Slice synthesis of a three dimensional “work of fracture” specimen

In the evaluation of brittle materials such as ceramics, the “work of fracture” specimen is enjoying considerable interest. That specimen, basically a beam bending specimen with rectangular cross section has inclined notches machined such that the remaining ligament is an isoceles triangle with the apex on the tension surface. The specimen is of particular interest because it tends to provide for slow stable crack propagation in such materials. The usual use of the test involves the recording of the load-deformation curve and the identification of the total area under the curve with the “work of fracture”. This then in turn is related to the fracture toughness.The present paper presents the results of an attempt to analyze this truly three dimensional problem in an approximate “two dimensional” fashion, treating the specimen as a series of slices and neglecting in effect the inter slice shear effects. Both beam bending and beam shear effects on compliance are considered. Plasticity effects are considered negligible for the class of brittle materials for which the test specimen is most frequently utilized. Comparison of experimental and analytical results is discussed. The observed stability characteristics of this “work of fracture” specimen is discussed in light of these results.