Decoupling the effects of surface topography and material heterogeneity on indentation modulus: A simple numerical linear-elastic model

Abstract

One complication in interpreting indentation modulus measurements in inhomogeneous structural materials is the coupling between surface topography and material heterogeneity. Typically, the specimen surface is prepared to be as smooth and flat as possible, yet there are always limits to how flat a sample surface will be. Moreover, when a compositional interface is sensed mechanically, via a change in modulus, any non-flat surface topography near the interface is combined with the phase changes to influence the total elastic-modulus measurement. This paper uses a linear elastic finite element model to suggest how to decouple these two phenomena. Three axisymmetric models are presented: (1) convex and concave surfaces with material uniformity, (2) a flat surface with a lateral-graded material interface, and (3) convex and concave surfaces with a laterally-graded material interface. Using the exact Hertzian formulae, the indentation modulus is computed assuming that all the models have flat surfaces, like physical experiments often assume, and are elastically uniform. The results of (1) and (2), which have only a non-flat surface topography or material heterogeneity, are used to interpret (3), which has both. The competition between the contact radius and the distance from the indentation point to the material interface significantly influences the calculated elastic modulus. The flat-surface assumption can yield significant errors when extracting the elastic modulus in solids with pronounced curved surfaces. An empirical relation based upon contact pressure and displacement data is used to accurately extract the true material elastic modulus when both surface curvature and material interface are present.