A technique for measuring the dynamic behaviour of ... - WIT Press

Computational Methods and Experiments in Material Characterisation II

153

A technique for measuring the dynamic behaviour of materials at elevated temperatures with a compressive SHPB B. Davoodi, A. Gavrus & E. Ragneau The Civil and Mechanical Engineering Laboratory (LGCGM), Institut National des Sciences Appliquées (INSA) de Rennes, France

Abstract In order to facilitate the characterization of materials at high strain rate and high temperature, this paper introduces a very simple technique for using the traditional Split Hopkinson Pressure Bar (SHPB) system at elevated temperatures, with a different geometry for the specimen. This particular specimen is used to avoid a complicated SHPB system at an elevated temperature, and to keep things as simple as possible. The limitations of the compression SHPB in use at high temperatures, the need for extra computations and the requirement for additional equipment may be reasons why there is such a scarcity of reliable flow stress data for various materials at high temperatures in the literature. In the layout of the high temperature test set up at our laboratory, in addition to the conventional compression SHPB, an induction coil heater is used as the heating system and a simple holder is used to hold the specimen at the correct position during the test. The thermal behaviour of the new specimen will make it possible to bring the cold bars in contact with the heated specimen manually and without using cumbersome mechanisms, increasing the likelihood that the experiments will be successfully carried out at the desired temperatures. This simple, easy, and practical, system has been used to test metallic materials at high temperature and high strain rates. Keywords: Compression Split Hopkinson Pressure Bar, high strain rate testing, elevated temperature, aluminium 5083, dynamic behaviour.

1

Introduction

The design of many engineering structures or structural elements when subjected to high strain rate dynamic loading is based on material data, usually in the form WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

154 Computational Methods and Experiments in Material Characterisation II of a stress-strain relationship. It is often necessary to predict the response of the structural elements in a wide range of engineering applications including high speed machining, metal forming operation, high velocity impact, explosive welding and crash-worthiness of vehicles. Materials behave differently at high strain rates and temperatures. The consideration of strain-rate and temperature dependence of material behaviour is very critical in the design of structures, because the mechanical behaviours of materials for example yield stress, ductility and strength, change under different strain-rate loadings and temperatures. Temperature has proportionately a much greater effect on material strength than strain rate if the deformation is performed at both high strain rate and high temperature conditions [1, 2]. But though its effects on high strain rate deformation have long been studied, it has not really been given the attention it deserves [1]. The Split Hopkinson Pressure Bar system is an excellent tool for studying the material strain rate sensitivity of various engineering materials that undergoes large strains at high strain rates, generally in the range of 102 to 104 s-1 compared with quasi-static loading rates of 10-3 s-1. Useful information for many materials has been extracted using this technique. In systems of SHPB currently in use, the standard cylindrical specimen is in contact with the pressure bars, and heating it creates temperature changes in the bars, which leads to changes in their mechanical characteristics, creating error in the obtained results. On the other hand, the fact that the bars are very long means that it is not practical to heat the entire system and this makes the use of this system in determination of the dynamic behaviour of materials at elevated temperatures challenging and difficult. Other systems are employed to preheat the specimen, while the incident and transmission bars are not in contact with the specimen. A mechanical or pneumatic device is needed to bring the bars in contact with the heated specimen just before the impact of the striker on the incident bar. The limitations of the SHPB in use at high temperatures, the need for extra computations and the requirement for additional equipment may be one of the reasons why there is such a scarcity of reliable information and flow stress for various materials at high temperatures in the literatures [3].

2

The Split Hopkinson Pressure Bar

The compression Split Hopkinson Pressure Bar, as shown in Fig. 1, is the most effective way to determine the characteristics of dynamic behaviour of materials under dynamic loading. The SHPB technique was initially used for a specimen loaded in compression [4]. As can be seen from the Figure 1, a conventional SHPB consists of a striker bar, an incident bar and a transmitter bar, typically made of high-strength steel. A specimen of suitable dimensions is sandwiched between the two long incident and transmitter bars which remain elastic throughout the impact. The diameter of the specimen is smaller than the bars to allow for radial expansion during plastic deformation. The interface between the specimen and the bars is lubricated in order to minimize frictional boundary restraint. The use of two pressure bars on either side of the specimen allows recording of the displacement, velocity and stress boundary conditions on each WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


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end of the specimen [5]. A gas gun launches the striker bar at a predetermined velocity at the incident bar that its impact causes an elastic compression wave to travel in the incident bar toward the specimen. The velocity of the striker just prior to impact is measured by means of electronic equipment. The duration of the pulse is equal to the round trip travel time of the longitudinal wave in the striker bar. When the impedance of the specimen is less than that of the bars, an elastic tensile wave is reflected into the incident bar and an elastic compression wave is transmitted into the transmitter bar. Electrical resistance strain gauges are the most direct, reliable method for strain measurement in high-speed testing. Therefore, strain gauges are used to measure the elastic deformations versus time in the half-bars, and these measurements are used to calculate the stress, strain and strain rate of the specimen, using one dimensional elastic wave theory. If the elastic stress pulses in the bars are no dispersive, the elementary theory for wave propagation in bars can be used. The strain gauge output signals are recorded on a PC. The basic formulas that provide the stress, strain, and strain-rate in a material specimen, can be deduced from the physical properties of the tested material. The basic formulas that provide the stress, strain, and strain-rate in a material specimen, can be deduced from the three known elastic strain in the pressure bars if two basic conditions are met. First, the wave propagation within the pressure bars must be one-dimensional and second, the specimen must deform uniformly [6].

Figure 1:

(a) Schematic outline of the compression SHPB experiment, (b) typical strain histories recorded from the strain gauge mounted on the incident and transmitter bars during an experiment, (c) typical final results in the form of true stress-true strain curve.

2.1 Strain-rate, strain and stress computation for small and large deformation (classical analysis) Nominal values of the strain rate, strain and the stress in the specimen up to any time duration are given by (available only for small deformations): WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

156 Computational Methods and Experiments in Material Characterisation II εn (t ) =

c (ε i (t ) − ε r (t ) − ε t (t )) l0

(1)

t

ε n (t ) =

c ε i (τ ) − ε r (τ ) − ε t (τ ))dτ l0 0

∫

(2)

EA [(ε i (t ) + ε r (t ) + ε t (t )] (3) 2 A0 where E and A are the Young's modulus and the cross-sectional area of the bar, c is the longitudinal elastic wave speed of the stress wave in the bar. The cylindrical specimen has initial cross-sectional area A0 and initial length l 0 . For an ideal SHPB test, the specimen should be in dynamic stress equilibrium, thus: ε i (t ) + ε r (t ) = ε t (t ) (4) In this case, the strain rate, strain and the stress are given by: c (5) εns (t ) = −2 ε r (t ) l0

σ n (t ) =

t

ε ns (t ) = −2

c ε r (τ )dτ l0 0

∫

(6)

EA (7) ε t (t ) A0 The equations (5), (6) and (7) can be used only for small deformations of the specimen. For large plastic deformations they may provide wrong results for material flow stress. Consequently, for ductile materials we must use the true values defined by [7]: ε (t ) (8) ε (t ) = n 1 − ε n (t )

σ ns (t ) =

ε (t ) = − ln[1 − ε n (t )] σ (t ) = σ n (t )[1 − ε n (t )] If the dynamic equilibrium of the specimen is valid we have: ε s (t ) ε (t ) = n s 1 − ε n (t )

ε (t ) = − ln[1 − ε ns (t )]

σ (t ) =

3

σ (t ) 1 − ε ns (t ) s n

(9) (10) (11) (12) (13)

High temperature test principle

For high temperature tests in SHPB, a heating system is needed for preheat the specimen at desired temperatures. Several types of heating devices have been developed. There are two general methods for high temperature testing: WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


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1.

Heating of the specimen and the whole pressure bars, or short portion of them adjacent to the specimen. 2. Heating only the specimen while the pressure bars are not in contact with the specimen and keeping them at room temperature. The very long pressure bars make the heating of the whole system impractical. Heating the specimen while in contact with bars also results in heating the ends of the bars. Thus, a temperature gradient is established in the two bars, which in turn affects the Young’s modulus and the density of the bars and hence variation in the stress wave propagation and potentially introduces further distortions into the measured signals. If the temperature gradient is large enough that it cannot be ignored, in order to obtain accurate stress-strain curves, it becomes necessary to correct the measured signals to compensate for the temperature dependent wave velocity and Young’s modulus by measuring the temperature distribution in the heated bars. In the second method, the cold bars automatically come in contact with the hot specimen just a fraction of a second before the impact of the striker on the incident bar or a few microseconds before the stress pulse reaches the end of the incident bar by mechanical or pneumatic devices. The transfer devices must be very fast and accurate and controlling the time between bringing the bars in contact and the arrival of the pulse is critical.

4

High temperature testing set-up for compression SHPB

4.1 SHPB apparatus A compressive SHPB system was designed and built by the P.S.F. (Procédés et Systèmes de Fabrication) team in the LGCGM. The 16 mm diameter striker, incident and transmitter bars shown in Fig. 1 had lengths of 600 mm, 2000 mm and 1300 mm, respectively. The bars were made from MARVAL 18 and have density ρ = 8000 Kg/m3, Young’s module E =186 GPa, and bar wave velocity c = 4821 m/s. The bars are designed to remain elastic throughout the test, and by virtue of their slenderness, one dimensional stress-wave theory applies to the bars to a good approximation. They were instrumented with strain gauges. The strain gauges are located respectively at 1000 mm from the impact surface on the incident bar and 650 mm from the specimen-bar interface on the transmitter bar. 4.2 Specimen geometry The specimen geometry is very important for obtaining reliable results with the SHPB system. For reducing the friction effects and the elastic punching of the bars in the compression SHPB tests using the standard cylindrical specimen, a new geometry for the specimen has been proposed by Deltort et al. [8] and was modified in the LGCGM, fig. 2. The diameter of the two ends is the same value as the diameter of the bars. The suitability of the thermal behaviour of this specimen between the times that the heat source is cut-off, until the stress pulse reaches the end of the incident bar, has been confirmed by experimental tests and

WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

158 Computational Methods and Experiments in Material Characterisation II the finite element method, and the possibility of it replacing the standard cylindrical specimen in the compression SHPB at high temperatures was investigated [9]. Figure 3 shows the drop in temperatures for the two forms of specimen at different temperatures, after contact with the bars. It can be seen from the figure that the cylindrical specimen loses its temperature very rapidly after contact with the bars, while the drop in temperature for the new shape is much less rapid. An original specimen and the deformed specimen after the high temperature compression SHPB tests are shown in Fig. 4.

Figure 2:

Figure 3:

Halter specimen.

Cooling of the specimen in contact with bars.

Figure 4:

Original and deformed specimen.

4.3 Heating system To avoid annealing and micro structural changes in the specimen which can occur at elevated temperatures, the use of the high frequency induction coil is preferable because of its rapidity in heating the specimen. Therefore, a high



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frequency induction coil is used to heat the specimen. This allows higher temperature tests for any material in less time without changing the micro structural. A semi-circular coil, whose diameter is slightly larger than that of the bars and the specimen, is utilized. Only 30 s is required to heat an aluminium specimen in the form of halter, fig. 2, to 500 °C using 50% of the full power of power supply. 4.4 Holder In experiments with compression SHPB at room temperature, a cylindrical specimen is held between two pressure bars, while in experiments at temperatures above room temperature, the specimen is not usually in contact with the bars, and during the heating of the specimen, the bars are kept away from the heat source, and the specimen. In such experiments, a holder to hold the specimen in a suitable place is therefore necessary until contact between the specimen and the bars is effected. Two types of holders may be considered: 1. Mobile Holder: the capability of this holder includes the holding of the specimen at a precise location relative to the bars and the release of the specimen after contact is made with the bars. This type of holder requires a pneumatic system or a mechanical system. 2. Fixed Holder: this type of holder holds the specimen in a precise location in the centreline of the bars throughout the test. The total time it takes to conduct the test is made up of: the heating time of the specimen, the time it takes for the two pressure bars to move towards the specimen, and the launch time of the projectile. Several methods for holding the specimen by means of a fixed holder have been utilized. Jaspers and Dautzenberg. [10] mounted the specimens in a ring discharge machined out of Inconel X750 with three springs holding the specimens at the centreline of the bars. According to Nemat-Nasser and Isaacs [11], the specimen was held between the bars by thermocouple wire and was attached by suitable wires to a sleeve. In the study by Lennon and Ramesh [12] the specimen was held between the pressure bars by means of thermocouple wire. Thermocouple wires would break apart during the experiments. In high temperature high strain-rate experiments with a halter specimen, a fixed holder, simply and precisely designed, has been used. The use of this holder has not been found to have any negative effects on the normal performance of the SHPB, and the heating system, and repeated experiments at various temperatures have demonstrated its precision and usefulness. This holder is adjustable, and does not require any exchanging in a series of experiments where dimensions of the specimen and temperatures are varied systematically. After each experiment, it can be immediately used in the next experiment. The layout of the high temperature test set up at LGCGM is shown in Figure 5. Although SHPB system does have the ability to effect contact between the cold pressure bars and the hot specimen, by means of a fast acting electropneumatic actuation system, controlled by a PC, the thermal behaviour of the halter specimen will make it possible to bring the bars in contact with the


160 Computational Methods and Experiments in Material Characterisation II specimen manually. Following the verification of the specimen and SHPB equipment, a number of dynamic uniaxial compression tests were conducted.

Figure 5:

5

The layout of the high temperature tests set up at LGCGM.

Dynamic compression experiments

5.1 Material To investigate the effects of temperature as well as strain rate, the aluminium alloy 5083 was selected as the high temperature SHPB test material. The specimen in the form of halter has density 2660 Kg/m3, Young's modulus 71 GPa, full length of 27 mm and length and diameter of central part are 5 and 9 mm, respectively (fig. 2). 5.2 Experimental procedure A specimen is held by the holder at correct position and quickly is heated up to the desired test temperature (usually 15 to 20°C higher than the test temperature), by using a high frequency induction coil. When a quasi stable temperature distribution in the specimen is achieved and just before the impact bar is projected from gas gun, the bars are brought manually and simultaneously in contact with the hot specimen. The bars were located 80 mm from the specimen during heating the specimen. The specimen temperature is continuously monitored by means of a thermocouple in contact with it. The estimated inaccuracy of the temperature measurements does not exceed ±3 °C. 5.3 Some experimental results By testing a number of specimens at the primary velocity of the striker bar of 10.6, 13.5 and 15.9 m/s at temperatures ranging from room temperature to 400 °C and recording as the incidence, reflected and transmitted strains, the WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)


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following results were achieved. In these experiments the impact velocity of the striker bar were varied so as to obtain different strain rates. A velocity equal to 10.6 m/s gives average true strain rate between 1200 and 1800 s-1, and a velocity equal to 13.5 m/s gives average true strain rate between 1800 and 2400 s-1, whereas a 15.9 m/s velocity results in average true strain rate between 2400 and 3000 s-1. The average strain rate for these tests is only an “estimate” because strain rate is not constant in this type of SHPB test. Selection of these values makes the investigation of the effects of temperature on flow stress at a constant strain-rate possible. Figure 6 shows incident, reflected and transmitted strain-time signals obtained from the dynamic compressive tests for striking velocity of 15.9 m/s at dissimilar temperatures. In Fig. 6, the reflected waves, which are related to the strain rate of the specimen, were increased as the temperature increased, while the incident waves remained at the same magnitude. The transmitted waves can be related to the flow stress of the specimen, changed as the temperature increased. Therefore, the flow stress was reduced as the temperature increased. To obtain the dynamic characterisation inverse analysis must be used; use of classic analysis can cause error. The obtained flow curves and the dynamic characterisation in these experiments will be studied in future articles.

Figure 6:

6

Incident, reflected and transmitted strain profiles obtained from high strain rate compression SHPB experiments at room temperature to 400°C (measured striking velocity is 15.9 m/s).

Conclusions

A simple technique which has been used in experiments of high strain rate at temperatures higher than room temperature was described. Using the halter WIT Transactions on Engineering Sciences, Vol 51, © 2005 WIT Press www.witpress.com, ISSN 1743-3533 (on-line)

162 Computational Methods and Experiments in Material Characterisation II specimen makes it possible to place the cold bars next to the hot specimen by hand, and without using cumbersome mechanisms, making it possible to perform the compression SHPB experiments at high temperatures with more confidence. Following the verification of the SHPB equipment, a number of dynamic uniaxial compression SHPB tests are conducted on aluminium 5083 alloys specimens. The influence of temperature and strain rate on the signals recorded by strain gauges in various experiments of Al 5083 has been presented.

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