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

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Show that it occurs at the periphery of contact, r = a : Describe qualitatively how a layer of residual compressive stress at the surface would affect the magnitude and location of this maximum stress |

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