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kCRSS.f
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kCRSS.f
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********************************************************
** KCRSS calculates the CRSS of slip and twin systems **
********************************************************
SUBROUTINE kCRSS(iphase,tauc,nSys,G12,burgerv,gndtot,irradiate,
+ tauSolute,gndcut,rhofor,rhosub,Temperature,homogtwin,
+ nTwinStart,nTwinEnd,twinvolfrac,tauctwin,nTwin,TwinIntegral,
+ twinvolfractotal,twinon)
INCLUDE 'ABA_PARAM.INC'
! crystal type
INTEGER,intent(in) :: iphase
! number of slip systems
INTEGER,intent(in) :: nSys
! total number of twin systems
INTEGER,intent(in) :: nTwin
! shear modulus for Taylor dislocation law
REAL*8,intent(in) :: G12
! Burgers vectors
REAL*8,intent(in) :: burgerv(nSys)
! scalar total GND density
REAL*8,intent(in) :: gndtot
! activate irradiation effect
INTEGER,intent(in) :: irradiate
! increase in tauc due to solute force
REAL*8,intent(in) :: tauSolute
! GND density (immobile)
REAL*8,intent(in) :: gndcut(nSys)
! forest dislocation density
REAL*8,intent(in) :: rhofor(nSys)
! substructure dislocation density
REAL*8,intent(in) :: rhosub
! Current temperature
REAL*8,intent(in) :: Temperature
! homogenize twin model
INTEGER,intent(in) :: homogtwin
! the active twins are the ones in the
! interval [nTwinStart,nTwinEnd] in the
! twin system file
INTEGER,intent(in) :: nTwinStart,nTwinEnd
! twin systems activation flag
INTEGER,intent(in) :: twinon
! twin volume fraction
REAL*8,intent(in) :: twinvolfrac(nTwin)
! average of the twin volume fraction
! over the neighbourhood
! two twin systems
REAL*8,intent(in) :: TwinIntegral(nTwin)
! total twin volume fraction
REAL*8,intent(in) :: twinvolfractotal
! critical resolved shear stress of slip systems
REAL*8,intent(inout) :: tauc(nSys)
! critical resolved shear stress of twin systems
REAL*8,intent(inout) :: tauctwin(nTwin)
INTEGER :: i
! check crystal type
if (iphase == 1) then
! Taylor dislocation law
tauc = tauc + 0.0065*G12*(burgerv(1))*sqrt(gndtot)
if (irradiate == 1) then
tauc = tauc + tauSolute
end if
else if (iphase == 2) then
! Taylor dislocation law
tauc = tauc + 0.32*G12*(burgerv(1))*sqrt(gndcut)
else if (iphase == 5) then
! alpha-Uranium model with forest and substructure dislocations
! R.J. McCabe, L. Capolungo, P.E. Marshall, C.M. Cady, C.N. Tomé
! Deformation of wrought uranium: Experiments and modeling
! Acta Materialia 58 (2010) 5447–5459
tauc(1) = tauc(1) + 19.066 * sqrt(rhofor(1)) + 1.8218 * sqrt(rhosub) * log(1.0 / (burgerv(1) * sqrt(rhosub)))
tauc(2) = tauc(2) + 18.832 * sqrt(rhofor(2)) + 1.7995 * sqrt(rhosub) * log(1.0 / (burgerv(2) * sqrt(rhosub)))
tauc(3) = tauc(3) + 54.052 * sqrt(rhofor(3)) + 5.1650 * sqrt(rhosub) * log(1.0 / (burgerv(3) * sqrt(rhosub)))
tauc(4) = tauc(4) + 54.052 * sqrt(rhofor(4)) + 5.1650 * sqrt(rhosub) * log(1.0 / (burgerv(4) * sqrt(rhosub)))
tauc(5) = tauc(5) + 123.357 * sqrt(rhofor(5)) + 11.7875 * sqrt(rhosub) * log(1.0 / (burgerv(5) * sqrt(rhosub)))
tauc(6) = tauc(6) + 123.357 * sqrt(rhofor(6)) + 11.7875 * sqrt(rhosub) * log(1.0 / (burgerv(6) * sqrt(rhosub)))
tauc(7) = tauc(7) + 123.357 * sqrt(rhofor(7)) + 11.7875 * sqrt(rhosub) * log(1.0 / (burgerv(7) * sqrt(rhosub)))
tauc(8) = tauc(8) + 123.357 * sqrt(rhofor(8)) + 11.7875 * sqrt(rhosub) * log(1.0 / (burgerv(8) * sqrt(rhosub)))
! Zecevic 2016 temperature dependence
tauc(1) = tauc(1) * exp(-(Temperature-293.0)/140.0)
tauc(2) = tauc(2) * exp(-(Temperature-293.0)/140.0)
tauc(3) = tauc(3) * exp(-(Temperature-293.0)/140.0)
tauc(4) = tauc(4) * exp(-(Temperature-293.0)/140.0)
tauc(5) = tauc(5) * exp(-(Temperature-293.0)/140.0)
tauc(6) = tauc(6) * exp(-(Temperature-293.0)/140.0)
tauc(7) = tauc(7) * exp(-(Temperature-293.0)/140.0)
tauc(8) = tauc(8) * exp(-(Temperature-293.0)/140.0)
! Daniel, Lesage, 1971 minimum value as minima
tauc(1) = max(tauc(1),4.0)
tauc(2) = max(tauc(2),4.0)
tauc(3) = max(tauc(3),4.0)
tauc(4) = max(tauc(4),4.0)
tauc(5) = max(tauc(5),4.0)
tauc(6) = max(tauc(6),4.0)
tauc(7) = max(tauc(7),4.0)
tauc(8) = max(tauc(8),4.0)
if (twinon == 1) then ! twin active
if (homogtwin == 1) then ! homogenized twin model
! add cross hardening of one twin system on the other
DO i=nTwinStart,nTwinEnd
tauctwin(i) = tauctwin(i) + 96.79*twinvolfractotal
END DO
else ! discrete twin model
! add hardening in the nucleation stage
! 50% is the critical twin volume fraction at which the
! softest value is reached
DO i=nTwinStart,nTwinEnd
if (twinvolfrac(i) < 0.5) then
tauctwin(i) = tauctwin(i) + 37.5*(0.5-twinvolfrac(i))
tauctwin(i) = tauctwin(i) + 2000.0*TwinIntegral(i)
else ! twinvolfrac(i) > 0.5
tauctwin(i) = tauctwin(i) + 37.5*(twinvolfrac(i)-0.5)
tauctwin(i) = tauctwin(i) + 2000.0*TwinIntegral(i)
end if
END DO
! local interaction between twin systems
! only when threshold is passed
if (twinvolfrac(nTwinEnd) > 0.5) then
tauctwin(nTwinStart) = tauctwin(nTwinStart) + 200.0*twinvolfrac(nTwinEnd)
end if
if (twinvolfrac(nTwinStart) > 0.5) then
tauctwin(nTwinEnd) = tauctwin(nTwinEnd) + 200.0*twinvolfrac(nTwinStart)
end if
end if ! choice of twin model (homogeneous/discrete)
end if ! twin active
end if ! check crystal type
RETURN
END