# Elastic Limit

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## What is Elastic Limit?

We know that elasticity is the ability of a body to regain its original shape after an external force is removed. However, all the bodies have a certain elastic limit up to which they remain in their original shape if they are stretched beyond this limit, their orientation changes.

So, we define elastic limit as the upper limit for deforming force up to which if deforming force is removed from the body, it comes back to its original configuration, and stretching beyond this limit can permanently change the body’s shape.

So, if the deforming force is increased, the body loses its elasticity attribute and gets permanently deformed.

### Elastic Limit

According to the experimental study done by Hooke’s in connection with the extension produced in the wire and load applied, he devised a law known by his name viz: Hooke’s law.

Hooke’s Law statement: Within the elastic limit, the extension produced in the wire is directly proportional to the load applied to it.

After some time, this law became applicable to all types of deformations viz: compression, bending and twisting, etc. In mathematical form, we can restate this law as:

Hooke’s law states that in the elastic limit, stress developed is directly proportional to the strain produced in the body. It is given by:

Stress α Strain

Now, removing the sign of proportionality, we get the equation as:

Stress = E x Strain

Here, E is proportionality constant and is called the coefficient of elasticity or the Modulus of Elasticity of the material of the body.

Also, E = $\frac{Stress}{Strain}$ = a constant

Here, the stress is the deforming force applied per unit area and strain is the deformation that occurred. Therefore, stress & strain are interlinked.

The unit of stress is Nm² and that of strain is unity (a dimensionless quantity).

### What is Elastic Limit in Physics?

As we got the stress-strain relationship in wire, now let’s understand the elastic limit in Physics.

Suspend a wire of uniform area vertically from a rigid support and on the other end, attach a hanger on which known weights can be placed.

Now, attach a vernier scale V to the wire’s lower end that can slide over the main scale M, as we can see in Fig.1 below:

Further, keep trying with different weights, place them one-by-one on the hanger, and note the reading.

After noting down the readings of extensions caused by different known weights on the wire, draw a graph. Going according to the reading, we plot the graph in the following manner:

Looking at Graph.1, till the portion OA, the Hooke’s law is fully obeyed, which means, the wire could gain its configuration. Therefore, OA is a linear region that represents the elastic limit.

As the stress doubles, the strain also doubles, we can see in Graph 2, a non-linear relationship is maintained between the stress & strain. Here, point A is considered the proportional limit.

So, what is the limit of proportionality? We define the proportional limit as the highest stress at which the stress-strain curve is a straight line.

Therefore, the difference between elastic limit and proportional limit is, elastic limit is the point at which there is no permanent deformation in a structure or the point at which the body regains its original shape, while the proportional limit is the point at which stress is directly proportional to the strain.

In Graph.1, after point A, point B indicates the limit of elastic behaviour and the beginning of the plastic behaviour, however, till point C, it regains its original shape after the applied force is removed.

At this point, the wire shows an increase in strain without any increase in stress, as the strain increases after point C, the wire begins to flow down and continues till point D. A time comes when it reaches point D, the wire becomes perfectly plastic.

Further deformation after point D, the weaker sections of the wire break, and point E is the ultimate or fracture point.

So, the difference between elastic limit and yield point is, elastic limit is the point at which the body shows complete elastic behaviour, while reaching the yield point, the body limits its elastic behaviour and initiates the plastic behaviour.

In simple words, elastic limit is the point at which the body regains its structure after removing the applied force, while yield point is the point after the permanent deformation and even after unloading, the body (wire) doesn’t gain its original shape.

### Difference Between Proportional Limit and Yield Point

Proportional limit or the limit of proportionality specifies the direct relation of stress with strain. Till this point, Hooke’s law is fully obeyed.

However, a point at which the stress remains constant, while the strain keeps on elongating the wire, a time comes when it reaches the perfectly plastic stage. Thus stage occurs at the point called the yield point.

Question 1: Which One has a Maximum Elastic Limit Rubber or Steel?

Answer: Elastic limit is the point till which the body regains its original shape after the load is removed. Elastomers like rubber have the maximum elastic limit, as per Young’s modulus of elasticity.

Question 2: What is the Difference Between Stress and Strain?