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Dynamic compressive behavior of selected aluminum alloy at low temperature
Materials Science and Engineering A 553 (2012) 176–180
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Dynamic compressive behavior of selected aluminum alloy at low temperature Yonggang Wang ∗ , Zhaoxiu Jiang Mechanics and Materials Science Research Center, Ningbo University, Zhejiang 315211, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 21 October 2011 Received in revised form 24 April 2012 Accepted 5 June 2012 Available online 9 June 2012 Keywords: Compressive behavior Low temperature Aluminum alloy High strain rate
a b s t r a c t This paper deals with the effect of low temperature on the compressive behavior at high strain rate of two aluminum alloys, 2024-T4 and 7075-T6 using a modified split Hopkinson pressure bar (SHPB) with a pulse shaper technique. A cooling device is specially designed to be coupled to the SHPB, which can reach temperatures as low as 123 K. Using experimentally determined stress–strain curves, the effect of low temperature on the dynamic compressive behavior is determined and discussed, showing that flow stress increases with the decrease of temperature, and the strain hardening behavior is almost independent of temperature ranging from 123 to 300 K. A simplified constitutive model based on the consideration of thermally activated dislocation motion is proposed. The prediction provided by the model gets satisfactory agreement with the experiments. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Aluminum alloys have been the most widely used structural materials in aeronautics and aerospace industry for several decades on account of their high stiffness/weight and strength/weight [1,2]. Two types of alloys make up the bulk of the aluminum found in modern aircraft. They are the 2000 series (Al–Cu–Mg) and the 7000 series alloys (Al–Zn–Mg–Cu). Many experiments have been conducted to investigate the mechanical behavior of aluminum alloy under the static loading [3–5]. In some of these applications, structures may be subjected to impulsive loading such as the impact of debris during take off or landing of a plane, or to the release of a turbine blade. The mechanical response of aluminum alloy may be sensitive to the loading rate. A comprehensive characterization of the behavior of aluminum alloys under dynamic loading had prompted numerous investigations in recent years [6–8]. Some authors reported the dynamic compressive test on 2000 and 7000 series by using SHPB or by a computer servo-controlled Gleeble 1500 system at normal and elevated temperature [9,10]. It is found that the mechanical properties of aluminum alloy seriously depend on the temperature. Furthermore, in aeronautical and aerospace applications, structural components made of aluminum alloys may be subjected to low temperatures. Such is the case of high-flying aircrafts (−60 ◦ C) and spacecraft orbiting around the Earth (−150 ◦ C when not directly exposed to solar radiation). The specific behavior of aluminum alloys under the low temperature did not obtain enough
∗ Corresponding author. Tel.: +86 574 87609958; fax: +86 574 87608358. E-mail address: [email protected] (Y. Wang). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.06.010
attention in the literature. Few of the reports related to low temperature had studied the static behavior [11,12]. However, little has been published on aluminum alloys at both high strain rates and low temperatures, probably due to the great difficulty in obtaining valid results. In this paper, the compressive behavior of 2024 T4 and 7075 T6 aluminum alloys at high strain rate and low temperature is studied by means of axial compressive tests using SHPB. A cooling device cooled by liquid nitrogen is particularly designed to reach temperatures as low as −150 ◦ C. The measured stress–strain diagrams at different low temperature show notable increase of flow stress with the decrease of temperature. The physical mechanism of the influence of low temperature on the dynamic mechanical properties of aluminum alloys is also discussed. 2. Experiments 2.1. Material characterization The materials tested were the aluminum alloy 2024-T4 and 7075-T6, which was received as-extruded bar commercially produced by ALCOA. 2024-T4 is the most widely used alloy of the 2000 series, which takes advantage of cold working followed by natural aging. The alloy has moderate yield strength but good damage tolerance. Strength is derived from the formation of a high-volume fraction of Guinier–Preston zones and coherent CuMgAl2 precipitate phase in the grain interiors, as well as by the presence of Al–Cu–Mn dispersions [1]. 7075-T6 has been the most widely used alloy of the 7000 series alloy, which has the highest strengths by far. Their strength is derived from the precipitation of coherent MgZn2 phase in the grain interiors and noncoherent MgZn2
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
177
Fig. 1. Microstructures in the polished and etched longitudinal section of 2024-T4.
Fig. 2. Microstructures in the polished and etched longitudinal section of 7075-T6.
along the grain boundaries [1]. Their microstructures in the polished and etched longitudinal sections of 2024-T4 and 7075-T6 aluminum alloys are shown in Figs. 1 and 2, respectively, which show the distribution of precipitates along the extrusion direction for strengthening. Fig. 1(a) and (b) shows that the CuMgAl2 precipitate phase are uniformly distributed in the grain interiors, and the grains are extruded as a narrow strip. Fig. 2(a) and (b) shows that the MgZn2 precipitation phase are distributed in both grain interiors and grain boundaries, and the grains are also extruded as a narrow strip. 2.2. Experimental set-up Dynamic compressive tests were performed using a modified SHPB as sketched in Fig. 3 [13]. The whole set-up mainly consists of a striker bar, a specimen placed between the incident bar and transmitted bars, a compressed-air gun and a cooling device. The striker and both bars are of high-yield steel, 14.5 mm in diameter and 1.2 m long, and they can move horizontally without any
restriction. The striker bar propelled by the compressed-air gun impact the incident bar, and the impact results in an incident elastic wave generated at the impact face of the incident bar. The elastic compressive wave propagates through the incident bar. At the incident bar–specimen interface, part of the wave due to the impedance mismatch between the specimen and the bars is reflected and part of the wave is transmitted through the specimen to the transmitted bar. The resulting time dependent strains are measured by strain gauges attached at the incident, for the incident εi (t) and reflected εr (t) signal and at the transmitted bar for the transmitted εt (t) signal. Based on the one-dimensional elastic wave propagation theory with the assumptions 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) [13]: (t) =
Eb Ab εt (t) As
2C0 ε(t) = − l ˙ ε(t) =−
Fig. 3. Configuration of SHPB.
(1)
t
εr (t)dt
(2)
0
2C0 εr (t) l
(3)
where C0 is the elastic wave velocity of bar, l is the initial length of specimen, Eb and Ab are the Young’s modulus and area of bar, respectively, As is the area of specimen. To reach low temperatures in the specimen a cooling device was specially designed to be coupled to the SHPB, in such a way that a small portion of the incident and transmitted bars remained inside it. The cooling device mainly consists of a low temperature
178
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
800 -1
Strain rate 2500 s
700
True stress / MPa
600 500 400 300 123 K 173 K 223 K 300 K
200 100
Fig. 4. The whole cooling device. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
0 0.00
0.05
0.10
0.15
0.20
True strain
3. Results and discussion
Fig. 5. Typical stress–strain curves for 2024-T4 aluminum alloys with four different temperatures.
100 0 Strain rate 2000 s-1
800
True stress / MPa
chamber produce by two polytetrafluoroethylene (PTFE) columns, a low temperature thermocouple, a temperature controller and a liquid nitrogen Dewar. The whole cooling device placed on the SHPB is shown in Fig. 4. The low temperature chamber is composed by two polytetrafluoroethylene (PTFE) columns. The separated two PTFE columns will be connected when it is placed on the SHPB, which have two circular holes along the axial and radial directions. The specimen sandwiched between the bars is placed into the circular hole along the radial direction of PTFE columns. A low temperature thermocouple attached the specimen through the circular hole along the axial direction is used to measure the temperature, which connected to a temperature controller to control a heating apparatus inside the liquid nitrogen Dewar. The intended experimental temperature can be pre-assigned in the temperature controller. From Fig. 4, it is observed that the intended temperature (−100 ◦ C) is the red number and the actual temperature of specimen is the green number. If the temperature of specimen is lower than the intended temperature, the heating apparatus inside the Dewar will work to heat the liquid nitrogen. Then the low temperature liquid nitrogen gas quickly flows along a black pipeline from the Dewar to the chamber, which is used to cool the specimen. The heating apparatus can be used to adjust the speed of low temperature gas flow from the Dewar. The cooling temperature of specimen depends on the speed of gas flow. Once the desired temperature is reached in the specimen, the cooling system keeps it enough time before impact to ensure a uniform distribution of temperature.
600
400 12 3 17 3 22 3 30 0
200
0 0.00
0.05
0.10
K K K K
0.15
0.20
True strain Fig. 6. Typical stress–strain curves for 7075-T6 aluminum alloys with four different temperatures.
are the results for the high strain rates of about 2.5 × 103 s−1 and 2.0 × 103 s−1 , respectively. By comparing Figs. 5 and 6, it is observed that the strain hardening rate of 2024-T4 alloy is higher than that of 7075-T6 alloy. It is well known that the physical mechanism of the strain hardening for pure metal is attributed to both the increase of
3.1. True stress–true strain relation 3500
-1
3000
True strain rate / s
Typical true stress–true strain curves for 2024-T4 and 7075T6 aluminum alloys with four different temperatures are shown in Figs. 5 and 6, respectively. To obtain a family of dynamic stress–strain curves as a function of low temperature, the strain rate in specimen is desired to be a constant during each experiment, which is not automatically achieved in a conventional SHPB experiment. Variations in strain rates during a SHPB experiment have been demonstrated to significantly affect the resultant stress–strain data. Therefore, in our experiments, the pulse shaping technique was used to produce a desired profile of incident pulse to ensure constant strain-rate deformation in specimen [14,15]. The true strain rate vs. true strain curves for 2024-T4 aluminum alloy are shown in Fig. 7. From Fig. 7, it is clearly noted that the strain rate is an almost steady state in the range of true strain from 0.05 to 0.25. Note that the oscillation in the strain rate is neglected because early stress–strain data measured by SHPB is not valid due to non-equilibrated stress state in specimen. All of above stress–strain curves of 2024-T4 and 7075-T6 aluminum alloy
2500 2000 1500 1000
123 K 173 K 223 K 300 K
500 0 0.00
0.05
0.10
0.15
0.20
0.25
True strain Fig. 7. Typical strain rate–strain curves for 2024-T4 aluminum alloys with different temperatures.
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
850
Table 1 Parameters for the constitutive relation of materials. A (MPa)
B (MPa)
n
C (K−1 )
2024-T4 7075-T6
445 562
460 207
0.4037 0.10
6.25 × 10−4 3.80 × 10−4
dislocation density and dislocation pile-ups during plastic deformation. It becomes increasingly saturated with new dislocations. This resistance to dislocation–formation manifests itself as a resistance to plastic deformation, hence, the observed strengthening. However, for 2024-T4 and 7075-T6 with many precipitates, the strain hardening may be depend considerably on these precipitates solution in Al matrix. Comparison of Fig. 1 with Fig. 2, at initial state both aluminum alloys have different grain size and precipitates. The precipitates volume fraction of 2024-T4 is larger than that of 7075T6, and the distribution of precipitates in 2024-T4 are more uniform than that of 7075-T6. Strain hardening results from the obstruction of these precipitates for dislocations gliding and intersecting. Less precipitates in 7075-T6 lead to its lower hardening behavior. On the other hand, the grain size of 2024-T4 is larger than that of 7075-T6 as shown in Figs. 1(b) and 2(b). Grain size also affects the strain hardening of polycrystalline metals [16]. Large grains have enough space for significant numbers of dislocation intersections during plastic deformation [16], which also results in the higher strain hardening behavior. The mathematical description of strain hardening is a power low relationship between the stress and the amount of plastic strain: A + Bεnp
(4)
where is the flow stress, A is the initial yield stress, B is the strength index, εp is the plastic strain and n is the strain hardening exponent. Model constants B and n represent the strain hardening effects of the materials, which can be evaluated from the plastic portion of stress–strain curves at 300 K temperature in Figs. 5 and 6. The values of A, B and n for both 2024-T4 and 7075-T6 alloys are listed in Table 1. 3.2. Influence of low temperature The variation of flow stresses as a function of temperature at two different strains of 0.5 and 0.15 for both alloys are presented in Figs. 8 and 9, respectively. The tested results show that the flow stress linearly decreases with the increase of temperature. In the microscopic respect, the temperature dependence of the flow 700
800
Flow stress (MPa)
Materials
=
750
700 ε=0.05 ε=0.15
650 100
150
Flow stress (MPa)
250
300
350
Fig. 9. Flow stress versus temperature on 7075-T6 alloy at the true strains of 0.05 and 0.15.
stress can be explained by the dependence of dislocation velocity on stress and temperature, mainly based on various thermal activation mechanisms of dislocation motion. In general, the complete description of the flow stress should be decomposed in two components [17]: = a + th
(5)
The first term ( a ) is an athermal component of stress, which is independent of the strain rate and temperature. The second term ( th ) is the contribution of strain rate and temperature to the flow stress. Based on the theory of dislocation, the average strain rate ˙ can be explained as [18]: (ε)
U
ε˙ = ε˙ 0 exp −
(6)
kT
where ε˙ 0 is the limiting strain rate, U is the activation energy that must be applied thermally to overcome the obstacle, k is the Boltzmann constant and T is the absolute temperature. In order to find ˙ T and th , it is assumed that the actithe relationship between ε, vation energy U can be expressed as a linear relationship of the form:
U = U0 1 −
th
(7)
0
where U0 and 0 are the activation energy and the stress at 0 K. Substituting Eq. (7) into (6), and solving for stress ( th ) yield the following result:
650
200
Temperature (K)
th = 0 1 −
kT ln U0
ε˙ ε˙ 0
(8)
The most evident result from this formulation is the logarithmic dependence of the flow stress on the strain rate and its linear dependence on temperature. In Figs. 8 and 9, it is observed that the slope of flow stress versus temperature curves at the different strain changes very little, which indicates that the plastic strain does not influence the temperature sensitivities of aluminum alloys in the temperature range of 123–300 K.
600
550 strain =0.05 strain=0.15
500 100
179
150
3.3. Constitutive relation 200
250
300
350
Temperature (K) Fig. 8. Flow stress versus temperature on 2024-T4 alloy at the true strains of 0.05 and 0.15.
Based on the discussion about Eq. (5), the flow stress is an addition of two terms a and th . The term of a can be defined to express the stain hardening process, the formulation described as Eq. (4). Meanwhile, it is found that the strain hardening and temperature sensitivity are independent of each other. Combined the
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the above experimental data. The values of model parameters are listed in Table 1. The predictions (denoted by four color lines) provided by the proposed model are compared with experiments (denoted by four different symbols) shown in Figs. 10 and 11 for 2024-T4 and 7075-T6 alloys, respectively. It is observed that the simulation results get satisfactory agreement with the experimental data.
Strain rate 2500 s-1
Flow stress / MPa
700
600
4. Conclusion
500 123 K 173 K 223 K 300 K
400
300 0.00
0.05
0.10
0.15
True plastic strain Fig. 10. Flow stress versus true plastic strain using the proposed simple model and comparison with experiments on 2024-T4 alloy. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
900 -1
Strain rate 2000 s
Acknowledgments
800
Flow stress / MPa
We studied the dynamic compressive behavior of two aluminum alloys, 2024-T4 and 7075-T6, at low temperature performing a modified SHPB tests. The pulse shaping technique was used to produce a desired profile of incident pulse to ensure constant strain-rate deformation in specimen. The cooling device matched with SHPB was used successfully at temperatures down to −150 ◦ C. The results of the dynamic tests showed obviously influence of temperature on the compressive flow stress of two aluminum alloys. Low temperature has little effect on the strain hardening behavior. Based on the assumption of a linear relationship between the activation energy and flow stress, a simple constitutive model is proposed to describe the material flow behavior of the investigated aluminum alloys at low temperature condition.
This research was supported by the National Science Foundation of China under Grant No. 11072119, the National Defence Industrial Scientific Research Program under Grant No. B1520110003, the K.C. Wong Magna Foundation of Ningbo University, China, and a grant from the Department of Education of Zhejiang Province through the Impact and Safety of Costal Engineering Initiative, a COE Program at Ningbo University.
700 123 K 173 K 223 K 300 K
600
500 0.00
0.05
0.10
References 0.15
True plastic strain Fig. 11. Flow stress versus true plastic strain using the proposed simple model and comparison with experiments on 7075-T6 alloy. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Eqs. (4) and (8) by the multiplicative nature like as the well-known Johnson–Cook constitutive model [19], a simplified physicallybased constitutive model developed based on the consideration of thermally activated dislocation motion is proposed as:
= (A + Bεnp ) 1 − CT ln
ε˙ ε˙ 0
(9)
In our tests, because the stain rate is almost constant, Eq. (9) can be simplified as: = (A + Bεnp )[1 − CT ]
(10)
where C is the material constant. Such simple formulation is applied to describe the dynamic mechanical behavior of two commercial aluminum alloys (2024-T4 and 7075-T6) at low temperature using
[1] J.-P. Immarigeon, R.T. Holt, A.K. Koul, L. Zhao, W. Wallace, J.C.Beddoes., Mater. Charact. 35 (1995) 41–67. [2] A. Heinz, A. Haszler, C. Keidel, S. Moldenhauer, R. Benedictus, W.S. Miller, Mater. Sci. Eng. A 280 (2000) 102–107. [3] H.T. Lee, G.H. Shaue, Mater. Sci. Eng. A 268 (1999) 154–164. [4] L.X. Hu, Z.Y. Liu, E. Wang, Mater. Sci. Eng. A 323 (2002) 213–217. [5] K.O. Pedersen, H.J. Roven, O.G. Lademo, O.S. Hopperstad, Mater. Sci. Eng. A 473 (2008) 81–89. [6] Y. Chen, A.H. Clausen, O.S. Hopperstad, M. Langseth, Int. J. Solid Struct. 46 (2009), 3835-3835. [7] K.O. Pedersen, T. Borvik, O.S. Hopperstad, Mater. Des. 32 (2011) 97–107. [8] R. Smerd, S. Winkler, C. Salisbury, W. Worswick, D. Lloyd, M. Finn, Int. J. Impact Eng. 32 (2005) 541–560. [9] N.P. Jin, H. Zhang, Y. Han, W.X. Wu, J.H. Chen, Mater. Charact. 60 (2009) 530–536. [10] E. El-Magd, M. Abouridouane, Int. J. Impact Eng. 32 (2006) 741–758. [11] D.A. Wigley, Mechanical Properties of Materials at Low Temperature, Plenum Press, New York, 1971. [12] S.J. Shigeoki, Light Metal (Japan) 39 (1989) 574–589. [13] H. Kolsky, Proc. R. Soc. B 62 (1949) 676–700. [14] D.J. Frew, M.J. Forrestal, W. Chen, Exp. Mech. 42 (2002) 93–106. [15] D.J. Frew, M.J. Forrestal, W. Chen, Exp. Mech. 45 (2005) 186–195. [16] P.L. Sun, E.K. Cerreta, G.T. Gray III, J.F. Bingert, Metall. Mater. Trans. A 37A (2006) 2983–2994. [17] F.J. Zerilli, R.W. Armstrong, J. Appl. Phys. 61 (1987) 1816–1825. [18] L.L. Wang, J. Eng. Mater. Technol. 106 (1984) 331–336. [19] G.R. Johnson, W.H. Cook, Eng. Fract. Mech. 21 (1985) 31–48.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Dynamic compressive behavior of selected aluminum alloy at low temperature Yonggang Wang ∗ , Zhaoxiu Jiang Mechanics and Materials Science Research Center, Ningbo University, Zhejiang 315211, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 21 October 2011 Received in revised form 24 April 2012 Accepted 5 June 2012 Available online 9 June 2012 Keywords: Compressive behavior Low temperature Aluminum alloy High strain rate
a b s t r a c t This paper deals with the effect of low temperature on the compressive behavior at high strain rate of two aluminum alloys, 2024-T4 and 7075-T6 using a modified split Hopkinson pressure bar (SHPB) with a pulse shaper technique. A cooling device is specially designed to be coupled to the SHPB, which can reach temperatures as low as 123 K. Using experimentally determined stress–strain curves, the effect of low temperature on the dynamic compressive behavior is determined and discussed, showing that flow stress increases with the decrease of temperature, and the strain hardening behavior is almost independent of temperature ranging from 123 to 300 K. A simplified constitutive model based on the consideration of thermally activated dislocation motion is proposed. The prediction provided by the model gets satisfactory agreement with the experiments. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Aluminum alloys have been the most widely used structural materials in aeronautics and aerospace industry for several decades on account of their high stiffness/weight and strength/weight [1,2]. Two types of alloys make up the bulk of the aluminum found in modern aircraft. They are the 2000 series (Al–Cu–Mg) and the 7000 series alloys (Al–Zn–Mg–Cu). Many experiments have been conducted to investigate the mechanical behavior of aluminum alloy under the static loading [3–5]. In some of these applications, structures may be subjected to impulsive loading such as the impact of debris during take off or landing of a plane, or to the release of a turbine blade. The mechanical response of aluminum alloy may be sensitive to the loading rate. A comprehensive characterization of the behavior of aluminum alloys under dynamic loading had prompted numerous investigations in recent years [6–8]. Some authors reported the dynamic compressive test on 2000 and 7000 series by using SHPB or by a computer servo-controlled Gleeble 1500 system at normal and elevated temperature [9,10]. It is found that the mechanical properties of aluminum alloy seriously depend on the temperature. Furthermore, in aeronautical and aerospace applications, structural components made of aluminum alloys may be subjected to low temperatures. Such is the case of high-flying aircrafts (−60 ◦ C) and spacecraft orbiting around the Earth (−150 ◦ C when not directly exposed to solar radiation). The specific behavior of aluminum alloys under the low temperature did not obtain enough
∗ Corresponding author. Tel.: +86 574 87609958; fax: +86 574 87608358. E-mail address: [email protected] (Y. Wang). 0921-5093/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.06.010
attention in the literature. Few of the reports related to low temperature had studied the static behavior [11,12]. However, little has been published on aluminum alloys at both high strain rates and low temperatures, probably due to the great difficulty in obtaining valid results. In this paper, the compressive behavior of 2024 T4 and 7075 T6 aluminum alloys at high strain rate and low temperature is studied by means of axial compressive tests using SHPB. A cooling device cooled by liquid nitrogen is particularly designed to reach temperatures as low as −150 ◦ C. The measured stress–strain diagrams at different low temperature show notable increase of flow stress with the decrease of temperature. The physical mechanism of the influence of low temperature on the dynamic mechanical properties of aluminum alloys is also discussed. 2. Experiments 2.1. Material characterization The materials tested were the aluminum alloy 2024-T4 and 7075-T6, which was received as-extruded bar commercially produced by ALCOA. 2024-T4 is the most widely used alloy of the 2000 series, which takes advantage of cold working followed by natural aging. The alloy has moderate yield strength but good damage tolerance. Strength is derived from the formation of a high-volume fraction of Guinier–Preston zones and coherent CuMgAl2 precipitate phase in the grain interiors, as well as by the presence of Al–Cu–Mn dispersions [1]. 7075-T6 has been the most widely used alloy of the 7000 series alloy, which has the highest strengths by far. Their strength is derived from the precipitation of coherent MgZn2 phase in the grain interiors and noncoherent MgZn2
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
177
Fig. 1. Microstructures in the polished and etched longitudinal section of 2024-T4.
Fig. 2. Microstructures in the polished and etched longitudinal section of 7075-T6.
along the grain boundaries [1]. Their microstructures in the polished and etched longitudinal sections of 2024-T4 and 7075-T6 aluminum alloys are shown in Figs. 1 and 2, respectively, which show the distribution of precipitates along the extrusion direction for strengthening. Fig. 1(a) and (b) shows that the CuMgAl2 precipitate phase are uniformly distributed in the grain interiors, and the grains are extruded as a narrow strip. Fig. 2(a) and (b) shows that the MgZn2 precipitation phase are distributed in both grain interiors and grain boundaries, and the grains are also extruded as a narrow strip. 2.2. Experimental set-up Dynamic compressive tests were performed using a modified SHPB as sketched in Fig. 3 [13]. The whole set-up mainly consists of a striker bar, a specimen placed between the incident bar and transmitted bars, a compressed-air gun and a cooling device. The striker and both bars are of high-yield steel, 14.5 mm in diameter and 1.2 m long, and they can move horizontally without any
restriction. The striker bar propelled by the compressed-air gun impact the incident bar, and the impact results in an incident elastic wave generated at the impact face of the incident bar. The elastic compressive wave propagates through the incident bar. At the incident bar–specimen interface, part of the wave due to the impedance mismatch between the specimen and the bars is reflected and part of the wave is transmitted through the specimen to the transmitted bar. The resulting time dependent strains are measured by strain gauges attached at the incident, for the incident εi (t) and reflected εr (t) signal and at the transmitted bar for the transmitted εt (t) signal. Based on the one-dimensional elastic wave propagation theory with the assumptions 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) [13]: (t) =
Eb Ab εt (t) As
2C0 ε(t) = − l ˙ ε(t) =−
Fig. 3. Configuration of SHPB.
(1)
t
εr (t)dt
(2)
0
2C0 εr (t) l
(3)
where C0 is the elastic wave velocity of bar, l is the initial length of specimen, Eb and Ab are the Young’s modulus and area of bar, respectively, As is the area of specimen. To reach low temperatures in the specimen a cooling device was specially designed to be coupled to the SHPB, in such a way that a small portion of the incident and transmitted bars remained inside it. The cooling device mainly consists of a low temperature
178
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
800 -1
Strain rate 2500 s
700
True stress / MPa
600 500 400 300 123 K 173 K 223 K 300 K
200 100
Fig. 4. The whole cooling device. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
0 0.00
0.05
0.10
0.15
0.20
True strain
3. Results and discussion
Fig. 5. Typical stress–strain curves for 2024-T4 aluminum alloys with four different temperatures.
100 0 Strain rate 2000 s-1
800
True stress / MPa
chamber produce by two polytetrafluoroethylene (PTFE) columns, a low temperature thermocouple, a temperature controller and a liquid nitrogen Dewar. The whole cooling device placed on the SHPB is shown in Fig. 4. The low temperature chamber is composed by two polytetrafluoroethylene (PTFE) columns. The separated two PTFE columns will be connected when it is placed on the SHPB, which have two circular holes along the axial and radial directions. The specimen sandwiched between the bars is placed into the circular hole along the radial direction of PTFE columns. A low temperature thermocouple attached the specimen through the circular hole along the axial direction is used to measure the temperature, which connected to a temperature controller to control a heating apparatus inside the liquid nitrogen Dewar. The intended experimental temperature can be pre-assigned in the temperature controller. From Fig. 4, it is observed that the intended temperature (−100 ◦ C) is the red number and the actual temperature of specimen is the green number. If the temperature of specimen is lower than the intended temperature, the heating apparatus inside the Dewar will work to heat the liquid nitrogen. Then the low temperature liquid nitrogen gas quickly flows along a black pipeline from the Dewar to the chamber, which is used to cool the specimen. The heating apparatus can be used to adjust the speed of low temperature gas flow from the Dewar. The cooling temperature of specimen depends on the speed of gas flow. Once the desired temperature is reached in the specimen, the cooling system keeps it enough time before impact to ensure a uniform distribution of temperature.
600
400 12 3 17 3 22 3 30 0
200
0 0.00
0.05
0.10
K K K K
0.15
0.20
True strain Fig. 6. Typical stress–strain curves for 7075-T6 aluminum alloys with four different temperatures.
are the results for the high strain rates of about 2.5 × 103 s−1 and 2.0 × 103 s−1 , respectively. By comparing Figs. 5 and 6, it is observed that the strain hardening rate of 2024-T4 alloy is higher than that of 7075-T6 alloy. It is well known that the physical mechanism of the strain hardening for pure metal is attributed to both the increase of
3.1. True stress–true strain relation 3500
-1
3000
True strain rate / s
Typical true stress–true strain curves for 2024-T4 and 7075T6 aluminum alloys with four different temperatures are shown in Figs. 5 and 6, respectively. To obtain a family of dynamic stress–strain curves as a function of low temperature, the strain rate in specimen is desired to be a constant during each experiment, which is not automatically achieved in a conventional SHPB experiment. Variations in strain rates during a SHPB experiment have been demonstrated to significantly affect the resultant stress–strain data. Therefore, in our experiments, the pulse shaping technique was used to produce a desired profile of incident pulse to ensure constant strain-rate deformation in specimen [14,15]. The true strain rate vs. true strain curves for 2024-T4 aluminum alloy are shown in Fig. 7. From Fig. 7, it is clearly noted that the strain rate is an almost steady state in the range of true strain from 0.05 to 0.25. Note that the oscillation in the strain rate is neglected because early stress–strain data measured by SHPB is not valid due to non-equilibrated stress state in specimen. All of above stress–strain curves of 2024-T4 and 7075-T6 aluminum alloy
2500 2000 1500 1000
123 K 173 K 223 K 300 K
500 0 0.00
0.05
0.10
0.15
0.20
0.25
True strain Fig. 7. Typical strain rate–strain curves for 2024-T4 aluminum alloys with different temperatures.
Y. Wang, Z. Jiang / Materials Science and Engineering A 553 (2012) 176–180
850
Table 1 Parameters for the constitutive relation of materials. A (MPa)
B (MPa)
n
C (K−1 )
2024-T4 7075-T6
445 562
460 207
0.4037 0.10
6.25 × 10−4 3.80 × 10−4
dislocation density and dislocation pile-ups during plastic deformation. It becomes increasingly saturated with new dislocations. This resistance to dislocation–formation manifests itself as a resistance to plastic deformation, hence, the observed strengthening. However, for 2024-T4 and 7075-T6 with many precipitates, the strain hardening may be depend considerably on these precipitates solution in Al matrix. Comparison of Fig. 1 with Fig. 2, at initial state both aluminum alloys have different grain size and precipitates. The precipitates volume fraction of 2024-T4 is larger than that of 7075T6, and the distribution of precipitates in 2024-T4 are more uniform than that of 7075-T6. Strain hardening results from the obstruction of these precipitates for dislocations gliding and intersecting. Less precipitates in 7075-T6 lead to its lower hardening behavior. On the other hand, the grain size of 2024-T4 is larger than that of 7075-T6 as shown in Figs. 1(b) and 2(b). Grain size also affects the strain hardening of polycrystalline metals [16]. Large grains have enough space for significant numbers of dislocation intersections during plastic deformation [16], which also results in the higher strain hardening behavior. The mathematical description of strain hardening is a power low relationship between the stress and the amount of plastic strain: A + Bεnp
(4)
where is the flow stress, A is the initial yield stress, B is the strength index, εp is the plastic strain and n is the strain hardening exponent. Model constants B and n represent the strain hardening effects of the materials, which can be evaluated from the plastic portion of stress–strain curves at 300 K temperature in Figs. 5 and 6. The values of A, B and n for both 2024-T4 and 7075-T6 alloys are listed in Table 1. 3.2. Influence of low temperature The variation of flow stresses as a function of temperature at two different strains of 0.5 and 0.15 for both alloys are presented in Figs. 8 and 9, respectively. The tested results show that the flow stress linearly decreases with the increase of temperature. In the microscopic respect, the temperature dependence of the flow 700
800
Flow stress (MPa)
Materials
=
750
700 ε=0.05 ε=0.15
650 100
150
Flow stress (MPa)
250
300
350
Fig. 9. Flow stress versus temperature on 7075-T6 alloy at the true strains of 0.05 and 0.15.
stress can be explained by the dependence of dislocation velocity on stress and temperature, mainly based on various thermal activation mechanisms of dislocation motion. In general, the complete description of the flow stress should be decomposed in two components [17]: = a + th
(5)
The first term ( a ) is an athermal component of stress, which is independent of the strain rate and temperature. The second term ( th ) is the contribution of strain rate and temperature to the flow stress. Based on the theory of dislocation, the average strain rate ˙ can be explained as [18]: (ε)
U
ε˙ = ε˙ 0 exp −
(6)
kT
where ε˙ 0 is the limiting strain rate, U is the activation energy that must be applied thermally to overcome the obstacle, k is the Boltzmann constant and T is the absolute temperature. In order to find ˙ T and th , it is assumed that the actithe relationship between ε, vation energy U can be expressed as a linear relationship of the form:
U = U0 1 −
th
(7)
0
where U0 and 0 are the activation energy and the stress at 0 K. Substituting Eq. (7) into (6), and solving for stress ( th ) yield the following result:
650
200
Temperature (K)
th = 0 1 −
kT ln U0
ε˙ ε˙ 0
(8)
The most evident result from this formulation is the logarithmic dependence of the flow stress on the strain rate and its linear dependence on temperature. In Figs. 8 and 9, it is observed that the slope of flow stress versus temperature curves at the different strain changes very little, which indicates that the plastic strain does not influence the temperature sensitivities of aluminum alloys in the temperature range of 123–300 K.
600
550 strain =0.05 strain=0.15
500 100
179
150
3.3. Constitutive relation 200
250
300
350
Temperature (K) Fig. 8. Flow stress versus temperature on 2024-T4 alloy at the true strains of 0.05 and 0.15.
Based on the discussion about Eq. (5), the flow stress is an addition of two terms a and th . The term of a can be defined to express the stain hardening process, the formulation described as Eq. (4). Meanwhile, it is found that the strain hardening and temperature sensitivity are independent of each other. Combined the
180
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800
the above experimental data. The values of model parameters are listed in Table 1. The predictions (denoted by four color lines) provided by the proposed model are compared with experiments (denoted by four different symbols) shown in Figs. 10 and 11 for 2024-T4 and 7075-T6 alloys, respectively. It is observed that the simulation results get satisfactory agreement with the experimental data.
Strain rate 2500 s-1
Flow stress / MPa
700
600
4. Conclusion
500 123 K 173 K 223 K 300 K
400
300 0.00
0.05
0.10
0.15
True plastic strain Fig. 10. Flow stress versus true plastic strain using the proposed simple model and comparison with experiments on 2024-T4 alloy. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
900 -1
Strain rate 2000 s
Acknowledgments
800
Flow stress / MPa
We studied the dynamic compressive behavior of two aluminum alloys, 2024-T4 and 7075-T6, at low temperature performing a modified SHPB tests. The pulse shaping technique was used to produce a desired profile of incident pulse to ensure constant strain-rate deformation in specimen. The cooling device matched with SHPB was used successfully at temperatures down to −150 ◦ C. The results of the dynamic tests showed obviously influence of temperature on the compressive flow stress of two aluminum alloys. Low temperature has little effect on the strain hardening behavior. Based on the assumption of a linear relationship between the activation energy and flow stress, a simple constitutive model is proposed to describe the material flow behavior of the investigated aluminum alloys at low temperature condition.
This research was supported by the National Science Foundation of China under Grant No. 11072119, the National Defence Industrial Scientific Research Program under Grant No. B1520110003, the K.C. Wong Magna Foundation of Ningbo University, China, and a grant from the Department of Education of Zhejiang Province through the Impact and Safety of Costal Engineering Initiative, a COE Program at Ningbo University.
700 123 K 173 K 223 K 300 K
600
500 0.00
0.05
0.10
References 0.15
True plastic strain Fig. 11. Flow stress versus true plastic strain using the proposed simple model and comparison with experiments on 7075-T6 alloy. (For interpretation of the references to colour in the text, the reader is referred to the web version of this article.)
Eqs. (4) and (8) by the multiplicative nature like as the well-known Johnson–Cook constitutive model [19], a simplified physicallybased constitutive model developed based on the consideration of thermally activated dislocation motion is proposed as:
= (A + Bεnp ) 1 − CT ln
ε˙ ε˙ 0
(9)
In our tests, because the stain rate is almost constant, Eq. (9) can be simplified as: = (A + Bεnp )[1 − CT ]
(10)
where C is the material constant. Such simple formulation is applied to describe the dynamic mechanical behavior of two commercial aluminum alloys (2024-T4 and 7075-T6) at low temperature using
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