Concurrently Modeling Multiple Length Scales by Coupling the Phase-Field Method to Spatially-Resolved Cluster Dynamics

DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING
Concurrently Modeling Multiple Length
Scales by Coupling the Phase-Field
Method to Spatially-Resolved Cluster
Dynamics
Dong-Uk Kim, Ali Muntaha, Michael R Tonks, University of Florida
Sophie Blondel, Brian Wirth, University of Tennessee-Knoxville
David Bernholdt, Phillip Roth, Oak Ridge National Laboratory
David Andersson, Los Alamos National Laboratory
Work is funded by Joint NE/SciDAC Project on the simulation of fission gas

View Slide

Phase field methods can efficiently model small features or
large features but not both in the same simulation

View Slide

n Nucleation and growth
n Grain boundary segregation
n Grain growth with small precipitates
There are various examples of where microstructural
features of very different sizes impact material behavior
Dendritic growth of precipitates in Ni-
based super alloys
Henry, M. F., Yoo, Y. S., Yoon, D. Y., & Choi, J.
(1993). Metallurgical Transactions A, 24(8), 1733-
1743.

View Slide

Fission gas release in irradiated fuel occurs due to materials
processes that occur across various length and time scales
Kashibe, S., K. Une, and
Kazuhiro Nogita. JNM 206, no. 1
(1993): 22-34.
Rest, J., et al. JNM 513 (2019): 310-345.

View Slide

n Initial bubble radius: 44 nm
n Interfacial width: 30 nm
n Initial bubble radius: 1.5 nm
n Interfacial width: 0.7 nm
Intergranular bubble analysis
Phase field simulations of fission gas bubbles currently target
specific length scale of interest
Intragranular bubble analysis
L.K. Aagesen, D. Schwen, M.R. Tonks, Y. Zhang,
Computational Materials Science. 161 (2019) 35–45.
M.R. Tonks, et al., In proceedings M&C 2013, May 5 –
9, 2013, Sun Valley ID
20×20×20 nm
1.2×1.04×0.45 *m

View Slide

We have developed a hybrid model that uses cluster
dynamics to model small bubbles and phase field for large
Cluster Dynamics (Xolotl) Phase Field (MOOSE)
Both codes are open source

View Slide

+ =
n
!"#
!$
= ̇
'()
+ +)
,-.)
− 0 .)
, where n = 1, 2, …,
>1000
n +)
= 0 for n > 1
n Reactions are represented by 0 .)
n 0 .)
= 3)
.)
.4
− 3 )54
. )54
.4
+ 3)
678$.)
−
3 )94
678$ . )94
+ 3)
:6;<.)
− 3 )94
:6;< . )94
n Include
n Clustering: Xe1
+ Xen
→ Xen+1
n Emission and resolution: Xen
→ Xe1
+ Xen-1
The cluster dynamics model uses a series of coupled
reaction diffusion equations to model Xe atom clusters
+ =
…

View Slide

n Solves the coupled equations using implicit finite difference
n Nonlinear solves are carried out using PETSc
n Scales well to 10,000’s of processors
n GPU acceleration is underway
Xolotl is an open source spatially-resolved cluster dynamics
code developed at the University of Tennessee-Knoxville
Limitations:
• Cannot represent large bubbles due to high computational expense
• Cannot represent interfacial motion such as grain boundary migration

View Slide

n Predicts the growth and coalescence of fission gas bubbles and grain boundary
migration
n Grand potential model (Plapp) with multiphase field grain growth model
n Xe atom and U vacancy chemical potentials (2 DOF).
n Bubble order parameter (1 DOF).
n Grain order parameters (1 – 20 DOF, reused for multiple grains).
n The model uses 4 – 22 DOF per node.
We are building our work on the most recent fission gas
model in MOOSE/MARMOT (developed by Larry Aagesen)
Aagesen et al. Computational Materials Science 161 (2019): 35-45.

View Slide

The phase field fission gas model in MOOSE/MARMOT
predicts bubble and grain boundary evolution
33 days 77 days 145 days
Limitations:
• Cannot represent bubbles that are much smaller than the grain size
• Cannot directly represent bubble nucleation
• Cannot directly represent re-solution

View Slide

Xolotl describes all behavior in the grains while MARMOT
models grain boundary bubbles and migration
Cluster Dynamics (Xolotl)
• Xe production
• Intragranular diffusion
• Clustering
• Resolution
Phase Field (MARMOT)
• Intergranular bubble
growth and
coalescence
• Grain boundary
migration
Gas atom arrival rate at
Interfaces
Interface locations

View Slide

Xolotl and MARMOT are coupled using the Multiapps and
Transfers systems in the MOOSE framework
MARMOT mesh MOOSE-Xolotl wrapper mesh Xolotl grid
Interpolation transfer Direct copy
Microstructure
Gas source
Interface coordinates
Gas source

View Slide

The coupled code provides the capability to represent small
intragranular bubbles and large intergranular bubbles
20 µm
̇
& = 1.09×10,-
fissions/(m3s)
. = 1800 K

View Slide

We verified that the codes are coupled correctly by comparing
a hybrid model simulation to stand-alone MARMOT
0 200 400 600 800 1000 1200 1400
Time (days)
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
Intergranular bubble fraction
Stand-alone MARMOT
Coupled (No Clu. & No Re-s.)
̇
" = 1.09×10)*
fissions/(m3s)
+ = 1800 K
Initial microstructure
Stand-alone MARMOT Coupled

View Slide

Clu. & Re-s.
4 8 16 32 64 128
# of processors
0
1000
2000
3000
4000
5000
6000
Computation time (s)
Data transfer
MARMOT
Xolotl
Clu. & No Re-s.
4 8 16 32 64 128
# of processors
0
1000
2000
3000
4000
5000
6000
Data transfer
MARMOT
Xolotl
The computational cost of Xolotl and MARMOT are similar
and cost of the data transfer is negligible
No Clu. & No Re-s.
4 8 16 32 64 128
# of processors
0
1000
2000
3000
4000
5000
6000
Data transfer
MARMOT
Xolotl

View Slide

The parallel scalability of the hybrid model is excellent
20 40 60 80 100 120
# of processors
10
20
30
40
50
60
Speedup
Ideal
Stand-alone MARMOT
Coupled (Clu. & No Re-s.)
Coupled (Clu. & Re-s.)
4 16 36 64 100
# of processors
0
0.5
1
1.5
2
Speedup
Ideal
Stand-alone MARMOT
Coupled (Clu. & No Re-s.)
Coupled (Clu. & Re-s.)
Strong Scaling Weak Scaling

View Slide

We will demonstrate the capabilities of the hybrid model by
investigating three aspects of fission gas behavior
Intragranular physics Grain size
Temperature
200 400 600 800 1000 1200 1400
Time (days)
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
No clustering & no re-solution
Clustering & no re-solution
Clustering & re-solution
Effective diffusion
200 400 600 800 1000 1200 1400
Time (days)
0.0145
0.015
0.0155
0.016
0.0165
0.017
@1800K, no re-solution
@1800K, re-solution
@1000K, re-solution
200 400 600 800 1000 1200 1400
Time (days)
0.014
0.015
0.016
0.017
0.018
0.019
0.02
10 grains
20 grains
30 grains

View Slide

The intragranular physics included in Xolotl has a large
impact on the overall fission gas behavior
20 µm
1800 K
̇
& = 1.09×10,-
fissions/(m3s)
Note: Initial intergranular bubbles are used to avoid
the need to model nucleation in MARMOT

View Slide

Clustering results in as much as 70% of the fission gas being
trapped within the grains
200 400 600 800 1000 1200 1400
Time (days)
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Effective diffusion
200 400 600 800 1000 1200 1400
Time (days)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Xe fraction in grains
1800 K

View Slide

Temperature results in much less gas arriving at grain
boundaries and less grain growth
20 µm
̇
& = 1.09×10,-
fissions/(m3s)

View Slide

Temperature results in much less gas arriving at grain
boundaries and less grain growth
1000 K, No re-solution 1000 K, Re-solution
1800 K, No re-solution 1800 K, Re-solution
20 µm
̇
& = 1.09×10,-
fissions/(m3s)

View Slide

More gas is trapped in the grains at lower temperature and
the intergranular bubbles grow much slower
200 400 600 800 1000 1200 1400
Time (days)
0.0145
0.015
0.0155
0.016
0.0165
0.017
@1800K, re-solution
@1000K, re-solution
200 400 600 800 1000 1200 1400
Time (days)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
@1800K, re-solution
@1000K, re-solution

View Slide

More grain growth occurs with more grains, resulting in more
sweeping up of gas by migrating grain boundaries
20 µm
1800 K, Clustering, Re-solution
̇
& = 1.09×10,-
fissions/(m3s)

View Slide

Decreasing grain size accelerates bubble growth, even
though we do not include fast grain boundary diffusion
200 400 600 800 1000 1200 1400
Time (days)
0.014
0.015
0.016
0.017
0.018
0.019
0.02
10 grains
20 grains
30 grains
200 400 600 800 1000 1200 1400
Time (days)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
10 grains
20 grains
30 grains
1800 K, Clustering, Re-solution

View Slide

We are currently working on 3D simulations with our hybrid
model
Microstructure Intragranular fission gas

View Slide

Direct coupling between phase field and cluster dynamics
could be used to model other phenomena
Cluster Dynamics
• Diffusion and atom
clustering
• Nucleation and growth
of small precipitates
Phase Field
• Large precipitate
evolution
• Interface evolution
• Grain boundary evolution

View Slide

Our hybrid model provides a means of modeling the impact
of small scale precipitates on large scale evolution

View Slide


View Slide

Concurrently Modeling Multiple Length Scales by Coupling the Phase-Field Method to Spatially-Resolved Cluster Dynamics

Concurrently Modeling Multiple Length Scales by Coupling the Phase-Field Method to Spatially-Resolved Cluster Dynamics

Daniel Wheeler

More Decks by Daniel Wheeler

Other Decks in Science

Featured

Transcript