Introduction and synopsis the performance p of a

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Introduction and synopsis The performance, P , of a component is characterized by a performance equation. The performance equation contains groups of material properties. These groups are the material indices. Sometimes the "group" is a single property; thus if the performance of a beam is measured by its stiffness, the performance equation contains only one property, the elastic modulus E. It is the material index for this problem. More commonly the performance equation contains a group of two or more properties. Familiar examples are the specific stiffness, ρ / E , and the specific strength, ρ σ / y , (where y σ is the yield strength or elastic limit, and ρ is the density), but there are many others. They are a key to the optimal selection of materials. Details of the method, with numerous examples are given in Chapters 5 and 6 and in the book “Case studies in materials selection”. This Appendix compiles indices for a range of common applications. Uses of material indices Material selection . Components have functions: to carry loads safely, to transmit heat, to store energy, to insulate, and so forth. Each function has an associated material index. Materials with high values of the appropriate index maximize that aspect of the performance of the component. For reasons given in Chapter 5, the material index is generally independent of the details of the design. Thus the indices for beams in the tables that follow are independent of the detailed shape of the beam; that for minimizing thermal distortion of precision instruments is independent of the configuration of the instrument, and so forth. This gives them great generality. Material deployment or substitution . A new material will have potential application in functions for which its indices have unusually high values. Fruitful applications for a new material can be identified by evaluating its indices and comparing them with those of existing, established materials. Similar reasoning points the way to identifying viable substitutes for an incumbent material in an established application. How to read the tables . The indices listed in the Tables 1 to 7 are, for the most part, based on the objective of minimizing mass. To minimize cost, use the index for minimum mass, replacing the density ρ by the cost per unit volume, ρ m C , where m C is the cost per kg. To minimize energy content or CO 2 burden, replace ρ by ρ p H or by ρ 2 CO where p H is the production energy per kg and 2 CO is the CO 2 burden per kg.
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© Granta Design, January 2009 Table A1 Stiffness-limited design at minimum mass (cost, energy, eco-impact) FUNCTION and CONSTRAINTS Maximize TIE (tensile strut) stiffness, length specified; section area free ρ / E SHAFT (loaded in torsion) stiffness, length, shape specified, section area free stiffness, length, outer radius specified; wall thickness free stiffness, length, wall-thickness specified; outer radius free ρ / G 2 / 1 ρ / G ρ / G 3 / 1 BEAM (loaded in bending) stiffness, length, shape specified; section area free stiffness, length, height specified; width free
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