2D Crack-Tip Stress Field: Paris Law & Wheeler Retardation

A fatigue crack doesn't just get longer — the elastic stress field surrounding its tip has a very specific, well-known shape (the Williams/Irwin asymptotic solution), and it's that field's magnitude, expressed as the stress-intensity factor K, that actually drives the Paris-law growth rate da/dN = C(ΔK)^m. This simulator computes that 2D near-tip field directly on a grid around the moving crack tip every frame — the von-Mises heatmap you see, capped at the material's yield stress, is the real elastic solution, and where it saturates traces out the true angle-dependent plastic-zone shape rather than a simplified circle. The crack grows cycle by cycle under the same Paris law and Wheeler (1972) overload-retardation model as the 3D version, but here you can watch its signature directly on a log-log da/dN vs ΔK plot: steady growth is a straight line of slope m, and firing an overload cycle visibly knocks the live point below that line until the tip re-grows through the oversized plastic zone the overload left behind. Switch between steel, aluminum and titanium, tune the load and overload severity, and see how the Wheeler exponent changes the shape of the dip.