Multiscale modeling of cemented tungsten carbide in hard rock drilling

Mechanical behavior of rotary-percussive drilling tools made of tungsten carbide (WC) hardmetal in impact interaction with hard rock is investigated. This study presents a three-step multiscale simulation strategy, developed for evaluation of stress and strain heterogeneity within the hardmetal microstructure when subjected to loadings representative for drilling applications. Two homogenization approaches are used: a full-field finite-element model and a Beta-model (a nonlinear extension of the Kröner's uniform field model). Both models combine isotropic Drucker-Prager elasto-plastic behavior of WC grains and isotropic von Mises elasto-plastic behavior of the binder, and include nonlinear hardening. First, a three-dimensional finite-element model of a representative volume element is constructed, which closely resembles the hardmetal microstructure. Full-field simulation with applied proportional loadings allows to determine the hardmetal effective elastic properties for different binder content, and an initial yield surface, resembling in shape a Drucker-Prager surface with a cap. These simulations are also used to calibrate the Beta-model, which, however, cannot predict the correct plastic behavior for the loadings with high hydrostatic component. Second, macroscopic finite-element simulations of normal and oblique frictional impact of an elastic rock by a hardmetal spherical tip are performed using a macroscopic set-up. The calibrated Beta-model is used at every Gauss-point of the hardmetal impactor. Finally, the most critical for the hardmetal's integrity points are identified on the impactor's surface, and complex non-proportional stress paths associated with these points are extracted. These stress paths are used as boundary conditions in a full-field simulations employing representative volume elements of hardmetal microstructure. Analysis of stress and plastic-strain fields at the microstructural scale suggests that the major source of wear of drilling inserts may come from tensile failure of WC grains.