Some concerns about the current interpretation and analyses of indentation unloading P – h curves highlighted with Young's modulus studies of single crystals of MgO (100)

Abstract

Indentation tests using indenter load, P, and indentation penetration, h, curves obtained from instrumented indentation machines have been in use for over 30 years. The unloading part of a P – h curve is frequently used for determining the indentation size at the maximum applied indenter load and for determining the elastic modulus of the test solid. To do this, four fundamental assumptions have been made. We show here experimentally that, unfortunately, none of the assumptions is correct. Therefore, these assumptions lead to incorrect determinations. Examples highlighting the concerns are given from our own work on single crystals of Cu and MgO and from the work of others. It is shown here that for both isotropic and anisotropic solids, the elastic moduli determined using the current methods of data analysis vary very considerably with the applied maximum indenter load. Furthermore, the obtained values do not correlate well with the literature values of the elastic moduli, despite the claim [see abstract of W. C. Oliver and G. M. Pharr (J. Mater. Res. 7, 1564 (1992)] that the agreement is within 5%. To remedy this problem, an alternative approach employing only elastic loading with an elastic sphere is used and the resulting load versus displacement data are analyzed using the Hertzian equation for the normal loading of a sphere on an elastic half-space. This experimental technique yields satisfactory values of the elastic moduli of test surfaces of single crystals of Cu (111), Cu (100), and MgO (100); the elastic moduli thus determined do not vary with the applied indenter load.Indentation tests using indenter load, P, and indentation penetration, h, curves obtained from instrumented indentation machines have been in use for over 30 years. The unloading part of a P – h curve is frequently used for determining the indentation size at the maximum applied indenter load and for determining the elastic modulus of the test solid. To do this, four fundamental assumptions have been made. We show here experimentally that, unfortunately, none of the assumptions is correct. Therefore, these assumptions lead to incorrect determinations. Examples highlighting the concerns are given from our own work on single crystals of Cu and MgO and from the work of others. It is shown here that for both isotropic and anisotropic solids, the elastic moduli determined using the current methods of data analysis vary very considerably with the applied maximum indenter load. Furthermore, the obtained values do not correlate well with the literature values of the elastic moduli, despite the claim [see abstract...