Elastic and Plastic Behaviour

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Understand and use the terms elastic deformation, plastic deformation, and elastic limit
  2. Understand that the area under the force-extension graph represents the work done
  3. Determine the elastic potential energy of a material deformed within its limit of proportionality from the area under the force-extension graph
  4. Recall and use EP = ½Fx = ½kx² for a material deformed within its limit of proportionality

Main Content

https://cambridgeassistant.com

1. Understanding Deformation: Elastic vs Plastic

When you apply a force to a material (like stretching a spring or pulling a wire), the material changes shape. This change in shape is called deformation. There are two main types of deformation:

Elastic Deformation

Elastic deformation occurs when a material stretches or compresses, but returns to its original shape when you remove the force.

  • Think of a spring: when you pull it and then let go, it bounces back to its original length
  • The material "remembers" its original shape
  • Example: A rubber band stretched gently will return to its original size when released

Plastic Deformation

Plastic deformation occurs when a material is stretched or compressed so much that it does not return to its original shape when you remove the force.

  • The material has been permanently changed
  • It stays deformed even after the force is removed
  • Example: If you bend a paper clip too far, it stays bent even when you stop applying force

The Elastic Limit

The elastic limit is the maximum amount you can stretch or compress a material while it still behaves elastically (i.e., still returns to its original shape).

  • Below the elastic limit: The material shows elastic behaviour and springs back to its original shape
  • Beyond the elastic limit: The material shows plastic behaviour and stays permanently deformed

Think of it as a point of no return. Once you cross this point, the material won't fully recover its original shape.

The Limit of Proportionality

There's another important point called the limit of proportionality. This is the point up to which the force and extension are directly proportional to each other (meaning they follow a straight-line relationship).

  • Below this limit, Hooke's Law applies: Force = k × extension (where k is the spring constant)
  • The limit of proportionality usually comes just before the elastic limit
  • They are very close together but not exactly the same point

Sign in to view full notes