# Characterization of Dolomite Stone Broken Under Axial Impact
## 2 Numerical Simulation of Single-Cutter Rock Breaking Under Axial Impacts
### Methods of Numerical Simulation  
The specimen being analyzed was a rectangular rock with dimensions of 30 mm * 20 mm * 15 mm, which contained an encrypted grid in its central cutting area. Previous studies have demonstrated that the cutting speed had a negligible effect on both the rock fragmentation process and the cutting force in numerical simulations. Therefore, the cutting tool was set to progress through the rock at a speed of 100 mm/s, with a forward inclination angle of 20\({}^{\circ}\), as depicted in Figure 1.  
The Drucker-Prager code was the primary framework for evaluating the damage and fracture characteristics of geological materials, especially rocks [37]. Within this framework, uniaxial compressive strength was used to determine the hardening behavior of materials. In addition, the shear damage criterion, together with damage evolution coefficients, was used to assess the conditions leading to rock fracture. The contact between the rock and the cutter was in the form of a \"cutting face-rock mesh node set\" contact, with the specific contact function set to be a nonlinear elastic slip contact, the normal contact property to be a hard contact, and the rock mesh to be designed as a hexahedral structural mesh. Moreover, an encrypted mesh was set in the contact part between the rock and the PDC cutter, with the maximum size of the mesh not exceeding 0.5 mm, and the encrypted area of the mesh was set to 0.1 mm in order to improve the accuracy of the simulation. In the cutting simulation process, the rotary cutting of the PDC cutter around the center axis of the drill bit was simplified to a linear cutting motion, and the cutters were regarded as rigid parts because of the strength difference between the PDC cutter and the rock. In order to simulate the real rock-breaking process of the PDC cutter at the bottom of the well, the  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Parameter Value** \\ \hline Young’s modulus & 9.29 GPa \\ Poisson’s ratio & 0.43 \\ Dilation angle & 5\({}^{\circ}\) \\ Internal friction angle & 41.24\({}^{\circ}\) \\ Cohesion yield three & 54.98 MPa \\ \hline Dolomite & 68.52\% \\ Calcite & 7.09\% \\ Sapphire & 0.85\% \\ Galena & 5.65\% \\ Micas & 7.57\% \\ Loam & 10.32\% \\ \hline \hline \end{tabular}
\end{table}
Table 1: Other parameters of damage plasticity model and mineralogical composition.  
Figure 1: Schematic representation of the numerical simulation framework.  
degrees of freedom of the bottom surface boundary of the simulated rock were set to 0. The main purpose of this simulation was to analyze the stress response and the response of the cutting characteristic parameters during the cutting process under the effect of axial impact, so the actual formation pressure conditions were not taken into account [38; 39; 40].  
A simulation scenario was developed in which the cutting tool progressed at a uniform velocity in the cutting direction. After consideration, the dynamic load acting on the drill bit generally did not exceed 50% of the static load, after exceeding which the PDC cutter damage phenomenon was very likely to occur; therefore, with reference to the previous parameter design, the static load was set to 2000 N, and the maximum impact force was set to 2500 N [41]. At the same time, taking into account the current mechanical and hydraulic impact tool design principles and test data, the impact frequency in the range of 20-40 Hz did not exceed 100 Hz [20]. Simultaneously, a dynamic load, characterized by a sinusoidal waveform with a defined period, was applied while maintaining a constant drilling pressure. The specifics of the simulation framework are detailed in Table 2. The amplitude of the impact inputs was configured at 1.0, 1.2, 1.3, 1.4, and 1.5, while the impact frequency was set at 10 Hz, 20 Hz, 40 Hz, 60 Hz, and 80 Hz. The axial external force, denoted as F, is illustrated in Figure 2.