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

Abstract

Nanoindentation testing using a Berkovich indenter was conducted to explore the relationships among indentation hardness (H), elastic work energy (We), plastic work energy (Wp), and total energy (Wt = We + Wp) 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, We/Wt and Wp/Wt showed positive and negative linear relationships with elastic strain resistance (H/Er), respectively, where Er is the reduced Young’s modulus obtained by using the nanoindentation. It is typically considered that Wp has no relationship with We; however, we found that Wp/We correlated well with H/Er for all the studied materials. With increasing H/Er, the curve converged toward Wp/We = 1, because the Gibbs free energy should not become negative when indents remain after the indentation. Moreover, H/Er must be less than or equal to 0.08. Thermodynamic analyses emphasized the physical meaning of hardness obtained by nanoindentation; that is, when Er is identical, harder materials show smaller values of Wp/We 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).

Enhancing Wear Resistance in Functionally Graded Metallic Components: Insights from Nanoindentation and Mechanical Analysis

“…where a and b are the constants equal to at −1 and 0.16, respectively. This equation is in good agreement with the findings of Yang et al [29] and Yamamoto et al [28], who established a linear relationship between H/E r and W e /W t (Equation ( 2)). Moreover, the relationship between H/E r and W p /W t determined by Cheng and Cheng [30] and Yamamoto et al [28] is expressed by Equation (3).…”

“…Okoro et al [27] performed nanoindentation testing to explore the effect of multiwalled carbon nanotubes (MWCNTs) on the mechanical properties of Ti 6 Al 4 V sintered materials and established correlations between W e /W t , W p /W t , H/E r , H 3 /E r 2 , and the added amount of MWCNTs. Previously, Yamamoto et al determined the relationship between H/E r and W p /W e for austenitic stainless steels, high-purity copper, single-crystal tungsten, and the quasielastically heat-treated 45mass%Ti-55mass%Ni alloy [28]. As a result, the following formula was derived:…”

Mechanical Characteristics Generation in the Workpiece Subsurface Layers through Cutting

“…The effect of machining conditions on the strain energy of the subsurface layers is presented in a study by Bezyazychny and colleagues [58]. Yamamoto et al studied the relationship between the elastic and plastic components, as well as the total energy of the indentation, and the microhardness of the tested metals [59]. Ren and Liu [60] and Wang with colleagues [61] devoted their research to studying the relationship between the mechanical properties of hard-working metals and alloys and the cutting process conditions.…”

Generation of Mechanical Characteristics in Workpiece Subsurface Layers through Milling

“…In this regard, it is necessary to note the study of Bezyazychnyy et al [81], devoted to the establishment of the relationship between cutting modes and physical and mechanical characteristics of the machined material, and the specific accumulated strain energy of this material along the workpiece depth. The relationship between the elastic and plastic components, as well as the total indentation energy and microhardness of the investigated specimens was the topic of the study of Yamamoto et al [82]. The relationship between the mechanical properties of carbide metals and alloys and the cutting process conditions has been studied by Wang and coworkers [83] and Ren and Liu [20].…”