Martensite volume fraction evolution
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Su Leen Wong
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@ -1595,7 +1595,7 @@ subroutine plastic_dislotwin_microstructure(temperature,ipc,ip,el)
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state(ph)%invLambdaSlipTrans(1_pInt:ns,of) = 0.0_pReal
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if (nr > 0_pInt .and. ns > 0_pInt) &
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state(ph)%invLambdaSlipTrans(1_pInt:ns,of) = &
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ftransOverLamellarSize(1:nr)/(1.0_pReal-sumftr)
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matmul(plastic_dislotwin_interactionMatrix_SlipTrans(1:ns,1:nr,instance),ftransOverLamellarSize(1:nr))/(1.0_pReal-sumftr)
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!* 1/mean free distance between 2 martensite stacks from different systems seen by a growing martensite (1/lambda_trans)
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if (nr > 0_pInt) &
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@ -1733,14 +1733,15 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
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real(pReal), dimension(9,9), intent(out) :: dLp_dTstar99
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integer(pInt) :: instance,ph,of,ns,nt,nr,f,i,j,k,l,m,n,index_myFamily,s1,s2
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real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0_twin,stressRatio
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real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,StressRatio_r,BoltzmannRatio,DotGamma0,Ndot0_twin,stressRatio, &
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Ndot0_trans,StressRatio_s
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real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333
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real(pReal), dimension(plastic_dislotwin_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip,dgdot_dtauslip,tau_slip
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real(pReal), dimension(plastic_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_twin,dgdot_dtautwin,tau_twin
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real(pReal), dimension(plastic_dislotwin_totalNtrans(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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V_trans,Vdot_trans,dVdot_dtautrans,tau_trans,fstress_trans
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gdot_trans,dgdot_dtautrans,tau_trans
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real(pReal), dimension(6) :: gdot_sb,dgdot_dtausb,tau_sb
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real(pReal), dimension(3,3) :: eigVectors, sb_Smatrix
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real(pReal), dimension(3) :: eigValues, sb_s, sb_m
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@ -1930,7 +1931,7 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
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end select
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gdot_twin(j) = &
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(1.0_pReal-sumf-sumftr)*lattice_shearTwin(index_myFamily+i,ph)*&
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state(ph)%twinvolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
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state(ph)%twinVolume(j,of)*Ndot0_twin*exp(-StressRatio_r)
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dgdot_dtautwin(j) = ((gdot_twin(j)*plastic_dislotwin_rPerTwinFamily(f,instance))/tau_twin(j))*StressRatio_r
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endif
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@ -1947,8 +1948,8 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
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enddo twinFamiliesLoop
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!* Phase transformation part
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Vdot_trans = 0.0_pReal
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dVdot_dtautrans = 0.0_pReal
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gdot_trans = 0.0_pReal
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dgdot_dtautrans = 0.0_pReal
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j = 0_pInt
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transFamiliesLoop: do f = 1_pInt,lattice_maxNtransFamily
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index_myFamily = sum(lattice_NtransSystem(1:f-1_pInt,ph)) ! at which index starts my family
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@ -1958,27 +1959,39 @@ subroutine plastic_dislotwin_LpAndItsTangent(Lp,dLp_dTstar99,Tstar_v,Temperature
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!* Resolved shear stress on transformation system
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tau_trans(j) = dot_product(Tstar_v,lattice_Strans_v(:,index_myFamily+i,ph))
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!* Total martensite volume fraction for transformation system
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V_trans(j) = state(ph)%stressTransFraction(j,of) + state(ph)%strainTransFraction(j,of)
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!* Driving force for stress-assisted martensite growth on transformation system
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fstress_trans(j) = tau_trans(j) - &
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plastic_dislotwin_Cdwp(instance)*(2*V_trans(j) - 6*V_trans(j)**2 + 4*V_trans(j)**3) - &
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12*plastic_dislotwin_deltaG(instance)*(V_trans(j)**2 - V_trans(j)**3)
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!* Transformation rate of stress-assisted martensite and its derivative
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if (fstress_trans(j) > tol_math_check) then
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Vdot_trans(j) = plastic_dislotwin_Cgro(instance)*(1.0_pReal - sumf - sumftr)*fstress_trans(j)
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dVdot_dtautrans(j) = plastic_dislotwin_Cgro(instance)*(1.0_pReal - sumf - sumftr)
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!* Stress ratios
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if (tau_trans(j) > tol_math_check) then
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StressRatio_s = (state(ph)%threshold_stress_trans(j,of)/tau_trans(j))**plastic_dislotwin_sPerTransFamily(f,instance)
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!* Shear rates and their derivatives due to transformation
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select case(lattice_structure(ph))
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case (LATTICE_fcc_ID)
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s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
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s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
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if (tau_trans(j) < plastic_dislotwin_tau_r_trans(j,instance)) then
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Ndot0_trans=(abs(gdot_slip(s1))*(state(ph)%rhoEdge(s2,of)+state(ph)%rhoEdgeDip(s2,of))+& !!!!! correct?
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abs(gdot_slip(s2))*(state(ph)%rhoEdge(s1,of)+state(ph)%rhoEdgeDip(s1,of)))/&
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(plastic_dislotwin_L0_trans(instance)*plastic_dislotwin_burgersPerSlipSystem(j,instance))*&
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(1.0_pReal-exp(-plastic_dislotwin_VcrossSlip(instance)/(kB*Temperature)*&
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(plastic_dislotwin_tau_r_trans(j,instance)-tau_trans(j))))
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else
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Ndot0_trans=0.0_pReal
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end if
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case default
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Ndot0_trans=plastic_dislotwin_Ndot0PerTransSystem(j,instance)
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end select
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gdot_trans(j) = &
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(1.0_pReal-sumf-sumftr)*&
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state(ph)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
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dgdot_dtautrans(j) = ((gdot_trans(j)*plastic_dislotwin_sPerTransFamily(f,instance))/tau_trans(j))*StressRatio_s
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endif
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!* Plastic velocity gradient for phase transformation
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Lp = Lp + Vdot_trans(j)*lattice_Strans(:,:,index_myFamily+i,ph)
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Lp = Lp + gdot_trans(j)*lattice_Strans(:,:,index_myFamily+i,ph)
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!* Calculation of the tangent of Lp
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forall (k=1_pInt:3_pInt,l=1_pInt:3_pInt,m=1_pInt:3_pInt,n=1_pInt:3_pInt) &
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dLp_dTstar3333(k,l,m,n) = &
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dLp_dTstar3333(k,l,m,n) + dVdot_dtautrans(j)*&
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dLp_dTstar3333(k,l,m,n) + dgdot_dtautrans(j)*&
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lattice_Strans(k,l,index_myFamily+i,ph)*&
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lattice_Strans(m,n,index_myFamily+i,ph)
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@ -2035,14 +2048,15 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
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ph, &
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of
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real(pReal) :: sumf,sumftr,StressRatio_p,StressRatio_pminus1,BoltzmannRatio,DotGamma0,&
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EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio
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EdgeDipMinDistance,AtomicVolume,VacancyDiffusion,StressRatio_r,Ndot0_twin,stressRatio,&
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Ndot0_trans,StressRatio_s
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real(pReal), dimension(plastic_dislotwin_totalNslip(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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gdot_slip,tau_slip,DotRhoMultiplication,EdgeDipDistance,DotRhoEdgeEdgeAnnihilation,DotRhoEdgeDipAnnihilation,&
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ClimbVelocity,DotRhoEdgeDipClimb,DotRhoDipFormation
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real(pReal), dimension(plastic_dislotwin_totalNtwin(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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tau_twin
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real(pReal), dimension(plastic_dislotwin_totalNtrans(phase_plasticityInstance(material_phase(ipc,ip,el)))) :: &
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V_trans,tau_trans,fstress_trans,shear_trans,shearrate_trans,probrate_trans
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tau_trans
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!* Shortened notation
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of = mappingConstitutive(1,ipc,ip,el)
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@ -2162,7 +2176,6 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
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StressRatio_r = (state(ph)%threshold_stress_twin(j,of)/&
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tau_twin(j))**plastic_dislotwin_rPerTwinFamily(f,instance)
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!* Shear rates and their derivatives due to twin
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select case(lattice_structure(ph))
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case (LATTICE_fcc_ID)
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s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
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@ -2190,66 +2203,43 @@ subroutine plastic_dislotwin_dotState(Tstar_v,Temperature,ipc,ip,el)
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enddo
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!* Transformation volume fraction evolution
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shear_trans = 0.0_pReal
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shearrate_trans = 0.0_pReal
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probrate_trans = 0.0_pReal
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j = 0_pInt
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do f = 1_pInt,lattice_maxNtransFamily ! loop over all trans families
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index_myFamily = sum(lattice_NtransSystem(1:f-1_pInt,ph)) ! at which index starts my family
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!* Projection of shear and shear rate on fault band (twin) systems
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if (nr > 0_pInt) then
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shear_trans = matmul(plastic_dislotwin_projectionMatrix_Trans(:,:,instance), &
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state(ph)%accshear_slip(1_pInt:ns,of))
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shearrate_trans = matmul(plastic_dislotwin_projectionMatrix_Trans(:,:,instance), &
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dotState(ph)%accshear_slip(1_pInt:ns,of))
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endif
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do i = 1_pInt,plastic_dislotwin_Ntrans(f,instance) ! process each (active) trans system in family
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j = j+1_pInt
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!* Resolved shear stress on transformation system
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tau_trans(j) = dot_product(Tstar_v,lattice_Strans_v(:,index_myFamily+i,ph))
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!* Total martensite volume fraction for transformation system
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V_trans(j) = state(ph)%stressTransFraction(j,of) + state(ph)%strainTransFraction(j,of)
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!* Driving force for stress-assisted martensite growth
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fstress_trans(j) = tau_trans(j) - &
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plastic_dislotwin_Cdwp(instance)*(2*V_trans(j) - 6*V_trans(j)**2 + 4*V_trans(j)**3) - &
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12*plastic_dislotwin_deltaG(instance)*(V_trans(j)**2 - V_trans(j)**3)
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!* Dotstate for stress-assisted martensite volume fraction
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if (fstress_trans(j) > tol_math_check) then
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dotState(ph)%stressTransFraction(j,of) = plastic_dislotwin_Cgro(instance)*&
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(1.0_pReal - sumf - sumftr)*fstress_trans(j)
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else
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dotState(ph)%stressTransFraction(j,of) = 0.0_pReal
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endif
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!* Probability rate of fault band intersection for strain-induced martensite nucleation
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!* Stress ratios
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if (tau_trans(j) > tol_math_check) then
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StressRatio_s = (state(ph)%threshold_stress_trans(j,of)/&
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tau_trans(j))**plastic_dislotwin_sPerTransFamily(f,instance)
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!* Shear rates and their derivatives due to transformation
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select case(lattice_structure(ph))
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case (LATTICE_fcc_ID)
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a = lattice_fccTobcc_transNucleationTwinPair(1,j)
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b = lattice_fccTobcc_transNucleationTwinPair(2,j)
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sa = sign(1_pInt, a)
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sb = sign(1_pInt, b)
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ssa = int(sign(1.0_pReal, shearrate_trans(a)),pInt)
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ssb = int(sign(1.0_pReal, shearrate_trans(b)),pInt)
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if (sa == ssa .and. sb == ssb) then
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probrate_trans(j) = (abs(shear_trans(a)*shearrate_trans(b)) + abs(shear_trans(b)*shearrate_trans(a)))
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s1=lattice_fcc_twinNucleationSlipPair(1,index_myFamily+i)
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s2=lattice_fcc_twinNucleationSlipPair(2,index_myFamily+i)
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if (tau_trans(j) < plastic_dislotwin_tau_r_trans(j,instance)) then
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Ndot0_trans=(abs(gdot_slip(s1))*(state(ph)%rhoEdge(s2,of)+state(ph)%rhoEdgeDip(s2,of))+&
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abs(gdot_slip(s2))*(state(ph)%rhoEdge(s1,of)+state(ph)%rhoEdgeDip(s1,of)))/&
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(plastic_dislotwin_L0_trans(instance)*plastic_dislotwin_burgersPerSlipSystem(j,instance))*&
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(1.0_pReal-exp(-plastic_dislotwin_VcrossSlip(instance)/(kB*Temperature)*&
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(plastic_dislotwin_tau_r_trans(j,instance)-tau_trans(j))))
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else
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probrate_trans(j) = 0.0_pReal
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endif
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probrate_trans(j) = probrate_trans(j)/lattice_fccTobcc_shearCritTrans**2
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!* Dotstate for strain-induced martensite volume fraction
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dotState(ph)%strainTransFraction(j,of) = plastic_dislotwin_Cnuc(instance)*&
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(1.0_pReal - sumf - sumftr)*probrate_trans(j)
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Ndot0_trans=0.0_pReal
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end if
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case default
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dotState(ph)%strainTransFraction(j,of) = 0.0_pReal
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Ndot0_trans=plastic_dislotwin_Ndot0PerTransSystem(j,instance)
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end select
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dotState(ph)%strainTransFraction(j,of) = &
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(1.0_pReal-sumf-sumftr)*&
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state(ph)%martensiteVolume(j,of)*Ndot0_trans*exp(-StressRatio_s)
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!* Dotstate for accumulated shear due to transformation
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!dotState(ph)%accshear_trans(j,of) = dotState(ph)%strainTransFraction(j,of) * &
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! lattice_sheartrans(index_myfamily+i,ph)
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endif
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enddo
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enddo
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