Analysis of Deformation Kinetics in Seven Body-Centered-Cubic Pure Metals Using a Two-Obstacle Model
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INTRODUCTION
METALS with a body-centered-cubic (bcc) crystal structure exhibit markedly different deformation kinetics than those with a close-packed (CP) structure. In particular, the yield stress of pure CP metals is either independent or at least highly insensitive to test temperature and strain rate. Pure bcc metals, on the other hand, exhibit a distinct temperature and strain-rate sensitivity. This well-known behavior has been attributed to the presence of an intrinsic lattice resistance, which often is referred to as the Peierls barrier[1–6] and further described as the resistance to motion of dislocation kinks.[1,5] A complication in interpretation of experimental results has been the challenge posed by producing high-purity single or polycrystalline test material. Minor interstitial impurities in niobium and iron, for instance, contribute to the measured yield stress.[7–9] While the role of an intrinsic lattice resistance in bcc metals is generally accepted, the confounding nature of the added lattice resistance offered by impurities continues to complicate interpretation of test results.[7] The intent of this article is to re-examine historic data as well as newer data in seven bcc metals of varying purity and to analyze this data set collectively in light of a simple deformation model that considers both the influences of the Peierls barrier and that of impurity constituents. It will be shown that such a model offers insight into the deformation mechanisms in bcc metals.
PAUL S. FOLLANSBEE, James F. Will Professor of Engineering Science, is with Saint Vincent College, Latrobe, PA 15650-2690. Contact e-mail: [email protected] Manuscript submitted October 15, 2009. Article published online August 11, 2010 3080—VOLUME 41A, DECEMBER 2010
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EXPERIMENTAL DATA
A wealth of data exists cataloging the dependence of the yield strength measured mostly in compression but also in tension and bending as a function of test temperature and strain rate in Fe, Mo, Nb, and Ta metals of varying purity. A limited data set exists for pure W, V, and Cr. Tables I and II list the sources of data considered for the analysis presented here. Some of the data is quite old and is not completely complemented by explicit chemical analysis. In compiling and selecting these data sets, particular attention was given to low test temperatures (below room temperature) and high strain rates (greater than 103 s1). A complication of high strain-rate testing (greater than 103 s1) is the difficulty in precisely measuring the yield point or proportional limit in the presence of a yield drop or given the lack of initial strain homogeneity accompanying common high strain-rate test techniques (e.g., Split Hopkinson Pressure Bar). To overcome these limitations, this investigator has relied upon a definition of yield based on the back extrapolated hardening behavior. The nearly perfect plastic hardening in many bcc metals enables this approximation and minimizes associated error. Figure 1 shows raw data for W, Mo, Nb, Ta, V, and Cr, an
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