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Keywords:
crack propagation; energy principle; stress intensity factor
crack propagation; energy principle; stress intensity factor
Summary:
Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a small crack extension.
References:
[1] Argatov, I. I., Nazarov, S. A.: Energy release caused by the kinking of a crack in a plane anisotropic solid. Translated from the Russian. J. Appl. Math. Mech. 66 (2002), 491-503. DOI 10.1016/S0021-8928(02)00059-X | MR 1937462
[2] Bach, M., Nazarov, S. A., Wendland, W. L.: Stable propagation of a mode-1 planar crack in an isotropic elastic space. Comparison of the Irwin and the Griffth approaches. Problemi attuali dell'analisi e della fisica matematica P. E. Ricci Dipartimento di Matematica, Univ. di Roma (2000), 167-189. MR 1809025
[3] Bourdin, B., Francfort, G. A., Marigo, J.-J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 (2000), 797-826. DOI 10.1016/S0022-5096(99)00028-9 | MR 1745759 | Zbl 0995.74057
[4] Ciarlet, P. G.: An introduction to differential geometry with applications to elasticity. J. Elasticity 78-79 (2005), 1-215. MR 2196098 | Zbl 1086.74001
[5] Costabel, M., Dauge, M.: General edge asymptotics of solutions of second-order elliptic boundary value problems I. Proc. R. Soc. Edinb., Sect. A 123 (1993), 109-155. DOI 10.1017/S0308210500021272 | MR 1204855 | Zbl 0791.35032
[6] Costabel, M., Dauge, M.: General edge asymptotics of solutions of second-order elliptic boundary value problems II. Proc. R. Soc. Edinb., Sect. A 123 (1993), 157-184. DOI 10.1017/S0308210500021284 | MR 1204855 | Zbl 0791.35033
[7] Costabel, M., Dauge, M.: Crack singularities for general elliptic systems. Math. Nachr. 235 (2002), 29-49. DOI 10.1002/1522-2616(200202)235:1<29::AID-MANA29>3.0.CO;2-6 | MR 1889276 | Zbl 1094.35038
[8] Costabel, M., Dauge, M., Yosibash, Z.: A quasi-dual function method for extracting edge stress intensity functions. SIAM J. Math. Anal. 35 (2004), 1177-1202. DOI 10.1137/S0036141002404863 | MR 2050197 | Zbl 1141.35363
[9] Dauge, M.: Elliptic Boundary Value Problems on Corner Domains. Lecture Notes in Mathematics 1341 Springer, Berlin (1988). MR 0961439 | Zbl 0668.35001
[10] Lorenzi, H. G. de: On the energy release rate and the $J$-integral for 3-D crack configurations. Int. J. Fract. 19 (1982), 183-193. DOI 10.1007/BF00017129
[11] Favier, E., Lazarus, V., Leblond, J.-B.: Coplanar propagation paths of 3D cracks in infinite bodies loaded in shear. Int. J. Solids Struct. 43 (2006), 2091-2109. DOI 10.1016/j.ijsolstr.2005.06.041 | Zbl 1121.74449
[12] Griffith, A. A.: The phenomena of rupture and flow in solids. Philos. Trans. Roy. Soc. London 221 (1921), 163-198. DOI 10.1098/rsta.1921.0006
[13] Hartranft, R. J., Sih, G. C.: Stress singularity for a crack with an arbitrarily curved front. Engineering Fracture Mechanics 9 (1977), 705-718. DOI 10.1016/0013-7944(77)90083-2
[14] Il'in, A. M.: Matching of Asymptotic Expansions of Solutions of Boundary Value Problems. Translated from the Russian. Translations of Mathematical Monographs 102 American Mathematical Society, Providence (1992). DOI 10.1090/mmono/102 | MR 1182791 | Zbl 0754.34002
[15] Irwin, G.: Fracture. Handbuch der Physik. Bd. 6: Elastizität und Plastizität S. Flügge Springer, Berlin 551-590 (1958). MR 0094946
[16] Kondrat'ev, V. A.: Boundary value problems for elliptic equations in domains with conical or angular points. Trans. Mosc. Math. Soc. 16 (1967), 227-313. MR 0226187
[17] Kozlov, V. A., Maz'ya, V. G., Rossmann, J.: Elliptic Boundary Value Problems in Domains with Point Singularities. Mathematical Surveys and Monographs 52 American Mathematical Society, Providence (1997). MR 1469972 | Zbl 0947.35004
[18] Kühnel, W.: Differential Geometry. Curves--Surfaces--Manifolds. Translated from the German. Student Mathematical Library 16 American Mathematical Society, Providence (2002). MR 1882174
[19] Lazarus, V.: Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading. Int. J. Fract. 122 (2003), 23-46. DOI 10.1023/B:FRAC.0000005373.73286.5d
[20] Leblond, J.-B., Torlai, O.: The stress field near the front of an arbitrarily shaped crack in a three-dimensional elastic body. J. Elasticity 29 (1992), 97-131. DOI 10.1007/BF00044514 | Zbl 0777.73054
[21] Maz'ya, V. G., Plamenevsky, B. A.: The coefficients in the asymptotic of the solutions of elliptic boundary-value problems in domains with conical points. Russian Math. Nachr. 76 (1977), 29-60.
[22] Maz'ya, V. G., Rossmann, J.: Über die Asymptotik der Lösungen elliptischer Randwertaufgaben in der Umgebung von Kanten. German Math. Nachr. 138 (1988), 27-53. DOI 10.1002/mana.19881380103 | MR 0975198 | Zbl 0672.35020
[23] Nazarov, S. A.: Stress intensity factors and crack deviation conditions in a brittle anisotropic solid. J. Appl. Mech. Techn. Phys. 46 (2005), 386-394. DOI 10.1007/s10808-005-0088-3 | MR 2144814 | Zbl 1088.74025
[24] Nazarov, S. A., Plamenevsky, B. A.: Elliptic Problems in Domains with Piecewise Smooth Boundaries. De Gruyter Expositions in Mathematics 13 Walter de Gruyter, Berlin (1994). MR 1283387 | Zbl 0806.35001
[25] Nazarov, S. A., Polyakova, O. R.: Rupture criteria, asymptotic conditions at crack tips, and selfadjoint extensions of the Lamé operator. Russian Tr. Mosk. Mat. Obs. 57 (1996), 16-74. MR 1468975
[26] Parks, D. M.: A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int. J. Fract. 10 (1974), 487-502. DOI 10.1007/BF00155252
[27] Sih, G. C., Paris, P. C., Irwin, G. R.: On cracks in rectilinearly anisotropic bodies. Int. J. Fract. 1 (1965), 189-203.
[28] Steigemann, M.: Verallgemeinerte Eigenfunktionen und lokale Integralcharakteristiken bei quasi-statischer Rissausbreitung in anisotropen Materialien. German Berichte aus der Mathematik Shaker, Aachen (2009). Zbl 1181.35286
[29] Williams, M. L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19 (1952), 526-528.
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