Dynamic crushing of aluminum foams: Part I – Experiments

The two-part series of papers presents the results of a study of the crushing behavior of open-cell Al foams under impact. In Part I, direct and stationary impact tests are performed on cylindrical foam specimens at impacts speeds in the range of 20–160 m/s using a gas gun. The stress at one end is recorded using a pressure bar, while the deformation of the entire foam specimen is monitored with high-speed photography. Specimens impacted at velocities of 60 m/s and above developed nearly planar shocks that propagated at well-defined velocities crushing the specimen. The shock speed vs. impact speed, and the strain behind the shock vs. impact speed representations of the Hugoniot were both extracted directly from the high-speed images. The former follows a linear relationship and the latter asymptotically approaches a strain of about 90% at higher velocities. The Hugoniot enables calculation of all problem variables without resorting to an assumed constitutive model. The compaction energy dissipation across the shock is shown to increase with impact velocity and to be significantly greater than the corresponding quasi-static value. Specimens impacted at velocities lower than 40 m/s exhibited response and deformation patterns that are very similar to those observed under quasi-static crushing. Apparently, in this impact speed regime inertia increases the energy absorption capacity very modestly.     

An experimental investigation of wave propagation in a rubber string impacted by a projectile2

Transverse perpendicular impact on long rubber strings of 0.140 and 0.277 in. dia was studied using a special apparatus consisting of a system of oscilloscopes, stroboscopes, camera and air pressure gun. The rubbers used in tests came from two manufacturers and were classified as pure gum rubbers. Three different initial stretches λ₀ were chosen for each string, and the impact velocities ranged from 1000 to 3000 in. sec. Maximum stretch, kink angles and impact velocities were measured and the following relations recorded : nominal stress vs stretch, kink angle vs impact velocity, maximum stretch λ_max vs impact velocity and the difference λ_max ? λ₀ vs non-dimensional impact velocity. Some of the results are compared with the theoretical data for the Mooney-Rivlin and the Isihara-Hashitsume-Tatibana-Zahorski materials, and others with the results of theoretical equations upon inserting experimental data.     

Stretchable hydrophobic surfaces and droplet heating

Silicon elastomer surface is treated towards achieving the hydrophobic state. Functionalized nano-silica units are coated onto elastomer surface and resulting texture characteristics are examined prior to stretching, stretched and after stretching. The droplet heating of the hydrophobic elastomer surface is carried out when the surface is subjected to unstretching, stretching and stretch releasing conditions. The thermal-flow field in the liquid is simulated and validated incorporating high speed recording system. Nano-size silica units coated elastomer surface demonstrates the hydrophobic wetting state. The hydrophobic wetting state changes slightly for stretched and stretched released surface. The contact angle is about 154° ± 2° for unstretched surface while it is 152° ± 2° for the stretched released surface; hence, stretch relaxing provides reversible change of the surface wetting state of the elastomer surface. The contact angle reduces to 142° ± 2° when surface is under stretched, which is related to increased pillar spacing on the surface. The droplet heating results in development of Marangoni current in the fluid, which significantly affects the flow and temperature fields and it becomes more apparent for the large size droplets. The maximum flow velocity increases almost 9% in 45 µL as the surface is stretched. The Nusselt number increases with droplet size and the Bond number has the values less than unity; hence, stretching increases the Nusselt number by 60% for droplet of 45 µL.     

A theoretical consideration of the ballistic response of continuous graphene membranes

The remarkable properties of graphene, including unusually high mechanical strength and stiffness, have been well-documented. In this paper, we combine an analytical solution for ballistic impact into a thin isotropic membrane, with ab initio density functional theory calculations for graphene under uniaxial tension, to predict the penetration resistance of multi-layer graphene membranes. The calculations show that continuous graphene membranes could enable ballistic barriers of extraordinary performance, enabling resistance to penetration at masses up to 100× lighter than existing state-of-the-art barrier materials. The very high elastic wave speed and strain energy to failure are the major drivers of this increase in performance. However, the in-plane mechanical isotropy of graphene, as compared to conventional orthotropic woven textiles, also contributes significantly to the efficiency of graphene as a barrier material. This result suggests that, for barrier applications, isotropic membranes composed of covalently bonded two-dimensional molecular networks could provide distinct advantages over fiber-based textiles derived from linear polymers.     

Measurement of extensional viscosity of polymer solutions

A filament stretching technique for measuring the extensional viscosity of polymer solutions at constant stretch rate is presented. The liquid sample is held between two coaxial discs and stretched by moving the bottom disc downwards with a speed that increases exponentially with time. This is illustrated using a constant viscosity, elastic fluid consisting of 0.185% polyisobutylene in a solvent of kerosene and polybutene. For the case of this particular fluid, two distinct stretch rate regions are found to arise. The stretch rate in the first region is much higher than in the second, which is, in most cases, close to the overall stretch rate imposed on the sample. Nonetheless, all the results of any given run can be represented using an average extensional rate. The extensional stress growth data, plotted as the Trouton ratio against time, show an initial linear viscoelastic region where T_R rises to a value of 3, independent of extensional rate. Beyond this region, T_R depends on the stretch rate and rises dramatically to values in excess of 10³; the higher the extensional rate, the faster is the increase in T_R. These data do not seem to reach a steady state and appear to be similar to polymer melt data obtained by others in the past. The reproducibility of the results is very good and all this suggests that it is now possible to obtain unambiguous constant-stretch-rate stress-growth data for polymer solutions stretched from a state of rest.     

Shock enhancement of cellular structures under impact loading: Part I Experiments

This paper aims at showing experimental proof of the existence of a shock front in cellular structures under impact loading, especially at low critical impact velocities around 50 m/s. First, an original testing procedure using a large diameter Nylon Hopkinson bar is introduced. With this large diameter soft Hopkinson bar, tests under two different configurations (pressure bar behind/ahead of the supposed shock front) at the same impact speed are used to obtain the force/time histories behind and ahead of the assumed shock front within the cellular material specimen.Stress jumps (up to 60% of initial stress level) as well as shock front speed are measured for tests at 55 m/s on Alporas foams and nickel hollow sphere agglomerates, whereas no significant shock enhancement is observed for Cymat foams and 5056 aluminium honeycombs. The corresponding rate sensitivity of the studied cellular structures is also measured and it is proven that it is not responsible for the sharp strength enhancement.A photomechanical measurement of the shock front speed is also proposed to obtain a direct experimental proof. The displacement and strain fields during the test are obtained by correlating images shot with a high speed camera. The strain field measurements at different times show that the shock front discontinuity propagates and allows for the measurement of the propagation velocity.All the experimental evidences enable us to confirm the existence of a shock front enhancement even at quite low impact velocities for a number of studied materials.     

On the Fiber Stretch in Shearing Deformations of Fibrous Soft Materials

The behavior of the fiber stretch in simple shear of soft materials fiber-reinforced with a single family of oriented parallel fibers is examined. The analysis is purely kinematical and the results are valid for both compressible and incompressible materials. It is shown that for a given amount of shear, for all fiber orientation angles in the range \(0 < \theta < \pi /4\), the fiber stretch increases with increasing \(\theta\) whereas in the range \(\pi /4 < \theta < \pi /2\), this is no longer the case and there is a particular fiber orientation for which the fiber stretch is a maximum. For a particular amount of shear corresponding to a special angle of shear (a “magic” angle of \(35.26^{\circ}\)), the fiber-orientation angle at which the fiber stretch is a maximum is its geometric complement namely a magic angle of \(54.74^{\circ}\). The results are also valid for torsion of a circular cylinder reinforced with a single family of helically wound fibers.     

Damage percolation during stretch flange forming of aluminum alloy sheet

A multi-scale finite element (FE)-damage percolation model was employed to simulate stretch flange forming of aluminum alloys AA5182 and AA5754. Material softening and strain gradients were captured using a Gurson-based FE model. FE results were then fed into the so-called damage percolation code, from which the damage development was modelled within measured microstructures. The formability of the stretch flange samples was predicted based upon the onset of catastrophic failure triggered by profuse void coalescence within the measured second-phase particle field. Damage development is quantified in terms of crack and void areal fractions, and compared to metallographic results obtained from interrupted stretch flange specimens. Parametric study is conducted on the effect of void nucleation strain in the prediction of formability of stretch flanges to “calibrate” proper nucleation strains for both alloys.     

The reptation model with segmental stretch

The Doi-Edwards model with segmental stretch and a non-linear finitely extensible spring law is described and examined in simple flow situations where analytic results are derivable; namely oscillatory flow and steady state flow at high deformation rates. The model is shown to be consistent with the Bueche-Ferry hypothesis in fast large strain unidirectional flows but to violate this rule in small strain reversing flows. The discrepancy is identified with a preaveraging approximation used to describe the relative tube-chain velocity. Experimentally verifiable scaling rule for the birefringence as a universal function of a planar flow-type parameter and deformation rate are identified. Sensitivity to the extensional flow character, absent in the original tube model, manifests itself with the introduction of segmental stretch. Although the model generates a non-separable memory function kernel the deformation dependence of the memory function is quantitatively shown to have negligible impact on the predicted theological properties relative to the original Doi-Edwards model. With this simplification, relatively uncomplicated approximations to the segmental stretch model can be deduced.     

Experimental investigation of the stress–stretch behavior of EPDM rubber with loading rate effects

The tensile stress–stretch behavior of an ethylene–propylene–diene terpolymer (EPDM) was experimentally investigated, both in a quasi-static stretching rate range (<0.4/s) with a conventional material test machine and in a dynamic stretching rate range (2800/s–3200/s) with a split Hopkinson tension bar (SHTB) technique. Experimental data were then analyzed using the Ogden and Roxburgh’s idealized Mullins effect modeling theory. Results show that the stress–stretch behavior is significantly dependent on stretching rate and the Mullins effect exists under dynamic loading. Furthermore, stretching rate only affects the material properties. The degree of damage in a stretched specimen is a function of only the maximum stretch ratio the specimen experienced.     

Particle velocimetry inside Newtonian and non-Newtonian droplets impacting a hydrophobic surface

A particle velocimetry technique is described which enables the measurement of the fluid velocity inside impacting drops. Using high speed photography of 2 μm fluorescent tracer particles suspended in the fluid, the velocity field was measured as a function of time and radial position. The potential of the technique is illustrated using velocimetry measurements of drops of pure water and aqueous solutions of 200 ppm poly-(ethylene oxide) (PEO). Dilute solutions of PEO have been known for some time to suppress the rebound of water from hydrophobic surfaces. The dissipation has traditionally been attributed to an increased extensional viscosity as the polymers stretch in the extensional flow of the droplet. Our results enable us to infer that the extensional viscosity of PEO drops, during both the spreading and retraction phase, is similar to that of pure water. The data suggest that the true source of dissipation lies at the droplet edge. We also show, by analysing the spreading of water drops, that the Roisman-Yarin theory for a droplet spreading on a surface is valid in the bulk of the droplet prior to the final stages of spreading.     

Discrete element method study of parameter optimization and particle mixing behaviour in a soil mixer

Soil mixing is an emerging research in the field of construction resource recovery. In this study, the mixing behaviour of soil particles in a mixer is numerically simulated by the discrete element method (DEM). A four-factor, three-level orthogonal experiment is designed to optimize the mixer design by selecting the fly-cutter speed, spindle speed, number of blades and fly-cutter diameter, using Lacey mixing index and power consumption as evaluation indicators. Then, the impact of soil cohesion and type on the mixing behaviour is investigated. The results show that the optimal parameter combination of this experiment is 280 rpm fly-cutter speed, 40 rpm spindle speed, 4 blades and 250 mm fly-cutter diameter. This optimal combination reaches a comparatively uniform state mix in 5.9 s with an average power consumption of 704.11 W. In addition, the wear and tear of the mixer increases as soil cohesion increases, while the mixing quality of materials declines, resulting in a “shaft hugging” phenomenon. The mixing efficiency varies greatly among different soil types, but the radial and tangential velocities have a similar law. This work can provide some guidance for the optimization design of a mixer and study of soil mixing.     

Effect of chamber pressure on spreading and splashing of liquid drops upon impact on a dry smooth stationary surface

Liquid drop impacts on a smooth surface were studied at elevated chamber pressures to characterize the effect of gas pressure on drop spreading and splashing. Five common liquids were tested at impact speeds between 1.0 and 3.5 m/s and pressure up to 12 bars. Based on experiments at atmospheric pressure, a modification to the “free spreading” model (Scheller and Bousfield in AIChE Paper 41(6):1357–1367, 1995) has been proposed that improves the prediction accuracy of maximum spread factors from an error of 15–5%. At high chamber pressures, drop spreading and maximum spread factor were found to be independent of pressure. The splash ratio (Xu et al. in Phys Rev Lett 94:184505, 2005) showed a non-constant behavior, and a power-law model was demonstrated to predict the increase in splash ratio with decreasing impact speed in the low impact speed regime. Also, drop shape was found to affect splash promotion or suppression for an asymmetry greater than 7–8% of the equivalent drop diameter. The observations of the current work could be especially useful for the study of formation of deposits and wall combustion in engine cylinders.     

Impact on a plate on the surface of a fluid

Questions of the interaction between solid and elastic structures with an ideal fluid which are associated with the initial stage of the impact and penetration of bodies in the fluid were considered in [1–4]. Results are presented below of an analysis of a central impact on a solid weightless plate which is on the surface of a compressible fluid. The impact velocity is much less than the speed of sound in the medium. Computations are performed by a finite-difference Lagrange method according to a program for plane motions of a continuous medium [5] by using a volume artificial viscosity of Neumann-Richtmayer type [6].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 143–145, May–June, 1978.     

Stress and neutron scattering measurements on linear polymer melts undergoing steady elongational flow

We use small-angle neutron scattering to measure the molecular stretching in polystyrene melts undergoing steady elongational flow at large stretch rates. The radius of gyration of the central segment of a partly deuterated polystyrene molecule is, in the stretching direction, increasing with the steady stretch rate to a power of about 0.25. This value is about half of the exponent observed for the increase in stress value σ, in agreement with Gaussian behavior. Thus, finite chain extensibility does not seem to play an important role in the strongly non-linear extensional stress behavior exhibited by the linear polystyrene melt.     

Identification of response functions from axisymmetric membrane inflation tests: Implications for biomechanics

There is a need in biomechanics to identify classes of experiments that allow direct determination of constitutive relations while preserving the natural geometry of the tissue. In this paper, we show how specific forms of response functions can be identified for nonlinear hyperelastic membranes by measuring principal stretch ratios, principal curvatures and distending pressures during quasi-static axisymmetric inflation tests. For completeness, we also list all of the equations that are needed to experimentally implement this new constitutive approach.     

Experimental investigation of hydrodynamic loads and pressure distribution during a pyramid water entry

In the maritime environment slamming is a phenomenon known as short duration impact of water on a floating or sailing structure. Slamming loads are local and could induce very high local stresses. This paper reports a series of impact test results and investigate the slamming loads and pressures acting on a square based pyramid. In this study the slamming tests have been conducted at constant velocity impact with a hydraulic high speed shock machine. This specific experimental equipment avoids the deceleration of the structure observed usually during water entry with drop tests. Three velocities of the rigid pyramid have been used (10, 13 and 15 m s⁻¹). Time-histories of local pressures, accelerations and slamming loads were successfully measured. The relationship between the pressure magnitude and the impact velocity is obtained and the spatial distribution of pressures on pyramid sides is characterized. The impact velocity was found to have a negligible influence in predicting the maximum pressure coefficient.     

致密砂岩巷道模型试件动态起裂及止裂全过程分析

为了开展在不同冲击载荷作用下巷道围岩内裂纹的起裂、扩展及止裂等问题,以可调速冲击试验机进行动态加载试验,采用致密青砂岩制作裂纹巷道模型试件,并利用裂纹扩展计分别记录了动态起裂、扩展、止裂等时刻,对裂纹扩展速度的变化规律进行分析;随后采用AUTODYN有限差分法软件进行相应的数值模拟,数值模拟得到的裂纹扩展路径与试验结果基本一致。经过两者对比分析可知:随着冲击载荷作用的增加,裂纹平均扩展速度逐渐增大,随后趋于稳定值;预制裂纹的起裂时间随着冲击速度载荷的增加而逐渐降低,并在稳定值上下波动;随着冲击速度载荷的增加,裂纹扩展路径过程中的止裂时段逐渐变短。