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High temperature deformation of a Cu40Zr44Ag8Al8 bulk metallic glass
Materials Science and Engineering A 528 (2011) 3748–3753
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
High temperature deformation of a Cu40 Zr44 Ag8 Al8 bulk metallic glass Y. Liu a , J.J. Blandin b , G. Kapelski b , M. Suéry b,∗ a b
Department of Mechanical Engineering, Nanchang University, 330031 Nanchang, China SIMAP/GPM2, Grenoble-INP, CNRS, UJF, ENSE3, BP 46, 38402 Saint-Martin d’Hères Cedex, France
a r t i c l e
i n f o
Article history: Received 14 October 2010 Received in revised form 14 January 2011 Accepted 17 January 2011 Available online 22 January 2011 Keywords: Bulk metallic glasses High temperature deformation Constitutive law Viscosity
a b s t r a c t The deformation behavior of a Cu40 Zr44 Ag8 Al8 bulk metallic glass in its supercooled liquid region was investigated in compression. Strain rate jumps were carried out at various temperatures ranging from about Tg to Tg + 20 K. The results show that the alloy exhibits quasi-Newtonian behavior at the highest temperature with a transition to non Newtonian flow when temperature decreases and strain rate increases. The mechanical behavior has been analyzed in the framework of the free volume model. The material has been characterized after deformation at Tg + 20 K by XRD and comparison has been made with the same material simply held at high temperature for the same duration. It was observed that deformation slightly accelerates crystallization which results in a very important hardening on the stress–strain curve. However, even if there is no hardening at high temperature which suggests that no crystallization has occurred, some hardening is observed at room temperature even for short holding times at high temperature. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Bulk metallic glasses (BMG) exhibit not only unique mechanical properties at room temperature, such as high strength and large elastic domain [1] but also superplastic-like behavior in the viscous state at high temperatures above Tg , where Tg is the glass transition temperature [2,3]. Consequently, near net shape fabrication of structural components is increasingly considered by using various processing techniques [4–7]. The homogeneous viscous flow behavior of BMG in the supercooled liquid region (SLR) can be Newtonian or non-Newtonian, depending on testing temperature and strain rate [8]. The Newtonian flow (i.e. flow stress linearly dependent on the applied strain rate or viscosity independent of strain rate) is typically obtained at high temperature and low strain rates. The transition from Newtonian to non-Newtonian flow behavior when the strain rate is increased or when the temperature is reduced, has been attributed to the stress-induced formation of defects in the bulk glassy alloy, which limits the increase of the flow stress when the strain rate is increased [9–11]. In the SLR, significant microstructural transformations can occur and consequently affect the flow behavior of the alloy [12,13]. In the case of nanocrystallization, a huge increase of viscosity is frequently observed and this important hardening can be attributed to several causes: the phase decomposition which may occur in the alloy
∗ Corresponding author. Tel.: +33 4 76 82 63 42; fax: +33 4 76 82 63 82. E-mail addresses: [email protected], [email protected] (M. Suéry). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.01.045
before crystallization, the development of nanocrystals in the viscous matrix but also a change in the composition of the residual glass when crystallization occurs. Cu-based bulk metallic glasses have been widely investigated in the past in particular because they contain relatively low cost elements [14–16]. Moreover, for some compositions, plastic deformation in compression at room temperature has been reported. Some limited information concerning the mechanical properties in compression at room temperature of the Cu36 Zr48 Ag8 Al8 glass was also reported but to our knowledge, the high temperature deformation of this family of bulk metallic glasses has not been investigated in detail. It is the aim of this paper to study the mechanical behavior of a Cu40 Zr44 Ag8 Al8 BMG deformed in its SLR. 2. Experiments An alloy with a composition of Cu40 Zr44 Ag8 Al8 (at%) was prepared by casting in copper molds. The pure metals were melted in a cold crucible in an argon atmosphere and the resulting alloy was injected under pressure into a water-cooled copper mold. The composition of the pure metals was controlled within 0.01%. The alloy was solidified under various sample shapes but rods with diameter equal to 3 mm were selected for the high temperature deformation tests. The thermal stability of the glass was characterized by differential scanning calorimetry (DSC) at a heating rate equal to 20 K/min. Fig. 1 displays the corresponding DSC spectrum. From this spectrum, a glass transition temperature Tg = 706 K and a crystallization temperature Tx = 784 K were measured, leading to a value of T = Tx − Tg = 78 K. This value suggests that a quite large
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 1. DSC at a scan rate of 20 K/min of the Cu40 Zr44 Ag8 Al8 rod with diameter of 3 mm.
window for high temperature forming can be expected with this metallic glass. However, it is not necessarily an indicator of its good formability. Indeed, Schroers [17] suggested that the width of the supercooled liquid region T = Tx − Tg normalized by the width of the undercooled liquid region (Tl − Tg ) shows the best correlation with formability, where Tl is the liquidus temperature. For this alloy, Tl was measured and it is equal to 1186 K. T/(Tl − Tg ) is thus equal to 0.162 which is a quite small value compared to other BMGs. It can then be concluded that this alloy should exhibit limited formability in its SLR. The values of Tg , Tx and Tl are in relatively good agreement with previously published data on the same glass composition [18]. Cylindrical samples with a diameter of 3 mm and a height of 5 mm were machined from the as-cast rods. Compression tests were performed at five temperatures (703 K, 711 K, 716 K, 721 K, 726 K) in the temperature interval from about Tg to Tg + 20 K with strain rates typically between 2.5 × 10−4 s−1 and 5 × 10−3 s−1 . In order to get information about the rheological behavior of the glass, strain rate jump tests were carried out. In this study, jumps with an increase of the strain rate were applied. The test started at a strain rate of 2.5 × 10−4 s−1 and after a strain of about 0.15, the strain rate was suddenly increased to 5 × 10−4 s−1 , and then again to 10−3 s−1 , 2.5 × 10−3 s−1 and finally to 5 × 10−3 s−1 . The strain achieved during the test was about 0.70 and the total time for the strain rate jumps was about 20 min. The structure of the as-cast rod and of specimens after thermal treatments and deformation was examined by conventional X-ray diffractometry (XRD) with monochromatic CuK␣ radiation. Micro hardness measurements of specimens were also carried out using a load of 300 g applied during 15 s. The reported values are the average of five measurements. 3. Results and discussion 3.1. Mechanical behavior at high temperature From the strain rate jump tests, the variation with strain rate of ˙ where the apparent viscosity was calculated according to = /3ε, is the flow stress and ε˙ is the strain-rate. Fig. 2 shows the variation of the apparent viscosity with both temperature and strain rate. For high temperatures (726 K and 721 K), the viscosity is nearly independent of strain rate, which corresponds to a Newtonian behavior. As expected, a reduction of the temperature promotes a non Newtonian behavior and for the lowest investigated temperature, the apparent viscosity decreases continuously with increasing strain
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Fig. 2. Variation of the apparent viscosity with both temperature and applied strain rate.
rates. One can also mention that such behavior is also associated with stress overshoots, as frequently observed for many BMGs [10]. High temperature deformation in uniaxial condition of metallic glasses is frequently described according to:
Gm
ε˙ = 2cf D exp −
kT
sinh
V √ 2 3kT
= ε˙ 0 sinh
V √ 2 3kT
(1)
with cf the concentration in flow defects, D the Debye frequency, Gm the activation free energy for defect migration, V the activation volume (which is frequently given by V = 0 ˝f with 0 the local shear strain at a defect and ˝f the defect volume) and the hyperbolic sine term taking into account the effect of the applied stress on the energy barrier. If the flow stress is increased, it will affect the energy barrier via the activation volume, defined as the volume of matter involved in each elementary defect jump. Practically speaking, it will reduce the flow stress which would be obtained if the Newtonian regime was maintained. However, it must be kept in mind that significant overshoots observed after a strain rate jump suggest that a step with values of cf different from the equilibrium value (i.e. controlled only by temperature) is present. The nature of the defects involved in the high temperature deformation of BMG is still under debate but in the framework of a deformation mechanism based on free volumes, one must keep in mind that the defect concentration cf is very sensitive to a slight variation in free volume concentration [10]. Relation (1) can also be rewritten more simply according to: ε˙ = ε˙ 0 sinh
V √ 2 3kT
(2)
In this work, the activation volume was estimated from the measured plateau stresses, Fig. 3 showing the variation of this stress with the applied strain rate. The values of V and ε˙ 0 are given in Table 1. Activation volumes of about 240 A˚ 3 are obtained for test temperatures between 711 K and 721 K. These values are in relatively good agreement with previously published data in zirconium based BMG [10] or in magnesium based BMG [19] deformed in their SLR. The activation volume was not determined at 726 K since the Table 1 Variation with temperature of the activation volume and the frequency factor. Temperature (K)
Activation volume (Å3 )
ε˙ 0 (s−1 )
703 711 716 721
372 245 236 237
8.78 × 10−5 5.54 × 10−4 1.15 × 10−3 2.43 × 10−3
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Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 3. Variation of the strain rate with the plateau stress for the various temperatures investigated.
Fig. 4. Master curve derived from Eq. (7).
√ eq c V/2 3kT x = = f √ cf sinh (V/2 3kT ) cf sinh (x) eq
glass behaves with a quasi-Newtonian rheology at this temperature. A higher value was obtained at 703 K which may be linked to the fact that this temperature is below Tg . Data corresponding to this temperature will not be considered in the following. The values of ε˙ 0 are more difficult to compare since they generally exhibit a large scattering, keeping in mind that ε˙ 0 is a function of both the concentration in flow defects cf and the activation free energy Gm for defect migration. Eq. (1) can also be rewritten by considering the viscosity: =
exp(Gm /kT )
= √ 3ε˙ 2cf D sinh(V/2 3kT )
(3)
At the equilibrium, the flow defect concentration is thus given by:
cf = c0 exp
Gf − kT
(4)
where Gf can be considered as the free energy for the formation of the flow defects. Depending on the applied conditions, cf may be different from the equilibrium value. It may result from strain assisted nucleation of defects or relaxation kinetics [10,11]. However, in the Newtonian regime, the flow defect concentration is assumed to correspond to the equilibrium value and V kT. Consequently, Eq. (3) can be rewritten in this regime as: kT N = √ exp 3c0 D V
G kT
(5)
If V is assumed to be constant in the studied temperature interval, the associated activation energy G can be calculated. A value of about 5.3 eV (510 kJ mol−1 ) is measured for the low strain rates (<5 × 10−4 s−1 ). This value is close to values reported for other BMGs like ZrTiCuNiBe [13] and Pd40 Ni10 Cu30 P20 [20]. Nevertheless, one must mention that in the case of the Cu47.5 Zr47.5 Al5 bulk metallic glass, a value of Q = 654 kJ mol−1 was measured [21] in agreement with results reported in the case of a Zr49 Cu45 Al6 glass [22]. These authors noted that these values are higher than those usually reported in the case of zirconium based BMG and suggested that the creation of a unit shear event could require a higher energy in Cu–Zr based glasses. Combining Eqs. (2), (3) and (5) leads to: √ eq 2cf D (V/2 3kT ) exp(Gm /kT ) = √ N 2cf D sinh (V/2 3kT ) exp(Gm /kT )
cf
(6)
If the defect concentration is assumed to remain at the equilibrium (i.e. no variation with strain or strain rate), Eq. (6) can lead to the construction of a master curve [23]: x = N sinh(x)
(7)
with x=
V √ 2 3kT
Fig. 4 shows the variation of /N with V/2kT and the experimental data points obtained at various temperatures and strain rates fall on this master curve. This agreement supports the idea that the same mechanisms of deformation are operating in the investigated experimental domain and validates the hypothesis that the defect concentration remains roughly constant for the investigated strain rates at a given temperature of deformation. 3.2. Characterization of the material after deformation When the BMG is held at high temperature even below the crystallization temperature for sufficient time, crystallization may occur and affect the mechanical response of the material both at room and high temperatures. This effect is obviously enhanced when temperature increases. Moreover, deformation may accelerate crystallization. To check this possible effect, specimens were either deformed by compression at 726 K at a strain rate of 5 × 10−4 s−1 up to a strain of 1 or simply held without deformation at the same temperature for the same duration (33 min). Fig. 5 shows the XRD spectra corresponding to these specimens together with the spectrum of the as-cast material. The presence of only broad and diffuse maxima in the as-cast state confirms that the alloy is fully amorphous. After simple holding for 33 min at 726 K, no peaks are detected which indicates that no crystallization has occurred yet. Deformation, however, seems to promote crystallization since small peaks can be detected on the corresponding spectrum. Indexation of these peaks suggests that Cu10 Zr7 and AgZr crystals have started to form in the material. In order to confirm the effect of deformation, longer holding treatments up to 240 min were performed at 726 K. Fig. 6 shows the XRD spectra after holding treatments of 43, 55, 120 and 240 min. The spectra obtained after 43 and 55 min holding are very similar to that obtained after deformation during 33 min, which indicates that
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 5. XRD spectra for various specimens: (1) as-cast material; (2) specimen held for 33 min at 726 K; (3) specimen deformed in compression at 726 K at 5 × 10−4 s−1 up to a strain of 1: the total time at 726 K is 33 min.
acceleration of crystallization has occurred during deformation but remains quite limited. Holding for 120 and 240 min leads to very sharp peaks corresponding to the previously mentioned Cu10 Zr7 and AgZr phases with in addition two other peaks corresponding to the CuZr2 and AlCu2 Zr phases. These results are partly in agreement with the results obtained by Louzguine-Luzgin et al. [24] who observed that the phases formed at the first exothermic reaction are Cu10 Zr7 , AlCu2 Zr and AgZr in a Cu45 Zr45 Al5 Ag5 BMG (for which the initial crystallization reaction is of eutectic type). Conversely in a Cu36 Zr48 Al8 Ag8 BMG (for which the initial crystallization reaction is of primary type), the phase formed is mainly AgZr. The slight acceleration of crystallization due to deformation has been confirmed by deforming specimens by compression at 726 K at a given strain rate of 2.5 × 10−4 s−1 after various initial holding times at this temperature. Fig. 7 shows the variation of stress as a function of time for initial holding times of 5, 25 and 43 min. For the specimen initially held for 5 min at 726 K before deformation, stress shows a plateau up to a time of about 2000 s (33 min) and then sharply increases indicating that crystallization has started after this time (curve 1). When the material is held for 25 min before deformation, a similar behavior is observed but stress starts to increase sharply after about 2200 s (37 min) (curve 2). The specimen held for 43 min before deformation shows a different behavior (curve 3). Indeed, it was shown previously that 43 min holding is sufficient to induce crystallization: stress therefore increases
Fig. 6. XRD spectra of specimens annealed for various times (43, 55, 120 and 240 min) at 726 K.
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Fig. 7. Effect of holding at 726 K before deformation on the stress–time curves obtained during compression at 726 K at a strain rate of 2.5 × 10−4 s−1 .
sharply from the beginning of compression. These results concerning acceleration of crystallization in bulk metallic glasses by compression are in agreement with previous results reported in the case of Zr based BMG [22]. Nevertheless, this acceleration remains limited since the glass is deformed in a quasi Newtonian regime for which no significant creation of defects is expected. Fig. 7 shows that specimens corresponding to curves 1 and 2 were finally held for 43 min at 726 K but they have experienced different strains: 0.56 for specimen 1 and 0.27 for specimen 2. In addition, a specimen has been simply annealed at this temperature for the same time so that for this specimen the strain is 0. In order to evaluate the influence of these treatments on the mechanical properties of the material at room temperature, microhardness measurements were carried out on the various specimens and Table 2 shows the results of these measurements. The microhardness values are close to 650 whatever the treatment,which indicates that deformation at high temperature, even if it accelerates slightly the crystallization of the glass, does not influence the mechanical properties at room temperature for such durations. Nevertheless, these values are higher than the hardness value of the as-cast material (=540) which confirms that crystallization of the glass increases its hardness. Table 2 includes also the hardness value for specimen 3 in Fig. 7 for which the holding time before compression was 43 min. This specimen was deformed during 160 s up to a strain of 0.04 which leads therefore to a total time at 726 K of 2740 s. Its hardness is 660, which is very similar to the values found for the other specimens. These results lead to the conclusion that the crystallization states of the various specimens are probably very similar. This is confirmed by the XRD spectra of specimens 2 and 3 as shown in Fig. 8. Table 2 shows that holding at 726 K for 43 min is sufficient to lead to a significant increase of the hardness of the glass induced by some crystallization as demonstrated by the appearance of small peaks on the XRD spectrum of Fig. 6. For shorter holding times, crystallization was not detected yet but it is nevertheless interesting to see whether the hardness has varied or not compared with the initial as-cast state. Fig. 9 shows the hardness variation as a function of holding time up to 55 min at 726 K. Even for short holding times of 15 or 25 min, hardness increases significantly compared with the as-cast state. Such an increase is probably correlated with some clustering effect preceding crystallization. It is also possible that crystallization has started but the nanocrystals formed at this stage are not detected through XRD. They have no influence on the high temperature behavior of the materials but influence the properties at room temperature such as the microhardness. For 55 min
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Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Table 2 Microhardness values of specimens deformed up to various strains at 726 K after different annealing times at 726 K. Specimen
Strain
Total time (s)
Annealing time before deformation (s)
Deformation time (s)
Microhardness (HV)
1 2 3
0.00 0.56 0.27 0.04
2580 2580 2580 2740
2580 340 1500 2580
0 2240 1080 160
650 660 650 660
± ± ± ±
24 15 12 10
Fig. 8. XRD spectra of specimens 2 and 3 in Table 2 and Fig. 7.
holding at 726 K, the hardness has slightly increased compared to that after 43 min. The evolution of the amorphous state of the alloy for holding times of 15 and 25 min compared with the as-cast state can be put into evidence by performing DSC scans after these holding treatments. Fig. 10 shows DSC scans carried out at a heating rate of 20 K/min for these specimens together with scans carried out on an as-cast specimen and on specimens held for 43 and 55 min. The figure shows that the DSC curves look similar for the as-cast and for the specimens held for 15 and 25 min but the crystallization peak reduces with increasing holding time and in addition some shift of the characteristic temperatures has occurred. Tg seems to increase slightly whereas Tx decreases. The curves corresponding to 43 and 55 min holding are completely different: the previously observed crystallization peak has disappeared and has been replaced by another peak at higher temperature suggesting that crystallization has already started which confirms the results obtained previously
Fig. 9. Effect of holding time at 726 K on the micro hardness measured at room temperature (micro hardness of the as cast glass is also shown).
Fig. 10. DSC curves at a heating rate of 20 K/min of specimens previously held for various times at 726 K. The arrows show the position of the glass transition temperature Tg and of the crystallization temperature Tx .
by XRD in particular. It should be noted that this new peak was already detected on the curves corresponding to the specimens held for 15 and 25 min. Another confirmation of the evolution of the as-cast material during holding for various times at 726 K can be obtained by performing isothermal DSC. For this experiment, the specimen was heated very quickly (500 K/min) up to the desired temperature (726 K) and held isothermally at this temperature. Fig. 11 shows the corresponding DSC curve which exhibits two distinct crystallization peaks, one between 25 and 30 min and the other between 80 and 85 min. This curve confirms that some crystallization has occurred after 15 min and 25 min holding. 43 and 55 min holdings correspond to the end of the first peak so that it is not surprising to observe a significant hardness increase at room temperature and some important hardening at high temperature for these spec-
Fig. 11. Isothermal DSC curve at 726 K for a specimen initially heated up to this temperature at 500 K/min.
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
imens. The second crystallization is finished after less than 100 min so that holdings of specimens for 120 min and 240 min obviously lead to a well crystallized state as observed on the XRD spectra of Fig. 6. 4. Conclusions The thermal stability and the deformation behavior in compression of a Cu40 Zr44 Ag8 Al8 bulk metallic glass in its supercooled liquid region (SLR) have been investigated. The main conclusions of this work are the following: - The glass transition Tg and the crystallization Tx temperatures of the BMG are 706 K and 784 K respectively leading to a T of 78 K. - When deformed in compression at various temperatures in the SLR, the BMG exhibits quasi-Newtonian behavior at the highest temperature with a transition to nonNewtonian flow when temperature decreases and strain rate increases. - The high temperature behavior can be interpreted in the framework of the free volume model and the associated activation volumes and activation energy have been determined. - Holding the glass for sufficient time in the SLR leads to nanocrystallisation and the resulting crystalline phases have been identified. - Nanocrystallisation leads to hardening at room temperature even if it is not detected by XRD (i.e. short holding times) whereas hardening at high temperature seems to require a more advanced state of crystallization (i.e. longer holding times). - Deformation accelerates slightly crystallization compared with simple holding for the same duration at the same temperature.
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Acknowledgements Yong Liu acknowledges the financial support of the Centre National de la Recherche Scientifique (CNRS, France) and of the National Natural Science Foundation of China (NSFC, China) (No. 51001058). Dr. Jean-Louis SOUBEYROUX (CRETA, Institut Néel, CNRS Grenoble, France) is also acknowledged for his help in alloy elaboration. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
Z.F. Zhang, J. Eckert, L. Schultz, Acta Mater. 51 (2003) 1167. K.S. Lee, T.K. Ha, S. Ahn, Y.W. Chang, J. Non-Cryst. Solids 317 (2003) 193. J.P. Chu, C.L. Chiang, T. Mahalingam, T.G. Nieh, Scripta Mater. 49 (2003) 435. J. Schroers, Adv. Mater. 22 (2010) 1566. Y. Kawamura, T. Shibata, A. Inoue, T. Masumoto, Acta Mater. 46 (1998) 253. Y. Saotome, K. Itoh, T. Zhang, A. Inoue, Scripta Mater. 44 (2001) 1541. Y. Saotome, Y. Fukuda, I. Yamaguchi, A. Inoue, J. Alloys Compd. 434–435 (2007) 97. F. Spaepen, Acta Metall. 25 (1977) 407. J. Lu, G. Ravichandran, W.L. Johnson, Acta Mater. 51 (2003) 3429. M. Blétry, P. Guyot, J.J. Blandin, J.L. Soubeyroux, Acta Mater. 54 (2006) 1257. M. Blétry, P. Guyot, Y. Bréchet, J.J. Blandin, J.L. Soubeyroux, Acta. Mater. 55 (2007) 6331. T.A. Waniuk, R. Busch, A. Masuhr, W.L. Johnson, Acta Mater. 46 (1998) 5229. S. Gravier, J.J. Blandin, P. Donnadieu, Philos. Mag. 88 (2008) 2357. A. Inoue, W. Zhang, T. Zhang, K. Kurosaka, Mater. Trans. 42 (2001) 1149. A. Inoue, W. Zhang, Mater. Trans. 43 (2002) 2921. T. Zhang, A. Inoue, Mater. Trans. 43 (2002) 1367. J. Schroers, Acta Mater. 56 (2008) 471. W. Zhang, Q. Zhang, A. Inoue, Adv. Eng. Mater. 10 (2008) 1034. S. Puech, J.J. Blandin, J.L. Soubeyroux, Rev. Adv. Mater. Sci. 18 (2008) 311. H. Kato, Y. Kawamura, A. Inoue, H.S. Chen, Appl. Phys. Lett. 73 (1998) 3665. K.S. Lee, H.J. Jun, S. Pauly, B. Bartusch, Y.W. Chang, J. Eckert, Intermetallics 17 (2009) 65. X.L. Fu, Y. Li, C.A. Schuh, Acta Mater. 55 (2007) 3059. M. Blétry, P. Guyot, Y. Brechet, J.J. Blandin, J.L. Soubeyroux, Intermetallics 12 (2004) 1051. D.V. Louzguine-Luzgin, G. Xie, Q. Zhang, C. Suryanarayana, A. Inoue, Metall. Mater. Trans. A 41 (2010) 1664.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
High temperature deformation of a Cu40 Zr44 Ag8 Al8 bulk metallic glass Y. Liu a , J.J. Blandin b , G. Kapelski b , M. Suéry b,∗ a b
Department of Mechanical Engineering, Nanchang University, 330031 Nanchang, China SIMAP/GPM2, Grenoble-INP, CNRS, UJF, ENSE3, BP 46, 38402 Saint-Martin d’Hères Cedex, France
a r t i c l e
i n f o
Article history: Received 14 October 2010 Received in revised form 14 January 2011 Accepted 17 January 2011 Available online 22 January 2011 Keywords: Bulk metallic glasses High temperature deformation Constitutive law Viscosity
a b s t r a c t The deformation behavior of a Cu40 Zr44 Ag8 Al8 bulk metallic glass in its supercooled liquid region was investigated in compression. Strain rate jumps were carried out at various temperatures ranging from about Tg to Tg + 20 K. The results show that the alloy exhibits quasi-Newtonian behavior at the highest temperature with a transition to non Newtonian flow when temperature decreases and strain rate increases. The mechanical behavior has been analyzed in the framework of the free volume model. The material has been characterized after deformation at Tg + 20 K by XRD and comparison has been made with the same material simply held at high temperature for the same duration. It was observed that deformation slightly accelerates crystallization which results in a very important hardening on the stress–strain curve. However, even if there is no hardening at high temperature which suggests that no crystallization has occurred, some hardening is observed at room temperature even for short holding times at high temperature. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Bulk metallic glasses (BMG) exhibit not only unique mechanical properties at room temperature, such as high strength and large elastic domain [1] but also superplastic-like behavior in the viscous state at high temperatures above Tg , where Tg is the glass transition temperature [2,3]. Consequently, near net shape fabrication of structural components is increasingly considered by using various processing techniques [4–7]. The homogeneous viscous flow behavior of BMG in the supercooled liquid region (SLR) can be Newtonian or non-Newtonian, depending on testing temperature and strain rate [8]. The Newtonian flow (i.e. flow stress linearly dependent on the applied strain rate or viscosity independent of strain rate) is typically obtained at high temperature and low strain rates. The transition from Newtonian to non-Newtonian flow behavior when the strain rate is increased or when the temperature is reduced, has been attributed to the stress-induced formation of defects in the bulk glassy alloy, which limits the increase of the flow stress when the strain rate is increased [9–11]. In the SLR, significant microstructural transformations can occur and consequently affect the flow behavior of the alloy [12,13]. In the case of nanocrystallization, a huge increase of viscosity is frequently observed and this important hardening can be attributed to several causes: the phase decomposition which may occur in the alloy
∗ Corresponding author. Tel.: +33 4 76 82 63 42; fax: +33 4 76 82 63 82. E-mail addresses: [email protected], [email protected] (M. Suéry). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.01.045
before crystallization, the development of nanocrystals in the viscous matrix but also a change in the composition of the residual glass when crystallization occurs. Cu-based bulk metallic glasses have been widely investigated in the past in particular because they contain relatively low cost elements [14–16]. Moreover, for some compositions, plastic deformation in compression at room temperature has been reported. Some limited information concerning the mechanical properties in compression at room temperature of the Cu36 Zr48 Ag8 Al8 glass was also reported but to our knowledge, the high temperature deformation of this family of bulk metallic glasses has not been investigated in detail. It is the aim of this paper to study the mechanical behavior of a Cu40 Zr44 Ag8 Al8 BMG deformed in its SLR. 2. Experiments An alloy with a composition of Cu40 Zr44 Ag8 Al8 (at%) was prepared by casting in copper molds. The pure metals were melted in a cold crucible in an argon atmosphere and the resulting alloy was injected under pressure into a water-cooled copper mold. The composition of the pure metals was controlled within 0.01%. The alloy was solidified under various sample shapes but rods with diameter equal to 3 mm were selected for the high temperature deformation tests. The thermal stability of the glass was characterized by differential scanning calorimetry (DSC) at a heating rate equal to 20 K/min. Fig. 1 displays the corresponding DSC spectrum. From this spectrum, a glass transition temperature Tg = 706 K and a crystallization temperature Tx = 784 K were measured, leading to a value of T = Tx − Tg = 78 K. This value suggests that a quite large
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 1. DSC at a scan rate of 20 K/min of the Cu40 Zr44 Ag8 Al8 rod with diameter of 3 mm.
window for high temperature forming can be expected with this metallic glass. However, it is not necessarily an indicator of its good formability. Indeed, Schroers [17] suggested that the width of the supercooled liquid region T = Tx − Tg normalized by the width of the undercooled liquid region (Tl − Tg ) shows the best correlation with formability, where Tl is the liquidus temperature. For this alloy, Tl was measured and it is equal to 1186 K. T/(Tl − Tg ) is thus equal to 0.162 which is a quite small value compared to other BMGs. It can then be concluded that this alloy should exhibit limited formability in its SLR. The values of Tg , Tx and Tl are in relatively good agreement with previously published data on the same glass composition [18]. Cylindrical samples with a diameter of 3 mm and a height of 5 mm were machined from the as-cast rods. Compression tests were performed at five temperatures (703 K, 711 K, 716 K, 721 K, 726 K) in the temperature interval from about Tg to Tg + 20 K with strain rates typically between 2.5 × 10−4 s−1 and 5 × 10−3 s−1 . In order to get information about the rheological behavior of the glass, strain rate jump tests were carried out. In this study, jumps with an increase of the strain rate were applied. The test started at a strain rate of 2.5 × 10−4 s−1 and after a strain of about 0.15, the strain rate was suddenly increased to 5 × 10−4 s−1 , and then again to 10−3 s−1 , 2.5 × 10−3 s−1 and finally to 5 × 10−3 s−1 . The strain achieved during the test was about 0.70 and the total time for the strain rate jumps was about 20 min. The structure of the as-cast rod and of specimens after thermal treatments and deformation was examined by conventional X-ray diffractometry (XRD) with monochromatic CuK␣ radiation. Micro hardness measurements of specimens were also carried out using a load of 300 g applied during 15 s. The reported values are the average of five measurements. 3. Results and discussion 3.1. Mechanical behavior at high temperature From the strain rate jump tests, the variation with strain rate of ˙ where the apparent viscosity was calculated according to = /3ε, is the flow stress and ε˙ is the strain-rate. Fig. 2 shows the variation of the apparent viscosity with both temperature and strain rate. For high temperatures (726 K and 721 K), the viscosity is nearly independent of strain rate, which corresponds to a Newtonian behavior. As expected, a reduction of the temperature promotes a non Newtonian behavior and for the lowest investigated temperature, the apparent viscosity decreases continuously with increasing strain
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Fig. 2. Variation of the apparent viscosity with both temperature and applied strain rate.
rates. One can also mention that such behavior is also associated with stress overshoots, as frequently observed for many BMGs [10]. High temperature deformation in uniaxial condition of metallic glasses is frequently described according to:
Gm
ε˙ = 2cf D exp −
kT
sinh
V √ 2 3kT
= ε˙ 0 sinh
V √ 2 3kT
(1)
with cf the concentration in flow defects, D the Debye frequency, Gm the activation free energy for defect migration, V the activation volume (which is frequently given by V = 0 ˝f with 0 the local shear strain at a defect and ˝f the defect volume) and the hyperbolic sine term taking into account the effect of the applied stress on the energy barrier. If the flow stress is increased, it will affect the energy barrier via the activation volume, defined as the volume of matter involved in each elementary defect jump. Practically speaking, it will reduce the flow stress which would be obtained if the Newtonian regime was maintained. However, it must be kept in mind that significant overshoots observed after a strain rate jump suggest that a step with values of cf different from the equilibrium value (i.e. controlled only by temperature) is present. The nature of the defects involved in the high temperature deformation of BMG is still under debate but in the framework of a deformation mechanism based on free volumes, one must keep in mind that the defect concentration cf is very sensitive to a slight variation in free volume concentration [10]. Relation (1) can also be rewritten more simply according to: ε˙ = ε˙ 0 sinh
V √ 2 3kT
(2)
In this work, the activation volume was estimated from the measured plateau stresses, Fig. 3 showing the variation of this stress with the applied strain rate. The values of V and ε˙ 0 are given in Table 1. Activation volumes of about 240 A˚ 3 are obtained for test temperatures between 711 K and 721 K. These values are in relatively good agreement with previously published data in zirconium based BMG [10] or in magnesium based BMG [19] deformed in their SLR. The activation volume was not determined at 726 K since the Table 1 Variation with temperature of the activation volume and the frequency factor. Temperature (K)
Activation volume (Å3 )
ε˙ 0 (s−1 )
703 711 716 721
372 245 236 237
8.78 × 10−5 5.54 × 10−4 1.15 × 10−3 2.43 × 10−3
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Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 3. Variation of the strain rate with the plateau stress for the various temperatures investigated.
Fig. 4. Master curve derived from Eq. (7).
√ eq c V/2 3kT x = = f √ cf sinh (V/2 3kT ) cf sinh (x) eq
glass behaves with a quasi-Newtonian rheology at this temperature. A higher value was obtained at 703 K which may be linked to the fact that this temperature is below Tg . Data corresponding to this temperature will not be considered in the following. The values of ε˙ 0 are more difficult to compare since they generally exhibit a large scattering, keeping in mind that ε˙ 0 is a function of both the concentration in flow defects cf and the activation free energy Gm for defect migration. Eq. (1) can also be rewritten by considering the viscosity: =
exp(Gm /kT )
= √ 3ε˙ 2cf D sinh(V/2 3kT )
(3)
At the equilibrium, the flow defect concentration is thus given by:
cf = c0 exp
Gf − kT
(4)
where Gf can be considered as the free energy for the formation of the flow defects. Depending on the applied conditions, cf may be different from the equilibrium value. It may result from strain assisted nucleation of defects or relaxation kinetics [10,11]. However, in the Newtonian regime, the flow defect concentration is assumed to correspond to the equilibrium value and V kT. Consequently, Eq. (3) can be rewritten in this regime as: kT N = √ exp 3c0 D V
G kT
(5)
If V is assumed to be constant in the studied temperature interval, the associated activation energy G can be calculated. A value of about 5.3 eV (510 kJ mol−1 ) is measured for the low strain rates (<5 × 10−4 s−1 ). This value is close to values reported for other BMGs like ZrTiCuNiBe [13] and Pd40 Ni10 Cu30 P20 [20]. Nevertheless, one must mention that in the case of the Cu47.5 Zr47.5 Al5 bulk metallic glass, a value of Q = 654 kJ mol−1 was measured [21] in agreement with results reported in the case of a Zr49 Cu45 Al6 glass [22]. These authors noted that these values are higher than those usually reported in the case of zirconium based BMG and suggested that the creation of a unit shear event could require a higher energy in Cu–Zr based glasses. Combining Eqs. (2), (3) and (5) leads to: √ eq 2cf D (V/2 3kT ) exp(Gm /kT ) = √ N 2cf D sinh (V/2 3kT ) exp(Gm /kT )
cf
(6)
If the defect concentration is assumed to remain at the equilibrium (i.e. no variation with strain or strain rate), Eq. (6) can lead to the construction of a master curve [23]: x = N sinh(x)
(7)
with x=
V √ 2 3kT
Fig. 4 shows the variation of /N with V/2kT and the experimental data points obtained at various temperatures and strain rates fall on this master curve. This agreement supports the idea that the same mechanisms of deformation are operating in the investigated experimental domain and validates the hypothesis that the defect concentration remains roughly constant for the investigated strain rates at a given temperature of deformation. 3.2. Characterization of the material after deformation When the BMG is held at high temperature even below the crystallization temperature for sufficient time, crystallization may occur and affect the mechanical response of the material both at room and high temperatures. This effect is obviously enhanced when temperature increases. Moreover, deformation may accelerate crystallization. To check this possible effect, specimens were either deformed by compression at 726 K at a strain rate of 5 × 10−4 s−1 up to a strain of 1 or simply held without deformation at the same temperature for the same duration (33 min). Fig. 5 shows the XRD spectra corresponding to these specimens together with the spectrum of the as-cast material. The presence of only broad and diffuse maxima in the as-cast state confirms that the alloy is fully amorphous. After simple holding for 33 min at 726 K, no peaks are detected which indicates that no crystallization has occurred yet. Deformation, however, seems to promote crystallization since small peaks can be detected on the corresponding spectrum. Indexation of these peaks suggests that Cu10 Zr7 and AgZr crystals have started to form in the material. In order to confirm the effect of deformation, longer holding treatments up to 240 min were performed at 726 K. Fig. 6 shows the XRD spectra after holding treatments of 43, 55, 120 and 240 min. The spectra obtained after 43 and 55 min holding are very similar to that obtained after deformation during 33 min, which indicates that
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Fig. 5. XRD spectra for various specimens: (1) as-cast material; (2) specimen held for 33 min at 726 K; (3) specimen deformed in compression at 726 K at 5 × 10−4 s−1 up to a strain of 1: the total time at 726 K is 33 min.
acceleration of crystallization has occurred during deformation but remains quite limited. Holding for 120 and 240 min leads to very sharp peaks corresponding to the previously mentioned Cu10 Zr7 and AgZr phases with in addition two other peaks corresponding to the CuZr2 and AlCu2 Zr phases. These results are partly in agreement with the results obtained by Louzguine-Luzgin et al. [24] who observed that the phases formed at the first exothermic reaction are Cu10 Zr7 , AlCu2 Zr and AgZr in a Cu45 Zr45 Al5 Ag5 BMG (for which the initial crystallization reaction is of eutectic type). Conversely in a Cu36 Zr48 Al8 Ag8 BMG (for which the initial crystallization reaction is of primary type), the phase formed is mainly AgZr. The slight acceleration of crystallization due to deformation has been confirmed by deforming specimens by compression at 726 K at a given strain rate of 2.5 × 10−4 s−1 after various initial holding times at this temperature. Fig. 7 shows the variation of stress as a function of time for initial holding times of 5, 25 and 43 min. For the specimen initially held for 5 min at 726 K before deformation, stress shows a plateau up to a time of about 2000 s (33 min) and then sharply increases indicating that crystallization has started after this time (curve 1). When the material is held for 25 min before deformation, a similar behavior is observed but stress starts to increase sharply after about 2200 s (37 min) (curve 2). The specimen held for 43 min before deformation shows a different behavior (curve 3). Indeed, it was shown previously that 43 min holding is sufficient to induce crystallization: stress therefore increases
Fig. 6. XRD spectra of specimens annealed for various times (43, 55, 120 and 240 min) at 726 K.
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Fig. 7. Effect of holding at 726 K before deformation on the stress–time curves obtained during compression at 726 K at a strain rate of 2.5 × 10−4 s−1 .
sharply from the beginning of compression. These results concerning acceleration of crystallization in bulk metallic glasses by compression are in agreement with previous results reported in the case of Zr based BMG [22]. Nevertheless, this acceleration remains limited since the glass is deformed in a quasi Newtonian regime for which no significant creation of defects is expected. Fig. 7 shows that specimens corresponding to curves 1 and 2 were finally held for 43 min at 726 K but they have experienced different strains: 0.56 for specimen 1 and 0.27 for specimen 2. In addition, a specimen has been simply annealed at this temperature for the same time so that for this specimen the strain is 0. In order to evaluate the influence of these treatments on the mechanical properties of the material at room temperature, microhardness measurements were carried out on the various specimens and Table 2 shows the results of these measurements. The microhardness values are close to 650 whatever the treatment,which indicates that deformation at high temperature, even if it accelerates slightly the crystallization of the glass, does not influence the mechanical properties at room temperature for such durations. Nevertheless, these values are higher than the hardness value of the as-cast material (=540) which confirms that crystallization of the glass increases its hardness. Table 2 includes also the hardness value for specimen 3 in Fig. 7 for which the holding time before compression was 43 min. This specimen was deformed during 160 s up to a strain of 0.04 which leads therefore to a total time at 726 K of 2740 s. Its hardness is 660, which is very similar to the values found for the other specimens. These results lead to the conclusion that the crystallization states of the various specimens are probably very similar. This is confirmed by the XRD spectra of specimens 2 and 3 as shown in Fig. 8. Table 2 shows that holding at 726 K for 43 min is sufficient to lead to a significant increase of the hardness of the glass induced by some crystallization as demonstrated by the appearance of small peaks on the XRD spectrum of Fig. 6. For shorter holding times, crystallization was not detected yet but it is nevertheless interesting to see whether the hardness has varied or not compared with the initial as-cast state. Fig. 9 shows the hardness variation as a function of holding time up to 55 min at 726 K. Even for short holding times of 15 or 25 min, hardness increases significantly compared with the as-cast state. Such an increase is probably correlated with some clustering effect preceding crystallization. It is also possible that crystallization has started but the nanocrystals formed at this stage are not detected through XRD. They have no influence on the high temperature behavior of the materials but influence the properties at room temperature such as the microhardness. For 55 min
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Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
Table 2 Microhardness values of specimens deformed up to various strains at 726 K after different annealing times at 726 K. Specimen
Strain
Total time (s)
Annealing time before deformation (s)
Deformation time (s)
Microhardness (HV)
1 2 3
0.00 0.56 0.27 0.04
2580 2580 2580 2740
2580 340 1500 2580
0 2240 1080 160
650 660 650 660
± ± ± ±
24 15 12 10
Fig. 8. XRD spectra of specimens 2 and 3 in Table 2 and Fig. 7.
holding at 726 K, the hardness has slightly increased compared to that after 43 min. The evolution of the amorphous state of the alloy for holding times of 15 and 25 min compared with the as-cast state can be put into evidence by performing DSC scans after these holding treatments. Fig. 10 shows DSC scans carried out at a heating rate of 20 K/min for these specimens together with scans carried out on an as-cast specimen and on specimens held for 43 and 55 min. The figure shows that the DSC curves look similar for the as-cast and for the specimens held for 15 and 25 min but the crystallization peak reduces with increasing holding time and in addition some shift of the characteristic temperatures has occurred. Tg seems to increase slightly whereas Tx decreases. The curves corresponding to 43 and 55 min holding are completely different: the previously observed crystallization peak has disappeared and has been replaced by another peak at higher temperature suggesting that crystallization has already started which confirms the results obtained previously
Fig. 9. Effect of holding time at 726 K on the micro hardness measured at room temperature (micro hardness of the as cast glass is also shown).
Fig. 10. DSC curves at a heating rate of 20 K/min of specimens previously held for various times at 726 K. The arrows show the position of the glass transition temperature Tg and of the crystallization temperature Tx .
by XRD in particular. It should be noted that this new peak was already detected on the curves corresponding to the specimens held for 15 and 25 min. Another confirmation of the evolution of the as-cast material during holding for various times at 726 K can be obtained by performing isothermal DSC. For this experiment, the specimen was heated very quickly (500 K/min) up to the desired temperature (726 K) and held isothermally at this temperature. Fig. 11 shows the corresponding DSC curve which exhibits two distinct crystallization peaks, one between 25 and 30 min and the other between 80 and 85 min. This curve confirms that some crystallization has occurred after 15 min and 25 min holding. 43 and 55 min holdings correspond to the end of the first peak so that it is not surprising to observe a significant hardness increase at room temperature and some important hardening at high temperature for these spec-
Fig. 11. Isothermal DSC curve at 726 K for a specimen initially heated up to this temperature at 500 K/min.
Y. Liu et al. / Materials Science and Engineering A 528 (2011) 3748–3753
imens. The second crystallization is finished after less than 100 min so that holdings of specimens for 120 min and 240 min obviously lead to a well crystallized state as observed on the XRD spectra of Fig. 6. 4. Conclusions The thermal stability and the deformation behavior in compression of a Cu40 Zr44 Ag8 Al8 bulk metallic glass in its supercooled liquid region (SLR) have been investigated. The main conclusions of this work are the following: - The glass transition Tg and the crystallization Tx temperatures of the BMG are 706 K and 784 K respectively leading to a T of 78 K. - When deformed in compression at various temperatures in the SLR, the BMG exhibits quasi-Newtonian behavior at the highest temperature with a transition to nonNewtonian flow when temperature decreases and strain rate increases. - The high temperature behavior can be interpreted in the framework of the free volume model and the associated activation volumes and activation energy have been determined. - Holding the glass for sufficient time in the SLR leads to nanocrystallisation and the resulting crystalline phases have been identified. - Nanocrystallisation leads to hardening at room temperature even if it is not detected by XRD (i.e. short holding times) whereas hardening at high temperature seems to require a more advanced state of crystallization (i.e. longer holding times). - Deformation accelerates slightly crystallization compared with simple holding for the same duration at the same temperature.
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Acknowledgements Yong Liu acknowledges the financial support of the Centre National de la Recherche Scientifique (CNRS, France) and of the National Natural Science Foundation of China (NSFC, China) (No. 51001058). Dr. Jean-Louis SOUBEYROUX (CRETA, Institut Néel, CNRS Grenoble, France) is also acknowledged for his help in alloy elaboration. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
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