1113 lines
60 KiB
Fortran
1113 lines
60 KiB
Fortran
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!************************************
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!* Module: CONSTITUTIVE_NONLOCAL *
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!************************************
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!* contains: *
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!* - constitutive equations *
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!* - parameters definition *
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!************************************
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MODULE constitutive_nonlocal
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!* Include other modules
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use prec, only: pReal,pInt
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implicit none
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!* Definition of parameters
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character (len=*), parameter :: constitutive_nonlocal_label = 'nonlocal'
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character(len=16), dimension(7), parameter :: constitutive_nonlocal_stateList = (/ 'rhoEdgePos ', &
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'rhoEdgeNeg ', &
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'rhoScrewPos ', &
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'rhoScrewNeg ', &
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'rhoForest ', &
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'tauSlipThreshold', &
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'backStress_v ' /) ! list of microstructural state variables
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character(len=16), dimension(4), parameter :: constitutive_nonlocal_stateListBasic = constitutive_nonlocal_stateList(1:4) ! list of "basic" microstructural state variables that are independent from other state variables
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character(len=16), dimension(3), parameter :: constitutive_nonlocal_stateListDependent = constitutive_nonlocal_stateList(5:7) ! list of microstructural state variables that depend on other state variables
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real(pReal), parameter :: kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin
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!* Definition of global variables
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integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_sizeDotState, & ! number of dotStates
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constitutive_nonlocal_sizeState, & ! total number of microstructural state variables
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constitutive_nonlocal_sizePostResults ! cumulative size of post results
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integer(pInt), dimension(:,:), allocatable, target :: constitutive_nonlocal_sizePostResult ! size of each post result output
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character(len=64), dimension(:,:), allocatable, target :: constitutive_nonlocal_output ! name of each post result output
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character(len=32), dimension(:), allocatable :: constitutive_nonlocal_structureName ! name of the lattice structure
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integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_structure, & ! number representing the kind of lattice structure
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constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance
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integer(pInt), dimension(:,:), allocatable :: constitutive_nonlocal_Nslip, & ! number of active slip systems for each family and instance
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constitutive_nonlocal_slipFamily, & ! lookup table relating active slip system to slip family for each instance
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constitutive_nonlocal_slipSystemLattice ! lookup table relating active slip system index to lattice slip system index for each instance
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real(pReal), dimension(:), allocatable :: constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice
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constitutive_nonlocal_C11, & ! C11 element in elasticity matrix
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constitutive_nonlocal_C12, & ! C12 element in elasticity matrix
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constitutive_nonlocal_C13, & ! C13 element in elasticity matrix
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constitutive_nonlocal_C33, & ! C33 element in elasticity matrix
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constitutive_nonlocal_C44, & ! C44 element in elasticity matrix
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constitutive_nonlocal_Gmod, & ! shear modulus
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constitutive_nonlocal_nu ! poisson's ratio
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real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance
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real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance
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real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_rhoEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance
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constitutive_nonlocal_rhoScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance
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constitutive_nonlocal_v0BySlipFamily, & ! initial dislocation velocity [m/s] for each family and instance
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constitutive_nonlocal_v0BySlipSystem, & ! initial dislocation velocity [m/s] for each slip system and instance
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constitutive_nonlocal_burgersBySlipFamily, & ! absolute length of burgers vector [m] for each family and instance
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constitutive_nonlocal_burgersBySlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
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constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
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real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each instance
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constitutive_nonlocal_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance
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constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance
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CONTAINS
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!****************************************
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!* - constitutive_init
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!* - constitutive_stateInit
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!* - constitutive_homogenizedC
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!* - constitutive_microstructure
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!* - constitutive_LpAndItsTangent
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!* - constitutive_dotState
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!* - constitutive_dotTemperature
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!* - constitutive_postResults
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!****************************************
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!**************************************
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!* Module initialization *
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!**************************************
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subroutine constitutive_nonlocal_init(file)
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use prec, only: pInt, pReal
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use math, only: math_Mandel3333to66, &
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math_Voigt66to3333, &
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math_mul3x3
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use IO, only: IO_lc, &
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IO_getTag, &
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IO_isBlank, &
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IO_stringPos, &
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IO_stringValue, &
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IO_floatValue, &
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IO_intValue, &
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IO_error
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use material, only: phase_constitution, &
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phase_constitutionInstance, &
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phase_Noutput
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use lattice, only: lattice_maxNslipFamily, &
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lattice_maxNtwinFamily, &
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lattice_maxNslip, &
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lattice_maxNtwin, &
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lattice_maxNinteraction, &
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lattice_NslipSystem, &
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lattice_NtwinSystem, &
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lattice_initializeStructure, &
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lattice_Qtwin, &
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lattice_sd, &
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lattice_sn, &
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lattice_st, &
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lattice_interactionSlipSlip
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!*** output variables
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!*** input variables
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integer(pInt), intent(in) :: file
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!*** local variables
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integer(pInt), parameter :: maxNchunks = 21
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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integer(pInt) section, &
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maxNinstance, &
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maxTotalNslip, &
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myStructure, &
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f, & ! index of my slip family
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i, & ! index of my instance of this constitution
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j, &
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k, &
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l, &
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o, & ! index of my output
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s, & ! index of my slip system
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s1, & ! index of my slip system
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s2, & ! index of my slip system
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output, &
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mySize
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character(len=64) tag
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character(len=1024) line
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write(6,*)
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write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_nonlocal_label,' init -+>>>'
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write(6,*)
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maxNinstance = count(phase_constitution == constitutive_nonlocal_label)
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if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law
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!*** space allocation for global variables
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allocate(constitutive_nonlocal_sizeDotState(maxNinstance)); constitutive_nonlocal_sizeDotState = 0_pInt
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allocate(constitutive_nonlocal_sizeState(maxNinstance)); constitutive_nonlocal_sizeState = 0_pInt
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allocate(constitutive_nonlocal_sizePostResults(maxNinstance)); constitutive_nonlocal_sizePostResults = 0_pInt
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allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance));constitutive_nonlocal_sizePostResult = 0_pInt
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allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance)); constitutive_nonlocal_output = ''
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allocate(constitutive_nonlocal_structureName(maxNinstance)); constitutive_nonlocal_structureName = ''
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allocate(constitutive_nonlocal_structure(maxNinstance)); constitutive_nonlocal_structure = 0_pInt
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allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_Nslip = 0_pInt
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allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance)); constitutive_nonlocal_slipFamily = 0_pInt
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allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance)); constitutive_nonlocal_slipSystemLattice = 0_pInt
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allocate(constitutive_nonlocal_totalNslip(maxNinstance)); constitutive_nonlocal_totalNslip = 0_pInt
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allocate(constitutive_nonlocal_CoverA(maxNinstance)); constitutive_nonlocal_CoverA = 0.0_pReal
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allocate(constitutive_nonlocal_C11(maxNinstance)); constitutive_nonlocal_C11 = 0.0_pReal
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allocate(constitutive_nonlocal_C12(maxNinstance)); constitutive_nonlocal_C12 = 0.0_pReal
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allocate(constitutive_nonlocal_C13(maxNinstance)); constitutive_nonlocal_C13 = 0.0_pReal
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allocate(constitutive_nonlocal_C33(maxNinstance)); constitutive_nonlocal_C33 = 0.0_pReal
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allocate(constitutive_nonlocal_C44(maxNinstance)); constitutive_nonlocal_C44 = 0.0_pReal
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allocate(constitutive_nonlocal_Gmod(maxNinstance)); constitutive_nonlocal_Gmod = 0.0_pReal
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allocate(constitutive_nonlocal_nu(maxNinstance)); constitutive_nonlocal_nu = 0.0_pReal
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allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance)); constitutive_nonlocal_Cslip_66 = 0.0_pReal
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allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance)); constitutive_nonlocal_Cslip_3333 = 0.0_pReal
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allocate(constitutive_nonlocal_rhoEdgePos0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoEdgePos0 = 0.0_pReal
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allocate(constitutive_nonlocal_rhoEdgeNeg0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoEdgeNeg0 = 0.0_pReal
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allocate(constitutive_nonlocal_rhoScrewPos0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoScrewPos0 = 0.0_pReal
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allocate(constitutive_nonlocal_rhoScrewNeg0(lattice_maxNslipFamily, maxNinstance)); constitutive_nonlocal_rhoScrewNeg0 = 0.0_pReal
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allocate(constitutive_nonlocal_v0BySlipFamily(lattice_maxNslipFamily, maxNinstance));
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constitutive_nonlocal_v0BySlipFamily = 0.0_pReal
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allocate(constitutive_nonlocal_burgersBySlipFamily(lattice_maxNslipFamily, maxNinstance));
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constitutive_nonlocal_burgersBySlipFamily = 0.0_pReal
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allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction, maxNinstance))
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constitutive_nonlocal_interactionSlipSlip = 0.0_pReal
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!*** readout data from material.config file
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rewind(file)
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line = ''
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section = 0
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do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
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read(file,'(a1024)',END=100) line
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enddo
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do ! read thru sections of phase part
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read(file,'(a1024)',END=100) line
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if (IO_isBlank(line)) cycle ! skip empty lines
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if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
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if (IO_getTag(line,'[',']') /= '') then ! next section
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section = section + 1
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output = 0 ! reset output counter
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endif
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if (section > 0 .and. phase_constitution(section) == constitutive_nonlocal_label) then ! one of my sections
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i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
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positions = IO_stringPos(line,maxNchunks)
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tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
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select case(tag)
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case ('(output)')
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output = output + 1
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constitutive_nonlocal_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
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case ('lattice_structure')
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constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
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case ('covera_ratio')
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constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2)
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case ('c11')
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constitutive_nonlocal_C11(i) = IO_floatValue(line,positions,2)
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case ('c12')
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constitutive_nonlocal_C12(i) = IO_floatValue(line,positions,2)
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case ('c13')
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constitutive_nonlocal_C13(i) = IO_floatValue(line,positions,2)
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case ('c33')
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constitutive_nonlocal_C33(i) = IO_floatValue(line,positions,2)
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case ('c44')
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constitutive_nonlocal_C44(i) = IO_floatValue(line,positions,2)
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case ('nslip')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1+f)
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case ('rhoedgepos0')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgePos0(f,i) = IO_floatValue(line,positions,1+f)
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case ('rhoedgeneg0')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeNeg0(f,i) = IO_floatValue(line,positions,1+f)
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case ('rhoscrewpos0')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewPos0(f,i) = IO_floatValue(line,positions,1+f)
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case ('rhoscrewneg0')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewNeg0(f,i) = IO_floatValue(line,positions,1+f)
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case ('v0')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_v0BySlipFamily(f,i) = IO_floatValue(line,positions,1+f)
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case ('burgers')
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forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_burgersBySlipFamily(f,i) = IO_floatValue(line,positions,1+f)
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case ('interaction_slipslip')
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forall (f = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(f,i) = IO_floatValue(line,positions,1+f)
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end select
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endif
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enddo
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100 do i = 1,maxNinstance
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constitutive_nonlocal_structure(i) = &
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lattice_initializeStructure(constitutive_nonlocal_structureName(i), constitutive_nonlocal_CoverA(i)) ! our lattice structure is defined in the material.config file by the structureName (and the c/a ratio)
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!*** sanity checks
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if (constitutive_nonlocal_structure(i) < 1 .or. constitutive_nonlocal_structure(i) > 3) call IO_error(205)
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if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0) call IO_error(225)
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if (any( constitutive_nonlocal_rhoEdgePos0(:,i) < 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(220)
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if (any( constitutive_nonlocal_rhoEdgeNeg0(:,i) < 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(220)
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if (any( constitutive_nonlocal_rhoScrewPos0(:,i) < 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(220)
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if (any( constitutive_nonlocal_rhoScrewNeg0(:,i) < 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(220)
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if (any( constitutive_nonlocal_burgersBySlipFamily(:,i) <= 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(221)
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if (any( constitutive_nonlocal_v0BySlipFamily(:,i) <= 0.0_pReal &
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.and. constitutive_nonlocal_Nslip(:,i) > 0)) call IO_error(-1)
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!*** determine total number of active slip systems
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constitutive_nonlocal_Nslip(:,i) &
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= min( lattice_NslipSystem(:, constitutive_nonlocal_structure(i)), constitutive_nonlocal_Nslip(:,i) ) ! we can't use more slip systems per family than specified in lattice
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constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(:,i))
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enddo
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|
||
|
|
!*** allocation of variables whose size depends on the total number of active slip systems
|
||
|
|
|
||
|
|
maxTotalNslip = maxval(constitutive_nonlocal_totalNslip)
|
||
|
|
allocate(constitutive_nonlocal_burgersBySlipSystem(maxTotalNslip, maxNinstance))
|
||
|
|
constitutive_nonlocal_burgersBySlipSystem = 0.0_pReal
|
||
|
|
allocate(constitutive_nonlocal_v0BySlipSystem(maxTotalNslip, maxNinstance))
|
||
|
|
constitutive_nonlocal_v0BySlipSystem = 0.0_pReal
|
||
|
|
allocate(constitutive_nonlocal_forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance))
|
||
|
|
constitutive_nonlocal_forestProjectionEdge = 0.0_pReal
|
||
|
|
allocate(constitutive_nonlocal_forestProjectionScrew(maxTotalNslip, maxTotalNslip, maxNinstance))
|
||
|
|
constitutive_nonlocal_forestProjectionScrew = 0.0_pReal
|
||
|
|
allocate(constitutive_nonlocal_interactionMatrixSlipSlip(maxTotalNslip, maxTotalNslip, maxNinstance))
|
||
|
|
constitutive_nonlocal_interactionMatrixSlipSlip = 0.0_pReal
|
||
|
|
|
||
|
|
do i = 1,maxNinstance
|
||
|
|
|
||
|
|
myStructure = constitutive_nonlocal_structure(i) ! lattice structure of this instance
|
||
|
|
|
||
|
|
!*** Inverse lookup of my slip system family and the slip system in lattice
|
||
|
|
|
||
|
|
l = 0_pInt
|
||
|
|
do f = 1,lattice_maxNslipFamily
|
||
|
|
do s = 1,constitutive_nonlocal_Nslip(f,i)
|
||
|
|
l = l + 1
|
||
|
|
constitutive_nonlocal_slipFamily(l,i) = f
|
||
|
|
constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1, myStructure)) + s
|
||
|
|
enddo; enddo
|
||
|
|
|
||
|
|
|
||
|
|
!*** determine size of state array
|
||
|
|
|
||
|
|
constitutive_nonlocal_sizeState(i) = (size(constitutive_nonlocal_stateList)-1) * constitutive_nonlocal_totalNslip(i) + 6_pInt ! the size of the list of states times the number of active slip systems gives the required size for the state array
|
||
|
|
constitutive_nonlocal_sizeDotState(i) = size(constitutive_nonlocal_stateListBasic) * constitutive_nonlocal_totalNslip(i) ! the size of the list of basic states times the number of active slip systems gives the required size for the dotState array
|
||
|
|
|
||
|
|
|
||
|
|
!*** determine size of postResults array
|
||
|
|
|
||
|
|
do o = 1,maxval(phase_Noutput)
|
||
|
|
select case(constitutive_nonlocal_output(o,i))
|
||
|
|
case( 'dislocationdensity', &
|
||
|
|
'shearrate_slip', &
|
||
|
|
'resolvedstress_slip', &
|
||
|
|
'resistance_slip')
|
||
|
|
mySize = constitutive_nonlocal_totalNslip(i)
|
||
|
|
case default
|
||
|
|
mySize = 0_pInt
|
||
|
|
end select
|
||
|
|
|
||
|
|
if (mySize > 0_pInt) then ! any meaningful output found
|
||
|
|
constitutive_nonlocal_sizePostResult(o,i) = mySize
|
||
|
|
constitutive_nonlocal_sizePostResults(i) = constitutive_nonlocal_sizePostResults(i) + mySize
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
|
||
|
|
|
||
|
|
!*** elasticity matrix and shear modulus according to material.config
|
||
|
|
|
||
|
|
select case (myStructure)
|
||
|
|
case(1:2) ! cubic(s)
|
||
|
|
forall(k=1:3)
|
||
|
|
forall(j=1:3) constitutive_nonlocal_Cslip_66(k,j,i) = constitutive_nonlocal_C12(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(k,k,i) = constitutive_nonlocal_C11(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(k+3,k+3,i) = constitutive_nonlocal_C44(i)
|
||
|
|
end forall
|
||
|
|
case(3:) ! all hex
|
||
|
|
constitutive_nonlocal_Cslip_66(1,1,i) = constitutive_nonlocal_C11(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(2,2,i) = constitutive_nonlocal_C11(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(3,3,i) = constitutive_nonlocal_C33(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(1,2,i) = constitutive_nonlocal_C12(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(2,1,i) = constitutive_nonlocal_C12(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(1,3,i) = constitutive_nonlocal_C13(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(3,1,i) = constitutive_nonlocal_C13(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(2,3,i) = constitutive_nonlocal_C13(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(3,2,i) = constitutive_nonlocal_C13(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(4,4,i) = constitutive_nonlocal_C44(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(5,5,i) = constitutive_nonlocal_C44(i)
|
||
|
|
constitutive_nonlocal_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_nonlocal_C11(i)- constitutive_nonlocal_C12(i))
|
||
|
|
end select
|
||
|
|
constitutive_nonlocal_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i)))
|
||
|
|
constitutive_nonlocal_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i))
|
||
|
|
|
||
|
|
constitutive_nonlocal_Gmod(i) = constitutive_nonlocal_C44(i) ! shear modulus is given by elastic constant C44
|
||
|
|
constitutive_nonlocal_nu(i) = constitutive_nonlocal_C12(i) / constitutive_nonlocal_C11(i)
|
||
|
|
|
||
|
|
|
||
|
|
!*** burgers vector and initial dislocation velocity for each slip system
|
||
|
|
|
||
|
|
do s = 1,constitutive_nonlocal_totalNslip(i)
|
||
|
|
constitutive_nonlocal_burgersBySlipSystem(s,i) &
|
||
|
|
= constitutive_nonlocal_burgersBySlipFamily( constitutive_nonlocal_slipFamily(s,i), i )
|
||
|
|
constitutive_nonlocal_v0BySlipSystem(s,i) = constitutive_nonlocal_v0BySlipFamily(constitutive_nonlocal_slipFamily(s,i),i)
|
||
|
|
enddo
|
||
|
|
|
||
|
|
|
||
|
|
!*** calculation of forest projections for edge and screw dislocations
|
||
|
|
|
||
|
|
do s1 = 1,constitutive_nonlocal_totalNslip(i)
|
||
|
|
do s2 = 1,constitutive_nonlocal_totalNslip(i)
|
||
|
|
|
||
|
|
constitutive_nonlocal_forestProjectionEdge(s1, s2, i) &
|
||
|
|
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
|
||
|
|
lattice_st(:, constitutive_nonlocal_slipSystemLattice(s2,i), myStructure))) ! forest projection of edge dislocations is the projection of (b x n) onto the slip normal of the respective splip plane
|
||
|
|
|
||
|
|
|
||
|
|
constitutive_nonlocal_forestProjectionScrew(s1, s2, i) &
|
||
|
|
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
|
||
|
|
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s2,i), myStructure))) ! forest projection of screw dislocations is the projection of b onto the slip normal of the respective splip plane
|
||
|
|
|
||
|
|
enddo; enddo
|
||
|
|
|
||
|
|
!*** calculation of interaction matrices
|
||
|
|
|
||
|
|
do s1 = 1,constitutive_nonlocal_totalNslip(i)
|
||
|
|
do s2 = 1,constitutive_nonlocal_totalNslip(i)
|
||
|
|
|
||
|
|
constitutive_nonlocal_interactionMatrixSlipSlip(s1, s2, i) &
|
||
|
|
= constitutive_nonlocal_interactionSlipSlip( lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), &
|
||
|
|
constitutive_nonlocal_slipSystemLattice(s2,i), &
|
||
|
|
myStructure), &
|
||
|
|
i )
|
||
|
|
|
||
|
|
enddo; enddo
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
endsubroutine
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* initial microstructural state (just the "basic" states) *
|
||
|
|
!*********************************************************************
|
||
|
|
pure function constitutive_nonlocal_stateInit(myInstance)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt
|
||
|
|
use lattice, only: lattice_maxNslipFamily
|
||
|
|
use IO, only: IO_error
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!*** input variables
|
||
|
|
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution
|
||
|
|
|
||
|
|
!*** output variables
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
|
||
|
|
constitutive_nonlocal_stateInit
|
||
|
|
|
||
|
|
!*** local variables
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(myInstance)) :: &
|
||
|
|
rhoEdgePos, & ! positive edge dislocation density
|
||
|
|
rhoEdgeNeg, & ! negative edge dislocation density
|
||
|
|
rhoScrewPos, & ! positive screw dislocation density
|
||
|
|
rhoScrewNeg, & ! negative screw dislocation density
|
||
|
|
rhoForest, & ! forest dislocation density
|
||
|
|
tauSlipThreshold ! threshold shear stress for slip
|
||
|
|
integer(pInt) ns, & ! short notation for total number of active slip systems
|
||
|
|
f, & ! index of lattice family
|
||
|
|
s0, &
|
||
|
|
s1, &
|
||
|
|
s ! index of slip system
|
||
|
|
|
||
|
|
|
||
|
|
constitutive_nonlocal_stateInit = 0.0_pReal
|
||
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
||
|
|
|
||
|
|
|
||
|
|
!*** set the basic state variables
|
||
|
|
|
||
|
|
s1 = 0_pInt
|
||
|
|
do f = 1,lattice_maxNslipFamily
|
||
|
|
|
||
|
|
s0 = s1 + 1_pInt
|
||
|
|
s1 = s0 + constitutive_nonlocal_Nslip(f,myInstance) - 1_pInt
|
||
|
|
|
||
|
|
do s = s0,s1
|
||
|
|
rhoEdgePos(s) = constitutive_nonlocal_rhoEdgePos0(f, myInstance)
|
||
|
|
rhoEdgeNeg(s) = constitutive_nonlocal_rhoEdgeNeg0(f, myInstance)
|
||
|
|
rhoScrewPos(s) = constitutive_nonlocal_rhoScrewPos0(f, myInstance)
|
||
|
|
rhoScrewNeg(s) = constitutive_nonlocal_rhoScrewNeg0(f, myInstance)
|
||
|
|
|
||
|
|
enddo; enddo
|
||
|
|
|
||
|
|
|
||
|
|
!*** calculate the dependent state variables
|
||
|
|
|
||
|
|
! forest dislocation density
|
||
|
|
forall (s = 1:ns) &
|
||
|
|
rhoForest(s) = dot_product( (rhoEdgePos + rhoEdgeNeg), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) &
|
||
|
|
+ dot_product( (rhoScrewPos + rhoScrewNeg), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
|
||
|
|
|
||
|
|
|
||
|
|
! threshold shear stress for dislocation slip
|
||
|
|
forall (s = 1:ns) &
|
||
|
|
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
|
||
|
|
* constitutive_nonlocal_burgersBySlipSystem(s, myInstance) &
|
||
|
|
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg), &
|
||
|
|
constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) )
|
||
|
|
|
||
|
|
|
||
|
|
!*** put everything together and in right order
|
||
|
|
|
||
|
|
constitutive_nonlocal_stateInit( 1: ns) = rhoEdgePos
|
||
|
|
constitutive_nonlocal_stateInit( ns+1:2*ns) = rhoEdgeNeg
|
||
|
|
constitutive_nonlocal_stateInit(2*ns+1:3*ns) = rhoScrewPos
|
||
|
|
constitutive_nonlocal_stateInit(3*ns+1:4*ns) = rhoScrewNeg
|
||
|
|
constitutive_nonlocal_stateInit(4*ns+1:5*ns) = rhoForest
|
||
|
|
constitutive_nonlocal_stateInit(5*ns+1:6*ns) = tauSlipThreshold
|
||
|
|
|
||
|
|
endfunction
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* calculates homogenized elacticity matrix *
|
||
|
|
!*********************************************************************
|
||
|
|
pure function constitutive_nonlocal_homogenizedC(state,g,ip,el)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt, &
|
||
|
|
p_vec
|
||
|
|
use mesh, only: mesh_NcpElems, &
|
||
|
|
mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains, &
|
||
|
|
material_phase, &
|
||
|
|
phase_constitutionInstance
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!*** input variables
|
||
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
||
|
|
ip, & ! current integration point
|
||
|
|
el ! current element
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! microstructural state
|
||
|
|
|
||
|
|
!*** output variables
|
||
|
|
real(pReal), dimension(6,6) :: constitutive_nonlocal_homogenizedC ! homogenized elasticity matrix
|
||
|
|
|
||
|
|
!*** local variables
|
||
|
|
integer(pInt) myInstance ! current instance of this constitution
|
||
|
|
|
||
|
|
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
|
||
|
|
|
||
|
|
constitutive_nonlocal_homogenizedC = constitutive_nonlocal_Cslip_66(:,:,myInstance)
|
||
|
|
|
||
|
|
endfunction
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* calculates quantities characterizing the microstructure *
|
||
|
|
!*********************************************************************
|
||
|
|
subroutine constitutive_nonlocal_microstructure(Temperature, Fp, state, g, ip, el)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt, &
|
||
|
|
p_vec
|
||
|
|
use math, only: math_Plain3333to99, &
|
||
|
|
math_Mandel33to6, &
|
||
|
|
math_Mandel6to33, &
|
||
|
|
math_mul33x33, &
|
||
|
|
math_mul3x3, &
|
||
|
|
math_mul33x3, &
|
||
|
|
math_transpose3x3, &
|
||
|
|
pi
|
||
|
|
use mesh, only: mesh_NcpElems, &
|
||
|
|
mesh_maxNips, &
|
||
|
|
mesh_element, &
|
||
|
|
FE_NipNeighbors, &
|
||
|
|
mesh_ipNeighborhood, &
|
||
|
|
mesh_ipVolume, &
|
||
|
|
mesh_ipCenterOfGravity
|
||
|
|
use material, only: homogenization_maxNgrains, &
|
||
|
|
material_phase, &
|
||
|
|
phase_constitutionInstance
|
||
|
|
use lattice, only: lattice_Sslip, &
|
||
|
|
lattice_Sslip_v, &
|
||
|
|
lattice_maxNslipFamily, &
|
||
|
|
lattice_NslipSystem, &
|
||
|
|
lattice_maxNslip, &
|
||
|
|
lattice_sd, &
|
||
|
|
lattice_sn, &
|
||
|
|
lattice_st
|
||
|
|
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!*** input variables
|
||
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
||
|
|
ip, & ! current integration point
|
||
|
|
el ! current element
|
||
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
||
|
|
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
||
|
|
Fp ! plastic deformation gradient
|
||
|
|
|
||
|
|
!*** input/output variables
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
|
||
|
|
state ! microstructural state
|
||
|
|
|
||
|
|
!*** output variables
|
||
|
|
|
||
|
|
!*** local variables
|
||
|
|
integer(pInt) myInstance, & ! current instance of this constitution
|
||
|
|
myStructure, & ! current lattice structure
|
||
|
|
ns, & ! short notation for the total number of active slip systems
|
||
|
|
neighboring_el, & ! element number of my neighbor
|
||
|
|
neighboring_ip, & ! integration point of my neighbor
|
||
|
|
n, & ! index of my current neighbor
|
||
|
|
s, & ! index of my current slip system
|
||
|
|
sLattice ! index of my current slip system as specified by lattice
|
||
|
|
real(pReal) gb, & ! short notation for G*b/2/pi
|
||
|
|
x, & ! coordinate in direction of lvec
|
||
|
|
y, & ! coordinate in direction of bvec
|
||
|
|
z ! coordinate in direction of nvec
|
||
|
|
real(pReal), dimension(3) :: connectingVector ! vector connecting the centers of gravity of me and my neigbor
|
||
|
|
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress in Mandel notation
|
||
|
|
real(pReal), dimension(3,3) :: transform, & ! orthogonal transformation matrix from slip coordinate system with e1=bxn, e2=b, e3=n to lattice coordinate system
|
||
|
|
sigma ! backstress resulting from the excess dislocation density of a single slip system and a single neighbor calculated in the coordinate system of the slip system
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
rhoEdgePos, & ! positive edge dislocation density
|
||
|
|
rhoEdgeNeg, & ! negative edge dislocation density
|
||
|
|
rhoScrewPos, & ! positive screw dislocation density
|
||
|
|
rhoScrewNeg, & ! negative screw dislocation density
|
||
|
|
rhoForest, & ! forest dislocation density
|
||
|
|
tauSlipThreshold, & ! threshold shear stress
|
||
|
|
neighboring_rhoEdgePos, & ! positive edge dislocation density of my neighbor
|
||
|
|
neighboring_rhoEdgeNeg, & ! negative edge dislocation density of my neighbor
|
||
|
|
neighboring_rhoScrewPos, & ! positive screw dislocation density of my neighbor
|
||
|
|
neighboring_rhoScrewNeg, & ! negative screw dislocation density of my neighbor
|
||
|
|
neighboring_rhoEdgeExcess, &! edge excess dislocation density of my neighbor
|
||
|
|
neighboring_rhoScrewExcess,&! screw excess dislocation density of my neighbor
|
||
|
|
neighboring_Nedge, & ! total number of edge excess dislocations in my neighbor
|
||
|
|
neighboring_Nscrew
|
||
|
|
|
||
|
|
|
||
|
|
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
|
||
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
||
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
||
|
|
|
||
|
|
|
||
|
|
!**********************************************************************
|
||
|
|
!*** get basic states
|
||
|
|
|
||
|
|
rhoEdgePos = state(g,ip,el)%p( 1: ns)
|
||
|
|
rhoEdgeNeg = state(g,ip,el)%p( ns+1:2*ns)
|
||
|
|
rhoScrewPos = state(g,ip,el)%p(2*ns+1:3*ns)
|
||
|
|
rhoScrewNeg = state(g,ip,el)%p(3*ns+1:4*ns)
|
||
|
|
|
||
|
|
|
||
|
|
!**********************************************************************
|
||
|
|
!*** calculate dependent states
|
||
|
|
|
||
|
|
!*** calculate the forest dislocation density
|
||
|
|
|
||
|
|
forall (s = 1:ns) &
|
||
|
|
rhoForest(s) = dot_product( (rhoEdgePos + rhoEdgeNeg), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) &
|
||
|
|
+ dot_product( (rhoScrewPos + rhoScrewNeg), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
|
||
|
|
|
||
|
|
|
||
|
|
!*** calculate the threshold shear stress for dislocation slip
|
||
|
|
|
||
|
|
forall (s = 1:ns) &
|
||
|
|
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
|
||
|
|
* constitutive_nonlocal_burgersBySlipSystem(s, myInstance) &
|
||
|
|
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg), &
|
||
|
|
constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) )
|
||
|
|
|
||
|
|
|
||
|
|
!*** calculate the backstress of the neighboring excess dislocation densities
|
||
|
|
|
||
|
|
backStress_v = 0.0_pReal
|
||
|
|
|
||
|
|
|
||
|
|
! loop through my neighbors (if it exists!)
|
||
|
|
|
||
|
|
do n = 1,FE_NipNeighbors(mesh_element(2,el))
|
||
|
|
|
||
|
|
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
|
||
|
|
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
|
||
|
|
|
||
|
|
if ( neighboring_el == 0 .or. neighboring_ip == 0 ) cycle
|
||
|
|
|
||
|
|
|
||
|
|
! calculate the connecting vector between me and my neighbor and his excess dislocation density
|
||
|
|
|
||
|
|
connectingVector = math_mul33x3( Fp(:,:,g,ip,el), &
|
||
|
|
(mesh_ipCenterOfGravity(:,ip,el) - mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el)) )
|
||
|
|
|
||
|
|
neighboring_rhoEdgePos = state(1, neighboring_ip, neighboring_el)%p( 1: ns)
|
||
|
|
neighboring_rhoEdgeNeg = state(1, neighboring_ip, neighboring_el)%p( ns+1:2*ns)
|
||
|
|
neighboring_rhoScrewPos = state(1, neighboring_ip, neighboring_el)%p(2*ns+1:3*ns)
|
||
|
|
neighboring_rhoScrewNeg = state(1, neighboring_ip, neighboring_el)%p(3*ns+1:4*ns)
|
||
|
|
|
||
|
|
neighboring_rhoEdgeExcess = neighboring_rhoEdgePos - neighboring_rhoEdgeNeg
|
||
|
|
neighboring_rhoScrewExcess = neighboring_rhoScrewPos - neighboring_rhoScrewNeg
|
||
|
|
|
||
|
|
neighboring_Nedge = neighboring_rhoEdgeExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
|
||
|
|
neighboring_Nscrew = neighboring_rhoScrewExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
|
||
|
|
|
||
|
|
! loop over slip systems and get their slip directions, slip normals, and sd x sn
|
||
|
|
|
||
|
|
do s = 1,ns
|
||
|
|
|
||
|
|
transform = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
|
||
|
|
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
|
||
|
|
lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) )
|
||
|
|
|
||
|
|
|
||
|
|
! coordinate transformation of p from the lattice coordinate system to the slip coordinate system
|
||
|
|
x = math_mul3x3(connectingVector, transform(:,1))
|
||
|
|
y = math_mul3x3(connectingVector, transform(:,2))
|
||
|
|
z = math_mul3x3(connectingVector, transform(:,3))
|
||
|
|
|
||
|
|
|
||
|
|
! calculate the back stress in the slip coordinate system for this slip system
|
||
|
|
gb = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) / (2.0_pReal*pi)
|
||
|
|
|
||
|
|
sigma(2,2) = - gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
|
||
|
|
* z * (3.0_pReal*y**2.0_pReal + z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
|
||
|
|
|
||
|
|
sigma(3,3) = gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
|
||
|
|
* z * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
|
||
|
|
|
||
|
|
sigma(1,1) = constitutive_nonlocal_nu(myInstance) * (sigma(2,2) + sigma(3,3))
|
||
|
|
|
||
|
|
sigma(1,2) = gb * neighboring_Nscrew(s) * z / (x**2.0_pReal + z**2.0_pReal)
|
||
|
|
|
||
|
|
sigma(2,3) = gb * ( neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
|
||
|
|
* (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal) &
|
||
|
|
- neighboring_Nscrew(s) * x / (x**2.0_pReal + z**2.0_pReal) )
|
||
|
|
|
||
|
|
sigma(2,1) = sigma(1,2)
|
||
|
|
sigma(3,2) = sigma(2,3)
|
||
|
|
sigma(1,3) = 0.0_pReal
|
||
|
|
sigma(3,1) = 0.0_pReal
|
||
|
|
|
||
|
|
! coordinate transformation from the slip coordinate system to the lattice coordinate system
|
||
|
|
backStress_v = backStress_v + math_Mandel33to6( math_mul33x33(math_transpose3x3(transform), math_mul33x33(sigma, transform) ) )
|
||
|
|
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
|
||
|
|
|
||
|
|
!**********************************************************************
|
||
|
|
!*** set dependent states
|
||
|
|
|
||
|
|
state(g,ip,el)%p(4*ns+1:5*ns) = rhoForest
|
||
|
|
state(g,ip,el)%p(5*ns+1:6*ns) = tauSlipThreshold
|
||
|
|
state(g,ip,el)%p(6*ns+1:6*ns+6) = backstress_v
|
||
|
|
|
||
|
|
endsubroutine
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* calculates plastic velocity gradient and its tangent *
|
||
|
|
!*********************************************************************
|
||
|
|
subroutine constitutive_nonlocal_LpAndItsTangent(Lp, dLp_dTstar99, Tstar_v, Temperature, state, g, ip, el)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt, &
|
||
|
|
p_vec
|
||
|
|
use math, only: math_Plain3333to99, &
|
||
|
|
math_mul6x6, &
|
||
|
|
math_Mandel6to33
|
||
|
|
use debug, only: debugger
|
||
|
|
use mesh, only: mesh_NcpElems, &
|
||
|
|
mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains, &
|
||
|
|
material_phase, &
|
||
|
|
phase_constitutionInstance
|
||
|
|
use lattice, only: lattice_Sslip, &
|
||
|
|
lattice_Sslip_v
|
||
|
|
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!*** input variables
|
||
|
|
integer(pInt), intent(in) :: g, & ! current grain number
|
||
|
|
ip, & ! current integration point
|
||
|
|
el ! current element number
|
||
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
||
|
|
state ! microstructural state
|
||
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
|
||
|
|
|
||
|
|
!*** output variables
|
||
|
|
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
|
||
|
|
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99 ! derivative of Lp with respect to Tstar (9x9 matrix)
|
||
|
|
|
||
|
|
!*** local variables
|
||
|
|
integer(pInt) myInstance, & ! current instance of this constitution
|
||
|
|
myStructure, & ! current lattice structure
|
||
|
|
ns, & ! short notation for the total number of active slip systems
|
||
|
|
i, &
|
||
|
|
j, &
|
||
|
|
k, &
|
||
|
|
l, &
|
||
|
|
t, & ! dislocation type
|
||
|
|
s, & ! index of my current slip system
|
||
|
|
sLattice ! index of my current slip system as specified by lattice
|
||
|
|
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress
|
||
|
|
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix)
|
||
|
|
real(pReal), dimension(4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
rho ! dislocation densities
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
rhoForest, & ! forest dislocation density
|
||
|
|
tauSlipThreshold, & ! threshold shear stress
|
||
|
|
tauSlip, & ! resolved shear stress
|
||
|
|
gdotSlip, & ! shear rate
|
||
|
|
dgdot_dtauSlip, & ! derivative of the shear rate with respect to the shear stress
|
||
|
|
v ! dislocation velocity
|
||
|
|
|
||
|
|
|
||
|
|
!*** initialize local variables
|
||
|
|
|
||
|
|
v = 0.0_pReal
|
||
|
|
tauSlip = 0.0_pReal
|
||
|
|
gdotSlip = 0.0_pReal
|
||
|
|
Lp = 0.0_pReal
|
||
|
|
dLp_dTstar3333 = 0.0_pReal
|
||
|
|
|
||
|
|
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
|
||
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
||
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
||
|
|
|
||
|
|
!*** shortcut to state variables
|
||
|
|
|
||
|
|
forall (t = 1:4) rho(t,:) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
|
||
|
|
rhoForest = state(g,ip,el)%p(4*ns+1:5*ns)
|
||
|
|
tauSlipThreshold = state(g,ip,el)%p(5*ns+1:6*ns)
|
||
|
|
backStress_v = state(g,ip,el)%p(6*ns+1:6*ns+6)
|
||
|
|
! if (debugger) write(6,'(a20,3(i3,x),/,3(3(f12.3,x)/))') 'backstress / MPa at ', g,ip,el, math_Mandel6to33(backStress_v/1e6)
|
||
|
|
! if (debugger) write(6,'(a15,3(i3,x),/,3(3(f12.3,x)/))') 'Tstar / MPa at ',g,ip,el, math_Mandel6to33(Tstar_v/1e6)
|
||
|
|
|
||
|
|
!*** loop over slip systems
|
||
|
|
|
||
|
|
do s = 1,constitutive_nonlocal_totalNslip(myInstance)
|
||
|
|
|
||
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
||
|
|
|
||
|
|
|
||
|
|
!*** Calculation of Lp
|
||
|
|
|
||
|
|
tauSlip(s) = math_mul6x6( Tstar_v + backStress_v, lattice_Sslip_v(:,sLattice,myStructure) )
|
||
|
|
|
||
|
|
if (rhoForest(s) > 0.0_pReal) &
|
||
|
|
v(s) = constitutive_nonlocal_v0BySlipSystem(s,myInstance) &
|
||
|
|
* exp( - ( tauSlipThreshold(s) - abs(tauSlip(s)) ) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
|
||
|
|
/ ( kB * Temperature * sqrt(rhoForest(s)) ) ) &
|
||
|
|
* sign(1.0_pReal,tauSlip(s))
|
||
|
|
|
||
|
|
gdotSlip(s) = sum(rho(:,s)) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) * v(s)
|
||
|
|
|
||
|
|
Lp = Lp + gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure)
|
||
|
|
|
||
|
|
|
||
|
|
!*** Calculation of the tangent of Lp
|
||
|
|
|
||
|
|
dgdot_dtauSlip(s) = gdotSlip(s) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
|
||
|
|
/ ( kB * Temperature * sqrt(rhoForest(s)) )
|
||
|
|
|
||
|
|
forall (i=1:3,j=1:3,k=1:3,l=1:3) &
|
||
|
|
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) + dgdot_dtauSlip(s) * lattice_Sslip(i,j, sLattice,myStructure) &
|
||
|
|
* lattice_Sslip(k,l, sLattice,myStructure)
|
||
|
|
enddo
|
||
|
|
!if (debugger) write(6,'(a26,3(i3,x),/,12(f10.3,x),/)') 'tauSlipThreshold / MPa at ',g,ip,el, tauSlipThreshold/1e6
|
||
|
|
!if (debugger) write(6,'(a15,3(i3,x),/,12(f10.3,x),/)') 'tauSlip / MPa at ',g,ip,el, tauSlip/1e6
|
||
|
|
!if (debugger) write(6,'(a15,3(i3,x),/,12(e10.3,x),/)') 'gdotSlip at ',g,ip,el, gdotSlip
|
||
|
|
|
||
|
|
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
|
||
|
|
|
||
|
|
endsubroutine
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* rate of change of microstructure *
|
||
|
|
!*********************************************************************
|
||
|
|
subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, Fp, invFp, Temperature, state, g, ip, el)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt, &
|
||
|
|
p_vec
|
||
|
|
use debug, only: debugger
|
||
|
|
use math, only: math_norm3, &
|
||
|
|
math_mul6x6, &
|
||
|
|
math_mul3x3, &
|
||
|
|
math_mul33x3, &
|
||
|
|
math_transpose3x3
|
||
|
|
use mesh, only: mesh_NcpElems, &
|
||
|
|
mesh_maxNips, &
|
||
|
|
mesh_element, &
|
||
|
|
FE_NipNeighbors, &
|
||
|
|
mesh_ipNeighborhood, &
|
||
|
|
mesh_ipVolume, &
|
||
|
|
mesh_ipCenterOfGravity, &
|
||
|
|
mesh_ipArea, &
|
||
|
|
mesh_ipAreaNormal
|
||
|
|
use material, only: homogenization_maxNgrains, &
|
||
|
|
material_phase, &
|
||
|
|
phase_constitutionInstance
|
||
|
|
use lattice, only: lattice_Sslip, &
|
||
|
|
lattice_Sslip_v, &
|
||
|
|
lattice_sd, &
|
||
|
|
lattice_sn, &
|
||
|
|
lattice_st, &
|
||
|
|
lattice_maxNslipFamily, &
|
||
|
|
lattice_NslipSystem
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!*** input variables
|
||
|
|
integer(pInt), intent(in) :: g, & ! current grain number
|
||
|
|
ip, & ! current integration point
|
||
|
|
el ! current element number
|
||
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
||
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
|
||
|
|
real(pReal), dimension(3,3), intent(in) :: Fp, & ! plastic deformation gradient
|
||
|
|
invFp ! inverse of plastic deformation gradient
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
||
|
|
state ! microstructural state
|
||
|
|
|
||
|
|
!*** input/output variables
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
|
||
|
|
dotState ! evolution of state variables / microstructure
|
||
|
|
|
||
|
|
!*** output variables
|
||
|
|
|
||
|
|
!*** local variables
|
||
|
|
integer(pInt) myInstance, & ! current instance of this constitution
|
||
|
|
myStructure, & ! current lattice structure
|
||
|
|
ns, & ! short notation for the total number of active slip systems
|
||
|
|
neighboring_el, & ! element number of my neighbor
|
||
|
|
neighboring_ip, & ! integration point of my neighbor
|
||
|
|
n, & ! index of my current neighbor
|
||
|
|
t, & ! type of dislocation
|
||
|
|
s, & ! index of my current slip system
|
||
|
|
sLattice ! index of my current slip system as specified by lattice
|
||
|
|
real(pReal), dimension(4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
rho, & ! dislocation densities
|
||
|
|
gdot ! shear rates
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
rhoForest, & ! forest dislocation density
|
||
|
|
tauSlipThreshold, & ! threshold shear stress
|
||
|
|
tauSlip, & ! resolved shear stress
|
||
|
|
v ! dislocation velocity
|
||
|
|
real(pReal), dimension(3,4,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
|
||
|
|
m ! direction of dislocation motion
|
||
|
|
real(pReal), dimension(6) :: backStress_v ! backstress resulting from the neighboring excess dislocation densities as 2nd Piola-Kirchhoff stress
|
||
|
|
real(pReal), dimension(4) :: leavingRho ! dislocation densities leaving the current interface
|
||
|
|
real(pReal), dimension(3) :: surfaceNormal ! surface normal of the current interface
|
||
|
|
real(pReal) norm_surfaceNormal, & ! euclidic norm of the surface normal
|
||
|
|
area ! area of the current interface
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
|
||
|
|
myStructure = constitutive_nonlocal_structure(myInstance)
|
||
|
|
ns = constitutive_nonlocal_totalNslip(myInstance)
|
||
|
|
|
||
|
|
|
||
|
|
!*** shortcut to state variables
|
||
|
|
|
||
|
|
forall (t = 1:4) rho(t,:) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
|
||
|
|
rhoForest = state(g,ip,el)%p(4*ns+1:5*ns)
|
||
|
|
tauSlipThreshold = state(g,ip,el)%p(5*ns+1:6*ns)
|
||
|
|
backStress_v = state(g,ip,el)%p(6*ns+1:6*ns+6)
|
||
|
|
|
||
|
|
|
||
|
|
do s = 1,ns
|
||
|
|
|
||
|
|
!*** Calculate gdot for each type of dislocation
|
||
|
|
|
||
|
|
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
|
||
|
|
tauSlip(s) = math_mul6x6( Tstar_v + backStress_v, lattice_Sslip_v(:,sLattice,myStructure) )
|
||
|
|
|
||
|
|
v(s) = constitutive_nonlocal_v0BySlipSystem(s,myInstance) &
|
||
|
|
* exp( - ( tauSlipThreshold(s) - abs(tauSlip(s)) ) &
|
||
|
|
* constitutive_nonlocal_burgersBySlipSystem(s,myInstance)**2.0_pReal &
|
||
|
|
/ ( kB * Temperature * sqrt(rhoForest(s)) ) ) &
|
||
|
|
* sign(1.0_pReal,tauSlip(s))
|
||
|
|
|
||
|
|
forall (t = 1:4) gdot(t,s) = rho(t,s) * constitutive_nonlocal_burgersBySlipSystem(s,myInstance) * v(s)
|
||
|
|
|
||
|
|
|
||
|
|
!*** Direction of dislocation motion
|
||
|
|
|
||
|
|
m(:,1,s) = lattice_sd(:, sLattice, myStructure)
|
||
|
|
m(:,2,s) = -lattice_sd(:, sLattice, myStructure)
|
||
|
|
m(:,3,s) = lattice_st(:, sLattice, myStructure)
|
||
|
|
m(:,4,s) = -lattice_st(:, sLattice, myStructure)
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
|
||
|
|
!*** loop through my neighbors if existent and calculate the area and the surface normal of the interface
|
||
|
|
|
||
|
|
do n = 1,FE_NipNeighbors(mesh_element(2,el))
|
||
|
|
|
||
|
|
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
|
||
|
|
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
|
||
|
|
|
||
|
|
surfaceNormal = math_mul33x3(math_transpose3x3(invFp), mesh_ipAreaNormal(:,n,ip,el))
|
||
|
|
norm_surfaceNormal = math_norm3(surfaceNormal)
|
||
|
|
surfaceNormal = surfaceNormal / norm_surfaceNormal
|
||
|
|
area = mesh_ipArea(n,ip,el) / norm_surfaceNormal
|
||
|
|
|
||
|
|
|
||
|
|
!*** loop through my interfaces
|
||
|
|
!*** subtract dislocation densities that leave through an interface from my dotState and add them to the neighboring dotState
|
||
|
|
|
||
|
|
do s = 1,ns
|
||
|
|
|
||
|
|
leavingRho = 0.0_pReal
|
||
|
|
do t = 1,4
|
||
|
|
if ( sign(1.0_pReal,math_mul3x3(m(:,t,s),surfaceNormal)) == sign(1.0_pReal,gdot(t,s)) ) then
|
||
|
|
|
||
|
|
leavingRho(t) = gdot(t,s) / constitutive_nonlocal_burgersBySlipSystem(s,myInstance) &
|
||
|
|
* math_mul3x3(m(:,t,s),surfaceNormal) * area
|
||
|
|
|
||
|
|
dotState(1,ip,el)%p((t-1)*ns+s) = dotState(1,ip,el)%p((t-1)*ns+s) - leavingRho(t)
|
||
|
|
|
||
|
|
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then
|
||
|
|
!*****************************************************************************************************
|
||
|
|
!*** OMP locking for this neighbor missing
|
||
|
|
!*****************************************************************************************************
|
||
|
|
dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) = &
|
||
|
|
dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) + leavingRho(t)
|
||
|
|
endif
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
endsubroutine
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* rate of change of temperature *
|
||
|
|
!*********************************************************************
|
||
|
|
pure function constitutive_nonlocal_dotTemperature(Tstar_v,Temperature,state,g,ip,el)
|
||
|
|
|
||
|
|
use prec, only: pReal, &
|
||
|
|
pInt, &
|
||
|
|
p_vec
|
||
|
|
use mesh, only: mesh_NcpElems, &
|
||
|
|
mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!* input variables
|
||
|
|
integer(pInt), intent(in) :: g, & ! current grain ID
|
||
|
|
ip, & ! current integration point
|
||
|
|
el ! current element
|
||
|
|
real(pReal), intent(in) :: Temperature ! temperature
|
||
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
|
||
|
|
state ! microstructural state
|
||
|
|
|
||
|
|
!* output variables
|
||
|
|
real(pReal) constitutive_nonlocal_dotTemperature ! evolution of Temperature
|
||
|
|
|
||
|
|
!* local variables
|
||
|
|
|
||
|
|
constitutive_nonlocal_dotTemperature = 0.0_pReal
|
||
|
|
|
||
|
|
endfunction
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
!*********************************************************************
|
||
|
|
!* return array of constitutive results *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - Temperature : temperature *
|
||
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
||
|
|
!* - dt : current time increment *
|
||
|
|
!* - ipc : component-ID at current integration point *
|
||
|
|
!* - ip : current integration point *
|
||
|
|
!* - el : current element *
|
||
|
|
!*********************************************************************
|
||
|
|
pure function constitutive_nonlocal_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
|
||
|
|
|
||
|
|
use prec, only: pReal,pInt,p_vec
|
||
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
|
||
|
|
use lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
||
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
||
|
|
real(pReal), intent(in) :: dt,Temperature
|
||
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
|
||
|
|
integer(pInt) matID,structID,ns,nt,f,o,i,c,j,index_myFamily
|
||
|
|
real(pReal) sumf,tau
|
||
|
|
real(pReal), dimension(constitutive_nonlocal_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
||
|
|
constitutive_nonlocal_postResults
|
||
|
|
|
||
|
|
!* Shortened notation
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
structID = constitutive_nonlocal_structure(matID)
|
||
|
|
ns = constitutive_nonlocal_totalNslip(matID)
|
||
|
|
|
||
|
|
|
||
|
|
!* Required output
|
||
|
|
c = 0_pInt
|
||
|
|
constitutive_nonlocal_postResults = 0.0_pReal
|
||
|
|
|
||
|
|
do o = 1,phase_Noutput(material_phase(ipc,ip,el))
|
||
|
|
select case(constitutive_nonlocal_output(o,matID))
|
||
|
|
|
||
|
|
case ('dislocationdensity')
|
||
|
|
constitutive_nonlocal_postResults(c+1:c+ns) = state(ipc,ip,el)%p(1:ns)
|
||
|
|
c = c + ns
|
||
|
|
|
||
|
|
end select
|
||
|
|
enddo
|
||
|
|
|
||
|
|
endfunction
|
||
|
|
|
||
|
|
END MODULE
|