Problem

Many advanced materials consist of fibers (made of glass, Kevlar, carbon, etc.) placed wit...

Many advanced materials consist of fibers (made of glass, Kevlar, carbon, etc.) placed within a matrix (such as epoxy, a titanium alloy, etc.). For these materials it is important to assess the bond strength between fibers and matrix, and this is often done via a pullout test, in which the tip of a fiber is exposed, the material sampled is properly clamped, and the fiber is pulled out of the matrix. The data collected often consists of a graph like the one shown, in which the force exerted on the fiber is recorded as a function of pullout displacement. With this in mind, the interface toughness assessment process may require a measure of the energy expended to pull out the fiber. Use the force-displacement graph shown, which is typical for a glass-fiber reinforced epoxy, to measure the total pullout energy. Hint: The work of the pullout force is given by the area under the curve.