A two-layer beam model with interlayer slip based on two-dimensional elasticity

The objective of this paper is the computation of the Airy stress function of a two-layer composite beam with interlayer slip. For the calculation of the upper and lower layer stress functions an iterative solution procedure from Boley-Tolins is adapted, which was originally introduced for isotropic single layer beams under plane stress assumptions. Considering the continuity equations for the interface stress, for the vertical deflection and a linear law between the interlayer slip and the shear stress, Boley-Tolins' method may be extended to derive an ordinary differential equation for the slip. The order of the ordinary differential equation depends on the number of iterations and the desired accuracy, ranging from an elementary, second order ordinary differential equation for the slip to a more refined, fourth order ordinary differential equation for the slip. Finally the derived slip models are compared by considering a thick simply-supported two-layer beam subjected to a sinusoidal transverse load. The results from the iterative approaches are compared to two-dimensional results under plane stress assumptions for two limit cases: a perfectly bonded beam and a composite beam without bonding. It is found that the refined higher order slip model almost coincides with the elasticity solution, even for very thick composite beams, whereas the elementary slip model only yields accurate results for a thin beam.