Actual relationship between load and deflection for cellular ceramic substrates: effective moduli of substrates and materials

Many practically important ceramic materials show inelastic behavior well beyond the elastic limit. However, because the appropriate load-deflection (stress–strain) diagrams are usually unavailable, particularly for thin-walled substrates, the elastic (Youngʹs) moduli, E, are commonly used for estimating mechanical and thermal stresses. We have developed an experimental device to directly measure deflection of outer layers of round cellular ceramic substrates under uniform radial pressure, which allowed us to obtain the complete load-deflection diagram up to the crush point, providing the ultimate (crush) strength of the ceramic substrates and eventually the ultimate (wall) strength of substrate materials. The materials were ASMT hematite Fe2O3 and titania TiO2 (as well as common cordierite), and the substrates had both closed and open cell designs with straight and skewed channels. We found that at all applied loads the substrate deflections were inelastic. However, in all diagrams a basic part was found to be nearly linear providing for the radial modulus, which we defined as the effective modulus of the substrate, Eq*. On this basis, we have determined the effective modulus of the substrate material, Eq. We found Eq to be much smaller than E, typically by an order of magnitude or more. Advantages of using Eq instead of E are discussed. We also argue that evaluation of the allowable pressure on a substrate should be based on the ultimate pressure corrected by the safety/load factor, k, whose estimates are discussed.