True Hardness Evaluation of Bulk Metallic Materials in the Presence of Pile Up: Analytical and Enhanced Lobes Method Approaches

Abstract

In the last few decades, a great deal of attention has been paid to understanding the factors controlling the detailed shape of loading-unloading curves obtained by the Oliver and Pharr's nanoindentation analysis, to enable us estimate material parameters such as true contact area, Young’s modulus, and hardness. In fact, it is well known that the Oliver and Pharr's analysis can overestimate hardness, especially in such cases where the material plastically deforms by piling up around the indentation. In recent years, different direct and analytic methods have been proposed. Direct visual methods are based on measurements of the produced indentation by scanning probe microscopy (SPM) or by atomic force microscopy (AFM). Some other analytic methods are based on the work of indentation analysis, that is to say, the analysis of the area of the load-displacement curve. In the case of the current study, DHP-copper hardness measurements using nanoindentation, in both H58 and annealed metallurgical conditions, were investigated by both direct and analytic methods. Three different SPM-based methods and work of indentation analysis methods were used to determine the true hardness. Among the three SPM-based methods, one showed quite a good agreement with the literature data and microhardness tests. This method was therefore developed and improved to make it dependent on curve parameters and no longer dependent on SPM or AFM, the measurements of the real contact area. The correlation between the pile-up phenomenon and the m exponent of the P = B(h − h f)m relationship is also discussed.