Statistical Estimation of Dislocation Pinning at Precipitates, Voids and Bubbles

"Pinning of dislocations at nanosized obstacles like precipitates, voids and bubbles, is a crucial mechanism in the context of phenomena like hardening and creep. The interaction between such an obstacle and a dislocation is often explored at fundamental level by means of analytical tools, atomistic simulations and finite element methods. Nevertheless, such studies fail to predict the effect on the overall plasticity on account of insufficient information about the underlying statistics of this process comprising a large number of dislocations and obstacles in a system. Here we propose a new statistical approach, where the statistics of pinning at idealized spherical obstacles is explored by taking into account the generalized size distribution of the obstacle along with the dislocation density within a three-dimensional framework. The application of this approach has been demonstrated for dislocation pinning at nanovoids in neutron irradiated type 316-stainless steel.IntroductionPresence of nanoscale obstacles like precipitates, voids and bubbles play a crucial role in determining the deformation behavior of a crystalline solid on account of the interactions between the line defects and such localized obstacles. In the context of the glide motion of dislocations, the obstacles can offer resistance to a moving dislocation, thereby causing a hardening effect [l-3]. In some other cases, inclusions like voids and bubbles can affect the rate of dislocation climb through diffusive [4] and non-diffusive [5] mechanisms. Over the last few decades, numerous studies have been performed to gain an insight of the dislocation-obstacle interactions at a fundamental level. These include the interactions responsible for the hardening effect, in addition to those pertaining to the non-conservative motion of dislocations.Although the elementary mechanisms of the various dislocation-obstacle interactions have been vastly explored and understood by means of analytical theory and numerical simulations, it remains difficult to quantitatively understand their effects on the macroscopic deformation behavior. This is due to the fact that their influence on the gross plastic deformation of a bulk sample would be the collective outcome of a large ensemble of such interactions. As a result, it becomes infeasible to predict the bulk deformation behavior of a material until the statistics of pinning of the dislocations at the localized obstacles is available. In the context of precipitate hardening, some well known attempts to extract the pinning-statistics were made by Friedel-Fleischer [6] and Mott [7] by analytical means, which were later tested through simplified 2-dimensional in-silica modeling [8]."