Volume 18 - Friction, Lubrication, and Wear Technology Part 11 doc

Fig. 2 Nanoindentation instrument with CDR; xyz, three-dimensional specimen micromanipulator; H, removable specimen holder; S, specimen; D, diamond indenter; W, balance weight for indenter assembly; E, electromagnet (load application); C, capacitor (depth transducer). Courtesy of Micro Materials Limited With hard machines (Ref 10, 16, 17), the indentation depth is controlled, for example, by means of a piezoelectric actuator. Force transducers used in existing designs include: a load cell with a range from a few tens of N to 2 N (Ref 17, 18); a digital electrobalance with a resolution of 0.1 N, and a maximum of 0.3 N (Ref 16); and a linear spring whose extension is measured by polarization interferometry (Ref 10). As noted in Table 2, it should be possible to vary the load or, in hard machines, the displacement, either in ramp mode or with a discontinuous increment (step mode). The important effects of varying the ramp speed, that is, the loading rate, will be discussed in the section "Choosing to Measure Deformation or Flow" in this article. The ramp function needs to be smooth, as well as linear, and there is evidence (Ref 19) that if the ramp is digitally controlled, the data will vary for the same mean loading rate according to the size of the digitally produced load increments, unless these are very small. The basic requirements include a system for data logging and processing. Scatter in nanoindentation data tends to be greater than with microindentation, partly as a result of unavoidable surface roughness, but principally because the specimen volume being sampled in a single indentation is often small, compared with inhomogeneities in the specimen (such as grain size or mean separation between inclusions). Thus, unless such indent is to be located at a particular site, it is usually necessary to make perhaps five, ten, or more tests, and to average the data. The spacing between indents must be large enough for each set of data to be unaffected by deformation resulting from nearby indents, and the total span should be at least one or two orders of magnitude greater than the size of the specimen inhomogeneities whose effect is to be minimized by averaging. On the other hand, if the test results turn out to be grouped in such a way that reveals differences between phases or grains, then each group should be averaged separately. In either case, the number of data points to be processed is large. A real-time display helps the operator to monitor the data for consistency between indents and for any systematic trend and arises, for example, from a change in the effective geometry of the indenter, if traces of material from the specimen become transferred to it. The most common reason for an inconsistent set of data is a vibration transient, the effect of which is visible at the time. A subjective decision can then be made to discard that particular data set. Rather than use a real-time display for this purpose, a more reliable approach is to use the output signal from a stylus vibration monitor (a simple modification of the detection system itself) to abort any individual test during which the vibration exceeds a certain level. Options that can greatly increase the scope and convenience of a nanoindentation instrument are listed in Table 2, in addition to basic requirements. With many specimen types, it is essential to record the exact location of each indent. This is achieved with the help of a specimen stage driven by either stepping motors or dc motors fitted with encoders. However, such devices must not be allowed to increase the total elastic compliance of the instrument to a value comparable with the smallest specimen compliance likely to be measured (the measurement of compliance is discussed in the section "Slow-Loading Test" of this article). It is useful to be able to displace the specimen, as smoothly as possible, toward and away from the indenter, as well as to minimize impact effects at contact. This also facilitates recalibration of the displacement transducer, which in some designs varies according to the location of the plane of the specimen surface. In at least one design (Ref 3), the specimen displacement stage allows the surface to be brought into the field of view of an optical microscope, by using computer control. Another system (Ref 18) uses a closed-loop TV camera to help reposition the indenter rapidly and safely. Refinements to the electronic hardware and software have been introduced to give, for instance, servocontrol of the selected load, loading rate, or displacement. This allows automatic compensation for nonideal transducer parameters, such as finite load cell compliance. Furthermore, the choice of loading mode (constant ramp speed or discontinuous step) can be extended to include more elaborate modes, such as constant strain rate or constant stress. Useful refinements include automatic control of the speed with which the specimen approaches the indenter and detection of the instant of contact. Thus, the whole loading-unloading cycle, and any required series of cycles, can be automated. As described in the section "Averaging of Multiple Tests" of this article, one design (Ref 6) includes provision for ac modulation of the load, which allows the continuous measurement of the compliance of the contact. Of course, drift can be a problem, and attention must be paid to temperature stability. On occasion, temperature compensation is necessary in connection with depth or load transducers. Thus far, the introduction of specimen heating stages has been delayed by the consequent major problems of thermal drift. Other physical measurements that require the use of the transducers mentioned also can be carried out, in principle, by means of a modified indentation procedure. One example is the determination of Young's modulus for thin films and other small specimens in the form of simple or composite beams whose elastic compliance is measured (Ref 16). As with optical scanning techniques, values of film stress can be derived from measurements of deflection and curvature of the film/substrate composite. Likewise, biaxial tensile testing of free-standing films can be carried out by means of the bulge test: if the bulge shape is profiled at a number of locations by probing with the indenter, then the strains can be calculated without the need to assume that the bulge is spherical. In effect, this represents a specialized type of profilometry, of which other examples include the measurement of film thickness and scratch width, as discussed below. Film adhesion can be characterized by various methods, two of which can be used, in principle, with the help of a nanoindentation instrument modified to act as a film failure mechanism simulator. The indentation fracture technique (Ref 20, 21) has the advantage that normal loading only is required, thus avoiding complications of interpretation that arise from groove formation. In addition, values of fundamental parameters, such as critical stress-intensity factor, can be derived, in principle. A variant of the CDR technique, which monitors the load-depth curve, together with acoustic emission, in order to detect debonding at fiber-matrix interfaces in composites is described in Ref 22. The thin-film scratch test has successfully been carried out by Wu et al. (Ref 23), who used conical indenters with hemispherical tips of radii down to l m, and a tangential load cell. These were fitted to a nanoindentation instrument, for which the servo system could be set to give either constant indentation speed or constant rate of normal loading while the specimen was being translated at constant speed. As with conventional scratch testing, the critical load at which film cracking or delamination begins is used as an empirical measurement of adhesion. It was found that a reliable indication of this load was the value at which a load drop first occurred during a scratch loading curve. Thus, in many cases, fractography by SEM was not required for the detection of delamination. Other established methods of detection, such as acoustic (Ref 24) or use of friction signal (Ref 25), can readily be used in conjunction with this technique. Wu et al. (Ref 18, 23) discuss the prospects of thus deriving values of fracture toughness of film/substrate assemblies. They also describe how scratch hardness is derived from measurement of the width of the scratch track when this is contained solely within one material (either bulk specimen or film only). The instrument could be operated in a simple profilometer mode, and values of track width were obtained from the observed difference between transverse depth profiles measured before and after the scratch was made. Likewise, microfriction tests can readily be performed (Ref 26) if the indenter is replaced by the required friction stylus mounted on a device for measuring transverse force, such as a piezoresistive transducer. Again, the flat specimen is translated at constant speed. Simultaneous measurement of the stylus motion normal to the specimen surface, using the existing depth transducer of the basic nanoindentation instrument, when correlated with the peaks and troughs of the friction trace, can help to either confirm or eliminate different alternative models of the friction process (Ref 27). Nanoindentation has been used to characterize individual submicron-sized powder grains (Fig. 3), and the deformation and brittle fracture of spray-dried agglomerates has been recently quantified (Ref 28) with the help of an instrument modified by the addition of a crushing device. Fig. 3 Single test on individual 150 m size grain of powder (lactose), with values of elastic recovery parameter, R, calculated by two methods: R 1 = ' e / p = 0.095, and R 2 = [(P m T /2W e ) - 1] -1 = 0.107 (symbols defined in text and Fig. 5) Test Procedures Choosing to Measure Deformation or Flow. As yet, there is no universally accepted standard procedure or hardness scale that applies to nanoindentation with CDR. Consequently, the literature to date describes a variety of different data handling procedures, which generally have not yet been universally established. However, close examination shows that the differences are almost always a matter of presentation, rather than scientific content. This review attempts to summarize all the principal techniques that have been published to date. Although the terminology used here has not necessarily been accepted in entirety, its usage is intended to emphasize the distinction made in Fig. 1 between the measurement of intrinsic material properties and the less ambitious task of characterizing particular specimens. Strictly speaking, terms such as loading rate will apply only when soft loading machines are used, but the equivalent hard loading procedure will be evident. An assumption underlying the concept of hardness as a material property is that at or below some particular value of contact pressure, the plastic strain rate is zero. Unless the test is performed at the absolute zero of temperature, this is not strictly true. In many materials near the surface, indentation creep (including low-temperature plasticity) is often noticeable. As discussed in an earlier review (Ref 3), if indentation depth varies significantly with timeas well as load, then even if the loading rate is held constant, and even if the material properties are independent of depth, there is no simple relation between load and depth. Furthermore, unless the indentation depth can be expressed in terms of separable functions of stress and time, the hardness, even if defined for a particular (constant) value of loading time or rate, will not be independent of load. Thus, as indicated in Fig. 4, a preliminary check is advisable. Fig. 4 Two principal types of test The simplest way to measure deformation is by means of "slow-loading" tests, where the indentation depth is plotted as a function of slowly varying load, but it is wise to check the creep rate first by means of a load held constant for a time that is comparable to the duration of the proposed ramping load tests. Suppose that after that time, the creep rate is still x nm/s. Then, it would be reasonable to perform slow-loading tests in which the loading rate is always fast enough to produce a rate of indentation that is large, compared with x. If this is impractical, then rather than attempt a hardness test, it is logical to characterize the flow behavior, as discussed in the section "Flow Behavior" of this article. Slow-Loading Test. Figure 5 shows a typical depth-load cycle, with load as the independent variable. Typically, a fresh location on the specimen surface is selected, and contact is made at a load of a few N or less. The load is then raised at the required rate until the desired maximum is reached, and is then decreased, at the same rate, to zero. The "unloading curve," as shown, is not horizontal. The indenter is forced back as the specimen shows partial elastic recovery, and it is this phenomenon that allows the derivation of information on modulus. The amount of plastic deformation determines the residual, or "off-load" indentation depth, p , and the plastic work, W p (Fig. 5). Fig. 5 Raw slow-loading data. (a) Depth, , as a function of load, P. (b) As (a), showing plastic and elastic work A simple scheme for extracting information from such a test is shown in Fig. 6. Although there is no complete theory of elasto-plastic indentation, a useful approach is that of Loubet et al. (Ref 4). They used a simple approximation, namely that the total "on-load" elasto-plastic indentation depth, T (Fig. 5), can be expressed as the sum of plastic and elastic components, p and e . It is further assumed that the area of contact between indenter ad specimen is determined by the plastic deformation only, and that e represents the movement of this area as a result of elastic deformation (Fig. 7). If this were exact, e would be given by Sneddon's relation (Ref 29) for a flat cylindrical punch normally loaded onto the plane surface of a smooth elastic body: (Eq 1) where P is the applied load, a is the radius of the contact region, E is Young's modulus, and v is Poisson's ratio. Thus, the unloading curve of as a function of P would be linear. Fig. 6 Information from a single slow-loading test Fig. 7 Regions of elastic and plastic deformation (symbols as in Fig. 5); I, indenter; P, plastic zone; E, approximate limit of significant elastic deformation In practice, there is some significant departure from linearity that occurs after a certain point (A in Fig. 5). This is attributed to a decrease in contact area arising from an opening of the apical angle of the indent, and a corrected value, ' e , is recommended instead of e in Eq 1. Because ' e , as well as T , can be determined experimentally, p can be found. It is therefore possible to derive separate values of appropriate parameters describing the elastic and plastic behavior of the specimen. Quite often, a typical specimen will show sizable variations in composition or structure, even within the small depth range sampled in these tests. Thus, before any attempt is made to derive values of material properties such as modulus, it is logical to define the most convenient indices that will provide a fingerprint characterizing an individual indent (Fig. 6). Ideally, these indices should relate directly to the raw test data, without the need for a sophisticated model or assumptions. In the simplest case of a homogeneous specimen whose material properties are constant, the values of these indices should also be constant, independent of depth. These conditions are satisfied by a fingerprint consisting of two numbers, an elastic recovery parameter, R, and a plastic hysteresis index, I h . The concept of an elastic recovery parameter was introduced by Lawn and Howes (Ref 30), who described its value in predicting how energy release provokes fracture in brittle materials. The definition was later modified (Ref 3, 31), so as to be consistent with the Loubet description above. It is defined as R = ' e / p , and, as shown in Appendix , it is readily calculated from the area W e (Fig. 5) that represents the mechanical work released during unloading: (Eq 2) where P m is the maximum load. Alternatively, ' e can be found by fitting a tangent to the unloadingcurve at the maximum. In effect, this gives the contact compliance d /dP, and thus (Appendix ): (Eq 3) Figure 3 shows an example. The physical significance of R is that for a homogeneous material, it is proportional to the ratio of hardness, H, to modulus E/(1 - v 2 ), according to the formula (Appendix ): (Eq 4) where k 1 is the geometrical factor that applies to the pyramidal geometry of the indenter used, namely the ratio of contact area ( a 2 ) to the square of the plastic depth ( ). The value R is a useful index, because it is a dimensionless quantity and because, in the case of an ideally homogeneous specimen, it will be independent of depth or load. Since R is derived from the contact compliance d /dP (according to Eq 3), any formula that includes R can of course be rewritten in terms of compliance. The hardness will be proportional to , but a more direct measure of the resistance to plastic deformation is the hysteresis index, I h , based on the plastic work, W p . It is easy to show this in the simplest case of a specimen that shows fully plastic behavior with H independent of depth, W p 3 (Ref 3). Thus, I h has the same dimensions as hardness if defined as: I h = P 3 / (Eq 5) In the simple case mentioned, the value of H will be I h /(9 k 1 ). Figure 8 shows an example of indents located within individual grains in a two-phase material (cermet), illustrating the differences in R and I h . It is important to realize that although I h characterizes a plastically deformed zone whose dimensions are not much greater than p , the value of R is determined by the behavior of a much larger elastic hinterland (Fig. 7). Fig. 8 SEM images of indents in a two-phase material (nichrome/chromium carbide cermet). Different maximum loads were used to give approximately the same indent depth in each case. Nanoindentation fingerprints, from left to right: Indent in dark region (carbide), R = 0.19, I h = 754; mixed region, R = 0.19, I h = 509; light region (nichrome), R = 0.12, I h = 282 Averaging of Multiple Tests. In principle, a major advantage of CDR is the ability to obtain graphs of hardness as a function of depth from a single test. However, for the reasons outlined earlier, it is usually necessary to perform a number of tests on each specimen and to average the data (see Fig. 9). As it has been shown, each test yields only a single value of R, and it is advantageous to vary the maximum load between tests, so that R can be obtained as a function of depth. If the compliance of the instrument itself is significant, compared with the contact compliance d /dP, it can be eliminated with the help of a plot of compliance against reciprocal of depth (Ref 32), extrapolated to infinite depth, before Eq 3 is used to calculate R. If E/(1 - v 2 ) is known, the value of k 1 can be derived from a plot of this type (Ref 33). Fig. 9 Averaging of multiple tests The need for discrete loading and unloading cycles to different values of maximum load is avoided if d /dP is continuously measured by means of a differential loading technique (Ref 6). An ac current source is used to add a small oscillatory modulation to the load, and the resulting oscillations in depth are detected with a lock-in amplifier. It is necessary to allow for the machine compliance and for damping inherent in the depth-sensing transducer. No indenter pyramid is perfectly sharp, and with an indenter of finite tip curvature, plastic deformation is initiated at a finite depth below the surface. For this reason, and because of other complications (vibrational noise, pile-up around the indentation, and specimen roughness), the accuracy with which the instant of contact and the depth-zero can be identified is much poorer than the resolution of the depth measurement (typically, 1 nm or better). Methods that allow for the exact indent geometry are discussed in the section "Hardness and Modulus" of this article. In practice, the zero of plastic indentation depth can be determined with reasonable precision, for example, as shown in Fig. 9 and described below. First, polynomials are fitted to the averaged loading curves and the graph of R against depth. From the relation p = T - ' e , this allows p to be plotted as a function of P 1/2 . This function is chosen simply because, for an ideal material, it would be linear. In practice, after a certain depth has been exceeded, linearity is often seen over a considerable depth range, and the appropriate depth-zero can be found by extrapolation back to zero load (Fig. 10a). The result can be confirmed (Ref 3) by means of a (linear) plot of against depth, with extrapolation back to zero W p . Fig. 10 Alternative data presentations, showing effect of changes in chosen depth- zero; numbers against curves indicate the depth offset in nm (specimen: multienergy boron implant into titanium). (a) Depth against square root of load. (b) l p against depth. (c) l' p against depth. Source: Ref 34 Subsequently derived profiles of relative hardness, in particular their shape at small depths, can show wild variations according to the choice of depth-zero (Fig. 10b), and should be interpreted with caution. For some materials (Ref 3), this near-surface difficulty is exaggerated by the interesting "critical load effect," whereby no permanent (plastic) indent size is made below a certain indent size. To study this, nanoindentation with depth recording was first used by Tazaki et al. [...]... 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