Indentation of spherical and conical punches into piezoelectric half-space with frictional sliding: Applications to scanning probe microscopy

A proper quantitative interpretation of scanning probe microscopy (SPM) experiments requires solutions for both normal and tangential indentations of punches into a piezoelectric material. Such indentation solutions, their dependence on the indenter shape, and implications for SPM are considered here. More specifically, indentation of the spherical and conically sharp indenters into a piezoelectric half-space accompanied by frictional sliding is addressed. The tangential part of the problem, which involves friction, is solved to complement the solution of the normal indentation problem obtained earlier. Exact stiffness relations between vertical load, tangential displacement, and material properties are obtained. The piezoelectric coupling is found to have a relatively weak effect on lateral contact stiffness. In contrast, the contact area depends noticeably on the tangential effects. The full electroelastic fields are derived in elementary functions and their implications are discussed.