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I will proceed step by step. 

constitutive_dislo.f90 contains a modified version of Anxin's dislocation based model. As far as tested it, I consider it now error free. Mechanical twinning is NOT implemented YET.
mattex.mpie file is modified in accordance with the changes in constitutive_dislo.f90
It would be a great help if someone else can check the implementation. I may have overseen something.
This commit is contained in:
Luc Hantcherli 2008-11-06 13:09:12 +00:00
parent 9692f2f3d3
commit 6e13ed0566
2 changed files with 98 additions and 299 deletions
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351
trunk/constitutive_dislo.f90
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@ -55,6 +55,8 @@ 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_Qsd
real(pReal), dimension(:) , allocatable :: material_D0
real(pReal), dimension(:) , allocatable :: material_GrainSize
real(pReal), dimension(:) , allocatable :: material_StackSize
real(pReal), dimension(:) , allocatable :: material_ActivationLength
@ -67,6 +69,7 @@ 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_q1
real(pReal), dimension(:) , allocatable :: material_q2
real(pReal), dimension(:,:) , allocatable :: material_SlipIntCoeff
@ -360,6 +363,12 @@ do while(.true.)
case ('qedge')
material_Qedge(section)=IO_floatValue(line,positions,2)
write(6,*) 'Qedge', material_Qedge(section)
case ('qsd')
material_Qsd(section)=IO_floatValue(line,positions,2)
write(6,*) 'Qsd', material_Qsd(section)
case ('diff0')
material_D0(section)=IO_floatValue(line,positions,2)
write(6,*) 'diff0', material_D0(section)
case ('grain_size')
material_GrainSize(section)=IO_floatValue(line,positions,2)
write(6,*) 'grain_size', material_GrainSize(section)
@ -393,6 +402,9 @@ 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 ('q1')
material_q1(section)=IO_floatValue(line,positions,2)
write(6,*) 'q1', material_q1(section)
@ -550,6 +562,8 @@ 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_Qsd(material_maxN)) ; material_Qsd=0.0_pReal
allocate(material_D0(material_maxN)) ; material_D0=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
@ -562,6 +576,7 @@ 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_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=''
@ -655,7 +670,7 @@ use math, only: math_sampleGaussOri,math_sampleFiberOri,math_sampleRandomOri,mat
math_Mandel3333to66,math_Mandel66to3333
use mesh, only: mesh_NcpElems,FE_Nips,mesh_maxNips,mesh_element
use IO, only: IO_hybridIA
use lattice, only: lattice_SlipIntType,lattice_sn,lattice_st,lattice_Qtwin,lattice_Sslip_v,lattice_Sslip
use lattice, only: lattice_SlipSlipIntType,lattice_sn,lattice_st,lattice_Qtwin,lattice_Sslip_v,lattice_Sslip
implicit none
!* Definition of variables
@ -709,7 +724,7 @@ 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 = 2_pInt
constitutive_maxNresults = 26_pInt
! -----------------------------------------------------------------------------------------------------------------------
@ -811,7 +826,7 @@ 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) = 2 ! number of constitutive results output by constitutive_post_results
constitutive_Nresults(g,i,e) = 26 ! 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
@ -861,9 +876,9 @@ do i=1,material_maxN
x=dot_product(lattice_sn(:,j,i),lattice_st(:,k,i))
y=1.0_pReal-x**(2.0_pReal)
!* Interaction matrix *
constitutive_Pforest(j,k,i)=abs(x)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
constitutive_Pforest(j,k,i)=abs(x)*material_SlipIntCoeff(lattice_SlipSlipIntType(j,k,i),i)
if (y>0.0_pReal) then
constitutive_Pparallel(j,k,i)=sqrt(y)*material_SlipIntCoeff(lattice_SlipIntType(j,k,i),i)
constitutive_Pparallel(j,k,i)=sqrt(y)*material_SlipIntCoeff(lattice_SlipSlipIntType(j,k,i),i)
else
constitutive_Pparallel(j,k,i)=0.0_pReal
endif
@ -888,21 +903,16 @@ use prec, only: pReal,pInt
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,startIdxTwin
integer(pInt) i,ipc,ip,el
integer(pInt) matID
real(pReal), dimension(6,6) :: constitutive_homogenizedC
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
startIdxTwin = material_Nslip(matID)
!* Homogenization scheme
constitutive_homogenizedC=(1-sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID)))))*&
material_Cslip_66(:,:,matID)
do i=1,material_Ntwin(matID)
constitutive_homogenizedC=constitutive_homogenizedC+state(startIdxTwin+i)*material_Ctwin_66(:,:,i,matID)
enddo
constitutive_homogenizedC = material_Cslip_66(:,:,matID)
return
end function
@ -920,20 +930,16 @@ subroutine constitutive_Microstructure(state,Tp,ipc,ip,el)
!*********************************************************************
use prec, only: pReal,pInt
use math, only: pi
use lattice, only: lattice_TwinIntType,lattice_SlipTwinIntType
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,j,startIdxTwin
real(pReal) Tp,Ftwin
integer(pInt) i,j,ipc,ip,el
integer(pInt) matID
real(pReal) Tp
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)
startIdxTwin = material_Nslip(matID)
!* Quantities derived from state - slip
!$OMP CRITICAL (evilmatmul)
@ -941,88 +947,20 @@ constitutive_rho_f=matmul(constitutive_Pforest (1:material_Nslip(matID),1:mater
constitutive_rho_p=matmul(constitutive_Pparallel(1:material_Nslip(matID),1:material_Nslip(matID),matID),state)
!$OMP END CRITICAL (evilmatmul)
do i=1,material_Nslip(matID)
constitutive_passing_stress(i) = material_c1(matID)*material_Gmod(matID)*material_bg(matID)*&
sqrt(constitutive_rho_p(i))
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))
constitutive_activation_volume(i) = material_c3(matID)*constitutive_jump_width(i)*material_bg(matID)**2.0_pReal
constitutive_rho_m(i) = (2.0_pReal*kB*Tp*sqrt(constitutive_rho_p(i)))/&
(material_c1(matID)*material_c3(matID)*material_Gmod(matID)*constitutive_jump_width(i)*&
material_bg(matID)**3.0_pReal)
constitutive_g0_slip(i) = constitutive_rho_m(i)*material_bg(matID)*attack_frequency*constitutive_jump_width(i)*&
exp(-(material_Qedge(matID)+constitutive_passing_stress(i)*constitutive_activation_volume(i))/&
(kB*Tp))
exp(-material_Qedge(matID)/(kB*Tp))
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_t(i)=0.0_pReal
do j=1,material_Ntwin(matID)
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_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 *
@ -1039,168 +977,48 @@ subroutine constitutive_LpAndItsTangent(Lp,dLp_dTstar,Tstar_v,state,Tp,ipc,ip,el
!* - dLp_dTstar : derivative of Lp (4th-order tensor) *
!*********************************************************************
use prec, only: pReal,pInt
use lattice, only: lattice_Sslip,lattice_Sslip_v,lattice_Stwin,lattice_Stwin_v,lattice_TwinShear
use lattice, only: lattice_Sslip,lattice_Sslip_v
use math, only: pi,math_Plain3333to99
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,startIdxTwin,i,j,k,l,m,n
real(pReal) Tp,Ftwin
integer(pInt) i,j,k,l,m,n,ipc,ip,el
integer(pInt) matID
real(pReal) Tp
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(3,3) :: Lp,Sslip,Stwin
real(pReal), dimension(3,3) :: Lp,Sslip
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))))
Lp = 0.0_pReal
dLp_dTstar3333 = 0.0_pReal
!* Calculation of Lp - slip
gdot_slip = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
Lp = 0.0_pReal
gdot_slip = 0.0_pReal
dgdot_dtauslip = 0.0_pReal
do i=1,material_Nslip(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))
Sslip = lattice_Sslip(:,:,i,material_CrystalStructure(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)*(tau_slip(i)/abs(tau_slip(i)))*&
sinh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp))
dgdot_dtauslip(i) = (constitutive_g0_slip(i)*constitutive_activation_volume(i))/(Kb*Tp)*&
cosh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp))
endif
Lp=Lp+(1.0_pReal-Ftwin)*gdot_slip(i)*lattice_Sslip(:,:,i,material_CrystalStructure(matID))
Lp = Lp + gdot_slip(i) * Sslip
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
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_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)*dgdot_dtauslip(i)*Sslip(k,l)*Sslip(m,n) !force m,n symmetry
dLp_dTstar3333(k,l,m,n) = dLp_dTstar3333(k,l,m,n) + dgdot_dtauslip(i) * Sslip(k,l) * Sslip(m,n)
endforall
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
@ -1223,56 +1041,37 @@ function constitutive_dotState(Tstar_v,state,Tp,ipc,ip,el)
!*********************************************************************
use prec, only: pReal,pInt
use math, only: pi
use lattice, only: lattice_Sslip_v,lattice_Stwin_v
use lattice, only: lattice_Sslip_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,j,startIdxTwin
real(pReal) Tp,Ftwin
integer(pInt) i,j,ipc,ip,el
integer(pInt) matID
real(pReal) Tp
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
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: locks,grainboundaries
real(pReal), dimension(material_Nslip(constitutive_matID(ipc,ip,el))) :: athermal_recovery,thermal_recovery
!* 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)
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
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)
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)*(tau_slip(i)/abs(tau_slip(i)))*&
sinh(((abs(tau_slip(i))-constitutive_passing_stress(i))*constitutive_activation_volume(i))/(Kb*Tp))
endif
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))
athermal_recovery(i) = material_c7(matID)*state(i)*abs(gdot_slip(i))
thermal_recovery(i) = material_c8(matID)*abs(tau_slip(i))*state(i)**2*((material_D0(matID)*material_bg(matID)**3)/&
(kB*Tp))*exp(-material_Qsd(matID)/(kB*Tp))
constitutive_dotState(i) = locks(i)+grainboundaries(i)-athermal_recovery(i)-thermal_recovery(i)
enddo
return
@ -1293,32 +1092,26 @@ function constitutive_post_results(Tstar_v,state,Tp,dt,ipc,ip,el)
!* constitutive_Nresults has to be set accordingly in _Assignment *
!*********************************************************************
use prec, only: pReal,pInt
use lattice, only: lattice_Sslip_v
implicit none
!* Definition of variables
integer(pInt) ipc,ip,el
integer(pInt) matID,i,startIdxTwin
real(pReal) dt,Tp,tau_slip
integer(pInt) i,ipc,ip,el
integer(pInt) matID
real(pReal) Tp,dt
real(pReal), dimension(6) :: Tstar_v
real(pReal), dimension(constitutive_Nstatevars(ipc,ip,el)) :: state
real(pReal), dimension(constitutive_Nresults(ipc,ip,el)) :: constitutive_post_results
!* Get the material-ID from the triplet(ipc,ip,el)
matID = constitutive_matID(ipc,ip,el)
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
!* Output variables
if(constitutive_Nresults(ipc,ip,el)==0) return
constitutive_post_results(1) = sum(state(1:material_Nslip(matID)))
constitutive_post_results(2) = sum(state((startIdxTwin+1):(startIdxTwin+material_Ntwin(matID))))
do i=1,material_Nslip(matID)
constitutive_post_results(2+i) = state(i)
enddo
return
end function

46
trunk/mattex.mpie
View File

@ -2,12 +2,12 @@
[TWIP steel FeMnC]
lattice_structure 1
Nslip 12
Ntwin 12
Ntwin 0
## Elastic constants
# Unit in [Pa]
C11 245.0e9
C12 105.0e9
C44 65.0e9
C11 183.9e9
C12 101.9e9
C44 115.4e9
## Parameters for phenomenological modeling
# Unit in [Pa]
@ -23,39 +23,45 @@ hardening_coefficients 1.0 1.4
## Parameters for dislocation-based modeling
# Burgers vector [m]
burgers 2.56e-10
# Activation energy for dislocation glide [J/K]
Qedge 3.0e-19
# Initial dislocation density [m]²
rho0 2.8e13
# Activation energy for dislocation glide [J/K] (0.5*G*b^3)
Qedge 5.5e-19
# Activation energy for self diffusion [J/K] (gamma-iron)
Qsd 4.7e-19
# Vacancy diffusion coeffficent (gamma-iron)
diff0 4.0e-5
# Average grain size [m]
grain_size 2.0e-5
# Dislocation interaction coefficients
interaction_coefficients 1.0 2.2 3.0 1.6 3.8 4.5
# Initial dislocation density [m]²
rho0 6.0e12
# Passing stress adjustment
c1 0.1
# Jump width adjustment
c2 2.0
# Activation volume adjustment
c3 1.2
c3 1.0
# Average slip distance adjustment for lock formation
# = c4(Anxin)*c2(Anxin) !!!!!!
c4 14.25
c4 50.0
# Average slip distance adjustment when grain boundaries
c5 1.0
# Average slip distance adjustment when twin boundaries
c6 0.1
c5 1.0
# Athermal recovery adjustment
c7 23.5
# Dislocation interaction coefficients
interaction_coefficients 1.0 2.2 3.0 1.6 3.8 4.5
c7 8.0
# Thermal recovery adjustment (plays no role for me)
c8 1.0e10
## Parameters for mechanical twinning
# Average twin thickness (stacks) [m]
stack_size 5.0e-8
# Total twin volume fraction saturation
f_sat 0.2
f_sat 1.0
# Average slip distance adjustment when twin boundaries
c6
# Scaling potential nucleation sites
site_scaling 1.0e-7
site_scaling 1.0e-6
# Scaling the P-K force on the twinning dislocation
q1 0.75
q1 1.0
# Scaling the resolved shear stress
q2 1.0