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Dynamic Problem Concerning Mode I Semi-Infinite Crack Propagation

Published online by Cambridge University Press:  29 January 2013

N. C. Lü ,
Y. H. Cheng ,
X. G. Li  and
J. Cheng
N. C. Lü*
Affiliation:
School of Material Science and Engineering, Shenyang Ligong University, Shenyang 110168, P. R., China Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P. R., China
Y. H. Cheng
Affiliation:
Department of Civil Engineering, Northeastern University, Shenyang 110006, P. R., China
X. G. Li
Affiliation:
Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P. R., China
J. Cheng
Affiliation:
Department of Astronautics and Mechanics, Harbin Institute of Technology, Harbin 150001, P. R., China
*
*Corresponding author (lnc_65@163.com)
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Abstract

By the approaches of the theory of complex functions, dynamic problem concerning mode I semi-infinite crack propagation was studied. Analytical solutions are very easily obtained by application of the measures of self-similar functions. The problems researched can be changed into Riemann-Hilbert problems and analytical solutions to semi-infinite crack under the condition of impulse loads and increasing loads Pt located at the origin of the coordinates, respectively, are attained.

Keywords

Complex functionsMode I semi-infinite crackDynamic problemSelf-similar functionsAnalytical solutions

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Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 309 - 318
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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References

REFERENCES

1.Charepanov, G. P., Mechanics of Brittle Fracture, Nauka, Moscow, pp. 732–792 (1973).Google Scholar
2.Hasebe, N. and Inohara, S., “Stress Analysis of a Semi- Infinite Plate with an Oblique Edge Crack,” Ingen Arch, 49, pp. 51–62 (1980).Google Scholar
3.Hasebe, N., “An Edge Crack in Semi-Infinite Plate Welded to a Rigid Stiffener,” Transactions of Japan Society of Civil Engineers, 314, pp. 149–157 (1981).Google Scholar
4.Chen, Y. Z. and Hasebe, N., “An Edge Crack Problem in a Semi-Infinite Plane Subjected to Concentrated Forces,” Applied Mathematics and Mechanics, 22, pp. 1279–1290 (2001).Google Scholar
5.Matbluly, M. S. and Nassar, M., “Elastostatic Analysis of Edge Cracked Orthotropic Strips,” ACTA Mechanica, 165, pp. 17–25 (2003).Google Scholar
6.Freund, L. B., Dynamic Fracture Mechanics, Cambridge University Press, UK (1990).Google Scholar
7.Huang, Y., Wang, W., Liu, C. and Rosakis, A. J., “Analysis of Intersonic Crack Growth in Unidirectional Rein- Forced Materials,” Journal of Mechanics and Physics of Solids, 47, pp. 1893–1916 (1999).CrossRefGoogle Scholar
8.Wu, K C., “Dynamic Crack Growth in Anisotropic Material,” International Journal of Fracture, 106, pp. 1–12 (2000).Google Scholar
9.Yao, X. F., Jin, G. C., Arakawa, K. and Takashi, K., “Experimental Studies on Dynamic Fracture Behavior of Thin Plates with Parallel Single Edge Cracks,” Polymer Testing, 21, pp. 933–940 (2002).Google Scholar
10.Sih, G. C. and MacDonald, B., “Fracture of Mechanics Applied to Engineering Problems. Strain Energy Density Fracture Criterion,” Engineering Fracture Mechanics, 6, pp. 361–386 (1974).Google Scholar
11.Rice, J. R., “Comment on Stress in an Infinite Strip Containing a Semi-Infinite Cracks,” Journal of Applied Mechanics, 34, pp. 248–249 (1967).Google Scholar
12.Hartranft, R. J. and Sih, G. C., “Alternating Method Applied to Edge and Surface Crack Problems,” In. G C Sih Edition Mechanics Fracture, pp. 177–238 (1973).Google Scholar
13.Solommer, E. and Soltesz, U., “Crack-Opening-Displacement Measurements of a Dynamically Loaded Crack,” Engineering Fracture Mechanics, 2, pp. 235–241 (1971).Google Scholar
14.Sih, G. C., Handbook of Stress Intensity Factors, Lehigh University, Bethlehem (1973).Google Scholar
15.Sih, G. C., Mechanics of Fracture Initiation and Propagation, Kluwer Academic Publisher, Boston (1991).Google Scholar
16.Parton, V. Z. and Boriskovsky, V. G., Dynamic Fracture Mechanics, Vol. 2 Propagation cracks, Revised Edition. Hemisphere Publishing Corporation, New York (1990).Google Scholar
17.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
18.Baker, B. R., “Dynamic Stresses Created by Moving Crack,” Journal of Applied Mechanics, 29, pp. 449–458 (1962).Google Scholar
19.Lü, N.-C., Li, X.-G., Cheng, Y.-H. and Cheng, J., “Fracture Dynamics Problem on Mode I Semi-Infinite Crack,” Archive of Applied Mechanics, 81, pp. 1181–1193 (2011).Google Scholar
20.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
21.Muskhelishvili, N. I., Singular Integral Equations. Nauka, Moscow (1968).Google Scholar
22.Muskhelishvili, N. I., Some Fundamental Problems in the Mathematical Theory of Elasticity. Nauka, Moscow (1968).Google Scholar
23.Atkinson, C., “The Propagation of a Brittle Crack in Anisotropic Material,” International Journal of Engineering Science, 3, pp. 77–91 (1965).Google Scholar
24.Lü, N.-C., Cheng, J. and Cheng, Y.-H., “Models of Fracture Dynamics of Bridging Fiber Pull-out of Composite Materials,” Mechanics Research Communications, 32, pp. 1–14 (2005).Google Scholar
25.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
26.Hoskins, R. F., Generalized Functions, Ellis Horwood (1979).Google Scholar
27.Gahov, F. D., Boundary-Value Problems, Fitzmatigiz, Moscow (1963).Google Scholar
28.Wang, X.-S., Singular Functions and Their Applications in Mechanics, Scientific Press, Beijing (1993).Google Scholar
29.Sih, G. C., Mechanics of Fracture 4. Elastodynamics Crack Problems, Noordhoff, Leyden (1977).Google Scholar
30.Kanwal, R. P. and Sharma, D. L., “Singularity Methods for Elastostatics,” Journal of Elasticity, 6, pp. 405–418 (1976).Google Scholar
31.Teaching Office of Mathematics of Tongji University, Advanced Mathematics (Vol. 1), Advanced Education Press, Beijing (1994).Google Scholar
32.Editorial Group of Mathematics Handbook, Mathematics Handbook, Advanced Education Press, Beijing (2002).Google Scholar
33.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
34.Lü, N. C., Cheng, Y. and Cheng, H. J., “Mode I Crack Tips Propagating at Different Speeds Under Differential Surface Tractions,” Theoretical and Applied Fracture Mechanics, 46, pp. 262–275 (2006).Google Scholar
35.KalthofJ, F. J, F., Beinert, J. and Winkler, S., “Measurements of Dynamic Stress Intensity Factors for Fastrunning and Arresting Cracks in Double-Cantilever-Beam Specimens,” Fast Fracture and crack Arrest, ASTM, STP 627, Philadelphia, Pa Publisher, pp. 161–176 (1977).Google Scholar
36.Kobayashi, A. S., “Dynamic Fracture Analysis by Dynam Ic Finite Element Method, Generation and Prediction Analyses,” Nonlinear and Dynarnic Fracture Mechanics, AMD, ASME, Publisher, 35, pp. 19–36, New York (1979).Google Scholar
36.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Fracture: Part 1, Crack Initiation and Arrest,” International Journal of Fracture, 25, pp. 247–262 (1984).Google Scholar
37.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynam Ic Fracture: Part 2, Microstructural Aspects,” International Journal of Fracture, 26, pp. 65–80 (1984).Google Scholar
38.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Frac Ture: Part 3, on Steady-State Crack Propagation and Crack Branching [J],” International Journal of Fracture, 26, pp. 141–152 (1984).Google Scholar
39.Ravi-Chandar, K. and Knauss, W. G., “An Experimental Investigation Into Dynamic Frac Ture: Part 4, on the Interaction of Stress Waves with Propagation Cracks,” International Journal of Fracture, 26, pp. 189–200 (1984).Google Scholar
40.Freund, L. B., “Crack Propagation in an Elastic Solid Subjected to General Loading- I. Constant Rate of Extension,” Journal of the Mechanics and Physics of Solids, 20, pp. 129–140 (1972).Google Scholar
41.Sneddon, N. I., Fourier Transform, McGraw- Hill, New York (1951).Google Scholar
42.Muskhelishvili, N. I., Some Basic Problems from the Mathematical Theory of Elasticity, Noordoff, Groningen (1953).Google Scholar
43.Galin, L. A., Contact Problems in Elasticity Theory, Gittl, Moscow (1953).Google Scholar
44.Broberg, K. B., “Crack Expanding with Constant Velocity in an Anisotropic Solid Under Anti-Plane Strain,” International Journal of Fracture, 93, pp. 1–12 (1998).Google Scholar
45.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).Google Scholar
46.Lü, N.-C., Cheng, Y.-H., Wang, Y.-T., Cheng, J., “Fracture Dynamics Problems of Orthotropic Solids Under Anti-Plane Shear Loading,” Nonlinear Dynamics, 63, pp. 793–806 (2011).Google Scholar
47.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
48.Kostrov, B. V., “Self-similar Problems of Propagation of Shear Cracks,” Journal of Applied Mathematics Mechanics, 28, pp. 1077–1087 (1964).Google Scholar
49.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).CrossRefGoogle Scholar
50.Lü, N.-C., Cheng, Y.-H., Li, X.-G. and Cheng, J., “Dynamic Propagation Problems Concerning the Surfaces of Asymmetrical Mode III Crack Subjected to Moving Loads,” Applied Mathematics Mechanics, 29, pp. 1279–1290 (2008).Google Scholar
51.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, 13, pp. 491–506 (1975).Google Scholar
52.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
53.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
54.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
55.Lü, N.-C., Yang, D.-N., Cheng, Y.-H. and Cheng, J., “Asymmetrical Dynamic Propagation Problems on Mode III Interface Crack,” Applied Mathematics Mechanics, 28, pp. 501–510 (2007).Google Scholar
56.Lü, N.-C., Cheng, J., Tian, X.-B. and Cheng, Y.-H., “Dynamic Propagation Problem on Dugdale Model of Mode III Interface Crack,” Applied Mathematics Mechanics, 26, pp. 1212–1221 (2005).Google Scholar
57.Lü, N.-C., Cheng, Y.-H. and Cheng, Jin., “Dynamic Propagation Problems Concerning Asymmetrical Mode III Interface Crack,” International Journal for Computational Methods in Engineering Science and Mechanics, 9, pp. 246–253 (2008).Google Scholar
58.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
69.Lü, N.-C., Cheng, J. and Cheng, Y.-H., “Self-Similar Solutions of Fracture Dynamics Problems on Axially Symmetry,” Applied Mathematics Mechanics, 22, pp. 1429–1435 (2001).Google Scholar
60.Broberg, K. B., “The Propagation of a Brittle Crack,” Archiv fur Fysik, 3, pp. 159–192 (1960).Google Scholar