Abstract
Quasistatic extension of a penny-shaped crack, which occurs prior to its spontaneous propagation, is studied by means of nonlinear fracture mechanics analogous to the methods used to describe plastic deformation in metals. Wnuk's model of final stretch is employed to describe the displacement and stress fields in the vicinity of the crack border. Three kinds of thermal loadings are considered: (a)prescribed heat flux across the surface of the crack, (b) prescribed temperature difference, and (c) given heat extraction rate resulting from the steady-state flow of a cooling fluid circulating in and out of the crack. The latter case is directly applicable to power-generating geothermal systems. All three problems, if treated by linear elastic fracture mechanics methods, lead to singular thermal stresses around the circumference of the crack. Although the first two problems are of a positive K-gradient nature, i.e., inherently unstable, the third one results in a negative K-gradient. Through the approach used in this work the existence of a preliminary phase of stable crack growth, which precedes the catastrophic (cases a and b) or the spontaneous (case c) crack extension, has been demonstrated. The critical parameters involving the thermal load and the terminal dimension of the crack, at which the transition from stable to unstable propagation takes place, are predicted.
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