Elastic waves in truncated cones

An experimental investigation of elastic waves produced by the axial collision of strikers with truncated 2024 aluminum cones with apex angles of 0.48, 5.38, 20, and 30 deg was performed. Wave propagation was initiated at the small end of all four cones and at the large end of the 0.48-deg and 5.38-deg cones. The striker consisted of a 1/2-in.-diam steel ball or a soft phenol-impregnated fiber cylinder. In most cases, impact was caused by firing the striker from an air gun at approximately 1300 ips; in an additional series of tests, a steel ball was dropped on the cone. The metamorphosis of the pulse at the surface of the target was recorded using both foil and semiconductor resistance strain gages. Data were obtained for periods ranging from 200 to 500 μsec; this permitted the observation of several reflections from the ends of the specimen. In several instances, cylindrical aluminum rods were glued to the cone to form a composite target; this permitted observation of the initial pulse incident on the conical section both from surface strain gage and sandwiched crystal records. Studies were also conduced to ascertain the stress distribution across the base of the 20-deg cone. Initial pulse records were employed to predict the surface response in the target using the one-dimensional equation of elastic wave propagation in a cone of infinite length. Reasonable agreement between the data and the results of calculations based on the analysis was obtained.     

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.     

钙质砂的SHPB实验技术及其动态力学性能

开展了11组南海钙质砂和福建石英砂的分离式霍普金森压杆（SHPB）实验,试样相对密实度为90%,厚度分别为10、30和50 mm,得到了冲击荷载下钙质砂和石英砂的应变率时程曲线、应变时程曲线和应力应变关系。实验结果表明:通过严格装样技术可以减小实验设备产生的误差,改变试样厚度、子弹长度、整形器等是实现钙质砂应力平衡和恒应变率的主要手段。在相同的密实度和加载条件下,钙质砂的体积模量和剪切模量约为石英砂的10%,压缩强度和抗剪强度约为石英砂的30%。冲击荷载作用下钙质砂的动态力学性能与石英砂存在较大的差异,因此不能将已有石英砂的研究结果直接用于钙质砂。     

Interface Forces in Laterally Impacted Steel Tubes

In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.     

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.     

Spline-approximation solution of two-dimensional problems of statics for orthotropic conical shells in a refined formulation

An approach to solving two-dimensional stress-strain problems for orthotropic conical shells of variable thickness in a refined formulation is developed. The approach is based on the spline-approximation and the stable discrete-orthogonalization method, which is used to solve the one-dimensional problem. The dependence of the deflection and stresses on the thickness and apex angle of a shell of constant volume is given as an example __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 43–54, November 2007.     

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.     

聚能炸药逆向环形起爆形成高速射流研究

设计了一种长径比为 0 .375 ,罩锥角为 12 0的大锥角小长径比聚能装药。利用闪光X射线摄影技术观察了小长径比聚能装药正向起爆时形成的射流图象以及逆向起爆时药型罩的压垮图象和射流图象。给出了形成射流的头部速度、射流的质量分布等射流特性参数。试验的聚能装药逆向起爆时射流头部速度为 7.48km/s,而正向起爆时仅为 4.34km/s。试验研究表明通过逆向环形起爆 ,小长径比聚能装药获得高速射流是可行的。     

A split Hopkinson pressure bar technique to determine compressive stress-strain data for rock materials

This paper presents a split Hopkinson pressure bar technique to obtain compressive stress-strain data for rock materials. This technique modifies the conventional split Hopkinson bar apparatus by placing a thin copper disk on the impact surface of the incident bar. When the striker bar impacts the copper disk, a nondispersive ramp pulse propagates in the incident bar and produces a nearly constant strain rate in a rock sample. Data from experiments with limestone show that the samples are in dynamic stress equilibrium and have constant strain rates over most of the test durations. In addition, the ramp pulse durations can be controlled such that samples are unloaded just prior to failure. Thus, intact samples that experience strains beyond the elastic region and postpeak stresses can be retrieved for microstructural evaluations. The paper also presents analytical models that predict the time durations for sample equilibrium and constant strain rate. Model predictions are in good agreement with measurements.     

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 %.     

Analysis of a rubber cone tensioned by a concentrated force

Using the constitutive equation of a rubber-like materials given by Gao (1997), this paper investigates the problem of a cone under tension of a concentrated force at its apex. Under consideration is the axial-symmetry case and the large strain is taken into account. The stress strain fields near the apex are obtained by both asymptotic analysis and finite element calculation. The two results are consistent well. When the cone angle is 180°, the solution becomes that of non-linear Boussinesq's problem for tension case.     

Elastic-pulse propagation in thin hollow cones

Elastic pulses were generated in a thin (3-mm) right circular conical shell with apex angle of 20 deg, by an axial impact of a drop weight. Radial-strain pulses of about 250-μs duration were measured at three locations along the cone by semiconductor strain gages. The relative amplitude decrease of the strain pulse was determined as a function of the distance traveled. An approximate analytical solution for this problem is presented. It is shown that, for cones made of material with Poisson's ratio ν=1/3, the approximation leads to the one-dimensional spherical-wave equation and the wave velocity is that of longitudinal waves in thin plates. The decay of amplitude predicted by the model depends on the distance traveled and on the wavelength and it agrees fairly well with the experimental results. The model also gives an upper bound on the amplitude decrease of the pulse.     

A methodology to assess the rate and pressure sensitivity of polymers over a wide range of strain rates

This paper details a methodology to test the mechanical response of soft, pressure sensitive materials, over a wide range of strain rates. A hybrid experimental-numerical procedure is used to assess the constitutive parameters. The experimental phase involves axial compression of a cylindrical specimen which is confined by a tightly-fit sleeve that is allowed to yield plastically, thus applying a constant confining pressure. The usually neglected frictional effects between the specimen and the sleeve are fully accounted for and characterized in detail. With commercial polycarbonate as a typical example, it is shown that pressure sensitivity and rate sensitivity are not coupled, thus reducing the number of tests needed to characterize a material. The results of numerical simulations indicate that the pressure sensitivity index (angle β in the Drucker-Prager material model) has little influence on the hydrostatic and confining pressures, whereas the equivalent stress sustained by the specimen increases with β, which for commercial polycarbonate is found to be β=15°.     

Upper limit of constant strain rates in a split Hopkinson pressure bar experiment with elastic specimens

The upper limit of the achievable constant strain rates in linearly elastic specimens loaded by a split Hopkinson pressure bar is estimated based on the specimen properties and a linear ramp loading. The criterion for a plateau of constant strain rate is derived and discussed. Dynamic experimental results on an S-2 glass/SC15 composite and polymethyl-methacrylate subjected to various ramp loadings verify the modeling results.     

Transient stresses in axisymmetric bodies of varying area

The purpose of this paper is to report on an experimental and theoretical investigation of one-dimensional stress-wave propagation in axisymmetric bodies of varying area. An experimental investigation of elastic waves produced by the axial collision of strikers with truncated 7075 aluminum cones and conical shells with a half angle of 5 deg was performed using an air gun. Strain distributions along the 5-deg conical specimens were obtained by strain gages mounted on the specimen. The method of characteristics was utilized in the theoretical analysis of the propagation of elastic stress waves. Procedures of numerical integration along the characteristic directions are established and carried out for all the experimentally tested cases on a digital computer. Good agreement between the data and the results of calculations based on the analysis was obtained.     

On the Plastic Wave Propagation Along the Specimen Length in SHPB Test

To observe the plastic wave propagation, an experimental setup is designed with a SHPB facility and a high speed digital camera. Two types of OFHC copper were selected as specimen materials: in the cold work condition and after total annealing, which represent non strain hardening and strain hardening material respectively. The rise time of incident impulse in the SHPB test is relevant to bar’s radius. A maximum allowable specimen length and a maximum allowable impact velocity (MAIV) of striker are proposed for the SHPB test. The propagation of plastic waves is observed along specimen length at the beginning of specimen’s plastic deformation in SHPB test. However, for both types of material, no plastic wave motion is caught along specimen length for large plastic strain level. Side confinement effect of friction is found to be significant, even with lubricant in the experiment.     

Dual-indentation technique for the assessment of strength properties of cohesive-frictional materials

We propose a dual indentation technique for the assessment of the cohesion and friction angle of cohesive-frictional materials of the Mohr–Coulomb type. The technique is based on a computational implementation of the yield design theorems applied to conical indentation tests with different apex angles. The upper bound solutions are found to be very close to flat indentation solutions available for cohesive-frictional materials. On this basis we derive fundamental hardness-to-cohesion solutions in function of the friction angle and the apex angle. By studying the property of these dimensionless relations, we show that the ratio of two hardness measurements obtained from indentation tests with different apex angles, allows one to determine the friction angle. This dual indentation method is applied to Berkovich and Corner Cube indenter assimilated to equivalent cones of different apex angle. The method is validated for a ‘model’ material, metallic glass, which has recently been identified as a cohesive-frictional materials. The only input to the method are two hardness values which we obtain by microindentation on metallic glass. The outcome are values of the cohesion and friction angle, which are found to be in excellent agreement with reported cohesion and friction angle values of metallic glass obtained by macroscopic triaxial testing and comprehensive finite-element backanalysis of indentation curves.     

锥体料斗内散料流动相对速度分布的实验研究

用示踪法进行了散粒体在圆锥料斗内不同出口直径条件下流动时相对速度分布的试验，并以此对Jenike轴向应力和共轴理论进行了实验验证，发现有些散料与Jenike轴向应力和共轴理论符合较好，而有些与之偏差较大。分析了内摩擦角、壁面摩擦角对最大主应变率方向的影响。     

Dynamic fracture toughness of high strength metals under impact loading: increase or decrease

An elusive phenomenon is observed in previous investigations on dynamic fracture that the dynamic fracture toughness(DFT) of high strength metals always increases with the loading rate on the order of TPa.m 1 /2.s 1.For the purpose of verification,variation of DFT with the loading rate for two high strength steels commonly used in the aviation industry,30CrMnSiA and 40Cr,is studied in this work.Results of the experiments are compared,which were conducted on the modified split Hopkinson pressure bar(SHPB) apparatus,with striker velocities ranging from 9.2 to 24.1 m/s and a constant value of 16.3 m/s for 30CrMnSiA and 40Cr,respectively.It is observed that for 30CrMnSiA,the crack tip loading rate increases with the increase of the striker velocity,while the fracture initiation time and the DFT simultaneously decrease.However,in the tests of 40Cr,there is also an increasing tendency of DFT,similar to other reports.Through an in-depth investigation on the relationship between the dynamic stress intensity factor(DSIF) and the loading rate,it is concluded that the generally increasing tendency in previous studies could be false,which is induced from a limited striker velocity domain and the errors existing in the experimental and numerical processes.To disclose the real dependency of DFT on the loading rate,experiments need to be performed in a comparatively large striker velocity range.     

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.