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up at grain boundaries or inclusions. The planes along which slip occurs are called slip planes. Slip occurs only with relatively high stresses, greater than the yield strength, and it causes plastic deformation. When a crystalline solid or a single crystal is subjected to low loads, the atoms move slightly from their normal lattice sites and return to their proper positions when the load is removed. The displacements of the individual atoms are very small during elastic deformation. They are submicroscopic, a fraction of an atomic distance. Although there are some dislocation movements, they are few in number, involve very short distances, and are reversible. Slip, however, is microscopic in size and causes plastic (permanent) deformation that is macroscopic. Figure 32.11 contains several two-dimensional lattice arrays which, in a simplified manner, illustrate the mechanism by means of which slip takes place. A typical perfect cubic lattice is shown in Fig. 32.11a, which is a small part of a single crystal. If sufficiently large shear stresses are placed on the crystal, all the atoms above the labeled slip plane move to the right simultaneously with respect to the atoms below the slip plane, as shown in Fig. 32.11b. The lattice is still a perfect cubic structure; only the outline or exterior shape of the single crystal has changed. It is believed, on the basis of the theories of elasticity, that the shear stress must be equal to the value of G/2 , where G is the shear modulus of elasticity. Young s modulus of elasticity E, Poisson s ratio , and G are related to one another by the equation G= E 2(1 + ) (32.1)
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For iron, E = 30 Mpsi and = 0.30, and so G = 11.5 Mpsi. Therefore, the so-called theoretical shear strength for slip to occur in iron is
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FIGURE 32.11 Two-dimensional sketch of the slip mechanism. (a) A perfect crystal; (b) idealized slip in a perfect crystal; (c) part of a crystal with one edge dislocation; (d) movement of dislocation subject to shear stress; (e) jog produced in the crystal face by dislocation motion.
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Downloaded from Digital Engineering Library @ McGraw-Hill ( 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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G 11.5 = = 1.83 Mpsi 2 2
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However, slip occurs in iron crystals with shear stresses of only 4 to 5 kpsi, which is more than two orders of magnitude smaller. The theoretical shear strength of the other pure metals is also 400 to 500 times larger than the actual shear strength. The commonly accepted explanation of why the actual shear stress is so much lower than the theoretical value is that slip does not occur by the simultaneous movement of all the atoms along the slip plane; rather, it occurs by the movement of individual rows (the dislocation row or plane) of atoms. Thus it is the movement of dislocations along the slip plane to the grain boundary that causes the actual shear stress for plastic deformation to be so low. Figure 32.11c, d, and e illustrates the movement of a dislocation that results in slip. In real crystals of metals, slip terminates at the grain boundaries or the freesurface faces and causes substantial jogs or steps, much larger than shown in Fig. 32.11. Experimental study of the spacings of the slip planes and the sizes of the jog have been made on some of the common metals. The spacing of the parallel planes along which slip occurs varies randomly, with an average distance between slip planes of about 2000 atom diameters. The length of the step or jog at the surface of the grain is approximately 200 to 700 atom diameters. The atomic displacements associated with slip, unlike those of the initial movements of dislocations, are irreversible in that the slip jog remains when the shear stresses are removed. That is, slip causes a permanent change in shape, or plastic deformation, as it is called. The evidence of slip is seen on metallurgically prepared samples as slip lines when examined under a microscope. The slip lines are the intersection of the crystallographic planes along which slip occurred with the etched surface of the specimen. Slip results in a narrow band on either side of the slip plane within which the lattice structure is severely distorted. These slip lines do not appear on the face of a specimen that is metallurgically polished after slip occurs; they appear only after etching with a suitable chemical reagent that dissolves the metal being studied. The slip lines become visible for the same reason that grain boundaries are visible after etching: The internal energy of the material within the distorted area is considerably higher than that of the material within the rest of the crystal. The metal in the higher energy level dissolves into the reagent much more rapidly than the rest of the crystal, leaving a narrow groove where the severely distorted band intersects the surface. Slip lines can also be seen on specimens that are polished prior to being plastically deformed and that have not been etched.
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