Foreword: Advances in Crack Growth Modelling

Fatigue failure of strucutres is normally caused by cracks that extend beyond a safe size. Flaws are present to some extend in all structural parts, either as a result of manufacturing fabrication defects or damage in service. Crack growth is a complex phenomenon to model and simplifications are assumed. In recent years, there has been an increasing realisation that advanced computational methods such as the Finite Element Method, the Boundary Element Method and Meshfree Methods can be used to simulate crack growth in complex structural parts. Early works to model crack growth using the Finite Element Method (FEM) can be traced back to works of Shephard et al [1] and, Valliappan and Marti[2]. More recent advances in the finite element method can be found in the work of Theilig et al [3] for two-dimensional mixed-mode crack problems, Buchholz and Richard [4], Citarella and Buchholz [5] and Li et al [6] for three – dimensional mixed-mode problems. A recent successful application of the FEM to mixed-model crack growth modelling is due to the development of eXtended Finite Element Method (XFEM). The XFEM as developed by Black and Belytscho[7] and Rethore et al [8] are inspired by the enriched finite elements originally proposed by Benzely [9] and Foschi and Barrett[10] (see Aliabadi and Rooke[11] for an overview of enriched FEM). The work by Belytschko and Black enabled the enrichment of finite element approximations requiring minimal remeshing to solve crack growth problems. The partition of unity property of finite elements was later used in XFEM which allowed enriching of regions near the discontinuities. This method offers some unique advantages over earlier FEM methods proposed to model crack growth in structures. It does not require any projections between the meshes and has proved to be far better than finite element methods with continuous remeshing. The advantage of XFEM lies in the fact that it subdivides the crack problem into two parts where a mesh is generated without cracks/inclusions and then finite element functions can be enriched to simulate discontinuities. Belytschko and Black treated curved discontinuities by mapping a straight crack enrichment field which was further developed by Dolbow et al. [12]and Moes et al.[13]. Sukumar et al. [14] implemented the concept of Partition of Unity and XFEM to three dimensional problems by using a discontinuous function to simulate the crack surface and enriching the crack front by 2D asymptotic crack tip displacement fields.