An extended Isogeometric Boundary Element formulation for the three-dimensional fatigue crack propagation modelling

Resumo

The fatigue crack propagation is responsible for the failure of various engineering components, which justifies the importance of its proper modelling. Its accurate prediction in real-life applications requires a numerical approach to account for complex details in geometry, boundary conditions and mechanical response. In this sense, the Boundary Element Method (BEM) has proven to be as a highly attractive approach to fracture mechanics applications, especially for three-dimensional models, since its boundary-only discretisation simplifies the re-meshing process and allows for the precise representation of the singular stress field near the crack front in these problems. The isogeometric approach in the BEM enables a smooth coupling with models built in CAD software. This stems from using the same approximation functions for the mechanical fields as these models use for their geometric description, in this study, the Non-Uniform Rational B-Splines (NURBS). However, the standard isogeometric BEM does not capture the asymptotic behaviour close to the crack front, and it also introduces a non-physical jump displacement at this region. The enrichment approach has demonstrated to be a successful strategy to circumvent these issues, in which the Williams solution expands the displacement approximation close to the crack front. Additionally, it introduces Stress Intensity Factors (SIFs) parameters that directly interpolate them, dismissing the need for computationally costly strategies such as the J-integral. In this context, this study proposes the fatigue crack growth modelling with the eXtended Isogeometric Boundary Element Method (XIGABEM) in which the SIFs are directly obtained by the XIGABEM formulation. Two different crack growth criteria are responsible for defining the crack growth advance: the hoop stress and the Schollmann criteria. In addition, a curve fitting algorithm defines the new crack front by finding the position of both control points and weights. Furthermore, a fine-tuning strategy guarantees C^0 and C^1 continuity between adjacent patches, which is required by the enrichment functions and enables a multi-patch description of cracks. One numerical application demonstrates the robustness and accuracy of the proposed scheme through its comparison with a reference solution. Thus, the XIGABEM strategy demonstrates its suitability for the three-dimensional fatigue crack growth analysis.