Temperature and rise-time effects on dynamic strain measurement

Strain pulses in a test specimen were measured over a temperature range of ?73 to +149°C with foil and semiconductor strain gages. These tests were performed to determine if the rise time and amplitude of the gage output change as a function of temperature. The existence of a constant that should be added to the theoretical rise times of resistance strain gages, as suggested by Koshiro Oi, was reexamined. ‘Long’ rise-time strain pulses were produced in the test specimen by an impacting steel ball. The rise times of these pulses were on the order of 7 μs and the amplitudes were approximately 65 μm/m. The results of these tests show that the rise time and amplitude of the gage do not change as a function of temperature. ‘Short’ rise-time strain pulses of approximately 500 μm/m with a rise time of 2 μs were produced in a test specimen by a short pendulum-type hammer apparatus. The results of these tests showed that the amplitude of the gage output was relatively independent of test temperatures but exhibited a slight hysteresis effect. The rise times for these tests remained constant up to a temperature of 93°C, then started to increase. The rise times at 149°C were approximately 100 percent longer than at room temperature. Under optimum conditions, a pulse with a measured rise time of 0.18 μs could be generated. The results of these tests indicated that the theoretical rise-time additive constant of resistance strain gages is 0.05 μs or less. This is one-half the value that Bickle arrived at by reevaluating Oi's data. However, since the real rise time of the pulse was unknown, this additive constant is not necessarily a property of the gage.     

Performance evaluation of accelerometers used for penetration experiments

We present a Hopkinson bar technique to evaluate the performance of accelerometers that measure large amplitude pulses, such as those experienced during projectile penetration tests. An aluminum striker bar impacts a thin Plexiglas or copper disk placed on the impact surface of an aluminum incident bar. The Plexiglas or copper disk pulse shaper produces a nondispersive stress wave that propagates in the aluminum incident bar and eventually interacts with a tungsten disk at the end of the bar. A quartz stress gage is placed between the aluminum bar and tungsten disk, and an accelerometer is mounted to the free end of the tungsten disk. An analytical model shows that the rise time of the incident stress pulse in the aluminum bar is long enough and the tungsten disk length is short enough that the response of the tungsten disk can be accurately approximated as rigid-body motion. We measure stress at the aluminum bar-tungsten disk interface with the quartz gage and we calculate rigid-body acceleration of the tungsten disk from Newton's Second Law and the stress gage data. In addition, we measure strain-time at two locations on the aluminum incident bar to show that the incident strain pulse is nondispersive and we calculate rigid-body acceleration of the tungsten disk from a model that uses this strain-time data. Thus, we can compare accelerations measured with the accelerometer and accelerations calculated with models that use stress gage and strain gage measurements. We show that all three acceleration-time pulses are in very close agreement for acceleration amplitudes to about 20,000 G.     

Pulse shaping techniques for testing brittle materials with a split hopkinson pressure bar

We present pulse shaping techniques to obtain compressive stress-strain data for brittle materials with the split Hopkinson pressure bar apparatus. The conventional split Hopkinson pressure bar apparatus is modified by shaping the incident pulse such that the samples are in dynamic stress equilibrium and have nearly constant strain rate over most of the test duration. A thin disk of annealed or hard C11000 copper is placed on the impact surface of the incident bar in order to shape the incident pulse. After impact by the striker bar, the copper disk deforms plastically and spreads the pulse in the incident bar. We present an analytical model and data that show a wide variety of incident strain pulses can be produced by varying the geometry of the copper disks and the length and striking velocity of the striker bar. Model predictions are in good agreement with measurements. In addition, we present data for a machineable glass ceramic material, Macor, that shows pulse shaping is required to obtain dynamic stress equilibrium and a nearly constant strain rate over most of the test duration.     

基于Hopkinson杆和人工神经网络的三轴冲击力传感器同步解耦标定方法

三分量冲击力载荷的同步激励与输入输出间的精准建模是三轴冲击力传感器标定所面临的主要挑战。为了实现对三轴冲击力传感器的有效标定,使其能够准确测量空间中的三维冲击力载荷。首先,基于Hopkinson杆与矢量分解原理建立了一种高幅值（104 N量级）、窄脉宽（10?4 s量级）可计量三分量冲击力载荷的同步激励方法,实现了对三轴冲击力传感器的同步加载。然后,基于最小二乘原理与矩阵微分构建了三轴冲击力传感器的线性标定模型,并通过改变子弹结构与冲击气压揭示了线性解耦标定模型中传感器主灵敏度系数与轴间耦合灵敏度系数并非固定常数而均与冲击力载荷脉冲构型（幅值、脉宽）相关的冲击特性。最后,将能够反映载荷构型信息的传感器各轴输出电压脉冲的幅值与脉宽作为影响因素,并以神经元的形式添加到人工神经网络（artificial neural network, ANN）的输入层,建立了基于ANN的三轴冲击力传感器输出电压与输入载荷间的代理模型,实现了数据驱动的三轴冲击力传感器非线性解耦标定。结果表明,相对最小二乘模型,ANN标定精度更高,采用ANN进行三轴冲击力传感器标定具有可行性和有效性。     

Properties of dynamic rupture and energy partition in a solid with a frictional interface

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.     

Shock pulse attenuation in a nonlinear viscoelastic solid

Thin, one-dimensional shock pulses were generated in a nonlinear viscoelastic material (polymethyl methacrylate) by a new experimental technique. The observed pulse attenuation was compared with an approximate theory based on the viscoelastic shock amplitude equation. The central assumption of this approximate theory is that the unloading wave propagates as a simple wave. Given an initial pulse shape it is shown that the attenuation and the pulse shape at any later time are accurately approximated. The calculated attenuation in polymethyl methacrylate agreed well with the experimental results.     

Dynamic compressive responses of intact and damaged ceramics from a single split Hopkinson pressure bar experiment

A novel dynamic compressive experimental technique has been developed based on a split Hopkinson pressure bar. This new method dynamically loads the ceramic specimen by two consecutive stress pulses. The first pulse determines the dynamic response of the intact ceramic materiaal and then crushes the specimen, and the second pulse determines the dynamic compressive constitutive behavior of the ceramic rubble. Precise pulse shaping ensures that the specimen deforms at nearly constant strain rates under dynamic stress equilibrium during the loading by both stress pulses. Pulse shaping also controls the amplitudes of loading pulses, the values of strain rates, the maximum strains in the rubble specimens, and the proper separation time between the two loading pulses. The feasibility of the new technique is demonstrated by the experimental results obtained on an AD995 alumina.     

One-dimensional pulse propagation in composite materials modelled as interpenetrating solid continua

Modulated simple wave theory is used to study the propagation of one dimensional, finite amplitude, high frequency pulses in composites which are modelled as interpenetrating solid continua with two identifiable constituents. The equations which govern the propagation of high frequency pulses are derived and their properties are studied in detail. Particular attention is paid to small amplitude high frequency pulses and results for pulses propagating into composites of a rather general nature are presented. The special results which hold for pulses which propagate into uniform regions are discussed in detail. The influence of the structure of the composite on pulse propagation is also assessed by examining pulse propagation in a number of different types of composite.     

水下爆炸对重力坝的毁伤效应及最优爆距

为研究不同爆距水下爆炸对重力坝的毁伤效应,并探讨是否存在“最优爆距”,基于离心模型试验建立了炸药-库水-空气-重力坝结构的全耦合数值模型,并设计了60组数值计算工况。不同工况水深均为600 mm,炸药量为2.2 g,重力坝模型几何比尺为1/80,包含5组爆深（50～250 mm）,每组爆深对应12组爆距,爆距范围为10～200 mm,相应比例爆距范围为0.077～1.54 m/kg1/3。对比分析了不同爆距水下爆炸对重力坝的毁伤程度,并定量比较了重力坝平均损伤、单元删除率、应力、应变等参数。结果表明,对于重力坝整体结构破坏,如重力坝整体弯曲导致的拉伸破坏,水下爆炸对重力坝的毁伤效应存在“最优爆距”,即随着爆距增加重力坝毁伤程度先增加后降低;与之类似,随着爆距的增加,重力坝上游坝面损伤区域的平均损伤、重力坝单元删除率、坝踵最大拉应力平均值和坝踵最大拉应变平均值先增加后降低且在40 mm爆距附近达到最大值。保持水深、炸药量和重力坝几何模型相同,5组不同爆深近水面水下爆炸对重力坝毁伤效应的“最优爆距”均在40 mm附近,表明近水面水下爆炸时爆深对“最优爆距”不存在显著影响。     

Safety distance for preventing hot particle ignition of building insulation materials

Trajectories of flying hot particles were predicted in this work, and the temperatures during the movement were also calculated. Once the particle temperature decreased to the critical temperature for a hot particle to ignite building insulation materials, which was predicted by hot-spot ignition theory, the distance particle traveled was determined as the minimum safety distance for preventing the ignition of building insulation materials by hot particles. The results showed that for sphere aluminum particles with the same initial velocities and diameters, the horizontal and vertical distances traveled by particles with higher initial temperatures were higher. Smaller particles traveled farther when other conditions were the same. The critical temperature for an aluminum particle to ignite rigid polyurethane foam increased rapidly with the decrease of particle diameter. The horizontal and vertical safety distances were closely related to the initial temperature, diameter and initial velocity of particles. These results could help update the safety provision of firework display.     

A newly developed interatomic potential of Nb−Al−Ti ternary systems for high-temperature applications

The application of hard/soft composite structure in personnel armor for blast mitigation is relatively practical and effective in realistic protection engineering, such as the shell/liner system of the helmet. However, there is still lacking a reliable experimental methodology to effectively evaluate the blast mitigation performance when the structure directly contacts the protected target, which limits the development of protection structures. In this paper, we proposed a new method to evaluate experimentally and numerically the blast mitigation performance of hard/soft composite structures. The blast mitigation mechanism is analyzed. The hard/soft structures were composed of ultra-high molecular weight polyethylene (UHMWPE) composite and expanded polyethylene (EPE) foam. In field explosion experiment, a 7.0 kg trinitrotoluene (TNT) spherical charge is used to generate blast waves at a 3.8 m stand-off distance. A pressure test device is designed to support the tested structure and measure the transmitted blast pressure pulses after passing through the structure. Experimental results indicate that the hard/soft structures can mitigate the blast pressure pulse into the triangular pressure pulse, through making the pulse profile flatter, reducing the pressure amplitude, and delaying the pulse arrival time. Specifically, the combination of 7 mm UHMWPE composite and 20 mm EPE foam can reduce the blast pressure amplitude by 40%. Correspondingly, the finite element simulation is also carried out to understand the blast mitigation mechanism. The numerical results indicate that the regulation for blast pressure pulses mainly complete at the hard/soft interface, which is attributed to the reflection of pressure waves at the interface and the deformation of the soft layer compressed by the hard layer possessing kinetic energy. Furthermore, based on these analyses, the corresponding theoretical model is proposed, and it can well explain the experimental and numerical results. This study is meaningful for evaluating and designing high-performance blast mitigation structures.

     

The dynamic behaviour of sharp V-notches under impact loading

The dynamic behaviour of sharp V-notches which are either symmetric or oblique to the longitudinal boundary of a homogeneous elastic and isotropic strip subjected to an impact plane pulse was studied by the method of caustics. The stress pulse impinging on the flanks of the notch reflects and diffracts in different ways depending on the geometry of the notch relative to the coming pulse. For compressive stress pulses a stress concentration at the bottom of the notch does not create a crack propagation phenomenon, whereas for tensile pulses there is a possibility for an incubation, nucleation and eventual propagation of a crack. A complete experimental study of the incubation nucleation and propagation of cracks from the bottoms of notches in thin strips under tensile stress pulses was undertaken, whereas for compressive stress pulses the stress concentration at the bottom of the notch was evaluated. Interesting results were disclosed concerning the reinforcement of pulses by reflection and caging in, the evolution of stress concentration at the notch and the mode of crack propagation inside the plate. Dynamic stress intensity factors were evaluated all over the paths of crack propagation indicating a close intimacy between crack velocity and values of SIFs.     

Evolution of a laser-generated shock wave in iron and its interaction with martensitic transformation and twinning

Effects of shock waves (generated by a nanosecond laser pulse in plates of Armco-iron) on structural changes are analysed. Localisation of processes of martensitic transformation and twinning – for various values of laser pulse duration – is studied both experimentally and numerically. A proposed model accounts for interaction of shock wave propagation and structure changes. Realisation of martensitic transformation and twin formation influences wave front modification. A stress amplitude decrease with increasing distance from a microcrater determines, together with the pulse duration, a character of spatial localisation of structural changes. Numerical results are compared with experimental data and serve as a basis for additional interpretation of phenomena. Received 9 August 1994 / Accepted 30 June 1997     

Pulse shaping techniques for testing elastic-plastic materials with a split Hopkinson pressure bar

We present pulse shaping techniques to obtain compressive stress-strain data for elastic-plastic materials with a split Hopkinson pressure bar. The conventional split Hopkinson pressure bar apparatus is modified by placing a combination of copper and steel pulse shapers on the impact surface of the incident bar. After impact by the striker bar, the copper-steel pulse shaper deforms plastically and spreads the pulse in the incident bar so that the sample is nearly in dynamic stress equilibrium and has a nearly constant strain rate in the plastic response region. We present analytical models and data that show a broad range of incident strain pulses can be obtained by varying the pulse shaper geometry and striking velocity. For an application, we present compressive stress-strain data for 4340 R_c 43 steel.     

A theory of pulse propagation in anisotropic elastic solids

A theory is described for the propagation of pulses in anisotropic elastic media. The pulse is initially defined by a harmonically modulated Gaussian envelope. As it propagates the pulse remains Gaussian, its spatial form characterized by a complex-valued envelope tensor. The center of the pulse follows the ray path defined by the initial velocity direction of the pulse. Relatively simple expressions are presented for the evolution of the amplitude and phase of the pulse in terms of the wave velocity, the phase slowness and unit displacement vectors. The spreading of the pulse is characterized by a spreading matrix. Explicit equations are given for this matrix in a transversely isotropic material. The rate of spreading can vary considerably, depending upon the direction of propagation. New reflected and transmitted pulses are created when a pulse strikes an interface of material discontinuity. Relations are given for the new envelope tensors in terms of the incident pulse parameters. The theory provides a convenient method to describe the evolution and change of shape of an ultrasonic pulse as it traverses a piecewise homogeneous solid. Numerical simulations are presented for pulses in a strongly anisotropic fiber reinforced composite.     

Rayleigh wave in a quadratic nonlinear elastic half-space (Murnaghan model)

The nonlinear equations that underlie the analysis of classical Rayleigh waves are derived for the two-dimensional case of nonlinear elastic deformation described by the Murnaghan model. In addition to the case of presence of both geometrical and physical nonlinearities, two special cases are considered where one only type of nonlinearity is taken into account. It is shown that unlike the one-dimensional problems for plane waves where only three types of nonlinear interaction should be allowed for, the two-dimensional problems should include 24 types of nonlinear interaction. In the case of geometrical nonlinearity alone, a preliminary analysis of the nonlinear equations is carried out. Second-order equations are derived. The second approximation includes the second harmonics of the wave itself and its attenuating amplitude and is nonlinearly dependent on the initial amplitude of the Rayleigh wave and linearly increasing with the distance traveled by the wave     

On the universality of nonthermal electron acceleration due to quasi-turbulent wakefields

Nonthermal acceleration of relativistic electrons in a wakefield induced by large amplitude light waves is discussed. It is considered that large amplitude light waves are excited as the precursor waves in the upstream of relativistic perpendicular shocks in the universe, and that the wakefield is excited by the light ponderomotive force. Thus, the wakefield acceleration is possible in the astrophysical circumstances. We model such shock environments in a laboratory plasma by substituting an intense laser pulse for the large amplitude light waves. By performing 2-D particle-in-cell simulations, we discuss the properties of the wakefield acceleration in various laser and plasma conditions. With the relativistic intensities of the laser pulses, the electrons are nonthermally accelerated by the wakefield. When the pulse length and the spot size are comparable to the electron inertial scale, the energy distribution functions of the electrons can be monoenergetic. On the other hand, when the pulse spatial scales are much larger than the electron inertial scale, which occurs in the case of the shock precursor light waves, the distribution functions are universally represented by power law spectra with an index of 2, independent of the laser intensity, the plasma density, and the laser pulse size.     

Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth

A problem for a central crack in a plate subjected to plane strain conditions is investigated. Mode I crack loading is created by a dynamic pressure pulse applied at large distance from the crack. It was found that for a certain combination of amplitude and duration of the pulse applied, energy transmitted to the sample has a strongly marked minimum, meaning that with the pulse amplitude or duration moving away from the optimal values minimum energy required for initiation of crack growth increases rapidly. Results received indicate a possibility to optimize energy consumption of different industrial processes connected with fracture. Much could be gained in for example drilling or rock pounding where energy input accounts for the largest part of the process cost. Presumably further investigation of the effect observed can make it possible to predict optimal energy saving parameters, i.e., frequency and amplitude of impacts, for industrial devices, e.g., bores, grinding machines, etc. and hence significantly reduce the process cost. The prediction can be given based on the parameters of the media fractured (material parameters, prevalent crack length and orientation, etc.).     

The Payne effect in finite viscoelasticity: constitutive modelling based on fractional derivatives and intrinsic time scales

As we know from experimental testing, the stiffness behaviour of carbon black-filled elastomers under dynamic deformations is weakly dependent on the frequency of deformation but strongly dependent on the amplitude. Increasing strain amplitudes lead to a decrease in the dynamic stiffness, which is known as the Payne effect. In this essay, we develop a constitutive approach of finite viscoelasticity to represent the Payne effect in the context of continuum mechanics. The starting point for the constitutive model resulting from this development is the theory of finite linear viscoelasticity for incompressible materials, where the free energy is assumed to be a linear functional of the relative Piola strain tensor. Motivated by the weak frequency dependence of the dynamic stiffness of reinforced rubber, the memory kernel of the free energy functional is of the Mittag Leffler type. We demonstrate that the model is compatible with the Second Law of Thermodynamics and equal to a fractional differential equation between the overstress of the Second Piola Kirchhoff type and the Piola strain tensor. In order to represent the dependence of the dynamic stiffness on the amplitude of strain, we replace the physical time by an intrinsic time variable. The temporal evolution of the intrinsic time is driven by an internal variable, which is a measure for the current state of the material's microstructure. The material constants of the model are estimated using a stochastic identification algorithm of the Monte Carlo type. We demonstrate that the constitutive approach pursued here represents the combined frequency and amplitude dependence of filler-reinforced rubber. In comparison with the micromechanical Kraus model developed for sinusoidal strains, the theory set out in this essay allows the representation of the stress response under arbitrary loading histories.     

Comparison of different methods of measurement of pressure of underwater shock waves generated by electrical discharge

Different methods for measurement of strong underwater shock waves pressure pulses with peak pressures of up to 200 MPa and rise time of tens to hundreds of nanoseconds are described and compared. The experimental techniques include direct methods of pressure measurement using various electromechanical gauges such as quartz, carbon-based, and commercially available PCB gauges, and nondirect methods based on measurement of the velocity of the shock wave such as time-of-flight and fast-streak photography. Advantages and disadvantages of the used gauges and methods are discussed. The shock waves were produced by underwater electrical discharge (discharge current amplitude ≤100 kA, pulse duration ≤5 μs) initiated by an exploding wire. A good correspondence between the pressure amplitudes measured by the various gauges and methods was observed. The obtained dependence of the shock wave pressure on the distance from the discharge channel was found to be best fitted by a r ^−0.7 law. It is also shown that none of these methods can be used to determine the time evolution of the pressure behind the front of the shock wave.