Fatigue Cracking at a Vibrating-Screen Bracket Fillet
A vibrating-screen manufacturer welds a 50 mm wide × 12 mm thick flat bracket to a support frame; the bracket carries a bearing housing on an 80 mm overhang. Field strain measurements show the vertical load on the bracket fluctuates between 0.5 kN and 2.5 kN at 24 Hz, in phase with the screen drive. The critical location is the fillet where the bracket meets the frame, where finite-element analysis gives a theoretical stress concentration factor Kt = 2.6; notch sensitivity for this steel at the service hardness is q = 0.88. The bracket is AISI 1045 hot-rolled steel with Sut = 620 MPa and Sy = 360 MPa. The machined fillet gives a surface factor ka = 0.82 and a size factor kb = 0.95. A prototype survived 3 × 10⁶ cycles on the test rig, but field units crack at the fillet within 8–14 months, roughly 6 × 10⁸ cycles. The drawing specifies a 1.0 mm fillet radius; the shop has been producing 0.6 mm radii because of tool wear.
1. Compute the fatigue factor of safety at the fillet using the Goodman criterion and state whether infinite life is predicted.
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Section modulus: Z = bt²/6 = 50 × 12²/6 = 1200 mm³. Bending moment at the fillet is F × 80 mm.
At 2.5 kN: M = 200 000 N·mm, σ = 200000/1200 = 166.7 MPa. At 0.5 kN: M = 40 000 N·mm, σ = 33.3 MPa. Nominal alternating and mean stresses: σa = (166.7 − 33.3)/2 = 66.7 MPa; σm = (166.7 + 33.3)/2 = 100.0 MPa.
Kf = 1 + q(Kt − 1) = 1 + 0.88(1.6) = 2.41. Applying Kf to both components (the conservative Shigley convention): σa = 160.5 MPa, σm = 240.8 MPa.
Endurance limit: Se = ka·kb·(0.5 Sut) = 0.82 × 0.95 × 310 = 241.5 MPa.
Goodman: 1/n = 160.5/241.5 + 240.8/620 = 0.665 + 0.388 = 1.053, so n = 0.95.
Even with the less conservative practice of applying Kf only to the alternating term, 1/n = 0.665 + 0.161 gives n = 1.21, and the Gerber criterion gives about 1.19. All three are below the 1.5–2.0 normally demanded for a high-cycle machine part, and the field record of cracking confirms the calculation. Note also that the FEA Kt = 2.6 corresponds to a 1.0 mm radius; the 0.6 mm radius actually produced has a higher Kt, so 0.95 is optimistic.
2. Compare three corrective actions - restoring the 1.0 mm fillet radius, shot peening, and switching to a 900 MPa steel - and recommend one.
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Restoring the radius: assume Kt falls to about 2.0 at r = 1.0 mm, giving Kf = 1.88 and local stresses σa = 125.4 MPa, σm = 188.0 MPa. Then 1/n = 125.4/241.5 + 188.0/620 = 0.519 + 0.303 = 0.822, so n = 1.22. Better, but barely above the non-conservative estimate for the current part; it removes the tool-wear variability but not the fundamental stress level.
Shot peening: it introduces a compressive residual of the order of −250 to −300 MPa at the surface, which offsets the mean stress. Treating the effective mean as roughly zero, 1/n = 160.5/241.5 = 0.665, giving n ≈ 1.5. Peening is cheap, but it is a process control that must be audited and cannot be applied to a welded joint after fabrication without re-validation.
Higher-strength steel: at Sut = 900 MPa, ka = 4.51 × 900⁻⁰·²⁶⁵ = 0.74, so Se = 0.74 × 0.95 × 450 = 317 MPa. Then 1/n = 160.5/317 + 240.8/900 = 0.506 + 0.268 = 0.774, so n = 1.29. This is only a marginal gain because the surface factor falls as strength rises, and weldability and cost both worsen.
Recommendation: increase the section (for example 16 mm thick, giving n ≈ 1.4 on its own) together with a controlled 1.0 mm radius, and audit the radius on current stock. Geometry buys more than metallurgy here.
3. Why is the prototype's 3 × 10⁶-cycle pass not evidence of infinite life?
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For steel, the endurance limit is established at about 10⁶–10⁷ cycles, so 3 × 10⁶ cycles sits right at the knee of the S–N curve, not beyond it. A specimen that survives a few million cycles has demonstrated nothing more than survival in the finite-life region.
Field duty is roughly 6 × 10⁸ cycles, two orders of magnitude beyond the rig test, so any slope still present in the S–N curve becomes decisive. In addition, the rig test almost certainly used nominal loading with a well-aligned fixture, whereas field units see preload from assembly, frame distortion, and the change in load sharing when a neighbouring bracket loosens. Corrosion or condensation at the fillet, and the 0.6 mm production radius with a correspondingly higher Kf, add further damage mechanisms that the rig does not reproduce.
The correct test is either a run-out at 10⁷ cycles at a stress level above the service stress with a defined margin, or a damage-tolerance approach that accepts a defined crack-growth life and sets an inspection interval. Reporting a pass at 3 × 10⁶ cycles without stating the stress level is not a fatigue qualification.