Nuclear Future Volume 9 issue 1
Figure 1: St ress (von Mises) contour plot of post heat-up contact between the cladding and the fuel in an AGR. Showing the enhancement brought to fuel performance modelling via the use of adaptive remeshing within an industrially verifi ed commercial modelling platform.
Figure 2: Two-dimensional representation of point connectivity within peridynamics formalism. Material points that are within a given cut-off of each other (the horizon, here represented by a dashed red line) are linked by bonds. Here the bonds for a single material point are highl ighted in red.
sorts of features. With this we have been able not only to perform convergent calculations for the stress state surrounding a discontinuity, such as a crack, over large time periods, but also to follow their nucleation, growth and propagation. Additionally, we now have the ability to study crack growth and bubble formation in nuclear fuel, which offers huge potential when coupled with a f uel performance code of the kind described earlier.
Within industry the information and insight obtained from atomistic simulation could, for example, provide additional data to augment safety cases
Another area in which we are employing peridynamics is to
consider PCI. Fuel and cladding can come into contact due to the combined effects of fuel swelling and cladding creep-down. The large stresses induced by this interaction, leading to fuel-cladding bonding, can encourage fuel cracking during power transients. Understanding interfaces between ductile and brittle materials could have benefi ts in understanding, and possibly help prevent fuel and cladding failures. Figure 3 shows an example of a peridynamics simulation of
the fracture of a bi-material strip where the top layer is a brittle material on a ductile substrate that has been taken through a heating cycle. This acts as an analogue to the behaviour where brittle oxide fuel adheres to ductile cladding. Such simulations can serve as a mechanism for explaining the features found in irradiated fuel micrographs and for integrity testing other reactor components.
46 Materials modelling at Imperial
Atomic scale modelling The FE and peridynamic methods described so far are continuum techniques in which the behaviour and interaction of the model elements are generally parameterised from material properties measured at the macroscopic scale. As described above, this means that such methods are relatively straightforward to set up and support a length-scale that allows simulation of entire components and sub-assemblies to be performed. However, the combination of microstructure, defect structure and atomic interactions determine the properties of a material, and although FE and peridynamics have been used to consider microstructural effects, their continuum nature makes them ill-suited to the task of describing atomic-level processes. By comparison, atomistic simulation techniques include an
explicit description of atoms and the forces acting between them. As such, the position of individual atoms under different conditions of composition, temperature and pressure can be probed in response to point and line defects, surfaces, grain- boundaries and interfaces. This makes atomistic techniques particularly well-suited to elucidating property trends and predicting the atomic-level mechanisms that give rise to the sometimes unexpected behaviour of nuclear materials. Within industry, the kind of information and insight obtained
from atomistic simulation could, for example, help add physical basis to fuel performance codes or provide additional data to augment safety cases. Already, data for gas migration, obtained using atomistic simulation, is used in the fuel performance code described earlier. Furthermore, the atomic-level understanding obtained from atomistic methods could be used to help design the next generation of fuel and structural materials for application within future reactor designs. As yet, atomic-level simulation techniques are perhaps not as widely deployed within
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