Mechanical modeling of granite subjected to indentation loading
Abstract: The understanding of the mechanical response of Bohus granite, as typical of hard rocks, to percussive drilling is important to improve the efficiency of such an operation. The resulting problem includes material modeling of the selected type of rock under indentation loading conditions. An elastoplastic constitutive material model combined with a damage description is employed for this purpose. The material model parameters are calibrated based on experimental results. Linear Drucker-Prager (DP) plasticity model with pressure-dependent dilatancy and an anisotropic damage model (DFH model) are considered to account for the inelastic deformations and the tensile failure (i.e., mode I fracture), respectively. The resulting constitutive model is implemented numerically into a finite element (FE) commercial software to simulate the material behavior under indentation loading up to its load capacity. In Paper A, the DP material model parameters are determined based on quasi-oedometric tests performed in a previous work and the yield surface and dilation angle are determined. The calibrated material model is implemented numerically taking advantage of Abaqus FE software. The established numerical model is then used to simulate quasi-static indentation test and the force-penetration (P-h) response is predicted. Moreover, a high-speed camera is utilized to monitor the surface of specimens, made of Bohus granite, at different load levels in indentation tests. It is detected that the load-drops observed in the P-hresponse are associated with the material removals on the surface. In Paper B, the anisotropic DFH damage model is employed to predict the material fracture pattern subjected to quasi-static indentation loading. The employed damage model considers the heterogeneity in the material tensile strength using Weibull statistics. It is described how the Weibull parameters are calibrated. The calibrated DFH model is combined with the DP model. The resulting DP-DFH model is used to simulate the material elastoplastic response and the fragmentation process. Furthermore, the frictional effects on the P-hresponse, fracture pattern and plastic zone are numerically investigated in Paper C. In doing so, friction is introduced between the indenter and the granite surface in numerical simulations. A parametric study of frictional coefficients is also carried out. Finally, in situ spherical indentation test is performed and monitored by X-ray microtomography in Paper D. The test is then analyzed by Digital Volume Correlation (DVC), with the aim of validating the calibrated constitutive model. FE simulations of the indentation problem, using different constitutive models, namely, elasticity, compressible elastoplasticity (DP) and compressible elastoplasticity with damage description (DP-DFH) are carried out and the results are compared based on DVC residuals. The frictional contact effects are also studied. It is concluded that compressible elastoplasticity should be accounted for to predict the load level and displacement fields beneath the indenter. It is also concluded that frictional effects lead to damage extension. However, the frictional effects on the P-hresponse and the size of the plastic zone underneath the indenter are negligible. Finally, it is shown that the employed damage model can determine the indentation fracture pattern prior to extensive failure of the chosen type of rock.
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