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.

使用裂缝的相场模型研究了由压痕载荷引起的脆性固体中裂纹的形成和随后的扩展。乍一看，这种方法似乎是解决当前问题的有前途的工具，包括从最初没有缺陷的表面产生裂纹在内的当前问题，但其实际应用却揭示了许多关键问题。本文阐述了基于变结构的常见相场模型的固有缺陷。讨论了适当的修改，这些修改至少在某种程度上使该方法适合于模拟压痕断裂。特别强调材料的拉伸强度和断裂韧性作为定量描述裂纹形成所必需的独立物理特性的重要性。将数值预测与其他理论结果以及文献中的实验结果进行了比较。