PSI - Issue 66

G. Cricrì et al. / Procedia Structural Integrity 66 (2024) 282–286 Author name / Structural Integrity Procedia 00 (2025) 000–000

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models the FE method must be adopted and a series of numerical issues have necessarily to be preliminary faced. To fill this gap, an analytical lap-joint model able to account for the adhesive damage by the cohesive crack modelling technique is proposed. The closed form solution we derive from it, may provide insight into joint progressive failure and be a valid starting point for more sophisticated analyses. Present paper is organized as follows. In Section 2, the model basic assumptions are discussed, the corresponding governing equations are given to gather with the model closed form solution. Moreover, we will show how theoretical results may be usefully employed for joint designing. In Section 3, the results of a validation study carried out by the outcomes of a series of finite element lap joints are analysed to identify the application field of the proposed model. Finally, in Section 4, main results of present study are summarized. 2. The adhesive joint model The joint model is very simple: it is constituted of two linear elastic straight elements having rectangular cross section, that may deform only axially. They are connected by an adhesive layer, whose length is L , that instead may deform only by shear. In the following, we denote by h 1 and h 2 the thicknesses of the lower and upper adherend respectively and by w the common width of their cross section, fig. 1-a). The thickness t of the adhesive layer is assumed equal to zero, in the limit. The joint is subjected to the overall tensile force P acting in the same plane of the adhesive layer.

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Fig. 1. (a) simple lap joint; (b) adhesive shear deformation; (c) adhesive shear stress – shear deformation diagram.

The adhesive shear deformation  may be evaluated in terms of the axial displacement of the upper and lower adherends 1 u and 2 u , fig. 1-b). Furthermore, its mechanical behaviour is linear up to a perfectly brittle rupture, as shown in fig. 1- c). When reaches � , the shear stress drops from  c to zero. The green area of fig. 1-c), denoted as Γ , represents the fracture energy of the adhesive. Under these assumptions, observing that the onset of joint failure take place when the maximum shear deformation  L/2  attains the critical value c  , the value c P of the failure load may be derived: � ��� � ℎ � � � � � � �� �� ��� � �� �� ��� ��� � �������� � � � � � � � � � � ������ � � � � �� � � �� � � � . (1) Further, the joint elongation s(  ) corresponding to the load P c (  ) for a crack increment L-  is given by: ����� ��� � � � �� � � �� �� ��� � �� �� ��� ��� � �� �� �� �� ��� � ����� � � � ��� � �� � �� (2)