Abstract: Stress-strain (σ-ε) relationship is the important guidance for materials design and development. The uniaxial tensile and compression testing are commonly used to obtain the σ-ε relationship of materials. However, suffered from the limitation of sample shape and size, these conventional approaches can hardly apply to the materials in micro/nano scale. Benefiting from the high resolutions of load and depth, instrumented nanoindentation based upon depth-sensoring technique has been widely used to extract mechanical properties (such as Young’s modulus, hardness, strain rate sensitivity exponent and creep parameters) at micro/nano scales. In recent years, researchers have developed novel protocols to extract σ-ε curves from load-depth (P-h) curves. Among these studies, the spherical indenter attract considerable attention as it possesses smooth and non-self-similar distribution of stress. The major challenge for analyzing the spherical indentation lies in the three axial states of the material under the rigid indenter, and the heterogeneous distributions of stress and strain make the direct measurement difficult to realize. For the sake of simplifying the analysis, various definitions, such as indentation strain, representative stress and representative strain, are introduced. Moreover, there are diverse analysis approaches as well, which can be classified into the empirical physics method and the simulation analysis method according the analysis procedure.As regard to empirical physics method, the transition between P-h curve and σ-ε are conducted by defining represen-tative stress and representative strain of the primary indentation zone, which are equivalent to uniaxial flow stress and strain, respectively. This approach is simple and has been validated on a broad variety of materials, nevertheless, the results strongly depend on the reliable definition of corresponding physical quantities and exhibit great sensitivity to the precision of experimental measurement.Concerning the simulation analysis method, the indentation P-h curves are firstly obtained by simulation with a wide range of constitutive para-meter, and then a function is derived by the analysis of P-h curves and the constitutive equation, finally the σ-ε can be inversely determined from the experimental P-h. Obviously, the establishment of the function is critical for this method, and the commonly employed approaches consist of dimension analysis and curve fitting. However, the stability and applicability of these functions constitute the major bottlenecks that hinder their widespread applications. Very recently, thanks to the fast development of compu-ter science and technology, researchers adopt algorithms to screen constitutive parameter intelligently, achieving a good agreement between predicted data and experimental results. Such novel analysis has shown great potentials in measuring the mechanical properties of materials. In summary, we offers a retrospection of the research efforts with respect to the extraction of σ-ε relationship from spherical nanoindentation from empirical physics and simulation analysis in this article. The basic concept and model, definitions of related physical quantities and establishment of these methods are summarized. Moreover, their merits and drawbacks are also discussed to provide experimental and guidance for the mechanical characterization at micro/nano scales.
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2019, Vol. 33 
