Y. N. Osetsky

Oak Ridge National Laboratory, Oak Ridge, TN, USA D. J. Bacon

The University of Liverpool, Liverpool, UK Published by Elsevier Ltd.

1.12.1 Introduction 334

1.12.2 Radiation Effects on Mechanical Properties 334

1.12.2.1 Radiation-Induced Obstacles to Dislocation Glide 334

1.12.2.2 Effects on Mechanical Properties 335

1.12.3 Method 336

1.12.3.1 Why Atomic-Scale Modeling? 336

1.12.3.2 Atomic-Level Models for Dislocations 336

1.12.3.3 Input Parameters 338

1.12.3.4 Output Information 338

1.12.4 Results on Dislocation-Obstacles Interaction 339

1.12.4.1 Inclusion-Like Obstacles 339

1.12.4.1.1 Temperature T — 0K 339

1.12.4.1.2 Temperature T> 0K 342

1.12.4.2 Dislocation-Type Obstacles 345

1.12.4.2.1 Stacking fault tetrahedra 345

1.12.4.2.2 Dislocation loops 348

1.12.4.3 Microstructure Modifications due to Plastic Deformation 352

1.12.5 Concluding Remarks 353

References 355

1.12.1 Introduction

Structural materials in nuclear power plants suffer a significant degradation of their properties under the intensive flux of energetic atomic particles (see Chapter 1.03, Radiation-Induced Effects on Microstructure). This is due to the evolution of microstructures associated with the extremely high concentration of radiation-induced defects. The high supersaturation of lattice defects leads to microstruc­tures that are unique to irradiation conditions. Irra­diation with high energy neutrons or ions creates initial damage in the form of displacement cascades that produce high local supersaturations of point defects and their clusters (see Chapter 1.11, Pri­mary Radiation Damage Formation). Evolution of the primary damage under the high operating tem­perature (^600 K to >1000 K) leads to a micro­structure containing a high concentration of defect clusters, such as voids, dislocation loops (DLs), stack­ing fault tetrahedra (SFTs), gas-filled bubbles, and precipitates, and an increase in the total dislocation network density (see Chapter 1.13, Radiation Dam­age Theory; Chapter 1.14, Kinetic Monte Carlo Simulations of Irradiation Effects and Chapter 1.15, Phase Field Methods). These changes affect material properties, including mechanical ones, which are the subject of this chapter.

A general theory of radiation effects has not yet been developed, and currently the most promising way to predict materials behavior is based on multi­scale materials modeling (MMM). In this framework, phenomena are considered at the appropriate length and times scales using specific theoretical and/or modeling approaches, and the different scales are linked by parameters/mechanisms/rules to provide integrated information from a lower to a higher level.

Research on the mechanical properties of irradiated materials, a topic of crucial importance for engineering solutions, provides a good example of this. The lowest level treats individual atoms by first principles, ab initio methods, by solving Schrodinger’s equation for moving electrons and ions. Calculations based on electron den­sity functional theory (DFT) (see Chapter 1.08, Ab Initio Electronic Structure Calculations for Nuclear Materials) and its approximations, such as bond order potentials (BOPs), can consider a few hundred atoms over a very short time of femtoseconds to picoseconds. Delivery of the resulting information to higher level models can be achieved through effective interatomic potentials (IAPs) (see Chapter 1.10, Interatomic Potential Development), in which the adjustable parameters are fitted to the basic chemical and struc­tural properties obtained ab initio. IAPs are required for atomic-scale modeling methods such as molecular stat­ics (MS) and molecular dynamics (MD), which are used to simulate millions of atoms. Time spanning nanose­conds to microseconds can be simulated by MD if the number of atoms is not large (see Section 1.12.3.3). This level can provide properties of point and extended defects and interactions between them (see Chapter 1.09, Molecular Dynamics). For mechanical properties, important interactions are between moving dislocations, which are responsible for plasticity, and defects created by irradiation. Mechanisms and para­meters determined at this level can then inform dislo­cation dynamics (DD) models based on elasticity theory of the continuum (see Chapter 1.16, Disloca­tion Dynamics). DD models can simulate processes at the micrometer scale and mesh with the mechanical properties of larger volumes of material used in finite elements (FEs) methods, that is, realistic models for the design of core components. In this chapter, we consider direct interactions at the atomic scale between moving dislocations and obstacles to their motion.

The structure of the chapter is as follows. First, we summarize the main features of the irradiation microstructure of concern. Then we provide a short description of atomic-scale methods applied to dislo­cation modeling, bearing in mind the details pre­sented in Chapter 1.09, Molecular Dynamics. This is followed by a review of important results from simulations of the interaction between disloca­tions and obstacles. We then describe how dislocations modify microstructure in irradiated metals. Finally, we indicate some issues that will hopefully be resolved by atomic-scale modeling in the near future. Our main aim is to give the reader a general picture of the phenomena involved and encourage further research in this area. The following sources1-4 provide a more general and deeper understanding of disloca­tions and modeling of plasticity issues.