Kolsky Bar Wave Separation Using a Photon Doppler Velocimeter

A method to permit wave separation with a Kolsky bar is described. A photon Doppler velocimeter (PDV) is used to measure particle velocity at the location of each strain-gage. These measurements are used with the measured strain to separate wave-trains that in general exist in each bar (for example, an incident and reflected pulse) even when they are superimposed at the gage location. This can extend the duration of the experiment and permit more freedom in the types of loadings that can be applied to a specimen. It was found that the PDV measurement of particle velocity often contains a significant component due to bending waves. A method to account for bending is described but requires multiple PDV measurements at each gage position.     

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 %.     

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.     

Compression response of a thermoplastic elastomer gel tissue surrogate over a range of strain-rates

The mechanical response of a thermoplastic elastomer synthetic ballistic gel is studied over a range of strain-rates. Experiments were conducted at room temperature under uniaxial stress compression at rates ranging from 0.001 to 500/s. Low-rate experiments (<1/s) were conducted with a servo-hydraulic load frame. High-rate experiments (>100/s) were conducted with a polymeric Kolsky bar, along with several modifications to improve data quality. These modifications include the use of a commercial force transducer, a normal displacement interferometer, and a line laser extensometer. Because of the low shear strength and comparatively high compressibility of these materials, inertial effects are very pronounced. Specimen size is varied in an effort to study inertial effects at various loading rates. High speed photography is also used to demonstrate the presence of non-uniform deformation, due to both inertia and friction between the specimen and the loading surfaces. Finally, numerical simulation is used to verify trends observed in the experiments and further validate the data. It is concluded that this material is rate sensitive, with an almost three-fold increase in stiffness over the range of strain-rates studied.     

A rigorous assessment of the benefits of miniaturization in the Kolsky bar system

A rigorous experimental and numerical assessment is made of the benefits and limits of miniaturization in the Kolsky bar system. The primary issues that arise in very high strain rate testing (stress equilibration, inertial effects, wave dispersion, friction, and controllability of deformations) are addressed through experiments coupled with explicit finite element analyses. A miniaturized Kolsky bar system that includes the input bar is developed, together with the use of the laser occlusive radius detector to obtain local measurements of specimen strain during the very high rate deformations. It is demonstrated that this miniaturized Kolsky bar system can be used to provide fully validated results, including the explicit determination of equilibration, over a very wide range of strain rates (1×10³ to 5×10⁴ s⁻¹). The desired high strain rate can be achieved even at low accumulated strains, and the total strain developed can be controlled very effectively. Specific conditions are developed for determining the range of utility of the technique for a given material. The technique is applied to the characterization of 6061-T651 aluminum, and the results are compared with the results obtained using a conventional Kolsky bar.     

On the Testing of the Dynamic Mechanical Properties of Soft Gelatins

This research focuses on the measurement of the static and dynamic mechanical properties of ballistic gelatin. We present a simple, novel experimental setup for measuring the dynamic material properties of ballistic gelatin that includes the classic metallic incident and transmission bars as opposed to the polymeric Kolsky bars used by additional research groups. This method is mathematically validated, while providing sought out for stress–strain curves for three different ballistic gelatin concentrations. The results are then compared to two additional research groups, while being consistent with one and contradictory to the other. Finally, an empirical constitutive law is presented that is consistent with the results obtained through the experimental setup.     

Development of a New Method to Investigate the Dynamic Friction Behavior of Interfaces Using a Kolsky Tension Bar

To understand interfacial interaction of a bi-material during an impact loading event, the dynamic friction coefficient is one of the key parameters that must be characterized and quantified. In this study, a new experimental method to determine the dynamic friction coefficient between two metals was developed by using a Kolsky tension bar and a custom-designed friction fixture. Polyvinylidene fluoride (PVDF) force sensors were used to measure the normal force applied to the friction tribo pairs and the friction force was measured with conventional Kolsky tension bar method. To evaluate the technique, the dynamic friction coefficient between 4340 steel and 7075-T6 aluminum was investigated at an impact speed of approximately 8 m/s. In addition, the dynamic friction coefficient of the tribo pairs with varied surface roughness was also investigated. The data suggest that higher surface roughness leads to higher friction coefficients at the same speed of 8 m/s.     

A Kolsky bar: Tension,tension-tension

The present paper introduces a new technique which combines rotation disk and traditional Kolsky bar (often termed as split-Hopkinson bar). This technique can be employed to study the tension stress-strain relations and tension-unloading-tension strain-rate history effects of materials in the strain rate range from 10²–10³s⁻¹. The rise time of the incident wave is as short as 15 μs because of the particular design. An attempt is made to estimate strain error caused by the thread connection between the specimen and the bars, and stress error due to the mismatch of the cross section of the specimen and bars. A short rise-time incident wave appears to be most advantageous in view of maintaining the accuracy of the stress-strain curve obtained near the initiation. Preliminary tests are performed on the instrument. Comments are made for this design configuration. M. Li (Student Member of SEM), presently at the Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL 32611, was Research Associate; R. Wang (formerly A.J. Wang) is Professor; and M.-B. Han is Associate Professor, Department of Mechanics, Peking University, Beijing 100871, P.R. China.     

Interferometric spark calorimetry

 We present a technique based on interferometry for the measurement of the quantity of energy transferred from a spark to the gases surrounding it. The primary advantage of this new technique is that it can be used to make accurate measurements not only in stagnant, but also in flowing gases. It has been used to make measurements with an estimated accuracy of better than ±5% in gases flowing at up to 6 m/s. We present the interferometric measurement technique, a simple phase-stepping holographic interferometer for making the measurement, and measurements made using a standard automotive ignition system. Measurements in flowing air at 1 bar show that the amount of energy transferred from a spark to the air doubles when the flow speed is increased from 0 to 2.2 m/s. Received: 3 March 1998/Accepted: 5 April 1999     

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.     

Modification of the kolsky method for studying properties of low‐density materials under high‐velocity cyclic strain

A modification of the Kolsky method with the use of the split Hopkinson bar is proposed, which allows testing lowdensity materials under cyclic loads of an identical sign. Cyclic dynamic testing of specimens is based on the essential difference of acoustic impedances of the material of the specimen tested from the material of pressure bars. The choice of the supportbar length several times greater than the loadingbar length allows registration of strain pulses in several cycles. Results are presented for the proposed modification of the Kolsky method used for tests in compression of foam plastic of two densities under three loading cycles.     

A magnetic method for the determination of residual stress

A magnetic method for the measurement of residual longitudinal stress in the outer portions of cylindrical bars is developed and applied to nickel and steel. It involves measurement of the reversible effective permeability over a range of frequency of the applied alternating field. Special composites specimens, in which any desired level of residual stress can be produced, serve as idealized test specimens. Magnetic stress measurements made on cold-drawn, machined and quenched rods are compared with measurements by X-ray diffraction and mechanical relaxation (slitting). A combination of magnetic and X-ray measurements yields qualitative information about the stress gradient in the outer portion of a bar. A rapid magnetic-test method, suitable for practical application, is described.     

An experimental method for considering dispersion and attenuation in a viscoelastic Hopkinson bar

An experimental method is developed to perform Hopkinson tests by means of viscoelastic bars by considering the wave propagation attenuation and dispersion due to the material rheological properties and the bar radial inertia (geometric effect). A propagation coefficient, representative of the wave dispersion and attenuation, is evaluated experimentally. Thus, the Pochhammer and Chree frequency equation is not necessary. Any bar cross-section shapes can be employed, and the knowledge of the bar mechanical properties is useless. The propagation coefficients for two PMMA bars with different diameters and for an elastic aluminum alloy bar are evaluated. These coefficients are used to determine the normal forces at the free end of a bar and at the ends of two bars held in contact. As an application, the mechanical impedance of an accelerometer is evaluated. A part of this work has been performed in the Laboratoire Matériaux Endommagement Fiabilité of the Ecole Nationale Supérieure des Arts et Métiers de Bordeaux.     

A novel technique for time-resolved detection and tracking of interfacial and matrix fracture in layered materials

A novel experimental technique is developed for time-resolved detection and tracking of damage in the forms of delamination and matrix cracking in layered materials such as composite laminates. The technique is non-contact in nature and uses dual or quadruple laser interferometers for high temporal resolution. Simultaneous measurements of differential displacement and velocity at individual locations are obtained to analyze the initiation and progression of interfacial fracture and/or matrix cracking/delamination in a polymer matrix composite laminate system reinforced by graphite fibers. The measurements at multiple locations allow the speeds at which interfacial crack front (mode-I) or matrix cracking/delamination front (mode-II dominated) propagates to be determined. Experiments carried out use three-point bend configurations. Impact loading is achieved using a modified Kolsky bar apparatus with a complete set of diagnostics for load, deformation, deformation rate, and input energy measurement. This technique is used to characterize the full process of damage initiation and growth. The experiments also focused on the quantification of the speed at which delamination or damage propagates under primarily mode-I and mode-II conditions. The results show that the speed of delamination (mode-I) or the speed of matrix cracking/delamination (primarily mode-II) increases linearly with impact velocity. Furthermore, speeds of matrix failure/delamination under primarily mode-II conditions are much higher than the speeds of mode-I crack induced delamination under mode-I conditions.     

Biaxial Testing of Sheet Materials at High Strain Rates Using Viscoelastic Bars

A dynamic bulge testing technique is developed to perform biaxial tests on metals at high strain rates. The main component of the dynamic testing device is a movable bulge cell which is directly mounted on the measuring end of the input bar of a conventional split Hopkinson pressure bar system. The input bar is used to apply and measure the bulging pressure. The experimental system is analyzed in detail and the measurement accuracy is discussed. It is found that bars made of low impedance materials must be used to achieve a satisfactory pressure measurement accuracy. A series of dynamic experiments is performed on aluminum 6111-T4 sheets using viscoelastic nylon bars to demonstrate the capabilities of the proposed experimental technique. The parameters of the rate-dependent Hollomon–Cowper–Symonds J2 plasticity model of the aluminum are determined using an inverse analysis method in conjunction with finite element simulations.     

应用杆束系统研究水泥砂浆节理面的压剪动特性

基于分离式Hopkinson压杆系统提出一套Hopkinson束杆装置,研究水泥砂浆节理面在压剪复合加载下的动态界面滑移特性。应用三根小杆作为接收杆,分别采用单杆和三杆两种入射方式,对含有节理面的水泥砂浆试件进行冲击加载。在节理面发生滑动时,由三根接收杆测试得到水泥砂浆试件不同位置滑移状态,进而得出节理面的整体滑移速度。此研究初步揭示了节理面在发生滑移时的局部滑移状态以及整体滑移状态,为节理面的动摩擦特性研究提供了较可靠的实验技术。     

Necking evolution in dynamically stretched bars: New experimental and computational insights

This paper presents new results on dynamic neck evolution in steel bars of varying diameters. Dynamic tensile tests were carried out in a Kolsky apparatus using cylindrical steel specimens with various cross-section diameters ranging from 1.5 mm to 4 mm. A high speed digital camera was used to record the deformation of the specimen during the loading process. Video recording of the tests enabled accurate experimental measurements of the necking evolution, specifically its growth rate as a function of the diameter. The experiments show that increasing the specimen cross-section slows down the neck development. This behavior has been further investigated using two different kinds of numerical calculations: (1) axisymmetric finite element simulations and (2) one-dimensional finite difference computations. While the finite difference model only considers the normal stress along the longitudinal direction of the bar, the finite element model does not entail any simplification on the stress state of the specimen during the loading process. In agreement with the experiments, the finite element calculations show a decrease of the necking growth rate with the increase in the cross-section of the sample. On the contrary, the damping effect of the specimen cross-section on the necking evolution is not captured by the finite difference computations. We postulate that this result comes from the one-dimensional nature of the finite difference model. This work uncovers, by means of combined experiments and modelling, the key role played by stress multiaxiality in the growth rate of dynamic necks.     

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.     

Flattened Brazilian Disc Method for Determining the Dynamic Tensile Stress-Strain Curve of Low Strength Brittle Solids

An indirect tensile testing method is proposed to measure the full dynamic tensile stress-strain curve of low strength brittle solids. In this method, the flattened-Brazilian disc (FBD) sample is loaded by modified split Hopkinson pressure bars (SHPB) system. Low amplitude dynamic forces were measured with a pair of piezoelectric force transducers embedded in the incident bar and the transmitted bar. The evolution of tensile stress at the center of the disc sample was determined through finite element analyses using the measured stress in SHPB as inputs. In a traditional Brazilian test, a strain gauge is mounted at the center of the specimen to measure the tensile strain, which is difficult to apply for low strength brittle materials. Thus, two types of non-contact methods, the Digital Image Correlation (DIC) technique and the Laser Gap Gauge (LGG), were used to measure the strain. The DIC method was used to monitor the displacement and the strain map of the specimen during the test, from which the strain at the center of the specimen can be obtained. The accuracy of the DIC results was assessed, and the displacement and strain uncertainties of our system were 0.003 mm and 0.003, respectively. LGG was used to monitor the expansion of the disc perpendicular to the loading axis, from which the average tensile strain is deduced. The numerical simulation revealed that the tensile strain at the center of the specimen is proportional to the average tensile strain and that the ratio is not sensitive to the material elastic parameters. The strain measured through LGG was compared with that measured by the DIC method using photos captured with a synchronized high-speed camera. The result of the LGG method was 20 % smaller than that of the DIC process. However, the latter was limited by the number of frames of the high-speed camera. The feasibility of this methodology was demonstrated using a polymer-bonded explosive (PBX).     

Mechanical Properties of Ballistic Gelatin at High Deformation Rates

The characterization of soft or low impedance materials is of increasing importance since these materials are commonly used in impact and energy absorbing applications. The increasing role of numerical modeling in understanding impact events requires high-rate material properties, where the mode of loading is predominantly compressive and large deformations may occur at high rates of deformation. The primary challenge in measuring the mechanical properties of soft materials is balancing the competing effects of material impedance, specimen size, and rate of loading. The traditional Split Hopkinson Pressure Bar approach has been enhanced through the implementation of polymeric bars to allow for improved signal to noise ratios and a longer pulse onset to ensure uniform specimen deformation. The Polymeric Split Hopkinson Pressure Bar approach, including the required viscoelastic bar analysis, has been validated using independent measurement techniques including bar-end displacement measurement and high speed video. High deformation rate characterization of 10% and 20% ballistic gelatin, commonly used as a soft tissue simulant, has been undertaken at nominal strain rates ranging from 1,000 to 4,000/s. The mechanical properties of both formulations of gelatin exhibited significant strain rate dependency. The results for 20% gelatin are in good agreement with previously reported values at lower strain rates, and provide important mechanical properties required for this material.