Fatigue Life
Fatigue life is the number of stress cycles that a material or component can endure at a given stress amplitude before fracture or failure occurs due to progressive crack initiation and propagation under cyclic loading. It is a critical design parameter for components subjected to repeated loading such as shafts, aircraft wings, and turbine blades. The S-N (Wöhler) curve relates the stress amplitude (S) to the number of cycles to failure (N) for a given material.
Key Formula
S^b × N = C
LaTeX: S^b \cdot N = C
| Symbol | Meaning | Unit |
|---|---|---|
| S | Stress amplitude | MPa |
| N | Number of cycles to failure | cycles |
| b | Basquin exponent (material constant) | dimensionless |
| C | Material constant from S-N curve | MPa^b·cycles |
Worked Example
Problem
An aluminium alloy has a fatigue strength of 200 MPa at 10⁶ cycles and 150 MPa at 10⁷ cycles. A component is subjected to a stress amplitude of 175 MPa. Using Basquin's law, estimate the fatigue life.
Solution
Step 1: Find exponent b: log(S1/S2) / log(N2/N1) = log(200/150) / log(10⁷/10⁶) = log(1.333) / log(10) = 0.1249 / 1 = 0.1249. So b = −1/0.1249 ≈ −8.0 (note: conventional Basquin uses negative b). Step 2: Find C using data point: C = S^b × N = 200⁸ × 10⁶ (using positive b formulation S^b × N = C where b ≈ 8). Step 3: For S = 175 MPa: N = C / S^b = (200^8 × 10⁶) / 175^8 = 10⁶ × (200/175)^8 = 10⁶ × (1.143)^8 ≈ 10⁶ × 2.99 ≈ 3.0 × 10⁶.
Answer
Fatigue life N ≈ 3.0 × 10⁶ cycles at 175 MPa
Fatigue Life (S-N) Data for Common Engineering Materials
| Material | UTS (MPa) | Endurance Limit (MPa) | Typical N at Endurance Limit |
|---|---|---|---|
| Mild steel (AISI 1020) | 395 | 200 | 10⁶ cycles |
| Stainless steel 316 | 580 | 230 | 10⁷ cycles |
| Aluminium 7075-T6 | 572 | 160 (no true limit) | 5 × 10⁸ cycles |
| Titanium Ti-6Al-4V | 950 | 620 | 10⁷ cycles |
| Carbon fibre (CFRP) | 600 | No true limit | Design dependent |
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Related Terms
Fracture Toughness
Fracture toughness is a material property that quantifies a material's resistance to crack propagation and catastrophic brittle fracture when subjected to stress. Denoted K_Ic for plane-strain mode I (opening mode) fracture, it has units of MPa·√m and represents the critical stress intensity factor at which a crack begins to propagate unstably. High fracture toughness is essential in safety-critical structural applications such as pressure vessels, aircraft fuselages, and pipelines, where the presence of flaws must not lead to sudden failure.
Composite Material
A composite material is an engineered material made from two or more constituent materials with significantly different physical or chemical properties, which remain distinct at the macroscopic level within the finished structure. The resulting composite typically exhibits superior performance characteristics — such as high strength-to-weight ratio, corrosion resistance, and tailored stiffness — compared to either constituent alone. Common composites include carbon fibre reinforced polymers (CFRP), glass fibre reinforced polymers (GFRP), and metal matrix composites (MMC).
Mechanical Vibration
Mechanical vibration is the oscillatory motion of a mechanical system about an equilibrium position, arising from elastic restoring forces and inertia. It occurs in structures, machines, and vehicles and can be free (natural), forced, or self-excited in nature. Understanding and controlling vibration is critical to prevent fatigue failure, noise generation, and resonance-induced catastrophic damage in engineering systems.
From Latin "fatigare" meaning "to tire or exhaust". The term "metal fatigue" was introduced by German engineer August Wöhler in the 1860s after his systematic study of railway axle failures under cyclic loading.