Phase Field Modeling of Hertzian Cone Cracks Under Spherical Indentation

Phase-Field Modeling of Fused Silica Cone-Crack Vickers Indentation

“…By increasing the load, the crack starts to propagate orthogonally to the surface towards the interior of the material (see the dimension, d , in Figure 4 c). This propagation direction has been well-captured in both 2D numerical [ 8 , 13 ] and 3D experimental [ 5 , 6 ] observations. With increasing load, the crack continues to propagate with an incline angle of around 45° with respect to the surface ( Figure 4 b).…”

“…The loading is prescribed as the displacement as the flat top side of the indenter, which is assumed to be rigid. This assumption has been adopted by different finite element studies [8,13,36], where simulations have exhibited little or no difference between the simulations with a rigid or deformable indenter. Material parameters for our brittle fracture phase-field formulation are shown in Table 4.…”

“…Despite all mentioned restrictions, for a certain choice of input variables for which all required conditions are satisfied, their modified model was able to reproduce the main features of cone-crack initiation and propagation: the formation of the initiation ring around the indenter, a vertical crack propagation, and the conical crack propagation with an inclination to the sample surface. Kindrachuk and Klunker [ 13 ] used a similar brittle phase-field formulation for the axis-symmetric 2D simulation of spherical indentation to investigate a kinked cone-crack propagation, caused by the changing contact conditions between the propagating spherical indenter and the sample surface. They performed a frictionless contact analysis by employing an ad-hoc crack driving force based on the strain measure, similar to the Beltrami criterion of failure, instead of a stress-based crack driving force.…”