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general polishing

This commit is contained in:
Martin Diehl 2018-08-31 16:08:01 +02:00
parent 912926e604
commit 7a67922c5f
1 changed files with 160 additions and 209 deletions
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src/plastic_dislotwin.f90
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@ -17,6 +17,8 @@ module plastic_dislotwin
real(pReal), parameter, private :: & real(pReal), parameter, private :: &
kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin kB = 1.38e-23_pReal !< Boltzmann constant in J/Kelvin
! START: Do something here
real(pReal), dimension(:,:), allocatable, private :: & real(pReal), dimension(:,:), allocatable, private :: &
tau_r_twin, & !< stress to bring partial close together for each twin system and instance tau_r_twin, & !< stress to bring partial close together for each twin system and instance
tau_r_trans !< stress to bring partial close together for each trans system and instance tau_r_trans !< stress to bring partial close together for each trans system and instance
@ -25,6 +27,7 @@ module plastic_dislotwin
projectionMatrix_Trans !< matrix for projection of slip system shear on fault band (twin) systems for each instance projectionMatrix_Trans !< matrix for projection of slip system shear on fault band (twin) systems for each instance
real(pReal), dimension(:,:,:,:,:), allocatable, private :: & real(pReal), dimension(:,:,:,:,:), allocatable, private :: &
sbSv sbSv
! END: Do something here
enum, bind(c) enum, bind(c)
enumerator :: undefined_ID, & enumerator :: undefined_ID, &
@ -232,7 +235,7 @@ subroutine plastic_dislotwin_init(fileUnit)
integer(pInt) :: NofMyPhase integer(pInt) :: NofMyPhase
integer(kind(undefined_ID)) outputID integer(kind(undefined_ID)) outputID
real(pReal), dimension(:,:,:,:,:), allocatable :: & real(pReal), dimension(:,:,:,:,:), allocatable :: &
Ctwin3333, & !< twin elasticity matrix Ctwin3333, & !< twin elasticity matrix
Ctrans3333 !< trans elasticity matrix Ctrans3333 !< trans elasticity matrix
@ -282,9 +285,8 @@ subroutine plastic_dislotwin_init(fileUnit)
allocate(param(maxNinstance)) allocate(param(maxNinstance))
allocate(state(maxNinstance)) allocate(state(maxNinstance))
allocate(dotState(maxNinstance)) allocate(dotState(maxNinstance))
allocate(sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), source=0.0_pReal)
allocate(sbSv(6,6,homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), source=0.0_pReal)
do p = 1_pInt, size(phase_plasticityInstance) do p = 1_pInt, size(phase_plasticityInstance)
if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle if (phase_plasticity(p) /= PLASTICITY_DISLOTWIN_ID) cycle
@ -389,7 +391,10 @@ subroutine plastic_dislotwin_init(fileUnit)
if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then if (prm%totalNslip > 0_pInt .and. prm%totalNtwin > 0_pInt) then
prm%interaction_SlipTwin = spread(config_phase(p)%getFloats('interaction_sliptwin'),2,1) prm%interaction_SlipTwin = spread(config_phase(p)%getFloats('interaction_sliptwin'),2,1)
prm%interaction_TwinSlip = spread(config_phase(p)%getFloats('interaction_twinslip'),2,1) prm%interaction_TwinSlip = spread(config_phase(p)%getFloats('interaction_twinslip'),2,1)
endif prm%p = math_expand(prm%p,prm%Nslip)
prm%q = math_expand(prm%q,prm%Nslip)
prm%tau_peierls = math_expand(prm%tau_peierls,prm%Nslip)
endif
if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then if (prm%totalNslip > 0_pInt .and. prm%totalNtrans > 0_pInt) then
prm%interaction_TransSlip = spread(config_phase(p)%getFloats('interaction_transslip'),2,1) prm%interaction_TransSlip = spread(config_phase(p)%getFloats('interaction_transslip'),2,1)
@ -578,11 +583,8 @@ subroutine plastic_dislotwin_init(fileUnit)
prm%qShearBand <= 0.0_pReal) & prm%qShearBand <= 0.0_pReal) &
call IO_error(211_pInt,el=instance,ext_msg='qShearBand ('//PLASTICITY_DISLOTWIN_label//')') call IO_error(211_pInt,el=instance,ext_msg='qShearBand ('//PLASTICITY_DISLOTWIN_label//')')
prm%p = math_expand(prm%p,prm%Nslip)
prm%q = math_expand(prm%q,prm%Nslip)
prm%tau_peierls = math_expand(prm%tau_peierls,prm%Nslip)
enddo enddo
! ToDo: this works only for one instance!
allocate(forestProjectionEdge(prm%totalNslip,prm%totalNslip,maxNinstance), source=0.0_pReal) allocate(forestProjectionEdge(prm%totalNslip,prm%totalNslip,maxNinstance), source=0.0_pReal)
allocate(projectionMatrix_Trans(prm%totalNtrans,prm%totalNslip,maxNinstance), source=0.0_pReal) allocate(projectionMatrix_Trans(prm%totalNtrans,prm%totalNslip,maxNinstance), source=0.0_pReal)
@ -1184,17 +1186,19 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
real(pReal), dimension(3,3), intent(out) :: Lp real(pReal), dimension(3,3), intent(out) :: Lp
real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99 real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99
integer(pInt) :: instance,ph,of,f,i,j,k,l,m,n,index_myFamily,s1,s2 integer(pInt) :: instance,ph,of,j,k,l,m,n,s1,s2
real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0_twin,stressRatio, & real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,&
Ndot0_trans,StressRatio_s StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0_twin,stressRatio, &
real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 Ndot0_trans,StressRatio_s, &
tau_twin, tau_trans, &
gdot_twin,dgdot_dtautwin, &
gdot_trans,dgdot_dtautrans, &
dgdot_dtauslip, &
tau_slip
real(pReal), dimension(3,3,3,3) :: dLp_dS
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: & real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
gdot_slip,dgdot_dtauslip,tau_slip gdot_slip
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: & real(pReal):: gdot_sb,dgdot_dtausb,tau_sb
gdot_twin,dgdot_dtautwin,tau_twin
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntrans) :: &
gdot_trans,dgdot_dtautrans,tau_trans
real(pReal), dimension(6) :: gdot_sb,dgdot_dtausb,tau_sb
real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix
real(pReal), dimension(3) :: eigValues, sb_s, sb_m real(pReal), dimension(3) :: eigValues, sb_s, sb_m
logical :: error logical :: error
@ -1229,46 +1233,43 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
Lp = 0.0_pReal Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal dLp_dS = 0.0_pReal
S = math_Mandel6to33(Tstar_v) S = math_Mandel6to33(Tstar_v)
associate(prm => param(instance)) associate(prm => param(instance))
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! Dislocation glide part ! Dislocation glide part
gdot_slip = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
slipSystems: do j = 1_pInt, prm%totalNslip slipSystems: do j = 1_pInt, prm%totalNslip
tau_slip = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
tau_slip(j) = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j)) significantSlipStress: if((abs(tau_slip)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
stressRatio =((abs(tau_slip)- state(instance)%threshold_stress_slip(j,of))/&
if((abs(tau_slip(j))-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
stressRatio =((abs(tau_slip(j))- state(instance)%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+prm%tau_peierls(j))) (prm%SolidSolutionStrength+prm%tau_peierls(j)))
StressRatio_p = stressRatio** prm%p(j) StressRatio_p = stressRatio** prm%p(j)
StressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal) ! ToDo: no very helpful StressRatio_pminus1 = stressRatio**(prm%p(j)-1.0_pReal) ! ToDo: no very helpful
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature) BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j) DotGamma0 = state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
gdot_slip(j) = DotGamma0 *sign(exp(-BoltzmannRatio*(1-StressRatio_p)** prm%q(j)), tau_slip)
!* Shear rates due to slip
gdot_slip(j) = DotGamma0 *sign(exp(-BoltzmannRatio*(1-StressRatio_p)** prm%q(j)), tau_slip(j))
!* Derivatives of shear rates !* Derivatives of shear rates
dgdot_dtauslip(j) = abs(gdot_slip(j))*BoltzmannRatio*prm%p(j) * prm%q(j) & dgdot_dtauslip = abs(gdot_slip(j))*BoltzmannRatio*prm%p(j) * prm%q(j) &
/ (prm%SolidSolutionStrength+prm%tau_peierls(j)) & / (prm%SolidSolutionStrength+prm%tau_peierls(j)) &
* StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal) * StressRatio_pminus1*(1-StressRatio_p)**(prm%q(j)-1.0_pReal)
endif else significantSlipStress
gdot_slip(j) = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
endif significantSlipStress
Lp = Lp + gdot_slip(j)*prm%Schmid_slip(1:3,1:3,j) Lp = Lp + gdot_slip(j)*prm%Schmid_slip(1:3,1:3,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtauslip(j) * prm%Schmid_slip(k,l,j) * prm%Schmid_slip(m,n,j) + dgdot_dtauslip * prm%Schmid_slip(k,l,j) * prm%Schmid_slip(m,n,j)
enddo slipSystems enddo slipSystems
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! correct Lp and dLp_dTstar3333 for twinned and transformed fraction ! correct Lp and dLp_dS for twinned and transformed fraction
!* Total twin volume fraction !* Total twin volume fraction
sumf = sum(state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0 sumf = sum(state(instance)%twinFraction(1_pInt:prm%totalNtwin,of)) ! safe for prm%totalNtwin == 0
@ -1276,13 +1277,11 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + & sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of)) sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of))
Lp = Lp * (1.0_pReal - sumf - sumftr) Lp = Lp * (1.0_pReal - sumf - sumftr)
dLp_dTstar3333 = dLp_dTstar3333 * (1.0_pReal - sumf - sumftr) dLp_dS = dLp_dS * (1.0_pReal - sumf - sumftr)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! Shear banding (shearband) part ! Shear banding (shearband) part
if(dNeq0(prm%sbVelocity)) then if(dNeq0(prm%sbVelocity)) then
gdot_sb = 0.0_pReal
dgdot_dtausb = 0.0_pReal
call math_eigenValuesVectorsSym(S,eigValues,eigVectors,error) call math_eigenValuesVectorsSym(S,eigValues,eigVectors,error)
do j = 1_pInt,6_pInt do j = 1_pInt,6_pInt
sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j)) sb_s = 0.5_pReal*sqrt(2.0_pReal)*math_mul33x3(eigVectors,sb_sComposition(1:3,j))
@ -1292,122 +1291,99 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
!* Calculation of Lp !* Calculation of Lp
!* Resolved shear stress on shear banding system !* Resolved shear stress on shear banding system
tau_sb(j) = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el)) tau_sb = dot_product(Tstar_v,sbSv(1:6,j,ipc,ip,el))
!* Stress ratios !* Stress ratios
if (abs(tau_sb(j)) < tol_math_check) then if (abs(tau_sb) < tol_math_check) then
StressRatio_p = 0.0_pReal StressRatio_p = 0.0_pReal
StressRatio_pminus1 = 0.0_pReal StressRatio_pminus1 = 0.0_pReal
else else
StressRatio_p = (abs(tau_sb(j))/prm%sbResistance)& StressRatio_p = (abs(tau_sb)/prm%sbResistance)**prm%pShearBand
**prm%pShearBand StressRatio_pminus1 = (abs(tau_sb)/prm%sbResistance)**(prm%pShearBand-1.0_pReal)
StressRatio_pminus1 = (abs(tau_sb(j))/prm%sbResistance)& endif
**(prm%pShearBand-1.0_pReal)
endif
BoltzmannRatio = prm%sbQedge/(kB*Temperature) BoltzmannRatio = prm%sbQedge/(kB*Temperature)
!* Initial shear rates gdot_sb = sign(prm%sbVelocity*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%qShearBand), tau_sb)
DotGamma0 = prm%sbVelocity dgdot_dtausb = ((abs(gdot_sb)*BoltzmannRatio* prm%pShearBand*prm%qShearBand)/ prm%sbResistance) &
* StressRatio_pminus1*(1_pInt-StressRatio_p)**(prm%qShearBand-1.0_pReal)
!* Shear rates due to shearband Lp = Lp + gdot_sb*sb_Smatrix
gdot_sb(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
prm%qShearBand)*sign(1.0_pReal,tau_sb(j))
!* Derivatives of shear rates
dgdot_dtausb(j) = &
((abs(gdot_sb(j))*BoltzmannRatio*&
prm%pShearBand*prm%qShearBand)/&
prm%sbResistance)*&
StressRatio_pminus1*(1_pInt-StressRatio_p)**(prm%qShearBand-1.0_pReal)
Lp = Lp + gdot_sb(j)*sb_Smatrix
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtausb(j)* sb_Smatrix(k,l) * sb_Smatrix(m,n) + dgdot_dtausb * sb_Smatrix(k,l) * sb_Smatrix(m,n)
enddo enddo
end if end if
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
twinSystems: do j = 1_pInt, prm%totalNtwin twinSystems: do j = 1_pInt, prm%totalNtwin
tau_twin = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,j))
tau_twin(j) = math_mul33xx33(S,prm%Schmid_twin(1:3,1:3,j)) significantTwinStress: if (tau_twin > tol_math_check) then
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/tau_twin)**prm%r(j)
if (tau_twin(j) > tol_math_check) then isFCCtwin: if (lattice_structure(ph) == LATTICE_FCC_ID) then
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/tau_twin(j))**prm%r(f)
!* Shear rates and their derivatives due to twin
if (lattice_structure(ph) == LATTICE_FCC_ID) then
s1=prm%fcc_twinNucleationSlipPair(1,j) s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j) s2=prm%fcc_twinNucleationSlipPair(2,j)
if (tau_twin(j) < tau_r_twin(j,instance)) then if (tau_twin < tau_r_twin(j,instance)) then
Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(ph)%rhoEdgeDip(s2,of))+& !!!!! correct? Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(ph)%rhoEdgeDip(s2,of))+& !!!!! correct?
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/& abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
(prm%L0_twin*prm%burgers_slip(j))*& (prm%L0_twin*prm%burgers_slip(j))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(tau_r_twin(j,instance)-tau_twin(j)))) (tau_r_twin(j,instance)-tau_twin)))
else else
Ndot0_twin=0.0_pReal Ndot0_twin=0.0_pReal
end if end if
else else isFCCtwin
Ndot0_twin=prm%Ndot0_twin(j) Ndot0_twin=prm%Ndot0_twin(j)
endif endif isFCCtwin
gdot_twin(j) = & gdot_twin = (1.0_pReal-sumf-sumftr)*prm%shear_twin(j)*&
(1.0_pReal-sumf-sumftr)*prm%shear_twin(j)*&
state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r) state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
dgdot_dtautwin(j) = ((gdot_twin(j)*prm%r(j))/tau_twin(j))*StressRatio_r dgdot_dtautwin = ((gdot_twin*prm%r(j))/tau_twin)*StressRatio_r
endif else significantTwinStress
gdot_twin = 0.0_pReal
dgdot_dtautwin = 0.0_pReal
endif significantTwinStress
Lp = Lp + gdot_twin(j)*prm%Schmid_twin(1:3,1:3,j) Lp = Lp + gdot_twin*prm%Schmid_twin(1:3,1:3,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) & forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) & dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtautwin(j)* prm%Schmid_twin(k,l,j)*prm%Schmid_twin(m,n,j) + dgdot_dtautwin* prm%Schmid_twin(k,l,j)*prm%Schmid_twin(m,n,j)
enddo twinSystems enddo twinSystems
!* Phase transformation part
gdot_trans = 0.0_pReal
dgdot_dtautrans = 0.0_pReal
j = 0_pInt
transSystems: do j = 1_pInt, prm%totalNtrans transSystems: do j = 1_pInt, prm%totalNtrans
tau_trans(j) = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j)) tau_trans = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j))
significantTransStress: if (tau_trans > tol_math_check) then
!* Stress ratios StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/tau_trans)**prm%s(j)
if (tau_trans(j) > tol_math_check) then isFCCtrans: if (lattice_structure(ph) == LATTICE_FCC_ID) then
StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/tau_trans(j))**prm%s(f)
!* Shear rates and their derivatives due to transformation
if (lattice_structure(ph) == LATTICE_FCC_ID) then
s1=prm%fcc_twinNucleationSlipPair(1,j) s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j) s2=prm%fcc_twinNucleationSlipPair(2,j)
if (tau_trans(j) < tau_r_trans(j,instance)) then if (tau_trans < tau_r_trans(j,instance)) then
Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+& !!!!! correct? Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+& !!!!! correct?
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/& abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
(prm%L0_trans*prm%burgers_slip(j))*& (prm%L0_trans*prm%burgers_slip(j))*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(tau_r_trans(j,instance)-tau_trans(j)))) (tau_r_trans(j,instance)-tau_trans)))
else else
Ndot0_trans=0.0_pReal Ndot0_trans=0.0_pReal
end if end if
else else isFCCtrans
Ndot0_trans=prm%Ndot0_trans(j) Ndot0_trans=prm%Ndot0_trans(j)
endif endif isFCCtrans
gdot_trans(j) = & gdot_trans = (1.0_pReal-sumf-sumftr)* state(instance)%martensiteVolume(j,of) &
(1.0_pReal-sumf-sumftr)*& * Ndot0_trans*exp(-StressRatio_s)
state(instance)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s) dgdot_dtautrans = ((gdot_trans*prm%s(j))/tau_trans)*StressRatio_s
dgdot_dtautrans(j) = ((gdot_trans(j)*prm%s(f))/tau_trans(j))*StressRatio_s else significantTransStress
endif gdot_trans = 0.0_pReal
dgdot_dtautrans = 0.0_pReal
endif significantTransStress
!* Plastic velocity gradient for phase transformation Lp = Lp + gdot_trans*prm%Schmid_trans(1:3,1:3,j)
Lp = Lp + gdot_trans(j)*prm%Schmid_trans(1:3,1:3,j)
!* Calculation of the tangent of Lp
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) &
+ dgdot_dtautrans(j) * prm%Schmid_trans(k,l,j)* prm%Schmid_trans(m,n,j)
forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
dLp_dS(k,l,m,n) = dLp_dS(k,l,m,n) &
+ dgdot_dtautrans * prm%Schmid_trans(k,l,j)* prm%Schmid_trans(m,n,j)
enddo transSystems enddo transSystems
end associate end associate
dLp_dTstar99 = math_Plain3333to99(dLp_dTstar3333)
dLp_dTstar99 = math_Plain3333to99(dLp_dS)
end subroutine plastic_dislotwin_LpAndItsTangent end subroutine plastic_dislotwin_LpAndItsTangent
@ -1443,20 +1419,19 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
ip, & !< integration point ip, & !< integration point
el !< element el !< element
integer(pInt) :: instance,f,i,j,index_myFamily,s1,s2, & integer(pInt) :: instance,j,s1,s2, &
ph, & ph, &
of of
real(pReal) :: sumf,sumftr,StressRatio_p,BoltzmannRatio,DotGamma0,& real(pReal) :: sumf,sumftr,StressRatio_p,BoltzmannRatio,DotGamma0,&
EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,& EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,&
Ndot0_trans,StressRatio_s,EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, & Ndot0_trans,StressRatio_s,EdgeDipDistance, ClimbVelocity,DotRhoEdgeDipClimb,DotRhoEdgeDipAnnihilation, &
DotRhoDipFormation,DotRhoMultiplication,DotRhoEdgeEdgeAnnihilation DotRhoDipFormation,DotRhoMultiplication,DotRhoEdgeEdgeAnnihilation, &
tau_twin, &
tau_trans, &
tau_slip
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: & real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Nslip) :: &
gdot_slip,tau_slip gdot_slip
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntwin) :: &
tau_twin
real(pReal), dimension(plasticState(material_phase(ipc,ip,el))%Ntrans) :: &
tau_trans
real(pReal), dimension(3,3) :: & real(pReal), dimension(3,3) :: &
S !< Second-Piola Kirchhoff stress S !< Second-Piola Kirchhoff stress
@ -1478,46 +1453,35 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + & sumftr = sum(state(instance)%stressTransFraction(1_pInt:prm%totalNtrans,of)) + &
sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of)) sum(state(instance)%strainTransFraction(1_pInt:prm%totalNtrans,of))
!* Dislocation density evolution
gdot_slip = 0.0_pReal
slipSystems: do j = 1_pInt, prm%totalNslip slipSystems: do j = 1_pInt, prm%totalNslip
tau_slip(j) = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j)) tau_slip = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
significantSlipStress1: if((abs(tau_slip)-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then
if((abs(tau_slip(j))-state(instance)%threshold_stress_slip(j,of)) > tol_math_check) then stressRatio =((abs(tau_slip)- state(instance)%threshold_stress_slip(j,of))/&
stressRatio =((abs(tau_slip(j))- state(instance)%threshold_stress_slip(j,of))/&
(prm%SolidSolutionStrength+prm%tau_peierls(j))) (prm%SolidSolutionStrength+prm%tau_peierls(j)))
StressRatio_p = stressRatio** prm%p(j) StressRatio_p = stressRatio** prm%p(j)
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature) BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
!* Initial shear rates
DotGamma0 = plasticState(ph)%state(j, of)*prm%burgers_slip(j)*prm%v0(j) DotGamma0 = plasticState(ph)%state(j, of)*prm%burgers_slip(j)*prm%v0(j)
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**prm%q(j))*sign(1.0_pReal,tau_slip)
!* Shear rates due to slip else significantSlipStress1
gdot_slip(j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)** & gdot_slip(j) = 0.0_pReal
prm%q(j))*sign(1.0_pReal,tau_slip(j)) endif significantSlipStress1
endif
!* Multiplication
DotRhoMultiplication = abs(gdot_slip(j))/(prm%burgers_slip(j)*state(instance)%mfp_slip(j,of)) DotRhoMultiplication = abs(gdot_slip(j))/(prm%burgers_slip(j)*state(instance)%mfp_slip(j,of))
!* Dipole formation
EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip(j) EdgeDipMinDistance = prm%CEdgeDipMinDistance*prm%burgers_slip(j)
if (dEq0(tau_slip(j))) then significantSlipStress2: if (dEq0(tau_slip)) then
DotRhoDipFormation = 0.0_pReal DotRhoDipFormation = 0.0_pReal
else else significantSlipStress2
EdgeDipDistance = & EdgeDipDistance = (3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j))/&
(3.0_pReal*lattice_mu(ph)*prm%burgers_slip(j))/& (16.0_pReal*PI*abs(tau_slip))
(16.0_pReal*pi*abs(tau_slip(j)))
if (EdgeDipDistance>state(instance)%mfp_slip(j,of)) EdgeDipDistance=state(instance)%mfp_slip(j,of) if (EdgeDipDistance>state(instance)%mfp_slip(j,of)) EdgeDipDistance=state(instance)%mfp_slip(j,of)
if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance if (EdgeDipDistance<EdgeDipMinDistance) EdgeDipDistance=EdgeDipMinDistance
DotRhoDipFormation = & DotRhoDipFormation = ((2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance))/prm%burgers_slip(j))*&
((2.0_pReal*(EdgeDipDistance-EdgeDipMinDistance))/prm%burgers_slip(j))*&
state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))*prm%dipoleFormationFactor state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))*prm%dipoleFormationFactor
endif endif significantSlipStress2
!* Spontaneous annihilation of 2 single edge dislocations !* Spontaneous annihilation of 2 single edge dislocations
DotRhoEdgeEdgeAnnihilation = & DotRhoEdgeEdgeAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j))*&
((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j))*& state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))
state(instance)%rhoEdge(j,of)*abs(gdot_slip(j))
!* Spontaneous annihilation of a single edge dislocation with a dipole constituent !* Spontaneous annihilation of a single edge dislocation with a dipole constituent
DotRhoEdgeDipAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j)) & DotRhoEdgeDipAnnihilation = ((2.0_pReal*EdgeDipMinDistance)/prm%burgers_slip(j)) &
* state(instance)%rhoEdgeDip(j,of)*abs(gdot_slip(j)) * state(instance)%rhoEdgeDip(j,of)*abs(gdot_slip(j))
@ -1525,7 +1489,7 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
!* Dislocation dipole climb !* Dislocation dipole climb
AtomicVolume = prm%CAtomicVolume*prm%burgers_slip(j)**(3.0_pReal) ! no need to calculate this over and over again AtomicVolume = prm%CAtomicVolume*prm%burgers_slip(j)**(3.0_pReal) ! no need to calculate this over and over again
VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature)) VacancyDiffusion = prm%D0*exp(-prm%Qsd/(kB*Temperature))
if (dEq0(tau_slip(j))) then if (dEq0(tau_slip)) then
DotRhoEdgeDipClimb = 0.0_pReal DotRhoEdgeDipClimb = 0.0_pReal
else else
if (dEq0(EdgeDipDistance-EdgeDipMinDistance)) then if (dEq0(EdgeDipDistance-EdgeDipMinDistance)) then
@ -1537,72 +1501,62 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
(EdgeDipDistance-EdgeDipMinDistance) (EdgeDipDistance-EdgeDipMinDistance)
endif endif
endif endif
dotState(instance)%rhoEdge(j,of) = DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation dotState(instance)%rhoEdge(j,of) = DotRhoMultiplication-DotRhoDipFormation-DotRhoEdgeEdgeAnnihilation
dotState(instance)%rhoEdgeDip(j,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb dotState(instance)%rhoEdgeDip(j,of) = DotRhoDipFormation-DotRhoEdgeDipAnnihilation-DotRhoEdgeDipClimb
dotState(instance)%accshear_slip(j,of) = abs(gdot_slip(j)) dotState(instance)%accshear_slip(j,of) = abs(gdot_slip(j))
enddo slipSystems enddo slipSystems
twinSystems: do j = 1_pInt, prm%totalNtwin twinSystems: do j = 1_pInt, prm%totalNtwin
tau_twin(j) = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j)) tau_twin = math_mul33xx33(S,prm%Schmid_slip(1:3,1:3,j))
if (tau_twin(j) > tol_math_check) then significantTwinStress: if (tau_twin > tol_math_check) then
StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/& StressRatio_r = (state(instance)%threshold_stress_twin(j,of)/tau_twin)**prm%r(j)
tau_twin(j))**prm%r(j) isFCCtwin: if (lattice_structure(ph) == LATTICE_FCC_ID) then
if (lattice_structure(ph) == LATTICE_FCC_ID) then
s1=prm%fcc_twinNucleationSlipPair(1,j) s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j) s2=prm%fcc_twinNucleationSlipPair(2,j)
if (tau_twin(j) < tau_r_twin(j,instance)) then if (tau_twin < tau_r_twin(j,instance)) then
Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+& Ndot0_twin=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/& abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
(prm%L0_twin*prm%burgers_slip(j))*& (prm%L0_twin*prm%burgers_slip(j))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (tau_r_twin(j,instance)-tau_twin)))
(tau_r_twin(j,instance)-tau_twin(j)))) else
else Ndot0_twin=0.0_pReal
Ndot0_twin=0.0_pReal end if
end if else isFCCtwin
else Ndot0_twin=prm%Ndot0_twin(j)
Ndot0_twin=prm%Ndot0_twin(j) endif isFCCtwin
endif dotState(instance)%twinFraction(j,of) = (1.0_pReal-sumf-sumftr)*&
dotState(instance)%twinFraction(j,of) = & state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
(1.0_pReal-sumf-sumftr)*& dotState(instance)%accshear_twin(j,of) = dotState(instance)%twinFraction(j,of) * prm%shear_twin(j)
state(instance)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r) endif significantTwinStress
dotState(instance)%accshear_twin(j,of) = dotState(instance)%twinFraction(j,of) * &
prm%shear_twin(j)
endif
enddo twinSystems enddo twinSystems
transSystems: do j = 1_pInt, prm%totalNtrans transSystems: do j = 1_pInt, prm%totalNtrans
tau_trans = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j))
tau_trans(j) = math_mul33xx33(S,prm%Schmid_trans(1:3,1:3,j)) significantTransStress: if (tau_trans > tol_math_check) then
StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/tau_trans)**prm%s(j)
if (tau_trans(j) > tol_math_check) then isFCCtrans: if (lattice_structure(ph) == LATTICE_FCC_ID) then
StressRatio_s = (state(instance)%threshold_stress_trans(j,of)/&
tau_trans(j))**prm%s(f)
if (lattice_structure(ph) == LATTICE_FCC_ID) then
s1=prm%fcc_twinNucleationSlipPair(1,j) s1=prm%fcc_twinNucleationSlipPair(1,j)
s2=prm%fcc_twinNucleationSlipPair(2,j) s2=prm%fcc_twinNucleationSlipPair(2,j)
if (tau_trans(j) < tau_r_trans(j,instance)) then if (tau_trans < tau_r_trans(j,instance)) then
Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+& Ndot0_trans=(abs(gdot_slip(s1))*(state(instance)%rhoEdge(s2,of)+state(instance)%rhoEdgeDip(s2,of))+&
abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/& abs(gdot_slip(s2))*(state(instance)%rhoEdge(s1,of)+state(instance)%rhoEdgeDip(s1,of)))/&
(prm%L0_trans*prm%burgers_slip(j))*& (prm%L0_trans*prm%burgers_slip(j))*(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*&
(1.0_pReal-exp(-prm%VcrossSlip/(kB*Temperature)*& (tau_r_trans(j,instance)-tau_trans)))
(tau_r_trans(j,instance)-tau_trans(j)))) else
else Ndot0_trans=0.0_pReal
Ndot0_trans=0.0_pReal end if
end if else isFCCtrans
else Ndot0_trans=prm%Ndot0_trans(j)
Ndot0_trans=prm%Ndot0_trans(j) endif isFCCtrans
endif dotState(instance)%strainTransFraction(j,of) = (1.0_pReal-sumf-sumftr)*&
dotState(instance)%strainTransFraction(j,of) = & state(instance)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
(1.0_pReal-sumf-sumftr)*&
state(instance)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
!* Dotstate for accumulated shear due to transformation !* Dotstate for accumulated shear due to transformation
!dotState(instance)%accshear_trans(j,of) = dotState(instance)%strainTransFraction(j,of) * & !dotState(instance)%accshear_trans(j,of) = dotState(instance)%strainTransFraction(j,of) * &
! lattice_sheartrans(index_myfamily+i,ph) ! lattice_sheartrans(index_myfamily+i,ph)
endif endif significantTransStress
enddo transSystems enddo transSystems
end associate
end associate
end subroutine plastic_dislotwin_dotState end subroutine plastic_dislotwin_dotState
@ -1708,13 +1662,10 @@ function plastic_dislotwin_postResults(Tstar_v,Temperature,ipc,ip,el)
!* Boltzmann ratio !* Boltzmann ratio
BoltzmannRatio = prm%Qedge(j)/(kB*Temperature) BoltzmannRatio = prm%Qedge(j)/(kB*Temperature)
!* Initial shear rates !* Initial shear rates
DotGamma0 = & DotGamma0 = state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* prm%v0(j)
state(instance)%rhoEdge(j,of)*prm%burgers_slip(j)* &
prm%v0(j)
!* Shear rates due to slip !* Shear rates due to slip
plastic_dislotwin_postResults(c+j) = & plastic_dislotwin_postResults(c+j) = DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
DotGamma0*exp(-BoltzmannRatio*(1_pInt-StressRatio_p)**&
prm%q(j))*sign(1.0_pReal,tau) prm%q(j))*sign(1.0_pReal,tau)
else else
plastic_dislotwin_postResults(c+j) = 0.0_pReal plastic_dislotwin_postResults(c+j) = 0.0_pReal