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in nonlocal_microstructure: at the model surface the excess density is now extrapolated from opposite neighbor instead of assuming zero density; this results in better modeling of the dislocation stress at the surface 

restructured nonlocal_dotstate, to be able to easily switch on and off particular effects in the microstructure evolution
nonlocal_dotstate now enforces a cutback when single density runs the risk of becoming negative; in the case of a state already below the relevantState dotState is set to zero
introduced two new output variables: rho_dot_edge and rho_dot_screw
This commit is contained in:
Christoph Kords 2010-05-21 08:51:15 +00:00
parent dba4ae7ef1
commit 0c5bc83469
3 changed files with 238 additions and 189 deletions
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2
code/constitutive.f90
View File

@ -467,7 +467,7 @@ select case (phase_constitution(material_phase(ipc,ip,el)))
case (constitutive_nonlocal_label) case (constitutive_nonlocal_label)
call constitutive_nonlocal_dotState(constitutive_dotState, Tstar_v, subTstar0_v, Fe, Fp, Temperature, misorientation, subdt, & call constitutive_nonlocal_dotState(constitutive_dotState, Tstar_v, subTstar0_v, Fe, Fp, Temperature, misorientation, subdt, &
constitutive_state, constitutive_subState0, subdt, ipc, ip, el) constitutive_state, constitutive_subState0, constitutive_relevantState, subdt, ipc, ip, el)
end select end select

423
code/constitutive_nonlocal.f90
View File

@ -82,8 +82,7 @@ real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_
constitutive_nonlocal_rhoDotFlux ! dislocation convection term constitutive_nonlocal_rhoDotFlux ! dislocation convection term
real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_forestProjectionEdge, & ! matrix of forest projections of edge dislocations for each 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_forestProjectionScrew, & ! matrix of forest projections of screw dislocations for each instance
constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance constitutive_nonlocal_interactionMatrixSlipSlip ! interaction matrix of the different slip systems for each instance
CONTAINS CONTAINS
!**************************************** !****************************************
@ -354,10 +353,10 @@ enddo
enddo enddo
do f = 1,lattice_maxNslipFamily do f = 1,lattice_maxNslipFamily
if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then if (constitutive_nonlocal_Nslip(f,i) > 0_pInt) then
if (constitutive_nonlocal_rhoSglEdgePos0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoSglEdgePos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoSglEdgeNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoSglScrewPos0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoSglScrewNeg0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(220) if (constitutive_nonlocal_rhoDipScrew0(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_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221)
@ -495,6 +494,8 @@ do i = 1,maxNinstance
'rho_dot_ann_ath', & 'rho_dot_ann_ath', &
'rho_dot_ann_the', & 'rho_dot_ann_the', &
'rho_dot_flux', & 'rho_dot_flux', &
'rho_dot_flux_edge', &
'rho_dot_flux_screw', &
'dislocationvelocity', & 'dislocationvelocity', &
'fluxdensity_edge_pos_x', & 'fluxdensity_edge_pos_x', &
'fluxdensity_edge_pos_y', & 'fluxdensity_edge_pos_y', &
@ -748,6 +749,7 @@ use math, only: math_Plain3333to99, &
math_det3x3, & math_det3x3, &
pi pi
use debug, only: debugger, & use debug, only: debugger, &
verboseDebugger, &
selectiveDebugger selectiveDebugger
use mesh, only: mesh_NcpElems, & use mesh, only: mesh_NcpElems, &
mesh_maxNips, & mesh_maxNips, &
@ -796,6 +798,9 @@ integer(pInt) myInstance, & ! current instance
neighboring_ip, & ! integration point of my neighbor neighboring_ip, & ! integration point of my neighbor
c, & ! index of dilsocation character (edge, screw) c, & ! index of dilsocation character (edge, screw)
n, & ! index of my current neighbor n, & ! index of my current neighbor
opposite_n, & ! index of my opposite neighbor
opposite_ip, & ! ip of my opposite neighbor
opposite_el, & ! element index of my opposite neighbor
s, & ! index of my current slip system s, & ! index of my current slip system
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-) t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
sLattice ! index of my current slip system according to lattice order sLattice ! index of my current slip system according to lattice order
@ -805,7 +810,7 @@ real(pReal) gb, & ! short notation f
z, & ! coordinate in direction of nvec z, & ! coordinate in direction of nvec
detFe, & ! determinant of elastic deformation gradient detFe, & ! determinant of elastic deformation gradient
neighboring_detFe ! determinant of my neighboring 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(3,6) :: connectingVector ! vector connecting the centers of gravity of me and my neigbor (for each neighbor)
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(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 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 neighboringSlip2myLattice, &! mapping from my neighbors slip coordinate system to my lattice coordinate system
@ -868,44 +873,68 @@ forall (s = 1:ns) &
!*** calculate the dislocation stress of the neighboring excess dislocation densities !*** calculate the dislocation stress of the neighboring excess dislocation densities
Tdislocation_v = 0.0_pReal Tdislocation_v = 0.0_pReal
connectingVector = 0.0_pReal
F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el)) F = math_mul33x33(Fe(:,:,g,ip,el), Fp(:,:,g,ip,el))
detFe = math_det3x3(Fe) detFe = math_det3x3(Fe)
invFe = math_inv3x3(Fe) invFe = math_inv3x3(Fe)
! loop through my neighbors (if existent!)
do n = 1,FE_NipNeighbors(mesh_element(2,el)) 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)
if ( neighboring_el == 0 .or. neighboring_ip == 0 ) cycle neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
if ( neighboring_ip == 0 ) &
cycle
neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el)) neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
Favg = 0.5_pReal * (F + neighboring_F) Favg = 0.5_pReal * (F + neighboring_F)
neighboring_detFe = math_det3x3(Fe(:,:,g,neighboring_ip,neighboring_el)) neighboring_detFe = math_det3x3(Fe(:,:,g,neighboring_ip,neighboring_el))
neighboring_invFe = math_inv3x3(Fe(:,:,g,neighboring_ip,neighboring_el)) neighboring_invFe = math_inv3x3(Fe(:,:,g,neighboring_ip,neighboring_el))
connectingVector = math_mul33x3(neighboring_invFe, math_mul33x3(Favg, & connectingVector(:,n) = math_mul33x3(neighboring_invFe, math_mul33x3(Favg, &
(mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el)) ) ) ! calculate connection vector between me and my neighbor in its lattice configuration (mesh_ipCenterOfGravity(:,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(:,ip,el)) ) ) ! calculate connection vector between me and my neighbor in its lattice configuration
forall (t = 1:8) neighboring_rhoSgl(:,t) = state(1, neighboring_ip, neighboring_el)%p((t-1)*ns+1:t*ns) opposite_n = n - 1_pInt + 2_pInt*mod(n,2_pInt)
opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el)
opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el)
if ( opposite_ip == 0 ) & ! if no opposite neighbor present...
connectingVector(:,opposite_n) = -connectingVector(:,n) ! ... assume "ghost" IP at mirrored position of this neighbor
enddo
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)
if ( neighboring_ip == 0 ) then ! if no neighbor present...
opposite_n = n - 1_pInt + 2_pInt*mod(n,2_pInt)
opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el)
opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el)
neighboring_el = opposite_el
neighboring_ip = opposite_ip
forall (t = 1:8) neighboring_rhoSgl(:,t) = max(0.0_pReal, 2.0_pReal * state(g,ip,el)%p((t-1)*ns+1:t*ns) &
- state(g,opposite_ip,opposite_el)%p((t-1)*ns+1:t*ns) ) ! ... extrapolate density from opposite neighbor (but assure positive value for density)
else
forall (t = 1:8) neighboring_rhoSgl(:,t) = state(g,neighboring_ip,neighboring_el)%p((t-1)*ns+1:t*ns)
endif
neighboring_rhoEdgeExcess = sum(abs(neighboring_rhoSgl(:,(/1,5/))),2) - sum(abs(neighboring_rhoSgl(:,(/2,6/))),2) neighboring_rhoEdgeExcess = sum(abs(neighboring_rhoSgl(:,(/1,5/))),2) - sum(abs(neighboring_rhoSgl(:,(/2,6/))),2)
neighboring_rhoScrewExcess = sum(abs(neighboring_rhoSgl(:,(/3,7/))),2) - sum(abs(neighboring_rhoSgl(:,(/4,8/))),2) neighboring_rhoScrewExcess = sum(abs(neighboring_rhoSgl(:,(/3,7/))),2) - sum(abs(neighboring_rhoSgl(:,(/4,8/))),2)
neighboring_Nedge = neighboring_rhoEdgeExcess * mesh_ipVolume(neighboring_ip, neighboring_el) ** (2.0_pReal/3.0_pReal) 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) neighboring_Nscrew = neighboring_rhoScrewExcess * mesh_ipVolume(neighboring_ip,neighboring_el) ** (2.0_pReal/3.0_pReal)
do s = 1,ns do s = 1,ns
lattice2slip = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice2slip = reshape( (/lattice_st(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice_sd(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) ) lattice_sn(:, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/) )
x = math_mul3x3(lattice2slip(1,:), -connectingVector) ! coordinate transformation of connecting vector from the lattice coordinate system to the slip coordinate system x = math_mul3x3(lattice2slip(1,:), -connectingVector(:,n)) ! coordinate transformation of connecting vector from the lattice coordinate system to the slip coordinate system
y = math_mul3x3(lattice2slip(2,:), -connectingVector) y = math_mul3x3(lattice2slip(2,:), -connectingVector(:,n))
z = math_mul3x3(lattice2slip(3,:), -connectingVector) z = math_mul3x3(lattice2slip(3,:), -connectingVector(:,n))
gb = constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) / (2.0_pReal*pi) 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)) & sigma(2,2) = - gb * neighboring_Nedge(s) / (1.0_pReal-constitutive_nonlocal_nu(myInstance)) &
@ -928,7 +957,7 @@ do n = 1,FE_NipNeighbors(mesh_element(2,el))
sigma(3,1) = 0.0_pReal sigma(3,1) = 0.0_pReal
neighboringSlip2myLattice = math_mul33x33(invFe,math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el),transpose(lattice2slip))) ! 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))) ! coordinate transformation from the slip coordinate system to the lattice coordinate system
Tdislocation_v = Tdislocation_v + math_Mandel33to6( detFe / neighboring_detFe & Tdislocation_v = Tdislocation_v + math_Mandel33to6( detFe / math_det3x3(Fe(:,:,g,neighboring_ip,neighboring_el)) &
* math_mul33x33(neighboringSlip2myLattice, math_mul33x33(sigma, transpose(neighboringSlip2myLattice))) ) * math_mul33x33(neighboringSlip2myLattice, math_mul33x33(sigma, transpose(neighboringSlip2myLattice))) )
enddo enddo
enddo enddo
@ -1023,8 +1052,8 @@ if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out) !$OMP CRITICAL (write2out)
write(6,*) '::: kinetics',g,ip,el write(6,*) '::: kinetics',g,ip,el
write(6,*) 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)/))') '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,/,3(3(f12.3,x)/))') 'Tstar / MPa', math_Mandel6to33(Tstar_v/1e6)
write(6,'(a,/,12(f12.5,x),/)') 'tau / MPa', tau/1e6_pReal write(6,'(a,/,12(f12.5,x),/)') 'tau / MPa', tau/1e6_pReal
write(6,'(a,/,12(f12.5,x),/)') 'tauThreshold / MPa', tauThreshold/1e6_pReal write(6,'(a,/,12(f12.5,x),/)') 'tauThreshold / MPa', tauThreshold/1e6_pReal
write(6,'(a,/,4(12(f12.5,x),/))') 'v / 1e-3m/s', constitutive_nonlocal_v(:,:,g,ip,el)*1e3 write(6,'(a,/,4(12(f12.5,x),/))') 'v / 1e-3m/s', constitutive_nonlocal_v(:,:,g,ip,el)*1e3
@ -1137,17 +1166,17 @@ enddo
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333) dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
if (verboseDebugger .and. selectiveDebugger) then !if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out) ! !$OMP CRITICAL (write2out)
write(6,*) '::: LpandItsTangent',g,ip,el ! write(6,*) '::: LpandItsTangent',g,ip,el
write(6,*) ! write(6,*)
! write(6,'(a,/,12(f12.5,x),/)') 'v', constitutive_nonlocal_v(:,t,g,ip,el) ! ! write(6,'(a,/,12(f12.5,x),/)') 'v', constitutive_nonlocal_v(:,t,g,ip,el)
write(6,'(a,/,12(f12.5,x),/)') 'gdot /1e-3',gdot*1e3_pReal ! write(6,'(a,/,12(f12.5,x),/)') 'gdot /1e-3',gdot*1e3_pReal
write(6,'(a,/,12(f12.5,x),/)') 'gdot total /1e-3',gdotTotal*1e3_pReal ! write(6,'(a,/,12(f12.5,x),/)') 'gdot total /1e-3',gdotTotal*1e3_pReal
write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp ! write(6,'(a,/,3(3(f12.7,x)/))') 'Lp',Lp
! call flush(6) ! ! call flush(6)
!$OMPEND CRITICAL (write2out) ! !$OMPEND CRITICAL (write2out)
endif !endif
endsubroutine endsubroutine
@ -1156,8 +1185,8 @@ endsubroutine
!********************************************************************* !*********************************************************************
!* rate of change of microstructure * !* rate of change of microstructure *
!********************************************************************* !*********************************************************************
subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, previousTstar_v, Fe, Fp, Temperature, misorientation, dt_previous, & subroutine constitutive_nonlocal_dotState(dotState, Tstar_v, previousTstar_v, Fe, Fp, Temperature, disorientation, dt_previous, &
state, previousState, timestep, g,ip,el) state, previousState, relevantState, timestep, g,ip,el)
use prec, only: pReal, & use prec, only: pReal, &
pInt, & pInt, &
@ -1174,7 +1203,8 @@ use math, only: math_norm3, &
math_inv3x3, & math_inv3x3, &
math_det3x3, & math_det3x3, &
math_Mandel6to33, & math_Mandel6to33, &
pi pi, &
NaN
use mesh, only: mesh_NcpElems, & use mesh, only: mesh_NcpElems, &
mesh_maxNips, & mesh_maxNips, &
mesh_maxNipNeighbors, & mesh_maxNipNeighbors, &
@ -1208,13 +1238,14 @@ real(pReal), intent(in) :: Temperature, & ! temperat
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation
previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: & real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: &
misorientation ! crystal misorientation between me and my neighbor (axis, angle pair) disorientation ! crystal disorientation between me and my neighbor (axis, angle pair)
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient Fp ! plastic deformation gradient
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
state, & ! current microstructural state state, & ! current microstructural state
previousState ! previous microstructural state previousState, & ! previous microstructural state
relevantState ! relevant microstructural state
!*** input/output variables !*** input/output variables
type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: & type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
@ -1235,12 +1266,21 @@ integer(pInt) myInstance, & ! current
opposite_el, & ! element index of my opposite neighbor opposite_el, & ! element index of my opposite neighbor
t, & ! type of dislocation t, & ! type of dislocation
s, & ! index of my current slip system s, & ! index of my current slip system
sLattice ! index of my current slip system according to lattice order sLattice, & ! index of my current slip system according to lattice order
i
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),10) :: &
rhoDot, & ! density evolution
rhoDotRemobilization, & ! density evolution by remobilization
rhoDotMultiplication, & ! density evolution by multiplication
rhoDotFlux, & ! density evolution by flux
rhoDotSingle2DipoleGlide, & ! density evolution by dipole formation (by glide)
rhoDotAthermalAnnihilation, & ! density evolution by athermal annihilation
rhoDotThermalAnnihilation, & ! density evolution by thermal annihilation
rhoDotDipole2SingleStressChange, & ! density evolution by dipole dissociation (by stress increase)
rhoDotSingle2DipoleStressChange ! density evolution by dipole formation (by stress decrease)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: &
rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles) rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
previousRhoSgl, & ! previous single dislocation densities (positive/negative screw and edge without dipoles) previousRhoSgl ! previous single dislocation densities (positive/negative screw and edge without dipoles)
totalRhoDotSgl, & ! total rate of change of single dislocation densities
thisRhoDotSgl ! rate of change of single dislocation densities for this mechanism
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),4) :: &
fluxdensity, & ! flux density at central material point fluxdensity, & ! flux density at central material point
neighboring_fluxdensity, &! flux density at neighbroing material point neighboring_fluxdensity, &! flux density at neighbroing material point
@ -1255,8 +1295,6 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstan
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles) rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
previousRhoDip, & ! previous dipole dislocation densities (screw and edge dipoles) previousRhoDip, & ! previous dipole dislocation densities (screw and edge dipoles)
totalRhoDotDip, & ! total rate of change of dipole dislocation densities
thisRhoDotDip, & ! rate of change of dipole dislocation densities for this mechanism
dLower, & ! minimum stable dipole distance for edges and screws dLower, & ! minimum stable dipole distance for edges and screws
dUpper, & ! current maximum stable dipole distance for edges and screws dUpper, & ! current maximum stable dipole distance for edges and screws
previousDUpper, & ! previous maximum stable dipole distance for edges and screws previousDUpper, & ! previous maximum stable dipole distance for edges and screws
@ -1304,10 +1342,6 @@ dLower = 0.0_pReal
dUpper = 0.0_pReal dUpper = 0.0_pReal
previousDUpper = 0.0_pReal previousDUpper = 0.0_pReal
dUpperDot = 0.0_pReal dUpperDot = 0.0_pReal
totalRhoDotSgl = 0.0_pReal
thisRhoDotSgl = 0.0_pReal
totalRhoDotDip = 0.0_pReal
thisRhoDotDip = 0.0_pReal
!*** shortcut to state variables !*** shortcut to state variables
@ -1328,7 +1362,13 @@ if (timestep <= 0.0_pReal) then
endif endif
if (any(constitutive_nonlocal_v(:,:,g,ip,el)*timestep > mesh_ipVolume(ip,el)**(1.0_pReal/3.0_pReal))) then ! if timestep is too large,... if (any(constitutive_nonlocal_v(:,:,g,ip,el)*timestep > mesh_ipVolume(ip,el)**(1.0_pReal/3.0_pReal))) then ! if timestep is too large,...
dotState(1,ip,el)%p(1:10*ns) = sqrt(-1.0_pReal) ! ...create NaN and enforce a cutback dotState(1,ip,el)%p(1:10*ns) = NaN ! ...assign NaN and enforce a cutback
if (verboseDebugger) then
!$OMP CRITICAL (write2out)
write(6,*) 'exceeded maximum allowed dislocation velocity at ',g,ip,el
write(6,*)
!$OMPEND CRITICAL (write2out)
endif
return return
endif endif
@ -1370,54 +1410,37 @@ if (dt_previous > 0.0_pReal) dUpperDot = (dUpper - previousDUpper) / dt_previous
!**************************************************************************** !****************************************************************************
!*** dislocation remobilization (bauschinger effect) !*** dislocation remobilization (bauschinger effect)
thisRhoDotSgl = 0.0_pReal rhoDotRemobilization = 0.0_pReal
if (timestep > 0.0_pReal) then if (timestep > 0.0_pReal) then
do t = 1,4 do t = 1,4
do s = 1,ns do s = 1,ns
if (rhoSgl(s,t+4) * constitutive_nonlocal_v(s,t,g,ip,el) < 0.0_pReal) then if (rhoSgl(s,t+4) * constitutive_nonlocal_v(s,t,g,ip,el) < 0.0_pReal) then
thisRhoDotSgl(s,t) = abs(rhoSgl(s,t+4)) / timestep rhoDotRemobilization(s,t) = abs(rhoSgl(s,t+4)) / timestep
rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4)) rhoSgl(s,t) = rhoSgl(s,t) + abs(rhoSgl(s,t+4))
thisRhoDotSgl(s,t+4) = - rhoSgl(s,t+4) / timestep rhoDotRemobilization(s,t+4) = - rhoSgl(s,t+4) / timestep
rhoSgl(s,t+4) = 0.0_pReal rhoSgl(s,t+4) = 0.0_pReal
endif endif
enddo enddo
enddo enddo
endif endif
totalRhoDotSgl = totalRhoDotSgl + thisRhoDotSgl
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation remobilization', thisRhoDotSgl * timestep
!$OMPEND CRITICAL (write2out)
endif
!**************************************************************************** !****************************************************************************
!*** calculate dislocation multiplication !*** calculate dislocation multiplication
thisRhoDotSgl(:,1:2) = spread(0.5_pReal * sum(abs(gdot(:,3:4)),2) * sqrt(rhoForest) & rhoDotMultiplication(:,1:2) = spread(0.5_pReal * sum(abs(gdot(:,3:4)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) & / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2)
thisRhoDotSgl(:,3:4) = spread(0.5_pReal * sum(abs(gdot(:,1:2)),2) * sqrt(rhoForest) & rhoDotMultiplication(:,3:4) = spread(0.5_pReal * sum(abs(gdot(:,1:2)),2) * sqrt(rhoForest) &
/ constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) & / constitutive_nonlocal_lambda0PerSlipSystem(:,myInstance) &
/ constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance), 2, 2)
thisRhoDotSgl(:,5:8) = 0.0_pReal ! used dislocation densities don't multiplicate rhoDotMultiplication(:,5:10) = 0.0_pReal ! used dislocation densities and dipoles don't multiplicate
thisRhoDotDip = 0.0_pReal ! dipoles don't multiplicate
totalRhoDotSgl = totalRhoDotSgl + thisRhoDotSgl
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', thisRhoDotSgl(:,1:4) * timestep
!$OMPEND CRITICAL (write2out)
endif
!**************************************************************************** !****************************************************************************
!*** calculate dislocation fluxes !*** calculate dislocation fluxes
thisRhoDotSgl = 0.0_pReal rhoDotFlux = 0.0_pReal
m(:,:,1) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,1) = lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
m(:,:,2) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure) m(:,:,2) = -lattice_sd(:, constitutive_nonlocal_slipSystemLattice(:,myInstance), myStructure)
@ -1429,15 +1452,16 @@ detFe = math_det3x3(Fe(:,:,g,ip,el))
fluxdensity = rhoSgl(:,1:4) * constitutive_nonlocal_v(:,:,g,ip,el) fluxdensity = rhoSgl(:,1:4) * constitutive_nonlocal_v(:,:,g,ip,el)
do n = 1,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors do n = 1,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors
opposite_n = n - 1_pInt + 2_pInt*mod(n,2_pInt) opposite_n = n - 1_pInt + 2_pInt*mod(n,2_pInt)
neighboring_el = mesh_ipNeighborhood(1,n,ip,el) neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
neighboring_ip = mesh_ipNeighborhood(2,n,ip,el) neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el) opposite_el = mesh_ipNeighborhood(1,opposite_n,ip,el)
opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el) opposite_ip = mesh_ipNeighborhood(2,opposite_n,ip,el)
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then ! if neighbor exists, average deformation gradient if ( neighboring_el > 0_pInt .and. neighboring_ip > 0_pInt ) then ! if neighbor exists, average deformation gradient
neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el)) neighboring_F = math_mul33x33(Fe(:,:,g,neighboring_ip,neighboring_el), Fp(:,:,g,neighboring_ip,neighboring_el))
Favg = 0.5_pReal * (F + neighboring_F) Favg = 0.5_pReal * (F + neighboring_F)
else ! if no neighbor, take my value as average else ! if no neighbor, take my value as average
@ -1449,7 +1473,7 @@ do n = 1,FE_NipNeighbors(mesh_element(2,el))
area = mesh_ipArea(n,ip,el) * math_norm3(surfaceNormal) area = mesh_ipArea(n,ip,el) * math_norm3(surfaceNormal)
surfaceNormal = surfaceNormal / math_norm3(surfaceNormal) ! normalize the surface normal to unit length surfaceNormal = surfaceNormal / math_norm3(surfaceNormal) ! normalize the surface normal to unit length
transmissivity = constitutive_nonlocal_transmissivity(misorientation(:,n)) transmissivity = constitutive_nonlocal_transmissivity(disorientation(:,n))
highOrderScheme = .false. highOrderScheme = .false.
if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then ! if neighbor exists... if ( neighboring_el > 0 .and. neighboring_ip > 0 ) then ! if neighbor exists...
@ -1483,10 +1507,13 @@ do n = 1,FE_NipNeighbors(mesh_element(2,el))
endif endif
lineLength = average_fluxdensity * math_mul3x3(m(:,s,t), surfaceNormal) * area ! line length that wants to leave this interface lineLength = average_fluxdensity * math_mul3x3(m(:,s,t), surfaceNormal) * area ! line length that wants to leave this interface
thisRhoDotSgl(s,t) = thisRhoDotSgl(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract positive dislocation flux that leaves the material point rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract positive dislocation flux that leaves the material point
thisRhoDotSgl(s,t+4) = thisRhoDotSgl(s,t+4) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) & rhoDotFlux(s,t+4) = rhoDotFlux(s,t+4) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) &
* sign(1.0_pReal, average_fluxdensity) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point * sign(1.0_pReal, average_fluxdensity) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
! if (selectiveDebugger .and. s==1) &
! write(6,'(a22,i2,a15,i2,a3,4(e20.10,x))') 'outgoing flux of type ',t,' to neighbor ',n,' : ', &
! -lineLength / mesh_ipVolume(ip,el), average_fluxdensity, maximum_fluxdensity, &
! average_fluxdensity / maximum_fluxdensity
else ! incoming flux else ! incoming flux
if ( highOrderScheme ) then if ( highOrderScheme ) then
average_fluxdensity = fluxdensity(s,t) + weight * (neighboring_fluxdensity(s,t) - fluxdensity(s,t)) average_fluxdensity = fluxdensity(s,t) + weight * (neighboring_fluxdensity(s,t) - fluxdensity(s,t))
@ -1498,23 +1525,19 @@ do n = 1,FE_NipNeighbors(mesh_element(2,el))
endif endif
lineLength = average_fluxdensity * math_mul3x3(m(:,s,t), surfaceNormal) * area ! line length that wants to leave this interface lineLength = average_fluxdensity * math_mul3x3(m(:,s,t), surfaceNormal) * area ! line length that wants to leave this interface
thisRhoDotSgl(s,t) = thisRhoDotSgl(s,t) - lineLength / mesh_ipVolume(ip,el) * transmissivity ! subtract negative dislocation flux that enters the material point rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) * transmissivity ! subtract negative dislocation flux that enters the material point
! if (selectiveDebugger .and. s==1) &
! write(6,'(a22,i2,a15,i2,a3,4(e20.10,x))') 'incoming flux of type ',t,' from neighbor ',n,' : ', &
! -lineLength / mesh_ipVolume(ip,el) * transmissivity, average_fluxdensity, maximum_fluxdensity, &
! average_fluxdensity / maximum_fluxdensity
endif endif
enddo enddo
enddo enddo
enddo enddo
constitutive_nonlocal_rhoDotFlux(:,:,g,ip,el) = thisRhoDotSgl constitutive_nonlocal_rhoDotFlux(:,:,g,ip,el) = rhoDotFlux
totalRhoDotSgl = totalRhoDotSgl + thisRhoDotSgl
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation flux', thisRhoDotSgl * timestep
!$OMPEND CRITICAL (write2out)
endif
!**************************************************************************** !****************************************************************************
@ -1522,109 +1545,128 @@ endif
!*** formation by glide !*** formation by glide
thisRhoDotSgl = 0.0_pReal
thisRhoDotDip = 0.0_pReal
do c = 1,2 do c = 1,2
thisRhoDotSgl(:,2*c-1) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & rhoDotSingle2DipoleGlide(:,2*c-1) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! negative mobile <-> positive mobile * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! negative mobile <-> positive mobile
+ abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1))) ! negative immobile <-> positive mobile + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1)))! negative immobile <-> positive mobile
thisRhoDotSgl(:,2*c) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & rhoDotSingle2DipoleGlide(:,2*c) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! negative mobile <-> positive mobile * (rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) & ! negative mobile <-> positive mobile
+ abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile <-> positive immobile + abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c))) ! negative mobile <-> positive immobile
thisRhoDotSgl(:,2*c+3) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & ! negative mobile <-> positive immobile rhoDotSingle2DipoleGlide(:,2*c+3) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & ! negative mobile <-> positive immobile
* rhoSgl(:,2*c+3) * abs(gdot(:,2*c)) * rhoSgl(:,2*c+3) * abs(gdot(:,2*c))
thisRhoDotSgl(:,2*c+4) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & rhoDotSingle2DipoleGlide(:,2*c+4) = - 2.0_pReal * dUpper(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! negative immobile <-> positive mobile * rhoSgl(:,2*c+4) * abs(gdot(:,2*c-1)) ! negative immobile <-> positive mobile
thisRhoDotDip(:,c) = - thisRhoDotSgl(:,2*c-1) - thisRhoDotSgl(:,2*c) + abs(thisRhoDotSgl(:,2*c+3)) + abs(thisRhoDotSgl(:,2*c+4)) rhoDotSingle2DipoleGlide(:,c+8) = - rhoDotSingle2DipoleGlide(:,2*c-1) - rhoDotSingle2DipoleGlide(:,2*c) &
+ abs(rhoDotSingle2DipoleGlide(:,2*c+3)) + abs(rhoDotSingle2DipoleGlide(:,2*c+4))
enddo enddo
totalRhoDotSgl = totalRhoDotSgl + thisRhoDotSgl
totalRhoDotDip = totalRhoDotDip + thisRhoDotDip
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by glide', thisRhoDotSgl * timestep, thisRhoDotDip * timestep
!$OMPEND CRITICAL (write2out)
endif
!*** athermal annihilation !*** athermal annihilation
rhoDotAthermalAnnihilation = 0.0_pReal
forall (c=1:2) & forall (c=1:2) &
thisRhoDotDip(:,c) = - 2.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) & rhoDotAthermalAnnihilation(:,c+8) = - 2.0_pReal * dLower(:,c) / constitutive_nonlocal_burgersPerSlipSystem(:,myInstance) &
* ( 2.0_pReal * ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) ) & ! was single hitting single * ( 2.0_pReal * ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) ) & ! was single hitting single
+ 2.0_pReal * ( abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1)) ) & ! was single hitting immobile single or was immobile single hit by single + 2.0_pReal * ( abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1)) ) & ! was single hitting immobile single or was immobile single hit by single
+ rhoDip(:,c) * ( abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)) ) ) ! single knocks dipole constituent + rhoDip(:,c) * ( abs(gdot(:,2*c-1)) + abs(gdot(:,2*c)) ) ) ! single knocks dipole constituent
totalRhoDotDip = totalRhoDotDip + thisRhoDotDip
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', thisRhoDotDip * timestep
!$OMPEND CRITICAL (write2out)
endif
!*** thermally activated annihilation of dipoles !*** thermally activated annihilation of dipoles
rhoDotThermalAnnihilation = 0.0_pReal
D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature)) D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( 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)) ) & * constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &
* 2.0_pReal / ( dUpper(:,1) + dLower(:,1) ) * 2.0_pReal / ( dUpper(:,1) + dLower(:,1) )
thisRhoDotDip(:,1) = - 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) ) ! edge climb rhoDotThermalAnnihilation(:,9) = - 4.0_pReal * rhoDip(:,1) * vClimb / ( dUpper(:,1) - dLower(:,1) ) ! edge climb
thisRhoDotDip(:,2) = 0.0_pReal !!! cross slipping still has to be implemented !!! rhoDotThermalAnnihilation(:,10) = 0.0_pReal !!! cross slipping still has to be implemented !!!
totalRhoDotDip = totalRhoDotDip + thisRhoDotDip
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out)
write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', thisRhoDotDip * timestep
!$OMPEND CRITICAL (write2out)
endif
!*** formation/dissociation by stress change = alteration in dUpper !*** formation/dissociation by stress change = alteration in dUpper
thisRhoDotSgl = 0.0_pReal rhoDotDipole2SingleStressChange = 0.0_pReal
thisRhoDotDip = 0.0_pReal forall (c=1:2, s=1:ns, dUpperDot(s,c) < 0.0_pReal) & ! increased stress => dipole dissociation
rhoDotDipole2SingleStressChange(s,8+c) = rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c))
! forall (c=1:2, s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! stress decrease => dipole formation
! thisRhoDotDip(s,c) = 8.0_pReal * rhoSgl(s,2*c-1) * rhoSgl(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c)
forall (c=1:2, s=1:ns, dUpperDot(s,c) < 0.0_pReal) & ! increased stress => dipole dissociation
thisRhoDotDip(s,c) = rhoDip(s,c) * dUpperDot(s,c) / (previousDUpper(s,c) - dLower(s,c))
forall (t=1:4) & forall (t=1:4) &
thisRhoDotSgl(:,t) = -0.5_pReal * thisRhoDotDip(:,(t-1)/2+1) rhoDotDipole2SingleStressChange(:,t) = -0.5_pReal * rhoDotDipole2SingleStressChange(:,(t-1)/2+9)
totalRhoDotSgl = totalRhoDotSgl + thisRhoDotSgl
totalRhoDotDip = totalRhoDotDip + thisRhoDotDip
if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out) rhoDotSingle2DipoleStressChange = 0.0_pReal
write(6,'(a,/,10(12(e12.5,x),/))') 'dipole stability by stress change', thisRhoDotSgl * timestep, thisRhoDotDip * timestep do c = 1,2
!$OMPEND CRITICAL (write2out) do s = 1,ns
endif if (dUpperDot(s,c) > 0.0_pReal) then ! stress decrease => dipole formation
rhoDotSingle2DipoleStressChange(s,2*(c-1)+1) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+1) &
* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+2) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+2) &
* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+5) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+5) &
* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
rhoDotSingle2DipoleStressChange(s,2*(c-1)+6) = -4.0_pReal * dUpperDot(s,c) * previousDUpper(s,c) * rhoSgl(s,2*(c-1)+6) &
* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
endif
enddo
enddo
forall (c = 1:2) &
rhoDotSingle2DipoleStressChange(:,8+c) = abs(rhoDotSingle2DipoleStressChange(:,2*(c-1)+1)) &
+ abs(rhoDotSingle2DipoleStressChange(:,2*(c-1)+2)) &
+ abs(rhoDotSingle2DipoleStressChange(:,2*(c-1)+5)) &
+ abs(rhoDotSingle2DipoleStressChange(:,2*(c-1)+6))
!**************************************************************************** !****************************************************************************
!*** assign the rates of dislocation densities to my dotState !*** assign the rates of dislocation densities to my dotState
dotState(1,ip,el)%p(1:8*ns) = dotState(1,ip,el)%p(1:8*ns) + reshape(totalRhoDotSgl,(/8*ns/)) rhoDot = 0.0_pReal
dotState(1,ip,el)%p(8*ns+1:10*ns) = dotState(1,ip,el)%p(8*ns+1:10*ns) + reshape(totalRhoDotDip,(/2*ns/)) forall (t = 1:10) &
rhoDot(:,t) = rhoDotFlux(:,t) &
+ rhoDotSingle2DipoleGlide(:,t) &
+ rhoDotAthermalAnnihilation(:,t) &
+ rhoDotRemobilization(:,t) &
+ rhoDotMultiplication(:,t) &
+ rhoDotThermalAnnihilation(:,t)
! + rhoDotDipole2SingleStressChange(:,t) &
! + rhoDotSingle2DipoleStressChange(:,t)
dotState(g,ip,el)%p(1:10*ns) = dotState(g,ip,el)%p(1:10*ns) + reshape(rhoDot,(/10*ns/))
do i = 1,4*ns
if (previousState(g,ip,el)%p(i) + dotState(g,ip,el)%p(i)*timestep < 0.0_pReal) then ! if single mobile densities become negative...
if (previousState(g,ip,el)%p(i) < relevantState(g,ip,el)%p(i)) then ! ... and density is already below relevance...
dotState(g,ip,el)%p(i) = 0.0_pReal ! ... set dotState to zero
else ! ... otherwise...
if (verboseDebugger) then
!$OMP CRITICAL (write2out)
write(6,*) 'negative dislocation density at ',g,ip,el
write(6,*)
!$OMPEND CRITICAL (write2out)
endif
dotState(g,ip,el)%p(i) = NaN ! ... assign NaN and enforce a cutback
endif
endif
enddo
if (verboseDebugger .and. selectiveDebugger) then if (verboseDebugger .and. selectiveDebugger) then
!$OMP CRITICAL (write2out) !$OMP CRITICAL (write2out)
write(6,'(a,/,8(12(e12.5,x),/))') 'deltaRho:', totalRhoDotSgl * timestep write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation remobilization', rhoDotRemobilization(:,1:8) * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'deltaRhoDip:', totalRhoDotDip * timestep write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', rhoDotMultiplication(:,1:4) * timestep
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation flux', rhoDotFlux(:,1:8) * timestep
write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', rhoDotAthermalAnnihilation(:,1:2) * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', rhoDotThermalAnnihilation(:,9:10) * timestep
! write(6,'(a,/,10(12(e12.5,x),/))') 'dipole dissociation by stress increase', rhoDotDipole2SingleStressChange * timestep
! write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by stress decrease', rhoDotSingle2DipoleStressChange * timestep
write(6,'(a,/,10(12(e12.5,x),/))') 'total density change', rhoDot * timestep
!$OMPEND CRITICAL (write2out) !$OMPEND CRITICAL (write2out)
endif endif
@ -1635,40 +1677,35 @@ endsubroutine
!********************************************************************* !*********************************************************************
!* transmissivity of IP interface * !* transmissivity of IP interface *
!********************************************************************* !*********************************************************************
function constitutive_nonlocal_transmissivity(misorientation) function constitutive_nonlocal_transmissivity(disorientation)
use prec, only: pReal, & use prec, only: pReal, &
pInt pInt
use math, only: inDeg, & use math, only: math_QuaternionToAxisAngle
math_norm3
implicit none implicit none
!* input variables !* input variables
real(pReal), dimension(4), intent(in) :: misorientation ! misorientation as quaternion real(pReal), dimension(4), intent(in) :: disorientation ! disorientation as quaternion
!* output variables !* output variables
real(pReal) constitutive_nonlocal_transmissivity ! transmissivity of an IP interface for dislocations real(pReal) constitutive_nonlocal_transmissivity ! transmissivity of an IP interface for dislocations
!* local variables !* local variables
real(pReal) misorientationAngle, & real(pReal) disorientationAngle
axisNorm real(pReal), dimension(3) :: disorientationAxis
real(pReal), dimension(3) :: misorientationAxis real(pReal), dimension(4) :: disorientationAxisAngle
misorientationAngle = 2.0_pReal * dacos(min(1.0_pReal, max(-1.0_pReal, misorientation(1)))) * inDeg disorientationAxisAngle = math_QuaternionToAxisAngle(disorientation)
misorientationAxis = misorientation(2:4) disorientationAxis = disorientationAxisAngle(1:3)
axisNorm = math_norm3(misorientationAxis) disorientationAngle = disorientationAxisAngle(4)
if (axisNorm > tiny(axisNorm)) &
misorientationAxis = misorientationAxis / axisNorm if (disorientationAngle < 3.0_pReal) then
if (misorientationAngle < 3.0_pReal) then
constitutive_nonlocal_transmissivity = 1.0_pReal constitutive_nonlocal_transmissivity = 1.0_pReal
elseif (misorientationAngle < 10.0_pReal) then
constitutive_nonlocal_transmissivity = 0.5_pReal
else else
constitutive_nonlocal_transmissivity = 0.01_pReal constitutive_nonlocal_transmissivity = 0.5_pReal
endif endif
endfunction endfunction
@ -1711,7 +1748,7 @@ endfunction
!********************************************************************* !*********************************************************************
!* return array of constitutive results * !* return array of constitutive results *
!********************************************************************* !*********************************************************************
function constitutive_nonlocal_postResults(Tstar_v, previousTstar_v, Fe, Fp, Temperature, misorientation, dt, dt_previous, & function constitutive_nonlocal_postResults(Tstar_v, previousTstar_v, Fe, Fp, Temperature, disorientation, dt, dt_previous, &
state, previousState, dotState, g,ip,el) state, previousState, dotState, g,ip,el)
use prec, only: pReal, & use prec, only: pReal, &
@ -1758,7 +1795,7 @@ real(pReal), intent(in) :: Temperature, & ! temperat
real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(6), intent(in) :: Tstar_v, & ! current 2nd Piola-Kirchhoff stress in Mandel notation
previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation previousTstar_v ! previous 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: & real(pReal), dimension(4,mesh_maxNipNeighbors), intent(in) :: &
misorientation ! crystal misorientation between me and my neighbor (axis, angle pair) disorientation ! crystal disorientation between me and my neighbor (axis, angle pair)
real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: & real(pReal), dimension(3,3,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
Fe, & ! elastic deformation gradient Fe, & ! elastic deformation gradient
Fp ! plastic deformation gradient Fp ! plastic deformation gradient
@ -2009,11 +2046,11 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
+ (rhoSgl(:,3) + abs(rhoSgl(:,7))) - (rhoSgl(:,4) + abs(rhoSgl(:,8))) + (rhoSgl(:,3) + abs(rhoSgl(:,7))) - (rhoSgl(:,4) + abs(rhoSgl(:,8)))
cs = cs + ns cs = cs + ns
case ('excess_rhoSgl_edge') case ('excess_rho_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = (rhoSgl(:,1) + abs(rhoSgl(:,5))) - (rhoSgl(:,2) + abs(rhoSgl(:,6))) constitutive_nonlocal_postResults(cs+1:cs+ns) = (rhoSgl(:,1) + abs(rhoSgl(:,5))) - (rhoSgl(:,2) + abs(rhoSgl(:,6)))
cs = cs + ns cs = cs + ns
case ('excess_rhoSgl_screw') case ('excess_rho_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = (rhoSgl(:,3) + abs(rhoSgl(:,7))) - (rhoSgl(:,4) + abs(rhoSgl(:,8))) constitutive_nonlocal_postResults(cs+1:cs+ns) = (rhoSgl(:,3) + abs(rhoSgl(:,7))) - (rhoSgl(:,4) + abs(rhoSgl(:,8)))
cs = cs + ns cs = cs + ns
@ -2099,11 +2136,11 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
* ( 2.0_pReal * ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) ) & ! was single hitting single * ( 2.0_pReal * ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) + rhoSgl(:,2*c) * abs(gdot(:,2*c-1)) ) & ! was single hitting single
+ 2.0_pReal * ( abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1)) ) ) ! was single hitting immobile/used single + 2.0_pReal * ( abs(rhoSgl(:,2*c+3)) * abs(gdot(:,2*c)) + abs(rhoSgl(:,2*c+4)) * abs(gdot(:,2*c-1)) ) ) ! was single hitting immobile/used single
enddo enddo
! do c=1,2 ! do c=1,2
! forall (s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! dipole formation by stress decrease ! forall (s=1:ns, dUpperDot(s,c) > 0.0_pReal) & ! dipole formation by stress decrease
! constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) + & ! constitutive_nonlocal_postResults(cs+s) = constitutive_nonlocal_postResults(cs+s) + &
! 8.0_pReal * rho(s,2*c-1) * rho(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c) ! 8.0_pReal * rhoSgl(s,2*c-1) * rhoSgl(s,2*c) * previousDUpper(s,c) * dUpperDot(s,c)
! enddo ! enddo
cs = cs + ns cs = cs + ns
case ('rho_dot_dip2sgl') case ('rho_dot_dip2sgl')
@ -2139,7 +2176,17 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(:,1:4,g,ip,el),2) & constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(:,1:4,g,ip,el),2) &
+ sum(abs(constitutive_nonlocal_rhoDotFlux(:,5:8,g,ip,el)),2) + sum(abs(constitutive_nonlocal_rhoDotFlux(:,5:8,g,ip,el)),2)
cs = cs + ns cs = cs + ns
case ('rho_dot_flux_edge')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(:,1:2,g,ip,el),2) &
+ sum(abs(constitutive_nonlocal_rhoDotFlux(:,5:6,g,ip,el)),2)
cs = cs + ns
case ('rho_dot_flux_screw')
constitutive_nonlocal_postResults(cs+1:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(:,3:4,g,ip,el),2) &
+ sum(abs(constitutive_nonlocal_rhoDotFlux(:,7:8,g,ip,el)),2)
cs = cs + ns
case ('dislocationvelocity') case ('dislocationvelocity')
constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_v(:,1,g,ip,el) constitutive_nonlocal_postResults(cs+1:cs+ns) = constitutive_nonlocal_v(:,1,g,ip,el)
cs = cs + ns cs = cs + ns

2
code/material.config
View File

@ -195,6 +195,8 @@ constitution nonlocal
(output) rho_dot_ann_ath (output) rho_dot_ann_ath
(output) rho_dot_ann_the (output) rho_dot_ann_the
(output) rho_dot_flux (output) rho_dot_flux
(output) rho_dot_flux_edge
(output) rho_dot_flux_screw
(output) dislocationvelocity (output) dislocationvelocity
(output) fluxDensity_edge_pos_x (output) fluxDensity_edge_pos_x
(output) fluxDensity_edge_pos_y (output) fluxDensity_edge_pos_y