dipole dissociation and formation by change in stress as new mechanism in deltaState; had to add dipole height to state variables, which is however updated by deltaState instead of microstructure; alternatively microstructure had to know the current stress state
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Christoph Kords
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4da6907648
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5b02d4e8eb
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@ -831,7 +831,7 @@ select case (phase_plasticity(material_phase(ipc,ip,el)))
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constitutive_deltaState(ipc,ip,el)%p = constitutive_dislotwin_deltaState(Tstar_v,Temperature,constitutive_state,ipc,ip,el)
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case (constitutive_nonlocal_label)
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constitutive_deltaState(ipc,ip,el)%p = constitutive_nonlocal_deltaState(Tstar_v,Temperature,constitutive_state,ipc,ip,el)
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call constitutive_nonlocal_deltaState(constitutive_deltaState(ipc,ip,el),constitutive_state, Tstar_v,Temperature,ipc,ip,el)
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end select
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@ -58,11 +58,13 @@ constitutive_nonlocal_listDependentStates = (/'rhoForest ', &
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'tauThreshold ', &
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'tauBack ' /) ! list of microstructural state variables that depend on other state variables
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character(len=16), dimension(4), parameter, private :: &
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constitutive_nonlocal_listOtherStates = (/'velocityEdgePos ', &
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'velocityEdgeNeg ', &
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'velocityScrewPos', &
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'velocityScrewNeg' /) ! list of other dependent state variables that are not updated by microstructure
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character(len=20), dimension(6), parameter, private :: &
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constitutive_nonlocal_listOtherStates = (/'velocityEdgePos ', &
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'velocityEdgeNeg ', &
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'velocityScrewPos ', &
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'velocityScrewNeg ', &
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'maxDipoleHeightEdge ', &
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'maxDipoleHeightScrew' /) ! list of other dependent state variables that are not updated by microstructure
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real(pReal), parameter, private :: &
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kB = 1.38e-23_pReal ! Physical parameter, Boltzmann constant in J/Kelvin
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@ -1524,7 +1526,7 @@ endsubroutine
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!*********************************************************************
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!* incremental change of microstructure *
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!*********************************************************************
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function constitutive_nonlocal_deltaState(Tstar_v, Temperature, state, g,ip,el)
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subroutine constitutive_nonlocal_deltaState(deltaState, state, Tstar_v, Temperature, g,ip,el)
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use prec, only: pReal, &
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pInt, &
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@ -1536,6 +1538,9 @@ use debug, only: debug_what, &
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debug_g, &
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debug_i, &
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debug_e
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use math, only: pi, &
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math_mul6x6
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use lattice, only: lattice_Sslip_v
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use mesh, only: mesh_NcpElems, &
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mesh_maxNips
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use material, only: homogenization_maxNgrains, &
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@ -1550,12 +1555,13 @@ integer(pInt), intent(in) :: g, & ! current
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el ! current element number
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real(pReal), intent(in) :: Temperature ! temperature
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real(pReal), dimension(6), intent(in) :: Tstar_v ! current 2nd Piola-Kirchhoff stress in Mandel notation
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(in) :: &
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!*** input/output variables
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type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), intent(inout) :: &
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state ! current microstructural state
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!*** output variables
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real(pReal), dimension(constitutive_nonlocal_sizeDotState(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
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constitutive_nonlocal_deltaState ! change of state variables / microstructure
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type(p_vec), intent(out) :: deltaState ! change of state variables / microstructure
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!*** local variables
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integer(pInt) myInstance, & ! current instance of this plasticity
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@ -1564,16 +1570,26 @@ integer(pInt) myInstance, & ! current
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c, & ! character of dislocation
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n, & ! index of my current neighbor
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t, & ! type of dislocation
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s ! index of my current slip system
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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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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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deltaRhoRemobilization, & ! density increment by remobilization
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deltaRhoSingle2DipoleStress, & ! density increment by dipole formation (by stress change)
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deltaRhoDipole2SingleStress ! density increment by dipole dissociation (by stress change)
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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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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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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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dUpper, & ! current maximum stable dipole distance for edges and screws
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dUpperOld, & ! old maximum stable dipole distance for edges and screws
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deltaDUpper ! change in maximum stable dipole distance for edges and screws
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#ifndef _OPENMP
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@ -1599,8 +1615,11 @@ 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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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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forall (c = 1_pInt:2_pInt) &
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dUpperOld(1_pInt:ns,c) = state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns)
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@ -1622,13 +1641,75 @@ enddo
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!****************************************************************************
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!*** assign the rates of dislocation densities to my dotState
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!*** if evolution rates lead to negative densities, a cutback is enforced
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!*** calculate dipole formation and dissociation by stress change
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!*** calculate limits for stable dipole height
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do s = 1_pInt,ns
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sLattice = constitutive_nonlocal_slipSystemLattice(s,myInstance)
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tau(s) = math_mul6x6(Tstar_v, lattice_Sslip_v(1:6,sLattice,myStructure)) + tauBack(s)
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if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
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enddo
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dLower = constitutive_nonlocal_minimumDipoleHeight(1:ns,1:2,myInstance)
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dUpper(1:ns,2) = min(1.0_pReal / sqrt(sum(abs(rhoSgl),2) + sum(rhoDip,2)), &
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constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgers(1:ns,myInstance) &
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/ (8.0_pReal * pi * abs(tau)))
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dUpper(1:ns,1) = dUpper(1:ns,2) / (1.0_pReal - constitutive_nonlocal_nu(myInstance))
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deltaDUpper = dUpper - dUpperOld
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!*** dissociation by stress increase
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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) / (dUpper(s,c) - dLower(s,c))
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forall (t=1_pInt:4_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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!*** formation by stress decrease
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deltaRhoSingle2DipoleStress = 0.0_pReal
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do c = 1,2
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do s = 1,ns
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if (deltaDUpper(s,c) > 0.0_pReal) then
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deltaRhoSingle2DipoleStress(s,2*(c-1)+1) = -4.0_pReal * deltaDUpper(s,c) * dUpper(s,c) * rhoSgl(s,2*(c-1)+1) &
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* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
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deltaRhoSingle2DipoleStress(s,2*(c-1)+2) = -4.0_pReal * deltaDUpper(s,c) * dUpper(s,c) * rhoSgl(s,2*(c-1)+2) &
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* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
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deltaRhoSingle2DipoleStress(s,2*(c-1)+5) = -4.0_pReal * deltaDUpper(s,c) * dUpper(s,c) * rhoSgl(s,2*(c-1)+5) &
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* ( rhoSgl(s,2*(c-1)+2) + abs(rhoSgl(s,2*(c-1)+6)) )
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deltaRhoSingle2DipoleStress(s,2*(c-1)+6) = -4.0_pReal * deltaDUpper(s,c) * dUpper(s,c) * rhoSgl(s,2*(c-1)+6) &
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* ( rhoSgl(s,2*(c-1)+1) + abs(rhoSgl(s,2*(c-1)+5)) )
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endif
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enddo
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enddo
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forall (c = 1:2) &
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deltaRhoSingle2DipoleStress(1:ns,8+c) = abs(deltaRhoSingle2DipoleStress(1:ns,2*(c-1)+1)) &
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+ abs(deltaRhoSingle2DipoleStress(1:ns,2*(c-1)+2)) &
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+ abs(deltaRhoSingle2DipoleStress(1:ns,2*(c-1)+5)) &
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+ abs(deltaRhoSingle2DipoleStress(1:ns,2*(c-1)+6))
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!*** store new maximum dipole height in state
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forall (c = 1_pInt:2_pInt) &
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state(g,ip,el)%p((16_pInt+c)*ns+1_pInt:(17_pInt+c)*ns) = dUpper(1_pInt:ns,c)
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!****************************************************************************
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!*** assign the rates of dislocation densities to deltaState
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deltaRho = 0.0_pReal
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deltaRho = deltaRhoRemobilization
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deltaRho = deltaRhoRemobilization &
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+ deltaRhoDipole2SingleStress &
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+ deltaRhoSingle2DipoleStress
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constitutive_nonlocal_deltaState = reshape(deltaRho,(/10_pInt*ns/))
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deltaState%p = reshape(deltaRho,(/10_pInt*ns/))
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@ -1641,7 +1722,7 @@ constitutive_nonlocal_deltaState = reshape(deltaRho,(/10_pInt*ns/))
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endif
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#endif
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endfunction
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endsubroutine
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