Ceramic Technology and Processing, King

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The four-point-bend fixture is at the top of the support column. There is a central rod touching the bottom of the test bar and transmitting the deflection to the extensometer at the lower right. This method is a direct measure of deflection.

Sonic Measurements

There are two types of sonic measurements: sonic velocity and resonate frequency.

Sonic Velocity. By placing a transducer on one side of the sample and the receiver on the other, the sonic velocity can be measured. Some instruments (V meter, James) have only one probe and use the reflected sonic wave from the other side for the measurement. In order to obtain a true MOE, the velocity of the shear wave must also be determined; this is harder to do. Sonic velocity by itself is a useful and easy measurement. Coupled with a measure of the amplitude attenuation, one obtains a fairly good idea about the nature of the ceramic body. For example, sonic velocity has sufficient sensitivity to discern the pressing direction in a part, as the velocity is higher in the pressing direction than along the sides. Attenuation is an empirical method to estimate how well a body is bonded. This is easily accomplished by measuring the reduction of wave amplitude across the sample. Techniques of this sort are useful quality control tools. They can even pick up interior cracks and laminations, as the reflected wave has traveled only half of the distance that it would have if the piece were whole.

Resonate Frequency. This technique is based on the resonate frequency or ring of a sample as it is tapped while suspended on end supports. A sonic probe is placed in contact with the side of the sample as it is tapped. The MOE measurement appears in a display. Shear modulus can also be measured by relocating the probe, but it is a little more difficult to get a reading. An instrument is shown in Figure 11.72.

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Figure 11.72: Resonate Frequency Measurement Apparatus for MOE measurements. Easy to use. (Courtesy of Grindosonic/Lemmings)

The device is commercially available and inexpensive. The test is fast and easy and can be made on any cylindrical sample of sufficient (3-4") length. Bar or cylindrical rod samples are usually tested.

Hardness

Hardness measurements are made by pressing a precision diamond point onto the polished surface of the sample with a certain load, and then measuring the size of the indentation. A special instrument is used for this purpose. Before purchasing it, ensure that the instrument is also capable of measuring fracture toughness. Fracture toughness requires a higher load than micro-hardness.

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The load for hardness measurements is between 100-200 grams, as it is not advisable to induce fractures around the indent. In comparison, for fracture toughness, the indent must be fractured and loads of a few kilograms are used.

There are two types of diamond configurations commonly used for ceramics: Vickers and Knoop. Vickers produces a symmetrical indent of pyramidal shape. The Knoop indenter produces an elongated pyramidal shape. Vickers is more commonly used as it is also the shape for fracture toughness measurements. As previously mentioned, it is much easier to see the ends of the indentations when the sample is coated with a reflective metal film such as gold. Now that the ends are clearly visible, the measurement is longer. This results in a lower hardness calculated for an indent without the reflective film. It is to be consistant, one way or the other.

A sketch of an indent will be shown in the next section along with the measurements for fracture toughness.

Fracture Toughness

There are a variety of configurations used on samples for measuring fracture toughness.7 These are shown redrawn, in Figure 11.73.

In addition to these five configurations, another also exists which will be described shortly. In Figure 11.73 each of the specimen geometries is as follows:

"A". Double Cantilever Beam. It is required that the crack length be followed, making it difficult for opaque materials.

"B". Single Edged Notched Beam. This is similar to fourpoint bending. Only a initial crack must be formed and presents complications.

"C". Double Torsion. This sketch is shown from the end view. From the top, the specimen is rectangular where the length is 3-4 times the plate width. The initial crack extends in only a short distance. The test is not too difficult to perform.

"D". Chevron Notch. A notch is sawed in the specimen as seen in the shaded area in the end view. This eliminates the need for pre-cracking, which can be tricky. On the other hand, cutting the chevron notch can be difficult to do correctly.

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"E". Indentation strength. The sample is indented with a load high enough to initiate cracks out of the indent corners. Then the specimen is broken in bending.

Figure 11.73: Fracture Toughness Specimen Configurations, Sketch. Pick the one that fits your needs.

An additional method that is fairly simple is the "Indentation Crack Length" method where the specimen is indented with a Vickers diamond point at a load high enough to cause fracturing at the corners, as seen in Figure 11.74.

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Figure 11.74: Fracture Toughness Test by the Indentation Crack Length Method. Arrows point to the measurements needed.

When working with a fine-grained, dense specimen, the Indentation Crack Length is most commonly used as it is easy to preform the test and make the measurements. However, there are also problems with this method, as shown in Figure 11.75.

The sample has been coated with gold/palladium and is viewed with Nomarsky interference contrast. While the indent and corner cracks are clearly seen, there are also circular cracks around the indent that compromise the test results. In this case, the load should be reduced or another method used to measure fracture toughness.

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Figure 11.75: Vickers Indentation with Cracking. Polished section with polarized light and Nomarski interference contrast illumination.Ring cracks compromise the toughness measurement. Scale bar 200 μm.

A simple equation is used to calculate toughness (KIC).

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There are three independent variables in the test: speed, load, and lubrication conditions. The wear maps are quite different for each set of conditions. The authors rationalized this behavior by calculating a critical velocity with an equation containing material thermal properties and friction, which affect thermal shock in the ceramic. Above that velocity, the surface breaks down and spalls. Wear is then by fracture and displacement. Below that transition, wear behavior is not so clear-cut.

Other examples of wear surfaces on ceramics were seen in the previous section on microscopy and illustrate that, as conditions change, the wear mechanism can change. There is the additional complication of the consequences of introducing other materials. Then, chemical reactions can influence wear rates as well as normal load and velocity.

One helpful way to envision wear, as previously mentioned, is to consider the following mass transport mechanisms: plastic deformation, diffusion, viscous flow, and fracture with kinetic displacement. Any, or all, of these may be involved in the wear process at one point or another. Microscopic examination and surface analysis provide clues to the mass transport mechanism that is active. A brief discussion on the four mass transport mechanisms (wear) appears below.

Plastic Deformation

Surfaces on wear couples are subjected to very severe conditions of pressure, shear, and temperature. Either the materials themselves or reaction products can be transported by plastic deformation along the sliding direction. This proves tricky, as the rate-controlling step can be the chemical reaction step, deluding the investigator into thinking that diffusion is the wear mechanism itself. To take an example, alumina sliding on steel results in a chemical reaction forming a spinel ( Al2O3-Fe2O3). This reaction was first recognized by Coes9 and later by Brown.10 While that reaction does displace Al, it does not displace it very far. Something else dominates the wear phenomena. The spinel crystallizes in the cubic system that has sufficient (at least three) slip systems for volumetric plastic deformation. Under the conditions of shear, pressure, and temperature at the interface, the spinel is whisked away as soon as it is formed. Coes found the spinel in the