DAMASK_EICMD/code/constitutive_dislobased.f90

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!* $Id$
2009-03-05 21:45:24 +05:30
!************************************
!* 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
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!*** 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
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!*************************************
!* 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
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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,*) '$Id$'
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
2009-03-05 21:45:24 +05:30
!* 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
2009-03-05 21:45:24 +05:30
2009-03-26 14:13:31 +05:30
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
2009-03-26 14:13:31 +05:30
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
2009-03-05 21:45:24 +05:30
END MODULE