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.     

Dynamic Tensile Characterization of a 4330-V Steel with Kolsky Bar Techniques

Dynamic tensile experimental techniques of high-strength alloys using a Kolsky tension bar implemented with pulse shaping and advanced analytical and diagnostic techniques have been developed. The issues that include minimizing abnormal stress peak, determining strain in specimen gage section, evaluating uniform deformation, as well as developing pulse shaping for constant strain rate and stress equilibrium have been addressed in this study to ensure valid experimental conditions and obtainment of reliable high-rate tensile stress–strain response of alloys with a Kolsky tension bar. The techniques were applied to characterize the tensile stress–strain response of a 4330-V steel at two high strain rates. Comparing these high-rate results with quasi-static data, the strain rate effect on the tensile stress–strain response of the 4330-V steel was determined. The 4330-V steel exhibits slight work-hardening behavior in tension and the tensile flow stress is significantly sensitive to strain rate.     

Inertial effects of quartz force transducers embedded in a split Hopkinson pressure bar

An aluminum split Hopkinson pressure bar is instrumented with quartz force transducers and used to test low impedance materials. Two transducers are used, one at the interface between the specimen and the incident bar and the other at the interface between the specimen and the transmitter bar. It is shown that the stress measured by the incident bar gage often contains a substantial acceleration component, i.e., a significant portion of the signal recorded by the gage is due to its own inertia and not representative of the stress within the sample. Attempts are made to actively compensate for this with measurements of the acceleration of the gage. This is done in three ways: (i) by differentiation of the interface velocity, as determined by a standard strain gage analysis; (ii) by a more direct determination of acceleration, using a measurement of the strain gradient within the bar; (iii) by adding a compensation crystal and mass to the gage to remove the inertial component from the output. It is shown that all three techniques successfully mitigate inertial effects.     

PVDF应力测量技术及在混凝土冲击实验中的应用

介绍了使用PVDF(polyvinylidene fluoride,聚偏二氟乙烯)应力计的应力直接测量技术。在SHPB装置上进行自制PVDF应力计动态压电系数的标定实验,分析了应力集中、横向泊松效应、摩擦效应对PVDF应力计信号及动态压电系数的影响。用PVDF应力计进行了混凝土的冲击压缩实验。利用混凝土前后端面PVDF应力计信号分析了实验过程中混凝土试样的应力均匀性。与应变计直测应变技术相结合得到了混凝土的动态应力-应变关系。     

Embedded optical fiber Bragg grating sensor in a nonuniform strain field: Measurements and simulations

This paper investigates the use of embedded optical fiber Bragg gratings to measure strain near a stress concentration within a solid structure. Due to the nature of a stress concentration (i.e., the strong nonuniformity of the strain field), the assumption that the grating spectrum in reflection remains a single peak with a constant bandwidth is not valid. Compact tension specimens including a controlled notch shape are fabricated, and optical fiber Bragg gratings with different gage lengths are embedded near the notch tip. The form of the spectra in transmission varies between gages that are at different distances from the notch tip under given loading conditions. This variation is shown to be due to the difference in the distribution of strain along the gage length. By using the strain field measured using electronic speckle pattern interferometry on the specimen surface and a discretized model of the grating, the spectra in transmission are then calculated analytically. For a known strain distribution, it is then shown that one can determine the magnitude of the applied force on the specimen. Thus, by considering the nonuniformity of the strain field, the optical fiber Bragg gage functions well as an embedded strain gage near the stress concentration.     

An experimental method for determining dynamic fracture toughness

The boundary and loading conditions in many dynamic fracture test methods are frequently not well defined and, therefore, introduce a degree of uncertainty in the modeling of the experiment to extract the dynamic fracture resistance for a rapidly propagating crack. A new dynamic fracture test method is presented that overcomes many of these difficulties. In this test, a precracked, three-point bend specimen is loaded by a transmitter bar that is impacted by a striker bar fired from a gas gun. Different levels of energy can be imparted to the specimen by varying the speed and length of the striker to induce different crack growth rates in the material. The specimen is instrumented with a crack ladder gage, crack-opening displacement gage and strain gages to develop requisite data to determine toughness. Typical data for AISI 4340 steel specimen are presented. A simple quasi-dynamic analysis model for deducing the fracture toughness for a running crack from these data is presented, and the results are compared with independent measurements.     

不同尺寸砂岩动态力学性质和应力平衡性的试验研究

采用大直径分离式霍普金森压杆系统获得的不同尺寸试样的实验冲击动态力学参数有差异,因此在直径100 mm压杆上进行了3种直径（50、75和100 mm）和5种长径比（0.4、0.5、0.6、0.8和1.0）的砂岩试样冲击试验,分析了不同尺寸试样应力-应变曲线和应变率曲线随尺寸的变化,提出了用于比较波形对齐重合度的波形叠加系数,并与应力平衡因子共同构建了动态应力平衡性研究体系,由此确定大直径霍普金森压杆试验的试样建议尺寸。同时,利用高速摄影机监测试样的动态破坏状况。结果表明:当长径比相同时,直径75与100 mm岩石试样的动态抗压强度测试值相近,直径50 mm试样具有更明显的长度效应;随着试样直径的增大,应变率曲线从单峰变为双峰;小尺寸试样更易发生轴向劈裂破坏,大尺寸试样受内部应力波叠加影响产生了较大的拉应力,易发生层裂拉伸和轴向劈裂的复合型破坏;对直径75 mm且长径比0.3~0.4的试样,波形对齐后重合度较高,在起始破坏前拥有充足的应力平衡时间,应变率加载效果较好。获得了砂岩试样冲击压缩试验的尺寸效应,可为大直径岩石试样的尺寸选择提供参考。     

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 quartz-crystal-embedded split Hopkinson pressure bar for soft materials

A dynamic experimental technique that is three orders of magnitude as sensitive in stress measurement as a conventional split Hopkinson pressure bar (SHPB) has been developed. Experimental results show that this new method is effective and reliable for determining the dynamic compressive stress-strain responses of materials with low mechanical impedance and low compressive strengths, such as elastomeric materials and foams at high strain rates. The technique is based on a conventional SHPB. Instead of a surface strain gage mounted on the transmission bar, a piezoelectric force transducer was embedded in the middle of the transmission bar of a high-strength aluminum alloy to directly measure the weakly transmitted force profile from a soft specimen. In addition, a pulse-shape technique was used for increasing the rise time of the incident pulse to ensure stress equilibrium and homogeneous deformation in the low-impedance and low-strength specimen.     

Dynamic force-penetration curves in rock by matching theoretical to experimental wave propagation response

A methodology to obtain the dynamic force-penetration curve of a rock specimen is presented. For this, a simple portable experimental setup is used. On one end, a hand-held hammer strikes a slender chisel. On the other end the chisel is in contact with the rock specimen into which the generated stress wave propagates. Strain gages installed at a selected section of the chisel are recorded throughout the impact duration. The theoretical signal at the same section is simulated using a numerical method based on the impulsemomentum principle previously developed by the author. Essentially the shape of the simulated theoretical response at the strain gage section depends on the impact velocity of the hammer and the slope of the assumed force-penetration curve. These two parameters are adjusted until the shape of the theoretical signal at the strain gage closely matches the experimental signal. Due to its simplicity, the proposed methodology has the potential of becoming a standard dynamic test for obtaining the force-penetration curvs in rocks.     

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。     

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。     

平面应变下紧凑拉伸试样的动态断裂韧性的实验研究

材料的动态断裂韧性是衡量材料在动载荷作用下抵杭裂纹扩展能力的重要指标,以往的材料动态断裂韧性测试多采用三点弯曲试样,而针对紧凑拉伸试样的动态断裂韧性研究很少.本文将紧凑拉伸试样(即CT试样)简化成等效弹簧质量模型,得到了CT试样动态应力强度因子的近似表达式.对Hopkinson压杆装置进行了改进,利用改进后的实验装置进...     

A New Shear-Compression-Specimen for Determining Quasistatic and Dynamic Polymer Properties

A new design of the shear compression specimen (SCS) for investigating the viscoelastic shear response of polymers is presented. The specimen consists of a polymer gage section with two metal ends that remain essentially rigid during deformation. Two closed-form analytic models are developed to predict the average stress and strain in the gage section from the deformation-load histories. This new SCS design and its analytic models are thoroughly evaluated via laboratory measurements and numerical simulations. These simulations show that the deformations in the gage section are more uniform than in the original design, and the distribution of the average shear stress and strain are highly homogenous. The simulation results yield good agreement with those of closed-form analytic results and the experiments demonstrate that the new SCS geometry and its analytic models are as reliable as other commonly employed specimens. It can also generate higher strain rates under usual loading conditions because of its smaller specimen gage length. The need for care in specimen preparation is also discussed in detail as illuminated by the experimental and simulation results.

M-shaped Specimen for the High-strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus

An experimental technique is proposed to determine the tensile stress–strain curve of metals at high strain rates. An M-shaped specimen is designed which transforms a compressive loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems associated with the gripping of tensile specimens under dynamic loading. The M-specimen geometry provides plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique is validated both experimentally and numerically for true equivalent plastic strain rates of up to 4,250/s.     

On testing of charpy specimens using the one-point bend impact technique

This paper reports our methodology and results for the assessment of the dynamic fracture energy of notched Charpy A508 steel specimens. The fracture tests consist of one-point bend impact applied to the specimen in contact with an instrumented bar. Fracture is caused by the inertia of the unsupported specimen only. The fracture energy is determined from the incident, reflected and single wire fracture gage signals. High-speed photographic recordings show that for all the specimens investigated in the “lower shelf” temperature regime, fracture occurs relatively early and prior to “taking off” of the bar by rigid body motion. It also confirms that the fracture gage readings indeed coincide with the formation of a crack from the notch tip. The present methodology is relatively easy to implement, and it allows the investigation of the fracture properties of materials at loading rates (and velocities) that are substantially higher than those achieved in a conventional Charpy test. Moreover, this test is attractive for modeling purposes since its boundary conditions are simple and well defined.     

Novel Design of Cruciform Specimens for Planar Biaxial Testing of Soft Materials

Cruciform specimens have long been used in planar biaxial testing of inanimate materials such as metals and composite materials. The efforts to improve the geometric design of cruciform specimens have focused on maximizing the degree of uniformity of stress and strain in the gage section. The standardization of the procedure for the determination of the mean stress in the gage section is lacking, however, because the exact load transferred from the grippers to the gage section during testing is unknown. Here, we introduce a novel split-arm design for cruciform specimens by taking into account three important factors: i) the effectiveness of load transfer from the grippers to the gage section, ii) the uniformity of normal stress (in the loading direction) over the symmetry line, and iii) the compatibility between the nominal stress and the true stress. By ensuring these conditions, one can estimate more accurately the mean stress in the gage section based on the measured force at the grippers and the deformed configuration of a reference length. A genetic algorithm coupled with finite element analysis was utilized to optimize the geometric shape of the novel cruciform design. The identified optimum design provides a load transfer effectiveness of 100 %. The calculated nominal stress deviates from the true stress at the center of the specimen by only ?0.49 %. A numerical experiment was conducted to validate the substantially improved performance of the optimized new design. Experiments were also conducted for natural latex rubber to demonstrate the application of the proposed design.     

Dynamic strain measurement with the interferometric strain gage

The interferometric strain gage has a short gage length, high-frequency response and the capability of measuring large plastic strains. Furthermore, the gage is easily ruled directly onto the specimen, and no mechanical or electrical contact needs to be made during the measurement. These features make the interferometric strain gage particularly suitable for dynamic plastic-strain measurement. In this paper, the details of an experimental setup for generating and measuring dynamic plastic strain are given. The photometric techniques of measuring the fringe motion of the interference patterns are describle as well as the data-reduction procedure. A typical result is presented, and the validity of the method is established.     

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。     

A basic study of a strain gage made of nickel foil

Strain gages made of nickel foil are devised for measuring the elastic surface stress of a specimen subjected to repeated loads. Sticking nickel foil on the surface of a specimen, the elastic stress is measured by observing slip-bands in the foil resulting from repeated strains. Calibration studies with rotating-bending tests are performed on round steel bars with nickel foil to determine the applicable test temperatures for the gage, and to establish the relation between the first appearance of slip-bands and the magnitude of cyclic stress. The peak stresses in grooved shafts under bending are measured with the nickel foil gages. The accuracy of the results is examined.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.