Monotonic Strength and Fracture

Abstract

In this chapter we describe the monotonic strength and fracture behavior of fiber reinforced composites at ambient temperatures. The term monotonic behavior means behavior under an applied stress that increases in one direction, i.e., not a cyclic loading condition. We discuss the behavior of composites under fatigue or cyclic loading as well as under conditions of creep in Chap. 13.

Problems

• 12.1. For a ceramic fiber with μ = 12 %, show that β ≈ 10. Show also that if the fiber length is changed by an order of magnitude, the corresponding drop in the average strength is about 20 %.

• 12.2. In a series of tests on boron fibers, it was found that μ = 10 %. Compute the ratio ${\overline{\sigma }_{\rm{B}}}/\overline{\sigma }$, where ${\overline{\sigma }_{\rm{B}}}$ is the average strength of the fiber bundle and $\overline{\sigma }$ is the average strength of fibers tested individually.

• 12.3. Estimate the work of fiber pullout in a 40 % carbon fiber/epoxy composite. Given σ _fu = 0.2 GPa, d = 8 μm, and τ _i = 2 MPa.

• 12.4. How would you go about testing a single fine-diameter fiber (recall that carbon fiber has a diameter of about 7 μm)? Do discuss the effect of variability in diameter of the fiber along its length in computing the strength of the fiber.