XFEM simulation of cracks, holes and inclusions in functionally graded materials
Source abstract
Abstract
The present work aims at the numerical simulation of inhomogeneities/discontinuities (cracks, holes and inclusions) in functionally graded materials (FGMs) using extended finite element method (XFEM). A FGM with unidirectional gradation in material properties is modeled under plane strain condition. The domain contains a major crack either at the center or at the edge of the domain along with multiple minor discontinuities/flaws such as minor cracks and/or voids/inclusions distributed all over the domain. The effect of the variation in stress intensity factor (SIF) of the major crack due to the presence of the minor cracks and voids/inclusions is studied in detail. The simulations show that the presence of minor discontinuities significantly affects the values of SIFs.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Geotechnical Engineering and Underground Structures · Fatigue and fracture mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (39)
Show source-provided references
1. Bordas, S., Nguyen, P., Dunant, C., Guidoum, A., Dang, H.: An extended finite element library. Int. J. Numer. Methods Eng. 71, 703–732 (2007)10.1002/nme.1966 ↗
2. Carpinteri, A., Paggi, M., Pugno, N.: An analytical approach for fracture and fatigue in functionally graded materials. Int. J. Fract. 141, 535–547 (2006)10.1007/s10704-006-9012-y ↗
3. Chen, S.C., Wang, T.C.: Finite element solutions for plane strain mode-I crack with strain gradient effects. Int. J. Solids Struct. 39, 1241–1257 (2002)10.1016/S0020-7683(01)00233-5 ↗
4. Cheng, Z., Zhong, Z.: Analysis of a moving crack in a functionally graded strip between two homogeneous layers. Int. J. Mech. Sci. 49, 1038–1046 (2007)10.1016/j.ijmecsci.2007.01.003 ↗
5. Cheng, Z., Gao, D., Zhong, Z.: Crack propagating in functionally graded coating with arbitrarily distributed material properties bonded to a homogeneous substrate. Acta Mech. Solida Sin. 23, 437–446 (2011)10.1016/S0894-9166(10)60046-8 ↗
6. Chudnovsky, A., Kachanov, M.: Interaction of a crack with a field of micro cracks. Appl. Eng. Sci. 21, 1009–1018 (1983)
7. Comi, C., Mariani, S.: Extended finite element simulation of quasi-brittle fracture in functionally graded materials. Comput. Methods Appl. Mech. Eng. 196, 4013–4026 (2007)10.1016/j.cma.2007.02.014 ↗
8. Dag, S., Yildirim, B., Sarikaya, D.: Mixed-mode fracture analysis of orthotropic functionally graded materials under mechanical and thermal loads. Int. J. Solids Struct. 44, 7816–7840 (2007)10.1016/j.ijsolstr.2007.05.010 ↗
9. Dolbow, J.E., Gosz, M.: On the computation of mixed-mode stress intensity factors in functionally graded materials. Int. J. Solids Struct. 39, 2557–2574 (2002)10.1016/S0020-7683(02)00114-2 ↗
10. Gong, S.X., Horii, H.: General solution to the problem of micro cracks near the tip of a main crack. J. Mech. Phys. Solids 37, 27–46 (1989)10.1016/0022-5096(87)90003-2 ↗
11. Gong, S.X., Meguid, S.A.: A general solution to the antiplane problem of an arbitrarily located elliptical hole near the tip of a main crack. Int. J. Solids Struct. 28, 249–263 (1991)10.1016/0020-7683(91)90209-X ↗
12. Guo, L.-C., Noda, N.: Modeling method for a crack problem of functionally graded materials with arbitrary properties-piecewise exponential model. Int. J. Solids Struct. 44, 6768–6790 (2007)10.1016/j.ijsolstr.2007.03.012 ↗
13. Huang, G.Y., Wang, Y.S., Dietmar, G.: Fracture analysis of functionally graded coatings: plane deformation. Eur. J. Mech. A Solids 22, 535–544 (2003)10.1016/S0997-7538(03)00064-0 ↗
14. Lee, S., Song, J., Yoon, Y., Zi, G., Belytschko, T.: Combined extended and superimposed finite element method for cracks. Int. J. Numer. Methods Eng. 59, 1119–1136 (2009)10.1002/nme.908 ↗
15. Ma, J., Zhong, Z., Zhang, C.: Analysis of a crack in a functionally graded strip with a power form shear modulus. Acta Mech. Solida Sin. 22(5), (2009)10.1016/S0894-9166(09)60297-4 ↗
16. Meguid, S.A., Gaultier, P.E., Gong, S.X.: A comparison between analytical and finite element analysis of main crack-micro crack interaction. Eng. Fract. Mech. 38, 451–465 (1991)10.1016/0013-7944(91)90095-I ↗
17. Meguid, S.A., Gong, S.X.: Stress concentration around interacting circular holes: a comparison between theory and experiments. Eng. Fract. Mech. 44, 247–256 (1993)10.1016/0013-7944(93)90049-X ↗
18. Meguid, S.A., Wang, X.D.: The dynamic interaction of a micro crack with a main crack under antiplane loading. Int. J. Solids Struct. 31, 1085–1097 (1994)10.1016/0020-7683(94)90165-1 ↗
19. Meguid, S.A., Zhu, Z.-H.: A novel finite element for treating inhomogeneous solids. Int. J. Numer. Methods Eng. 38, 1579–1592 (1995a)10.1002/nme.1620380908 ↗
20. Meguid, S.A., Zhu, Z.-H.: Stress distribution in dissimilar materials containing inhomogeneities near the interface using novel finite element. Finite Elem. Anal. Des. 20, 283–298 (1995b)10.1016/0168-874X(95)00036-S ↗
21. Meguid, S.A.: Main crack-micro crack interaction of hydrogenated and outgassed austenitic steels. Int. J. Hydrogen Energy 22, 377–381 (1997)10.1016/S0360-3199(96)00088-2 ↗
22. Meguid, S.A., Wang, X.D.: On the dynamic behavior of interacting micro defects in advanced composite materials. Int. J. Impact Eng. 19(5–6), 503–514 (1997)10.1016/S0734-743X(97)00011-0 ↗
23. Moes, N., Dolbow, J., Belytschko, T.: A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng. 46, 131–150 (1999)10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J ↗
24. Mohammadi, S.: Extended Finite Element Method for Fracture Analysis of Structures, 1st edn. Blackwell Publishing Limited, Oxford (2008)10.1002/9780470697795 ↗
25. Mori, T., Saito, K., Mura, T.: An inclusion model for crack arrest in a composite reinforced by sliding fibers. Mech. Mater. 7, 49–58 (1988)10.1016/0167-6636(88)90005-1 ↗
26. Mori, K., Tabarrok, B., Tong, X.: A new method for analysis of arbitrarily shaped cracks by the body force method. Int. J. Mech. Sci. 36, 881–895 (1994)10.1016/0020-7403(94)90052-3 ↗
27. Nelli Silva, E.C., Paulino, G.H.: Topology optimization applied to the design of functionally graded materials (FGM) structures. In: XXI ICTAM, Warsaw, Poland, 15–21 Aug 2004
28. Prabhakar, R.M., Tippur, H.V.: Numerical analysis of crack-tip fields in functionally graded materials with a crack normal to the elastic gradient. Int. J. Solids Struct. 37, 5353–5370 (2000)10.1016/S0020-7683(99)00207-3 ↗
29. Rao, B.N., Rahman, S.: An interaction integral method for analysis of cracks in orthotropic functionally graded materials. Comput. Mech. 32, 40–51 (2003)10.1007/s00466-003-0460-1 ↗
30. Rao, B.N., Rahman, S.: A continuum shape sensitivity method for fracture analysis of orthotropic functionally graded materials. Mech. Mater. 37, 1007–1025 (2005)10.1016/j.mechmat.2005.01.001 ↗
31. Rao, B.N., Rahman, S.: A continuum shape sensitivity method for fracture analysis of isotropic functionally graded materials. Comput. Mech. 38, 133–150 (2006)10.1007/s00466-005-0726-x ↗
32. Sukumar, N., Chopp, D., Moes, N., Belytschko, T.: Modeling holes and inclusions by level sets in the extended finite element method. Comput. Methods Appl. Mech. Eng. 190, 6183–6200 (2001)10.1016/S0045-7825(01)00215-8 ↗
33. Wang, X.D., Meguid, S.A.: Dynamic interaction between a matrix crack and a circular inhomogenity with a distinct interphase. Int. J. Solids Struct. 36, 517–531 (1999)10.1016/S0020-7683(98)00039-0 ↗
34. Wang, B.-L., Mai, Y.-W.: Multiple surface cracks in a piezoelectric layer bonded to an elastic substrate under transient electromechanical loads. Mech. Mater. 39, 564–579 (2007)10.1016/j.mechmat.2006.08.009 ↗
35. Wang, S., Dempsey, J.P.: A cohesive edge crack. Eng. Fract. Mech. 78, 1353–1373 (2011)10.1016/j.engfracmech.2011.02.018 ↗
36. Zhang, Ch., Sladek, J., Sladek, V.: Crack analysis in unidirectionally and bidirectionally functionally graded materials. Int. J. Fract. 129, 385–406 (2004)10.1023/B:FRAC.0000049495.13523.94 ↗
37. Zhang, Ch., Sladek, J., Sladek, V.: Antiplane crack analysis of a functionally graded material by a BIEM. Comput. Mater. Sci. 32, 611–619 (2005)10.1016/j.commatsci.2004.09.002 ↗
38. Zhang, L., Kim, J.-H.: A complex variable approach for asymptotic mode-III crack-tip fields in an anisotropic functionally graded material. Eng. Fract. Mech. 76, 2512–2525 (2009)10.1016/j.engfracmech.2009.09.002 ↗
39. Zhu, Z.-H., Meguid, S.A.: On the thermoelastic stress of multiple interacting inhomogeneities. Int. J. Solids Struct. 37, 2313–2330 (2000)10.1016/S0020-7683(98)00342-4 ↗