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This lesson introduces the concepts of stress, strain, and Young's modulus at a level appropriate for AQA GCSE D&T (8552), Section 3.2.2. While detailed mathematical analysis is not required at GCSE, understanding these concepts helps you explain why materials behave differently under force and why engineers choose specific materials for specific applications.
Stress is the force applied per unit area of a material's cross-section. It measures how concentrated the force is within the material.
Formula:
Stress (sigma) = Force (F) / Cross-sectional Area (A)
Units: Pascals (Pa) or Newtons per square metre (N/m squared). In practice, stress values for engineering materials are often given in megapascals (MPa) — millions of Pascals.
Two wires made of the same material but with different thicknesses will break at different forces — the thicker wire can withstand more force because the load is spread over a larger area. However, they will break at the same stress because stress accounts for the cross-sectional area.
| Scenario | Force | Area | Stress | Outcome |
|---|---|---|---|---|
| Thin wire (1 mm squared) | 100 N | 1 mm squared | 100 MPa | Breaks |
| Thick wire (2 mm squared) | 100 N | 2 mm squared | 50 MPa | Survives |
| Thick wire (2 mm squared) | 200 N | 2 mm squared | 100 MPa | Breaks |
AQA Exam Tip: At GCSE, you are not expected to perform stress calculations, but you should understand the concept. If asked why a thicker component is stronger, explain that "the same force is spread over a larger cross-sectional area, resulting in lower stress, so the material is less likely to fail."
Strain is a measure of how much a material has deformed relative to its original dimensions. It is the ratio of extension (change in length) to original length.
Formula:
Strain (epsilon) = Extension (delta L) / Original Length (L)
Units: Strain has no units — it is a ratio. It is sometimes expressed as a percentage.
If a 1-metre-long wire stretches by 2 mm (0.002 m) under load:
Strain = 0.002 / 1.0 = 0.002 (or 0.2%)
This means the wire has stretched by 0.2% of its original length.
| Material | Typical Strain at Failure | Behaviour |
|---|---|---|
| Cast iron | Less than 0.5% | Brittle — breaks with almost no stretching |
| Mild steel | About 15-25% | Ductile — stretches significantly before breaking |
| Rubber | Up to 500%+ | Highly elastic — can stretch to several times its original length |
| Glass | Less than 0.1% | Very brittle — shatters with negligible deformation |
| Copper | About 30-40% | Very ductile — can be drawn into thin wire |
Young's modulus (also called the modulus of elasticity) measures how stiff a material is — that is, how much it resists being deformed when a force is applied.
Formula:
Young's modulus (E) = Stress / Strain
Units: Pascals (Pa) or Gigapascals (GPa).
| Material | Young's Modulus (GPa) | Stiffness Description |
|---|---|---|
| Diamond | ~1,200 | Extremely stiff |
| Steel | ~200 | Very stiff |
| Aluminium | ~70 | Moderately stiff |
| Oak (along grain) | ~12 | Moderately flexible |
| Nylon | ~2-3 | Flexible |
| Natural rubber | ~0.01-0.1 | Very flexible |
AQA Exam Tip: You do not need to memorise Young's modulus values at GCSE, but you should be able to explain what a high or low value means. "A material with a high Young's modulus is stiff and resists deformation; a material with a low Young's modulus is flexible and deforms more easily under the same force."
These three quantities are interconnected and describe the full picture of how a material responds to force:
A stress-strain graph plots stress on the y-axis and strain on the x-axis:
Understanding stress, strain, and stiffness helps designers make informed decisions:
| Design Scenario | Required Property | Material Choice |
|---|---|---|
| Aircraft wing spar | High stiffness, low weight | Aluminium alloy or CFRP (high Young's modulus, low density) |
| Climbing rope | High tensile strength, some stretch to absorb falls | Nylon (good strength with low Young's modulus allowing energy absorption) |
| Bridge support columns | High compressive strength and stiffness | Reinforced concrete (high compressive strength, high Young's modulus) |
| Phone case | Moderate stiffness with some flexibility to absorb impacts | TPU or silicone (low to moderate Young's modulus) |
| Cutting tool blade | Very high hardness and stiffness | High-speed steel or tungsten carbide (very high Young's modulus and hardness) |
Real-world example: The Airbus A350 uses approximately 53% carbon fibre reinforced polymer (CFRP) by weight. CFRP has a Young's modulus comparable to aluminium but is about 40% lighter. This stiffness-to-weight advantage reduces fuel consumption and carbon emissions.
| Term | Definition | Key Point |
|---|---|---|
| Stress | Force per unit area | Measured in Pa or MPa |
| Strain | Extension divided by original length | Dimensionless ratio (no units) |
| Young's modulus | Stress divided by strain | Measures stiffness; units are Pa or GPa |
| Stiffness | Resistance to deformation | High Young's modulus = stiff |
| Strength | Maximum stress before failure | Not the same as stiffness |
| Elastic limit | Point beyond which deformation becomes permanent | Below this, deformation is elastic (reversible) |
AQA Exam Tip: Do not confuse stiffness and strength. A material can be stiff but not strong (e.g. glass — very stiff but brittle and breaks at relatively low stress). A material can be strong but not stiff (e.g. nylon rope — high tensile strength but stretches significantly under load). The exam may test this distinction.
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