An Automated Technique to Analyze Micro Indentation Load-Displacement Curve

Abstract

High-throughput methods of measuring mechanical properties can accelerate materials discovery and processing route developments. These metrics of material performance get incorporated into both physics-based (ICME) and statistical machine-learning Processing-Microstructure-Properties (PMP) models. Conventional mechanical testing techniques, such as tensile testing, require large material volumes and become expensive and challenging when quantifying a statistically significant number of observations to enable process optimization thru PMP models of homogeneous materials; not to mention the added complexity of purposefully engineered inhomogeneous materials. Instrumented microhardness machines enable the extraction of indentation stress-strain curves from load-displacement curves as a proxy metric for more time/cost intensive uniaxial stress-strain curves. This versatile technique characterizes the local stress-strain behavior from small material volumes by modifying Hertz theory on the stresses between elastic solids. In this paper, an automated algorithm, written in Python (v2.7), is presented to apply modified Hertz’s theory to extract the Elastic Modulus and indentation stress-strain curve from the load-displacement data. Two methods of assuming the contribution of the elastic deformation of the indenter are presented. First, the algorithm works through the assumptions made by Khosravani et al. and presents these results in comparison to a second method of assuming that the contribution of the indenter elastic deformation is sufficiently small that it is assumed constant and can be approximated from the size of the indent on the sample surface. The algorithms are compared using microhardness measurements from a nickel-base superalloy, LSHR and show that the Elastic Modulus and the yield strength values are in reasonable agreement with the reference literature. The assumptions on the effect of the indenter elastic properties has effects on the shapes of the plastic part of the curve; the Khosravani et al. method seems to underestimate the work hardening properties of the material; while the other method overestimates the work hardening properties. Therefore, utilizing both methods provides proxy measurements of the potential upper and lower bounds of the work hardening behavior beyond the yield strength of the material which could be helpful for PMP models.