DAMASK_EICMD/code/constitutive_dislobased.f90

824 lines
40 KiB
Fortran

!************************************
!* Module: CONSTITUTIVE *
!************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!* - orientations *
!************************************
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
character(len=64), dimension(:,:), allocatable :: constitutive_dislobased_output
character(len=32), dimension(:), allocatable :: constitutive_dislobased_structureName
integer(pInt), dimension(:), allocatable :: constitutive_dislobased_structure
integer(pInt), dimension(:), allocatable :: constitutive_dislobased_Nslip
integer(pInt), dimension(:), allocatable :: constitutive_dislobased_Ntwin
real(pReal), dimension(:), allocatable :: constitutive_dislobased_C11
real(pReal), dimension(:), allocatable :: constitutive_dislobased_C12
real(pReal), dimension(:), allocatable :: constitutive_dislobased_C13
real(pReal), dimension(:), allocatable :: constitutive_dislobased_C33
real(pReal), dimension(:), allocatable :: constitutive_dislobased_C44
real(pReal), dimension(:), allocatable :: 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
real(pReal), dimension(:), allocatable :: constitutive_dislobased_bg
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Qedge
real(pReal), dimension(:), allocatable :: constitutive_dislobased_grainsize
real(pReal), dimension(:), allocatable :: constitutive_dislobased_stacksize
real(pReal), dimension(:), allocatable :: constitutive_dislobased_fmax
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Ndot0
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cmfpslip
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cmfptwin
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cthresholdslip
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cthresholdtwin
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cactivolume
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Cstorage
real(pReal), dimension(:), allocatable :: constitutive_dislobased_Carecovery
real(pReal), dimension(:), allocatable :: constitutive_dislobased_CoverA
real(pReal), dimension(:,:), allocatable :: constitutive_dislobased_SlipIntCoeff
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iparallel
real(pReal), dimension(:,:,:), allocatable :: constitutive_dislobased_Iforest
!*************************************
!* 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 :: Rgaz = 8.314_pReal
CONTAINS
!****************************************
!* - constitutive_init
!* - 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, only: lattice_sn,lattice_st,lattice_interactionSlipSlip,lattice_initializeStructure,lattice_Qtwin,lattice_tn
integer(pInt), intent(in) :: file
integer(pInt), parameter :: maxNchunks = 7
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section,maxNinstance,i,j,k,l,m,n,o,p,q,r,s,output
character(len=64) tag
character(len=1024) line
real(pReal) x,y
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_structureName(maxNinstance)) ; constitutive_dislobased_structureName = ''
allocate(constitutive_dislobased_structure(maxNinstance)) ; constitutive_dislobased_structure = 0_pInt
allocate(constitutive_dislobased_Nslip(maxNinstance)) ; constitutive_dislobased_Nslip = 0_pInt
allocate(constitutive_dislobased_Ntwin(maxNinstance)) ; constitutive_dislobased_Ntwin = 0_pInt
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_Ctwin_3333 = 0.0_pReal
allocate(constitutive_dislobased_rho0(maxNinstance)) ; constitutive_dislobased_rho0 = 0.0_pReal
allocate(constitutive_dislobased_bg(maxNinstance)) ; constitutive_dislobased_bg = 0.0_pReal
allocate(constitutive_dislobased_Qedge(maxNinstance)) ; constitutive_dislobased_Qedge = 0.0_pReal
allocate(constitutive_dislobased_grainsize(maxNinstance)) ; constitutive_dislobased_grainsize = 0.0_pReal
allocate(constitutive_dislobased_stacksize(maxNinstance)) ; constitutive_dislobased_stacksize = 0.0_pReal
allocate(constitutive_dislobased_fmax(maxNinstance)) ; constitutive_dislobased_fmax = 0.0_pReal
allocate(constitutive_dislobased_Ndot0(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_Cstorage(maxNinstance)) ; constitutive_dislobased_Cstorage = 0.0_pReal
allocate(constitutive_dislobased_Carecovery(maxNinstance)) ; constitutive_dislobased_Carecovery = 0.0_pReal
allocate(constitutive_dislobased_CoverA(maxNinstance)) ; constitutive_dislobased_CoverA = 0.0_pReal
allocate(constitutive_dislobased_SlipIntCoeff(6,maxNinstance)) ; constitutive_dislobased_SlipIntCoeff = 0.0_pReal
allocate(constitutive_dislobased_output(maxval(phase_Noutput),maxNinstance)) ; constitutive_dislobased_output = ''
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 ('nslip')
constitutive_dislobased_Nslip(i) = IO_intValue(line,positions,2)
case ('ntwin')
constitutive_dislobased_Ntwin(i) = IO_intValue(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 ('rho0')
constitutive_dislobased_rho0(i) = IO_floatValue(line,positions,2)
case ('burgers')
constitutive_dislobased_bg(i) = IO_floatValue(line,positions,2)
case ('qedge')
constitutive_dislobased_Qedge(i) = IO_floatValue(line,positions,2)
case ('grainsize')
constitutive_dislobased_grainsize(i) = IO_floatValue(line,positions,2)
case ('stacksize')
constitutive_dislobased_stacksize(i) = IO_floatValue(line,positions,2)
case ('fmax')
constitutive_dislobased_fmax(i) = IO_floatValue(line,positions,2)
case ('ndot0')
constitutive_dislobased_Ndot0(i) = IO_floatValue(line,positions,2)
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 ('cstorage')
constitutive_dislobased_Cstorage(i) = IO_floatValue(line,positions,2)
case ('carecovery')
constitutive_dislobased_Carecovery(i) = IO_floatValue(line,positions,2)
case ('interaction_coefficients')
forall (j=2:min(7,positions(1))) &
constitutive_dislobased_SlipIntCoeff(j-1,i) = IO_floatValue(line,positions,j)
end select
endif
enddo
100 do i = 1,maxNinstance
constitutive_dislobased_structure(i) = lattice_initializeStructure(constitutive_dislobased_structureName(i), &
constitutive_dislobased_CoverA(i))
! sanity checks
if (constitutive_dislobased_structure(i) < 1) call IO_error(201)
if (constitutive_dislobased_Nslip(i) < 1) call IO_error(202)
if (constitutive_dislobased_rho0(i) < 0.0_pReal) call IO_error(220)
if (constitutive_dislobased_bg(i) <= 0.0_pReal) call IO_error(221)
if (constitutive_dislobased_Qedge(i) <= 0.0_pReal) call IO_error(222)
enddo
allocate(constitutive_dislobased_Iparallel(maxval(constitutive_dislobased_Nslip),maxval(constitutive_dislobased_Nslip),maxNinstance))
constitutive_dislobased_Iparallel = 0.0_pReal
allocate(constitutive_dislobased_Iforest(maxval(constitutive_dislobased_Nslip),maxval(constitutive_dislobased_Nslip),maxNinstance))
constitutive_dislobased_Iforest = 0.0_pReal
allocate(constitutive_dislobased_Ctwin_66(6,6,maxval(constitutive_dislobased_Ntwin),maxNinstance))
constitutive_dislobased_Ctwin_66 = 0.0_pReal
allocate(constitutive_dislobased_Ctwin_3333(3,3,3,3,maxval(constitutive_dislobased_Ntwin),maxNinstance))
constitutive_dislobased_Ctwin_3333 = 0.0_pReal
do i = 1,maxNinstance
constitutive_dislobased_sizeDotState(i) = constitutive_dislobased_Nslip(i)+constitutive_dislobased_Ntwin(i)
constitutive_dislobased_sizeState(i) = 10*constitutive_dislobased_Nslip(i)+5*constitutive_dislobased_Ntwin(i)
do j = 1,maxval(phase_Noutput)
select case(constitutive_dislobased_output(j,i))
case('state_slip')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
case('rateofshear_slip')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
case('mfp_slip')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
case('thresholdstress_slip')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Nslip(i)
case('state_twin')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Ntwin(i)
case('rateofshear_twin')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Ntwin(i)
case('mfp_twin')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Ntwin(i)
case('thresholdstress_twin')
constitutive_dislobased_sizePostResults(i) = constitutive_dislobased_sizePostResults(i) + constitutive_dislobased_Ntwin(i)
end select
enddo
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)))
!* Construction of the twin elasticity matrices
!* Iteration over the systems
constitutive_dislobased_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_dislobased_Cslip_66(:,:,i))
do j=1,constitutive_dislobased_Ntwin(i)
do k=1,3
do l=1,3
do m=1,3
do n=1,3
do p=1,3
do q=1,3
do r=1,3
do s=1,3
constitutive_dislobased_Ctwin_3333(k,l,m,n,j,i) = constitutive_dislobased_Ctwin_3333(k,l,m,n,j,i) + &
constitutive_dislobased_Cslip_3333(p,q,r,s,i)*&
lattice_Qtwin(k,p,j,i)*lattice_Qtwin(l,q,j,i)*lattice_Qtwin(m,r,j,i)*lattice_Qtwin(n,s,j,i)
enddo
enddo
enddo
enddo
enddo
enddo
enddo
enddo
constitutive_dislobased_Ctwin_66(:,:,j,i) = math_Mandel3333to66(constitutive_dislobased_Ctwin_3333(:,:,:,:,j,i))
enddo
!* Construction of the hardening matrices
!* Iteration over the systems
do j = 1,constitutive_dislobased_Nslip(i)
do k = 1,constitutive_dislobased_Nslip(i)
!* Projection of the dislocation *
x = math_mul3x3(lattice_sn(:,j,i),lattice_st(:,k,i))
y = 1.0_pReal-x**(2.0_pReal)
!* Interaction matrix *
constitutive_dislobased_Iforest(j,k,i) = abs(x)*&
constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i)
if (y>0.0_pReal) &
constitutive_dislobased_Iparallel(j,k,i) = sqrt(y)*&
constitutive_dislobased_SlipIntCoeff(lattice_interactionSlipSlip(j,k,constitutive_dislobased_structure(i)),i)
enddo
enddo
enddo
return
end subroutine
function constitutive_dislobased_stateInit(myInstance)
!*********************************************************************
!* initial microstructural state *
!*********************************************************************
use prec, only: pReal,pInt
implicit none
!* Definition of variables
integer(pInt), intent(in) :: myInstance
real(pReal), dimension(constitutive_dislobased_sizeState(myInstance)) :: constitutive_dislobased_stateInit
constitutive_dislobased_stateInit = 0.0_pReal
constitutive_dislobased_stateInit(1:constitutive_dislobased_Nslip(myInstance)) = constitutive_dislobased_rho0(myInstance)
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_Nslip(matID)
nt = constitutive_dislobased_Ntwin(matID)
!* Total twin volume fraction
sumf = 0.0_pReal
if (nt > 0_pInt) sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt)))
!* 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
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
!* Shortened notation
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
ns = constitutive_dislobased_Nslip(matID)
nt = constitutive_dislobased_Ntwin(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 = 0.0_pReal
if (nt > 0_pInt) sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt)))
!* Forest and parallel dislocation densities
!$OMP CRITICAL (evilmatmul)
state(ipc,ip,el)%p((ns+nt+1):(2*ns+nt)) = matmul(constitutive_dislobased_Iforest (1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns))
state(ipc,ip,el)%p((2*ns+nt+1):(3*ns+nt)) = matmul(constitutive_dislobased_Iparallel(1:ns,1:ns,matID),state(ipc,ip,el)%p(1:ns))
!$OMP END CRITICAL (evilmatmul)
!* 1/mean free distance between 2 forest dislocations seen by a moving dislocation
do i=1,ns
state(ipc,ip,el)%p(3*ns+nt+i) = sqrt(state(ipc,ip,el)%p(ns+nt+i))
enddo
!* 1/mean free distance between 2 twin stacks from different systems seen by a moving dislocation
!$OMP CRITICAL (evilmatmul)
state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = 0.0_pReal
if (nt > 0_pInt) state(ipc,ip,el)%p((4*ns+nt+1):(5*ns+nt)) = &
matmul(lattice_interactionSlipTwin(1:ns,1:nt,constitutive_dislobased_structure(matID)),state(ipc,ip,el)%p((ns+1):(ns+nt)))/&
(2.0_pReal*constitutive_dislobased_stacksize(matID)*(1.0_pReal-sumf))
!$OMP END CRITICAL (evilmatmul)
!* 1/mean free distance between 2 twin stacks from different systems seen by a growing twin
!$OMP CRITICAL (evilmatmul)
if (nt > 0_pInt) state(ipc,ip,el)%p((5*ns+nt+1):(5*ns+2*nt)) = &
matmul(lattice_interactionTwinTwin(1:nt,1:nt,constitutive_dislobased_structure(matID)),state(ipc,ip,el)%p((ns+1):(ns+nt)))/&
(2.0_pReal*constitutive_dislobased_stacksize(matID)*(1.0_pReal-sumf))
!$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
do 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))
enddo
!* threshold stress for dislocation motion
do i=1,ns
state(ipc,ip,el)%p(6*ns+3*nt+i) = constitutive_dislobased_Cthresholdslip(matID)*&
constitutive_dislobased_bg(matID)*constitutive_dislobased_Gmod(matID)*sqrt(state(ipc,ip,el)%p(2*ns+nt+i))
enddo
!* threshold stress for growing twin
do 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_bg(matID)+&
(constitutive_dislobased_bg(matID)*constitutive_dislobased_Gmod(matID))/state(ipc,ip,el)%p(5*ns+2*nt+i))
enddo
!* activation volume for dislocation glide
do i=1,ns
state(ipc,ip,el)%p(7*ns+4*nt+i) = constitutive_dislobased_Cactivolume(matID)*&
constitutive_dislobased_bg(matID)*constitutive_dislobased_bg(matID)*state(ipc,ip,el)%p(5*ns+2*nt+i)
enddo
!* final twin volume after growth
do i=1,nt
state(ipc,ip,el)%p(8*ns+4*nt+i) = (pi/6.0_pReal)*constitutive_dislobased_stacksize(matID)*&
state(ipc,ip,el)%p(6*ns+2*nt+i)*state(ipc,ip,el)%p(6*ns+2*nt+i)
enddo
!* mobile dislocation densities
do 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))
enddo
!* initial shear rate for slip
do 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_bg(matID)*attack_frequency*&
state(ipc,ip,el)%p(5*ns+2*nt+i)*exp(-constitutive_dislobased_Qedge(matID)/(kB*Temperature))
enddo
end subroutine
subroutine constitutive_dislobased_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,Temperature,state,ipc,ip,el)
!*********************************************************************
!* 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_Stwin,lattice_Sslip_v,lattice_Stwin_v,lattice_shearTwin
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,k,l,m,n,ns,nt
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_Nslip(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
gdot_slip,dgdot_dtauslip,tau_slip
real(pReal), dimension(constitutive_dislobased_Ntwin(phase_constitutionInstance(material_phase(ipc,ip,el)))) :: &
gdot_twin,dgdot_dtautwin,tau_twin
!* Shortened notation
matID = phase_constitutionInstance(material_phase(ipc,ip,el))
ns = constitutive_dislobased_Nslip(matID)
nt = constitutive_dislobased_Ntwin(matID)
!* Total twin volume fraction
sumf = 0.0_pReal
if (nt > 0_pInt) sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt)))
!* Calculation of Lp from dislocation glide
Lp = 0.0_pReal
gdot_slip = 0.0_pReal
do i = 1,ns
tau_slip(i) = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
if ( abs(tau_slip(i)) > state(ipc,ip,el)%p(6*ns+3*nt+i) ) &
gdot_slip(i) = state(ipc,ip,el)%p(9*ns+5*nt+i)*sign(1.0_pReal,tau_slip(i))*&
sinh(((abs(tau_slip(i))-state(ipc,ip,el)%p(6*ns+3*nt+i))*state(ipc,ip,el)%p(7*ns+4*nt+i))/(kB*Temperature))
Lp = Lp + (1.0_pReal - sumf)*gdot_slip(i)*lattice_Sslip(:,:,i,constitutive_dislobased_structure(matID))
enddo
!* Calculation of Lp from deformation twinning
gdot_twin = 0.0_pReal
do i = 1,nt
tau_twin(i) = dot_product(Tstar_v,lattice_Stwin_v(:,i,constitutive_dislobased_structure(matID)))
if ( tau_twin(i) > 0.0_pReal ) &
gdot_twin(i) = (constitutive_dislobased_fmax(matID) - sumf)*lattice_shearTwin(i,constitutive_dislobased_structure(matID))*&
state(ipc,ip,el)%p(8*ns+4*nt+i)*constitutive_dislobased_Ndot0(matID)*&
exp(-(state(ipc,ip,el)%p(7*ns+3*nt+i)/tau_twin(i))**10.0_pReal)
Lp = Lp + gdot_twin(i)*lattice_Stwin(:,:,i,constitutive_dislobased_structure(matID))
enddo
!* Calculation of the tangent of Lp from dislocation glide
dLp_dTstar3333 = 0.0_pReal
dLp_dTstar = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
do i = 1,ns
if ( abs(tau_slip(i)) > state(ipc,ip,el)%p(6*ns+3*nt+i) ) &
dgdot_dtauslip(i) = (state(ipc,ip,el)%p(9*ns+5*nt+i)*state(ipc,ip,el)%p(7*ns+4*nt+i))/(kB*Temperature)*&
cosh(((abs(tau_slip(i))-state(ipc,ip,el)%p(6*ns+3*nt+i))*state(ipc,ip,el)%p(7*ns+4*nt+i))/(kB*Temperature))
forall (k=1:3,l=1:3,m=1:3,n=1:3) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + &
dgdot_dtauslip(i)*lattice_Sslip(k,l,i,constitutive_dislobased_structure(matID))&
*lattice_Sslip(m,n,i,constitutive_dislobased_structure(matID))
enddo
!* Calculation of the tangent of Lp from deformation twinning
dgdot_dtautwin = 0.0_pReal
do i = 1,nt
if ( tau_twin(i) > 0.0_pReal ) &
dgdot_dtautwin(i) = (gdot_twin(i)*10.0_pReal*state(ipc,ip,el)%p(7*ns+3*nt+i)**10.0_pReal)/(tau_twin(i)**11.0_pReal)
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(i)*lattice_Stwin(k,l,i,constitutive_dislobased_structure(matID)) &
*lattice_Stwin(m,n,i,constitutive_dislobased_structure(matID))
enddo
dLp_dTstar = math_Plain3333to99(dLp_dTstar3333)
return
end subroutine
function constitutive_dislobased_dotState(Tstar_v,Temperature,state,ipc,ip,el)
!*********************************************************************
!* rate of change of microstructure *
!* INPUT: *
!* - 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_v,lattice_Stwin_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,ns,nt
real(pReal) Temperature,sumf,tau_slip,tau_twin,gdot_slip,gdot_twin,storage,arecovery
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: state
real(pReal), dimension(6) :: Tstar_v
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))
ns = constitutive_dislobased_Nslip(matID)
nt = constitutive_dislobased_Ntwin(matID)
!* Total twin volume fraction
sumf = 0.0_pReal
if (nt > 0_pInt) sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt)))
!* Dislocation density evolution
constitutive_dislobased_dotState = 0.0_pReal
do i = 1,ns
tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
if ( abs(tau_slip) > state(ipc,ip,el)%p(6*ns+3*nt+i) ) then
gdot_slip = state(ipc,ip,el)%p(9*ns+5*nt+i)*sign(1.0_pReal,tau_slip)*&
sinh(((abs(tau_slip)-state(ipc,ip,el)%p(6*ns+3*nt+i))*state(ipc,ip,el)%p(7*ns+4*nt+i))/(kB*Temperature) )
storage = (constitutive_dislobased_Cstorage(matID)*abs(gdot_slip))/&
(constitutive_dislobased_bg(matID)*state(ipc,ip,el)%p(5*ns+2*nt+i))
arecovery = constitutive_dislobased_Carecovery(matID)*state(ipc,ip,el)%p(i)*abs(gdot_slip)
constitutive_dislobased_dotState(i) = storage - arecovery
endif
enddo
!* Twin volume fraction evolution
do i = 1,nt
tau_twin = dot_product(Tstar_v,lattice_Stwin_v(:,i,constitutive_dislobased_structure(matID)))
if ( tau_twin > 0.0_pReal ) &
constitutive_dislobased_dotState(ns+i) = (constitutive_dislobased_fmax(matID) - sumf)*&
state(ipc,ip,el)%p(8*ns+4*nt+i)*constitutive_dislobased_Ndot0(matID)*&
exp(-(state(ipc,ip,el)%p(7*ns+3*nt+i)/tau_twin)**10.0_pReal)
enddo
return
end function
function constitutive_dislobased_dotTemperature(Tstar_v,Temperature,state,ipc,ip,el)
!*********************************************************************
!* rate of change of microstructure *
!* INPUT: *
!* - Tstar_v : 2nd Piola Kirchhoff stress tensor (Mandel) *
!* - ipc : component-ID at current integration point *
!* - ip : current integration point *
!* - el : current element *
!* OUTPUT: *
!* - constitutive_dotTemperature : evolution of Temperature *
!*********************************************************************
use prec, only: pReal,pInt,p_vec
use lattice, only: lattice_Sslip_v
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase, phase_constitutionInstance
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,n
real(pReal) Temperature
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: *
!* - 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 lattice, only: lattice_Sslip_v,lattice_Stwin_v,lattice_shearTwin
use mesh, only: mesh_NcpElems,mesh_maxNips
use material, only: homogenization_maxNgrains,material_phase,phase_constitutionInstance,phase_Noutput
implicit none
!* Definition of variables
integer(pInt), intent(in) :: ipc,ip,el
real(pReal), intent(in) :: dt,Temperature
real(pReal), dimension(6), intent(in) :: Tstar_v
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state
integer(pInt) matID,o,i,c,ns,nt
real(pReal) sumf,tau_slip,tau_twin
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))
ns = constitutive_dislobased_Nslip(matID)
nt = constitutive_dislobased_Ntwin(matID)
!* Total twin volume fraction
sumf = 0.0_pReal
if (nt > 0_pInt) sumf = sum(state(ipc,ip,el)%p((ns+1):(ns+nt)))
!* 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 ('state_slip')
constitutive_dislobased_postResults(c+1:c+ns) = state(ipc,ip,el)%p(1:ns)
c = c + ns
case ('rateofshear_slip')
do i = 1,ns
tau_slip = dot_product(Tstar_v,lattice_Sslip_v(:,i,constitutive_dislobased_structure(matID)))
if ( abs(tau_slip) > state(ipc,ip,el)%p(6*ns+3*nt+i) ) then
constitutive_dislobased_postResults(c+i) = state(ipc,ip,el)%p(9*ns+5*nt+i)*sign(1.0_pReal,tau_slip)*&
sinh(((abs(tau_slip)-state(ipc,ip,el)%p(6*ns+3*nt+i))*state(ipc,ip,el)%p(7*ns+4*nt+i))/(kB*Temperature) )
else
constitutive_dislobased_postResults(c+i) = 0.0_pReal
endif
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 ('thresholdstress_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 ('state_twin')
if (nt > 0_pInt) constitutive_dislobased_postResults(c+1:c+nt) = state(ipc,ip,el)%p((ns+1):(ns+nt))
c = c + nt
case ('rateofshear_twin')
if (nt > 0_pInt) then
do i = 1,nt
tau_twin = dot_product(Tstar_v,lattice_Stwin_v(:,i,constitutive_dislobased_structure(matID)))
if ( tau_twin > 0.0_pReal ) then
constitutive_dislobased_postResults(c+i) = (constitutive_dislobased_fmax(matID) - sumf)*&
lattice_shearTwin(i,constitutive_dislobased_structure(matID))*&
state(ipc,ip,el)%p(8*ns+4*nt+i)*constitutive_dislobased_Ndot0(matID)*&
exp(-(state(ipc,ip,el)%p(7*ns+3*nt+i)/tau_twin)**10.0_pReal)
else
constitutive_dislobased_postResults(c+i) = 0.0_pReal
endif
enddo
endif
c = c + nt
case ('mfp_twin')
if (nt > 0_pInt) 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 ('thresholdstress_twin')
if (nt > 0_pInt) 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