Research On Dynamic Fragmentation Of Ductile Metals

Materials usually break into many pieces (fragments) under high strain-rate tension. Understanding the fragmentation properties of solids is important to the researchers in fields of physics, mechanics, aerospace and defense engineering. For a given set of material, structure and loading parameters, estimating the average fragment size is a crucial issue. The further question remains on how to determine this characteristic size distribution.By introducing a cohesive fracture model into the Mott momentum diffusion analysis, Grady and Kipp deduced a formula for predicting the average size of the fragments during a ductile fragmentation process. To quantitatively evaluate the accuracy of the Grady-Kipp formula, in this paper, we numerically simulated the fragmentation processes of an elastic-plastic bar undergoing initially uniform high strainrate tensile deformation. The key material parameters, including the fracture energy, the material density, yield stress A, and the strain-rate sensitivity C, were varied intentionally for evaluating their effects on the fragmentation process. The average fragment sizes were calculated for a wide range of the prescribed strainrates and the material parameters. It was concluded that the Grady-Kipp model provides reasonably close predictions of the lower limit of the ductile fragment sizes, though slight deviations exist in the cases when the fundamental assumptions in the Grady-Kipp analysis do not apply.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 be2;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 distributions. 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.Actually during the fabrication and the machining process, metallic components are inevitably brought with defects or inhomogeneities. Generally such defects or inhomogeneities have fixed geometric distributions. In this paper, we use the explicit FEM code to simulate the dynamic fragmentation processes of a thin elastic-plastic bar undergoing uniform high strain-rate tensile deformations. The thin bar is prescribed with periodical geometrical defects. Through numerical experiments, it was found that the bar with the initial defects usually broke into pieces earlier than the bar without defects. For periodically distributed defects, there exists a strain-rate region in which the fragmentation process is completely controlled by the defects. This is called the "defect controlled fragmentation" process. The spacing and the size of the defect also affect the fragmentation process, by moving the strain-rate region of the "defect controlled fragmentation". The effects of the combined defect distribution on the ductile fragmentation process are also investigated.A new loading experimental technology was developed for conducting expanding ring tests, basing on the Split Hopkinson Pressure Bar (SHPB). The tests are useful for the studies on the dynamic tensile deformation and the fracture (fragmentation) properties of materials. The loading fixture includes a hydraulic cylinder full of incompressible fluid, which is pushed by a piston connected to the input bar. As the liquid is driven, it compresses and expands the metallic ring specimen in the radial direction. The approximately incompressible property of the liquid makes it possible to transfer a low piston-velocity to a very high radial velocity of the specimen, as the sectional areas of the cylinder narrows extremely. Using this experimental technology the ring specimens made of ductile metals were dynamically expanded and fragmentized. Results show apparent increases of the fragment numbers and the fracture strain of the specimen with the increase of the impact velocity.One-dimensional theoretical models are established to study the unloading processes of the ductile materials due to an array of internal equally-spaced defects. By symmetry, a unit region containing one defect is considered. The Mott wave propagations and the interactions in the region were analyzed theoretically or numerically, leading to the historical curves of the average stress across the region. The critical time of fracture, defined as the time at which the average stress dropped to zero, is determined from these curves. It appears that for a prescribed strainrate, there always exists an optimum defect spacing corresponding to the rapidest unloading process. Fortunately, the optimum defect spacings for different strainrates approximate the fragment sizes given by Grady-Kipp formula.To quantitatively evaluate the accuracy of the Grady-Kipp formula for2D fragmentation, we numerically simulated the fragmentation processes of an elastic-plastic plate undergoing initially uniform high strainrate tensile deformation. Through numerical experiments, it was found that the calculated fragment size is significantly different from Grady’s theoretic estimate, which is four or five times of the numerical value.