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local stress correction of gradient in dead dislocations and neighboring excess density is additive

This commit is contained in:
Christoph Kords 2012-03-14 15:24:19 +00:00
parent 06c93435f2
commit 6bca2150f2
1 changed files with 40 additions and 95 deletions
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121
code/constitutive_nonlocal.f90
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@ -951,7 +951,6 @@ integer(pInt) neighboring_el, & ! element number o
s, & ! slip system index s, & ! slip system index
t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-) t, & ! index of dilsocation type (e+, e-, s+, s-, used e+, used e-, used s+, used s-)
dir, & dir, &
side, &
n n
integer(pInt), dimension(2) :: neighbor integer(pInt), dimension(2) :: neighbor
real(pReal) nu, & ! poisson's ratio real(pReal) nu, & ! poisson's ratio
@ -959,28 +958,20 @@ real(pReal) nu, & ! poisson's ratio
b, & b, &
detFe, & detFe, &
detFp, & detFp, &
FVsize, & FVsize
rhoExcessGradient real(pReal), dimension(2) :: rhoExcessGradient, &
real(pReal), dimension(2) :: rhoExcessGradient_over_rho, & rhoExcessGradient_over_rho, &
gradient, & rhoTotal
gradientDeads, &
gradientInter, &
gradientDistance, &
gradientDistanceDeads, &
gradientDistanceInter, &
rhoExcessAtSampledPoint
real(pReal), dimension(3) :: ipCoords, & real(pReal), dimension(3) :: ipCoords, &
neighboring_ipCoords neighboring_ipCoords, &
real(pReal), dimension(FE_maxNipNeighbors) :: & rhoExcessDifferences
distance ! length of connection vector
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el)))) :: &
rhoForest, & ! forest dislocation density rhoForest, & ! forest dislocation density
tauBack, & ! back stress from pileup on same slip system tauBack, & ! back stress from pileup on same slip system
tauThreshold ! threshold shear stress tauThreshold ! threshold shear stress
real(pReal), dimension(3,2) :: rhoExcessDifferences, &
sampledPoint
real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient real(pReal), dimension(3,3) :: invFe, & ! inverse of elastic deformation gradient
invFp ! inverse of plastic deformation gradient invFp, & ! inverse of plastic deformation gradient
connections
real(pReal), dimension(3,FE_maxNipNeighbors) :: & real(pReal), dimension(3,FE_maxNipNeighbors) :: &
connection_latticeConf, & connection_latticeConf, &
areaNormal_latticeConf areaNormal_latticeConf
@ -990,7 +981,6 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance
rhoDip ! dipole dislocation density (edge, screw) rhoDip ! dipole dislocation density (edge, screw)
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),8) :: &
rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-) rhoSgl ! single dislocation density (edge+, edge-, screw+, screw-, used edge+, used edge-, used screw+, used screw-)
real(pReal), dimension(3,3,2) :: connections
real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip),FE_maxNipNeighbors) :: & real(pReal), dimension(2,maxval(constitutive_nonlocal_totalNslip),FE_maxNipNeighbors) :: &
neighboring_rhoExcess ! excess density at neighboring material point neighboring_rhoExcess ! excess density at neighboring material point
real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: & real(pReal), dimension(3,constitutive_nonlocal_totalNslip(phase_plasticityInstance(material_phase(g,ip,el))),2) :: &
@ -1075,7 +1065,7 @@ if (.not. phase_localPlasticity(phase)) then
- state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*ns+s) ! negative mobiles - state(g,neighboring_ip,neighboring_el)%p((2_pInt*c-1_pInt)*ns+s) ! negative mobiles
else else
! thats myself! probably using periodic images ! thats myself! probably using periodic images
connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize connection_latticeConf(1:3,n) = 0.0_pReal
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
endif endif
else else
@ -1084,99 +1074,54 @@ if (.not. phase_localPlasticity(phase)) then
endif endif
else else
! local neighbor or different lattice structure or different plasticity instance ! local neighbor or different lattice structure or different plasticity instance
connection_latticeConf(1:3,n) = math_mul33x3(invFe, neighboring_ipCoords - ipCoords) connection_latticeConf(1:3,n) = 0.0_pReal ! use central values instead
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
endif endif
else else
! free surface ! free surface
connection_latticeConf(1:3,n) = areaNormal_latticeConf(1:3,n) * FVsize connection_latticeConf(1:3,n) = 0.0_pReal ! use central values instead
neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess neighboring_rhoExcess(1:2,1:ns,n) = rhoExcess
endif endif
distance(n) = math_norm3(connection_latticeConf(1:3,n))
enddo enddo
!* loop through the slip systems
!* calculate the dislocation gradient in both directions of m with two different methods: !* loop through the slip systems and calculate the dislocation gradient by
!* 1. gradient between central excess density and dead dislocations in central ip !* 1. interpolation of the excess density in the neighorhood
!* 2. interpolate gradient from excess density in three neighboring ips !* 2. interpolation of the dead dislocation density in the central volume
!* take the heigher gradient in both directions and do a weighted sum with weights according to the distance
m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct) m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
m(1:3,1:ns,2) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct) m(1:3,1:ns,2) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,instance), latticeStruct)
do s = 1_pInt,ns do s = 1_pInt,ns
rhoExcessGradient_over_rho = 0.0_pReal
!* gradient from interpolation of neighboring excess density
do c = 1_pInt,2_pInt do c = 1_pInt,2_pInt
if (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c) < 1.0_pReal) then
cycle ! no siginificant density
endif
!* gradient from dead dislocations
gradientDeads = 0.0_pReal
if (rhoSgl(s,2_pInt*c+3_pInt) > 0.0_pReal) then ! positive deads
gradientDeads(1) = + 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on positive side
else
gradientDeads(2) = - 2.0_pReal * rhoSgl(s,2_pInt*c+3_pInt) / FVsize ! on negative side
endif
if (rhoSgl(s,2_pInt*c+4_pInt) > 0.0_pReal) then ! negative deads
gradientDeads(2) = gradientDeads(2) + 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on negative side
else
gradientDeads(1) = gradientDeads(1) - 2.0_pReal * rhoSgl(s,2_pInt*c+4_pInt) / FVsize ! on positive side
endif
gradientDistanceDeads(1:2) = 0.5_pReal * FVsize
!* gradient from interpolation
gradientInter = 0.0_pReal
rhoExcessDifferences = 0.0_pReal
connections = 0.0_pReal
gradientDistanceInter = 0.0_pReal
do dir = 1_pInt,3_pInt do dir = 1_pInt,3_pInt
if (math_mul3x3(areaNormal_latticeConf(1:3,2_pInt*dir-1_pInt),m(1:3,s,c)) > 0.0_pReal) then ! on positive side
neighbor(1) = 2_pInt * dir - 1_pInt neighbor(1) = 2_pInt * dir - 1_pInt
neighbor(2) = 2_pInt * dir neighbor(2) = 2_pInt * dir
else ! on negative side connections(dir,1:3) = connection_latticeConf(1:3,neighbor(1)) - connection_latticeConf(1:3,neighbor(2))
neighbor(1) = 2_pInt * dir rhoExcessDifferences(dir) = neighboring_rhoExcess(c,s,neighbor(1)) - neighboring_rhoExcess(c,s,neighbor(2))
neighbor(2) = 2_pInt * dir - 1_pInt
endif
do side = 1_pInt,2_pInt
n = neighbor(side)
rhoExcessDifferences(dir,side) = neighboring_rhoExcess(c,s,n) - rhoExcess(c,s)
connections(dir,1:3,side) = connection_latticeConf(1:3,n)
gradientDistanceInter(side) = gradientDistanceInter(side) &
+ (math_mul3x3(connection_latticeConf(1:3,n),m(1:3,s,c))) ** 2.0_pReal / distance(n)
enddo enddo
rhoExcessGradient(c) = math_mul3x3(math_mul33x3(math_inv33(connections), rhoExcessDifferences), m(1:3,s,c))
enddo enddo
sampledPoint(1:3,1) = + gradientDistanceInter(1) * m(1:3,s,c)
sampledPoint(1:3,2) = - gradientDistanceInter(2) * m(1:3,s,c)
do side = 1_pInt,2_pInt
rhoExcessAtSampledPoint(side) = math_mul3x3(math_mul33x3(math_inv33(connections(1:3,1:3,side)), &
rhoExcessDifferences(1:3,side)), &
sampledPoint(1:3,side)) &
+ rhoExcess(c,s)
enddo
gradientInter(1) = (rhoExcessAtSampledPoint(1) - rhoExcess(c,s)) / gradientDistanceInter(1)
gradientInter(2) = (rhoExcess(c,s) - rhoExcessAtSampledPoint(2)) / gradientDistanceInter(2)
!* take maximum of both gradients and mix contributions from both sides according to weighted distances !* plus gradient from deads
do dir = 1_pInt,2_pInt do t = 1_pInt,4_pInt
if (abs(gradientDeads(dir)) > abs(gradientInter(dir))) then c = (t - 1_pInt) / 2_pInt + 1_pInt
gradient(dir) = gradientDeads(dir) rhoExcessGradient(c) = rhoExcessGradient(c) + rhoSgl(s,t+4_pInt) / FVsize
gradientDistance(dir) = gradientDistanceDeads(dir)
else
gradient(dir) = gradientInter(dir)
gradientDistance(dir) = gradientDistanceInter(dir)
endif
enddo enddo
rhoExcessGradient = (gradient(1) * gradientDistance(2) + gradient(2) * gradientDistance(1)) &
/ (gradientDistance(1) + gradientDistance(2))
!* excess gradient over density: in case of vanishing central total density we take the distance squared instead!!! !* normalized with the total density
rhoExcessGradient_over_rho(c) = rhoExcessGradient / (rhoSgl(s,2_pInt*c-1_pInt) + rhoSgl(s,2_pInt*c)) rhoExcessGradient_over_rho = 0.0_pReal
enddo rhoTotal(1_pInt) = sum(abs(rhoSgl(s,[1_pInt,2_pInt,5_pInt,6_pInt]))) + rhoDip(s,1_pInt)
rhoTotal(2_pInt) = sum(abs(rhoSgl(s,[3_pInt,4_pInt,7_pInt,8_pInt]))) + rhoDip(s,2_pInt)
forall (c = 1_pInt:2_pInt, rhoTotal(c) > 0.0_pReal) &
rhoExcessGradient_over_rho(c) = rhoExcessGradient(c) / rhoTotal(c)
!* gives the local stress correction when multiplied with a factor
b = constitutive_nonlocal_burgers(s,instance) b = constitutive_nonlocal_burgers(s,instance)
tauBack(s) = - mu * b / (2.0_pReal * pi) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu) + rhoExcessGradient_over_rho(2)) tauBack(s) = - mu * b / (2.0_pReal * pi) * (rhoExcessGradient_over_rho(1) / (1.0_pReal - nu) + rhoExcessGradient_over_rho(2))