Abstract
Spherical or Hertzian indentation is used to characterize and guide the development of engineered ceramics under consideration for diverse applications involving contact, wear, rolling fatigue, and impact. Ring crack initiation can be one important damage mechanism of Hertzian indentation. It is caused by sufficiently-high, surface-located, radial tensile stresses in an annular ring located adjacent to and outside of the Hertzian contact circle. While the maximum radial tensile stress is known to be dependent on the elastic properties of the sphere and target, the diameter of the sphere, the applied compressive force, and the coefficient of friction, the Weibull effective area too will be affected by those parameters. However, the estimations of a maximum radial tensile stress and Weibull effective area are difficult to obtain because the coefficient of friction during Hertzian indentation is complex, likely intractable, and not known a priori. Circumventing this, the Weibull effective area expressions are derived here for the two extremes that bracket all coefficients of friction; namely, (1) the classical, frictionless, Hertzian case where only complete slip occurs, and (2) the case where no slip occurs or where the coefficient of friction is infinite.
