Page 52 - Mechanical Behavior of Materials

Section 2.4 Elastic Deformation and Theoretical Strength 51

Figure 2.15 Low-angle boundary in a crystal formed by an array of edge dislocations.
(From [Boyer 85] p. 2.15; used with permission.)

creep deformation. Elastic deformation is discussed next, and this leads to some rough theoretical
estimates of strength for solids.

2.4.1 Elastic Deformation
Elastic deformation is associated with stretching, but not breaking, the chemical bonds between the
atoms in a solid. If an external stress is applied to a material, the distance between the atoms changes
by a small amount that depends on the material and the details of its structure and bonding. These
distance changes, when accumulated over a piece of material of macroscopic size, are called elastic
deformations.
If the atoms in a solid were very far apart, there would be no forces between them. As the
distance x between atoms is decreased, they begin to attract one another according to the type of
bonding that applies to the particular case. This is illustrated by the upper curve in Fig. 2.16. A
repulsive force also acts that is associated with resistance to overlapping of the electron shells of
the two atoms. This repulsive force is smaller than the attractive force at relatively large distances,
but it increases more rapidly, becoming larger at short distances. The total force is thus attractive
at large distances, repulsive at short distances, and zero at one particular distance x e , which is the
equilibrium atomic spacing. This is also the point of minimum potential energy.
Elastic deformations of engineering interest usually represent only a small perturbation about
the equilibrium spacing, typically less than 1% strain. The slope of the total force curve over this
small region is approximately constant. Let us express force on a unit area basis as stress, σ = P/A,
where A is the cross-sectional area of material per atom. Also, note that strain is the ratio of the
change in x to the equilibrium distance x e .

P x − x e
σ = , ε = (2.1)
A x e