Strain Rate and Dynamic Fracturing in Planetary - Scale Impacts

Introduction: Impacts initiate dynamic fracturing on macro-and micro-scales, and the resulting fragmentation can be related to strain rate. The dynamic fracture process has been directly observed at low strain rates (~10-2 to 10-3 s-1 , during earthquakes) and at high strain rates (~10 5 to 10 6 s-1 , during laboratory-scale hypervelocity impact experiments) [1]. Based on first order estimates of the strain rate in the projectile (~ impact velocity/projectile diameter) [2], the strain rates encountered during a typical planetary-scale impact range from ~10 0 to 10 2 s-1. These intermediate values lie within an strain rate regime that is extremely difficult to observe naturally. Using numerical simulations and new dynamic fragmentation models, we investigate what strain rates might be generated during large scale impacts and assess implications for fragmentation considering new dynamic fragmentation models. Fragmentation Models: To first order, higher strain rates yield smaller fragment sizes. However, in reality the relationship is more complex. Experiments [3] have found that classical energy models of dynamic fracture (e.g., Grady-Kipp [4]) overestimate the average fragment size produced for a given strain rate. Observations of lunar craters report large amounts of very fine fragments, more so than would be predicted by classical models [5]. This indicates that the classical models are not accounting for important factors. In fragmentation modeling, it is important to account for residual kinetic energy associated with crack dynamics. A recent analytical-numerical model (ZMR) incorporated the elastic wave propagation, crack nucleation, growth, and interactions into the analysis. Here, kinetic energy is extracted from the system and applied to additional fracturing, creating new cracks and resulting in smaller fragment sizes [6]. This effect is pronounced at intermediate to low strain rates, and allows this model to predict fragment sizes in closer agreement to experimental observations [3,7]. Figure 1 compares the normalized average fragment size to the strain rate for basalt. The expected strain rate regimes for earthquakes, planetary-scale impacts, and laboratory-scale impacts are indicated. At high strain rates, the two models differ by approximately an order of magnitude. A significant turnover in average fragment size is observed between ~10 4 to 10