Collinear micro-shear-bands model for grain-size and precipitate-size effects on the yield strength

Numerous experimental evidences show that the grain size may significantly alter the yield strength of metals. Similarly, in γ‘-strengthened nickel-based superalloys, the precipitate size also influences their yield strength. Then, how to describe such two kinds of size effects on the yield strength is a very practical challenge. In this study, according to experimental observations, a collinear micro-shear-bands model is proposed to explore these size effects on metal materials’ yield strength. An analytical solution for the simple model is derived. It reveals that the yield strength is a function of average grain-size or precipitate-size, which is able to reasonably explain size effects on yield strength. The typical example validation shows that the new relationship is not only able to precisely describe the grain-size effect in some cases, but also able to theoretically address the unexplained Hall-Petch relationship between the γ’ precipitate size and the yield strength of nickel-based superalloys.