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Materials Science and Engineering: An Introduction

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Unformatted text preview: Hall-Fetch equation— dependence of yield strength on grain size REVISED PAGES 7.8 Strengthening by Grain Size Reduction - 189 across this common boundary—say, from grain A to grain B in Figure 7.14. The grain boundary acts as a barrier to dislocation motion for two reasons: 1. Since the two grains are of different orientations, a dislocation passing into grain B will have to change its direction of motion; this becomes more diffi- cult as the crystallographic misorientation increases. 2. The atomic disorder within a grain boundary region will result in a disconti- nuity of slip planes from one grain into the other. It should be mentioned that. for high-angle grain boundaries, it may not be the case that dislocations traverse grain boundaries during deformation; rather, dislocations tend to “pile up" (or back up) at grain boundaries. These pile-ups introduce stress concentrations ahead of their slip planes, which generate new dislocations in adja- cent grains A fine-grained material (one that has small grains) is harder and stronger than one that is coarse grained, since the former has a greater total grain boundary area to impede dislocation motion. For many materials, the yield strength cry varies with grain size according to a), : .70 + mm (7.7) In this expression, termed the Hall-Perch equation, of is the average grain diameter, and 0-” and ky are constants for a particular material. Note that Equation 7.7 is not valid for both very large (i.e., coarse) grain and extremely fine grain polycrystalline materials. Figure 7.15 demonstrates the yield strength dependence on grain size for a brass alloy. Grain size may be regulated by the rate of solidification from the liq- uid phase, and also by plastic deformation followed by an appropriate heat treat- ment, as discussed in Section 7.13. It should also be mentioned that grain size reduction improves not only strength, but also the toughness of many alloys. Small-angle grain boundaries (Section 4.6) are not effective in interfering with the slip process because of the slight crystallographic misalignment across the boundary. On the other hand. twin boundaries (Section 4.6) will effectively block Grain size. of (mm) Figure 7.15 rIhe influence of grain size on the yield strength of 30 a 70 {Zn—30 Zn brass alloy. Note that the grain diameter increases from right to left and is not linear. (Adapted from H. Suzuki, 150 a— ' “The Relation Between the Structure and Mechanical Properties of Metals,” Vol. II, National Physical Laboratory, Symposium No. 15, 1963, p. 524.) 10*1 10*? 5 x 10*3 200 M C) Yield strength tksi) IUD Yield strength tMPa} H D 50 0 | i | n 4 s 12 15 d—lt2 (mm-IQ, EQA ...
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