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* "constitutive_nonlocal_flux" is set to zero in "constitutive_nonlocal_dotState", not in "constitutive_nonlocal_microstructure" 

* dislocation flux and internal stress calculation now consistent with new definition of slip system lattice according to paper (polarity of screws inverted)
This commit is contained in:
Christoph Kords 2011-02-23 08:08:06 +00:00
parent 3c944e79fa
commit d835380bc0
1 changed files with 42 additions and 41 deletions
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81
code/constitutive_nonlocal.f90
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@ -804,6 +804,7 @@ use math, only: math_Plain3333to99, &
math_mul33x3, & math_mul33x3, &
math_inv3x3, & math_inv3x3, &
math_det3x3, & math_det3x3, &
math_transpose3x3, &
pi pi
use debug, only: debugger, & use debug, only: debugger, &
verboseDebugger verboseDebugger
@ -851,6 +852,7 @@ type(p_vec), dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems), in
!*** local variables !*** local variables
integer(pInt) myInstance, & ! current instance of this constitution integer(pInt) myInstance, & ! current instance of this constitution
myStructure, & ! current lattice structure myStructure, & ! current lattice structure
myPhase, &
ns, & ! short notation for the total number of active slip systems ns, & ! short notation for the total number of active slip systems
neighboring_el, & ! element number of my neighbor neighboring_el, & ! element number of my neighbor
neighboring_ip, & ! integration point of my neighbor neighboring_ip, & ! integration point of my neighbor
@ -869,13 +871,13 @@ real(pReal), dimension(3,3) :: sigma, & ! dislocation stre
F, & ! total deformation gradient F, & ! total deformation gradient
neighboring_F, & ! total deformation gradient of neighbor neighboring_F, & ! total deformation gradient of neighbor
invFe, & ! inverse elastic deformation gradient invFe, & ! inverse elastic deformation gradient
invPositionDifference ! inverse of a 3x3 matrix containing finite differences of pairs of position vectors Q ! inverse transpose of 3x3 matrix with finite differences of opposing position vectors
real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation real(pReal), dimension(6) :: Tdislocation_v ! dislocation stress (resulting from the neighboring excess dislocation densities) as 2nd Piola-Kirchhoff stress in Mandel notation
real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & real(pReal), dimension(2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
rhoExcess ! central excess density rhoExcess ! central excess density
real(pReal), dimension(6,2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: & real(pReal), dimension(6,2,constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el)))) :: &
neighboring_rhoExcess ! excess density for each neighbor, dislo character and slip system neighboring_rhoExcess ! excess density for each neighbor, dislo character and slip system
real(pReal), dimension(6,3) :: neighboring_position ! position vector of each neighbor when seen from the centreal material point's lattice frame real(pReal), dimension(3,6) :: neighboring_position ! position vector of each neighbor when seen from the centreal material point's lattice frame
real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),8) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(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(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: & real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstance(material_phase(g,ip,el))),2) :: &
@ -886,17 +888,12 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstan
tauThreshold, & ! threshold shear stress tauThreshold, & ! threshold shear stress
tau ! resolved shear stress tau ! resolved shear stress
myInstance = phase_constitutionInstance(material_phase(g,ip,el)) myPhase = material_phase(g,ip,el)
myInstance = phase_constitutionInstance(myPhase)
myStructure = constitutive_nonlocal_structure(myInstance) myStructure = constitutive_nonlocal_structure(myInstance)
ns = constitutive_nonlocal_totalNslip(myInstance) ns = constitutive_nonlocal_totalNslip(myInstance)
!**********************************************************************
!*** set fluxes to zero
constitutive_nonlocal_rhoDotFlux(1:ns,1:10,g,ip,el) = 0.0_pReal
!********************************************************************** !**********************************************************************
!*** get basic states !*** get basic states
@ -934,7 +931,7 @@ forall (s = 1:ns) &
Tdislocation_v = 0.0_pReal Tdislocation_v = 0.0_pReal
if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only calculate dislocation stress for nonlocal material if (.not. phase_localConstitution(myPhase)) then ! only calculate dislocation stress for nonlocal material
F = math_mul33x33(Fe(1:3,1:3,g,ip,el), Fp(1:3,1:3,g,ip,el)) F = math_mul33x33(Fe(1:3,1:3,g,ip,el), Fp(1:3,1:3,g,ip,el))
invFe = math_inv3x3(Fe(1:3,1:3,g,ip,el)) invFe = math_inv3x3(Fe(1:3,1:3,g,ip,el))
@ -949,67 +946,67 @@ if (.not. phase_localConstitution(material_phase(g,ip,el))) then
if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then ! at free surfaces ... if ( neighboring_ip == 0 .or. neighboring_el == 0 ) then ! at free surfaces ...
neighboring_el = el ! ... use central values instead of neighboring values neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip neighboring_ip = ip
neighboring_position(n,1:3) = 0.0_pReal neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution elseif (phase_localConstitution(material_phase(1,neighboring_ip,neighboring_el))) then ! for neighbors with local constitution
neighboring_el = el ! ... use central values instead of neighboring values neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip neighboring_ip = ip
neighboring_position(n,1:3) = 0.0_pReal neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
elseif (myStructure /= & elseif (myPhase /= material_phase(1,neighboring_ip,neighboring_el)) then ! for neighbors with different phase
constitutive_nonlocal_structure(phase_constitutionInstance(material_phase(1,neighboring_ip,neighboring_el)))) then ! for neighbors with different crystal structure
neighboring_el = el ! ... use central values instead of neighboring values neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip neighboring_ip = ip
neighboring_position(n,1:3) = 0.0_pReal neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
else else
forall (s = 1:ns, c = 1:2) &
neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) &
+ abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) &
- state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) &
- abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s))
transmissivity = sum(constitutive_nonlocal_compatibility(2,1:ns,1:ns,n,ip,el)**2.0_pReal, 1) transmissivity = sum(constitutive_nonlocal_compatibility(2,1:ns,1:ns,n,ip,el)**2.0_pReal, 1)
if ( any(transmissivity < 0.99_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ... if ( any(transmissivity < 0.9_pReal) ) then ! at grain boundary (=significantly decreased transmissivity) ...
neighboring_el = el ! ... use central values instead of neighboring values neighboring_el = el ! ... use central values instead of neighboring values
neighboring_ip = ip neighboring_ip = ip
neighboring_position(n,1:3) = 0.0_pReal neighboring_position(1:3,n) = 0.0_pReal
neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess neighboring_rhoExcess(n,1:2,1:ns) = rhoExcess
else else
neighboring_F = math_mul33x33(Fe(1:3,1:3,g,neighboring_ip,neighboring_el), Fp(1:3,1:3,g,neighboring_ip,neighboring_el)) neighboring_F = math_mul33x33(Fe(1:3,1:3,g,neighboring_ip,neighboring_el), Fp(1:3,1:3,g,neighboring_ip,neighboring_el))
neighboring_position(n,1:3) = & neighboring_position(1:3,n) = &
0.5_pReal * math_mul33x3(math_mul33x33(invFe,neighboring_F) + Fp(1:3,1:3,g,ip,el), & 0.5_pReal * math_mul33x3(math_mul33x33(invFe,neighboring_F) + Fp(1:3,1:3,g,ip,el), &
mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(1:3,ip,el)) mesh_ipCenterOfGravity(1:3,neighboring_ip,neighboring_el) - mesh_ipCenterOfGravity(1:3,ip,el))
forall (s = 1:ns, c = 1:2) &
neighboring_rhoExcess(n,c,s) = state(g,neighboring_ip,neighboring_el)%p((2*c-2)*ns+s) &
+ abs(state(g,neighboring_ip,neighboring_el)%p((2*c+2)*ns+s)) &
- state(g,neighboring_ip,neighboring_el)%p((2*c-1)*ns+s) &
- abs(state(g,neighboring_ip,neighboring_el)%p((2*c+3)*ns+s))
endif endif
endif endif
enddo enddo
invPositionDifference = math_inv3x3(neighboring_position((/1,3,5/),1:3) - neighboring_position((/2,4,6/),1:3)) Q = math_inv3x3(math_transpose3x3(neighboring_position(1:3,(/1,3,5/)) - neighboring_position(1:3,(/2,4,6/))))
do s = 1,ns do s = 1,ns
lattice2slip = transpose( reshape( (/ lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice2slip = math_transpose3x3(reshape((/ &
lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), & lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure) /), & -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure), &
(/ 3,3 /) ) ) lattice_sn(1:3, constitutive_nonlocal_slipSystemLattice(s,myInstance), myStructure)/), (/3,3/)))
rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),1:2,s) - neighboring_rhoExcess((/2,4,6/),1:2,s) rhoExcessDifference = neighboring_rhoExcess((/1,3,5/),1:2,s) - neighboring_rhoExcess((/2,4,6/),1:2,s)
forall (c = 1:2) & forall (c = 1:2) &
disloGradients(1:3,c) = math_mul33x3( lattice2slip, math_mul33x3(invPositionDifference, rhoExcessDifference(1:3,c)) ) disloGradients(1:3,c) = math_mul33x3(lattice2slip, math_mul33x3(Q, rhoExcessDifference(1:3,c)))
sigma = 0.0_pReal sigma = 0.0_pReal
sigma(1,1) = + (-0.06066_pReal + nu*0.41421_pReal) / (1.0_pReal-nu) * disloGradients(3,1) sigma(1,1) = + 0.375_pReal / (1.0_pReal-nu) * disloGradients(3,1)
sigma(2,2) = + 0.32583_pReal / (1.0_pReal-nu) * disloGradients(3,1) sigma(2,2) = + 0.5_pReal * nu / (1.0_pReal-nu) * disloGradients(3,1)
sigma(3,3) = + 0.14905_pReal / (1.0_pReal-nu) * disloGradients(3,1) sigma(3,3) = + 0.125_pReal / (1.0_pReal-nu) * disloGradients(3,1)
sigma(1,2) = + 0.20711_pReal * disloGradients(3,2) sigma(1,2) = + 0.25_pReal * disloGradients(3,2)
sigma(2,3) = - 0.08839_pReal / (1.0_pReal-nu) * disloGradients(2,1) - 0.20711_pReal * disloGradients(1,2) sigma(1,3) = - 0.125_pReal / (1.0_pReal-nu) * disloGradients(1,1) - 0.25_pReal * disloGradients(2,2)
sigma(2,1) = sigma(1,2) sigma(2,1) = sigma(1,2)
sigma(3,2) = sigma(2,3) sigma(3,1) = sigma(1,3)
forall (i=1:3, j=1:3) & forall (i=1:3, j=1:3) &
sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) & sigma(i,j) = sigma(i,j) * constitutive_nonlocal_Gmod(myInstance) * constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) &
* constitutive_nonlocal_R(myInstance)**2.0_pReal * constitutive_nonlocal_R(myInstance)**2.0_pReal
Tdislocation_v = Tdislocation_v + math_Mandel33to6( math_mul33x33(transpose(lattice2slip), math_mul33x33(sigma, lattice2slip) ) ) Tdislocation_v = Tdislocation_v + math_Mandel33to6(math_mul33x33(math_transpose3x3(lattice2slip), &
math_mul33x33(sigma, lattice2slip)))
enddo enddo
@ -1558,14 +1555,18 @@ where (rhoSgl(1:ns,1:2) > 0.0_pReal) &
!**************************************************************************** !****************************************************************************
!*** calculate dislocation fluxes (only for nonlocal constitution) !*** calculate dislocation fluxes (only for nonlocal constitution)
constitutive_nonlocal_rhoDotFlux(:,:,g,ip,el) = 0.0_pReal
rhoDotFlux = 0.0_pReal rhoDotFlux = 0.0_pReal
if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only for nonlocal constitution if (.not. phase_localConstitution(material_phase(g,ip,el))) then ! only for nonlocal constitution
!*** take care of the definition of lattice_st = lattice_sd x lattice_sn !!!
!*** opposite sign to our p vector in the (s,p,n) triplet !!!
m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,1) = lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,2) = -lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,2) = -lattice_sd(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,3) = lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,3) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
m(1:3,1:ns,4) = -lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure) m(1:3,1:ns,4) = lattice_st(1:3, constitutive_nonlocal_slipSystemLattice(1:ns,myInstance), myStructure)
my_Fe = Fe(1:3,1:3,g,ip,el) my_Fe = Fe(1:3,1:3,g,ip,el)
my_F = math_mul33x33(my_Fe, Fp(1:3,1:3,g,ip,el)) my_F = math_mul33x33(my_Fe, Fp(1:3,1:3,g,ip,el))
@ -1780,7 +1781,7 @@ if (verboseDebugger .and. (debug_g==g .and. debug_i==ip .and. debug_e==el)) then
!$OMP CRITICAL (write2out) !$OMP CRITICAL (write2out)
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation remobilization', rhoDotRemobilization(1:ns,1:8) * timestep write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation remobilization', rhoDotRemobilization(1:ns,1:8) * timestep
write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep write(6,'(a,/,4(12(e12.5,x),/))') 'dislocation multiplication', rhoDotMultiplication(1:ns,1:4) * timestep
write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation flux (outgoing)', rhoDotFlux(1:ns,1:8) * timestep write(6,'(a,/,8(12(e12.5,x),/))') 'dislocation flux', rhoDotFlux(1:ns,1:8) * timestep
write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by glide', rhoDotSingle2DipoleGlide * timestep write(6,'(a,/,10(12(e12.5,x),/))') 'dipole formation by glide', rhoDotSingle2DipoleGlide * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', rhoDotAthermalAnnihilation(1:ns,1:2) * timestep write(6,'(a,/,2(12(e12.5,x),/))') 'athermal dipole annihilation', rhoDotAthermalAnnihilation(1:ns,1:2) * timestep
write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', rhoDotThermalAnnihilation(1:ns,9:10) * timestep write(6,'(a,/,2(12(e12.5,x),/))') 'thermally activated dipole annihilation', rhoDotThermalAnnihilation(1:ns,9:10) * timestep
@ -2181,7 +2182,7 @@ endif
!*** dislocation motion !*** dislocation motion
m(1:3,1:ns,1) = lattice_sd(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure) m(1:3,1:ns,1) = lattice_sd(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure)
m(1:3,1:ns,2) = lattice_st(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure) m(1:3,1:ns,2) = -lattice_st(1:3,constitutive_nonlocal_slipSystemLattice(1:ns,myInstance),myStructure)
forall (c = 1:2, s = 1:ns) & forall (c = 1:2, s = 1:ns) &
m_currentconf(1:3,s,c) = math_mul33x3(Fe(1:3,1:3,g,ip,el), m(1:3,s,c)) m_currentconf(1:3,s,c) = math_mul33x3(Fe(1:3,1:3,g,ip,el), m(1:3,s,c))