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* kinetics now according to Mohles; enables solid solution hardening 

* changed example in material.config accordingly
This commit is contained in:
Christoph Kords 2011-01-26 10:17:42 +00:00
parent 6ac06af517
commit 05d4d5fef2
3 changed files with 95 additions and 51 deletions
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6
code/IO.f90
View File

@ -1222,7 +1222,11 @@ endfunction
case (234)
msg = 'Negative cutoff radius'
case (235)
msg = 'Non-positive activation energy for dislocation glide'
msg = 'Non-positive attack frequency'
case (236)
msg = 'Non-positive wall depth'
case (237)
msg = 'Non-positive obstacle strength'
case (240)
msg = 'Non-positive Taylor factor'
case (241)

114
code/constitutive_nonlocal.f90
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@ -54,12 +54,15 @@ real(pReal), dimension(:), allocatable :: constitutive_nonlocal_
constitutive_nonlocal_C44, & ! C44 element in elasticity matrix
constitutive_nonlocal_Gmod, & ! shear modulus
constitutive_nonlocal_nu, & ! poisson's ratio
constitutive_nonlocal_Q0, & ! activation energy for dislocation glide
constitutive_nonlocal_atomicVolume, & ! atomic volume
constitutive_nonlocal_D0, & ! prefactor for self-diffusion coefficient
constitutive_nonlocal_Dsd0, & ! prefactor for self-diffusion coefficient
constitutive_nonlocal_Qsd, & ! activation enthalpy for diffusion
constitutive_nonlocal_aTolRho, & ! absolute tolerance for dislocation density in state integration
constitutive_nonlocal_R ! cutoff radius for dislocation stress
constitutive_nonlocal_R, & ! cutoff radius for dislocation stress
constitutive_nonlocal_d0, & ! wall depth as multiple of b
constitutive_nonlocal_tauObs, & ! obstacle strength in Pa
constitutive_nonlocal_fattack, & ! attack frequency in Hz
constitutive_nonlocal_vs ! maximum dislocation velocity = velocity of sound
real(pReal), dimension(:,:,:), allocatable :: constitutive_nonlocal_Cslip_66 ! elasticity matrix in Mandel notation for each instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_Cslip_3333 ! elasticity matrix for each instance
real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_rhoSglEdgePos0, & ! initial edge_pos dislocation density per slip system for each family and instance
@ -68,8 +71,6 @@ real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_
constitutive_nonlocal_rhoSglScrewNeg0, & ! initial screw_neg dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoDipEdge0, & ! initial edge dipole dislocation density per slip system for each family and instance
constitutive_nonlocal_rhoDipScrew0, & ! initial screw dipole dislocation density per slip system for each family and instance
constitutive_nonlocal_v0PerSlipFamily, & ! dislocation velocity prefactor [m/s] for each family and instance
constitutive_nonlocal_v0PerSlipSystem, & ! dislocation velocity prefactor [m/s] for each slip system and instance
constitutive_nonlocal_lambda0PerSlipFamily, & ! mean free path prefactor for each family and instance
constitutive_nonlocal_lambda0PerSlipSystem, & ! mean free path prefactor for each slip system and instance
constitutive_nonlocal_burgersPerSlipFamily, & ! absolute length of burgers vector [m] for each family and instance
@ -78,6 +79,7 @@ real(pReal), dimension(:,:), allocatable :: constitutive_nonlocal_
constitutive_nonlocal_dLowerEdgePerSlipSystem, & ! minimum stable edge dipole height for each slip system and instance
constitutive_nonlocal_dLowerScrewPerSlipFamily, & ! minimum stable screw dipole height for each family and instance
constitutive_nonlocal_dLowerScrewPerSlipSystem, & ! minimum stable screw dipole height for each slip system and instance
constitutive_nonlocal_Qeff0, & ! prefactor for activation enthalpy for dislocation glide in J
constitutive_nonlocal_interactionSlipSlip ! coefficients for slip-slip interaction for each interaction type and instance
real(pReal), dimension(:,:,:,:,:), allocatable :: constitutive_nonlocal_v, & ! dislocation velocity
constitutive_nonlocal_rhoDotFlux ! dislocation convection term
@ -209,14 +211,17 @@ allocate(constitutive_nonlocal_C33(maxNinstance))
allocate(constitutive_nonlocal_C44(maxNinstance))
allocate(constitutive_nonlocal_Gmod(maxNinstance))
allocate(constitutive_nonlocal_nu(maxNinstance))
allocate(constitutive_nonlocal_Q0(maxNinstance))
allocate(constitutive_nonlocal_atomicVolume(maxNinstance))
allocate(constitutive_nonlocal_D0(maxNinstance))
allocate(constitutive_nonlocal_Dsd0(maxNinstance))
allocate(constitutive_nonlocal_Qsd(maxNinstance))
allocate(constitutive_nonlocal_aTolRho(maxNinstance))
allocate(constitutive_nonlocal_Cslip_66(6,6,maxNinstance))
allocate(constitutive_nonlocal_Cslip_3333(3,3,3,3,maxNinstance))
allocate(constitutive_nonlocal_R(maxNinstance))
allocate(constitutive_nonlocal_d0(maxNinstance))
allocate(constitutive_nonlocal_tauObs(maxNinstance))
allocate(constitutive_nonlocal_vs(maxNinstance))
allocate(constitutive_nonlocal_fattack(maxNinstance))
constitutive_nonlocal_CoverA = 0.0_pReal
constitutive_nonlocal_C11 = 0.0_pReal
constitutive_nonlocal_C12 = 0.0_pReal
@ -224,15 +229,18 @@ constitutive_nonlocal_C13 = 0.0_pReal
constitutive_nonlocal_C33 = 0.0_pReal
constitutive_nonlocal_C44 = 0.0_pReal
constitutive_nonlocal_Gmod = 0.0_pReal
constitutive_nonlocal_Q0 = 0.0_pReal
constitutive_nonlocal_atomicVolume = 0.0_pReal
constitutive_nonlocal_D0 = 0.0_pReal
constitutive_nonlocal_Dsd0 = 0.0_pReal
constitutive_nonlocal_Qsd = 0.0_pReal
constitutive_nonlocal_aTolRho = 0.0_pReal
constitutive_nonlocal_nu = 0.0_pReal
constitutive_nonlocal_Cslip_66 = 0.0_pReal
constitutive_nonlocal_Cslip_3333 = 0.0_pReal
constitutive_nonlocal_R = 0.0_pReal
constitutive_nonlocal_R = -1.0_pReal
constitutive_nonlocal_d0 = 0.0_pReal
constitutive_nonlocal_tauObs = 0.0_pReal
constitutive_nonlocal_vs = 0.0_pReal
constitutive_nonlocal_fattack = 0.0_pReal
allocate(constitutive_nonlocal_rhoSglEdgePos0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoSglEdgeNeg0(lattice_maxNslipFamily, maxNinstance))
@ -240,7 +248,6 @@ allocate(constitutive_nonlocal_rhoSglScrewPos0(lattice_maxNslipFamily, maxNinsta
allocate(constitutive_nonlocal_rhoSglScrewNeg0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoDipEdge0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_rhoDipScrew0(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_v0PerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_burgersPerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_Lambda0PerSlipFamily(lattice_maxNslipFamily, maxNinstance))
allocate(constitutive_nonlocal_interactionSlipSlip(lattice_maxNinteraction, maxNinstance))
@ -252,7 +259,6 @@ constitutive_nonlocal_rhoSglScrewPos0 = -1.0_pReal
constitutive_nonlocal_rhoSglScrewNeg0 = -1.0_pReal
constitutive_nonlocal_rhoDipEdge0 = -1.0_pReal
constitutive_nonlocal_rhoDipScrew0 = -1.0_pReal
constitutive_nonlocal_v0PerSlipFamily = 0.0_pReal
constitutive_nonlocal_burgersPerSlipFamily = 0.0_pReal
constitutive_nonlocal_lambda0PerSlipFamily = 0.0_pReal
constitutive_nonlocal_interactionSlipSlip = 0.0_pReal
@ -313,8 +319,6 @@ do
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoDipEdge0(f,i) = IO_floatValue(line,positions,1+f)
case ('rhodipscrew0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_rhoDipScrew0(f,i) = IO_floatValue(line,positions,1+f)
case ('v0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_v0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('lambda0')
forall (f = 1:lattice_maxNslipFamily) constitutive_nonlocal_lambda0PerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case ('burgers')
@ -327,18 +331,24 @@ do
case('ddipminscrew')
forall (f = 1:lattice_maxNslipFamily) &
constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) = IO_floatValue(line,positions,1+f)
case('q0')
constitutive_nonlocal_Q0(i) = IO_floatValue(line,positions,2)
case('atomicvolume')
constitutive_nonlocal_atomicVolume(i) = IO_floatValue(line,positions,2)
case('d0')
constitutive_nonlocal_D0(i) = IO_floatValue(line,positions,2)
case('dsd0')
constitutive_nonlocal_Dsd0(i) = IO_floatValue(line,positions,2)
case('qsd')
constitutive_nonlocal_Qsd(i) = IO_floatValue(line,positions,2)
case('atol_rho')
constitutive_nonlocal_aTolRho(i) = IO_floatValue(line,positions,2)
case ('interaction_slipslip')
forall (it = 1:lattice_maxNinteraction) constitutive_nonlocal_interactionSlipSlip(it,i) = IO_floatValue(line,positions,1+it)
case('d0')
constitutive_nonlocal_d0(i) = IO_floatValue(line,positions,2)
case('tauobs')
constitutive_nonlocal_tauObs(i) = IO_floatValue(line,positions,2)
case('vs')
constitutive_nonlocal_vs(i) = IO_floatValue(line,positions,2)
case('fattack')
constitutive_nonlocal_fattack(i) = IO_floatValue(line,positions,2)
end select
endif
enddo
@ -366,7 +376,6 @@ enddo
if (constitutive_nonlocal_rhoDipEdge0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_rhoDipScrew0(f,i) < 0.0_pReal) call IO_error(220)
if (constitutive_nonlocal_burgersPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(221)
if (constitutive_nonlocal_v0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(226)
if (constitutive_nonlocal_lambda0PerSlipFamily(f,i) <= 0.0_pReal) call IO_error(227)
if (constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228)
if (constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i) <= 0.0_pReal) call IO_error(228)
@ -374,12 +383,15 @@ enddo
enddo
if (any(constitutive_nonlocal_interactionSlipSlip(1:maxval(lattice_interactionSlipSlip(:,:,myStructure)),i) < 0.0_pReal)) &
call IO_error(229)
if (constitutive_nonlocal_Q0(i) <= 0.0_pReal) call IO_error(235)
if (constitutive_nonlocal_R(i) < 0.0_pReal) call IO_error(234)
if (constitutive_nonlocal_atomicVolume(i) <= 0.0_pReal) call IO_error(230)
if (constitutive_nonlocal_D0(i) <= 0.0_pReal) call IO_error(231)
if (constitutive_nonlocal_Dsd0(i) <= 0.0_pReal) call IO_error(231)
if (constitutive_nonlocal_Qsd(i) <= 0.0_pReal) call IO_error(232)
if (constitutive_nonlocal_aTolRho(i) <= 0.0_pReal) call IO_error(233)
if (constitutive_nonlocal_d0(i) <= 0.0_pReal) call IO_error(236)
if (constitutive_nonlocal_tauObs(i) <= 0.0_pReal) call IO_error(237)
if (constitutive_nonlocal_vs(i) <= 0.0_pReal) call IO_error(226)
if (constitutive_nonlocal_fattack(i) <= 0.0_pReal) call IO_error(235)
!*** determine total number of active slip systems
@ -397,9 +409,6 @@ maxTotalNslip = maxval(constitutive_nonlocal_totalNslip)
allocate(constitutive_nonlocal_burgersPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_burgersPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_v0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_v0PerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_lambda0PerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_lambda0PerSlipSystem = 0.0_pReal
@ -409,6 +418,9 @@ constitutive_nonlocal_dLowerEdgePerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_dLowerScrewPerSlipSystem(maxTotalNslip, maxNinstance))
constitutive_nonlocal_dLowerScrewPerSlipSystem = 0.0_pReal
allocate(constitutive_nonlocal_Qeff0(maxTotalNslip, maxNinstance))
constitutive_nonlocal_Qeff0 = 0.0_pReal
allocate(constitutive_nonlocal_forestProjectionEdge(maxTotalNslip, maxTotalNslip, maxNinstance))
constitutive_nonlocal_forestProjectionEdge = 0.0_pReal
@ -573,10 +585,9 @@ do i = 1,maxNinstance
f = constitutive_nonlocal_slipFamily(s1,i)
!*** burgers vector, dislocation velocity prefactor, mean free path prefactor and minimum dipole distance for each slip system
!*** burgers vector, mean free path prefactor and minimum dipole distance for each slip system
constitutive_nonlocal_burgersPerSlipSystem(s1,i) = constitutive_nonlocal_burgersPerSlipFamily(f,i)
constitutive_nonlocal_v0PerSlipSystem(s1,i) = constitutive_nonlocal_v0PerSlipFamily(f,i)
constitutive_nonlocal_lambda0PerSlipSystem(s1,i) = constitutive_nonlocal_lambda0PerSlipFamily(f,i)
constitutive_nonlocal_dLowerEdgePerSlipSystem(s1,i) = constitutive_nonlocal_dLowerEdgePerSlipFamily(f,i)
constitutive_nonlocal_dLowerScrewPerSlipSystem(s1,i) = constitutive_nonlocal_dLowerScrewPerSlipFamily(f,i)
@ -603,6 +614,12 @@ do i = 1,maxNinstance
enddo; enddo
!*** calculation of prefactor for activation enthalpy for dislocation glide
constitutive_nonlocal_Qeff0(:,i) = constitutive_nonlocal_burgersPerSlipSystem(:,i) ** 3.0_pReal &
* dsqrt(0.5_pReal * constitutive_nonlocal_d0(i) ** 3.0_pReal &
* constitutive_nonlocal_Gmod(i) * constitutive_nonlocal_tauObs(i))
enddo
endsubroutine
@ -965,6 +982,7 @@ do s = 1,ns
enddo
!**********************************************************************
!*** set states
@ -1026,7 +1044,10 @@ real(pReal), dimension(constitutive_nonlocal_totalNslip(phase_constitutionInstan
tauThreshold, & ! threshold shear stress
tau, & ! resolved shear stress
rhoForest ! forest dislocation density
real(pReal) boltzmannProbability
real(pReal) boltzmannProbability, &
tauRel, & ! relative thermally active resolved shear stress
wallFunc, & ! functions reflecting the shape of the obstacle wall (see PhD thesis Mohles p.53)
timeRatio ! ratio of travel to dwell time
myInstance = phase_constitutionInstance(material_phase(g,ip,el))
@ -1041,23 +1062,40 @@ tau = 0.0_pReal
constitutive_nonlocal_v(:,:,g,ip,el) = 0.0_pReal
if (present(dv_dtau)) dv_dtau = 0.0_pReal
if (Temperature > 0.0_pReal) then
do s = 1,ns
tau(s) = math_mul6x6(Tstar_v + Tdislocation_v, &
lattice_Sslip_v(:,constitutive_nonlocal_slipSystemLattice(s,myInstance),myStructure))
if ( abs(tau(s)) > 0.0_pReal ) then
boltzmannProbability = dexp( -constitutive_nonlocal_Q0(myInstance) * dsqrt(rhoForest(s)) / ( abs(tau(s)) * kB * Temperature) )
constitutive_nonlocal_v(s,:,g,ip,el) = sign(constitutive_nonlocal_v0PerSlipSystem(s,myInstance), tau(s)) &
/ ( boltzmannProbability + constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) * dsqrt(rhoForest(s)) ) &
* boltzmannProbability
!*** only if the resolved shear stress exceeds the threshold stress, dislocations are able to cut the dislocation forest
!*** the forest can't be overcome by thermal activation
tauRel = (abs(tau(s)) - tauThreshold(s)) / constitutive_nonlocal_tauObs(myInstance)
if (tauRel > 0.0_pReal .and. tauRel < 1.0_pReal) then
wallFunc = 4.0_pReal * dsqrt(2.0_pReal) / 3.0_pReal * dsqrt(1.0_pReal - tauRel) / tauRel
boltzmannProbability = dexp(- constitutive_nonlocal_Qeff0(s,myInstance) * wallFunc / (kB * Temperature))
timeRatio = boltzmannProbability * constitutive_nonlocal_fattack(myInstance) &
/ (constitutive_nonlocal_vs(myInstance) * dsqrt(rhoForest(s)))
if (present(dv_dtau)) &
dv_dtau(s) = abs(constitutive_nonlocal_v(s,1,g,ip,el)) * constitutive_nonlocal_Q0(myInstance) &
* constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) * rhoForest(s) / ( tau(s)**2.0_pReal * kB * Temperature ) &
/ ( boltzmannProbability + constitutive_nonlocal_burgersPerSlipSystem(s,myInstance) * dsqrt(rhoForest(s)) )
constitutive_nonlocal_v(s,:,g,ip,el) = sign(constitutive_nonlocal_vs(myInstance),tau(s)) * timeRatio / (1.0_pReal + timeRatio)
if (present(dv_dtau)) then
dv_dtau(s) = abs(constitutive_nonlocal_v(s,1,g,ip,el)) * constitutive_nonlocal_Qeff0(s,myInstance) &
/ (kB * Temperature * (1.0_pReal + timeRatio)) &
* 0.5_pReal * wallFunc * (2.0_pReal - tauRel) &
/ ((1.0_pReal - tauRel) * (abs(tau(s)) - tauThreshold(s)))
endif
!*** if resolved stress exceeds even threshold plus obstacle stress, then allow for maximum travel velocity
!*** the tangent is zero, since no dependency of tau
elseif (tauRel >= 1.0_pReal) then
constitutive_nonlocal_v(s,:,g,ip,el) = sign(constitutive_nonlocal_vs(myInstance), tau(s)) &
* constitutive_nonlocal_fattack(myInstance) &
/ (constitutive_nonlocal_vs(myInstance) * dsqrt(rhoForest(s)) &
+ constitutive_nonlocal_fattack(myInstance))
endif
enddo
endif
@ -1620,7 +1658,7 @@ forall (c=1:2) &
rhoDotThermalAnnihilation = 0.0_pReal
D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
D = constitutive_nonlocal_Dsd0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) &
* constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &
@ -2295,7 +2333,7 @@ do o = 1,phase_Noutput(material_phase(g,ip,el))
cs = cs + ns
case ('rho_dot_ann_the')
D = constitutive_nonlocal_D0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
D = constitutive_nonlocal_Dsd0(myInstance) * exp(-constitutive_nonlocal_Qsd(myInstance) / (kB * Temperature))
vClimb = constitutive_nonlocal_atomicVolume(myInstance) * D / ( kB * Temperature ) &
* constitutive_nonlocal_Gmod(myInstance) / ( 2.0_pReal * pi * (1.0_pReal-constitutive_nonlocal_nu(myInstance)) ) &

14
code/material.config
View File

@ -231,15 +231,17 @@ rhoSglScrewNeg0 1e11 0 0 0 # Initial negative screw single
rhoDipEdge0 1e8 0 0 0 # Initial edge dipole dislocation density in m/m**3
rhoDipScrew0 1e8 0 0 0 # Initial screw dipole dislocation density in m/m**3
r 10e-6 # cutoff radius for dislocation stress in m
v0 3500 0 0 0 # maximum dislocation velocity (velocity of sound)
Q0 5e-19 # activation energy for dislocation glide
vs 3500 0 0 0 # maximum dislocation velocity (velocity of sound) in m/s
dDipMinEdge 1e-9 0 0 0 # minimum distance for stable edge dipoles in m
dDipMinScrew 1e-9 0 0 0 # minimum distance for stable screw dipoles in m
lambda0 100 0 0 0 # prefactor for mean free path
atomicVolume 1.7e-29
D0 1e-4 # prefactor for self-diffusion coefficient
Qsd 2.3e-19 # activation enthalpy for seld-diffusion
atol_rho 1e2 # dislocation density considered relevant
atomicVolume 1.7e-29 # atomic volume in m**3
Dsd0 1e-4 # prefactor for self-diffusion coefficient in m**2/s
Qsd 2.3e-19 # activation enthalpy for seld-diffusion in J
d0 2.0 # obstacle depth in multiples of the burgers vector length
tauObs 2e6 # obstacle strength in Pa
fattack 50e9 # attack frequency in Hz
atol_rho 1e2 # dislocation density considered relevant in m/m**3
interaction_SlipSlip 0.122 0.122 0.625 0.07 0.137 0.122 # Dislocation interaction coefficient
[BCC_Ferrite]