Estimation of mixed-mode fracture parameters by gene expression programming

Document Type : Article

Authors

Department of Civil Engineering, Engineering Faculty, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

Abstract

The linear elastic fracture phenomenon has been characterized with stress intensity factors (SIFs). In this study a general function is obtained in order to predict the fracture parameters. Numerical calculation of the SIFs in a mixed-mode condition is a cumbersome task. In this research, more than 6800 numerical analyses using extended finite element method are conducted to simulate the fracture problem. States are considered for a plate with an arbitrary edge or center crack. Mixed mode SIFs were calculated using of interaction integral. Then, Gene Expression Programming (GEP) method is utilized to extraction of a function. Results show acceptable correlations between numerical calculations and genetic programming functions. R-square (R2) values are in a range of 0.91 to 0.96 that guarantees the accuracy of the inferred functions.

Keywords

Main Subjects


References:
1. Zahnder, A.T., Fracture Mechanics, Springer (2012). 
2. Gdoutos, E.E., Fracture Mechanics: An Introduction,Springer (2005).
3. Janssen, M., Zuidema, J., and Wanhill, R., Fracture Mechanics, Second Edition, Taylor & Francis (2004).
4. Aliha, M.R.M., Behbahani, H., Fazaeli, H., and Rezaifar, M.H. "Experimental study on mode I fracture toughness of diff:erent asphalt mixtures", Scientia Iranica, 22(1), pp. 120-130 (2015). (en). 
5. Likeb, A., Gubeljak, N., and Matvienko, Y. "Stress intensity factor and limit load solutions for new pipering specimen with axial cracks", Procedia Mater. Sci.,3, pp. 1941-1946 (2014).
6. Joseph, R.P., Purbolaksono, J., Liew, H.L., Ramesh, S., and Hamdi, M. "Stress intensity factors of a corner crack emanating from a pinhole of a solid cylinder",Eng. Fract. Mech., 128, pp. 1-7 (2014).
7. Evans, R., Clarke, A., Gravina, R., Heller, M., and Stewart, R. "Improved stress intensity factors for selected configurations in cracked plates", Eng. Fract. Mech., 127, pp. 296-312 (2014).
8. Duan, J., Li, X., and Lei, Y. "A note on stress intensity factors for a crack emanating from a sharp V-notch", Eng. Fract. Mech., 90, pp. 180-187 (2012).
9. De Luycker, E., Benson, D.J., Belytschko, T., Bazilevs, Y., and Hsu, M.C. "X-FEM in isogeometric analysis for linear fracture mechanics", Int. J. Numer. Methods Eng., 87(6), pp. 541-565 (2011).
10. De Klerk, A., Visser, A.G., and Groenwold, A.A."Lower and upper bound estimation of isotropic and orthotropic fracture mechanics problems using elements with rotational degrees of freedom", Commun. Numer. Methods Eng., 24(5), pp. 335-353 (2008).
11. Yoneyama, S., Ogawa, T. and Kobayashi, Y. "Evaluating mixed-mode stress intensity factors from full-field displacement fields obtained by optical methods", Eng. Fract. Mech., 74(9), pp. 1399-1412 (2007).
12. Banks-Sills, L., Wawrzynek, P.A., Carter, B., Ingraffea, A.R., and Hershkovitz, I. "Methods for calculating stress intensity factors in anisotropic materials: Part II-Arbitrary geometry", Eng. Fract. Mech., 74(8), pp. 1293-1307 (2007).
13. Ayhan, A.O. "Stress intensity factors for threedimensional cracks in functionally graded materials using enriched finite elements", Int. J. Solids Struct., 44(25-26), pp. 8579-8599 (2007).
14. Shahani, A.R. and Nabavi, S.M. "Closed form stress intensity factors for a semi-elliptical crack in a thickwalled cylinder under thermal stress", International Journal of Fatigue, 28(8), pp. 926-933 (2006).
15. Chen, D-C., Chang, D-Y., Chen, F-H., and Kuo, TY. "Application of ductile fracture criterion for tensile test of zirconium alloy 702", Scientia Iranica, 25(2), pp. 824-829 (2018). (en) .
16. Khademalrasoul, A. "Linear and curvature internal heterogeneous boundaries influences on mixed mode crack propagation using level set method", Journal of Structural and Construction Engineering, 4(3), pp. 42-54 (2017). 
17. Sukumar, N. and Prevost, J.H. "Modeling quasi-static crack growth with the extended finite element method. Part I: Computer implementation", Int. J. Solids Struct., 40(26), pp. 7513-7537 (2003).
18. Moes, N. and Belytschko, T. "Extended finite element method for cohesive crack growth", Eng. Fract. Mech., 69(7), pp. 813-833 (2002).
19. Yin, S., Yu, T., Bui, T.Q., Liu, P., and Hirose, S. "Buckling and vibration extended isogeometric analysis of imperfect graded Reissner-Mindlin plates with internal defects using NURBS and level sets",Computers & Structures, 177, pp. 23-38 (2016).
20. Bui, T.Q. "Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS", Comput. Meth. Appl. Mech. Eng., 295, pp. 470-509 (2015).
21. Bhardwaj, G., Singh, I.V., Mishra, B.K., and Kumar, V. "Numerical simulations of cracked plate using XIGA under different loads and boundary conditions", Mech. Adv. Mater. Struct., 23(6), pp. 704-714 (2016).
22. Bhardwaj, G., Singh, I.V., and Mishra, B.K. "Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA", Comput. Meth. Appl. Mech. Eng., 284, pp. 186-229 (2015).
23. Arzani, H., Kaveh, A., and Taheri Taromsari, M. "Optimum two-dimensional crack modeling in discrete least-squares meshless method by charged system search algorithm", Scientia Iranica, 24(1), pp. 143-152 (2017).  
24. Sukumar, N., Huang, Z.Y., Prevost, J.H., and Suo, Z. "Partition of unity enrichment for bimaterial interface cracks", Int. J. Numer. Methods Eng., 59(8), pp. 1075- 1102 (2004).
25. Moes, N., Dolbow, J., and Belytschko, T. "A finite element method for crack growth without remeshing", Int. J. Numer. Methods Eng., 46(1), pp. 131-150 (1999).
26. Babuska, I. and Zhang, Z. "The partition of unity method for the elastically supported beam", Comput. Meth. Appl. Mech. Eng., 152(1-2), pp. 1-18 (1998).
27. Nasiri, S., Khosravani, M.R., and Weinberg, K. "Fracture mechanics and mechanical fault detection by artificial intelligence methods: A review", Eng. Fail. Anal., 81(Supplement C), pp. 270-293 (2017).
28. Greenbaum, J., Wu, K., Zhang, L., Shen, H., Zhang, J., and Deng, H-W. "Increased detection of genetic loci associated with risk predictors of osteoporotic fracture using a pleiotropic cFDR method", Bone. 99(Supplement C), pp. 62-68 (2017). 
29. Xue, Y., Cheng, L., Mou, J., and Zhao, W. "A new fracture prediction method by combining genetic algorithm with neural network in low-permeability reservoirs", Journal of Petroleum Science and Engineering, 121(Supplement C), pp. 159-166 (2014).
30. Mohammadi, S., Extended Finite Element Method: for Fracture Analysis of Structures, Wiley (2008). 
31. Ferreira, C., Gene Expression Programming: Mathematical Modeling by an Artificial Intelligence, Springer (2006).
32. Belytschko, T. and Black, T. "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Methods Eng., 45(5), pp. 601-620 (1999).
33. Babuska, I. and Melenk, J. "The partition of unity method", Int. J. Numer. Methods Eng., 40, pp. 727- 758 (1997).
34. Melenk, J.M. and Babuska, I. "The partition of unity finite element method: Basic theory and applications", Comput. Meth. Appl. Mech. Eng., 139(1-4), pp. 289- 314 (1996).
35. Yau, J.F., Wang, S.S., and Corten, H.T. "A mixedmode crack analysis of isotropic solids using conservation laws of elasticity", Journal of Applied Mechanics- Transactions of the ASME, 47(2), pp. 335-341 (1980).
Volume 27, Issue 1
Transactions on Mechanical Engineering (B)
January and February 2020
Pages 229-238
  • Receive Date: 04 November 2017
  • Revise Date: 05 August 2018
  • Accept Date: 29 October 2018