Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations

Abstract

A new method for evaluating modulus and hardness from nanoindentation load/ displacement curves is presented. As a spherical indenter penetrates an elastoplastic half-space, the elastic displacement above the contact line is presumed to diminish in proportion to the total elastic displacement under the indenter. Applying boundary conditions on the elastic and plastic displacements for elastic and rigid plastic contacts leads to an expression that can be best fit to the entire unloading curve to determine E ‫ء‬ , the reduced modulus. Justification of the formulation is presented, followed by the results of a preliminary survey conducted on three predominantly isotropic materials: fused quartz, polycrystalline Al, and single crystal W. Diamond tips with radii ranging from 130 nm to 5 mm were used in combination with three different nanoindentation devices. Results indicate that the method gives property values consistent with accepted values for modulus and hardness. The importance of surface roughness and indentation depth are also considered.

Nanoindentation stress–strain curves of plasma-enhanced chemical vapor deposited silicon oxide thin films

“…For the fused quartz, σ II is approximately 9 GPa. σ II corresponds to its measured hardness value, and compares favorably to the literature (for example, 8.8 GPa by Gerberich et al [29], and 8.5 GPa by Oliver and Pharr [8]). The initial yielding point, σ I cannot be clearly distinguished in Fig.…”

Microstructure and Mechanical Properties of Electroplated Cu Thin Films

“…Also the surface roughness increases significantly with the film thickness (Figure 1), which affects the contact area determination in the indentation analysis. The effect of surface roughness on thin film modulus measurements by nanoindentation is discussed in [15] and in [16].…”

An investigation into the dynamic indentation response of metallic materials

“…However, experimentally the index can be lower than 2 in certain situations due to a range of effects that may occur singly or together [27,[34][35][36]. These include (1) improper fitting [32], (2) indenter radius effects, where the bluntness of the real tip reduces n at low depths toward the value of 1.5 for a sphere [30,37,38], (3) surface roughness, where n * 1 [39], (4) instrumental factors such as machine compliance and thermal drift [40], (5) indentation size effects [41,42], (6) ratedependent deformation [43], (7) material inhomogeneity, and (8) fracture [44].…”