Length effect of rods under three-point bending for determining the Weibull parameters of brittle materials

Brittle materials, such as ceramics, are commonly characterised using two parameters: one is a measure of the strength, the other a measure of the scatter. To determine these parameters three-point bending tests of circular rods are often used and the parameters determined using simple bending theory. However, the simple bending theory can be a poor representation of the stresses near the loading points particularly for small length:diameter ratio. To overcome the shortcomings of the simple theory, finite element analyses have been performed for rods of varying length:diameter ratio and correction factors for the simple theory have been determined. These factors depend on both the length:depth ratio and the material property defining the scatter.