Effective Area and Effective Volume Calculations for Ceramic Test Specimens

Abstract

The calculation of the effective volume and/or effective area is a key step in estimating the reliability of ceramic component life cycles. Most common tests performed to assess the strength of components made from ceramics are bend bar specimens tested in three-point and four-point flexure, C-ring and O-ring specimens under diametral compressive or tensile loads, and biaxial ring-on-ring specimens. ASTM closed form solutions [1] for the effective volume and area exist for specimen geometries based on classical theories with underlying assumptions. In general, the closed form expressions are valid for limited specimen geometry bounds. A discussion regarding the validity is presented via a numerical approach that computationally determines the effective volume and area for ceramic test specimens. The results obtained utilizing the numerical approach are compared with the closed form solutions. These comparisons point to the need for revisiting the underlying assumptions used in developing the closed form expressions. Finally, simple power law approximations are developed based on numerical results that directly give the effective volume and/or the effective area based on the Weibull modulus for the test geometries investigated in this research effort.