Semiempirical Formulae for Mechanical Properties Controlled by Strength and Ductility of Power-Law Hardening Metallic Materials

Abstract

Some subordinate mechanical properties, such as the strain hardening exponent (n) and the fracture true stress ($\sigma_{\text{f}}$), are not available in general material property handbooks, although they are important in choosing materials. This paper investigated the relations between the subordinate mechanical properties to the basic ones for power-law hardening materials. Our semiempirical analysis shows that, in uniaxial tensile experiment, the strain hardening exponent is controlled by the ratio of the yield strength ($\sigma_{\text{s}}$) and the ultimate tensile strength ($\sigma_{\text{b}}$), and the value also equals to the maximum uniform strain. The absolute calculation errors of n on various metal materials are approximately within ± 0.03. Physically, n expresses the ability of the strength rising from the yield strength to the ultimate tensile strength during uniform deformation; it may also denote the maximum ability of uniform deformation before necking. The fracture strength is controlled directly by n, $\sigma_{\text{b}}$ and the reduction in area (ψ_K) in our concise expression. The relative errors of the fracture strength between the calculations and the measurements on metal materials are approximately within 20%. Results also indicate that the fracture true stress represents the increased stress during uniform deformation plus the concentrated stress caused by necking.