Name: Modulus of Elasticity
Uploaded: 2019-07-19
Duration: 8 min 54 s
Description: Why are most long bridges made of steel? Can we replace it with another material? Learn about the types of elastic modulus and use them to know the strength...

Question

Draw stress strain curve for a loaded steel wire and hence define the term permanent set, elastic limit, yield point and tensile strength.

Accepted Answer

Given below is a typical stress-strain curve for a metal.

From the graph, we can see that in the region between $O$ to $A$ , the curve is linear. The point $A$ is known as the proportionality limit. In this region, Hooke’s law is obeyed.

In the region from $A$ to $B$ , stress and strain are not proportional. Still, the body will return to its original dimension when the load is removed. The point $B$ in the curve is known as elastic limit (or yield point) and the corresponding stress is known as yield strength ( $σ_{y}$ ) of the material.

If the load is increased further, the stress developed exceeds the yield strength and strain increases rapidly even for a small change in the stress. The portion of the curve between $B$ and $D$ shows this. When the load is removed, say at some point $C$ between $B$ and $D$ , the body does not regain its original dimension. In this case, even when the stress is zero, the strain is not zero. The material is said to have a permanent set. The deformation is said to be plastic deformation. The point $D$ on the graph is the ultimate tensile strength ( $σ_{u}$ ) of the material.

Therefore, from the graph, we can define:

Permanent set:- A material is said to have a permanent set if it has a non-zero strain even if the stress associated with it is zero.

Elastic limit or yield point:- Elastic limit is defined as the maximum stress that a material can withstand before the permanent deformation. It is the highest limit of the material before plastic deformation of the material can occur. Once the stress or force is removed from the material, the material comes back to its original shape.

Tensile strength:- It is defined as the maximum stress that a material can withstand when a force is applied.

Draw stress strain curve for a loaded steel wire and hence define the term permanent set, elastic limit, yield point and tensile strength.

Important Questions on Mechanical Properties of Solids

Learn and Prepare for any exam you want !