Composite materials
When a short fiber embedded in a matrix is loaded in tension along its length, which correctly describes the distribution of tensile stress within the fiber? Assume the interface does not slip and transfers load at a constant shear stress.
- ANear zero at the ends, rising away from them through interfacial shear, and constant in the middle if the fiber is long enough
- BUniform along the whole length because the interfacial shear stress is constant, and independent of fiber length
- CMaximum at both ends, because the end faces take the load directly, and decreasing toward the middle of the fiber
Show answer and explanation
Answer: A. Near zero at the ends, rising away from them through interfacial shear, and constant in the middle if the fiber is long enough
Almost no load is transferred through the end faces of the fiber, so the stress in the fiber is nearly zero at its ends. Moving away from the ends, load enters little by little through the interfacial shear stress τ, and the stress rises roughly in proportion to the distance from the end. If the fiber is long enough, beyond a certain distance the strains of fiber and matrix match and the stress reaches a constant maximum. The length needed for this maximum to reach the tensile strength of the fiber is the critical fiber length lc, and the strength is reached at a distance lc/2 from the end. If the fiber is much longer than lc, the low-stress end portions are a small fraction, and the reinforcing effect approaches that of continuous fibers. A constant interfacial shear stress means that the fiber stress rises at a constant rate, not that the stress itself is uniform. The explanation that load enters through the end faces and the stress is greatest at the ends is the reverse.