Strengthening by Grain Size Reduction

Because the two grains are of different orientations, a dislocation passing into grain B must change its direction of motion this becomes more difficult as the crystallographic misorientation increases. 

The atomic disorder within a grain boundary region results in a discontinuity 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 

Figore 7.14 The motion of a dislocation as it encounters a grain bonndary, illustrating how the botmdary acts as a barrier to continued shp. Slip planes are discontinnons and change directions across the boundary. (From L. H. Van Vlack, A Textbook of Materials Technology, Addison-Wesley Publishing Co., 1973. Reproduced with the permission of the Estate of Lawrence H. Van Vlack.) 

Hall-Petch equation— dependence of yield strength on grain size 

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In summary, we have discussed the three mechanisms that may be used to strengthen and harden single-phase metal alloys strengthening by grain size reduction, solid-solution strengthening, and strain hardening. Of course, they may be used in conjunction with one another for example, a solid-solution strengthened alloy may also be strain hardened. 

It should also be noted that the strengthening effects due to grain size reduction and strain hardening can be eliminated or at least reduced by an elevated-temperature heat treatment (Sections 7.12 and 7.13). In contrast, solid-solution strengthening is unaffected by heat treatment. 

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