Significance of the deviations of the crack front into the plane perpendicular to the crack propagation direction - II. Crack-front vibration

Abstract

In this part II, the influence of thermal vibration on the shape of a crack front and on the conditions for crack motion are investigated. We have considered a static crack model in mode I loading in a linear isotropic elastic medium whose front vibrates in the form of a standing wave with displacement ξ perpendicular to both the average crack plane and the crack propagation direction; ξis assumed to be sum of standing sine waves and the crack to be represented by a continuous distribution of vibrating edge dislocations. The displacement and stress fields due to an infinitely long edge dislocation, oscillating in the form of a standing wave, are first given. Then it is shown that, in free vibration conditions, ξ would satisfy the d'Alembert wave equation with a constant phase velocity corresponding to the velocity of a travelling sine wave along an edge dislocation. It is also shown that the sites for the initiation of crack motion are located on the average crack plane at the nodes of the vibrating crack front. The crack opening force G per unit length of the crack front, at the sites of crack propagation initiation, is found to be different from that of the rigid planar crack, when averaged over time, but the magnitude of the difference is relatively small. G decreases with increasing temperature T and is found to be proportional to T ² at very low temperature and to T at higher temperatures. The relation for G leads to view the vibrating crack front as being non straight on average over time. In tungsten, a nearly isotropic material, the theory yields a mean crack front inclination angle of about 1° at absolute zero, 3.2° at room temperature and 10.6° at the melting point.