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IntegrateCrystalEqns.f90
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IntegrateCrystalEqns.f90
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!***********************************************************************
subroutine ComputeStressResidual(rhs, stress, stressini, estran, rss, &
mudot, gamdot, kappa, dtime, argmin, argmax, dstrain, VecM, &
VecS, ZVec, grainid)
!***********************************************************************
use NumType
use FILEIO
use PlaPar
use ElasMod
implicit none
REAL(KIND=8) :: stress(NVEC),stressini(NVEC)
REAL(KIND=8) :: kappa(MaxNumSlip)
REAL(KIND=8) :: argmin, argmax, dtime,dstrain(NVEC)
REAL(KIND=8) :: rhs(NVec), PartResid(NVec)
REAL(KIND=8) :: estran(NVEC)
INTEGER :: is,ip, i,j, ip1,ip2, numslip, grainid
REAL(KIND=8) :: InnerProductVec, SSKineticEqn
REAL(KIND=8) :: crss(MaxNumSlip),rss(MaxNumSlip), gamdot(MaxNumSlip),mudot(6)
REAL(KIND=8) :: ZTen(NSD,NSD,MaxNumSlip),ZVec(NVEC,MaxNumSlip)
INTEGER :: StressSolveflat
REAL(KIND=8) :: VecM(NSD,MaxNumSlip)
REAL(KIND=8) :: VecS(NSD,MaxNumSlip)
!-----------------------------------------------------------------------
! initialize eigenstrain rate
mudot=pzero
! determine number of slip systems
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip = PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip = PhSlip(2)
else
call RunTimeError(FILE_O,'Error: crystalID exceed the existing lattice!')
end if
do is = 1, numslip
rss(is) = InnerProductVec(stress(:), ZVec(:,is), NVEC)
crss(is) = kappa(is)
gamdot(is) = SSKineticEqn(rss(is),crss(is),KDDGAM, argmin, argmax,is,grainid)
mudot(:) = mudot(:)+gamdot(is)*ZVec(:,is)
end do
rhs = (stress-stressini)/dtime-MATMUL(Lijkl(:,:,grainid),(dstrain/dtime-mudot))
return
END
!***********************************************************************
SUBROUTINE ComputeStressJacobian(lhs, rss, kappa, dtime, stress, VecM, &
VecS, Zvec, grainid)
!***********************************************************************
use NumType
use PlaPar
use FILEIO
use ElasMod
implicit none
real(kind=8) :: dtime
real(kind=8) :: lhs(NVEC,NVEC), rss(MaxNumSlip)
real(kind=8) :: kappa(MaxNumSlip)
real(kind=8) :: lhsPart(6,6)
real(kind=8) :: dmudotdsigma(6,6), I_P(6,6), Term1(6,6), Term2(6,6)
real(kind=8) :: delta,tem
integer :: is, ip, ip1, ip2, i, numslip, grainid
real(kind=8) :: crss(MaxnumSlip)
real(kind=8) :: stress(6)
real(kind=8) :: temp2(6,6),omega(MaxNumSlip)
real(kind=8) :: InnerProductVec
real(kind=8) :: SignOf
real(kind=8) :: VecM(3,MaxNumSlip)
real(kind=8) :: VecS(3,MaxNumSlip)
real(kind=8) :: ZTen(3,3,MaxNumSlip),ZVec(6,MaxNumSlip)
!-----------------------------------------------------------------------
! initialization
tem = 295.0
dmudotdsigma = pzero
omega = pzero
! omega and dudotdsigma
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
do is = 1, numslip
if (is.le.3) then
omega(is)=0.5*Plap%ddavg(1,1)*Plap%vid(1,1)*Plap%burgers(1,1)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,1)/Plap%detV(1,1))*Plap%detV(1,1)/Plap%kbolt/tem)*Plap%detV(1,1)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.6) then
omega(is)=0.5*Plap%ddavg(1,2)*Plap%vid(1,2)*Plap%burgers(1,2)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,2)/Plap%detV(1,2))*Plap%detV(1,2)/Plap%kbolt/tem)*Plap%detV(1,2)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.12) then
omega(is)=0.5*Plap%ddavg(1,3)*Plap%vid(1,3)*Plap%burgers(1,3)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,3)/Plap%detV(1,3))*Plap%detV(1,3)/Plap%kbolt/tem)*Plap%detV(1,3)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.30) then
omega(is)=0.5*Plap%ddavg(1,4)*Plap%vid(1,4)*Plap%burgers(1,4)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,4)/Plap%detV(1,4))*Plap%detV(1,4)/Plap%kbolt/tem)*Plap%detV(1,4)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else
call RunTimeError(File_o, 'ComputeJacobian: is exceed number of slip')
end if
call OuterProductVec(ZVec(1,is),ZVec(1,is),temp2,6)
dmudotdsigma(:,:)=dmudotdsigma(:,:)+omega(is)*temp2
enddo
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
do is = 1, numslip
omega(is)=0.5*Plap%ddavg(2,1)*Plap%vid(2,1)*Plap%burgers(2,1)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(2,1)/Plap%detV(2,1))*Plap%detV(2,1)/Plap%kbolt/tem)*Plap%detV(2,1)/Plap%kbolt/tem!*SignOf(rss(is,ip)
call OuterProductVec(ZVec(1,is),ZVec(1,is),temp2,6)
dmudotdsigma(:,:)=dmudotdsigma(:,:)+omega(is)*temp2
enddo
else
call RunTimeError(FILE_O,'Error: crystalID exceed the existing lattice!')
end if
! loacal jacobian
lhs = 1/dtime*Ident4th+MATMUL(Lijkl(:,:,grainid),dmudotdsigma)
return
end
!***********************************************************************
SUBROUTINE ComputeStress(rhs, stress, stressini, estran, rss, mudot, &
gamdot, kappa, dtime, argmin, argmax, dstrain, VecM, VecS, &
ZVec, iterCounterN, tolerNewt, kstep, kinc, ierr, noel, grainid)
!***********************************************************************
use NumType
use FILEIO
implicit none
INTEGER :: iterCounterN, kstep, kinc, info, ierr, grainid
REAL(KIND=8) :: stress(NVEC), stress0(NVEC), stressini(NVEC)
REAL(KIND=8) :: kappa(MaxNumSlip)
REAL(KIND=8) :: argmin, argmax, dtime,dstrain(NVEC), tolerNewt
REAL(KIND=8) :: rhs(6), PartResid(6), lhs(6, 6)
REAL(KIND=8) :: estran(NVEC)
REAL(KIND=8) :: norm_stress0, norm_kappa0, norm_stress, norm_kappa
REAL(KIND=8) :: rhs_norm, rhs_norm0
REAL(KIND=8) :: delstress(NVEC), delstressvec(NVEC)
INTEGER :: is,ip, i,j, ip1,ip2, iterNewt, noel
INTEGER :: indx(NVEC)
REAL(KIND=8) :: InnerProductVec, SSKineticEqn, search
REAL(KIND=8) :: crss(MaxNumSlip),rss(MaxNumSlip), gamdot(MaxNumSlip)
REAL(KIND=8) :: delIdent4th(6,6)
REAL(KIND=8) :: mudot(6), I_P(6,6), mult1(6), mult2(6),temp1(6)
INTEGER :: StressSolveflat
LOGICAL :: converged, converged2
REAL(KIND=8) :: VecM(NSD,MaxNumSlip)
REAL(KIND=8) :: VecS(NSD,MaxNumSlip)
REAL(KIND=8) :: ZTen(NSD,NSD,MaxNumSlip),ZVec(NVEC,MaxNumSlip)
!-----------------------------------------------------------------------
if (debug==1) write(file_e,*) '-------------Begin Stress Solve-----------------'
call ComputeStressResidual(rhs, stress, stressini, estran, rss, &
mudot, gamdot, kappa, dtime, argmin, argmax, dstrain, VecM, &
VecS, ZVec, grainid)
if (debug==1 .and. noel==1) write(FILE_E, '(A30, /, 6e12.5)') 'Initial Residual is:', rhs
! initial valuies for the norm of stress of each part
rhs_norm0=norm2(rhs)
iterNewt = 0
converged = .false.
do while (iterNewt .lt. iterCounterN .and. .not. converged )
iterNewt=iterNewt+1
if (debug==1 .and. noel==1) write(file_e, *) 'iterNewt= ', iterNewt
stress0=stress
if (debug==1) then
write(file_E, *) 'stress= '
write(file_E, *) stress(:)
endif
! solve for the crystal stresses
! compute local jacobian
call ComputeStressJacobian(lhs, rss, kappa, dtime, stress, VecM, &
VecS, Zvec, grainid)
if (debug==1 .and. noel==1) then
write(file_E, *) 'kinc=', kinc
write(file_E, *) 'lhs= '
write(file_E, '( 6(2x, E12.5))') lhs
write(file_E, *) 'rhs= '
write(file_E, '( 6(2x, E12.5))') rhs
write(file_E,*) 'dstrain='
write(file_E, '( 6(2x, E12.5))') dstrain
endif
!
! solve for the increment of stress
CALL DGESV( 6, 1, lhs, 6, indx, rhs, 6, INFO )
if (debug==1) write(File_E,*) 'INFO= ', INFO
if (INFO<0) then
ierr=XTAL_SING_JACOBIAN
write(File_o,*) 'StressSolve: Jacobian is singular when kinc=', kinc
return
endif
! Please notice that here both delstress and rhs are 6*NPart by one vector
! we just rearrange them to be in the matrix form
delstressVec=rhs
delstress=reshape(delstressVec, shape(delstress))
search = pone
stress=stress0-search*delstress
if (debug==1 .and. noel==1) then
write(file_E,*) 'delstress='
write(file_E, '( 6(2x, E12.5))') delstress
endif
call ComputeStressResidual(rhs, stress, stressini, estran, rss, &
mudot, gamdot, kappa, dtime, argmin, argmax, dstrain, VecM, &
VecS, ZVec, grainid)
if (debug==1) write(FILE_E, '(A30, /, 12e12.5)') 'New Residual is:', rhs
! update stresses
rhs_norm=norm2(rhs)
! Add a linear search
do while ((rhs_norm .gt. rhs_norm0) .and. (kinc .gt. 1) )
search = search*0.5
if (search .lt. TINY(1.d0)) then
call WriteWarning(File_O, 'StressSolveDeviatoric: LS Failed, search < TINY')
ierr = XTAL_LS_FAILED
return
endif
stress=stress0-search*delstress
call ComputeStressResidual(rhs, stress, stressini, estran, rss, &
mudot, gamdot, kappa, dtime, argmin, argmax, dstrain, VecM, &
VecS, ZVec, grainid)
rhs_norm=norm2(rhs)
enddo
rhs_norm0 = rhs_norm
converged=converged2(rhs, tolerNewt, 6)
enddo
if (noel==1 .and. debug==1) then
write(file_e,*) 'at kinc = ', kinc, 'stress increment is:'
write(file_e,'(6E20.10)') stressini
write(file_E,*) 'dstrain='
write(file_E, '( 6(2x, E12.5))') dstrain
end if
if (iterNewt.ge. iterCounterN) then
call WriteWarning(FILE_O, 'ComputeStress: Netwon iters > iterCounterN')
ierr = XTAL_MAX_ITERS_HIT
return
endif
! echo data if convergence is achieved
if (converged .and. debug==1) then
write(File_E,*) 'stress is'
write(File_E,'(6E15.8)') stress(:)
end if
return
end
!***********************************************************************
SUBROUTINE PlasticModuli(cepmod, stress, kappa, dtime, VecM, VecS, ZVec, grainid, noel)
!***********************************************************************
use NumType
use PlaPar
USE FILEIO
use ElasMod
implicit none
real(kind=8) :: cepmod(NVEC,NVEC)
real(kind=8) :: Stress(NVEC)
real(kind=8) :: kappa(MaxNumSlip)
real(kind=8) :: dmudotdsigma(6,6),dmudotdrss
real(kind=8) :: rss(MaxNumSlip), ZZT(6,6,MaxNumSlip)
integer :: ip,is,i,j,numslip, grainid, noel
real(kind=8) :: del, I_P(6,6)
real(kind=8) :: InnerProductVec
real(kind=8), ALLOCATABLE :: A(:,:), ATemp(:,:), F(:,:)
real(kind=8) :: phiab(6,6),etaab(6,6),fb(6,6)
real(kind=8) :: dtime,tem
real(kind=8) :: ddd
real(kind=8) :: SignOf
integer :: Cepmodflag
integer :: indx(6)
REAL(kind=8) :: VecM(3,MaxNumSlip)
REAL(kind=8) :: VecS(3,MaxNumSlip)
REAL(kind=8) :: ZTen(3,3,MaxNumSlip),ZVec(6,MaxNumSlip)
REAL(kind=8) :: start_time, end_time
!-----------------------------------------------------------------------
! Caculate d(sigma_n+1^(beta))/d(epsilonbar_(n+1))
allocate (A(6,6), ATemp(6,6), F(6,6))
tem = 295.0d0
Cepmodflag = 0
A = pzero
dmudotdsigma = pzero
dmudotdrss = pzero
! Caculate the rss
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
do is=1,NumSlip
rss(is)=InnerProductVec(stress(:),ZVec(:,is),6)
Call OuterProductVec(ZVec(:,is),ZVec(:,is),ZZT(:,:,is),6)
if (is.le.3) then
dmudotdrss=0.5*Plap%ddavg(1,1)*Plap%vid(1,1)*Plap%burgers(1,1)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,1)/Plap%detV(1,1))*Plap%detV(1,1)/Plap%kbolt/tem)*Plap%detV(1,1)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.6) then
dmudotdrss=0.5*Plap%ddavg(1,2)*Plap%vid(1,2)*Plap%burgers(1,2)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,2)/Plap%detV(1,2))*Plap%detV(1,2)/Plap%kbolt/tem)*Plap%detV(1,2)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.12) then
dmudotdrss=0.5*Plap%ddavg(1,3)*Plap%vid(1,3)*Plap%burgers(1,3)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,3)/Plap%detV(1,3))*Plap%detV(1,3)/Plap%kbolt/tem)*Plap%detV(1,3)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else if (is.le.30) then
dmudotdrss=0.5*Plap%ddavg(1,4)*Plap%vid(1,4)*Plap%burgers(1,4)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(1,4)/Plap%detV(1,4))*Plap%detV(1,4)/Plap%kbolt/tem)*Plap%detV(1,4)/Plap%kbolt/tem!*SignOf(rss(is,ip))
else
call RunTimeError(File_o, 'Plastic Moduli: is exceed number of slip')
end if
dmudotdsigma(:,:)=dmudotdsigma(:,:)+dmudotdrss*ZZT(:,:,is)
enddo
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
do is=1,NumSlip
rss(is)=InnerProductVec(stress(:),ZVec(:,is),6)
Call OuterProductVec(ZVec(:,is),ZVec(:,is),ZZT(:,:,is),6)
dmudotdrss=0.5*Plap%ddavg(2,1)*Plap%vid(2,1)*Plap%burgers(2,1)**2.*exp(((dabs(rss(is))&
-kappa(is))-Plap%detF(2,1)/Plap%detV(2,1))*Plap%detV(2,1)/Plap%kbolt/tem)*Plap%detV(2,1)/Plap%kbolt/tem!*SignOf(rss(is,ip))
dmudotdsigma(:,:)=dmudotdsigma(:,:)+dmudotdrss*ZZT(:,:,is)
enddo
else
call RunTimeError( FILE_O, 'Error: crystalID exceed the existing lattice!')
end if
!---> LY changed
call CheckMatriceZero(dmudotdsigma(1,1),6)
!---> LY changed
A(:,:) = Ident4th/dtime + MATMUL(Lijkl(:,:,grainid),dmudotdsigma)
F(:,:) = Lijkl(:,:,grainid)/dtime
! Solve for cepmod as a whole and cepmod in each part is stored in cepmod
CALL DGESV( 6, 6, A, 6, indx, F, 6, Cepmodflag )
! Split cepmodm into cepmod(:,:,ip)
cepmod = F
deallocate (A, ATemp, F)
! echo data for debugging
if(debug==1) then
write(FILE_E,*) 'at noel',noel,'tangential moduli is'
write(FILE_E,'(6E20.10)') cepmod(:,:)
end if
return
END
!***********************************************************************
SUBROUTINE IntegrateHardening(kappa, kappa_n, eqvalues, mu, mu_n, &
estran, estran_n, stress, rss, mudot, gamdot, dtime, &
kInteg_Code, VecM, VecS,ZVec, argmin, argmax, dd_for, &
dd_revp, dd_revn, stressf, dd_rev0, dd_deb, time, dstrain, &
dd_all, dd_max, noel, grainid)
!***********************************************************************
use NumType
use PlaPar
use FileIO
implicit none
real(kind=8) :: estran(6),estran_n(6)
real(kind=8) :: kappa(MaxNumSlip), kappa_n(MaxNumSlip)
real(kind=8) :: Stress(NVEC), eqvalues(NEQVA)
real(kind=8) :: crss(MaxNumSlip),rss(MaxNumSlip)
real(kind=8) :: gamdot(MaxNumSlip), SHEARATE(MaxNumSlip)
real(kind=8) :: mu(NVEC), mudot(NVEC)
real(kind=8) :: dd_for (MaxNumSlip)
real(kind=8) :: dd_revp (MaxNumSlip)
real(kind=8) :: dd_revn (MaxNumSlip)
real(kind=8) :: stressf (MaxNumSlip)
real(kind=8) :: dd_rev0 (MaxNumSlip)
real(kind=8) :: dd_deb (MaxNumSlip)
real(kind=8) :: dstrain (NVEC)
real(kind=8) :: dd_deb_tot
real(kind=8) :: dd_all
real(kind=8) :: argmin, argmax, kappa_sat
real(kind=8) :: c, g_n, g_s, g
real(kind=8) :: dkappa, gamtot_n, mu_n(NVEC), delgam, fac
real(kind=8) :: kTHETA
real(kind=8) :: dtime, time
real(kind=8) :: erate
real(kind=8) :: k2
real(kind=8) :: dfordsh
real(kind=8) :: drevpdsh
real(kind=8) :: drevndsh
real(kind=8) :: ddebdsh
real(kind=8) :: dkappa1
real(kind=8) :: dkappa2
real(kind=8) :: dkappa3
real(kind=8) :: dkappa3_s
real(kind=8) :: tem
real(kind=8) :: temrate
real(kind=8) :: pcoef
real(kind=8) :: rate_ref
real(kind=8) :: inter_ref
real(kind=8) :: kdeb
real(kind=8) :: dd_max
real(kind=8) :: dd_min
real(kind=8) :: dd_tot(MaxNumSlip)
real(kind=8) :: InnerProductVec, SSKineticEqn
real(kind=8) :: VecM(3,MaxNumSlip)
real(kind=8) :: VecS(3,MaxNumSlip)
real(kind=8) :: ZTen(3,3,MaxNumSlip),ZVec(6,MaxNumSlip)
integer :: is, ip, jk, kInteg_Code, numslip, grainid, noel
data tem /295.0d0/
data temrate /0.0d0/
data pcoef /0.5d0/
data rate_ref /1.0d7/
data inter_ref /0.9d0/
data kdeb /0.86d0/
data kTHETA /1.0d0/
!-----------------------------------------------------------------------
if (debug==1) write(File_E,*) '---- Start IntegrateHardening! ----'
crss = pzero
dd_deb_tot = pzero
! dd
mudot(:)=pzero
! determine phase
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
else
call RunTimeError( FILE_O, 'Error: crystalID exceed the existing lattice!')
end if
dd_all=0.0d0
do is = 1, numslip
rss(is) = DOT_PRODUCT(stress(:), ZVec(:,is))
crss(is)= kappa(is)
gamdot(is) = SSKineticEqn(rss(is),crss(is),KDDGAM, argmin, argmax,is,grainid)
mudot(:)=mudot(:) + gamdot(is)*ZVec(:, is)
dd_tot(is)=dd_for(is)+dd_revp(is)+dd_revn(is)
dd_deb_tot=dd_deb_tot+dd_deb(is)
if ((dd_deb(is)+dd_tot(is)) .GE. dd_all) dd_all=dd_deb(is)+dd_tot(is)
if (sign(1.0,rss(is)) .ne. stressf(is)) then
stressf(is)=sign(1.0,rss(is))
dd_rev0(is)=dd_tot(is)
end if
enddo
if (debug==1) write(FILE_E,*) dd_all
! dd_max
dd_max=0.0d0
if (dd_all .GE. dd_max) dd_max=dd_all
! echo some data for debugging
if (debug==1 .and. noel==1) then
write(FILE_E,*) 'rss:'
write(FILE_E,*) rss(:)
write(FILE_E,*) 'dd_for:'
write(FILE_E,*) dd_for(:)
write(FILE_E,*) 'dd_revp:'
write(FILE_E,*) dd_revp(:)
write(FILE_E,*) 'dd_revn:'
write(FILE_E,*) dd_revn(:)
write(FILE_E,*) 'stressf:'
write(FILE_E,*) stressf(:)
write(FILE_E,*) 'dd_rev0:'
write(FILE_E,*) dd_rev0(:)
write(FILE_E,*) 'dd_deb:'
write(FILE_E,*) dd_deb(:)
endif
eqvalues(kSHRATE) = pzero
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
else
call RunTimeError( FILE_O, 'Error: crystalID exceed the existing lattice!')
end if
do is = 1, numslip
eqvalues(kSHRATE) = eqvalues(kSHRATE) + dabs(gamdot(is))
enddo
! accumulated shear strain: gamtot
eqvalues(kGAMTOT) = eqvalues(kGAMTOT_n) + eqvalues(kSHRATE)*dtime
eqvalues(kMISES) = 0.5d0 *sqrt((Stress(1))**2 &
+ (Stress(2))**2 &
+ (Stress(3))**2 &
+ 6.d0*(Stress(6)**2+Stress(5)**2+Stress(4)**2))
! inelastic strain mu and total elastic strain for each part.
mu = mu_n
mu(:) = mu_n(:) + mudot(:)*dtime
if (debug==1) then
write(file_e,*) 'gamdot(:): '
write(file_e,*) gamdot(:)
write(file_e,*) 'eqvalues(kshrate), eqvalues(kgamtot), mu: '
write(file_e,*) eqvalues(kshrate), eqvalues(kgamtot), mu(:)
endif
! integration of hardening law (one hardness/slip system)
if (debug==1) write(FILE_E, *) 'kinteg_code =', kinteg_code
if (kInteg_Code .eq. kHARD_EXPL) then
! explicit update
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
else
call RunTimeError( FILE_O,'Error: crystalID exceed the existing lattice!')
end if
do is = 1, numslip
kappa_sat = Plap%taus0 * ((eqvalues(kSHRATE) / Plap%gamss0)**Plap%xms) !saturated stress
c = dtime*Plap%h0
g_s = kappa_sat - Plap%tausi
g_n = kappa_n(is) - Plap%tausi
if ( (g_n/g_s) .le. 1.0 ) then
g = g_n + c*(1.0-g_n/g_s)*eqvalues(kSHRATE)
else
g = g_n
endif
kappa(is) = g + Plap%tausi
if(debug==1) then
write(file_e,*) 'dkappa, dkappa/dtime='
write(file_e,*) kappa(is)-kappa_n(is), (kappa(is)-kappa_n(is))/dtime
write(File_E,*) 'kappa(is) is:'
write(File_E,*) kappa(is)
end if
enddo
else if (kInteg_Code .eq. kHARD_MIDP) then
! generalized mid-point rule
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
else
call RunTimeError( FILE_O,'Error: crystalID exceed the existing lattice!')
end if
do is = 1, numslip
kappa_sat = Plap%taus0 * ((eqvalues(kSHRATE) / Plap%gamss0)**Plap%xms)
c = dtime*Plap%h0
g_s = kappa_sat - Plap%tausi
g_n = kappa_n(is) - Plap%tausi
if ( (g_n/g_s) .le. 1.0 ) then
g = g_n + c*((1.0-kTHETA)*(1.0-g_n/g_s)*eqvalues(kSHRATE_n)+(kTHETA)*eqvalues(kSHRATE))
g = g / (1.0 + c*kTHETA*eqvalues(kSHRATE)/g_s)
else
g = g_n
endif
kappa(is) = g + Plap%tausi
enddo
else if (kInteg_Code .eq. kHARD_ANAL) then
! annihilation
gamtot_n = eqvalues(kGAMTOT_n)
delgam = eqvalues(kSHRATE) * dtime
!write(*,*) 'gamtot_n, delgam=', gamtot_n, delgam
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
else
call RunTimeError( FILE_O,'Error: crystalID exceed the existing lattice!')
end if
do is= 1, numslip
kappa_sat = Plap%taus0 * ((eqvalues(kSHRATE) / Plap%gamss0)**Plap%xms)
g_s = kappa_sat - Plap%tausi
fac = dabs(Plap%h0/g_s)
dkappa = 0.0
do jk = 1, numslip
dkappa = dkappa + dabs(gamdot(jk))*dtime/delgam
enddo
dkappa = dkappa * g_s * exp(-gamtot_n*fac) * (1.0 - exp(-delgam*fac))
if (debug==1) then
write(file_e,*) 'kappa_sat, g_s, fac, dkappa: ', kappa_sat, g_s, fac, dkappa
endif
kappa(is) = kappa_n(is) + dkappa
if (debug==1) write(*,*) kappa(is)
enddo
else if (kInteg_Code .eq. kHARD_DD) then
if (debug==1) write(File_E,*) '------------------- kHARD_DD begin ------------------------------'
dkappa3=pzero
if (Plap%crystalID(grainid) .eq. kHCP) then
numslip=PhSlip(1)
do is= 1, numslip
erate=dabs(gamdot(is))
if (is.le.3) then
k2 = Plap%k1(1,1)*Plap%burgers(1,1)*inter_ref/Plap%gref(1,1)*(1.-Plap%kbolt*tem &
*log(erate/rate_ref)/(Plap%Drag(1,1))/Plap%burgers(1,1)**3.0)
dfordsh=(1.-pcoef)*Plap%k1(1,1)*sqrt(dd_tot(is))-k2*dd_for(is)
if (stressf(is) .ge. 0.0d0) then
drevpdsh=pcoef*Plap%k1(1,1)*sqrt(dd_tot(is))-k2*dd_revp(is)
drevndsh=-Plap%k1(1,1)*sqrt(dd_tot(is))*(dd_revn(is)/dd_rev0(is))
else
drevndsh=pcoef*Plap%k1(1,1)*sqrt(dd_tot(is))-k2*dd_revn(is)
drevpdsh=-Plap%k1(1,1)*sqrt(dd_tot(is))*(dd_revp(is)/dd_rev0(is))
end if
dkappa1=Plap%sref(1,1)/Plap%sita(1,1)*(1.-exp((tem-Plap%sita_ref(1,1))&
/Plap%sita(1,1)))*temrate*dtime
dkappa2=0.5*Plap%burgers(1,1)*inter_ref*Plap%shmu(1,1)/sqrt(dd_tot(is))&
*(dfordsh+drevndsh+drevpdsh)*abs(gamdot(is))*dtime
kappa(is)=kappa(is)+dkappa1+dkappa2
dd_for(is)=dd_for(is)+dfordsh*abs(gamdot(is))*dtime
dd_revp(is)=dd_revp(is)+drevpdsh*abs(gamdot(is))*dtime
dd_revn(is)=dd_revn(is)+drevndsh*abs(gamdot(is))*dtime
ddebdsh=Plap%qsub(1,1)*Plap%burgers(1,1)*sqrt(dd_deb_tot)*k2*dd_for(is)
dkappa3_s=-0.5*kdeb*Plap%shmu(1,1)*Plap%burgers(1,1)/sqrt(dd_deb_tot)*&
(log(Plap%burgers(1,1)*sqrt(dd_deb_tot))+1.0)*ddebdsh*abs(gamdot(is))*dtime
dkappa3=dkappa3+dkappa3_s
dd_deb(is)=dd_deb(is)+ddebdsh*abs(gamdot(is))*dtime
else if (is.le.6) then
k2=Plap%k1(1,2)*Plap%burgers(1,2)*inter_ref/Plap%gref(1,2)*(1.-Plap%kbolt*tem &
*log(erate/rate_ref)/(Plap%Drag(1,2))/Plap%burgers(1,2)**3.0)
dfordsh=(1.-pcoef)*Plap%k1(1,2)*sqrt(dd_tot(is))-k2*dd_for(is)
if (stressf(is) .ge. 0.0d0) then
drevpdsh=pcoef*Plap%k1(1,2)*sqrt(dd_tot(is))-k2*dd_revp(is)
drevndsh=-Plap%k1(1,2)*sqrt(dd_tot(is))*(dd_revn(is)/dd_rev0(is))
else
drevndsh=pcoef*Plap%k1(1,2)*sqrt(dd_tot(is))-k2*dd_revn(is)
drevpdsh=-Plap%k1(1,2)*sqrt(dd_tot(is))*(dd_revp(is)/dd_rev0(is))
end if
dkappa1=Plap%sref(1,2)/Plap%sita(1,2)*(1.-exp((tem-Plap%sita_ref(1,2))&
/Plap%sita(1,2)))*temrate*dtime
dkappa2=0.5*Plap%burgers(1,2)*inter_ref*Plap%shmu(1,2)/sqrt(dd_tot(is))&
*(dfordsh+drevndsh+drevpdsh)*abs(gamdot(is))*dtime
kappa(is)=kappa(is)+dkappa1+dkappa2
dd_for(is)=dd_for(is)+dfordsh*abs(gamdot(is))*dtime
dd_revp(is)=dd_revp(is)+drevpdsh*abs(gamdot(is))*dtime
dd_revn(is)=dd_revn(is)+drevndsh*abs(gamdot(is))*dtime
ddebdsh=Plap%qsub(1,2)*Plap%burgers(1,2)*sqrt(dd_deb_tot)*k2*dd_for(is)
dkappa3_s=-0.5*kdeb*Plap%shmu(1,2)*Plap%burgers(1,2)/sqrt(dd_deb_tot)*&
(log(Plap%burgers(1,2)*sqrt(dd_deb_tot))+1.0)*ddebdsh*abs(gamdot(is))*dtime
dkappa3=dkappa3+dkappa3_s
dd_deb(is)=dd_deb(is)+ddebdsh*abs(gamdot(is))*dtime
else if (is.le.12) then
k2=Plap%k1(1,3)*Plap%burgers(1,3)*inter_ref/Plap%gref(1,3)*(1.-Plap%kbolt*tem &
*log(erate/rate_ref)/(Plap%Drag(1,3))/Plap%burgers(1,3)**3.0)
dfordsh=(1.-pcoef)*Plap%k1(1,3)*sqrt(dd_tot(is))-k2*dd_for(is)
if (stressf(is) .ge. 0.0d0) then
drevpdsh=pcoef*Plap%k1(1,3)*sqrt(dd_tot(is))-k2*dd_revp(is)
drevndsh=-Plap%k1(1,3)*sqrt(dd_tot(is))*(dd_revn(is)/dd_rev0(is))
else
drevndsh=pcoef*Plap%k1(1,3)*sqrt(dd_tot(is))-k2*dd_revn(is)
drevpdsh=-Plap%k1(1,3)*sqrt(dd_tot(is))*(dd_revp(is)/dd_rev0(is))
end if
dkappa1=Plap%sref(1,3)/Plap%sita(1,3)*(1.-exp((tem-Plap%sita_ref(1,3))&
/Plap%sita(1,3)))*temrate*dtime
dkappa2=0.5*Plap%burgers(1,3)*inter_ref*Plap%shmu(1,3)/sqrt(dd_tot(is))&
*(dfordsh+drevndsh+drevpdsh)*abs(gamdot(is))*dtime
kappa(is)=kappa(is)+dkappa1+dkappa2
dd_for(is)=dd_for(is)+dfordsh*abs(gamdot(is))*dtime
dd_revp(is)=dd_revp(is)+drevpdsh*abs(gamdot(is))*dtime
dd_revn(is)=dd_revn(is)+drevndsh*abs(gamdot(is))*dtime
ddebdsh=Plap%qsub(1,3)*Plap%burgers(1,3)*sqrt(dd_deb_tot)*k2*dd_for(is)
dkappa3_s=-0.5*kdeb*Plap%shmu(1,3)*Plap%burgers(1,3)/sqrt(dd_deb_tot)*&
(log(Plap%burgers(1,3)*sqrt(dd_deb_tot))+1.0)*ddebdsh*abs(gamdot(is))*dtime
dkappa3=dkappa3+dkappa3_s
dd_deb(is)=dd_deb(is)+ddebdsh*abs(gamdot(is))*dtime
else if (is.le.30) then
k2=Plap%k1(1,4)*Plap%burgers(1,4)*inter_ref/Plap%gref(1,4)*(1.-Plap%kbolt*tem &
*log(erate/rate_ref)/(Plap%Drag(1,4))/Plap%burgers(1,4)**3.0)
dfordsh=(1.-pcoef)*Plap%k1(1,4)*sqrt(dd_tot(is))-k2*dd_for(is)
if (stressf(is) .ge. 0.0d0) then
drevpdsh=pcoef*Plap%k1(1,4)*sqrt(dd_tot(is))-k2*dd_revp(is)
drevndsh=-Plap%k1(1,4)*sqrt(dd_tot(is))*(dd_revn(is)/dd_rev0(is))
else
drevndsh=pcoef*Plap%k1(1,4)*sqrt(dd_tot(is))-k2*dd_revn(is)
drevpdsh=-Plap%k1(1,4)*sqrt(dd_tot(is))*(dd_revp(is)/dd_rev0(is))
end if
dkappa1=Plap%sref(1,4)/Plap%sita(1,4)*(1.-exp((tem-Plap%sita_ref(1,4))&
/Plap%sita(1,4)))*temrate*dtime
dkappa2=0.5*Plap%burgers(1,4)*inter_ref*Plap%shmu(1,4)/sqrt(dd_tot(is))&
*(dfordsh+drevndsh+drevpdsh)*abs(gamdot(is))*dtime
kappa(is)=kappa(is)+dkappa1+dkappa2
dd_for(is)=dd_for(is)+dfordsh*abs(gamdot(is))*dtime
dd_revp(is)=dd_revp(is)+drevpdsh*abs(gamdot(is))*dtime
dd_revn(is)=dd_revn(is)+drevndsh*abs(gamdot(is))*dtime
ddebdsh=Plap%qsub(1,4)*Plap%burgers(1,4)*sqrt(dd_deb_tot)*k2*dd_for(is)
dkappa3_s=-0.5*kdeb*Plap%shmu(1,4)*Plap%burgers(1,4)/sqrt(dd_deb_tot)*&
(log(Plap%burgers(1,4)*sqrt(dd_deb_tot))+1.0)*ddebdsh*abs(gamdot(is))*dtime
dkappa3=dkappa3+dkappa3_s
dd_deb(is)=dd_deb(is)+ddebdsh*abs(gamdot(is))*dtime
else
call RunTimeError(File_o, 'Hardening rule: is exceed maxinum number')
endif
if (debug==1) then
write(file_e,*) 'is =', is
write(file_e,*) 'k2 =', k2
write(file_e,*) 'dfordsh, drevpdsh,drevndsh,ddebdsh='
write(file_e,*) dfordsh, drevpdsh,drevndsh,ddebdsh
write(file_e,*) 'dkappa1, dkappa2,dkappa3='
write(file_e,*) dkappa1,dkappa2,dkappa3_s
endif
enddo
do is= 1, numslip
if (debug==1) then
write(file_e,*) 'is =', is
write(file_e,*) 'dkappa, akappa3,ratio='
write(file_e,*) dkappa1+dkappa2+dkappa3,dkappa3,(dkappa1+dkappa2+dkappa3)/kappa(is)
kappa(is)=kappa(is)+dkappa3
endif
end do
else if (Plap%crystalID(grainid) .eq. kBCC) then
numslip=PhSlip(2)
do is= 1, numslip
erate=dabs(gamdot(is))
k2=Plap%k1(2,1)*Plap%burgers(2,1)*inter_ref/Plap%gref(2,1)*(1.-Plap%kbolt*tem &
*log(erate/rate_ref)/(Plap%Drag(2,1))/Plap%burgers(2,1)**3.0)
dfordsh=(1.-pcoef)*Plap%k1(2,1)*sqrt(dd_tot(is))-k2*dd_for(is)
if (stressf(is) .ge. 0.0d0) then
drevpdsh=pcoef*Plap%k1(2,1)*sqrt(dd_tot(is))-k2*dd_revp(is)
drevndsh=-Plap%k1(2,1)*sqrt(dd_tot(is))*(dd_revn(is)/dd_rev0(is))
else
drevndsh=pcoef*Plap%k1(2,1)*sqrt(dd_tot(is))-k2*dd_revn(is)
drevpdsh=-Plap%k1(2,1)*sqrt(dd_tot(is))*(dd_revp(is)/dd_rev0(is))
end if
dkappa1=Plap%sref(2,1)/Plap%sita(2,1)*(1.-exp((tem-Plap%sita_ref(2,1))&
/Plap%sita(2,1)))*temrate*dtime
dkappa2=0.5*Plap%burgers(2,1)*inter_ref*Plap%shmu(2,1)/sqrt(dd_tot(is))&
*(dfordsh+drevndsh+drevpdsh)*abs(gamdot(is))*dtime
kappa(is)=kappa(is)+dkappa1+dkappa2
dd_for(is)=dd_for(is)+dfordsh*abs(gamdot(is))*dtime
dd_revp(is)=dd_revp(is)+drevpdsh*abs(gamdot(is))*dtime
dd_revn(is)=dd_revn(is)+drevndsh*abs(gamdot(is))*dtime
ddebdsh=Plap%qsub(2,1)*Plap%burgers(2,1)*sqrt(dd_deb_tot)*k2*dd_for(is)
dkappa3_s=-0.5*kdeb*Plap%shmu(2,1)*Plap%burgers(2,1)/sqrt(dd_deb_tot)*&
(log(Plap%burgers(2,1)*sqrt(dd_deb_tot))+1.0)*ddebdsh*abs(gamdot(is))*dtime
dkappa3=dkappa3+dkappa3_s
dd_deb(is)=dd_deb(is)+ddebdsh*abs(gamdot(is))*dtime
if (debug==1) then
write(file_e,*) 'is =', is
write(file_e,*) 'k2 =', k2
write(file_e,*) 'dfordsh, drevpdsh,drevndsh,ddebdsh='
write(file_e,*) dfordsh, drevpdsh,drevndsh,ddebdsh
write(file_e,*) 'dkappa1, dkappa2,dkappa3='
write(file_e,*) dkappa1,dkappa2,dkappa3_s
end if
end do
do is= 1, numslip
if (debug==1) then
write(file_e,*) 'is =', is
write(file_e,*) 'dkappa, akappa3,ratio='
write(file_e,*) dkappa1+dkappa2+dkappa3,dkappa3,(dkappa1+dkappa2+dkappa3)/kappa(is)
end if
kappa(is)=kappa(is)+dkappa3
end do
else
call RunTimeError( FILE_O, 'Error: crystalID exceed the existing lattice!')
end if
else
! wrong code number
call RunTimeError(FILE_O, 'IntegrateHardening: Wrong kInteg_Code!')
endif
return
END
!***********************************************************************
SUBROUTINE IntegrateCrystalEqns2(s_ij, stress, estran, kappa, mu, &
mu_n, eqvalues, gamdot, rss, mudot, stress_n, estran_n, &
kappa_n, dtime, iterCounterS, iterCounterN, ierr, &
iterState, tolerState, tolerNewt, cepmod, dstrain, kinc, &
kstep, argmin, argmax, VecM, VecS,ZVec, dd_for_n, dd_for, &
dd_revp_n, dd_revp, dd_revn_n, dd_revn, stressf_n, stressf, &
dd_rev0_n, dd_rev0, dd_deb_n, dd_deb, time, dd_tot, dd_max, &
noel, grainid)
!***********************************************************************
USE NumType
USE FileIO
USE Timing
USE SlipGeo
IMPLICIT NONE
REAL(KIND=8) :: s_ij(NSD,NSD)
REAL(KIND=8) :: Stress(NVEC),Stressini(NVEC), Stressvec(NVEC)
REAL(KIND=8) :: estran(NVEC), kappa(MaxNumSlip)
INTEGER :: iterCounterS, iterCounterN, ierr
REAL(KIND=8) :: argmin, argmax, dtime, dstrain(NVEC)
REAL(KIND=8) :: search, tolerState, tolerNewt
REAL(KIND=8) :: dd_for_n (MaxNumSlip)
REAL(KIND=8) :: dd_revp_n (MaxNumSlip)
REAL(KIND=8) :: dd_revn_n (MaxNumSlip)
REAL(KIND=8) :: stressf_n (MaxNumSlip)
REAL(KIND=8) :: dd_rev0_n (MaxNumSlip)
REAL(KIND=8) :: dd_deb_n (MaxNumSlip)
REAL(KIND=8) :: dd_for (MaxNumSlip)
REAL(KIND=8) :: dd_revp (MaxNumSlip)
REAL(KIND=8) :: dd_revn (MaxNumSlip)
REAL(KIND=8) :: stressf (MaxNumSlip)
REAL(KIND=8) :: dd_rev0 (MaxNumSlip)
REAL(KIND=8) :: dd_deb (MaxNumSlip)
REAL(KIND=8) :: dd_tot
REAL(KIND=8) :: R_G_all
REAL(KIND=8) :: dd_min, dd_max
REAL(KIND=8) :: R_Ghosh
REAL(KIND=8) :: time
REAL(KIND=8) :: gamdot(MaxNumSlip), mu(NVEC), eqvalues(NEQVA)
REAL(KIND=8) :: stress_n(NVEC), estran_n(NVEC), kappa_n(MaxNumSlip), mu_n(NVEC)
REAL(KIND=8) :: cepmod(NVEC,NVEC)
REAL(KIND=8) :: rss(MaxNumSlip), mudot(NVEC)
LOGICAL :: converged, NConverged
REAL(KIND=8) :: norm_stress0, norm_kappa0, norm_stress, norm_kappa, normtau, normk, normtau0, normk0
REAL(KIND=8) :: vec1(NVEC), vec2(MaxNumSlip)
REAL(KIND=8) :: delstress(NVEC), stress0(NVEC)
REAL(KIND=8) :: delstressvec(NVEC)
REAL(KIND=8) :: rhs(NVEC), lhs(NVEC,NVEC)
REAL(KIND=8) :: rhs_norm0, rhs_norm
REAL(KIND=8) :: ddd
REAL(KIND=8) :: T_n, T_eff
REAL(KIND=8) :: T_tot(NSD),T_t(NSD)
REAL(KIND=8) :: VecMT(NSD)
INTEGER :: c10, c20
LOGICAL :: ConvergeState
REAL(KIND=8) :: InnerProductVec
INTEGER :: is, ip, iterState, kinc, INFO, kstep, noel, grainid
REAL(KIND=8) :: VecM(NSD,MaxNumSlip)
REAL(KIND=8) :: VecS(NSD,MaxNumSlip)
REAL(KIND=8) :: ZVec(NVEC,MaxNumSlip)
REAL(KIND=8) :: start_time, end_time
integer :: iflag
CHARACTER(LEN=20) :: ErroInfo
!-----------------------------------------------------------------------
if (debug==1) write(FILE_E, *) '*----Begin IntegrateCrystalEqns!----*'
! initialize
stress=Stress_n
kappa=kappa_n
dd_for=dd_for_n
dd_revp=dd_revp_n