Abstract:
The length-to-diameter ratio has a significant impact on the mechanical properties and energy evolution of rock samples under impact loads, and the current constitutive model for rock damage that considers the coupling of length-to-diameter ratio and strain rate still needs to be improved. The split Hopkinson pressure bar (SHPB) system was used to conduct dynamic compression tests with four length-to-diameter ratios (0.4, 0.6, 0.8, 1.0) and five levels of impact air pressure (0.2–0.6 MPa). The relationships between parameters such as strength, deformation, and energy with length-to-diameter ratio were analyzed. The theoretical slopes of reflection energy, transmission energy, fragmentation energy, and incident energy have been derived. Based on the Weber distribution and D-P criterion, a damage constitutive model considering the coupling of length-to-diameter ratio and strain rate was established. The research results show that: ① The dynamic stress-strain curve of sandy mudstone specimens under impact loads can be divided into the compaction stage, quasi-elastic stage, plastic stage, and failure stage. Within the range of impact air pressure involved in the experiment, the dynamic strength growth factor is positively correlated with the aspect ratio, while the softening coefficient is negatively correlated with the aspect ratio. ② With the increase in length-to-diameter ratio, the energy density of specimen fragmentation decreases. As the length-to-diameter ratio of the sample increases from 0.4 to 1.0, the proportion of reflected energy increases from 19% to 31%, the proportion of transmitted energy decreases from 37% to 21%, and the proportion of dissipated energy ranges from 43% to 48%. By fitting the experimental data, it was found that there is a positive correlation between reflected energy, transmitted energy, dissipated energy, and incident energy. Based on the interface reflection coefficient \lambda of stress waves transmitted from the incident bar to the specimen, the theoretical slopes of reflected energy, transmitted energy, dissipated energy, and incident energy are are derived as \lambda^10 , \left(1-\lambda^6\right)^2 and 1-\lambda^10-\left(1-\lambda^6\right)^2, respectively. ③ Based on the dynamic strength obtained from experiments and its function with strain rate and length-to-diameter ratio, the initial constitutive model derived from the Weber distribution and D-P criterion was modified. The resulting damage constitutive model shows good consistency with the experimental curves and can be used to characterize the dynamic mechanical properties of sandy mudstone.