Indentation Problems

Abstract

If an elastic–plastic material is indented by a rigid quadratic indenter such as a sphere, the contact problem will exhibit an elastic range, in which the stress field and the force–displacement relation are defined by the Hertzian analysis. The maximum shear stress associated with the axisymmetric Hertzian problem occurs at a depth of 0.48a, where a is the radius of the contact circle and this point reaches both the Tresca and von Mises yield conditions when P=PY=21.2SY3R2E∗2, where SY is the yield stress in uniaxial tension (Johnson in Contact Mechanics, Cambridge University Press, Cambridge, 1985, Johnson 1985).