Stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates

Abstract

An elastic two-dimensional finite element analysis was used to evaluate the modes II and I stress intensity factors of a shortly kinked slant central crack with frictional surfaces in uniaxially loaded plates. Four main crack angles measured from the load direction, i.e. 45, 60, 75, and 85°, with crack length to plate width of 0.1, 0.3, and 0.5 were considered. The coefficients of friction of the crack surfaces were 0, 0.25, 0.5, 0.75 and 1. The kink angle was measured from the main crack line in a counterclockwise direction and varied in increments of 5° between 0 and –120° for the plates loaded in tension and between 0 and +120° for the compressed plates. The ratio of the kink length and the main crack length was 0.0065. The arrangement and the size of the elements around the crack tip were the same for all the meshes generated for the present work. The variation of the computed modes II and I stress intensity factors was dependent on the type of the remotely applied axial load and both main crack and kinking angles. For a fully opened crack, there was a negative kink angle at which mode I stress intensity factor attained a maximum value. That corresponded to approximately zero mode II stress intensity factor. The maximum value of mode I stress intensity factor increased as the main crack angle increased, i.e. the mode I stress intensity factor reached a maximum when the main crack was at 90° to the loading direction. In axially compressed plates, relatively sliding crack surfaces in contact showed opened crack tips only at positive kink angles, which were larger than an angle dependent on the main crack angle. The resulting mode II and mode I stress intensity factors decreased as the coefficient of friction increased. Further, the mode I stress intensity factor increased with the increasing positive kink angle and reached a maximum value before it decreased. On the other hand, the absolute value of the mode II stress intensity factor decreased with the increasing positive kink angle and had a zero value before it increased again. In both types of loading, the measure of the kink angle for the maximum mode I stress intensity factor was independent of the main crack length. The present results showed that the kink angles corresponding to maximum mode I stress intensity factors agreed well with predicted and experimentally observed initial crack growth directions found in the literature.