Mechanical Properties & Testing
Stress, strain and Young's modulus; the tensile test, hardness, ductility and toughness; fatigue and creep.
Mechanical properties & testing, summary notes
- 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'.
- Stress
- σ = F / A (Pa = N/m²)
- Strain
- ε = ΔL / L (dimensionless)
- Young's modulus
- E = σ / ε (stiffness, elastic region)
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.
Stress, strain & the tensile test
Properties & testing concept map
Mechanical Properties & Testing
Mechanical properties quiz
Mechanical Properties & Testing, quiz
1. On the stress against strain curve shown, the point beyond which the material will not return to its original length is:
QPS2. On the curve shown, the ultimate tensile strength of the material is at point:
RQS3. A steel bar of 200 mm² cross-section fails at a load of 90 kN. Its ultimate tensile strength is:
450 MPa45 MPa180 MPa4. A 2 m aluminium rod is heated through 100 K. Taking the coefficient of linear expansion as 23 × 10⁻⁶ per K, it expands by:
4.6 mm0.46 mm46 mm5. A tensile load of 20 kN is carried by a bar of cross-sectional area 100 mm². The stress is:
200 MPa20 MPa2000 MPa6. A bar 500 mm long stretches by 0.5 mm under load. The strain is:
0.0010.0110007. A material is stressed to 200 MPa and the resulting strain is 0.001. Its modulus of elasticity is:
200 GPa200 MPa0.2 GPa8. A material has an ultimate tensile strength of 400 MPa and is working at 100 MPa. The factor of safety is:
40.25300