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annihilation of screws

This commit is contained in:
Christoph Kords 2012-11-17 13:50:20 +00:00
parent dc5cd8a4c4
commit 467c186f0f
1 changed files with 37 additions and 39 deletions
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code/constitutive_nonlocal.f90
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@ -162,8 +162,7 @@ constitutive_nonlocal_interactionMatrixSlipSlip ! interacti
real(pReal), dimension(:,:,:,:), allocatable, private :: & real(pReal), dimension(:,:,:,:), allocatable, private :: &
constitutive_nonlocal_lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!) constitutive_nonlocal_lattice2slip, & ! orthogonal transformation matrix from lattice coordinate system to slip coordinate system (passive rotation !!!)
constitutive_nonlocal_accumulatedShear, & ! accumulated shear per slip system up to the start of the FE increment constitutive_nonlocal_accumulatedShear ! accumulated shear per slip system up to the start of the FE increment
constitutive_nonlocal_rhoDotEdgeJogs
real(pReal), dimension(:,:,:,:,:), allocatable, private :: & real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
constitutive_nonlocal_Cslip_3333, & ! elasticity matrix for each instance constitutive_nonlocal_Cslip_3333, & ! elasticity matrix for each instance
@ -716,13 +715,11 @@ allocate(constitutive_nonlocal_rhoDotMultiplication(maxTotalNslip, 2, homogeniza
allocate(constitutive_nonlocal_rhoDotSingle2DipoleGlide(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotSingle2DipoleGlide(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(constitutive_nonlocal_rhoDotAthermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotAthermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(constitutive_nonlocal_rhoDotThermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_rhoDotThermalAnnihilation(maxTotalNslip, 2, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
allocate(constitutive_nonlocal_rhoDotEdgeJogs(maxTotalNslip, homogenization_maxNgrains, mesh_maxNips, mesh_NcpElems))
constitutive_nonlocal_rhoDotFlux = 0.0_pReal constitutive_nonlocal_rhoDotFlux = 0.0_pReal
constitutive_nonlocal_rhoDotMultiplication = 0.0_pReal constitutive_nonlocal_rhoDotMultiplication = 0.0_pReal
constitutive_nonlocal_rhoDotSingle2DipoleGlide = 0.0_pReal constitutive_nonlocal_rhoDotSingle2DipoleGlide = 0.0_pReal
constitutive_nonlocal_rhoDotAthermalAnnihilation = 0.0_pReal constitutive_nonlocal_rhoDotAthermalAnnihilation = 0.0_pReal
constitutive_nonlocal_rhoDotThermalAnnihilation = 0.0_pReal constitutive_nonlocal_rhoDotThermalAnnihilation = 0.0_pReal
constitutive_nonlocal_rhoDotEdgeJogs = 0.0_pReal
allocate(constitutive_nonlocal_compatibility(2,maxTotalNslip, maxTotalNslip, FE_maxNipNeighbors, mesh_maxNips, mesh_NcpElems)) allocate(constitutive_nonlocal_compatibility(2,maxTotalNslip, maxTotalNslip, FE_maxNipNeighbors, mesh_maxNips, mesh_NcpElems))
constitutive_nonlocal_compatibility = 0.0_pReal constitutive_nonlocal_compatibility = 0.0_pReal
@ -1866,14 +1863,16 @@ integer(pInt) myInstance, & ! current
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
deltaRho, & ! density increment deltaRho, & ! density increment
deltaRhoRemobilization, & ! density increment by remobilization deltaRhoRemobilization, & ! density increment by remobilization
deltaRhoDipole2SingleStress ! density increment by dipole dissociation (by stress change) deltaRhoDipole2SingleStress, & ! density increment by dipole dissociation (by stress change)
deltaRhoScrewDipoleAnnihilation ! density incrmeent by annihilation of screw dipoles
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(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)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),4) :: &
v ! dislocation glide velocity v ! dislocation glide velocity
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
tau, & ! current resolved shear stress tau, & ! current resolved shear stress
tauBack ! current back stress from pileups on same slip system tauBack, & ! current back stress from pileups on same slip system
rhoForest
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
rhoDip, & ! current dipole dislocation densities (screw and edge dipoles) rhoDip, & ! current dipole dislocation densities (screw and edge dipoles)
dLower, & ! minimum stable dipole distance for edges and screws dLower, & ! minimum stable dipole distance for edges and screws
@ -1905,6 +1904,7 @@ forall (s = 1_pInt:ns, t = 5_pInt:8_pInt) &
rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s) rhoSgl(s,t) = state(g,ip,el)%p((t-1_pInt)*ns+s)
forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) & forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal) rhoDip(s,c) = max(state(g,ip,el)%p((7_pInt+c)*ns+s), 0.0_pReal)
rhoForest = state(g,ip,el)%p(10_pInt*ns+1:11_pInt*ns)
tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns) tauBack = state(g,ip,el)%p(12_pInt*ns+1:13_pInt*ns)
forall (t = 1_pInt:4_pInt) & forall (t = 1_pInt:4_pInt) &
v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns) v(1_pInt:ns,t) = state(g,ip,el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
@ -1959,17 +1959,15 @@ dUpper = max(dUpper,dLower)
deltaDUpper = dUpper - dUpperOld deltaDUpper = dUpper - dUpperOld
!*** dissociation by stress increase !*** dissociation by stress increase (only edge dipoles)
deltaRhoDipole2SingleStress = 0.0_pReal deltaRhoDipole2SingleStress = 0.0_pReal
forall (c=1_pInt:2_pInt, s=1_pInt:ns, deltaDUpper(s,c) < 0.0_pReal) & forall (s=1_pInt:ns, deltaDUpper(s,1) < 0.0_pReal) &
deltaRhoDipole2SingleStress(s,8_pInt+c) = rhoDip(s,c) * deltaDUpper(s,c) / (dUpperOld(s,c) - dLower(s,c)) deltaRhoDipole2SingleStress(s,9) = rhoDip(s,1) * deltaDUpper(s,1) / (dUpperOld(s,1) - dLower(s,1))
forall (t=1_pInt:2_pInt) &
forall (t=1_pInt:4_pInt) &
deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal * deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt) deltaRhoDipole2SingleStress(1_pInt:ns,t) = -0.5_pReal * deltaRhoDipole2SingleStress(1_pInt:ns,(t-1_pInt)/2_pInt+9_pInt)
!*** store new maximum dipole height in state !*** store new maximum dipole height in state
forall (c = 1_pInt:2_pInt) & forall (c = 1_pInt:2_pInt) &
@ -1977,12 +1975,28 @@ forall (c = 1_pInt:2_pInt) &
!****************************************************************************
!*** annihilation of screw dipoles
! we assume that all screws annihilate instantaneously by cross-slipping on the colinear system
! (so right now this is actually an athermal process, could be enriched by a thermally activated probability for cross-slip)
! annihilated screw dipoles leave edge jogs behind on the colinear system
deltaRhoScrewDipoleAnnihilation = 0.0_pReal
if (myStructure == 1_pInt) then ! only fcc
deltaRhoScrewDipoleAnnihilation(1:ns,10) = -rhoDip(1:ns,2)
forall (s = 1:ns, constitutive_nonlocal_colinearSystem(s,myInstance) > 0_pInt) &
deltaRhoScrewDipoleAnnihilation(constitutive_nonlocal_colinearSystem(s,myInstance),1:2) = rhoDip(s,2) &
* 0.25_pReal * sqrt(rhoForest(s)) * (dUpperOld(s,2) + dLower(s,2))
endif
!**************************************************************************** !****************************************************************************
!*** assign the changes in the dislocation densities to deltaState !*** assign the changes in the dislocation densities to deltaState
deltaRho = 0.0_pReal deltaRho = 0.0_pReal
deltaRho = deltaRhoRemobilization & deltaRho = deltaRhoRemobilization &
+ deltaRhoDipole2SingleStress + deltaRhoDipole2SingleStress &
+ deltaRhoScrewDipoleAnnihilation
deltaState%p = reshape(deltaRho,(/10_pInt*ns/)) deltaState%p = reshape(deltaRho,(/10_pInt*ns/))
@ -1994,6 +2008,7 @@ deltaState%p = reshape(deltaRho,(/10_pInt*ns/))
.or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then .or. .not. iand(debug_level(debug_constitutive),debug_levelSelective) /= 0_pInt )) then
write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation remobilization', deltaRhoRemobilization(1:ns,1:8) write(6,'(a,/,8(12x,12(e12.5,1x),/))') '<< CONST >> dislocation remobilization', deltaRhoRemobilization(1:ns,1:8)
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole dissociation by stress increase', deltaRhoDipole2SingleStress write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole dissociation by stress increase', deltaRhoDipole2SingleStress
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> screw dipole annihilation', deltaRhoScrewDipoleAnnihilation
write(6,*) write(6,*)
endif endif
#endif #endif
@ -2447,22 +2462,18 @@ do c = 1_pInt,2_pInt
enddo enddo
!*** athermal annihilation !*** athermal annihilation (only edge dipoles)
rhoDotAthermalAnnihilation = 0.0_pReal rhoDotAthermalAnnihilation = 0.0_pReal
rhoDotAthermalAnnihilation(1:ns,9) = -2.0_pReal * dLower(1:ns,1) / constitutive_nonlocal_burgers(1:ns,myInstance) &
forall (c=1_pInt:2_pInt) & * ( 2.0_pReal * (rhoSgl(1:ns,1) * abs(gdot(1:ns,2)) + rhoSgl(1:ns,2) * abs(gdot(1:ns,1))) & ! was single hitting single
rhoDotAthermalAnnihilation(1:ns,c+8_pInt) = -2.0_pReal * dLower(1:ns,c) / constitutive_nonlocal_burgers(1:ns,myInstance) & + 2.0_pReal * (abs(rhoSgl(1:ns,5)) * abs(gdot(1:ns,2)) + abs(rhoSgl(1:ns,6)) * abs(gdot(1:ns,1))) & ! was single hitting immobile single or was immobile single hit by single
* ( 2.0_pReal * (rhoSgl(1:ns,2*c-1) * abs(gdot(1:ns,2*c)) + rhoSgl(1:ns,2*c) * abs(gdot(1:ns,2*c-1))) & ! was single hitting single + rhoDip(1:ns,1) * (abs(gdot(1:ns,1)) + abs(gdot(1:ns,2)))) ! single knocks dipole constituent
+ 2.0_pReal * (abs(rhoSgl(1:ns,2*c+3)) * abs(gdot(1:ns,2*c)) + abs(rhoSgl(1:ns,2*c+4)) * abs(gdot(1:ns,2*c-1))) & ! was single hitting immobile single or was immobile single hit by single
+ rhoDip(1:ns,c) * (abs(gdot(1:ns,2*c-1)) + abs(gdot(1:ns,2*c)))) ! single knocks dipole constituent
!*** thermally activated annihilation of dipoles !*** thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal rhoDotThermalAnnihilation = 0.0_pReal
! edge annihilation by thermally activate climb
D = constitutive_nonlocal_Dsd0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature)) D = constitutive_nonlocal_Dsd0(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)) ) &
@ -2472,15 +2483,7 @@ forall (s = 1_pInt:ns, dUpper(s,1) > dLower(s,1)) &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) - rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) - rhoDotSingle2DipoleGlide(s,9)) ! make sure that we do not annihilate more dipoles than we have
! annihilation of screw dipoles: we assume that all screws annihilate instantaneously by cross-slipping on the colinear system ! annihilation of screw dipoles: we assume that all screws annihilate instantaneously by cross-slipping on the colinear system
! (so right now this is actually an athermal process, could be enriched by a thermally activated probability for cross-slip) ! so this mechanism is modeled in the deltaState
! annihilated screw dipoles leave edge jogs behind on the colinear system
if (myStructure == 1_pInt) then ! only fcc
rhoDotThermalAnnihilation(1:ns,10) = -rhoDip(1:ns,2) / timestep
forall (s = 1:ns, constitutive_nonlocal_colinearSystem(s,myInstance) > 0_pInt) &
rhoDotThermalAnnihilation(constitutive_nonlocal_colinearSystem(s,myInstance),1:2) = -rhoDotThermalAnnihilation(s,10) &
* 0.25_pReal * sqrt(rhoForest(s)) * (dUpper(s,2) + dLower(s,2))
endif
!**************************************************************************** !****************************************************************************
@ -2500,7 +2503,6 @@ if (numerics_integrationMode == 1_pInt) then
constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1:2,g,ip,el) = rhoDotSingle2DipoleGlide(1:ns,9:10) constitutive_nonlocal_rhoDotSingle2DipoleGlide(1:ns,1:2,g,ip,el) = rhoDotSingle2DipoleGlide(1:ns,9:10)
constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotAthermalAnnihilation(1:ns,9:10) constitutive_nonlocal_rhoDotAthermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotAthermalAnnihilation(1:ns,9:10)
constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotThermalAnnihilation(1:ns,9:10) constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,1:2,g,ip,el) = rhoDotThermalAnnihilation(1:ns,9:10)
constitutive_nonlocal_rhoDotEdgeJogs(1:ns,g,ip,el) = 2.0_pReal * rhoDotThermalAnnihilation(1:ns,1)
endif endif
@ -2513,8 +2515,8 @@ endif
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', rhoDotSingle2DipoleGlide * timestep write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', & write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> athermal dipole annihilation', &
rhoDotAthermalAnnihilation(1:ns,9:10) * timestep rhoDotAthermalAnnihilation(1:ns,9:10) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', & write(6,'(a,/,2(12x,12(e12.5,1x),/))') '<< CONST >> thermally activated dipole annihilation', &
rhoDotThermalAnnihilation * timestep rhoDotThermalAnnihilation(1:ns,9:10) * timestep
write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', rhoDot * timestep write(6,'(a,/,10(12x,12(e12.5,1x),/))') '<< CONST >> total density change', rhoDot * timestep
write(6,'(a,/,10(12x,12(f12.7,1x),/))') '<< CONST >> relative density change', & write(6,'(a,/,10(12x,12(f12.7,1x),/))') '<< CONST >> relative density change', &
rhoDot(1:ns,1:8) * timestep / (abs(rhoSgl)+1.0e-10), & rhoDot(1:ns,1:8) * timestep / (abs(rhoSgl)+1.0e-10), &
@ -3482,10 +3484,6 @@ do o = 1_pInt,phase_Noutput(material_phase(g,ip,el))
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el) constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotThermalAnnihilation(1:ns,2,g,ip,el)
cs = cs + ns cs = cs + ns
case ('rho_dot_edgejogs')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = constitutive_nonlocal_rhoDotEdgeJogs(1:ns,g,ip,el)
cs = cs + ns
case ('rho_dot_flux') case ('rho_dot_flux')
constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,1:4,g,ip,el),2) & constitutive_nonlocal_postResults(cs+1_pInt:cs+ns) = sum(constitutive_nonlocal_rhoDotFlux(1:ns,1:4,g,ip,el),2) &
+ sum(abs(constitutive_nonlocal_rhoDotFlux(1:ns,5:8,g,ip,el)),2) + sum(abs(constitutive_nonlocal_rhoDotFlux(1:ns,5:8,g,ip,el)),2)