Fatigue Life Calculator

Fatigue is the accumulation of localized damage under repeated loading at stresses far below yield, and it accounts for most in-service failures of moving machinery. Stress-life analysis characterizes it with an S-N curve of alternating stress against cycles to failure on logarithmic axes. Wrought steels show a knee near 10^6 to 10^7 cycles below which the curve flattens into an endurance limit, conventionally about 0.5 times ultimate tensile strength and capped near 700 MPa for very high strength grades; aluminium and most non-ferrous alloys have no true limit, so infinite-life design is unavailable. Laboratory data come from polished rotating-bend specimens, so Marin factors scale them to reality: roughly 0.7 to 0.9 for machined surfaces, 0.7 to 0.9 for size on shafts larger than the 7.6 mm test bar, and about 0.814 to move from median survival to 99 percent reliability. Two corrections complete the picture. Tensile mean stress holds cracks open and shortens life; the Goodman line Sa/Se + Sm/Su = 1 handles this conservatively, the parabolic Gerber relation fits ductile-metal data more closely, and Soderberg substitutes yield for ultimate strength. Variable-amplitude histories are summed by the Palmgren-Miner rule, D = sum of ni/Nfi, with failure at D = 1. The limitations are serious: Miner's rule ignores load sequence, and experiments show failure anywhere from D near 0.7 to over 2. Life is dominated by crack initiation at notches, welds and surface defects, and scatter of a factor of three in cycles at one stress level is normal even for identical specimens.

Fatigue entered engineering through railway accidents. Repeated fractures of apparently sound wrought-iron axles prompted W. J. M. Rankine's 1843 paper to the Institution of Civil Engineers on unexpected axle breakage, and the systematic answer came from August Wohler, an engineer with the Royal Prussian railways, whose rotating-bend tests from the late 1850s through the 1860s established that failure depended on the range of stress rather than its peak, producing the stress-life plot that still carries his name. Gerber proposed his parabolic mean-stress correction in 1874, and the linear alternative is associated with John Goodman's textbook Mechanics Applied to Engineering. The toolkit assembled steadily thereafter. O. H. Basquin published the power-law relation between stress amplitude and cycles in 1910. Arvid Palmgren introduced linear damage summation in 1924 while working on ball-bearing life at SKF, and M. A. Miner independently formalized it in a 1945 Journal of Applied Mechanics paper written at Douglas Aircraft, which is why the rule carries both names. C. R. Soderberg advanced the yield-based conservative criterion around 1930, and Joseph Marin systematized the surface, size, reliability and temperature correction factors in his mid-century work. The field acquired urgency after the de Havilland Comet disasters of 1954, whose investigation traced pressure-cabin cracking to stress concentrations at cutouts, pushing aerospace toward damage-tolerant design based on crack growth rather than stress-life alone.