A review of nanoindentation continuous stiffness measurement technique and its applications
Introduction
Indentation has been the most commonly used technique to measure the mechanical properties of materials because of the ease and speed with which it can be carried out. At the beginning of the 20th century, indentation tests were first performed by Brinell, using spherical and smooth balls from ball bearings as indenters to measure the plastic properties of materials [1], [2]. The Brinell test was quickly adopted as an industrial test method soon after its introduction and prompted the development of various macro- and microindentation tests [3]. Traditional indentation testing involves optical imaging of the indent. This clearly imposes a lower limit on the length scale of the indentation. During the past two decades, the scope of indentation testing has been extended down to the nanometer range. This has been achieved principally through the development of instruments capable of continuously measuring load and displacement throughout an indentation [2], [4], [5], [6]. In recently developed systems, loads as small as a nanonewton and displacements of about 0.1 nm can be accurately measured. On the other hand, the recognition in the early 1970s that elastic modulus could potentially be measured from an indentation load–displacement curve [7] greatly promoted the development of instrumented-indentation testing methodologies. In recent years, the study of mechanical properties of materials on the nanoscale has received much attention, as these properties are size-dependent [2], [8], [9]. These studies have been motivated partly by the development of nanocomposites and the application of nanometer thick films for miniaturization of engineering and electronic components [2], [10], and partly by newly available methods of probing mechanical properties in small volumes [2], [5], [6]. The nanoindenter is maturing as an important tool for probing the mechanical properties of small volumes of material. Indentation load–displacement data contain a wealth of information. From the load–displacement data, many mechanical properties such as hardness and elastic modulus can be determined without imaging the indentations [2], [5]. The nanoindenter has also been used to estimate the fracture toughness of ultrathin films [11], [12], [13], which cannot be measured by conventional indentation tests. With a tangential force sensor, nanoscratch and wear tests can be performed at ramping loads [14], [15], [16], [17], [18], [19], [20]. Atomic force microscopes are ideal for imaging of nanometer-scale indents, providing useful information about nanoindentation deformation and cracking. When an indentation system is used in conjunction with an atomic force microscope, in situ imaging can be obtained [8]. With the rapid development of instruments and analytical procedures, more material properties will be measured or estimated using nanoindentation in the near future.
Diamond is the most frequently used indenter material, because its high hardness and elastic modulus minimize the contribution of the indenter itself to the measured displacement [2]. For probing properties such as hardness and elastic modulus at the smallest possible scales, the Berkovich triangular pyramidal indenter is preferred over the four-sided Vickers or Knoop indenter because a three-sided pyramid is more easily ground to a sharp point [1], [2], [6]. Another three-sided pyramidal indenter, the cube corner indenter, can displace more than three times the volume of the Berkovich indenter at the same load, thereby producing much higher stresses and strains in the vicinity of the contact and reducing the cracking threshold. This makes this indenter ideal for the estimation of fracture toughness at relatively small scales [11], [12]. The spherical indenter initiates elastic contact and then causes elastic–plastic contact at higher loads. This indenter, then is well suited for the examination of yielding and work hardening. However, it is very difficult to obtain a precise sphere with a diameter of less than 100 μm made of diamond. This fact limits its application in nanoindentation testing [6].
A recently developed technique, continuous stiffness measurement (CSM) [5], [21], [22], offers a significant improvement in nanoindentation testing. The CSM is accomplished by imposing a small, sinusoidally varying signal on top of a DC signal that drives the motion of the indenter. By analyzing the response of the system by means of a frequency specific amplifier data are obtained. This allows the measurement of contact stiffness at any point along the loading curve and not just at the point of unloading as in the conventional measurement. The CSM technique makes the continuous measurement of mechanical properties of materials possible in one sample experiment without the need for discrete unloading cycles, and with a time constant that is at least three orders of magnitude smaller than the time constant of the more conventional method of determining stiffness from the slope of an unloading curve. The measurements can be made at exceedingly small penetration depths. Thus, this technique is ideal for mechanical property measurements of nanometer-thick films. Furthermore, its small time constant makes it especially useful for measuring the properties of polymeric materials. In nonuniform materials, such as graded materials and multilayers, the microstructure and mechanical properties change with indentation depth. Continuous measurements of mechanical properties of these materials during indentation are greatly needed.
Utilizing the CSM technique, creep measurements on the nanoscale can be performed by monitoring changes in displacement and stress relaxation. Because the CSM is carried out at frequencies greater than 40 Hz, it is less sensitive to thermal drift [22]. Also utilizing the CSM technique, load cycles of a sinusoidal shape at high frequencies allow the performance of fatigue tests at the nanoscale. The fatigue behavior of thin films and microbeams can be studied by monitoring the change in contact stiffness because the contact stiffness is sensitive to damage formation.
The purpose of this review paper is to present the recent work on the nanoindentation CSM technique and its applications. Emphasis is placed on the CSM analytical methodologies and how they can be used to study hardness, elastic modulus, creep, and fatigue properties for layered materials and nonhomogeneous composites, especially those designed for use in magnetic storage and microelectromechanical systems (MEMS) devices. Discussion on the CSM results in conjunction with nanoindentation scratch and wear data are also presented.
Section snippets
Hardness and elastic modulus measurements
The two mechanical properties measured most frequently using indentation techniques are the hardness, H, and the elastic modulus, E. As the indenter is pressed into the sample, both elastic and plastic deformation occurs, which results in the formation of a hardness impression conforming to the shape of the indenter. During indenter withdrawal, only the elastic portion of the displacement is recovered, which facilitates the use of an elastic solution in modeling the contact process [2], [5], [6]
Uniform and multilayered hard structures
According to Eq. (13), the contact stiffness, S, of a uniform material is linearly proportional to the contact depth, hc. For a nonuniform material, however, the linear relationship between S and hc does not exist [25]. Li and Bhushan [27] conducted CSM tests on fused silica, PTFE, and styrene butadiene rubber (SBR). Fused silica and PTFE are rigid plastic, uniform materials with constant elastic modulus values. SBR is a uniform soft viscoelastic material. Fig. 8 shows CSM results for fused
Conclusions
In this paper, the nanoindentation CSM technique and its methodologies are reviewed. Applications of the CSM technique to the measurement of contact stiffness, elastic modulus, hardness, creep resistance, and fatigue properties of the materials used in magnetic storage devices are presented and discussed in conjunction with the data of nanoscratch, and friction and wear tests. We conclude the following:
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The CSM technique probes the mechanical property changes in situ during indentation, and
Acknowledgements
The authors would like to thank Nano Innovation Center, MTS, Knoxville, TN, for the technical support and several useful discussions. The research reported in this paper was supported by the industrial membership of the Nanotribology Laboratory for Information Storage and MEMS/NEMS, Ohio State University, Columbus, OH. The authors thank Dr. W.W. Scott for useful discussions that aided the preparation of the manuscript.
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