波分离技术在混凝土冲击压缩试验中的应用

介绍了SHPB实验中的波分离技术基本原理,该方法利用两相距很近应变计测量信号分离重叠的入射波和反射波。由于两应变计的距离很近,在弹性杆可以忽略应力波传播的弥散。由于应变计的位置可以非常接近试样,减少了实验中因应力波弥散产生的误差。利用该方法对混凝土进行了冲击压缩实验研究,得到了混凝土的动态应力-应变关系。讨论了测量误差导致波分离技术的误差。     

Flow visualization study of the macromechanics of abrasive-waterjet turning

This paper reports the results of a visualization study conducted to develop further understanding of the macromechanics of the abrasive-waterjet-turning process. The paper describes details of the experiments and visualization results and their implications to the abrasive-waterjet-turning process. A high-speed movie camera was used to record the experiments for the entry and steady-state stages of the turning operation. The study demonstrates that the material removal takes place on the face of the workpiece and that the process involves a mechanism of step formation and removal similar to that of linear cutting with an abrasive waterjet. Moreover, the observations suggest that the abrasive waterjet does not undergo any significant radial deflection in the region where material removal takes place.A.I. Ansari, presently at Mechanical Engineering Department, University of Maryland, College Park, MD 20742, was Doctoral Student, Mechanical Engineering-Engineering Mechanics Department, Michigan Technological University, Houghton, MI 49931.presently at Mechanical Engineering Department, University of Maryland, was Associate Professor, Mechanical Engineering-Engineering Mechanics Department, Michigan Technological University.     

直撞式霍普金森压杆二次加载技术

利用传统分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验技术来实现试件在较低应变率下的大变形时,需要使用超长的压杆系统,杆件的加工和实验空间限制了该技术的推广应用。鉴于此,提出一种直撞式霍普金森压杆二次加载实验技术,利用透射杆中的应力波在其末端的准刚性壁反射实现对试件的二次加载,并分析了准刚性质量块尺寸对二次加载的影响规律;采用二点波分离方法对叠加的应力波进行了有效分离和计算,在总长4 m的压杆系统中实现了1.2 ms的长历时加载,并可以准确获得试件的加载应变率曲线和应力应变关系。建立了直撞式霍普金森压杆二次加载有限元模型,数值仿真结果表明,该实验技术能有效地实现试件的二次加载,与超长SHPB系统获得的仿真结果相比较,两者的试件应力应变关系完全一致。利用该技术对1100铝合金材料进行动态压缩实验,实现了其在102 s?1量级应变率下的大变形动态力学性能测试。     

Distribution and dispersion in the Euler-Lagrange random walk

Summary In a new kind of random walk, displaying both Lagrangian and Eulerian statistical properties¹⁾, calculations were made previously of the Eulerian and Lagrangian velocity auto-correlations. Now the characteristic function of particle displacement has been calculated, and possible continuum limit forms for the probability density equation have been deduced. One of these turns out to be the telegraph equation, given by Goldstein²⁾ as the limit of a different kind of random walk. For this case the auto-correlation functions have been determined.This work was supported by the Mechanics Branch, U.S. Office of Naval Research, under contract Nonr 248 (38) and was presented in Session F of the 1959 Annual Meeting of the American Physical Society at New York under the title A Random Walk with both Lagrangian and Eulerian Statistics.Associate Professor of Engineering Research, Ordnance Research Laboratory, The Pennsylvania State University. This work was done as Research Associate, Post-Doctoral Fellow, Mechanical Engineering Department, The Johns Hopkins University.     

Stress-strain relationships for spruce wood: Influence of strain rate,moisture content and loading direction

The influence of strain rate, moisture content and loading direction on the stress-strain relationships for spruce wood has been investigated. The strain rates were approximately 8×10⁻³ s⁻¹, 17s⁻¹ and 1000 s⁻¹, and the states of moisture content were those corresponding to oven dry, fiber saturated and fully saturated. Compressive loads were applied along the principal directions of the stem of the tree, i.e., radially, tangentially and axially. The low and medium strain-rate tests were performed with the aid of a servohydraulic testing machine, while the high strain-rate tests were carried out using the split Hopkinson pressure bar (SHPB) technique. Magnesium or steel bars were used in the different SHPB tests in order to reduce impedance mismatch for the different directions of the wood specimens. The strain rate was found to have large influence on the behavior of the wood, especially under the condition of full saturation, where water transport in the deforming specimen is of major importance.     

Modified Kolsky Formulas for an Increased Measurement Duration of SHPB Systems

The so-called incident, reflected and transmitted strain histories are typically recorded during standard Split Hopkinson Pressure Bar (SHPB) experiments. Subsequently, the stress-strain curve for the specimen material is determined based on these recordings. Unless wave deconvolution techniques are employed, the reliable measurement of the reflected wave requires an input bar which is at least twice as long as the striker bar (of equal impedance). The present brief technical note elucidates the advantages of a simple alternative configuration which has only been seldom used in the past. Based on the assumption of quasi-static equilibrium at the specimen level, we present a modification of Kolsky’s formulas such that the stress-strain curve for the specimen material can be obtained from the measurement of the incident and transmitted strain histories only. As a result, the measurement of the reflected wave may be omitted and a much shorter input bar can be chosen. Conversely, a much longer striker bar may be used for a given input bar length, thereby increasing the valid duration of standard SHPB experiments by up to 100 % through the use of the modified Kolky formulas. An example experiment is shown where the duration of valid measurements has been increased by more than 70 %.     

Characterization of shock accelerometers using Davies bar and laser interferometer

In this paper, we propose a novel method for evaluating the frequency response of shock accelerometers using Davies bar and interferometry. The method adopts elastic wave pulses propagating in a thin circular bar for the generation of high accelerations. The accelerometer to be examined is attached to one end of the bar and experiences high accelerations of the order of 10³∼10⁵ m/s². A laser interferometer system is newly designed for the absolute measurement of the bar end motion. It can measure the motion of a diffuse surface specimen at a speed of 10⁻³ ∼10⁰ m/s. Uncertainty of the velocity measurement is estimated to be±6×10⁻⁴ m/s, proving a high potential for use in the primary calibration of shock accelerometers. Frequency characteristics of the accelerometer are determined by comparing the accelerometer's output with velocity data of the interferometry in the frequency domain. Two piezoelectric-type accelerometers are tested in the experiment, and their frequency characteristics are obtained over a wide frequency range up to several ten kilohertz. It is also shown that the results obtained using strain gages are consistent with those by this new method. Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11.     

Technique for Combined Dynamic Compression–Shear Testing of PBXs

We modify the split Hopkinson pressure bar and propose a compression–shear experimental method to investigate the dynamic behavior of polymer-bonded explosives (PBXs). The main apparatuses used include an incident bar with a wedge-shaped end and two transmission bars. We employ Y-cut quartzes with a rotation angle of 17.7° to measure the shear force and an optical system for shear strain measurement. A PBX with a density of 1.7 g/cm³ is investigated using the proposed method. Experimental results show that the specimen endures both compression and shear failure. Compression failure stress rises, and shear failure stress decreases as the strain rate increases. The sequences of shear and compression failure times are various at different strain rates. Based on the maximum shear failure criterion, we conclude that these phenomena are related to the experimental loading path.     

Dynamic characterization of compliant materials using an all-polymeric split Hopkinson bar

The split Hopkinson bar is a reliable experimental technique for measuring high strain rate properties of high-strength materials. Attempts to apply the split Hopkinson bar in measurement on more compliant materials, such as plastics, rubbers and foams, suffer from limitations on the maximum achievable strain and from high noise-to-signal ratios. The present work introduces and all-polymeric split Hopkinson bar (APSHB) experiment, which overcomes these limitations. The proposed method uses polymeric pressure bars to achieve a closer impedance match between the pressure bars and the specimen materials, thus providing both a low noise-to-signal ratio data and a longer input pulse for higher maximum strain. The APSHB requires very careful data reduction procedures because of the viscoelastic behavior of the incident and transmitter pressure bars. High-quality stress-strain data for a variety of compliant materials, such as polycarbonate, polyurethane foam and styrofoam, are presented.     

Experimental analysis of dynamic mechanical properties for artificially frozen clay by the split Hopkinson pressure bar

A device for impact compression experiments is the split Hopkinson pressure bar with a refrigerating attemperator. Data for incident and reflected waves are obtained by the measuring technique with strain gauges, and data for transmitted waves are obtained by the measuring technique with semiconductor gauges. Static compression tests of frozen clay are conducted at an identical temperature and different strain rates of 0.001 and 0.01 sec ⁻¹ . Dynamic stress-strain curves are obtained at strain rates of 360–1470 sec ⁻¹ . The low and high temperatures correspond to high and low strain rates, respectively. It is shown that both the temperature and strain rate affect the frozen soil deformation process. Different dynamic stress-strain curves obtained at the same temperature but different strain rates are found to converge. The test results indicate that frozen soil has both temperature-brittleness and impact-brittleness.     

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。     

Preface to the Special Issue in Celebration of Professor Shouwen Yu’s 70th Birthday

Shouwen Yu,emeritus Professor of Applied Mechanics at Tsinghua University,was born on May 4,1939 in Xianyou County,Fujian Province of China.From 1955 to 1958,he studied as an undergraduate     

Full Field Strain Measurement in Compression and Tensile Split Hopkinson Bar Experiments

The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128 × 80 (compression tests) and 258 × 48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.     

Two-dimensional analysis of the split hopkinson pressure bar system

The split Hopkinson pressure bar is widely used to measure the dynamic properties of solid materials. This paper presents the results of the first comprehensive two-dimensional numerical analysis of the technique, and quantitatively describes the effects of realistic friction and of variations in both the specimen geometry and the imposed strain-rate on the validity of the assumptions used in analyzing experimental data. A two-dimensional axisymmetric numerical analysis is used to compute all components of the stress, strain and strain-rate tensors at each mesh point within the specimen and the elastic bars. The calculated response of the pressure bars is used to reconstruct the stress-strain behavior of the specimen and this is compared to both the input stress-strain curve and the actual calculated stress-strain states in the specimen. Thus, the validity of the assumptions and the corrections used in the analysis of the data is determined.Inertia and friction between the specimen and the elastic bars affect the response of the specimen differently for different length-to-diameter ratios. Inertia effects produce stress waves propagating radially and axially in the specimen and may result in an oscillating reconstructed stress-strain curve. If the ends of the specimen are well lubricated and care is taken to minimize the effects of inertia, the reconstructed stress-strain curve agrees with the input. However, serious stress and strain nonuniformity exists when the ends are not lubricated and this results in a reconstructed stress-strain curve where, for any given strain, the stress magnitude is larger than the correct value. A comparison of the calculations with experiment shows excellent agreement for various interface conditions. Finally, the inertia correction of E.D.H. Davies and S.C. Hunter (1963) is found to be reasonable.     

High-strain-rate compressive behavior of a rigid polyurethane foam with various densities

The dynamic compressive stress-strain behavior of a rigid polyurethane foam with four values of density (78, 154, 299, and 445 kg/m³) has been determined in the strain-rate range of 1000–5000 s⁻¹. A pulse shaping technique was used with a split Hopkinson pressure bar to ensure homogeneous deformation in the foam specimens under dynamic compression. Dynamic stress equilibrium in the specimen was monitored during each experiment using piezoelectric force transducers mounted close to the specimen end-faces. Quasi-static experiments were also performed to demonstrate rate effects. Experimental results show that both the quasistatic and the dynamic stress-strain curves of the foam exhibit linear elasticity at small strains until a peak is reached. After the peak, the stress-strain curves have a plateau region followed by a densification region. The peak stress is strain-rate sensitive and depends on the square of the foam density.     

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.     

基于Hopkinson压杆的M型试样动态拉伸实验方法研究

采用传统分离式Hopkinson压杆进行M型试样的动态拉伸实验,可避免试样与杆的连接问题,但该方法并未得到发展和验证。本文中,采用有限元数值分析和实验方法,对M型试样动态拉伸实验进行分析和改进。结果表明:（1）改进的封闭M型试样,可以增强试样整体刚度,有效减少试样畸变引起的附加弯矩对拉伸标段的影响,方便通过Hopkinson压杆加载实现一维拉伸变形;（2）采用试样刚度系数修正法,可消除M型试样整体结构的弹性变形对测试的影响,精确获得试样拉伸标段的塑性应变;（3）高加载率下,建议采用波形整器加载,可显著减少试样结构引起的载荷震荡现象、改善两端的应力平衡,获得准确的动态拉伸应力应变曲线,实现5 900 s?1甚至更高应变率下的动态拉伸实验。研究方法可为M型试样拉伸实验设计和应用提供参考。     

应力平衡和接触状态在Hopkinson杆测试聚合物动态弹性模量中的影响研究

针对用Hopkinson杆试验能否准确测量聚合物动态弹性模量以及其中主要影响因素的问题,本文基于重构试样初始加载阶段的应力波反射透射过程,分别计算了6个特征时间内的前三次反射波和透射波,得到试样的应力平衡度和试样的应力应变曲线。对于所研究的聚合物材料,通过比较重构的应力应变曲线的弹性模量与输入的材料弹性模量,发现在4个特征时间后,误差仅在3%左右。因此试样变形过程中的应力平衡与否不是材料在Hopkinson杆试验中弹性模量测不准的原因。通过环氧树脂试样试验发现,根据Hopkinson杆理论计算的应变结果要大于试样上应变片实测的结果,误差在11%左右。相应的数值模拟研究发现:试样和杆子端面接触状态直接决定着试样弹性模量测量的精度。关于惯性效应和压痕效应的研究也证实它们的影响是可以忽略的。     

A tension split Hopkinson bar for investigating the dynamic behavior of sheet metals

The dynamic response of sheet metals at high strain rate is investigated with a tensile split Hopkinson bar test using plate type specimens. The tension split Hopkinson bar inevitably causes some errors in the strain at grips with the plate type specimens, since the grip and specimens disturb the one-dimensional wave propagation in bars. To validate the experiment, the level of error induced from the grips is estimated by comparing the waves acquired from experiments with the Pochhammer-Chree solution. The optimum geometry of the specimen is determined to minimize the loading equilibrium error. High strain rate tensile tests are then performed with auto-body sheet metals in order to construct their appropriate constitutive models for use in crash-worthiness evaluation.     

J^＊ INTEGRAL OF THE SPECIFIC DEVIATOR STRAIN ENERGY AND ITS APPLICATION

First the deviator strain energy is introduced, then the problem of plane-crack critical growth was discussed, a path independent line integral J^* was defined, furthermore its conservation was proved strictly. As application examples, Mode-Ⅰ stress intensity factors of cracked beams were obtained with present approach. The results are shown to agree well with those available in the open literature.