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# Materials Science and Engineering: An Introduction

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Unformatted text preview: REVISED PAGES 7.5 Slip in Single Crystals - 181 Burgers vectors for face-centered cubic, body-centered cubic, and hexagonal close- packed crystal structures are given as follows: b(FCC) = 2(110) (7.1a) b(BCC) = gnu) (7.1s) b(HCP) : 2min} (7.1.2) '— Concept Check 7.1 Which of the following is the slip system for the simple cubic crystal structure? Why? {100K110} {110}(110) {100K010} {110K111} (Note: a unit cell for the simple cubic crystal structure is shown in Figure 3.23.) [The answer may be found at www.Wiley.conv’college/wllister (Student Companion Sife).] 7.5 SLIP IN SINGLE CRYSTALS resolved shear stress Resolved shear stress—dependence on applied stress and orientation of stress direction relative to slip plane normal and slip direction critical resolved shear stress A further explanation of slip is simpliﬁed by treating the process in single crystals, then making the appropriate extension to polycrystalline materials. As mentioned previously, edge, screw, and mixed dislocations move in response to shear stresses ap- plied along a slip plane and in a slip direction. As noted in Section 6.2, even though an applied stress may be pure tensile (or compressive), shear components exist at all but parallel or perpendicular alignments to the stress direction (Equation 6.4b). These are termed resolved shear stresses, and their magnitudes depend not only on the ap- plied stress, but also on the orientation of both the slip plane and direction within that plane. Let «p represent the angle between the normal to the slip plane and the applied stress direction, and A the angle between the slip and stress directions, as in- dicated in Figure 7.7; it can then be shown that for the resolved shear stress 7R 1-,, = o-oosrt: cosA (7.2) where 0' is the applied stress. In general, d) + A as 90°, since it need not be the case that the tensile axis. the slip plane normal. and the slip direction all lie in the same plane. A metal single crystal has a number of different slip systems that are capable of operating. The resolved shear stress normally differs for each one because the orientation of each relative to the stress axis (46 and A angles) also differs. How- ever, one slip system is generally oriented most favorably—that is, has the largest resolved shear stress, rR(max): 73(max) = cr(cos ()5 cos A)”, (7.3) In response to an applied tensile or compressive stress. slip in a single crystal com— mences on the most favorably oriented slip system when the resolved shear stress reaches some critical value, termed the critical resolved shear stress rm; it repre- sents the minimum shear stress required to initiate slip, and is a property of the EQA ...
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