The stress amplitude below which a material effectively no longer fails under cyclic loading. It often appears at around 10⁶–10⁷ cycles in carbon steels but is not distinct in aluminum alloys.
Japanese name: 疲労限度
Fatigue limit appears in 2 practice questions across 2 topics, including Fracture mechanics and fatigue, Mechanical properties and fracture.
The S–N curve is a log–log plot of the number of cycles to failure under repeated loading at various stress amplitudes. For carbon and low-alloy steels, the curve becomes nearly horizontal from around 10⁶ to 10⁷ cycles, and below that stress amplitude the material effectively does not fail. The stress amplitude of this horizontal part is the fatigue limit, often given as the fully reversed value from a rotating-bending test. Aluminum and copper alloys show no clear horizontal part, so they are evaluated instead by the fatigue strength at a set number of cycles, such as 10⁷.
There is an empirical guideline that the rotating-bending fatigue limit of steel, for smooth polished specimens, is roughly half the tensile strength. For high-strength steels above about 1400 MPa in tensile strength, however, internal defects such as inclusions become crack origins, so raising strength no longer raises the fatigue limit much. Proportionality to hardness is also used as a guideline, but all of these are statistical trends that also vary with material lot and microstructure. In actual part design, test data or standard values are used and corrected for the size and surface effects described next.
Even for the same material, the fatigue limit is lowered by surface roughness, part size, notches, tensile mean stress and corrosive environments. For notches, the correction uses not the stress concentration factor itself but the fatigue notch factor, which includes the material's notch sensitivity. In corrosive environments, pits keep forming on the surface, so no fatigue limit appears. In the very-high-cycle range beyond 10⁸ cycles, failure can start from internal inclusions and leave a pattern called a fish-eye on the fracture surface, so the fatigue limit is not an absolute limit.
In infinite-life design, the fatigue limit of specimens is multiplied by factors for surface, size, reliability and so on to estimate the value for the part, and mean stress is corrected with a Goodman diagram or similar. Most fatigue cracks start at the surface, so treatments that introduce compressive residual stress at the surface are effective. Examples include shot peening, carburizing, nitriding and induction hardening; polishing the surface to reduce scratches and reducing inclusions in steel also raise the fatigue limit. Welded joints have much lower fatigue strength than the base metal because of the weld toe shape and residual stress, so they are handled by separate design standards.
Answer: B. About 225 MPa
σm/σB = 200/800 = 0.25, so σa = 300×(1 − 0.25) = 225 MPa. A tensile mean stress acts to open cracks, so the allowable stress amplitude is smaller than the fully reversed value (σm = 0). The modified Goodman diagram is a conservative guide that joins σw on the vertical axis and σB on the horizontal axis with a straight line. About 281 MPa is the value from the parabolic Gerber relation, which squares the mean stress ratio, 300×(1 − 0.25²), and is a less conservative estimate than Goodman. About 100 MPa divides by σw instead of σB. A compressive mean stress often works in favor of fatigue resistance, but designs usually do not take credit for that effect.
Fatigue strength is the stress amplitude that causes failure at a set number of cycles (such as 10⁷), also called the fatigue strength at N cycles. The fatigue limit is the stress amplitude below which failure effectively does not occur, used for materials such as steel whose S–N curve has a horizontal part.
Many specimens are tested in rotating-bending or axial fatigue tests at various stress amplitudes, their cycles to failure are measured, and the limit is found from the horizontal part of the S–N curve. Statistical methods such as the staircase method, which raises or lowers the stress one step at a time, may be used to estimate the mean and scatter.
For materials such as aluminum alloys that have no horizontal part, use the fatigue strength at the number of cycles the product will experience during its life. If the stress amplitude varies, damage is summed with Miner's rule to estimate life.
For carbon and low-alloy steels, the S-N curve often flattens out at around 10⁶–10⁷ cycles, showing a fatigue limit below which failure becomes unlikely.
Which statement about fatigue S-N curves is correct?Modified Goodman diagram 0.2% offset yield strength Creep Fracture toughness Young's modulus