Crack propagation by XFEM

Description

Before explaining the XFEM model, let’s learn more about crack in metals.

What is crack in metals?

Cracks are surface or subsurface fissures that develop in a material. Propagation energy derived from mechanical, thermal, chemical, and metallurgical effects, or a combination of these may influence crack initiation and growth. Various types of cracks exist in metals and can be categorized as cooling, solidification, centreline, crater, grinding, pickling, heat treatment, machining tears, plating, fatigue, creep, stress corrosion and hydrogen cracks. Cracks can grow and lead to complete fracture of the component posing significant threats to component life and may lead to serious injuries or loss of life. Brittle fracture in metals occurs with little or no visible warning. The Discovery of any cracks warrants immediate interventions to arrest the cracks before they propagate to the point of fracture.

Simulating the crack

Evaluating the behaviour of metals during crack propagation requires expensive and time-consuming experiments. This makes the FEA method a great tool to have a comprehensive study. Since the model needs to predict the complex behaviour of the material during the propagation, various types of simulations are proposed. Each method has a specific benefit which makes them an appropriate technique for each purpose or material. XFEM models are the most popular among them which is explained here.

XFEM model

The extended finite element method (XFEM), also known as generalized finite element method (GFEM) or partition of unity method (PUM) is a numerical technique that extends the classical finite element method (FEM) approach by extending the solution space for solutions to differential equations with discontinuous functions. The extended finite element method was developed to ease difficulties in solving problems with localized features that are not efficiently resolved by mesh refinement. One of its initial applications was the modelling of fractures in a material. In this original implementation, discontinuous basis functions are added to standard polynomial basis functions to provide a basis that included crack opening displacements.

advantages

A key advantage of XFEM is that in such problems the finite element mesh does not need to be updated to track the crack path. Subsequent research has illustrated the more general use of this method for problems involving singularities, material interfaces, the regular meshing of micro-structural features such as voids, and other problems where a localized feature can be described by an appropriate set of basis functions. It was shown that for some problems, such as embedding the problem’s feature into the approximation space, can significantly improve convergence rates and accuracy. Moreover, treating problems with discontinuities with eXtended Finite Element Methods suppresses the need to mesh and remesh the discontinuity surfaces, thus alleviating the computational costs and projection errors associated with conventional finite element methods.

Obtained from: https://arxiv.org/ftp/arxiv/papers/1308/1308.5208.pdf

Tutorial video

In this video, you will learn how to create a simple model to predict crack propagation through a part. XFEM model allows you to assign more than one crack in part. In addition, this method is very fast and suitable for  creating large models. The video is short; less than 10 minutes and includes the output and Abaqus CAE file.

 In this video, we avoid giving too many details so you can easily use the products. Here you can find the following files:

Abaqus files: CAE, ODB, INP, and JNL

Video files: How to create this model.

PowerPoint and Solidworks files

For more information please send me an Email:

rezatangestani@hyperlyceum.com