Introduction

 

Any body deforms under external stresses, i.e. changes in size and shape. When the action of force stops and the body restores its shape and size the deformation is called elastic. Under plastic deformation shape and size of a body is not restored when external stresses is eliminated.

Elastic deformation occurs when external force that creates this deformation doesn’t extend a certain limit which is called elastic limit. Under the effect of applied loading only insignificant change in the distances between atoms ore crystal clusters turning occurs. When stretching the distance between the crystal atoms grows and this distance decreases when compressing. For this case the balance of attraction and repulsion forces is violated, that is why the displaced atoms in the result of the action of attraction or repulsion forcers return to the initial state of equilibrium, and the crystals regain their original size and shape.

Let us apply external force F to the rigid rod fixed at one end (fig. 6.1). Let the initial length l increased by Δ l. The ratio of the force to the cross section area - S is called the mechanical stress:

. (6.1)

For a cylinder specimen (wire) of the diameter the cross section aria is:

(6.2)

and the mechanical stress is:

. (6.3)

 

 

The value:

(6.4)

is called relative deformation that is the ratio of absolute lengthening to initial length .

 

Figure 6.1

 

The experiment proves that linear dependency occurs between σ; and ε; in elastic deformation area. In fig.6.2 OA region is the elastic deformation area where Hook’s Law is true:

(6.5)

In the AB region a plastic deformation takes place, i.e. in the case when residual deformations ε_r originates as soon as external forces stop acting upon. Stress is called limit of elasticity of the material.

Figure 6.2

 

Relation (6.5) proves Hook’s Law, where E is elasticity module or Yung module that characterizes the elastic properties of a material. Yung module is equal to mechanical stress at which the rod length is doubled. The value of Yung’s modulus basically is determined by the type of crystal lattice, i.e. by the forces of atomic bonds.

The value of Yung’s modulus for some materials is shown in the table 6.1.

 

Table 6.1

№	Material	Е × 109, Pа
	Steel	195 ÷206
	Cast iron
	Ті
	Сu
	Ag
	Al
	Mg
	Glass	49 ÷ 78
	Plastic	1.7 ÷ 1.9