Stress analysis of adhesively-bonded single stepped-lap joints with functionally graded adherends based on the four-parameter fractional viscoelastic model

Abstract

This paper presents a viscoelastic stress analysis of adhesively-bonded single stepped-lap joints under tension with functionally graded adherends. This analysis is based on the four-parameter fractional viscoelastic model and is considered the shear, peel, and axial stress components in the adhesive layer. The adhesive layer is assumed to exhibit a linear viscoelastic behavior, which is modeled using the fractional Zener model. The adherends is made of functionally graded Al2O3–Ni and are modeled using Timoshenko beam theory. The governing differential equations of the joint are derived in terms of the internal forces and moments in the Laplace domain using the structural, equilibrium, and compatibility equations of the adhesive layer and adherends. The governing equations are solved simultaneously and transformed from the Laplace domain into the time domain via the numerical inverse Laplace method. The results are compared to finite element results obtained from ANSYS Workbench, and a good agreement is observed. The results indicate that the axial stress in the adhesive layer is remarkable compared to the peel and shear stresses and must be considered in studies. Moreover, the variation in stress along the adhesive layer's thickness at both sides of the overlap region is significant.