Analysis of the effects of conical indentation variables on the indentation response of elastic–plastic materials through factorial design of experiment

Abstract

In this work, the effects of conical indentation variables on the load–depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 26 was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/hmax, n, θ, E, and hmax. The dimensional variables E and hmax were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/hmax was obtained with two different hmax values. A set of dimensionless functions was defined to analyze the effect of the input variables: Π1 = Pl/Eh2, Π2 = hc/h, Π3 = H/Y, Π4= S/Ehmax, Π6 = hmax/hf, and Π7 = Wp/WT. These six functions were found to depend only on the dimensionless variables studied (Y/E, R/hmax, n, θ). Another dimensionless function, Π5 = β, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on β was θ. However, β showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that β is especially susceptible to the error in the calculation of the initial unloading slope.