Fatigue

4 tools in the Structures area.

Notch Sensitivity

Fatigue notch factor K_f = 1 + q (K_t − 1) of a notch, hole or fillet from its elastic stress concentration factor K_t, its root radius r and the notch sensitivity q of the material. Two forms of q are evaluated: Neuber's, q = 1 / [1 + (π/(π − ω)) √(ρ′/r)] with the flank angle ω and the Neuber constant ρ′ (Kuhn and Hardrath 1952), and Peterson's, q = 1 / (1 + α/r) with the Peterson constant α (Peterson 1959). The constants come from the material and its ultimate tensile strength F_tu: for steels ρ′ is read from the NACA TN 2805 curve and α from Dowling's fit; for aluminum alloys ρ′ from the Kuhn and Figge curves (NASA TN D-1259) and α = 0.02 in; for titanium alloys α = 0.0015 in from the KAPL-3158 tests; any constant typed on the form overrides. Small notches are the point: as r shrinks q falls toward zero and K_f stays well below K_t, and an optional threshold bound K_f ≤ √(1 + d/a_0) from the notch depth d, the fatigue limit S_e and the threshold ΔK_th caps the factor for notches too small to start a crack.

Low-Cycle Fatigue

Estimates the fatigue life at a point from an elastic stress range using the Ramberg-Osgood cyclic curve, the Coffin-Manson strain-life relation and the Smith-Watson-Topper and Walker mean-stress corrections.

Spectrum Fatigue Life

Fatigue life of a part under a variable-amplitude stress history: the history is rainflow counted (ASTM E1049), every cycle's life comes from the MIL-HDBK-5J best-fit S/N equation of the chosen material and notch condition (log N = A − B log(S_eq − C) with the equivalent stress S_eq = S_max (1 − R)^p, which carries the mean-stress effect), and Miner's rule sums the damage to give the blocks and hours to failure with a scatter factor. 139 handbook equations are on the dropdown (steel, aluminum, magnesium, heat-resistant and titanium alloys, unnotched and notched), harvested from the handbook figures and filed with their figure numbers; custom constants can be typed.

2 worked examples reproduced, listed on the tool page.

Random Vibration Fatigue

Fatigue damage and life of a structure under a stationary Gaussian random vibration given as an acceleration power spectral density: the input PSD by breakpoints (log-log segments) or one of the standard profiles (NAVMAT P-9492, the NASA and USAF minimum workmanship levels of NASA-HDBK-7005, MIL-STD-810H common-carrier truck, jet-aircraft cargo and minimum-integrity exposures) with its exact rms; the response PSD of a single-degree-of-freedom structure (f_n and Q or damping ratio, or an entered transmissibility table) with the response rms by integration and by Miles' equation; the spectral moments, rates of zero crossings and peaks and the irregularity factor; the stress rms from a stress per g; and the fatigue damage of the entered duration and the time to failure by the narrow-band (Bendat) Rayleigh-peak formula, Dirlik's rainflow-range density, Steinberg's three-band method and the Wirsching–Light correction, with the S-N curve as a Basquin law or a MIL-HDBK-5J equivalent-stress equation, a fatigue damage spectrum over natural frequency and charts of the PSDs and range densities. The default case is illustrative: the NAVMAT P-9492 profile (6.06 g rms) on an SDOF at 100 Hz with Q = 10 (7.82 g rms response), 1 ksi of stress per g and the handbook's unnotched 7075-T6 sheet curve.

1 worked example reproduced, listed on the tool page.

Other Structures sections

Materials · Composites · Frames and Trusses · Beams · Loads and Dynamics · Joints · Stress and Strain · Stability · Plates and Shells · Thin-Walled Structures · Contact · Stress Concentrations · Damage Tolerance