Peak Shear Stress in a Bonded Lap Joint (Volkersen)

A bonded joint that fails at half the predicted load was almost always sized on average stress: divide the load by the bonded area and compare with the adhesive shear strength. The adhesive, though, does not work uniformly along the overlap. The adherends stretch unevenly, load piles up at both ends and the middle stays nearly unloaded. This calculator returns the peak stress at the ends from the Volkersen model, the number that actually drives the design, and shows how far it sits above the average.

Three steps. Average stress is τ_avg = F/(b·L). The dimensionless parameter λ = L·√(2·G_a/(E·t·t_a)) weighs adhesive shear stiffness against adherend axial stiffness. The peak follows from τ_max = τ_avg·(λ/2)·coth(λ/2). With the defaults — 5000 N, a 25 by 25 mm joint, 2 mm aluminium adherends at 70000 MPa, a 0.2 mm adhesive layer at 1000 MPa — the average reads 8.000 MPa, λ works out to 6.682, coth(3.341) to 1.0025 and the peak climbs to 26.793 MPa, 3.35 times the average. Check the limiting case: drop G_a to 0.000001 MPa, the adhesive turns too soft to sustain a gradient, the factor tends to 1 and the page prints exactly 8.000 MPa.

The model sees shear only. In a real single lap the load path runs eccentric, the joint rotates under load and peel stress appears at the ends — usually what starts the failure, and what Goland-Reissner models, not Volkersen. The formulation here assumes a balanced joint, both adherends of the same material and thickness; the factor 2 inside λ follows from that. It also assumes a linear elastic adhesive up to rupture, whereas a ductile adhesive yields at the ends and redistributes load, so the elastic peak overstates real severity by a wide margin. Edge fillets and residual thermal stress sit outside. Treat the number as a way to rank design options, never as an allowable stress.