Simplified stress analysis of functionally graded single-lap joints subjected to combined thermal and mechanical loads

Functionally graded adhesive (FGA) joints involve a continuous variation of the adhesive properties along the overlap allowing for the homogenization of the stress distribution and load transfer, in order to increase the joint strength. The use of FGA joints made of dissimilar adherends under combined mechanical and thermal loads could then be an attractive solution. This paper aims at presenting a 1D-bar and a 1D-beam simplified stress analyses of such multimaterial joints, in order to predict the adhesive stress distribution along the overlap, as a function of the adhesive graduation. The graduation of the adhesive properties leads to differential equations which coefficients can vary the overlap length. For the 1D-bar analyses, two different resolution schemes are employed. The first one makes use of Taylor expansion power series (TEPS) as already published under pure mechanical load. The second one is based on the macro-element (ME) technique. For the 1D-beam analysis, the solution is only based on the ME technique. A comparative study against balanced and unbalanced joint configurations under pure mechanical and/or thermal loads involving constant or graduated adhesive properties are provided to assess the presented stress analyses. The mathematical description of the analyses is provided.