778 lines
36 KiB
Fortran
778 lines
36 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Philip Eisenlohr, Michigan State University
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!> @author Zhuowen Zhao, Michigan State University
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Phenomenological crystal plasticity using a power law formulation for the shear rates
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!! and a Voce-type kinematic hardening rule
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!--------------------------------------------------------------------------------------------------
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module plastic_kinehardening
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use prec, only: &
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pReal,&
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pInt
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implicit none
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private
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integer(pInt), dimension(:,:), allocatable, target, public :: &
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plastic_kinehardening_sizePostResult !< size of each post result output
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character(len=64), dimension(:,:), allocatable, target, public :: &
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plastic_kinehardening_output !< name of each post result output
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integer(pInt), dimension(:), allocatable, target, public :: &
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plastic_kinehardening_Noutput !< number of outputs per instance
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integer(pInt), dimension(:), allocatable, public, protected :: &
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plastic_kinehardening_totalNslip !< no. of slip system used in simulation
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integer(pInt), dimension(:,:), allocatable, private :: &
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plastic_kinehardening_Nslip !< active number of slip systems per family (input parameter, per family)
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enum, bind(c)
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enumerator :: &
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undefined_ID, &
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crss_ID, & !< critical resolved stress
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crss_back_ID, & !< critical resolved back stress
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sense_ID, & !< sense of acting shear stress (-1 or +1)
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chi0_ID, & !< backstress at last switch of stress sense (positive?)
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gamma0_ID, & !< accumulated shear at last switch of stress sense (at current switch?)
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accshear_ID, &
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shearrate_ID, &
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resolvedstress_ID
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end enum
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type, private :: tParameters !< container type for internal constitutive parameters
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real(pReal) :: &
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gdot0, & !< reference shear strain rate for slip (input parameter)
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n_slip, & !< stress exponent for slip (input parameter)
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aTolResistance, &
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aTolShear
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real(pReal), dimension(:), allocatable, private :: &
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crss0, & !< initial critical shear stress for slip (input parameter, per family)
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theta0, & !< initial hardening rate of forward stress for each slip
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theta1, & !< asymptotic hardening rate of forward stress for each slip >
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theta0_b, & !< initial hardening rate of back stress for each slip >
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theta1_b, & !< asymptotic hardening rate of back stress for each slip >
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tau1, &
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tau1_b, &
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nonSchmidCoeff
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real(pReal), dimension(:,:), allocatable, private :: &
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interaction_slipslip !< latent hardening matrix
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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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real(pReal), dimension(:,:), allocatable, private :: &
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hardeningMatrix_SlipSlip
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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
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type, private :: tKinehardeningState
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real(pReal), pointer, dimension(:,:) :: & !< vectors along NipcMyInstance
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crss, & !< critical resolved stress
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crss_back, & !< critical resolved back stress
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sense, & !< sense of acting shear stress (-1 or +1)
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chi0, & !< backstress at last switch of stress sense
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gamma0, & !< accumulated shear at last switch of stress sense
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accshear !< accumulated (absolute) shear
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end type
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type(tParameters), dimension(:), allocatable, private :: &
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param, & !< containers of constitutive parameters (len Ninstance)
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paramNew ! temp
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type(tKinehardeningState), allocatable, dimension(:), private :: &
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dotState, &
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deltaState, &
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state, &
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state0
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public :: &
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plastic_kinehardening_init, &
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plastic_kinehardening_LpAndItsTangent, &
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plastic_kinehardening_dotState, &
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plastic_kinehardening_deltaState, &
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plastic_kinehardening_postResults
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private :: &
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plastic_kinehardening_shearRates
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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_kinehardening_init
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran 4.6 at the moment)
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use prec, only: &
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dEq0
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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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use IO, only: &
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IO_error, &
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IO_timeStamp
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use material, only: &
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phase_plasticity, &
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phase_plasticityInstance, &
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phase_Noutput, &
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material_allocatePlasticState, &
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PLASTICITY_kinehardening_label, &
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PLASTICITY_kinehardening_ID, &
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material_phase, &
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plasticState
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use config, only: &
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config_phase, &
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MATERIAL_partPhase
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use lattice
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implicit none
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integer(kind(undefined_ID)) :: &
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output_ID
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integer(pInt) :: &
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o, i, p, &
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phase, &
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instance, &
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maxNinstance, &
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NipcMyPhase, &
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outputSize, &
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offset_slip, &
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startIndex, endIndex, &
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nSlip, &
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sizeDotState, &
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sizeState, &
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sizeDeltaState
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integer(pInt), dimension(0), parameter :: emptyIntArray = [integer(pInt)::]
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real(pReal), dimension(0), parameter :: emptyRealArray = [real(pReal)::]
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character(len=65536), dimension(0), parameter :: emptyStringArray = [character(len=65536)::]
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integer(kind(undefined_ID)) :: &
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outputID !< ID of each post result output
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character(len=65536), dimension(:), allocatable :: &
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outputs
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character(len=65536) :: &
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tag = '', &
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extmsg = '', &
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structure = ''
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write(6,'(/,a)') ' <<<+- constitutive_'//PLASTICITY_KINEHARDENING_label//' init -+>>>'
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write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
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#include "compilation_info.f90"
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maxNinstance = int(count(phase_plasticity == PLASTICITY_KINEHARDENING_ID),pInt)
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if (maxNinstance == 0_pInt) return
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if (iand(debug_level(debug_constitutive),debug_levelBasic) /= 0_pInt) &
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write(6,'(a,1x,i5,/)') '# instances:',maxNinstance
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allocate(plastic_kinehardening_sizePostResult(maxval(phase_Noutput),maxNinstance), &
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source=0_pInt)
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allocate(plastic_kinehardening_output(maxval(phase_Noutput),maxNinstance))
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plastic_kinehardening_output = ''
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allocate(plastic_kinehardening_Noutput(maxNinstance), source=0_pInt)
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allocate(plastic_kinehardening_Nslip(lattice_maxNslipFamily,maxNinstance), source=0_pInt)
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allocate(plastic_kinehardening_totalNslip(maxNinstance), source=0_pInt)
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allocate(param(maxNinstance)) ! one container of parameters per instance
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allocate(paramNew(maxNinstance))
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allocate(state(maxNinstance))
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allocate(state0(maxNinstance))
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allocate(dotState(maxNinstance))
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allocate(deltaState(maxNinstance))
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do p = 1_pInt, size(phase_plasticityInstance)
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if (phase_plasticity(p) /= PLASTICITY_KINEHARDENING_ID) cycle
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instance = phase_plasticityInstance(p) ! which instance of my phase
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associate(prm => paramNew(phase_plasticityInstance(p)), &
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dot => dotState(phase_plasticityInstance(p)), &
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delta => deltaState(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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!--------------------------------------------------------------------------------------------------
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! optional parameters that need to be defined
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prm%aTolResistance = config_phase(p)%getFloat('atol_resistance',defaultVal=1.0_pReal)
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prm%aTolShear = config_phase(p)%getFloat('atol_shear', defaultVal=1.0e-6_pReal)
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! sanity checks
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if (prm%aTolResistance <= 0.0_pReal) extmsg = trim(extmsg)//'aTolresistance '
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if (prm%aTolShear <= 0.0_pReal) extmsg = trim(extmsg)//'aTolShear '
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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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prm%crss0 = config_phase(p)%getFloats('crss0', requiredShape=shape(prm%Nslip))
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prm%tau1 = config_phase(p)%getFloats('tau1', requiredShape=shape(prm%Nslip))
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prm%tau1_b = config_phase(p)%getFloats('tau1_b', requiredShape=shape(prm%Nslip))
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prm%theta0 = config_phase(p)%getFloats('theta0', requiredShape=shape(prm%Nslip))
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prm%theta1 = config_phase(p)%getFloats('theta1', requiredShape=shape(prm%Nslip))
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prm%theta0_b = config_phase(p)%getFloats('theta0_b', requiredShape=shape(prm%Nslip))
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prm%theta1_b = config_phase(p)%getFloats('theta1_b', requiredShape=shape(prm%Nslip))
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! expand: family => system
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!prm%crss0 = math_expand(prm%crss0, prm%Nslip)
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prm%tau1 = math_expand(prm%tau1,prm%Nslip)
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prm%tau1_b = math_expand(prm%tau1_b, prm%Nslip)
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prm%theta0 = math_expand(prm%theta0,prm%Nslip)
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prm%theta1 = math_expand(prm%theta1,prm%Nslip)
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prm%theta0_b = math_expand(prm%theta0_b,prm%Nslip)
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prm%theta1_b = math_expand(prm%theta1_b,prm%Nslip)
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prm%gdot0 = config_phase(p)%getFloat('gdot0')
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prm%n_slip = config_phase(p)%getFloat('n_slip')
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endif slipActive
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!--------------------------------------------------------------------------------------------------
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! output pararameters
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outputs = config_phase(p)%getStrings('(output)',defaultVal=emptyStringArray)
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allocate(prm%outputID(0))
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do i=1_pInt, size(outputs)
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outputID = undefined_ID
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select case(outputs(i))
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case ('resistance')
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outputID = merge(crss_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('accumulatedshear')
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outputID = merge(accshear_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('shearrate')
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outputID = merge(shearrate_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('resolvedstress')
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outputID = merge(resolvedstress_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('backstress')
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outputID = merge(crss_back_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('sense')
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outputID = merge(sense_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('chi0')
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outputID = merge(chi0_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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case ('gamma0')
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outputID = merge(gamma0_ID,undefined_ID,prm%totalNslip>0_pInt)
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outputSize = prm%totalNslip
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end select
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if (outputID /= undefined_ID) then
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plastic_kinehardening_Noutput(instance) = plastic_kinehardening_Noutput(instance) + 1_pInt
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plastic_kinehardening_output(i,phase_plasticityInstance(p)) = outputs(i)
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plastic_kinehardening_sizePostResult(i,phase_plasticityInstance(p)) = outputSize
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prm%outputID = [prm%outputID , outputID]
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endif
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end do
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param(instance)%outputID = prm%outputID
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nslip = prm%totalNslip
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!--------------------------------------------------------------------------------------------------
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! allocate state arrays
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sizeDotState = nSlip & !< crss
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+ nSlip & !< crss_back
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+ nSlip !< accumulated (absolute) shear
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sizeDeltaState = nSlip & !< sense of acting shear stress (-1 or +1)
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+ nSlip & !< backstress at last switch of stress sense
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+ nSlip !< accumulated shear at last switch of stress sense
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sizeState = sizeDotState + sizeDeltaState
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NipcMyPhase = count(material_phase == p) ! number of IPCs containing my phase
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call material_allocatePlasticState(p,NipcMyPhase,sizeState,sizeDotState,sizeDeltaState, &
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nSlip,0_pInt,0_pInt)
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plasticState(p)%sizePostResults = sum(plastic_kinehardening_sizePostResult(:,phase_plasticityInstance(p)))
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plasticState(p)%offsetDeltaState = sizeDotState
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endindex = 0_pInt
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o = endIndex ! offset of dotstate index relative to state index
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%crss => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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dot%crss => plasticState(p)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
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plasticState(p)%aTolState(startIndex-o:endIndex-o) = prm%aTolResistance
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! .............................................
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%crss_back => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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dot%crss_back => plasticState(p)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
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plasticState(p)%aTolState(startIndex-o:endIndex-o) = prm%aTolResistance
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! .............................................
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%accshear => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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dot%accshear => plasticState(p)%dotState (startIndex-o:endIndex-o,1:NipcMyPhase)
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plasticState(p)%aTolState(startIndex-o:endIndex-o) = prm%aTolShear
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!----------------------------------------------------------------------------------------------
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!locally define deltaState alias
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o = endIndex
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! .............................................
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%sense => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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delta%sense => plasticState(p)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
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! .............................................
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%chi0 => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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delta%chi0 => plasticState(p)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
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! .............................................
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + nSlip
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stt%gamma0 => plasticState(p)%state (startIndex :endIndex ,1:NipcMyPhase)
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delta%gamma0 => plasticState(p)%deltaState(startIndex-o:endIndex-o,1:NipcMyPhase)
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end associate
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end do
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!--------------------------------------------------------------------------------------------------
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! allocation of variables whose size depends on the total number of active slip systems
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initializeInstances: do phase = 1_pInt, size(phase_plasticity) ! loop through all phases in material.config
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myPhase2: if (phase_plasticity(phase) == PLASTICITY_KINEHARDENING_ID) then ! only consider my phase
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NipcMyPhase = count(material_phase == phase) ! number of IPCs containing my phase
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instance = phase_plasticityInstance(phase) ! which instance of my phase
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!--------------------------------------------------------------------------------------------------
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! sanity checks
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! if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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! .and. param(instance)%crss0 (1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' crss0'
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! if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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! .and. param(instance)%tau1 (1:nSlipFamilies) <= 0.0_pReal)) extmsg = trim(extmsg)//' tau1'
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! if (any(plastic_kinehardening_Nslip (1:nSlipFamilies,instance) > 0_pInt &
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! .and. param(instance)%tau1_b(1:nSlipFamilies) < 0.0_pReal)) extmsg = trim(extmsg)//' tau1_b'
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! if (param(instance)%gdot0 <= 0.0_pReal) extmsg = trim(extmsg)//' gdot0'
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! if (param(instance)%n_slip <= 0.0_pReal) extmsg = trim(extmsg)//' n_slip'
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if (extmsg /= '') then
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extmsg = trim(extmsg)//' ('//PLASTICITY_KINEHARDENING_label//')' ! prepare error message identifier
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call IO_error(211_pInt,ip=instance,ext_msg=extmsg)
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endif
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offset_slip = plasticState(phase)%nSlip
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plasticState(phase)%slipRate => &
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plasticState(phase)%dotState(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
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plasticState(phase)%accumulatedSlip => &
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plasticState(phase)%state(offset_slip+1:offset_slip+plasticState(phase)%nSlip,1:NipcMyPhase)
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endindex = 0_pInt
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o = endIndex ! offset of dotstate index relative to state index
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startIndex = endIndex + 1_pInt
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endIndex = endIndex + paramNew(instance)%totalNslip
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state0 (instance)%crss => plasticState(phase)%state0 (startIndex :endIndex ,1:NipcMyPhase)
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state0(instance)%crss = spread(math_expand(paramNew(instance)%crss0,&
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|
paramNew(instance)%Nslip), &
|
|
2, NipcMyPhase)
|
|
endif myPhase2
|
|
enddo initializeInstances
|
|
|
|
end subroutine plastic_kinehardening_init
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculation of shear rates (\dot \gamma)
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Mp,instance,of)
|
|
|
|
use math
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp
|
|
integer(pInt), intent(in) :: &
|
|
instance, & !< instance of that phase
|
|
of !< index of phaseMember
|
|
real(pReal), dimension(paramNew(instance)%totalNslip), intent(out) :: &
|
|
gdot_pos, & !< shear rates from positive line segments
|
|
gdot_neg, & !< shear rates from negative line segments
|
|
tau_pos, & !< shear stress on positive line segments
|
|
tau_neg !< shear stress on negative line segments
|
|
|
|
integer(pInt) :: &
|
|
i
|
|
|
|
associate(prm => paramNew(instance), stt => state(instance))
|
|
do i = 1_pInt, prm%totalNslip
|
|
tau_pos(i) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))
|
|
tau_neg(i) = math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,i))
|
|
enddo
|
|
|
|
tau_pos = tau_pos - stt%crss_back(:,of)
|
|
tau_neg = tau_neg - stt%crss_back(:,of)
|
|
|
|
gdot_pos = sign(0.5_pReal * prm%gdot0 *(abs(tau_pos)/ state(instance)%crss(:,of))**prm%n_slip,tau_pos)
|
|
gdot_neg = sign(0.5_pReal * prm%gdot0 *(abs(tau_neg)/ state(instance)%crss(:,of))**prm%n_slip,tau_neg)
|
|
|
|
end associate
|
|
end subroutine plastic_kinehardening_shearRates
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates plastic velocity gradient and its tangent
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_LpAndItsTangent(Lp,dLp_dMp,Mp,instance,of)
|
|
use prec, only: &
|
|
dNeq0
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(out) :: &
|
|
Lp !< plastic velocity gradient
|
|
real(pReal), dimension(3,3,3,3), intent(out) :: &
|
|
dLp_dMp !< derivative of Lp with respect to the Mandel stress
|
|
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer(pInt), intent(in) :: &
|
|
instance, &
|
|
of
|
|
|
|
integer(pInt) :: &
|
|
j,k,l,m,n
|
|
|
|
|
|
real(pReal), dimension(paramNew(instance)%totalNslip) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg, &
|
|
dgdot_dtau_pos,dgdot_dtau_neg
|
|
|
|
associate(prm => paramNew(instance), stt => state(instance))
|
|
Lp = 0.0_pReal
|
|
dLp_dMp = 0.0_pReal
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Mp,instance,of)
|
|
where (dNeq0(gdot_pos))
|
|
dgdot_dtau_pos = gdot_pos*prm%n_slip/tau_pos
|
|
else where
|
|
dgdot_dtau_pos = 0.0_pReal
|
|
end where
|
|
|
|
where (dNeq0(gdot_neg))
|
|
dgdot_dtau_neg = gdot_neg*prm%n_slip/tau_neg
|
|
else where
|
|
dgdot_dtau_neg = 0.0_pReal
|
|
end where
|
|
|
|
do j = 1_pInt, prm%totalNslip
|
|
Lp = Lp + (gdot_pos(j)+gdot_neg(j))*prm%Schmid_slip(1:3,1:3,j)
|
|
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
|
|
dLp_dMp(k,l,m,n) = dLp_dMp(k,l,m,n) &
|
|
+ dgdot_dtau_pos(j)*prm%Schmid_slip(k,l,j)*prm%nonSchmid_pos(m,n,j) &
|
|
+ dgdot_dtau_neg(j)*prm%Schmid_slip(k,l,j)*prm%nonSchmid_neg(m,n,j)
|
|
enddo
|
|
end associate
|
|
|
|
end subroutine plastic_kinehardening_LpAndItsTangent
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates (instantaneous) incremental change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_deltaState(Mp,instance,of)
|
|
use prec, only: &
|
|
dNeq, &
|
|
dEq0
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer(pInt), intent(in) :: &
|
|
instance, &
|
|
of
|
|
|
|
real(pReal), dimension(paramNew(instance)%totalNslip) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg, &
|
|
sense
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Mp,instance,of)
|
|
sense = merge(state(instance)%sense(:,of), & ! keep existing...
|
|
sign(1.0_pReal,gdot_pos+gdot_neg), & ! ...or have a defined
|
|
dEq0(gdot_pos+gdot_neg,1e-10_pReal)) ! current sense of shear direction
|
|
|
|
#ifdef DEBUG
|
|
! if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
|
|
! .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
|
|
! .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
! write(6,'(a)') '======= kinehardening delta state ======='
|
|
! endif
|
|
#endif
|
|
|
|
|
|
#ifdef DEBUG
|
|
! if (iand(debug_level(debug_constitutive), debug_levelExtensive) /= 0_pInt &
|
|
! .and. ((el == debug_e .and. ip == debug_i .and. ipc == debug_g) &
|
|
! .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt)) then
|
|
! write(6,'(i2,1x,f7.4,1x,f7.4)') j,sense(j),state(instance)%sense(j,of)
|
|
! endif
|
|
#endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! switch in sense of shear?
|
|
where(dNeq(sense,state(instance)%sense(:,of),0.1_pReal))
|
|
deltaState(instance)%sense (:,of) = sense - state(instance)%sense(:,of) ! switch sense
|
|
deltaState(instance)%chi0 (:,of) = abs(state(instance)%crss_back(:,of)) - state(instance)%chi0(:,of) ! remember current backstress magnitude
|
|
deltaState(instance)%gamma0(:,of) = state(instance)%accshear(:,of) - state(instance)%gamma0(:,of) ! remember current accumulated shear
|
|
else where
|
|
deltaState(instance)%sense (:,of) = 0.0_pReal ! no change
|
|
deltaState(instance)%chi0 (:,of) = 0.0_pReal
|
|
deltaState(instance)%gamma0(:,of) = 0.0_pReal
|
|
end where
|
|
|
|
end subroutine plastic_kinehardening_deltaState
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates the rate of change of microstructure
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine plastic_kinehardening_dotState(Mp,instance,of)
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer(pInt), intent(in) :: &
|
|
instance, &
|
|
of !< element !< microstructure state
|
|
|
|
integer(pInt) :: &
|
|
j
|
|
|
|
real(pReal), dimension(paramNew(instance)%totalNslip) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg
|
|
real(pReal) :: &
|
|
sumGamma
|
|
|
|
|
|
associate( prm => paramNew(instance), stt => state(instance), dot => dotState(instance))
|
|
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Mp,instance,of)
|
|
|
|
dot%accshear(:,of) = abs(gdot_pos+gdot_neg)
|
|
sumGamma = sum(stt%accshear(:,of))
|
|
|
|
do j = 1_pInt, prm%totalNslip
|
|
dot%crss(j,of) = &
|
|
dot_product(prm%interaction_SlipSlip(j,:),dot%accshear(:,of)) * &
|
|
( prm%theta1(j) + (prm%theta0(j) - prm%theta1(j) &
|
|
+ prm%theta0(j)*prm%theta1(j)*sumGamma/prm%tau1(j)) &
|
|
*exp(-sumGamma*prm%theta0(j)/prm%tau1(j)) & ! V term depending on the harding law
|
|
)
|
|
enddo
|
|
dot%crss_back(:,of) = &
|
|
stt%sense(:,of)*dot%accshear(:,of) * &
|
|
( prm%theta1_b + &
|
|
(prm%theta0_b - prm%theta1_b &
|
|
+ prm%theta0_b*prm%theta1_b/(prm%tau1_b+stt%chi0(:,of))*(stt%accshear(:,of)-stt%gamma0(:,of))&
|
|
) &
|
|
*exp(-(stt%accshear(:,of)-stt%gamma0(:,of)) *prm%theta0_b/(prm%tau1_b+stt%chi0(:,of))) &
|
|
) ! V term depending on the harding law for back stress
|
|
|
|
end associate
|
|
|
|
end subroutine plastic_kinehardening_dotState
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief return array of constitutive results
|
|
!--------------------------------------------------------------------------------------------------
|
|
function plastic_kinehardening_postResults(Mp,instance,of) result(postResults)
|
|
use math, only: &
|
|
math_mul33xx33
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp !< Mandel stress
|
|
integer(pInt), intent(in) :: &
|
|
instance, &
|
|
of
|
|
|
|
real(pReal), dimension(sum(plastic_kinehardening_sizePostResult(:,instance))) :: &
|
|
postResults
|
|
integer(pInt) :: &
|
|
o,c,j
|
|
|
|
real(pReal), dimension(paramNew(instance)%totalNslip) :: &
|
|
gdot_pos,gdot_neg, &
|
|
tau_pos,tau_neg
|
|
|
|
postResults = 0.0_pReal
|
|
c = 0_pInt
|
|
|
|
call plastic_kinehardening_shearRates(gdot_pos,gdot_neg,tau_pos,tau_neg, &
|
|
Mp,instance,of)
|
|
associate( prm => paramNew(instance), stt => state(instance))
|
|
outputsLoop: do o = 1_pInt,plastic_kinehardening_Noutput(instance)
|
|
select case(prm%outputID(o))
|
|
case (crss_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%crss(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case(crss_back_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%crss_back(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case (sense_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%sense(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case (chi0_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%chi0(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case (gamma0_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%gamma0(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case (accshear_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = stt%accshear(:,of)
|
|
c = c + prm%totalNslip
|
|
|
|
case (shearrate_ID)
|
|
postResults(c+1_pInt:c+prm%totalNslip) = gdot_pos+gdot_neg
|
|
c = c + prm%totalNslip
|
|
|
|
case (resolvedstress_ID)
|
|
do j = 1_pInt, prm%totalNslip
|
|
postResults(c+j) = math_mul33xx33(Mp,prm%Schmid_slip(1:3,1:3,j))
|
|
enddo
|
|
c = c + prm%totalNslip
|
|
|
|
end select
|
|
enddo outputsLoop
|
|
end associate
|
|
|
|
end function plastic_kinehardening_postResults
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates shear rates on slip systems and derivatives with respect to resolved stress
|
|
!> @details: Shear rates 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(prm,stt,of,Mp,gdot_pos,gdot_neg,dgdot_dtau_pos,dgdot_dtau_neg)
|
|
use prec, only: &
|
|
dNeq0
|
|
use math, only: &
|
|
math_mul33xx33
|
|
|
|
implicit none
|
|
type(tParameters), intent(in) :: &
|
|
prm
|
|
type(tKinehardeningState), intent(in) :: &
|
|
stt
|
|
integer(pInt), intent(in) :: &
|
|
of
|
|
real(pReal), dimension(prm%totalNslip), intent(out) :: &
|
|
gdot_pos, &
|
|
gdot_neg
|
|
real(pReal), dimension(prm%totalNslip), optional, intent(out) :: &
|
|
dgdot_dtau_pos, &
|
|
dgdot_dtau_neg
|
|
real(pReal), dimension(3,3), intent(in) :: &
|
|
Mp
|
|
|
|
real(pReal), dimension(prm%totalNslip) :: &
|
|
tau_pos, &
|
|
tau_neg
|
|
integer(pInt) :: i
|
|
logical :: nonSchmidActive
|
|
|
|
nonSchmidActive = size(prm%nonSchmidCoeff) > 0_pInt
|
|
|
|
do i = 1_pInt, prm%totalNslip
|
|
tau_pos(i) = math_mul33xx33(Mp,prm%nonSchmid_pos(1:3,1:3,i))
|
|
tau_neg(i) = merge(math_mul33xx33(Mp,prm%nonSchmid_neg(1:3,1:3,i)), &
|
|
0.0_pReal, nonSchmidActive)
|
|
enddo
|
|
|
|
tau_pos = tau_pos - stt%crss_back(:,of)
|
|
tau_neg = tau_neg - stt%crss_back(:,of)
|
|
|
|
where(dNeq0(tau_pos))
|
|
gdot_pos = prm%gdot0 * merge(0.5_pReal,1.0_pReal, nonSchmidActive) & ! 1/2 if non-Schmid active
|
|
* sign(abs(tau_pos/stt%crss(:,of))**prm%n_slip, tau_pos)
|
|
else where
|
|
gdot_pos = 0.0_pReal
|
|
end where
|
|
|
|
where(dNeq0(tau_neg))
|
|
gdot_neg = prm%gdot0 * 0.5_pReal & ! only used if non-Schmid active, always 1/2
|
|
* sign(abs(tau_neg/stt%crss(:,of))**prm%n_slip, tau_neg)
|
|
else where
|
|
gdot_neg = 0.0_pReal
|
|
end where
|
|
|
|
if (present(dgdot_dtau_pos)) then
|
|
where(dNeq0(gdot_pos))
|
|
dgdot_dtau_pos = gdot_pos*prm%n_slip/tau_pos
|
|
else where
|
|
dgdot_dtau_pos = 0.0_pReal
|
|
end where
|
|
endif
|
|
if (present(dgdot_dtau_neg)) then
|
|
where(dNeq0(gdot_neg))
|
|
dgdot_dtau_neg = gdot_neg*prm%n_slip/tau_neg
|
|
else where
|
|
dgdot_dtau_neg = 0.0_pReal
|
|
end where
|
|
endif
|
|
|
|
end subroutine kinetics
|
|
|
|
end module plastic_kinehardening
|