Hardness, Toughness, and Brittleness: An Indentation Analysis

TLDR

Hardness and toughness are fundamental material properties, and their ratio H/Kc has been considered. The authors propose the ratio H/Kc as an index of brittleness. Indentation mechanics and normalization of characteristic dimensions and load in terms of H and Kc enable construction of a universal deformation/fracture diagram. The model shows that materials deform more readily under small‑scale loading and fracture under large‑scale loading, and the diagram predicts mechanical response for any material and loading condition, providing a simple classification tool for design.

Abstract

The ratio H/K c , wjere His hardness (resistance to deformation) and K c . is toughness (resistance to fracture), is proposed as an index of brittleness. Indentation mechanics provides the scientific basis for this proposal. The analysis, developed in terms of a model contact system, indicates that all materials are more susceptible to deformation in small‐scale loading events and to fracture in large‐scale events. By normalizing the characteristic dimensions of the two competing processes and the contact load in terms of appropriate functions of H and K c a universal deformation/fracture diagram can be constructed. From this diagram the mechanical response of any material of known hardness and toughness may be predicted for any prospective in‐service contact loading conditions. The concept offers a simple approach to materials classification for design purposes.