NONLINEAR HERTZIAN INDENTATION FRACTURE-MECHANICS

Indentation cracking under blunt indenters is analyzed using nonlinear fracture mechanics. The usual assumptions of linear elastic fracture mechanics have been replaced with a nonlinear load vs load-point displacement curve while assuming the material is linear elastic, The load, the load-point displacement, and a function of the crack area have been related to the crack driving force, J, while assuming a cone fracture under the Hertzian sphere, Experimentally, it was found that the load-displacement curve during loading, cracking, and unloading is nonlinear. The crack length is empirically shown to be proportional to the load-point displacement for several indenters, The experimentally measured relations between indenter load, load-point displacement, and crack geometries are then analyzed with mechanical energy balances based on the similitude of crack lengths with load-point displacements. The Hertz hardness that describes the nonlinear load vs load-point displacement relation during cracking is derived on the constant J line in load-displacement space. Finally, well-known experimental expressions that relate load to crack length are shown to be indistinguishable from the load-point displacement analysis reported.