From 434ac7f06edc3b27b39451cd143f1c38d0527217 Mon Sep 17 00:00:00 2001 From: Luc Hantcherli Date: Tue, 17 Jun 2008 14:40:46 +0000 Subject: [PATCH] In dislo: - model for stacking fault energy computation w.r.t temperature and orientation - classical thermodynamical approach to twin nucleation (delta_E) - rename some parameters In crystallite: - add msg='ok', even if components in consistent tangent are not re-computed - allow for pseudo-convergence in the outer-loop (case of slow convergence of dislocation densities) in mattex: - add new parameters --- trunk/constitutive_dislo.f90 | 415 ++++++++++++++++++++++------------- trunk/crystallite.f90 | 10 +- trunk/mattex.mpie | 57 ++--- 3 files changed, 304 insertions(+), 178 deletions(-) diff --git a/trunk/constitutive_dislo.f90 b/trunk/constitutive_dislo.f90 index 661280125..05efd4e85 100644 --- a/trunk/constitutive_dislo.f90 +++ b/trunk/constitutive_dislo.f90 @@ -24,6 +24,10 @@ character(len=300), parameter :: mattexFile = 'mattex.mpie' real(pReal), parameter :: attack_frequency = 1.0e10_pReal !* Physical parameter, Boltzmann constant in J/Kelvin real(pReal), parameter :: kB = 1.38e-23_pReal +!* Physical parameter, Avogadro number in 1/mol +real(pReal), parameter :: avogadro = 6.022e23_pReal +!* Physical parameter, Gaz constant in J.mol/Kelvin +real(pReal), parameter :: Rgaz = 8.314_pReal !************************************* !* Definition of material properties * @@ -31,7 +35,7 @@ real(pReal), parameter :: kB = 1.38e-23_pReal !* Number of materials integer(pInt) material_maxN !* Lattice structure and number of selected slip or twin systems per material -integer(pInt), dimension(:) , allocatable :: material_LatticeStructure +integer(pInt), dimension(:) , allocatable :: material_CrystalStructure integer(pInt), dimension(:) , allocatable :: material_Nslip integer(pInt), dimension(:) , allocatable :: material_Ntwin !* Maximum number of selected slip or twin systems over materials @@ -47,15 +51,15 @@ real(pReal), dimension(:) , allocatable :: material_Gmod real(pReal), dimension(:,:,:) , allocatable :: material_Cslip_66 real(preal), dimension(:,:,:,:) , allocatable :: material_Ctwin_66 !* Visco-plastic material parameters +real(pReal) material_sfe real(pReal), dimension(:) , allocatable :: material_rho0 real(pReal), dimension(:) , allocatable :: material_bg real(pReal), dimension(:) , allocatable :: material_Qedge -real(pReal), dimension(:) , allocatable :: material_tau0 real(pReal), dimension(:) , allocatable :: material_GrainSize real(pReal), dimension(:) , allocatable :: material_StackSize real(pReal), dimension(:) , allocatable :: material_ActivationLength real(pReal), dimension(:) , allocatable :: material_TwinSaturation -real(pReal), dimension(:) , allocatable :: material_twin_res +real(pReal), dimension(:) , allocatable :: material_SiteScaling real(pReal), dimension(:) , allocatable :: material_c1 real(pReal), dimension(:) , allocatable :: material_c2 real(pReal), dimension(:) , allocatable :: material_c3 @@ -63,8 +67,8 @@ real(pReal), dimension(:) , allocatable :: material_c4 real(pReal), dimension(:) , allocatable :: material_c5 real(pReal), dimension(:) , allocatable :: material_c6 real(pReal), dimension(:) , allocatable :: material_c7 -real(pReal), dimension(:) , allocatable :: material_c8 -real(pReal), dimension(:) , allocatable :: material_c9 +real(pReal), dimension(:) , allocatable :: material_q1 +real(pReal), dimension(:) , allocatable :: material_q2 real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff !************************************ @@ -126,7 +130,8 @@ real(pReal), dimension(:) , allocatable :: constitutive_rho_f real(pReal), dimension(:) , allocatable :: constitutive_rho_p real(pReal), dimension(:) , allocatable :: constitutive_g0_slip real(pReal), dimension(:) , allocatable :: constitutive_twin_volume -real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len +real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_s +real(pReal), dimension(:) , allocatable :: constitutive_inv_intertwin_len_t real(pReal), dimension(:) , allocatable :: constitutive_twin_mfp !************************************ @@ -318,8 +323,8 @@ do while(.true.) !$OMP CRITICAL (write2out) select case(tag) case ('lattice_structure') - material_LatticeStructure(section)=IO_intValue(line,positions,2) - write(6,*) 'lattice_structure', material_LatticeStructure(section) + material_CrystalStructure(section)=IO_intValue(line,positions,2) + write(6,*) 'lattice_structure', material_CrystalStructure(section) case ('nslip') material_Nslip(section)=IO_intValue(line,positions,2) write(6,*) 'nslip', material_Nslip(section) @@ -355,24 +360,18 @@ do while(.true.) case ('qedge') material_Qedge(section)=IO_floatValue(line,positions,2) write(6,*) 'Qedge', material_Qedge(section) - case ('tau0') - material_tau0(section)=IO_floatValue(line,positions,2) - write(6,*) 'tau0', material_tau0(section) case ('grain_size') material_GrainSize(section)=IO_floatValue(line,positions,2) write(6,*) 'grain_size', material_GrainSize(section) case ('stack_size') material_StackSize(section)=IO_floatValue(line,positions,2) write(6,*) 'stack_size', material_StackSize(section) - case ('d_star') - material_ActivationLength(section)=IO_floatValue(line,positions,2) - write(6,*) 'activation length', material_ActivationLength(section) case ('f_sat') material_TwinSaturation(section)=IO_floatValue(line,positions,2) write(6,*) 'twin saturation', material_TwinSaturation(section) - case ('twin_resistance') - material_twin_res(section)=IO_floatValue(line,positions,2) - write(6,*) 'twin_resistance', material_twin_res(section) + case ('site_scaling') + material_SiteScaling(section)=IO_floatValue(line,positions,2) + write(6,*) 'site_scaling', material_SiteScaling(section) case ('c1') material_c1(section)=IO_floatValue(line,positions,2) write(6,*) 'c1', material_c1(section) @@ -394,12 +393,12 @@ do while(.true.) case ('c7') material_c7(section)=IO_floatValue(line,positions,2) write(6,*) 'c7', material_c7(section) - case ('c8') - material_c8(section)=IO_floatValue(line,positions,2) - write(6,*) 'c8', material_c8(section) - case ('c9') - material_c9(section)=IO_floatValue(line,positions,2) - write(6,*) 'c9', material_c9(section) + case ('q1') + material_q1(section)=IO_floatValue(line,positions,2) + write(6,*) 'q1', material_q1(section) + case ('q2') + material_q2(section)=IO_floatValue(line,positions,2) + write(6,*) 'q2', material_q2(section) end select !$OMP END CRITICAL (write2out) endif @@ -536,7 +535,7 @@ do while (part/='') end select enddo !* Array allocation -allocate(material_LatticeStructure(material_maxN)) ; material_LatticeStructure=0_pInt +allocate(material_CrystalStructure(material_maxN)) ; material_CrystalStructure=0_pInt allocate(material_Nslip(material_maxN)) ; material_Nslip=0_pInt allocate(material_Ntwin(material_maxN)) ; material_Ntwin=0_pInt allocate(material_C11(material_maxN)) ; material_C11=0.0_pReal @@ -551,12 +550,11 @@ allocate(material_rho0(material_maxN)) ; mate allocate(material_SlipIntCoeff(lattice_MaxMaxNslipOfStructure,material_maxN)) ; material_SlipIntCoeff=0.0_pReal allocate(material_bg(material_maxN)) ; material_bg=0.0_pReal allocate(material_Qedge(material_maxN)) ; material_Qedge=0.0_pReal -allocate(material_tau0(material_maxN)) ; material_tau0=0.0_pReal allocate(material_GrainSize(material_maxN)) ; material_GrainSize=0.0_pReal allocate(material_StackSize(material_maxN)) ; material_StackSize=0.0_pReal allocate(material_ActivationLength(material_maxN)) ; material_ActivationLength=0.0_pReal allocate(material_TwinSaturation(material_maxN)) ; material_TwinSaturation=0.0_pReal -allocate(material_twin_res(material_maxN)) ; material_twin_res=0.0_pReal +allocate(material_SiteScaling(material_maxN)) ; material_SiteScaling=0.0_pReal allocate(material_c1(material_maxN)) ; material_c1=0.0_pReal allocate(material_c2(material_maxN)) ; material_c2=0.0_pReal allocate(material_c3(material_maxN)) ; material_c3=0.0_pReal @@ -564,8 +562,8 @@ allocate(material_c4(material_maxN)) allocate(material_c5(material_maxN)) ; material_c5=0.0_pReal allocate(material_c6(material_maxN)) ; material_c6=0.0_pReal allocate(material_c7(material_maxN)) ; material_c7=0.0_pReal -allocate(material_c8(material_maxN)) ; material_c8=0.0_pReal -allocate(material_c9(material_maxN)) ; material_c9=0.0_pReal +allocate(material_q1(material_maxN)) ; material_q1=0.0_pReal +allocate(material_q2(material_maxN)) ; material_q2=0.0_pReal allocate(texture_ODFfile(texture_maxN)) ; texture_ODFfile='' allocate(texture_Ngrains(texture_maxN)) ; texture_Ngrains=0_pInt allocate(texture_symmetry(texture_maxN)) ; texture_symmetry='' @@ -612,7 +610,7 @@ close(fileunit) !* Construction of the elasticity matrices do i=1,material_maxN - select case (material_LatticeStructure(i)) + select case (material_CrystalStructure(i)) case(1:2) ! cubic(s) material_Gmod(i)=material_C44(i) forall(k=1:3) @@ -711,7 +709,7 @@ material_maxNslip = maxval(material_Nslip) ! max of slip systems among mat material_maxNtwin = maxval(material_Ntwin) ! max of twin systems among materials present constitutive_maxNstatevars = maxval(material_Nslip) + maxval(material_Ntwin) ! ----------------------------------------------------------------------------------------------------------------------- -constitutive_maxNresults = 24_pInt +constitutive_maxNresults = 2_pInt ! ----------------------------------------------------------------------------------------------------------------------- @@ -754,7 +752,8 @@ allocate(constitutive_jump_width(material_maxNslip)) ; constitutive_jump_ allocate(constitutive_activation_volume(material_maxNslip)) ; constitutive_activation_volume=0.0_pReal allocate(constitutive_g0_slip(material_maxNslip)) ; constitutive_g0_slip=0.0_pReal allocate(constitutive_twin_volume(material_maxNtwin)) ; constitutive_twin_volume=0.0_pReal -allocate(constitutive_inv_intertwin_len(material_maxNtwin)) ; constitutive_inv_intertwin_len=0.0_pReal +allocate(constitutive_inv_intertwin_len_s(material_maxNslip)) ; constitutive_inv_intertwin_len_s=0.0_pReal +allocate(constitutive_inv_intertwin_len_t(material_maxNtwin)) ; constitutive_inv_intertwin_len_t=0.0_pReal allocate(constitutive_twin_mfp(material_maxNtwin)) ; constitutive_twin_mfp=0.0_pReal allocate(constitutive_tau_slip(material_maxNslip)) ; constitutive_tau_slip=0.0_pReal allocate(constitutive_tau_twin(material_maxNtwin)) ; constitutive_tau_twin=0.0_pReal @@ -812,7 +811,7 @@ do e=1,mesh_NcpElems constitutive_TexVolFrac(g,i,e) = texVolfrac(s)/multiplicity(texID)/Nsym(texID) constitutive_Nstatevars(g,i,e) = material_Nslip(matID) + material_Ntwin(matID)! number of state variables (i.e. tau_c of each slip system) ! ----------------------------------------------------------------------------------------------------------------------- - constitutive_Nresults(g,i,e) = 24 ! number of constitutive results output by constitutive_post_results + constitutive_Nresults(g,i,e) = 2 ! number of constitutive results output by constitutive_post_results ! ----------------------------------------------------------------------------------------------------------------------- constitutive_EulerAngles(:,g,i,e) = Euler(:,s) ! store initial orientation forall (l=1:material_Nslip(matID)) ! initialize state variables @@ -829,7 +828,7 @@ enddo ! cp_element do i=1,material_maxN C_3333=math_Mandel66to3333(material_Cslip_66(:,:,i)) do j=1,material_Ntwin(i) - Qtwin=lattice_Qtwin(:,:,j,material_LatticeStructure(i)) + Qtwin=lattice_Qtwin(:,:,j,material_CrystalStructure(i)) do k=1,3 do l=1,3 do m=1,3 @@ -872,6 +871,7 @@ do i=1,material_maxN enddo enddo + end subroutine @@ -920,7 +920,7 @@ subroutine constitutive_Microstructure(state,Tp,ipc,ip,el) !********************************************************************* use prec, only: pReal,pInt use math, only: pi -use lattice, only: lattice_TwinIntType +use lattice, only: lattice_TwinIntType,lattice_SlipTwinIntType implicit none !* Definition of variables @@ -928,6 +928,8 @@ integer(pInt) ipc,ip,el integer(pInt) matID,i,j,startIdxTwin real(pReal) Tp,Ftwin real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state +real(pReal) x_fe,x_Mn,x_C,beta_mart,Tp_mart,f_mart,beta_aust,Tp_aust,f_aust +real(pReal) deltaG1,deltaG2,deltaG3,deltaG4,deltaG5 !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) @@ -936,10 +938,10 @@ startIdxTwin = material_Nslip(matID) !* Quantities derived from state - slip !$OMP CRITICAL (evilmatmul) constitutive_rho_f=matmul(constitutive_Pforest (1:material_Nslip(matID),1:material_Nslip(matID),matID),state) -constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state) -!$OMP END CRITICAL (evilmatmul) +constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state) +!$OMP END CRITICAL (evilmatmul) do i=1,material_Nslip(matID) - constitutive_passing_stress(i) = material_tau0(matID)+material_c1(matID)*material_Gmod(matID)*material_bg(matID)*& + constitutive_passing_stress(i) = material_c1(matID)*material_Gmod(matID)*material_bg(matID)*& sqrt(constitutive_rho_p(i)) constitutive_jump_width(i) = material_c2(matID)/sqrt(constitutive_rho_f(i)) @@ -957,22 +959,70 @@ enddo !* Quantities derived from state - twin Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) +do i=1,material_Nslip(matID) + !* Inverse of the average distance between 2 twins of the same familly + constitutive_inv_intertwin_len_s(i)=0.0_pReal + do j=1,material_Ntwin(matID) + constitutive_inv_intertwin_len_s(i)=constitutive_inv_intertwin_len_s(i)+& + (lattice_SlipTwinIntType(i,j,material_CrystalStructure(matID))*state(startIdxTwin+j))/& + (2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin)) + enddo +enddo do i=1,material_Ntwin(matID) !* Inverse of the average distance between 2 twins of the same familly - constitutive_inv_intertwin_len(i)=0.0_pReal + constitutive_inv_intertwin_len_t(i)=0.0_pReal do j=1,material_Ntwin(matID) - constitutive_inv_intertwin_len(i)=constitutive_inv_intertwin_len(i)+& - (lattice_TwinIntType(i,j,material_LatticeStructure(matID))*state(startIdxTwin+j))/& - (2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin)) + constitutive_inv_intertwin_len_t(i)=constitutive_inv_intertwin_len_t(i)+& + (lattice_TwinIntType(i,j,material_CrystalStructure(matID))*state(startIdxTwin+j))/& + (2.0_pReal*material_StackSize(matID)*(1.0_pReal-Ftwin)) enddo - constitutive_twin_mfp(i)=(1.0_pReal)/((1.0_pReal/material_GrainSize(matID))+constitutive_inv_intertwin_len(i)) - constitutive_twin_volume(i)=(pi/6.0_pReal)*material_StackSize(matID)*constitutive_twin_mfp(i)**2.0_pReal + constitutive_twin_mfp(i)=1.0_pReal/((1.0_pReal/material_GrainSize(matID))+constitutive_inv_intertwin_len_t(i)) + constitutive_twin_volume(i)=((4.0_pReal*pi)/3.0_pReal)*material_StackSize(matID)*constitutive_twin_mfp(i)**2.0_pReal enddo +!* Stacking fault energy as function of temperature (see Allain PhD Thesis p40-42) * +x_Fe=0.774_pReal ! atomic % +x_Mn=0.218_pReal ! atomic % +x_C =0.027_pReal ! atomic % + +!* Chemical contribution * +deltaG1=x_Fe*(4.309_pReal*Tp-2243.38_pReal) +deltaG2=x_Mn*(1.123_preal*Tp-1000.0_pReal) +deltaG3=x_Fe*x_Mn*(2873.0_pReal+717.0_pReal*(x_Fe-x_Mn)) +deltaG4=1246.0_pReal*(1.0_pReal-exp(-24.29_pReal*x_C))-17175.0_pReal*x_Mn*x_C + +!* Magnetical contribution * +beta_mart=0.62_pReal*x_Mn-4.0_pReal*x_C ! Magnetic spin in µB +Tp_mart=580.0_pReal*x_Mn ! Néel Temperature +beta_aust=0.7_pReal*x_Fe+0.62_pReal*x_Mn-0.64_pReal*x_Fe*x_Mn-4.0_pReal*x_C ! Magnetic spin in µB +Tp_aust=669.27_pReal*(1.0_pReal-exp(-5.46_pReal*x_Mn))-2408.0_pReal*x_C*x_Fe-109.0_pReal ! Néel Temperature +if (Tp<=Tp_mart) then + f_mart=1.0_pReal-(1.0_pReal/2.34_pReal)*((79.0_pReal*Tp_mart)/(140.0_pReal*0.28_pReal*Tp)+& + (474.0_pReal/497.0_pReal)*((1.0_pReal/0.28_pReal)-1.0_pReal)*(((Tp/Tp_mart)**3.0_pReal)/6.0_pReal+& + ((Tp/Tp_mart)**9.0_pReal)/135.0_pReal+((Tp/Tp_mart)**15.0_pReal)/600.0_pReal)) +else + f_mart=-(1.0_pReal/2.34_pReal)*(((Tp/Tp_mart)**-5.0_pReal)/10.0_pReal+((Tp/Tp_mart)**-15.0_pReal)/315.0_pReal+& + ((Tp/Tp_mart)**-25.0_pReal)/1500.0_pReal) +endif +if (Tp<=Tp_aust) then + f_aust=1.0_pReal-(1.0_pReal/2.34_pReal)*((79.0_pReal*Tp_aust)/(140.0_pReal*0.28_pReal*Tp)+& + (474.0_pReal/497.0_pReal)*((1.0_pReal/0.28_pReal)-1.0_pReal)*(((Tp/Tp_aust)**3.0_pReal)/6.0_pReal+& + ((Tp/Tp_aust)**9.0_pReal)/135.0_pReal+((Tp/Tp_aust)**15.0_pReal)/600.0_pReal)) +else + f_aust=-(1.0_pReal/2.34_pReal)*(((Tp/Tp_aust)**-5.0_pReal)/10.0_pReal+((Tp/Tp_aust)**-15.0_pReal)/315.0_pReal+& + ((Tp/Tp_aust)**-25.0_pReal)/1500.0_pReal) +endif +deltaG5=Rgaz*Tp*(log(beta_mart+1.0_pReal)*f_mart-log(beta_aust+1.0_pReal)*f_aust) + +!* Final expression * +material_sfe=(4.0_pReal/(sqrt(3.0_pReal)*avogadro*material_bg(matID)**2.0_pReal))*& + (deltaG1+deltaG2+deltaG3+deltaG4+deltaG5)+2.0_pReal*0.0035_pReal + return end subroutine + subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el) !********************************************************************* !* This subroutine contains the constitutive equation for * @@ -990,7 +1040,7 @@ subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el !********************************************************************* use prec, only: pReal,pInt use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_TwinShear -use math, only: math_Plain3333to99 +use math, only: pi,math_Plain3333to99 implicit none !* Definition of variables @@ -1002,92 +1052,155 @@ real(pReal), dimension(3,3) :: Lp,Sslip,Stwin real(pReal), dimension(3,3,3,3) :: dLp_dTstar3333 real(pReal), dimension(9,9) :: dLp_dTstar real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state +real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,dgdot_dtauslip,tau_slip +real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el))) :: sfe_eff,fdot_twin,dfdot_dtautwin,tau_twin,tauc_twin +real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el)),material_Nslip(constitutive_matID(ipc,ip,el))) :: dfdot_dtauslip !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) startIdxTwin = material_Nslip(matID) +Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) !* Calculation of Lp - slip -Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) -Lp = 0.0_pReal +gdot_slip = 0.0_pReal +dgdot_dtauslip = 0.0_pReal +Lp = 0.0_pReal do i=1,material_Nslip(matID) - constitutive_tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_LatticeStructure(matID))) - if (abs(constitutive_tau_slip(i))>constitutive_passing_stress(i)) then - constitutive_gdot_slip(i) = constitutive_g0_slip(i)*& - sinh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) - constitutive_dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(kB*Tp)*& - cosh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) - else - constitutive_gdot_slip(i) = 0.0_pReal - constitutive_dgdot_dtauslip(i) = 0.0_pReal - endif - Lp=Lp+(1.0_pReal-Ftwin)*constitutive_gdot_slip(i)*lattice_Sslip(:,:,i,material_LatticeStructure(matID)) + tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID))) + if (abs(tau_slip(i))>constitutive_passing_stress(i)) then + gdot_slip(i) = constitutive_g0_slip(i)*sinh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) + dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(kB*Tp)*& + cosh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) + endif + Lp=Lp+(1.0_pReal-Ftwin)*gdot_slip(i)*lattice_Sslip(:,:,i,material_CrystalStructure(matID)) enddo +!write(6,*) '##############' +!write(6,*) '##############' + +!write(6,*) 'Schmid_1', lattice_Sslip_v(:,1,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_2', lattice_Sslip_v(:,2,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_3', lattice_Sslip_v(:,3,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_4', lattice_Sslip_v(:,4,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_5', lattice_Sslip_v(:,5,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_6', lattice_Sslip_v(:,6,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_7', lattice_Sslip_v(:,7,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_8', lattice_Sslip_v(:,8,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_9', lattice_Sslip_v(:,9,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_10', lattice_Sslip_v(:,10,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_11', lattice_Sslip_v(:,11,material_CrystalStructure(matID)) +!write(6,*) 'Schmid_12', lattice_Sslip_v(:,12,material_CrystalStructure(matID)) +!write(6,*) 'Tstar_v',Tstar_v +!write(6,*) 'state',state +!write(6,*) 'Tp', Tp +!write(6,*) 'ssd_f', constitutive_rho_f +!write(6,*) 'ssd_p', constitutive_rho_p +!write(6,*) 'jump_width', constitutive_jump_width +!write(6,*) 'activation_volume', constitutive_activation_volume +!write(6,*) 'passing_stress', constitutive_passing_stress +!write(6,*) 'ssd_m', constitutive_rho_m +!write(6,*) 'g0_slip', constitutive_g0_slip +!write(6,*) 'tau_slip',tau_slip +!write(6,*) 'gdot_slip', gdot_slip +!write(6,*) 'dgdot_dtauslip', dgdot_dtauslip + + !* Calculation of Lp - twin -!do i=1,material_Ntwin(matID) -! constitutive_tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_LatticeStructure(matID))) -! if (constitutive_tau_twin(i)>0.0_pReal) then -! constitutive_fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*& -! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*& -! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*& -! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID))) -! constitutive_dfdot_dtautwin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*& -! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*& -! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*& -! (material_c9(matID)/constitutive_tau_twin(i))*& -! (material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID)*& -! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID))) -! do j=1,material_Nslip(matID) -! if (constitutive_gdot_slip(i)>0.0_pReal) then -! constitutive_dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*& -! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*& -! (material_ActivationLength(matID)/material_bg(matID))*constitutive_dgdot_dtauslip(j)*& -! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID))) -! else -! constitutive_dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*& -! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*& -! (material_ActivationLength(matID)/material_bg(matID))*(-constitutive_dgdot_dtauslip(j))*& -! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID))) -! endif -! enddo -! else -! constitutive_fdot_twin(i)=0.0_pReal -! constitutive_dfdot_dtautwin(i)=0.0_pReal -! do j=1,material_Nslip(matID) -! constitutive_dfdot_dtauslip(i,j)=0.0_pReal -! enddo -! endif -! Lp=Lp+state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*constitutive_fdot_twin(i)*& -! lattice_Stwin(:,:,i,material_LatticeStructure(matID)) +sfe_eff = 0.0_pReal +fdot_twin = 0.0_pReal +dfdot_dtautwin = 0.0_pReal +dfdot_dtauslip = 0.0_pReal +do i=1,material_Ntwin(matID) + tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_CrystalStructure(matID))) + if ((tau_twin(i) > 0.0_pReal).AND.(material_TwinSaturation(matID)-Ftwin>=0)) then + sfe_eff(i)=material_sfe-(sqrt(3.0_pReal)/3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i) + if (sfe_eff(i)<0.0_pReal) sfe_eff(i) = 0.0_pReal + fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*& + constitutive_twin_volume(i)*& + ((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*& + sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*& + exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& + (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) + + dfdot_dtautwin(i) = (material_TwinSaturation(matID)-Ftwin)*& + constitutive_twin_volume(i)*& + ((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*& + sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*& + ((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**2.0_pReal)/& + (3.0_pReal*Kb*Tp*material_q2(matID)**4.0_pReal*tau_twin(i)**5.0_pReal))*& + (-sqrt(3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i)-& + 4.0_pReal*sfe_eff(i))*& + exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& + (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) + + do j=1,material_Nslip(matID) + if (gdot_slip(j)>0.0_pReal) then + dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*& + constitutive_twin_volume(i)*& + ((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*dgdot_dtauslip(j)*& + sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*& + exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& + (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) + else + dfdot_dtauslip(i,j) = (material_TwinSaturation(matID)-Ftwin)*& + constitutive_twin_volume(i)*& + ((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*(-dgdot_dtauslip(j))*& + sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*& + exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& + (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) + endif + enddo + endif + Lp=Lp+state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*constitutive_fdot_twin(i)*& + lattice_Stwin(:,:,i,material_CrystalStructure(matID)) +enddo + + +!write(6,*) 'twin_mfp', constitutive_twin_mfp +!write(6,*) 'twin_volume', constitutive_twin_volume +!write(6,*) 'tau_twin',tau_twin +!write(6,*) 'part1:',material_TwinSaturation(matID)-Ftwin +!write(6,*) 'part2:',constitutive_twin_volume +!write(6,*) 'part3:',((2.0_pReal*sqrt(6.0_pReal)*sum(abs(gdot_slip))*& +! sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal) +!do i=1,12 +!write(6,*) 'part4:',exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& +! (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) +!write(6,*) 'part5:',(-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& +! (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal) !enddo +!write(6,*) 'sfe', material_sfe +!write(6,*) 'sfe_eff',sfe_eff +!write(6,*) 'fdot_twin', fdot_twin +!write(6,*) 'dfdot_dtautwin', dfdot_dtautwin +!write(6,*) 'dfdot_dtauslip', dfdot_dtauslip - + !* Calculation of the tangent of Lp dLp_dTstar3333=0.0_pReal do i=1,material_Nslip(matID) - Sslip = lattice_Sslip(:,:,i,material_LatticeStructure(matID)) + Sslip = lattice_Sslip(:,:,i,material_CrystalStructure(matID)) forall (k=1:3,l=1:3,m=1:3,n=1:3) dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ & - (1.0_pReal-Ftwin)*constitutive_dgdot_dtauslip(i)*Sslip(k,l)*Sslip(m,n) !force m,n symmetry + (1.0_pReal-Ftwin)*dgdot_dtauslip(i)*Sslip(k,l)*Sslip(m,n) !force m,n symmetry endforall enddo -!do i=1,material_Ntwin(matID) -! Stwin = lattice_Stwin(:,:,i,material_LatticeStructure(matID)) -! forall (k=1:3,l=1:3,m=1:3,n=1:3) -! dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ & -! state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*& -! constitutive_dfdot_dtautwin(i)*Stwin(k,l)*Stwin(m,n) !force m,n symmetry -! endforall -! do j=1,material_Nslip(matID) -! Sslip = lattice_Sslip(:,:,j,material_LatticeStructure(matID)) -! forall (k=1:3,l=1:3,m=1:3,n=1:3) -! dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ & -! state(material_Nslip(matID)+i)*lattice_TwinShear(material_LatticeStructure(matID))*& -! constitutive_dfdot_dtauslip(i,j)*Stwin(k,l)*Sslip(m,n) !force m,n symmetry -! endforall -! enddo -!enddo +do i=1,material_Ntwin(matID) + Stwin = lattice_Stwin(:,:,i,material_CrystalStructure(matID)) + forall (k=1:3,l=1:3,m=1:3,n=1:3) + dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ & + state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*& + dfdot_dtautwin(i)*Stwin(k,l)*Stwin(m,n) !force m,n symmetry + endforall + do j=1,material_Nslip(matID) + Sslip = lattice_Sslip(:,:,j,material_CrystalStructure(matID)) + forall (k=1:3,l=1:3,m=1:3,n=1:3) + dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n)+ & + state(material_Nslip(matID)+i)*lattice_TwinShear(material_CrystalStructure(matID))*& + dfdot_dtauslip(i,j)*Stwin(k,l)*Sslip(m,n) !force m,n symmetry + endforall + enddo +enddo dLp_dTstar = math_Plain3333to99(dLp_dTstar3333) return @@ -1109,6 +1222,7 @@ function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el) !* - constitutive_DotState : evolution of state variable * !********************************************************************* use prec, only: pReal,pInt +use math, only: pi use lattice, only: lattice_Sslip_v,lattice_Stwin_v implicit none @@ -1118,51 +1232,48 @@ integer(pInt) matID,i,j,startIdxTwin real(pReal) Tp,Ftwin real(pReal), dimension(6) :: Tstar_v real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: constitutive_dotState,state +real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: gdot_slip,tau_slip +real(pReal), dimension(material_Ntwin(constitutive_matID(ipc,ip,el))) :: sfe_eff,fdot_twin,tau_twin,tauc_twin +real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: locks,grainboundaries,recovery +real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: twinboundaries !* Get the material-ID from the triplet(ipc,ip,el) matID = constitutive_matID(ipc,ip,el) startIdxTwin = material_Nslip(matID) +Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) constitutive_dotState = 0.0_pReal !* Dislocation density evolution +gdot_slip = 0.0_pReal do i=1,material_Nslip(matID) - constitutive_tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_LatticeStructure(matID))) - if (abs(constitutive_tau_slip(i))>constitutive_passing_stress(i)) then - constitutive_gdot_slip(i) = constitutive_g0_slip(i)*& - sinh((constitutive_tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) - else - constitutive_gdot_slip(i) = 0.0_pReal - endif - constitutive_locks(i) = (sqrt(constitutive_rho_f(i))*abs(constitutive_gdot_slip(i)))/& - (material_c4(matID)*material_bg(matID)) - - constitutive_grainboundaries(i) = abs(constitutive_gdot_slip(i))/(material_c5(matID)*material_bg(matID)*material_GrainSize(matID)) -! if (material_Ntwin(matID)>0) then -! constitutive_twinboundaries(i) = (abs(constitutive_gdot_slip(i))*constitutive_inv_intertwin_len(i))/& -! (material_c6(matID)*material_bg(matID)) -! endif - constitutive_recovery(i) = material_c7(matID)*state(i)*abs(constitutive_gdot_slip(i)) - constitutive_dotState(i) = constitutive_locks(i)+constitutive_grainboundaries(i)-constitutive_recovery(i) -! constitutive_dotState(i) = constitutive_locks(i)+constitutive_grainboundaries(i)+constitutive_twinboundaries(i)& -! -constitutive_recovery(i) + tau_slip(i)=dot_product(Tstar_v,lattice_Sslip_v(:,i,material_CrystalStructure(matID))) + if (abs(tau_slip(i))>constitutive_passing_stress(i)) & + gdot_slip(i) = constitutive_g0_slip(i)*sinh((tau_slip(i)*constitutive_activation_volume(i))/(kB*Tp)) + + locks(i) = (sqrt(constitutive_rho_f(i))*abs(gdot_slip(i)))/(material_c4(matID)*material_bg(matID)) + grainboundaries(i) = abs(gdot_slip(i))/(material_c5(matID)*material_bg(matID)*material_GrainSize(matID)) + twinboundaries(i) = (abs(gdot_slip(i))*constitutive_inv_intertwin_len_s(i))/(material_c6(matID)*material_bg(matID)) + recovery(i) = material_c7(matID)*state(i)*abs(gdot_slip(i)) + + constitutive_dotState(i) = locks(i)+grainboundaries(i)+twinboundaries(i)-recovery(i) enddo !* Twin volume fraction evolution -!Ftwin = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) -!do i=1,material_Ntwin(matID) -! constitutive_tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_LatticeStructure(matID))) -! if (constitutive_tau_twin(i)>0.0_pReal) then -! constitutive_fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*constitutive_twin_volume(i)*& -! material_c8(matID)*sum(state(1:material_Nslip(matID)))**(1.5_pReal)*& -! (material_ActivationLength(matID)/material_bg(matID))*sum(abs(constitutive_gdot_slip))*& -! exp(-((material_twin_res(matID)/constitutive_tau_twin(i))**material_c9(matID))) -! else -! constitutive_fdot_twin(i) = 0.0_pReal -! endif -! constitutive_dotState(startIdxTwin+i)=constitutive_fdot_twin(i) -!enddo - -!constitutive_dotState=0.0_pReal +fdot_twin = 0.0_pReal +do i=1,material_Ntwin(matID) + tau_twin(i)=dot_product(Tstar_v,lattice_Stwin_v(:,i,material_CrystalStructure(matID))) + if (tau_twin(i)>0.0_pReal) then + sfe_eff(i)=material_sfe-(sqrt(3.0_pReal)/3.0_pReal)*material_q1(matID)*material_q2(matID)*material_bg(matID)*tau_twin(i) + if (sfe_eff(i)<0.0_pReal) sfe_eff(i) = 0.0_pReal + fdot_twin(i) = (material_TwinSaturation(matID)-Ftwin)*& + constitutive_twin_volume(i)*& + ((2.0_pReal*sqrt(6.0_pReal)*material_SiteScaling(matID)*sum(abs(gdot_slip))*& + sum(state(1:material_Nslip(matID)))**1.5_pReal)/3.0_pReal)*& + exp((-25.0_pReal*pi**3.0_pReal*material_Gmod(matID)**2.0_pReal*sfe_eff(i)**3.0_pReal)/& + (3.0_pReal*Kb*Tp*(material_q2(matID)*tau_twin(i))**4.0_pReal)) + endif + constitutive_dotState(startIdxTwin+i) = fdot_twin(i) +enddo return end function @@ -1200,12 +1311,14 @@ startIdxTwin = material_Nslip(matID) if(constitutive_Nresults(ipc,ip,el)==0) return constitutive_post_results=0.0_pReal -do i=1,material_Nslip(matID) - constitutive_post_results(i) = state(i) -enddo -do i=1,material_Ntwin(matID) - constitutive_post_results(startIdxTwin+i) = state(startIdxTwin+i) -enddo +!do i=1,material_Nslip(matID) +! constitutive_post_results(i) = state(i) +!enddo +!do i=1,material_Ntwin(matID) +! constitutive_post_results(startIdxTwin+i) = state(startIdxTwin+i) +!enddo +constitutive_post_results(1) = sum(state(1:material_Nslip(matID))) +constitutive_post_results(2) = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))) return end function diff --git a/trunk/crystallite.f90 b/trunk/crystallite.f90 index 38a45f0da..6ce7d9c8a 100644 --- a/trunk/crystallite.f90 +++ b/trunk/crystallite.f90 @@ -176,6 +176,8 @@ CONTAINS enddo enddo endif +! + msg = 'ok' ! a new consistent tangent was computed even if msg was not ok for all components ! return ! @@ -418,7 +420,13 @@ Inner: do ! inner iteration: Lp dt*constitutive_dotState(Tstar_v,state,Temperature,& grain,ip,cp_en) ! residuum from evolution of microstructure !!$OMP END CRITICAL (stateupdate) - state = state - ROuter ! update of microstructure + state = state - ROuter ! update of microstructure + if (iOuter==nOuter) then +!$OMP CRITICAL (write2out) + write (6,*) 'WARNING: Outer loop has not really converged' +!$OMP END CRITICAL (write2out) + exit Outer + endif if (maxval(abs(Router/state),state /= 0.0_pReal) < reltol_Outer) exit Outer enddo Outer ! diff --git a/trunk/mattex.mpie b/trunk/mattex.mpie index d5d09100d..4fe9fdd78 100644 --- a/trunk/mattex.mpie +++ b/trunk/mattex.mpie @@ -21,52 +21,57 @@ w0 1.0 hardening_coefficients 1.0 1.4 ## Parameters for dislocation-based modeling -# Initial dislocation density [m]² -rho0 2.8e13 # Burgers vector [m] burgers 2.56e-10 # Activation energy for dislocation glide [J/K] Qedge 3.0e-19 -# Reference for passing stress [Pa] -tau0 0.0 +# Initial dislocation density [m]² +rho0 2.8e13 +# Average grain size [m] +grain_size 2.0e-5 # Passing stress adjustment c1 0.1 # Jump width adjustment c2 2.0 # Activation volume adjustment c3 1.2 -# Dislocation storage adjustment +# Average slip distance adjustment for lock formation # = c4(Anxin)*c2(Anxin) !!!!!! c4 14.25 -# Grain boundaries storage adjustment +# Average slip distance adjustment when grain boundaries c5 1.0 -# Athermal annihilation adjustment +# Average slip distance adjustment when twin boundaries +c6 0.1 +# Athermal recovery adjustment c7 23.5 # Dislocation interaction coefficients interaction_coefficients 1.0 2.2 3.0 1.6 3.8 4.5 -# Twin parameters -# Grain size [m] -grain_size 2.0e-5 -# Twin thickness (stacks) [m] +## Parameters for mechanical twinning +# Average twin thickness (stacks) [m] stack_size 5.0e-8 -# Activation length for twin nucleation [m] -d_star 5.0e-10 -# Twin saturation value -f_sat 0.3 -# Twin boundaries storage adjustment -c6 0.425 -# Scaling of really activated nucleation sites -c8 2.0e-3 -# Selection of active twin systems -c9 10.0 -# Twin resistance [Pa] -twin_resistance 1000.0e6 -stacking_fault_energy 2.0e-2 +# Total twin volume fraction saturation +f_sat 0.2 +# Scaling potential nucleation sites +site_scaling 1.0e-7 +# Scaling the P-K force on the twinning dislocation +q1 0.75 +# Scaling the resolved shear stress +q2 1.0 + [cube SX] symmetry no /monoclinic /orthorhombic -Ngrains 1 /2 /4 -(gauss) phi1 0.0 phi 0.0 phi2 0.0 scatter 0.0 fraction 1.0 +Ngrains 10 /2 /4 +#(gauss) phi1 0.0 phi 29.21 phi2 -26.57 scatter 0.0 fraction 1.0 +#(gauss) phi1 0.0 phi 54.74 phi2 -45.0 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 45.0 phi2 0.0 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 0.0 phi2 0.0 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 35.26 phi2 -45.0 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 48.19 phi2 -26.57 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 26.57 phi2 0.0 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 42.03 phi2 -33.69 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 40.36 phi2 -11.31 scatter 0.0 fraction 0.1 +#(gauss) phi1 0.0 phi 15.62 phi2 -26.57 scatter 0.0 fraction 0.1