A non-linear crack model

Abstract

Elliott's crack model which accounts for non-linearity of material behaviour in the vicinity of a crack tip is difficult to investigate analytically in view of the mathematical complexities associated with the governing singular integral equation. However, with a particular force law, the governing equation can be transformed into one that arises in the theory of the lift coefficient of a thin jet-flapped wing, and for which a solution has been obtained. The displacement variation ahead of the crack tip is therefore known, and the results show that the width of the crack front decreases as the force law becomes sharper, a state of affairs which is analogous to that for the dislocation width in the Peierls-Nabarro model. The fact that a solution of the governing equation has been obtained without the use of inverse methods, should act as a spur to the search for solutions for other force laws.