Laminate Orientation Code The example shown ear lier of how an eight ply

Laminate orientation code the example shown ear lier

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Laminate Orientation Code. The example shown ear- lier of how an eight-ply laminated composite structure, shown in Figure 2–25, is produced is convenient but that method becomes complicated and extensive for structures made from a large number of plies. The laminate orienta- tion code seeks to simplify and shorten the designation for a given fabricated composite structure. Note in the previ- ous example that the eight plies are symmetrical about the midplane between plies four and five. This is typical for many practical designs of composite structures and it is un- necessary to repeat the names of all plies. At times, two or more adjacent plies of the same orientation are used and it TABLE 2–18 Examples of the Effect of Laminate Construction on Strength and Stiffness Tensile strength Modulus of elasticity Longitudinal Transverse Longitudinal Transverse Laminate type ksi MPa ksi MPa 10 6 psi GPa 10 6 psi GPa Unidirectional 200 1380 5 34 21 145 1.6 11 Quasi-isotropic 80 552 80 552 8 55 8 55 – 45 ° +45 ° 0º: Longitudinal direction 90º: Transverse direction FIGURE 2–25 Multilayer, laminated, composite construction designed to produce quasi-isotropic properties
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CHAPTER TWO Materials in Mechanical Design 69 Rule of Mixtures for Ultimate Strength s uc = s uf V f + σ′ m V m (2–10) At any lower level of stress, the relationship among the over- all stress in the composite, the stress in the fibers, and the stress in the matrix follows a similar pattern: Rule of Mixtures for Stress in a Composite σ c = σ f V f + σ m V m (2–11) Figure 2–27 illustrates this relationship on a stress–strain diagram. 10. For symmetrical structures, only half of the plies are defined and the subscript s is added to the final bracket. 11. For a structure having an odd number of plies, but which is otherwise symmetrical, the orientation of the central ply is written with a horizontal bar over it. Some examples are: (a) Symmetrical, as in Figure 2–25: 0 ° , 90 ° , + 45 ° , - 45 ° , - 45 ° , + 45 ° , 90 ° , 0 ° S [0/90/ { 45] s (b) Multiple plies at same orientation: 0 ° , 0 ° , 90 ° , 90 ° , + 45 ° , - 45 ° , - 45 ° , + 45 ° , 90 ° , 90 ° , 0 ° , 0 ° S [0 2 /90 2 / { 45] s (c) Odd number of plies: 0 ° , 90 ° , + 45 ° , - 45 ° , 90 ° , - 45 ° , + 45 ° , 90 ° , 0 ° S [0/90/ { 45/90 ] s (d) Nonsymmetrical: 90 ° , 90 ° , + 30 ° , + 30 ° , - 30 ° , - 30 ° , 0 ° , 0 ° S [90 2 /30 2 / - 30 2 /0 2 ] (e) Repeating sets of plies with the same orientation: 0 ° , 90 ° , + 45 ° , 0 ° , 90 ° , + 45 ° , 0 ° , 90 ° , + 45 ° S [0/90/45] 3 Predicting Composite Properties The following discussion summarizes some of the important variables needed to define the properties of a composite. The subscript c refers to the composite, m refers to the ma- trix, and f refers to the fibers. The strength and the stiffness of a composite material depend on the elastic properties of the fiber and matrix components. But another parameter is the relative volume of the composite composed of fibers, V f , and that composed of the matrix material, V m . That is, V f = volume fraction of fiber in the composite V m = volume fraction of matrix in the composite Note that for a unit volume, V f + V m = 1; thus, V m = 1 - V f .
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