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X-FEM simulation of 2-D fracture mechanics problem
| Content Provider | Semantic Scholar |
|---|---|
| Author | Sharma, Kamal Bhasin, Vivek Singh, I. V. Mishra, Brij K. Vaze, K. K. |
| Copyright Year | 2011 |
| Abstract | In this paper, edge crack problems under mechanical loads have been analysed using extended finite element method (XFEM) as it has proved to be a competent method for handling problems with discontinuities. The XFEM provides a versatile technique to model discontinuities in the solution domain without re-meshing or conformal mesh. The stress intensity factors (SIF) have been calculated by domain based interaction integral method. The effect of crack orientation and interaction under mechanical loading has been studied. Analytical solutions, which are available for two dimensional displacement fields in linear elastic fracture mechanics, have been used for crack tip enrichment. From the present analysis, it has been observed that there is monotonous decrease in the SIF-1 value with the increase in inclination, while SIF-II values first increases then it also decreases. Next study was performed for first edge crack in the presence of second crack on opposite edge. The results were obtained by changing the distance between the crack tips as well as by changing the orientation of second crack. SIFs values decrease with increase in distances between the crack tips for collinear cracks. In next study, for the first crack in presence of inclined second edge crack and it was found that SIFs increase initially with the increase in inclination and decrease after that. It emphasizes the fact that cracks at larger distances act more or less independently. In next study, with the use of level set method crack growth path is evaluated without remeshing for plate with hole, soft inclusion & hard inclusion under mode-I loading and compare with available published results. INTRODUCTION Many structural systems, which are comprised of piping systems, can be found in nuclear power plants, offshore drilling platforms, fossil power generation plants, gas pipelines and others. The unavoidable existence of cracks in some components may lead to increased safety concerns about the loss of structural strength and possibly failure of these structural systems. In assessing the integrity of structures containing such cracks, it is important to quantify the relevant crack driving force so that its load-carrying capacity can be predicted. As opposed to earlier FE approaches, in recent years the X-FEM has proven to be a very efficient tool for the numerical modeling of cracks. In comparison to the standard FEM, the X-FEM provides significant benefits in the numerical modeling of crack propagation. The main advantages are that the finite element mesh need not to conform to the crack boundaries (crack faces) to account for the geometric discontinuity, and furthermore, mesh regeneration is not needed in crack growth simulations. Therefore, only a single mesh, which is often easily generated, can be used for any crack length and orientation. The X-FEM is based on the introduction of additional degrees of freedom (DOFs), which are associated with the nodes of the elements intersected by the crack geometry. In this method, both discontinuous displacement fields along the crack faces and the leading singular crack tip asymptotic displacement fields are added to the displacement based FEM approximation for crack modeling through the partition of unity approach. This enables the method for accurate modeling of the crack. REVIEW OF EARLIER WORK Numerical methods, especially the finite element (FE) method, have been widely used in computational fracture mechanics. However, modeling of multiple crack configurations, crack growth and cracks intersecting with other discontinuities is still a laborious task since the crack topology is generally complicated and difficult to be explicitly modeled by the FE. Moreover, the crack tip singularity needs to be accurately represented by the approximation. Belytschko and Black [1] introduced a method for solving crack problems in the FE framework which is independent of the mesh. In this method the meshing task is reduced by enriching the elements near the crack tip and along the crack faces with the leading singular crack tip asymptotic displacement fields using the partition of unity (PU) method [2, 3] to account for the presence of the crack. When multiple crack segments are needed to be enriched with the near tip fields, a mapping algorithm introduced by Fleming et al. [4] is used to align the |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://repository.lib.ncsu.edu/bitstream/handle/1840.20/32573/p303.pdf?isAllowed=y&sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
