Four-parameter fractional thermo-viscoelastic model to stress analysis of single stepped-lap adhesive joints of FGM adherends

Abstract

This paper develops an analytical framework to investigate the thermo-viscoelastic stress distribution in adhesively bonded single stepped-lap (SSL) joints with functionally graded (FG) adherends subjected to tensile loading. The adhesive layer (AL) is modeled by the fractional Zener formulation within a four-parameter fractional thermo-viscoelastic framework, capturing its linear viscoelastic behavior. The FG adherends, consisting of nickel–aluminum oxide (Ni–Al₂O₃), are described using Timoshenko beam theory. Governing differential equations are derived from constitutive, equilibrium, and compatibility conditions at the reference temperature and subsequently extended to arbitrary temperatures through thermoelastic relations for the adherends and the time–temperature superposition principle for the adhesive. These equations are solved in the Laplace domain and inverted to the time domain using the Gaver–Stehfest algorithm. The proposed model provides a time- and temperature-dependent prediction of axial, shear, and peel stresses at any point within the adhesive layer or interfaces. Validation against finite element simulations in ANSYS Workbench demonstrates excellent agreement. Results reveal that temperature variations strongly influence the stress field, while elevated temperatures significantly accelerate the relaxation and stabilization of reduced stress components.