Enhanced elastic-foundation analysis of balanced single lap adhesive joints

Abstract Conventional single-lap adhesive joints between identical adherends achieve ultimate strength only after significant inelastic deformation of the adhesive and perhaps also the adherends. However purely elastic analysis provides insights and is relevant to fatigue initiation or brittle failure. We extend classical beam-based elastic results, both ‘within the bond’ (deriving more-accurate peak peel stress from the joint-edge moment) and ‘beyond the bond’ (determining the edge moment from adherend dimensions, remote boundary conditions, and load). Within the bond, we show that peak adhesive equivalent stress and principal stress are minimized when the bond length exceeds four characteristic lengths of the elastic-foundation shear stress equation. This makes simplified ‘long’ joint formulas attractive for initial design. We then examine how well the long-joint predicted peak peel stress matches plane strain finite element analysis, and empirically capture a peel-stress end effect due to nonzero adhesive Poisson ratio. With this end-effect correction, the limit of useful accuracy can be expressed as a ratio R a of (adherend axial stiffness) to (adhesive axial stiffness) being > a number of order 10 2 - 10 3 depending on Poisson ratio. This limit supplements the Goland and Reissner proposed applicability limit for elastic foundation analysis, expressed as a limiting ratio R v of through-thickness or vertical stiffnesses. Outside the bond, Timoshenko-style beam-column expressions are used to derive a simplified joint-edge moment factor. While similar in spirit to the edge-moment determination of Goland and Reissner for infinite-length pinned adherends, treating the bond region as a rigid block leads to simpler nonlinear expressions, and captures the moment-reducing benefits of shorter (finite-length) adherends and fixed-slope end conditions. Joint rotation effects become dominant when T L 2 > E I ( L is adherend free length, T is tensile load), then joint rotation magnitude depends on T D 2 / E I ( D is lap length).