Tag Archives: Polycrystal

Uranium Dioxide (UO2)

Different kinds of oxide fuels are used in nuclear power plants, most commonly used – and for the longest time – is Uranium Dioxide (UO2). A solid understanding of the fuel performance is central to control in-service performance, properties and degradation of the fuel as well as for safe handling of it.

As fuel material, UO2 is usually sintered into small cylindrical pellets, measuring about 10 mm in diameter and similar in length. These cylinders are stacked in fuel rods inside a Zircalloy cladding. The small radial gap between the pellets and the cladding is usually filled with a pressurized gas such as Helium. A number of such fuel rods are mounted in fuel assemblies together with control rods with a high capacity for neutron absorption. The fuel assemblies are then used as heat source in fission power plants.

As the fuel pellets are “burnt” in the reactor, fission processes take place and the degree of irradiation of the fuel pellets is usual measured in terms of the “burnup”, that is the fraction of the initial material that has undergone fission.

Under common in-service conditions, the core of the fuel pellets can be maintained at a temperature of 2000K while the pellet surface is at around 800K (the melting point of UO2 is approximately 3140K). The outside temperature is maintained by a constant flow of coolant through the fuel assemblies. Under such extreme thermal gradient conditions, the fuel material undergoes drastic changes. These changes have a strong influence on fuel performance and properties such as the thermal conductivity and structural rigidity. The grain structure will have different morphologies in different regions. This is schematically illustrated below.

UO2_cross_section
Cross-section of a UO2 fuel pellet, showing characteristic microstructure variations.

The extreme thermal gradients will also cause so-called “hourglassing” of the fuel pellets along with cracking – both radially and circumferentially – due to thermally induced stresses and swelling due to solid fission products.

By the release of fission gasses (e.g., Xe, Kr, I and Cs), gas-filled pores or voids will form in the microstructure. The gas bubbles form in the grain interiors and migrate by diffusion to coalesce along the grain boundaries.

UO2_gas_bubbles
Formation of gas-filled bubbles, pores and voids in the grain structure of UO2 during irradiation.

The presence of gas bubbles can cause swelling and cracking of the fuel pellet and the gas can also be released inside the Zircalloy cladding, lowering the heat conduction capacity of the Helium that surrounds the pellets. In either case, the integrity of the Zircalloy cladding is compromised.

In Hallberg & Zhu (2015), the stability of grain boundary texture under grain growth in UO2 is studied through level set modeling, taking anisotropic grain boundary properties into account. The characteristic morphologies of faceted voids in UO2, due to heterogeneous interface energies, is studied in Zhu & Hallberg (2015) by 3D phase field simulations.

New paper on grain boundary texture stability in UO2

A paper was recently published in Journal of Nuclear Materials on the stability of certain grain boundary configurations in UO2 (Uranium Dioxide) during grain growth. The paper is titled Stability of grain boundary texture during isothermal grain growth in UO2 considering anisotropic grain boundary properties, and can be found here or at the at Science Direct.

HallbergZhu2015_jnm_cover

Paper published on evolution of grain boundary character distribution during grain growth

A new paper, titled "Influence of anisotropic grain boundary properties on the evolution of grain boundary character distribution during grain growth - A 2D level set study", was recently published in Modelling and Simulation in Materials Science and Engineering and can be found at the publisher's site following this link or here.

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Dislocation and grain boundary interaction

Mesoscale models of microstructure evolution allow studying of heterogeneous dislocation density distributions and related gradient effects. This is closely connected to the well-renowned Hall-Petch effect, stating a proportionality between the yield stress \sigma_{\mathrm{y}} and the inverse of the square-root of the average grain size d according to

\sigma_{\mathrm{y}}\propto\frac{1}{\sqrt{d}}

The interaction between dislocation motion and grain boundaries can be modeled by different approaches. Some examples are given below.

In Hallberg and Ristinmaa (2013) (also discussed in this conference presentation), a hybrid finite difference/cellular automaton model is established where dislocation density gradient are modeled in a reaction-diffusion system. This approach results in the expected Hall-Petch behavior of the macroscopic flow stress – without including an explicit dependence on the grain size – in addition to providing a physically sound dislocation density distribution, indicated in the figure below.

Simulated distribution of total dislocation density in an artificial polycrystal. Due to the reaction-diffusion modeling of dislocation density evolution and the presence of grain boundaries, dislocation pile-ups are formed along the grain boundaries and particularly at triple junctions.
Simulated distribution of total dislocation density in an artificial polycrystal. Due to the reaction-diffusion modeling of dislocation density evolution and the presence of grain boundaries, dislocation pile-ups are formed along the grain boundaries and particularly at triple junctions.

By this modeling approach, the dislocation density will be concentrated at grain boundaries and particularly at triple junctions, directly providing the sites for nucleation of recrystallization. This is in contrast to the common modeling approach where nuclei are placed manually at appropriate sites in the microstructure.

Another approach to modeling of dislocation and grain boundary interaction is taken in Hallberg (2013) where a level set formulation is used to model polycrystal grain structures.

Dislocation density distribution influenced by the presence of grain boundaries. The microstructure model is based on level sets, representing the individual grains. The extent of dislocation accumulation at grain boundaries can be controlled by the parameter w, as illustrated in images a-d.
Dislocation density distribution influenced by the presence of grain boundaries. The microstructure model is based on level sets, representing the individual grains. The extent of dislocation accumulation at grain boundaries can be controlled by the parameter w, as illustrated in images a-d.

Animation showing a 2D level set simulation of Dynamic Discontinuous Recrystallization (DDRX)

A simple 2D simulation of dynamic discontinuous recrystallization (DDRX) in pure Cu at an elevated temperature. The simulation is based on level sets in a finite element setting. Adaptive remeshing is performed in each step. The animation speed is increased compared to actual time.