|
phase_plasticityInstance, &
|
2016-01-15 05:49:44 +05:30
|
|
|
phaseAt, phasememberAt
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
implicit none
|
2015-01-29 19:26:09 +05:30
|
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
2014-11-06 00:41:09 +05:30
|
|
|
real(pReal), intent(in) :: Temperature
|
2018-11-28 11:14:32 +05:30
|
|
|
real(pReal), dimension(3,3), intent(in) :: Mp
|
2014-11-06 00:41:09 +05:30
|
|
|
real(pReal), dimension(3,3), intent(out) :: Lp
|
2018-11-28 11:14:32 +05:30
|
|
|
real(pReal), dimension(3,3,3,3), intent(out) :: dLp_dMp
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-30 12:16:26 +05:30
|
|
|
integer(pInt) :: instance,of,i,k,l,m,n
|
2018-11-28 00:19:04 +05:30
|
|
|
|
2015-01-21 20:44:00 +05:30
|
|
|
real(pReal), dimension(plastic_disloUCLA_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
|
2018-11-27 23:31:55 +05:30
|
|
|
gdot_slip_pos,gdot_slip_neg,tau_slip_pos,tau_slip_neg,dgdot_dtauslip_pos,dgdot_dtauslip_neg
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* Shortened notation
|
2016-01-15 05:49:44 +05:30
|
|
|
of = phasememberAt(ipc,ip,el)
|
2018-11-30 12:16:26 +05:30
|
|
|
instance = phase_plasticityInstance(phaseAt(ipc,ip,el))
|
2018-11-29 11:57:35 +05:30
|
|
|
associate(prm => param(instance))
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
Lp = 0.0_pReal
|
2018-11-28 11:14:32 +05:30
|
|
|
dLp_dMp = 0.0_pReal
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-30 12:16:26 +05:30
|
|
|
call kinetics(Mp,Temperature,instance,of, &
|
2018-11-27 23:49:36 +05:30
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
|
2018-11-29 03:08:14 +05:30
|
|
|
slipSystems: do i = 1_pInt, prm%totalNslip
|
|
|
|
Lp = Lp + (gdot_slip_pos(i)+gdot_slip_neg(i))*prm%Schmid_slip(1:3,1:3,i)
|
|
|
|
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
|
|
|
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
|
|
|
+ dgdot_dtauslip_pos(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_pos(m,n,i) &
|
|
|
|
+ dgdot_dtauslip_neg(i) * prm%Schmid_slip(k,l,i) * prm%nonSchmid_neg(m,n,i)
|
|
|
|
enddo slipSystems
|
2018-11-29 02:52:13 +05:30
|
|
|
end associate
|
2018-11-29 03:08:14 +05:30
|
|
|
|
|
|
|
Lp = 0.5_pReal * Lp
|
|
|
|
dLp_dMp = 0.5_pReal * dLp_dMp
|
|
|
|
|
2015-01-21 20:44:00 +05:30
|
|
|
end subroutine plastic_disloUCLA_LpAndItsTangent
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
!> @brief calculates the rate of change of microstructure
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
2018-11-30 14:34:41 +05:30
|
|
|
subroutine plastic_disloUCLA_dotState(Mp,Temperature,instance,of)
|
2014-11-06 00:41:09 +05:30
|
|
|
use prec, only: &
|
2016-05-29 14:15:03 +05:30
|
|
|
tol_math_check, &
|
2016-10-29 13:09:08 +05:30
|
|
|
dEq0
|
2014-11-06 00:41:09 +05:30
|
|
|
use math, only: &
|
|
|
|
pi
|
|
|
|
|
|
|
|
implicit none
|
2018-11-28 11:14:32 +05:30
|
|
|
real(pReal), dimension(3,3), intent(in):: &
|
|
|
|
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
2014-11-06 00:41:09 +05:30
|
|
|
real(pReal), intent(in) :: &
|
|
|
|
temperature !< temperature at integration point
|
|
|
|
integer(pInt), intent(in) :: &
|
2018-11-30 14:34:41 +05:30
|
|
|
instance, of
|
|
|
|
integer(pInt) :: ns,j
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
real(pReal) :: &
|
|
|
|
EdgeDipMinDistance,&
|
|
|
|
AtomicVolume,&
|
|
|
|
VacancyDiffusion,&
|
|
|
|
DotRhoMultiplication,&
|
|
|
|
EdgeDipDistance, &
|
|
|
|
DotRhoEdgeDipAnnihilation, &
|
|
|
|
DotRhoEdgeEdgeAnnihilation, &
|
|
|
|
ClimbVelocity, &
|
|
|
|
DotRhoEdgeDipClimb, &
|
2018-11-28 00:19:04 +05:30
|
|
|
DotRhoDipFormation
|
2018-11-30 14:34:41 +05:30
|
|
|
real(pReal), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
|
2018-11-27 23:11:33 +05:30
|
|
|
gdot_slip_pos, gdot_slip_neg,&
|
|
|
|
tau_slip_pos,&
|
2018-11-27 23:23:01 +05:30
|
|
|
tau_slip_neg, &
|
|
|
|
dgdot_dtauslip_neg,dgdot_dtauslip_pos
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2016-04-25 02:06:35 +05:30
|
|
|
ns = plastic_disloUCLA_totalNslip(instance)
|
2018-11-30 14:34:41 +05:30
|
|
|
dotState(instance)%whole(:,of) = 0.0_pReal
|
2016-04-25 02:06:35 +05:30
|
|
|
|
2018-11-29 13:26:57 +05:30
|
|
|
associate(prm => param(instance), stt => state(instance),mse => microstructure(instance))
|
2014-11-06 00:41:09 +05:30
|
|
|
!* Dislocation density evolution
|
2018-11-30 12:16:26 +05:30
|
|
|
call kinetics(Mp,Temperature,instance,of, &
|
2018-11-27 23:23:01 +05:30
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
|
2018-11-29 03:08:14 +05:30
|
|
|
dotState(instance)%accshear_slip(:,of) = (gdot_slip_pos+gdot_slip_neg)*0.5_pReal
|
|
|
|
|
2018-11-30 12:55:23 +05:30
|
|
|
do j = 1_pInt, prm%totalNslip
|
2018-11-28 00:19:04 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
!* Multiplication
|
2018-11-28 00:19:04 +05:30
|
|
|
DotRhoMultiplication = abs(dotState(instance)%accshear_slip(j,of))/&
|
2018-11-29 03:32:46 +05:30
|
|
|
(prm%burgers(j)* &
|
2018-11-29 13:26:57 +05:30
|
|
|
mse%mfp(j,of))
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* Dipole formation
|
|
|
|
EdgeDipMinDistance = &
|
2018-11-29 03:32:46 +05:30
|
|
|
plastic_disloUCLA_CEdgeDipMinDistance(instance)*prm%burgers(j)
|
2018-11-27 23:11:33 +05:30
|
|
|
if (dEq0(tau_slip_pos(j))) then
|
2014-11-06 00:41:09 +05:30
|
|
|
DotRhoDipFormation = 0.0_pReal
|
|
|
|
else
|
|
|
|
EdgeDipDistance = &
|
2018-11-30 12:55:23 +05:30
|
|
|
(3.0_pReal*prm%mu*prm%burgers(j))/&
|
2018-11-27 23:11:33 +05:30
|
|
|
(16.0_pReal*pi*abs(tau_slip_pos(j)))
|
2018-11-29 13:26:57 +05:30
|
|
|
if (EdgeDipDistance>mse%mfp(j,of)) EdgeDipDistance=mse%mfp(j,of)
|
2014-11-06 00:41:09 +05:30
|
|
|
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
|
|
|
|
DotRhoDipFormation = &
|
2018-11-29 03:32:46 +05:30
|
|
|
((2.0_pReal*EdgeDipDistance)/prm%burgers(j))*&
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%rhoEdge(j,of)*abs(dotState(instance)%accshear_slip(j,of))*plastic_disloUCLA_dipoleFormationFactor(instance)
|
2014-11-06 00:41:09 +05:30
|
|
|
endif
|
|
|
|
|
|
|
|
!* Spontaneous annihilation of 2 single edge dislocations
|
|
|
|
DotRhoEdgeEdgeAnnihilation = &
|
2018-11-29 03:32:46 +05:30
|
|
|
((2.0_pReal*EdgeDipMinDistance)/prm%burgers(j))*&
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%rhoEdge(j,of)*abs(dotState(instance)%accshear_slip(j,of))
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent
|
|
|
|
DotRhoEdgeDipAnnihilation = &
|
2018-11-29 03:32:46 +05:30
|
|
|
((2.0_pReal*EdgeDipMinDistance)/prm%burgers(j))*&
|
2018-11-29 11:57:35 +05:30
|
|
|
stt%rhoEdgeDip(j,of)*abs(dotState(instance)%accshear_slip(j,of))
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
!* Dislocation dipole climb
|
|
|
|
AtomicVolume = &
|
2018-11-29 03:32:46 +05:30
|
|
|
plastic_disloUCLA_CAtomicVolume(instance)*prm%burgers(j)**(3.0_pReal)
|
2014-11-06 00:41:09 +05:30
|
|
|
VacancyDiffusion = &
|
2015-01-21 20:44:00 +05:30
|
|
|
plastic_disloUCLA_D0(instance)*exp(-plastic_disloUCLA_Qsd(instance)/(kB*Temperature))
|
2018-11-27 23:11:33 +05:30
|
|
|
if (dEq0(tau_slip_pos(j))) then
|
2014-11-06 00:41:09 +05:30
|
|
|
DotRhoEdgeDipClimb = 0.0_pReal
|
|
|
|
else
|
|
|
|
ClimbVelocity = &
|
2018-11-30 12:55:23 +05:30
|
|
|
((3.0_pReal*prm%mu*VacancyDiffusion*AtomicVolume)/(2.0_pReal*pi*kB*Temperature))*&
|
2014-11-06 00:41:09 +05:30
|
|
|
(1/(EdgeDipDistance+EdgeDipMinDistance))
|
|
|
|
DotRhoEdgeDipClimb = &
|
2018-11-29 11:57:35 +05:30
|
|
|
(4.0_pReal*ClimbVelocity*stt%rhoEdgeDip(j,of))/(EdgeDipDistance-EdgeDipMinDistance)
|
2014-11-06 00:41:09 +05:30
|
|
|
endif
|
|
|
|
|
|
|
|
!* Edge dislocation density rate of change
|
2016-01-15 20:56:24 +05:30
|
|
|
dotState(instance)%rhoEdge(j,of) = &
|
2014-11-06 00:41:09 +05:30
|
|
|
DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
|
|
|
|
|
|
|
|
!* Edge dislocation dipole density rate of change
|
2016-01-15 20:56:24 +05:30
|
|
|
dotState(instance)%rhoEdgeDip(j,of) = &
|
2014-11-06 00:41:09 +05:30
|
|
|
DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
|
2018-11-28 00:19:04 +05:30
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-11-30 12:55:23 +05:30
|
|
|
enddo
|
2018-11-29 03:32:46 +05:30
|
|
|
end associate
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2015-01-21 20:44:00 +05:30
|
|
|
end subroutine plastic_disloUCLA_dotState
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
!> @brief return array of constitutive results
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
2018-11-30 14:34:41 +05:30
|
|
|
function plastic_disloUCLA_postResults(Mp,Temperature,instance,of) result(postResults)
|
2014-11-06 00:41:09 +05:30
|
|
|
use prec, only: &
|
2017-11-21 04:13:06 +05:30
|
|
|
dEq, dNeq0
|
2014-11-06 00:41:09 +05:30
|
|
|
use math, only: &
|
2018-11-28 11:14:32 +05:30
|
|
|
pi, &
|
2018-12-03 15:18:37 +05:30
|
|
|
math_mul33xx33
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
implicit none
|
2018-12-03 15:18:37 +05:30
|
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
|
|
Mp !< Mandel stress
|
|
|
|
real(pReal), intent(in) :: &
|
|
|
|
Temperature !< Mandel stress
|
|
|
|
integer(pInt), intent(in) :: &
|
|
|
|
instance, &
|
|
|
|
of
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2018-12-03 15:18:37 +05:30
|
|
|
real(pReal), dimension(sum(plastic_disloUCLA_sizePostResult(:,instance))) :: &
|
|
|
|
postResults
|
2014-11-06 00:41:09 +05:30
|
|
|
|
|
|
|
integer(pInt) :: &
|
2018-12-03 15:18:37 +05:30
|
|
|
o,c,i
|
|
|
|
real(pReal), dimension(param(instance)%totalNslip) :: &
|
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos, &
|
|
|
|
gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
|
2018-11-30 14:34:41 +05:30
|
|
|
|
2018-12-03 15:18:37 +05:30
|
|
|
associate( prm => param(instance), stt => state(instance), mse => microstructure(instance))
|
2018-11-30 14:34:41 +05:30
|
|
|
|
2018-11-29 03:32:46 +05:30
|
|
|
postResults = 0.0_pReal
|
2018-12-03 15:18:37 +05:30
|
|
|
c = 0_pInt
|
|
|
|
|
|
|
|
outputsLoop: do o = 1_pInt,size(prm%outputID)
|
|
|
|
select case(prm%outputID(o))
|
|
|
|
|
|
|
|
case (rho_ID)
|
|
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdge(1_pInt:prm%totalNslip,of)
|
|
|
|
case (rhoDip_ID)
|
|
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%rhoEdgeDip(1_pInt:prm%totalNslip,of)
|
|
|
|
case (shearrate_ID,stressexponent_ID)
|
|
|
|
call kinetics(Mp,Temperature,instance,of, &
|
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
|
|
|
|
|
|
|
|
if (prm%outputID(o) == shearrate_ID) then
|
|
|
|
postResults(c+1:c+prm%totalNslip) = (gdot_slip_pos + gdot_slip_neg)*0.5_pReal
|
|
|
|
elseif(prm%outputID(o) == stressexponent_ID) then
|
|
|
|
where (dNeq0(gdot_slip_pos+gdot_slip_neg))
|
|
|
|
postResults(c+1_pInt:c + prm%totalNslip) = (tau_slip_pos+tau_slip_neg) * 0.5_pReal &
|
|
|
|
/ (gdot_slip_pos+gdot_slip_neg) &
|
|
|
|
* (dgdot_dtauslip_pos+dgdot_dtauslip_neg)
|
|
|
|
else where
|
|
|
|
postResults(c+1_pInt:c + prm%totalNslip) = 0.0_pReal
|
|
|
|
end where
|
|
|
|
endif
|
|
|
|
case (accumulatedshear_ID)
|
|
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear_slip(1_pInt:prm%totalNslip, of)
|
|
|
|
case (mfp_ID)
|
|
|
|
postResults(c+1_pInt:c+prm%totalNslip) = mse%mfp(1_pInt:prm%totalNslip, of)
|
|
|
|
case (resolvedstress_ID)
|
|
|
|
do i = 1_pInt, prm%totalNslip
|
|
|
|
postResults(c+i) =math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))
|
|
|
|
enddo
|
|
|
|
case (thresholdstress_ID)
|
|
|
|
postResults(c+1_pInt:c+prm%totalNslip) = mse%threshold_stress(1_pInt:prm%totalNslip,of)
|
|
|
|
case (dipoleDistance_ID)
|
|
|
|
do i = 1_pInt, prm%totalNslip
|
|
|
|
if (dNeq0(abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))) then
|
|
|
|
postResults(c+i) = (3.0_pReal*prm%mu*prm%burgers(i)) &
|
|
|
|
/ (16.0_pReal*pi*abs(math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))))
|
|
|
|
else
|
|
|
|
postResults(c+i) = huge(1.0_pReal)
|
|
|
|
endif
|
|
|
|
postResults(c+i)=min(postResults(c+i),mse%mfp(i,of))
|
|
|
|
enddo
|
|
|
|
end select
|
|
|
|
|
|
|
|
c = c + prm%totalNslip
|
|
|
|
enddo outputsLoop
|
|
|
|
end associate
|
2018-11-27 22:55:06 +05:30
|
|
|
|
|
|
|
end function plastic_disloUCLA_postResults
|
|
|
|
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
|
|
!> @brief return array of constitutive results
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
2018-11-30 12:16:26 +05:30
|
|
|
subroutine kinetics(Mp,Temperature,instance,of, &
|
2018-11-27 22:55:06 +05:30
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg)
|
|
|
|
use prec, only: &
|
|
|
|
tol_math_check, &
|
|
|
|
dEq, dNeq0
|
|
|
|
use math, only: &
|
2018-11-28 11:14:32 +05:30
|
|
|
pi, &
|
|
|
|
math_mul33xx33
|
2018-11-27 22:55:06 +05:30
|
|
|
|
|
|
|
implicit none
|
2018-11-28 11:14:32 +05:30
|
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
|
|
Mp !< 2nd Piola Kirchhoff stress tensor in Mandel notation
|
2018-11-27 22:55:06 +05:30
|
|
|
real(pReal), intent(in) :: &
|
|
|
|
temperature !< temperature at integration point
|
|
|
|
integer(pInt), intent(in) :: &
|
2018-11-30 12:16:26 +05:30
|
|
|
instance,of
|
2018-11-27 22:55:06 +05:30
|
|
|
|
|
|
|
integer(pInt) :: &
|
2018-11-30 12:55:23 +05:30
|
|
|
i,j
|
2018-11-27 22:55:06 +05:30
|
|
|
real(pReal) :: StressRatio_p,StressRatio_pminus1,&
|
|
|
|
BoltzmannRatio,DotGamma0,stressRatio,&
|
|
|
|
dvel_slip, vel_slip
|
2018-11-28 11:48:50 +05:30
|
|
|
real(pReal), intent(out), dimension(plastic_disloUCLA_totalNslip(instance)) :: &
|
2018-11-27 22:55:06 +05:30
|
|
|
gdot_slip_pos,dgdot_dtauslip_pos,tau_slip_pos,gdot_slip_neg,dgdot_dtauslip_neg,tau_slip_neg
|
2018-11-29 13:26:57 +05:30
|
|
|
associate(prm => param(instance), stt => state(instance),mse => microstructure(instance))
|
2018-11-30 12:16:26 +05:30
|
|
|
|
2018-11-27 22:55:06 +05:30
|
|
|
|
|
|
|
|
2014-11-06 00:41:09 +05:30
|
|
|
gdot_slip_pos = 0.0_pReal
|
2014-11-06 02:23:25 +05:30
|
|
|
gdot_slip_neg = 0.0_pReal
|
|
|
|
dgdot_dtauslip_pos = 0.0_pReal
|
|
|
|
dgdot_dtauslip_neg = 0.0_pReal
|
2018-11-30 12:16:26 +05:30
|
|
|
do j = 1_pInt, prm%totalNslip
|
2014-11-07 16:53:34 +05:30
|
|
|
!* Boltzmann ratio
|
2018-11-29 03:32:46 +05:30
|
|
|
BoltzmannRatio = prm%H0kp(j)/(kB*Temperature)
|
2014-11-07 16:53:34 +05:30
|
|
|
!* Initial shear rates
|
2018-11-29 15:01:02 +05:30
|
|
|
DotGamma0 = stt%rhoEdge(j,of)*prm%burgers(j)*prm%v0(j)
|
2014-11-06 01:09:23 +05:30
|
|
|
!* Resolved shear stress on slip system
|
2018-11-29 03:32:46 +05:30
|
|
|
tau_slip_pos(j) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,j))
|
|
|
|
tau_slip_neg(j) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,j))
|
2014-11-07 16:53:34 +05:30
|
|
|
|
2018-11-29 13:26:57 +05:30
|
|
|
significantPositiveTau: if((abs(tau_slip_pos(j))-mse%threshold_stress(j, of)) > tol_math_check) then
|
2015-01-21 20:44:00 +05:30
|
|
|
!* Stress ratio
|
2018-11-29 13:26:57 +05:30
|
|
|
stressRatio = ((abs(tau_slip_pos(j))-mse%threshold_stress(j, of))/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+&
|
2018-11-29 13:14:31 +05:30
|
|
|
prm%tau_Peierls(j)))
|
2018-11-29 03:32:46 +05:30
|
|
|
stressRatio_p = stressRatio** prm%p(j)
|
|
|
|
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
|
2015-01-21 20:44:00 +05:30
|
|
|
!* Shear rates due to slip
|
2018-11-29 03:32:46 +05:30
|
|
|
vel_slip = 2.0_pReal*prm%burgers(j) &
|
|
|
|
* prm%kink_height(j) * prm%omega(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
* (tau_slip_pos(j) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
/ ( &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
)
|
2014-11-06 00:41:09 +05:30
|
|
|
|
2014-11-06 01:09:23 +05:30
|
|
|
gdot_slip_pos(j) = DotGamma0 &
|
2015-01-15 16:26:15 +05:30
|
|
|
* vel_slip &
|
2014-11-06 02:23:25 +05:30
|
|
|
* sign(1.0_pReal,tau_slip_pos(j))
|
|
|
|
!* Derivatives of shear rates
|
2015-01-21 20:44:00 +05:30
|
|
|
|
2014-11-06 02:23:25 +05:30
|
|
|
dvel_slip = &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*prm%burgers(j) &
|
|
|
|
* prm%kink_height(j) * prm%omega(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
* ( &
|
2018-11-29 03:32:46 +05:30
|
|
|
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
+ tau_slip_pos(j) &
|
2018-11-30 11:57:23 +05:30
|
|
|
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
|
2018-11-29 03:32:46 +05:30
|
|
|
*BoltzmannRatio*prm%p(j)&
|
|
|
|
*prm%q(j)/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+prm%tau_Peierls(j))*&
|
2018-11-30 11:57:23 +05:30
|
|
|
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
|
|
|
- (tau_slip_pos(j) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
|
|
|
|
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-30 11:57:23 +05:30
|
|
|
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
|
2018-11-29 03:32:46 +05:30
|
|
|
*BoltzmannRatio*prm%p(j)&
|
|
|
|
*prm%q(j)/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+prm%tau_Peierls(j))*&
|
2018-11-30 11:57:23 +05:30
|
|
|
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )&
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
|
|
|
) &
|
|
|
|
/ ( &
|
|
|
|
( &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_pos(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
)**2.0_pReal &
|
|
|
|
)
|
2015-01-15 16:26:15 +05:30
|
|
|
|
|
|
|
dgdot_dtauslip_pos(j) = DotGamma0 * dvel_slip
|
|
|
|
|
2016-01-15 20:56:24 +05:30
|
|
|
endif significantPositiveTau
|
2018-11-30 12:16:26 +05:30
|
|
|
|
|
|
|
|
2018-11-29 13:26:57 +05:30
|
|
|
significantNegativeTau: if((abs(tau_slip_neg(j))-mse%threshold_stress(j, of)) > tol_math_check) then
|
2014-11-06 02:23:25 +05:30
|
|
|
!* Stress ratios
|
2018-11-29 13:26:57 +05:30
|
|
|
stressRatio = ((abs(tau_slip_neg(j))-mse%threshold_stress(j, of))/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+&
|
2018-11-29 13:14:31 +05:30
|
|
|
prm%tau_Peierls(j)))
|
2018-11-29 03:32:46 +05:30
|
|
|
stressRatio_p = stressRatio** prm%p(j)
|
|
|
|
stressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal)
|
2014-11-06 02:23:25 +05:30
|
|
|
!* Shear rates due to slip
|
2018-11-29 03:32:46 +05:30
|
|
|
vel_slip = 2.0_pReal*prm%burgers(j) &
|
|
|
|
* prm%kink_height(j) * prm%omega(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
* (tau_slip_neg(j) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
/ ( &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
)
|
2015-01-15 16:26:15 +05:30
|
|
|
|
2014-11-06 02:23:25 +05:30
|
|
|
gdot_slip_neg(j) = DotGamma0 &
|
2015-01-15 16:26:15 +05:30
|
|
|
* vel_slip &
|
2014-11-06 02:23:25 +05:30
|
|
|
* sign(1.0_pReal,tau_slip_neg(j))
|
2014-11-06 01:09:23 +05:30
|
|
|
!* Derivatives of shear rates
|
|
|
|
dvel_slip = &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*prm%burgers(j) &
|
|
|
|
* prm%kink_height(j) * prm%omega(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
* ( mse%mfp(j,of) - prm%kink_width(j) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
* ( &
|
2018-11-29 03:32:46 +05:30
|
|
|
(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
+ tau_slip_neg(j) &
|
2018-11-30 11:57:23 +05:30
|
|
|
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
|
2018-11-29 03:32:46 +05:30
|
|
|
*BoltzmannRatio*prm%p(j)&
|
|
|
|
*prm%q(j)/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+prm%tau_Peierls(j))*&
|
2018-11-30 11:57:23 +05:30
|
|
|
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) ) &
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* (2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
|
|
|
- (tau_slip_neg(j) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) ) &
|
|
|
|
* (2.0_pReal*(prm%burgers(j)**2.0_pReal) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-30 11:57:23 +05:30
|
|
|
* (abs(exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)))&
|
2018-11-29 03:32:46 +05:30
|
|
|
*BoltzmannRatio*prm%p(j)&
|
|
|
|
*prm%q(j)/&
|
2018-11-29 15:01:02 +05:30
|
|
|
(prm%solidSolutionStrength+prm%tau_Peierls(j))*&
|
2018-11-30 11:57:23 +05:30
|
|
|
StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) )&
|
2015-01-16 04:10:17 +05:30
|
|
|
) &
|
|
|
|
) &
|
|
|
|
/ ( &
|
|
|
|
( &
|
2018-11-29 03:32:46 +05:30
|
|
|
2.0_pReal*(prm%burgers(j)**2.0_pReal)*tau_slip_neg(j) &
|
2018-11-29 15:07:06 +05:30
|
|
|
+ prm%omega(j) * prm%B(j) &
|
2018-11-29 13:26:57 +05:30
|
|
|
*(( mse%mfp(j,of) - prm%kink_width(j) )**2.0_pReal) &
|
2018-11-29 03:32:46 +05:30
|
|
|
* exp(-BoltzmannRatio*(1-StressRatio_p) ** prm%q(j)) &
|
2015-01-16 04:10:17 +05:30
|
|
|
)**2.0_pReal &
|
|
|
|
)
|
2015-01-15 16:26:15 +05:30
|
|
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|
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|
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dgdot_dtauslip_neg(j) = DotGamma0 * dvel_slip
|
2018-11-30 12:16:26 +05:30
|
|
|
endif significantNegativeTau
|
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enddo
|
2018-11-29 03:32:46 +05:30
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|
end associate
|
2018-11-27 22:55:06 +05:30
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|
end subroutine kinetics
|
2014-11-06 00:41:09 +05:30
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|
2015-01-21 20:44:00 +05:30
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|
end module plastic_disloUCLA
|