Computers and Concrete

  • 제32권1호
  • /
  • Pages.99-117
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  • 2023
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  • 1598-8198(pISSN)
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  • 1598-818X(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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Stochastic fracture behavior analysis of infinite plates with a separate crack and a hole under tensile loading

  • Khubi Lal Khatri (Department of Mechanical Engineering, Swarrnim institute of Technology) ;
  • Kanif Markad (Department of Mechanical Engineering, DVVP College of Engineering)
  • 투고 : 2022.11.28
  • 심사 : 2023.04.11
  • 발행 : 2023.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

The crack under the influence of the higher intensities of the stresses grows and the structure gets collapsed with the time when the crack length reaches to critical value. Therefore, the fracture behavior of a structure in terms of stress intensity factors (SIF) becomes important to determine the remaining fracture strength and capacity of material and structure for avoiding catastrophic failure, increasing safety and further improvement in the design. The robustness of the method has been demonstrated by comparing the numerical results with analytical and experimental results of some problems. XFEM is used to model cracks and holes in structures and predict their strength and reliability under service conditions. Further, XFEM is extended with a stochastic method for predicting the sensitivity in terms of output COVs and fracture strength in terms of mean values of stress intensity factors (SIFs) of a structure with discontinuities (cracks and holes) under tensile loading condition with input individual and combined randomness in different system parameters. In stochastic technique, the second order perturbation technique (SOPT) has been used for the predicting the fracture behavior of the structures. The stochastic/perturbation technique is also known as Taylor series expansion method and it provides the reliable results if the input randomness is less than twenty percentage. From the present numerical analysis it is observed that, the crack tip near to the hole is under the influence of the stress concentration and the variational effect of the input random parameters on the crack tip in terms of the SIFs are lesser so the COVs are the less sensitive. The COVs of mixed mode SIFs are the most sensitive for the crack angles (α=45° to 90°) for all the values of c1 and d1. The plate with the shorter distance between hole and crack is the most sensitive with all the crack angles but the crack tip which is much nearer to the hole has the highest sensitivity.

키워드

참고문헌

  1. Abdelaziz, Y. and Hamouine, A. (2008), "A survey of the extended finite element", Comput. Struct., 86, 1141-1151. https://doi.org/10.1016/j.compstruc.2007.11.001.
  2. Ahmed, A. (2009), "Extended finite element method (XFEM) - Modeling arbitrary discontinuities and failure analysis", Master's thesis, University of Pavia, Pavia, Lombardy, Italy.
  3. Akhondzadeh, S., Khoei, A.R. and Broumand, P. (2017), "An efficient enrichment strategy for modeling stress singularities in isotropic composite materials with X-FEM technique", Eng. Fract. Mech., 169, 201-225. https://doi.org/10.1016/j.engfracmech.2016.11.019.
  4. Arregui-Mena, J.D., Margetts, L. and Mummery, P.M. (2016), "Practical application of the stochastic finite element method", Arch. Comput. Methods Eng., 23, 171-190. https://doi.org/10.1007/s11831-014-9139-3.
  5. Awang, M., Khalili, A.A. and Pedapati, S.R. (2020), "A review: Thin protective coating for wear protection in high-temperature application", Metal., 10, 42. https://doi.org/10.3390/met10010042.
  6. Bahloul, A., Ahmed, A.B. and Bouraoui, C. (2017), "Probabilistic fatigue crack growth assessment of Al 7075-T6 aerospace component", Proc. Struct. Integr., 5, 430-437. https://doi.org/10.1016/j.prostr.2017.07.192.
  7. Bhardwaj, G., Singh, I.V. and Mishra, B.K. (2015), "Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA", Comput. Method. Appl. Mech. Eng., 284, 186-229. https://doi.org/10.1016/j.cma.2014.08.015.
  8. Chakraborty, A. and Rahman, S. (2008), "Stochastic multiscale models for fracture analysis of functionally graded materials", Eng. Fract. Mech., 75, 2062-2086. https://doi.org/10.1016/j.engfracmech.2007.10.013.
  9. Choi, S.K., Canfield, R.A. and Grandhi, R.V. (2007), Reliability-Based Structural Design, Springer London, UK.
  10. Chowdhury, M.S., Song, C. and Gao, W. (2011), "Probabilistic fracture mechanics by using Monte Carlo simulation and the scaled boundary finite element method", Eng. Fract. Mech., 78, 2369-2389. https://doi.org/10.1016/j.engfracmech.2011.05.008.
  11. Daux, C., Moes, N., Dolbow, J., Sukumar, N. and Belytschko, T. (2000), "Arbitrary branched and intersecting cracks with the extended finite element method", Int. J. Numer. Method. Eng., 48, 1741-1760. https://doi.org/10.1002/1097-0207(20000830)48:12%3C1741::AID-NME956%3E3.0.CO;2-L.
  12. Evangelatos, G.I. and Spanos, P.D. (2011), "A collocation approach for spatial discretization of stochastic peridynamic modeling of fracture", J. Mech. Mater. Struct., 6, 1171-1195. http://doi.org/10.2140/jomms.2011.6.1171.
  13. Faisal, N., Cora, O.N., Bekci, M.L., Sliwa R.E., Sternberg Y., Pant, S., Degenhardt, R. and Prathuru, A. (2021), "Defect types", Structural Health Monitoring Damage Detection Systems for Aerospace, Springer, Cham, Switzerland.
  14. Guo, J.H., Lu, Z.X., Han, H.T. and Yang, Z. (2009), "Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material", Int. J. Solids Struct., 46, 3799-3809. https://doi.org/10.1016/j.ijsolstr.2009.07.002.
  15. Haldar, A. and Mahadevan, S. (2000), Probability, Reliability, and Statistical Methods in Engineering Design, Wiley, Hoboken, NJ, USA.
  16. Khasin, V.L. (2014), "Stochastic model of crack propagation in brittle heterogeneous materials", Int. J. Eng. Sci., 82, 101-123. https://doi.org/10.1016/j.ijengsci.2014.04.002.
  17. Kumar, S., Singh, I.V. and Mishra, B.K. (2014), "XFEM simulation of stable crack growth using J-R curve under finite strain plasticity", Int. J. Mech. Mater. Des., 10, 165-177. https://doi.org/10.1007/s10999-014-9238-1.
  18. Lal, A. and Markad K.M. (2021), "Probabilistic based nonlinear progressive failure analysis of piezoelectric laminated composite shell panels in hygrothermal environment", J. Aerosp. Eng. (ASCE), 34(6), https://doi.org/10.1061/(ASCE)AS.1943-5525.0001345.
  19. Lal, A. and Palekar, S.P. (2017), "Stochastic fracture analysis of laminated composite plate with arbitrary cracks using X-FEM", Int. J. Mech. Mater. Des., 13, 195-228. https://doi.org/10.1007/s10999-015-9325-y.
  20. Li, F.Z., Shih, C.F. and Needleman, A. (1985), "A comparison of methods for calculating energy release rates", Eng. Fract. Mech., 21, 405-421. https://doi.org/10.1016/0013-7944(85)90029-3.
  21. Lyathakula, K.R. and Yuan, F.G. (2021), "A probabilistic fatigue life prediction for adhesively bonded joints via ANNs-based hybrid model", Int. J. Fatig., 151, 106352. https://doi.org/10.1016/j.ijfatigue.2021.106352.
  22. Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Eng., 46, 131-150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO,2-J.
  23. Niu, X.P., Wang, R.Z., Liao, D., Zhu, S.P., Zhang, X.C. and Keshtegar, B. (2021), "Probabilistic modeling of uncertainties in fatigue reliability analysis of turbine bladed disks", Int. J. Fatig., 142, 105912. https://doi.org/10.1016/j.ijfatigue.2020.105912.
  24. Pais, M. (2011a), MATLAB Extended Finite Element (MXFEM) Code v1.2, www.matthewpais.com.
  25. Pais, M.J. (2011b), "Variable amplitude fatigue analysis using surrogate models and exact XFEM reanalysis", Ph.D. Dissertation, University of Florida, Gainesville, Florida, USA.
  26. Pawel, S. (2017), "An improved XFEM for the poisson equation with discontinuous coefficients", Arch. Mech. Eng., 64(1), 1-22. https://doi.org/10.1515/meceng-2017-0008.
  27. Pietruszczak, S. and Haghighat, E. (2014), "Modeling of fracture propagation in concrete structures using a constitutive relation with embedded discontinuity", Stud. Geotech. Mech., 36(4), 27-33. https://doi.org/10.2478/sgem-2014-0033.
  28. Rahman, S. and Chakraborty, A. (2011), "Stochastic multiscale fracture analysis of three-dimensional functionally graded composites", Eng. Fract. Mech., 78, 27-46. https://doi.org/10.1016/j.engfracmech.2010.09.006.
  29. Rahman, S. and Chen, G. (2005), "Continuum shape sensitivity and reliability analyses of nonlinear cracked structures", Int. J. Fract., 131, 189-209. https://doi.org/10.1007/s10704-004-3948-6.
  30. Rahman, S. and Rao, B.N. (2001a), "A perturbation method for stochastic meshless analysis in elastostatics", Int. J. Numer. Method. Eng., 50, 1969-1991. https://doi.org/10.1002/nme.106.
  31. Rahman, S. and Rao, B.N. (2001b), "An element-free Galerkin method for probabilistic mechanics and reliability", Int. J. Solids Struct., 38, 9313-9330. https://doi.org/10.1016/S0020-7683(01)00193-7.
  32. Rao, B.N. and Rahman, S. (2003), "An interaction integral method for analysis of cracks in orthotropic functionally graded materials", 32, 40-51. https://doi.org/10.1007/s00466-003-0460-1.
  33. Reddy, R.M. and Rao, B.N. (2008), "Stochastic fracture mechanics by fractal finite element method", Comput. Method. Appl. Mech. Eng., 198, 459-474. https://doi.org/10.1016/j.cma.2008.08.014.
  34. Rhee, H.C. and Salama, M.M. (1987), "Mixed-mode stress intensity factor solutions of a warped surface flaw by three-dimensional finite element analysis", Eng. Fract. Mech., 28, 203-209. https://doi.org/10.1016/0013-7944(87)90214-1.
  35. Rizov, V.I. (2021), "Viscoelastic inhomogeneous beam under time-dependent strains: A longitudinal crack analysis", Adv. Comput. Des., 6(2), pp.153-168. https://doi.org/10.12989/acd.2021.6.2.153.
  36. Soni, A., Sahin, K. and Navin, K. (2020), "Effect of parametric uncertainties on fracture behavior of cortical bone using XIGA", Eng. Fract. Mech., 233, 107079. https://doi.org/10.1016/j.engfracmech.2020.107079.
  37. Stefanou, G. (2009), "The stochastic finite element method: Past, present and future", Comput. Method. Appl. Mech. Eng., 198, 1031-1051. https://doi.org/10.1016/j.cma.2008.11.007.
  38. Tanaka, K. (1974), "Fatigue crack propagation from a crack inclined to the cyclic tensile axis", Eng. Fract. Mech., 6, 493-507. https://doi.org/10.1016/0013-7944(74)90007-1.
  39. Tian, R., Wen, L. and Wang, L. (2019), "Three-dimensional improved XFEM (IXFEM) for static crack problems", Comput. Method. Appl. Mech. Eng., 343, 339-367. https://doi.org/10.1016/j.cma.2018.08.029.
  40. Venanzio, G. (2020), "On the statistical nature of fatigue crack-growth through Monte Carlo simulations and experimental data", IOP Conf. Ser. Mat. Sci. Eng., 1214(1), 012020. https://doi.org/10.1088/1757-899x/1214/1/012020.
  41. Ventura, G., Budyn, E. and Belytschko, T. (2003), "Vector level sets for description of propagating cracks in finite elements", Int. J. Numer. Method. Eng., 58, 1571-1592. https://doi.org/10.1002/nme.829.
  42. Wang, L., Liang, J., Yang, Y.W. and Zheng, Y. (2018), "Time-dependent reliability assessment of fatigue crack growth modeling based on perturbation series expansions and interval mathematics", Theor. Appl. Fract. Mech., 95, 104-118. https://doi.org/10.1016/j.tafmec.2018.02.010.
  43. Wei, D. and Rahman, S. (2007), "Structural reliability analysis by univariate decomposition and numerical integration", Probab. Eng. Mech., 22(1), 27-38. https://doi.org/10.1016/j.probengmech.2006.05.004.
  44. Xu, H. and Rahman, S. (2005), "Decomposition methods for structural reliability analysis", Probab. Eng. Mech., 20, 239-250. https://doi.org/10.1016/j.probengmech.2005.05.005.
  45. Zhao, J., Xie, L., Liu, J. and Zhao, Q. (2012), "A method for stress intensity factor calculation of infinite plate containing multiple hole-edge cracks", Int. J. Fatig., 35, 2-9. https://doi.org/10.1016/j.ijfatigue.2011.06.001.
  46. Zhao, M., Gu, W. and Warner, D.H. (2022), "Atomic mechanism of near threshold fatigue crack growth in vacuum", Nat. Commun., 13, 812. https://doi.org/10.1038/s41467-022-28481-8.
  47. Zhou, X.Y., Gosling, P.D., Pearce, C.J., Ullah, Z. and Kaczmarczyk, L. (2016), "Perturbation-based stochastic multi-scale computational homogenization method for woven textile composites", Int. J. Solid. Struct., 80, 368-380. https://doi.org/10.1016/j.ijsolstr.2015.09.008.
  48. Zhu, S.P., Foletti, S. and Beretta S. (2017), "Probabilistic framework for multiaxial LCF assessment under material variability", Int. J. Fatig., 103, 371-385. https://doi.org/10.1016/j.ijfatigue.2017.06.019.
  49. Zhu, S.P., Liu, Q., Peng, W. and Zhang, X.C. (2018), "Computational-experimental approaches for fatigue reliability assessment of turbine bladed disks", Int. J. Mech. Sci., 142-143, 502-517. https://doi.org/10.1016/j.ijmecsci.2018.04.050.
  50. Zhuang, Z., Liu, Z., Cheng, B. and Liao, J. (2014), The Extended Finite Element Method, 1st Edition, Tsinghua University Press, Beijing, China.