Fracture sequences during elastic–plastic indentation of brittle materials

A fracture analysis is developed for crack initiation sequences occurring during sharp indentation of brittle materials. Such indentations, generated by pyramidal or conical loading, generate elastic and plastic deformation. The analysis uses a nonlinear elements-in-series model to describe indentation load–displacement responses, onto which lateral, radial, cone, and median crack initiation points are located. The crack initiation points are determined by extension and application of a contact stress-field model coupled to the indentation load, originally developed by Yoffe, in combination with crack nuclei coupled to the indentation displacement to arrive at an explicit fracture model. Parameters in the analysis are adapted directly from experimental fracture and deformation measurements, and the analysis outputs are directly comparable to experimental observations. After adaptation, crack initiation loads and sequences during indentation loading and unloading of glasses and crystals are predicted by the model from material modulus, hardness, and toughness values to within about 25% of peak contact load. This work is dedicated to George M. Pharr IV on the occasion of his 65th birthday in recognition of his contributions to indentation mechanics.