Regularization of torsional stresses in tubular lap bonded joints by means of functionally graded adhesives

This paper describes the analytical stress analysis of a tubular single lap joint under torsion with a functionally graded modulus adhesive (FGA). The adhesive technology offers several advantages in structural applications, such as bonding dissimilar materials, but suffers from severe stress concentrations in the bondline which often act as a trigger for fracture phenomena. To overcome these problems, FGA with nanoparticles distributed inside the polymer can be used, as proposed recently in technical literature. The aim of the work is to retrieve which is the optimal stiffness of the adhesive layer to regularize the stresses. The peculiar geometry analyzed permits a straightforward analytical approach since pure torsion on tubes do not cause any bending and no Poisson's effect creates peel stress in the adhesive, therefore only shear stress are to be considered. The work first develops the equations which govern the shear stress distribution in the adhesive and then by forcing the shear stress to be constant is able to find out which is the stiffness profile along the bondline. The axial distribution of the stiffness of the FGA layer along the overlap is provided and the dependence on the elasto-geometrical parameters is discussed. The findings of the paper can be used to tailor the reinforcement distribution, under the hypothesis of a continuously changing adhesive stiffness.