PSI - Issue 54

I.R.S. Araújo et al. / Procedia Structural Integrity 54 (2024) 406–413 Araújo et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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edge of the joint were chosen to ensure greater refinement in the critical regions of the joint. This variation aims to reduce computational effort and time in obtaining results without compromising their accuracy. Fig. 3 illustrates the effect of the bias along the length of the scarf joint.

Fig. 2. Representation of the mesh constituent elements.

Fig. 3. Bias effect along the length of the joint.

To simulate real experimental test conditions, boundary and loading conditions were applied to the models in the ABAQUS ® software. The joint was fixed at one end and constrained in the transverse direction at the opposite end. 2.4. XFEM formulation The XFEM serves as an enhancement to the conventional FEM. The XFEM integrates enrichment functions into the FEM formulation, primarily designed to represent displacement jumps between crack faces during crack propagation (Pike and Oskay 2015). When simulating damage within Abaqus ® , damage initiation and propagation are triggered in regions where the stresses and/or strains exceed predetermined thresholds. Abaqus ® offers a choice of six crack initiation criteria. In this work, the quadratic nominal stress (QUADS) was considered 2 2 n s 0 0 n s t t f t t     =   +      (1) t n and t s are the current normal and shear traction components to the cracked surface, and t n 0 and t s 0 the respective limit values. Damage initiates when f reaches unity. For damage growth, the fundamental expression of the displacement vector u , including the displacements enrichment, is written as (Abaqus® 2013) ( ) ( ) 1 N i i N x H x = =  +     u u a i i . (2) N i ( x ) and u i relate to the conventional Finite Element formulation. N i ( x ) represents the nodal shape functions, while u i stands for the nodal displacement vector associated with the continuous part of the formulation. The second term enclosed in brackets, H ( x ) a i , is only active in the nodes for which any relating shape function is cut by the crack and can be expressed by the product of the nodal enriched degree of freedom vector including the mentioned nodes, a i , with the associated discontinuous shape function, H ( x ), across the crack surfaces. This method is built upon the concept of introducing phantom nodes that subdivide elements intersected by a crack, effectively simulating the separation between newly created sub-elements. These phantom nodes initially share the same coordinates as the real nodes, and remain entirely constrained to the real nodes until damage initiation occurs. Once crossed by a crack, the element gets divided into two sub-domains. The discontinuity in displacements is achieved by adding phantom nodes atop the original nodes. When an element undergoes cracking,