PSI - Issue 18

V. Dattoma et al. / Procedia Structural Integrity 18 (2019) 719–730 Author name / Structural Integrity Procedia 00 (2019) 000–000

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considered. The significance of friction in the calculated stresses has been studied by the authors and the results has been discussed below. 3.2. Model B The second model (denoted model B) was generated starting from the laminae characteristics calculated as in model A and consists of homogeneous orthotropic material variable from lamina to lamina. It is generated in order to evaluate the progressive damage of the composite material (either for matrix and fibers damage) and eventually the delamination consequences. Starting from a sketch in 2D, aa “shell model” is generated and the geometry was discretized adopting the same divisions used in the model A. Composite laminate is created using “ACP Tools” combining sixteen-layered elements together with one element thickness for ply, in according with the sequence of lamination. . The jointed geometry is modelled as in the model A. In Figure 4a is shown an example of lamination generated with this procedure, while in Figure 4b is shown the mesh around the bolt in the composite laminate.

(a) (b) Fig. 4. (a) Fiber orientation in plies 3-4; (b) Refined element mesh around the hole in the laminate.

The model thus generated aims to provide an accurate representation of 3D stress field developed around the bolt, due to combined bending and shear effects, clamping force of the fastener and related through-thickness pressures in the region of the bolted hole. This model allows the accurate addressing of all 3D damage types, including delamination. In this model, the 3-D Hashin-type failure criteria (Hashin, 1980) were used to predict matrix the fiber damage. In a second calculation, the delamination effect is also included and its effects are considered. 3.3. Delamination model for the case B In this work, the exponential cohesive zone law was used, since delamination is a mixed-mode decohesion process and thus a coupled cohesive zone law is required. The coupling in the Exponential Cohesive Zone Law of Xu and Needleman (X.-P. Xu and A. Needleman, 1993) is controlled by two parameters: q and r, where q is the relationship between the normal and tangential work of separation (q= ϕ n / ϕ t ) and r is a coupling parameter, depending on the characteristic length (δ n ) associated with the decohesion process in the normal direction. The exponential law of Xu and Needleman is based on a potential that represent the work of separation as following: � � � � ���� �� � � ��� � � � � � � � � � � � � �� � � � � � � � � � � � ��� � � � � � (1) with q and δ n previously described and δ t is another characteristic length associated with the slip separation process in the tangential direction. Adequate calibrated coupling between the normal and tangential directions is required to describe the interface behaviour realistically. If complete loss of interfacial integrity is important and a cohesive zone completely fails in shear, its load-carrying capacity in normal traction should completely diminish as well and vice versa.