Polishing and Etching Techniques for Dense Alumina

Abstract

Both of these moduli for aluminum oxide have shown excellent fit to a scmi-empirical relation of the type shown in equation (1). Poisson's ratio calculated from equation (2) is shown in Fig. 1 for one set of data. The reinterpreted data of Lang2 for longitudinal ( E 2 ) arid torsional (GI) resonant frequency moduli of coldpressed and sintcred specimens of alumina were employed here.The relation bctween Poisson's ratio (y) and porosity ( P ) is of the type y + 1 = (yo + l)e-(be-bbu)P (3)A vcry close approximation to equation ( 3 ) , relating p and P, is a straight-line equation of the type y = yo -mP (4) yo = Poisson's ratio of nonporous specimen. m = an cmpirical constant. The constants in Fig 1 arc in good agreement with Knudsen's' assumption of :I value of 0.26 for pa (also after Lung2) and his "very arbitrary working assumption that Ap/AP = -0.30 for porous alumina bodies."The value of m depends primarily on the difference between the empirical constant for the relation of porosity to elastic modulus (call it be) and shear modulus ( b g ) but also depends on the zero porosity moduli Eu and GO. If both b values were the same, y would not vary with porosity. In Fig. 1, b, is greater than b,, and the slope is negative. Indirect evidence suggests that Poisson's ratio depends on pore morphology more than on total porosity. It is possible that differences in b, and b, values in series of similar specimens and between groups of dissimilar specimens could be employed to determine the degree of anisotropic internal structure and the nature of the porosity (e.g., pore morphology). It must be remembered, however, that in using equation (2), one is dealing with small differences in large numbers, and the uncertainty of the data must be established. F. P. Knudsen, "Effect of Porosity on Young's Modulus of Alumina." J. Am. Ceranz. Soc., 45 [ 2 ] 94-95 (1962).