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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

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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, sf1 ( ) + , at the midpoint of the fiber. Neglect the stress transmitted across the ends of the fiber.