List of Symbols
2.4 Ductile Regime Machining of Brittle Materials
2.4.2 Nanoindentation
Since past few decades, the hardness measurement techniques have been improved with sophisticated instruments. Numerous methods and instruments have been developed to determine the mechanical properties of a material, e.g. tensile/compressive, shear, triaxial, scratch test, nanoindentation etc. For brittle materials such as Si and SiC, tensile/compressive testing is not suitable as it is difficult to obtain sufficient amount of strain before the material specimen fails.
Nanoindentation test is used to measure mechanical properties of materials such as hardness and Young’s modulus. In this test the softer material of interest (specimen) is deformed by a harder material (indenter) whose properties are known. Indentation techniques can also be used to obtain the strain-hardening exponent, creep, fracture toughness, viscoelastic properties and stress-strain data. Nanoindentation is similar to the conventional hardness testing method in which the scale of the penetration is measured in nanometers rather than in micron or millimeters. It is also considered as nondestructive characterization technique as only a small area scale is considered for deformation. Literature reveals that the hypothesis of ductile-mode machining has emerged from the indentation of brittle materials.
Nanoindentation helps in understanding of ductile to brittle transition and evaluation of plastic deformation of brittle materials. Many researchers [Rao et al. (2007), Yan et al. (2005a, TH-2306_10610325
23 2005b, 2006b, 2010), Goel et al. (2014a, b)] worked on nanoindentation of brittle materials and suggested that under a specified hydrostatic pressure or below a certain thickness (in the range of few nanometers to submicron), brittle materials behave as ductile material even at ambient temperature. This concept is especially useful in the machining of brittle materials, since this ductile phase transition due to hydrostatic pressure can be used as a guideline to remove the material in ductile mode. Moreover, it is possible to extract strain-strain data for brittle material, which is not possible through conventional tensile/compressive testing as it is difficult to obtain sufficient amount of strain before it fails during tensile loading.
In general, two types of nanoindentation systems are used for indentation purpose, i.e., MTS NANO Indenter XP (MTS Corporation, Nano Instruments Innovation Center, TN, USA) and a micro-force tester (Instron Corporation, Norwood, MA, USA) [Zhang ( 2007)]. A typical nanoindentation instrument consists of three basic components: (a) an indenter mounted onto a rigid column or load frame, (b) an actuator for applying the force and (c) a sensor for measuring the indenter displacements. The indenter (generally Berkovich indenter) is attached to the holder using a rigid metal-bonding process. Diamond is mostly preferred in making of the indenters because it has high hardness and elastic modulus. Moreover, it minimizes the deformation of the indenter during indentation as compared to other less-stiff materials in which the elastic displacements of the indenter must be considered.
Figure 2.8 (a) Schematic of typical nanoindentation tester, (b) Force actuator, (c) Capacitive displacement gauge [Nair et al. (2014), Sun et al. (2018)]
Figure 2.8 (a) shows the schematic of a typical nanoindentation tester with a force actuator and a capacitive displacement sensor. Small forces are generated either (a)
Force actuator Capacitive displacement gauge Indenter tip
Specimen
Load frame P
Lateral motion stage
Permanent magnet
Stylus
Coil
Power source
P Stylus Outer electrodes
Center plate C
C1
C2
(a)
(b)
(c)
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electromagnetically with a coil and magnet assembly or (b) electrostatically using a capacitor with fixed and moving plates or (c) piezoelectric actuators. The force actuator with coil and permanent magnet assembly is shown in Figure 2.8 (b). The most common and earliest means of applying force is to insert a coil inside a permanent magnet. The magnetic field is gen- erated by varying the current inside the coil. This generated field interacts with the field of the permanent magnet, which generates the necessary force to push the holder with indenter onto the sample. However, the current that is used to actuate the magnet produces joule heating effect that leads to thermal drift in the instrument. In case of electrostatic force actuation, the voltage is applied between the middle and upper/lower plate, and the generated force is proportional to the square of the voltage. The advantage of the electrostatic force actuation lies in its temperature stability and good control over thermal drift. The vertical displacement is measured using a capacitance technique, i.e., by measuring the downward displacement of the plate at the center with respect to those of the two outer plates (Figure 2.8 (c)).
For brittle materials, nanoindentation finds a very important and useful technique as it is capable of finding physical parameters which are difficult to obtain from general tensile/compression tests. It is capable of providing nanometric displacement to the tip of the indenter and recording of a very small load value in the range of mN with high degree of precision. The capital cost involved in nanoindentation instrument is very high in comparison to that of conventional micro hardness testing instruments. Lawn et al. (1994) observed distributed irreversible deformation in brittle ceramics during Hertzian indentation tests. It was concluded that brittle material shows an effective ductility behavior in the indentation stress-strain response. A model was developed to quantitatively represent the relationship of the radial crack size and the fracture toughness of the material. Later, Oliver and Pharr (1992, 2004) taken up the model and derived an analytical model to determine mechanical properties such as Young’s modulus and hardness from the nanoindentation simulation.
Yan et al. (2005a, 2005b, 2006b) and Pandey et al. (2011) investigated the phase change and amorphization of silicon by carrying out nanoindentation tests before and after the diamond machining. Transmission electron microscopic observation confirmed the formation of amorphous phase during diamond turning that affects the surface function of the machined part. It was observed that the machining-induced amorphous silicon is softer than diamond- cubic silicon. Rao et al. (2007) studied the phase transformation in both crystalline silicon (c- Si) and relaxed amorphous silicon (a-Si) during nanoindentation using sharp Berkovich tip. It was found that relaxed a-Si matrix is more prone to high pressure phase transformation (HPPT) compared to c-Si. Similar observations were reported by Goel et al. (2014a) during
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25 experimental and numerical studies on nanoindentation on polysilicon and single crystal silicon. It was reported that the HPPT was observed to occur more preferentially along the grain boundaries than across the grain boundaries. In the subsequent work, Goel et al. (2014b) presented extensive experimental work on nanoindentation tests on 4H-SiC.Authors observed yielding or incipient plasticity in 4H-SiC typically at a shear stress of about 21 GPa (an indentation depth of 33.8 nm) through a pop-in event. Recently, Yao et al. (2018) reported phase transformation of SiC from 4H to 3C in the vicinity of a crack during nanoindentation.
Observations:
Nanoindentation is found to be a very useful tool to obtain various mechanical properties such as Young’s modulus, hardness, strain-hardening exponent, creep, fracture toughness, viscoelastic properties, and stress-strain data. However, it is very difficult to obtain the in-situ information about the stress and pressure developed, temperature profile, and displacement underneath the indenter during physical experiments. Therefore, the use of numerical techniques such as MD and FEM can thought to be simple, easy and economical alternatives to costly, tedious and time-consuming physical experiments. Literature reports experimental studies on nanoindentation of silicon and silicon carbide to understand the phase transition during the nanoindentation test. Scant literature has been reported on MD simulation of nanoindentation process; whilst, very scant literature has been reported on FEM simulation of nanoindentation of silicon and silicon carbide. Moreover, none of the literature has attempted to determine the ductile to brittle transition thickness.