Phase field modeling of Hertzian indentation fracture

Abstract The formation and subsequent growth of cracks in brittle solids caused by indentation loading is investigated using a phase field modeling of fracture. While this methodology, at first glance, appears to be a promising tool for handling problems like the present one including crack initiation from an initially defect-free surface, its actual application reveals a number of critical issues. The paper illustrates inherent shortcomings of common phase field models for fracture based on a variational structure. Appropriate modifications are discussed which render the method – at least to some extent – suitable for the simulation of indentation fracture. Particular emphasis is placed on the significance of the material’s tensile strength and fracture toughness as independent physical properties necessary for the quantitative description of crack formation. Numerical predictions are compared with other theoretical results as well as experimental findings from the literature.