Tension of Ductile Ceramics

Most ceramic materials are brittle at room temperature. However, in the case of ductile materials, namely when the elastic limit and the fracture stress do not coincide due to some plasticity observed in the deformation process, the relation can be given, similarly to Eq. 1.7, as  

Here clearly, Ij is the instantaneous length of the test specimen. Equation 1.9 is the summation of all the small changes between the two values and, thus, may be expressed as  

Sometimes, it is necessary to alternate between these two definitions of strain, namely e and s, which can be easily done, as shown below, by rendering Eq. (1.6) as  

for example, a load is acting on an elastic body in x direction, it elongates not only in the direction of the acting load, but contracts laterally, as well. Thus, contraction must occur in the transverse y and z directions. Empirically, it was observed that transverse strains are constant fractions of longitudinal extension. The ratio of the lateral contractive strain to the axial strain is called Poisson s ratio , denoted by v and expressed as  

This ratio denotes a reduction in cross-section elongation. In brittle materials, there is a small change in the cross-section with elongation, so v is low. Thus, when a sample of material is stretched on one axis, it tends to get thinner also on the other two axes. If, during the uniaxial tension, no lateral contraction occurs, then v = 0. 

---