Fractal behavior and shape characteristics of fragments produced by the impact of quasi-brittle spheres
Impact induced fragmentation has been extensively studied in mechanical, geotechnical, aerospace and mining communities due to its direct relevance to a variety of engineering applications. In the present work, we investigated the fragmentation of quasi-brittle spheres subjected to a range of impact velocities using the combined finite and discrete element method (FDEM) coupled with a rate-dependent cohesive zone fracture model. The statistics of fragment mass distribution and shape characteristics are collected and interpreted using fractal analysis.
The fragment mass distribution can be described by a power law with the exponential coefficient depending on the impact velocity. Whereas some previous experimental and numerical studies have revealed a high degree of robustness of the exponent against the impact velocity. At higher velocities, the concentrated local stress at the contact point initiates an increased number of microcracks which evolve into finer fragments as the kinetic energy converts to surface energy during the comminution.
Such mechanism results in finer post-impact fragment size distributions that correspond to higher power law coefficients. The variation of fragment shape with respect to impact velocity is characterized by the Domokos shape descriptor and aspect ratio. It is found that all the fragment shapes will cease their variation and reach stable distributions as the impact velocities elevate. The variations of fracture patterns, the two largest fragments, and the average fragment mass with impact velocity are in good qualitative agreement with the existing experimental and numerical results.
The present study demonstrates that the combined FDEM coupled with the cohesive zone model is a promising tool in fragmentation studies for its physical soundness and its convenience in conducting detailed post-impact fragment size and shape analyses.
Keywords: Impact, Cohesive zone model, Fragmentation, Fractal behavior, Shape characterization.