Eric Herbold

Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals

One-dimensional strongly nonlinear phononic crystals were assembled from chains of PTFE (polytetrafluoroethylene) and stainless-steel spheres with gauges installed inside the beads. Trains of strongly nonlinear solitary waves were excited by impacts. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same magnitude of dynamic contact force) were achieved through a noncontact magnetically induced precompression of the chains. The data for the PTFE based chains are presented for the first time and the data for the stainless-steel beads chains are extended into a range of maximum dynamic forces more than one order of magnitude lower than previously reported. Experimental results agreed reasonably well with the long-wave approximation and numerical calculations based on the Hertz interaction law for particles interactions.

Highly nonlinear solitary waves in periodic dimer granular chains.

We investigate the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously studied examples as special cases and also provides key insights into the influence of the dimer lattice on the properties (width and propagation speed) of the highly nonlinear wave solutions.

Particle size effect on strength, failure, and shock behavior in polytetrafluoroethylene-Al-W granular composite materials

The variation of metallic particle size and sample porosity significantly alters the dynamic mechanical properties of high density granular composite materials processed using a cold isostatically pressed mixture of polytetrafluoroethylene (PTFE), aluminum (Al), and tungsten (W) powders. Quasistatic and dynamic experiments are performed with identical constituent mass fractions with variations in the size of the W particles and pressing conditions. The relatively weak polymer matrix allows the strength and fracture modes of this material to be governed by the granular type behavior of agglomerated metal particles. A higher ultimate compressive strength was observed in relatively high porosity samples with small W particles compared to those with coarse W particles in all experiments. Mesoscale granular force chains of the metallic particles explain this unusual phenomenon as observed in hydrocode simulations of a drop-weight test. Macrocracks forming below the critical failure strain for the matrix and un...

Shock wave structure in a strongly nonlinear lattice with viscous dissipation

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Solitary and shock waves in discrete strongly nonlinear double power-law materials

Solitary and shock waves in discrete double power-law materials E.B. Herbold Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, California 92093-0411, USA V.F. Nesterenko Department of Mechanical and Aerospace Engineering, University of California at San Diego, La Jolla, California 92093-0411, USA; Materials Science and Engineering Program, University of California at San Diego, La Jolla, California 92093-0418, USA (Received April 24, 2007)

The influence of metallic particle size on the mechanical properties of polytetraflouroethylene-Al–W powder composites

The dynamic mechanical properties of high density mixtures of polytetraflouroethylene, aluminum (Al), and tungsten (W) powders are tailored by changing the morphology of the particles and porosity. Powder composites with fine metallic particles exhibited higher ultimate compressive strength, despite higher porosity, than less porous composites containing coarse W particles with equivalent mass fractions. The mesoscale force chains between the fine metallic particles are responsible for this unusual phenomenon. Macrocracks forming in the sample below the critical failure strain in the matrix and a competition between densification and fracture were observed in dynamic tests.

SIMULATION OF PARTICLE SIZE EFFECT ON DYNAMIC PROPERTIES AND FRACTURE OF PTFE‐W‐Al COMPOSITES

Recent investigations of the dynamic compressive strength of cold isostatically pressed composites of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) powders show significant differences depending on the size of metallic particles. The addition of W increases the density and changes the overall strength of the sample depending on the size of W particles. To investigate relatively large deformations, multi‐material Eulerian and arbitrary Lagrangian‐Eulerian methods, which have the ability to efficiently handle the formation of free surfaces, were used. The calculations indicate that the increased sample strength with fine metallic particles is due to the dynamic formation of force chains. This phenomenon occurs for samples with a higher porosity of the PTFE matrix compared to samples with larger particle size of W and a higher density PTFE matrix.

Influence of Controlled Viscous Dissipation on the Propagation of Strongly Nonlinear Waves in Stainless Steel Based Phononic Crystals

Strongly nonlinear phononic crystals were assembled from stainless steel spheres. Single solitary waves and splitting of an initial pulse into a train of solitary waves were investigated in different viscous media using motor oil and non‐aqueous glycerol to introduce a controlled viscous dissipation. Experimental results indicate that the presence of a viscous fluid dramatically altered the splitting of the initial pulse into a train of solitary waves. Numerical simulations qualitatively describe the observed phenomena only when a dissipative term based on the relative velocity between particles is introduced.

Linking initial microstructure and local response during quasistatic granular compaction

We performed experiments combining three-dimensional x-ray diffraction and x-ray computed tomography to explore the relationship between microstructure and local force and strain during quasistatic granular compaction. We found that initial void space around a grain and contact coordination number before compaction can be used to predict regions vulnerable to above-average local force and strain at later stages of compaction. We also found correlations between void space around a grain and coordination number, and between grain stress and maximum interparticle force, at all stages of compaction. Finally, we observed grains that fracture to have an above-average initial local void space and a below-average initial coordination number. Our findings provide (1) a detailed description of microstructure evolution during quasistatic granular compaction, (2) an approach for identifying regions vulnerable to large values of strain and interparticle force, and (3) methods for identifying regions of a material with large interparticle forces and coordination numbers from measurements of grain stress and local porosity.

EXPLOSIVE COMPATIONS OF INTERMETALLIC‐FORMING POWDER MIXTURES FOR FABRICATING STRUCTURAL ENERGETIC MATERIALS

A double‐tube implosion geometry is used to explosively shock consolidate intermetallic‐forming Ni‐Al, Ta‐Al, Nb‐Al, Mo‐Al and W‐Al powder mixtures for fabricating bulk structural energetic materials, with mechanical strength and ability to undergo impact‐initiated exothermic reactions. The compacts are characterized based on uniformity of micro structure and degree of densification. Mechanical properties of the compacts are characterized over the strain‐rate range of 10−3 to 104 s−1. The impact reactivity is determined using rod‐on‐anvil experiments, in which disk‐shaped compacts mounted on a copper projectile, are impacted against a steel anvil in using a 7.62 mm gas gun. The impact reactivity of the various explosively‐consolidated reactive powder mixture compacts is correlated with overall kinetic energy and impact stress to determine their influence on threshold for reaction initiation. The characteristics of the various compacts, their mechanical properties and impact‐initiated chemical reactivity w...