Elastic Limit

The elastic limit is the greatest stress or force per unit area that can occur within a solid material before permanent deformation. The material returns to its original size and shape when forces up to the elastic limit are removed. When a material is stressed beyond its elastic limit, it yields or flows. For such materials, the elastic limit signifies the transition from elastic to plastic behaviour. Stresses that exceed the elastic limit in most brittle materials result in fracture with little or no plastic deformation.

In principle, the elastic limit differs from the proportional limit, which denotes the end of the type of elastic behaviour described by Hooke’s law, namely, that in which the stress is proportional to the strain (relative deformation) or, alternatively, that in which the load is proportional to the displacement. For some elastic materials, the elastic limit roughly coincides with the proportional limit, making the two difficult to differentiate at times; nevertheless, for other materials, a zone of non proportional elasticity occurs between the two. The proportionate limit is the point at which linearly elastic behaviour comes to a halt.

Stress and Strain

When a thing is deformed by an external force, it creates an equal and opposite restorative force within itself. Stress is defined as the force divided by the area of the unit.

Stress = ForceArea

The newton per metre square (N/m2) or pascal (Pa) is the SI unit of stress. 

The dimensions of a strained object vary. Strain is calculated by dividing the changes in dimension by the original dimension. The strain is categorised as longitudinal, shearing, or volumetric strain depending on the type of change.

Longitudinal Strain = Change in length Original length

Shearing Strain → Change in displacement Original length

Volume Strain → Change in  volumeOriginal volume

There are no units or dimensional formula for strain.

Elastic and Plastic Deformation

When an object reverts to its original shape when an external force is removed, it is said to have undergone elastic deformation. The elastic deformation, on the other hand, develops into plastic deformation when the external force is significant. Plastic deformation, unlike elastic deformation, results in a permanent change in the object’s dimensions.

 Stress-Strain Relationship

A graph can be used to depict the relationship between stress and strain. The graph below depicts a typical representation of a metal’s stress-strain relationship. The stress-strain graph will differ depending on the material. Several conclusions can be derived from this graph:

• The graph’s region O to A is linear. The Hooke’s law is followed here.

• The graph is non-linear from point A to point B, indicating that stress is no longer proportional to strain. The metal, on the other hand, returns to its former shape at this point.

• The elastic limit, often known as the yield point, is located at point B. The Yield Strength of the material is the associated stress at this point.

• Even though there is a slight change in stress, the strain in the metal grows fast in the region from B to D.

• The region of elastic deformation on the graph is where Hooke’s law is observed.

• Even if the force is removed at point C, the metal still deforms, and this deformation is plastic.

• The ultimate tensile strength of the material is represented by point D on the graph. Even if only a small amount of force is exerted beyond this point, the metal breaks at point E.

• The material is said to be fragile when the distance between points D and E is tiny. The material is said to be ductile when the space between these two sites is significant. 

Limit of Proportionality

The highest potential applied stress at which stress and strain are directly proportional is the limit of proportionality. The stress-strain graph is a straight line inside the proportional limit, and Hooke’s law applies.

Yield Point

Plastic deformation occurs when a material is stressed beyond its elastic limit. The Yield point of a material is the point at which it transitions from elastic to plastic deformation.

Difference Between Elastic Limit & Proportional Limit

• The elastic limit differs from the proportional limit in that the elastic limit is the maximum pressure that may be given to a material without it deforming. The proportional limit of a material is defined as the point at which stress and strain are directly proportional to one another. 

• Another important distinction is that in the elastic limit, the stress and strain have a linear relationship, whereas in the proportional limit, the relationship between the stress and strain does not matter.

Difference Between Elastic Limit & Yield Point

The main distinction between the elastic limit and the yield point is that the yield point denotes the end of the elasticity, whereas the elastic limit denotes the beginning of the elasticity. The elastic limit of a solid material is the highest stress that can be applied before the solid body begins to deform permanently. Engineers invented the yield point to designate the point of permanent deformation defined by bond rupture for engineering purposes.

Difference Between Proportional Limit and Yield Point

The proportional limit, also known as the limit of proportionality, defines the direct relationship between stress and strain. Hooke’s law has been strictly followed up to this point.

However, there comes a point where the stress remains constant while the strain continues to lengthen the wire, and the wire enters the perfectly plastic state. The yield point is where this step takes place.

Real life Examples of Elastic Limit

1. Rubber is regarded as one of the most pliable materials.

2. Glass is more elastic than steel and other materials.

3. A nail bends permanently when subjected to the shear stress of a hammer strike, indicating that it has hit its elastic limit.

4. Quartz and copper, as well as Phosphorus, are almost plastic bodies.

5. The bodies of paraffin wax and dirt are regarded to be fully plastic.

Conclusion

The ability of a body to restore its previous shape after an external force has been eliminated is known as elasticity. All bodies, however, have an elastic limit within which they may maintain their original shape. Their orientation shifts if they are stretched past this limit.

As a result, we define the elastic limit as the top limit for deforming force beyond which the body returns to its original configuration when the deforming force is released, and stretching beyond this limit can permanently modify the body’s shape.

The elastic limit of a material is the greatest value of force or stress at which it begins to exhibit elastic behaviour. It is the highest limit before the plastic substance deforms. When a material reaches its elastic limit, it begins to deform when more stress or force is applied to it. When stress is applied to brittle materials beyond their elastic limitations, the consequence is a fracture.

As a result, increasing the deforming force causes the body to lose its flexibility and become permanently misshapen.