Stress and Strain
NoteStress 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.
