CHARACTERISTICS OF FRAGMENT SIZE DISTRIBUTION OF DUCTILE MATERIALS FRAGMENTIZED UNDER HIGH STRAINRATE TENSION

Finite Element Method has been used to simulate the fracture and fragmentations of ductile metallic rings undergoing high rate expansions. In this paper, the numerical fragments obtained from the FEM simulations were collected for statistical analysis. It is found that: (1) The cumulative distributions of the normalized fragment sizes at different initial expansion velocities are similar, and collectively the fragment size distributions are modeled as a Weibull distribution with an initial threshold. Approximately, this distribution can be further simplified as a Rayleigh distribution, which is the special case with the Weibull parameter to be 2; (2) The cumulative distribution of the fragment sizes exhibits a step-like nature, which means that the fragment sizes may be "quantized". A Monte-Carlo model is established to describe the origination of such quantization. In the model, the fractures occur at the sites where the tensioned material necks. The spacing of the necking sites follows a narrow Weibull distribution. As the fragment size is the sum of several (a random integer) necking spacing, the distributions of the fragment sizes automatically inherit the quantum properties of the random integers as long as the spacing distributions are not so wide. The experimental results conducted on Al L04 and on OFHC agree with the analysis.