Bend Flexural Tests of Ceramics

It has been stated that brittle materials, such as ceramics, are preferentially tested by means of compressive and bending deformations. The main reason for this is that specimens of this nature tend to fail at relatively low stresses, not only because of the flaws and cracks commonly found in various sized ceramics, but for other reasons as well, as listed below  

Two methods are used for bend testing—three- and four-point bending tests. Here, the specimens are rectangular, without notches. It is obvious from Fig. 1.48 that the applied force (downward arrows) is compressive by nature, resisted by the tensional force (upward arrows). Thus, the longitudinal stresses at the lower surfaces (convex) in the specimens are tensile and compressive at their upper surfaces (concave). As a consequence, a calculable bending moment develops. The modulus of rupture is the stress of the specimen at its failure and represents the flexural strength of the specimen. 

The arrow pointing downwards in a, for example, is the center point for the load application. A large variety of machines are available for flexural tests, such as MTS, Instron, Universal Testing Machine, etc. The basic assumption in flexural tests may be summarized briefly as follows  

A circular cross-section is not used as frequently as the rectangular beam shown above. 

M is the bending moment, c is half the specimen width, t is the thickness and I is the moment of inertia of the cross-sectional area. Lists of the moments of inertia of plane figures and areas are found in the literature and also in the Appendix of Timoshenko s book [19]. Basically, the plane under consideration is divided into small pieces and the contribution of each individual piece to the moment of inertia is evaluated by integration  

---