[MUSIC] Hi, this is Rick Neu. In this lesson we're going to look at high-throughput methods to measure fracture toughness. The learning outcome is to explain the principles and methods for measuring fracture toughness. So first of all let's review what a conventional fracture toughness test might look like. This is a compact tensile specimen. It's not really compact in the sense that we need to be compact. The wheat varies anywhere from a quart of an inch to an inch to could be much larger. In fact, sometimes it has to be really large if your material has a fairly good amount of ductility. And basically what you do is you apply a load after you've pre-cracked the specimen usually in fatigue. You apply a load. And you measure the load at which fracture occurs, and that load is correlated to a measure of fracture toughness. One measure of fracture toughness is the critical stress and tensity factor, this Kc. And so we'll just use that as an example. And this is a standard test. There's actually two ASTM standards that deal with this particular test, E399 and the more comprehensive E1820. To measure the crack growth and you typically put a clip gauge on here. Say you get load displacement information from this sort of test. That isn't going to work for high-throughput. An so we pointed out the best way to do a high-throughput test on small samples is through indentation but in this case instead of using spherical indenters like we did for strength and modulus, we're going to purposely use a sharp indenter to create a stress concentration. If you press a sharp indenter in something that's brittle, what happens is cracks will form in the body where tensile stresses naturally will form. Gotta understand a little bit about why cracks would form, when you're indenting a brittle material with a sharp indenter. So first of all, you have to realize tensile stresses are induced as the plastic zone size around the indenter increases in a certain regions. Now during loading the tensile stresses are below the indenter and so that's shown and you create what's known as median cracks. During unloading you get spring back and you get tensile stresses that tend to form lateral to the surface, and these are called lateral cracks. And then there is a hoop stress around the indenter at the tips of those hoop stress is where they are magnified the most and you get cracks formed there, those are radial cracks. And often what happens is the median cracks and the radial cracks link up to form this median radial cracks. And so, when you indent something there's going to be subsurface cracks, which you often can't see, unless you're use some sort of an x-ray type source, but there'll be cracks along the surface that you do see. And the length of the cracks relates to the fracture toughness of the material. In fact, if the materials not brittle the cracks won't form. So in some sense there's a threshold where your fracture toughness is high enough where cracks don't form at all There's really two types of indenters that are often used in this. One is a vickers type indenter. So this has four corners and the fracture toughness is based on the length of the radial surface cracks that form. The crack length, turns out, varies as a function of load. So as you increase the load, make the indent larger, your crack length also grows in size. And in fact, for a range of loads, generally, you get the same measure of fracture toughness. Work done by Lawn, Evans and Marshall, back in the early 1980's, showed that fracture toughness can be correlated to the properties of the material, the Young's modulus and the hardness, the load applied and the size of the cracks. Later an extensive study on many materials was done and basically a similar form, a little bit more comprehensive form shown at the bottom was developed. And this is fairly realistic in relating some measure of fracture toughness to the crack lengths that form with some scaling factor and I show this scaling factors that are typically used. So, that's a Vickers Indenter, now if you go to Berkovich Indenter this Indenters are commonly use in nanoindentation. You lose symmetry and you only have three corners. So this modifies that equation, but just slightly. It actually depends on the number of radial cracks that form. And in fact, it basically just affects the scaling factor in front. In fact the ratio changes from four radial cracks to two radial cracks, that ratio is 1.073. And so that basically, you come up with a similar relationship, that relates those properties to the cracks that measure. Now you have to measure all these different things. But this can be done. I mean, and this is just an application, example application. Let's say you want to measure the fracture toughness of silicon carbide, a brittle material. And so you start out with a diamond indenter, we use a particular instrument. There's a few out there. Hysitron Triboscope is one of the common instruments you use to do these measurements. You apply the load and you perform in-situ imagine. No cracks are observed if you don't load it high enough. So there's some threshold where there's no cracks and once you go above that threshold the cracks appear. And then once you've continuously increased the load your cracks will grow. Now what you typically do to get the E and H. The Young's modulus and the hardness is you use the load displacement information below that threshold where there is no cracks, because once there is a crack that changes your modulus hardness measurements. So you get that information from the same instrument. And then for loads both the threshold, you measure the crack and then you plug that into one of these factor toughness relationships. In this example We just used the simpler relationship and found that the fractured toughness was around 3MPa square root of meter and it was found you can measure this at different load levels and it was relatively independent on load up to 40 millinewtons. And on the left it shows an image of the indent and there's cracks coming from the corners that are measured. So in this lesson, we've explained the principles and methods for measuring fracture toughness. And the way to do it is using indentation methods but using sharpened indenters. They provide fine space resolution, rapid speed and measurement, and possibility of automation. But we should point out there's still some limitations. You can only really obtained quantifiable information when the materials is relatively brittle. If your material has fairly good fracture toughness capability already Cracks aren't going to form in the indent and you're not going to get any additional information. But the way this could be used is, for example, on the right here we have one of our samples, material libraries, with a gradient. And let's say we put an array of indents and go to this fracture mechanics protocol. And if you look closely, you'll see that there's a region on here where cracks form at the indents and there's other regions where they don't. And so we can quickly assess that well, that region or those processing conditions, those microstructures are more brittle than other parts on that sample. And so we can quickly identify what conditions might lead to lower fracture toughness. So what's next? We'll turn our attention to chemical properties. Thank you. [SOUND]