Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 118

Because of their high hardness, most ceramics are difficult and expensive to machine into the shape required for tensile testing. Ceramic specimens are also more difficult to grip stably at their ends when compared to metals and polymers. The ease of testing in a flexural (bending) mode, coupled with the simple geometry and low cost of the specimens makes this test very popular for ceramics. There are two ways of performing flexural testing, referred to as three‐point bending and four‐point bending, but four‐point bending is often preferred and commonly used in testing ceramics when design data are required.

In four‐point bending, the specimen, commonly in the shape of a beam, is supported on two rollers, a distance l apart (called the outer span), the load (force) F is applied by means of two upper rollers that are symmetrically arranged, and the deflection at the center of the beam is measured (Figure 4.1e). In a common testing configuration, the distance d between the upper rollers (called the inner span) is equal to l/2. As the specimen is bent, the lower surface of the beam is in tension whereas the upper surface is in compression. Halfway across the thickness, called the neutral axis, the length of the beam is unchanged and, thus, the resultant stress is zero. The highest tensile stress σ is at the bottom surface of the beam and is constant over the inner span. It is given by

(4.11)

where, h is the thickness and w the width of the beam. The deflection of the center of the beam δ, relative to the outer support points, is given by

(4.12)

where, E is the Young’s modulus.

In three‐point bending, the load is applied by means of a single roller midway between the two lower rollers. The corresponding relations for the highest tensile stress σ (at the bottom surface below the upper roller) and deflection at the center of the beam are

(4.13)

(4.14)