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).

Highlights

  • The mechanical properties of a material, its strength and ductility, are the most fundamental metrics for evaluating its deformation behavior under applied stress

  • Table shows the nanoindentation test results measured under load ofof9.8

  • Nanoindentation tests were performed to evaluate the relationships among the indentation hardness and energy components of various metals and alloys

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Summary

Introduction

The mechanical properties of a material, its strength and ductility, are the most fundamental metrics for evaluating its deformation behavior under applied stress. Ductility involves both uniform and local deformation, which occur by different mechanisms. Hu et al [1] showed that an increase in the local elongation of dual phase (DP) 980 steel correlated with an improvement in the hole expansion ratio obtained during hole piercing tests, classified as the edge stretchability. Taylor et al [2] reported that the hole expansion ratio of DP980 steel decreased as the martensite hardness and martensite/ferrite hardness ratio (as determined by nanoindentation tests) increased. Using synchrotron X-ray laminography of nanoscale precipitated steel and bainitic steel, Mugita et al [3] showed that an increase in the nanoindentation hardness at the grain boundaries correlated with a decrease in local elongation, because the growth of voids was accelerated

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