Atomistic simulations of the effects of segregated elements on grain-boundary fracture in body-centered-cubic Fe
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I. INTRODUCTION
THE structure of high-angle grain boundaries in metals and alloys has been the subject of a large amount of simulation work in the past 30 years. In particular, symmetrical-tilt grain boundaries have been the subject of numerous studies and structural models.[1] In contrast, the fracture properties of these boundaries have not been studied extensively. In a direct study using computer simulation, it was shown that the fracture of special coincident-site-lattice grain boundaries is very closely related to the structural unit of the grain boundary.[2] In that work, it was shown that the periodicity of the grain boundary plays a critical role in the energy evolution as the crack advances along the boundary. That work points out the importance of lattice trapping effects on the fracture behavior of grain boundaries, which may be more significant than expected for the fracture inside the grains. In addition, the segregation of impurities to grain boundaries can affect the fracture response of the boundaries in a very significant way. From a theoretical point of view, the effects of impurities on grain-boundary fracture have been studied only in an indirect way. Segregation energies of various impurities to the grain boundary and to a free surface of similar orientation are calculated, and, from these results, the effects of the impurities on the cohesive energy of the boundary can be inferred.[3–6] It can be assumed, then, that the changes induced by the impurities on grain-boundary cohesion are the controlling factor D. FARKAS, Professor, and B. HYDE, Graduate Student, are with the Department of Materials Science and Engineering, Virginia Tech, Blacksburg, VA 24060. Contact e-mail: [email protected] R. NOGUEIRA, Researcher, is with Escola Politécnica, USP, São Paulo, Brazil. M. RUDA, Researcher, is with the Centro Atómico Bariloche, CNEA, Bariloche and CRUB– Universidad Nacional del Comahue, Argentina. Manuscript submitted August 6, 2004. METALLURGICAL AND MATERIALS TRANSACTIONS A
in the grain-boundary fracture behavior. However, since lattice trapping effects are also very important in grain boundaries, this assumption is not necessarily true. A recent review on the importance of segregated impurities in the behavior of grain boundaries was given by Briant.[7] Overall, this is a complex phenomenon, and the direct simulation of the fracture response using atomistic techniques can help one understand the basic mechanisms of interplay between the chemistry of the grain boundaries and the fracture response. The Griffith criterion[8] for the mechanical stability of a crack can be formulated as a balance of the energy release rate and the surface energy of the two fracture surfaces that are created as the crack advances and is usually taken as the starting point of the analysis of fracture. In contrast to this approach, from an atomistic point of view, crack-propagation resistance should be characterized by the force required to break individual atomic bonds rather than a global energetic criterion. This latter
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