If the volume fraction of bers is 025 what are the

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Unformatted text preview: ith a center-to-center spacing of 100 m, the volume fraction of fibers is 0.2 and the interface area is approximately 157 cm2. Assume that the composite is a continuous fiber composite. Calculate the volume fraction of fibers and the interface area if the fibers are arranged in a hexagonal array and the nearest-neighbor distance is 50 m. 32. Explain how delamination at the fiber-matrix interface can enhance the fracture toughness of composites. 33. Ceramic matrix and fiber materials often contain porosity levels on the order of 10%. How will porosity influence the elastic modulus and the tensile strength of these materials? 34. What is fiber bridging, and how does it enhance the fracture toughness of ceramic-matrix composites? Give an example of a composite system where fiber bridging is the dominant mechanism for toughness. 35. In an epoxy/S-glass composite system, it is desired that the longitudinal elastic modulus be at least twice the transverse elastic modulus. What volume fraction of fibers is necessary to achieve this condition? 36. Show that the critical volume fraction of fibers necessary for fiber strengthening is given by Equation 14.5–15. 37. Explain why the rule of mixtures does not yield a reasonable estimate for the coefficient of thermal expansion. 38. E-glass and epoxy both exhibit isotropic thermal expansion. Do you expect that the coefficient of thermal expansion of an E-glass/epoxy composite will also be isotropic? Explain your answer. 39. Explain why carbon fibers have a modulus of elasticity that is so different along the fiber axis compared with the value in the transverse direction. Do you expect the elastic modulus of a diamond fiber to be different in different directions? Explain. 40. List and briefly describe the three stages of fatigue failure in laminate composites. 41. Explain why the fracture toughness is high in composites with distributed damage. 42. A unidirectional fiber–reinforced composite has a modulus of 20 GPa in the longitudinal direction and 3 GPa in the transverse direction. If the volume fraction of fibers is 0.25, what are the elastic moduli of the matrix and fibers? 43. The pictures shown in Figure 14.5–1 and Figure 14.5–10a, b, and c belong to the same Al-Li/alumina composite system. Construct a grid of test points and estimate the volume fraction of the fibers using all four pictures. Select one of the pictures and measure the area of the composite and fibers directly. Then compute the volume fraction. Compare the two estimates and comment. Now double the test point spacing in the grid and make the same measurements. Compare your answers. 44. Consider a unidirectional fiber-reinforced composite loaded p...
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