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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This note was uploaded on 02/25/2013 for the course PHYS 2202 taught by Professor Sowell during the Spring '10 term at Georgia Tech.

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