A coupled approach to predict cone-cracks in spherical indentation tests with smooth or rough indenters

Indentation tests are largely exploited in experiments to characterize the mechanical and fracture properties of the materials from the resulting crack patterns. This work proposes an efficient theoretical and computational framework, whose implementation is detailed for 2D axisymmetric and for 3D geometries, to simulate indentation-induced cracking phenomena caused by non-conforming contacts with indenter profiles of an arbitrary shape. The formulation hinges on the coupling of the MPJR (eMbedded Profile for Joint Roughness) interface finite elements which embed the indenter profile to efficiently solve the contact problem between non-planar bodies, and the phase-field model for brittle fracture to simulate crack evolution and nonlocal damage in the substrate. The novel framework is applied to predict cone-crack formation in the case of indentation tests with smooth spherical indenters, with validation against experimental data. Then, the methodology is employed for the very first time in the literature to assess the effect of surface roughness superimposed on the shape of the smooth spherical indenter. In terms of physical insights, numerical predictions quantify the dependencies of the critical load for crack nucleation and the crack radius on the amplitude of roughness in comparison with the behavior of smooth indenters. Again, the consistency with available experimental trends is noticed.