Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

Abstract

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed on three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

“…and a c can be determined by By considering the effect of piling-up on the volume displaced by hydrostatic core, a modified expanding cavity model (ECM) was developed in our previous study 23 to describe the relationship between indentation work and plastic properties as follows…”

“…Recently, it has been shown that, with a spherical indenter, plastic properties can be determined from a single loading curve. 18,19,23 By reviewing the spherical indentation methods that have been developed, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] the five models selected for this study were those of Field and Swain, 14 Cao and Lu, 18 Zhao et al, 19 Lee, 11 and Jiang et al 23 Although there have certainly been many more studies performed on this topic, these five were selected for three reasons. First, they can be simply reproduced step by step according to only the procedures provided by the original literature; second, they offer a means of identifying the plastic properties solely by analyzing the load-depth data (that is, they do not rely on the physical measurement of residual impression); third, they are easy to implement experimentally (no difficulty is caused by repetitive loading and unloading, and only a small number of empirical parameters are used).…”

“…In addition, the effectiveness of our computation model is proven by our previous test data. 23 With these numerical results, the accuracy of each model was studied. Furthermore, considering that the sensitivity characteristic has been recognized as another important factor for the evaluation of indentation-based methods, stability analysis of these five models was also performed.…”

Determining the elastic-plastic properties of metallic materials through instrumented indentation

“…Kang et al [14,15] tried to reduce the pile up effect by measuring the residual indentation. Jiang et al [16] also introduced a correction factor related to the indentation value to take this pile up into account. However, it should be noted that these corrections are limited to a certain range of selected material properties.…”

“…This method needs a large number of FEM computations within a certain range of the material properties defined as the power law equation. The dimensional function has established a relationship between the indentation characteristics and material properties [16,[73][74][75][76][77][78][79][80].  theorem is the key theorem in dimensional analysis, which could reduce complex physical problems to their simplest form [81,82].…”