Simulation of mixed mode I/II cyclic deformation at the tip of a short kinked inclined crack with frictional surfaces

Abstract

The paper presents a model for near tip-displacements of a short kinked slant crack in a two-dimensional plate subjected to uniaxial cyclic loading. Possible regimes of sticking and sliding contact and separation along the two frictional surfaces of the main crack and the kink were identified. Both stationary and artificially advancing central cracks were analysed with an inhouse finite element package and compared in terms of plastically deformed zones and crack tip relative displacements. An artificial crack tip advance equivalent to one element was allowed along the direction of the assumed kink. Three stress ratios of 0.2, 0 and −1 were assumed. The main crack angle was 45° with a crack length to plate width ratio of 0.3 and the coefficient of friction varied from 0 to 1. The kink angle varied between 60 and −80° measured in a counter-clockwise direction from the main crack line. In the case of a negative stress ratio, extents of both monotonic and cyclic crack tip deformation decreased with increasing the coefficient of friction between the crack surfaces. For positive stress ratios, such an effect was not obvious. The extent of the cyclic crack tip opening displacement appeared as an appropriate candidate to predict the crack initiation angle in the case of mixed mode I/II loading. The present results did not support the use of a maximum effective stress range based on crack tip closure for such prediction. The maximum extent of the crack tip opening displacement corresponded to a kink angle which was nearly the same as that measure obtained from an elastic analysis. The extent of the crack tip sliding displacement at that kink angle was negligible.