Frictionless normal indentation of a surface by a sphere was considered in Section 13.2.1.1.
(a) Prove the statement in that section that the maximum tensile normal stress is
(b) Show that it occurs at the periphery of contact, r = a.
(c) Discuss the consequences of this maximum stress for fatigue cracking in
(a) polycrystalline aluminum oxide, (b) PMMA and (c) commercially pure aluminum during cyclic indentation.
(d) Describe qualitatively how a layer of residual compressive stress at the surface would affect the magnitude and location of this maximum stress