Strain Energy During Mechanical Milling: Part I. Mathematical Modeling
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INTRODUCTION
SEVERE plastic deformation (SPD) techniques provide a relatively straightforward approach to synthesize nanostructured (grain dimensions 10 to 100 nm) and ultrafine-grained (hundreds of nm) materials, via dislocation generation, accumulation, and rearrangement mechanisms. Among the various SPD approaches developed, mechanical milling has received particular attention because of its potential for high-tonnage manufacturing.[1–3] During mechanical milling, the strain energy stored in powders provides the driving force for dislocation generation and accumulation, as described in mechanistic models.[4,5] An inspection of the published literature shows that the mechanisms responsible for the generation and storage of strain energy during milling remain poorly understood.[3,6] Consequently, critical information on how the processing parameters influence the strain energy and microstructural YAOJUN LIN, formerly Postdoctoral Scholar with the Department of Chemical Engineering and Materials Science, University of California, Davis, CA 95616, is now Professor with the State Key Laboratory of Metastable Materials Science and Technology and College of Materials Science and Engineering, Yanshan University, Qinhuangdao, Hebei 066004, P.R. China. Contact e-mail: yjlin@ysu. edu.cn BO YAO, formerly Postdoctoral Research Associate with the Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL 32816, is now Postdoctoral Research Associate, Pacific Northwest National Laboratory, Richland, WA 99354. ZHIHUI ZHANG, formerly Assistant Project Scientist with the Department of Chemical Engineering and Materials Science, University of California, Davis, is now Research Scientist with the Center for Technology Innovation, Baker Hughes, Houston, TX 77040. JULIE M. SCHOENUNG and ENRIQUE J. LAVERNIA, Professors, are with the Department of Chemical Engineering and Materials Science, University of California, Davis. YING LI, formerly Postdoctoral Researcher with the Department of Chemical Engineering and Materials Science, University of California, Davis, is now Director’s Postdoctoral Fellow, Los Alamos National Laboratory, Los Alamos, NM 87545. YONGHO SOHN, Professor, is with the Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida. Manuscript submitted October 6, 2011. Article published online May 26, 2012 4258—VOLUME 43A, NOVEMBER 2012
features of stored energy remains unknown. To provide insight into these questions, Part I of the current study describes a mathematical framework to (1) quantify the contributions of normal and shear strains to the strain energy introduced to powders Ui, (2) calculate the magnitude of the strain energy stored in powders Us based on the Us/Ui ratio v estimated using an equation included in the mathematical framework, and (3) establish the influence of processing parameters on Ui and Us. The modeling results can be summarized as follows: (1) The normal strain and the shear strain make comparable contributions
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