Crack propagation thresholds: A measure of surface energy
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I. INTRODUCTION Crack propagation velocities in brittle materials, notably ceramics and glasses, are enhanced by the presence of reactive species, especially water, at the crack tip. Examination of the crack velocity characteristics of these brittle materials reveals apparent thresholds where the crack velocity tends to zero at finite values of the applied loading. '"6 Early explanations of this phenomenon suggested that at low applied loadings the crack tip was "blunting," reducing the stress concentration at the tip, thereby reducing the effectiveness of the applied loading for driving the crack.3'7 Much of this work relied on inference of crack-tip geometry rather than observation, and recent studies show marked inconsistencies between the predictions of blunting models of crack propagation and careful measurements of crack propagation behavior.3 A recent explanation for crack propagation thresholds is that the applied loading is not a complete specification of the driving force for crack propagation in many material/environment combinations. This explanation suggests that the net driving force is more properly described by the sum of a force driving crack propagation, arising from the applied loading, and a force impeding propagation, arising from surface interactions across the barely separated crack walls near the crack tip.4"6 At small applied loadings the aiding and impeding influences become comparable and the net driving force for crack propagation reduces to zero. Evidence for the existence of strong forces between surfaces separated by a small distance, such as would occur in the vicinity of a crack tip, is reviewed briefly in Refs. 4 and 6 and includes direct measurement of the force/separation characteristics of mica surfaces separated by various fluids,8 the adhesion of elastomers to flat surfaces,9'10 measurements of crack healing forces in 852
J. Mater. Res. 1 (6), Nov/Dec 1986
http://journals.cambridge.org
glasses and mica, 511 13 and transmission electron microscopy (TEM) observations of healing of cracks in a variety of materials, particularly alumina, indicative of a strong closure force between the adjacent crack walls.14 There have, however, been no direct observations of the influence of such forces at crack tips, such as perturbations in crack shape behind the tip. Here we will show that thresholds in crack propagation characteristics arise naturally out of simple fracture mechanics considerations of the surface energy, or work to fracture, for a propagating crack. The arguments used are thermodynamic and are very similar to those used by Griffith15 in his seminal work on crack equilibrium and by Rice16 in consideration of nonequilibrium cracks. The analysis will allow us to use the results of an indentation fracture experiment to estimate the surface energy of a material in a reactive environment. Sapphire is chosen as the material for study on the basis of the crack healing observations of Hockey14 and the dispersion force calculations of Clarke et al.4 II. THEORY A. Fracture mechanics
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