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Materials Science and Engineering: An Introduction

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Unformatted text preview: REVISED PAGES 182 - Chapter 1 i‘ Dislocations and Strengthening Mechanisms Yield strength of a single crystal— dcpcndencc on the critical resolved shear stress and the orientation of most favorably oriented slip system Figure 1.7 Geometrical relationships between the tensile axis, slip plane, and slip direction used in calculating the resolved shear stress for a single crystal. Normal to slip plane Slip direction material that determines when yielding occurs. The single crystal plastically deforms or yields when rflmax) = 7cm, and the magnitude of the applied stress required to initiate yielding (i.e., the yield strength 0}.) is TCI’SS 0” _ (cosqb cos Mm“ (7'4) The minimum stress necessary to introduce yielding occurs when a single crystal is oriented such that qb = A = 45“; under these conditions, a"), = 27““ (7.5) For a single-crystal specimen that is stressed in tension, deformation will be as in Figure 7.8, where slip occurs along a number of equivalent and most favorably oriented planes and directions at various positions along the specimen length. This slip deformation forms as small steps on the surface of the single crystal that are parallel to one another and loop around the circumference of the specimen as in- dicated in Figure 7.8. Each step results from the movement of a large number of Direction Figure 7.8 Macroscopic slip in a single crystal. of force ,- .. ._.__ in! Slip piane EQA ...
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