ON LINEAR ELASTIC STRAIN ENERGY-RELEASE RATE AND THE J-INTEGRAL

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Department of Engineering

ABSTRACT
A brief review of the trend in Fracture Mechanics studies was provided. Some solutions of elementary fracture mechanics problems were re-investigated. Many of those solutions were shown to have some limitations. These limitations were in the form of introducing some unrealistic stress and displacement distributions. The general applicability of the strain energy-release rate and the J-integral as crack tip parameters are based on viewing the stress and strain fields at the crack tip with an appropriate rationale. Therefore, based on the elementary problems considered and their reported solutions, some inconsistencies in the application and interpretation of the Irwin crack extension force, G and the J-integral as crack tip parameters, were pointed out. For the purpose of eliminating some of the limitations noted in the review, a plane quasi-static problem was reconsidered. By employing the well-known Kolosov- Muskhelishvili equations, some new formulae were derived. The new formulae are, in fact, the generalized Westergaard formulae. It was furthermore proved that the new formulae satisfy all necessary equations of motion and conditions of plane elasticity. Applying the new formulae, some special problems in both the main body of the thesis and the appendix, were solved. From the problems considered, the crack extension force, G, was evaluated from the new solutions developed. Furthermore, a new crack tip characterizing parameter, denoted by I, (after G.R. Irwin) was developed. The effect of biaxial loading on the Irwin crack tip parameter, I, was investigated. It was furthermore shown that characterization via the crack extension force concept is equivalent to crack tip characterization via the Irwin parameter. Also from the problems considered, the J—integral was investigated. For all the cases considered, it was shown that the J-integral at a crack tip is not equal to the Irwin crack extension force, G, at the same crack tip. From the solutions again, by consi— dering some appropriate rationale, the J-integral was shown to yield unrealistic results for some loadings. Finally, some experiments were conducted on glass to determine its fracture toughness values. All the experiments were conducted at room temperature and a loading rate of 2.0 cm/min. From the different experiments conducted, consistent values of the fracture toughness values were obtained. A critical strain energy-release rate, G1 = 6.93 N/m and a critical Irwin parameter, I1c = 997.6 x 103 N/m1/for the glass were obtained.