Illustrative: Thermal Fatigue from Cyclic Temperature Gradients
How repeated thermal cycling produced fatigue cracking at a constraint location — the interaction of thermal expansion, structural constraint and cyclic stress.
Case type
Illustrative engineering case. This case demonstrates thermal fatigue — a well-documented mechanism in high-temperature equipment and thermally constrained structures.
1. The system or structure
A steel exhaust manifold bolted rigidly to a cylinder head. The manifold experiences temperature cycling from ambient to approximately 600°C during engine operation. The bolts are rigid, preventing thermal expansion of the manifold.
2. What failed?
Cracks appeared in the manifold flange after approximately 5,000 thermal cycles. The cracks initiated at the bolt holes and propagated radially outward.
3. Operating and load environment
Each engine start-up and shut-down produces a thermal cycle: the manifold heats from ambient to 600°C, then cools back. The rigid bolting prevents free thermal expansion, generating compressive stress at temperature and tensile residual stress on cooling.
4. Failure location
The cracks initiated at the bolt holes in the manifold flange — the locations of maximum constraint and stress concentration.
5. Physical failure mechanism
The mechanism is thermal fatigue — cyclic stress generated by constrained thermal expansion.
- Thermal expansion: ΔL = α × L × ΔT. For steel, α ≈ 12×10⁻⁶/°C. A 580°C temperature rise produces a strain of approximately 0.7%
- Constraint: rigid bolting prevents expansion. The thermal strain converts to compressive stress at temperature: σ = E × α × ΔT ≈ 200,000 × 0.007 = 1,400 MPa — well above yield
- Plastic compression: at temperature, the manifold yields in compression. On cooling, it is left in tension — a residual tensile stress near yield
- Cyclic stress: each cycle produces a stress range from near-yield tension to near-yield compression at the constraint — a low-cycle fatigue regime
- Stress concentration at bolt holes: Kt ≈ 3 elevates the local stress, accelerating crack initiation
6. Why did it happen?
- Physical cause: low-cycle thermal fatigue from constrained expansion at the bolt holes
- Contributing factor: rigid bolting provided no compliance for thermal expansion
- Contributing factor: bolt holes created stress concentrations at the point of maximum thermal stress
- Contributing factor: no thermal fatigue analysis was performed — the design assumed static thermal stress only
9. Engineering lessons
- Thermal cycling with constraint produces fatigue loading — it is not a static stress problem
- Compliance (flexible joints, bellows, or compliant fasteners) reduces thermal stress by allowing expansion
- Stress concentrations at constraint points are thermal fatigue initiation sites
- Low-cycle fatigue from thermal cycling requires strain-life (Coffin-Manson) analysis, not S-N methods