الجامعة المستنصرية كلية الهندسة قسم الهندسة الميكانيكية مواد هندسية مرحلة 3 COMPOSITE MATERIALSد. ناظم مجبل فالحمواد هندسية 1-4
MECH 473 ~ LECTURE 15: COMPOSITES For particulate composites, the rule of mixtures predicts the density of the composite as well as other properties (although other properties may vary depending on how the dispersed phase is arranged) Density, r, is given as a fraction, f, as: RULE OF MIXTURES Where the subscripts m and f refer to the matrix and fiber.
MECH 473 ~ LECTURE 15: COMPOSITES For fiber reinforced composites, the rule of mixtures predicts the density of the composite as well as electrical and thermal conductivity along the direction of the fibers if they are continuous and unidirectional. Density, r, is given as a fraction, f, as: RULE OF MIXTURES For thermal conductivity: For electrical conductivity: Thermal and electrical energy can be transferred through the composite at a rate that is proportional to the volume fraction, f of the conductive material
MECH 473 ~ LECTURE 15: COMPOSITES In a composite material with a metal matrix and ceramic fibers, the bulk of the energy would be transferred through the matrix. In a composite consisting of a polymer matrix containing metallic fibers, the energy would be transferred through the fibers. When the fibers are not continuous or unidirectional, the simple rule of mixtures may not apply. For example, in a metal fiber-polymer matrix composite, electrical conductivity would be low and would depend on the length of the fibers, the volume fraction of fibers and how often the fibers touch one another. RULE OF MIXTURES
MECH 473 ~ LECTURE 15: COMPOSITES The rule of mixtures can also be used to predict the modulus of elasticity when the fibers are continuous and unidirectional. Parallel to the fibers, the modulus of elasticity may be as high as: RULE OF MIXTURES However, when the applied load is very large, the matrix begins to deform and the stress-strain curve is no longer linear. Since the matrix now contributes little to the stiffness, the modulus is approximated by:
MECH 473 ~ LECTURE 15: COMPOSITES Perpendicular to the fibers, the modulus of elasticity may be as high as: RULE OF MIXTURES There are many good examples provided in your text by Askland and Phule in the chapter, “Composites: Teamwork and Synergy in Materials”. Review this chapter and the examples provided.
MECH 473 ~ LECTURE 15: COMPOSITES -Fiber reinforced composites provide improved strength, fatigue resistance, Young’s modulus and strength to weight ratio over the constituent materials. -This is achieved by incorporating strong, stiff, yet brittle fibers into a more ductile matrix. -Generally speaking the fiber supplies the strength and stiffness while the matrix binds the fibers together and provides a means of transferring the load between fibers -The matrix also provides protection for the fibers FIBER REINFORCED COMPOSITES
MECH 473 ~ LECTURE 15: COMPOSITES -Many factors must be considered when designing a fiber-reinforced composite including the length, diameter, orientation, amount and properties of the constituents, and the bonding between them. -The method used to produce the final product is also very important as it dictates the type of properties just mentioned as well as the quality of the product. CHARACTERISTICS OF FIBER REINFORCED COMPOSITES
MECH 473 ~ LECTURE 15: COMPOSITES Fiber length and diameter: Fiber dimensions are characterized by their aspect ratio l/d where l is the fiber length and d is the diameter. The strength improves when the aspect ratio is large. Typical fiber diameters are from 10 mm to 150 mm. Fibers often fracture because of surface imperfections. Making the diameter small reduces its surface area, which has fewer flaws. Long fibers are preferred because the ends of the fiber carry less of the load. Thus the longer the fiber, the fewer the ends and the higher the load carrying capacity of the fibers. CHARACTERISTICS OF FIBER REINFORCED COMPOSITES
MECH 473 ~ LECTURE 15: COMPOSITES -As can be seen from this plot, the strength of the composite increases as the fiber length increases (this is a chopped E-glass-epoxy composite) CHARACTERISTICS OF FIBER REINFORCED COMPOSITES