On the Correspondence between Two- and Three-Dimensional Elastic Solutions of Crack Problems

Abstract:

The classical two-dimensional solutions of the theory of elasticity provide a framework of Linear Elastic Fracture Mechanics. However, these solutions, in fact, are approximations despite that the corresponding governing equations of the plane theories of elasticity are solved exactly. This paper aims to elucidate the main differences between the approximate (two-dimensional) and exact (three-dimensional) elastic solutions of crack problems. The latter demonstrates many interesting features, which cannot be analysed within the plane theories of elasticity. These features include the presence of scale effects of deterministic nature, the existence of new singular stress states and fracture modes. Furthermore, the deformation and stress fields near the tip of the crack is essentially three-dimensional and do not follow plane stress or plane strain simplifications. Moreover, in certain situations the two-dimensional solutions can provide misleading results; and several characteristic examples are outlined in this paper.

• Periodical: Key Engineering Materials (Volume 713)
• Pages: 18-21
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.713.18
• Online since: September 2016
• Authors: Andrei G. Kotousov*, Zhuang He, Aditya Khanna
• Keywords: Linear Elastic Fracture Mechanics, Stress Intensity Factor, Thickness Effect, Through-the-Thickness Crack, Williams’ Crack Tip Solution

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