Hertzian fracture at finite friction: A parametric study

Friction has a profound influence on Hertzian fracture initiation when dissimilar materials are involved. Experimental studies show that the presence of friction results in higher fracture loads and fracture radii as compared to the frictionless case. It has also been shown recently that the experimental observations concerning Hertzian fracture initiation at unloading may be explained by the effect friction has on a surface tensile stress distribution. Presently a contact cycle between two dissimilar elastic bodies at finite Coulomb friction has been investigated numerically for a wide range of material parameters and contact geometries. Emphasis has been given to the surface tensile stress distribution which is assumed to be a governing parameter for Hertzian fracture initiation. In particular it was found that during loading the contact region divides into invariant stick and inward slip regions and the presence of outward frictional shear tractions reduces the maximum surface tensile stress and shifts it away from the contact contour as compared to the frictionless case. At unloading, the distributions of stick-slip zones were found to be severely history- and geometry-dependent and shear tractions reversed their direction over part of the contact area. Consequently, tensile stresses were found to grow at unloading. Results concerning the influence of the friction coefficient, Dundurʹs parameter and the specimenʹs Poissonʹs ratio on the absolute maximum surface tensile stress obtained at a frictional contact cycle are reported along with the magnitudes of the relative increase of maximum tensile stresses at unloading. Based on a critical stress fracture criterion it is discussed how the predicted increases will influence the critical loads required for crack initiation.