Representative Stress-Strain Curve by Spherical Indentation on Elastic-Plastic Materials

Chao Chang,M A Garrido,J Ruiz-Hervias,Zhu Zhang,Le-Le Zhang

doi:10.1155/2018/8316384

Abstract

Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation. Tabor empirically determined the stress constraint factor (stress CF), ψ, and strain constraint factor (strain CF), β, but the choice of value for ψ and β is still under discussion. In this study, a new insight into the relationship between constraint factors of stress and strain is analytically described based on the formation of Tabor’s equation. Experiment tests were performed to evaluate these constraint factors. From the results, representative stress-strain curves using a proposed strain constraint factor can fit better with nominal stress-strain curve than those using Tabor’s constraint factors.

Highlights

Tensile stress-strain curve of metallic materials can be determined by the representative stress-strain curve from the spherical indentation
Introduction e instrumented indentation technique consists of applying load to the sample by means of an indenter of known geometry, while the applied load and the penetration depth of the indenter are recorded simultaneously during a loading and unloading cycle. e load-penetration data can be used to determine the mechanical properties of the material without having to image the residual impression left on the material’s surface
These properties are not sufficient to characterize a material. e present work focuses on the methodology to determine the stress-strain curve of metallic materials by the depth-sensing indentation technique using a spherical indenter

Summary

Theoretical Background

2.1. e Analytical Relationship between Stress and Strain Factors. In 1908, Meyer had found that for many materials, the mean pressure increased with a/R according to the simple power law [18]. Following Meyer’s work, Tabor had proposed the concept of representative strain or stress, by which the mean pressure in Meyer’s equation and the a/R ratio can be converted into the true stress-strain curve. Which represents the relationship between load, F, and the ratio of contact radius to indenter radius according to the power law at the fully plastic regime. According to Hertz equation under the elastic regime, the loading and contact radius can be expressed as. The procedure assumes that elastic-plastic transition is negligible, and the relationship between stress and strain constraint factors is a rmed from Hertz’s theory. We utilize the Hertz equation to study the relationship between the stress and strain constraint factors to extract the stress-strain curve based on Tabor’s representative method. When reduced Young’s modulus and initial unloading slope of the unloading are known. e procedure to estimate the contact radius is consistent with Kalidindi et al.’s [32, 33] work

Experimental Procedure

Results and Discussion

Conclusion e main conclusion in the paper can be summarized as follows: