Abstract
Based on the ABAQUS platform for finite element analysis, the extended finite element method (XFEM) considering elastoplastic constitutive relationship is developed, by which the displacement discontinuity across the crack surface and the strong nonlinearity near the crack tip can be described more accurately. The strip specimens with unilateral cracks and central cracks under uniaxial tension are simulated using the XFEM and the FEM, respectively. The J-integral across the crack on each increment is calculated using the equivalent domain integral method (EDIM), the interaction integral method and the FEM, respectively. The effects of mesh size and mesh shape near the crack tip, element type and different calculation methods on the accuracy of J-integral are analyzed. The simulation results show that the XFEM is more accurate than the FEM with the same element size and type. The fracture tests of cast iron specimens with unilateral cracks under uniaxial tension are performed, and the J-integral criterion is valid to predict the fracture initiation in numerical simulation. The critical value of J-integral is calculated using the EDIM of the XFEM. The comparisons demonstrate that the simulated elastoplastic load–displacement curves with the XFEM are in good agreement with the experimental results.
Similar content being viewed by others
References
Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech. 1968;35(2):379–86.
Kumar V, German MD, Shih CF. Engineering approach for elastic-plastic fracture analysis. EPRI Report NP-1931, Electric Power Research Institute (94); 1981.
Wu S, Lu Y, Kuo K, et al. Combustion-induced crack/debond propagation in a metalized propellant. American Institute of Aeronautics and Astronautics; 1992.
Liu JH, Wang DR, Liu Y. Evaluation asphalt mixture fracture resistance using the J-integral. J Solid Mech. 2010;31(01):16–22.
Zhu CL, Li JB, Lin G. J-integral method for calculation of fracture energy of mixed mode inclined cracks based on SBFEM. J Civ Eng. 2011;44(04):16–22.
Moura B, Shih CF. A treatment of crack tip contour integrals. Int J Fract. 1987;35:295–310.
Shivakumar KN, Raju IS. An equivalent domain integral method for three-dimensional mixed-mode fracture problems. Eng Fract Mech. 1992;42(6):935–59.
Stern M, Becker EB, Dunham RS. A contour integral computation of mixed-mode stress intensity factors. Int J Fract. 1976;12(3):359–68.
Yau J, Wang S, Corten H. A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity. J Appl Mech. 1980;47(2):335–41.
Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng. 1999;45(5):601–20.
Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Methods Eng. 2015;46(1):131–50.
Deb D, Das KC. Enriched finite element procedures for analyzing decoupled bolts installed in rock mass. Int J Numer Anal Methods Geomech. 2011;35(15):1636–55.
He B, Zhuang X. Modeling hydraulic cracks and inclusion interaction using XFEM. In: Underground space; 2018;3(3):218–228
Yu TT. Numerical aspects of the extended finite element method. Rock Soil Mech. 2007;28(S1):305–10.
Zeng QL, Zhuang Z, Liu ZL, et al. Fully coupled modeling for multiple clusters growth of hydraulic fractures in shale. J Comput Mech. 2016;33(04):643–8.
Giner E, Sukumar N, Tarancón JE, et al. An Abaqus implementation of the extended finite element method. Eng Fract Mech. 2009;76(3):347–68.
China Institute of Aeronautics. Handbook of stress intensity Factor. Beijing: Science Press; 1993.
Huang Y, Song Q, Luo XF, Chang YJ. Calculating two dimensional stress intensity factor based on the extended finite element method. J Guangxi Univ (Nat Sci Ed). 2018;43(01):365–70.
Cheng J, Zhao SS. Fracture mechanics. Beijing: Beijing Science Press; 2006.
Song XL, An JR. The new Chinese and foreign metal materials manual. 2nd ed. Beijing: Chemical Industry Press; 2012.
Acknowledgements
This project was supported by the National Natural Science Foundation of China (Grant 51465002, 11262001, 51675110, 11632007) and the Systematic Project of Guangxi Key Laboratory Project of Disaster Prevention and Engineering Safety (Grant 2016ZDX07).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, Y., Song, Q., Kuang, Z. et al. Fracture Analysis of Cast Iron Materials with Cracks Based on Elastoplastic Extended Finite Element Method. Acta Mech. Solida Sin. 32, 201–214 (2019). https://doi.org/10.1007/s10338-019-00078-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-019-00078-7