Exploring the origins of the indentation size effect at submicron scales

Abstract

The origin of the indentation size effect has been extensively researched over the last three decades, following the establishment of nanoindentation as a broadly used small-scale mechanical testing technique that enables hardness measurements at submicrometer scales. However, a mechanistic understanding of the indentation size effect based on direct experimental observations at the dislocation level remains limited due to difficulties in observing and quantifying the dislocation structures that form underneath indents using conventional microscopy techniques. Here, we employ precession electron beam diffraction microscopy to “look beneath the surface,” revealing the dislocation characteristics (e.g., distribution and total length) as a function of indentation depth for a single crystal of nickel. At smaller depths, individual dislocation lines can be resolved, and the dislocation distribution is quite diffuse. The indentation size effect deviates from the Nix–Gao model and is controlled by dislocation source starvation, as the dislocations are very mobile and glide away from the indented zone, leaving behind a relatively low dislocation density in the plastically deformed volume. At larger depths, dislocations become highly entangled and self-arrange to form subgrain boundaries. In this depth range, the Nix–Gao model provides a rational description because the entanglements and subgrain boundaries effectively confine dislocation movement to a small hemispherical volume beneath the contact impression, leading to dislocation interaction hardening. The work highlights the critical role of dislocation structural development in the small-scale mechanistic transition in indentation size effect and its importance in understanding the plastic deformation of materials at the submicron scale.

Micromechanical Contrast of Ordos Basin Sandstone‐Mudstone Interbedded Layered Rocks

“…During nanoindentation tests in the CSM mode, the Young's modulus and hardness are sensitive to the indentation depth, especially in the shallow depth, as illustrated in Figure 3. Initially, the larger Young's modulus and hardness measured below 100 nm was severely influenced by the tip blunting and surface quality (Ma et al., 2021; Zonana et al., 2020). With the increase of indentation depth, the Young's modulus fluctuated within a small range and exhibited nearly independent of the indentation depth, while the hardness gradually decreased with varying degrees.…”

A further look at the nano/micro-indentation method for measuring and ranking Young’s modulus and hardness of materials

“…The above-described method for measuring intrinsic Young's modulus and ranking Young's moduli of different materials using the indentation technique also applies to other types of material, such as metallic materials. For metals, the measured Young's modulus is influenced by plastic deformation rather than cracking or fracture [67]. Plastic deformation also lowers Young's modulus due to decreased density and lowered electron work function [68], so the measured Young's modulus is not the intrinsic Young's modulus but that of plastically deformed material.…”

“…This happens because the induced cracks make further penetration of the indenter head easier. The increase in hardness at lowered indentation loads was explained by the Indentation Size Effect [67], which stated that as the indentation load decreased or the indent became smaller, geometrically necessary dislocation density rose, resulting in a higher hardness [20,31]. For ceramic material with little or limited slip systems, the situation underneath the indenter is however complicated.…”

Study on Size Effect in Indentation Tests

“…At the micron or nanoscale, it has been extensively confirmed that mechanical behaviors of small structures can exhibit strong size dependence. This fantastic phenomenon is often observed and presented as the depth dependence of hardness in shallow indentation tests, namely, the indentation size effect (ISE) [3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Numerous experiments showed that the ISE becomes intense when the penetration depths of indenters are less than 1 µm [6,8,13,14,16].…”

“…In contrast to the normal ISE, the reverse ISE is infrequent and is manifested as a decreasing hardness with a decreasing depth. For instance, Ma et al [8] experimentally examined the nanohardness of single-crystal Ni and observed a normal ISE phenomenon. Wang et al [13] reported that the hardness of sintered EPD ZrO 2 first appears as a reverse ISE and then turns to a normal ISE behavior.…”