Stress, strain and Young's modulus; the tensile test, hardness, ductility and toughness; fatigue and creep.
Notes
Mechanical properties & testing — summary notes
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Main ideas
Stress is force per unit area (σ = F/A, in pascals); strain is the fractional change in length (ε = ΔL/L, dimensionless). In the elastic region their ratio is Young's modulus E = σ/ε, a measure of stiffness — not strength.
Loading a metal: it deforms elastically (returns to shape) up to the elastic limit / yield point; beyond that it deforms plastically (permanent). The ultimate tensile strength (UTS) is the highest stress it carries before necking and fracture.
Key properties: ductility (drawn into wire, high % elongation), malleability (rolled/hammered into sheet), toughness (energy absorbed before fracture — the Izod/Charpy impact test), hardness (resistance to indentation — Brinell/Rockwell/Vickers) and brittleness (fractures with little plastic warning).
Fatigue is failure under repeated cyclic loading at stresses well BELOW the static UTS; most in-service structural failures are fatigue, starting at a stress raiser — a hole, scratch, sharp corner or corrosion pit.
Creep is slow permanent stretching under a sustained load at high temperature (turbine discs and blades), and is a life-limiting mechanism for hot engine parts.
⚠ Exam trap: yield/elastic limit is NOT the same as UTS, and a strong material (high UTS) can still be brittle (low toughness). Because fatigue fails below the static strength, a part can break after many cycles at a load that looked 'safe'.
Key formulas
Stress
σ = F / A (Pa = N/m²)
Strain
ε = ΔL / L (dimensionless)
Young's modulus
E = σ / ε (stiffness, elastic region)
Solved examples
A control rod repeatedly sees a load far below its rated tensile strength, yet cracks after a few thousand flights. What is the mechanism, and where would the crack start?
This is fatigue — cyclic loading below the static UTS. The crack initiates at a stress raiser such as a fastener hole, a machining mark or a corrosion pit, then propagates a little on each cycle until the remaining section fails. It is why edges are deburred, holes are smooth, and life limits and inspections exist.