Wave-crack interaction in finite elastic bodies
Source abstract
Abstract
This paper continues studies in Lalegname et al. (Int J Fract 152:97–125, 2008) on crack propagation in a bounded linear elastic body under the influence of incident waves. In Lalegname et al. (2008) we have considered shear waves, whereas in this paper we discuss the influence of plane elastic waves to a running crack. Actually, the time dependent problem is formulated in a two-dimensional current cracked configuration by a system of linear elasto-dynamic equations. In order to describe the behaviour of the elastic fields near the straight crack tip, we transform these equations to a reference configuration and derive the dynamic stress singularities. Furthermore, we assume that an energy balance law is valid. Exploiting the knowledge on the singular behaviour of the crack fields, we derive from the energy balance law a dynamic energy release rate. Comparing this energy release rate with an experimentally given fracture toughness we get an ordinary differential equation for the crack tip motion. We present first numerical simulations for a Mode I crack propagation.
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Research context
OpenAlex topics: Numerical methods in engineering · Ultrasonics and Acoustic Wave Propagation · Contact Mechanics and Variational Inequalities
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References (34)
Show source-provided references
1. ASTM E 1823-96 (1996) Standard terminology relating to fatigue and fracture testing-Annual Book of ASTM Standards, volume 03.01. American Society for Testing and Materials, West Conshohocken
2. Barenblatt GI, Cherepanov LR (1960) On the wedging of brittle bodies. J Appl Math Mech 23: 993–101410.1016/0021-8928(60)90076-9 ↗
3. Bourdin B, Larsen CJ, Richardson CL (2011) A time-discrete model for dynamic fracture based on crack regularization. Int J Fract 168: 133–14310.1007/s10704-010-9562-x ↗
4. Bratov V, Petrov Y (2007) Application of incubation time approach to simulate dynamic crack propagation. Int J Fract 146: 53–6010.1007/s10704-007-9135-9 ↗
5. Broberg KB (1960) The propagation of a brittle crack. Arkiv för Fysik 18: 159–192
6. Brokate M, Khludnev A (2004) On crack propagation shapes in elastic bodies. Z Angew Math Phys 55: 318–32910.1007/s00033-003-3026-3 ↗
7. Buehler MJ, Gao H, Huang Y (2003) Atomistic and continuum studies of a suddenly stopping supersonic crack. Comput Mater Sci 28: 385–40810.1016/j.commatsci.2003.08.001 ↗
8. Destuynder P, Jaoua M (1981) Sur une interprétation mathématique de l’intégrale de rice en théorie de la rupture fragile. Math Methods Appl Sci 3: 70–8710.1002/mma.1670030106 ↗
9. Francfort GA, Marigo JJ (1998) Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids 46(8): 1319–134210.1016/S0022-5096(98)00034-9 ↗
10. Freund LB (1990) Dynamic fracture mechanics. Cambridge University Press, New York10.1017/CBO9780511546761 ↗
11. Friedman A, Hu B, Velazquez JJL (2000) The evolution of stress intensity factors and the propagation of cracks in elastic media. Arch Rational Mech Anal 152: 103–13910.1007/s002050000072 ↗
12. Giaquinta M, Hildebrandt S (1996) Calculus of variations. Springer, Berlin
13. Gross D (1996) Bruchmechanik. Springer, Berlin10.1007/978-3-662-06174-9 ↗
14. Haboussa D, Grégoire D, Elguedj T, Maigre H, Combescure A (2011) X-FEM analysis of the effects of holes or other cracks on dynamic crack propagations. Int J Numer Meth Eng 86: 618–63610.1002/nme.3128 ↗
15. Kovtunenko VA (2001) Sensitivity of cracks in 2d-Lamé problem via material derivatives. Z Angew Math Phys 52: 1071–108710.1007/PL00001584 ↗
16. Lalegname A, Sändig A-M, Sewell G (2008) Analytical and numerical treatment of a dynamic crack model. Int J Fract 152: 97–12510.1007/s10704-008-9274-7 ↗
17. Lalegname A (2009) Modeling, analysis and simulation of 2D dynamic crack propagation. PhD thesis, Stuttgart University
18. Lalegname A, Sändig A-M (2011) Wave-crack interaction in finite elastic bodies. Report of the Institute of Applied Analysis and Numerical Simulation 2011/002 http://preprints.ians.uni-stuttgart.de/downloads/show-preprintvolume.php?volume=201110.1007/s10704-011-9650-6 ↗
19. Lamé G (1852) Leçons sur la Théorie Mathématique de l’Elasticité des Corps Solides. Bachelier, Paris
20. Marder M (1999) Molecular dynamics of cracks, volume 1. Comput Sci Eng 5: 48–5510.1109/5992.790587 ↗
21. Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Englewood Cliffs
22. Malvern LE (1953) Methods of theoretical physics, volume I and II. McGraw-Hill, New York
23. Neuber H (1986) Ein neuer Ansatz zur Lösung raumlicher Probleme der Elastizitätstheorie. Z Angew Math Mech 23: 585–614
24. Nicaise S, Sändig A-M (2007) Dynamic crack propagation in a 2d elastic body: the out-of-plane case. J Math Anal Appl 329: 1–3010.1016/j.jmaa.2006.06.043 ↗
25. Owen DM, Zhuang S, Rosakis AJ, Ravichandran G (1998) Experimental determination of dynamic crack initiation and propagation fracture toughness in thin aluminum sheets. Int J Fract 90: 153–17410.1023/A:1007439301360 ↗
26. Papkovich PF (1932) The representation of the general integral of the fundamental equations of elasticity theory in terms of harmonic functions (in russian). Izv Akad Nauk SSSR Phys Math Ser 10: 1425
27. Rèthorè J, Gravouil A, Combescure A (2005) An energy-conserving scheme for dynamic crack growth using the eXtended finite element method. Int J Numer Meth Eng 63: 631–65910.1002/nme.1283 ↗
28. Rosakis AJ, Ravichandran G (2000) Dynamic failure mechanics. Int J Solids Struct 37: 331–34810.1016/S0020-7683(99)00097-9 ↗
29. Sändig A-M, Nicaise S, Lalegname A (2007) Dynamic crack propagation in a 2d elastic body. the out-of plane case. ICIAM 07. ETH Zürich10.1016/j.jmaa.2006.06.043 ↗
30. Sewell G (2005a) The numerical solution of ordinary and partial differential equations. 2. Wiley, New York10.1002/0471742015 ↗
31. Sewell G (2005b) PDE2D. University of Texas, El Paso, http://www.pde2d.com
32. Tvergaard V, Hutchinson J (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40: 1377–139710.1016/0022-5096(92)90020-3 ↗
33. Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J Appl Mech 19: 526–52810.1115/1.4010553 ↗
34. Yang B, Ravi-Chandar K (1996) On the role of the process zone in dynamic fracture. J Mech Phys Solids 44: 1955–197610.1016/S0022-5096(96)00067-1 ↗