Metrological Comparison of Available Methods to Correct Edge-Effect Local Plasticity in Instrumented Indentation Test

Abstract

The Instrumented Indentation Test (IIT) mechanically characterizes materials from the nano to the macro scale, enabling the evaluation of microstructure and ultra-thin coatings. IIT is a non-conventional technique applied in strategic sectors, e.g., automotive, aerospace and physics, to foster the development of innovative materials and manufacturing processes. However, material plasticity at the indentation edge biases the characterization results. Correcting such effects is extremely challenging, and several methods have been proposed in the literature. However, comparisons of these available methods are rare, often limited in scope, and neglect metrological performance of the different methods. After reviewing the main available methods, this work innovatively proposes a performance comparison within a metrological framework currently missing in the literature. The proposed framework for performance comparison is applied to some available methods, i.e., work-based, topographical measurement of the indentation to evaluate the area and the volume of the pile-up, Nix-Gao model and the electrical contact resistance (ECR) approach. The accuracy and measurement uncertainty of the correction methods is compared considering calibrated reference materials to establish traceability of the comparison. Results, also discussed in light of the practical convenience of the methods, show that the most accurate method is the Nix-Gao approach (accuracy of 0.28 GPa, expanded uncertainty of 0.57 GPa), while the most precise is the ECR (accuracy of 0.33 GPa, expanded uncertainty of 0.37 GPa), which also allows for in-line and real-time corrections.

Keywords: measurement uncertainty; nanoindentation; pile-up.

Figure 1

Example of indentation curve (IC), highlighting the main parameters: first contact point h₀, maximum penetration h_max and force F_max, residual plastic penetration h_p, total measured contact stiffness S_m and the plastic (red area) and elastic (yellow area) work, W_p and W_el, respectively.

Figure 2

Edge effect: pile-up and sink-in. Note how the calibrated area shape function respectively underestimates and overestimates the actual contact area.

Figure 3

Quantity definition for the pile-up correction based on topographical measurement and geometrical description of the edge effect. Upper case letters correspond to geometry points, while lower case letters are used for empirical evaluations. a is a side length of the indented pyramid; r the radius of circle circumcising the projected pile-up arc BDC with center at A; h is indentation depth after elastic recovery; h_pile-up the height of the pile up; θ the half-dihedral angle of the indenter.

Figure 4

(a) Schematic of ECR set-up. (b) Anton Paar MCT3 and NHT3 with wiring for ECR. (c) CSI Zygo NewView9000.

Figure 5

(a) Trend of H_IT as a function of characterization force: notice the onset of ISE at forces smaller than 1 N, and pile-up leading to an overestimation of the hardness at forces larger than 10 N (error bars represent measurement uncertainty at a 95% confidence level). Red dashed lines are calibrated values. (b) Nix and Gao ISE modeling (red solid line) overlapping raw data: notice a strong deviation from linearity at small 1/h, i.e., at large penetration depths, indicating the occurrence of pile-up.

Figure 6

Measured surface topography of an indentation. Notice the relevant and not homogeneous pile-up.

Figure 7

Results of the pile-up correction by the considered approaches: error bars at 95% confidence level. Black: raw data, blue: corrected data, red: calibrated values (upper and lower limit of confidence level at 95%).