Elastic and Plastic Behaviour of Materials
When a force is applied to a material, it deforms. This deformation can be either elastic or plastic.
Elastic Deformation
Elastic deformation is a temporary deformation where the material returns to its original shape and size once the force is removed. This occurs when the force applied is less than the material’s elastic limit. The elastic limit, typically slightly beyond the limit of proportionality, is the maximum force that can be applied while still allowing the material to return to its original dimensions.
Think of a rubber band—you can stretch it, and it snaps back to its original shape when you let go. This is elastic deformation.
Plastic Deformation
Plastic deformation, on the other hand, is a permanent deformation where the material does not return to its original shape and size even after the force is removed. This happens when the applied force exceeds the elastic limit.
An example of this is bending a metal paperclip. Once bent past a certain point, it remains deformed even after you remove the force.
Graphical Representation
The sources provide a graph (Figure 6.5) illustrating the force-extension behavior of a wire, highlighting key points:
- Elastic limit (E): The point beyond which the material transitions from elastic to plastic deformation.
- Permanent extension (B): The residual deformation that remains after the force is removed, characteristic of plastic deformation.
Energy Involved in Deformation
The energy involved in deformation is stored as potential energy within the material. In the case of elastic deformation, this stored energy is called elastic potential energy, also known as strain energy. All the elastic potential energy is recovered when the force is removed, as the material returns to its original shape and size.
For a spring deformed within its limit of proportionality, the elastic potential energy (Ep) is calculated using the following equations:
- $$E_p = \frac{1}{2}Fe$$
- $$E_p = \frac{1}{2}ke^2$$
Where:
- F is the force applied to the spring
- e is the extension of the spring
- k is the spring constant
Work Done During Deformation
The work done in deforming a material is represented by the area under the force-extension graph. This holds true for both elastic and plastic deformations:
- In elastic deformation, the work done is completely recovered as elastic potential energy when the force is removed.
- In plastic deformation, some energy is dissipated as heat and is not recovered.