Marlin E. Kipp

Geometric statistics and dynamic fragmentation

The present study is focused on the distributions in particle size produced in dynamic fragmentation processes. Previous work on this subject is reviewed. We then examine the one‐dimensional fragmentation problem as a random Poisson process and provide comparisons with expanding ring fragmentation data. Next we explore the two‐dimensional (area) and, less extensively, the three‐dimensional (volume) fragmentation problem. Mott’s theory of random area fragmentation is developed, and we propose an alternative application of Poisson statistics which leads to an exponential distribution in fragment size. Both theoretical distributions are compared with analytic and computer studies of random area geometric fragmentation problems, including those suggested by Mott, the Voronoi construction, a variation of the Johnson–Mehl construction, and several methods of our own. We find that size distributions from random geometric fragmentation are construction dependent, and that a conclusive choice between the two distr...

Dynamic Fracture and Fragmentation

The dynamic fracture and fragmentation of a solid body or structure can result from the application of an intense impulsive load. The scale of such events ranges from shaped-charge jet breakup and rock blasting to astro-physical impacts and creation of planetary debris. In rock blasting, for example, specific information on ejecta velocities and fragment size distributions is sought, and methods to control resulting fragment sizes by proper placement and type of explosives are of interest (Grady and Kipp, 1987). In stretching shaped-charge jets, fragmentation characteristics, such as time-to-breakup and particle size are intimately tied to performance (Chou and Carleone, 1977). Ejecta from planetary and meteoric impact provide information on the evolution and dynamics of the solar system (Melosh, 1984). The applications in which solids or structures are subjected to intense dynamic loading and when breakup must be mitigated or controlled are numerous and varied. The need to understand the dynamic fracture mechanisms for such applications has provided the impetus for research in this rich area, and the field is currently quite active. The response of a single crack or void, within a solid body, to both static and impulsive loading has received considerable attention over the past several decades and is reasonably well understood (Freund, 1973; Chen and Sih, 1977; Kipp et al., 1980). The mechanics of a system of cracks or voids under impulsive or stress-wave loading, and how the cooperative response of such a system relates to the transient strength and ultimate failure and fragmentation of a solid body is less well understood, and has been a subject of study over the past decade (Curran et al., 1977; Davison and Graham, 1979; Meyer and Aimone, 1983; Grady and Kipp, 1987; Curran et al., 1987). Experimental studies of fracture under high-rate loading have revealed unusual features associated with the phenomenon, such as enhanced material strength and failure-stress dependence on loading conditions. Although such observations have led to the postulation of rate-dependent material properties, most of the features can be understood through fundamental fracture concepts when considered in terms of a system of interacting cracks or voids.

Shock compression and release in high-strength ceramics

Shock compression and release particle velocity data have been obtained for silicon carbide, titanium diboride, boron carbide, and zirconium dioxide with a laser velocity interferometer (VISAR). Peak impact stresses in these experiments range between 20 and 50 GPa. Iterative numerical methods were used to obtain dynamic compression and release stress-strain behavior of the ceramics. 16 refs., 4 figs., 3 tabs.

Numerical and experimental studies of high-velocity impact fragmentation

Abstract Developments are reported in both numerical and experimental capabilities for characterizing the debris spray produced in penetration events. We have performed a series of high-velocity experiments specifically designed to examine the fragmentation of the projectile during impact. High-strength, well-characterized steel spheres (6.35 mm diameter) were launched with a two-stage light-gas gun to velocities in the range of 3 to 5 km/s. Normal impact with PMMA plates, thicknesses of 0.6 to 11 mm, applied impulsive loads of various amplitudes and durations to the steel sphere. The extent of fragmentation, loss in momentum, and divergence of the debris are shown to correspond to the impact conditions. Multiple flash radiography was used to monitor material motion and fragmentation of the steel sphere during the impact event. Dynamic fragmentation theories, based on energy-balance principles, were used to evaluate local material deformation and fracture state information from CTH, a three-dimensional Eulerian solid dynamics shock wave propagation code. The local fragment characterization of the material defines a weighted fragment size distribution, and the sum of these distributions provides a composite particle size distribution for the steel sphere. The calculated axial and radial velocity changes agree well with experimental data, and the calculated fragment sizes for a specific experiment are in qualitative agreement with the radiographic data.

Fragmentation properties of metals

In the present study we are developing an experimental fracture material property test method specific to dynamic fragmentation. Spherical test samples of the metals of interest are subjected to controlled impulsive stress loads by acceleration to high velocities with a light-gas launcher facility and subsequent normal impact on thin plates. Motion, deformation and fragmentation of the test samples are diagnosed with multiple flash radiography methods. The impact plate materials are selected to be transparent to the x-ray method so that only test metal material is imaged. Through a systematic series of such tests, both strain-to-failure and fragmentation resistance properties are determined through this experimental method. Fragmentation property data for several steels, copper, aluminum, tantalum and titanium have been obtained to date. Aspects of the dynamic data have been analyzed with computational methods to achieve a better understanding of the processes leading to failure and fragmentation, and to test an existing computational fragmentation model.

Modeling of shock‐induced chemical reactions in powder mixtures

Chemical reactions in inorganic powder mixtures under high‐pressure shock wave loading are described by two mathematical models, one homogeneous and the other heterogeneous. The models are formulated based upon existing results of observations on post‐shock samples of Al‐Ni, Al‐Ti, and ZnO‐Fe2O3 mixtures. Two mechanisms were isolated for the development of the initial models: (1) the creation of a nonequilibrium mixture by dynamic mass mixing, and (2) ensuing chemical reactions. The homogeneous model was evaluated under shock conditions using a one‐dimensional wave propagation code, and suggested requisite conditions for the thermal excursion of localized reactions: a localized initial peak temperature of 1000–2000 K and reaction time constants of 1 μs or less. Calculations indicate that reactions occur while the sample is under shock loading, consistent with observations of post‐shock samples.

Elastic shock response and spall strength of concrete

Impact experiments have been performed to obtain shock compression, release response, and spall strength of two scaled concrete formulations. Wave profiles from a suite of ten experiments, with shock amplitudes of 0.08 to 0.55 GPa, focus primarily on the elastic regime. Despite considerable wave structure that develops as the shock transits these heterogeneous targets, consistent pullback signals were identified in the release profiles, indicating a spall strength of about 30 MPa. Explicit modeling of the concrete aggregate structure in numerical simulations provides insight into the particle velocity records.

Fracture resistant properties of AerMet steels

Abstract The purpose of this study is to report well-controlled experiments conducted to determine the fracture resistant properties of AerMet® 100 steels. One of the objectives of this study is to determine the influence of fracture toughness properties on the fracture and fragmentation process. Both sphere impact tests and cylinder expansion test geometry were used to determine the dynamic fracture resistant coefficients. These experiments were conducted at strain rates of ∼ 14 × 10 3 /s for the cylinder expansion tests; the strain rates for the sphere impact tests varied over 50 to 100 × 10 3 /s. Fracture resistant coefficients of 60 MPa √m and 20 MPa √m are obtained from the cylinder test and the sphere impact test, respectively. These measurements do not agree with the static fracture toughness values reported in the literature.

Experimental and computational simulation of the high velocity impact of copper spheres on steel plates

Summary High-velocity impact experiments were performed in which copper spheres struck hardened 4340 steel target plates. Velocities range between 3 and 5 km/s, and both normal and oblique impacts were performed. High-resolution flash radiography was used to diagnose the impact crater formation and debris motion within a time frame accessible to computational simulation. Witness plate and fragment capture methods were used to evaluate size and trajectory statistics of the ejecta fragment debris. The three-dimensional wave-code CTH was used to analyze the crater formation and debris evolution process. Simulated radiographs were constructed for direct comparison with X-ray data.

Polyurethane foam impact experiments and simulations

Uniaxial strain impact experiments have been performed to obtain shock compression and release response of a 0.22 g/cm3 polyurethane foam in a configuration where the foam impacts a thin target witness plate. Wave profiles from a suite of ten experiments have been obtained, where shock amplitudes range from 40 to 600 MPa. A traditional P-α porous material model generally captures the material response. A fully three-dimensional explicit representation of the heterogeneous foam structure modeled with numerical simulations recovers some of the high frequency aspects of the particle velocity records.