A model for microcrack initiation and propagation beneath hertzian contacts in polycrystalline ceramics

Abstract

A fracture mechanics model of damage evolution within Hertzian stress fields in heterogeneous brittle ceramics is developed. Discrete microcracks generate from shear faults associated with the heterogeneous ceramic microstructure; e.g. in polycrystalline alumina, they initiate at the ends of intragrain twin lamellae and extend along intergrain boundaries. Unlike the well-defined classical cone fracture that occurs in the weakly tensile region outside the surface contact in homogeneous brittle solids, the fault-microcrack damage in polycrystalline ceramics is distributed within a subsurface shear-compression zone below the contact. The shear faults are modelled as sliding interfaces with friction, in the manner of established rock mechanics descriptions but with provision for critical nucleation and matrix restraining stresses. This allows for constrained microcrack pop-in during the loading half-cycle. Ensuing stable microcrack extension is then analyzed in terms of a K-dfield formulation. For simplicity, only mode I extensions is considered specifically here, although provision exists for including mode II. The compressive stresses in the subsurface field constrain microcrack growth during the loading half-cycle, such that enhanced extension occurs during unloading. Data from damage observations in alumina ceramics are used to illustrate the theoretical predictions. Microstructural scaling is a vital element in the microcrack description: initition is unstable only above a critical grain size, and extension increases as the grain size increases. Internal residual stresses also play an important role in determining the extent of microcrack damage. Implications of the results in the practical context of wear and fatigue properties are discussed.