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internal functions need no prefix

This commit is contained in:
Martin Diehl 2020-03-16 15:22:44 +01:00
parent 47f91d08ca
commit ecd74ff8b5
1 changed files with 131 additions and 177 deletions
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src/constitutive_plastic_nonlocal.f90
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@ -851,145 +851,6 @@ module subroutine plastic_nonlocal_dependentState(F, Fp, ip, el)
end subroutine plastic_nonlocal_dependentState end subroutine plastic_nonlocal_dependentState
!--------------------------------------------------------------------------------------------------
!> @brief calculates kinetics
!--------------------------------------------------------------------------------------------------
subroutine plastic_nonlocal_kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, &
tauThreshold, c, Temperature, instance, of)
integer, intent(in) :: &
c, & !< dislocation character (1:edge, 2:screw)
instance, of
real(pReal), intent(in) :: &
Temperature !< temperature
real(pReal), dimension(param(instance)%totalNslip), intent(in) :: &
tau, & !< resolved external shear stress (without non Schmid effects)
tauNS, & !< resolved external shear stress (including non Schmid effects)
tauThreshold !< threshold shear stress
real(pReal), dimension(param(instance)%totalNslip), intent(out) :: &
v, & !< velocity
dv_dtau, & !< velocity derivative with respect to resolved shear stress (without non Schmid contributions)
dv_dtauNS !< velocity derivative with respect to resolved shear stress (including non Schmid contributions)
integer :: &
ns, & !< short notation for the total number of active slip systems
s !< index of my current slip system
real(pReal) :: &
tauRel_P, &
tauRel_S, &
tauEff, & !< effective shear stress
tPeierls, & !< waiting time in front of a peierls barriers
tSolidSolution, & !< waiting time in front of a solid solution obstacle
vViscous, & !< viscous glide velocity
dtPeierls_dtau, & !< derivative with respect to resolved shear stress
dtSolidSolution_dtau, & !< derivative with respect to resolved shear stress
meanfreepath_S, & !< mean free travel distance for dislocations between two solid solution obstacles
meanfreepath_P, & !< mean free travel distance for dislocations between two Peierls barriers
jumpWidth_P, & !< depth of activated area
jumpWidth_S, & !< depth of activated area
activationLength_P, & !< length of activated dislocation line
activationLength_S, & !< length of activated dislocation line
activationVolume_P, & !< volume that needs to be activated to overcome barrier
activationVolume_S, & !< volume that needs to be activated to overcome barrier
activationEnergy_P, & !< energy that is needed to overcome barrier
activationEnergy_S, & !< energy that is needed to overcome barrier
criticalStress_P, & !< maximum obstacle strength
criticalStress_S, & !< maximum obstacle strength
mobility !< dislocation mobility
associate(prm => param(instance))
ns = prm%totalNslip
v = 0.0_pReal
dv_dtau = 0.0_pReal
dv_dtauNS = 0.0_pReal
if (Temperature > 0.0_pReal) then
do s = 1,ns
if (abs(tau(s)) > tauThreshold(s)) then
!* Peierls contribution
!* Effective stress includes non Schmid constributions
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) ! ensure that the effective stress is positive
meanfreepath_P = prm%burgers(s)
jumpWidth_P = prm%burgers(s)
activationLength_P = prm%doublekinkwidth *prm%burgers(s)
activationVolume_P = activationLength_P * jumpWidth_P * prm%burgers(s)
criticalStress_P = prm%peierlsStress(s,c)
activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) ! ensure that the activation probability cannot become greater than one
tPeierls = 1.0_pReal / prm%fattack &
* exp(activationEnergy_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**prm%p)**prm%q)
if (tauEff < criticalStress_P) then
dtPeierls_dtau = tPeierls * prm%p * prm%q * activationVolume_P / (KB * Temperature) &
* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) &
* tauRel_P**(prm%p-1.0_pReal)
else
dtPeierls_dtau = 0.0_pReal
endif
!* Contribution from solid solution strengthening
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = abs(tau(s)) - tauThreshold(s)
meanfreepath_S = prm%burgers(s) / sqrt(prm%solidSolutionConcentration)
jumpWidth_S = prm%solidSolutionSize * prm%burgers(s)
activationLength_S = prm%burgers(s) / sqrt(prm%solidSolutionConcentration)
activationVolume_S = activationLength_S * jumpWidth_S * prm%burgers(s)
activationEnergy_S = prm%solidSolutionEnergy
criticalStress_S = activationEnergy_S / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) ! ensure that the activation probability cannot become greater than one
tSolidSolution = 1.0_pReal / prm%fattack &
* exp(activationEnergy_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**prm%p)**prm%q)
if (tauEff < criticalStress_S) then
dtSolidSolution_dtau = tSolidSolution * prm%p * prm%q &
* activationVolume_S / (KB * Temperature) &
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal) &
* tauRel_S**(prm%p-1.0_pReal)
else
dtSolidSolution_dtau = 0.0_pReal
endif
!* viscous glide velocity
tauEff = abs(tau(s)) - tauThreshold(s)
mobility = prm%burgers(s) / prm%viscosity
vViscous = mobility * tauEff
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
!* free flight at glide velocity in between.
!* adopt sign from resolved stress
v(s) = sign(1.0_pReal,tau(s)) &
/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / meanfreepath_S + mobility /vViscous**2.0_pReal)
dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / meanfreepath_P
endif
enddo
endif
#ifdef DEBUGTODO
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauThreshold / MPa', tauThreshold * 1e-6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tau / MPa', tau * 1e-6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> tauNS / MPa', tauNS * 1e-6_pReal
write(6,'(a,/,12x,12(f12.5,1x))') '<< CONST >> v / mm/s', v * 1e3
write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtau', dv_dtau
write(6,'(a,/,12x,12(e12.5,1x))') '<< CONST >> dv_dtauNS', dv_dtauNS
#endif
end associate
end subroutine plastic_nonlocal_kinetics
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief calculates plastic velocity gradient and its tangent !> @brief calculates plastic velocity gradient and its tangent
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -1009,7 +870,6 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp, dLp_dMp, &
real(pReal), dimension(3,3,3,3), intent(out) :: & real(pReal), dimension(3,3,3,3), intent(out) :: &
dLp_dMp !< derivative of Lp with respect to Tstar (9x9 matrix) dLp_dMp !< derivative of Lp with respect to Tstar (9x9 matrix)
integer :: & integer :: &
instance, & !< current instance of this plasticity instance, & !< current instance of this plasticity
ns, & !< short notation for the total number of active slip systems ns, & !< short notation for the total number of active slip systems
@ -1017,7 +877,6 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp, dLp_dMp, &
j, & j, &
k, & k, &
l, & l, &
ph, & !phase number
of, & !offset of, & !offset
t, & !< dislocation type t, & !< dislocation type
s !< index of my current slip system s !< index of my current slip system
@ -1035,10 +894,9 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp, dLp_dMp, &
gdotTotal !< shear rate gdotTotal !< shear rate
!*** shortcut for mapping !*** shortcut for mapping
ph = material_phaseAt(1,el)
of = material_phasememberAt(1,ip,el) of = material_phasememberAt(1,ip,el)
instance = phase_plasticityInstance(ph) instance = phase_plasticityInstance(material_phaseAt(1,el))
associate(prm => param(instance),dst=>microstructure(instance),stt=>state(instance)) associate(prm => param(instance),dst=>microstructure(instance),stt=>state(instance))
ns = prm%totalNslip ns = prm%totalNslip
@ -1063,9 +921,8 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp, dLp_dMp, &
tau = tau + dst%tau_back(:,of) tau = tau + dst%tau_back(:,of)
! edges ! edges
call plastic_nonlocal_kinetics(v(:,1), dv_dtau(:,1), dv_dtauNS(:,1), & call kinetics(v(:,1), dv_dtau(:,1), dv_dtauNS(:,1), &
tau, tauNS(:,1), dst%tau_pass(:,of), & tau, tauNS(:,1), dst%tau_pass(:,of),1,Temperature, instance, of)
1, Temperature, instance, of)
v(:,2) = v(:,1) v(:,2) = v(:,1)
dv_dtau(:,2) = dv_dtau(:,1) dv_dtau(:,2) = dv_dtau(:,1)
dv_dtauNS(:,2) = dv_dtauNS(:,1) dv_dtauNS(:,2) = dv_dtauNS(:,1)
@ -1079,9 +936,8 @@ module subroutine plastic_nonlocal_LpAndItsTangent(Lp, dLp_dMp, &
endforall endforall
else else
do t = 3,4 do t = 3,4
call plastic_nonlocal_kinetics(v(:,t), dv_dtau(:,t), dv_dtauNS(:,t), & call kinetics(v(:,t), dv_dtau(:,t), dv_dtauNS(:,t), &
tau, tauNS(:,t), dst%tau_pass(:,of), & tau, tauNS(:,t), dst%tau_pass(:,of),2,Temperature, instance, of)
2, Temperature, instance, of)
enddo enddo
endif endif
@ -1302,10 +1158,6 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
lineLength, & !< dislocation line length leaving the current interface lineLength, & !< dislocation line length leaving the current interface
selfDiffusion !< self diffusion selfDiffusion !< self diffusion
logical :: &
considerEnteringFlux, &
considerLeavingFlux
ph = material_phaseAt(1,el) ph = material_phaseAt(1,el)
if (timestep <= 0.0_pReal) then if (timestep <= 0.0_pReal) then
plasticState(ph)%dotState = 0.0_pReal plasticState(ph)%dotState = 0.0_pReal
@ -1436,6 +1288,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
Favg = my_F Favg = my_F
endif endif
neighbor_v0 = 0.0_pReal ! needed for check of sign change in flux density below
!* FLUX FROM MY NEIGHBOR TO ME !* FLUX FROM MY NEIGHBOR TO ME
!* This is only considered, if I have a neighbor of nonlocal plasticity !* This is only considered, if I have a neighbor of nonlocal plasticity
@ -1445,16 +1298,10 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
!* my neighbor's interface. !* my neighbor's interface.
!* The entering flux from my neighbor will be distributed on my slip systems according to the !* The entering flux from my neighbor will be distributed on my slip systems according to the
!* compatibility !* compatibility
considerEnteringFlux = .false.
neighbor_v0 = 0.0_pReal ! needed for check of sign change in flux density below
if (neighbor_n > 0) then if (neighbor_n > 0) then
if (phase_plasticity(material_phaseAt(1,neighbor_el)) == PLASTICITY_NONLOCAL_ID & if (phase_plasticity(material_phaseAt(1,neighbor_el)) == PLASTICITY_NONLOCAL_ID .and. &
.and. any(compatibility(:,:,:,n,ip,el) > 0.0_pReal)) & any(compatibility(:,:,:,n,ip,el) > 0.0_pReal)) then
considerEnteringFlux = .true.
endif
enteringFlux: if (considerEnteringFlux) then
forall (s = 1:ns, t = 1:4) forall (s = 1:ns, t = 1:4)
neighbor_v0(s,t) = plasticState(np)%state0(iV (s,t,neighbor_instance),no) neighbor_v0(s,t) = plasticState(np)%state0(iV (s,t,neighbor_instance),no)
neighbor_rhoSgl0(s,t) = max(plasticState(np)%state0(iRhoU(s,t,neighbor_instance),no),0.0_pReal) neighbor_rhoSgl0(s,t) = max(plasticState(np)%state0(iRhoU(s,t,neighbor_instance),no),0.0_pReal)
@ -1464,7 +1311,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
.or. neighbor_rhoSgl0 < prm%significantRho) & .or. neighbor_rhoSgl0 < prm%significantRho) &
neighbor_rhoSgl0 = 0.0_pReal neighbor_rhoSgl0 = 0.0_pReal
normal_neighbor2me_defConf = math_det33(Favg) * matmul(math_inv33(transpose(Favg)), & normal_neighbor2me_defConf = math_det33(Favg) * matmul(math_inv33(transpose(Favg)), &
IPareaNormal(1:3,neighbor_n,neighbor_ip,neighbor_el)) ! calculate the normal of the interface in (average) deformed configuration (now pointing from my neighbor to me!!!) IPareaNormal(1:3,neighbor_n,neighbor_ip,neighbor_el)) ! normal of the interface in (average) deformed configuration (pointing neighbor => me)
normal_neighbor2me = matmul(transpose(neighbor_Fe), normal_neighbor2me_defConf) & normal_neighbor2me = matmul(transpose(neighbor_Fe), normal_neighbor2me_defConf) &
/ math_det33(neighbor_Fe) ! interface normal in the lattice configuration of my neighbor / math_det33(neighbor_Fe) ! interface normal in the lattice configuration of my neighbor
area = IParea(neighbor_n,neighbor_ip,neighbor_el) * norm2(normal_neighbor2me) area = IParea(neighbor_n,neighbor_ip,neighbor_el) * norm2(normal_neighbor2me)
@ -1480,7 +1327,6 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) & where (compatibility(c,:,s,n,ip,el) > 0.0_pReal) &
rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) & rhoDotFlux(:,t) = rhoDotFlux(1:ns,t) &
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to equally signed mobile dislocation type + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to equally signed mobile dislocation type
where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) & where (compatibility(c,:,s,n,ip,el) < 0.0_pReal) &
rhoDotFlux(:,topp) = rhoDotFlux(:,topp) & rhoDotFlux(:,topp) = rhoDotFlux(:,topp) &
+ lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to opposite signed mobile dislocation type + lineLength/IPvolume(ip,el)*compatibility(c,:,s,n,ip,el)**2.0_pReal ! transferring to opposite signed mobile dislocation type
@ -1488,7 +1334,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
endif endif
enddo enddo
enddo enddo
endif enteringFlux endif; endif
!* FLUX FROM ME TO MY NEIGHBOR !* FLUX FROM ME TO MY NEIGHBOR
@ -1498,17 +1344,11 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
!* leaving flux to neighbor == entering flux from opposite neighbor !* leaving flux to neighbor == entering flux from opposite neighbor
!* In case of reduced transmissivity, part of the leaving flux is stored as dead dislocation density. !* In case of reduced transmissivity, part of the leaving flux is stored as dead dislocation density.
!* That means for an interface of zero transmissivity the leaving flux is fully converted to dead dislocations. !* That means for an interface of zero transmissivity the leaving flux is fully converted to dead dislocations.
considerLeavingFlux = .true.
if (opposite_n > 0) then if (opposite_n > 0) then
if (phase_plasticity(material_phaseAt(1,opposite_el)) /= PLASTICITY_NONLOCAL_ID) & if (phase_plasticity(material_phaseAt(1,opposite_el)) == PLASTICITY_NONLOCAL_ID) then
considerLeavingFlux = .false.
endif
leavingFlux: if (considerLeavingFlux) then
normal_me2neighbor_defConf = math_det33(Favg) & normal_me2neighbor_defConf = math_det33(Favg) &
* matmul(math_inv33(transpose(Favg)), & * matmul(math_inv33(transpose(Favg)),IPareaNormal(1:3,n,ip,el)) ! normal of the interface in (average) deformed configuration (pointing me => neighbor)
IPareaNormal(1:3,n,ip,el)) ! calculate the normal of the interface in (average) deformed configuration (pointing from me to my neighbor!!!)
normal_me2neighbor = matmul(transpose(my_Fe), normal_me2neighbor_defConf) & normal_me2neighbor = matmul(transpose(my_Fe), normal_me2neighbor_defConf) &
/ math_det33(my_Fe) ! interface normal in my lattice configuration / math_det33(my_Fe) ! interface normal in my lattice configuration
area = IParea(n,ip,el) * norm2(normal_me2neighbor) area = IParea(n,ip,el) * norm2(normal_me2neighbor)
@ -1531,7 +1371,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
endif endif
enddo enddo
enddo enddo
endif leavingFlux endif; endif
enddo neighbors enddo neighbors
endif endif
@ -1583,10 +1423,9 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
!*** thermally activated annihilation of edge dipoles by climb !*** thermally activated annihilation of edge dipoles by climb
rhoDotThermalAnnihilation = 0.0_pReal rhoDotThermalAnnihilation = 0.0_pReal
selfDiffusion = prm%Dsd0 * exp(-prm%selfDiffusionEnergy / (KB * Temperature)) selfDiffusion = prm%Dsd0 * exp(-prm%selfDiffusionEnergy / (kB * Temperature))
vClimb = prm%atomicVolume * selfDiffusion / ( KB * Temperature ) & vClimb = prm%atomicVolume * selfDiffusion * prm%mu &
* prm%mu / ( 2.0_pReal * PI * (1.0_pReal-prm%nu) ) & / ( kB * Temperature * PI * (1.0_pReal-prm%nu) * (dUpper(:,1) + dLower(:,1)))
* 2.0_pReal / ( dUpper(:,1) + dLower(:,1) )
forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) & forall (s = 1:ns, dUpper(s,1) > dLower(s,1)) &
rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), & rhoDotThermalAnnihilation(s,9) = max(- 4.0_pReal * rhoDip(s,1) * vClimb(s) / (dUpper(s,1) - dLower(s,1)), &
- rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) & - rhoDip(s,1) / timestep - rhoDotAthermalAnnihilation(s,9) &
@ -1640,6 +1479,7 @@ module subroutine plastic_nonlocal_dotState(Mp, F, Fp, Temperature,timestep, &
end subroutine plastic_nonlocal_dotState end subroutine plastic_nonlocal_dotState
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief Compatibility update !> @brief Compatibility update
!> @detail Compatibility is defined as normalized product of signed cosine of the angle between the slip !> @detail Compatibility is defined as normalized product of signed cosine of the angle between the slip
@ -1828,6 +1668,120 @@ module subroutine plastic_nonlocal_results(instance,group)
end subroutine plastic_nonlocal_results end subroutine plastic_nonlocal_results
!--------------------------------------------------------------------------------------------------
!> @brief calculates kinetics
!--------------------------------------------------------------------------------------------------
subroutine kinetics(v, dv_dtau, dv_dtauNS, tau, tauNS, tauThreshold, c, Temperature, instance, of)
integer, intent(in) :: &
c, & !< dislocation character (1:edge, 2:screw)
instance, of
real(pReal), intent(in) :: &
Temperature !< temperature
real(pReal), dimension(param(instance)%totalNslip), intent(in) :: &
tau, & !< resolved external shear stress (without non Schmid effects)
tauNS, & !< resolved external shear stress (including non Schmid effects)
tauThreshold !< threshold shear stress
real(pReal), dimension(param(instance)%totalNslip), intent(out) :: &
v, & !< velocity
dv_dtau, & !< velocity derivative with respect to resolved shear stress (without non Schmid contributions)
dv_dtauNS !< velocity derivative with respect to resolved shear stress (including non Schmid contributions)
integer :: &
ns, & !< short notation for the total number of active slip systems
s !< index of my current slip system
real(pReal) :: &
tauRel_P, &
tauRel_S, &
tauEff, & !< effective shear stress
tPeierls, & !< waiting time in front of a peierls barriers
tSolidSolution, & !< waiting time in front of a solid solution obstacle
vViscous, & !< viscous glide velocity
dtPeierls_dtau, & !< derivative with respect to resolved shear stress
dtSolidSolution_dtau, & !< derivative with respect to resolved shear stress
meanfreepath_S, & !< mean free travel distance for dislocations between two solid solution obstacles
meanfreepath_P, & !< mean free travel distance for dislocations between two Peierls barriers
jumpWidth_P, & !< depth of activated area
jumpWidth_S, & !< depth of activated area
activationLength_P, & !< length of activated dislocation line
activationLength_S, & !< length of activated dislocation line
activationVolume_P, & !< volume that needs to be activated to overcome barrier
activationVolume_S, & !< volume that needs to be activated to overcome barrier
activationEnergy_P, & !< energy that is needed to overcome barrier
activationEnergy_S, & !< energy that is needed to overcome barrier
criticalStress_P, & !< maximum obstacle strength
criticalStress_S, & !< maximum obstacle strength
mobility !< dislocation mobility
associate(prm => param(instance))
ns = prm%totalNslip
v = 0.0_pReal
dv_dtau = 0.0_pReal
dv_dtauNS = 0.0_pReal
do s = 1,ns
if (abs(tau(s)) > tauThreshold(s)) then
!* Peierls contribution
!* Effective stress includes non Schmid constributions
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = max(0.0_pReal, abs(tauNS(s)) - tauThreshold(s)) ! ensure that the effective stress is positive
meanfreepath_P = prm%burgers(s)
jumpWidth_P = prm%burgers(s)
activationLength_P = prm%doublekinkwidth *prm%burgers(s)
activationVolume_P = activationLength_P * jumpWidth_P * prm%burgers(s)
criticalStress_P = prm%peierlsStress(s,c)
activationEnergy_P = criticalStress_P * activationVolume_P
tauRel_P = min(1.0_pReal, tauEff / criticalStress_P) ! ensure that the activation probability cannot become greater than one
tPeierls = 1.0_pReal / prm%fattack &
* exp(activationEnergy_P / (kB * Temperature) &
* (1.0_pReal - tauRel_P**prm%p)**prm%q)
if (tauEff < criticalStress_P) then
dtPeierls_dtau = tPeierls * prm%p * prm%q * activationVolume_P / (kB * Temperature) &
* (1.0_pReal - tauRel_P**prm%p)**(prm%q-1.0_pReal) * tauRel_P**(prm%p-1.0_pReal)
else
dtPeierls_dtau = 0.0_pReal
endif
!* Contribution from solid solution strengthening
!* The derivative only gives absolute values; the correct sign is taken care of in the formula for the derivative of the velocity
tauEff = abs(tau(s)) - tauThreshold(s)
meanfreepath_S = prm%burgers(s) / sqrt(prm%solidSolutionConcentration)
jumpWidth_S = prm%solidSolutionSize * prm%burgers(s)
activationLength_S = prm%burgers(s) / sqrt(prm%solidSolutionConcentration)
activationVolume_S = activationLength_S * jumpWidth_S * prm%burgers(s)
activationEnergy_S = prm%solidSolutionEnergy
criticalStress_S = activationEnergy_S / activationVolume_S
tauRel_S = min(1.0_pReal, tauEff / criticalStress_S) ! ensure that the activation probability cannot become greater than one
tSolidSolution = 1.0_pReal / prm%fattack &
* exp(activationEnergy_S / (kB * Temperature)* (1.0_pReal - tauRel_S**prm%p)**prm%q)
if (tauEff < criticalStress_S) then
dtSolidSolution_dtau = tSolidSolution * prm%p * prm%q * activationVolume_S / (kB * Temperature) &
* (1.0_pReal - tauRel_S**prm%p)**(prm%q-1.0_pReal)* tauRel_S**(prm%p-1.0_pReal)
else
dtSolidSolution_dtau = 0.0_pReal
endif
!* viscous glide velocity
tauEff = abs(tau(s)) - tauThreshold(s)
mobility = prm%burgers(s) / prm%viscosity
vViscous = mobility * tauEff
!* Mean velocity results from waiting time at peierls barriers and solid solution obstacles with respective meanfreepath of
!* free flight at glide velocity in between.
!* adopt sign from resolved stress
v(s) = sign(1.0_pReal,tau(s)) &
/ (tPeierls / meanfreepath_P + tSolidSolution / meanfreepath_S + 1.0_pReal / vViscous)
dv_dtau(s) = v(s)**2.0_pReal * (dtSolidSolution_dtau / meanfreepath_S + mobility /vViscous**2.0_pReal)
dv_dtauNS(s) = v(s)**2.0_pReal * dtPeierls_dtau / meanfreepath_P
endif
enddo
end associate
end subroutine kinetics
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief returns copy of current dislocation densities from state !> @brief returns copy of current dislocation densities from state
!> @details raw values is rectified !> @details raw values is rectified