Hardness–Deformation Energy Relationship in Metals and Alloys: A Comparative Evaluation Based on Nanoindentation Testing and Thermodynamic Consideration

Nanoindentation testing using a Berkovich indenter was conducted to explore the relationships among indentation hardness (H), elastic work energy (W(e)), plastic work energy (W(p)), and total energy (W(t) = W(e) + W(p)) for deformation among a wide range of pure metal and alloy samples with different hardness, including iron, steel, austenitic stainless steel (H ≈ 2600–9000 MPa), high purity copper, single-crystal tungsten, and 55Ni–45Ti (mass%) alloy. Similar to previous studies, W(e)/W(t) and W(p)/W(t) showed positive and negative linear relationships with elastic strain resistance (H/E(r)), respectively, where E(r) is the reduced Young’s modulus obtained by using the nanoindentation. It is typically considered that W(p) has no relationship with W(e); however, we found that W(p)/W(e) correlated well with H/E(r) for all the studied materials. With increasing H/E(r), the curve converged toward W(p)/W(e) = 1, because the Gibbs free energy should not become negative when indents remain after the indentation. Moreover, H/E(r) must be less than or equal to 0.08. Thermodynamic analyses emphasized the physical meaning of hardness obtained by nanoindentation; that is, when E(r) is identical, harder materials show smaller values of W(p)/W(e) than those of softer ones during nanoindentation under the same applied load. This fundamental knowledge will be useful for identifying and developing metallic materials with an adequate balance of elastic and plastic energies depending on the application (such as construction or medical equipment).