Analysis of Mixed-Mode Crack Propagation Using the Boundary Integral Method

Abstract

Crack propagation in a rotating inner raceway of a high speed roller bearing is analyzed using the boundary integral equation method. The model consists of an edge crack in a plate under tension, upon which varying Hertzian stress fields are superimposed. A computer program for the boundary integral equation method was written using quadratic elements to determine the stress and displacement fields for discrete roller positions. Mode I and Rode II stress intensity factors and crack extension forces Gee (energy release rate due to tensile opening mode) and GrB (energy release rate due to shear displacement mode) were computed. These calculations permit determination of that crack growth angle for which the change in the crack extension forces is maximum. The crack driving force was found to be the alternating mixed-mode loading that occurs with each passage of the most heavily loaded roller. This alternating mixed-mode loading is due to the superposition of the Hertzian stress fields on the tangential stresses due to rotation and press fit. The crack is predicted to propagate in a step-like fashion alternating between radial and inclined segments, and this pattern was observed experimentally. Themaxin_Jmchanges AGee and AGre of the crack extension forces are found to be good measures of the crack propagation rate and direction. The time-to-failure of the inner race- way of the high speed bearing was estimated to be very short for a DN value of three million, where D is the bearing bore diameter in nm and N is the speed in RPM. The predicted short lifetime was confirmed by limited testing of a ball bearing of similar load capabilities. A modified Forman type crack propagation law as a function of the crack extension forces was used in calculating the time-to-failure. 17.