Stress and Strain
Stress and strain are fundamental concepts that describe how materials respond to external forces.
Stress
Stress
A force applied to a material divided by its cross-sectional area. Measured in Pascals (Pa).
Formula:
Stress = Force ÷ Area
$$σ = \frac{F}{A}$$
- σ = stress (in Pascals, Pa)
- F = force applied (in Newtons, N)
- A = cross-sectional area (in square metres, m²)
Strain
Strain
The change in length of a material divided by its original length, caused by stress.
Formula:
Strain = Change in Length ÷ Original Length
$$ε = \frac{ΔL}{ L}$$
- ε = strain (no units – it's a ratio)
- ΔL = change in length (in metres, m)
- L = original length (in metres, m)
Strain is a ratio, meaning it has no units. It simply describes how much a material has stretched or compressed.
The Stress-Strain Relationship
Stress-strain graph
A visual representation of how a material responds to a load.
- Elastic deformation: The material returns to its original shape when the force is removed.
- Plastic deformation: The material is permanently stretched or bent and does not return to its original shape.
Key Points on a Stress-Strain Graph
1. Young's Modulus
Young's Modulus
A measure of a material’s stiffness, defined as stress divided by strain.
A steeper slope indicates a stiffer material, while a gentler slope indicates a more flexible material.
2. Yield Strength
Yield Strength
The maximum stress a material can handle before plastic deformation begins.
Beyond this point, the material will not return to its original shape when the load is removed.
3. Ultimate Strength
Ultimate Strength
The maximum stress a material can withstand before breaking.
This point represents the peak of the stress-strain curve.
Ultimate strength is often used to determine the safety limits of a material.
4. Fracture Point
Fracture Point
The point where a material breaks after reaching its stress and strain limits, beyond elastic and plastic deformation.
Fracture occurs after the material has undergone significant plastic deformation.
Material Failure: Understanding the Limits
When materials are pushed beyond their limits, they fail in different ways:
- Brittle Failure – Snaps suddenly with no stretch. Examples: glass, ceramics
- Ductile Failure – Stretches and deforms before breaking. Examples: steel, aluminium
- Fatigue Failure – Cracks from repeated stress over time. Examples: plane wings, bridges, bike frames
