A centre-cracked metal plate is pulled and relaxed again and again. Each cycle the crack grows a tiny step by the Paris law; the stress at the tips rises until the plate fractures. Constants are typical textbook-range values for teaching, not design data.
Runs the full crack-growth march for 12 stress ranges and compares it with the quadrature of the same law and with the closed form for an infinite plate. The log-log slope should be close to -m.
Press the button.
The science
Stress intensity. For a through-crack of half-length a in a wide plate under remote stress σ, K = Y σ √(πa). For a finite plate of width W (centre crack) the Feddersen secant factor Y = √sec(πa/W) is used (textbook check: Y = 1.189 at a/W = 0.25). Valid for a/W below about 0.45.
Cycle loading. The stress ratio is R = σmin/σmax; the range is Δσ = σmax(1-R) and ΔK = Y Δσ √(πa). The slider sets Δσ and R; the peak stress follows.
Paris law. da/dN = C (ΔK)m in the middle ("Region II") of the growth curve; below a threshold ΔKth cracks do not grow (run-out). The optional Forman-type law multiplies by Kc/(Kc - ΔK) with Kc = (1-R)KIC so growth accelerates as Kmax approaches the toughness. Units here: MPa, m, MPa√m, m/cycle.
Life. N = ∫ da / (C ΔKm). For an infinite plate (Y = 1) and m ≠ 2 it has the closed form N = [af1-m/2 - a01-m/2] / (C (1-m/2) (Δσ√π)m), used here as an independent check of the numerical march. Because m is about 3, life scales roughly as Δσ-m: a 10 % higher stress range cuts life by roughly a quarter.
End of life. The crack stops being stable at the first of: Kmax = KIC (fast fracture, ac = (KIC/(Yσmax))2/π when Y = 1), net-section yield σmax W/(W-2a) = σy (plastic collapse; tough steels), or the width limit a/W = 0.45.
Stress field. The colour overlay is the Westergaard solution for a crack in an infinite sheet, σyy/σ, drawn for the current crack length; it ignores the plate edges and plasticity. The plastic-zone radius shown is Irwin's plane-stress estimate rp = (Kmax/σy)2/(2π).
What is simplified. Constant-amplitude loading, no crack closure, no environment, no short-crack or threshold R-dependence, plane stress, a single material constant set per alloy (real scatter is a factor of 2-10 in life). The crack opening in the 3D view is exaggerated about 60x, the load cycle is shown at a slow visual rate, and the time-lapse integrator grows the crack by a fixed small fraction per step, so the cycle counter runs faster early in life. Material constants are typical values, to be spot-checked against a handbook before any real use. Not an engineering design tool.
Test frame and plate built in Blender and rendered with Three.js. Educational model.