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Asymmetrical Dynamic Propagation Problem on the Edges of Mode III Interface Crack Subjected to Superimpose Loads

Published online by Cambridge University Press:  29 January 2013

N.-C. Lü ,
X.-G. Li ,
Y.-H. Cheng  and
J. Cheng
N.-C. Lü
Affiliation:
School of Material Science and Engineering, Shenyang Ligong University, Shenyang 110159, P R, China Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P R, China
X.-G. Li
Affiliation:
School of Civil Engineering, Harbin Engineering University, Harbin 150001, P R, China
Y.-H. Cheng*
Affiliation:
Department of Civil Engineering, Northeastern University, Shenyang 110006, P R, China
J. Cheng
Affiliation:
Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P R, China
*
*Corresponding author (cyh_neu@163.com)
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Abstract

By application of the theory of complex variable functions, asymmetrical dynamic propagation problem on the edges of mode III interface crack subjected to superimpose loads was studied. Analytical solutions of the stresses displacements and dynamic stress intensity factors are obtained by means of self- similar functions. The problems researched can be facilely transformed into Riemann-Hilbert problems and their closed solutions are attained rather simple according to this measure. After those solutions are utilized by superposition theorem, the solutions of arbitrarily complex problems can be gained.

Keywords

Complex variable functionsMode III interface crackAsymmetrical dynamic propagationSelf- similar functionAnalytical solutions
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 319 - 326
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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References

REFERENCES

1.Liu, X. F., “Closed-Form Solution for a Mode-III Interface Crack Between Two Bonded Dissimilar Elastic Layers,” International Journal of Fracture, 109, pp. L3–L8 (2001).Google Scholar
2.Comninou, M., “The Interface Crack,” ASME Journal of Applied Mechanics, 44, pp. 631–636 (1977).Google Scholar
3.Korsunsky, A. M., “Debonding of a Weak Interface in Front of a Through-Thickness Crack,” International Journal of Fracture, 109, pp. L35–L40 (2001).CrossRefGoogle Scholar
4.Wei, P. J., Zhang, S. Y., Wu, Y. L. and Li, R. K. Y. “Dynamic SIF of Interface Crack between Two Dissimilar Viscoelastic Bodies Under Impact Loading,” International Journal of Fracture, 105, pp. 127–136 (2000).Google Scholar
5.Needleman, A. and Rosakis, A J., “The Effect of Bond Strength and Loading Rate on the Conditions Governing the Attainment of Intersonic Crack Growth Along Interfaces,” Journal of the Mechanics and Physics of Solids, 47, pp. 2411–2449 (1999).CrossRefGoogle Scholar
6.Lee, K. W. and Earmme, Y. Y., “An Interfacial Edge Crack Anistropic Bimaterial Under Anti-Plane Singularity,” International Journal of Fracture, 104, pp. 15–23 (2000).Google Scholar
7.Choi, S. R., Chong, C. H. and Chai, Y. S., “Interfacial Edge Cracking in Two Bonded Dissimilar Orthotropic Quarter Planes Under Anti-plane Shear,” International Journal of Fracture, 67, pp. 143–150 (1994).CrossRefGoogle Scholar
8.Marur, P. R. and Tippur, H. V., “Dynamic Response of Bimaterial and Graded Interface Cracks Under Impact Loading,” International Journal of Fracture, 103, pp. 95–109 (2000).Google Scholar
9.Arata, J. J. M., Needleman, A., Kumar, K. S. and Curtin, W. A., “Dynamic Response of Bimaterial and Graded Interface Cracks Under Impact Loading,” International Journal of Fracture, 105, pp. 321–342 (2000).CrossRefGoogle Scholar
10.Brock, L. M., “Dynamic Intensity Factors for an Interface Flaw Extending at a Non-uniform Rate,” Journal of Elasticity, 4, pp. 51–63 (1974).CrossRefGoogle Scholar
11.Rubin-Gonzalea, C. and Mason, J. J., “Dynamic Intensity Factors at the Tip of a Uniformly Loaded Semi-Infinite Crack in an Orthotropic Material,” Journal of Mechanics and Physics of Solids, 48, pp. 899–925 (2000).Google Scholar
12.Comninou, Maria., “On the Behaviour of Interface Cracks,” International Journal of Structural Mechanics and Materials Science, 1, pp. 249–264 (1980).Google Scholar
13.Sih, G. C., Mechanics of Fracture Initiation and Propagation, Kluwer Academic Publisher, Boston (1991).Google Scholar
14.Knauss, W. G., “Dynamic Fracture,” International Journal of Fracture, 25, pp. 35–91 (1987).Google Scholar
15.Lü, N.-C., Cheng, Y.-H. and Wang, Y.-T., Two “Dynamic Propagation Problems of Mode III Interface Crack,”Advanced Materials Research, pp. 477–481 (2011).Google Scholar
16.Wang, Y.-S. and Wang, D., “Transient Motion of an Interface Dislocation and Self-Similar Propagation of an Interface Crack: Anti-Plane Motion,” Engineering Fracture Mechanics, 55, pp. 717–725 (1996).Google Scholar
17.Lü, N. C., Cheng, J. and Cheng, Y. H., “Mode III Interface Crack Propagation in Two Joined Media with Weak Dissimilarity and Strong Orthotropy,” Theoretical and Applied Fracture Mechanics, 36, pp. 219–231 (2001).Google Scholar
18.Cheng, J., “Crack Propagation Problem in Interface Between Dissimilar Othotropic Media,” Acta Mechanica Solida Sinica, 8, pp. 108–116 (1987).Google Scholar
19.Lü, N.-C., Tang, L.-Q. and Cheng, Y.-H., “Solution of Anti-Plane Dynamic Self-Similar Propagation Crack Problem Along Interfaces of Orthotropic Composite Materials,” Chinese Quarterly of Mechanics, 24, pp. 108–112 (2003).Google Scholar
20.Yang, J.-Y., Lü, N.-C. and Tang, L.-Q., “A Dynamic Propagation Problem on Mode III Interface Crack Subjected to Homogeneous Loads at the Central Zone Along a Weak Interface,” Journal of Harbin Institute of Technology, 37, pp. 414–417 (2004).Google Scholar
21.Lü, N.-C., Yang, D.-N., Cheng, Y.-H. and Cheng, J., “Asymmetrical Dynamic Propagation Problems on Mode III Interface Crack,” Applied Mathematics and Mechanics, 28, pp. 501–510 (2007).CrossRefGoogle Scholar
22.Lü, N. C., Cheng, Y. H., Li, X. G. and Cheng, J., “Asymmetrical Dynamic Propagation Problems Concerning Mode III Interface Crack,” Composite Interfaces, 17, pp. 37–48 (2010).Google Scholar
23.Wu, K.-C., “Transient Motion of an Interfacial Line Force or Dislocation in an Anisotropic Elastic Material,” International Journal of Solids and Structures, 40, pp. 1811–1823 (2003).Google Scholar
24.Wu, K.-C.Chen, S.-H., “Transient Motion of an Anisotropic Elastic Bimaterial Due to a Line Source,” International Journal of Solids and Structures, 44, pp. 2269–2284 (2007).Google Scholar
25.Muskhelishvili, N. I., Some Fundamental Problems in the Mathematical Theory of Elasticity. Nauka, Moscow (1966).Google Scholar
26.Muskhelishvili, N. I., Singular Integral Equations, Nauka, Moscow (1966).Google Scholar
27.Atkinson, C., “On the Dynamic Stress and Displacement Field Associated with a Crack Propagating Across the Interface Between Two Media,” International Journal of Engineering Science, pp. 491–506 (1974).Google Scholar
28.Atkinson, C., “The Propagation of a Brittle Crack in Anisotropic Material,” International Journal of Engineering Science, 3, pp. 77–91 (1965).Google Scholar
29.Lü, N.-C., Cheng, Y.-H., Tian, X.-B. and Cheng, J., “Dynamic Propagation Problem on Dugdale Model of Mode III Interface Crack,” Applied Mathematics and Mechanics, 26, pp. 1212–1221 (2005).Google Scholar
30.Charepanov, G. P., Mechanics of Brittle Fracture, Nauka, Moscow (1973).Google Scholar
31.Lü, N. C., Cheng, Y. H., Li, X. G. and Cheng, J., “Dynamic Propagation Problem of Mode I Semi-Infinite Crack Subjected to Superimpose Loads,” Fatigue & Fracture of Engineering Materials & Structures, 33, pp. 141–148 (2010).Google Scholar
32.Charepanov, G. P. and Afanasov, E. F., “Some Dynamic Problems of the Theory of Elasticity. A Review,” International Journal of Engineering Science, 12, pp. 665–690 (1970).Google Scholar
33.Lü, N. C., Cheng, Y. H. and Cheng, J., “Mode I Crack Tips Propagating at Different Speeds Under Differential Surface Tractions,” Fatigue & Fracture of Engineering Materials & Structures, 46, pp. 262–275 (2006).Google Scholar
34.Hoskins, R. F., Generalized Functions. Ellis Horwood, New York (1979).Google Scholar
35.Gahov, F. D., Boundary-value problems, Fizmatgiz, Moscow (1963).Google Scholar
36.Sih, G. C., Mechanics of Fracture 4. Elastodynamics Crack Problems, Noordhoff, Leyden (1977).Google Scholar
37.Kanwal, R. P. and Sharma, D. L., “Singularity Methods for Elastostatics,” Journal of Elasticity, 6, pp. 405–418 (1976).Google Scholar
38. Teaching Office of Mathematics of Tongji University, Advanced Mathematics, Advanced Education Press, Beijing (1994).Google Scholar
39.Wu, K. C., “Dynamic Crack Growth in Anisotropic Material,” International Journal of Fracture, 106, pp. 1–12 (2000).Google Scholar
40.Knauss, W. G. and Ravi-Chandar, K, “Some Basic Problems in Stress Wave Dominated Fracture,” International Journal of Fracture, 27, pp. 127–143 (1985).Google Scholar
41.Knauss, W. G. and Ravi-Chandar, K., “An Experimental Investigation Into Dynamic Fracture: Part 1, Crack Initiation and Arrest,” International Journal of Fracture, 25, pp. 247–262 (1984).Google Scholar
42.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Fracture: Pt. 2, Microstructural Aspects,” International Journal of Fracture, 26, pp. 65–80 (1984).Google Scholar
43.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Fracture: Pt. 3, on Steady-State Crack Propagation and Crack Branching,” International Journal of Fracture, 26, pp. 141–154 (1984).CrossRefGoogle Scholar
44.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Fracture: Pt. 4, on the Interaction of Stress Waves with Propagation Cracks,” International Journal of Fracture, 26, pp. 189–200 (1984).Google Scholar
45.Schovanec, L. and Walton, J. R., “On the Order of the Stress Singularity for an Antiplane Shear Crack at the Interface of Two Bonded Inhomogeneous Elastic Materials,” Journal of Applied Mechanics, 55, pp. 234–236 (1988).CrossRefGoogle Scholar
46.Lü, N. C., Cheng, Y. H., Si, H. L. and Cheng, J., “Dynamics of Asymmetrical Crack Propagation in Composite Materials,” Theoretical and Applied Fracture Mechanics, 47, pp. 260–273 (2007).Google Scholar
47.Lü, N. C., Cheng, J. and Cheng, Y. H., “A Dynamic Model of Bridging Fiber Pull-out of Composite Materials,” Mechanics Research Communications, 32, pp. 1–14 (2005).Google Scholar
48.Sneddon, N. I., Fourier Transform, McGraw-Hill, New York (1951).Google Scholar
49.Muskhelishvili, N. I., Some Basic Problems from the Mathematical Theory of Elasticity, P. Noordoff, Groningen, Holland (1953).Google Scholar
50.Galin, L. A., Contact Problems in Elasticity Theory, GITTL, Moscow (1953).Google Scholar
51.Broberg, K. B., “The Propagation of a Brittle Crack,” Arch. fur Fysik, pp. 159–192 (1960).Google Scholar
52.Lü, N.-C., Cheng, Y.-H. and Cheng, J., “An Asymmetrical Self-Similar Dynamic Crack Model of Bridging Fiber Pull-Out in Unidirectional Composite Materials,” International Journal for Computational Methods in Engineering Science and Mechanics, 9, pp. 171–179 (2008).Google Scholar
53.Lü, N.-C., Li, X.-G., Cheng, Y.-H. and Cheng, J., “An Asymmetrical Dynamic Crack Model of Bridging Fiber Pull-Out of Composite Materials,” Fibers and Polymers, 12, pp. 79–88 (2011).Google Scholar
54.Lü, N. C., Cheng, Y. H., Li, X. G. and Cheng, J., “Asymmetrical Dynamic Fracture Model of Bridging Fiber Pull-Out of Unidirectional Composite Materials,” Nonlinear Dynamics, 66, pp. 1–14 (2011).Google Scholar
55.Wang, Y. H., Cheung, Y. K. and Woo, C. W., “Anti-Plane Shear Problem for an Edge Crack in a Finite Orthotropic Plate,” Engineering Fracture Mechanics, 42, pp. 971–976 (1992).Google Scholar
56.Lü, N.-C., Cheng, Y.-H. and Wang, Y.-T., “Two Dynamic Propagation Problems of Symmetrical Mode III Crack,” Applied Mechanics and Materials, 44–47, pp. 693–696 (2011).Google Scholar
57.Lü, N.-C., Cheng, Y.-H., Wang, Y.-T. and Cheng, J., “Dynamic Extension Problems Concerning Asymmetrical Mode III Crack,” Applied Mathematical Modelling, 35, pp. 2499–2507 (2011).CrossRefGoogle Scholar
58.Lü, N.-C., Cheng, Y.-H., Wang, Y.-T. and Cheng, J., “Fracture Dynamics Problems of Orthotropic Solids Under Anti-Plane Shear Loading,” Nonlinear Dynamics, 63, pp. 793–806 (2011).Google Scholar
59.Lü, N. C., Cheng, Y. H., Wang, Y. T. and Cheng, J., “Dynamic Fracture of Orthotropic Solids Under Anti-Plane Shear Loading,” Mechanics of Advanced Materials and Structures, 17, pp. 215–224 (2010).Google Scholar
60.Wang, Y. H., “Analysis of an Edge-Cracked Body Subjected to a Longitudinal Shear Force,” Engineering Fracture Mechanics, 42, pp. 45–50 (1992).Google Scholar
61.Lü, N.-C., Cheng, J. and Cheng, Y.-H., “Self-similar Solutions of Fracture Dynamics Problems on Axially Symmetry,” Applied Mathematics and Mechanics, 22, pp. 1429–1435 (2001).Google Scholar