Deformation Behavior of Fine Grained Al-Mg Alloy under Biaxial Stress

Masafumi Noda1,a and Kunio Funami2,b

1Department of Seismic Control Business, Sankyo Oilless Industry, Inc. 1-1-5, Nisshin-cho, Fuchu-shi, Tokyo, 183-0036, Japan

2Department of Mechanical Engineering, Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba, 275-0016, Japan a noda@sankyo-oilless.co.jp,bfunami@pf.it-chiba.ac.jp

Keywords: Biaxial tension, Superplastic deformation, Grain separation, Cavities,Strain rate Abstract. The grain boundary sliding and the formation of slipped bands and cavitations during biaxial tensile deformation were examined in fine grained Al-Mg alloy. Biaxial tensile testing was conducted with cruciform specimens at initial strain rates of 10-4 to 101s-1. It was found that at the same equivalent strain conditions, the number of cavities under biaxial tension is significantly greater than that under uniaxial tension. A greater prevalence of slipped bands and grain separations were clearly observed under biaxial stress than under uniaxial stress. It was suggested that development of slipped bands resulted from the formation of elongated cavities and multiple deformed bands under biaxial stress. Additionally, the m-value under biaxial stress remained at about 0.3 over a wide range of strain rates. The effects of grain separation and formation of cavities were related to the motion of grain boundary sliding, grain size and loading conditions.

1.Introduction

The development of ultra-fine materials with high strength and capable of superplastic deformation has recently been implemented through various methods using high strain working methods [1-6]. Simulation methods for forming working have been proposed for setting the loading conditions for plastic deformation into various shapes using these materials [7-11]. The plastic working parameters introduced in the above, however, are all experimental values obtained under uniaxial stress, not under biaxial stress. In the case of application of superplastic deformation to the working of complex shapes, if working parameters are not applied by linking structural changes with both loading rates and stress states, appropriate simulations cannot be achieved.

This report includes studies on relationships of superplastic properties and working parameters of Al-Mg alloy with a fine-grain structure obtained under biaxial stress, using a prototyped biaxial testing machine with structural changes, and comparisons with those obtained under uniaxial stress. 2. Experimental methods 2.1 Materials

The test material was a cast 5083 Al-Mg alloy (crystal grain size:70µm) with a chemical composition in mass% of Si 0.08, Fe 0.2,Cu 0.02,Mn 0.5,Mg 4.83,Zn 0.01,Cr 0.06,with Al comprising the remainder. Rolled material with a crystal grain size refined down to 2–3 µm by warm rolling after keeping at 523 K for 1.8 ks was used. For the warm rolling of the material, the reduction rate per pass was 20%, the material was re-heated for 300 s after each pass, the total reduction rate was 90%, and the final thickness was 1 mm.

Materials Science Forum Vols. 503-504 (2006) pp 475-480Online available since 2006/Jan/15 at www.scientific.net© (2006) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/MSF.503-504.475

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b

2.2 Mechanical properties Mechanical properties under biaxial stress were measured using a prototyped biaxial tensile

testing machine. At the test temperature employed (673 K), the temperature variations of a specimen could be suppressed to within 15 K inside a 6 mm circular region.

The specimen used in the biaxial stress-loading test was the cruciform specimen shown in Fig.1 with a plate thickness of 1 mm. The plate thickness of the central portion was made thinner than the nominal thickness by machining 0.25 mm down from both surfaces in a 6 mm circular region to sustain a large deformation in the central region of the specimen. The same equivalent strain was confirmed by an FEM analysis to be maintained inside the region after plastic deformation of and over 30%. The tensile tests were carried out at a constant displacement rate. The surface and internal structures, respectively, were observed after testing using an FE-SEM and an SEM. 3. Experimental results 3.1 Stress-strain relationships at elevated temperatures

The nominal stress-strain relationships and the equivalent stress-strain relationships obtained by the uniaxial and the equi-biaxial tensile tests with various strain rates at 673 K are shown in Fig.2. A comparison of both diagrams at each strain rate reveals that the uniaxial tensile tests show a gradual decrease in the stress beyond the peak stress, followed by rupture, whereas the biaxial tensile tests also show a decrease in the stress beyond the peak stress, but the decrease until rupture stress is minimal.

The peak stress and m value–strain rate relationships are shown in Fig.3. As shown in Fig.3, the peak stresses in the biaxial loading are lower than those in the uniaxial loading in the tested strain rate range. A uniaxial tensile test at a strain rate 3.3x10-4s-1 showed an m-value of 0.33 and a large fracture elongation of 225%. The above behavior agrees with the superplastic behavior reported on Al alloys [8]. The biaxial tensile test at a strain rate of 3.3x10-4s-1 showed an m-value of 0.32 and a fracture elongation of 85%. While the m-value maintained values over 0.30, which is the criterion for the

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Fig.1 Geometrical shape and dimensions of cruciform specimen used in biaxial tensile test

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Fig.2 Nominal stress-strain curves at 673 K for uniaxial specimens (a) and cruciform specimens (b) at various strain rates.

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expression of superplasticity [6,7], up to 8.3x10-4s-1 under uniaxial stress, a value over 0.30 was maintained up to a strain rate of 3.3 x10-1 s-1 in the biaxial stress state. The m-value is said to correspond closely to fracture elongation in uniaxial tensile testing [8]. Although, in the biaxial tensile test, the fracture elongation remained at 60 ~ 80% in the strain rate range of 3.3x10-4 ~ 3.3x10-1 s-1 where the m-value maintains a value of over 0.30, the fracture elongation also decreases beyond the strain rate of 5.0x10-1s-1 where the m-value begins to decrease sharply. The major characteristic observed in the biaxial tensile test, as described in the above, is that the m-value remains at 0.3 up to the high strain rate region.

3.2 Structural changes during uniaxial and biaxial tensile deformations 3.2.1 SEM structural observations

The surface structural observations by an FE-SEM of the fine-structure Al-Mg material are shown in Fig.4 at various deformation amounts after the uniaxial and the biaxial tensile tests conducted at the test temperature of 673 K and a strain rate of 8.3 x 10-4 s-1. Those for the strain rate increased to 8.3 x 10-2 s-1, as shown in Fig.5. As shown in Fig.4 (a), crystal grains become elongated in the tensile direction when a deformation of 30% was applied in the uniaxial tensile test. Voids and grain boundary sliding at the grain boundaries normal to the tensile direction as well as fibrous structures can be confirmed. In Fig.4 (c), which illustrates the biaxial stress state, fibrous structures are observed in random directions, and are found more often than in the uniaxial stress state. When the strain rate is increased, as shown in Fig.5 (a), voids and grain boundary sliding are observed at the grain boundaries normal to the tensile direction under uniaxial stress. Grain boundary sliding can be confirmed by inclination of the scratches made in advance by alumina powder. In the biaxial stress state shown in Fig.5 (c), in contrast, voids and grain boundary sliding are observed in random directions. When the deformation amount is increased to approximately 60%, as shown in Fig. 5 (b) and (d), it was found that the voids observed for the deformation amount 30 under uniaxial stress grew, and that the grain boundary sliding significantly increased. Voids grow in the biaxial stress state as well, where

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Fig.3 Relationship between (a) peak stress and (b) m-value and initial strain rate under uniaxial and biaxial loading at 673 K

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Fig.4 SEM microstructure of the specimen surface deformed at 673 K using (a): 35%, (b): 60% uniaxial and (c): 22%, (d): 60% cruciform tensile specimen under an initial strain rate of 8.3 x 10-4s-1.

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they are more often observed than in the uniaxial stress state. Grain boundary sliding also occurs to a significant extent. Comparisons of Fig.4 (b) and (d) and Fig.5 (b) and (d) show that when a large deformation is applied, crystal grains become finer, with an increase in strain rate under both uniaxial and biaxial stresses. It is assumed that this is caused by a greater deformation rate than the recrystallization and grain growth rates. In the uniaxial stress state, the crystal grains are elongated in the tensile direction, and voids and grain boundary sliding occur normal to the tensile direction; however, in the biaxial stress state, the crystal grains maintain their equiaxiality and voids, and grain boundary sliding occurs in random directions. When the strain rate is low in these cases, fibrous structures are observed at grain boundaries in the portions where voids and grain boundary sliding are observed in both the uniaxial and the biaxial stress states.

Dynamic recrystallization and grain growth are considered to contribute to the above, since the amounts of rotation of crystal grains and grain boundary sliding are large under uniaxial stress. The scratches are bent in undulations at grain boundaries, but straight inside grains, and their inclinations are varied at grain boundaries. These agree with the facts described in the previous report [4]. On the other hand, in the biaxial stress state, the scratches showed larger changes in their inclinations at grain boundaries due to larger amounts of rotation of crystal grains and grain boundary sliding than in the uniaxial stress state, and no transgranular deformation was found. 3.2.2 TEM structural observations TEM structures of the uniaxial and the biaxial tensile specimens are shown in Fig.6 when a 60% deformation is applied at the test temperature 673 K and strain rates 8.3 x 10-2 s-1 and 8.3 x 10-4 s-1.

As observed in the surface structures, crystal grains are elongated in the tensile direction in Fig.6 (a)

( a ) (b)

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Fig.6 TEM microstructures taken from the uniaxial and the biaxial tensile specimens showing fiber formation in regions where surface grains were separated (εe = 60%).

(a) and (c): uniaxial loading at initial strain rates of 8.3 x 10-2s-1 and 8.3 x 10-4s-1. (b), (d), and (e): biaxial loading with initial strain rates of 8.3 x 10-2s-1and 8.3 x 10-4s-1.

(c )

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Fig.5 SEM microstructure of the specimen surdeformed at 673 K using the (a): 30%, (b): 60%uniaxial and (c): 25%, (d): 60% cruciform tensilspecimen under an initial strain rate 8.3 x 10-2s-1

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for a strain rate 8.3x10-2s-1 under uniaxial stress. Grain growth took place as shown in Fig.6 (c) on reducing the strain rate. This was assumed to be due to the recrystallization rate being higher than the deformation rate, and the dynamic recrystallization and the grain growth are concluded to contribute during the deformation. This result is similar to that described in the previous report [4]. Figure 6 (b), on the other hand, indicates that the crystal grain shapes maintain their equiaxiality at a strain rate of 8.3 x10-2 s-1 under biaxial stress. Figure 6 (d) showing a low strain rate indicates that, in comparison with Fig.6 (b) for a high strain rate, grain growth did not occur, but instead grain refining took place. Figure 6(d) showing a lower strain rate under biaxial stress, reveals the presence of precipitation at grain boundaries. This is not found in the uniaxial stress state. 4. Discussions 4.1 Deformation mechanisms in the uniaxial and the biaxial tensile tests at elevated temperatures

Differences are observed in the deformation tresses, the fracture elongations and the m-values between the uniaxial and the biaxial stress states in the tensile tests conducted at 673 K. These are due to grain boundary sliding being more active in the biaxial stress state than in the uniaxial stress state, as clearly observed in the FE-SEM observations shown in Figs.4 and 5. These are, in other words, the result of relaxation of stress made possible by grain boundary sliding. While the reduction is significant in the cross-sectional area due to plastic flows in the plate thickness and the plate width in the uniaxial tensile specimen, the deformation is constrained in the cruciform specimen due to the principal stresses working in two orthogonal directions [8]. It is believed that the deformations contributing in the tensile directions are limited in the plate thickness alone, which led to poorer flow ability, and hence lower deformation stresses in the biaxial stress state than in the uniaxial stress state.

This difference in flow ability is believed to lead to the differences seen in the deformation stresses and the elongations between the uniaxial and the biaxial tensile tests. Accordingly, because the greater the deformation becomes, the greater the deformation capability required, the difference in the deformation behaviors becomes clearer between the uniaxial and the biaxial tensile tests. The differences in deformation behaviors between the uniaxial and the biaxial stress also appear as differences in m-values. The loci of each point become larger when they are located more distantly from the origin in the uniaxial stress state, and the strain rate, becomes more important when the loci of each point become larger. Changes in strain rate exert a major influence on deformation stress. On the other hand, in the biaxial stress state, since the loci of each point are constant, regardless of the distances from the origin, the deformation stress is affected by the strain rate only in the high strain rate region, and keeps a constant variation in the low strain rate region. These are assumed to yield the observed differences in m-values. 4.2 Influences of crystal grain sizes on the mechanical properties in the uniaxial and the biaxial tensile tests at elevated temperatures

Specimens with different crystal grain sizes were prepared by changing the annealing temperature. The crystal grain sizes were obtained by the intercept method. The grain size becomes larger with higher annealing temperature. Rapid grain growth is observed between 523 K and 573 K in particular. It was assumed that the rapid grain growth was caused in this temperature range because of its proximity to the recovery and recrystallization temperature of the Al alloy. It has been made clear that the Hall-Petch equation holds true for ultrafine grains no larger than 1 µm. Although a similar degree of scatter, as in the uniaxial stress state, is observed, a linear relationship can be seen between the 0.2% proof stress and

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the –1/2 power of the grain size in the biaxial stress state as well, indicating that the Hall-Petch law holds true. The slopes of the straight lines for the both stress states yield the same values; however, a difference in the intercept, i.e., the σi's, was observed. We believe the reason a difference is shown in the σi's, is due to the difference in the applied stress modes in the uniaxial and biaxial stress states.

Consequently, different mechanical properties are observed in materials with the same grain size due to the difference in applied stress modes. The influences exerted on the mechanical properties can be markedly different for the same change in grain size as a result of applying different stress modes, either uniaxial or biaxial. 5. Conclusions Various mechanical properties in the biaxial stress state factors necessary for sophistication of forming working and its simulations were obtained by carrying out biaxial tensile tests using the cruciform specimens under a variety of conditions. The following results were obtained. 1. Although the m-value decreases with increased strain rate under uniaxial stress, it maintains a value over 0.3 up to 1.7 x 10-1 s-1, which is a high deformation rate under biaxial stress. 2. The mechanical properties under uniaxial and biaxial stresses were different for specimens with the same crystal grain size because the deformation mechanisms were different. The influences of grain size on the mechanical properties were also different between the uniaxial and the biaxial stress states. 3. The grain sizes observed were 10 µm and 4 µm, respectively, after an approximately 60% deformation at the test temperature of 673 K and a strain rate of 8.3 x 10-2 s-1 under uniaxial and biaxial stresses; formation of fine grains due to dynamic recrystallization was confirmed in the biaxial stress state which does not involve shear deformation. 4. On the other hand, at the test temperature 673 K, crystal grains were elongated in the tensile direction and voids were generated normal to the tensile direction under uniaxial stress; crystal grains maintained equiaxiality, and voids were generated in random directions. 6. References [1] K. Ameyama: Scripta Mater., 38 (1998) 726. [2] M. Furukawa, Z. Horita, M. Nemoto, R.Z. Valiev and T.G. Langdon: Acta Mater., 44 (1996) 4619. [3] R.Z. Abdulov, R.Z. Valiev and N.A. Krashilnikov: J. Mater. Sci. Lett., 9 (1990) 1445. [4] M. Noda, M. Hirohashi and K. Funami: J. Japan Inst. Metals, 67 (2003) 98-105. [5] Y. Saito, H. Utsunomiya, N. Tsuji and T. Sakai: Acta Mater., 47 (1999) 579-583. [6] Y.J. Kwon, I. Shigematsu and N. Saito: J. Japan Inst. Metals, 66 (2002) 1325-1332. [7] T. Kuwabara, S. Ikeda and A. Yoshizawa: Proc. 53rd Japanese Joint Conference for the Technology of Plasticity (2002) 405. [8] T.R. Chen and J.C. Huang: Metall. and Mater. Transactions A, 53-30A (1999) 53-65. [9] M. Sakane, M. Ohnami, T. Hisano and T. Itsumura, J. JSMS (in Japanese), 37-414 (1988) 340-346. [10] K. Hatanaka, Y. Motosawa and S. Ogawa: Trans. JSME, 62-603 (1996) 2601-2608. [11] M. Yoshinaga, T. Kuwabara, T. Sugibayashi et. al.: Keikinzoku (Journal of the Japan Institute of Light Metals (in Japanese)), 3-7 (2003) 284-289.

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Nanomaterials by Severe Plastic Deformation 10.4028/www.scientific.net/MSF.503-504 Deformation Behavior of Fine Grained Al-Mg Alloy under Biaxial Stress 10.4028/www.scientific.net/MSF.503-504.475

DOI References

[1] K. Ameyama: Scripta Mater., 38 (1998) 726.

doi:10.1016/S1359-6462(97)00465-X [3] R.Z. Abdulov, R.Z. Valiev and N.A. Krashilnikov: J. Mater. Sci. Lett., 9 (1990) 1445.

doi:10.1007/BF00721611 [4] M. Noda, M. Hirohashi and K. Funami: J. Japan Inst. Metals, 67 (2003) 98-105.

doi:10.2320/matertrans.44.2288 [5] Y. Saito, H. Utsunomiya, N. Tsuji and T. Sakai: Acta Mater., 47 (1999) 579-583.

doi:10.1016/S1359-6454(98)00365-6