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Compressive deformation behaviour of magnesium alloys
Journal of Materials Processing Technology 162–163 (2005) 416–421
Compressive deformation behaviour of magnesium alloys Z. Trojanov´a ∗ , P. Luk´acˇ Charles University, Faculty of Mathematics and Physics, Department of Metal Physics, Ke Karlovu 5, CZ 12116 Praha 2, Czech Republic
Abstract The compressive deformation behaviour of magnesium alloys AZ91, AE42, AS21, QE22, ZE41, Mg4Li, and Mg8Li has been studied. The alloys were tested in the temperature range 23–300 ◦ C. The differences in the deformation behaviour of the alloys are discussed in terms of hardening and softening processes. Non-dislocation obstacles and forest dislocations are considered as the main obstacles for the moving dislocations, hence, responsible for hardening. Cross slip and climb of dislocations may control softening at higher temperatures. © 2005 Elsevier B.V. All rights reserved. Keywords: Deformation behaviour; Mechanical properties; Magnesium alloys
1. Introduction Lightweight materials are attractive for many applications. Although aluminium-based alloys are used for a considerable number of components, the use of magnesium alloys, which are structural materials with lowest density, is limited. Recent research on both types of alloys has been focused on their deformation behaviour. The magnesium-based alloys exhibit a high specific strength, i.e. the ratio of the yield stress (hardness) to the density at room temperature. The strength of Mg alloys decreases very rapidly with increasing temperature. On the other hand, magnesium alloys have a poor ductility, especially at room temperature. Usually, the ductility of magnesium alloys increases with increasing temperature. Equal channel angle pressing (ECAP) may improve the mechanical properties: an increase in the strength at 23 and 100 ◦ C and the ductility increase at temperatures between 23 and 300 ◦ C as was found for AZ91 magnesium alloy (e.g. [1]). Magnesium alloys also exhibit a high thermal conductivity and high coefficient of thermal expansion (CTE). The values of the CTE for pure Mg are higher than those for Mg alloys and composites [2–4]. Magnesium alloys possess a low corrosion resistance and low resistance to creep. Aune and Westengen [5] have reported that Mg–Al–Si (AS41 and AS21) and Mg–Al–RE (AE41 and AE42) alloys exhibit a ∗
Corresponding author. Tel.: +420 2 2191 1357; fax: +420 2 2191 1490. E-mail address: [email protected] (Z. Trojanov´a).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.024
major improvement in creep resistance due to a suppression of the formation of the Mg17 Al12 phase. Magnesium alloys containing zinc and rare-earth (RE) elements, e.g. ZE41 magnesium alloy, exhibit moderate strength after ageing [6]. The testing temperature influences significantly the deformation behaviour. In contrast to aluminium alloys, limited information is available on the deformation behaviour of magnesium alloys at temperatures, i.e. above room temperature. The room temperature (295 K = 0.32TM , where TM is the absolute melting temperature), is a relative high temperature. The differences in the deformation behaviour of aluminium and magnesium alloys are influenced by the limited crystallographic same slip systems in the hcp structure. As known, homogeneous deformation of polycrystals is possible, if five independent slip systems are active. The dominant slip system in magnesium and magnesium alloys at room temperature is the basal one. The number of independent mode of the basal slip is only two, which is not sufficient for the satisfying of the von Mises criterion [7]. Therefore, to fulfil von Mises criterion [7], a non-basal slip system should be active. The activity of any slip system depends on the critical resolved shear stress (CRSS); the activity of a non-basal slip system requires a high stress. The CRSS for the non-basal slip systems of Mg and its alloys depends very significantly on the testing temperature. It decreases rapidly with increasing temperature. The aim of present paper is to give an overview on the deformation behaviour of selected magnesium alloys, to es-
Z. Trojanov´a, P. Luk´acˇ / Journal of Materials Processing Technology 162–163 (2005) 416–421
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timate the temperature variation of the yield stress as well as the maximum stress and to discuss possible hardening and softening mechanisms.
2. Experimental The materials used in this study are the following magnesium alloys: AZ91 (nominal composition in wt.%: 9Al, 1Zn, balance Mg), AE42 (4Al, 2Nd), AS21 (2Al, 1Si), ZE41 (4Zn, 1Nd), QE22 (2Ag, 2Nd), Mg4Li (Mg–4 wt.% Li) and Mg8Li (Mg–8 wt.% Li). The alloys except Mg8Li form a hexagonal close-packed structure. Mg8Li alloy exhibits twophase structure, consisting of the ␣ (hcp) magnesium-rich and  (bcc) lithium-rich phases at room temperature. Lithium is lighter than magnesium and therefore, Mg–Li alloys exhibit ultralow densities. The alloys were squeeze cast. Test specimens were machined from the bars and they had a rectangular section of 6 mm × 6 mm and a gauge length of 12 mm. Compression tests were performed in an Instron machine in the temperature range from 20 to 300 ◦ C with a constant crosshead speed giving an initial strain rate of 1.33 × 10−4 s−1 . The yield stress, σ 0.2 , was estimated as the flow stress at 0.2% offset strain and the maximum stress, σ max , as the maximum value of the flow stress.
Fig. 2. Temperature dependence of the yield stress and the maximum stress for AZ91 alloy.
yield stress and the maximum stress as plotted in Fig. 2. A very small or no difference between the maximum stress and the yield stress at higher temperatures is also apparent. The true stress–true strain curves for AE42 magnesium alloy are plotted in Fig. 3. The temperature dependences of the yield stress and the maximum stress are shown in Fig. 4. It can be seen a significant influence of the testing temperature on the deformation behaviour. The values of the flow stress, yield stress and maximum stress decrease with increasing
3. Experimental results Fig. 1 shows the true stress–true strain curves of the AZ91 specimens deformed in compression at various temperatures. It can be seen that the shape of the deformation curves is significantly affected by the testing temperature. At temperatures T ≤ 150 ◦ C, hardening followed by softening is apparent whereas at T ≥ 200 ◦ C, a dynamic equilibrium between hardening and softening starts at the very beginning of deformation. The flow stress of specimens deformed at T ≥ 200 ◦ C is independent of strain. One may assume that the deformation behaviour at T ≤ 150 ◦ C is different from that at T ≥ 200 ◦ C. This is also obvious from the temperature dependences of the
Fig. 1. True stress–true strain curves obtained for AZ91 alloy and various temperatures.
Fig. 3. True stress–true strain curves obtained for AE42 alloy and various temperatures.
Fig. 4. Temperature dependence of the yield stress and the maximum stress for AE42 alloy.
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Fig. 5. True stress–true strain curves obtained for AS21 alloy and various temperatures.
temperature. The yield stress as well as the maximum stress of AE42 at selected temperatures is lower than those of the AZ91 alloy. A dynamic equilibrium between hardening and softening of the AE42 alloy begins at a temperature of about 250 ◦ C, which can also be seen from the plots of the yield stress and maximum stress against the testing temperature (Fig. 4). Fig. 5 shows the true stress–true strain curves of AS21 alloy for various testing temperatures. The influence of temperature on the course of the deformation curves of AS21 alloy is very similar to that observed for AE42 alloy. The values of the yield stress as well as the maximum stress of AS21 alloy and their variation with temperature (Fig. 6) are very close to those obtained for AE42 alloy. It can be seen from Figs. 7 and 8 that a dynamic equilibrium between hardening and softening in QE22 alloy starts at a temperature of 300 ◦ C. The values of the yield stress and maximum stress of QE22 alloy are higher than those of AZ91 alloy—compare Figs. 2 and 8. A rapid decrease in the yield stress of QE22 alloy with increasing temperature is observed at the testing temperatures higher than 300 ◦ C. The true stress–true strain curves of ZE41 alloys are shown in Fig. 9. From Fig. 10, it can be seen that both the yield stress and maximum stress of the alloy exhibit anomalous
Fig. 6. Temperature dependence of the yield stress and the maximum stress for AS21 alloy.
Fig. 7. True stress–true strain curves obtained for QE22 alloy and various temperatures.
Fig. 8. Temperature dependence of the yield stress and the maximum stress for QE22 alloy.
temperature dependence. The values of both the yield stress and maximum stress measured at 150 ◦ C are higher than those estimated at 100 ◦ C; a local minimum is observed at 100 ◦ C. The true stress–true strain curves in Fig. 9 indicate that the hardening rate of the alloy is close to zero at a temperature of 300 ◦ C; a dynamic equilibrium between hardening and softening.
Fig. 9. True stress–true strain curves obtained for ZE41 alloy and various temperatures.
Z. Trojanov´a, P. Luk´acˇ / Journal of Materials Processing Technology 162–163 (2005) 416–421
Fig. 10. Temperature dependence of the yield stress and the maximum stress for ZE41 alloy.
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Fig. 13. True stress–true strain curves obtained for Mg8Li alloy and various temperatures.
Fig. 11 shows the true stress–true strain curves of Mg4Li alloy. Fig. 12 includes the temperature dependences of the yield stress and maximum stress of the alloy. From Figs. 11 and 12, it can be seen that (a) the yield stress decreases slowly with temperature, whereas the maximum stress decreases rapidly with the testing temperature and (b) a relative high work hardening rate is observed at the beginning of the deformation at temperatures.
Fig. 14. Temperature dependence of the yield stress and the maximum stress for Mg8Li alloy.
Fig. 11. True stress–true strain curves obtained for Mg4Li alloy and various temperatures.
The true stress–true strain curves of a two-phase Mg8Li alloys and the temperature variations of the yield stress and maximum stress are shown in Figs. 13 and 14, respectively. It is evident that the values of the yield stress of Mg8Li alloy are higher than those of Mg4Li alloy. On the other hand, the values of the maximum stress of Mg8Li are lower than those of Mg4Li alloys. The hardening in Mg8Li alloy is lower than in Mg4Li alloy. The testing temperature influences significantly the work hardening rate. At T ≥ 150 ◦ C, the flow stress is practically independent of strain.
4. Discussion
Fig. 12. Temperature dependence of the yield stress and the maximum stress for Mg4Li alloy.
The presented results show that the shape of the stress–strain curves change at certain temperatures; the temperature depends on the composition of the investigated alloy. At and above this temperature, the work hardening rate is very close to zero. The changes in the shape of the deformation behaviour also indicate the activity of some softening processes. At higher temperatures, there is a dynamic balance between storage of dislocations leading to hardening and annihilation of dislocations leading to softening.
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As mention above, the activity of five independent slip systems is required for plastic deformation of polycrystals. In Mg and its alloys, beside the basal slip system, i.e. slip in a direction, slip in c + a direction is necessary [8]. Slip in 1 1 2¯ 3 directions and on second order pyramidal {1 1 2¯ 2} planes are very probable. The pyramidal slip systems can be considered as non-basal slip systems. When a slip system with c + a Burgers vector is active, the von Mises [7] criterion is obeyed. During deformation of magnesium-based polycrystalline alloys, the motion of not only a (basal) dislocations but also c + a (pyramidal) dislocations is assumed. Different dislocation reactions between the a dislocations and the c + a dislocations may occur [8]. One type of dislocation reactions may produce obstacles of the dislocation type. These dislocation obstacles for moving dislocation can be stored and they cause an increase in hardening. An interaction among the c + a pyramidal dislocations can take place. Some dislocation reactions can result in softening [8]. On the other hand, screw components of the c + a dislocations can move to the parallel slip planes by double cross slip and then annihilate, which causes a decrease in the work hardening rate; softening is observed. The activity of any non-basal slip system depends on the critical resolved shear stress that is necessary for the dislocation motion in the slip system. The value of the CRSS for the second-order pyramidal slip of Mg single crystals at room temperature is approximately 100 times higher than that for the basal slip system. The CRSS decreases very rapidly with temperature. It should be pointed out that it shows anomalous temperature dependence in a certain temperature range [9,10]. The CRSS can decrease with addition of solute atoms, e.g. of lithium [11,12] or zinc [13], if single crystals are deformed at certain temperatures. The main strengthening effect of Mg4Li alloy is solid solution hardening. Precipitates are the main non-dislocation obstacles in the other alloys investigated in this study. The density and strength of these obstacles influence the yield stress, which characterises the beginning of the deformation. The flow stress, σ, of alloys depends on the average dislocation density, ρ, as σ = σy + αGbρ1/2
(1)
where σ y is the yield stress and it is a function of the concentration of solute atoms, grain size, precipitates and temperature, α is a constant, G is the shear modulus and b is the magnitude of the Burgers vector. The dislocation structure can change during deformation and therefore, the flow stress also changes with strain and temperature. The change of the flow stress with strain is characterized by the work hardening rate Θ = ∂σ/∂ε, which decreases with strain. In the alloys investigated, there are obstacles nondislocation types such as precipitates and the dislocation obstacles (forest dislocations). A part of the moving dislocations stored at the obstacles contributes substantially to hardening.
On the other hand, processes such as cross slip and climb of dislocations contribute to softening. The dislocation microstructure can change. For simplicity, the density of the total dislocations is considered as the characteristic parameter of the evolution of microstructure during deformation. According to the model of Luk´acˇ and Bal´ık [14], we take into account storage of dislocations at both impenetrable obstacles and forest dislocations, and annihilation of dislocations due to both cross slip and climb. The evolution equation has the following form ∂ρ/∂e = K1 + K2 ρ1/2 − K3 ρ − K4 ρ3/2
(2)
Here K1 = 1/s, where s is the spacing between impenetrable (non-dislocation) obstacles. K2 is a coefficient of the dislocation multiplication intensity due to interaction with forest dislocations. K3 = LCS /b is the coefficient of the dislocation annihilation intensity due to cross slip, LCS is the dislocation segment length recovered by one slip event. K4 = Db2 ψτ/χγkT, where D is an abbreviation that includes the diffusion coefficient and the stacking fault energy, ψ a fraction of dislocation which can be annihilated by climb of dislocations with jogs, χ the ratio between dislocation climb distance and the average dislocation spacing, τ the shear stress, γ the shear strain rate, k is the Boltzmann’s constant and T is the absolute temperature. The stress dependence of the work hardening rate for polycrystals can thus be expressed in the following form Θ = A/(σ − σy ) + B − C(σ − σy ) − D(σ − σ)3
(3)
Parameter A is connected with the interaction of dislocations with the non-dislocation obstacles (incoherent precipitates). Parameter B characterises the work hardening due to the interaction with the forest dislocations. Both parameters A and B do not change with temperature, except at higher temperatures, when the activity of non-basal slip increases and it may change the forest dislocation density. The parameter C relates to recovery due to cross slip and increases with increasing temperature because of thermally activated character of cross slip. The parameter D is connected with a local climb of dislocation and should also increase with temperature. It is evident that the activity of non-basal slip system increases with increasing temperature. At higher temperatures, cross slip becomes a significant recovery process responsible for softening. The work hardening rate should decrease, which is observed experimentally. To the decrease in the work hardening rate may also contribute the B parameter that, in hexagonal metals may decrease with increasing temperature. The result may be a quasi steady state character of the true stress–true strain curves at higher temperatures.
5. Conclusions Shape of the true stress–true strain curves of magnesium alloys indicate that the deformation behaviour of the
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alloys depends significantly on the testing temperature. Nondislocation obstacle which was impenetrable for the moving dislocations and forest dislocations are responsible for hardening. At and above a certain temperature, softening processes influence the course of the work hardening curve. Increasing activity of softening processes with increasing temperature causes the differences in the deformation behaviour. Cross slip and climb of dislocations may be responsible for the observed softening.
Acknowledgements The authors appreciate support from the Grant Agency of the Academy of Sciences of the Czech Republic under Grant No. A2112303 and the Grant Agency of the Czech Republic under Grant No. 106/03/0843.
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References [1] K. M´athis, A. Mussi, Z. Trojanov´a, P. Luk´acˇ , E. Rauch, Kovove Mater. 41 (2003) 293. [2] P. Luk´acˇ , A. Rudajevov´a, Kovove Mater. 41 (2003) 281. [3] A. Rudajevov´a, P. Luk´acˇ , Acta Mater. 51 (2003) 5579. [4] A. Rudajevov´a, P. Luk´acˇ , J. Alloys Compd. 378 (2004) 172. [5] T.K. Aune, H. Westengen, SAE Technical Paper No. 950424, Detroit, MI, 1995. [6] M.O. Pekguleryuz, A.A. Kaya, Adv. Eng. Mater. 5 (2003) 866. [7] R. von Mises, Z. Angew. Math. Mech. 8 (1928) 161. [8] P. Luk´acˇ , K. M´athis, Kovove Mater. 40 (2002) 281. [9] J.F. Stohr, J.P. Poirier, Phil. Mag. 25 (1972) 1313. [10] S. Ando, K. Nakamura, K. Takashima, H. Tonda, J. Jpn. Inst. Light Met. 42 (1992) 765. [11] A. Urakami, M. Meshi, M.E. Fine, Proceedings of the ICSMA 2, vol. 1, ASM, Asilomar, 1970, p. 272. [12] S. Ando, H. Tonda, Mater. Sci. Forum 350/351 (2000) 43. [13] A. Akhtar, E. Teghtsoonian, Acta Metall. 17 (1969) 1351. [14] P. Luk´acˇ , J. Bal´ık, Key Eng. Mater. 97/98 (1994) 307.
Compressive deformation behaviour of magnesium alloys Z. Trojanov´a ∗ , P. Luk´acˇ Charles University, Faculty of Mathematics and Physics, Department of Metal Physics, Ke Karlovu 5, CZ 12116 Praha 2, Czech Republic
Abstract The compressive deformation behaviour of magnesium alloys AZ91, AE42, AS21, QE22, ZE41, Mg4Li, and Mg8Li has been studied. The alloys were tested in the temperature range 23–300 ◦ C. The differences in the deformation behaviour of the alloys are discussed in terms of hardening and softening processes. Non-dislocation obstacles and forest dislocations are considered as the main obstacles for the moving dislocations, hence, responsible for hardening. Cross slip and climb of dislocations may control softening at higher temperatures. © 2005 Elsevier B.V. All rights reserved. Keywords: Deformation behaviour; Mechanical properties; Magnesium alloys
1. Introduction Lightweight materials are attractive for many applications. Although aluminium-based alloys are used for a considerable number of components, the use of magnesium alloys, which are structural materials with lowest density, is limited. Recent research on both types of alloys has been focused on their deformation behaviour. The magnesium-based alloys exhibit a high specific strength, i.e. the ratio of the yield stress (hardness) to the density at room temperature. The strength of Mg alloys decreases very rapidly with increasing temperature. On the other hand, magnesium alloys have a poor ductility, especially at room temperature. Usually, the ductility of magnesium alloys increases with increasing temperature. Equal channel angle pressing (ECAP) may improve the mechanical properties: an increase in the strength at 23 and 100 ◦ C and the ductility increase at temperatures between 23 and 300 ◦ C as was found for AZ91 magnesium alloy (e.g. [1]). Magnesium alloys also exhibit a high thermal conductivity and high coefficient of thermal expansion (CTE). The values of the CTE for pure Mg are higher than those for Mg alloys and composites [2–4]. Magnesium alloys possess a low corrosion resistance and low resistance to creep. Aune and Westengen [5] have reported that Mg–Al–Si (AS41 and AS21) and Mg–Al–RE (AE41 and AE42) alloys exhibit a ∗
Corresponding author. Tel.: +420 2 2191 1357; fax: +420 2 2191 1490. E-mail address: [email protected] (Z. Trojanov´a).
0924-0136/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2005.02.024
major improvement in creep resistance due to a suppression of the formation of the Mg17 Al12 phase. Magnesium alloys containing zinc and rare-earth (RE) elements, e.g. ZE41 magnesium alloy, exhibit moderate strength after ageing [6]. The testing temperature influences significantly the deformation behaviour. In contrast to aluminium alloys, limited information is available on the deformation behaviour of magnesium alloys at temperatures, i.e. above room temperature. The room temperature (295 K = 0.32TM , where TM is the absolute melting temperature), is a relative high temperature. The differences in the deformation behaviour of aluminium and magnesium alloys are influenced by the limited crystallographic same slip systems in the hcp structure. As known, homogeneous deformation of polycrystals is possible, if five independent slip systems are active. The dominant slip system in magnesium and magnesium alloys at room temperature is the basal one. The number of independent mode of the basal slip is only two, which is not sufficient for the satisfying of the von Mises criterion [7]. Therefore, to fulfil von Mises criterion [7], a non-basal slip system should be active. The activity of any slip system depends on the critical resolved shear stress (CRSS); the activity of a non-basal slip system requires a high stress. The CRSS for the non-basal slip systems of Mg and its alloys depends very significantly on the testing temperature. It decreases rapidly with increasing temperature. The aim of present paper is to give an overview on the deformation behaviour of selected magnesium alloys, to es-
Z. Trojanov´a, P. Luk´acˇ / Journal of Materials Processing Technology 162–163 (2005) 416–421
417
timate the temperature variation of the yield stress as well as the maximum stress and to discuss possible hardening and softening mechanisms.
2. Experimental The materials used in this study are the following magnesium alloys: AZ91 (nominal composition in wt.%: 9Al, 1Zn, balance Mg), AE42 (4Al, 2Nd), AS21 (2Al, 1Si), ZE41 (4Zn, 1Nd), QE22 (2Ag, 2Nd), Mg4Li (Mg–4 wt.% Li) and Mg8Li (Mg–8 wt.% Li). The alloys except Mg8Li form a hexagonal close-packed structure. Mg8Li alloy exhibits twophase structure, consisting of the ␣ (hcp) magnesium-rich and  (bcc) lithium-rich phases at room temperature. Lithium is lighter than magnesium and therefore, Mg–Li alloys exhibit ultralow densities. The alloys were squeeze cast. Test specimens were machined from the bars and they had a rectangular section of 6 mm × 6 mm and a gauge length of 12 mm. Compression tests were performed in an Instron machine in the temperature range from 20 to 300 ◦ C with a constant crosshead speed giving an initial strain rate of 1.33 × 10−4 s−1 . The yield stress, σ 0.2 , was estimated as the flow stress at 0.2% offset strain and the maximum stress, σ max , as the maximum value of the flow stress.
Fig. 2. Temperature dependence of the yield stress and the maximum stress for AZ91 alloy.
yield stress and the maximum stress as plotted in Fig. 2. A very small or no difference between the maximum stress and the yield stress at higher temperatures is also apparent. The true stress–true strain curves for AE42 magnesium alloy are plotted in Fig. 3. The temperature dependences of the yield stress and the maximum stress are shown in Fig. 4. It can be seen a significant influence of the testing temperature on the deformation behaviour. The values of the flow stress, yield stress and maximum stress decrease with increasing
3. Experimental results Fig. 1 shows the true stress–true strain curves of the AZ91 specimens deformed in compression at various temperatures. It can be seen that the shape of the deformation curves is significantly affected by the testing temperature. At temperatures T ≤ 150 ◦ C, hardening followed by softening is apparent whereas at T ≥ 200 ◦ C, a dynamic equilibrium between hardening and softening starts at the very beginning of deformation. The flow stress of specimens deformed at T ≥ 200 ◦ C is independent of strain. One may assume that the deformation behaviour at T ≤ 150 ◦ C is different from that at T ≥ 200 ◦ C. This is also obvious from the temperature dependences of the
Fig. 1. True stress–true strain curves obtained for AZ91 alloy and various temperatures.
Fig. 3. True stress–true strain curves obtained for AE42 alloy and various temperatures.
Fig. 4. Temperature dependence of the yield stress and the maximum stress for AE42 alloy.
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Fig. 5. True stress–true strain curves obtained for AS21 alloy and various temperatures.
temperature. The yield stress as well as the maximum stress of AE42 at selected temperatures is lower than those of the AZ91 alloy. A dynamic equilibrium between hardening and softening of the AE42 alloy begins at a temperature of about 250 ◦ C, which can also be seen from the plots of the yield stress and maximum stress against the testing temperature (Fig. 4). Fig. 5 shows the true stress–true strain curves of AS21 alloy for various testing temperatures. The influence of temperature on the course of the deformation curves of AS21 alloy is very similar to that observed for AE42 alloy. The values of the yield stress as well as the maximum stress of AS21 alloy and their variation with temperature (Fig. 6) are very close to those obtained for AE42 alloy. It can be seen from Figs. 7 and 8 that a dynamic equilibrium between hardening and softening in QE22 alloy starts at a temperature of 300 ◦ C. The values of the yield stress and maximum stress of QE22 alloy are higher than those of AZ91 alloy—compare Figs. 2 and 8. A rapid decrease in the yield stress of QE22 alloy with increasing temperature is observed at the testing temperatures higher than 300 ◦ C. The true stress–true strain curves of ZE41 alloys are shown in Fig. 9. From Fig. 10, it can be seen that both the yield stress and maximum stress of the alloy exhibit anomalous
Fig. 6. Temperature dependence of the yield stress and the maximum stress for AS21 alloy.
Fig. 7. True stress–true strain curves obtained for QE22 alloy and various temperatures.
Fig. 8. Temperature dependence of the yield stress and the maximum stress for QE22 alloy.
temperature dependence. The values of both the yield stress and maximum stress measured at 150 ◦ C are higher than those estimated at 100 ◦ C; a local minimum is observed at 100 ◦ C. The true stress–true strain curves in Fig. 9 indicate that the hardening rate of the alloy is close to zero at a temperature of 300 ◦ C; a dynamic equilibrium between hardening and softening.
Fig. 9. True stress–true strain curves obtained for ZE41 alloy and various temperatures.
Z. Trojanov´a, P. Luk´acˇ / Journal of Materials Processing Technology 162–163 (2005) 416–421
Fig. 10. Temperature dependence of the yield stress and the maximum stress for ZE41 alloy.
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Fig. 13. True stress–true strain curves obtained for Mg8Li alloy and various temperatures.
Fig. 11 shows the true stress–true strain curves of Mg4Li alloy. Fig. 12 includes the temperature dependences of the yield stress and maximum stress of the alloy. From Figs. 11 and 12, it can be seen that (a) the yield stress decreases slowly with temperature, whereas the maximum stress decreases rapidly with the testing temperature and (b) a relative high work hardening rate is observed at the beginning of the deformation at temperatures.
Fig. 14. Temperature dependence of the yield stress and the maximum stress for Mg8Li alloy.
Fig. 11. True stress–true strain curves obtained for Mg4Li alloy and various temperatures.
The true stress–true strain curves of a two-phase Mg8Li alloys and the temperature variations of the yield stress and maximum stress are shown in Figs. 13 and 14, respectively. It is evident that the values of the yield stress of Mg8Li alloy are higher than those of Mg4Li alloy. On the other hand, the values of the maximum stress of Mg8Li are lower than those of Mg4Li alloys. The hardening in Mg8Li alloy is lower than in Mg4Li alloy. The testing temperature influences significantly the work hardening rate. At T ≥ 150 ◦ C, the flow stress is practically independent of strain.
4. Discussion
Fig. 12. Temperature dependence of the yield stress and the maximum stress for Mg4Li alloy.
The presented results show that the shape of the stress–strain curves change at certain temperatures; the temperature depends on the composition of the investigated alloy. At and above this temperature, the work hardening rate is very close to zero. The changes in the shape of the deformation behaviour also indicate the activity of some softening processes. At higher temperatures, there is a dynamic balance between storage of dislocations leading to hardening and annihilation of dislocations leading to softening.
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As mention above, the activity of five independent slip systems is required for plastic deformation of polycrystals. In Mg and its alloys, beside the basal slip system, i.e. slip in a direction, slip in c + a direction is necessary [8]. Slip in 1 1 2¯ 3 directions and on second order pyramidal {1 1 2¯ 2} planes are very probable. The pyramidal slip systems can be considered as non-basal slip systems. When a slip system with c + a Burgers vector is active, the von Mises [7] criterion is obeyed. During deformation of magnesium-based polycrystalline alloys, the motion of not only a (basal) dislocations but also c + a (pyramidal) dislocations is assumed. Different dislocation reactions between the a dislocations and the c + a dislocations may occur [8]. One type of dislocation reactions may produce obstacles of the dislocation type. These dislocation obstacles for moving dislocation can be stored and they cause an increase in hardening. An interaction among the c + a pyramidal dislocations can take place. Some dislocation reactions can result in softening [8]. On the other hand, screw components of the c + a dislocations can move to the parallel slip planes by double cross slip and then annihilate, which causes a decrease in the work hardening rate; softening is observed. The activity of any non-basal slip system depends on the critical resolved shear stress that is necessary for the dislocation motion in the slip system. The value of the CRSS for the second-order pyramidal slip of Mg single crystals at room temperature is approximately 100 times higher than that for the basal slip system. The CRSS decreases very rapidly with temperature. It should be pointed out that it shows anomalous temperature dependence in a certain temperature range [9,10]. The CRSS can decrease with addition of solute atoms, e.g. of lithium [11,12] or zinc [13], if single crystals are deformed at certain temperatures. The main strengthening effect of Mg4Li alloy is solid solution hardening. Precipitates are the main non-dislocation obstacles in the other alloys investigated in this study. The density and strength of these obstacles influence the yield stress, which characterises the beginning of the deformation. The flow stress, σ, of alloys depends on the average dislocation density, ρ, as σ = σy + αGbρ1/2
(1)
where σ y is the yield stress and it is a function of the concentration of solute atoms, grain size, precipitates and temperature, α is a constant, G is the shear modulus and b is the magnitude of the Burgers vector. The dislocation structure can change during deformation and therefore, the flow stress also changes with strain and temperature. The change of the flow stress with strain is characterized by the work hardening rate Θ = ∂σ/∂ε, which decreases with strain. In the alloys investigated, there are obstacles nondislocation types such as precipitates and the dislocation obstacles (forest dislocations). A part of the moving dislocations stored at the obstacles contributes substantially to hardening.
On the other hand, processes such as cross slip and climb of dislocations contribute to softening. The dislocation microstructure can change. For simplicity, the density of the total dislocations is considered as the characteristic parameter of the evolution of microstructure during deformation. According to the model of Luk´acˇ and Bal´ık [14], we take into account storage of dislocations at both impenetrable obstacles and forest dislocations, and annihilation of dislocations due to both cross slip and climb. The evolution equation has the following form ∂ρ/∂e = K1 + K2 ρ1/2 − K3 ρ − K4 ρ3/2
(2)
Here K1 = 1/s, where s is the spacing between impenetrable (non-dislocation) obstacles. K2 is a coefficient of the dislocation multiplication intensity due to interaction with forest dislocations. K3 = LCS /b is the coefficient of the dislocation annihilation intensity due to cross slip, LCS is the dislocation segment length recovered by one slip event. K4 = Db2 ψτ/χγkT, where D is an abbreviation that includes the diffusion coefficient and the stacking fault energy, ψ a fraction of dislocation which can be annihilated by climb of dislocations with jogs, χ the ratio between dislocation climb distance and the average dislocation spacing, τ the shear stress, γ the shear strain rate, k is the Boltzmann’s constant and T is the absolute temperature. The stress dependence of the work hardening rate for polycrystals can thus be expressed in the following form Θ = A/(σ − σy ) + B − C(σ − σy ) − D(σ − σ)3
(3)
Parameter A is connected with the interaction of dislocations with the non-dislocation obstacles (incoherent precipitates). Parameter B characterises the work hardening due to the interaction with the forest dislocations. Both parameters A and B do not change with temperature, except at higher temperatures, when the activity of non-basal slip increases and it may change the forest dislocation density. The parameter C relates to recovery due to cross slip and increases with increasing temperature because of thermally activated character of cross slip. The parameter D is connected with a local climb of dislocation and should also increase with temperature. It is evident that the activity of non-basal slip system increases with increasing temperature. At higher temperatures, cross slip becomes a significant recovery process responsible for softening. The work hardening rate should decrease, which is observed experimentally. To the decrease in the work hardening rate may also contribute the B parameter that, in hexagonal metals may decrease with increasing temperature. The result may be a quasi steady state character of the true stress–true strain curves at higher temperatures.
5. Conclusions Shape of the true stress–true strain curves of magnesium alloys indicate that the deformation behaviour of the
Z. Trojanov´a, P. Luk´acˇ / Journal of Materials Processing Technology 162–163 (2005) 416–421
alloys depends significantly on the testing temperature. Nondislocation obstacle which was impenetrable for the moving dislocations and forest dislocations are responsible for hardening. At and above a certain temperature, softening processes influence the course of the work hardening curve. Increasing activity of softening processes with increasing temperature causes the differences in the deformation behaviour. Cross slip and climb of dislocations may be responsible for the observed softening.
Acknowledgements The authors appreciate support from the Grant Agency of the Academy of Sciences of the Czech Republic under Grant No. A2112303 and the Grant Agency of the Czech Republic under Grant No. 106/03/0843.
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