Characterization of shock accelerometers using davies bar and strain-gages

This paper proposes a novel method for evaluating the dynamic characteristics of shock accelerometers under high acceleration levels and a wide frequency bandwidth. High accelerations of 10³∼10⁵m/s² can be generated by the reflection of an elastic wave pulse propagating in a metal bar known as the Davies bar. The elastic wave pulse is produced by the collision of a projectile against one end of the bar, and is detected by straingages. The accelerometer to be characterized is attached to the other end of the bar. The one-dimensional theory of elastic waves enables the derivation of an input acceleration to the accelerometer from the measured strain. The dispersion of the elastic waves caused by the lateral inertia of the bar is compensated for by using a two-dimensional analytical solution. This method was validated by an experiment characterizing a piezoelectric-type accelerometer within the frequency band approximately 1 kHz∼70 kHz.     

Miniaturized Compression Test at Very High Strain Rates by Direct Impact

A modified miniaturized version of the Direct Impact Compression Test (DICT) technique is described in this paper. The method permits determination of the rate-sensitive plastic properties of materials up to strain rate ∼10⁵ s⁻¹. Miniaturization of the experimental setup with specimen dimensions: diameter d _S = 2.0 mm and thickness l _S = 1.0 mm, Hopkinson bar diameter 5.2 mm, with application of a novel optical arrangement in measurement of specimen strain, makes possible compression tests at strain rates from ∼10³ s⁻¹ to ∼10⁵ s⁻¹. In order to estimate the rate sensitivity of a low-alloy construction steel, quasi-static, Split Hopkinson Pressure Bar (SHPB) and DICT tests have been performed at room temperature within the rate spectrum ranging from 5*10⁻⁴ s⁻¹ to 5*10⁴ s⁻¹. Adiabatic heating and friction effects are analyzed and the final true stress versus true strain curves at different strain rates are corrected to a constant temperature and zero friction. The results have been analyzed in the form of true stress versus the logarithm of strain rate and they show two regions of a constant rate sensitivity : relatively low up to the strain rate threshold ∼50 s⁻¹, and relatively high above the threshold, up to strain rate ∼4.5*10⁴ s⁻¹.     

The influence of acceleration and deceleration on shock wave movement on and around aerofoils in transonic flight

This paper examines the shock wave dynamics of a biconvex aerofoil in transonic flight during acceleration and retardation. The aerofoil has a cord length of 1 m and air at infinity is at 101.325 kPa and 300 K. Using Fluent as the CFD software, constant velocity (steady state) simulations were conducted at transonic Mach numbers. The aerofoil was then accelerated at 1041m/s² (106 g), starting at Mach 0.1, and decelerated at −1041m/s², starting at Mach 1.6, through the same range of Mach numbers using time-dependent (unsteady) simulations. Significant differences were found in the transonic region between the steady and the unsteady aerodynamic forces. Analysis of the flow field in this region showed that acceleration-dependent variations in the position of the shock wave on the surfaces of the aerofoil were the main reason for this. As very high accelerations were used in order to emphasize differences, which do not have many practical applications, simulations using accelerations lower than 9 g were also conducted in order to confirm the results. The acceleration-dependent behaviour of other shock waves around the aerofoil, such as the bow shock in front of the aerofoil and the trailing wave were also examined. The trailing wave followed behind the aerofoil changing position with different accelerations at the same Mach number.      

Thermal optimization on micromachined convective accelerometer

 A kind of micromachined convective accelerometer without solid proof mass is numerically and experimentally studied in this paper. The accelerometer consists of a micro heater and two temperature sensors which measure the temperature difference between two symmetrical positions on both sides of the micro heater. The temperature difference is caused by free convection due to acceleration. Thermal optimization on the accelerometer is conducted based on numerical simulation. Three important indexes of the accelerometer, linearity, sensitivity and frequency response are discussed respectively. The results show that linearity relates with the non-dimensional number Gr, only when Gr is in the range from 10⁻² to 10³, good linearity can be achieved. The optimum sensor position for high sensitivity and good linearity is near at x/D=0.3. An increase of heating power or cavity size leads to an increase in the sensitivity. The working media that has small density ρ and large thermal diffusivity α is favorable for fast frequency response, the one having large density ρ and small kinematic viscosity υ will be advantageous for high sensitivity. Experimental tests prove that the optimized convective accelerometer has good linearity, high sensitivity and preferable frequency response. Received on 9 March 2001 / Published online: 29 November 2001     

Dynamic shearing resistance of molten metal films under high pressures and extremely high shearing rates

In the present study plate-impact pressureshear experiments have been conducted to study the dynamic shearing resistance of molten metal films at shearing rates of approximately 10⁷ s⁻¹. These molten films are generated by pressure-shear impact of relatively low melt-point metals such as 7075-T6 Al alloy with high hardness and high flow-strength tool-steel plates. By employing high impact speeds and relatively smooth impacting surfaces, normal interfacial pressures ranging from 1–3 GPa and slip speeds of over 100 m/s are generated during the pressure-shear loading. The resulting friction stress (∼100 to 400 MPa) combined with the high slip speeds generate conditions conductive to interfacial temperatures approaching the fully melt temperature regime of the lower melt-point metal (7075-T6 aluminum alloy) comprising the tribo-pair. During pressure-shear loading, laser interferometry is employed to measure normal and transverse motion at the rear surface of the target plate. The normal component of the particle velocity provides the interfacial normal traction while the transverse component provides the shearing resistance of the interface as it passes through melt. In order to extract the critical interfacial parameters, such as the interfacial slip-speed and interfacial temperatures, a Lagrangian finiteelement code is developed. The computational procedure accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below melt the flyer and target materials are described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point, a purely Newtonian fluid constitutive model is employed. The results of this hybrid experimental-computational study provide insights into the dynamic shearing resistance of molten metal films at high pressures and extremely high shearing rates.     

Measurement of laser driven shock wave transit time through thin aluminium targets by optical shadowgraphy

Laser driven shock wave transit time in thin aluminium targets was experimentally estimated by determining the shock emergence time at the rear of thin aluminium foils of varying thickness from 5 to 35 μm. A 20 J, 5 ns Nd:glass laser was focused to produce laser intensity of 10¹² to 5 × 10¹³ W/cm² on the targets which were placed in vacuum. Target foil movement was measured to an accuracy of 10 μm using optical shadowgraphy technique. This technique was used to accurately measure the shock transit time by recording the optical shadowgrams at various instants of time and thus identify the instant at which the foil is just set into motion. Shock transit time measured in foils of different thickness can give the value of shock velocity at a given laser intensity. Target motion recorded by shadowgraphy can also give the target foil velocity from which shock pressure can be estimated. Experimental values of shock transit time, shock velocity and shock pressure were observed to agree well with the values using one-dimensional multi-group radiation hydrodynamic simulations. PACS 52.50Jm; 52.50Lp; 52.25 Communicated by K. Takayama     

Testing Aluminum Alloy from Quasi-static to Dynamic Strain-rates with a Modified Split Hopkinson Bar Method

An aluminum alloy¹ was tested at quasi-static to dynamic strain-rates (from 10⁻¹ to 5 10³ s⁻¹), using a single measuring device, a modified Split Hopkinson Bar. A wave separation technique [Bussac et al., J Mech Phys Solids 50:321–350, 2002] based on the maximum likelihood method was applied to process the strain and velocity measurements recorded at various points on each bar. With this method, it is possible to compute the stress, strain, displacement and velocity at any point on the bar. Since the measurement time is unlimited, the maximum strain measured in a given specimen no longer decreases with the strain-rate, as occurs with the classical Split Hopkinson Bar method. ¹The authors wish to thank the automobile manufacturer who provided samples of the alloy used in this study. For reasons of commercial and industrial confidentiality, we were not informed about the composition of this alloy.     

A cryomechanics technique to measure dissipated energies of 10 nJ

A new cryomechanics measurement technique has been developed to measure fracture-induced dissipated energies as small as 10 nJ (10×10⁻⁹ J) at temperatures near 4.2 K. The technique, with much less stringent instrumentation requirements than those used for measurement of ∼10 nJ energies, was applied to an induced fracture experiment where dissipation energies were of the order of ∼100 μJ. Fracture of 0.5-mm diameter pencil leads of two different hardnesses gave rise to measured energies of 65 ∼ 110 μJ. A two-dimensional finite-element analysis was used to interpret the experimental measurements. Based on the analysis, approximately 50 μJ of 65 ∼ 110 μJ measured is estimated to be the dissipated energy associated with crack formation and propagation.     

Method for identification of the filled polymer material relaxation kernel in millisecond time range

The filled polymer materials exhibit viscoelastic properties in a wide time range including the millisecond range (∼10⁻²–10 ms) characteristic of different shock loadings of structures made of these materials. We propose a method for the identification of the filled polymer material relaxation kernel in the millisecond time range; this method is based on a shock loading test of a cylindrical sample made of this material. In this test, the disk indenter acceleration is measured by using a piezotransducer. The test scheme does not impose any rigid constraints on the sample dimensions. In particular, it is possible to use samples of typical dimensions of the order of 10 cm, for which the conditions that the sample material is representative of the structure material are necessarily satisfied. The relaxation kernel parameters are identified by numerical minimization of the theoretically predicted indenter velocity deviation from the velocity-time dependence obtained by integrating the acceleration transducer readings. The minimization problem is solved by using a genetic algorithm. The problem of theoretical prediction of the indenter velocity is solved numerically by using a reduced computational scheme whose parameters are chosen from the minimum condition for the deviation from the prediction obtained in the framework of the detailed computational scheme. The use of the reduced computational scheme permits decreasing the computational costs by 3–4 orders of magnitude compared with the detailed computational scheme, which is a necessary condition for the practical applicability of the genetic algorithm in identification problems. We present examples of relaxation kernel identification in the range of 0.1–10ms from the results of the test where the disk indenter raised to the height of 1m falls on the sample end surface.     

Shock waves in molecular solids: ultrafast vibrational spectroscopy of the first nanosecond

A novel technique which uses a microfabricated shock target array assembly is described, where the passage of a shock front through a thin (0.5μm) polycrystalline layer and the subsequent unloading process is monitored in real time with ultrafast coherent Raman spectroscopy. Using a high repetition rate laser shock generation technique, high resolution, coherent Raman spectra are obtained in shocked anthracene and in a high explosive material, NTO, with time resolution of ∼ 50 ps. Spectroscopic measurements are presented which yield the shock pressure (up to 5 GPa), the shock velocity (∼ 4 km/s), the shock front risetime (t _r < 25 ps), and the temperature (∼ 400°C). A brief discussion is presented, how this new technique can be used to determine the Hugoniot, the equation of state, the entropy increase across the shock front, and monitor shock induced chemical reactions in real time. Received 28 October 1996 / Accepted 12 November 1996     

Non-linear Mechanical Behaviour of Metallic Micro-wires under Dynamic Axial Loads

Metallic micro-wires (diameter ≈10 μm) are widely used to suspend reference bodies and isolate them from micro-seismic vibration because of their low bending and torsional stiffness. They make it possible to realize torsion/swing low-resonant frequency oscillators, spectrally separable from the higher frequency physics of interest. In this study, metallic micro-wires are used to provide both seismic isolation through flexural compliance and high-speed actuation thanks to axial stiffness. An experimental apparatus is realized to characterize the dynamic response of a 25 μm diameter tungsten wire used to actuate a suspended mass (10^-2 kg) subjected to accelerations up to 0.2 m/s². A theoretical non-linear model taking into account flexural and axial behaviour of the wire is developed and validated experimentally. Such a model makes it possible to predict the actual motion of the object, which significantly differs from that of the actuator.     

Microscopic high-speed liquid-metal jets in vacuum

The operation of microscopic high-speed liquid-metal jets in vacuum has been investigated. We show that such jets may be produced with good stability and collimation at higher speeds than previously demonstrated, provided that the nozzle design is appropriate and that cavitation-induced instabilities are avoided. The experiments with a medium-speed tin jet (u ∼ 60 m/s, Re=1.8×10⁴, Z=2.9×10⁻³) showed that it operated without any signs of instabilities, whereas the stability of high-speed tin jets (d=30 μm, u=500 m/s, Re=5.6×10⁴, Z=4.7×10⁻³) has been investigated via dynamic similarity using a water jet. Such a 500-m/s tin jet is required as the anode for high-brightness operation of a novel electron-impact X-ray source.     

An investigation of ball-on-ball impact

The Bureau of Mines, U.S. Department of the Interior, has used a shock accelerometer to measure deceleration in ball-on-ball impact. The accelerometer signal was analyzed by a fast-Fourier-transform (FFT) technique, and signal components were identified from the accelerometer characteristics, solid mechanics, and finite-element modal and spectral analysis. Following frequency-domain digital filtering to remove extraneous frequencies, the remaining signal was reconstituted by an inverse FFT. Supporting Hertzian quasistatic and elastic and elastic-plastic dynamic finite-element calculations were carried out. All calculations predicted similar peak decelerations and contact times. The former agreed well with experiment. However, stress-wave effects make it difficult to use deceleration measurements to define contact times, even at an impact velocity of 8 ms⁻¹. Such an impact must be analyzed as dynamic rather than static.     

An investigation of electromagnetic wave propagation in plasma by shock tube

This paper presents the electromagnetic wave propagation characteristics in plasma and the attenuation coefficients of the microwave in terms of the parameters he, v, w, L, wb. The φ800 mm high temperature shock tube has been used to produce a uniform plasma. In order to get the attenuation of the electromagnetic wave through the plasma behind a shock wave, the microwave transmission has been used to measure the relative change of the wave power. The working frequency is f = (2-35)GHz (ω=2πf, wave length A =15cm-8mm). The electron density in the plasma is ne = (3&#215;10^10-1&#215;10^14) cm^-3. The collision frequency v = (1&#215;10^8-6&#215;10^10) Hz. The thickness of the plasma layer L = (2-80)cm. The electron circular frequency ωb=eBo/me, magnetic flux density B0 = (0-0.84)T. The experimental results show that when the plasma layer is thick (such as L/λ≥10), the correlation between the attenuation coefficients of the electromagnetic waves and the parameters ne,v,ω, L determined from the measurements are in good agreement with the theoretical predictions of electromagnetic wave propagations in the uniform infinite plasma. When the plasma layer is thin (such as when both L and A are of the same order), the theoretical results are only in a qualitative agreement with the experimental observations in the present parameter range, but the formula of the electromagnetic wave propagation theory in an uniform infinite plasma can not be used for quantitative computations of the correlation between the attenuation coefficients and the parameters ne,v,ω, L. In fact, if ω&lt;ωp, v^2&lt;&lt;ω^2, the power attenuations K of the electromagnetic waves obtained from the measurements in the thin-layer plasma are much smaller than those of the theoretical predictions. On the other hand, if ω&gt;ωp, v^2&lt;&lt;ω^2 (just v≈f), the measurements are much larger than the theoretical results. Also, we have measured the electromagnetic wave power attenuation value under the magnetic field and without a magnetic field. The result indicates that the value measured under the magnetic field shows a distinct improvement.     

Geometric methods in determining rigid-body dynamics

This research develops a measurement system using linear accelerometers to determine the three-dimensional, six degrees of freedom, impact response of an anthropomorphic test device (dummy). A procedure using spherical geometric analysis (SGA) was developed. It uses three triaxial accelerometer clusters for determining angular velocity, angular acceleration, and linear acceleration. SGA differs in its calculation of angular velocity from other procedures which determine rigid-body motion. Unlike procedures which use linear accelerometers to determine angular velocity by integration of angular acceleration, SGA uses the topology of the sphere to obtain both angular acceleration and angular velocity through algebraic manipulation of the output from the linear accelerations. The validation of SGA is accomplished by the use of hypothetical as well as experimental data.     

Comparison of experimental data with results of some drying models for regularly shaped products

This paper presents an experimental and theoretical investigation of drying of moist slab, cylinder and spherical products to study dimensionless moisture content distributions and their comparisons. Experimental study includes the measurement of the moisture content distributions of slab and cylindrical carrot, slab and cylindrical pumpkin and spherical blueberry during drying at various temperatures (e.g., 30, 40, 50 and 60°C) at specific constant velocity (U = 1 m/s) and the relative humidity φ = 30%. In theoretical analysis, two moisture transfer models are used to determine drying process parameters (e.g., drying coefficient and lag factor) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate the dimensionless moisture content distributions. The calculated results are then compared with the experimental moisture data. A considerably high agreement is obtained between the calculations and experimental measurements for the cases considered. The effective diffusivity values were evaluated between 0.741 × 10⁻⁵ and 5.981 × 10⁻⁵ m²/h for slab products, 0.818 × 10⁻⁵ and 6.287 × 10⁻⁵ m²/h for cylindrical products and 1.213 × 10⁻⁷ and 7.589 × 10⁻⁷ m²/h spherical products using the Model-I and 0.316 × 10⁻⁵–5.072 × 10⁻⁵ m²/h for slab products, 0.580 × 10⁻⁵–9.587 × 10⁻⁵ m²/h for cylindrical products and 1.408 × 10⁻⁷–13.913 × 10⁻⁷ m²/h spherical products using the Model-II.     

Determination of dynamic yield strengths with embedded manganin gages in plate-impact and long-rod experiments

The dynamic yield strengths of three steels were determined at strain rates of about 10³ s⁻¹ and 10⁶ s⁻¹. The measurements at 10³ s⁻¹ were obtained by a new technique based on measurements of large amplitude elastic waves in long bars struck by rigid flyer plates. Embedded manganin gages were used to measure stress, and the gage records were long enough to observe subsequent reverberations between the bar free end and the plastically deformed impact end. The measurements at 10⁶ s⁻¹ were made with a slightly modified version of a conventional flyer-plate impact configuration. The data are combined with static results to show the behavior of these steels at strain rates of 10⁻³ s⁻¹ to 10⁶ s⁻¹.     

Precursor vacuum-ultraviolet radiation ahead of strong shock waves in a shock tube

The profile and excitation mechanism of vacuum-ultraviolet radiation emitted from shock wave is investigated in a shock tube. For shock wave in argon, the rdiation is due to resonant transition excited by argon-argon collision in the shock front with excitation cross section coefficientS ^*=1.0×10⁻¹⁷ cm²·ev⁻¹ and activation energyE ^*=11.4 ev. For shock wave in air the radition is emitted from a very thin shock layer in which the mechanism ofX ¹∑→b ¹∑ of N₂ is excited with excitation cross sectionQ=2×10⁻¹⁶cm² and activation energyE ^*=12.1 ev. Institute of Mechanics, Academia Sinica     

A pulse-expansion wave tube for nucleation studies at high pressures

 The design and performance of a new pulse-expansion wave tube for nucleation studies at high pressures are described. The pulse-expansion wave tube is a special shock tube in which a nucleation pulse is formed at the endwall of the high pressure section. The nucleation pulse is due to reflections of the initial shock wave at a local widening situated in the low pressure section at a short distance from the diaphragm. The nucleation pulse has a duration of the order of 200 μs, while nucleation pressures that can be achieved range from 1 to 50 bar total pressure. Droplet size and droplet number density can accurately be determined by a 90°-Mie light scattering method and a light extinction method. The range of nucleation rates that can be measured is 10⁸ cm^-3 s^-1<J<10¹¹ cm^-3 s^-1. We will illustrate the functioning and possibilities of the new pulse-expansion wave tube by nucleation rate measurements in the gas-vapour mixture nitrogen/water in the temperature range 200–260 K, and in the mixture methane/n-nonane as a function of supersaturation S at various total pressures up to 40 bar and temperatures around 240 K. Received: 5 June 1996/Accepted: 9 December 1996     

Simultaneous determination of shear and extensional viscosities and wall slip by on-line rheometry with parameter fitting: an application to EPDM rubber

Shear and extensional viscosities and wall slip are determined simultaneously under extrusion processing conditions using an on-line rheometer. Because it is not possible to independently control flow rate and temperature, classical methods for interpretation of capillary data cannot be used with on-line rheometry. This limitation is overcome using computational optimization to fit parameters in a flow model. This consists of three parts, representing shear viscosity, extensional viscosity, and wall slip. Three-parameter, power law forms, based on local instantaneous deformation rates and including temperature dependence, are used for each, and analytic solutions applied for entry flow and flow in the capillary. For entry flow, the Cogswell–Binding approach is used, and for developed flow in the capillary a solution incorporating wall slip is derived. The rheometer, with interchangeable capillaries, is mounted in place of the die on a rubber profile extrusion line. Pressure drops and temperatures for extrusion of an EPDM rubber through 2 mm diameter capillaries of length 0, 2, 3, 4, and 5 mm are logged and flow rates determined for a range of extruder speeds (5 to 20 rpm). Pressures ranged from 60 to 75 bar and temperatures from 86 to 116 °C. Mean flow velocity in the capillaries was between 5 × 10⁻³ and 5 × 10⁻¹ m s⁻¹. The nine material parameters are optimized for best fit of the analytic pressure drops to experimental data, using about 100 data points, with the Levenberg–Marquardt method. It is concluded that flow is dominated by extension and wall slip. Shear flow appears to play little part. The slip model indicates that slip velocity increases much more rapidly than the wall shear stress (in the range 0.5–1 MPa) and decreases with temperature for a given stress level. Results for the (uniaxial) extensional viscosity represent an engineering approximation to this complex phenomenon at the high strains (approximately 200) and high extension rates (up to 800 s⁻¹) applying in the extrusion. Results indicate a slight extension hardening and a decrease with temperature. Results are put into the context of the available studies in the literature, which, particularly with regard to wall-slip and extensional flow, consider conditions far removed from those applying in industrial extrusion. The present methods provide a powerful means for flow characterization under processing conditions, providing data suitable for use in computer simulations of extrusion and optimization of die design.