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Balanced 2024-T3 double-lap bonded joint: Volkersen peak, Hart-Smith elastic-plastic strength, plateau and peel

Tool	Adhesive Bonded Joint
Source	Hart-Smith, L. J. (1973). Adhesive-Bonded Double-Lap Joints. NASA Contractor Report 112235, National Aeronautics and Space Administration, Langley Research Center, Hampton, VA. Equations (22), (83), (112), (113) and the material properties of Table II (p. 80).
Level	Professional

Problem

Two 0.125 in 2024-T3 splice plates are bonded to a 0.25 in 2024-T3 plate over a 2.5 in overlap with the ductile film adhesive of NASA CR-112235 Table II (τ_p = 6 ksi, bond thickness 0.005 in, γ_p/γ_e = 20). The joint carries an ultimate tensile load of 12,000 lb/in. Find the elastic (Volkersen) peak shear stress, the elastic-plastic state of the adhesive, the adhesive shear strength at this overlap and on the long-overlap plateau, the peel stress at the ends of the splice plates and the margins of safety.

Inputs to Enter

Double lap, overlap L = 2.5 in, P = 12,000 lb/in entered as an ultimate load, no temperature change
Adherends: t_1 = 0.125 in (each outer), t_2 = 0.25 in (inner), E = 10.5 Msi, F_tu = 65 ksi, F_ty = 47 ksi, ν = 0.3
Adhesive: η = 0.005 in, G = 60 ksi, τ_p = 6 ksi (γ_e = 0.10), γ_p = 2.0, E_c′ = 500 ksi, peel strength 10 ksi
FS = 1.5, FS_yld = 1.15

Open the Adhesive Bonded Joint tool (loaded with this example)

Answers

λ = √((G/η)(1/(E_1 t_1) + 2/(E_2 t_2))) = 4.276 1/in, λL = 10.69; average stress 2.400 ksi; elastic peak (P/2)(λ/2) coth(λL/2) = 12.83 ksi; the adhesive first yields at 5,612 lb/in
Elastic-plastic state at 12,000 lb/in: plastic zones 0.2663 in at each end, elastic zone 1.9675 in, end strain 0.279 against a failure strain of 2.10, trough stress 3.0 % of τ_p
Adhesive shear strength at this overlap 30,000 lb/in (fully plastic, 2 τ_p L); plateau P = 4 √(E t) √(τ_p η (γ_e/2 + γ_p)) = 35,937 lb/in (CR-112235 eq. 22)
Design overlap P/(2 τ_p) + 2/λ = 1.468 in (eq. 112); plastic zones + 6/λ = 1.936 in (MIL-HDBK-17-3F)
Peel σ_c = τ_p (3 E_c′ (1 − ν²) t_o / (E_o η))^¼ = 8.056 ksi (eq. 83)
M.S.: adhesive shear +1.50 (ULT), peel +0.24 (ULT), adherends F_tu +0.35 (ULT), F_ty +0.28 (LIM)

Notes

The tool's default inputs are this joint; press Submit. The joint is illustrative: the adhesive and aluminum properties are those of CR-112235 Table II (with γ_e 0.10 and γ_p 2.0, η(γ_e/2 + γ_p) = 0.01025 in against the table's 0.0102 in), the geometry and load are the tool's own. The report prints no dimensional worked example; the tool reproduces its non-dimensional strength tables (Appendix A.2) in test_bonded_joint.php.