Elastic and plastic behaviour

When a force is applied to a solid material, it changes shape (deforms). The way a material responds to force depends on its elastic and plastic behaviour.

Elastic Deformation

• Elastic deformation occurs when a material returns to its original shape after the deforming force is removed.
• This happens because the atoms or molecules are displaced from their equilibrium positions but return when the force is gone.
• The deformation is reversible.

Plastic Deformation

• Plastic deformation occurs when a material does not return to its original shape after the force is removed.
• The material is permanently deformed because the atomic structure has been altered.
• The deformation is irreversible.

Elastic Limit

• The elastic limit is the maximum force (or stress) that can be applied to a material without causing permanent deformation.
• If the force exceeds the elastic limit, the material will undergo plastic deformation.

Force–Extension Graph

• A force–extension graph plots the applied force (vertical axis) against the extension (horizontal axis) of a material.
• The initial straight-line portion obeys Hooke’s law (force is proportional to extension).
• The area under the force–extension graph represents the work done on the material.

Work Done and Elastic Potential Energy

• The work done to stretch a material (within its elastic limit) is stored as elastic potential energy.
• For a material obeying Hooke’s law, the force–extension graph is a straight line, and the area under the line (a triangle) gives the elastic potential energy.

Summary

• Elastic deformation is reversible; plastic deformation is permanent.
• The elastic limit is the maximum stress/force for reversible deformation.
• The area under a force–extension graph gives the work done on the material.
• For materials obeying Hooke’s law, use $E_p = \frac{1}{2} F x = \frac{1}{2} k x^2$ to calculate elastic potential energy.