Controlling Plastic Flow across Grain Boundaries in a Continuum Model
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A grain boundary is an interface between two grains of different orientation. It may act as a source/sink or an obstruction to the flow of dislocations. Any of these possibilities significantly affect the evolution of microstructure of polycrystalline solids, which subsequently affects their mechanical response. It is not possible to model these features in classical crystal plasticity theory due to the absence of an explicit characterization of dislocations. In discrete dislocation modeling, the correct rules for dislocation transmission through grain boundaries are not known yet. In this article, a recently proposed continuum approach, phenomenological mesoscopic field dislocation mechanics (PMFDM, Acharya and Roy[1]), is used to model controlled plastic flow through grain boundaries in crystalline materials. PMFDM is a combination of (a) field dislocation mechanics theory (Acharya[2–4]), as a model for the plastic flow of polar, mobile dislocation density, and long-range internal stress; and (b) gradient crystal plasticity, which is used as a model for plastic flow of statistical dislocation distributions and strength arising from short-range interactions. In the PMFDM framework, a polycrystal is set up by using appropriate slip systems for different grains. However, by doing so, the structure of equations allows free flow of excess dislocations through grain boundaries. A jump condition at an interface for excess dislocation density in the context of PMFDM theory is developed in Acharya.[5] In this article, we use a finite element implementation of this SAURABH PURI, Postdoctoral Scholar, is with the Department of Mechanical Engineering, California Institute of Technology, Pasadena, CA 91101. Contact e-mail: [email protected] AMIT ACHARYA, Professor, Department of Civil and Environmental Engineering, and ANTHONY D. ROLLETT, Professor, Department of Materials Science and Engineering, are with Carnegie Mellon University, Pittsburgh, PA 15213. Manuscript submitted December 16, 2009. Article published online May 29, 2010 METALLURGICAL AND MATERIALS TRANSACTIONS A
jump condition (Puri[6] and Puri et al.[7]) to study the effect of grain boundary constraints to plastic flow on the deformation of a bicrystal. It was observed in the experiments done by Robach et al.[8] that most of the dislocation motion started from the grain boundary. They did not observe any dislocation sources within the grain. Motivated by these experiments, a particular case with dislocation sources localized to the region adjacent to the grain boundary is considered in this article. This article is organized as follows: the governing equations of PMFDM theory are summarized in Section II. The jump condition at an interface for excess dislocation density evolution is discussed briefly in Section III. An illustration of the effect of grain boundary constraints on the mechanical response of a bicrystal is presented in Section IV. We end with some concluding remarks in Section V. A comment regarding terminology: Given a scale of resolution l, we refer to the
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