Numerical Investigation of the Fragmentation Process in Marble Spheres Upon Dynamic Impact

Three-dimensional discrete element simulations are performed to better understand the impact-induced complex fragmentation process of marble spheres. A 3D clumped particle method is used and a new calibration procedure to match both the quasi-static and dynamic mechanical behaviors of marble is proposed. The impact simulation results show that radial macrocracks occur, which break the intact marble spheres into large orange-slice-shaped fragments. Secondary macrocracks occur for impact velocities larger than 9 m/s, and the fragment size is further reduced. The fracture mechanisms due to local damage, radial, and secondary macrocracks significantly affect the impact process, energy dissipation, evolutions of the masses of the first and second largest fragments, and damage ratio. The numerical model is able to accurately capture all mechanisms, from local damage to disintegration, of the impact-induced fragmentation. Due to local damage and macrocracks, the obtained fragments consist of large and small fragments. The fragment size distributions based on mass and number can be fitted using a generalized extreme value law. The numerical predictions indicate that the translational velocities of some small fragments can be significantly higher than the impact velocity due to the instant high-tensile stress wave near the contact area. The results also suggest that there is no correlation between fragment mass and fragment kinetic energy.