XFEM investigation on Knoop indentation cracking: Fracture toughness and aspect-ratio of radial-median cracks

• Knoop indentation cracking is simulated with XFEM.
• Values for damage model parameters are suggested for indentation cracking.
• The influence of material properties on the final crack size is investigated.
• Functions for estimating fracture toughness and crack aspect-ratio are proposed.

In sharp indentation of brittle materials, cracks form below the impression or at its corners and propagate further during unloading. The dimensions of radial-median cracks can be exploited to derive the fracture toughness. Knoop indentation has the merit that only one large crack is produced. This and the shallow plastic zone make it the preferred method for crack growth experiments, but which require information on the initial crack shape. For investigation of the complex indentation stress field, which is moreover perturbed by cracking, the extended finite element method (XFEM) is an ideal tool. Results show that the point load assumption holds for sufficient loading, which means that Knoop indentation can be used for fracture toughness evaluation. During loading the plastic zone evolves linearly with depth h, while crack depth cz is found to evolve according to h ∝ cz3/4. For well-developed cracks, the crack aspect-ratio ρ ≡ cz/c (c is the length of the crack on the surface) is load-independent. The XFE model is validated through comparison with experimental results from the literature. Based on parameter studies, we establish functions that allow determination of fracture toughness and crack aspect-ratio. It is demonstrated that the mapping functions work well.

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