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Materials Engineering DISCUSSION
A bracket made from steel with a yield strength of 350 MPa and a tensile strength of 600 MPa supports a vibrating pump. The calculated nominal stress in the bracket cycles between 30 and 270 MPa, so it never reaches yield, but after about three months a crack started at a bolt hole and the bracket broke.
The static calculation shows a safety factor above 1.2. How should this have been checked for fatigue, and why did the crack start at the hole?
Static strength says nothing about repeated loading. Under cyclic stress, a crack can start and grow at stresses well below yield, and what matters is the stress range and the number of cycles. Split your loading into a mean and an alternating part: mean = (270 + 30) / 2 = 150 MPa, amplitude = (270 - 30) / 2 = 120 MPa.
The cycle count is large even for a slow machine. A pump vibrating at 25 Hz accumulates 25 × 3600 × 24 = 2.16 million cycles per day, so ten million cycles pass in under five days. Three months puts this firmly in the high-cycle regime, where the part must sit below its endurance limit to survive.
A first estimate of the endurance limit for steel is about half the tensile strength for a polished laboratory specimen, so 300 MPa here. A real part is lower: surface finish, size, loading type and reliability factors commonly bring it down to 50 to 70 percent of that. Take 0.6 × 300 = 180 MPa as a working value.
Then allow for mean stress with the Goodman relation: σ_a / S_e + σ_m / S_ut = 1 / n. With your numbers, 120 / 180 + 150 / 600 = 0.67 + 0.25 = 0.92, so n = 1.09. On nominal stress the bracket is only just inside the line, before the hole is even considered.
The hole is why it started there. A round hole in a plate under tension raises the local stress by a theoretical factor K_t of about 3 at the edge of the hole. In fatigue the effective factor is K_f = 1 + q × (K_t - 1), where q is the notch sensitivity, typically 0.7 to 0.9 for steels with holes of normal size. With q = 0.8, K_f = 2.6.
Apply it to the alternating stress: 120 × 2.6 = 312 MPa at the hole edge against an endurance limit near 180 MPa. That is far above it, so finite life is expected, and a few months of vibration is consistent.
Fixes, roughly in order of effect. Reduce the alternating stress: stiffen the bracket, add a gusset, or deal with the vibration at its source with better balance or isolation mounts. Move holes and welds out of the highly stressed region, because both are crack starters. Make sure the bolts are properly preloaded; a joint that slips or a loose bolt puts the full load cycle through the hole edge and adds fretting.
A higher-strength steel helps less than people expect. The plain-specimen endurance limit rises with tensile strength, but notch sensitivity rises as well, and welded details in particular have about the same fatigue strength whatever the steel grade.
For loads that vary in amplitude, count the cycles at each stress level and sum the damage with Miner's rule: Σ(n_i / N_i), with failure predicted when the sum reaches 1. N_i is the life at that stress level from the S-N curve of the material or the detail category in a fatigue design code. The rule ignores the order of loading and real results scatter widely around 1, so codes apply extra factors.
The broken part itself is evidence. A fatigue fracture shows a smooth region with beach marks spreading from the origin and a rougher final-fracture zone. A small final zone means the nominal stress was low and the crack grew for a long time; a large one points to high stress.
