By utilizing numerical models and simulation, insights about the fracture process of brittle heterogeneous materials can be gained without the need for expensive, difficult, or even impossible, experiments. Brittle and heterogeneous materials like rocks usually exhibit a large spread of experimental data and there is a need for a stochastic model that can mimic this behaviour. In this work, a new numerical approach, based on the Bonded Discrete Element Method, for modelling of heterogeneous brittle materials is proposed and evaluated. The material properties are introduced into the model via two main inputs. Firstly, the grains are constructed as ellipsoidal subsets of spherical discrete elements. The sizes and shapes of these ellipsoidal subsets are randomized, which introduces a grain shape heterogeneity Secondly, the micromechanical parameters of the constituent particles of the grains are given by the Weibull distribution. The model was applied to the Brazilian Disc Test, where the crack initiation, propagation, coalescence and branching could be investigated for different sets of grain cement strengths and sample heterogeneities. The crack initiation and propagation was found to be highly dependent on the level of heterogeneity and cement strength. Specifically, the amount of cracks initiating from the loading contact was found to be more prevalent for cases with higher cement strength and lower heterogeneity, while a more severe zigzag shaped crack pattern was found for the cases with lower cement strength and higher heterogeneity. Generally, the proposed model was found to be able to capture typical phenomena associated with brittle heterogeneous materials, e.g. the unpredictability of the strength in tension and crack properties.
The dynamic fracture process of rock materials is of importance for several industrial applications, such as drilling for geothermal installation. Numerical simulation can aid in increasing the understanding about rock fracture; however, it requires precise knowledge about the dynamical mechanical properties alongside information about the initiation and propagation of cracks in the material. This work covers the detailed dynamic mechanical characterisation of two rock materials—Kuru grey granite and Kuru black diorite—using a Split-Hopkinson Pressure Bar complemented with high-speed imaging. The rock materials were characterised using the Brazilian disc and uniaxial compression tests. From the high-speed images, the instant of fracture initiation was estimated for both tests, and a Digital Image Correlation analysis was conducted for the Brazilian disc test. The nearly constant tensile strain in the centre was obtained by selecting a rectangular sensing region, sufficiently large to avoid complicated local strain distributions appearing between grains and at voids. With a significantly high camera frame rate of 671,000 fps, the indirect tensile strain and strain rates on the surface of the disc could be evaluated. Furthermore, the overloading effect in the Brazilian disc test is evaluated using a novel methodology consisting of high-speed images and Digital Image Correlation analysis. From this, the overloading effects were found to be 30 and 23%. The high-speed images of the compression tests indicated fracture initiation at 93 to 95% of the peak dynamic strength for granite and diorite, respectively. However, fracture initiation most likely occurred before this in a non-observed part of the sample. It is concluded that the indirect tensile strain obtained by selecting a proper size of the sensing region combined with the high temporal resolution result in a reliable estimate of crack formation and subsequent propagation.
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