Crack Interaction Studies Using XFEM Technique

Document Type: Research Paper

Author

Reactor Safety Divison, Bhabha Atomic Research Centre, Trombay, Mumbai

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.                                      

Keywords

[1] Belytschko T., Black T., 1999, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering 45: 601-620.
[2] Melenk J. M., Babuska I., 1996, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 139: 289-314.
[3] Babuska I., Melenk J. M., 1997, The partition of unity method, International Journal for Numerical Methods in Engineering 40: 727-758.
[4] Fleming M., Chu Y. A., Moran B., Belytschko T., 1997, Enriched element-free Galerkin methods for crack-tip fields, International Journal for Numerical Methods in Engineering 40 : 1483-1504.
[5] Moës N., Dolbow J., Belytschko T., 1999, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46: 131-150.
[6] Daux C., Moës N., Dolbow J., Sukumar N., Belytschko T., 2000, Arbitrary branched and intersecting cracks with the extended finite element method, International Journal for Numerical Methods in Engineering 48: 1741-1760.
[7] Sukumar N., Moës N., Moran B., Belytschko T., 2000, Extended finite element method for three-dimensional crack modelling, International Journal for Numerical Methods in Engineering 48: 1549-1570.
[8] Dolbow J., Moës N., Belytschko T., 2000, Modelling fracture in Mindlin–Reissner plates with the extended finite element method, International Journal of Solids and Structures 37: 7161-7183.
[9] Dolbow J., Moës N., Belytschko T., 2001, An extended finite element method for modeling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering 190: 6825-6846.
[10] Areias P., Belytschko T., 2005, Analysis of three-dimensional crack initiation and propagation using exteneded finite element method, International Journal for Numerical Methods in Engineering 63: 760-788.
[11] Nagashima T., Omoto Y., Tani S., 2003, Stress intensity factor analysis of interface cracks using X-FEM, International Journal of Numerical Methods in Engineering 56: 1151-1173.
[12] Liu X. Y., Xiao Q. Z., Karihaloo B. L., 2004, XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials, International Journal of Numerical Methods in Engineering 59: 1113-1118.
[13] Sukumar N., Chopp D. , Moes N., Belytschko T., 2001, Modelling holes and inclusions by level sets in the extended finite element method, Computer Methods in Applied Mechanics and Engineering 190: 6183-6200.
[14] Alves M., Rossi R., 2003, A modidied element-free galerkin method with essential boundary conditions enforced by an extended partition of unity finite element weight function, International Journal for Numerical Methods in Engineering 57 : 1523-1552.
[15] Sukumar N., Prévost J. H., 2003, Modelling quasi-static crack growth with the extended finite element method Part I: Computer implementation, International Journal of Solids and Structures 40: 7513-7537.
[16] Huang R., Sukumar N., Prévost J. H. , 2003, Modeling quasi-static crack growth with the extended finite element method Part II: Numerical applications, International Journal of Solids and Structures 40: 7539-7552.
[17] Zi G., Belytschko T., 2003, New crack-tip elements for XFEM and applications to cohesive cracks, International Journal for Numerical Methods in Engineering 57: 2221-2240.
[18] Mergheim J., Kuhl E., Steinmann P., 2005, A finite element method for the computational modelling of cohesive cracks, International Journal for Numerical Methods in Engineering 63: 276-289.
[19] Sukumar N., Huang Z. Y., Prévost J. H., Suo Z., 2004, Partition of unity enrichment for bimaterial interface cracks, International Journal for Numerical Methods in Engineering 59: 1075-1102.