Parameters
Applied load P5000 N
Joint width w25.0 mm
Overlap length L50.0 mm
Adherend modulus E₁70 GPa
Adherend thickness t₁2.0 mm
Adherend modulus E₂70 GPa
Adherend thickness t₂2.0 mm
Adhesive shear modulus Ga1.5 GPa
Adhesive thickness ta0.20 mm
Allowable shear τ_allow25 MPa
Volkersen Model
$$\tau(x) = \frac{P\kappa}{2w}\cdot\frac{\cosh(\kappa x)}{\sinh(\kappa L/2)}$$ $$\kappa = \sqrt{\frac{G_a}{t_a}\!\left(\frac{1}{E_1 t_1}+\frac{1}{E_2 t_2}\right)}$$Mean shear: $\bar{\tau} = P/(wL)$
Stress concentration: $K = \tau_{max}/\bar{\tau}$
0.0 MPa
Peak τ (end)
0.0 MPa
Mean τ
0.00
Stress Conc. K
0.00
Safety Factor
Shear Stress Distribution (Volkersen)
Overlap Length vs Peak Shear Stress
Hart-Smith Elastic-Plastic Model
Adhesive treated as elastic-perfectly plastic: elastic for $\tau \leq \tau_y$, plastic flow for $\tau > \tau_y$.
Failure load estimate: $P_f = w\!\left[2\tau_y\sqrt{\dfrac{2G_a t_a \gamma_p}{1/E_1t_1+1/E_2t_2}} + \tau_y L_{el}\right]$
Peel stress (linear elastic approx.): $\sigma_p(x) \approx \dfrac{6M(x)}{t_a^2}$
Engineering note: Structural epoxy adhesives: Ga ≈ 1–2 GPa, τ_y ≈ 25–40 MPa, failure strain ≈ 0.5–5%. Aerospace bonded joints designed per Hart-Smith method (FAA AC 20-107B). Automotive body panels: typical overlap/thickness ratio = 10–30.