The relationship between energy consumption and the rock fragment size distribution is a basic question in rock fragmentation. Based on fractal rock mechanics and fracture mechanics theory, a new model of energy consumption during rock fragmentation is proposed. Moreover, dynamic uniaxial compressive tests on granite and sandstone under five different impact velocities are conducted with the split Hopkinson pressure bar (SHPB) device, the fragment size distribution of broken rock is obtained by sieving and the energy dissipation in the process is analyzed. The results from the tests show that fragments resulting from rock breakage under impact loading exhibit fractal features; the larger the fractal dimension, the higher the degree of rock fragmentation. Notably, the energy consumption density is inversely correlated with the average size of the rock fragments: with an increasing energy consumption density, the average size decreases significantly and the fracture surface area increases accordingly. Additionally, the SHPB tests enable determination of the fracture surface energy of granite and sandstone, and the energy consumption density is calculated based on the theoretical model and found to be in good agreement with the experimental results.

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In this study, we report a theoretical model for the temperature and size dependent surface energy of metallic nanomaterials. The model is verified by making a comparison with the available simulation and experimental data. Reasonable agreement has been observed between these results. This study reveals that the decrease of surface energy at high temperatures is caused by cohesive energy weakening and bond expansion. With the same nanomaterial size, the sequence of size effects on the surface energy from weak to strong is thin films, nanowires, and nanoparticles. In particular, this work can provide a theoretical basis for the prediction of size dependent surface energy of metallic nanomaterials at different temperatures, which can help in the understanding of the mechanical and thermodynamic properties of metal surfaces.

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