[MUSIC] Dear students, today we are going to discuss the mechanical behavior of ceramic materials. In previous lectures, we have known that the stress strain response of metals is characterized by is a reversible elastic deformation followed by a substantial plastic deformation. The elastic deformation can proceed into 1-2% straight of metals which is called an elastic limit. The plastic deformation is carried by dislocation motion. For ceramics, the mechanical behavior is dramatically different from the metals. The first slide you can see is elastic limit is much smaller than the metals smaller than 0.1%. And this means the ceramics have very high elastic modulus and the high value of this modulus is a direct result from the nature of atomic bonding in the ceramics which is usually a mixture of ionic and covalent. They're both stronger than the metallic bonding in metals. Secondly, the ceramic materials doesn't have this plastic deformation at all. And its actual stress is much smaller than the theoretical estimation. And it's compressive strength is smaller than its tension strengths. And such a mechanical behavior of ceramics and particularly the brittle failure mechanism is caused by the flows generated during the fabrication, such as a pores and the cracks ceramics, because the very high melting point of the ceramic materials. So most ceramic components are not made by melting and casting like metals, but rather by the use of powder based the roots. In which a green buddy is formed, followed by a high temperature desertification process. And this figure shows a widely used green forming method which is called depressing, the powders are loaded into this mode and then external pressure is applied to make the powder into a compact. This compact is very porous, the porosity is around 50%. In a high temperature densification process which we also call the sintering. These pores will be eliminated from the green body with the driving force of decreasing surface energy, and most of the pores can be eliminated. But it's extremely difficult to get a rid of all of them. So you will always have pore in a final ceramic product. And there are many chances to introduce corrects during the green forming, during the pressing, the demolding and when you transfer to your green body. Therefore, there will always be pause and microcracks. And suppose your example contains the crack like this with a half lens a, and it's cracked tip with a radius curvature of r. And if a external stress is applied on to your sem example. The actual strength at the crack tip can be calculated using this equation that it equals to the applied stress plus the stress times the square root of the half length A divided by 2 times of the radius of curvature. In other words with the presence of a crack, the local stress at the crack tip may be much larger than the actual external stress applied to the sample. Then the sample will fracture was the local stress exceed the theoretical values. And moreover, although the growth of the crack will reduce the elastic strain energy stored in a sample, there will also be an energy cost. And this is because the growth of the crack is accompanied with new surface creation, and it will increase the total surface energy. The balance of the two energy contributions is described by this Griffith failure criterion. And in particular with stress sigma is applied to your sample containing a crack or populist a. T he condition for the stable crack growth is in this equation that the geometrically related factor y times the critical phillium stress times the square root of pi times the half length A equals to the square root of two times elastic modulus times the surface energy. And this elastic modulus and the surface energy are intrinsic properties of materials. So, for certain materials, the right hand side of this equation can be considered as constant. And if you want to make the left hand side of the equation constant, it means with larger crack size, your fragile strength of the sample will be smaller. And if the initial crack is smaller than you will need a larger valium stress for crack to grow. And from the above discussion, you may appreciate the importance of the size of the flow or the crack pre existing in the sample. And especially the strength of a ceramic depends on his largest flaw in a sample. And unconditioned that there is no interaction between the floors. And there's a good example in comparison of these two scenarios, in figure A sample A, you can see it has smaller pre-existing cracks with average flow size about five micron. But there is a single long flow with the size of 100 micron and in sample B the average flow size is larger than the sample a About 20 micron. But since the stress is determined by the largest flaw, we can simply predict that the sample A is weaker sample B. And before concluding this lecture, and we'll still get one more question, why ceramics do not have plastic deformation and fail by brittle fracture. In previous lectures, we have known that for crystal the lattice resistance to dislocation motion is determined by the Peierls-Nabarro stress. And therefore, in principle, as long as the stress is large enough, this ceramic crystals can also go through plastic deformation. However, ceramic have covalent and ionic bonds and have a complex crystal structure. And all these factor would lead to a large, modular, large bug vector and lack of asleep systems and small dislocation. And this would eventually give a very high Peierls-Nabarro stress. And as a result, the Pareto fracture stress is determined by the pre existing flows would normally be much smaller than that determined by the past Nabarro stress. In other words, ceramic would fracture before yielding. And having said so, when someone may argue, if there is no or very limited flaws in the ceramics. Then the stress magnitude may readily achieve the one determined by the past Nabarro stress at the ceramic crystals may have dislocation motion and subsequently plastic deformation. Indeed, this is what have been observed in small scale ceramics. And suppose we have a ceramic sample with manning is pre-existing floors. And as long as we pick a sample small enough to avoid any of the flaws, and it will be possible to preserve the plastic deformation and tactility when we do the tensile or compression test. And for example, in fact people have already observed that phenomenon. And this is gallium arsenide and underwear. And its diameter is about 100 nanometer, and in situ compression in transmitted electron microscope. We can clearly see this plastic deformation. And as long as they are made sufficiently small. So in today's lecture, we have learned the mechanical behavior of ceramics. Thank you very much. [MUSIC]
