Mode III stress intensity factor ahead of a rough crack

Journal of the Mechanics and Physics of Solids

Volumn 45, Issue 5, 1997, Pages 853-872

  Vandembroucq, Damien ^a   Roux, Stéphane ^a  

^a CNRS   (France)

Author keywords

A. stress intensity factor; B. crack mechanics; B. elastic material; C. analytic functions; C. numerical algorithms

Indexed keywords

ALGORITHMS; CONFORMAL MAPPING; CRACK PROPAGATION; ELASTICITY; NUMERICAL ANALYSIS; STRESS INTENSITY FACTORS;

MODE III CRACKS; STATIC STRESS FIELD;

FRACTURE MECHANICS;

EID: 0031141177     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(96)00091-9     Document Type: Article

References (38)

1. Ball, R. C. and Larralde, H. (1996) Linear stability analysis of planar straight cracks propagating quasistatically under type I loading. Int. J. Fract. 71, 365-377.
2. Borodich, F. M. (1994) In Fractals in the Natural and Applied Sciences, 2nd IFIP Working Conference, pp. 61-68. North Holland, Amsterdam.
3. Bouchaud, E., Lapasset, G. and Planés, J. (1990) Fractal dimension of fractured surfaces: a universal value? Europhys. Lett. 13, 73-79.
4. Bouchaud, E. and Bouchaud, J. P. (1994) Fracture surfaces: apparent roughness, relevant length scales, and fracture toughness. Phys. Rev. B. 50, 17752-17555.
5. Bower, A. F. and Ortiz, M. (1990) Solution of three dimensional crack problems by a finite perturbation method. J. Mech. Phys. Solids 38, 443-480.
6. Cotterell, B. and Rice, J. R. (1980) Slightly curved and kinked cracks. Int. J. Fract. 16, 155-169.
7. Dauskardt, R. H., Haubensak, F. and Richie, R. O. (1990) On the interpretation of the fractal character of fracture surfaces. Acta Met. Mater. 38, 143-159.
8. Davidson, D. L. (1989) Fracture surface roughness as a gauge of fracture toughness: aluminium-particulate SiC composites. J. Mater. Sci. 24, 681-687.
9. Fahmy, Y., Russ, J. C. and Koch, C. C. (1991) Application of fractal geometry measurements to the evaluation of fracture toughness of brittle intermetallics. J. Mater. Res. 6, 1856.
10. Fares, N. (1989) Crack fronts trapped by arrays of obstacles: numerical solution based on surface integral representation. J. Appl. Mech. 56, 837-843.
11. Feder, J. (1990) Fractals. Plenum Press, New York.
12. Gao, H. (1993) Surface roughening and branching instabilities in dynamic fracture. J. Mech. Phys. Solids 41, 457-486.
13. Gao, H. and Rice, J. R. (1989) A first order perturbation analysis of crack trapping by arrays of obstacles. J. Appl. Mech. 56, 828-836.
14. Gol'dshteǐn, R. V. and Mosolov, A. N. (1991) Cracks with a fractal surface. Sov. Phys. Dokl. 36, 603-611 ; ibid. (1992), J. Appl. Maths Mechs 56, 563-571.
15. Gol'dshteǐn, R. V. and Mosolov, A. N. (1991) Cracks with a fractal surface. Sov. Phys. Dokl. 36, 603-611 ; ibid. (1992), J. Appl. Maths Mechs 56, 563-571.
16. Gol'dshteǐn, R. V. and Mosolov, A. N. (1991) Cracks with a fractal surface. Sov. Phys. Dokl. 36, 603-611 ; ibid. (1992), J. Appl. Maths Mechs 56, 563-571.
17. Guilloteau, E. (1995) La fracture du verre: Phénomènes-clés à l'échelle nanométrique. Thèse (Ph. D. Dissertation), University Paris-Sud.
18. Gutknecht, M. H. (1981) Solving Theodorsen's integral equation for conformal maps with the fast Fourier transform and other iterative methods. Numer. Math. 36, 405-429.
19. Gutknecht, M. H. (1983) Numerical experiments on solving Theodorsen's integral equation for conformal maps with the fast Fourier transform and other iterative methods. SIAM J. Sci. Stat. Comput. 4, 1-30.
20. Henrici, P. (1985) Applied and Computational Complex Analysis, Volume III. Wiley, New York.
21. Lung, C. W. (1986) In Fractals in Physics (ed. L. Pietronero and E. Tossatti), p. 189. North-Holland, Amsterdam.
22. Lung, C. W. and Mu, Z. Q. (1988) Fractal dimension measured with perimeter-area relation and toughness of materials. Phys. Rev. B 38, 11781-11784.
23. Måløy, K. J., Hansen, A., Hinrichsen, E. L. and Roux, S. (1992) Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 68, 213-215.
24. Mandelbrot, B. B., Passoja, D. E. and Paullay, A. J. (1984) Fractal character of fracture surfaces of metals. Nature 308, 721-722.
25. Mecholsky, J. J., Passoja, D. E. and Finberg-Ringel, K. S. (1989) Quantitative analysis of brittle fracture surfaces using fractal geometry. J. Am. Ceram. Soc. 72, 60-65.
26. Movchan, A. B. and Willis, J. R. (1995) Dynamic weight functions for a moving crack. II. Shear loading. J. Mech. Phys: Solids 43, 1369-1383.
27. Mower, T. M. and Argon, A. S. (1995) Experimental investigation of crack trapping in brittle heterogeneous solids. Mech. Mater. 19, 343-364.
28. Passoja, D. E. (1988) Fundamental relationships between energy and geometry of fracture. Adv. Ceramics 22, 101.
29. Perrin, G. and Rice, J. R. (1994) Disordering of a planar crack front in a model elastic medium of randomly variable toughness. J. Mech. Phys. Solids 42, 1047-1064.
30. Rice, J. R. (1985) First-order variation in elastic fields due to variation in location of a planar crack front. J. Appl. Mech. 52, 571-579.
31. Rice, J. R., Ben-Zion, Y. and Kim, K. S. (1994) Three dimensional perturbation solution for a dynamic planar crack moving unsteadily in a model elastic solid. J. Mech. Phys. Solids 42, 813-843.
32. Schmittbuhl, J., Roux, S., Vilotte, J. P. and Maly, K. J. (1995a) Interfacial crack pinning: effect of nonlocal interactions. Phys. Rev. Lett. 74, 1787-1790.
33. Schmittbuhl, J., Vilotte, J. P. and Roux, S. (1995b) Reliability of self-affine measurements. Phys. Rev. E 51, 131-147.
34. Theocaris, P. S. and Panagiotopoulos, P. D. (1993) The 'fractal assumption' in cracks: bilateral calculation methods. Int. J. Num. Meth. Engng 36, 1597-1604.
35. Tzschichholz, F. and Pfuff, M. (1991) In Fracture Processes in Concrete Rocks and Ceramics, Vol. 1 (ed. J. G. M. Van Mier, J. G. Rots and A. Bakker), pp. 251-260. Cambridge University Press, Cambridge.
36. Vandembroucq, D. and Roux, S. (1996a) Conformal mapping on rough boundaries I: applications to harmonic problems, to appear in Phys. Rev. E.
37. Vandembroucq, D. and Roux, S. (1996b) Conformal mapping on rough boundaries II: applications to biharmonic problems, to appear in Phys. Rev. E.
38. Willis, J. R. and Movchan, A. B. (1995) Dynamic weight functions for a moving crack. I. Mode I loading. J. Mech. Phys. Solids 43, 319-341.