Dead dislocations are treated the same as mobile dislocations for the flux part though they do not contribute to slip. By that the pileup of dead dislocations is able to diminish with time (kinetics are the same as for the glide part; this is not correct but gives valuable results). Also remobilization of dead dislocations at neighbor is taken into account for flux.
This commit is contained in:
Christoph Kords
parent
6bca2150f2
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9cbbb7cab5
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@ -1544,7 +1544,8 @@ integer(pInt) myInstance, & ! current
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t, & ! type of dislocation
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topp, & ! type of dislocation with opposite sign to t
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s, & ! index of my current slip system
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sLattice ! index of my current slip system according to lattice order
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sLattice, & ! index of my current slip system according to lattice order
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deads
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),10) :: &
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rhoDot, & ! density evolution
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rhoDotRemobilization, & ! density evolution by remobilization
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@ -1554,11 +1555,11 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance
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rhoDotAthermalAnnihilation, & ! density evolution by athermal annihilation
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rhoDotThermalAnnihilation ! density evolution by thermal annihilation
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
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neighboring_rhoSgl, & ! current single dislocation densities (positive/negative screw and edge without dipoles)
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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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fluxdensity, & ! flux density at central material point
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neighboring_fluxdensity, & ! flux density at neighboring material point
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neighboring_v, & ! dislocation glide velocity
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gdot ! shear rates
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real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
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rhoForest, & ! forest dislocation density
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@ -1740,13 +1741,11 @@ if (.not. phase_localPlasticity(material_phase(g,ip,el))) then
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my_Fe = Fe(1:3,1:3,g,ip,el)
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my_F = math_mul33x33(my_Fe, Fp(1:3,1:3,g,ip,el))
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fluxdensity = rhoSgl(1:ns,1:4) * v
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do n = 1_pInt,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors
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do n = 1_pInt,FE_NipNeighbors(mesh_element(2,el)) ! loop through my neighbors
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neighboring_el = mesh_ipNeighborhood(1,n,ip,el)
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neighboring_ip = mesh_ipNeighborhood(2,n,ip,el)
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if (neighboring_el > 0_pInt .and. neighboring_ip > 0_pInt) then ! if neighbor exists ...
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do neighboring_n = 1_pInt,FE_NipNeighbors(mesh_element(2,neighboring_el)) ! find neighboring index that points from my neighbor to myself
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do neighboring_n = 1_pInt,FE_NipNeighbors(mesh_element(2,neighboring_el)) ! find neighboring index that points from my neighbor to myself
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if ( el == mesh_ipNeighborhood(1,neighboring_n,neighboring_ip,neighboring_el) &
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.and. ip == mesh_ipNeighborhood(2,neighboring_n,neighboring_ip,neighboring_el)) then ! possible candidate
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if (math_mul3x3(mesh_ipAreaNormal(1:3,n,ip,el),&
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@ -1776,7 +1775,8 @@ if (.not. phase_localPlasticity(material_phase(g,ip,el))) then
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!* The entering flux from my neighbor will be distributed on my slip systems according to the compatibility
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considerEnteringFlux = .false.
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neighboring_fluxdensity = 0.0_pReal ! needed for check of sign change in flux density below
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neighboring_v = 0.0_pReal ! needed for check of sign change in flux density below
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neighboring_rhoSgl = 0.0_pReal
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if (neighboring_el > 0_pInt .or. neighboring_ip > 0_pInt) then
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if (phase_plasticity(material_phase(1,neighboring_ip,neighboring_el)) == constitutive_nonlocal_label &
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.and. any(constitutive_nonlocal_compatibility(:,:,:,n,ip,el) > 0.0_pReal)) &
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@ -1785,8 +1785,15 @@ if (.not. phase_localPlasticity(material_phase(g,ip,el))) then
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if (considerEnteringFlux) then
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forall (t = 1_pInt:4_pInt) &
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neighboring_fluxdensity(1:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1)*ns+1:t*ns) &
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* state(g,neighboring_ip,neighboring_el)%p((12+t)*ns+1:(13+t)*ns)
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neighboring_v(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((12_pInt+t)*ns+1_pInt:(13_pInt+t)*ns)
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forall (t = 1_pInt:4_pInt) &
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neighboring_rhoSgl(1_pInt:ns,t) = max(state(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns), 0.0_pReal)
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forall (t = 5_pInt:8_pInt) &
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neighboring_rhoSgl(1_pInt:ns,t) = state(g,neighboring_ip,neighboring_el)%p((t-1_pInt)*ns+1_pInt:t*ns)
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forall (s = 1_pInt:ns, t = 1_pInt:4_pInt, neighboring_rhoSgl(s,t+4_pInt)*neighboring_v(s,t) < 0.0_pReal) ! remobilization of deads at neighbor
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neighboring_rhoSgl(s,t) = neighboring_rhoSgl(s,t) + abs(neighboring_rhoSgl(s,t+4_pInt))
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neighboring_rhoSgl(s,t+4_pInt) = 0.0_pReal
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endforall
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normal_neighbor2me_defConf = math_det33(Favg) &
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* math_mul33x3(math_inv33(transpose(Favg)), mesh_ipAreaNormal(1:3,neighboring_n,neighboring_ip,neighboring_el)) ! calculate the normal of the interface in (average) deformed configuration (now pointing from my neighbor to me!!!)
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normal_neighbor2me = math_mul33x3(transpose(neighboring_Fe), normal_neighbor2me_defConf) / math_det33(neighboring_Fe) ! interface normal in the lattice configuration of my neighbor
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@ -1796,15 +1803,18 @@ if (.not. phase_localPlasticity(material_phase(g,ip,el))) then
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do t = 1_pInt,4_pInt
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c = (t + 1_pInt) / 2
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topp = t + mod(t,2_pInt) - mod(t+1_pInt,2_pInt)
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if (neighboring_fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal & ! flux from my neighbor to me == entering flux for me
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.and. fluxdensity(s,t) * neighboring_fluxdensity(s,t) >= 0.0_pReal ) then ! ... only if no sign change in flux density
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lineLength = neighboring_fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
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where (constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility...
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rhoDotFlux(1:ns,t) = rhoDotFlux(1:ns,t) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed dislocation type
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* constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal
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where (constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility...
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rhoDotFlux(1:ns,topp) = rhoDotFlux(1:ns,topp) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed dislocation type
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* constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el) ** 2.0_pReal
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if (neighboring_v(s,t) * math_mul3x3(m(1:3,s,t), normal_neighbor2me) > 0.0_pReal & ! flux from my neighbor to me == entering flux for me
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.and. v(s,t) * neighboring_v(s,t) >= 0.0_pReal ) then ! ... only if no sign change in flux density
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do deads = 0_pInt,4_pInt,4_pInt
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lineLength = abs(neighboring_rhoSgl(s,t+deads)) * neighboring_v(s,t) &
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* math_mul3x3(m(1:3,s,t), normal_neighbor2me) * area ! positive line length that wants to enter through this interface
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where (constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) > 0.0_pReal) & ! positive compatibility...
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rhoDotFlux(1_pInt:ns,t) = rhoDotFlux(1_pInt:ns,t) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to equally signed mobile dislocation type
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* constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
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where (constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) < 0.0_pReal) & ! ..negative compatibility...
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rhoDotFlux(1_pInt:ns,topp) = rhoDotFlux(1_pInt:ns,topp) + lineLength / mesh_ipVolume(ip,el) & ! ... transferring to opposite signed mobile dislocation type
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* constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el) ** 2.0_pReal
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enddo
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endif
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enddo
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enddo
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@ -1834,16 +1844,18 @@ if (.not. phase_localPlasticity(material_phase(g,ip,el))) then
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do s = 1_pInt,ns
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do t = 1_pInt,4_pInt
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c = (t + 1_pInt) / 2_pInt
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if (fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from me to my neighbor == leaving flux for me (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
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lineLength = fluxdensity(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length that wants to leave through this interface
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if (fluxdensity(s,t) * neighboring_fluxdensity(s,t) >= 0.0_pReal) then ! no sign change in flux density
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transmissivity = sum(constitutive_nonlocal_compatibility(c,1:ns,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor
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if (v(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) > 0.0_pReal ) then ! flux from me to my neighbor == leaving flux for me (might also be a pure flux from my mobile density to dead density if interface not at all transmissive)
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if (v(s,t) * neighboring_v(s,t) >= 0.0_pReal) then ! no sign change in flux density
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transmissivity = sum(constitutive_nonlocal_compatibility(c,1_pInt:ns,s,n,ip,el)**2.0_pReal) ! overall transmissivity from this slip system to my neighbor
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else ! sign change in flux density means sign change in stress which does not allow for dislocations to arive at the neighbor
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transmissivity = 0.0_pReal
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endif
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rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract dislocation flux from current mobile type
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lineLength = rhoSgl(s,t) * v(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of mobiles that wants to leave through this interface
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rhoDotFlux(s,t) = rhoDotFlux(s,t) - lineLength / mesh_ipVolume(ip,el) ! subtract dislocation flux from current type
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rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) + lineLength / mesh_ipVolume(ip,el) * (1.0_pReal - transmissivity) &
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* sign(1.0_pReal, fluxdensity(s,t)) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
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* sign(1.0_pReal, v(s,t)) ! dislocation flux that is not able to leave through interface (because of low transmissivity) will remain as immobile single density at the material point
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lineLength = rhoSgl(s,t+4_pInt) * v(s,t) * math_mul3x3(m(1:3,s,t), normal_me2neighbor) * area ! positive line length of deads that wants to leave through this interface
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rhoDotFlux(s,t+4_pInt) = rhoDotFlux(s,t+4_pInt) - lineLength / mesh_ipVolume(ip,el) * transmissivity ! dead dislocations leaving through this interface
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endif
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enddo
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enddo
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