Thermal Stress Formation in a Functionally Graded Al2O3-Adhesive Single Lap Joint Subjected to a Uniform Temperature Field

Abstract

This study investigates the strain and stress states in an aluminum single lap joint bonded with a functionally graded Al2O3 micro particle reinforced adhesive layer subjected to a uniform temperature field. Navier equations of elasticity theory were designated by considering the spatial derivatives of Lamé constants and the coefficient of thermal expansion for local material composition. The set of partial differential equations and mechanical boundary conditions for a two-dimensional model was reduced to a set of linear equations by means of the central finite difference approximation at each grid point of a discretized joint. The through-thickness Al2O3-adhesive composition was tailored by the functional grading concept, and the mechanical and thermal properties of local adhesive composition were predicted by Mori–Tanaka’s homogenization approach. The adherend–adhesive interfaces exhibited sharp discontinuous thermal stresses, whereas the discontinuous nature of thermal strains along bi-material interfaces can be moderated by the gradient power index, which controls the through-thickness variation of particle amount in the local adhesive composition. The free edges of the adhesive layer were also critical due to the occurrence of high normal and shear strains and stresses. The gradient power index can influence the distribution and levels of strain and stress components only for a sufficiently high volume fraction of particles. The grading direction of particles in the adhesive layer was not influential because the temperature field is uniform; namely, it can only upturn the low and high strain and stress regions so that the neat adhesive–adherend interface and the particle-rich adhesive–adherend interface can be relocated.