Effect of surface roughness on nanoindentation test of thin films

Abstract

By using the two-dimensional quasicontinuum method, the nanoindentation process on a single crystal copper thin film with surface roughness is simulated to study the effect of surface morphology on the measurements of mechanical parameters. The nanohardness and elastic modulus are calculated according to Oliver–Pharr’s method. The obtained results show a good agreement with relevant theoretical and experimental results. It is found that surface roughness has a significant influence on both the nanohardness and elastic modulus of thin films determined from nanoindentation tests. The effect of such factors as the indenter size, indentation depth and surface morphology are also examined. To rule out the influence of surface morphology, the indentation depth should be much greater than the characteristic size of surface roughness and a reasonable indenter size should be chosen. This study is helpful for identifying the mechanical parameters of rough thin films by nanoindentation test and designing nanoindentation experiments.

Introduction

As an urgent requirement of the rapid development of micro/nanotechnology, the characterization of mechanical properties of materials at micro- and nanoscales has attracted much attention in the past decade [1], [2], [3], [4]. The mechanical properties of micro-/nanosized materials often exhibit significant size dependence due to such reasons as surface/interface effects [5], [6], [7]. Nanoindentation has become a widely adopted technique to identify the mechanical behaviors at the nanoscale. In such a test, a hard indenter, which can be of a spherical, conical or cylindrical shape, is pressed into a sample. An advantage of this technique is that both the load P and the displacement h of the indenter during loading and unloading can be continuously monitored with high resolution in the nanonewton and nanometer ranges. Such mechanical parameters as elastic modulus, hardness, and yield stress can be determined from the indentation force–depth curve. Most previous studies on nanoindentation have been concentrated on materials with a smooth surface [8], [9], [10], [11], [12], [13]. When the characteristic size of roughness is on the order of the indenter, the roughness may have a significant influence on the test. Therefore, it is of importance to investigate the effects of surface roughness on nanoindentation.

Recently, the effect of surface roughness during nanoindentation has been considered by experimental measurements and numerical simulations. Wang et al. [14] experimentally studied the influence of the sample surface condition on the hardness, elastic modulus, and other mechanical parameters of materials measured from nanoindentation test. Zhang et al. [2], [15] established a load-bearing area ratio model of nanoindentation on rough surfaces. They showed that the rougher the indented surface, the more the energy dissipated during the plastic deformation, and the more significant the indentation size effect. By means of finite element method (FEM), Chen et al. [16] studied the effect of the indenter tip roundness on the measured hardness for two typical elastic perfectly plastic materials. They found that the tip rounding can cause a pronounced increase in the measured hardness at an indentation depth comparable to the tip radius. Kreuzer and Pippan [17] studied the influence of different slip band orientations in a model material by means of a two-dimensional discrete dislocation model. Recently, the process of film nucleation and the surface morphology of the substrate were also analyzed by molecular dynamics (MD) simulations [18]. However, MD simulations are generally very time consuming due to the relatively large size and relatively long time involved in actual nanoindentation tests.

To minimize the limitation of MD simulations, Tadmor and coworkers [19], [20], [21], [22] established a quasicontinuum method by successfully coupling FEM and atomic methods. The basic idea is that in a crystal undergoing mechanical deformation, the majority of the lattice experiences a slowly varying deformation at the atomic scale which can be well described by the continuum approximation. It is only in the vicinity of defects or in the presence of mechanical manipulations on the order of the lattice spacing where discrete atomic effects become important. There is thus no need to explicitly treat every single atom in the crystal as is done in standard lattice statics and molecular dynamics approaches. A detailed overview of the quasicontinuum implementation is given by Shenoy et al. [22]. This novel method has been used to investigate the nanoindentation test of defect-free single crystals and proven capable of implementing large-scale simulations without losing calculation precision [23], [24], [25]. Using the quasicontinuum method, Li and Jiang [26] examined the effect of the indenter size by simulating the initial plastic deformation of Al and Cu single crystals. The predicted results of hardness and elastic modulus were in excellent agreement with relevant experiments. Shan et al. [10] studied the effects of surface steps on the first dislocation emission during nanoindentation by the quasicontinuum method. They found that surface steps significantly influence the critical load of first dislocation emission.

Thin films with a thickness on the order of microns or nanometers have a wide range of applications from functional to structural materials. In this paper, we use the quasicontinuum method to investigate the effects of surface roughness on the measurement results of the mechanical properties of thin films by the nanoindentation technique. We simulate the process of a rigid cylindrical indenter pressing into a smooth or a rough single crystal copper thin film. The single crystal copper is described by the embedded atomic method potential labeled by Ercolessi and Adams [27]. The well-known Oliver and Pharr method [1] is adopted to evaluate the nanohardness and elastic modulus. The influences of both the indenter size and surface roughness on the measurement results are examined.