Note
Please refer back to A3.2 on the introduction to Young's Modulus before progressing onto this section.
Young's Modulus and Stiffness
Definition
Young's Modulus
A measure of a material’s stiffness, defined as stress divided by strain.
Note
$$\text{Young’s Modulus (E)}= \frac{\text{Tensile Strain (ε)}}{\text{Tensile Stress (σ)}}$$
- Stress (σ) = Force / Cross-sectional Area
→ Unit: Pascals (Pa) - Strain (ε) = Extension / Original Length
→ Unit: No unit (ratio)
Interpreting Stress–Strain Graphs
Stress–strain graphs show how a material behaves when pulled:
| Point on Graph | Meaning |
|---|---|
| Gradient (Linear region) | Young’s Modulus (stiffness) |
| Yield Strength | Point where the material begins to deform permanently |
| Ultimate Strength | Maximum stress the material can handle before weakening |
| Fracture Point | Where the material breaks |
Example
- Steel has a high Young’s Modulus: it resists stretching, making it ideal for bridges and high-rise buildings.
- Rubber has a low Young’s Modulus: it stretches easily, which is useful for tyres and elastic bands.
Calculating Young's Modulus: Step-by-Step
- Measure the Original Length
- Record the initial length of the material sample.
- Apply a Force
- Gradually increase the force and measure the resulting extension.
- Calculate Tensile Stress
- Use the formula: stress = cross-sectional area / force
- Calculate Tensile Strain
- Use the formula: strain = change in length / original length
- Determine Young's Modulus
- Use the formula: Young's modulus = strain / stress
Analogy
- Think of Young's Modulus like a spring constant.
- A stiff spring (high Young's Modulus) resists stretching, while a soft spring (low Young's Modulus) stretches easily.
Real-World Applications
- Construction - Steel is chosen for its high Young's Modulus, providing structural integrity.
- Aerospace - Carbon fiber is used for its high stiffness-to-weight ratio, essential for lightweight and strong components.
- Consumer Products - Plastics with a low Young's Modulus are used in flexible packaging and wearable devices.
Self review
Calculate Young's Modulus for a material with a tensile stress of 500,000 Pa and a tensile strain of 0.002.
