chapter 9

Topics: Elasticity, Hooke's law, Tensile strength Pages: 16 (890 words) Published: August 18, 2014


Elasticity of Solids

Deformation: Changes in shape or size of an object through the application of external forces. Elasticity: Property which allows a material to regain its shape after being distorted. Elastic Limit: The maximum amounts by which an object or a material can be stretched and still regain its original shape after the distorting forces are removed. An object or a material which returns to its original length or size after being distorted suffers elastic deformation, i.e. it behaves within the elastic limit. Plastic deformation occurs when a material is deformed beyond its elastic limit.

Stress and Strain

The elastic properties of solids are discussed in terms of stress and strain. Stress, s is the force acting on a unit cross-section area.

Stress,

The unit of stress is N m-2 or Pascal (Pa)

There are three types of stress, they are:

(i) Tensile stress

(ii) Compressive stress

(iii) Shear stress

Strain, e is defined as the extension per unit length.

Strain,

Where = extension/elongation
= original length

There are two types of strain, they are:

(i) Tensile strain =

=

(ii) Compressive strain =
=

Strain is the ratio of the change in length to the original length, therefore it is a dimensionless quantity or it has no unit.

Force and Elongation

When a wire is being stretched, an elongation will occur. During this process, the attractive force between the atoms will increase (up to a point) and this will prevents the elongation process from occurring.

When the wire is being compressed, the compression process will be prevented by the force of repulsion which pushes the atoms away from each other.

The relationship between the force and elongation can be represented by a graph. The relationship between stress and strain can be represented by the same graph as force and elongation.

Consider, a wire is being stretched. By referring to the above stress-strain graph, some of the important features are as follows :-

Stress is proportional to strain up to the limit of proportionality, P. The gradient of the line OP is equal to the Young modulus. This follows the Hooke’s Law which stated:

For many objects the force F required to maintain an extension e, is directly proportional to the extension,

F µ e leading to F = ke

Where k is a constant which depends on the type of material.

The elastic limit, E, beyond which the wire becomes permanently stretched, where plastic deformation has occurred.

The yield point, Y is the point where at a certain stress the strain begins to increase rapidly with increasing stress.

The ultimate tensile strength (UTS) of the wire is the stress at which it breaks.

Ductile metals (e.g. copper) undergo a great deal of plastic deformation before they break.

Rubber is a polymer which has two striking mechanical properties, they are :

Its range of elasticity is great.
Its value of the Young modulus is about 104 times smaller than most solids and increases as the temperature rises.

Its stress-strain graph is a little bit different compared to a metal graph. Its stress-strain graph for unloading lies beneath its loading. This can be shown in the graph below.

The stress-strain graph for rubber does not obey the Hooke’s Law because there is no straight line (constant gradient) in the hysteresis loop.

The stress-strain graph for a loading-unloading cycle forms a closed loop called...
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