Introduction

The deformation and failure properties of many materials are sensitive to strain rate, and testing at various strain rates is required for determining the rate sensitivity. Quasi-static low strain rate tests in the range from 10−5 s−1 up to about 1 s−1 are usually done using servo hydraulic or screw driven machines. High strain rates tests ranging from about 400 s−1 to 5000 s−1 are most commonly done using the Split Hopkinson (Kolsky) Bar (SHB) technique. The strain rate gap between these techniques is often called the intermediate strain rate range. Testing with servo hydraulic machines at intermediate strain rates usually results in oscillatory data since the machines are not in a state of static equilibrium during the test, and inertia effects have to be considered. Testing with the SHB technique at strain rates below 400 s−1 is not practical since the possible test duration in a typical SHB apparatus is too short. The difficulties associated with testing at intermediate strain rates and proposed solutions are discussed next.

Low strain rate tests in the range from 10−5 s−1 up to about 1 s−1 done in a servo hydraulic testing machine are called quasi-static because the specimen and the all the components of the testing machine (frame, load cell, grips, etc.) are in a state of static equilibrium throughout the test. The stress strain curves that are determined from the force measured by the load cell and strain measured on the specimen are smooth. The actuators of many servo hydraulic machines can move fast enough to deform specimens at higher strain rates and have been used for conducting tests at strain rates higher than 1 s−1. In such tests, the actuator first accelerates to the required speed and then either impacts the specimen directly (compression test), or impacts a component of a sliding sleeve mechanism that loads the specimen. The impact introduces vibrations in the testing frame and data recorded in these tests is typically plagued with large oscillations in the force measurement (often referred to as ringing). During the test, the whole testing machine is not in a state of static equilibrium. The duration of the test is of the same order as the time that it takes for the various components of the testing machine to accelerate to the speed that they have to move in order to deform the specimen at the required strain rate. The testing machine is a complicated dynamic system of accelerating components that are affecting each others motion. The force measured by the load cell includes inertia effects from all the moving components and is not necessarily the same as the force in the specimen.

Various modifications have been suggested and implemented in standard servo hydraulic machines in order to obtain data at intermediate strain rates with minimal ringing. In general, increasing the stiffness of the testing frame increases its natural frequencies and reduces the ringing. Reducing the mass of components in the system (grips, connecting rods, sliding mechanism, etc.) reduces the ringing amplitude [1, 2]. The amplitude of the noise in the force measurement can be reduced by measuring the force closer to the specimen. This was done by adding a second stiff load cell next to the specimen, or by using a dog-bone shaped specimen with a long flange [3, 4]. The flange is instrumented with strain gages and since its deformation during the test is within the elastic range, the reading from the strain gage can be calibrated to give the force in the gage section. In a different arrangement [5] the force was measured by analyzing the waves in a long bar that was connected between the specimen and the frame. Smoothing the data was also done by measuring the vibrational frequencies of the testing machine and removing the noise frequencies from the data by using filters during the experiment or by applying fast Fourier transform analysis to the recorded data [1, 2, 6, 7]. Instead of eliminating the ringing, researchers have also used simulation for determining the property of the specimen tested. The whole experimental configuration (frame, grips, load cell, impact of the actuator, etc.) is simulated using time dependent finite element analysis and an assumed material model for the deformation of the specimen [1]. The assumed properties of the tested material are validated if the results from the simulation, which includes all the dynamic effects, agree with the test measurements.

The SHB technique was introduced in 1949 by Kolsky [8] with compressive loading and modified later for tensile testing [9,10,11]. In a SHB experiment, a short specimen is placed between two long bars (incident and transmitter). To conduct a test, a loading wave is introduced in the incident bar. When the wave reaches the specimen it is loaded and starts deforming between the two bars. Upon loading, part of the loading wave is transmitted through the specimen to the transmitter bar and part is reflected back to the incident bar. The experimental setup is designed such that the specimen is loaded beyond the elastic limit up to failure while the stresses in the bars are well below the elastic limit. The validity of the test is contingent on the assumptions that the specimen is in a state of equilibrium (inertia and wave effects within the specimen are not considered) and the deformation is uniform during most of the test duration (except in the very beginning of the test). To satisfy these assumptions, the specimen has to be short such that the time for a wave to traverse its length is short in comparison to the duration of the test. The incident and transmitter bars, however, are not in a state of static equilibrium. The stress waves that propagate in the bars (incident, reflected and transmitted) are recorded and subsequently are used, by applying elastic wave theory, to determine the deformation (average strain) and stress in the specimen throughout the test. The maximum duration of a SHB experiment is limited by the length of the bars and the duration of the loading wave. The maximum test duration is a little less than twice the time that it takes for a wave to travel the length of the transmitter transmission bar (depending on the position of the strain gages on the bar). In a typical SHB experiment the specimen’s length is 2 to 8 mm, and the loading wave is 200 to 400 μs long. Theoretically, the SHB technique can be used to conduct tests in which the specimen deforms at lower strain rates. However, it is not practical since in order to accumulate appreciable strain in the specimen in a lower strain rate test, the loading wave has to be of a long duration (4 ms for 20% deformation at strain rate of 50 s−1) and the incident and transmitter bars have to be very long. A compression SHB with 11 m long incident and transmitter bars and a 2.5 m long striker bar with a pulse shaper that generated a 3 ms long loading wave was used [12], to test foam at strain rates of about 50 s−1.

Modifications to the standard SHB technique have been proposed for conducting long duration tests at intermediate strain rates. Instead of generating the loading by an impact of a very long projectile, loading was applied by pushing the incident bar (as a rigid body) with a hydraulic oil jack [13, 14]. On the transmitter side, a short bar was used and a wave separation technique was applied to analyze the data from the multiple reflections of the waves. In place of using a long transmitter bar, a short (~1 m) serpentine bar was used in a direct impact intermediate strain rate test [15]. The serpentine bar is made of a solid bar that is placed inside several concentric tubes with matching impedance. The bar and the tubes are connected in series such that the transmitted wave propagates with no reflections. In this test, the specimen was impacted directly with a 2.5 m projectile (1 ms long loading wave).

The present paper introduces a new device for testing materials in tension and compression at strain rates between about 20 s−1 and 250−1. The operation of the apparatus is based on the logic of the split Hopkinson bar technique except that a hydraulic actuator replaces the incident bar. The hydraulic actuator applies load directly to the specimen that is attached on its other end to a very long transmitter bar. This arrangement provides a long loading duration and a clean (no ringing) force measurement in the specimen by measuring the force in the transmitter bar. Stress strain curves obtained from testing specimens in this apparatus are clean and smooth without any evidence of oscillations or ringing.

Experimental Setup

The intermediate strain rate testing apparatus, shown schematically in Fig. 1, is made up of a long round transmitter bar and a fast hydraulic actuator. Photographs of the actual apparatus are shown in Fig. 2. The specimen is placed between one end of the transmitter bar and the hydraulic actuator and can be loaded in tension or compression by a force applied by the actuator. The operation is similar to that of a SHB except that the incident bar is replaced by a hydraulic actuator that can apply load to the specimen for a long duration of time and the transmitter bar is very long. The hydraulic actuator is custom-built (Scott Industrial Systems, Dayton OH). It has a stroke of 102 mm, maximum speed of 7 m/s, and can apply a maximum force of about 18 kN. The transmitter bar is 40 m long. It is composed up of 3.6 m long segments of 22.2 mm diameter 304 L stainless steel bars that are connected together. The connection between two segments is made with 6.35 mm threaded studs. The connection is designed such that when the connection is tightened there is minimal gap between the end of the stud and the bottom of the threaded cup, and the end surfaces of the two bars are compressed against each other with no gap. The objective is to have a connection that allows the wave to propagate along the transmitter bar with no reflection. The transmitter bar remains elastic throughout the tests and the force that is applied to the specimen is determined from the amplitude of the transmitted wave (the same as in the SHB experiment). The wave in the transmitter bar propagates to the end of the bar and then reflects back toward the specimen. The experiment can continue until the reflected wave reaches the specimen. The 40 m long bar provides time for tests of up to approximately 15 ms in duration.

Fig. 1
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Schematic of the intermediate strain rate testing apparatus

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Fig. 2
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The intermediate strain rate testing apparatus

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In a tension test, the specimen has a dog-bone geometry with a short parallel gage section between two wider tabs, Fig. 3. In a tension test one end of the specimen (tab) is attached to the end of the transmitter bar and the other end is connected by means of a slack mechanism to the actuator. During a test, the actuator accelerates to the desired speed and then loads the specimen while moving at a nearly constant speed. In a compression test, the specimen is a short, small diameter cylinder. It is placed at the center of the cross-sectional surface of the transmitter bar. It is held in place by molybdenum disulfide grease, which acts also as a lubricant during the test. The actuator end has a flat surface, parallel to the surface of the transmitter bar, and the specimen is loaded by the actuator that impacts the specimen’s free end directly. Upon impact, the specimen starts to deform between the actuator and the transmitter bar end and a compression wave propagates in the transmitter bar.

Fig. 3
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Tensile test specimen geometry

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The wave’s amplitude in the bar (the force in the specimen) is measured at two locations by two sets of strain gages that are next to each other. One set consists of four foil strain gages (Micro-Measurements ED-DY-125 AC-10C) and the other of two semiconductor gages (KYOWA KSP-2-1 K-E4). The four foil gages are placed 355 mm from the interface with the specimen, such that two gages are in the axial direction (opposite sides of the bar) and two gages are in the transverse direction (opposite sides of the bar, rotated on the circumference 90° from the axial gages). The four gages are connected in a full Wheatstone bridge such that their signals add up. The two semiconductor strain gages are both in the axial direction (on opposite sides of the bar). The gages are connected to two opposite arms of a Wheatstone bridge and two dummy gages complete the bridge. The output from the bridges is connected through differential amplifiers (Tektronix ADA 400A) to an oscilloscope (Tektronix TDS 5034B) where the data is recorded. Both sets of gages have been calibrated by placing the section of the transmitter bar with the gages in a servo hydraulic testing machine. Since the cross sectional area of the transmitter bar is much larger than that of the specimen, the force (stress) in the transmitter bar during a test is relatively small. In a typical tensile test the output of the foil bridge is less than 1 mV while the output from the semiconductor bridge is over 20 mV. Consequently, the signal measured with the semiconductor gages has much less electrical noise than the signal from the foil gages. The force in a compression test (with metal specimens) is much larger (and increasing during the test) and the foil gages are sufficient for measuring the force.

Deformation during the test is measured directly on the specimen using a commercial Digital Image Correlation (DIC) system (VIC-2D or VIC-3D, Correlated Solutions Inc., Irmo, SC), using high-speed Photron cameras (45,000 or 75,000 fps, 0.03-0.07 mm/pixel, virtual gage length ~0.5 mm). DIC can also measure the displacement of the end of the transmitter bar and the end of the actuator.

Results from a Tensile Test

Figures 4, 5, 6 and 7 show the results from a tensile test on a specimen made of 304 stainless steel. The width (Fig. 3) of the gage section of the specimen is 2.667 mm and its thickness 0.914 mm. The force recorded by the foil and semiconductor strain gages on the transmitter bar are shown in Fig. 4. (The force signals that are presented in the paper are recorded raw data that have not been filtered or smoothed electronically or numerically.) The record from the foil strain gages has a very high frequency noise but the curve is smooth with no oscillations (ringing) and no evidence of wave reflection from the connections of the bars that make up the long transmitter bar. The record from the semiconductor gages is identical to that of the foil gages but without the electrical noise. A series of eight processed DIC images that show the full-field axial strain are shown in Fig. 5. This figure shows that the strain in the specimen gage is nearly uniform up to the strain when localization starts. The history of the strain, determined in three different ways, is shown in Fig. 6. One curve shows the engineering strain determined by the DIC software by selecting two points in the gage section (virtual extensometer). A second curve displays the average Hencky strain in a rectangular area on the surface of the specimen, and the third curve is the Hencky strain at one point on the surface of the specimen (the point where localized deformation develops at the end of the test). Figure 6 shows that the Hencky strain from the area and the point is essentially the same up to about strain of 0.35 when the localization at the point starts to develop. The engineering strain, as expected, is larger than the Hencky (true) strain (the difference starts to be noticeable at stains larger than 0.15). Up to the time where the localization starts, the true and engineering strains displayed in Fig. 6 agree with the relationship εtrue = ln(1 + εeng). The straight dashed line in Fig. 6 shows the average strain rate. It shows an essentially constant strain rate of about 75 s−1 up to the strain when the localization starts to develop. Figure 7 shows the engineering stress strain curve from this test. The solid-line and dashed-line curves are determined from the force measured by the foil and semiconductor strain gages, respectively. The stress strain curve is smooth with no ringing or large oscillations.

Fig. 4
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Tensile force measured on the transmitter bar

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Fig. 5
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Axial tensile strain measured with DIC

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Fig. 6
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Axial tensile strain during a tensile test

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Fig. 7
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Tensile engineering stress strain curves for 304 stainless steel at strain rate of 75 s−1

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Results from a Compressive Test

Results from a compression test on a specimen made of 6061-T6 aluminum are shown in Figs. 8, 9, 10 and 11. The specimen is a 5.08 mm long circular cylinder with a diameter of 4.57 mm. The force recorded during the test is displayed in Fig. 8. The figure shows a smooth curve with no oscillations which indicates that the compression wave travels through the long bar without any reflections. The actual test is taking place during the first 4 ms where the force increases monotonically. After that the actuator starts to slow down and eventually the force declines. Several DIC images during the test are shown in Fig. 9. The images show the specimen and the platens that compress the specimen. It is observed that the strain in the specimen is uniform throughout the test and that the strain in the platens is essentially zero (their cross-sectional area is much larger than that of the specimen). The strain history in the specimen is displayed in Fig. 10. The figure shows the engineering strain determined by placing a virtual extensometer on the specimen and the true strain that is determined from this strain. From the slope of these curves it can be observed that the strain rate (slope of the straight dashed line) during most of the test is nearly constant at about 85 s−1. At the very beginning of the test, the strain rate is higher (about 100 s−1) and toward the end of the test, at strain beyond 0.28, the strain rate is lower. The reduction of the strain rate in the beginning of the test is due to a slight reduction of the actuator speed upon impact. The reduction of the strain rate at large strains is due to the increase of the specimen’s cross-sectional area. The larger area applies a larger force to the transmitter bar which increases its particle velocity. Consequently, the difference between the actuator velocity and the transmitter bar velocity reduces. This is similar to the situation in a standard compression SHB experiment where the strain rate decreases during the test. The true stress strain curve from this test is shown in Fig. 11. The curve is smooth with no ringing or oscillations.

Fig. 8
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Force measured in a compression test

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Fig. 9
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DIC images from a compression test

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Fig. 10
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Axial strain measured during a compression test

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Fig. 11
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Compression stress strain curve for 6061-T6 aluminum

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Summary and Conclusions

A new device for tensile and compressive testing at intermediate strain rates ranging from about 20 s−1 to 250 s−1 is presented. The device is made up of a fast hydraulic actuator that loads (impacts) a specimen that is attached to a long bar. The operation of the device is based on the principles of the split Hopkinson bar technique, except that a hydraulic actuator replaces the incident bar and the transmitter bar is very long (40 m). Testing to appreciable amount of strain at intermediate strain rate requires significantly more time than at high strain rate. The new device provides a loading duration of up to about 15 ms, compared to about 500 μs in a typical SHB experiment. As in a SHB test, the force in the specimen is determined from the measured force in the transmitter bar. The deformation (strain) of the specimen is measured with DIC using high-speed cameras. Results from both tensile and compression tests show that the obtained stress strain curves are smooth without any oscillations (ringing) that are typical in tests conducted at these strain rates with standard hydraulic machines.