Dynamic fragmentation of planetary materials: Ejecta length quantification and semi-analytical modelling

The dynamic fragmentation of planetary materials during impact into finite targets has been examined. A particle tracking algorithm was implemented to estimate the size and velocity of fragments ejected from the rear of the target. A total of 76 experiments were performed for four materials, target thicknesses of 7 mm–55 mm, and impact energies of 10 J–6810 J. Semi-empirical models were developed from non-dimensional groups to predict key experimental results. This includes the transformation of incoming projectile kinetic energy to the ejecta kinetic energy. The amount of impact energy converted to kinetic energy of ejecta was found to increase from 2% to 18% over the range of test conditions. Energy dissipated into expanding the field laterally was found to be small in comparison to the streamwise direction (∑KEy/∑KEx = 4%). Percentiles of the distribution of mass, momentum and kinetic energy with respect to ejecta lengths were also examined. Percentile ejecta lengths decrease for increasing normalized impact energy. Fits of the non-dimensional ejecta lengths provide reasonable collapse for the percentile values. Lastly, the cumulative distributions of mass, momentum and kinetic energy among normalized 50% length values were quantified. Exponential function forms were found to fit all of the data over the range over normalized length scales of 0.3–4. When integrated, this predicts the probability density distribution of mass, momentum, and kinetic energy among ejecta lengths for the range of experimental conditions in this study. This data is important in the development and validation of numerical models.