Abstract
We analyze a kinked and curved crack in an elastic body by using the first order perturbation method, where the result is applied to a straight crack with a slightly kinked and curved crack extension in a finite body. Crack path criteria are discussed for the crack path prediction in brittle solids, which may also lead to some considerations about the crack path stability; i.e., whether the crack path keeps its direction or not. The first order perturbation is then applied to a system of kinked and curved cracks for the simulation of curved or wavy crack propagation in brittle solids, where attention is focused on the transition from straight to wavy crack propagation of edge cracks due to the penetration of surface cooling. The simulated results are compared with experimentally observed wavy cracks in a heated glass plate, whose edge was gradually immersed into a cooling bath filled with water, so as to identify the parameter which characterizes the straight versus wavy crack paths.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Amestoy M, Leblond JB (1992) Crack paths in plane situations-II. Detailed form of the expansion of the stress intensity factors. Int J Solids Struct 29:465–501
Banichuk NV (1970) Determination of the form of a curvilinear crack by small parameter technique. Mekhanika Tverdogo Tela 7–2: 130–137 (in Russian)
Bilby BA, Cardew GE (1975) The crack with a kinked tip. Int J Fract 11:708–712
Bilby BA, Cardew GE, Howard IC (1978) Stress intensity factors at the tips of kinked and forked cracks In: Taplin DMR (ed) Fracture 1977, vol 3. Pergamon Press, Oxford, p 197–200
Blacker TD, Sephenson MB (1991) Paving: a new approach to automated quadrilateral mesh generation. Int J Numer Meth Eng 32:811–847
Broberg KB (1987) On crack paths. Eng Fract Mech 28:663–679
Bueckner HF (1970) A novel principle for the computation of stress intensity factors. ZAMM 59:529–546
Bueckner HF (1973) Field singularities and related integral representation. In: Sih GC (ed) Mechanics of fracture, vol 1. Noordhoff, Leyden, p 239–314
Bueckner HF (1987) Weight function and fundamental fields for the penny-shaped and the half-plane crack in three-space. Int J Solids Struct 23:57–93
Cotterell B, Rice JR (1980) Slightly curved or kinked cracks. Int J Fract 16:155–169
Erdogan F, Sih GC (1963) On crack extension in plates under plane loading and transverse shear. J Basic Eng 85:519–527
Goldstein RV, Salganik RL (1970) Plane problem of curvilinear cracks in an elastic solid. Mekhanika Tverdogo Tela 7–3:69–82 (in Russian)
Goldstein RV, Salganik RL (1974) Brittle fracture of solids with arbitrary cracks. Int J Fract 10:507–523
Hayashi K, Nemat-Nasser S (1981a) Energy release rate and crack kinking. Int J Solids Struct 17:107–114
Hayashi K, Nemat-Nasser S (1981b) Energy-release rate and crack kinking under combined loading. J Appl Mech 48:520–524
Hirata M (1931) Experimental studies on form and growth of cracks in glass plate. Scientific Paper, Institute of Physics and Chemistry Research 16:172–195
Kantorovich LV, Krylov VI (1964) Chapter VII Schwarz’s method. Approximate methods of higher analysis. Noordhoff, Groningen, p 616–670
Karihaloo BL, Keer LM, Nemat-Nasser S, Oranratnachai A (1981) Approximate description of crack kinking and curving. J Appl Mech 48:515–519
Kawamura Y, Mu Y, Sumi Y (1999) Development of an automatic quadrilateral mesh generator for the simulation of curved crack growth. Trans Jpn Soc Comput Eng Sci 2:1–6
Kitagawa H, Yuuki R, Ohira T (1975) Crack morphological aspects in fracture mechanics. Eng Fract Mech 7:515–529
Leevers PS, Radon JC, Culver LE (1976) Fracture trajectories in a biaxially stressed plate. J Mech Phys Solids 24:381–395
Leblond JB (1989) Crack paths in plane situations-I. General form of the expansion of the stress intensity factors. Int J Solids Struct 25:1311–1325
Lo KK (1978) Analysis of branched cracks. J Appl Mech 45:797–802
Pook LP (2002) Crack paths. WIT Press, Southampton
Sumi Y, Nemat-Nasser S, Keer LM (1983) On crack branching and curving in a finite body. Int J Fract 21:67–79; Erratum (1984) Int J Fract 24:159
Sumi Y, Kagohashi Y (1983) A fundamental research on the growth pattern of cracks (second report). J Soc Naval Architects Jpn 152:397–404 (in Japanese)
Sumi Y, Nemat-Nasser S, Keer LM (1985) On crack path stability in a finite body. Eng Fract Mech 22:759–771
Sumi Y (1985) Computational crack path prediction. Theor Appl Fract Mech 4:149–156
Sumi Y (1986) A note on the first order perturbation solution of a straight crack with slightly branched and curved extension under a general geometric and loading condition. Eng Fract Mech 24:479–481
Sumi Y, Chen Y, Hayashi S (1996) Morphological aspects of fatigue crack propagation, Part I computational procedure. Int J Fract 82:205–220
Sumi Y, Wang ZN (1998) A fnite-element simulation method for a system of growing cracks in a heterogeneous material. Mech Mater 28:197–206
Sumi Y, Mu Y (2000) Thermally induced quasi-static wavy crack propagation in a brittle solid. Mech Mater 32:531–542
Wu CH (1978) Fracture under combined loads by maximum-energy-release-rate criterion. J Appl Mech 45:553–558
Yuse A, Sano M (1993) Transition between crack patterns in quenched glass plates. Nature 362:329–331
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this chapter
Cite this chapter
Sumi, Y. (2014). Crack Paths in Brittle Solids. In: Mathematical and Computational Analyses of Cracking Formation. Mathematics for Industry, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54935-2_7
Download citation
DOI: https://doi.org/10.1007/978-4-431-54935-2_7
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54934-5
Online ISBN: 978-4-431-54935-2
eBook Packages: EngineeringEngineering (R0)