PSI - Issue 57

Cristian Bagni et al. / Procedia Structural Integrity 57 (2024) 859–871 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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2.1. First methodology The first methodology assumes that the life of the hybrid joint as a whole corresponds to the life of the adhesive and neglects the life given by the mechanical joints after failure of the adhesive. In particular, in the proposed methodology the peel (or opening) stress is used to predict the fatigue damage and fatigue life of the joint, since it is well known that adhesives are very strong under shear loading, but quite weak under peel loading. The corresponding FE modelling strategy consists of modelling the adherends using mid-surface linear shell elements and the adhesive using linear solid elements. Furthermore, the exposed faces of the solid elements are wrapped with linear shell elements with membrane behaviour only (Fig. 1). The membrane shell elements are modelled using the properties of the adhesive and with a negligible thickness (e.g. 10 -6 mm) to avoid introducing any noticeable contribution to the behaviour of the joint. The mechanical joints (either rivets or spot welds) can be modelled either by using linear solid elements (Fig. 1) or by following one of the modelling strategies already recommended in the nCode DesignLife Theory Guide (Hottinger Brüel & Kjær (2023)), for example using beam elements, area contact method (ACM) or penta solid elements. The solid elements and the shell elements (both adherends and membrane shell elements) are connected using ‘bonded contacts’ (or similar tools, depending on the FE software used). With this modelling strategy, the adhesive is modelled from mid-surface to mid-surface of the adherends and therefore, it is thicker than in the physical joint. As a consequence, the Young’s modulus of the adhesive might need to be corrected to account for the larger thickness and preserve the real stiffness of the joint. Finally, the peel stresses are recovered from the centroid of the membrane shell elements.

Fig. 1. Example of the proposed modelling strategy applied to a lap shear specimen, with the adherends and the mechanical joints in grey and the adhesive in cyan.

The mechanical joints are included in the FE model to try to replicate their positive or detrimental effects on the fatigue performance of the adhesive, as described in Section 1. However, if considered reasonable, the FE model can be simplified by not modelling the mechanical joints and model the hybrid joint as a simple adhesively bonded joint. Modifications to the proposed modelling strategy can be used, such as modelling the adherends with solid elements or modelling the adherends with mid-surface shell elements or modelling the adhesive with solid elements and the actual adhesive thickness, and joining the adherends with the adhesive using bar/beam elements. However, these modifications would make the model more onerous from a modelling and/or computational point of view. Therefore, these modifications should be applied only if necessary. Finally, life/damage predictions can be performed using the DesignLife standard SN Analysis Engine, where the inputs are the peel stresses at the centroid of the membrane elements from the FE model, the load history and