PSI - Issue 72

Thomas Steffen Methfessel et al. / Procedia Structural Integrity 72 (2025) 105–112

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advantageous when the components to be joined are rather thin. Then there is no need of screws or rivets, the load transfer is distributed over a larger overlap area and this typically goes along with a comparatively high strength-to weight ratio. Beside these advantages, however, there are also challenges: Typically, the load transfer between two joined components or so-called adherends is not homogeneously distributed, but there are stress concentrations at the ends of the overlapping area. It is these stress concentrations that have a decisive impact on the effective strength or structural integrity of the adhesive bonding under mechanical and/or thermal loading since the stress concentrations trigger local failure as e.g. debonding between the adherends and the adhesive. For the example of a single-lap adhesive bonding the occurrence of the stress concentrations is schematically shown in Fig. 1. In the framework of linear elasticity theory due to the given geometrical and/or material discontinuities at the stress concentrations at the locations of the blue dots strictly speaking even have a singular character. This means they go along with locally infinite stresses which might lead to the paradox conclusion that this leads to failure already for very low loads which is not realistic. What actually is needed in this situation is a realistic analysis assessment tool which should be as simple and efficient as possible. It is the goal of the current contribution to present such an assessment tool. The problem to analyze adhesive bonding is not new and there are established models available. A kind of pioneering work for the case of single-lap joints is that of Volkersen (1938) which later was extended for instance by Goland and Reissner (1944) as well as by Ojalvo and Eidinoff (1978) among others. These works give approximate descriptions for the stress distribution within the adhesive layer which are easy to use, but they are only good for sufficiently thin adhesive layers. For larger thicknesses they get inaccurate and may lead to considerable errors. Thus, in the case of thicker adhesive layers there is a need for improved modeling and it is the purpose of the current contribution to do this by a well-adjusted higher-order modeling within the adhesive layer continuum. In doing so, for the sake of simplicity and generality, the consideration will be restricted to the overlap-area as it has originally been suggested by Bigwood and Crocombe (1989). As within the overlap-region the considered configuration in essence is a three-layer structure with an upper and lower adherend and the adhesive layer in between like within a sandwich, such kind of modeling is called a “sandwich - type model”. The effect of the adjacent structural parts of the adherends are taken into account by appropriately chosen boundary conditions for the respective cross-sectional forces or deformations.

Fig. 1. Example: Single-lap adhesive bonding.

2. Higher-order modeling approach In the sense of sandwich-type modeling the three-layer overlap configuration of total length l shown in Fig. 2 is to be considered. The upper adherend indicated by the index i=1 is of thickness h 1 , the lower adherend indicated by the index i=2 is of thickness h 2 . The adhesive layer in between indicated by the index a is of thickness t . The horizontal longitudinal coordinate is denoted by x, the vertical transverse coordinate by z starting in the midplane of the adhesive layer. Beyond this also local z -coordinates z 1 and z 2 each starting in the respective adherend midplane will be employed as well.