Page 65 - Manufacturing Engineering and Technology - Kalpakjian, Serope : Schmid, Steven R.

Chapter 1 The Structure of Metals

l.4 Deformation and Strength of Single Crystals

When a single crystal is subjected to an external force, it first undergoes elastic
deformation; that is, it returns to its original shape when the force is removed. A sim-
ple analogy to this type of behavior is a helical spring that stretches when loaded and
returns to its original shape when the load is removed. If the force on the crystal struc-
ture is increased sufficiently, the crystal undergoes plastic deformation or permanent
deformation; that is, it does not return to its original shape when the force is removed.
There are two basic mechanisms by which plastic deformation takes place in
crystal structures. One is the slipping of one plane of atoms over an adjacent plane
(called the slip plane) under a shear stress (Fig. 1.5a). Note that this behavior is
much like the sliding of playing cards against each other. Shear stress is defined as
the ratio of the applied shearing force to the cross-sectional area being sheared.
just as it takes a certain magnitude of force to slide playing cards against each
other, a single crystal requires a certain amount of shear stress (called critical shear stress)
to undergo permanent deformation. Thus, there must be a shear stress of sufficient mag-
nitude within a crystal for plastic deformation to occur; otherwise the deformation
remains elastic.
The shear stress required to cause slip in single crystals is directly proportional
to the ratio I9/a in Fig. 1.5a, where a is the spacing of the atomic planes and I9 is
inversely proportional to the atomic density in the atomic plane. As b/a decreases, the
shear stress required to cause slip decreases. Thus, slip in a single crystal takes place
along planes of maximum atomic density; in other words, slip takes place in closely
packed planes and in closely packed directions.
Because the 19/a ratio varies for different directions within the crystal, a single
crystal exhibits different properties when tested in different directions; this property
is called anisotropy. A simple example of anisotropy is the behavior of woven cloth,

which stretches differently when pulled in different directions. Another example is

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FIGURE l.5 Permanent deformation of a single crystal under a tensile load. The highlighted
grid of atoms emphasizes the motion that occurs within the lattice. (a) Deformation by slip. The
b/a ratio influences the magnitude of the shear stress required to cause slip. (b) Deformation by
twinning, involving the generation of a “twin” around a line of symmetry subjected to shear.
Note that the tensile load results in a shear stress in the plane illustrated.