1084 lines
58 KiB
Fortran
1084 lines
58 KiB
Fortran
|
|
!************************************
|
|
!* Module: CONSTITUTIVE *
|
|
!************************************
|
|
!* contains: *
|
|
!* - constitutive equations *
|
|
!* - parameters definition *
|
|
!* - orientations *
|
|
!************************************
|
|
|
|
! [TWIP steel FeMnC]
|
|
|
|
! C11 175.0e9 # elastic constants in Pa
|
|
! C12 115.0e9
|
|
! C44 135.0e9
|
|
! lattice_structure fcc
|
|
! Nslip 12
|
|
! Ntwin 12
|
|
! constitution dislobased
|
|
! (output) dislocationdensity
|
|
! (output) shearrate_slip
|
|
! (output) mfp_slip # mean free path
|
|
! (output) resolvedstress_slip
|
|
! (output) resistance_slip # passing stress
|
|
! (output) volumefraction
|
|
! (output) shearrate_twin
|
|
! (output) mfp_twin # mean free path
|
|
! (output) resolvedstress_twin
|
|
! (output) resistance_twin # "nucleation barrier"
|
|
|
|
! ### dislocation density-based constitutive parameters ###
|
|
! burgers 2.56e-10 # Burgers vector [m]
|
|
! Qedge 5.5e-19 # Activation energy for dislocation glide [J/K] (0.5*G*b^3)
|
|
! grainsize 2.0e-5 # Average grain size [m]
|
|
! stacksize 5.0e-8 # Twin stack mean thickness [m]
|
|
! interaction_slipslip 1.0 2.2 3.0 1.6 3.8 4.5 # Dislocation interaction coefficients
|
|
! interaction_sliptwin 0.0 1.0 # Dislocation interaction coefficients
|
|
! interaction_twintwin 0.0 1.0 # Dislocation interaction coefficients
|
|
! # dislocation glide
|
|
! rho0 2.5e12 # Initial dislocation density [m/m³]
|
|
! Cmfpslip 1.0 # Adjustable parameter controlling dislocation mean free path
|
|
! Cactivolume 1.0 # Adjustable parameter controlling activation volume
|
|
! Cthresholdslip 0.1 # Adjustable parameter controlling threshold stress for dislocation motion
|
|
! Cstorage 0.02 # Adjustable parameter controlling dislocation storage
|
|
! Carecovery 15.0 # Adjustable parameter controlling athermal recovery
|
|
! # mechanical twinning
|
|
! Ndot0 0.0 # Number of potential twin source per volume per time [1/m³.s]
|
|
! fmax 1.0 # Maximum admissible twin volume fraction
|
|
! Cmfptwin 1.0 # Adjustable parameter controlling twin mean free path
|
|
! Cthresholdtwin 1.0 # Adjustable parameter controlling threshold stress for deformation twinning
|
|
|
|
|
|
MODULE constitutive_dislobased
|
|
|
|
!*** Include other modules ***
|
|
use prec, only: pReal,pInt
|
|
implicit none
|
|
|
|
character (len=*), parameter :: constitutive_dislobased_label = 'dislobased'
|
|
|
|
integer(pInt), dimension(:), allocatable :: constitutive_dislobased_sizeDotState, &
|
|
constitutive_dislobased_sizeState, &
|
|
constitutive_dislobased_sizePostResults
|
|
integer(pInt), dimension(:,:), allocatable,target :: constitutive_dislobased_sizePostResult
|
|
character(len=64), dimension(:,:), allocatable,target :: constitutive_dislobased_output
|
|
|
|
character(len=32), dimension(:), allocatable :: constitutive_dislobased_structureName
|
|
integer(pInt), dimension(:), allocatable :: constitutive_dislobased_structure, &
|
|
constitutive_dislobased_totalNslip, &
|
|
constitutive_dislobased_totalNtwin
|
|
integer(pInt), dimension(:,:), allocatable :: constitutive_dislobased_Nslip, &
|
|
constitutive_dislobased_Ntwin, &
|
|
constitutive_dislobased_slipFamily, &
|
|
constitutive_dislobased_twinFamily
|
|
|
|
real(pReal), dimension(:), allocatable :: constitutive_dislobased_CoverA, &
|
|
constitutive_dislobased_C11, &
|
|
constitutive_dislobased_C12, &
|
|
constitutive_dislobased_C13, &
|
|
constitutive_dislobased_C33, &
|
|
constitutive_dislobased_C44, &
|
|
constitutive_dislobased_Gmod
|
|
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Cslip_66
|
|
real(pReal), dimension(:,:,:,:), allocatable :: constitutive_dislobased_Ctwin_66
|
|
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_dislobased_Cslip_3333
|
|
real(pReal), dimension(:,:,:,:,:,:), allocatable :: constitutive_dislobased_Ctwin_3333
|
|
real(pReal), dimension(:,:), allocatable :: constitutive_dislobased_rho0, &
|
|
constitutive_dislobased_Burgers, &
|
|
constitutive_dislobased_Qedge, &
|
|
constitutive_dislobased_stacksize, &
|
|
constitutive_dislobased_Ndot0, &
|
|
|
|
constitutive_dislobased_interaction_slipslip, &
|
|
constitutive_dislobased_interaction_sliptwin, &
|
|
constitutive_dislobased_interaction_twinslip, &
|
|
constitutive_dislobased_interaction_twintwin
|
|
real(pReal), dimension(:), allocatable :: constitutive_dislobased_grainsize, &
|
|
constitutive_dislobased_fmax, &
|
|
constitutive_dislobased_Cmfpslip, &
|
|
constitutive_dislobased_Cmfptwin, &
|
|
constitutive_dislobased_Cthresholdslip, &
|
|
constitutive_dislobased_Cthresholdtwin, &
|
|
constitutive_dislobased_Cactivolume, &
|
|
constitutive_dislobased_Carecovery, &
|
|
constitutive_dislobased_Cstorage
|
|
|
|
|
|
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_parall_interaction, &
|
|
constitutive_dislobased_forest_interaction, &
|
|
constitutive_dislobased_hardeningMatrix_sliptwin, &
|
|
constitutive_dislobased_hardeningMatrix_twinslip, &
|
|
constitutive_dislobased_hardeningMatrix_twintwin
|
|
|
|
!*************************************
|
|
!* Definition of material properties *
|
|
!*************************************
|
|
!* Physical parameter, attack_frequency != Debye frequency
|
|
real(pReal), parameter :: attack_frequency = 1.0e10_pReal
|
|
!* Physical parameter, Boltzmann constant in J/Kelvin
|
|
real(pReal), parameter :: kB = 1.38e-23_pReal
|
|
!* Physical parameter, Avogadro number in 1/mol
|
|
real(pReal), parameter :: avogadro = 6.022e23_pReal
|
|
!* Physical parameter, Gas constant in J.mol/Kelvin
|
|
real(pReal), parameter :: Rgas = 8.314_pReal
|
|
|
|
CONTAINS
|
|
!****************************************
|
|
!* - constitutive_init
|
|
!* - constitutive_stateInit
|
|
!* - constitutive_homogenizedC
|
|
!* - constitutive_microstructure
|
|
!* - constitutive_LpAndItsTangent
|
|
!* - consistutive_dotState
|
|
!* - constitutive_dotTemperature
|
|
!* - consistutive_postResults
|
|
!****************************************
|
|
|
|
|
|
subroutine constitutive_dislobased_init(file)
|
|
!**************************************
|
|
!* Module initialization *
|
|
!**************************************
|
|
use prec, only: pInt,pReal
|
|
use math, only: math_Mandel3333to66,math_Voigt66to3333,math_mul3x3
|
|
use IO
|
|
use material
|
|
use lattice
|
|
|
|
integer(pInt), intent(in) :: file
|
|
integer(pInt), parameter :: maxNchunks = 21
|
|
integer(pInt), dimension(1+2*maxNchunks) :: positions
|
|
integer(pInt) section,maxNinstance,i,j,k,l,m,n,o,p,q,r,s,output,mySize
|
|
character(len=64) tag
|
|
character(len=1024) line
|
|
real(pReal) x,y
|
|
|
|
write(6,*)
|
|
write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_dislobased_label,' init -+>>>'
|
|
write(6,*)
|
|
|
|
maxNinstance = count(phase_constitution == constitutive_dislobased_label)
|
|
if (maxNinstance == 0) return
|
|
|
|
allocate(constitutive_dislobased_sizeDotState(maxNinstance)) ; constitutive_dislobased_sizeDotState = 0_pInt
|
|
allocate(constitutive_dislobased_sizeState(maxNinstance)) ; constitutive_dislobased_sizeState = 0_pInt
|
|
allocate(constitutive_dislobased_sizePostResults(maxNinstance)) ; constitutive_dislobased_sizePostResults = 0_pInt
|
|
allocate(constitutive_dislobased_sizePostResult(maxval(phase_Noutput), &
|
|
maxNinstance)) ; constitutive_dislobased_sizePostResult = 0_pInt
|
|
allocate(constitutive_dislobased_output(maxval(phase_Noutput), &
|
|
maxNinstance)) ; constitutive_dislobased_output = ''
|
|
|
|
allocate(constitutive_dislobased_structureName(maxNinstance)) ; constitutive_dislobased_structureName = ''
|
|
allocate(constitutive_dislobased_structure(maxNinstance)) ; constitutive_dislobased_structure = 0_pInt
|
|
allocate(constitutive_dislobased_Nslip(lattice_maxNslipFamily,&
|
|
maxNinstance)) ; constitutive_dislobased_Nslip = 0_pInt
|
|
allocate(constitutive_dislobased_Ntwin(lattice_maxNtwinFamily,&
|
|
maxNinstance)) ; constitutive_dislobased_Ntwin = 0_pInt
|
|
|
|
allocate(constitutive_dislobased_slipFamily(lattice_maxNslip,&
|
|
maxNinstance)) ; constitutive_dislobased_slipFamily = 0_pInt
|
|
allocate(constitutive_dislobased_twinFamily(lattice_maxNtwin,&
|
|
maxNinstance)) ; constitutive_dislobased_twinFamily = 0_pInt
|
|
|
|
allocate(constitutive_dislobased_totalNslip(maxNinstance)) ; constitutive_dislobased_totalNslip = 0_pInt
|
|
allocate(constitutive_dislobased_totalNtwin(maxNinstance)) ; constitutive_dislobased_totalNtwin = 0_pInt
|
|
|
|
allocate(constitutive_dislobased_CoverA(maxNinstance)) ; constitutive_dislobased_CoverA = 0.0_pReal
|
|
allocate(constitutive_dislobased_C11(maxNinstance)) ; constitutive_dislobased_C11 = 0.0_pReal
|
|
allocate(constitutive_dislobased_C12(maxNinstance)) ; constitutive_dislobased_C12 = 0.0_pReal
|
|
allocate(constitutive_dislobased_C13(maxNinstance)) ; constitutive_dislobased_C13 = 0.0_pReal
|
|
allocate(constitutive_dislobased_C33(maxNinstance)) ; constitutive_dislobased_C33 = 0.0_pReal
|
|
allocate(constitutive_dislobased_C44(maxNinstance)) ; constitutive_dislobased_C44 = 0.0_pReal
|
|
allocate(constitutive_dislobased_Gmod(maxNinstance)) ; constitutive_dislobased_Gmod = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cslip_66(6,6,maxNinstance)) ; constitutive_dislobased_Cslip_66 = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cslip_3333(3,3,3,3,maxNinstance)) ; constitutive_dislobased_Cslip_3333 = 0.0_pReal
|
|
|
|
allocate(constitutive_dislobased_rho0(lattice_maxNslipFamily, &
|
|
maxNinstance)) ; constitutive_dislobased_rho0 = 0.0_pReal
|
|
allocate(constitutive_dislobased_Burgers(lattice_maxNslipFamily, &
|
|
maxNinstance)) ; constitutive_dislobased_Burgers = 0.0_pReal
|
|
allocate(constitutive_dislobased_Qedge(lattice_maxNslipFamily, &
|
|
maxNinstance)) ; constitutive_dislobased_Qedge = 0.0_pReal
|
|
allocate(constitutive_dislobased_grainsize(maxNinstance)) ; constitutive_dislobased_grainsize = 0.0_pReal
|
|
allocate(constitutive_dislobased_stacksize(lattice_maxNtwinFamily, &
|
|
maxNinstance)) ; constitutive_dislobased_stacksize = 0.0_pReal
|
|
allocate(constitutive_dislobased_fmax(maxNinstance)) ; constitutive_dislobased_fmax = 0.0_pReal
|
|
allocate(constitutive_dislobased_Ndot0(lattice_maxNtwinFamily, &
|
|
maxNinstance)) ; constitutive_dislobased_Ndot0 = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cmfpslip(maxNinstance)) ; constitutive_dislobased_Cmfpslip = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cmfptwin(maxNinstance)) ; constitutive_dislobased_Cmfptwin = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cthresholdslip(maxNinstance)) ; constitutive_dislobased_Cthresholdslip = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cthresholdtwin(maxNinstance)) ; constitutive_dislobased_Cthresholdtwin = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cactivolume(maxNinstance)) ; constitutive_dislobased_Cactivolume = 0.0_pReal
|
|
allocate(constitutive_dislobased_Carecovery(maxNinstance)) ; constitutive_dislobased_Carecovery = 0.0_pReal
|
|
allocate(constitutive_dislobased_Cstorage(maxNinstance)) ; constitutive_dislobased_Cstorage = 0.0_pReal
|
|
|
|
allocate(constitutive_dislobased_interaction_slipslip(lattice_maxNinteraction,&
|
|
maxNinstance)) ; constitutive_dislobased_interaction_slipslip = 0.0_pReal
|
|
allocate(constitutive_dislobased_interaction_sliptwin(lattice_maxNinteraction,&
|
|
maxNinstance)) ; constitutive_dislobased_interaction_sliptwin = 0.0_pReal
|
|
allocate(constitutive_dislobased_interaction_twinslip(lattice_maxNinteraction,&
|
|
maxNinstance)) ; constitutive_dislobased_interaction_twinslip = 0.0_pReal
|
|
allocate(constitutive_dislobased_interaction_twintwin(lattice_maxNinteraction,&
|
|
maxNinstance)) ; constitutive_dislobased_interaction_twintwin = 0.0_pReal
|
|
|
|
rewind(file)
|
|
line = ''
|
|
section = 0
|
|
|
|
do while (IO_lc(IO_getTag(line,'<','>')) /= 'phase') ! wind forward to <phase>
|
|
read(file,'(a1024)',END=100) line
|
|
enddo
|
|
|
|
do ! read thru sections of phase part
|
|
read(file,'(a1024)',END=100) line
|
|
if (IO_isBlank(line)) cycle ! skip empty lines
|
|
if (IO_getTag(line,'<','>') /= '') exit ! stop at next part
|
|
if (IO_getTag(line,'[',']') /= '') then ! next section
|
|
section = section + 1
|
|
output = 0 ! reset output counter
|
|
endif
|
|
if (section > 0 .and. phase_constitution(section) == constitutive_dislobased_label) then ! one of my sections
|
|
i = phase_constitutionInstance(section) ! which instance of my constitution is present phase
|
|
positions = IO_stringPos(line,maxNchunks)
|
|
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
|
|
select case(tag)
|
|
case ('(output)')
|
|
output = output + 1
|
|
constitutive_dislobased_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
|
|
case ('lattice_structure')
|
|
constitutive_dislobased_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
|
|
case ('covera_ratio')
|
|
constitutive_dislobased_CoverA(i) = IO_floatValue(line,positions,2)
|
|
case ('c11')
|
|
constitutive_dislobased_C11(i) = IO_floatValue(line,positions,2)
|
|
case ('c12')
|
|
constitutive_dislobased_C12(i) = IO_floatValue(line,positions,2)
|
|
case ('c13')
|
|
constitutive_dislobased_C13(i) = IO_floatValue(line,positions,2)
|
|
case ('c33')
|
|
constitutive_dislobased_C33(i) = IO_floatValue(line,positions,2)
|
|
case ('c44')
|
|
constitutive_dislobased_C44(i) = IO_floatValue(line,positions,2)
|
|
case ('nslip')
|
|
forall (j = 1:lattice_maxNslipFamily) constitutive_dislobased_Nslip(j,i) = IO_intValue(line,positions,1+j)
|
|
case ('ntwin')
|
|
forall (j = 1:lattice_maxNtwinFamily) constitutive_dislobased_Ntwin(j,i) = IO_intValue(line,positions,1+j)
|
|
case ('rho0')
|
|
forall (j = 1:lattice_maxNslipFamily) constitutive_dislobased_rho0(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('burgers')
|
|
forall (j = 1:lattice_maxNslipFamily) constitutive_dislobased_Burgers(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('qedge')
|
|
forall (j = 1:lattice_maxNslipFamily) constitutive_dislobased_Qedge(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('grainsize')
|
|
constitutive_dislobased_grainsize(i) = IO_floatValue(line,positions,2)
|
|
case ('stacksize')
|
|
forall (j = 1:lattice_maxNtwinFamily) constitutive_dislobased_stacksize(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('fmax')
|
|
constitutive_dislobased_fmax(i) = IO_floatValue(line,positions,2)
|
|
case ('ndot0')
|
|
forall (j = 1:lattice_maxNtwinFamily) constitutive_dislobased_Ndot0(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('cmfpslip')
|
|
constitutive_dislobased_Cmfpslip(i) = IO_floatValue(line,positions,2)
|
|
case ('cmfptwin')
|
|
constitutive_dislobased_Cmfptwin(i) = IO_floatValue(line,positions,2)
|
|
case ('cthresholdslip')
|
|
constitutive_dislobased_Cthresholdslip(i) = IO_floatValue(line,positions,2)
|
|
case ('cthresholdtwin')
|
|
constitutive_dislobased_Cthresholdtwin(i) = IO_floatValue(line,positions,2)
|
|
case ('cactivolume')
|
|
constitutive_dislobased_Cactivolume(i) = IO_floatValue(line,positions,2)
|
|
case ('carecovery')
|
|
constitutive_dislobased_Carecovery(i) = IO_floatValue(line,positions,2)
|
|
case ('cstorage')
|
|
constitutive_dislobased_Cstorage(i) = IO_floatValue(line,positions,2)
|
|
case ('interaction_slipslip')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislobased_interaction_slipslip(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interaction_sliptwin')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislobased_interaction_sliptwin(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interaction_twinslip')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislobased_interaction_twinslip(j,i) = IO_floatValue(line,positions,1+j)
|
|
case ('interaction_twintwin')
|
|
forall (j = 1:lattice_maxNinteraction) &
|
|
constitutive_dislobased_interaction_twintwin(j,i) = IO_floatValue(line,positions,1+j)
|
|
end select
|
|
endif
|
|
enddo
|
|
|
|
|
|
100 do i = 1,maxNinstance
|
|
constitutive_dislobased_structure(i) = lattice_initializeStructure(constitutive_dislobased_structureName(i), &
|
|
constitutive_dislobased_CoverA(i))
|
|
constitutive_dislobased_Nslip(:,i) = min(lattice_NslipSystem(:,constitutive_dislobased_structure(i)),&
|
|
constitutive_dislobased_Nslip(:,i))
|
|
constitutive_dislobased_Ntwin(:,i) = min(lattice_NtwinSystem(:,constitutive_dislobased_structure(i)),&
|
|
constitutive_dislobased_Ntwin(:,i))
|
|
constitutive_dislobased_totalNslip(i) = sum(constitutive_dislobased_Nslip(:,i))
|
|
constitutive_dislobased_totalNtwin(i) = sum(constitutive_dislobased_Ntwin(:,i))
|
|
|
|
! sanity checks (still under construction)
|
|
if (constitutive_dislobased_structure(i) < 1 .or. & ! sanity checks
|
|
constitutive_dislobased_structure(i) > 3) call IO_error(205)
|
|
if (any(constitutive_dislobased_rho0(:,i) < 0.0_pReal)) call IO_error(220)
|
|
if (any(constitutive_dislobased_Burgers(:,i) <= 0.0_pReal .and. &
|
|
constitutive_dislobased_Nslip(:,i) > 0)) call IO_error(221)
|
|
if (any(constitutive_dislobased_Qedge(:,i) <= 0.0_pReal .and. &
|
|
constitutive_dislobased_Nslip(:,i) > 0)) call IO_error(222)
|
|
enddo
|
|
|
|
allocate(constitutive_dislobased_parall_interaction(maxval(constitutive_dislobased_totalNslip),&
|
|
maxval(constitutive_dislobased_totalNslip),&
|
|
maxNinstance))
|
|
allocate(constitutive_dislobased_forest_interaction(maxval(constitutive_dislobased_totalNslip),&
|
|
maxval(constitutive_dislobased_totalNslip),&
|
|
maxNinstance))
|
|
allocate(constitutive_dislobased_hardeningMatrix_sliptwin(maxval(constitutive_dislobased_totalNslip),&
|
|
maxval(constitutive_dislobased_totalNtwin),&
|
|
maxNinstance))
|
|
allocate(constitutive_dislobased_hardeningMatrix_twinslip(maxval(constitutive_dislobased_totalNtwin),&
|
|
maxval(constitutive_dislobased_totalNslip),&
|
|
maxNinstance))
|
|
allocate(constitutive_dislobased_hardeningMatrix_twintwin(maxval(constitutive_dislobased_totalNtwin),&
|
|
maxval(constitutive_dislobased_totalNtwin),&
|
|
maxNinstance))
|
|
constitutive_dislobased_parall_interaction = 0.0_pReal
|
|
constitutive_dislobased_forest_interaction = 0.0_pReal
|
|
constitutive_dislobased_hardeningMatrix_sliptwin = 0.0_pReal
|
|
constitutive_dislobased_hardeningMatrix_twinslip = 0.0_pReal
|
|
constitutive_dislobased_hardeningMatrix_twintwin = 0.0_pReal
|
|
|
|
allocate(constitutive_dislobased_Ctwin_66(6,6,maxval(constitutive_dislobased_totalNtwin),maxNinstance))
|
|
constitutive_dislobased_Ctwin_66 = 0.0_pReal
|
|
|
|
allocate(constitutive_dislobased_Ctwin_3333(3,3,3,3,maxval(constitutive_dislobased_totalNtwin),maxNinstance))
|
|
constitutive_dislobased_Ctwin_3333 = 0.0_pReal
|
|
|
|
do i = 1,maxNinstance
|
|
do j = 1,maxval(phase_Noutput)
|
|
select case(constitutive_dislobased_output(j,i))
|
|
case('dislocationdensity', &
|
|
'shearrate_slip', &
|
|
'mfp_slip', &
|
|
'resolvedstress_slip', &
|
|
'resistance_slip' &
|
|
)
|
|
mySize = constitutive_dislobased_totalNslip(i)
|
|
case('volumefraction', &
|
|
'shearrate_twin', &
|
|
'mfp_twin', &
|
|
'resolvedstress_twin', &
|
|
'resistance_twin' &
|
|
)
|
|
mySize = constitutive_dislobased_totalNtwin(i)
|
|
case default
|
|
mySize = 0_pInt
|
|
end select
|
|
|
|
if (mySize > 0_pInt) then ! any meaningful output found
|
|
constitutive_dislobased_sizePostResult(j,i) = mySize
|
|
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + mySize
|
|
endif
|
|
enddo
|
|
|
|
constitutive_dislobased_sizeDotState(i) = constitutive_dislobased_totalNslip(i) + constitutive_dislobased_totalNtwin(i)
|
|
constitutive_dislobased_sizeState(i) = 10*constitutive_dislobased_totalNslip(i) + 5*constitutive_dislobased_totalNtwin(i)
|
|
|
|
constitutive_dislobased_Gmod(i) = constitutive_dislobased_C44(i)
|
|
|
|
select case (constitutive_dislobased_structure(i))
|
|
case(1:2) ! cubic(s)
|
|
forall(k=1:3)
|
|
forall(j=1:3) &
|
|
constitutive_dislobased_Cslip_66(k,j,i) = constitutive_dislobased_C12(i)
|
|
constitutive_dislobased_Cslip_66(k,k,i) = constitutive_dislobased_C11(i)
|
|
constitutive_dislobased_Cslip_66(k+3,k+3,i) = constitutive_dislobased_C44(i)
|
|
end forall
|
|
case(3:) ! all hex
|
|
constitutive_dislobased_Cslip_66(1,1,i) = constitutive_dislobased_C11(i)
|
|
constitutive_dislobased_Cslip_66(2,2,i) = constitutive_dislobased_C11(i)
|
|
constitutive_dislobased_Cslip_66(3,3,i) = constitutive_dislobased_C33(i)
|
|
constitutive_dislobased_Cslip_66(1,2,i) = constitutive_dislobased_C12(i)
|
|
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)))
|
|
constitutive_dislobased_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_dislobased_Cslip_66(:,:,i))
|
|
|
|
!* Inverse lookup of my slip system family
|
|
l = 0_pInt
|
|
do j = 1,lattice_maxNslipFamily
|
|
do k = 1,constitutive_dislobased_Nslip(j,i)
|
|
l = l + 1
|
|
constitutive_dislobased_slipFamily(l,i) = j
|
|
enddo; enddo
|
|
|
|
!* Inverse lookup of my twin system family
|
|
l = 0_pInt
|
|
do j = 1,lattice_maxNtwinFamily
|
|
do k = 1,constitutive_dislobased_Ntwin(j,i)
|
|
l = l + 1
|
|
constitutive_dislobased_twinFamily(l,i) = j
|
|
enddo; enddo
|
|
|
|
!* Construction of the twin elasticity matrices
|
|
do j=1,lattice_maxNtwinFamily
|
|
do k=1,constitutive_dislobased_Ntwin(j,i)
|
|
do l=1,3 ; do m=1,3 ; do n=1,3 ; do o=1,3 ; do p=1,3 ; do q=1,3 ; do r=1,3 ; do s=1,3
|
|
constitutive_dislobased_Ctwin_3333(l,m,n,o,sum(constitutive_dislobased_Nslip(1:j-1,i))+k,i) = &
|
|
constitutive_dislobased_Ctwin_3333(l,m,n,o,sum(constitutive_dislobased_Nslip(1:j-1,i))+k,i) + &
|
|
constitutive_dislobased_Cslip_3333(p,q,r,s,i)*&
|
|
lattice_Qtwin(l,p,sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k,constitutive_dislobased_structure(i))* &
|
|
lattice_Qtwin(m,q,sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k,constitutive_dislobased_structure(i))* &
|
|
lattice_Qtwin(n,r,sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k,constitutive_dislobased_structure(i))* &
|
|
lattice_Qtwin(o,s,sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k,constitutive_dislobased_structure(i))
|
|
enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo ; enddo
|
|
constitutive_dislobased_Ctwin_66(:,:,k,i) = math_Mandel3333to66(constitutive_dislobased_Ctwin_3333(:,:,:,:,k,i))
|
|
enddo
|
|
enddo
|
|
|
|
!* Construction of the hardening matrices
|
|
!* Iteration over the systems
|
|
do j=1,lattice_maxNslipFamily
|
|
do k=1,constitutive_dislobased_Nslip(j,i)
|
|
do l=1,lattice_maxNslipFamily
|
|
do m=1,constitutive_dislobased_Nslip(l,i)
|
|
!* Projection of the dislocation *
|
|
x = math_mul3x3(lattice_sn(:,sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
constitutive_dislobased_structure(i)), &
|
|
lattice_st(:,sum(lattice_NslipSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)))
|
|
y = 1.0_pReal-x**(2.0_pReal)
|
|
!* Interaction matrix *
|
|
constitutive_dislobased_forest_interaction(sum(constitutive_dislobased_Nslip(1:j-1,i))+k, &
|
|
sum(constitutive_dislobased_Nslip(1:l-1,i))+m,i) = &
|
|
abs(x)*constitutive_dislobased_interaction_slipslip(lattice_interactionSlipSlip( &
|
|
sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
sum(lattice_NslipSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)),i)
|
|
if (y>0.0_pReal) &
|
|
constitutive_dislobased_parall_interaction(sum(constitutive_dislobased_Nslip(1:j-1,i))+k, &
|
|
sum(constitutive_dislobased_Nslip(1:l-1,i))+m,i) = &
|
|
sqrt(y)*constitutive_dislobased_interaction_slipslip(lattice_interactionSlipSlip( &
|
|
sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
sum(lattice_NslipSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)),i)
|
|
enddo; enddo; enddo; enddo
|
|
|
|
do j=1,lattice_maxNslipFamily
|
|
do k=1,constitutive_dislobased_Nslip(j,i)
|
|
do l=1,lattice_maxNtwinFamily
|
|
do m=1,constitutive_dislobased_Ntwin(l,i)
|
|
constitutive_dislobased_hardeningMatrix_sliptwin(sum(constitutive_dislobased_Nslip(1:j-1,i))+k,&
|
|
sum(constitutive_dislobased_Ntwin(1:l-1,i))+m,i) = &
|
|
constitutive_dislobased_interaction_sliptwin(lattice_interactionSlipTwin( &
|
|
sum(lattice_NslipSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
sum(lattice_NtwinSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)),i)
|
|
enddo; enddo; enddo; enddo
|
|
|
|
do j=1,lattice_maxNtwinFamily
|
|
do k=1,constitutive_dislobased_Ntwin(j,i)
|
|
do l=1,lattice_maxNslipFamily
|
|
do m=1,constitutive_dislobased_Nslip(l,i)
|
|
constitutive_dislobased_hardeningMatrix_twinslip(sum(constitutive_dislobased_Ntwin(1:j-1,i))+k,&
|
|
sum(constitutive_dislobased_Nslip(1:l-1,i))+m,i) = &
|
|
constitutive_dislobased_interaction_twinslip(lattice_interactionTwinSlip( &
|
|
sum(lattice_NtwinSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
sum(lattice_NslipSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)),i)
|
|
enddo; enddo; enddo; enddo
|
|
|
|
do j=1,lattice_maxNtwinFamily
|
|
do k=1,constitutive_dislobased_Ntwin(j,i)
|
|
do l=1,lattice_maxNtwinFamily
|
|
do m=1,constitutive_dislobased_Ntwin(l,i)
|
|
constitutive_dislobased_hardeningMatrix_twintwin(sum(constitutive_dislobased_Ntwin(1:j-1,i))+k,&
|
|
sum(constitutive_dislobased_Ntwin(1:l-1,i))+m,i) = &
|
|
constitutive_dislobased_interaction_twintwin(lattice_interactionTwinTwin( &
|
|
sum(lattice_NtwinSystem(1:j-1,constitutive_dislobased_structure(i)))+k, &
|
|
sum(lattice_NtwinSystem(1:l-1,constitutive_dislobased_structure(i)))+m, &
|
|
constitutive_dislobased_structure(i)), i )
|
|
enddo; enddo; enddo; enddo
|
|
|
|
enddo
|
|
|
|
return
|
|
end subroutine
|
|
|
|
|
|
function constitutive_dislobased_stateInit(myInstance)
|
|
!*********************************************************************
|
|
!* initial microstructural state *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt
|
|
use lattice, only: lattice_maxNslipFamily,lattice_maxNtwinFamily
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), intent(in) :: myInstance
|
|
integer(pInt) i
|
|
real(pReal), dimension(constitutive_dislobased_sizeState(myInstance)) :: constitutive_dislobased_stateInit
|
|
|
|
constitutive_dislobased_stateInit = 0.0_pReal
|
|
|
|
do i = 1,lattice_maxNslipFamily
|
|
constitutive_dislobased_stateInit(1+sum(constitutive_dislobased_Nslip(1:i-1,myInstance)) : &
|
|
sum(constitutive_dislobased_Nslip(1:i ,myInstance))) = &
|
|
constitutive_dislobased_rho0(i,myInstance)
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
function constitutive_dislobased_homogenizedC(state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* calculates homogenized elacticity matrix *
|
|
!* - state : microstructure quantities *
|
|
!* - 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,ns,nt,i
|
|
real(pReal) sumf
|
|
real(pReal), dimension(6,6) :: constitutive_dislobased_homogenizedC
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
|
|
|
!* Shortened notation
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
|
ns = constitutive_dislobased_totalNslip(matID)
|
|
nt = constitutive_dislobased_totalNtwin(matID)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0
|
|
|
|
!* Homogenized elasticity matrix
|
|
constitutive_dislobased_homogenizedC = (1.0_pReal-sumf)*constitutive_dislobased_Cslip_66(:,:,matID)
|
|
do i=1,nt
|
|
constitutive_dislobased_homogenizedC = constitutive_dislobased_homogenizedC + &
|
|
state(ipc,ip,el)%p(ns+i)*constitutive_dislobased_Ctwin_66(:,:,i,matID)
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
subroutine constitutive_dislobased_microstructure(Temperature,state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* calculates quantities characterizing the microstructure *
|
|
!* - Temperature : temperature *
|
|
!* - state : microstructure quantities *
|
|
!* - ipc : component-ID of current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt,p_vec
|
|
use math, only: pi
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance
|
|
use lattice, only: lattice_interactionSlipTwin,lattice_interactionTwinTwin
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
|
integer(pInt) matID,ns,nt,i
|
|
real(pReal) Temperature,sumf
|
|
real(pReal), dimension(constitutive_dislobased_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: fOverStacksize
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
|
|
|
!* Shortened notation
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
|
ns = constitutive_dislobased_totalNslip(matID)
|
|
nt = constitutive_dislobased_totalNtwin(matID)
|
|
!* State: 1 : ns rho_ssd
|
|
!* State: ns+1 : ns+nt f
|
|
!* State: ns+nt+1 : 2*ns+nt rho_forest
|
|
!* State: 2*ns+nt+1 : 3*ns+nt rho_parallel
|
|
!* State: 3*ns+nt+1 : 4*ns+nt 1/lambda_slip
|
|
!* State: 4*ns+nt+1 : 5*ns+nt 1/lambda_sliptwin
|
|
!* State: 5*ns+nt+1 : 5*ns+2*nt 1/lambda_twin
|
|
!* State: 5*ns+2*nt+1 : 6*ns+2*nt mfp_slip
|
|
!* State: 6*ns+2*nt+1 : 6*ns+3*nt mfp_twin
|
|
!* State: 6*ns+3*nt+1 : 7*ns+3*nt threshold_stress_slip
|
|
!* State: 7*ns+3*nt+1 : 7*ns+4*nt threshold_stress_twin
|
|
!* State: 7*ns+4*nt+1 : 8*ns+4*nt activation volume
|
|
!* State: 8*ns+4*nt+1 : 8*ns+5*nt twin volume
|
|
!* State: 8*ns+5*nt+1 : 9*ns+5*nt rho_mobile
|
|
!* State: 9*ns+5*nt+1 : 10*ns+5*nt initial shear rate
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0
|
|
|
|
!* rescaled twin volume fraction for topology
|
|
forall (i = 1:nt) &
|
|
fOverStacksize(i) = state(ipc,ip,el)%p(ns+i)/constitutive_dislobased_stacksize(constitutive_dislobased_twinFamily(i,matID),matID)
|
|
|
|
!* Forest and parallel dislocation densities
|
|
!$OMP CRITICAL (evilmatmul)
|
|
state(ipc,ip,el)%p((ns+nt+1):(2*ns+nt)) = &
|
|
matmul(constitutive_dislobased_forest_interaction(1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns))
|
|
state(ipc,ip,el)%p((2*ns+nt+1):(3*ns+nt)) = &
|
|
matmul(constitutive_dislobased_parall_interaction(1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns))
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
|
|
forall (i=1:ns) state(ipc,ip,el)%p(3*ns+nt+i) = sqrt(state(ipc,ip,el)%p(ns+nt+i))
|
|
|
|
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
|
|
!$OMP CRITICAL (evilmatmul)
|
|
state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = 0.0_pReal
|
|
if (nt > 0_pInt) state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = &
|
|
matmul(constitutive_dislobased_hardeningMatrix_sliptwin(1:ns,1:nt,matID),fOverStacksize(1:nt))/&
|
|
(2.0_pReal*(1.0_pReal-sumf))
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
|
|
!$OMP CRITICAL (evilmatmul)
|
|
if (nt > 0_pInt) state(ipc,ip,el)%p((5*ns+nt+1):(5*ns+2*nt)) = &
|
|
matmul(constitutive_dislobased_hardeningMatrix_twintwin(1:nt,1:nt,matID),fOverStacksize(1:nt))/&
|
|
(2.0_pReal*(1.0_pReal-sumf))
|
|
!$OMP END CRITICAL (evilmatmul)
|
|
|
|
!* mean free path between 2 obstacles seen by a moving dislocation
|
|
do i=1,ns
|
|
if (nt > 0_pInt) then
|
|
state(ipc,ip,el)%p(5*ns+2*nt+i) = (constitutive_dislobased_Cmfpslip(matID)*constitutive_dislobased_grainsize(matID))/&
|
|
(1.0_pReal+constitutive_dislobased_grainsize(matID)*&
|
|
(state(ipc,ip,el)%p(3*ns+nt+i)+state(ipc,ip,el)%p(4*ns+nt+i)))
|
|
else
|
|
state(ipc,ip,el)%p(5*ns+i) = (constitutive_dislobased_Cmfpslip(matID)*constitutive_dislobased_grainsize(matID))/&
|
|
(1.0_pReal+constitutive_dislobased_grainsize(matID)*(state(ipc,ip,el)%p(3*ns+i)))
|
|
endif
|
|
enddo
|
|
|
|
!* mean free path between 2 obstacles seen by a growing twin
|
|
forall (i=1:nt) &
|
|
state(ipc,ip,el)%p(6*ns+2*nt+i) = (constitutive_dislobased_Cmfptwin(matID)*constitutive_dislobased_grainsize(matID))/&
|
|
(1.0_pReal+constitutive_dislobased_grainsize(matID)*state(ipc,ip,el)%p(5*ns+nt+i))
|
|
|
|
!* threshold stress for dislocation motion
|
|
forall (i=1:ns) &
|
|
state(ipc,ip,el)%p(6*ns+3*nt+i) = constitutive_dislobased_Cthresholdslip(matID)*&
|
|
constitutive_dislobased_Burgers(constitutive_dislobased_slipFamily(i,matID),matID)*&
|
|
constitutive_dislobased_Gmod(matID)*sqrt(state(ipc,ip,el)%p(2*ns+nt+i))
|
|
|
|
!* threshold stress for growing twin
|
|
forall (i=1:nt) &
|
|
state(ipc,ip,el)%p(7*ns+3*nt+i) = constitutive_dislobased_Cthresholdtwin(matID)*(sqrt(3.0_pReal)/3.0_pReal)*(&
|
|
(0.0002_pReal*Temperature-0.0396_pReal)/constitutive_dislobased_Burgers(constitutive_dislobased_slipFamily(i,matID),matID)+&
|
|
(constitutive_dislobased_Burgers(constitutive_dislobased_slipFamily(i,matID),matID)*&
|
|
constitutive_dislobased_Gmod(matID))/state(ipc,ip,el)%p(5*ns+2*nt+i))
|
|
|
|
!* activation volume for dislocation glide
|
|
forall (i=1:ns) &
|
|
state(ipc,ip,el)%p(7*ns+4*nt+i) = constitutive_dislobased_Cactivolume(matID)*&
|
|
constitutive_dislobased_Burgers(constitutive_dislobased_slipFamily(i,matID),matID)**2*state(ipc,ip,el)%p(5*ns+2*nt+i)
|
|
|
|
!* final twin volume after growth
|
|
forall (i=1:nt) &
|
|
state(ipc,ip,el)%p(8*ns+4*nt+i) = (pi/6.0_pReal)*&
|
|
constitutive_dislobased_stacksize(constitutive_dislobased_twinFamily(i,matID),matID)*&
|
|
state(ipc,ip,el)%p(6*ns+2*nt+i)*state(ipc,ip,el)%p(6*ns+2*nt+i)
|
|
|
|
!* mobile dislocation densities
|
|
forall (i=1:ns) &
|
|
state(ipc,ip,el)%p(8*ns+5*nt+i) = (2.0_pReal*kB*Temperature*state(ipc,ip,el)%p(2*ns+nt+i))/&
|
|
(state(ipc,ip,el)%p(6*ns+3*nt+i)*state(ipc,ip,el)%p(7*ns+4*nt+i))
|
|
|
|
!* initial shear rate for slip
|
|
forall (i=1:ns) &
|
|
state(ipc,ip,el)%p(9*ns+5*nt+i) = state(ipc,ip,el)%p(8*ns+5*nt+i)*&
|
|
constitutive_dislobased_Burgers(constitutive_dislobased_slipFamily(i,matID),matID)*&
|
|
attack_frequency*state(ipc,ip,el)%p(5*ns+2*nt+i)*&
|
|
exp(-constitutive_dislobased_Qedge(constitutive_dislobased_slipFamily(i,matID),matID)/&
|
|
! --------------------
|
|
(kB*Temperature))
|
|
|
|
end subroutine
|
|
|
|
|
|
subroutine constitutive_dislobased_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* calculates plastic velocity gradient and its tangent *
|
|
!* INPUT: *
|
|
!* - Temperature : temperature *
|
|
!* - state : microstructure quantities *
|
|
!* - 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
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,structID,ns,nt,f,i,j,k,l,m,n,index_myFamily
|
|
real(pReal) Temperature,sumf
|
|
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_totalNslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_slip,dgdot_dtauslip,tau_slip
|
|
real(pReal), dimension(constitutive_dislobased_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_twin,dgdot_dtautwin,tau_twin
|
|
|
|
!* Shortened notation
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
|
structID = constitutive_dislobased_structure(matID)
|
|
ns = constitutive_dislobased_totalNslip(matID)
|
|
nt = constitutive_dislobased_totalNtwin(matID)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0
|
|
|
|
Lp = 0.0_pReal
|
|
dLp_dTstar3333 = 0.0_pReal
|
|
dLp_dTstar = 0.0_pReal
|
|
|
|
!* Dislocation glide part
|
|
gdot_slip = 0.0_pReal
|
|
dgdot_dtauslip = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Nslip(f,matID) ! process each (active) slip system in family
|
|
j = j+1_pInt
|
|
|
|
!* Calculation of Lp
|
|
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID))
|
|
if ( abs(tau_slip(j)) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then
|
|
|
|
gdot_slip(j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau_slip(j))*&
|
|
sinh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature))
|
|
|
|
dgdot_dtauslip(j) = (state(ipc,ip,el)%p(9*ns+5*nt+j)*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature)*&
|
|
cosh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature))
|
|
|
|
endif
|
|
Lp = Lp + (1.0_pReal - sumf)*gdot_slip(j)*lattice_Sslip(:,:,index_myFamily+i,structID)
|
|
|
|
!* Calculation of the tangent of Lp
|
|
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(j)*lattice_Sslip(k,l,index_myFamily+i,structID) &
|
|
*lattice_Sslip(m,n,index_myFamily+i,structID)
|
|
enddo
|
|
enddo
|
|
|
|
!* Mechanical twinning part
|
|
gdot_twin = 0.0_pReal
|
|
dgdot_dtautwin = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Ntwin(f,matID) ! process each (active) slip system in family
|
|
j = j+1_pInt
|
|
|
|
!* Calculation of Lp
|
|
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID))
|
|
if ( tau_twin(j) > 0.0_pReal ) then
|
|
|
|
gdot_twin(j) = (constitutive_dislobased_fmax(matID) - sumf)*lattice_shearTwin(index_myFamily+i,structID)*&
|
|
state(ipc,ip,el)%p(8*ns+4*nt+j)*constitutive_dislobased_Ndot0(f,matID)*&
|
|
exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau_twin(j))**10.0_pReal)
|
|
|
|
dgdot_dtautwin(j) = (gdot_twin(j)*10.0_pReal*state(ipc,ip,el)%p(7*ns+3*nt+j)**10.0_pReal)/(tau_twin(j)**11.0_pReal)
|
|
|
|
endif
|
|
Lp = Lp + gdot_twin(j)*lattice_Stwin(:,:,index_myFamily+i,structID)
|
|
|
|
!* Calculation of the tangent of Lp
|
|
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_dtautwin(j)*lattice_Stwin(k,l,index_myFamily+i,structID) &
|
|
*lattice_Stwin(m,n,index_myFamily+i,structID)
|
|
enddo
|
|
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: *
|
|
!* - Temperature : temperature *
|
|
!* - state : microstructure quantities *
|
|
!* - 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 mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
|
|
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
integer(pInt) matID,structID,ns,nt,f,i,j,k,index_myFamily
|
|
real(pReal) Temperature,sumf
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal), dimension(constitutive_dislobased_totalNslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_slip,tau_slip,storage,arecovery
|
|
real(pReal), dimension(constitutive_dislobased_totalNtwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
gdot_twin,tau_twin
|
|
real(pReal), dimension(constitutive_dislobased_sizeDotState(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
constitutive_dislobased_dotState
|
|
|
|
!* Shortened notation
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
|
structID = constitutive_dislobased_structure(matID)
|
|
ns = constitutive_dislobased_totalNslip(matID)
|
|
nt = constitutive_dislobased_totalNtwin(matID)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0
|
|
|
|
constitutive_dislobased_dotState = 0.0_pReal
|
|
|
|
!* Dislocation density evolution
|
|
gdot_slip = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Nslip(f,matID) ! process each (active) slip system in family
|
|
j = j+1_pInt
|
|
|
|
!* Calculation of Lp
|
|
tau_slip(j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID))
|
|
if ( abs(tau_slip(j)) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then
|
|
|
|
gdot_slip(j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau_slip(j))* &
|
|
sinh(((abs(tau_slip(j))-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature))
|
|
|
|
storage(j) = (constitutive_dislobased_Cstorage(matID)*abs(gdot_slip(j)))/&
|
|
(constitutive_dislobased_Burgers(f,matID)*state(ipc,ip,el)%p(5*ns+2*nt+j))
|
|
|
|
arecovery(j) = constitutive_dislobased_Carecovery(matID)*state(ipc,ip,el)%p(j)*abs(gdot_slip(j))
|
|
|
|
constitutive_dislobased_dotState(j) = storage(j) - arecovery(j)
|
|
|
|
endif
|
|
enddo
|
|
enddo
|
|
|
|
!* Twin volume fraction evolution
|
|
gdot_twin = 0.0_pReal
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all twin families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Ntwin(f,matID) ! process each (active) twin system in family
|
|
j = j+1_pInt
|
|
|
|
!* Calculation of Lp
|
|
tau_twin(j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID))
|
|
if ( tau_twin(j) > 0.0_pReal ) &
|
|
constitutive_dislobased_dotState(ns+j) = (constitutive_dislobased_fmax(matID) - sumf)* &
|
|
lattice_shearTwin(index_myFamily+i,structID)*state(ipc,ip,el)%p(8*ns+4*nt+j)*constitutive_dislobased_Ndot0(f,matID)*&
|
|
exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau_twin(j))**10.0_pReal)
|
|
enddo
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
function constitutive_dislobased_dotTemperature(Tstar_v,Temperature,state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* rate of change of microstructure *
|
|
!* INPUT: *
|
|
!* - Temperature : temperature *
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
|
!* - ipc : component-ID at current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!* OUTPUT: *
|
|
!* - constitutive_dotTemperature : evolution of Temperature *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt) ipc,ip,el
|
|
real(pReal) Temperature
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
|
|
real(pReal), dimension(6) :: Tstar_v
|
|
real(pReal) constitutive_dislobased_dotTemperature
|
|
|
|
constitutive_dislobased_dotTemperature = 0.0_pReal
|
|
|
|
return
|
|
end function
|
|
|
|
|
|
pure function constitutive_dislobased_postResults(Tstar_v,Temperature,dt,state,ipc,ip,el)
|
|
!*********************************************************************
|
|
!* return array of constitutive results *
|
|
!* INPUT: *
|
|
!* - Temperature : temperature *
|
|
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
|
|
!* - dt : current time increment *
|
|
!* - ipc : component-ID at current integration point *
|
|
!* - ip : current integration point *
|
|
!* - el : current element *
|
|
!*********************************************************************
|
|
use prec, only: pReal,pInt,p_vec
|
|
use mesh, only: mesh_NcpElems,mesh_maxNips
|
|
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
|
|
use lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_maxNslipFamily,lattice_maxNtwinFamily, &
|
|
lattice_NslipSystem,lattice_NtwinSystem,lattice_shearTwin
|
|
implicit none
|
|
|
|
!* Definition of variables
|
|
integer(pInt), intent(in) :: ipc,ip,el
|
|
real(pReal), intent(in) :: dt,Temperature
|
|
real(pReal), dimension(6), intent(in) :: Tstar_v
|
|
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
|
|
integer(pInt) matID,structID,ns,nt,f,o,i,c,j,index_myFamily
|
|
real(pReal) sumf,tau
|
|
real(pReal), dimension(constitutive_dislobased_sizePostResults(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
|
|
constitutive_dislobased_postResults
|
|
|
|
!* Shortened notation
|
|
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
|
|
structID = constitutive_dislobased_structure(matID)
|
|
ns = constitutive_dislobased_totalNslip(matID)
|
|
nt = constitutive_dislobased_totalNtwin(matID)
|
|
|
|
!* Total twin volume fraction
|
|
sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt))) ! safe for nt == 0
|
|
|
|
!* Required output
|
|
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 ('dislocationdensity')
|
|
constitutive_dislobased_postResults(c+1:c+ns) = state(ipc,ip,el)%p(1:ns)
|
|
c = c + ns
|
|
|
|
case ('shearrate_slip')
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Nslip(f,matID) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
tau = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID))
|
|
if ( abs(tau) > state(ipc,ip,el)%p(6*ns+3*nt+j) ) then
|
|
constitutive_dislobased_postResults(c+j) = state(ipc,ip,el)%p(9*ns+5*nt+j)*sign(1.0_pReal,tau)* &
|
|
sinh(((abs(tau)-state(ipc,ip,el)%p(6*ns+3*nt+j))*state(ipc,ip,el)%p(7*ns+4*nt+j))/(kB*Temperature))
|
|
else
|
|
constitutive_dislobased_postResults(c+j) = 0.0_pReal
|
|
endif
|
|
enddo ; enddo
|
|
c = c + ns
|
|
|
|
case ('mfp_slip')
|
|
constitutive_dislobased_postResults(c+1:c+ns) = state(ipc,ip,el)%p((5*ns+2*nt+1):(6*ns+2*nt))
|
|
c = c + ns
|
|
|
|
case ('resolvedstress_slip')
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNslipFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NslipSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Nslip(f,matID) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
constitutive_dislobased_postResults(c+j) = dot_product(Tstar_v,lattice_Sslip_v(:,index_myFamily+i,structID))
|
|
enddo; enddo
|
|
c = c + ns
|
|
|
|
case ('resistance_slip')
|
|
constitutive_dislobased_postResults(c+1:c+ns) = state(ipc,ip,el)%p((6*ns+3*nt+1):(7*ns+3*nt))
|
|
c = c + ns
|
|
|
|
case ('volumefraction')
|
|
constitutive_dislobased_postResults(c+1:c+nt) = state(ipc,ip,el)%p((ns+1):(ns+nt))
|
|
c = c + nt
|
|
|
|
case ('shearrate_twin')
|
|
if (nt > 0_pInt) then
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Ntwin(f,matID) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
tau = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID))
|
|
if ( tau > 0.0_pReal ) then
|
|
constitutive_dislobased_postResults(c+j) = (constitutive_dislobased_fmax(matID) - sumf)* &
|
|
lattice_shearTwin(index_myFamily+i,structID)*state(ipc,ip,el)%p(8*ns+4*nt+j)* &
|
|
constitutive_dislobased_Ndot0(f,matID)*exp(-(state(ipc,ip,el)%p(7*ns+3*nt+j)/tau)**10.0_pReal)
|
|
else
|
|
constitutive_dislobased_postResults(c+j) = 0.0_pReal
|
|
endif
|
|
enddo ; enddo
|
|
endif
|
|
c = c + nt
|
|
|
|
case ('mfp_twin')
|
|
constitutive_dislobased_postResults(c+1:c+nt) = state(ipc,ip,el)%p((6*ns+2*nt+1):(6*ns+3*nt))
|
|
c = c + nt
|
|
|
|
case ('resolvedstress_twin')
|
|
if (nt > 0_pInt) then
|
|
j = 0_pInt
|
|
do f = 1,lattice_maxNtwinFamily ! loop over all slip families
|
|
index_myFamily = sum(lattice_NtwinSystem(1:f-1,structID)) ! at which index starts my family
|
|
do i = 1,constitutive_dislobased_Ntwin(f,matID) ! process each (active) slip system in family
|
|
j = j + 1_pInt
|
|
constitutive_dislobased_postResults(c+j) = dot_product(Tstar_v,lattice_Stwin_v(:,index_myFamily+i,structID))
|
|
enddo; enddo
|
|
endif
|
|
c = c + nt
|
|
|
|
case ('resistance_twin')
|
|
constitutive_dislobased_postResults(c+1:c+nt) = state(ipc,ip,el)%p((7*ns+3*nt+1):(7*ns+4*nt))
|
|
c = c + nt
|
|
|
|
end select
|
|
enddo
|
|
|
|
return
|
|
end function
|
|
|
|
END MODULE |