The big idea: Stress is the force divided by the area carrying it, so a thin bar reaches a high stress under a small force.
Strain, and why the graph matters
- Strain is how much it stretched divided by its original length, so it has no units.
- Plotting stress against strain describes the material, not the particular test piece — which is why the graph is worth learning.
Where the graph comes from: the tensile test
Pull a sample
A standard test piece is clamped and pulled slowly until it breaks.
Record two readings
The machine logs the force and the extension all the way.
Turn them into stress and strain
Stress = force ÷ cross-sectional area. Strain = extension ÷ original length.
Plot the curve
Stress against strain gives the graph below; its straight-line gradient is Young's modulus.
The curve built one landmark at a time. Every term in this statement is a point or a slope on it.
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| On the graph | What it is | What it means for a product |
|---|---|---|
| The straight line at the start | The elastic region — it springs back completely when the load is removed | Everything a product does in normal use should happen here |
| Its GRADIENT | Young's modulus, E — stress divided by strain in the elastic region | How stiff it is: how little it deflects under load |
| Where the line bends over | Yield strength — beyond it the material deforms permanently | For most products this is the real limit: a shelf that sags for ever has failed |
| The peak of the curve | Ultimate tensile strength — the greatest stress it reaches | After it the specimen necks, so the load falls while it keeps stretching |
| The end of the curve | Fracture — it breaks | How far past yield it got tells you how much WARNING you would have had |
Stiffness is a gradient. Strength is a height.: They are measured on different axes of the same graph and they are not related.
Glass is stiff and weak. Nylon is strong and floppy. Confusing them is the single commonest error in this topic, and it produces answers that recommend a stronger material for a deflection problem.
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Ductile
- A long plastic region after yield
- Stretches, necks and thins visibly before it breaks
- Absorbs a lot of energy — it is tough
- Gives WARNING: a bent part is a warning a cracked one is not
Brittle
- Almost no plastic region at all
- Fractures at or near the elastic limit
- Absorbs very little energy, however strong it is
- No warning — full load one moment, in pieces the next
Why a designer cares about the difference: An overloaded ductile part bends, somebody notices, and it is replaced.
An overloaded brittle part shatters without notice. So a ladder is aluminium, not cast iron; safety glass is laminated; and a brittle material in a safety-critical part gets a much larger safety factor.
Reading a graph you have not seen: Steep and short: stiff and brittle — glass, ceramic, cast iron.
Steep and long: stiff and ductile — mild steel, aluminium.
Shallow and long: springy and tough — rubber, nylon, polypropylene.
Words the papers ask for, and stress in a real design
Elasticity
Returns to its original shape when the load is removed (the straight start of the graph).
Plasticity
Past the yield point the change of shape is permanent: a bent coat hook stays bent. It has not broken.
Brittle
Fractures with little or no plastic deformation and often breaks into sharp pieces, like glass.
Using stress to size a part
A zip-line cable: the rider's weight ÷ the cable's cross-section is the stress. Choose a diameter that keeps it well under yield, with a safety factor.
How this is tested — describing the relationship between stress and strain, and reading a stress-strain graph. It comes up two ways:
Paper 1 — multiple choice
- Identify a landmark on a supplied stress-strain graph.
- Say what the gradient of the elastic region represents.
Paper 2 — analysing a product
- Interpret a stress-strain graph for a named material.
- Compare two materials from their curves.
The trap: Treating stiffness and strength as the same thing. Stiffness is the GRADIENT of the elastic line; strength is a HEIGHT on the stress axis. Glass is stiff and weak.
A stress-strain graph for mild steel shows a straight line to 250 MPa, a bend, a peak at 430 MPa and fracture at a strain of 0.22. Analyse what this tells a designer.
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