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).