Computer simulation of solid solution strengthening in Fcc alloys: Part I. Friedel and mott limits
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I.
INTRODUCTION
T H E O R I E S of solid solution strengthening in fcc solids have proceeded using analytical models it-2tl and computer simulation models. [22-271The analytical models often provide useful qualitative and, in some cases, quantitative insights into solid solution effects. However, in order to make the analytical models tractable, often somewhat arbitrary assumptions are introduced into the treatments. Computer simulation techniques afford the opportunity to solve for the behavior of a model over a wide range of parameters (such as concentration, obstacle strength, or dislocation line tension), with the only restriction being the numerical accuracy of the particular computer configuration or program. Two important limits may be identified in solid solution strengthening: the low concentration, high obstacle strength limit, or the Friedel limit, and the high concentration, low obstacle strength limit, or Mott limit.t2~ In this investigation, we will summarize some of the assumptions made in evaluating the yield stress behavior in these limits, particularly the Mott limit, and compare the results of some analytical models with our computer simulation. Not surprisingly, we will reproduce the key analytical result in the Friedel limit, namely, that the yield stress varies as the square root of concentration. However, we will report that this same square root of concentration dependence is also valid in the Mott limit. This is at variance with the concentration to the 2 / 3 power derived by a number of authors for the Mott limit. [8"9'16'17'2~ We will point out certain questionable assumptions made in these studies and further point out that our results are in agreement with the results of Kuo and Arsenault t271 in the extreme Mott limit of a straight dislocation line ( i . e . , infinite line tension). This paper concerns itself with establishing the behavior of our numerical model in these important limits R.J. ARSENAULT, Professor and Director, and S. PATU, Visiting Scholar from the Institute of Metals Research, Academica Sinica, Shenyang, The People's Republic of China, Research Associate, are with the Metallurgical Materials Laboratory, University of Maryland, College Park, MD 20742-2111. D.M. ESTERLING, Professor, is with the Civil, Mechanical, and Environmental Engineering Department, George Washington University, Washington, DC 20052. Manuscript submitted January 20, 1988. METALLURGICAL TRANSACTIONS A
and contrasts our results, particularly the concentration dependence, with those derived from analytical models. The succeeding paper will provide details of the simulation method and will derive the general dependence of the yield stress on line tension and obstacle strength as well as concentration. Section II provides some background on earlier work. Section III contains an analytical treatment of the Mott limit, showing the need to take special care of fluctuations in the restoring forces. Section IV summarizes the simulation method used to generate the numerical results in Section V. II.
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