Modeling dynamic fragmentation of heterogeneous brittle materials

Extreme high-rate loading of structural materials triggers a complex process of fragmentation involving probabilistic, energetic and mechanical aspects. One-dimensional modeling approaches based on elastodynamics have been successfully used to predict strain-rate dependence of average fragment-size. However, the ability of such approaches to correctly predict the statistical distribution of fragment-size has not been quantitatively compared with experiments. In this work, we use a one-dimensional approach based on the model suggested by Zhou et al. [1] to assess dynamic fragmentation in glass, concrete and masonry. The model considers a one-dimensional bar under a uniform initial tensile strain rate, with spatially varying strength to represent variations in the materials microstructure. The results include fragment-size, fragment-mass and time of formation distributions for strain rates between 103 and 105 s-1. Results show that the generalized gamma distribution is highly suitable for describing the fragment-size statistics. Given uncertainty in the standard deviation of the strength, a parametric study was performed to assess the effects of these variations on the fragmentation statistics. The trend in the rate-dependence of average fragment-size shows good agreement with measurements from shock tube experiments for all the materials studied. However, the estimated parameters of the fragment-size distribution from the 1D modeling approach do not compare well with the measurements from shock tube experiments for three common brittle materials studied in this work. Particularly, the predicted distribution of fragment-size extracted for a single value of strain rate exhibits a smaller variance than that observed in the experiments. A formulation that includes the heterogeneity of strain rates in the shock tube tests is proposed towards the development of quantitatively validated fragmentation models.