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viscosity term in kinetics law proportional to resolvedstress minus forest term

This commit is contained in:
Christoph Kords 2012-03-14 15:18:36 +00:00
parent 33ab391c14
commit 06c93435f2
1 changed files with 17 additions and 15 deletions
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32
code/constitutive_nonlocal.f90
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@ -1019,22 +1019,22 @@ forall (s = 1_pInt:ns, c = 1_pInt:2_pInt) &
!*** calculate the forest dislocation density !*** calculate the forest dislocation density
!*** (= projection of screw and edge dislocations) !*** (= projection of screw and edge dislocations)
forall (s = 1_pInt:ns) forall (s = 1_pInt:ns) &
rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)), & rhoForest(s) = dot_product((sum(abs(rhoSgl(1:ns,(/1,2,5,6/))),2) + rhoDip(1:ns,1)), &
constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) & constitutive_nonlocal_forestProjectionEdge(s,1:ns,instance)) &
+ dot_product((sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)), & + dot_product((sum(abs(rhoSgl(1:ns,(/3,4,7,8/))),2) + rhoDip(1:ns,2)), &
constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance)) constitutive_nonlocal_forestProjectionScrew(s,1:ns,instance))
!*** calculate the threshold shear stress for dislocation slip !*** calculate the threshold shear stress for dislocation slip
tauThreshold(s) = constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) & forall (s = 1_pInt:ns) &
* sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), & tauThreshold(s) = constitutive_nonlocal_Gmod(instance) * constitutive_nonlocal_burgers(s,instance) &
constitutive_nonlocal_interactionMatrixSlipSlip(s,1:ns,instance))) * sqrt(dot_product((sum(abs(rhoSgl),2) + sum(abs(rhoDip),2)), &
constitutive_nonlocal_interactionMatrixSlipSlip(s,1:ns,instance)))
end forall
!*** calculate the dislocation stress of the neighboring excess dislocation densities !*** calculate the dislocation stress of the neighboring excess dislocation densities
!*** zero for material points of local plasticity !*** zero for material points of local plasticity
@ -1252,7 +1252,8 @@ integer(pInt) instance, & ! curren
ns, & ! short notation for the total number of active slip systems ns, & ! short notation for the total number of active slip systems
s ! index of my current slip system s ! index of my current slip system
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)))) :: &
tauThreshold ! threshold shear stress tauThreshold, & ! threshold shear stress
tauEff ! effective shear stress
real(pReal) tauRel_P, & real(pReal) tauRel_P, &
tauRel_S, & tauRel_S, &
tPeierls, & ! waiting time in front of a peierls barriers tPeierls, & ! waiting time in front of a peierls barriers
@ -1281,6 +1282,7 @@ instance = phase_plasticityInstance(material_phase(g,ip,el))
ns = constitutive_nonlocal_totalNslip(instance) ns = constitutive_nonlocal_totalNslip(instance)
tauThreshold = state%p(11_pInt*ns+1:12_pInt*ns) tauThreshold = state%p(11_pInt*ns+1:12_pInt*ns)
tauEff = abs(tau) - tauThreshold
p = constitutive_nonlocal_p(instance) p = constitutive_nonlocal_p(instance)
q = constitutive_nonlocal_q(instance) q = constitutive_nonlocal_q(instance)
@ -1291,7 +1293,7 @@ if (present(dv_dtau)) dv_dtau = 0.0_pReal
if (Temperature > 0.0_pReal) then if (Temperature > 0.0_pReal) then
do s = 1_pInt,ns do s = 1_pInt,ns
if (abs(tau(s)) > tauThreshold(s)) then if (tauEff(s) > 0.0_pReal) then
!* Peierls contribution !* Peierls contribution
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity !* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
@ -1302,7 +1304,7 @@ if (Temperature > 0.0_pReal) then
activationVolume_P = activationLength_P * jumpWidth_P * constitutive_nonlocal_burgers(s,instance) activationVolume_P = activationLength_P * jumpWidth_P * constitutive_nonlocal_burgers(s,instance)
criticalStress_P = constitutive_nonlocal_peierlsStress(s,c,instance) criticalStress_P = constitutive_nonlocal_peierlsStress(s,c,instance)
activationEnergy_P = criticalStress_P * activationVolume_P activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = (abs(tau(s)) - tauThreshold(s)) / criticalStress_P tauRel_P = tauEff(s) / criticalStress_P
tPeierls = 1.0_pReal / constitutive_nonlocal_fattack(instance) & tPeierls = 1.0_pReal / constitutive_nonlocal_fattack(instance) &
* exp(activationEnergy_P / (kB * Temperature) * (1.0_pReal - tauRel_P**p)**q) * exp(activationEnergy_P / (kB * Temperature) * (1.0_pReal - tauRel_P**p)**q)
if (present(dv_dtau)) then if (present(dv_dtau)) then
@ -1321,7 +1323,7 @@ if (Temperature > 0.0_pReal) then
activationVolume_S = activationLength_S * jumpWidth_S * constitutive_nonlocal_burgers(s,instance) activationVolume_S = activationLength_S * jumpWidth_S * constitutive_nonlocal_burgers(s,instance)
activationEnergy_S = constitutive_nonlocal_solidSolutionEnergy(instance) activationEnergy_S = constitutive_nonlocal_solidSolutionEnergy(instance)
criticalStress_S = activationEnergy_S / activationVolume_S criticalStress_S = activationEnergy_S / activationVolume_S
tauRel_S = (abs(tau(s)) - tauThreshold(s)) / criticalStress_S tauRel_S = tauEff(s) / criticalStress_S
tSolidSolution = 1.0_pReal / constitutive_nonlocal_fattack(instance) & tSolidSolution = 1.0_pReal / constitutive_nonlocal_fattack(instance) &
* exp(activationEnergy_S / (kB * Temperature) * (1.0_pReal - tauRel_S**p)**q) * exp(activationEnergy_S / (kB * Temperature) * (1.0_pReal - tauRel_S**p)**q)
if (present(dv_dtau)) then if (present(dv_dtau)) then
@ -1333,7 +1335,7 @@ if (Temperature > 0.0_pReal) then
!* viscous glide velocity !* viscous glide velocity
mobility = constitutive_nonlocal_burgers(s,instance) / constitutive_nonlocal_viscosity(instance) mobility = constitutive_nonlocal_burgers(s,instance) / constitutive_nonlocal_viscosity(instance)
vViscous = mobility * abs(tau(s)) vViscous = mobility * tauEff(s)
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of !* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
@ -1341,13 +1343,12 @@ if (Temperature > 0.0_pReal) then
!* since those have the smallest activation volume, thus are decisive. !* since those have the smallest activation volume, thus are decisive.
v(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) & v(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) &
* (1.0_pReal - exp(-(abs(tau(s)) - tauThreshold(s)) * activationVolume_P / (kB * Temperature))) * (1.0_pReal - exp(-tauEff(s) * activationVolume_P / (kB * Temperature)))
v(s) = sign(v(s),tau(s)) v(s) = sign(v(s),tau(s))
if (present(dv_dtau)) then if (present(dv_dtau)) then
dv_dtau(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) & dv_dtau(s) = 1.0_pReal / (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous) &
* (abs(v(s)) * (dtPeierls_dtau + dtSolidSolution_dtau + 1.0_pReal / (mobility * tau(s) * tau(s))) & * (abs(v(s)) * (dtPeierls_dtau + dtSolidSolution_dtau + 1.0_pReal / (mobility * tauEff(s)*tauEff(s))) &
+ activationVolume_P / (kB * Temperature) * exp(-(abs(tau(s)) - tauThreshold(s)) * activationVolume_P & + activationVolume_P / (kB * Temperature) * exp(-tauEff(s) * activationVolume_P / (kB * Temperature)))
/ (kB * Temperature)))
endif endif
endif endif
@ -1363,6 +1364,7 @@ endif
write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g write(6,'(a,i8,1x,i2,1x,i1)') '<< CONST >> nonlocal_kinetics at el ip g',el,ip,g
write(6,*) write(6,*)
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauEff / MPa', tauEff / 1e6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3 write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / 1e-3m/s', v * 1e3
endif endif
#endif #endif