Youngs Modulus and the Strength of Perfect Solids

In addition to understanding the behavior of ceramics exposed to thermal energy, it is important to understand their behavior when they are subjected to an external load or stress. The objective of this section is to interrelate the shape of the energy versus distance curve E r), discussed in Chap. 2, to the elastic modulus, which is a measure of the stiffness of a material and the theoretical strength of that material. To accomplish this goal, one needs to examine the forces F r) that develop between atoms as a result of externally applied stresses. As noted in Sec. 2.4, F r) is defined as 

From the general shape of the E r) curve, one can easily sketch the shape of a typical force versus distance curve, as shown in Fig. 4.6. The following salient features are noteworthy  

In the remainder of this section, the relationships between stiffness and theoretical strength, on one hand, and E r) and F(r), on the other hand, are developed. 

Experience has shown that all solids will respond to small stresses a by stretching in proportion to the stress applied, a phenomenon that is described by Hooke s law  

Here L is the length under the applied stress, and Lq is the original length. 

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