Interaction Between a Nanofiber and an Arbitrarily Oriented Crack

Abstract

The interaction between a hollow cylindrical nanofiber and a crack in an infinite medium is investigated. The two-dimensional problem, when the crack lies in the cross-sectional plane of the fiber, is solved for a transversely isotropic fiber in an isotropic matrix phase. The reported work to date on crack—fiber interaction problems seems to be based on a conventional solid fiber cross-section, whereas in this study, a hollow fiber cross-section is considered. The crack is considered at various orientations with respect to the nanofiber. Mismatch between Young's modulus and Poisson's ratios of the fiber and matrix, fiber diameter, and fiber wall thickness, are some of the parameters in the study. Finite element method is used as the analysis tool to compute energy release rates in mixed mode conditions. Fiber—matrix interface tractions are also computed to investigate secondary failure mechanism. The behavior of a hollow nanofiber is shown to be significantly different from that of a fiber with a solid cross-section. However, with increasing nanofiber wall thickness the results of the present investigation are seen to converge to the solutions of a solid fiber. Finally, the influence of the properties of the interphase region between the hollow nanofiber and matrix on energy release rates is investigated.

Keywords

fracture finite element analysis crack interface energy release rate.

Get full access to this article

View all access options for this article.

References

Tamate, O. (1968). The Effect of the Circular Inclusion on the Stresses Around a Line Crack in a Sheet Under Tension, International Journal of Fracture Mechanics, 4(3): 257—265.

Erdogan, F. , Gupta, G.D. and Ratwani, M. (1974). Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack, Journal of Applied Mechanics, 41(4): 1007—1013.

Kunin, I. and Gommersstadt, B. (1985). On the Elastic Crack—Inclusion Interaction, International Journal of Solids and Structures, 21(7): 757—766.

Helsing, J. (1999). Stress Intensity Factors for a Crack in Front of an Inclusion, Engineering Fracture Mechanics, 64(2): 245—253.

Wang, J. , Mogilevskaya, S.G. and Crouch, S.L. (2003). Benchmark Results for the Problem of Interaction Between a Crack and a Circular Inclusion, Journal of Applied Mechanics, 70(4): 619—621.

Helsing, J. and Jonsson, A. (2002). On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature, Journal of Applied Mechanics, 69(1): 88—90.

Cheeseman, B.A. and Santare, M.H. (2000). The Interaction of a Curved Crack with a Circular Elastic Inclusion, International Journal of Fracture, 103(3): 259—277.

Atkinson, C. (1975). On the Stress Intensity Factors Associated with the Cracks Interacting with an Interface Between two Elastic Media, International Journal of Engineering Science , 13(5): 487—504.

Erdogan, F. , Gupta, G.D. and Cook, T.S. (1972). In: Sih, G.C. (ed.), Numerical Solutions of Singular Integral Equations, Vol. 1, pp. 1053—1067, Noordhoff International, Leyden, The Netherlands.

10.

Romeo, A. and Ballarini, R.A. (1995). A Crack Very Close to a Bimaterial Interface, ASME Journal of Applied Mechanics, 62(3): 614—619.

11.

Selvadurai, A.P.S. (1996). On Integral Equation Approaches to the Mechanics of Fibre-Crack Interaction, Engineering Analysis with Boundary Elements, 17(4): 287—294.

12.

Mao, R. and Sun, G. (1995). A Study of the Interaction Between Matrix Crack and Matrix-Fibre Interface, Engineering Fracture Mechanics , 51(3): 469—477.

13.

Li, Z. and Yang, L. (2002). The Near-Tip Stress Intensity Factor for a Crack Partially Penetrating an Inclusion, Journal of Applied Mechanics , 71(4): 465—469.

14.

Steif, P.S. (1987). A Semi-infinite Crack Partially Penetrating a Circular Inclusion, Journal of Applied Mechanics, 54(1): 87—92.

15.

Noda, N.A. , Takase, Y. and Hamashima, T. (2003). Generalized Stress Intensity Factors in the Interaction Within a Rectangular Array of Rectangular Inclusions, Archive of Applied Mechanics, 73(5—6): 311—322.

16.

Oiao, Y. , Kong, X. and Pan, E. (2004). Fracture Toughness of Thermoset Composites Reinforced by Perfectly Bonded Impenetrable Short Fiber, Engineering Fracture Mechanics, 71(18): 2621—2633.

17.

Bush, M.B. (1997). The Interaction Between a Crack and a Particle Cluster, International Journal of Fracture, 88(3): 215—232.

18.

Knight, M.G. , Wrobel, L.C. , Henshall, J.L. and De Lacerda , L.A. (2002). A Study of the Interaction Between a Propagating Crack and an Uncoated/Coated Elastic Inclusion using the BE Technique, International Journal of Fracture, 114(1): 47—61.

19.

Xiao, Z.M. and Chen, B.J. (2001). Stress Intensity Factor for a Griffith Crack Interacting with a Coated Inclusion, International Journal of Fracture , 108(3): 193—205.

20.

Liu, Y. , Ru, C.Q. , Schiavone, P. and Mioduchowski , A. (2001). New Phenomena Concerning the Effect of Imperfect Bonding on Radial Matrix Cracking in Fiber Composites, International Journal of Engineering Science, 39(18): 2033—2050.

21.

Yang, L. , Chen, Q. and Zhonghua, L. (2004). Crack—inclusion Interaction for Mode II Crack Analyzed by Eshelby Equivalent Inclusion Method, Engineering Fracture Mechanics, 71(9—10): 1421—1433.

22.

Li, R. and Chudnovsky, A. (1993). Variation of the Energy Release Rate as a Crack Approaches and Passes Through an Elastic Inclusion, International Journal of Fracture, 59(4): R69—R74.

23.

Li, R. and Chudnovsky, A. (1993). Energy Analysis of Crack Interaction with an Elastic Inclusion, International Journal of Fracture, 63(3): 247—261.

24.

Applied Sciences Incorporated , website at http://www.apsci.com/ppi-pyro3.html

25.

Lafdi, K. , University of Dayton Research Institute, Private communication .

26.

Ansys 8.1 (2002), SAS IP, Inc.

27.

Guo, X.E. , Liang, L.G. and Goldstein , S.A. (1998). Micromechanics of Osteonal Cortical Bone Fracture, ASME Journal of Biomechanical Engineering, 120: 112—117.