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32.6 MECHANICAL STRENGTH
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Although the specific mechanical properties of real materials are discussed in detail in the material that follows, it is very appropriate at this time to relate the concepts of the strengthening mechanisms to the previously described crystalline structures. Mechanical properties can best be studied on the basis of three precepts which encompass all the strengthening mechanisms. These three principles are stated here because they involve the distortion of the lattice structure that has just been discussed.
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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SOLID MATERIALS 32.20
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32.6.1 Principles of Mechanical Strength Strength can be defined as a material s ability to resist slip. Thus it follows that the first principle of mechanical strength is this: A material is strengthened when slip is made more difficult to initiate. Therefore, to make a material stronger, it must be given a treatment that retards the avalanche of dislocations or, in other words, pegs the slip planes. The second principle of mechanical strength is this: Slip is retarded by inducing mechanical strains, or distortions, in the lattice structure of the material. These distortions were discussed previously as lattice imperfections or defects. Thus it is a paradox that the source of strength in real polycrystalline materials is crystal imperfections or crystal defects. The third principle of mechanical strength is this: There are four methods to induce mechanical strains or lattice distortions in a material, namely, decreasing the grain size, low-temperature plastic deformation (cold work), single-phase alloying, and multiple-phase alloying.
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32.6.2 Grain Size Local distortion of the lattice structure at the grain boundaries induces substantial strain energy in those regions. This distortion impedes slip, or causes the dislocations to pile up, and consequently, the grain-boundary material is stronger than the material at the central portions of the crystal. This is true for most metals at room temperature. However, as additional energy is added to a polycrystalline material by raising the temperature, the grain-boundary material softens (and also melts) sooner or at a lower temperature than the bulk of the grain.At some temperature, called the equicohesive temperature, the strengths at these two regions are equal. Above the equicohesive temperature, the grain-boundary material is the weaker of the two. This explains why materials that are used at elevated temperatures have higher creep strengths when their grains are coarse rather than fine. The surface-area-to-volume ratio of a sphere is inversely proportional to its diameter. Therefore, as the diameter of a sphere decreases, its ratio of surface area to volume increases.This means that for a given weight or volume of a polycrystalline solid, the total grain-boundary surface increases as the grain size decreases. Since the grainboundary material is stronger than the interior material, the strength also varies inversely with the grain size.Also, since the surface area of a sphere is proportional to the square of its diameter, it can be assumed as a first approximation that the yield strength is proportional to the reciprocal of the square of the grain diameter. Figure 32.12a shows how the 0.2 percent offset yield strength of 70Cu-30Zn brass varies with grain size. In this case, the yield strength increases by a factor of 4 with a grain diameter ratio of 24. The strengths of some materials, such as aluminum or steel, are not so greatly affected by grain size alone.
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32.6.3 Cold Work Cold work is a more significant strengthening mechanism than decreasing the grain size for most metals. When a crystalline material is plastically deformed, there is an avalanche of dislocations (called slip) that terminates at the grain boundaries. It is a mass movement of a body of atoms along a crystallographic plane. This movement in a polycrystalline material distorts both the grain boundaries and the crystalline planes in the grain so that slip occurs in the adjacent grains as well. Actually, a por-
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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