DAMASK_EICMD/code/constitutive_nonlocal.f90

1798 lines
96 KiB
Fortran

!* $Id$
!************************************
!* Module: CONSTITUTIVE_NONLOCAL *
!************************************
!* contains: *
!* - constitutive equations *
!* - parameters definition *
!************************************
MODULE constitutive_nonlocal
!* Include other modules
use prec, only: pReal,pInt
implicit none
!* Definition of parameters
character (len=*), parameter :: constitutive_nonlocal_label = 'nonlocal'
character(len=16), dimension(6), parameter :: constitutive_nonlocal_listBasicStates = (/'rhoEdgePos ', &
'rhoEdgeNeg ', &
'rhoScrewPos ', &
'rhoScrewNeg ', &
'rhoEdgeDip ', &
'rhoScrewDip ' /) ! list of "basic" microstructural state variables that are independent from other state variables
character(len=16), dimension(3), parameter :: constitutive_nonlocal_listDependentStates = (/'rhoForest ', &
'tauSlipThreshold', &
'Tdislocation_v ' /) ! list of microstructural state variables that depend on other state variables
real(pReal), parameter :: kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin
!* Definition of global variables
integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_sizeDotState, & ! number of dotStates
constitutive_nonlocal_sizeState, & ! total number of microstructural state variables
constitutive_nonlocal_sizePostResults ! cumulative size of post results
integer(pInt), dimension(:,:), allocatable, target :: constitutive_nonlocal_sizePostResult ! size of each post result output
character(len=64), dimension(:,:), allocatable, target :: constitutive_nonlocal_output ! name of each post result output
character(len=32), dimension(:), allocatable :: constitutive_nonlocal_structureName ! name of the lattice structure
integer(pInt), dimension(:), allocatable :: constitutive_nonlocal_structure, & ! number representing the kind of lattice structure
constitutive_nonlocal_totalNslip ! total number of active slip systems for each instance
integer(pInt), dimension(:,:), allocatable :: constitutive_nonlocal_Nslip, & ! number of active slip systems for each family and instance
constitutive_nonlocal_slipFamily, & ! lookup table relating active slip system to slip family for each instance
constitutive_nonlocal_slipSystemLattice ! lookup table relating active slip system index to lattice slip system index for each instance
real(pReal), dimension(:), allocatable :: constitutive_nonlocal_CoverA, & ! c/a ratio for hex type lattice
constitutive_nonlocal_C11, & ! C11 element in elasticity matrix
constitutive_nonlocal_C12, & ! C12 element in elasticity matrix
constitutive_nonlocal_C13, & ! C13 element in elasticity matrix
constitutive_nonlocal_C33, & ! C33 element in elasticity matrix
constitutive_nonlocal_C44, & ! C44 element in elasticity matrix
constitutive_nonlocal_Gmod, & ! shear modulus
constitutive_nonlocal_nu, & ! poisson's ratio
constitutive_nonlocal_Q0, & ! activation energy for dislocation glide
constitutive_nonlocal_atomicVolume, & ! atomic volume
constitutive_nonlocal_D0, & ! prefactor for self-diffusion coefficient
constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion
constitutive_nonlocal_relevantRho ! dislocation density considered relevant
real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_rhoEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoEdgeNeg0, & ! initial edge_neg dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoScrewPos0, & ! initial screw_pos dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoEdgeDip0, & ! initial edge dipole dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoScrewDip0, & ! initial screw dipole dislocation density per slip system for each family and instance
constitutive_nonlocal_v0PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_nonlocal_v0PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance
constitutive_nonlocal_lambda0PerSlipSystem, & ! mean free path prefactor for each slip system and instance
constitutive_nonlocal_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each family and instance
constitutive_nonlocal_burgersPerSlipSystem, & ! absolute length of burgers vector [m] for each slip system and instance
constitutive_nonlocal_dLowerEdgePerSlipFamily, & ! minimum stable edge dipole height for each family and instance
constitutive_nonlocal_dLowerEdgePerSlipSystem, & ! minimum stable edge dipole height for each slip system and instance
constitutive_nonlocal_dLowerScrewPerSlipFamily, & ! minimum stable screw dipole height for each family and instance
constitutive_nonlocal_dLowerScrewPerSlipSystem, & ! minimum stable screw dipole height for each slip system and instance
constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each instance
constitutive_nonlocal_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance
constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance
logical :: periodicBC = .false.
CONTAINS
!****************************************
!* - constitutive_init
!* - constitutive_stateInit
!* - constitutive_homogenizedC
!* - constitutive_microstructure
!* - constitutive_LpAndItsTangent
!* - constitutive_dotState
!* - constitutive_dotTemperature
!* - constitutive_postResults
!****************************************
!**************************************
!* Module initialization *
!**************************************
subroutine constitutive_nonlocal_init(file)
use prec, only: pInt, pReal
use math, only: math_Mandel3333to66, &
math_Voigt66to3333, &
math_mul3x3
use IO, only: IO_lc, &
IO_getTag, &
IO_isBlank, &
IO_stringPos, &
IO_stringValue, &
IO_floatValue, &
IO_intValue, &
IO_error
use material, only: phase_constitution, &
phase_constitutionInstance, &
phase_Noutput
use lattice, only: lattice_maxNslipFamily, &
lattice_maxNtwinFamily, &
lattice_maxNslip, &
lattice_maxNtwin, &
lattice_maxNinteraction, &
lattice_NslipSystem, &
lattice_NtwinSystem, &
lattice_initializeStructure, &
lattice_Qtwin, &
lattice_sd, &
lattice_sn, &
lattice_st, &
lattice_interactionSlipSlip
!*** output variables
!*** input variables
integer(pInt), intent(in) :: file
!*** local variables
integer(pInt), parameter :: maxNchunks = 21
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt) section, &
maxNinstance, &
maxTotalNslip, &
myStructure, &
f, & ! index of my slip family
i, & ! index of my instance of this constitution
j, &
k, &
l, &
ns, & ! short notation for total number of active slip systems for the current instance
o, & ! index of my output
s, & ! index of my slip system
s1, & ! index of my slip system
s2, & ! index of my slip system
it, & ! index of my interaction type
output, &
mySize
character(len=64) tag
character(len=1024) line
write(6,*)
write(6,'(a20,a20,a12)') '<<<+- constitutive_',constitutive_nonlocal_label,' init -+>>>'
write(6,*) '$Id$'
write(6,*)
maxNinstance = count(phase_constitution == constitutive_nonlocal_label)
if (maxNinstance == 0) return ! we don't have to do anything if there's no instance for this constitutive law
!*** space allocation for global variables
allocate(constitutive_nonlocal_sizeDotState(maxNinstance))
allocate(constitutive_nonlocal_sizeState(maxNinstance))
allocate(constitutive_nonlocal_sizePostResults(maxNinstance))
allocate(constitutive_nonlocal_sizePostResult(maxval(phase_Noutput), maxNinstance))
allocate(constitutive_nonlocal_output(maxval(phase_Noutput), maxNinstance))
constitutive_nonlocal_sizeDotState = 0_pInt
constitutive_nonlocal_sizeState = 0_pInt
constitutive_nonlocal_sizePostResults = 0_pInt
constitutive_nonlocal_sizePostResult = 0_pInt
constitutive_nonlocal_output = ''
allocate(constitutive_nonlocal_structureName(maxNinstance))
allocate(constitutive_nonlocal_structure(maxNinstance))
allocate(constitutive_nonlocal_Nslip(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_slipFamily(lattice_maxNslip, maxNinstance))
allocate(constitutive_nonlocal_slipSystemLattice(lattice_maxNslip, maxNinstance))
allocate(constitutive_nonlocal_totalNslip(maxNinstance))
constitutive_nonlocal_structureName = ''
constitutive_nonlocal_structure = 0_pInt
constitutive_nonlocal_Nslip = 0_pInt
constitutive_nonlocal_slipFamily = 0_pInt
constitutive_nonlocal_slipSystemLattice = 0_pInt
constitutive_nonlocal_totalNslip = 0_pInt
allocate(constitutive_nonlocal_CoverA(maxNinstance))
allocate(constitutive_nonlocal_C11(maxNinstance))
allocate(constitutive_nonlocal_C12(maxNinstance))
allocate(constitutive_nonlocal_C13(maxNinstance))
allocate(constitutive_nonlocal_C33(maxNinstance))
allocate(constitutive_nonlocal_C44(maxNinstance))
allocate(constitutive_nonlocal_Gmod(maxNinstance))
allocate(constitutive_nonlocal_nu(maxNinstance))
allocate(constitutive_nonlocal_Q0(maxNinstance))
allocate(constitutive_nonlocal_atomicVolume(maxNinstance))
allocate(constitutive_nonlocal_D0(maxNinstance))
allocate(constitutive_nonlocal_Qsd(maxNinstance))
allocate(constitutive_nonlocal_relevantRho(maxNinstance))
allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance))
allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance))
constitutive_nonlocal_CoverA = 0.0_pReal
constitutive_nonlocal_C11 = 0.0_pReal
constitutive_nonlocal_C12 = 0.0_pReal
constitutive_nonlocal_C13 = 0.0_pReal
constitutive_nonlocal_C33 = 0.0_pReal
constitutive_nonlocal_C44 = 0.0_pReal
constitutive_nonlocal_Gmod = 0.0_pReal
constitutive_nonlocal_Q0 = 0.0_pReal
constitutive_nonlocal_atomicVolume = 0.0_pReal
constitutive_nonlocal_D0 = 0.0_pReal
constitutive_nonlocal_Qsd = 0.0_pReal
constitutive_nonlocal_relevantRho = 0.0_pReal
constitutive_nonlocal_nu = 0.0_pReal
constitutive_nonlocal_Cslip_66 = 0.0_pReal
constitutive_nonlocal_Cslip_3333 = 0.0_pReal
allocate(constitutive_nonlocal_rhoEdgePos0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoEdgeNeg0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoScrewPos0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoScrewNeg0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoEdgeDip0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoScrewDip0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_v0PerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction, maxNinstance))
allocate(constitutive_nonlocal_dLowerEdgePerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_dLowerScrewPerSlipFamily(lattice_maxNslipFamily, maxNinstance))
constitutive_nonlocal_rhoEdgePos0 = 0.0_pReal
constitutive_nonlocal_rhoEdgeNeg0 = 0.0_pReal
constitutive_nonlocal_rhoScrewPos0 = 0.0_pReal
constitutive_nonlocal_rhoScrewNeg0 = 0.0_pReal
constitutive_nonlocal_rhoEdgeDip0 = 0.0_pReal
constitutive_nonlocal_rhoScrewDip0 = 0.0_pReal
constitutive_nonlocal_v0PerSlipFamily = 0.0_pReal
constitutive_nonlocal_burgersPerSlipFamily = 0.0_pReal
constitutive_nonlocal_lambda0PerSlipFamily = 0.0_pReal
constitutive_nonlocal_interactionSlipSlip = 0.0_pReal
constitutive_nonlocal_dLowerEdgePerSlipFamily = 0.0_pReal
constitutive_nonlocal_dLowerScrewPerSlipFamily = 0.0_pReal
!*** readout data from material.config file
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_nonlocal_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_nonlocal_output(output,i) = IO_lc(IO_stringValue(line,positions,2))
case ('lattice_structure')
constitutive_nonlocal_structureName(i) = IO_lc(IO_stringValue(line,positions,2))
case ('covera_ratio')
constitutive_nonlocal_CoverA(i) = IO_floatValue(line,positions,2)
case ('c11')
constitutive_nonlocal_C11(i) = IO_floatValue(line,positions,2)
case ('c12')
constitutive_nonlocal_C12(i) = IO_floatValue(line,positions,2)
case ('c13')
constitutive_nonlocal_C13(i) = IO_floatValue(line,positions,2)
case ('c33')
constitutive_nonlocal_C33(i) = IO_floatValue(line,positions,2)
case ('c44')
constitutive_nonlocal_C44(i) = IO_floatValue(line,positions,2)
case ('nslip')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_Nslip(f,i) = IO_intValue(line,positions,1+f)
case ('rhoedgepos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgePos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoedgeneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoscrewpos0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewPos0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoscrewneg0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewNeg0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoedgedip0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoEdgeDip0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhoscrewdip0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoScrewDip0(f,i) = IO_floatValue(line,positions,1+f)
case ('v0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_v0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('lambda0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('burgers')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_burgersPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('ddipminedge')
forall (f = 1:lattice_maxNslipFamily) &
constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('ddipminscrew')
forall (f = 1:lattice_maxNslipFamily) &
constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('q0')
constitutive_nonlocal_Q0(i) = IO_floatValue(line,positions,2)
case('atomicvolume')
constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2)
case('d0')
constitutive_nonlocal_D0(i) = IO_floatValue(line,positions,2)
case('qsd')
constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2)
case('relevantrho')
constitutive_nonlocal_relevantRho(i) = IO_floatValue(line,positions,2)
case ('interaction_slipslip')
forall (it = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1+it)
end select
endif
enddo
100 do i = 1,maxNinstance
constitutive_nonlocal_structure(i) = &
lattice_initializeStructure(constitutive_nonlocal_structureName(i), constitutive_nonlocal_CoverA(i)) ! our lattice structure is defined in the material.config file by the structureName (and the c/a ratio)
myStructure = constitutive_nonlocal_structure(i)
!*** sanity checks
if (myStructure < 1 .or. myStructure > 3) call IO_error(205)
if (sum(constitutive_nonlocal_Nslip(:,i)) <= 0_pInt) call IO_error(225)
do o = 1,maxval(phase_Noutput)
if(len(constitutive_nonlocal_output(o,i)) > 64) call IO_error(666)
enddo
do f = 1,lattice_maxNslipFamily
if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then
if (constitutive_nonlocal_rhoEdgePos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoEdgeNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoScrewPos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoScrewNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoEdgeDip0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoScrewDip0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221)
if (constitutive_nonlocal_v0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(226)
if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(227)
if (constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228)
if (constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228)
endif
enddo
if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) &
call IO_error(229)
if (constitutive_nonlocal_Q0(i) <= 0.0_pReal) call IO_error(-1)
if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(230)
if (constitutive_nonlocal_D0(i) <= 0.0_pReal) call IO_error(231)
if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(232)
if (constitutive_nonlocal_relevantRho(i) <= 0.0_pReal) call IO_error(233)
!*** determine total number of active slip systems
constitutive_nonlocal_Nslip(:,i) = min( lattice_NslipSystem(:, myStructure), constitutive_nonlocal_Nslip(:,i) ) ! we can't use more slip systems per family than specified in lattice
constitutive_nonlocal_totalNslip(i) = sum(constitutive_nonlocal_Nslip(:,i))
enddo
!*** allocation of variables whose size depends on the total number of active slip systems
maxTotalNslip = maxval(constitutive_nonlocal_totalNslip)
allocate(constitutive_nonlocal_burgersPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_burgersPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_v0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_v0PerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_lambda0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_lambda0PerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_dLowerEdgePerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_dLowerEdgePerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_dLowerScrewPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_dLowerScrewPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance))
constitutive_nonlocal_forestProjectionEdge = 0.0_pReal
allocate(constitutive_nonlocal_forestProjectionScrew(maxTotalNslip, maxTotalNslip, maxNinstance))
constitutive_nonlocal_forestProjectionScrew = 0.0_pReal
allocate(constitutive_nonlocal_interactionMatrixSlipSlip(maxTotalNslip, maxTotalNslip, maxNinstance))
constitutive_nonlocal_interactionMatrixSlipSlip = 0.0_pReal
do i = 1,maxNinstance
myStructure = constitutive_nonlocal_structure(i) ! lattice structure of this instance
!*** Inverse lookup of my slip system family and the slip system in lattice
l = 0_pInt
do f = 1,lattice_maxNslipFamily
do s = 1,constitutive_nonlocal_Nslip(f,i)
l = l + 1
constitutive_nonlocal_slipFamily(l,i) = f
constitutive_nonlocal_slipSystemLattice(l,i) = sum(lattice_NslipSystem(1:f-1, myStructure)) + s
enddo; enddo
!*** determine size of state array
ns = constitutive_nonlocal_totalNslip(i)
constitutive_nonlocal_sizeState(i) = size(constitutive_nonlocal_listBasicStates) * ns &
+ ( size(constitutive_nonlocal_listDependentStates) - 1_pInt ) * ns + 6_pInt
constitutive_nonlocal_sizeDotState(i) = size(constitutive_nonlocal_listBasicStates) * ns
!*** determine size of postResults array
do o = 1,maxval(phase_Noutput)
select case(constitutive_nonlocal_output(o,i))
case( 'rho', &
'delta', &
'rho_edge', &
'rho_screw', &
'excess_rho', &
'excess_rho_edge', &
'excess_rho_screw', &
'rho_forest', &
'rho_dip', &
'delta_dip', &
'rho_edge_dip', &
'rho_screw_dip', &
'shearrate', &
'resolvedstress', &
'resistance', &
'rho_dot', &
'rho_dot_dip', &
'rho_dot_gen', &
'rho_dot_sgl2dip', &
'rho_dot_dip2sgl', &
'rho_dot_ann_ath', &
'rho_dot_ann_the', &
'rho_dot_flux', &
'd_upper_edge', &
'd_upper_screw', &
'd_upper_dot_edge', &
'd_upper_dot_screw' )
mySize = constitutive_nonlocal_totalNslip(i)
case default
mySize = 0_pInt
end select
if (mySize > 0_pInt) then ! any meaningful output found
constitutive_nonlocal_sizePostResult(o,i) = mySize
constitutive_nonlocal_sizePostResults(i) = constitutive_nonlocal_sizePostResults(i) + mySize
endif
enddo
!*** elasticity matrix and shear modulus according to material.config
select case (myStructure)
case(1:2) ! cubic(s)
forall(k=1:3)
forall(j=1:3) constitutive_nonlocal_Cslip_66(k,j,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(k,k,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(k+3,k+3,i) = constitutive_nonlocal_C44(i)
end forall
case(3:) ! all hex
constitutive_nonlocal_Cslip_66(1,1,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(2,2,i) = constitutive_nonlocal_C11(i)
constitutive_nonlocal_Cslip_66(3,3,i) = constitutive_nonlocal_C33(i)
constitutive_nonlocal_Cslip_66(1,2,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(2,1,i) = constitutive_nonlocal_C12(i)
constitutive_nonlocal_Cslip_66(1,3,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(3,1,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(2,3,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(3,2,i) = constitutive_nonlocal_C13(i)
constitutive_nonlocal_Cslip_66(4,4,i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_Cslip_66(5,5,i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_Cslip_66(6,6,i) = 0.5_pReal*(constitutive_nonlocal_C11(i)- constitutive_nonlocal_C12(i))
end select
constitutive_nonlocal_Cslip_66(:,:,i) = math_Mandel3333to66(math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i)))
constitutive_nonlocal_Cslip_3333(:,:,:,:,i) = math_Voigt66to3333(constitutive_nonlocal_Cslip_66(:,:,i))
constitutive_nonlocal_Gmod(i) = constitutive_nonlocal_C44(i)
constitutive_nonlocal_nu(i) = 0.5_pReal * constitutive_nonlocal_C12(i) &
/ (constitutive_nonlocal_C12(i) + constitutive_nonlocal_C44(i))
do s1 = 1,ns
f = constitutive_nonlocal_slipFamily(s1,i)
!*** burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system
constitutive_nonlocal_burgersPerSlipSystem(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i)
constitutive_nonlocal_v0PerSlipSystem(s1,i) = constitutive_nonlocal_v0PerSlipFamily(f,i)
constitutive_nonlocal_lambda0PerSlipSystem(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i)
constitutive_nonlocal_dLowerEdgePerSlipSystem(s1,i) = constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i)
constitutive_nonlocal_dLowerScrewPerSlipSystem(s1,i) = constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i)
do s2 = 1,ns
!*** calculation of forest projections for edge and screw dislocations. s2 acts as forest to s1
constitutive_nonlocal_forestProjectionEdge(s1, s2, i) &
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
lattice_st(:, constitutive_nonlocal_slipSystemLattice(s2,i), myStructure))) ! forest projection of edge dislocations is the projection of (t = b x n) onto the slip normal of the respective slip plane
constitutive_nonlocal_forestProjectionScrew(s1, s2, i) &
= abs(math_mul3x3(lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s1,i), myStructure), &
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s2,i), myStructure))) ! forest projection of screw dislocations is the projection of b onto the slip normal of the respective splip plane
!*** calculation of interaction matrices
constitutive_nonlocal_interactionMatrixSlipSlip(s1, s2, i) &
= constitutive_nonlocal_interactionSlipSlip( lattice_interactionSlipSlip(constitutive_nonlocal_slipSystemLattice(s1,i), &
constitutive_nonlocal_slipSystemLattice(s2,i), &
myStructure), &
i )
enddo; enddo
enddo
endsubroutine
!*********************************************************************
!* initial microstructural state (just the "basic" states) *
!*********************************************************************
pure function constitutive_nonlocal_stateInit(myInstance)
use prec, only: pReal, &
pInt
use lattice, only: lattice_maxNslipFamily
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
constitutive_nonlocal_stateInit
!*** local variables
real(pReal), dimension(constitutive_nonlocal_totalNslip(myInstance)) :: &
rhoEdgePos, & ! positive edge dislocation density
rhoEdgeNeg, & ! negative edge dislocation density
rhoScrewPos, & ! positive screw dislocation density
rhoScrewNeg, & ! negative screw dislocation density
rhoEdgeDip, & ! edge dipole dislocation density
rhoScrewDip, & ! screw dipole dislocation density
rhoForest, & ! forest dislocation density
tauSlipThreshold ! threshold shear stress for slip
integer(pInt) ns, & ! short notation for total number of active slip systems
f, & ! index of lattice family
from, &
upto, &
s ! index of slip system
constitutive_nonlocal_stateInit = 0.0_pReal
ns = constitutive_nonlocal_totalNslip(myInstance)
!*** set the basic state variables
do f = 1,lattice_maxNslipFamily
from = 1+sum(constitutive_nonlocal_Nslip(1:f-1,myInstance))
upto = sum(constitutive_nonlocal_Nslip(1:f,myInstance))
rhoEdgePos(from:upto) = constitutive_nonlocal_rhoEdgePos0(f, myInstance)
rhoEdgeNeg(from:upto) = constitutive_nonlocal_rhoEdgeNeg0(f, myInstance)
rhoScrewPos(from:upto) = constitutive_nonlocal_rhoScrewPos0(f, myInstance)
rhoScrewNeg(from:upto) = constitutive_nonlocal_rhoScrewNeg0(f, myInstance)
rhoEdgeDip(from:upto) = constitutive_nonlocal_rhoEdgeDip0(f, myInstance)
rhoScrewDip(from:upto) = constitutive_nonlocal_rhoScrewDip0(f, myInstance)
enddo
!*** calculate the dependent state variables
! forest dislocation density
forall (s = 1:ns) &
rhoForest(s) &
= dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip), constitutive_nonlocal_forestProjectionEdge(s, 1:ns, myInstance) ) &
+ dot_product( (rhoScrewPos + rhoScrewNeg + rhoScrewDip), constitutive_nonlocal_forestProjectionScrew(s, 1:ns, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
! threshold shear stress for dislocation slip
forall (s = 1:ns) &
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
* constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) &
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoScrewPos + rhoScrewNeg + rhoEdgeDip + rhoScrewDip), &
constitutive_nonlocal_interactionMatrixSlipSlip(s, 1:ns, myInstance) ) )
!*** put everything together and in right order
constitutive_nonlocal_stateInit( 1: ns) = rhoEdgePos
constitutive_nonlocal_stateInit( ns+1:2*ns) = rhoEdgeNeg
constitutive_nonlocal_stateInit(2*ns+1:3*ns) = rhoScrewPos
constitutive_nonlocal_stateInit(3*ns+1:4*ns) = rhoScrewNeg
constitutive_nonlocal_stateInit(4*ns+1:5*ns) = rhoEdgeDip
constitutive_nonlocal_stateInit(5*ns+1:6*ns) = rhoScrewDip
constitutive_nonlocal_stateInit(6*ns+1:7*ns) = rhoForest
constitutive_nonlocal_stateInit(7*ns+1:8*ns) = tauSlipThreshold
endfunction
!*********************************************************************
!* relevant microstructural state *
!*********************************************************************
pure function constitutive_nonlocal_relevantState(myInstance)
use prec, only: pReal, &
pInt
implicit none
!*** input variables
integer(pInt), intent(in) :: myInstance ! number specifying the current instance of the constitution
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizeState(myInstance)) :: &
constitutive_nonlocal_relevantState ! relevant state values for the current instance of this constitution
!*** local variables
constitutive_nonlocal_relevantState = constitutive_nonlocal_relevantRho(myInstance)
endfunction
!*********************************************************************
!* calculates homogenized elacticity matrix *
!*********************************************************************
pure function constitutive_nonlocal_homogenizedC(state,g,ip,el)
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
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: state ! microstructural state
!*** output variables
real(pReal), dimension(6,6) :: constitutive_nonlocal_homogenizedC ! homogenized elasticity matrix
!*** local variables
integer(pInt) myInstance ! current instance of this constitution
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
constitutive_nonlocal_homogenizedC = constitutive_nonlocal_Cslip_66(:,:,myInstance)
endfunction
!*********************************************************************
!* calculates quantities characterizing the microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_microstructure(state, Temperature, Fe, Fp, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_Plain3333to99, &
math_Mandel33to6, &
math_Mandel6to33, &
math_mul33x33, &
math_mul3x3, &
math_mul33x3, &
math_inv3x3, &
math_det3x3, &
pi
use debug, only: debugger
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipCenterOfGravity
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
lattice_maxNslipFamily, &
lattice_NslipSystem, &
lattice_maxNslip, &
lattice_sd, &
lattice_sn, &
lattice_st
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
state ! microstructural state
!*** output variables
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor
n, & ! index of my current neighbor
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal) gb, & ! short notation for G*b/2/pi
x, & ! coordinate in direction of lvec
y, & ! coordinate in direction of bvec
z, & ! coordinate in direction of nvec
detFe, & ! determinant of elastic deformation gradient
neighboring_detFe ! determinant of my neighboring elastic deformation gradient
real(pReal), dimension(3) :: connectingVector ! vector connecting the centers of gravity of me and my neigbor
real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(3,3) :: lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system with e1=bxn, e2=b, e3=n
neighboringSlip2myLattice, &! mapping from my neighbors slip coordinate system to my lattice coordinate system
sigma, & ! Tdislocation resulting from the excess dislocation density of a single slip system and a single neighbor calculated in the coordinate system of the slip system
F, & ! total deformation gradient
neighboring_F, & ! total deformation gradient of my neighbor
Favg, & ! average total deformation gradient of me and my neighbor
invFe, & ! inverse of elastic deformation gradient
neighboring_invFe ! inverse of my neighboring elastic deformation gradient
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoEdgePos, & ! positive edge dislocation density
rhoEdgeNeg, & ! negative edge dislocation density
rhoScrewPos, & ! positive screw dislocation density
rhoScrewNeg, & ! negative screw dislocation density
rhoEdgeDip, & ! edge dipole dislocation density
rhoScrewDip, & ! screw dipole dislocation density
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
neighboring_rhoEdgePos, & ! positive edge dislocation density of my neighbor
neighboring_rhoEdgeNeg, & ! negative edge dislocation density of my neighbor
neighboring_rhoScrewPos, & ! positive screw dislocation density of my neighbor
neighboring_rhoScrewNeg, & ! negative screw dislocation density of my neighbor
neighboring_rhoEdgeExcess, &! edge excess dislocation density of my neighbor
neighboring_rhoScrewExcess,&! screw excess dislocation density of my neighbor
neighboring_Nedge, & ! total number of edge excess dislocations in my neighbor
neighboring_Nscrew
logical flipConnectingVector
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
!**********************************************************************
!*** get basic states
rhoEdgePos = state(g,ip,el)%p( 1: ns)
rhoEdgeNeg = state(g,ip,el)%p( ns+1:2*ns)
rhoScrewPos = state(g,ip,el)%p(2*ns+1:3*ns)
rhoScrewNeg = state(g,ip,el)%p(3*ns+1:4*ns)
rhoEdgeDip = state(g,ip,el)%p(4*ns+1:5*ns)
rhoScrewDip = state(g,ip,el)%p(5*ns+1:6*ns)
!**********************************************************************
!*** calculate dependent states
!*** calculate the forest dislocation density
forall (s = 1:ns) &
rhoForest(s) &
= dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip), constitutive_nonlocal_forestProjectionEdge(1:ns, s, myInstance) ) &
+ dot_product( (rhoScrewPos + rhoScrewNeg + rhoScrewDip), constitutive_nonlocal_forestProjectionScrew(1:ns, s, myInstance) ) ! calculation of forest dislocation density as projection of screw and edge dislocations
! if (debugger) write(6,'(a23,3(i3,x),/,12(e10.3,x),/)') 'forest dislocation density at ',g,ip,el, rhoForest
!*** calculate the threshold shear stress for dislocation slip
forall (s = 1:ns) &
tauSlipThreshold(s) = constitutive_nonlocal_Gmod(myInstance) &
* constitutive_nonlocal_burgersPerSlipSystem(s, myInstance) &
* sqrt( dot_product( (rhoEdgePos + rhoEdgeNeg + rhoEdgeDip + rhoScrewPos + rhoScrewNeg + rhoScrewDip), &
constitutive_nonlocal_interactionMatrixSlipSlip(1:ns, s, myInstance) ) )
! if (debugger) write(6,'(a26,3(i3,x),/,12(f10.5,x),/)') 'tauSlipThreshold / MPa at ',g,ip,el, tauSlipThreshold/1e6
!*** calculate the dislocation stress of the neighboring excess dislocation densities
Tdislocation_v = 0.0_pReal
F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
detFe = math_det3x3(Fe)
invFe = math_inv3x3(Fe)
! loop through my neighbors (if existent!)
do n = 1,FE_NipNeighbors(mesh_element(2,el))
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
flipConnectingVector = .false.
if ( neighboring_el == 0 .or. neighboring_ip == 0 ) then
if (.not. periodicBC) then
cycle
else
flipConnectingVector = .true.
select case (n)
case (1)
neighboring_el = mesh_ipNeighborhood(1,2,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,2,ip,el)
case (2)
neighboring_el = mesh_ipNeighborhood(1,1,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,1,ip,el)
case (3)
neighboring_el = mesh_ipNeighborhood(1,4,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,4,ip,el)
case (4)
neighboring_el = mesh_ipNeighborhood(1,3,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,3,ip,el)
case (5)
neighboring_el = mesh_ipNeighborhood(1,6,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,6,ip,el)
case (6)
neighboring_el = mesh_ipNeighborhood(1,5,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,5,ip,el)
endselect
endif
endif
! deformation gradients needed for mapping between configurations
neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
Favg = 0.5_pReal * (F + neighboring_F)
neighboring_detFe = math_det3x3(Fe(:,:,g,neighboring_ip,neighboring_el))
neighboring_invFe = math_inv3x3(Fe(:,:,g,neighboring_ip,neighboring_el))
! calculate connection vector between me and my neighbor in its lattice configuration
if (flipConnectingVector) then
connectingVector = math_mul33x3(neighboring_invFe, math_mul33x3(Favg, &
-(mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el)) ) )
else
connectingVector = math_mul33x3(neighboring_invFe, math_mul33x3(Favg, &
(mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el)) ) )
endif
! neighboring dislocation densities
neighboring_rhoEdgePos = state(1, neighboring_ip, neighboring_el)%p( 1: ns)
neighboring_rhoEdgeNeg = state(1, neighboring_ip, neighboring_el)%p( ns+1:2*ns)
neighboring_rhoScrewPos = state(1, neighboring_ip, neighboring_el)%p(2*ns+1:3*ns)
neighboring_rhoScrewNeg = state(1, neighboring_ip, neighboring_el)%p(3*ns+1:4*ns)
neighboring_rhoEdgeExcess = neighboring_rhoEdgePos - neighboring_rhoEdgeNeg
neighboring_rhoScrewExcess = neighboring_rhoScrewPos - neighboring_rhoScrewNeg
neighboring_Nedge = neighboring_rhoEdgeExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
neighboring_Nscrew = neighboring_rhoScrewExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal)
! loop over slip systems and get their slip directions, slip normals, and sd x sn
do s = 1,ns
lattice2slip = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) )
! coordinate transformation of connecting vector from the lattice coordinate system to the slip coordinate system
x = math_mul3x3(lattice2slip(1,:), -connectingVector)
y = math_mul3x3(lattice2slip(2,:), -connectingVector)
z = math_mul3x3(lattice2slip(3,:), -connectingVector)
! calculate the back stress in the slip coordinate system for this slip system
gb = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) / (2.0_pReal*pi)
sigma(2,2) = - gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* z * (3.0_pReal*y**2.0_pReal + z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
sigma(3,3) = gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* z * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal
sigma(1,1) = constitutive_nonlocal_nu(myInstance) * (sigma(2,2) + sigma(3,3))
sigma(1,2) = gb * neighboring_Nscrew(s) * z / (x**2.0_pReal + z**2.0_pReal)
sigma(2,3) = gb * ( neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
* y * (y**2.0_pReal - z**2.0_pReal) / (y**2.0_pReal + z**2.0_pReal)**2.0_pReal &
- neighboring_Nscrew(s) * x / (x**2.0_pReal + z**2.0_pReal) )
sigma(2,1) = sigma(1,2)
sigma(3,2) = sigma(2,3)
sigma(1,3) = 0.0_pReal
sigma(3,1) = 0.0_pReal
! coordinate transformation from the slip coordinate system to the lattice coordinate system
neighboringSlip2myLattice = math_mul33x33(invFe,math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el),transpose(lattice2slip)))
Tdislocation_v = Tdislocation_v + math_Mandel33to6( detFe / neighboring_detFe &
* math_mul33x33(neighboringSlip2myLattice, math_mul33x33(sigma, transpose(neighboringSlip2myLattice))) )
enddo
enddo
! if (debugger) then
! !$OMP CRITICAL (write2out)
! write(6,*) '::: constitutive_nonlocal_microstructure at ',g,ip,el
! write(6,*)
! write(6,'(a,/,6(f12.5,x),/)') 'Tdislocation_v / MPa', Tdislocation_v/1e6_pReal
! !$OMP CRITICAL (write2out)
! endif
!**********************************************************************
!*** set dependent states
state(g,ip,el)%p(6*ns+1:7*ns) = rhoForest
state(g,ip,el)%p(7*ns+1:8*ns) = tauSlipThreshold
state(g,ip,el)%p(8*ns+1:8*ns+6) = Tdislocation_v
endsubroutine
!*********************************************************************
!* calculates plastic velocity gradient and its tangent *
!*********************************************************************
subroutine constitutive_nonlocal_LpAndItsTangent(Lp, dLp_dTstar99, Tstar_v, Temperature, state, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_Plain3333to99, &
math_mul6x6, &
math_Mandel6to33
use debug, only: debugger
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature ! temperature
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
!*** output variables
real(pReal), dimension(3,3), intent(out) :: Lp ! plastic velocity gradient
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99 ! derivative of Lp with respect to Tstar (9x9 matrix)
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
i, &
j, &
k, &
l, &
t, & ! dislocation type
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 ! derivative of Lp with respect to Tstar (3x3x3x3 matrix)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
rho ! dislocation densities
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
tauSlip, & ! resolved shear stress
gdotSlip, & ! shear rate
dgdot_dtauSlip, & ! derivative of the shear rate with respect to the shear stress
v ! dislocation velocity
!*** initialize local variables
v = 0.0_pReal
tauSlip = 0.0_pReal
gdotSlip = 0.0_pReal
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
!*** shortcut to state variables
forall (t = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
rhoForest = state(g,ip,el)%p(6*ns+1:7*ns)
tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns)
Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6)
!*** calculation of resolved stress
forall (s =1:ns) &
tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, &
lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure) )
!*** Calculation of gdot and its tangent
v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) &
* exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) &
* sign(1.0_pReal,tauSlip)
gdotSlip = sum(rho,2) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v
dgdot_dtauSlip = gdotSlip * constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature * tauSlipThreshold )
!*** Calculation of Lp and its tangent
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
Lp = Lp + gdotSlip(s) * lattice_Sslip(:,:,sLattice,myStructure)
forall (i=1:3,j=1:3,k=1:3,l=1:3) &
dLp_dTstar3333(i,j,k,l) = dLp_dTstar3333(i,j,k,l) + dgdot_dtauSlip(s) * lattice_Sslip(i,j, sLattice,myStructure) &
* lattice_Sslip(k,l, sLattice,myStructure)
enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,*) '::: LpandItsTangent',g,ip,el
write(6,*)
write(6,'(a,/,3(3(f12.3,x)/))') 'Tdislocation / MPa', math_Mandel6to33(Tdislocation_v/1e6)
write(6,'(a,/,3(3(f12.3,x)/))') 'Tstar / MPa', math_Mandel6to33(Tstar_v/1e6)
write(6,'(a,/,12(f12.5,x),/)') 'tauSlip / MPa', tauSlip/1e6_pReal
! write(6,'(a,/,12(f12.5,x),/)') 'tauSlipThreshold / MPa', tauSlipThreshold/1e6_pReal
! write(6,'(a,/,12(f12.5,x),/)') 'v', v
! write(6,'(a,/,12(f12.5,x),/)') 'gdot total /1e-3',gdotSlip*1e3_pReal
! write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp
call flush(6)
!$OMPEND CRITICAL (write2out)
endif
endsubroutine
!*********************************************************************
!* rate of change of microstructure *
!*********************************************************************
subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, subTstar0_v, Fe, Fp, Temperature, subdt, state, subState0, g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use debug, only: debugger
use math, only: math_norm3, &
math_mul6x6, &
math_mul3x3, &
math_mul33x3, &
math_mul33x33, &
math_inv3x3, &
math_det3x3, &
pi
use mesh, only: mesh_NcpElems, &
mesh_maxNips, &
mesh_element, &
FE_NipNeighbors, &
mesh_ipNeighborhood, &
mesh_ipVolume, &
mesh_ipArea, &
mesh_ipAreaNormal
use material, only: homogenization_maxNgrains, &
material_phase, &
phase_constitutionInstance
use lattice, only: lattice_Sslip, &
lattice_Sslip_v, &
lattice_sd, &
lattice_sn, &
lattice_st, &
lattice_maxNslipFamily, &
lattice_NslipSystem
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: Temperature, & ! temperature
subdt ! substepped crystallite time increment
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation
subTstar0_v ! 2nd Piola-Kirchhoff stress in Mandel notation at start of crystallite increment
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state, & ! current microstructural state
subState0 ! microstructural state at start of crystallite increment
!*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
dotState ! evolution of state variables / microstructure
!*** output variables
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor
c, & ! character of dislocation
n, & ! index of my current neighbor
t, & ! type of dislocation
s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
rho, & ! dislocation densities (positive/negative screw and edge without dipoles)
totalRhoDot, & ! total rate of change of dislocation densities
thisRhoDot, & ! rate of change of dislocation densities for this mechanism
gdot, & ! shear rates
lineLength ! dislocation line length leaving the current interface
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
tauSlip, & ! current resolved shear stress
subTauSlip0, & ! resolved shear stress at start of crystallite increment
v, & ! dislocation velocity
invLambda, & ! inverse of mean free path for dislocations
vClimb ! climb velocity of edge dipoles
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! dipole dislocation densities (screw and edge dipoles)
totalRhoDipDot, & ! total rate of change of dipole dislocation densities
thisRhoDipDot, & ! rate of change of dipole dislocation densities for this mechanism
dLower, & ! minimum stable dipole distance for edges and screws
dUpper, & ! current maximum stable dipole distance for edges and screws
dUpper0, & ! maximum stable dipole distance for edges and screws at start of crystallite increment
dUpperDot ! rate of change of the maximum stable dipole distance for edges and screws
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
m ! direction of dislocation motion
real(pReal), dimension(3,3) :: F, & ! total deformation gradient
neighboring_F, & ! total deformation gradient of my neighbor
Favg ! average total deformation gradient of me and my neighbor
real(pReal), dimension(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
subTdislocation0_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress at start of crystallite increment
real(pReal), dimension(3) :: surfaceNormal ! surface normal of the current interface
real(pReal) norm_surfaceNormal, & ! euclidic norm of the surface normal
area, & ! area of the current interface
detFe, & ! determinant of elastic defornmation gradient
D ! self diffusion
logical flipAreaNormal
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
tauSlip = 0.0_pReal
subTauSlip0 = 0.0_pReal
v = 0.0_pReal
gdot = 0.0_pReal
dLower = 0.0_pReal
dUpper = 0.0_pReal
dUpper0 = 0.0_pReal
dUpperDot = 0.0_pReal
totalRhoDot = 0.0_pReal
thisRhoDot = 0.0_pReal
totalRhoDipDot = 0.0_pReal
thisRhoDipDot = 0.0_pReal
!*** shortcut to state variables
forall (t = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDip(:,c) = state(g,ip,el)%p((3+c)*ns+1:(4+c)*ns)
rhoForest = state(g,ip,el)%p(6*ns+1:7*ns)
tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns)
Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6)
subTdislocation0_v = subState0(g,ip,el)%p(8*ns+1:8*ns+6)
!****************************************************************************
!*** Calculate shear rate
do s = 1,ns ! loop over slip systems
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) )
subTauSlip0(s) = math_mul6x6( subTstar0_v + subTdislocation0_v, lattice_Sslip_v(:,sLattice,myStructure) )
enddo
v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) &
* exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) &
* sign(1.0_pReal,tauSlip)
forall (t = 1:4) &
gdot(:,t) = rho(:,t) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,*) '::: constitutive_nonlocal_dotState at ',g,ip,el
write(6,*)
write(6,'(a,/,12(f12.5,x),/)') 'tauSlip / MPa', tauSlip/1e6_pReal
write(6,'(a,/,12(f12.5,x),/)') 'tauSlipThreshold / MPa', tauSlipThreshold/1e6_pReal
write(6,'(a,/,12(e12.3,x),/)') 'v', v
write(6,'(a,/,4(12(f12.5,x),/))') 'gdot / 1e-3', gdot*1e3_pReal
write(6,'(a,/,(12(f12.5,x),/))') 'gdot total/ 1e-3', sum(gdot,2)*1e3_pReal
call flush(6)
!$OMP CRITICAL (write2out)
endif
!****************************************************************************
!*** calculate limits for stable dipole height and its rate of change
dLower(:,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(:,myInstance)
dLower(:,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(:,myInstance)
dUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
/ ( 8.0_pReal * pi * abs(tauSlip) ), &
1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) )
dUpper(:,1) = dUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
dUpper0(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
/ ( 8.0_pReal * pi * abs(subTauSlip0) ), &
1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) )
dUpper0(:,1) = dUpper0(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
if (subdt > 0) dUpperDot = (dUpper - dUpper0) / subdt
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,2(12(e12.5,x),/))') 'dUpper:',dUpper
write(6,'(a,/,2(12(e12.5,x),/))') 'dUpperDot:',dUpperDot
call flush(6)
!$OMP CRITICAL (write2out)
endif
!****************************************************************************
!*** calculate dislocation multiplication
invLambda = sqrt(rhoForest) / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance)
thisRhoDot = spread(0.25_pReal * sum(abs(gdot),2) * invLambda / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 4)
thisRhoDipDot = 0.0_pReal ! dipoles don't multiplicate
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'dislocation multiplication', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!****************************************************************************
!*** calculate dislocation fluxes
thisRhoDot = 0.0_pReal
thisRhoDipDot = 0.0_pReal
m(:,:,1) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,:,2) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,:,3) = lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,:,4) = -lattice_st(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
detFe = math_det3x3(Fe(:,:,g,ip,el))
do n = 1,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors
neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
flipAreaNormal = .false.
! if neighbor exists, total deformation gradient is averaged over me and my neighbor
if (periodicBC .and. (neighboring_el == 0 .or. neighboring_ip == 0) ) then
flipAreaNormal = .true.
select case (n)
case (1)
neighboring_el = mesh_ipNeighborhood(1,2,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,2,ip,el)
case (2)
neighboring_el = mesh_ipNeighborhood(1,1,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,1,ip,el)
case (3)
neighboring_el = mesh_ipNeighborhood(1,4,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,4,ip,el)
case (4)
neighboring_el = mesh_ipNeighborhood(1,3,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,3,ip,el)
case (5)
neighboring_el = mesh_ipNeighborhood(1,6,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,6,ip,el)
case (6)
neighboring_el = mesh_ipNeighborhood(1,5,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,5,ip,el)
endselect
endif
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then
neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
Favg = 0.5_pReal * (F + neighboring_F)
else
Favg = F
endif
! calculate the area and the surface normal (of unit length) of the interface in lattice configuration
if (flipAreaNormal) then
surfaceNormal = math_det3x3(Favg) / detFe &
* math_mul33x3(transpose(Fe(:,:,g,ip,el)), math_mul33x3(Favg,-mesh_ipAreaNormal(:,n,ip,el)))
else
surfaceNormal = math_det3x3(Favg) / detFe &
* math_mul33x3(transpose(Fe(:,:,g,ip,el)), math_mul33x3(Favg,mesh_ipAreaNormal(:,n,ip,el)))
endif
norm_surfaceNormal = math_norm3(surfaceNormal)
surfaceNormal = surfaceNormal / norm_surfaceNormal
area = mesh_ipArea(n,ip,el) * norm_surfaceNormal
lineLength = 0.0_pReal
do s = 1,ns ! loop over slip systems
do t = 1,4 ! loop over dislocation types
if ( sign(1.0_pReal,math_mul3x3(m(:,s,t),surfaceNormal)) == sign(1.0_pReal,gdot(s,t)) ) then
lineLength(s,t) = gdot(s,t) / constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
* math_mul3x3(m(:,s,t),surfaceNormal) * area ! dislocation line length that leaves this interface per second
thisRhoDot(s,t) = thisRhoDot(s,t) - lineLength(s,t) / mesh_ipVolume(ip,el) ! subtract dislocation density rate (= line length over volume) that leaves through an interface from my dotState ...
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then
!*****************************************************************************************************
!*** OMP locking for this neighbor missing
!*****************************************************************************************************
dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) = dotState(1,neighboring_ip,neighboring_el)%p((t-1)*ns+s) &
+ lineLength(s,t) / mesh_ipVolume(neighboring_ip,neighboring_el) ! ... and add it to the neighboring dotState (if neighbor exists)
endif
endif
enddo
enddo
enddo
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'dislocation flux', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!****************************************************************************
!*** calculate dipole formation and annihilation
!*** formation by glide
forall (c=1:2) &
thisRhoDipDot(:,c) = 4.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) )
forall (t=1:4) &
thisRhoDot(:,t) = -0.5_pReal * thisRhoDipDot(:,(t-1)/2+1)
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'dipole formation by glide', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!*** athermal annihilation
forall (c=1:2) &
thisRhoDipDot(:,c) = - 4.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) & ! was single hitting single
+ 0.5_pReal * rhoDip(:,c) * (abs(gdot(:,2*c-1))+abs(gdot(:,2*c))) ) ! single knocks dipole constituent
thisRhoDot = 0.0_pReal ! singles themselves don't annihilate
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'athermal dipole annihilation', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!*** thermally activated annihilation of dipoles
D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) &
* constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &
* 2.0_pReal / ( dUpper(:,1) + dLower(:,1) )
thisRhoDipDot(:,1) = - 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) ) ! edge climb
thisRhoDipDot(:,2) = 0.0_pReal !!! cross slipping still has to be implemented !!!
thisRhoDot = 0.0_pReal
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'thermally activated dipole annihilation', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!*** formation by stress change = alteration in dUpper
thisRhoDipDot = 0.0_pReal
forall (c=1:2, s=1:ns, dUpperDot(s,c) > 0) & ! stress decrease
thisRhoDipDot(s,c) = 8.0_pReal * rho(s,2*c-1) * rho(s,2*c) * dUpper(s,c) * dUpperDot(s,c)
forall (c=1:2, s=1:ns, dUpperDot(s,c) < 0) & ! increased stress
thisRhoDipDot(s,c) = rhoDip(s,c) * dUpperDot(s,c) / (dUpper(s,c) - dLower(s,c))
forall (t=1:4) &
thisRhoDot(:,t) = -0.5_pReal * thisRhoDipDot(:,(t-1)/2+1)
totalRhoDot = totalRhoDot + thisRhoDot
totalRhoDipDot = totalRhoDipDot + thisRhoDipDot
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,6(12(e12.5,x),/))') 'dipole stability by stress change', thisRhoDot * subdt, thisRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
!****************************************************************************
!*** assign the rates of dislocation densities to my dotState
dotState(1,ip,el)%p(1:4*ns) = reshape(totalRhoDot,(/4*ns/)) ! one-dimension only (linear list)
dotState(1,ip,el)%p(4*ns+1:6*ns) = reshape(totalRhoDipDot,(/2*ns/))
if (debugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,4(12(e12.5,x),/))') 'deltaRho:', totalRhoDot * subdt
write(6,'(a,/,2(12(e12.5,x),/))') 'deltaRhoDip:', totalRhoDipDot * subdt
call flush(6)
!$OMP CRITICAL (write2out)
endif
endsubroutine
!*********************************************************************
!* rate of change of temperature *
!*********************************************************************
pure function constitutive_nonlocal_dotTemperature(Tstar_v,Temperature,state,g,ip,el)
use prec, only: pReal, &
pInt, &
p_vec
use mesh, only: mesh_NcpElems, &
mesh_maxNips
use material, only: homogenization_maxNgrains
implicit none
!* input variables
integer(pInt), intent(in) :: g, & ! current grain ID
ip, & ! current integration point
el ! current element
real(pReal), intent(in) :: Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v ! 2nd Piola-Kirchhoff stress in Mandel notation
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state ! microstructural state
!* output variables
real(pReal) constitutive_nonlocal_dotTemperature ! evolution of Temperature
!* local variables
constitutive_nonlocal_dotTemperature = 0.0_pReal
endfunction
!*********************************************************************
!* return array of constitutive results *
!*********************************************************************
pure function constitutive_nonlocal_postResults(Tstar_v, subTstar0_v, Temperature, dt, subdt, state, subState0, dotState, g, ip, el)
use prec, only: pReal, &
pInt, &
p_vec
use math, only: math_mul6x6, &
pi
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_NslipSystem
implicit none
!*** input variables
integer(pInt), intent(in) :: g, & ! current grain number
ip, & ! current integration point
el ! current element number
real(pReal), intent(in) :: dt, & ! time increment
subdt, & ! time increment of crystallite substep
Temperature ! temperature
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! 2nd Piola-Kirchhoff stress in Mandel notation
subTstar0_v ! 2nd Piola-Kirchhoff stress in Mandel notation at start of crystallite inc
type(p_vec), dimension(homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems), intent(in) :: &
state, & ! microstructural state
subState0, & ! microstructural state at start of crystallite inc
dotState ! evolution rate of microstructural state
!*** output variables
real(pReal), dimension(constitutive_nonlocal_sizePostResults(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
constitutive_nonlocal_postResults
!*** local variables
integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure
ns, & ! short notation for the total number of active slip systems
o, & ! index of current output
s, & ! index of current slip system
sLattice, & ! index of my current slip system according to lattice order
cs, & ! constitutive result index
c, & ! character of dislocation
t ! type of dislocation
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
rho, & ! dislocation densities (positive/negative screw and edge without dipoles)
rhoDot, & ! evolution rate of dislocation densities (positive/negative screw and edge without dipoles)
gdot ! shear rates
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density
tauSlipThreshold, & ! threshold shear stress
tauSlip, & ! current resolved shear stress
subTauSlip0, & ! resolved shear stress at start of crystallite increment
v, & ! dislocation velocity
invLambda, & ! inverse of mean free path for dislocations
vClimb ! climb velocity of edge dipoles
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! dipole dislocation densities (screw and edge dipoles)
rhoDipDot, & ! evolution rate of dipole dislocation densities (screw and edge dipoles)
dLower, & ! minimum stable dipole distance for edges and screws
dUpper, & ! current maximum stable dipole distance for edges and screws
dUpper0, & ! maximum stable dipole distance for edges and screws at start of crystallite increment
dUpperDot ! rate of change of the maximum stable dipole distance for edges and screws
real(pReal), dimension(6) :: Tdislocation_v, & ! current dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress
subTdislocation0_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress at start of crystallite increment
real(pReal) D ! self diffusion
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance)
cs = 0_pInt
constitutive_nonlocal_postResults = 0.0_pReal
! short hand notations for state variables
forall (t = 1:4) rho(:,t) = state(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDip(:,c) = state(g,ip,el)%p((3+c)*ns+1:(4+c)*ns)
rhoForest = state(g,ip,el)%p(6*ns+1:7*ns)
tauSlipThreshold = state(g,ip,el)%p(7*ns+1:8*ns)
Tdislocation_v = state(g,ip,el)%p(8*ns+1:8*ns+6)
subTdislocation0_v = subState0(g,ip,el)%p(8*ns+1:8*ns+6)
forall (t = 1:4) rhoDot(:,t) = dotState(g,ip,el)%p((t-1)*ns+1:t*ns)
forall (c = 1:2) rhoDipDot(:,c) = dotState(g,ip,el)%p((3+c)*ns+1:(4+c)*ns)
! Calculate shear rate
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
tauSlip(s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) )
subTauSlip0(s) = math_mul6x6( subTstar0_v + subTdislocation0_v, lattice_Sslip_v(:,sLattice,myStructure) )
enddo
v = constitutive_nonlocal_v0PerSlipSystem(:,myInstance) &
* exp( - constitutive_nonlocal_Q0(myInstance) / ( kB * Temperature) * (1.0_pReal - (abs(tauSlip)/tauSlipThreshold) ) ) &
* sign(1.0_pReal,tauSlip)
forall (t = 1:4) &
gdot(:,t) = rho(:,t) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) * v
! calculate limits for stable dipole height and its rate of change
dLower(:,1) = constitutive_nonlocal_dLowerEdgePerSlipSystem(:,myInstance)
dLower(:,2) = constitutive_nonlocal_dLowerScrewPerSlipSystem(:,myInstance)
dUpper(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
/ ( 8.0_pReal * pi * abs(tauSlip) ), &
1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) )
dUpper(:,1) = dUpper(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
dUpper0(:,2) = min( constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
/ ( 8.0_pReal * pi * abs(subTauSlip0) ), &
1.0_pReal / sqrt( sum(rho,2)+sum(rhoDip,2) ) )
dUpper0(:,1) = dUpper0(:,2) / ( 1.0_pReal - constitutive_nonlocal_nu(myInstance) )
if (subdt > 0) then
dUpperDot = (dUpper - dUpper0) / subdt
else
dUpperDot = 0.0_pReal
endif
do o = 1,phase_Noutput(material_phase(g,ip,el))
select case(constitutive_nonlocal_output(o,myInstance))
case ('rho')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rho,2)
cs = cs + ns
case ('delta')
constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt( sum(rho,2) )
cs = cs + ns
case ('rho_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) + rho(:,2)
cs = cs + ns
case ('rho_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,3) + rho(:,4)
cs = cs + ns
case ('excess_rho')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) - rho(:,2) + rho(:,3) - rho(:,4)
cs = cs + ns
case ('excess_rho_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,1) - rho(:,2)
cs = cs + ns
case ('excess_rho_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rho(:,3) - rho(:,4)
cs = cs + ns
case ('rho_forest')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoForest
cs = cs + ns
case ('rho_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDip,2)
cs = cs + ns
case ('delta_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = 1.0_pReal / sqrt( sum(rhoDip,2) )
cs = cs + ns
case ('rho_edge_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(:,1)
cs = cs + ns
case ('rho_screw_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = rhoDip(:,2)
cs = cs + ns
case ('shearrate')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(abs(gdot),2)
cs = cs + ns
case ('resolvedstress')
do s = 1,ns
sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
constitutive_nonlocal_postResults(cs+s) = math_mul6x6( Tstar_v + Tdislocation_v, lattice_Sslip_v(:,sLattice,myStructure) )
enddo
cs = cs + ns
case ('resistance')
constitutive_nonlocal_postResults(cs+1:cs+ns) = tauSlipThreshold
cs = cs + ns
case ('rho_dot')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDot,2)
cs = cs + ns
case ('rho_dot_dip')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(rhoDipDot,2)
cs = cs + ns
case ('rho_dot_gen')
invLambda = sqrt(rhoForest) / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance)
constitutive_nonlocal_postResults(cs+1:cs+ns) = &
sum(abs(gdot),2) * invLambda / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance)
cs = cs + ns
case ('rho_dot_sgl2dip')
do c=1,2 ! dipole formation by glide
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + &
4.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) )
enddo
do c=1,2
forall (s=1:ns, dUpperDot(s,c) > 0) & ! dipole formation by stress decrease
constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) + &
8.0_pReal * rho(s,2*c-1) * rho(s,2*c) * dUpper(s,c) * dUpperDot(s,c)
enddo
cs = cs + ns
case ('rho_dot_dip2sgl')
do c=1,2
forall (s=1:ns, dUpperDot(s,c) < 0) &
constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) - &
rhoDip(s,c) * dUpperDot(s,c) / (dUpper(s,c) - dLower(s,c))
enddo
cs = cs + ns
case ('rho_dot_ann_ath')
do c=1,2
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_postResults(cs+1:cs+ns) + &
4.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* ( rho(:,2*c-1)*abs(gdot(:,2*c)) + rho(:,2*c)*abs(gdot(:,2*c-1)) &
+ 0.5_pReal * rhoDip(:,c) * (abs(gdot(:,2*c-1))+abs(gdot(:,2*c))) )
enddo
cs = cs + ns
case ('rho_dot_ann_the')
D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) &
* constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &
* 2.0_pReal / ( dUpper(:,1) + dLower(:,1) )
constitutive_nonlocal_postResults(cs+1:cs+ns) = 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) )
! !!! cross-slip of screws missing !!!
cs = cs + ns
case ('rho_dot_flux')
! !!! still has to be implemented !!!
constitutive_nonlocal_postResults(cs+1:cs+ns) = 0.0_pReal
cs = cs + ns
case ('d_upper_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(:,1)
cs = cs + ns
case ('d_upper_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpper(:,2)
cs = cs + ns
case ('d_upper_dot_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(:,1)
cs = cs + ns
case ('d_upper_dot_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = dUpperDot(:,2)
cs = cs + ns
end select
enddo
endfunction
END MODULE