Determination of mechanical properties using micro- and nanoindentation

Zhiyong Li, Purdue University

Abstract

This thesis addresses three important problems in hardness testing that are of direct relevance to the determination of stress-strain curves of elastic-plastic materials using quasi-static indentation. First, a dimensional analysis is used to obtain a generalized load-penetration relation for conical indenters. It is found that the indenter load, P, is proportional to δ 2, where δ is the depth of penetration of the indenter into the specimen. This relation is shown to be applicable to a wide range of material models at other than small depths of indenter penetration. Dimensional analysis is also used to obtain insight into the indentation “size effect” which manifests itself as a dependence of hardness on indenter load. Results from indentation experiments on steels conducted over a range of penetration depths are found to be in agreement with the dimensional analysis. Second, a finite element analysis has been made of the phenomena of “piling-up” and “sinking-in” of material around hardness indentations. A criterion is developed using this analysis to characterize the conditions corresponding to “piling-up” and “sinking-in” for conical indentation. Since the true load-bearing area of a hardness indentation is obviously influenced by the degree of piling-up and sinking-in, the analysis is used to develop a procedure for reducing the errors in hardness estimation due to these factors. Lastly, spherical indentation of elastic-plastic solids is analyzed using the FEM. It is shown that the so-called constraint factor (c), which is the ratio of the hardness to the yield strength of a solid, is not a universal constant but depends on the ratio of yield strength (Y0) to Young's modulus (E) of the solid. The values for c are found to be in the range of 1.75–3.0 with higher c values occurring for materials with smaller values of Y0/E. It is also found that the threshold value of effective indentation strain at which full plasticity is reached during quasi-static indentation is a function of Y0/E. The feasibility of using Tabor's approach to extracting stress-strain data from spherical indentation tests is discussed in the light of the present results.

Degree

Ph.D.

Advisors

Chandrasekar, Purdue University.

Subject Area

Mechanics|Materials science

COinS