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