Chaitanya Deo

Nuclear and Radiological Engineering Programs, George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology USA

1. Introduction

In the process of energy production via fission — and fusion in the years to come — both fuel components and structural materials within nuclear reactors can sustain substantial radiation damage. Regardless of the type of reactor, this damage initially appears in the form of local intrinsic point defects within the material — vacancies and interstitials. The point defects agglomerate, interact with the underlying microstructure and produce effects such as void swelling and irradiation creep. Vacancies provide a pathway for solutes to segregate to grain boundaries and dislocation leading to chemical inhomogeneities that translate into phase transformations and/or property variations in these materials, rendering them unsuitable for the desired application.

Many deleterious effects of irradiation on material properties —e. g. void swelling, irradiation creep, radiation-induced hardening and embrittlement —can be traced back to the formation of the aforementioned point defect clusters and gas bubbles. These effects include such phenomena as swelling, growth, phase change, segregation, etc. For example (Was 2007), a block of pure nickel, 1cm on a side, irradiated in a reactor (to a fluence of say, 1022 n/cm2) will measure 1.06cm on a side, representing a volume change of 20%. The volume change, or swelling, is isotropic and is due to the formation of voids in the solid. Other examples are irradiation growth which is distortion at constant volume, phase changes under irradiation where new phases form as a consequence of diffusion of supersaturated defect concentrations and radiation induced segregation.

In addition, the transmutation of reactor elements produces extrinsic defects such as hydrogen, deuterium and helium. For example, Zircalloy high-pressure-tubes used in light water reactors are known to absorb deuterium which can cause delayed hydride cracking (Cirimello, G. et al. 2006). Similarly, in Pebble Bed Modular reactors and in other technologies based on inert gas cooling, formation of ionic gas bubbles within both fuel and structural materials is common(Was 2007). This is critical in structural materials as their behaviour depends on their microstructure, which is in turn affected by neutron radiation.

Cladding materials are also exposed to fission product gasses produced in the fuel during operation.

The effect of irradiation on materials is a classic example of an inherently multiscale phenomenon, as schematically illustrated in Figure 1 for the case of deformation and plasticity in irradiated materials. Irradiation changes the properties of cladding and duct materials as follows: increase in the ductile to brittle transition temperature; reduction of fracture toughness from low temperature irradiation (below 400oC); irradiation creep, helium embrittlement (above ~500C) and swelling. Experimental irradiation programs can be conducted to test the irradiation induced mechanical property changes, but these take significant time and the conditions are limited. As a consequence, it is desirable and efficient to develop models with reliable predictive capabilities for both, design of new reactor components, and simulation of the in-service response of existing materials.

Although these phenomena have been known for many years (Olander 1981; de la Rubia, Zbib et al. 2000; Was 2007) , the underlying fundamental mechanisms and their relation to the irradiation field have not been clearly demonstrated. Most models and theories of irradiation induced deformation and mechanical behavior rely on empirical parameters fit to experimental data. With improvements in computational techniques and algorithms, it is now possible to probe structure-property connections through the elucidation of fundamental atomic mechanisms. Often, these mechanisms involve defects of different dimensionality that exist and interact with each other to significantly affect material properties.

For irradiated materials, point defects and clusters affect crystal plasticity. Dislocation-defect interactions may be associated with defects in the matrix, the modification of the local elastic constants due to the presence of defects and defect clusters and the effects of clusters and voids on the stacking fault energy. The formation of self interstitial loop rafts and the decoration of dislocations with self interstitial clusters have become important issues for understanding radiation hardening and embrittlement under cascade damage conditions(Wen, Ghoniem et al. 2005). Dislocation motion is thought to be the main mechanism for deformation, because a fairly high density of network dislocations are generated during irradiation, and the dislocation sink strength for point defects is much higher that the grain boundary sink strength for point defects. Computational studies of dislocation activity can be performed at several different length and time scales(Ghoniem, Busso et al. 2003) that are shown in Fig. 1.

Pertinent processes span more than 10 orders of magnitude in length from the sub-atomic nuclear to structural component level, and span 22 orders of magnitude in time from the sub-picosecond of nuclear collisions to the decade-long component service lifetimes (Odette, Wirth et al. 2001; Wirth, G. R. et al. 2004). Many different variables control the mix of nano/microstructural features formed and the corresponding degradation of physical and mechanical properties in nuclear fuels, cladding and structural materials. The most important variables include the initial material composition and microstructure, the thermo­mechanical loads, and the irradiation history. While the initial material state and thermo­mechanical loading are of concern in all materials performance-limited engineering applications, the added complexity introduced by the effects of radiation is a large concern for materials in advanced nuclear energy systems.

The scientific challenge for next-generation extreme materials — whatever their composition — is to understand their failure modes, and to prolong their useful lifetimes by interrupting or arresting these failures. Damage starts with atomic displacements that create interstitials and vacancies, which then migrate and aggregate to form clusters and ever-larger extended structures. Eventually, the damage reaches macroscopic dimensions, leading to degradation of performance and failure. This problem is massively multiscale, covering nine orders of magnitude in its spatial dimension, and neither experiment nor theory has yet captured this complexity in a single framework.

On the experimental side, in situ measurements of neutron irradiation with atomic or nano­scale resolution are needed to observe the initial damage processes, followed by coarser — grained experiments to capture migration, aggregation and ultimately macroscopic failure. The modeling challenge is equally dramatic: kinetic energy from an incident particle is

transferred successively to electronic, atomic, vibrational and structural systems, requiring a diverse mix of theoretical formulations appropriate for different spatial scales.

This chapter will review choices for structural materials for these environments, and review the methods and techniques available for simulating these materials at various length and time scales Methods that will be reviewed will include first principles calculations, molecular dynamics calculations, kinetic Monte Carlo methods, and microstructural mechanics methods.