Specimen-Bar Impedance Mismatch Effects on Equilibrium and Rate Constancy for Kolsky Bar Experiments

During a Kolsky bar, also known as a split Hopkinson pressure bar (SHPB), experiment, stress equilibrium and strain rate constancy conditions directly contribute to the measurement quality for rate-sensitive materials. A Kolsky bar specimen is initially at rest, and then gradually accelerated to a desired rate. Stress equilibrium is incrementally achieved by multiple stress pulse reflections inside the specimen to reach the desired mean stress. The critical time to achieve constant strain rate and equilibrium stress depends on the impedance mismatch between the bars and the specimen. This paper examined this critical time based on using linear elastic specimens under uniaxial compression. In the first part, the critical time is experimentally measured for PMMA specimens loaded by aluminum, titanium, and steel bars using linear ramp incident pulses. The results show that increasing impedance mismatch increases the time to reach a constant rate, while the time to satisfy equilibrium remains nearly the same. In the second part, optimal bilinear-shaped incident loadings were evaluated and shown to achieve both conditions faster than linear loadings. The time to satisfy both conditions was mapped via simulation using various bilinear pulses over a wide range of impedance mismatches. The analysis shows bilinear loadings with initial rise time between 1.75 and 2.15 transits in the sample require minimum time to equilibrium. There exists an optimum region of bilinear loadings that can reduce the time to reach constant rate. Within such region, the bilinear slope ratio can be approximated to be a reciprocal function of initial rise time.     

Structure of weak shock waves in 2-D layered material systems

Shock waves in homogeneous materials in the absence of phase transitions are understood to have a one-wave structure. However, upon loading of a layered heterogeneous material system a two-wave structure is obtained––a leading shock front followed by a complex pattern that varies with time. This dual shock-wave pattern can be attributed to material architecture through which the shock wave propagates, i.e. the impedance (and geometric) mismatch present at various length scales, and nonlinearities arising from material inelasticity and failure.The objective of the present paper is to provide a better understanding of the role of material architecture in determining the structure of weak shock waves in 2-D layered material systems. Normal plate-impact experiments are conducted on 2-D layered material targets to obtain both the precursor decay and the late-time dispersion. The particle velocity at the free surface of the target plate is measured by using a multi-beam VALYN VISAR. In order to understand the effects of layer thickness and the distance of wave propagation on elastic precursor decay and late-time dispersion several different targets with various layer and target thicknesses are employed. Moreover, in order to understand the effects of material inelasticity both elastic–elastic and elastic–viscoelastic bilaminates are utilized.The results of these experiments are interpreted by using asymptotic techniques to analyze propagation of acceleration waves in 2-D layered material systems. The analysis makes use of the Laplace transform and Floquet theory for ODE’s with periodic coefficients [Asymptotic solutions for wave propagation in elastic and viscoelastic bilaminates. In: Developments in Mechanics, Proceedings of the 14th Mid-Eastern Mechanics Conference, vol. 26, no. 8, pp. 399–417]. Both wave-front and late-time solutions for step-pulse loading on layered half-space are compared with the experimental observations. The results of the study indicate that the structure of acceleration waves is strongly influenced by impedance mismatch of the layers constituting the laminates, density of interfaces, distance of wave propagation, and the material inelasticity.     

搓绳子的弹性力学分析

 用能量法解决了一个类似于搓绳子的问题. 两根相同的弹性直杆, 并在一起沿相同的方向扭转N 圈后, 把两端焊接起来, 看能够回绕几圈. 杆轴线在回绕后变成了螺旋线, 本文利用螺旋线的曲率和挠率求出了回 绕后的变形能, 并利用回绕前后杆的变形能相等求出了两杆回转的圈数. 并用相同的方法求出了三根杆时回转的圈数.     

A one-dimensional theory of wave-propagation in elastic rods based on the „method of internal constraints“

Conclusions The results obtained in this paper in the particular case of lateral vibrations of bars show an encouraging agreement between the values ofc/c ₀ andc _g/c₀ given by the approximate theory based on the assumption of internal constraints and the exact theory derived from the use of the equations of the Mathematical Theory of Elasticity.This approximate theory which will be referred to as the Theory of Internal Constraints is in the dynamic case completely contained in the constraint equation (1) and in the application ofHamiltons Principle. Accordingly the concept of Shear Coefficient is not used. In the general case of wave propagation in elastic straight rods this theory unifies a number of separate engineering treatments of the problem. Moreover, the same theory can be applied to the study of vibrations of curved bars taking into account the effects of shear and of rotatory inertia as has been shown in a previous paper.The mathematical simplicity of the theory and its degree of accuracy justify its use in dealing with engineering problems in vibrations of curved or straight bars for which more exact theories cannot be used because of their mathematical complexities.The author wants to express his best thanks to Mr.E. C. Zachmanoglou, student in the Department of Aeronautical Engineering, and to Mr.R. V. Milligan, graduate student in the Department of Mechanics, at Rensselaer Polytechnic Institute for the valuable help and assistance given to him in the preparation of the numerical tables and graphs which are presented in this paper.The material presented in this paper is based on an investigation which is being conducted under the sponsorship of the Office of Naval Research, Department of the U. S. Navy, Washington, D. C.; and is presented with the permission of the Office of Naval Research.     

Impact bifurcation of semi-infinite elastic thin bars

The dynamic buckling problem of elastic bars subjected to axial impact has been investigated by many authors in different ways. In this paper the problem, in which the elastic bars are assumed to be ideally straight, is reformulated in connection with the bifurcation due to the stress wave propagation. The example of a semi-infinite elastic bar is used for illustration.     

Eigenvibrations of curved elastic bars according to the „Method of internal constraints“

Conclusions In the present paper it has been shown how it is possible to discuss the problem of vibrations of curved bars once that the solution of the corresponding problem for the straight bar is known. The method of approach in deriving the equations of motion being completely contained in the constraint equation (5) and in the application of Hamilton Principle, while the method of solving the equations being based on a perturbation method which utilizes as first approximation the solution of the straight case.More general dynamic problems of elongated solids in which the inertia characteristics of the cross-section of the bar are known functions of the variable x can be attacked and solved by the same method which has so far been demonstrated for the simple cases of bars having constant inertia characteristics.The material in the paper is based on an investigation, conducted at the Rensselaer Polytechnic Institute, Troy, New York, under the sponsorship of the Office of Ordnance Research, Contract No. DA-30-115-ORD-709. Project No. 454.13.     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.     

STUDY ON AMPLIFICATION FACTOR OF FLEXURAL BUCKLING CRITICAL LOAD OF AXIAL COMPRESSION BARS1)

为了建立一般条件下轴压构件屈曲临界载荷的计算理论,首先对轴心受压构件发生屈曲时的总势能方程进行了推导,然后采用Rayleigh-Ritz法并基于势能驻值原理得到了4种不同端部约束条件下轴压构件的屈曲临界载荷,对比欧拉临界载荷,给出了临界载荷放大系数 的计算式,全面考虑了构件长细比、压缩变形、剪切变形以及截面形状系数对临界载荷的影响,推导的计算式可用于较小长细比轴压构件发生屈曲时临界载荷的计算.圆截面和双轴对称工字形截面轴压构件屈曲临界载荷的分析表明构件长细比是影响放大系数的主导因素。     

动态拉伸试验中试样应变测试的有效性分析

为了评估将试样通过胶粘连接到加载杆的Hopkinson杆装置所获得试样应变的有效性,对四种强度刚度差异较大的纤维增强复合材料进行了动态拉伸试验。试验时,试样通过环氧胶和杆夹层粘接,试样的应变分别按照Hopkinson杆一维应力波理论计算和试样上应变计直接准确测量得到。结果证明：对小变形碳纤维复合材料,按一维应力波理论计算的应变与试样上直接所测应变值偏差超过100%;对较大变形的GFRP和KFRP层合板,两者偏差小于40%。说明采用Hopkinson杆一维应力波理论计算的试样应变不准确。为修正不准确性,一是通过大量数据分析建立按一维应力波理论计算值与直接测量应变之间的关系式,用此式可使此试验装置获得有效的试样应变;二是借助ABAQUS有限元模拟分析得出粘胶层以及试样过渡弧段的变形,用一维应力波理论计算的应变减去此变形,也可获得有效的试样应变。     

Enhanced fracture energy and effects of temperature at spalling in ceramics: continuum damage modelling

Summary Enhanced fracture energy losses at spalling and the temperature dependence of the spalling strength of alumina ceramic bars are analysed on the basis of the experimental tests conducted both in room temperature and within the temperature range up to 1500°C at strain rates of some 500 s⁻¹. The experimental method and the measurements are first shortly outlined. The mechanical response of ceramic bars is modelled then as a heterogeneous distribution of brittle-elastic mesoelements undergoing continuum damage at the known strain history, corresponding to that registered in the experiments. The mesoelements are characterised by the values of initial damage randomly fluctuating within a given band-width superposed on a deterministic distribution, which corresponds to the fabrication conditions of the ceramic bars. The model has been tested in the evaluation of room-temperature experiments, its parameters: the average value of the initial damage, Young's modulus of the undamaged material and the energy absorption capacity in continuum damage are taken from the calibration fitting the experimental data. The registered energy losses at spalling, which exceed the static values of fracture energy by almost an order of magnitude, can be explained thus by the enhancement of the dissipation due to bulk damage, which is computed on the basis of the above parameters. The temperature change of the Young's modulus of the matrix material is taken as corresponding to the measured change of the uniaxial wave velocity in the bar, and corrected by the temperature change of the mass density. The analysis of the model shows that the drop in the spalling strength of the specimens with the increase of the temperature is phenomenologically related to the falling energy absorption capacity within the continuum damage mechanism. An explanation of this phenomenon is attempted, based on the grain-size-related mechanisms of the microfracture from pre-existing intergranular flaws distributed over the bulk of ceramics. Received 7 May 1999; accepted for publication 14 June 1999     

Crack bifurcation in laminar ceramics having large compressive stress

Crack bifurcation is observed in laminar ceramics that contain large residual compressive stress. In such composites, alternating material layers have tensile and compressive residual stress, due to thermal expansion mismatch or other sources. The compressive stress ensures that crack growth leading to failure in the laminar system is mediated by threshold strength, but, in some cases, it also leads to bifurcation of the propagating flaw. The phenomenon of bifurcation takes place when the crack tip is propagating in the compressive layer, and occurs typically at a distance equal to a few laminate thicknesses below the free surface and beyond. The observation of this phenomenon is usually associated with the presence of edge cracking in the compressive layers of the laminar ceramic, although it can also occur in the absence of such edge cracks. In the few cases where bifurcation occurs without edge cracks, the residual stresses and layer thicknesses are close to the condition in which edge cracks will occur. In addition, in this case the bifurcation is confined to near the specimen free surface, and below the bifurcation plane, the cracks are straight. The energy release rates for the straight and bifurcated cracks are calculated from the results of finite element computations and compared. When edge cracking is ignored, the crack is simulated as a through-thickness crack in an infinite body, and the energy release rate is used to predict crack deviation and bifurcation. Based on this, the finite element model successfully predicts bifurcation in only one material combination that was investigated in experiments. However, the experimental bifurcation takes place in two additional material combinations. When the effect of edge cracking is incorporated into the finite element simulations, the energy release rate calculations successfully predict the phenomenon of bifurcation in three material combinations, as observed in the experiments. Since no edge cracks are present in the fourth material combination tested experimentally, its lack of bifurcations is automatically predicted by the model. The presence of edge cracking, or its incipience, is thus concluded to be critical to the occurrence of crack bifurcation in laminar ceramic composites.     

Inspection of interfaces between corroded steel bars and concrete using the combination of a piezoelectric zirconate-titanate transducer and an electromagnetic acoustic transducer

We have conducted an inspection of the interface between a steel bar and concrete using the combination of a piezoelectric zirconate-titanate transducer (PZT) and an electromagnetic acoustic transducer (EMAT). The PZT is used for generating elastic waves by mechanical vibration and then the EMAT is used for receiving the transmitted ultrasonic guided waves. This arrangement is made in order to overcome the major shortcomings of the PZT, i.e., the requirement of a couplant, and of the EMAT, i.e., relatively low transmitted ultrasonic energy. To investigate the applicability of this technique in the field, outside the laboratory environment, the experiments are conducted on different types of steel bars: corrosion-free, naturally corroded, and zinc-coated as well as corroded bars. It is shown that the PZT-EMAT combination is very effective for inspecting the steel bar-concrete interface. Using this technique, small separation at the steel bar-concrete interface can be effectively detected for corroded as well as corrosion-free specimens. This method can be applied in the field to pre-stressed tendons and soil nails, where one side of the reinforcement is exposed.     

钢筋混凝土结构改进型分离式数值模型

提出一种考虑粘结滑移效应的钢筋混凝土改进型分离式数值模型。在混合物理论基础上,该模型兼顾混凝土基体和钢筋的力学行为,且基于钢筋混凝土界面粘结滑移模型,获得了钢筋等效模型。改进型分离式数值模型由于对钢筋及其界面无显式离散要求,使得钢筋的运用完全独立于其几何形状,同时对混凝土网格没有约束,并且不增加计算成本,因此该模型可适用于钢筋混凝土宏观结构层面分析。通过钢筋混凝土构件-结构的爆炸实验,对改进型分离式数值模型进行层次化验证。对比结果表明,考虑粘结滑移效应的有限元模型能够更好地预测钢筋混凝土结构的宏观力学行为。     

On the longitudinal impact of two phase transforming bars. Elastic versus a rate-type approach. Part I: The elastic case

Longitudinal impact experiments of thin bars are proposed as an effective mean for understanding the kinetics of stress-induced phase transformations. We consider on one side the elastic model and on the other side an augmented theory, which includes the Maxwellian rate-type viscoelasticity with finite instantaneous response and as a limiting case the Kelvin–Voigt viscoelasticity with infinite instantaneous response. By using the chord criterion, we investigate the complete set of Goursat and Riemann problems which could arise as a result of dynamic interactions when we consider a piecewise linear elastic model corresponding to a three phase material. Subsequently we use our Riemann solvers to construct solutions for the longitudinal impact of two elastic phase transforming bars for a variety of impact conditions. We focus on the results which can be measured in laboratory experiments like the time of separation of the two bars after impact, the profile of the particle velocity at the rear end of the target and the stress history at the contact point. In Part II of this paper we continue with a theoretical and numerical comparative analysis on the wave structure predicted by our general rate-type approach for the same impact problem.     

一种用于软材料测试的改进SHPB装置

本文提出了一种新的、用于测试橡胶、高弹体及高聚物软泡沫材料动态力学性能的SHPB改进装置。该装置取消了常见的入射杆而采用长杆弹直接撞击试件从而实现了持续的长时间加载，使得在相当大的应变率范围内试件的最大应变在一个加载过程中即可达到。配合该装置采用了瞬态响应优良、分辨率良好的光电式位移测试系统来测量试件的变形；为记录微弱的应变信号，在透射杆中使用了半导体应变片。本方案克服了传统SHPB在测试软材料时由于子弹长度限制带来的加载幅度不足及由于阻抗失配导致的应变信号微弱的困难；与采用高聚物杆的SHPB改进方案相比，本方案的测试结果也更为可靠。在试验装置中还运用了加载整形技术以改善试件中的应力均匀性。从测试结果看，该装置能有效地实现大变形范围、近似恒应变率持续加载以及相应的微弱应变信号的测量。     

Numerical study of the unsteady flow and heat transfer in channels with periodically mounted square bars

 Numerical investigations of unsteady laminar flow and heat transfer in a channel of height H with periodically mounted square bars of height d = 0.2H arranged side by side to the approaching flow have been conducted for different transverse separation distances of the bars. Five cases with transverse separation distance of 0, 0.5, 1, 1.5 and 2d for a Reynolds number of 300 in a channel with a periodicity length of 2H were studied. The unsteady Navier–Stokes equations and the energy equation have been solved by a finite volume code with staggered grids combined with the SIMPLEC algorithm and a fine grid resolution. Due to the arrangement of bars detached from the channel walls the flow is unsteady with vortex shedding from the bars. The amplitude and mean values of the drag coefficients, skin friction coefficients, friction factor and Nusselt numbers have a strong dependence of the transverse separation distance of the bars. Received on 28 January 2000     

921A钢纯剪切帽状试件在SHPB实验中的动态变形

应用ANSYS/LS-DYNA软件,开展了一系列基于921A钢纯剪切帽状试件的SHPB数值模拟.结合SHPB系统应力波理论,研究不同加载速率v0(或应力脉冲I(t))下,特别是高应变率(约106 s-1)下的压杆轴向应变波形以及相应的试件动态变形特性,并对高速撞击下压杆中应变波形的适用性作了相关讨论.     

On the impedance of the pipe in laminar and turbulent pulsating flows

The response of a facility, consisting of a valveless reciprocating pump, a large settling chamber and a long straight smooth pipe, to a periodic change in the volume was analysed. The impedance of the pipe was estimated in both laminar and turbulent flow regimes under otherwise identical flow conditions. A good agreement with theory was obtained for the laminar flow. The estimate of the pipe impedance from the experimental data in turbulent flow was based on the momentum equation as well as on the measured resonant frequency of the system. These independent methods show that the inertance of the pipe has a qualitatively different behavior in laminar and turbulent flow regimes.     

半无限长弹性直杆受轴向冲击载荷作用的分叉问题

受轴向冲击载荷作用的弹性杆的屈曲问题曾被许多作者从不同的角度研究过。本文以半无限长弹性直杆为研究对象,把这个问题作为由于轴向应力波的传播而导致的分叉问题,给出了它的正确提法,并通过实例作了具体的说明。     

Kinetische Stabilität gerader,insbesondere durch nichtkonservative Torsion beanspruchter Stäbe bei Beachtung der äußeren Dämpfung

Übersicht Nach Aufstellung allgemeiner Stabilitätsgleichungen für gerade Stäbe werden diese auf kinetische, durch Torsion bedingte Knickprobleme angewendet. Dann werden für zwei Stabilitätsfälle des tordierten Stabes die kritischen Lasten unter Berücksichtigung der äußeren Dämpfung ermittelt.

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Kinetic stability of straight bars, especially loaded by nonconservative torsion with regard to external damping

Summary After setting up general stability equations of straight bars these are applied to the problem of kinetic buckling caused by torsion. Then, the critical loads are determined for two conditions of the twisted bar with special regard to external damping.