Introduction of microcompression testing

by the Hertzian contact solution [44, 58]:

3

3

4E Rh P  _s

, (2-18)

where Er is the effective modulus of the pair of contacting solids, R is the indenter tip radius. The onset of plastic deformation during nanoindentation is marked by a large displacement burst, as shown in Figure 23 [69]. The large displacement does not imply that the specimen has undergone large plastic deformation. It is mainly a reflection of the major shearing along the slip plane which is called as the pop-in effect. The first pop-in is regard as the initiation of the first slip plane. One should notice that the critical pop-in depth could decrease with decreasing tip radius. The experimental equation of maximum shear stress can be estimated by

3 / 1 2

2

max 0.12( )

R E P_{crit s}

  , (2-19)

where Pcrit is the first pop-in load in nanoindentation. The maximum normal stress is given by [53]

(

)

max 16P E 9π R 0.39(P E /R )

σ = = . (2-20)

It can be seen that, under nanoindentation, max at the contact center is in the range 0.3max. Figure 24 shows the sketch of relationship between resolve shear stress and normal stress.

In 2004, Uchic et al. [61] published “sample dimensions influence strength and crystal plasticity” in the well known journal, Science. It contains the detailed study of the sign effect in single crystal of Ni, intermetallic alloy of Ni3Al-1%Ta and Ni superalloy single crystal on mechanical properties, using the focused ion beam (FIB) and the nanoindentation system to fabricate micrometer sized compression samples.

Three benefits of the microcompression process in this study are: (1) the microcompression samples remain attached to the substrate and easy to handle; (2) the microcompression samples are loaded with the commercial nanoindentation system; (3) the fabrication of microcompression samples by the FIB can be scripted and automated.

This technique has been used for the investigation of sample size effects on the mechanical properties of single crystals of metals and alloys, as well as metallic glasses. These methodologies are discussed in the following sections.

2.7.1. Micropillar preparation

The FIB is a very powerful instrument to make transmission electron microscopy (TEM) samples, advanced circuit editing, pattern machining and mostly, site-specific milling. Ga ions operating at 25-30 keV is generally used for fabricate fabricating micrometer sized compression samples, termed as the micropillars. Methods of microscale compression sample preparation can be mainly classified into two ways, the annular-milling method and the lathe-milling program method. Generally speaking, the annular-milling is used in preparing a small diameter sample (less than 2 m) and the lathe-milling program method is for the sample which is larger than 2 m. Comparisons are described below.

The standard procedure of the annular-milling microscale compression sample preparation process usually consists of two steps [48, 62]. In the first step, rough etching with a high beam current of Ga ions is used to mill the outer crater and outline a pillar. In this step, it is important to fabricate a large crater to make sure that the flat punch indenter will contact the pillar of interest. Additionally, this step is usually performed by using high current (5~20 nA) of the FIB, since the goal is to quickly remove the material around the sample of interest. In the second step, a series of concentric annular milling patterns by a finer beam current are made to reach the final desired diameter. But due to the convergence angle of the Ga ion beam, there is a tapered angle (Figure 25 [48, 62]). The stress or Young’s modulus would increase with increasing tapered angle and would cause overestimated values. To solve this problem, it is possible to minimize such taper angle by adjusting the annular milling patterns and decreasing the beam current. But still, it is nearly impossible to produce perfect micropillar samples which having both a uniform cross-section and a well-defined gauge length by using this method alone.

Thus, in order to eliminate the taper of the microcompression sample, Uchic et al.

[48, 62] developed another fabrication method of the FIB milling process, the lathe-milling program method, which can possibly lathe off the side of the microcompression sample with the FIB by tilting an angle (2~5^o). The automatic build-in program is developed to take place of user operating tedious and monotonous steps. Firstly, tilt the sample in 2~5^o, lathed off the side of the pillar with a relatively higher beam currents (1~7 nA), then rotated a small angle (5~10^o) and milled again.

The circular pattern on the top of the pillar is a fiducial mark used as a reference point to reorient the specimen during the incremental milling and unit rotation process. The radius of this mark is a half radius of the expected sample. Through 360^o trimming, then

finer beam currents (0.05~1 nA) were used for subsequent steps. Still, there are some disadvantages of this method. Holder should be able to rotate precisely and quickly, or procedure would take too much time. Secondly, there are difficulties in milling a well-defined circular fiducial marker with the diameter smaller than 0.5 m. Thus, microcompression samples smaller than 2 m in diameter would be difficult to prepare by the lathe-milling program method (Figure 26 [48, 62]). Considering the rate of milling (~1000 m³/min^-1) [49, 63], a large microscale sample need not to use this method as well. There are still other micro-machining methods, such as the micro-electrodischarge machining (micro-EDM), femto-second laser ablation, micro-electron-chemical milling and photolithography. The latter methods are used to prepare a slightly larger length scale relative to the previous mentions of two FIB milling methods.

In terms of the micro-electrodischarge machining, it is a critical technology to fabricate high-aspect-ratio 3D microscale samples. However, the surfaces of microscale samples fabricated by the micro-electrodischarge machining will exhibit micro-cracks, resulting in stress concentration and reduction of fatigue strength. For the micropillar preparation, the FIB milling technique seems to be the best choice for this research.

2.7.2. Force loading and measurement

Once the micropillars are fabricated, the samples are then tested in uniaxial compression by using a flat punch tip (Figure 27) in a commercially available nanoindentation system (MTS Nano indenter XP). Due to the conventional nanoindention system with angstrom displacement resolution of 0.1 nm and load

resolution of 1 nN, it makes the technique popular in many applications such as the measurement of mechanical properties of thin films and tribological measurements of coatings. In particular, the modified nanoindentation plays an important role in performing the microcompression test because the use of a flat punch tip enables the diamond indenter to act as a compression platen. The flat punch tip is also truncated by using FIB, and the schematic description of microcompression test is shown in Figure 28 [64].

2.7.3. Parameters of microcompression tests

According to the two-dimensional and three-dimensional finite element modeling, Zhang et al. [21] have made recommendations regarding allowable fillet radius (rc), pillar aspect ratio ( tapered angle () and misalignment of the system. Parameters are shown below respectively.

The first important geometric factor, fillet radius (rc), is defined as the curvature at the bottom of the pillar which connects to the base (Figure 29 [64]). Compared with input stress, 6% of flow stress error from microcompression would cause by radius/pillar radius ratio r_c/r = 1. Error decreases with decreasing r_c/r ratio. This would cause an overestimate of flow stress (Figure 30 [21]). Another issue should be addressed is the distribution of the von Mises stresses in the pillar and the base. The results show that with increase rc/r, the stress concentration at the fillet is alleviated. It is well known that the stress concentrations may result in localized the sample failure prior to yield. In the case of rc/r > 0.5, there was no obvious stress concentration. Thus, the choice of the rc/r ratio needs to be judicious. One needs a small rc/r ratio to obtain the accurate material behavior in the plastic region; another needs a large rc/r to avoid

the localized failure at the pillar root. In the 2D simulations, the value of r_c/r in the range of 0.2~0.5 is the optimum condition for the microcompression testing. Therefore, this suggests that if the r_c/r is well controlled, the microcompression test can still be used to probe the mechanical properties of materials.

The second important geometric factor is the pillar aspect ratio The aspect ratio of the pillars has a relatively small effect on the output flow stress curves when it is larger than 2. The smaller  is the larger output flow stress would be. Because of the constraint result from the pillar base and the output strain hardening of the pillar during the microcompression test, these two reasons will cause the output flow to deviate from the input value. However, the increase of the aspect ratio could increase the affects of the bucking, and causes the decreasing of the output stress. The reason is if pillars are not at just the same stress axis as the tip is, the friction between the pillar top and the indenter tip interface should be considered. Interacting due to these two conflicting affects is displaced in Figure 31 [21], leveling off or stress drop could be seen at the stress-strain curve. The results indicate that the plastic buckling is suppressed by the friction when the aspect ratio is less than 5. Hence, for both 2D and 3D simulation results, Zhang et al. [21] recommended that the aspect ratio of pillars should be around 2~3.

The third important geometric factor is the taper of the pillar. The angle of taper is defined as below:

2 ) ( tan ¹

h r r_bottom _top

 ^



, (2-21)

where r_bottom and r_top are the radius of the bottom and top of the pillar, respectively. h is the height of the pillar. The top surface of the pillar is often smaller than the bottom of the pillar caused by the fabrication of FIB or other micromachining processes. The effects of taper result in an overestimate of the elastic modulus. Due to the taper angle of ~2.86^o, the measured elastic modulus is obviously larger than the input data. Figure 32 [21] shows the contrast taper affects with different aspect ratios, though the small aspect ratio would cause overestimation. Figure 32 shows that the overestimation of output stress caused by taper is increased more than the aspect ratio did. Thus, to avoid the load drop and minimize the overestimate of the output stress, the small aspect ratio and small taper angle must be chosen.

Finally, the last important factor that might cause the primary deviation of the stress-strain curve and affect the accuracy of testing elastic region of microcompression is the effect of misalignment of the system. This misalignment is the angle between the normal direction of the flat punch indenter tip and the pillar axis. It gives rise to an underestimate of the elastic modulus of the material (Figure 33). [21] The measured elastic modulus decreases with misalignment increasing. The excessive misalignment may result in buckling of the pillar. From 3D simulation, the results indicate that even perfect alignment ( = 0^o) has 20% of underestimating the elastic modulus. Therefore, the elastic modulus should time at least 1.25 from the microcompression testing.

2.7.4. Microscale characterization of mechanical properties

In 2004, Uchic et al. [61] have discovered the size effect of Ni, intermetallic alloy of Ni3Al-1%Ta and Ni superalloy single crystal. In their results, the strength of small sample size (5 m, Ni3Al-1%Ta alloy) rose dramatically from 250 MPa for a

20-m-diameter sample to 2 GPa for a 0.5-m-diameter sample. Sample size larger than 20 m had similar mechanical properties with bulk samples. In contrast, 10-m-diameter Ni superalloy single crystal did not show the same effect as the Ni3Al-1%Ta alloy, due to its fine precipitates that provide the strong internal hardening mechanisms and preempt the influence of the external dimensions.

In 2005, Greer et al. [65] observed the same phenomenon on microscale Au samples too. Strength significant increased for more than one order of magnitude in submicron pillar samples. They claimed that the high strengths in microcompression were caused by an indication of dislocation starvation. Dislocations are believed to pass through the sample free surface and out of the crystal before they have an opportunity to interact and multiply. Without the contribution of dislocations, the strength will tend toward to theoretical strength. To confirm this explanation and to exhaust the artifact condition during the sample preparation process, Greer et al. [65] developed an alternative fabrication technique based on lithographic patterning and electroplating.

Their results on microspecimen fabricated by both FIB milling and lithographic patterning and electroplating indicate that the strength increase is not artificial. Volkert et al. [66] have also examined the similar sample size effects in submicron pillar sample and attributed their results to source-limited behavior in small volumes.

In 2006, Uchic and co-workers [67] demonstrated the microscale compressive behavior of the Ni76Al24 alloys by means of microcompression tests. They found that the events of strain burst were observed in the stress-strain curves of microscale samples. The strain burst means that the strain (or displacement) takes place almost instantly and it was much similar to the so-called the pop-in effect for the nanoindentation compression testing. Figure 34 [67] shows the SEM micrograph

analysis, indicating the number of observable slip bands is approximately the same as the number of strain bursts.

Similar research published in 2006 by Schuster et al. [68], the maximum yield strength of the microscale compressive properties of electrodeposited nanocrystalline Ni is 1498 MPa for the 20 m diameter samples. The result of the Mo-10Al-4-Ni alloy was reported by Bei and co-workers in 2007 [69]. The results show that the micropillars are all yielded, regardless of the size, at a critical resolved shear stress of G/26, where G is the shear modulus, it is in the range expected for the theoretical strength, from G/30 to G/10.

To date, the microcompression tests on single-phase metals have generally shown distinct size effects, the yield and flow strength increase with decreasing pillar diameter.

These dramatic effects are attributed to dislocation starvation because the size of the sample is smaller than the characteristic length scale of dislocation multiplication. It would result in a strength approaching to the theoretical strength.