Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical Engineering


Weapons systems--Design and construction., Fragmentation bombs., Metals--Fracture.


The dynamic fragmentation of shell cases has historically been treated with mixed physical and statistical models that have been applied with varying degrees of success. Mott developed the most commonly used physics-based model of fragmentation in the 1930’s. Mott also developed an unrelated, but more pervasive statistical distribution function. In this work, basic concepts of these analyses are extended to account for fracture energy and applied to the explosive fragmentation of shell elements and to the impact fragmentation of solid plates. An energy-based distribution function is developed and validated against experiment, and conclusions are drawn regarding the efficacy of the approach. The tools used to develop the energy-based distribution function are wave mechanics and survival statistics. The wave mechanics are parametrized using Kipp & Grady’s energy-based fracture extensions to Mott’s formulation. Survival statistics is a field developed initially to determine chemical kinetics parameters such as half-life from collision rates. In order to develop a physical basis for model derivations, established methods by Mott and Kipp & Grady are modified and used to determine the rate of fracture formation and associated tensile release wave propagation, which results in a deterministic estimate of mean particle length expected in the fragmentation process. Kinetic energy in the fracturing medium is converted into surface energy through crack growth during the formation phase. After a fracture has completed, energy is no longer absorbed, but the tensile release wave continues to propagate. The survival statistics method is used to determine the growth and coalescence of these release waves. From the growth and coalescence rates, the distribution in particle sizes is mathematically formulated. The process is carried out for both pre-completion and post-completion phases of fracture formation. The resulting distribution functions from both phases are statistically mixed using a constant derived from physical parameters and mechanical properties. Multi-layer effects are treated with statistical mixing of distribution functions calculated from the physical state parameters and mechanical properties of each constituent layer. These distribution functions are mixed using the ratio of layer masses as the mixing constant, with a notional physically based method for layer contribution presented, but not fully pursued. Hydrocode analysis is used in the course of this work to calculate the physical state of materials subjected to dynamic fragmentation. A hydrocode is a finite element analysis code that treats solid materials as viscous fluids, which closely approximates the behavior of most materials under high strain rate conditions. The fracture models are integrated with the ALE3D™ hydrocode from Lawrence Livermore National Laboratory and applied to diverse fragmentation problems ranging from dynamic fragmentation of an explosively loaded shell case to the impact fragmentation of single material plates. In the course of this research, a naturally fragmenting device was designed using the hydrocode coupled fragmentation models, fabricated, and subjected to experiment. The results and analysis from this experiment are presented as a validation case alongside experimental data from literature. Validation of the multi-layer formulations is accomplished through analysis of a series of 9 high velocity fragment impact experiments carried out by the present author in recent history, with the projectile and target plate treated as distinct layers resulting in divergence from the single layer simulation results.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.