1207 lines
56 KiB
Fortran
1207 lines
56 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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MODULE constitutive
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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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! MISSING consistency check after reading 'mattex.mpie'
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character(len=300), parameter :: mattexFile = 'mattex.mpie'
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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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!*************************************
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!* Definition of material properties *
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!*************************************
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!* Number of materials
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integer(pInt) material_maxN
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!* Lattice structure and number of selected slip or twin systems per material
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integer(pInt), dimension(:) , allocatable :: material_LatticeStructure
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integer(pInt), dimension(:) , allocatable :: material_Nslip
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integer(pInt), dimension(:) , allocatable :: material_Ntwin
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!* Maximum number of selected slip or twin systems over materials
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integer(pInt) material_maxNslip
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integer(pInt) material_maxNtwin
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!* Elastic constants and matrices
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real(pReal), dimension(:) , allocatable :: material_C11
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real(pReal), dimension(:) , allocatable :: material_C12
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real(pReal), dimension(:) , allocatable :: material_C13
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real(pReal), dimension(:) , allocatable :: material_C33
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real(pReal), dimension(:) , allocatable :: material_C44
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real(pReal), dimension(:) , allocatable :: material_Gmod
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real(pReal), dimension(:,:,:) , allocatable :: material_Cslip_66
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real(preal), dimension(:,:,:,:) , allocatable :: material_Ctwin_66
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!* Visco-plastic material parameters
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real(pReal), dimension(:) , allocatable :: material_rho0
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real(pReal), dimension(:) , allocatable :: material_bg
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real(pReal), dimension(:) , allocatable :: material_Qedge
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real(pReal), dimension(:) , allocatable :: material_tau0
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real(pReal), dimension(:) , allocatable :: material_GrainSize
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real(pReal), dimension(:) , allocatable :: material_StackSize
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real(pReal), dimension(:) , allocatable :: material_ActivationLength
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real(pReal), dimension(:) , allocatable :: material_TwinSaturation
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real(pReal), dimension(:) , allocatable :: material_twin_res
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real(pReal), dimension(:) , allocatable :: material_c1
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real(pReal), dimension(:) , allocatable :: material_c2
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real(pReal), dimension(:) , allocatable :: material_c3
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real(pReal), dimension(:) , allocatable :: material_c4
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real(pReal), dimension(:) , allocatable :: material_c5
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real(pReal), dimension(:) , allocatable :: material_c6
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real(pReal), dimension(:) , allocatable :: material_c7
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real(pReal), dimension(:) , allocatable :: material_c8
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real(pReal), dimension(:) , allocatable :: material_c9
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real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff
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!************************************
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!* Definition of texture properties *
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!************************************
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!* Number of textures, maximum number of Gauss and Fiber components
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integer(pInt) texture_maxN
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integer(pInt) texture_maxNGauss
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integer(pInt) texture_maxNFiber
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!* Textures definition
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character(len=80), dimension(:), allocatable :: texture_ODFfile
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character(len=80), dimension(:), allocatable :: texture_symmetry
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integer(pInt), dimension(:) , allocatable :: texture_Ngrains
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integer(pInt), dimension(:) , allocatable :: texture_NGauss
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integer(pInt),dimension(:) , allocatable :: texture_NFiber
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integer(pInt),dimension(:) , allocatable :: texture_NRandom
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integer(pInt),dimension(:) , allocatable :: texture_totalNgrains
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real(pReal), dimension(:,:,:) , allocatable :: texture_Gauss
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real(pReal), dimension(:,:,:) , allocatable :: texture_Fiber
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_EulerAngles
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!************************************
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!* Grains *
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!************************************
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integer(pInt) constitutive_maxNgrains
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integer(pInt), dimension(:,:) , allocatable :: constitutive_Ngrains
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integer(pInt), dimension(:,:,:) , allocatable :: constitutive_matID
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real(pReal), dimension(:,:,:) , allocatable :: constitutive_matVolFrac
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integer(pInt), dimension(:,:,:) , allocatable :: constitutive_texID
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real(pReal), dimension(:,:,:) , allocatable :: constitutive_texVolFrac
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!************************************
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!* Kinetics variables *
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!************************************
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real(pReal), dimension(:) , allocatable :: constitutive_tau_slip
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real(pReal), dimension(:) , allocatable :: constitutive_tau_twin
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real(pReal), dimension(:) , allocatable :: constitutive_gdot_slip
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real(pReal), dimension(:) , allocatable :: constitutive_fdot_twin
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real(pReal), dimension(:) , allocatable :: constitutive_dgdot_dtauslip
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real(pReal), dimension(:) , allocatable :: constitutive_dfdot_dtautwin
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real(pReal), dimension(:,:) , allocatable :: constitutive_dfdot_dtauslip
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real(pReal), dimension(:) , allocatable :: constitutive_locks
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real(pReal), dimension(:) , allocatable :: constitutive_grainboundaries
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real(pReal), dimension(:) , allocatable :: constitutive_twinboundaries
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real(pReal), dimension(:) , allocatable :: constitutive_recovery
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!************************************
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!* State variables *
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!************************************
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integer(pInt) constitutive_maxNstatevars
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integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nstatevars
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_old
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real(pReal), dimension(:,:,:,:), allocatable :: constitutive_state_new
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real(pReal), dimension(:) , allocatable :: constitutive_passing_stress
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real(pReal), dimension(:) , allocatable :: constitutive_jump_width
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real(pReal), dimension(:) , allocatable :: constitutive_activation_volume
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real(pReal), dimension(:) , allocatable :: constitutive_rho_m
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real(pReal), dimension(:) , allocatable :: constitutive_rho_f
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real(pReal), dimension(:) , allocatable :: constitutive_rho_p
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real(pReal), dimension(:) , allocatable :: constitutive_g0_slip
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real(pReal), dimension(:) , allocatable :: constitutive_twin_volume
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real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len
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real(pReal), dimension(:) , allocatable :: constitutive_twin_mfp
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!************************************
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!* Interaction matrices *
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!************************************
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real(pReal), dimension(:,:,:), allocatable :: constitutive_Pforest
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real(pReal), dimension(:,:,:), allocatable :: constitutive_Pparallel
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!************************************
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!* Results *
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!************************************
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integer(pInt) constitutive_maxNresults
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integer(pInt), dimension(:,:,:), allocatable :: constitutive_Nresults
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CONTAINS
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!****************************************
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!* - constitutive_Init
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!* - constitutive_CountSections
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!* - constitutive_Parse_UnknownPart
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!* - constitutive_Parse_MaterialPart
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!* - constitutive_Parse_TexturePart
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!* - constitutive_Parse_MatTexDat
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!* - constitutive_Assignment
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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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!****************************************
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subroutine constitutive_Init()
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!**************************************
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!* Module initialization *
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!**************************************
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call constitutive_Parse_MatTexDat(mattexFile)
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call constitutive_Assignment()
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end subroutine
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subroutine constitutive_CountSections(file,count,part)
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!*********************************************************************
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!* This subroutine reads a "part" from the input file until the next *
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!* part is reached and counts the number of "sections" in the part *
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!* INPUT: *
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!* - file : file ID *
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!* OUTPUT: *
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!* - part : name of the next "part" *
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!* - count : number of sections inside the current "part" *
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) part,line,tag
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integer(pInt) file,count
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integer(pInt), dimension(3) :: positions
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count=0
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part=''
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,1)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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part=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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count=count+1
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endif
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enddo
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100 return
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end subroutine
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character(len=80) function constitutive_assignNGaussAndFiber(file)
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!*********************************************************************
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt) file,section
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integer(pInt), dimension(3) :: positions
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constitutive_assignNGaussAndFiber=''
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section = 0_pInt
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,1)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_assignNGaussAndFiber=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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texture_NGauss(section) = 0_pInt
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texture_NFiber(section) = 0_pInt
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elseif (tag=='(gauss)') then
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texture_NGauss(section)=texture_NGauss(section)+1
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elseif (tag=='(fiber)') then
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texture_NFiber(section)=texture_NFiber(section)+1
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_UnknownPart(file)
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!*********************************************************************
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!* read an unknown "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt
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use IO, only: IO_stringPos,IO_stringValue,IO_lc
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 1
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integer(pInt) file
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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constitutive_parse_unknownPart=''
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do
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks)
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_Parse_UnknownPart=tag(2:len_trim(tag)-1)
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exit
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_MaterialPart(file)
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!*********************************************************************
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!* This function reads a material "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt,pReal
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use IO
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 7
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integer(pInt) i,file,section
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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section = 0
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constitutive_parse_materialPart = ''
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do while(.true.)
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_parse_materialPart=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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else
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if (section>0) then
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select case(tag)
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case ('lattice_structure')
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material_LatticeStructure(section)=IO_intValue(line,positions,2)
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write(6,*) 'lattice_structure', material_LatticeStructure(section)
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case ('nslip')
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material_Nslip(section)=IO_intValue(line,positions,2)
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write(6,*) 'nslip', material_Nslip(section)
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case ('ntwin')
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material_Ntwin(section)=IO_intValue(line,positions,2)
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write(6,*) 'ntwin', material_Ntwin(section)
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case ('c11')
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material_C11(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c11', material_C11(section)
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case ('c12')
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material_C12(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c12', material_C12(section)
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case ('c13')
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material_C13(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c13', material_C13(section)
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case ('c33')
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material_C33(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c33', material_C33(section)
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case ('c44')
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material_C44(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c44', material_C44(section)
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case ('rho0')
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material_rho0(section)=IO_floatValue(line,positions,2)
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write(6,*) 'rho0', material_rho0(section)
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case ('interaction_coefficients')
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do i=1,6
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material_SlipIntCoeff(i,section)=IO_floatValue(line,positions,i+1)
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write(6,*) 'interaction_coefficients', material_SlipIntCoeff(i,section)
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enddo
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case ('burgers')
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material_bg(section)=IO_floatValue(line,positions,2)
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write(6,*) 'burgers', material_bg(section)
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case ('qedge')
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material_Qedge(section)=IO_floatValue(line,positions,2)
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write(6,*) 'Qedge', material_Qedge(section)
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case ('tau0')
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material_tau0(section)=IO_floatValue(line,positions,2)
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write(6,*) 'tau0', material_tau0(section)
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case ('grain_size')
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material_GrainSize(section)=IO_floatValue(line,positions,2)
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write(6,*) 'grain_size', material_GrainSize(section)
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case ('stack_size')
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material_StackSize(section)=IO_floatValue(line,positions,2)
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write(6,*) 'stack_size', material_StackSize(section)
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case ('d_star')
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material_ActivationLength(section)=IO_floatValue(line,positions,2)
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write(6,*) 'activation length', material_ActivationLength(section)
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case ('f_sat')
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material_TwinSaturation(section)=IO_floatValue(line,positions,2)
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write(6,*) 'twin saturation', material_TwinSaturation(section)
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case ('twin_resistance')
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material_twin_res(section)=IO_floatValue(line,positions,2)
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write(6,*) 'twin_resistance', material_twin_res(section)
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case ('c1')
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material_c1(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c1', material_c1(section)
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case ('c2')
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material_c2(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c2', material_c2(section)
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case ('c3')
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material_c3(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c3', material_c3(section)
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case ('c4')
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material_c4(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c4', material_c4(section)
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case ('c5')
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material_c5(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c5', material_c5(section)
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case ('c6')
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material_c6(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c6', material_c6(section)
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case ('c7')
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material_c7(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c7', material_c7(section)
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case ('c8')
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material_c8(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c8', material_c8(section)
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case ('c9')
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material_c9(section)=IO_floatValue(line,positions,2)
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write(6,*) 'c9', material_c9(section)
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end select
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endif
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endif
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enddo
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100 return
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end function
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character(len=80) function constitutive_Parse_TexturePart(file)
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!*********************************************************************
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!* This function reads a texture "part" from the input file until *
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!* the next part is reached *
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!* INPUT: *
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!* - file : file ID *
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!*********************************************************************
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use prec, only: pInt
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use IO
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use math, only: inRad
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implicit none
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!* Definition of variables
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character(len=80) line,tag
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integer(pInt), parameter :: maxNchunks = 13 ! may be more than 10 chunks ..?
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integer(pInt) file,section,gaussCount,fiberCount,i
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integer(pInt), dimension(1+2*maxNchunks) :: positions
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section = 0
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gaussCount = 0
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fiberCount = 0
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constitutive_parse_texturePart = ''
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do while(.true.)
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read(file,'(a80)',END=100) line
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positions=IO_stringPos(line,maxNchunks) ! parse leading chunks
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tag=IO_lc(IO_stringValue(line,positions,1))
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if (tag(1:1)=='#' .OR. positions(1)==0) then ! skip comment and empty lines
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cycle
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elseif (tag(1:1)=='<'.AND.tag(len_trim(tag):len_trim(tag))=='>') then
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constitutive_parse_texturePart=tag(2:len_trim(tag)-1)
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exit
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elseif (tag(1:1)=='[') then
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section=section+1
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gaussCount=0
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fiberCount=0
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else
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if (section>0) then
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select case(tag)
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case ('hybridIA')
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texture_ODFfile(section)=IO_stringValue(line,positions,2)
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case ('(gauss)')
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gaussCount=gaussCount+1
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do i=2,10,2
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tag=IO_lc(IO_stringValue(line,positions,i))
|
|
select case (tag)
|
|
case('phi1')
|
|
texture_Gauss(1,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('phi')
|
|
texture_Gauss(2,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('phi2')
|
|
texture_Gauss(3,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('scatter')
|
|
texture_Gauss(4,gaussCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('fraction')
|
|
texture_Gauss(5,gaussCount,section)=IO_floatValue(line,positions,i+1)
|
|
end select
|
|
enddo
|
|
case ('(fiber)')
|
|
fiberCount=fiberCount+1
|
|
do i=2,12,2
|
|
tag=IO_lc(IO_stringValue(line,positions,i))
|
|
select case (tag)
|
|
case('alpha1')
|
|
texture_fiber(1,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('alpha2')
|
|
texture_fiber(2,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('beta1')
|
|
texture_fiber(3,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('beta2')
|
|
texture_fiber(4,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('scatter')
|
|
texture_fiber(5,fiberCount,section)=IO_floatValue(line,positions,i+1)*inRad
|
|
case('fraction')
|
|
texture_fiber(6,fiberCount,section)=IO_floatValue(line,positions,i+1)
|
|
end select
|
|
enddo
|
|
case ('ngrains')
|
|
texture_Ngrains(section)=IO_intValue(line,positions,2)
|
|
case ('symmetry')
|
|
texture_symmetry(section)=IO_stringValue(line,positions,2)
|
|
end select
|
|
endif
|
|
endif
|
|
enddo
|
|
100 return
|
|
|
|
end function
|
|
|
|
|
|
subroutine constitutive_Parse_MatTexDat(filename)
|
|
!*********************************************************************
|
|
!* This function reads the material and texture input file *
|
|
!* INPUT: *
|
|
!* - filename : name of input file *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use IO, only: IO_error, IO_open_file
|
|
use math, only: math_Mandel3333to66, math_Voigt66to3333
|
|
use lattice, only: lattice_MaxMaxNslipOfStructure,lattice_MaxMaxNtwinOfStructure
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
character(len=*) filename
|
|
character(len=80) part,formerPart
|
|
integer(pInt) sectionCount,i,j,k, fileunit
|
|
|
|
! set fileunit
|
|
fileunit=200
|
|
!-----------------------------
|
|
!* First reading: number of materials and textures
|
|
!-----------------------------
|
|
!* determine material_maxN and texture_maxN from last respective parts
|
|
if(IO_open_file(fileunit,filename)==.false.) goto 100
|
|
part = '_dummy_'
|
|
do while (part/='')
|
|
formerPart = part
|
|
call constitutive_CountSections(fileunit,sectionCount,part)
|
|
select case (formerPart)
|
|
case ('materials')
|
|
material_maxN = sectionCount
|
|
case ('textures')
|
|
texture_maxN = sectionCount
|
|
end select
|
|
enddo
|
|
!* Array allocation
|
|
allocate(material_LatticeStructure(material_maxN)) ; material_LatticeStructure=0_pInt
|
|
allocate(material_Nslip(material_maxN)) ; material_Nslip=0_pInt
|
|
allocate(material_Ntwin(material_maxN)) ; material_Ntwin=0_pInt
|
|
allocate(material_C11(material_maxN)) ; material_C11=0.0_pReal
|
|
allocate(material_C12(material_maxN)) ; material_C12=0.0_pReal
|
|
allocate(material_C13(material_maxN)) ; material_C13=0.0_pReal
|
|
allocate(material_C33(material_maxN)) ; material_C33=0.0_pReal
|
|
allocate(material_C44(material_maxN)) ; material_C44=0.0_pReal
|
|
allocate(material_Gmod(material_maxN)) ; material_Gmod=0.0_pReal
|
|
allocate(material_Cslip_66(6,6,material_maxN)) ; material_Cslip_66=0.0_pReal
|
|
allocate(material_Ctwin_66(6,6,lattice_MaxMaxNtwinOfStructure,material_maxN)) ; material_Ctwin_66=0.0_pReal
|
|
allocate(material_rho0(material_maxN)) ; material_rho0=0.0_pReal
|
|
allocate(material_SlipIntCoeff(lattice_MaxMaxNslipOfStructure,material_maxN)) ; material_SlipIntCoeff=0.0_pReal
|
|
allocate(material_bg(material_maxN)) ; material_bg=0.0_pReal
|
|
allocate(material_Qedge(material_maxN)) ; material_Qedge=0.0_pReal
|
|
allocate(material_tau0(material_maxN)) ; material_tau0=0.0_pReal
|
|
allocate(material_GrainSize(material_maxN)) ; material_GrainSize=0.0_pReal
|
|
allocate(material_StackSize(material_maxN)) ; material_StackSize=0.0_pReal
|
|
allocate(material_ActivationLength(material_maxN)) ; material_ActivationLength=0.0_pReal
|
|
allocate(material_TwinSaturation(material_maxN)) ; material_TwinSaturation=0.0_pReal
|
|
allocate(material_twin_res(material_maxN)) ; material_twin_res=0.0_pReal
|
|
allocate(material_c1(material_maxN)) ; material_c1=0.0_pReal
|
|
allocate(material_c2(material_maxN)) ; material_c2=0.0_pReal
|
|
allocate(material_c3(material_maxN)) ; material_c3=0.0_pReal
|
|
allocate(material_c4(material_maxN)) ; material_c4=0.0_pReal
|
|
allocate(material_c5(material_maxN)) ; material_c5=0.0_pReal
|
|
allocate(material_c6(material_maxN)) ; material_c6=0.0_pReal
|
|
allocate(material_c7(material_maxN)) ; material_c7=0.0_pReal
|
|
allocate(material_c8(material_maxN)) ; material_c8=0.0_pReal
|
|
allocate(material_c9(material_maxN)) ; material_c9=0.0_pReal
|
|
allocate(texture_ODFfile(texture_maxN)) ; texture_ODFfile=''
|
|
allocate(texture_Ngrains(texture_maxN)) ; texture_Ngrains=0_pInt
|
|
allocate(texture_symmetry(texture_maxN)) ; texture_symmetry=''
|
|
allocate(texture_NGauss(texture_maxN)) ; texture_NGauss=0_pInt
|
|
allocate(texture_NFiber(texture_maxN)) ; texture_NFiber=0_pInt
|
|
allocate(texture_NRandom(texture_maxN)) ; texture_NRandom=0_pInt
|
|
|
|
!-----------------------------
|
|
!* Second reading: number of Gauss and Fiber
|
|
!-----------------------------
|
|
rewind(fileunit)
|
|
part = '_dummy_'
|
|
do while (part/='')
|
|
select case (part)
|
|
case ('textures')
|
|
part = constitutive_assignNGaussAndFiber(fileunit)
|
|
case default
|
|
part = constitutive_Parse_UnknownPart(fileunit)
|
|
end select
|
|
enddo
|
|
!* Array allocation
|
|
texture_maxNGauss=maxval(texture_NGauss)
|
|
texture_maxNFiber=maxval(texture_NFiber)
|
|
allocate(texture_Gauss(5,texture_maxNGauss,texture_maxN)) ; texture_Gauss=0.0_pReal
|
|
allocate(texture_Fiber(6,texture_maxNFiber,texture_maxN)) ; texture_Fiber=0.0_pReal
|
|
|
|
!-----------------------------
|
|
!* Third reading: materials and textures are stored
|
|
!-----------------------------
|
|
rewind(fileunit)
|
|
part='_dummy_'
|
|
do while (part/='')
|
|
select case (part)
|
|
case ('materials')
|
|
part=constitutive_Parse_MaterialPart(fileunit)
|
|
case ('textures')
|
|
part=constitutive_Parse_TexturePart(fileunit)
|
|
case default
|
|
part=constitutive_Parse_UnknownPart(fileunit)
|
|
end select
|
|
enddo
|
|
close(fileunit)
|
|
|
|
|
|
!* Construction of the elasticity matrices
|
|
do i=1,material_maxN
|
|
select case (material_LatticeStructure(i))
|
|
case(1:2) ! cubic(s)
|
|
material_Gmod(i)=material_C44(i)
|
|
forall(k=1:3)
|
|
forall(j=1:3)
|
|
material_Cslip_66(k,j,i)=material_C12(i)
|
|
endforall
|
|
material_Cslip_66(k,k,i)=material_C11(i)
|
|
material_Cslip_66(k+3,k+3,i)=material_C44(i)
|
|
endforall
|
|
case(3) ! hcp
|
|
material_Gmod(i)=material_C44(i)
|
|
!* MISSING: Warning message: C44 in hexagonal structures?
|
|
material_Cslip_66(1,1,i)=material_C11(i)
|
|
material_Cslip_66(2,2,i)=material_C11(i)
|
|
material_Cslip_66(3,3,i)=material_C33(i)
|
|
material_Cslip_66(1,2,i)=material_C12(i)
|
|
material_Cslip_66(2,1,i)=material_C12(i)
|
|
material_Cslip_66(1,3,i)=material_C13(i)
|
|
material_Cslip_66(3,1,i)=material_C13(i)
|
|
material_Cslip_66(2,3,i)=material_C13(i)
|
|
material_Cslip_66(3,2,i)=material_C13(i)
|
|
material_Cslip_66(4,4,i)=material_C44(i)
|
|
material_Cslip_66(5,5,i)=material_C44(i)
|
|
material_Cslip_66(6,6,i)=0.5_pReal*(material_C11(i)-material_C12(i))
|
|
end select
|
|
material_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(material_Cslip_66(:,:,i)))
|
|
enddo
|
|
|
|
! MISSING some consistency checks may be..?
|
|
! if ODFfile present then set NGauss NFiber =0
|
|
return
|
|
100 call IO_error(200) ! corrupt materials_textures file
|
|
end subroutine
|
|
|
|
|
|
subroutine constitutive_Assignment()
|
|
!*********************************************************************
|
|
!* This subroutine assign material parameters according to ipc,ip,el *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use math, only: math_sampleGaussOri,math_sampleFiberOri,math_sampleRandomOri,math_symmetricEulers,math_EulerToR,&
|
|
math_Mandel3333to66,math_Mandel66to3333
|
|
use mesh, only: mesh_NcpElems,FE_Nips,mesh_maxNips,mesh_element
|
|
use IO, only: IO_hybridIA
|
|
use lattice, only: lattice_SlipIntType,lattice_sn,lattice_st,lattice_Qtwin,lattice_Sslip_v,lattice_Sslip
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) e,g,i,j,k,l,m,n,o,p,q,r,s
|
|
integer(pInt) matID,texID
|
|
real(pReal) x,y
|
|
integer(pInt), dimension(:,:,:), allocatable :: hybridIA_population
|
|
integer(pInt), dimension(texture_maxN) :: Ncomponents,Nsym,multiplicity,ODFmap,sampleCount
|
|
real(pReal), dimension(3,4*(1+texture_maxNGauss+texture_maxNfiber)) :: Euler
|
|
real(pReal), dimension(4*(1+texture_maxNGauss+texture_maxNfiber)) :: texVolfrac
|
|
real(pReal), dimension(texture_maxN) :: sumVolfrac
|
|
real(pReal), dimension(3,3,3,3) :: C_3333,Ctwin_3333
|
|
real(pReal), dimension(3,3) :: Qtwin
|
|
|
|
! process textures
|
|
o = 0_pInt ! ODF counter
|
|
ODFmap = 0_pInt ! blank mapping
|
|
sampleCount = 0_pInt ! count orientations assigned per texture
|
|
|
|
do texID=1,texture_maxN
|
|
select case (texture_symmetry(texID)) ! set symmetry factor
|
|
case ('orthotropic')
|
|
Nsym(texID) = 4_pInt
|
|
case ('monoclinic')
|
|
Nsym(texID) = 2_pInt
|
|
case default
|
|
Nsym(texID) = 1_pInt
|
|
end select
|
|
if (texture_ODFfile(texID)=='') then ! texture components
|
|
sumVolfrac(texID) = sum(texture_gauss(5,:,texID))+sum(texture_fiber(6,:,texID))
|
|
if (sumVolfrac(texID)<1.0_pReal) texture_NRandom(texID) = 1_pInt ! check whether random component missing
|
|
Ncomponents(texID) = texture_NGauss(texID)+texture_NFiber(texID)+texture_NRandom(texID)
|
|
else ! hybrid IA
|
|
o = o+1
|
|
ODFmap(texID) = o ! remember mapping
|
|
Ncomponents(texID) = 1_pInt ! single "component"
|
|
endif
|
|
! adjust multiplicity and number of grains per IP of components
|
|
multiplicity(texID) = max(1_pInt,texture_Ngrains(texID)/Ncomponents(texID)/Nsym(texID))
|
|
if (mod(texture_Ngrains(texID),Ncomponents(texID)*Nsym(texID)) /= 0_pInt) then
|
|
texture_Ngrains(texID) = multiplicity(texID)*Ncomponents(texID)*Nsym(texID)
|
|
write (6,*) 'changed Ngrains to',texture_Ngrains(texID),' for texture',texID
|
|
endif
|
|
enddo
|
|
|
|
!* publish globals
|
|
constitutive_maxNgrains = maxval(texture_Ngrains)
|
|
material_maxNslip = maxval(material_Nslip) ! max of slip systems among materials present
|
|
material_maxNtwin = maxval(material_Ntwin) ! max of twin systems among materials present
|
|
constitutive_maxNstatevars = maxval(material_Nslip) + maxval(material_Ntwin)
|
|
! -----------------------------------------------------------------------------------------------------------------------
|
|
constitutive_maxNresults = 24_pInt
|
|
! -----------------------------------------------------------------------------------------------------------------------
|
|
|
|
|
|
!* calc texture_totalNgrains
|
|
allocate(texture_totalNgrains(texture_maxN)) ; texture_totalNgrains=0_pInt
|
|
do i=1,mesh_NcpElems
|
|
texID = mesh_element(4,i)
|
|
texture_totalNgrains(texID) = texture_totalNgrains(texID) + FE_Nips(mesh_element(2,i))*texture_Ngrains(texID)
|
|
enddo
|
|
|
|
! generate hybridIA samplings for ODFfile textures to later draw from these populations
|
|
allocate(hybridIA_population(3,maxval(texture_totalNgrains/Nsym,ODFmap /= 0),o))
|
|
do texID = 1,texture_maxN
|
|
if (ODFmap(texID) > 0) &
|
|
hybridIA_population(:,:,ODFmap(texID)) = IO_hybridIA(texture_totalNgrains(texID)/Nsym(texID),texture_ODFfile(texID))
|
|
enddo
|
|
|
|
!* Array allocation
|
|
allocate(constitutive_Ngrains(mesh_maxNips,mesh_NcpElems)) ; constitutive_Ngrains=0_pInt
|
|
allocate(constitutive_matID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_matID=0_pInt
|
|
allocate(constitutive_texID(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_texID=0_pInt
|
|
allocate(constitutive_MatVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_MatVolFrac=0.0_pReal
|
|
allocate(constitutive_TexVolFrac(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_TexVolFrac=0.0_pReal
|
|
allocate(constitutive_EulerAngles(3,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_EulerAngles=0.0_pReal
|
|
allocate(constitutive_Nresults(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nresults=0_pInt
|
|
allocate(constitutive_Nstatevars(constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems)) ; constitutive_Nstatevars=0_pInt
|
|
allocate(constitutive_state_old(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
|
|
constitutive_state_old=0.0_pReal
|
|
allocate(constitutive_state_new(constitutive_maxNstatevars,constitutive_maxNgrains,mesh_maxNips,mesh_NcpElems))
|
|
constitutive_state_new=0.0_pReal
|
|
allocate(constitutive_Pforest(material_maxNslip,material_maxNslip,material_maxN))
|
|
constitutive_Pforest=0.0_pReal
|
|
allocate(constitutive_Pparallel(material_maxNslip,material_maxNslip,material_maxN))
|
|
constitutive_Pparallel=0.0_pReal
|
|
allocate(constitutive_rho_p(material_maxNslip)) ; constitutive_rho_p=0.0_pReal
|
|
allocate(constitutive_rho_f(material_maxNslip)) ; constitutive_rho_f=0.0_pReal
|
|
allocate(constitutive_rho_m(material_maxNslip)) ; constitutive_rho_m=0.0_pReal
|
|
allocate(constitutive_passing_stress(material_maxNslip)) ; constitutive_passing_stress=0.0_pReal
|
|
allocate(constitutive_jump_width(material_maxNslip)) ; constitutive_jump_width=0.0_pReal
|
|
allocate(constitutive_activation_volume(material_maxNslip)) ; constitutive_activation_volume=0.0_pReal
|
|
allocate(constitutive_g0_slip(material_maxNslip)) ; constitutive_g0_slip=0.0_pReal
|
|
allocate(constitutive_twin_volume(material_maxNtwin)) ; constitutive_twin_volume=0.0_pReal
|
|
allocate(constitutive_inv_intertwin_len(material_maxNtwin)) ; constitutive_inv_intertwin_len=0.0_pReal
|
|
allocate(constitutive_twin_mfp(material_maxNtwin)) ; constitutive_twin_mfp=0.0_pReal
|
|
allocate(constitutive_tau_slip(material_maxNslip)) ; constitutive_tau_slip=0.0_pReal
|
|
allocate(constitutive_tau_twin(material_maxNtwin)) ; constitutive_tau_twin=0.0_pReal
|
|
allocate(constitutive_gdot_slip(material_maxNslip)) ; constitutive_gdot_slip=0.0_pReal
|
|
allocate(constitutive_fdot_twin(material_maxNtwin)) ; constitutive_fdot_twin=0.0_pReal
|
|
allocate(constitutive_dgdot_dtauslip(material_maxNslip)) ; constitutive_dgdot_dtauslip=0.0_pReal
|
|
allocate(constitutive_dfdot_dtautwin(material_maxNtwin)) ; constitutive_dfdot_dtautwin=0.0_pReal
|
|
allocate(constitutive_dfdot_dtauslip(material_maxNtwin,material_maxNslip)) ; constitutive_dfdot_dtauslip=0.0_pReal
|
|
allocate(constitutive_locks(material_maxNslip)) ; constitutive_locks=0.0_pReal
|
|
allocate(constitutive_grainboundaries(material_maxNslip)) ; constitutive_grainboundaries=0.0_pReal
|
|
allocate(constitutive_twinboundaries(material_maxNslip)) ; constitutive_twinboundaries=0.0_pReal
|
|
allocate(constitutive_recovery(material_maxNslip)) ; constitutive_locks=0.0_pReal
|
|
|
|
!* Assignment of all grains in all IPs of all cp-elements
|
|
do e=1,mesh_NcpElems
|
|
matID=mesh_element(3,e)
|
|
texID=mesh_element(4,e)
|
|
do i=1,FE_Nips(mesh_element(2,e))
|
|
g = 0_pInt ! grain counter
|
|
do m = 1,multiplicity(texID)
|
|
o = 0_pInt ! component counter
|
|
if (texture_ODFfile(texID)=='') then
|
|
do k = 1,texture_nGauss(texID) ! *** gauss ***
|
|
o = o+1
|
|
Euler(:,o) = math_sampleGaussOri(texture_Gauss(1:3,k,texID),texture_Gauss(4,k,texID))
|
|
texVolFrac(o) = texture_Gauss(5,k,texID)
|
|
enddo
|
|
do k = 1,texture_nFiber(texID) ! *** fiber ***
|
|
o = o+1
|
|
Euler(:,o) = math_sampleFiberOri(texture_Fiber(1:2,k,texID),texture_Fiber(3:4,k,texID),texture_Fiber(5,k,texID))
|
|
texVolFrac(o) = texture_Fiber(6,k,texID)
|
|
enddo
|
|
do k = 1,texture_nRandom(texID) ! *** random ***
|
|
o = o+1
|
|
Euler(:,o) = math_sampleRandomOri()
|
|
texVolfrac(o) = 1.0_pReal-sumVolfrac(texID)
|
|
enddo
|
|
else ! *** hybrid IA ***
|
|
o = 1 ! only singular orientation, i.e. single "component"
|
|
Euler(:,o) = hybridIA_population(:,1+sampleCount(texID),ODFmap(texID))
|
|
texVolfrac(o) = 1.0_pReal
|
|
endif
|
|
if (Nsym(texID) > 1) then ! symmetry generates additional orientations
|
|
forall (k=1:o)
|
|
Euler(:,1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = &
|
|
math_symmetricEulers(texture_symmetry(texID),Euler(:,k))
|
|
texVolfrac(1+o+(Nsym(texID)-1)*(k-1):3+o+(Nsym(texID)-1)*(k-1)) = texVolfrac(k)
|
|
end forall
|
|
endif
|
|
do s = 1,Nsym(texID)*o ! loop over orientations to be assigned to ip (ex multiplicity)
|
|
g = g+1 ! next "grain"
|
|
constitutive_matID(g,i,e) = matID ! copy matID of element
|
|
constitutive_texID(g,i,e) = texID ! copy texID of element
|
|
constitutive_MatVolFrac(g,i,e) = 1.0_pReal ! singular material (so far)
|
|
constitutive_TexVolFrac(g,i,e) = texVolfrac(s)/multiplicity(texID)/Nsym(texID)
|
|
constitutive_Nstatevars(g,i,e) = material_Nslip(matID) + material_Ntwin(matID)! number of state variables (i.e. tau_c of each slip system)
|
|
! -----------------------------------------------------------------------------------------------------------------------
|
|
constitutive_Nresults(g,i,e) = 24 ! number of constitutive results output by constitutive_post_results
|
|
! -----------------------------------------------------------------------------------------------------------------------
|
|
constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation
|
|
forall (l=1:material_Nslip(matID)) ! initialize state variables
|
|
constitutive_state_old(l,g,i,e) = material_rho0(matID)
|
|
constitutive_state_new(l,g,i,e) = material_rho0(matID)
|
|
end forall
|
|
enddo ! components
|
|
sampleCount(texID) = sampleCount(texID)+1 ! next member of hybrid IA population
|
|
enddo ! multiplicity
|
|
enddo ! ip
|
|
enddo ! cp_element
|
|
|
|
!* Construction of the rotated elasticity matrices for twinning
|
|
do i=1,material_maxN
|
|
C_3333=math_Mandel66to3333(material_Cslip_66(:,:,i))
|
|
do j=1,material_Ntwin(i)
|
|
Qtwin=lattice_Qtwin(:,:,j,material_LatticeStructure(i))
|
|
do k=1,3
|
|
do l=1,3
|
|
do m=1,3
|
|
do n=1,3
|
|
Ctwin_3333(k,l,m,n)=0.0_pReal
|
|
do p=1,3
|
|
do q=1,3
|
|
do r=1,3
|
|
do s=1,3
|
|
Ctwin_3333(k,l,m,n)=Ctwin_3333(k,l,m,n)+C_3333(p,q,r,s)*Qtwin(k,p)*Qtwin(l,q)*Qtwin(m,r)*Qtwin(n,s)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
!* Mapping back to 66-format of the matrices
|
|
material_Ctwin_66(:,:,j,i) = math_Mandel3333to66(Ctwin_3333)
|
|
enddo
|
|
enddo
|
|
|
|
!* Construction of the hardening matrices
|
|
do i=1,material_maxN
|
|
!* Iteration over the systems
|
|
do j=1,material_Nslip(i)
|
|
do k=1,material_Nslip(i)
|
|
!* Projection of the dislocation *
|
|
x=dot_product(lattice_sn(:,j,i),lattice_st(:,k,i))
|
|
y=1.0_pReal-x**(2.0_pReal)
|
|
!* Interaction matrix *
|
|
constitutive_Pforest(j,k,i)=abs(x)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
|
|
if (y>0.0_pReal) then
|
|
constitutive_Pparallel(j,k,i)=sqrt(y)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
|
|
else
|
|
constitutive_Pparallel(j,k,i)=0.0_pReal
|
|
endif
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
end subroutine
|
|
|
|
|
|
function constitutive_HomogenizedC(state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* This function returns the 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
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,i,startIdxTwin
|
|
real(pReal), dimension(6,6) :: constitutive_homogenizedC
|
|
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
|
|
|
|
!* Get the material-ID from the triplet(ipc,ip,el)
|
|
matID = constitutive_matID(ipc,ip,el)
|
|
startIdxTwin = material_Nslip(matID)
|
|
|
|
!* Homogenization scheme
|
|
constitutive_homogenizedC=(1-sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))))*&
|
|
material_Cslip_66(:,:,matID)
|
|
do i=1,material_Ntwin(matID)
|
|
constitutive_homogenizedC=constitutive_homogenizedC+state(startIdxTwin+i)*material_Ctwin_66(:,:,i,matID)
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
subroutine constitutive_Microstructure(state,Tp,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* This function calculates from state needed variables *
|
|
!* INPUT: *
|
|
!* - state : state variables *
|
|
!* - Tp : temperature *
|
|
!* - ipc : component-ID of current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use math, only: pi
|
|
use lattice, only: lattice_TwinIntType
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,i,j,startIdxTwin
|
|
real(pReal) Tp,Ftwin
|
|
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
|
|
|
|
!* Get the material-ID from the triplet(ipc,ip,el)
|
|
matID = constitutive_matID(ipc,ip,el)
|
|
startIdxTwin = material_Nslip(matID)
|
|
|
|
!* Quantities derived from state - slip
|
|
constitutive_rho_f=matmul(constitutive_Pforest (1:material_Nslip(matID),1:material_Nslip(matID),matID),state)
|
|
constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state)
|
|
do i=1,material_Nslip(matID)
|
|
constitutive_passing_stress(i) = material_tau0(matID)+material_c1(matID)*material_Gmod(matID)*material_bg(matID)*&
|
|
sqrt(constitutive_rho_p(i))
|
|
|
|
constitutive_jump_width(i) = material_c2(matID)/sqrt(constitutive_rho_f(i))
|
|
|
|
constitutive_activation_volume(i) = material_c3(matID)*constitutive_jump_width(i)*material_bg(matID)**2.0_pReal
|
|
|
|
constitutive_rho_m(i) = (2.0_pReal*kB*Tp*sqrt(constitutive_rho_p(i)))/&
|
|
(material_c1(matID)*material_c3(matID)*material_Gmod(matID)*constitutive_jump_width(i)*&
|
|
material_bg(matID)**3.0_pReal)
|
|
|
|
constitutive_g0_slip(i) = constitutive_rho_m(i)*material_bg(matID)*attack_frequency*constitutive_jump_width(i)*&
|
|
exp(-(material_Qedge(matID)+constitutive_passing_stress(i)*constitutive_activation_volume(i))/&
|
|
(kB*Tp))
|
|
enddo
|
|
|
|
!* Quantities derived from state - twin
|
|
Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
|
do i=1,material_Ntwin(matID)
|
|
!* Inverse of the average distance between 2 twins of the same familly
|
|
constitutive_inv_intertwin_len(i)=0.0_pReal
|
|
do j=1,material_Ntwin(matID)
|
|
constitutive_inv_intertwin_len(i)=constitutive_inv_intertwin_len(i)+&
|
|
(lattice_TwinIntType(i,j,material_LatticeStructure(matID))*state(startIdxTwin+j))/&
|
|
(2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin))
|
|
enddo
|
|
constitutive_twin_mfp(i)=(1.0_pReal)/((1.0_pReal/material_GrainSize(matID))+constitutive_inv_intertwin_len(i))
|
|
constitutive_twin_volume(i)=(pi/6.0_pReal)*material_StackSize(matID)*constitutive_twin_mfp(i)**2.0_pReal
|
|
enddo
|
|
|
|
return
|
|
end subroutine
|
|
|
|
|
|
subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* This subroutine contains the constitutive equation for *
|
|
!* calculating the velocity gradient *
|
|
!* INPUT: *
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
|
!* - state : current microstructure *
|
|
!* - Tp : temperature *
|
|
!* - ipc : component-ID of current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!* OUTPUT: *
|
|
!* - Lp : plastic velocity gradient *
|
|
!* - dLp_dTstar : derivative of Lp (4th-order tensor) *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_TwinShear
|
|
use math, only: math_Plain3333to99
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,startIdxTwin,i,j,k,l,m,n
|
|
real(pReal) Tp,Ftwin
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal), dimension(3,3) :: Lp,Sslip,Stwin
|
|
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
|
|
real(pReal), dimension(9,9) :: dLp_dTstar
|
|
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
|
|
|
|
!* Get the material-ID from the triplet(ipc,ip,el)
|
|
matID = constitutive_matID(ipc,ip,el)
|
|
startIdxTwin = material_Nslip(matID)
|
|
|
|
!* Calculation of Lp - slip
|
|
Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
|
Lp = 0.0_pReal
|
|
do i=1,material_Nslip(matID)
|
|
constitutive_tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_LatticeStructure(matID)))
|
|
if (abs(constitutive_tau_slip(i))>constitutive_passing_stress(i)) then
|
|
constitutive_gdot_slip(i) = constitutive_g0_slip(i)*&
|
|
sinh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
|
constitutive_dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(kB*Tp)*&
|
|
cosh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
|
else
|
|
constitutive_gdot_slip(i) = 0.0_pReal
|
|
constitutive_dgdot_dtauslip(i) = 0.0_pReal
|
|
endif
|
|
Lp=Lp+(1.0_pReal-Ftwin)*constitutive_gdot_slip(i)*lattice_Sslip(:,:,i,material_LatticeStructure(matID))
|
|
enddo
|
|
|
|
!* Calculation of Lp - twin
|
|
!do i=1,material_Ntwin(matID)
|
|
! constitutive_tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_LatticeStructure(matID)))
|
|
! if (constitutive_tau_twin(i)>0.0_pReal) then
|
|
! constitutive_fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*&
|
|
! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*&
|
|
! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*&
|
|
! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)))
|
|
! constitutive_dfdot_dtautwin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*&
|
|
! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*&
|
|
! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*&
|
|
! (material_c9(matID)/constitutive_tau_twin(i))*&
|
|
! (material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)*&
|
|
! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)))
|
|
! do j=1,material_Nslip(matID)
|
|
! if (constitutive_gdot_slip(i)>0.0_pReal) then
|
|
! constitutive_dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*&
|
|
! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*&
|
|
! (material_ActivationLength(matID)/material_bg(matID))*constitutive_dgdot_dtauslip(j)*&
|
|
! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)))
|
|
! else
|
|
! constitutive_dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*&
|
|
! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*&
|
|
! (material_ActivationLength(matID)/material_bg(matID))*(-constitutive_dgdot_dtauslip(j))*&
|
|
! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)))
|
|
! endif
|
|
! enddo
|
|
! else
|
|
! constitutive_fdot_twin(i)=0.0_pReal
|
|
! constitutive_dfdot_dtautwin(i)=0.0_pReal
|
|
! do j=1,material_Nslip(matID)
|
|
! constitutive_dfdot_dtauslip(i,j)=0.0_pReal
|
|
! enddo
|
|
! endif
|
|
! Lp=Lp+state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*constitutive_fdot_twin(i)*&
|
|
! lattice_Stwin(:,:,i,material_LatticeStructure(matID))
|
|
!enddo
|
|
|
|
|
|
!* Calculation of the tangent of Lp
|
|
dLp_dTstar3333=0.0_pReal
|
|
do i=1,material_Nslip(matID)
|
|
Sslip = lattice_Sslip(:,:,i,material_LatticeStructure(matID))
|
|
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)+ &
|
|
(1.0_pReal-Ftwin)*constitutive_dgdot_dtauslip(i)*Sslip(k,l)*Sslip(m,n) !force m,n symmetry
|
|
endforall
|
|
enddo
|
|
!do i=1,material_Ntwin(matID)
|
|
! Stwin = lattice_Stwin(:,:,i,material_LatticeStructure(matID))
|
|
! 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)+ &
|
|
! state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*&
|
|
! constitutive_dfdot_dtautwin(i)*Stwin(k,l)*Stwin(m,n) !force m,n symmetry
|
|
! endforall
|
|
! do j=1,material_Nslip(matID)
|
|
! Sslip = lattice_Sslip(:,:,j,material_LatticeStructure(matID))
|
|
! 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)+ &
|
|
! state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*&
|
|
! constitutive_dfdot_dtauslip(i,j)*Stwin(k,l)*Sslip(m,n) !force m,n symmetry
|
|
! endforall
|
|
! enddo
|
|
!enddo
|
|
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
|
|
|
|
return
|
|
end subroutine
|
|
|
|
|
|
function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* This subroutine contains the constitutive equation for *
|
|
!* calculating rate of change of microstructure *
|
|
!* INPUT: *
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
|
!* - state : current microstructure *
|
|
!* - Tp : temperature *
|
|
!* - ipc : component-ID of current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!* OUTPUT: *
|
|
!* - constitutive_DotState : evolution of state variable *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use lattice, only: lattice_Sslip_v,lattice_Stwin_v
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,i,j,startIdxTwin
|
|
real(pReal) Tp,Ftwin
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state
|
|
|
|
!* Get the material-ID from the triplet(ipc,ip,el)
|
|
matID = constitutive_matID(ipc,ip,el)
|
|
startIdxTwin = material_Nslip(matID)
|
|
constitutive_dotState = 0.0_pReal
|
|
|
|
!* Dislocation density evolution
|
|
do i=1,material_Nslip(matID)
|
|
constitutive_tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_LatticeStructure(matID)))
|
|
if (abs(constitutive_tau_slip(i))>constitutive_passing_stress(i)) then
|
|
constitutive_gdot_slip(i) = constitutive_g0_slip(i)*&
|
|
sinh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp))
|
|
else
|
|
constitutive_gdot_slip(i) = 0.0_pReal
|
|
endif
|
|
constitutive_locks(i) = (sqrt(constitutive_rho_f(i))*abs(constitutive_gdot_slip(i)))/&
|
|
(material_c4(matID)*material_bg(matID))
|
|
|
|
constitutive_grainboundaries(i) = abs(constitutive_gdot_slip(i))/(material_c5(matID)*material_bg(matID)*material_GrainSize(matID))
|
|
! if (material_Ntwin(matID)>0) then
|
|
! constitutive_twinboundaries(i) = (abs(constitutive_gdot_slip(i))*constitutive_inv_intertwin_len(i))/&
|
|
! (material_c6(matID)*material_bg(matID))
|
|
! endif
|
|
constitutive_recovery(i) = material_c7(matID)*state(i)*abs(constitutive_gdot_slip(i))
|
|
constitutive_dotState(i) = constitutive_locks(i)+constitutive_grainboundaries(i)-constitutive_recovery(i)
|
|
! constitutive_dotState(i) = constitutive_locks(i)+constitutive_grainboundaries(i)+constitutive_twinboundaries(i)&
|
|
! -constitutive_recovery(i)
|
|
enddo
|
|
|
|
!* Twin volume fraction evolution
|
|
!Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
|
|
!do i=1,material_Ntwin(matID)
|
|
! constitutive_tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_LatticeStructure(matID)))
|
|
! if (constitutive_tau_twin(i)>0.0_pReal) then
|
|
! constitutive_fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*&
|
|
! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*&
|
|
! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*&
|
|
! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)))
|
|
! else
|
|
! constitutive_fdot_twin(i) = 0.0_pReal
|
|
! endif
|
|
! constitutive_dotState(startIdxTwin+i)=constitutive_fdot_twin(i)
|
|
!enddo
|
|
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!constitutive_dotState=0.0_pReal
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return
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end function
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function constitutive_post_results(Tstar_v,state,Tp,dt,ipc,ip,el)
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!*********************************************************************
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!* return array of constitutive results *
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!* INPUT: *
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!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
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!* - state : current microstructure *
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!* - dt : current time increment *
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!* - Tp : temperature *
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!* - ipc : component-ID of current integration point *
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!* - ip : current integration point *
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!* - el : current element *
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!* constitutive_Nresults has to be set accordingly in _Assignment *
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!*********************************************************************
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use prec, only: pReal,pInt
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use lattice, only: lattice_Sslip_v
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implicit none
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!* Definition of variables
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integer(pInt) ipc,ip,el
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|
integer(pInt) matID,i,startIdxTwin
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|
real(pReal) dt,Tp,tau_slip
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real(pReal), dimension(6) :: Tstar_v
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real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
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real(pReal), dimension(constitutive_Nresults(ipc,ip,el)) :: constitutive_post_results
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|
|
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!* Get the material-ID from the triplet(ipc,ip,el)
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|
matID = constitutive_matID(ipc,ip,el)
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|
startIdxTwin = material_Nslip(matID)
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|
|
|
if(constitutive_Nresults(ipc,ip,el)==0) return
|
|
|
|
constitutive_post_results=0.0_pReal
|
|
do i=1,material_Nslip(matID)
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|
constitutive_post_results(i) = state(i)
|
|
enddo
|
|
do i=1,material_Ntwin(matID)
|
|
constitutive_post_results(startIdxTwin+i) = state(startIdxTwin+i)
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
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END MODULE |