A Rate-Theory Approach to Irradiation Damage Modeling with Random Cascades in Space and Time
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ATE theory has been used to model the mechanical effects of irradiation damage since the late 1960s, originating with the work of Harkness et al.,[1] Brailsford and Bullough,[2] and Dollins.[3] The method tracks the production, transport, absorption, and recombination of vacancies and interstitials liberated by neutron bombardment, and then utilizes the point defect populations to drive models of microstructural evolution and in-pile deformation via stress-free growth,[3–5] creep,[6,7] or void swelling.[2] The standard rate-theory formalism utilizes balance equations for point defects in which all sources and sinks are considered uniform in both space and time and in which the concentration of defects is driven toward equilibrium where the rate of production equals the rate of mutual recombination plus absorption. As reviewed by Was,[8] the time-dependent point defect behavior in a non-evolving, spatially uniform medium has been addressed by Sizmann[9] and Lam.[10] Since the ability to accurately model the microstructural mechanisms of evolution and deformation relies heavily on the solution to the point defect balance equations, it is important to assess the degree to which JESSE J. CARTER and WILLIAM H. HOWLAND, Scientists, and RICHARD W. SMITH, Group Leader, are with the Bettis Atomic Power Laboratory, PO Box 79, West Mifflin, PA 15122. Contact e-mail: [email protected] Manuscript submitted May 8, 2013. Article published online June 25, 2014 METALLURGICAL AND MATERIALS TRANSACTIONS A
the basic mathematical assumptions of the model impact its ability to capture the key aspects of the true point defect behavior. Two assumptions of particular interest in regard to their effect on defect absorption rates are the averaging of point defect production via displacement cascades into a constant, average production rate density, and the replacement of distinct dislocations with a uniform, average removal rate. The purpose of this work is to assess the impact of these assumptions by performing detailed numerical simulations in which they may each be relaxed. Interstitials and vacancies are mostly liberated in the form of displacement damage cascades that result from the energetic interaction of fast neutrons with lattice atoms. Due to the random nature of neutron scattering, these cascades occur randomly in space and time, and are small in both physical size and temporal duration. It may be argued that point defect production via cascades would be better modeled as a series of distinct, local events followed by periods of production-free transport than by a uniform, space- and time-averaged source term. Due to mutual interstitial-vacancy recombination and absorption at sinks, point defects can only travel a finite distance from the specific cascade in which they were produced. If the range and lifetime of the defects is seen to be short with respect to the distance and period between cascade events, then the averaged source approximation may not properly capture local behavior in any given region. The degree to which the poi
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