×

Spring boundary model for a partially closed crack. (English) Zbl 1213.74280

Summary: The spring boundary conditions have been widely employed to describe the acoustic properties of rough surfaces in partial contact. Central to this model is the role of the interfacial stiffness. Recently, a singular stiffness model has been proposed to remove inconsistencies which arise when these boundary conditions are used to describe the acoustic response of partially closed cracks with a position-independent and finite stiffness. Here, an alternative solution to this problem is discussed which is based on the micromechanics of rough surfaces in contact. For cracks that are partially closed, it prescribes a finite crack stiffness that varies along the crack faces and, rather than diverging, becomes null within a small but finite neighborhood of the crack tip. The conditions under which the local stiffness of a non-planar crack can be evaluated are also reviewed.

MSC:

74R99 Fracture and damage
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Baik, J. M.; Thompson, R. B., Ultrasonic scattering from imperfect interfaces: a quasi static model, J. Nondestruct. Eval., 4, 177-196 (1984)
[2] Greenwood, J. A.; Williamson, J. B.P., Contact of nominally rough surfaces, Proc. R. Soc. London, Ser. A, 295, 300-319 (1966)
[3] Kendall, K.; Tabor, D., An ultrasonic study of the area of contact between stationary and sliding surfaces, Proc. R. Soc. London, Ser. A, 323, 321-340 (1971)
[4] A.B. Wooldridge, The effects of compressive stress on the ultrasonic response of steel-steel interfaces and fatigue cracks, CEGB Report NW-SSD-RR-42-79, Berkeley Nuclear Laboratories, 1971.; A.B. Wooldridge, The effects of compressive stress on the ultrasonic response of steel-steel interfaces and fatigue cracks, CEGB Report NW-SSD-RR-42-79, Berkeley Nuclear Laboratories, 1971.
[5] N.F. Haines, The theory of sound transmission and reflection at contacting interfaces, CEGB Report RD-B-N4744, Berkeley Nuclear Laboratories, 1980.; N.F. Haines, The theory of sound transmission and reflection at contacting interfaces, CEGB Report RD-B-N4744, Berkeley Nuclear Laboratories, 1980.
[6] Johnson, K. L., Contact Mechanics (1985), Cambridge University Press: Cambridge University Press New York · Zbl 0599.73108
[7] Brown, S. R.; Scholz, C. H., Closure of elastic random surfaces in contact, J. Geophys. Res., 90, 5531-5545 (1985)
[8] Drinkwater, B. W.; Dwyer-Joyce, R. S.; Cawley, P., A study of the interaction between ultrasound and partially contacting solid-solid interface, Proc. R. Soc. London, Ser. A, 452, 2613-2628 (1996)
[9] Lavrentyev, A. I.; Rokhlin, S. I., Ultrasonic spectroscopy of imperfect interfaces between a layer and two solids, J. Acoust. Soc. Am., 103, 657-664 (1998)
[10] Dwyer-Joyce, R. S.; Drinkwater, B. W.; Quinn, A. M., The use of ultrasound in the investigation of rough surface interfaces, ASME Trans. J. Tribol., 123, 8-16 (2001)
[11] Baltazar, A.; Rokhlin, S. I.; Pecorari, C., On the relationship between ultrasonic and micro-mechanic properties of contacting rough surfaces, J. Mech. Phys. Solids, 50, 1397-1416 (2002) · Zbl 1071.74663
[12] Bostrom, A.; Wickham, G., On the boundary conditions for ultrasonic transmission by partially closed cracks, J. Nondestruct. Eval., 10, 139-149 (1991)
[13] Bostrom, A.; Eriksson, A. S., Scattering of two penny-shaped cracks with spring boundary conditions, Proc. R. Soc. London, Ser. A, 443, 183-201 (1993) · Zbl 0922.73012
[14] Pecorari, C., Scattering of a Rayleigh wave by a surface-breaking crack with faces in partial contact, Wave Motion, 33, 259-270 (2001) · Zbl 1074.74575
[15] Pecorari, C.; Poznic, M., Nonlinear scattering by a partially closed surface-breaking crack, J. Acoust. Soc. Am., 117, 592-600 (2005)
[16] Ueda, S.; Biwa, S.; Watanabe, K.; Heuer, R.; Pecorari, C., On the stiffness of spring model for closed crack, Int. J. Eng. Sci., 44, 874-888 (2006) · Zbl 1213.74272
[17] Mendelsohn, D. A.; Achenbach, J. D.; Keer, L. M., Scattering of elastic waves by a surface-breaking crack, Wave Motion, 2, 277-292 (1980) · Zbl 0438.73016
[18] Brind, R. J.; Achenbach, J. D., Scattering of longitudinal and transverse waves by a sub-surface crack, J. Sound Vib., 78, 555-563 (1981) · Zbl 0477.73094
[19] Sayles, R. S.; Thomas, T. R., Surface topography as nonstationary random processes, Nature, 271, 431-434 (1978)
[20] Mandelbrot, B. B.; Passoja, D. E.; Paullay, A. J., Fractal character of fracture surfaces of metals, Nature, 308, 721-722 (1984)
[21] Daguier, P.; Nghiem, B.; Bouchaud, E.; Creuzet, F., Pinning and depinning off crack fronts in heterogeneous materials, Phys. Rev. Lett., 78, 1062-1065 (1997)
[22] Parisi, A.; Caldarelli, G.; Pietronero, L., Roughness of fracture surfaces, Europhys. Lett., 52, 304-310 (2000)
[23] Skjetne, B.; Helle, T.; Hansen, A., Roughness of crack interfaces in two-dimensional beam lattices, Phys. Rev. Lett., 87, 125503 (2001)
[24] Nukala, P. K.V. V.; Zapperi, S.; Simunovic, S., Crack roughness in three-dimensional random fuse network, Phys. Rev. E, 74, 026105 (2006)
[25] Hills, D. A.; Kelly, P. A.; Dai, D. N.; Korsunsky, A. M., Solution of Crack Problems (1996), Kluwer Academic Publishers · Zbl 0874.73001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.