 # Stress and Strain

You must have noticed that there are certain objects that you can stretch easily. Let’s say a rubber band. However, can you stretch an iron rod? Sound’s impossible right? Why? In this chapter, we will look at these properties of solids in greater detail. We will see how quantities like stress can help us guess the strength of solids.

Table of content

### Suggested Videos        ## Properties of Solids

### Intermolecular Force

In a solid, atoms and molecules are arranged in a way that neighbouring molecules exert a force on each other. These forces are intermolecular forces.

### Elasticity

A body regains its original configuration (length, shape or volume) after you remove the deforming forces. This is elasticity. ### Perfectly Elastic Body

A perfectly elastic body regains its original configuration immediately and completely after the removal of deforming force from it. Quartz and phosphor bronze are the examples of nearly perfectly elastic bodies.

### Plasticity

A plastic body is unable to return to its original size and shape even on removal of the deforming force.

## Stress

It is the ratio of the internal force F, produced when the substance is deformed, to the area A over which this force acts. In equilibrium, this force is equal in magnitude to the externally applied force. In other words, The SI Unit of stress is newton per square meter (Nm-2).In CGS units, stress is measured in dyne-cm-2. Dimensional formula of stress is ML-1T-2

### Types of Stress

• Normal stress: It is the restoring force per unit area perpendicular to the surface of the body.  It is of two types: tensile and compressive stress.
• (Tangential stress: When the elastic restoring force or deforming force acts parallel to the surface area, the stress is called tangential stress.

## Strain

It is the ratio of the change in size or shape to the original size or shape. It has no dimensions, it is just a number.

### Types of Strain

• Longitudinal strain: If the deforming force produces a change in length alone, the strain produced in the body is called longitudinal strain or tensile strain. It is given as: • Volumetric strain: If the deforming force produces a change in volume alone, the strain produced in the body is called volumetric strain. It is given as: • Shear strain: The angle tilt caused in the body due to tangential stress expressed is called shear strain. It is given as: The maximum stress to which the body can regain its original status on the removal of the deforming force is called the elastic limit.

## Hooke’s Law

Hooke’s law states that, within elastic limits, the ratio of stress to the corresponding strain produced is a constant. This constant is called the modulus of elasticity. Thus, ## Stress-Strain Curve

Stress-strain curves are useful to understand the tensile strength of a given material. The given figure shows a stress-strain curve of a given metal. • The curve from O to A is linear. In this region, the material obeys the Hooke’s Proportional limit law.
• In the region from A to C stress and strain are not proportional. Still, the body regains its original dimension, once we remove the load.
• Point B in the curve is the yield point or elastic limit and the corresponding stress is the yield strength of the material.
• The curve beyond B shows the region of plastic deformation.
• The point D on the curve shows the tensile strength of the material. Beyond this point, additional strain leads to fracture, in the given material.  ## Solved Example For You

Q: A and B are two steel wires and the radius of A is twice that of B, if we stretch them by the same load, then the stress on B is:

1. Four times that of A
2. Two times that of A
3. Three times that of A
4. Same

Sol: A) Since stress is inversely proportional to the area, and the area is proportional to the square of the radius, then we can write: [Strees on B]/[Stress on A] = [Radius of A]2/[Radius of B]2. Since the radius of A is = 2 times the radius of B, the ratio in the above equation will be equal to 4.

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