×

zbMATH — the first resource for mathematics

Conditions for mode I crack deviation in orthotropic plane subjected to biaxial loading. (English) Zbl 1423.74823
Summary: A problem of a Mode I crack deviation is considered. It is assumed that a crack is located initially on a symmetry axis of an orthotropic plane and subjected to biaxial loading. A crack is modeled as a thin elliptical hole. The maximal tensile stresses are taken as a crack growth criterion. To stress the role of elastic anisotropy for a crack rotation, the strength properties of the material are assumed to be isotropic. Conditions for a crack deviation and stability of a straight crack path are obtained. The obtained results generalize previous results of the authors, where an analogical problem was considered for the case of uniaxial tension. Presented results are compared with the results following from the traditional model of the crack, considering a crack as an ideal cut.
MSC:
74R10 Brittle fracture
74E10 Anisotropy in solid mechanics
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Cotterell, B.; Rice, J.R., Slightly curved or kinked cracks, International journal of fracture, 16, 2, 155-169, (1980)
[2] Goldstein, R.V.; Shifrin, E.I., Dependence of a crack growth path on the elastic moduli of an anisotropic solid, International journal of fracture, 150, 157-180, (2008) · Zbl 1143.74047
[3] Lekhnitskii, S.G., Theory of elasticity of an anisotropic elastic body, (1977), Nauka Moscow, in Russian · Zbl 0467.73012
[4] Rabotnov, Yu.N., Mechanics of an deformable body, (1979), Nauka Moscow, in Russian
[5] Savin, G.N., Stress concentration around holes, (1968), Naukova Dumka Kiev, in Russian · Zbl 0100.19808
[6] Stroh, A.N., Dislocations and cracks in anisotropic elasticity, Philosophical magazine, 3, 625-646, (1958) · Zbl 0080.23505
[7] Ting, T.C.T., Effects of change of reference coordinates on the stress analyses of anisotropic elastic materials, International journal of solids structures, 18, 2, 139-152, (1982) · Zbl 0468.73015
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.