Prediction of limit strains in superplastic materials
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9/27/03
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Prediction of Limit Strains in Superplastic Materials M.P. MILES, G.S. DAEHN, and R.H. WAGONER A simple model has been developed to study the effects of static and dynamic grain growth and strain rate on the ductility of superplastic materials. One-half of a tensile specimen was modeled numerically using a power-law creep constitutive equation, with either a constant strain rate or constant extension rate. Static grain growth was shown to reduce material ductility at all rates of growth, except when the imposed strain rate was very low. Dynamic grain growth was shown to enhance ductility at lower growth rates and for intermediate imposed strain rates, while decreasing ductility at higher growth rates. Comparison of simulated and experimental results reveals the relationship between strain and grain size, thus justifying the treatment of dynamic grain growth as a function of accumulated strain.
I. INTRODUCTION
SUPERPLASTIC behavior has been described as a function of how the grains in a polycrystalline material slide relative to each other at their boundaries. The process is diffusion controlled, and the grains maintain their relative shape and size as the material is strained on a macroscopic scale.[1] The Ashby and Verrall model of this behavior resulted in a constitutive equation relating stress, temperature, and diffusion rates to strain rate.[2] Although the grain-switching mechanism proposed by Ashby and Verrall has been criticized,[3] the general constitutive equation which resulted from their theory can be used to model the stress-strain rate behavior of some superplastic materials, such as the Zn-Al eutectic.[4] In this model, the behavior described as diffusionaccommodated flow operates at lower stresses, with strain rates typically lower than 104 s1. At higher stresses, with strain rates of 103 s1 and higher, a less-rate-sensitive “dislocation creep mechanism” dominates.[5] In the higher stress regime, there is little boundary sliding and grains can become elongated via normal plastic deformation, with simple instability necking usually limiting ductility. The constitutive equation is formed by summing the separate equations for diffusion-accommodated flow and dislocation creep,[2] which models flow over a large range of strain rates, with each mechanism being more or less active, depending on the stress level. A typical curve of strain rate sensitivity (m) vs strain rate is shown in Figure 1 (m d ln /d ln , taken either at constant strain or structure). Ductility is low at the very low and high imposed strain rates and is much higher at intermediate strain rates. A small and stable grain size is required for superplasticity;[1] usually, 10 m or smaller is necessary. A forming temperature of half the melting point of the material or greater is also required, which produces conditions for grain growth. As a result, most superplastic alloys are two-phase, where the second phase is in the form of a fine dispersion in order M.P. MILES, Assistant Professor, is with Manu
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