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Martin Diehl
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ae9a48c124
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12ca7428cf
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@ -744,17 +744,6 @@ module subroutine nonlocal_dependentState(ph, en, ip, el)
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enddo
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endif
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#ifdef DEBUG
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if (debugConstitutive%extensive &
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.and. ((debugConstitutive%element == el .and. debugConstitutive%ip == ip)&
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.or. .not. debugConstitutive%selective)) then
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print'(/,a,i8,1x,i2,1x,i1,/)', '<< CONST >> nonlocal_microstructure at el ip ',el,ip
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print'(a,/,12x,12(e10.3,1x))', '<< CONST >> rhoForest', stt%rho_forest(:,en)
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print'(a,/,12x,12(f10.5,1x))', '<< CONST >> tauThreshold / MPa', dst%tau_pass(:,en)*1e-6
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print'(a,/,12x,12(f10.5,1x),/)', '<< CONST >> tauBack / MPa', dst%tau_back(:,en)*1e-6
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endif
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#endif
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end associate
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end subroutine nonlocal_dependentState
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@ -1030,17 +1019,9 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
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forall (s = 1:ns, t = 1:4) v(s,t) = plasticState(ph)%state(iV(s,t,ph),en)
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gdot = rhoSgl(:,1:4) * v * spread(prm%b_sl,2,4)
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#ifdef DEBUG
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if (debugConstitutive%basic &
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.and. ((debugConstitutive%element == el .and. debugConstitutive%ip == ip) &
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.or. .not. debugConstitutive%selective)) then
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print'(a,/,10(12x,12(e12.5,1x),/))', '<< CONST >> rho / 1/m^2', rhoSgl, rhoDip
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print'(a,/,4(12x,12(e12.5,1x),/))', '<< CONST >> gdot / 1/s',gdot
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endif
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#endif
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!****************************************************************************
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!*** limits for stable dipole height
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! limits for stable dipole height
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do s = 1,ns
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tau(s) = math_tensordot(Mp, prm%Schmid(1:3,1:3,s)) + dst%tau_back(s,en)
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if (abs(tau(s)) < 1.0e-15_pReal) tau(s) = 1.0e-15_pReal
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@ -1057,8 +1038,8 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
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dUpper = max(dUpper,dLower)
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!****************************************************************************
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!*** dislocation multiplication
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! dislocation multiplication
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rhoDotMultiplication = 0.0_pReal
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isBCC: if (phase_lattice(ph) == 'cI') then
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forall (s = 1:ns, sum(abs(v(s,1:4))) > 0.0_pReal)
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@ -1080,9 +1061,9 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
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!****************************************************************************
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!*** calculate dipole formation and annihilation
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! dipole formation and annihilation
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!*** formation by glide
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! formation by glide
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do c = 1,2
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rhoDotSingle2DipoleGlide(:,2*c-1) = -2.0_pReal * dUpper(:,c) / prm%b_sl &
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* ( rhoSgl(:,2*c-1) * abs(gdot(:,2*c)) & ! negative mobile --> positive mobile
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@ -1107,7 +1088,7 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
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enddo
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!*** athermal annihilation
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! athermal annihilation
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rhoDotAthermalAnnihilation = 0.0_pReal
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forall (c=1:2) &
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rhoDotAthermalAnnihilation(:,c+8) = -2.0_pReal * dLower(:,c) / prm%b_sl &
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@ -1122,7 +1103,7 @@ module subroutine nonlocal_dotState(Mp, Temperature,timestep, &
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* 0.25_pReal * sqrt(stt%rho_forest(s,en)) * (dUpper(s,2) + dLower(s,2)) * prm%f_ed
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!*** thermally activated annihilation of edge dipoles by climb
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! thermally activated annihilation of edge dipoles by climb
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rhoDotThermalAnnihilation = 0.0_pReal
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selfDiffusion = prm%D_0 * exp(-prm%Q_cl / (kB * Temperature))
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vClimb = prm%V_at * selfDiffusion * prm%mu &
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@ -1650,13 +1631,13 @@ end subroutine stateInit
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates kinetics
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!--------------------------------------------------------------------------------------------------
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pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Temperature, ph)
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pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, T, ph)
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integer, intent(in) :: &
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c, & !< dislocation character (1:edge, 2:screw)
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ph
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real(pReal), intent(in) :: &
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Temperature !< temperature
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T !< T
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real(pReal), dimension(param(ph)%sum_N_sl), intent(in) :: &
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tau, & !< resolved external shear stress (without non Schmid effects)
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tauNS, & !< resolved external shear stress (including non Schmid effects)
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@ -1677,16 +1658,11 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Tem
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vViscous, & !< viscous glide velocity
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dtPeierls_dtau, & !< derivative with respect to resolved shear stress
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dtSolidSolution_dtau, & !< derivative with respect to resolved shear stress
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meanfreepath_S, & !< mean free travel distance for dislocations between two solid solution obstacles
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meanfreepath_P, & !< mean free travel distance for dislocations between two Peierls barriers
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jumpWidth_P, & !< depth of activated area
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jumpWidth_S, & !< depth of activated area
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activationLength_P, & !< length of activated dislocation line
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activationLength_S, & !< length of activated dislocation line
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lambda_S, & !< mean free distance between two solid solution obstacles
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lambda_P, & !< mean free distance between two Peierls barriers
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activationVolume_P, & !< volume that needs to be activated to overcome barrier
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activationVolume_S, & !< volume that needs to be activated to overcome barrier
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activationEnergy_P, & !< energy that is needed to overcome barrier
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activationEnergy_S, & !< energy that is needed to overcome barrier
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criticalStress_P, & !< maximum obstacle strength
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criticalStress_S, & !< maximum obstacle strength
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mobility !< dislocation mobility
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@ -1700,40 +1676,32 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Tem
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if (abs(tau(s)) > tauThreshold(s)) then
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!* Peierls contribution
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!* Effective stress includes non Schmid constributions
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!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
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tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) ! ensure that the effective stress is positive
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meanfreepath_P = prm%b_sl(s)
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jumpWidth_P = prm%b_sl(s)
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activationLength_P = prm%w *prm%b_sl(s)
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activationVolume_P = activationLength_P * jumpWidth_P * prm%b_sl(s)
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tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s))
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lambda_P = prm%b_sl(s)
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activationVolume_P = prm%w *prm%b_sl(s)**3.0_pReal
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criticalStress_P = prm%peierlsStress(s,c)
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activationEnergy_P = criticalStress_P * activationVolume_P
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tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) ! ensure that the activation probability cannot become greater than one
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tauRel_P = min(1.0_pReal, tauEff / criticalStress_P)
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tPeierls = 1.0_pReal / prm%nu_a &
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* exp(activationEnergy_P / (kB * Temperature) &
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* exp(activationEnergy_P / (kB * T) &
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* (1.0_pReal - tauRel_P**prm%p)**prm%q)
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if (tauEff < criticalStress_P) then
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dtPeierls_dtau = tPeierls * prm%p * prm%q * activationVolume_P / (kB * Temperature) &
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dtPeierls_dtau = tPeierls * prm%p * prm%q * activationVolume_P / (kB * T) &
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* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal)
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else
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dtPeierls_dtau = 0.0_pReal
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endif
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!* Contribution from solid solution strengthening
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!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
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! Contribution from solid solution strengthening
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tauEff = abs(tau(s)) - tauThreshold(s)
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meanfreepath_S = prm%b_sl(s) / sqrt(prm%c_sol)
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jumpWidth_S = prm%f_sol * prm%b_sl(s)
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activationLength_S = prm%b_sl(s) / sqrt(prm%c_sol)
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activationVolume_S = activationLength_S * jumpWidth_S * prm%b_sl(s)
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activationEnergy_S = prm%Q_sol
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criticalStress_S = activationEnergy_S / activationVolume_S
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tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) ! ensure that the activation probability cannot become greater than one
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lambda_S = prm%b_sl(s) / sqrt(prm%c_sol)
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activationVolume_S = prm%f_sol * prm%b_sl(s)**3.0_pReal / sqrt(prm%c_sol)
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criticalStress_S = prm%Q_sol / activationVolume_S
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tauRel_S = min(1.0_pReal, tauEff / criticalStress_S)
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tSolidSolution = 1.0_pReal / prm%nu_a &
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* exp(activationEnergy_S / (kB * Temperature)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
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* exp(prm%Q_sol / (kB * T)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
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if (tauEff < criticalStress_S) then
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dtSolidSolution_dtau = tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * Temperature) &
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dtSolidSolution_dtau = tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * T) &
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* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal)
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else
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dtSolidSolution_dtau = 0.0_pReal
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@ -1744,13 +1712,10 @@ pure subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Tem
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mobility = prm%b_sl(s) / prm%eta
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vViscous = mobility * tauEff
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!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
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!* free flight at glide velocity in between.
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!* adopt sign from resolved stress
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v(s) = sign(1.0_pReal,tau(s)) &
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/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
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dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / meanfreepath_S + mobility /vViscous**2.0_pReal)
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dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / meanfreepath_P
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/ (tPeierls / lambda_P + tSolidSolution / lambda_S + 1.0_pReal / vViscous)
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dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / lambda_S + mobility /vViscous**2.0_pReal)
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dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / lambda_P
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endif
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enddo
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