A shrink-fit shaft subject to torsion

The problem studied is an elastic, circular shaft, fitted into a cavity normal to the free surface of a half-space. The cavity is smaller than the shaft, so that there is a residual radial stress. A torque is applied to the shaft, giving rise to a region of slip between the shaft and the socket. Its extent is determined by forming an integral equation whose kernel is given by a circular ring dislocation, which has a Burgers vector whose magnitude is constant, oriented in the tangential direction. The problem has direct application to the study of shrink fitted shafts in wheels, whose diameter is large compared with the shaft.