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1 Pothnis, Jayaram R., Y. Perla, H. Arya and N.K. Naik High strain rate tensile behavior of aluminum alloy 7075 T651 and IS 2062 mild steel, ASME Journal of Engineering Materials and Technology, 133: paper number , pp 1-9. Post-print version MATS , Naik, Page 1

2 High Strain Rate Tensile Behavior of Aluminum Alloy 7075 T651 Abstract and IS 2062 Mild Steel Jayaram R. Pothnis 1, Yernamma Perla 2, H. Arya 3, N. K. Naik *, 4 Aerospace Engineering Department Indian Institute of Technology Bombay Powai, Mumbai , India * Corresponding author 4 Tel.: (+91-22) ; fax: (+91-22) nknaik@aero.iitb.ac.in 1 jpothnis@gmail.com 2 yernindh_p_h@yahoo.co.in 3 arya@aero.iitb.ac.in Background. Investigations on the effect of strain rate on tensile properties of two materials, namely, aluminum alloy 7075 T651 and IS 2062 mild steel are presented. Method of Approach. Experimental studies were carried out on tensile Split Hopkinson Pressure Bar (SHPB) apparatus in the strain rate range of 54 to 164 per sec. Uncertainty analysis for the experimental results is presented. Johnson-Cook material constitutive model was applied to predict the tensile yield strength of the tested materials at different strain rates. Results. It is observed that the tensile yield strength is enhanced compared with that at quasi-static loading. During tensile SHPB testing of the specimens, it was observed that the peak force obtained from the strain gauge mounted on the transmitter bar is lower than the peak force obtained from the strain gauge mounted on the incident bar. An explanation to this is provided based on increase in dislocation density and necking in the tested specimens during high strain rate loading and the consequent stress wave attenuation as it propagates within the specimen. The fracture behavior and effect of high strain rate testing on microstructure changes are examined. Conclusions. The peak force obtained based on strain gauge mounted on the transmitter bar is lower than the peak force obtained based on strain gauge mounted MATS , Naik, Page 2

3 on the incident bar. There is an increase in tensile yield strength at high strain rate loading compared with that at quasi-static loading for both the materials. The enhancement is more for IS 2062 mild steel than that for aluminum alloy 7075 T651. In the range of parameters considered, the strength enhancement factor was upto 1.3 for aluminum alloy 7075 T651 and it was upto 1.8 for IS 2062 mild steel. Generally, there was a good match between the experimental values and JC model predictions. Keywords: Tensile high strain rate behavior, Johnson-Cook material model, Stress wave attenuation, Aluminum alloy 7075 T651, IS 2062 mild steel, Uncertainty analysis 1 Introduction Over the years, different engineering materials are used for a variety of structural applications. During processing or over their service life, these engineering materials / structures undergo different loading conditions. For their effective use, they should be able to withstand different loading conditions. High strain rate loading is one of the critical conditions. Typical examples of high strain rate loading are: forging, high velocity machining, high energy rate forming, crash landing, collision and high velocity impact. In order to design structures used under such extreme loading conditions, the mechanical deformation behavior of materials should be known. It is well known that the mechanical behavior of most materials depends upon applied strain rate. While Izod / Charpy test and drop weight test are used for the evaluation of mechanical properties at intermediate strain rates, Split Hopkinson Pressure Bar (SHPB) or Kolsky apparatus is widely used for the study of mechanical behavior of materials at high strain rates. SHPB apparatus works based on onedimensional wave propagation theory in elastic bars. MATS , Naik, Page 3

4 After Kolsky [1] introduced SHPB technique for dynamic testing of specimens, it has become a widely used experimental technique to test the materials at high strain rates. The details regarding SHPB technique are presented in [2-5]. Considering the importance of this discipline, i.e., the mechanical behavior of materials at high strain rate loading, there are typical studies on this subject. But the information available on this subject is not exhaustive. Hence, further studies are planned on high strain rate behavior of typical materials under tensile loading. The tensile split Hopkinson pressure bar was originally introduced by Harding et al [6] and later by Lindholm et al [7]. Since then, there are typical studies on high strain rate behavior of different materials [8-30]. Based on the literature survey, an attempt is made to consolidate all the observations on the tensile behavior of materials under high strain rate loading. Accordingly, ranges of property change factors are worked out for different materials and are presented in Table 1. Property change factor is defined as the ratio of property at high strain rate (HSR) loading to the property at quasi-static (QS) loading. If the property at high strain rate loading is more than the property at quasi-static loading, property change factor would be more than one. For such cases, property change factor is termed as property enhancement factor. There may be cases where the property change factor could be less than one. This indicates that, for such cases, the property at high strain rate loading would be less than that at quasi-static loading. It can be noted that the property change factor is generally more than one for tensile strength. The results are presented mainly for different aluminum alloys and steels. The property change factor for tensile strength varies in the range of 0.96 to 1.5. High strain rate tensile properties are also given in Table 2. Comparing with the quasi-static tensile strength, it can be seen that the tensile strength is enhanced at high strain rate loading. MATS , Naik, Page 4

5 Comparing with the ultimate tensile strain values at quasi-static loading, it can be observed that the ultimate tensile strain decreases at high strain rate loading. Only two early papers by Harding et al [6] and Lindholm et al [7] indicate that the ultimate tensile strain increases at high strain rate compared with those at quasi-static loading. The objective of the present study is to determine the behavior of aluminum alloy 7075 T651 and IS 2062 mild steel under high strain rate tensile loading. Tensile yield strength and yield strain were evaluated and are presented. Quasi-static properties were also evaluated and are presented for comparison. Force versus time plots based on strain gauge signals obtained from incident bar and transmitter bar are derived and compared. During tensile testing of specimens, it was observed that the peak force obtained from the strain gauge mounted on the transmitter bar is lower than the peak force obtained from the strain gauge mounted on the incident bar. The explanation for this is provided later. Further, the Johnson-Cook (JC) model is employed for the prediction of high strain rate tensile yield strength for the tested materials. The experimental and predicted test results are compared. MATS , Naik, Page 5

6 Table 1 Behavior of materials under high strain rate tensile loading: property change factor (from literature) Material Strain rate, έ (per sec) Quasi-static properties ult (MPa) E (GPa) ult (%) Property change factor, HSR / QS for ult for E for ult Molybdenum х10-3 y RR77 aluminum Al Al 5454 H Al 6351 T Reference Harding et al (1960) Lindholm et al (1971) Al 6061 T Al 6061 T Al 7075 T Al 7017 T Rodriguez et al (1994) AISI stainless steel Steel S15C Itabashi and Kawata Steel S55C (2000) Brass y Wang et al (2004) Steel X6CrNiNb1810 Solomos et al Steel MnMoNi55 (2004) Steel 26NiCrMo Mild steel Beynon et al C - Mn steel (2005) Dual phase steel NiCrMoV y Rohr et al (2005) AA5182 Al Smerd et al AA5754 Al (2005) y yield strength MATS , Naik, Page 6

7 Table 2 High strain rate behavior of materials: tensile loading (from literature) Material Strain rate, έ (per sec) ult (MPa) High strain rate properties E (GPa) ult (%) Reference Al 6061-T Nicholas Al 7075-T (1981) 321 stainless steel Ellwood et al (1982) Al 6061-T Staab and Gilat (1991) Alminum alloy LF Li et al (1993) Copper sheet Tantalum sheet Al 2024-T Al 6061-T Al 7075-T PMMA AerMet 100 * Es-1c * HP * Modified 4340 * LeBlanc and Lassila (1993) Lee and Kim (2003) Boyce and Dilmore (2009) * Ultrahigh-strength steels 2 Tensile Split Hopkinson Pressure Bar Apparatus Different configurations of tensile SHPB apparatus are used over the years [2-5, 25]. Schematic arrangement of the tensile SHPB apparatus and the photograph of the apparatus used for the present study are given in Fig. 1. The main parts of the apparatus are: incident MATS , Naik, Page 7

8 bar, transmitter bar, high pressure propelling mechanism, specimen holders and the support stand. Working of tensile SHPB apparatus as given in Fig. 1 is presented in [25]. The diameter of the incident and transmitter bars is 16 mm and the length is 2000 mm each. The bars are made of SUS440C martensite stainless steel with Young s modulus of 203 GPa and density of 7667 kg/m Experimental Technique and Data Acquisition. The entire strain / deformation history within the specimen was obtained by taking measurements along the incident and transmitter bars from the strain gauges with the help of amplifier and oscilloscope. From these signals and using one-dimensional wave propagation theory, strain rate versus time, strain versus time, stress versus time and stress versus strain plots for the specimen were obtained [2,4,25]. 2.2 Specimen Configuration. The arrangement of specimen and holders is presented in Fig. 2. For the experimental study, end-threaded cylindrical specimens were used. Schematic of a typical end-threaded cylindrical specimen is shown in Fig. 2a. The gauge length l S is 15 mm and diameter d S of 4 mm and 4.5 mm were used. Right-handed and left-handed threads were provided on either side of the specimens for easy mounting of the specimen on to the holders. 3 Theory The design of SHPB is based on one-dimensional wave propagation in elastic bars which deals with the motion of particles in longitudinal direction. The one-dimensional system can ideally be considered to be of infinite length and negligible diameter. Since it is MATS , Naik, Page 8

9 not possible in practice, the theory is adopted with certain approximations. The analytical relations to calculate strain rate, strain and stress as a function of time in the specimen in SHPB testing are [2, 4, 25], where, Strain rate, ( t ) (2 C O/ l S ) R( t ) (1) S t Average strain, ( t) (2 C / l ) ( t). dt (2) S O S R O A Stress, ( ) B S t E T ( t) (3) A S C O is elastic wave velocity in the bars, l S is specimen gauge length, A B is crosssectional area of the bars, A is cross-sectional area of the specimen, E is Young s modulus S of the bars, R is reflected strain pulse, T is transmitted strain pulse and t is time duration. 4 Calibration of Tensile SHPB Apparatus For commissioning and assessing the accuracy of SHPB apparatus, calibration was carried out first. The incident and transmitter bars were joined together using the set of threaded holders with end-threaded cylindrical calibration specimen (Fig. 3a). Calibration details are given in [25]. The force history obtained based on the strain gauge mounted on the incident bar (F 1 ) and that obtained based on the strain gauge mounted on the transmitter bar (F 2 ) were derived and compared. It was noted that the forces F 1 and F 2 match very well throughout the duration of impact. This indicates that the stress states within the incident bar and transmitter bar are exactly the same. This ensures that the tensile SHPB apparatus is perfectly aligned and friction free. MATS , Naik, Page 9

10 5 Experimental Studies Experimental studies were carried out on high strain rate behavior under tensile loading using SHPB apparatus. Studies were carried out in the strain rate range of 54 to 164 per sec. Studies were also carried out at quasi-static loading for comparison. Strain rates used and tensile properties are given in Figs. 4-8 for aluminum alloy 7075 T651 and Fig. 9 for IS 2062 mild steel. The typical results are also given in Table 3. Table 3 Strain rate effect on tensile properties (present experimental study) Material Aluminum alloy 7075 T651 Strain rate, έ (per sec) Yield stress (MPa) Yield strain, (%) Quasi-static Quasi-static IS 2062 Mild steel Aluminum Alloy 7075 T651. Strain gauge signals obtained on oscilloscope during testing are presented in Fig. 4a. The durations of the incident and reflected signals are represented by a 1 a 2 and a 3 a 4 respectively. In the present case, a 1 a 2 = 460 sec and a 3 a 4 = 470 micro sec. Force versus time plots are obtained from the strain gauge signals and are presented in Fig. 4b. Force history on the incident bar is plotted based on strain gauge signal I+R, whereas force history on the transmitter bar is plotted based on strain gauge signal T. MATS , Naik, Page 10

11 Here I, R and T refer to incident, transmitted and reflected signals. The force history obtained based on signal I+R is referred to as F 1 and the force history obtained based on signal T is referred to as F 2 for further discussion. Force F 1 would be acting on the interface between the incident bar and the specimen whereas force F 2 would be acting on the interface between the transmitter bar and the specimen. It may be noted that the forces F 1 and F 2 are not matching (Fig. 4b). The magnitude of peak force F 2 is significantly lower than the magnitude of peak force F 1. An explanation to this behavior is provided based on increase in dislocation density and necking in specimens during high strain rate loading and the consequent stress wave attenuation as it propagates within the specimen. Sil and Varma [31] studied combined effect of grain size and tensile strain rate on the dislocation substructures and mechanical properties in pure aluminum. They studied with three grain sizes of 70, 278 and 400 μm and showed that there is a continuous decrease in cell size with increase in percentage strain for all the three grain sizes, irrespective of the strain rate. They further observed that with an increase in strain, there is an increase in dislocation density and decrease in cell size. Cordero and Labbe [32] observed that the deformation evolved from weakly to strongly heterogeneous during high strain rate tensile loading. Their studies were based on monitoring the strain rate progression in an aluminum sample undergoing tensile deformation by electron speckle-pattern interferometry. Lee and Liu [33] studied the effect of compressive strain rate on the dynamic flow behavior of different steels. They observed that with increasing strain rate, the number of dislocations inside the cell walls increases and the size of individual dislocation cells decreases. As the stress wave propagates and encounters a boundary between two materials, it would partly transmit and partly reflect. The boundary can be either because of impedance mismatch or area mismatch. Because of transmission and reflection of the incident stress MATS , Naik, Page 11

12 wave at the boundaries, attenuation of the incident stress wave would take place. At high strain rate loading, as the strain increases the dislocation density increases [31-33]. Hence, the incident stress wave would encounter more boundaries as the strain increases leading to more attenuation of the incident stress wave. Figures 3b-3d show deformation behavior of specimens during high strain rate tensile loading. Figure 3a shows end-threaded cylindrical calibration specimen with a set of holders. The calibration specimen and set of holders are made using the same material as that of the incident and transmitter bars and with the same diameter. There would not be necking in the calibration specimen. On the other hand, with aluminum alloy or mild steel specimens, necking of the specimen would take place. Figure 3b shows end-threaded cylindrical specimen held in a set of holders. Necking of the specimen during tensile loading is shown in Fig. 3c. Idealized representation of necked specimen is shown in Fig. 3d. It can be seen that this is a stepped specimen. Since there is cross-sectional area variation along the gauge length of the specimen for necked specimens, stress wave attenuation would take place as it propagates within the specimen. Figure 5 shows a typical aluminum alloy specimen subjected to high strain rate loading. The specimen has undergone deformation partially with specimen necking visible. Since there is cross-sectional area variation along the gauge length of the specimen for necked specimens, stress wave attenuation would take place as it propagates within the specimen. It may be noted that the necking is not at the centre, it is towards incident side. As can be seen from Fig. 4b, F 2 is lower than F 1. An explanation to this has been provided based on increase in dislocation density and necking in specimens during high strain rate loading and the consequent stress wave attenuation as it propagates within the specimen. The force F 1 at the time of yielding (52 micro sec) is KN while the force F 2 at the same MATS , Naik, Page 12

13 time is 8.66 KN. The tensile yield strength reported further is based on F 2. This is to obtain conservative estimate of tensile properties. Time versus strain rate, strain and stress plots are given in Fig. 6. These plots are obtained based on strain gauge signals and Eqs. (1-3). Point B in Fig. 6 indicates the stress, strain rate and strain pertaining to the yield point. It can be noticed that the strain rate increases gradually and no visible peak is observed before the strain rate corresponding to yield point is reached. The results are reported for a strain rate of 109 per sec. A typical true stress true strain plot is presented in Fig. 7. The stress-strain plot can be subdivided into two regions. Region one represents the behavior of the material until the yield point is reached (upto point B). Region two represents the behavior of the material during plastic deformation and final failure (after point B). The yield strain in this case is 0.36%. In this case the final failure also is observed to takes place at the same stress level. The strains presented in Table 3 are with respect to the yield point of the material. For comparison, tensile properties at quasi-static loading are also presented in Table 3. From Table 3 and Fig. 8, it can be observed that the tensile yield strength is enhanced at high strain rate loading compared with that at quasi-static loading. The property enhancement factor for tensile yield strength varies from 1.2 to 1.3 corresponding to strain rate varying from 77 to 164 per sec. Further, in the strain rate range considered, there is an increase of tensile yield strength as the strain rate is increased. However, no clear trend regarding the yield strain is observed. 5.2 IS 2062 Mild Steel. High strain rate tensile testing of IS 2062 mild steel specimens was also carried out on tensile SHPB apparatus. Evidence of necking before ultimate failure was clearly observed in this case too. Even during mild steel testing, difference between F 1 MATS , Naik, Page 13

14 and F 2 was observed. Stress attenuation in mild steel specimens can also be explained on the basis of same reasons as in aluminum alloy 7075 T651 specimens. In the case of IS 2062 mild steel, qualitative behavior was similar to that of aluminum alloy 7075 T651. From Table 3 and Fig. 9, it can be observed that high strain rate tensile yield strength of IS 2062 mild steel is enhanced as compared to that at quasi-static strain rate. In the strain rate range considered, there was an increase of tensile yield strength as the strain rate increased. However, no clear trend regarding the yield strain was observed. The property enhancement factor for tensile yield strength in case of IS 2062 mild steel varies from 1.5 to 1.8 corresponding to strain rate varying from 54 to 163 per sec. 5.3 Comparison. From Figs. 8, 9 and Table 3, it can be observed that the qualitative behavior of aluminum alloy 7075 T651 and IS 2062 mild steel is nearly the same. The tensile yield strength increases compared with that at quasi-static loading. But the increase in tensile strength at high strain rate loading is more for IS 2062 mild steel than for aluminum alloy 7075 T651. The type of crystal structure also influences deformation behavior [34]. While IS 2062 mild steel has Body Centered Cubic (BCC) crystal structure, aluminum alloy 7075 T651 has Face Centered Cubic (FCC) structure. Though both the crystal structures are influenced by strain rate, the increase is higher in case of BCC metals as compared to FCC metals [34]. 5.4 Uncertainty Analysis. Strain rate versus experimental tensile yield strength plots for aluminum alloy 7075 T651 and IS 2062 mild steel are presented in Figs. 8 and 9, respectively. For each case, experiments were conducted at four sets of strain rates. For each strain rate, 5-6 specimens were tested. MATS , Naik, Page 14

15 During SHPB testing, in spite of proper alignment of the SHPB apparatus and calibration, there can be scatter in yield strength and intended strain rate. The possible reasons are: valve operations for propelling the striker bar; specimen geometry, machining conditions and alignment; vibration and friction. Scatter band of tensile yield stress is indicated by vertical lines in Figs. 8 and 9 at four sets of strain rates. There was scatter of strain rates also for each set of intended strain rate. This scatter band is indicated by horizontal lines. For the case of aluminum alloy 7075 T651, and first set of strain rate, the tensile yield strength varied from 591 MPa to 637 MPa whereas the strain rate varied from 77 per sec to 85 per sec. For ascertaining the accuracy of SHPB test results, uncertainty analysis was carried out. The uncertainty analysis methodology [35, 36] used is presented in Appendix. Sample calculations are also presented. Combined standard uncertainty, u c is 7.87 MPa for aluminum alloy 7075 T651. Expanded uncertainty with confidence level of 95 % is, U = MPa. Compared with high strain rate yield strength of 684 MPa, combined standard uncertainty is 1.15 %, and expanded uncertainty is 2.3 %. Combined standard uncertainty, u c is MPa for IS 2062 mild steel. Expanded uncertainty with confidence level of 95 % is, U = 32.1 MPa. Compared with high strain rate yield strength of 921 MPa, combined standard uncertainty is 1.7 %, and expanded uncertainty is 3.4 %. MATS , Naik, Page 15

16 6 Fracture Features and Microstructure Observations The aluminum alloy 7075 T651 and IS 2062 mild steel specimens tested under quasistatic and high strain rate conditions were examined under a Hitachi make, S-3400 N model Scanning Electron Microscope (SEM) to observe the fracture features. Figure 10 presents SEM photographs of the fracture surface of an aluminum alloy 7075 T651 specimen subjected to quasi-static tensile test. Specimen necking was observed with the fracture surface appearing rough and irregular. The fracture could be categorized as ductile. Closer observation of the surface revealed many dimples and micro voids. Figure 11 presents SEM photographs of the fracture surface of an aluminum alloy 7075 T651 specimen tested under high strain rate loading. The fracture surface reveals a large region with smooth surface. In areas around the smooth surface dimples were seen. The presence of the smooth area that does not exhibit any deformation characteristics indicates brittle fracture. Hence, this could be termed as a combination of both ductile and brittle fracture. This also indicates that a complete transition from ductile to brittle fracture can be expected at even higher strain rates. Photomicrographs of aluminum alloy 7075 T651 specimens subjected to quasi-static and high strain rate testing are presented in Figs. 12 and 13, respectively. Keller s reagent (190 ml distilled water, 5 ml nitric acid, 3 ml hydrochloric acid, 2 ml hydrofluoric acid) was used to etch the polished specimen surfaces. An optical microscope (Olympus make, GX51 model) was used to examine the surfaces. The measurement of the grain sizes at a magnification of 500X revealed that for the quasi-static specimen, the average grain dimensions were 14 μm and 14.5 μm in horizontal and vertical directions respectively. At the same magnification, the average grain dimensions were 13.5 μm and 13.3 μm in horizontal and vertical directions for the specimen tested at high strain rate. Therefore, a reduction in MATS , Naik, Page 16

17 grain size is observed during high strain rate testing. These findings support the stress wave attenuation concept explained on the basis of grain size reduction at high strain rate. In case of IS 2062 mild steel specimens, ductile fracture was observed at both quasistatic and high strain rates. 2 % Nital etchant solution (nitric acid 2 % by volume, methyl alcohol 98% by volume) was used to study the grain structure. The average grain size for the quasi-static specimen was 12.3 μm and 12.1 μm in the horizontal and vertical directions, respectively. For high strain rate specimen, the average grain size was 9 μm in horizontal direction and 8.8 μm in the vertical direction at the same magnification. Therefore, even for this material a reduction in grain size is observed at high strain rate as compared to that quasistatic test conditions. Further inference follows as in the case of aluminum alloy 7075 T Material Constitutive Models In the area of material testing, development and use of constitutive models for predicting material properties has been a common practice. In the area of high strain rate characterization of metallic materials, constitutive models like Johnson-Cook (JC), revised Johnson-Cook (RJC) and Zerilli-Armstrong are available [37-39]. Johnson and Cook [37] presented an empirical model to determine flow stress considering the effects of strain, strain rate and temperature. The JC model was of the form given below: n m C1 C2 1 C3 ln 1 T (4) where σ is Von Misses flow stress, ε is the equivalent plastic strain, / 0 is the dimensionless plastic strain rate for 0 = 1 per sec and T* is the homologous temperature given by T* = (T T T Room ) / (T Melt T Room ). Here T T, T Melt, T Room are the test temperature, MATS , Naik, Page 17

18 material melt temperature and room temperature, respectively. C 1, C 2, C 3, n and m are material constants determined using experimental data. At higher strain rates (> 10 3 per sec), in case of ductile materials, the increase in the flow stress is observed to be much higher than that as predicted by the JC model. Hence, for increasing the sensitivity to strain rate of the JC model at higher strain rates, a revised JC model was proposed by Rule et al [38]. The revised JC model is given below. 1 1 C5 ln C5 n m C1 C2 1 C3 ln C4 1 T (5) Here C 1, C 2, C 3, C 4, C 5, n and m are material constants. Here C 4 and C 5 are additional material constants and this model provides for enhanced strain rate dependence of flow stress by introducing an additional strain rate dependence term 1/ (C 5 ln ε *). C 5 is the logarithm. of a critical strain rate. When the strain rate is equal to the critical value, the value of stress becomes infinity. Since this is not possible in practice, the model proposes a maximum value for strain rate dependence term. This is given by a non dimensional constant C 6 whose value is given by the relation mentioned below: ln C3 C4 C 5 ln C 5 C 6 (6) Using the constants, flow stress of different metallic materials can be determined at different strain rates, temperatures and strains. 7.1 Prediction of Tensile Yield Strength Using JC Model. The tensile yield strength of the tested materials was determined using the JC model. Past literature [40, 41] yielded the JC model material constants. Table 4 gives details about the JC model material constants used for the two materials. The yield strength was determined at different strain rates and for a constant strain value for each of the two materials. Eqs. (7) and (8) as given below were MATS , Naik, Page 18

19 used for aluminum alloy 7075 T651 and IS 2062 mild steel materials, respectively. Using Eqs. (7) and (8), yield strength was obtained at different strain rates. From the plot of rate of change of local modulus versus strain for different strain rates, the strain for predicting the yield strength was identified. For aluminum alloy 7075 T651, strain value used was 0.6 % and for IS 2062 mild steel it was 0.7 % ln 1 T (7) ln 1 T (8) Table 4 Johnson-Cook material constants Johnson-Cook model material constants Material C 1 (MPa) C 2 (MPa) C 3 m n Ref. Aluminum Brar et al alloy (2009) T651 Park et al Mild Steel (2005) Figure 8 presents the predicted yield strength versus strain rate for aluminum alloy 7075 T651. The experimental results are also given for comparison. Both the plots are closer to each other. Figure 9 present a comparison of the predicted and experimental values in case of IS 2062 mild steel. However, in case of mild steel, the JC model material constants for the material tested were not available and general values available for mild steel from literature MATS , Naik, Page 19

20 were used. This possibly explains the greater deviations in mild steel results between experimental and predicted as compared to that of aluminum alloy 7075 T Conclusions High strain rate behavior under tensile loading is studied for aluminum alloy 7075 T651 and IS 2062 mild steel. Results are presented based on experimental and JC model studies. General observations are: The peak force obtained based on strain gauge mounted on the transmitter bar is lower than the peak force obtained based on strain gauge mounted on the incident bar. This is explained based on increase in dislocation density and necking in aluminum alloy 7075 T651 and IS 2062 mild steel specimens during high strain rate loading and the consequent stress wave attenuation as it propagates within the specimen. There is an increase in tensile yield strength at high strain rate loading compared with that at quasi-static loading for both the materials. The enhancement is more for IS 2062 mild steel than that for aluminum alloy 7075 T651. In the range of parameters considered, the strength enhancement factor was upto 1.3 for aluminum alloy 7075 T651 and it was upto 1.8 for IS 2062 mild steel. Generally, the experimental and JC model prediction tensile yield strength values are comparable to each other. Combined standard uncertainty is 1.15 %, and expanded uncertainty is 2.3 % for aluminum alloy 7075 T651 for the experimental results presented. Combined standard uncertainty is 1.7 %, and expanded uncertainty is 3.4 % for IS 2062 mild steel for the experimental results presented. MATS , Naik, Page 20

21 Appendix: Uncertainty Analysis Uncertainty analysis methodology [35, 36] is presented below for the experimental results obtained. n 1 Average or mean of the values, X i X, n k 1 where, n is number of values for each set of data range n 1 Standard deviation, Xik, Xi ( n 1) k1 n 1 Standard uncertainty, u Xik, Xi nn ( 1) k1 ik Standard uncertainty for k th set of data range, uk k n k, k = 1 to n Combined standard uncertainty with parallel links, u c u1 u2 u3 u4... n 0 where, n0 is number of sets of data ranges Expanded uncertainty, U = k u c where, k is coverage factor For confidence level of 95 %, k = 2. For aluminum alloy 7075 T651 X 1 = MPa, X 2 = MPa, X 3 = MPa, X 4 = MPa 1 = 18.1 MPa, 2 = 21.5 MPa, 3 = 17.4 MPa, 4 = 18.1 MPa u 1 = 7.39 MPa, u 2 = 8.80 MPa, u 3 = 7.81 MPa, u 4 = 7.39 MPa Combined standard uncertainty, u c = 7.87 MPa Expanded uncertainty, U = MPa MATS , Naik, Page 21

22 For IS 2062 mild steel X 1 = MPa, X 2 = MPa, X 3 = MPa, X 4 = MPa 1 = 35.2 MPa, 2 = 51.0 MPa, 3 = 37.3 MPa, 4 = 30.5 MPa u 1 = 13.3 MPa, u 2 = 20.8 MPa, u 3 = 15.2 MPa, u 4 = 13.6 MPa Combined standard uncertainty, u c = MPa Expanded uncertainty, U = 32.1 MPa. MATS , Naik, Page 22

23 References [1] Kolsky, H., 1949, An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading, Proc. Phys. Soc. London, B62, pp [2] Meyers, M.A., 1994, Dynamic Behavior of Materials, Wiley Publications, New York, pp [3] Sierakowski, R.L., and Chaturvedi, S.K., 1997, Dynamic Loading and Characterization of Fiber Reinforced Composites, John Wiley & Sons, Inc., New York, pp [4] Kuhn, H., and Medlinm, D., (eds), Mechanical Testing and Evaluation, ASM Hand Book, ASM International, Materials Park, Ohio, Vol. 8, pp [5] Gama, B.A., Lopatnikov, S.L., and Gillespie Jr, J.W., 2004, Hopkinson Bar Experimental Technique, A Critical Review, Appl. Mech. Rev., 57, pp [6] Harding, J., Wood, E.O., and Campbell, J.D., 1960, Tensile Testing of Materials at Impact Rates of Strain, J. Mech. Eng. Sci., 2, pp [7] Lindholm, U.S., Bessey, R.L., and Smith, G.V., 1971, Effect of Strain Rate on Yield Strength, Tensile Strength, and Elongation of Three Aluminium Alloys, J. Mater., 6, pp [8] Nicholas, T., 1981, Tensile Testing of Materials at High Rates of Strain, Exp. Mech., 21, pp [9] Ellwood, S., Griffiths, L.J., and Parry, D.J., 1982, A Tensile Technique for Materials Testing at High Strain Rates, J. Phys., 15, pp [10] Cross, L.A., Bless, S.J., Rajendran, A.M., Strader, E.A., and Dawicke, D.S., 1984, New Technique to Investigate Necking in a Tensile Hopkinson bar, Exp. Mech., 24, pp [11] Ogawa, K., 1985, Mechanical Behaviour of Metals Under Tension-Compression Loading at High Strain Rate, Int. J. Plast., 1, pp [12] Staab, G.H., and Gilat, A., 1991, A Direct-Tension Split Hopkinson Bar for High Strain Rate Testing, Exp. Mech., 31, pp [13] Li, M., Wang, R., and Han, M.B., 1993, A Kolsky Bar: Tension, Tension-Tension, Exp. Mech., 33, pp [14] LeBlanc, M.M., and Lassila, D.H., 1993, Dynamic Tensile Testing of Sheet Material Using the Split-Hopkinson Bar Technique, Exp. Tech., 17, pp MATS , Naik, Page 23

24 [15] Rodriguez, J., Navarro, C., and Sanchez-Galvez, V., 1994, Numerical Assessment of the Dynamic Tension Test Using the Split Hopkinson Bar, J. Test. Eval., 22, pp [16] Noble, J.P., Goldthorpe, B.D., Church, P., and Harding, J., 1999, The Use of the Hopkinson Bar to Validate Constitutive Relations at High Rates of Strain, J. Mech. Phys. Solids, 47, pp [17] Itabashi, M., and Kawata, K., 2000, Carbon Content Effect on High-Strain-Rate Tensile Properties for Carbon Steels, Int. J. Impact Eng., 24, pp [18] Lee, O.S., and Kim, M.S., 2003, Dynamic Material Property Characterization by Using Split Hopkinson Pressure Bar (SHPB) Technique, Nucl. Eng. Des., 226, pp [19] Wang, Y., Zhou, Y., and Xia, Y., 2004, A Constitutive Description of Tensile Behaviour for Brass Over a Wide Range of Strain Rates, Mater. Sci. Eng., A, 372, pp [20] Solomos, G., Albertini, C., Labibes, K., Pizzinato, V., and Viaccoz, B., 2004, Strain Rate Effects in Nuclear Steels at Room and Higher Temperatures, Nucl. Eng. Des., 229, pp [21] Beynon, N.D., Jones, T.B., and Fourlaris, G., 2005, Effect of High Strain Rate Deformation on Microstructure of Strip Steels Tested Under Dynamic Tensile Conditions, Mater. Sci. Technol., 21, pp [22] Smerd, R., Winkler, S., Salisbury, C., Worswick, M., Lloyd, D., and Finn, M., 2005, High Strain Rate Tensile Testing of Automotive Aluminum Alloy Sheet, Int. J. Impact Eng., 32, pp [23] Rohr, I., Nahme, H., and Thoma, K., 2005, Material Characterization and Constitutive Modeling of Ductile High Strength Steel for a Wide Range of Strain Rates, Int. J. Impact Eng., 31, pp [24] Mohr, D., and Gary, G., 2006, High Strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus, J. Phys. IV, 134, pp [25] Naik, N.K., and Yernamma, P., 2008, Mechanical Behaviour of Acrylic Under High Strain Rate Tensile Loading, Polym. Test., 27, pp [26] Boyce, B.L., and Dilmore, M.F., 2009, The Dynamic Tensile Behavior of Tough, Ultrahigh-Strength Steels at Strain-Rates from s -1 to 200 s -1, Int. J. Impact Eng., 36, pp MATS , Naik, Page 24

25 [27] Huh, H., Lim, J.H. and Park, S.H., 2009, High Speed Tensile Test of Steel Sheets for the Stress-Strain Curve at the Intermediate Strain Rate, Int. J. Automot. Technol., 10, pp [28] Yu, H., Guo, Y., Zhang, K., Lai, X., 2009, Constitutive Model on the Description of Plastic Behavior of DP 600 steel at strain rate from 10-4 to 10 3 s -1, Comp. Mater. Sci., 46, pp [29] Chen, Y., Clausen, A.H., Hopperstad, O.S., Langseth, M., 2009, Stress strain Behaviour of Aluminium alloys at a Wide Range of Strain Rates, Int. J. Solids Struct., 46, pp [30] Torca, I., Aginagalde, A., Esnaola, J.A., Galdos, L., Azpilgain, Z., Garcia, C., 2010, Tensile Behaviour of 6082 Aluminium Alloy Sheet under Different Conditions of Heat Treatment, Temperature and Strain Rate, Key Eng. Mater., 423, pp [31] Sil, D., and Varma, S.K., 1993, The Combined Effect of Grain Size and Strain Rate on the Dislocation Substructures and Mechanical Properties in Pure Aluminum, Metall. Trans. A, 24A, pp [32] Cordero, R.R., and Labbe, F., 2006, Monitoring the Strain-Rate Progression of an Aluminium Sample Undergoing Tensile Deformation by Electronic Speckle-Pattern Interferometry (ESPI), J. Phys. D: Appl. Phys., 39, pp [33] Lee, W.S., and Liu, W.C.Y., 2006, The Effects of Temperature and Strain Rate on the Dynamic Flow Behaviour of Different Steels, Mater. Sci. Eng., A, 426, pp [34] Lennon, A.M. and Ramesh, K.T., 2004, The Influence of Crystal Structure on the Dynamic Behavior of Materials at High Temperatures, Int. J. Plast., 20, pp [35] Bell, S., 2001, A Beginner s Guide to Uncertainty of Measurement, National Physical Laboratory, Issue 2, Middlesex, UK. [36] United Kingdom Accreditation Service Publication M3003, 2007, The Expression of Uncertainty and Confidence in Measurement, UKAS Publications, Edition 2, Middlesex, UK. [37] Johnson, G. R., and Cook, W. H., 1983, A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures, Proc. 7th International Symposium on Ballistics, Hague, Netherlands, pp [38] Rule, W.K., and Jones, S.E., 1998, A Revised Form for the Johnson-Cook Strength Model, Int. J. Impact Eng., 21, pp [39] Zerilli, F. J., and Armstrong, R.W., 1987, Dislocation-Mechanics-Based Constitutive Relations for Material Dynamics Calculations, J. Appl. Phys., 61, pp MATS , Naik, Page 25

26 [40] Park, M., Yoo, J., Chung, D.T., 2005, An Optimization of a Multi-Layered Plate under Ballistic Impact, Int. J. Solids Struct., 42, pp [41] Brar, N., Joshi, V., and Harris, B., 2009, Constitutive Model Constants for Al T651 and Al 7075-T6, 16 th APS Topical Conference on Shock Compression of Condensed Matter, American Physical Society, Nashville, Tennessee. MATS , Naik, Page 26

27 Figure captions Fig. 1. Split Hopkinson Pressure Bar (SHPB) apparatus, tensile loading, a) schematic arrangement, b) photograph. Fig. 2. Arrangement of specimen and holders, a) end-threaded cylindrical specimen (dimensions in mm), b) end-threaded cylindrical specimen with holders. Fig. 3. Deformation behavior of specimens, a) end-threaded cylindrical calibration specimen with holders, b) end-threaded cylindrical specimen with holders, c) necking of the specimen during loading, d) idealized representation of necked specimen. Fig. 4. Tensile SHPB test results for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec, (a) strain gauge signals on oscilloscope, (b) comparison of force versus time behavior, derived from strain gauge signals. Fig. 5. A typical yielded Al alloy 7075 T651 specimen. Fig. 6. High strain rate tensile test results for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec, (a) time versus strain rate plot, (b) time versus strain plot, (c) time versus stress plot. Fig. 7. Stress versus strain plot from high strain rate tensile test on SHPB for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec. Fig. 8. Strain rate versus tensile yield strength plot, experimental and predicted using JC model for Al alloy 7075 T651. Fig.9. Strain rate versus tensile yield strength plot, experimental and predicted using JC model for IS 2062 mild steel. Fig.10. SEM images of Al alloy 7075 T651 specimen, tested at quasi-static strain rate, (a) specimen cross-section (magnification = 20X), (b) central region of the specimen cross-section showing dimples characteristic of ductile fracture (magnification = 500X). Fig.11. SEM images of Al alloy 7075 T651 specimen, tested at high strain rate, έ = 77 per sec, (a) specimen cross-section (magnification = 20X), (b) central region of the specimen cross-section showing dimples as well as flat regions characteristic of ductile and brittle fractures, respectively (magnification = 1000X). MATS , Naik, Page 27

28 Fig. 12. Photomicrograph of Al alloy 7075 T651 specimen, tested at quasi-static strain rate (magnification 500x). Fig. 13. Photomicrograph of Al alloy 7075 T651 specimen, tested at high strain rate, έ = 77 per sec (magnification 500x). Table captions Table 1 Behavior of materials under high strain rate tensile loading: property change factor (from literature) Table 2 High strain rate behavior of materials: tensile loading (from literature) Table 3 Strain rate effect on tensile properties (present experimental study) Table 4 Johnson-Cook material constants MATS , Naik, Page 28

29 Fig. 1. Split Hopkinson Pressure Bar (SHPB) apparatus, tensile loading, a) schematic arrangement, b) photograph. MATS , Naik, Page 29

30 Fig. 2. Arrangement of specimen and holders, a) end-threaded cylindrical specimen (dimensions in mm), b) end-threaded cylindrical specimen with holders. MATS , Naik, Page 30

31 Fig. 3. Deformation behavior of specimens, a) end-threaded cylindrical calibration specimen with holders, b) end-threaded cylindrical specimen with holders, c) necking of the specimen during loading, d) idealized representation of necked specimen. MATS , Naik, Page 31

32 (b) F 1 F 2 Fig. 4. Tensile SHPB test results for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec, (a) strain gauge signals on oscilloscope, (b) comparison of force versus time behavior, derived from strain gauge signals. MATS , Naik, Page 32

33 Fig. 5. A typical yielded Al alloy 7075 T651 specimen. MATS , Naik, Page 33

34 Fig. 6. High strain rate tensile test results for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec, (a) time versus strain rate plot, (b) time versus strain plot, (b) time versus stress plot. MATS , Naik, Page 34

35 Stress, σ (MPa) Strain, є (%) Fig. 7. Stress versus strain plot from high strain rate tensile test on SHPB for Al alloy 7075 T651, d s = 4 mm, l s = 15 mm, έ = 109 per sec. Fig. 8. Strain rate versus tensile yield strength plot, experimental and predicted using JC model for Al alloy 7075 T651. MATS , Naik, Page 35

36 Fig.9. Strain rate versus tensile yield strength plot, experimental and predicted using JC model for IS 2062 mild steel. MATS , Naik, Page 36

37 (a) (b) Fig.10. SEM images of Al alloy 7075 T651 specimen, tested at quasi-static strain rate, (a) specimen cross-section (magnification = 20X), (b) central region of the specimen cross-section showing dimples characteristic of ductile fracture (magnification = 500X). MATS , Naik, Page 37

38 (a) (b) Fig.11. SEM images of Al alloy 7075 T651 specimen, tested at high strain rate, έ = 77 per sec, (a) specimen cross-section (magnification = 20X), (b) central region of the specimen cross-section showing dimples as well as flat regions characteristic of ductile and brittle fractures, respectively (magnification = 1000X). Fig. 12. Photomicrograph of Al alloy 7075 T651 specimen, tested at quasi-static strain rate (magnification 500x). MATS , Naik, Page 38

39 Fig. 13. Photomicrograph of Al alloy 7075 T651 specimen, tested at high strain rate, έ = 77 per sec (magnification 500x). MATS , Naik, Page 39