591 lines
29 KiB
Fortran
591 lines
29 KiB
Fortran
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!************************************
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!* Module: CONSTITUTIVE *
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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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!* - orientations *
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!************************************
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! [Alu]
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! constitution dislobased
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! (output) dislodensity
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! (output) rateofshear
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! lattice_structure 1
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! Nslip 12
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!
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! c11 106.75e9
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! c12 60.41e9
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! c44 28.34e9
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!
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! burgers 2.86e-10 # Burgers vector [m]
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! Qedge 3e-19 # Activation energy for dislocation glide [J/K] (0.5*G*b^3)
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! Qsd 2.4e-19 # Activation energy for self diffusion [J/K] (gamma-iron)
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! diff0 1e-3 # prefactor vacancy diffusion coeffficent (gamma-iron)
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! interaction_coefficients 1.0 2.2 3.0 1.6 3.8 4.5 # Dislocation interaction coefficients
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!
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! rho0 6.0e12 # Initial dislocation density [m/m^3]
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!
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! c1 0.1 # Passing stress adjustment
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! c2 2.0 # Jump width adjustment
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! c3 1.0 # Activation volume adjustment
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! c4 50.0 # Average slip distance adjustment for lock formation
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! c7 8.0 # Athermal recovery adjustment
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! c8 1.0e10 # Thermal recovery adjustment (plays no role for me)
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MODULE constitutive_dislobased
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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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character (len=*), parameter :: constitutive_dislobased_label = 'dislobased'
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integer(pInt), dimension(:), allocatable :: constitutive_dislobased_sizeDotState, &
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constitutive_dislobased_sizeState, &
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constitutive_dislobased_sizePostResults
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character(len=64), dimension(:,:), allocatable :: constitutive_dislobased_output
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character(len=32), dimension(:), allocatable :: constitutive_dislobased_structureName
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integer(pInt), dimension(:), allocatable :: constitutive_dislobased_structure
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integer(pInt), dimension(:), allocatable :: constitutive_dislobased_Nslip
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_C11
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_C12
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_C13
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_C33
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_C44
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_Gmod
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real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Cslip_66
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!* Visco-plastic constitutive_phenomenological parameters
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_rho0
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_bg
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_Qedge
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_Qsd
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_D0
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c1
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c2
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c3
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c4
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c5
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c6
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c7
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_c8
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real(pReal), dimension(:), allocatable :: constitutive_dislobased_CoverA
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real(pReal), dimension(:,:), allocatable :: constitutive_dislobased_SlipIntCoeff
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real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iparallel
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real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iforest
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!*************************************
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!* Definition of material properties *
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!*************************************
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!* Physical parameter, attack_frequency != Debye frequency
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real(pReal), parameter :: attack_frequency = 1.0e10_pReal
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!* Physical parameter, Boltzmann constant in J/Kelvin
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real(pReal), parameter :: kB = 1.38e-23_pReal
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!* Physical parameter, Avogadro number in 1/mol
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real(pReal), parameter :: avogadro = 6.022e23_pReal
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!* Physical parameter, Gas constant in J.mol/Kelvin
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real(pReal), parameter :: Rgaz = 8.314_pReal
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CONTAINS
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!****************************************
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!* - constitutive_init
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!* - constitutive_homogenizedC
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!* - constitutive_microstructure
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!* - constitutive_LpAndItsTangent
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!* - consistutive_dotState
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!* - consistutive_postResults
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!****************************************
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subroutine constitutive_dislobased_init(file)
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!**************************************
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!* Module initialization *
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!**************************************
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use prec, only: pInt, pReal
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use math, only: math_Mandel3333to66, math_Voigt66to3333, math_mul3x3
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use IO
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use material
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use lattice, only: lattice_sn, lattice_st, lattice_interactionSlipSlip, lattice_initializeStructure
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integer(pInt), intent(in) :: file
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integer(pInt), parameter :: maxNchunks = 7
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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integer(pInt) section, maxNinstance, i,j,k,l, output
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character(len=64) tag
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character(len=1024) line
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real(pReal) x,y
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maxNinstance = count(phase_constitution == constitutive_dislobased_label)
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if (maxNinstance == 0) return
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allocate(constitutive_dislobased_sizeDotState(maxNinstance)) ; constitutive_dislobased_sizeDotState = 0_pInt
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allocate(constitutive_dislobased_sizeState(maxNinstance)) ; constitutive_dislobased_sizeState = 0_pInt
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allocate(constitutive_dislobased_sizePostResults(maxNinstance)); constitutive_dislobased_sizePostResults = 0_pInt
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allocate(constitutive_dislobased_output(maxval(phase_Noutput), &
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maxNinstance)) ; constitutive_dislobased_output = ''
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allocate(constitutive_dislobased_structureName(maxNinstance)) ; constitutive_dislobased_structureName = ''
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allocate(constitutive_dislobased_structure(maxNinstance)) ; constitutive_dislobased_structure = 0_pInt
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allocate(constitutive_dislobased_Nslip(maxNinstance)) ; constitutive_dislobased_Nslip = 0_pInt
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allocate(constitutive_dislobased_C11(maxNinstance)) ; constitutive_dislobased_C11 = 0.0_pReal
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allocate(constitutive_dislobased_C12(maxNinstance)) ; constitutive_dislobased_C12 = 0.0_pReal
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allocate(constitutive_dislobased_C13(maxNinstance)) ; constitutive_dislobased_C13 = 0.0_pReal
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allocate(constitutive_dislobased_C33(maxNinstance)) ; constitutive_dislobased_C33 = 0.0_pReal
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allocate(constitutive_dislobased_C44(maxNinstance)) ; constitutive_dislobased_C44 = 0.0_pReal
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allocate(constitutive_dislobased_Gmod(maxNinstance)) ; constitutive_dislobased_Gmod = 0.0_pReal
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allocate(constitutive_dislobased_Cslip_66(6,6,maxNinstance)) ; constitutive_dislobased_Cslip_66 = 0.0_pReal
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allocate(constitutive_dislobased_rho0(maxNinstance)) ; constitutive_dislobased_rho0 = 0.0_pReal
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allocate(constitutive_dislobased_bg(maxNinstance)) ; constitutive_dislobased_bg = 0.0_pReal
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allocate(constitutive_dislobased_Qedge(maxNinstance)) ; constitutive_dislobased_Qedge = 0.0_pReal
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allocate(constitutive_dislobased_Qsd(maxNinstance)) ; constitutive_dislobased_Qsd = 0.0_pReal
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allocate(constitutive_dislobased_D0(maxNinstance)) ; constitutive_dislobased_D0 = 0.0_pReal
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allocate(constitutive_dislobased_c1(maxNinstance)) ; constitutive_dislobased_c1 = 0.0_pReal
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allocate(constitutive_dislobased_c2(maxNinstance)) ; constitutive_dislobased_c2 = 0.0_pReal
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allocate(constitutive_dislobased_c3(maxNinstance)) ; constitutive_dislobased_c3 = 0.0_pReal
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allocate(constitutive_dislobased_c4(maxNinstance)) ; constitutive_dislobased_c4 = 0.0_pReal
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allocate(constitutive_dislobased_c5(maxNinstance)) ; constitutive_dislobased_c5 = 0.0_pReal
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allocate(constitutive_dislobased_c6(maxNinstance)) ; constitutive_dislobased_c6 = 0.0_pReal
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allocate(constitutive_dislobased_c7(maxNinstance)) ; constitutive_dislobased_c7 = 0.0_pReal
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allocate(constitutive_dislobased_c8(maxNinstance)) ; constitutive_dislobased_c8 = 0.0_pReal
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allocate(constitutive_dislobased_CoverA(maxNinstance)) ; constitutive_dislobased_CoverA = 0.0_pReal
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allocate(constitutive_dislobased_SlipIntCoeff(6,maxNinstance)) ; constitutive_dislobased_SlipIntCoeff = 0.0_pReal
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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_dislobased_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_dislobased_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
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case ('lattice_structure')
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constitutive_dislobased_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
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case ('covera_ratio')
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constitutive_dislobased_CoverA(i) = IO_floatValue(line,positions,2)
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case ('nslip')
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constitutive_dislobased_Nslip(i) = IO_intValue(line,positions,2)
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case ('c11')
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constitutive_dislobased_C11(i) = IO_floatValue(line,positions,2)
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case ('c12')
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constitutive_dislobased_C12(i) = IO_floatValue(line,positions,2)
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case ('c13')
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constitutive_dislobased_C13(i) = IO_floatValue(line,positions,2)
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case ('c33')
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constitutive_dislobased_C33(i) = IO_floatValue(line,positions,2)
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case ('c44')
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constitutive_dislobased_C44(i) = IO_floatValue(line,positions,2)
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case ('rho0')
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constitutive_dislobased_rho0(i) = IO_floatValue(line,positions,2)
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case ('burgers')
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constitutive_dislobased_bg(i) = IO_floatValue(line,positions,2)
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case ('qedge')
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constitutive_dislobased_Qedge(i) = IO_floatValue(line,positions,2)
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case ('qsd')
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constitutive_dislobased_Qsd(i) = IO_floatValue(line,positions,2)
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case ('diff0')
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constitutive_dislobased_D0(i) = IO_floatValue(line,positions,2)
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case ('c1')
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constitutive_dislobased_c1(i) = IO_floatValue(line,positions,2)
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case ('c2')
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constitutive_dislobased_c2(i) = IO_floatValue(line,positions,2)
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case ('c3')
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constitutive_dislobased_c3(i) = IO_floatValue(line,positions,2)
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case ('c4')
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constitutive_dislobased_c4(i) = IO_floatValue(line,positions,2)
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case ('c5')
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constitutive_dislobased_c5(i) = IO_floatValue(line,positions,2)
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case ('c6')
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constitutive_dislobased_c6(i) = IO_floatValue(line,positions,2)
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case ('c7')
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constitutive_dislobased_c7(i) = IO_floatValue(line,positions,2)
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case ('c8')
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constitutive_dislobased_c8(i) = IO_floatValue(line,positions,2)
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case ('interaction_coefficients')
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forall (j=2:min(7,positions(1))) &
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constitutive_dislobased_SlipIntCoeff(j-1,i) = IO_floatValue(line,positions,j)
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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_dislobased_structure(i) = lattice_initializeStructure(constitutive_dislobased_structureName(i), &
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constitutive_dislobased_CoverA(i))
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! sanity checks
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if (constitutive_dislobased_structure(i) < 1) call IO_error(201)
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if (constitutive_dislobased_Nslip(i) < 1) call IO_error(202)
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if (constitutive_dislobased_rho0(i) < 0.0_pReal) call IO_error(220)
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if (constitutive_dislobased_bg(i) <= 0.0_pReal) call IO_error(221)
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if (constitutive_dislobased_Qedge(i) <= 0.0_pReal) call IO_error(222)
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if (constitutive_dislobased_Qsd(i) <= 0.0_pReal) call IO_error(223)
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if (constitutive_dislobased_D0(i) <= 0.0_pReal) call IO_error(224)
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enddo
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allocate(constitutive_dislobased_Iparallel(maxval(constitutive_dislobased_Nslip),&
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maxval(constitutive_dislobased_Nslip),&
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maxNinstance))
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allocate(constitutive_dislobased_Iforest(maxval(constitutive_dislobased_Nslip),&
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maxval(constitutive_dislobased_Nslip),&
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maxNinstance))
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do i = 1,maxNinstance
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constitutive_dislobased_sizeDotState(i) = constitutive_dislobased_Nslip(i)
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constitutive_dislobased_sizeState(i) = 8*constitutive_dislobased_Nslip(i)
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do j = 1,maxval(phase_Noutput)
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select case(constitutive_dislobased_output(j,i))
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case('dislodensity')
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constitutive_dislobased_sizePostResults(i) = &
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constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
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case('rateofshear')
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constitutive_dislobased_sizePostResults(i) = &
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constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
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end select
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enddo
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constitutive_dislobased_Gmod(i) = constitutive_dislobased_C44(i)
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select case (constitutive_dislobased_structure(i))
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case(1:2) ! cubic(s)
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forall(k=1:3)
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forall(j=1:3) &
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constitutive_dislobased_Cslip_66(k,j,i) = constitutive_dislobased_C12(i)
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constitutive_dislobased_Cslip_66(k,k,i) = constitutive_dislobased_C11(i)
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constitutive_dislobased_Cslip_66(k+3,k+3,i) = constitutive_dislobased_C44(i)
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end forall
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case(3:) ! all hex
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constitutive_dislobased_Cslip_66(1,1,i) = constitutive_dislobased_C11(i)
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constitutive_dislobased_Cslip_66(2,2,i) = constitutive_dislobased_C11(i)
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constitutive_dislobased_Cslip_66(3,3,i) = constitutive_dislobased_C33(i)
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constitutive_dislobased_Cslip_66(1,2,i) = constitutive_dislobased_C12(i)
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constitutive_dislobased_Cslip_66(2,1,i) = constitutive_dislobased_C12(i)
|
||
|
|
constitutive_dislobased_Cslip_66(1,3,i) = constitutive_dislobased_C13(i)
|
||
|
|
constitutive_dislobased_Cslip_66(3,1,i) = constitutive_dislobased_C13(i)
|
||
|
|
constitutive_dislobased_Cslip_66(2,3,i) = constitutive_dislobased_C13(i)
|
||
|
|
constitutive_dislobased_Cslip_66(3,2,i) = constitutive_dislobased_C13(i)
|
||
|
|
constitutive_dislobased_Cslip_66(4,4,i) = constitutive_dislobased_C44(i)
|
||
|
|
constitutive_dislobased_Cslip_66(5,5,i) = constitutive_dislobased_C44(i)
|
||
|
|
constitutive_dislobased_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_dislobased_C11(i)- &
|
||
|
|
constitutive_dislobased_C12(i))
|
||
|
|
end select
|
||
|
|
constitutive_dislobased_Cslip_66(:,:,i) = &
|
||
|
|
math_Mandel3333to66(math_Voigt66to3333(constitutive_dislobased_Cslip_66(:,:,i)))
|
||
|
|
|
||
|
|
|
||
|
|
!* Construction of the hardening matrices
|
||
|
|
!* Iteration over the systems
|
||
|
|
do j = 1,constitutive_dislobased_Nslip(i)
|
||
|
|
do k = 1,constitutive_dislobased_Nslip(i)
|
||
|
|
!* Projection of the dislocation *
|
||
|
|
x = math_mul3x3(lattice_sn(:,j,i),lattice_st(:,k,i))
|
||
|
|
y = 1.0_pReal-x**(2.0_pReal)
|
||
|
|
!* Interaction matrix *
|
||
|
|
constitutive_dislobased_Iforest(j,k,i) = abs(x)*&
|
||
|
|
constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i)
|
||
|
|
if (y>0.0_pReal) &
|
||
|
|
constitutive_dislobased_Iparallel(j,k,i) = sqrt(y)*&
|
||
|
|
constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i)
|
||
|
|
enddo
|
||
|
|
enddo
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
return
|
||
|
|
|
||
|
|
end subroutine
|
||
|
|
|
||
|
|
|
||
|
|
function constitutive_dislobased_stateInit(myInstance)
|
||
|
|
!*********************************************************************
|
||
|
|
!* initial microstructural state *
|
||
|
|
!*********************************************************************
|
||
|
|
use prec, only: pReal,pInt
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt), intent(in) :: myInstance
|
||
|
|
real(pReal), dimension(constitutive_dislobased_Nslip(myInstance)) :: constitutive_dislobased_stateInit
|
||
|
|
|
||
|
|
constitutive_dislobased_stateInit = constitutive_dislobased_rho0(myInstance)
|
||
|
|
|
||
|
|
return
|
||
|
|
end function
|
||
|
|
|
||
|
|
function constitutive_dislobased_homogenizedC(state,ipc,ip,el)
|
||
|
|
!*********************************************************************
|
||
|
|
!* homogenized elacticity matrix *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - state : state variables *
|
||
|
|
!* - ipc : component-ID of current integration point *
|
||
|
|
!* - ip : current integration point *
|
||
|
|
!* - el : current element *
|
||
|
|
!*********************************************************************
|
||
|
|
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
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
||
|
|
integer(pInt) matID
|
||
|
|
real(pReal), dimension(6,6) :: constitutive_dislobased_homogenizedC
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
||
|
|
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
constitutive_dislobased_homogenizedC = constitutive_dislobased_Cslip_66(:,:,matID)
|
||
|
|
|
||
|
|
return
|
||
|
|
|
||
|
|
end function
|
||
|
|
|
||
|
|
|
||
|
|
subroutine constitutive_dislobased_microstructure(Temperature,state,ipc,ip,el)
|
||
|
|
!*********************************************************************
|
||
|
|
!* calculate derived quantities from state (not used here) *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - Tp : temperature *
|
||
|
|
!* - ipc : component-ID of current integration point *
|
||
|
|
!* - ip : current integration point *
|
||
|
|
!* - el : current element *
|
||
|
|
!*********************************************************************
|
||
|
|
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
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt) ipc,ip,el,matID,n,i
|
||
|
|
real(pReal) Temperature
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
||
|
|
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
n = constitutive_dislobased_Nslip(matID)
|
||
|
|
!* Quantities derived from state - slip
|
||
|
|
!* State: 1 : n rho
|
||
|
|
!* n+1 : 2n rho_f
|
||
|
|
!* 2n+1 : 3n rho_p
|
||
|
|
!* 3n+1 : 4n passing stress
|
||
|
|
!* 4n+1 : 5n jump width
|
||
|
|
!* 5n+1 : 6n activation volume
|
||
|
|
!* 6n+1 : 7n rho_m
|
||
|
|
!* 7n+1 : 8n g0_slip
|
||
|
|
!$OMP CRITICAL (evilmatmul)
|
||
|
|
state(ipc,ip,el)%p((n+1):(2*n)) = matmul(constitutive_dislobased_Iforest (1:n,1:n,matID),state(ipc,ip,el)%p(1:n))
|
||
|
|
state(ipc,ip,el)%p((2*n+1):(3*n)) = matmul(constitutive_dislobased_Iparallel(1:n,1:n,matID),state(ipc,ip,el)%p(1:n))
|
||
|
|
!$OMP END CRITICAL (evilmatmul)
|
||
|
|
|
||
|
|
do i=1,n
|
||
|
|
|
||
|
|
state(ipc,ip,el)%p(3*n+i) = &
|
||
|
|
constitutive_dislobased_c1(matID)*constitutive_dislobased_Gmod(matID)*&
|
||
|
|
constitutive_dislobased_bg(matID)*sqrt(state(ipc,ip,el)%p(2*n+i))
|
||
|
|
|
||
|
|
state(ipc,ip,el)%p(4*n+i) = &
|
||
|
|
constitutive_dislobased_c2(matID)/sqrt(state(ipc,ip,el)%p(n+i))
|
||
|
|
|
||
|
|
state(ipc,ip,el)%p(5*n+i) = &
|
||
|
|
constitutive_dislobased_c3(matID)*state(ipc,ip,el)%p(4*n+i)*constitutive_dislobased_bg(matID)**2.0_pReal
|
||
|
|
|
||
|
|
state(ipc,ip,el)%p(6*n+i) = &
|
||
|
|
(2.0_pReal*kB*Temperature*sqrt(state(ipc,ip,el)%p(2*n+i)))/&
|
||
|
|
(constitutive_dislobased_c1(matID)*constitutive_dislobased_c3(matID)*constitutive_dislobased_Gmod(matID)*&
|
||
|
|
state(ipc,ip,el)%p(4*n+i)*constitutive_dislobased_bg(matID)**3.0_pReal)
|
||
|
|
|
||
|
|
state(ipc,ip,el)%p(7*n+i) = &
|
||
|
|
state(ipc,ip,el)%p(6*n+i)*constitutive_dislobased_bg(matID)*attack_frequency*state(ipc,ip,el)%p(4*n+i)*&
|
||
|
|
exp(-constitutive_dislobased_Qedge(matID)/(kB*Temperature))
|
||
|
|
|
||
|
|
enddo
|
||
|
|
|
||
|
|
end subroutine
|
||
|
|
|
||
|
|
|
||
|
|
subroutine constitutive_dislobased_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
|
||
|
|
!*********************************************************************
|
||
|
|
!* plastic velocity gradient and its tangent *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
||
|
|
!* - ipc : component-ID at current integration point *
|
||
|
|
!* - ip : current integration point *
|
||
|
|
!* - el : current element *
|
||
|
|
!* OUTPUT: *
|
||
|
|
!* - Lp : plastic velocity gradient *
|
||
|
|
!* - dLp_dTstar : derivative of Lp (4th-rank tensor) *
|
||
|
|
!*********************************************************************
|
||
|
|
use prec, only: pReal,pInt,p_vec
|
||
|
|
use math, only: math_Plain3333to99, math_mul6x6
|
||
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v
|
||
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
|
||
|
|
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt) ipc,ip,el
|
||
|
|
integer(pInt) matID,i,k,l,m,n
|
||
|
|
real(pReal) Temperature
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
||
|
|
real(pReal), dimension(6) :: Tstar_v
|
||
|
|
real(pReal), dimension(3,3) :: Lp
|
||
|
|
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
||
|
|
real(pReal), dimension(9,9) :: dLp_dTstar
|
||
|
|
real(pReal), dimension(constitutive_dislobased_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
||
|
|
gdot_slip,dgdot_dtauslip,tau_slip
|
||
|
|
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
n = constitutive_dislobased_Nslip(matID)
|
||
|
|
|
||
|
|
!* Calculation of Lp
|
||
|
|
Lp = 0.0_pReal
|
||
|
|
gdot_slip = 0.0_pReal
|
||
|
|
do i = 1,constitutive_dislobased_Nslip(matID)
|
||
|
|
tau_slip(i) = math_mul6x6(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
|
||
|
|
if ((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))>0) &
|
||
|
|
gdot_slip(i) = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip(i))*&
|
||
|
|
sinh(((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature))
|
||
|
|
|
||
|
|
Lp = Lp + gdot_slip(i)*lattice_Sslip(:,:,i,constitutive_dislobased_structure(matID))
|
||
|
|
enddo
|
||
|
|
|
||
|
|
!* Calculation of the tangent of Lp
|
||
|
|
dLp_dTstar3333 = 0.0_pReal
|
||
|
|
dLp_dTstar = 0.0_pReal
|
||
|
|
dgdot_dtauslip = 0.0_pReal
|
||
|
|
do i = 1,constitutive_dislobased_Nslip(matID)
|
||
|
|
if ((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))>0) &
|
||
|
|
dgdot_dtauslip(i) = (state(ipc,ip,el)%p(7*n+i)*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature)*&
|
||
|
|
cosh(((abs(tau_slip(i))-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature))
|
||
|
|
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
|
||
|
|
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
|
||
|
|
dgdot_dtauslip(i)*lattice_Sslip(k,l,i,constitutive_dislobased_structure(matID))* &
|
||
|
|
lattice_Sslip(m,n,i,constitutive_dislobased_structure(matID))
|
||
|
|
enddo
|
||
|
|
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
|
||
|
|
|
||
|
|
return
|
||
|
|
end subroutine
|
||
|
|
|
||
|
|
|
||
|
|
function constitutive_dislobased_dotState(Tstar_v,Temperature,state,ipc,ip,el)
|
||
|
|
!*********************************************************************
|
||
|
|
!* rate of change of microstructure *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
||
|
|
!* - ipc : component-ID at current integration point *
|
||
|
|
!* - ip : current integration point *
|
||
|
|
!* - el : current element *
|
||
|
|
!* OUTPUT: *
|
||
|
|
!* - constitutive_dotState : evolution of state variable *
|
||
|
|
!*********************************************************************
|
||
|
|
use prec, only: pReal,pInt,p_vec
|
||
|
|
use lattice, only: lattice_Sslip_v
|
||
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
|
||
|
|
implicit none
|
||
|
|
|
||
|
|
!* Definition of variables
|
||
|
|
integer(pInt) ipc,ip,el
|
||
|
|
integer(pInt) matID,i,n
|
||
|
|
real(pReal) Temperature,tau_slip,gdot_slip,locks,athermal_recovery,thermal_recovery
|
||
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
||
|
|
real(pReal), dimension(6) :: Tstar_v
|
||
|
|
real(pReal), dimension(constitutive_dislobased_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
||
|
|
constitutive_dislobased_dotState
|
||
|
|
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
n = constitutive_dislobased_Nslip(matID)
|
||
|
|
|
||
|
|
!* Dislocation density evolution
|
||
|
|
constitutive_dislobased_dotState = 0.0_pReal
|
||
|
|
do i = 1,n
|
||
|
|
tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
|
||
|
|
if (abs(tau_slip) > state(ipc,ip,el)%p(3*n+i)) then
|
||
|
|
gdot_slip = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip)*&
|
||
|
|
sinh(((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature))
|
||
|
|
|
||
|
|
locks = (sqrt(state(ipc,ip,el)%p(n+i))*abs(gdot_slip))/&
|
||
|
|
(constitutive_dislobased_c4(matID)*constitutive_dislobased_bg(matID))
|
||
|
|
|
||
|
|
athermal_recovery = constitutive_dislobased_c7(matID)*state(ipc,ip,el)%p(i)*abs(gdot_slip)
|
||
|
|
|
||
|
|
!thermal_recovery = constitutive_dislobased_c8(matID)*abs(tau_slip)*state(ipc,ip,el)%p(i)**(2.0_pReal)*&
|
||
|
|
! ((constitutive_dislobased_D0(matID)*constitutive_dislobased_bg(matID)**(3.0_pReal))/&
|
||
|
|
! (kB*Temperature))*exp(-constitutive_dislobased_Qsd(matID)/(kB*Temperature))
|
||
|
|
|
||
|
|
constitutive_dislobased_dotState(i) = locks - athermal_recovery
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
|
||
|
|
return
|
||
|
|
end function
|
||
|
|
|
||
|
|
pure function constitutive_dislobased_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
|
||
|
|
!*********************************************************************
|
||
|
|
!* return array of constitutive results *
|
||
|
|
!* INPUT: *
|
||
|
|
!* - 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 *
|
||
|
|
!*********************************************************************
|
||
|
|
use prec, only: pReal,pInt,p_vec
|
||
|
|
use math, only: math_mul6x6
|
||
|
|
use lattice, only: lattice_Sslip_v
|
||
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
||
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
|
||
|
|
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,o,i,c,n
|
||
|
|
real(pReal) tau_slip, active_rate
|
||
|
|
real(pReal), dimension(constitutive_dislobased_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
||
|
|
constitutive_dislobased_postResults
|
||
|
|
|
||
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
||
|
|
n = constitutive_dislobased_Nslip(matID)
|
||
|
|
c = 0_pInt
|
||
|
|
constitutive_dislobased_postResults = 0.0_pReal
|
||
|
|
|
||
|
|
do o = 1,phase_Noutput(material_phase(ipc,ip,el))
|
||
|
|
select case(constitutive_dislobased_output(o,matID))
|
||
|
|
case ('dislodensity')
|
||
|
|
constitutive_dislobased_postResults(c+1:c+n) = state(ipc,ip,el)%p(1:n)
|
||
|
|
c = c + n
|
||
|
|
case ('rateofshear')
|
||
|
|
do i = 1,n
|
||
|
|
tau_slip = math_mul6x6(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
|
||
|
|
if ((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))>0) then
|
||
|
|
constitutive_dislobased_postResults(c+i) = state(ipc,ip,el)%p(7*n+i)*sign(1.0_pReal,tau_slip)*&
|
||
|
|
sinh(((abs(tau_slip)-state(ipc,ip,el)%p(3*n+i))*state(ipc,ip,el)%p(5*n+i))/(kB*Temperature))
|
||
|
|
else
|
||
|
|
constitutive_dislobased_postResults(c+i) = 0.0_pReal
|
||
|
|
endif
|
||
|
|
enddo
|
||
|
|
c = c + n
|
||
|
|
end select
|
||
|
|
enddo
|
||
|
|
|
||
|
|
return
|
||
|
|
|
||
|
|
end function
|
||
|
|
|
||
|
|
END MODULE
|