A linear elastic fiber of rectangular cross section is embedded in a linear elastic matrix material, and the composite is subjected to a uniaxial stress as shown in Figure 6.25a. The interfacial shear stress distribution along the fiber is to be approximated by a linear function, as shown in Figure 6.25b. Determine the fiber length, \(L\), that is required to develop the ultimate tensile stress, \(s_{\mathrm{fl}}^{(+)}\), at the midpoint of the fiber. Neglect the stress transmitted across the ends of the fiber.

Transcribed Image Text:

(a) Matrix (b) Tmax x 12 Fiber L FIGURE 6.25 (a) Fiber with rectangular cross section embedded in matrix. (b) Interfacial shear stress distri- bution along the fiber shown in (a).