Fatigue Test Rig

The test rig

A servo-hydraulic frame pushes and pulls the specimen with a piston while a load cell under the crosshead measures the force; the controller on the left shows load, stress and cycle count. Piston travel is exaggerated about 50x so you can see the cycle. The amber glow is the crack tip, and the beacon turns amber while a crack grows and flashes red at fracture.

Why metal breaks below its strength

A load that is far too small to break a part once can break it after many repetitions. Fatigue has two stages: initiation of a tiny crack at the surface or at a stress concentrator, then propagation of that crack a little more on every cycle until the remaining ligament can no longer carry the load.

Stage 1: Basquin S-N life

sigma_a = sigma_f' (2N)^b gives the cycles N to initiate a crack for a fully reversed stress amplitude sigma_a. Mean stress is handled with the Smith-Watson-Topper parameter sigma_eq = sqrt(sigma_max sigma_a), which makes tension harmful and compression helpful. Notches act through the fatigue notch factor Kf = 1 + q (Kt - 1) with Peterson sensitivity q = 1/(1 + a_n/r), and rough surfaces through a knock-down ks. Steels have a knee near 10⁶-10⁷ cycles below which the model reports run-out; aluminium and titanium do not, so run-out is declared at 10⁹ cycles. Damage is summed linearly with Miner's rule, D = N/N_init.

Stage 2: Paris crack growth

da/dN = C (Delta K)^m with Delta K = Y Delta sigma sqrt(pi a). Only the tensile part of the cycle opens the crack, so Delta sigma = sigma_max - max(sigma_min, 0). The geometry factor for a single edge crack in a finite-width plate is the Tada polynomial Y(x) = 1.12 - 0.231x + 10.55x^2 - 21.72x^3 + 30.39x^4, x = a/W. Below the threshold Delta K_th a crack arrests. Final fracture happens when K_max = Y sigma_max sqrt(pi a) reaches the fracture toughness K_Ic or when the net-section stress sigma_max W/(W - a) reaches the flow stress, whichever comes first. For constant Y and m != 2 the life has the closed form N = (a_c^(1-m/2) - a_0^(1-m/2)) / (C (1 - m/2) (Y Delta sigma sqrt(pi))^m).

What is simplified

Material constants are typical handbook values, not certified data. Plasticity at the crack tip, load-sequence effects, the R-ratio dependence of the threshold, corrosion fatigue and the scatter of real S-N data (a factor of 2-10 in life) are not modelled. Low-cycle behaviour above yield uses the elastic Basquin line and is only indicative. Visual stretch of the specimen is exaggerated. Educational model, not for design.

What to try

• Load the Infinite life preset, then raise the amplitude by 20 %: life drops by orders of magnitude (the slope of the S-N curve is only about b = -0.08).
• Add a notch (Kt 2) or a corroded surface and watch the equivalent stress point move up the S-N curve.
• Compare tensile and compressive mean stress at the same amplitude.
• Open the fracture surface: each ring is the crack front after 7 % growth, so the rings crowd together early and spread out late as da/dN accelerates.