David E. Lambert

Strain rate effects on dynamic fracture and strength

An experimental procedure and accompanying theoretical analysis is presented to produce a well-characterized technique for quantifying dynamic fracture properties of quasi-brittle materials. An analytical and experimental investigation of mode I fracture of concrete was conducted under the dynamic loading of a split Hopkinson pressure bar. Fracture specimens in the form of notched-cavity splitting tension cylinders were subjected to stress wave loading that produced strain rates nearing 10/s. Fracture parameters were extracted by the application of the two-parameter fracture model, a nonlinear fracture model for quasi-brittle materials. Finite element analysis verified the experimental configuration and addressed inertial contributions within the dynamic environment. Ultra-high-speed digital photography was synchronized with the fracture process to provide additional validation and insight to the experimental technique. Results show that the effective fracture toughness and specimen strength both increase significantly with loading rate. The numeric and photographic results validate the experimental technique as a new tool in determining rate dependent material properties.

Experimental Validation of Detonation Shock Dynamics in Condensed Explosives

Experiments in the HMX-based condensed explosive PBX-9501 were carried out to validate a reduced, asymptotically derived description of detonation shock dynamics (DSD) where it is assumed that the normal detonation shock speed is determined by the total shock curvature. The passover experiment has a lead disk embedded in a right circular cylindrical charge of PBX-9501 and is initiated from the bottom. The subsequent detonation shock experiences a range of dynamic states with both diverging (convex) and converging (concave) configurations as the detonation shock passes over the disk. The time of arrival of the detonation shock at the top surface of the charge is recorded and compared against DSD simulation and direct multi-material simulation. A new wide-ranging equation of state (EOS) and rate law that is constrained by basic explosive characterization experiments is introduced as a constitutive description of the explosive. This EOS and rate law is used to compute the theoretical normal shock velocity, curvature relation of the explosive for the reduced description, and is also used in the multi-material simulation. The time of arrival records are compared against the passover experiment and the dynamic motion of the shock front and states within the explosive are analysed. The experiment and simulation data are in excellent agreement. The level of agreement, both qualitative and quantitative, of theory and simulation with experiment is encouraging because it indicates that descriptions such as the wide-ranging EOS/rate law and the corresponding reduced DSD description can be used effectively to model real explosives and predict complex dynamic behaviors.

Explosively Driven Fragmentation Experiments for Continuum Damage Modeling

The explosively loaded right-circular tube geometry is used as the basis for dynamic fracture and fragmentation modeling. Details of the cylinder configuration are investigated to prescribe controlled loading conditions of uniaxial stress and plane strain. Earlier works by Goto [2008, “Investigation of the Fracture and Fragmentation of Explosively Driven Rings and Cylinders,” Int. J. Impact Eng. 35 (12), pp. 1547–1556] had used thin-walled tubes to provide plane strain loading and shorter “rings” to establish uniaxial stress conditions. This paper extends on that work to look at alternative cylinder dimensions and metals of interest. A tungsten alloy, Aero-224, and a high strength steel, Eglin Steel (ES-1), are the subject metals. Transient continuum-mechanics simulations evaluated whether the stress triaxiality conditions were being met as design parameters of cylinder material, cylinder wall-thickness, cylinder length, and initiation configuration were varied. Design analysis shows that the thin cylinders of ES-1 steel do establish the desired plane strain conditions as it expands to failure. Ultra-high speed photography experiments verify the time of fracture and correlate casewall expansion and velocity measurements. Synchronization of the code and diagnostics measurements is presented as a valuable analysis method. On the other hand, rings (i.e., uniaxial stress) of the Aero-224 tungsten alloy were failing just short of uniaxial stress approximating conditions. Analysis of the Aero-224 rings indicated it must be capable of achieving at least a 25% strain to failure in order to have the triaxiality condition satisfied. Strain to failure measurements directly from recovered fragments were less than 14%. Nevertheless, a Weibull distribution was fit to the empirical data set and used to drive a statistically compensated fracture model. Results and discussion of the failure strain distribution and the ability for continuum codes to adequately conduct such simulations are presented.

Cylindrical converging shock initiation of reactive materials

Recent research has been conducted that builds on the Forbes et al. (1997) study of inducing a rapid solid state reaction in a highly porous core using a converging cylindrical shock driven by a high explosive. The high explosive annular charge used in this research to compress the center reactive core was comparable to PBXN-110. Some modifications were made on the physical configuration of the test item for scale-up and ease of production. The reactive materials (I2O5/Al and I2O5/Al/Teflon) were hand mixed and packed to a tap density of about 32 percent. Data provided by a Cordon 114 high speed framing camera and a Photon Doppler Velocimetry instrument provided exit gas expansion, core particle and cylinder wall velocities. Analysis indicates that the case expansion velocity differs according to the core formulation and behaved similar to the baseline high explosive core with the exit gas of the reactive materials producing comparable velocities. Results from CTH hydrocode used to model the test item com...

Experimental Design and Data Collection for Dynamic Fragmentation Experiments

Experiments have been conducted to investigate the fracture and fragmentation characteristics of a liquid phased sintered (LPS) tungsten and high strength steel alloys. Metal cylinders, each of which was 20.32 cm tall and 5.08 cm inner/5.88 cm outer diameter, were explosively driven to failure. Two complimentary types of experiments were conducted in this series to determine input parameters for a related continuum mechanics based modeling effort. Open air experiments utilized ultra-high speed framing photography and a photonic Doppler velocimetry system (PDV). The information from these experiments provided a case wall velocity, relative time of breakup and strain-rate during the stress loading timeframe. Complimentary experiments were conducted in a water tank to perform a soft recovery of the fragments. The fragments were subsequently cleaned, massed, and characterized according to their mass and failure strain distributions. Various methods of analyzing the data (Mott & Weibull distributions) are discussed along with the calibration of the continuum damage model parameters. Results of the failure strain analysis, fragment distribution, and damage model are then supplied for use in subsequent modeling and application designs. Further details of the modeling and simulation approach are outlined in a complimentary set of two papers presented by Lambert [1] and Hopson [2].

Analysis of a Soft Catch for Conventional Warheads

A “soft catch” is a device with which an explosively formed projectile can be decelerated to zero velocity without sustaining significant damage. The recovered projectile provides data, via metallurgical analysis, on the deformation conditions found within the explosively formed projectile. At Eglin AFB, FL, the soft catch consists of a sequence of sections (Figures 1–3), each roughly one meter long, filled with various soft media. Velocity screens are placed at the entrance and exit of each section. This enables investigators to experimentally determine the time at which the projectile passes each station in the catch. Based on these experimental measurements, average velocity estimates for each section of the soft catch can be made. The purpose of this paper is to support the soft catch design process with a one-dimensional analysis. The mathematical modeling is based on observations presented in studies by Allen, Mayfield, and Morrison [1,2]. Their work addresses the penetration of sand, but their modeling is appropriate for materials in the soft catch. The current paper describes application of their model to interpreting three soft catch experiments where Tantalum projectiles with initial velocities of approximately 1400 m/s were successfully recovered.Copyright

Modeling a supersonic solid state detonation in an overdriven porous mixture of aluminum and teflon

In this paper, we demonstrate that an engineering device can be carefully designed in such a way that an overdriven solid state detonation can be initiated and propagated supersonically in a highly porous mixture of aluminum and Teflon. The equation of state and kinetics for the porous mixture are phenomenological models that were developed in our previous work [1]. This demonstration can be regarded as a good verification that the models which were used mainly in 1-D simulation are practically applicable and consistent to higher dimensional simulation of a shock dynamics in practical engineering devices.

MODELLING SOLID STATE DETONATION AND DETONATION WITH DESIGNED MICROSTRUCTURE

Solid state detonation (SSD) refers to nonclassical supersonic reactive wave phenomena in energetic materials that are not typically considered explosives. Reactive energetic materials include both metal/metal oxide and metal oxide/polymer systems with thermitic reaction. Like conventional solid explosives, the materials are manufactured composites with a well‐defined microstructure. Ingredients include nano‐engineered energetic materials with novel surface and reaction properties. The manufactured materials are still described by a continuum limit informed by the microstructural properties. We consider limit model formulations that include acoustic dispersion phenomena, void effect, macroscopic ignition and extinction of steady traveling reactive waves, in a modeling framework that can aid the design of new materials, which will be the basis for our continued work on SSD including the inter‐material heat transfer and kinetics.

Experimental validation of advanced explosive/metal interactions

The extremely high power density stored in explosives drives their selection of use in military, mining, demolition, cladding, shock consolidation of powders, shock-induced chemical synthesis and magnetic flux compression processes. The use of distributed initiation locations has emerged as a primary method to customize the detonation front and create desirable output. Explosive/metal systems with multiple, distributed initiation locations create detonation states that do not follow the simple line of sight, or Huygens model and, hence, advanced detonation physics with associated theory are required. The theory of detonation shock dynamics (DSD) is one such description used to provide high fidelity modeling of complex wave structures. A collection of experiments using simultaneous ultra-high speed digital framing and streak film cameras is presented as a means of obtaining spatial and temporal characteristics of complex detonation fronts that validate the DSD descriptions. The method of test, operational conditions and results are given to demonstrate the use of high rate imaging of detonation events and how this validates our understanding of the physics and the capability of advanced detonation wave tracking models.

Modeling kinetics for the reaction of aluminum and teflon and the simulation of its energetic flow motion

Simulations with reduced kinetic models are used to study shock ignition and detonation in reactive materials that may support non-classical detonation. Porous aluminum Teflon oxidizer mixtures that support combustion reactions in air are considered, as a member of a class of materials with intrinsic interest. We recast a phenomenological theory [4] with realistic kinetics with end products whose primary components are AlF3, CO, CO2 and Al2O3. Intermediate products include at least thirty elementary reactions; a sub-set can be selected to simplify, but a hard problem remains. Results of the multi-species evolution and its impact on rapid self-oxidizing combustion and possible detonation conditions and the computational methods are presented.