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7.8  Strengthening by Grain Size Reduction  •  229

                                                                Figure 7.13  For a single crystal subjected to
                                                           Twin  a shear stress t, (a) deformation by slip;
                                                          planes
                                                                (b) deformation by twinning.
              Slip
              planes
                                                         Twin




                       (a)                       (b)

              Mechanisms of Strengthening in Metals


                                 Metallurgical and materials engineers are often called on to design alloys having high
                                 strengths yet some ductility and toughness; typically, ductility is sacrificed when an alloy
                                 is strengthened. Several hardening techniques are at the disposal of an engineer, and
                                 frequently alloy selection depends on the capacity of a material to be tailored with the
                                 mechanical characteristics required for a particular application.
                                    Important to the understanding of strengthening mechanisms is the relation be-
                                 tween dislocation motion and mechanical behavior of metals. Because macroscopic
                                 plastic deformation corresponds to the motion of large numbers of dislocations, the abil-
                                 ity of a metal to deform plastically depends on the ability of dislocations to move. Because
                                 hardness and strength (both yield and tensile) are related to the ease with which plastic
                                 deformation can be made to occur, by reducing the mobility of dislocations, the me-
                                 chanical strength may be enhanced—that is, greater mechanical forces are required to
                                 initiate plastic deformation. In contrast, the more unconstrained the dislocation motion,
                                 the greater is the facility with which a metal may deform, and the softer and weaker it
                  Tutorial Video:  becomes. Virtually all strengthening techniques rely on this simple principle: Restricting
                Defects in Metals  or hindering dislocation motion renders a material harder and stronger.
                   How do Defects   The present discussion is confined to strengthening mechanisms for single-
                    Affect Metals?  phase metals by grain size reduction, solid-solution alloying, and strain hardening.
                                 Deformation and strengthening of multiphase alloys are more complicated, involving
                                 concepts beyond the scope of the present discussion; Chapter 10 and Section 11.9 treat
                                 techniques that are used to strengthen multiphase alloys.


              7.8  STRENGTHENING BY GRAIN SIZE REDUCTION
                                 The size of the grains, or average grain diameter, in a polycrystalline metal influences
                                 the mechanical properties. Adjacent grains normally have different crystallographic
                                 orientations and, of course, a common grain boundary, as indicated in Figure 7.14.
                                 During plastic deformation, slip or dislocation motion must take place across this com-
                                 mon 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.  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.
                                  2.  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
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