Elastic Strain Energy

ELASTIC STRAIN ENERGY

The dislocation lines have distortional energy associated with them since there are compressive and tensile strains around and shear strains around the edge dislocations dislocations. The elastic strain energy U per unit length of the dislocation line is given by

where μ is the shear modulus of the material and b is the length of the Burgers vector.

Larger the Burgers vector, larger is the strain energy. For a full dislocation, the Burgers vector is

where r is the lattice vector and n is any integer number.

The dislocation has a tendency to have smallest Burgers vector and hence least strain energy increases. There can be partial dislocation also, if the Burgers vector is a fraction of a lattice translation.

Note: In general, elastic energy per unit volume of elastic material is given by

Deformation of Metals

• When metals or alloys are stressed (i.e., subject to load), they get deformed.

• Deformation is the change in dimension of matter under the action of applied forces.

The deformation may be completely temporary that is elastic deformation. It disappears after the deforming load is removed

• The permanent deformation may also occur that is plastic deformation which remains even after the removal of the deforming load.

Elastic deformation

If a metal is loaded, a temporary deformation of the crystals takes place through displacement of the atoms.

As the deforming load is removed, the atoms return to their original position and the crystal recovers its original shape (Fig.1.45).

Plastic deformation

• Plastic deformation follows elastic deformation

• If the deforming load is such that the stresses in the metal piece cross the elastic limit, the specimen gets plastically deformed.

If the deforming load at this stage is removed, the metal piece does not regain its original shape; ie., a permanent set (plastic strain) is always retained (Fig.1.46).

Plastic deformation depends on the following factors

• Applied stress

• Temperature

• Strain rate

Plastic deformation is accompanied by changes in both the internal and external state and it is not reversible.

• Permanent deformation produces distortion of the crystal and microstructures.

It is intentionally carried out as in working and shaping processes such as bending, stamping, drawing, spinning, rolling, forging, extruding, etc.

• It is also carried out in order to improve some of the mechanical properties of metals and alloys.