Static and dynamic fracture analysis of 3D cracked orthotropic shells using XFEM method

Abstract

In this study, cracked shell-type structures with 3D geometries made of orthotropic materials are considered. Extended Finite Element Method (XFEM) is typically used for analysis of 2D orthotropic plates; however, the available commercial FEM packages like ABAQUS do not offer a solution for cracked orthotropic elements. As a result, authors have developed a programming code in MATLAB software, which is capable of solving 3D orthotropic structures with shell elements. Examples of 2D and 3D shell element problems with different crack angles and fibre orientations are investigated to validate the accuracy of the evaluated stress intensity factors under static and dynamic loading conditions. Parametric studies are also performed to observe the fracture behaviour of a pipe with different crack orientations at different fibre directions in composites.

Introduction

Various methods have been used to analyze cracked composite structures. Among the performed studies in this field, closed-form solutions to the fracture mechanics behaviour of such materials could be addressed [1], [2]. Some of these studies focused on stress and displacement fields around a linear crack on an inhomogeneous medium [3], [4], [5], [6].

Since most analytical solutions are applicable to limited geometries and boundary conditions, numerical techniques such as boundary element method [7], [8], and finite element method [9], [10], [11] have been proposed for fracture analysis of composites with complex geometries.

The extended finite element method is a powerful numerical method capable of solving cracked fields without the need for matching crack boundaries with edge elements or any change in the generated meshes. In this method, Heaviside enrichment functions are utilized to consider crack-tip discontinuity enrichment functions that evaluate the singular field around the crack tip. The XFEM was originally proposed by Belytschko and Black [12]. It was further developed by Daux et al. [13], Belytschko et al. [14], Sukumar et al. [15] and other researchers [16], [17], [18], [19], [20] for plate problems. It was then extended to shell-type structures by Areias and Belytschko [21], Wyart et al. [22] and Bayesteh and Mohammadi [23] for isotropic materials. This method was originally used for homogenous materials while it is further extended to orthotropic media. The method necessitates different crack tip enrichment functions derived based on analytical solutions derived for near crack tip displacement fields. Different analytical solutions have been proposed to be applied for the specific classes of orthotropic materials [24], [25], through the use of analytical displacement fields [26], [27], [28], [29], [30]. Asadpoure and Mohammadi [31] proposed a set of crack-tip enrichment functions for composite materials using a unified analytical formulation [2]. The XFEM adopted with the layer-wise method is studied and developed by Li et al. [32], [33], [34], [35], [36], [37].

Analytical solutions of the dynamic analysis of cracked anisotropic media has been developed by Viola et al. [26], Broberg [38], Lim et al. [1] and Nobile and Carloni [29]. As well, others utilized numerical methods such as boundary element solutions [7], [8] or finite element method [39] for analysis of cracked anisotropic media. Belytschko et al. [40] and Grégoire et al. [41] modelled dynamic crack propagation through the XFEM framework for isotropic materials. Motamedi and Mohammadi [42], [43], [44] adopted the XFEM method for dynamic analysis of cracked orthotropic plates.

This study investigates 3D analysis of cracked orthotropic shell structures under static and dynamic loading. For this purpose, a MATLAB stand-alone code is developed to solve and post-process the results of stress intensity factors for cracked orthotropic elements through XFEM method.