A Diffuse Interface Model for Void Formation under Non-Equilibrium Irradiation
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A Diffuse Interface Model for Void Formation under Non-Equilibrium Irradiation Srujan Rokkam1 and Anter El-Azab2 1 Mechanical Engineering Department, Florida State University, Tallahassee, FL 32310, USA 2 Department of Scientific Computing, Florida State University, 415 Dirac Science Library, Tallahassee, FL 32306-4120, USA ABSTRACT Void formation in irradiated materials is an intriguing and technologically important physical process associated with radiation damage. In this communication, we present a diffuse interface model for simulating void formation in materials under irradiation. Voids are treated as aggregates of vacancies left from the cascade damage. The emergence of the void ensembles in the irradiated material is modeled by an Allen-Cahn equation coupled with two Cahn-Hilliard equations governing the space and time evolution of vacancies and interstitials. The governing system of equations includes stochastic generation of point defects representing the cascade process, reaction of vacancies and interstitials, interaction of point defects with extended defects (viz., void surface and grain boundaries) and thermal fluctuations in defects. Numerical simulations demonstrating the model capabilities with respect to nucleation and growth of voids and swelling of the irradiated material are presented. INTRODUCTION Ever since the discovery of voids in irradiated metals by Cawthorne and Fulton [1], voids have been observed to form in almost all metals and alloys subject to irradiation. In many cases the occurrence of voids in these materials has been accompanied by volumetric swelling of the order of a few percent to as high as 20% or more [2,3]. Such high levels of volume changes can pose severe problems for the long-term reliability of structural materials used in the design of reactor components. Owing to their technological relevance, experimental [3,4] and theoretical studies [5,6] have been undertaken to understand the phenomenon of void nucleation, growth, swelling and the factors that influence their occurrence. The traditional approaches to model void formation treats both void nucleation and growth as separate processes which are studied respectively by means of classical nucleation theory and rate theory of void growth. This traditional route neglects the interactions between nucleating and growing voids, and lacks information pertaining to spatial distribution of point defects, the microstructure itself, or their coupling with the driving forces of void formation. As such, a comprehensive theory to model void nucleation, growth and associated phenomenon should account for the coupling between various processes as well as effects of the spatial distribution of defects and microstructural entities. Motivated by the need to develop spatially resolved models for microstructural evolution of materials under irradiation we recently developed a framework [7-9] for modeling irradiation induced microstructure using continuum fields whose temporal evolution indentifies the microstructural evolution in the mate
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