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 σ max and τ max 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 σ max and τ max 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 (σ max and τ max 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.