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This paper aims to develop a viscoelastic analytical model for adhesively bonded single stepped-lap joints subjected to tensile loading. The adherends are aluminum alloy A6063 and modeled as Timoshenko elastic beams and the adhesive is epoxy type B. A three-parameter fractional viscoelastic foundation (3PFVF) model is proposed to express the governing stresses in the joint and the fractional Zener model is used to model the viscoelastic behavior of the adhesive layer. The proposed 3PFVF model makes it possible to have different peel stresses between the two interfaces of adhesive and adherends. The governing differential equations are derived in the Laplace domain, and then solved and transformed simultaneously in the time domain using the Gaver-Stehfest inverse Laplace transform method. The finite element simulation with ANSYS is applied to validate the proposed method. The results show that a simple fractional viscoelastic model, which has a short differential equation, offers the same results as the classical viscoelastic models, which have higher and more complex differential equations. Moreover, the results show that the maximum shear and peel stresses in the single stepped-lap joints are about 20% less than single-lap joints.

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