Material Fatigue
Material fatigue is the progressive and localised structural damage that occurs in a material subjected to repeated cyclic loading, even when the peak stress is well below the material's static yield or ultimate strength. Fatigue cracks typically initiate at stress concentrations such as notches, holes, or surface defects, and propagate incrementally with each load cycle until sudden fracture occurs. It is responsible for the majority of mechanical failures in practice, including failures in aircraft, bridges, shafts, and biomedical implants.
Worked Example
Problem
A steel shaft experiences a fully reversed cyclic bending stress of amplitude 200 MPa. Given that the endurance limit of the steel is 280 MPa and the stress concentration factor Kf = 1.6, determine whether the shaft will survive indefinitely.
Solution
Step 1: Calculate the effective stress amplitude accounting for stress concentration. σ_eff = Kf × σ_a = 1.6 × 200 MPa = 320 MPa Step 2: Compare with endurance limit. σ_eff = 320 MPa > Endurance limit = 280 MPa Step 3: Conclusion. Because the effective stress amplitude exceeds the endurance limit, the shaft will eventually fail by fatigue.
Answer
The shaft will NOT survive indefinitely; fatigue failure is predicted.
Fatigue Life Terminology and Key Concepts
| Term | Symbol / Unit | Definition | Significance |
|---|---|---|---|
| Stress amplitude | σ_a (MPa) | Half the range of cyclic stress | Drives crack initiation |
| Mean stress | σ_m (MPa) | Average of max and min stress | Shifts S-N curve (Goodman) |
| Endurance limit | S_e (MPa) | Stress below which infinite life is predicted | Design target for steel |
| S-N curve | Wöhler curve | Plot of stress amplitude vs cycles to failure | Characterises fatigue life |
| Stress concentration | Kt / Kf | Local stress amplification at notches/holes | Primary crack initiator |
| Fatigue life | N (cycles) | Cycles to failure at given stress amplitude | Design life parameter |
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Related Terms
Material Hardness
Material hardness is the resistance of a material's surface to permanent plastic deformation, typically measured by pressing a standardised indenter into the surface under a controlled load and measuring the size or depth of the resulting indentation. It is a surface property that correlates with wear resistance, machinability, and (for steels) approximate tensile strength. Common hardness scales include Vickers (HV), Brinell (HB), and Rockwell (HR), each suited to different materials and applications.
Brittleness
Brittleness is a material property characterised by the tendency to fracture suddenly under stress with little or no prior plastic (permanent) deformation, typically showing less than 2–5% elongation at fracture in a tensile test. Brittle materials store elastic energy and release it catastrophically at fracture, giving virtually no warning of impending failure. Materials such as cast iron, glass, ceramics, and concrete exhibit brittle behaviour, and engineering designs using them must account for the absence of ductile redistribution of stress.
Engineering Stress
Engineering stress is defined as the applied force divided by the original cross-sectional area of a specimen, regardless of any deformation that occurs during loading. It is the conventional measure used in materials testing and structural analysis because the original dimensions are easily measured before the test begins. Engineering stress is widely used in design calculations, material data sheets, and stress-strain curves to characterise material behaviour under uniaxial loading.
The term "fatigue" was introduced by Jean-Victor Poncelet in 1839, borrowed from French/Latin "fatigare" (to weary or tire), describing how materials progressively weaken under repeated loading. August Wöhler conducted systematic fatigue testing on railway axles in the 1860s, producing the foundational S-N curves.