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 is how much it stretched divided by its original length, so it has no units.
Plotting one against the other describes the material, not the particular test piece — which is why the graph is worth learning.
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: A ductile part that is overloaded bends, somebody notices, and it is replaced.
A brittle part that is overloaded shatters without notice. That is why a ladder is aluminium rather than cast iron, why safety glass is laminated, and why a brittle material in a safety-critical part is designed to 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.
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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