Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 www.springerlink.com/content/1738-494x DOI 10.1007/s12206-010-1106-9 High-temperature dynamic deformation of aluminum alloys using SHPB Ouk Sub Lee 1,*, HyeBin Choi 2 and HongMin Kim 2 1 School of Mechanical Engineering, Inha University, Incheon, 402-751, Korea 2 Department of Mechanical Engineering, Inha University, Incheon, 402-751, Korea (Manuscript Received December 7, 2009; Revised June 25, 2010; Accepted September 2, 2010) ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Abstract This paper investigates the dynamic deformation behavior of two aluminum alloys, 2024-T4 and 6061-T6, using a modified split Hopkinson pressure bar (SHPB) with a pulse shaper technique at both elevated and room temperatures. An experimental strategy is proposed, and the dynamic deformation behaviors of two alloys are evaluated with the modified high-temperature SHPB apparatus. The experiments were carried out under varying strain rates and temperatures. The reflected waves modulated by the pulse shaper, the flow stressstrain relationships, the strain rates, the front- and back-ends stresses during the dynamic deformation period were measured at varying high temperatures. Experimentally obtained data were used to evaluate the parameters in the material constitutive equation, such as the Johnson-Cook (JC) constitutive model. Keywords: m-shpb (modified split Hopkinson pressure bar); Dynamic deformation behavior; Johnson-cook constitutive model; Flow stress; High strain rate; High temperature; Pulse shaper; Aluminum alloys ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1. Introduction Dynamic mechanical material properties generally differ from static values. The dynamic mechanical properties of a material are known to be highly dependent on strain, strainrate, and temperature [1]. The split Hopkinson pressure bar (SHPB) technique has been widely used to determine the mechanical properties of varying materials deformed under highstrain-rate conditions. This experimental technique measures the impact deformation response of varying materials for strain rates ranging from 10 2 s -1 to 10 4 s -1 [2]. Structural metallic materials for engineering applications frequently involve high temperatures [3, 4] under the dynamic or impact types of loadings. To analyze the dynamic deformation behavior at high-temperature ranges, modifying the classical SHPB apparatus is necessary. In this paper, a highfrequency induction heating system is introduced to raise the specimen temperatures. Some of the experimental results are presented, and the experimentally obtained data are used to evaluate the parameters in the material constitutive equation, such as the Johnson- Cook (JC) constitutive model. Parts of this paper were presented at the 9th International DYMAT conference on the Mechanical and Physical Behavior of Materials under Dynamic Loading, Brussels, Belgium, September 2009. This paper was recommended for publication in revised form by Associate Editor Youngseog Lee * Corresponding author. Tel.: +82 32 860 7315, Fax.: +82 32 860 1716 E-mail address: leeos@inha.ac.kr KSME & Springer 2011 2. Basic theory of SHPB technique The conventional SHPB technique mainly consists of a striker bar, pressure bars, a specimen placed between the incident and transmitted bars, and a compressed-air gun. A compressed-air gun is used to accelerate the striker bar to impact the incident bar, and the impact results in an incident elastic wave ( ε i ) generated at the impact face of the incident bar. The incident elastic compressive wave travels in the incident bar toward the specimen. Due to the impedance mismatch between the specimen and the pressure bars, part of the incident elastic compressive wave is reflected ( ε r ) and returns to the impact face. Once the elastic compressive wave reaches the specimen, a part of the incident pulse is reflected from the bar-specimen interface because of the material impedance mismatch. Part of the incident elastic compressive wave transmits through the specimen into the transmitted bar. The transmitted elastic compressive wave ( ε t ) emitted from the specimen travels along the transmitted bar until it hits the end of the bar. A strain gauge mounted on the incident bar measures the incident pulse ( ε i ) and reflected pulse ( ε r ), and a strain gauge mounted on the transmitted bar measures the transmitted pulse ( ε t ). Based on the one-dimensional elastic wave propagation theory with the assumption of homogeneous deformation of specimen, the engineering stress, the engineering strain, and the strain rate in the specimen can be estimated as Eqs. (1)-(3):
144 O. S. Lee et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 Fig. 1. Schematic of a modified SHPB apparatus. Fig. 2. High-frequency induction system and specimen set on the fixing system in a modified SHPB apparatus [5]. A σ = E ε i A s (1) C0 ε = 2 ε dt L r (2) C & 0 ε = 2 ε r ( t ) L (3) Fig. 3. Temperature variation of the specimen; (a) AA2024-T4, (b)aa6061-t6 [5]. where L is the initial length of the specimen, C 0 ( C0 = E ρ, ρ is the mass density of pressure bar) is wave propagation velocity; A and As are the cross-sectional areas of the pressure bar and the specimen, respectively; and E is the Young s modulus of the material of the two pressure bars [5]. 3. Experimental 3.1 High temperature SHPB apparatus The high-temperature compressive SHPB apparatus used in this study consists of a striker bar, two pressure bars, an impact-loading apparatus, a high-frequency induction heating system, and the measuring instruments. A schematic of the experimental system used in this paper is shown in Fig. 1. The incident bar, transmitted bar, and striker bar are made of STB2, a hard steel alloy having the Young s modulus of 225 GPa, and 16 mm in diameter. Each pressure bar is 1600 mm in length and the striker bar is 200 mm in length. A launching device is used to accelerate the striker bar to produce a compressive impact wave on the incident bar. The compressed air accelerates the striker bar. A Lecroy Wavepro 940 oscilloscope, Instruments Division 2311 signal conditioning amplifier, a photo sensor, and a Graphtec mini logger GL220 are Fig. 4. (a) Comparison of reflected pulse signals obtained with and without pulse shaper at a high temperature; (b) 1 mm thick copper pulse shaper before (left) and after experiment [5]. used to measure the dynamic strain outputs, the velocity of the striker bar, and the temperature of the specimen [5]. 3.2 Temperature measuring of specimen In the high-temperature SHPB experiment, the uneven high temperatures at the ends of two pressure bars in contact with the heated specimen may cause some experimental errors.
O. S. Lee et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 145 Thus, the following require close monitoring: (1) the thermal gradient occurring in the end parts of the pressure bars may change the Young s modulus. (2) This may result in a change in the mechanical impedance. (3) This may subsequently alter the configuration of reflected and transmitted waves. (4) A uniform temperature distribution over the entire specimen during the high-temperature experiment is required [6]. Due to the above reasons, a non-contact heating system is recommended. In this study, a non-contact heating system is utilized to heat the specimen to obtain the flow stress-strain relationship at high temperatures. The specimen is dynamically deformed at elevated temperatures in the high-frequency induction heating system. As shown in Fig. 2, the induction heating system is designed to heat the specimen attached to a mica plate on a Teflon bracket surrounded by the induction coil. This heating system does not affect the elastic wave propagation in the specimen. The pressure bars are located 70 mm away from the specimen during heating time to avoid the heating of the pressure bars. A required experimental temperature could be attained during a desired period using the control panel attached to the induction heating system. When the specimen reaches at the required temperature, the air gun is used to push the specimen in, in order for it to come in contact with the bars. The heating system used in this study, however, has two limitations in measuring the high temperature of specimens: (1) measuring the transient temperature at the impact moment is not possible and (2) the specimen temperature may be controlled by the period of heating time. Therefore, the profile of temperature variation should be obtained corresponding to the heating time before carrying out the main SHPB experiment. In this study, a K-type thermocouple inserted into the center of a specimen is used to measure the temperature before conducting the experiments. The transient temperatures in the specimen are measured during the heating period. The striker bar is set to impact the incident bar 1 s after the pressure bars come in contact with the specimen. The suitable experimental temperature depends on the heating period in the induction system. The temperature profiles of the specimen used in this study are shown in Fig. 3, with consideration of the contact time between the specimen and pressure bars [5]. 3.3 Lubrication Another important factor is the lubrication between the specimen and the pressure bars affecting the barreling of the specimen under dynamic compression loadings. In the hightemperature SHPB experiments, the viscosity of the lubricant and strength of the specimen decrease with the increase of the experiment temperature. Therefore, the barreling due to the lubrication may significantly affect the experimental results at high temperatures. The prevention of barreling in the specimen during a high-temperature SHPB experiment may be a very important experimental issue [6]. In this study, hightemperature EP grease with WS2 (manufactured by Rauh Chemical Co., Ltd.), which is appropriate for the temperature range from 253 to 1073 K, is used to lubricate the interface between the specimen and the pressure bars. 3.4 Specimen In this study, cylindrical compression specimens having a length of 5 mm and a diameter of 10 mm are used. The specimen dimensions are chosen to minimize the longitudinal and the radial inertia effects by noting that under LD= 3ν s 2 (where L is length, D is diameter, and ν s is the Poisson s ratio of the specimen) conditions, the inertia effects could be minimized even under non-uniform strain rate conditions [7]. 3.5 Pulse shaper A material for the pulse shaper is selected so that the pulse shaper deforms plastically in a designed manner upon impact, effectively controlling the shape of the incident pulse in the incident bar. The gradually increasing pulse shaper area upon impact of the striker bar allows greater momentum to transfer from the striker bar to the incident bar, significantly increasing the rising time of the incident pulse. The proper choice of the pulse shaper material and dimensions control the profile of the incident pulse. Multiple experiments are necessary to select the proper material and geometry of a pulse shaper. In this paper, copper with a thickness of 1 mm and a diameter of 10 mm is used as pulse shaper. The reflected signals with and without pulse shaper and the geometries of the pulse shaper before and after experiment are shown in Fig. 4 (a) and Fig. 4 (b), respectively [5, 7]. Approximately 10% signal fluctuation is achieved by the pulse shaper compared with the signals of 100% fluctuation without the pulse shaper. 4. Johnson-Cook constitutive model The Johnson-Cook (JC) model was introduced in 1983 and was primarily intended for application in the computational work. The JC model was initially formulated by gathering test data at different strain rates and temperatures for a wide range of test procedures [6, 8]. In this paper, the JC model is used to model the material behavior; however, the JC model is known to have some merits and demerits, as investigated by Dipti et al. [9]. The JC model defines the Ludwik law as a multiplicative law of three uncoupled terms. These terms are dependent on the plastic strain, the strain rate and the temperature, as shown in Eq. (4); σ [ + n A Bε ] & ε T T + 0 1 C ln 1 & ε 0 Tm T0 = m where A is the quasi-static yield stress at a reference strain rate and temperature; B is the modulus of strain hardening, n is the strain hardening exponent; C is the strain rate hardening constant; ε& 0 is the reference strain rate; T is the experimental temperature; T0 is the reference temperature; Tm is the melting temperature; and m is the thermal softening constant [7]. (4)
146 O. S. Lee et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 Fig. 5. Strain rate and the front- and the back-end stresses with respect to deformation time (a) 2024-T4 at a reference temperature; (b) 2024-T4 at a high temperature; (c) 6061-T6 at a reference temperature; (d) 6061-T6 at a high temperature [5]. 5. Results and discussions 5.1 Pulse shaper and stress equilibrium In this study, the high-temperature SHPB technique with a pulse shaper is employed to investigate the dynamic flow stress-strain relationship for two aluminum alloys, namely, 2024-T4 and 6061-T6 specimens, at varying elevated temperatures under a state of dynamic stress equilibrium during deformation. The material and geometry of the pulse shaper are shown to be significantly modulated, and the rising time and duration of the steady strain-rate are increased significantly with the help of the pulse shaper. The dynamic stress equilibrium in the specimen during a high-temperature SHPB experiment has been achieved by the modulation of the strain signals of the specimen. Fig. 5 shows the strain rate and stress histories of the front-end and backend of the specimen at both room and high temperatures. The front-end indicates the surface of specimen contacting with an incident bar, and the back-end indicates the surface of specimen in contact with a transmitted bar. In Fig. 5(b) and Fig. 5 (d), the larger discrepancies between the front-end and the back-end stresses at high temperatures are noted. The effect of contact time at high temperatures is noted in the early deformation period. This phenomenon, commonly occurring at high-temperature conditions, may be caused by the nonhomogeneous temperature distribution in the specimen, resulting from the limited heat conduction between the pressure bars and the specimen. A short delay in initiating the experiments after heating the specimens may accomplish the coincidence of the front-end and back-end stresses. In our experimental procedure, the contact time between specimen and pressure bars is minimized to reduce the effect of the temperature drop of the specimen on the dynamic deformation behavior. This means that the non-equilibrium state in the early deformation period may be negligible to the total deformation of specimen during this high temperature SHPB experiment [8, 10]. 5.2 The flow stress-strain relationship The dynamic flow stress-strain curves with strain rates from about 1300s -1 to 4300s -1 at elevated temperatures for the specimens are summarized in Fig. 6. The dynamic flow stressstrain curves at room temperature show a higher level of flow stresses than the flow stress-strain curves at high temperatures, as expected. The flow stress and the strain rate increases with the increase of temperature. Generally, the flow stresses increase with the increase of strain rate at room temperature due to the strain rate hardening effect, and the variation of the strain rate significantly affects the slope of plastic flow stress curves [11]. However, Fig. 6 shows that the flow stress is not obviously increased with the increase of strain rate at high temperatures. That is, the thermal softening effect is increased under the high-temperature condition [5]; however, some discrepancies are evident be-
O. S. Lee et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 147 Table 1. Parameters in the JC model for aluminum alloys. Material 2024-T4 6061-T6 A (MPa) 390 340 B (MPa) 1980 1018 N 0.4890 0.7789 C 0.0140 0.0568 M 0.6000 0.2526 Reference strain rate 0.0001 s -1 Reference temperature 298 K Melting point 775 K 855 K In this paper, we used a high-temperature SHPB apparatus and a pulse shaper technique [5] were used. The dynamic deformation behavior of aluminum alloys such as 2024-T4 and 6061-T6 under dynamic compressive loading conditions was evaluated at high temperatures using a modified pulse shaper SHPB technique with a high-frequency induction heating system. The experimental data shown in Fig. 6 were used to determine the parameters in the Johnson-Cook (JC) constitutive model, as shown in Table 1. The experimental results are as follows: (1) The strain rate and the high temperature significantly affect the plastic flow behavior. The effect of temperature on the plastic flow increases at higher temperatures, and its effects seem to be more pronounced than that of the increased strain rates. (2) A modified pulse shaper SHPB technique allows the acquisition of better dynamic stress equilibrium in the specimen at high temperatures, except in the early deformation period ranging from 20 to 60 microseconds. (3) The increased temperatures of the specimens reduce the strain rate hardening with pronounced sensitivity. (4) Further studies investigating the mismatch between the front-end and the back-end stress at a high temperature are required. Furthermore, the non-homogeneous temperature distribution in the specimen and ends of pressure bars should be improved through a well-equipped experimental procedure. Acknowledgment This work was supported by the Inha University Research Grant. References Fig. 6. Experimental flow stress-strain relationship under the different strain rates and experimental temperatures and Fit to Johnson-Cook model (a) AA2024-T4; (b) AA6061-T6. tween the experimental and the fitted curves at temperatures higher than 573 K, as shown in Fig 6 (b). Further investigation is needed regarding this matter. 6. Conclusions [1] H. Kolsky, Stress Wave in Solids, Dover Publications, Inc, New York, USA (1963). [2] O. S. Lee, G. H. Kim, M. S. Kim and S. W. Hwang, Dynamic deformation behavior of aluminum alloys under high strain rate compressive/tensile loading, Proc. of the KSME 2000 Fall Annual Meeting (2000) 268-273. [3] D. Gerlich, and E. S. Fisher, The high temperature elastic moduli of aluminum, J. Phys.Chem.Solid, 30 (1969)1197-1205. [4] Y. Y. Cho and H. S. Kim, State dependence of activation energies for high temperature creep of Al7075 alloy, KSME journal, 17 (1993)131-140. [5] O. S. Lee, S. W. Hwang, H. B. Choi, D. H. Kim and H. M. Kim, Dynamic deformation of aluminum alloys ay high temperature by using SHPB techniques, Proc. of 9th International Conference on the Mechanical Physical Behavior of Materials under Dynamic Loading (2009) 443-448. [6] S. W. Seo, O. K. Min and, H. M. Yang, Constitutive equation for Ti-6Al-4V at high temperatures measured using the SHPB technique, International Journal of Impact Engineering, 31 (2005) 735-754. [7] G. T. Gray, ASM Handbook Vol. 8 Mechanical Testing and Evaluation, ASM International Material Park, USA (2000). [8] Y. Li, Y. Guo, H. Hu and Q. Wei, A critical assessment of high temperature dynamic mechanical testing of metals,, In-
148 O. S. Lee et al. / Journal of Mechanical Science and Technology 25 (1) (2011) 143~148 ternational Journal of Impact Engineering, 36 (2009) 177-184. [9] D. Samantaray, S. Mandal and A. Bhaduri, A comparative study of Johnson-Cook, modified Zerilli-Armstrong and Arrehenius type constitutive models to predict evaluate temperature flow behavior in modified 9Cr-1Mo steel, Computational Materials Science, Available online 25, October (2009). [10] A. S. Khan and R. Liang, Behavior of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling, International Journal of Plasticity, 15 (1999) 1089-1109. [11] I. K. Lee, H. M. Yang and O. K. Min, The True Stress- Strain Relation of Aluminum Alloys in the SHPB Tension Test, KSME A, (2000) 7917-1922. Ouk Sub Lee received his Ph.D. degree in Mechanical Engineering from the University of Washington, USA, in 1983. Dr. Lee is currently a Professor at the School of Mechanical Engineering at Inha University in Incheon, Korea. Dr. Lee s research interests include dynamic fracture and reliability and failure analysis of engineering structures.