Relationships between the work recovery ratio of indentation and plastic parameters for instrumented spherical indentation

Abstract

This paper aims to obtain an analytical expression for the ratio of unloading work of indentation (W u ) to total loading work of indentation (W t ) (work recovery ratio of indentation) in instrumented spherical indentation. The expanding cavity model and Lamé solution are used. Three typical stress-strain relations (elastic-perfectly plastic, linear hardening, and power-law hardening) are analyzed. The results of finite-element method coincide with the expressions. The expressions show that the work recovery ratio of indentation is just related to plastic parameters. Furthermore, elastic work (W e ) are obtained, and it is proved that W e should be distinguished from W u in spherical indentation.

Modelling mechanical properties of the multilayer composite materials with the polyamide core

“…9), with the difference being that deformation here is the ratio of displacement to the total thickness of the belt, whereas for determining stresses the circular section with a diameter of 10 mm is used. In both cases, the base model of reinforced elastic-plastic material was used, in which after achieving certain displacement there is hardening of the material -Young's modulus increases [5]. In the case of shear tests, it is necessary to determine the pure shear deformation angle using the correlation 4.…”

Identification of the elastic–plastic constitutive model for measuring mechanical properties of metals by instrumented spherical indentation test

“…In our previous work, methods to determine elastic-plastic parameters for three typical constitutive models by instrumented spherical indentation had been developed. [9][10][11] Based on the spherically symmetric assumption in the expanding cavity model (ECM) [13] (see Fig. 2) and the Lamé's elastic solution, the equations of total loading work (W t ) and unloading work (W u ) were derived.…”

“…2) and the Lamé's elastic solution, the equations of total loading work (W t ) and unloading work (W u ) were derived. [11] There are two basic hypotheses for ECM: (1) the displacement field produced by the indenter is approximately spherically symmetric; (2) the material under the indenter can be divided into three parts, namely, a core zone (r < a), a plastic zone (a < r < c), and an elastic zone (r > c), where a is the radius of the core zone and c is the radius of the boundary of the plastic and elastic zones. They can be confirmed by the result of a popular finite-element method (FEM) modeling (see Fig.…”

“…(a) Linear elastic and perfectly plastic, (b) linear elastic and linear hardening, and (c) linear elastic and power-law hardening. [11] (© Materials Research Society, 2015, Reprinted with permission.) Figure 2.…”

“…It has been shown that the parameters of the typical constitutive models of metals can be determined by instrumented spherical indentation tests. [11] But the elastic-plastic constitutive models of the metals must be known in advance in order to choose the appropriate method. For a material with unknown elastic-plastic constitutive model, it is difficult to decide which method should be chosen.…”