Energy release rate of symmetric adhesive joints

Abstract A formula is derived for the mixed mode energy release rate of adhesive joints in terms of local stress concentrations σmax and τmax determined by beam theory. The formula G= 1 2 t E′ a σ 2 max 1 2 t G a τ 2 max is equivalent to a similar expression from two-dimensional elasticity theory in terms of the stress intensity factors K I and K II . The equivalence permits explicit determination of the two stress intensity factors K I and K II in terms of the finite stress concentrations σmax and τmax determined by technical beam theory. The reinterpretation of the stress concentration from beam theory in terms of stress intensity factors enables the use of simple beam-type calculations for fracture predictions without the need for a detailed three-dimensional analysis. While the stress concentrations (σmax and τmax increase with decreasing thickness t of the adhesive layer, the energy release rate ℷ is nearly independent of t . The centrally loaded symmetric lap joint is analysed in detail and explicit results for the mixed mode energy release rate ℷ and the corresponding load phase angle Ψ = tan −1 (K II /K I ) are given. For long joints Ψ = 49° , independent of adhesive properties, increasing for shorter joints.