The effect of heterogeneous deformation on the hot deformation of WE54 magnesium alloy

Materials and Design 58 (2014) 30–35

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The effect of heterogeneous deformation on the hot deformation of WE54 magnesium alloy Manuel Carsi a, M. Jesús Bartolome a, Ignacio Rieiro b, Félix Peñalba c, Oscar A. Ruano a,⇑ a

Dept. Metalurgia Física, Centro Nacional de Investigaciones Metalúrgicas, CENIM-CSIC, Av. Gregorio del Amo 8, 28040 Madrid, Spain Facultad de Matemática, Universidad de Castilla-La Mancha, Av. Carlos III s/n, 45071 Toledo, Spain c Tecnalia, Mikeletegi Pasealekua 2, Parque Tecnológico, 20009 San Sebastián, Spain b

a r t i c l e

i n f o

Article history: Received 4 November 2013 Accepted 18 January 2014 Available online 26 January 2014 Keywords: Magnesium alloy Recrystallization Hot compression Garofalo equation Efficiency and stability maps

a b s t r a c t The high temperature forming behavior of WE54 magnesium alloy is studied by means of compression and tension tests. Metallographic investigation was performed to evaluate the heterogeneous deformation of the compression samples at high temperature. Dynamic recrystallization was found to be related to the amount of deformation in the various regions of the compression sample. The compression data allowed determination of the Garofalo equation describing the hot deformation behavior. The parameters n and Q, stress exponent and activation energy, of this equation were 4.4 and 237 kJ/mol respectively. This equation was used to predict the formability behavior for the hot rolling process and also to determine the maximum forming efficiency and stability of the alloy. The optimum rolling temperature was found to be 520 °C. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Magnesium alloys are the lightest alloys used as structural metallic alloys. Various magnesium alloys of the AZ, AM and ZK series find applications, especially in automobile and motorcycle parts [1]. However, these alloys have poor mechanical and corrosion properties at temperatures above 250 °C [2,3]. Magnesium alloys containing yttrium and/or high amount of (heavy) rare earth (RE) metals have the best combination of mechanical properties [4,5] and corrosion resistance at high temperature [6]. The improved mechanical properties through RE addition have been attributed mainly to precipitation strengthening, and particularly the precipitation of a fine dispersion of intermetallic particles [5,7,8]. These intermetallic phases exhibit little diffusivity and a good coherence with the matrix [9], conferring the alloys excellent creep resistance [10,11] and also better tensile properties than other magnesium alloys [12,13]. In the conventional Mg–Al and Mg–Zn alloys, DRX occurred extensively at temperatures of about 300–450 °C by bulging of original grain boundaries and subsequent subgrain growth [14,15]. In the case of Mg–RE alloy the amount of stable precipitates should influence strongly this behavior and the recrystallization process at these temperatures should be more difficult [16]. These investi-

⇑ Corresponding author. Tel.: +34 915538900; fax: +34 915347425. E-mail address: [email protected] (O.A. Ruano). http://dx.doi.org/10.1016/j.matdes.2014.01.038 0261-3069/Ó 2014 Elsevier Ltd. All rights reserved.

gations and those on hot workability and constitutive modeling of high temperature magnesium alloys are quite limited [17]. Important for hot workability is the study of the conditions of strain, strain rate and temperature in order to obtain components free of defects. These conditions are best described by deformation maps that define regions without flow instability and free of damage [15,18]. These maps are drawn, according to Prasad instructions, by interpolating the experimental stress and strain rate data using polynomial functions, usually of third order, and then differentiated ‘‘point by point’’. The curves obtained are almost always wavy and this corresponds to ‘‘islands’’ in the maps. In contrast, our approach is based on recalculation of the data directly from constitutive equations that are later used to draw the processing maps [19]. In the present work, the heterogeneity of deformation during hot compression and the accompanied dynamic recrystallization of a precipitation strengthened magnesium-rare earth, WE54, alloy is investigated. Processing maps are constructed to determine the safe conditions of temperature and strain rate. 2. Material and experimental procedure A magnesium WE54 commercial alloy was used in the present study. The nominal composition of the cast ingot in wt.% is Mg–2.8HRE–5.1Y–1.8Nd–0.52Zr (HRE = heavy rare earth). The as-received material was in the form of an extruded bar of 40 mm diameter. Average grain size was determined according to

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M. Carsi et al. / Materials and Design 58 (2014) 30–35

1,4 1,2 1 0,8

eF

the standard ASTM: E-112. Cylindrical compression samples, 10 mm in diameter and 15 mm in length, were machined from the bar. The compression axis of the sample was parallel to the extruded axis of the bar. Hot axisymetric uniaxial compression testing was performed in the temperature range 301–461 °C using a Gleeble 3800 simulator at strain rates in the range 0.72–8.7 s1. The equipment uses a servo-hydraulic mechanism that deforms the sample to a desired strain, in this case e = 1. The samples are compressed in vacuum between two well lubricated platens to minimize friction problems and electrical heating is used to reach the desired temperature that is measured using a K-type thermocouple welded directly to the sample. In addition, tensile tests were conducted in an Instron 2518 testing machine at various temperatures and 0.9 s1 to determine the ductility of the alloy. The rectangular tensile samples, 3.5 mm in width, 2 mm in thickness and 15 mm in gauge length, were machined from the bar longitudinal section and cut in a Struers Accutom precision cut-off machine. The microstructure from the as-received material and that of the tested samples was evaluated using an optical microscope (OM) Olympus BH2-UM.

0,6 0,4 0,2 0.9 s

0 350

400

450

500

-1

550

600

T, ºC Fig. 2. Elongation to failure as a function of temperature for tensile tests conducted at 0.9 s1.

3. Results and discussion 3.1. Compression and tensile tests Compression tests were conducted at five temperatures and four strain rates. Fig. 1 presents an example of these tests at 8.7 s1 and various temperatures. This strain rate is similar to that used in the industry for hot rolling of magnesium alloys. All the hot compression curves are characterized by a sharp increase of stress with strain up to a maximum followed by a limited softening until a strain of about 1. This behavior is typical of dynamic recrystallization occurring during deformation [20]. The figure shows very limited ductility at 301 and 333 °C, especially at the former temperature. It is worth noting that at 301 °C most of the tensile samples failed in the elastic regime. As expected, the flow stress in compression increases with decreasing temperature and increasing strain rate. The values of the maximum stress are much higher than those of alloys of the AZ and ZK series. Compared to a ZK30 alloy the stress values are about twice at all temperatures [21]. Tensile tests at the maximum deformation rate allowed by the equipment, 0.9 s1, were conducted to have an estimation of the ductility of the alloy. Fig. 2 shows a representation of the

elongation to failure, eF, as a function of temperature at 0.9 s1 for the WE54 magnesium alloy. A peak in ductility is observed at about 520 °C. 3.2. Microstructural characterization The microstructure of the WE54 alloy in the as-extruded condition is shown in Fig. 3. It is a fully recrystallized microstructure consisting of equiaxic grains of about 20 lm in size. Some twins are present inside the grains. This microstructure is the result of the high temperature and strain developed during the extrusion process. Sections containing the compression axis were cut for metallographic observations. Fig. 4 shows a metallographic appearance of the flow line contours of a compression sample deformed at 461 °C, 8.7 s1 and e = 1. The compression axis is along locations 1, 2 and 3. The sample clearly presents a heterogeneous deformation pattern. During testing, the metal near the periphery of the billet can be seen as the ‘‘easy deformed region’’ and material near to the geometric center can be seen as the ‘‘difficult deformed region’’ [22]. In other words, the strain is higher in the center and decreases toward its periphery.

-300 301ºC 333ºC 379ºC 423ºC 461ºC

-250

, MPa

-200

-150

-100

-50 8.7 s

0

0

-0,2

-0,4

ε

-0,6

-1

-0,8

-1

Fig. 1. Stress vs strain curves from compression tests conducted at 8.7 s1 and various temperatures.

Fig. 3. Microstructure of the as-received WE54 alloy.

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M. Carsi et al. / Materials and Design 58 (2014) 30–35

10 e',301C 333ºC 379ºC 423ºC 461ºC

1

Fig. 4. Flow line contours of a longitudinal section of a compression sample deformed at 461 °C, 8.7 s1 and e = 1.

Fig. 5 shows micrographs taken at locations named 3, 5, 6 and 10 in Fig. 4. The order of presentation of the micrographs in Fig. 5 is proportional to the amount of deformation in the compression sample of Fig. 4. Location 3, Fig. 5a, with the highest deformation, presents an almost fully recrystallized condition, although some patches of unrecrystallized regions are also observed as bright and elongated islands in the micrograph. The recrystallized grains are about 3 lm in size. Furthermore, locations 5 and 6, Fig. 5b and c respectively, that are situated near the edge of the sample, show a higher amount of unrecrystallized regions. Finally, location 10, Fig. 5d, shows a deformed grain microstructure with the grains elongated perpendicularly to the compression axis. No hints of recrystallization is observed. This could be attributed to the effect of a change in the mode of deformation that is affected by the presence of the surface. It can be concluded that the heterogeneous microstructures obtained can be attributed to the heterogeneous distribution of the strain in the compression sample since the amount of deformation alters the amount of stored energy and the number of the nuclei necessary to start the dynamic recrystallization process. At his temperature, 461 °C, probably the entire sample would recrystallize completely if given enough time and/or strain. 3.3. Constitutive equations Fig. 6 shows plots of the strain-rate, e_ , against the flow stress, r, at various temperatures. The stress was calculated at the peak of

0,1

100

1000

σ , MPa Fig. 6. Strain rate as a function of stress at various temperatures for the WE 54 alloy.

the stress–strain curves. This is because recrystallization at the peak is clearly begun and is not influenced by grain or particle growth. Furthermore, the influence of adiabatic heating is negligible. This is important since for a correct determination of the activation energy the microstructural state of the samples at different temperatures should be the same. The data at 301 °C in Fig. 6 had a strong scatter at the highest strain rates which is attributed to the lack of ductility and therefore were eliminated. On these plots, the slope of the curves corresponds to the stress exponent, n, considering a power law relationship for creep. The n values increase with decreasing temperature from n = 8 at 461 °C up to n = 30 at 333 °C. On the other hand, the apparent activation energy for deformation, Q, cannot be calculated assuming a power law relation because the curves given in Fig. 3 are not parallel. Therefore, an analysis of the deformation behavior of this alloy was conducted by means of the Garofalo constitutive equation. This equation gives the envelopment of all possible power law equations along the

Fig. 5. Micrographs taken from Fig. 4 at: (a) location 3, (b) location 5, (c) location 6 and (d) location 10.

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M. Carsi et al. / Materials and Design 58 (2014) 30–35

strain rate and temperature ranges investigated. The hyperbolic sine Garofalo equation can be expressed as [23,24]:



e_ ¼ A exp 

 Q n ½sinh ar RT

54

0,5

52

ð1Þ

e_ exp 237 kJ=mol=RT ¼ 3:51  1015 sinh ð0:013rÞ4:4

ð2Þ

The Garofalo parameters are therefore: Q = 237 kJ/mol, A = 3.5146  1015, n = 4.4 and a = 0.013. The stress exponent of this equation can be related to a slip creep mechanism controlled by dislocation climb. However, the value of the activation energy for deformation, 237 kJ/mol, is much higher than the value of 136 kJ/mol measured for lattice self-diffusion of Mg [26] and also higher than those of other AZ magnesium alloys [27,28]. Nevertheless, they are similar to those derived in previous studies for the activation energy for plastic deformation in WE alloys [29]. The observation of activation energy values for deformation much higher than that for magnesium self-diffusion is an issue that is still to be solved. This difference might be attributable to impurities present since minor alloying constituents may affect diffusivity. Unfortunately, there are not diffusion measurements in this Mg-rare alloys that may corroborate this assumption. On the other hand, the presence of precipitates that are strong obstacles to dislocation movement could act in a similar way as in ODS alloy. However, in these materials high activation energies are accompanied by a high stress exponent and in this magnesium alloy n is low, 4.4. It is our contention that the high activation energies observed are apparent, since microstructure evolves in a different way depending on testing temperature. While samples deformed at 461 °C were almost completely recrystallized after testing, those tested at 333 °C showed very little recrystallization. It is inferred, therefore, that samples tested at lower temperatures would be more creep resistant than fully recrystallized. A correction of the slope of the ln e_ vs 1/T fit, should be included to calculate the activation energy for deformation. This correction would compensate the effect of a different kinetic of recrystallization, and would give lower values of the activation energy, probably close to that for self-diffusion. An usual representation of the creep data is based on the parameters obtained for the Garofalo equation showing the Zener–Hollomon parameter, Z, defined as Z ¼ e_ exp(Q/RT), as a function of sinh ar. This representation, given in Fig. 7, involves a groupment of original variables, e_ and T, into Z. The points given

50

46

lnZ

1,5

2,0

2,5

3,0

3,5 54 52

Mg WE54 Q=237 kJ/mol A= 3.5146 E15 n= 4.4 r=0,994 F= 1371

48

where A, a and n are material constants, R is the gas constant and T is the temperature. The n exponent of this equation is adjusted for the minimum stress exponent values of the power laws, which correspond to the lowest strain rates. The parameters of the Garofalo equation, A, Q, n, a, can be determined by a non-linear, RCR (Rieiro, Carsi, Ruano) method involving an algorithm specifically developed for the treatment of this equation [25]. This method allows an automatic calculation of the particular values of this equation for a given material. In addition, the method grants an evaluation of the conditioning of the tests, by means of the function F of Snedecor, and prediction of strain rates (or stresses). The adjustment and statistical treatment of this equation was conducted in three steps. In one of them, the multiple correlation of the initial solution parameters are determined allowing prediction with a higher confidence than those conducted by means of other iterative methods. A characteristic of this method is the integral data processing without any intervention or manipulation between the input (experimental data) and the output that gives the parameters of the Garofalo equation. The optimal solution of the parameters of the Garofalo equation obtained by this method is the following:

1,0

50 48 46

44

44

42

42

40

40

38

38

36

36

34

0,5

1,0

1,5

2,0

2,5

3,0

34 3,5

ln Sinh (0.013σ) Fig. 7. Zener–Hollomon parameter, Z ¼ e_ exp(Q/RT), as a function of sinh ar for the compression tests on the magnesium alloy WE54.

in the figure are obtained by means of the experimental data using the parameters A, Q, n, a, obtained from the non-linear, RCR, method. These points fall close to the central line given in the figure. This line corresponds to the best fit and the two adjacent lines define the 95% confidence band of this fit. The points also fall between the 95% confidence band for prediction given as the outer lines. This is a proof of the goodness of the fit by the non-linear method. The correlation coefficient of the final solution, r = 0.995, can be considered as satisfactory. The experimental function F of Snedecor of the initial values used to obtain the Garofalo equation is 1371. This value ensures a good prediction capacity. 3.5. Processing maps In a forming process, it is important to locate its maximum stability region. Various criteria have been used in the literature [30–34]. Thermodynamically, the stability is understood as the state where the system evolves by continuously diminishing the total energy. In the engineering system design the control of the supplied and the dissipated energy is often characterize by the Lyapunov criteria. The first Lyapunov criterion can be expressed as a function of the strain rate sensitivity, m, in the following manner [30,32]:

 L1 ¼

 dm <0 d ln e_ C;r

ð3Þ

where L1 is the first Lyapunov function for the stability characterization of a dynamic system applied to the plastic deformation that is considered within a thermomechanical framework. It is a stability criteria to the occurrence of processes leading the material away for its behavior described by the constitutive equation, for instance, band formation, flow localization, appearance of voids and cracks, etc. The calculations of the parameter L1, and also of the parameters g y f of efficiency and energy dissipation of Prasad and coworkers, are carried out by most of the authors using an adjustment of the curves log (r) vs log e_ by means of a second or third degree polynomial. Then, m is calculated from the slope in each point. Our approach for calculating these maps consists in the adjustment of all the measured points to a hyperbolic sine equation of Garofalo type and then calculation of m for each strain rate and temperature using this equation. In other words, we assume an equation f ðr; T; e_ Þ ¼ 0 for a given value of the strain, e, expressed as r = g(T, e_ ), that is the result of average values at the various test

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M. Carsi et al. / Materials and Design 58 (2014) 30–35

temperatures. From this equation, for each e, we can obtain the values of m and L1 using the corresponding expressions. These expressions are not incremental, since they are obtained from the Garofalo type equation, but are continuous. The optimum stability zone in the plane [T, e_ ] can be determined by the optimal regions of the maps given by Eq. (3). Fig. 8 is a representation of the first Lyapunov criteria as a function of strain rate and temperature. The most stable region corresponds to the most negative values of the Lyapunov functions. In Fig. 8, the zone comprised between the two level lines for 0.013 is that presenting the lower chance of crack appearance and therefore is recommended for a stable forming process. A stability band between 490 and 560 °C (optimum at 530 °C) is obtained for a strain rate of 8.7 s1. It is to be noted that forming temperatures below 450 °C can be reached in the last steps of forming. At this temperature, a value of contours of about 0.01 is obtained. This value is only 23% less than that expected in the optimum temperature zone and indicates a small risk of crack formation even at this low temperature. This is because of the small gradient existing in this temperature region. Once the maximum stability region for the forming process is determined, it is important to locate the maximum efficiency. The high temperature forming of metals can be analyzed by means of the supplied power to the material, P, that can be divided in two terms [35–37]:

P ¼ re_ ¼

Z

e_

rde_ þ

0

Z r

e_ dr

ð4Þ

0

or P = G + J where G, the dissipator content, is the power spent in the deformation without changing the internal structure and J, the dissipator co-content, is the power spent in the deformation with a change of the internal structure. A relation of efficiency factors for G and J, gG and gJ, can be obtained by dividing Eq. (4) by the supplied energy:

1 ¼ gG þ gJ

ð5Þ

Since the forming process of the WE54 alloy implies changes in the internal structure, it is more interesting to study the term gJ that is defined by the relation:

1

gJ ¼ _ re

Z r

e_ dr

ð6Þ

0

Fig. 8. Representation of the 1st Lyapunov criterion as a function of strain rate and temperature.

The resolution of this equation would be extremely difficult if power laws would have used. This difficulty is avoided by the use of the Garofalo equation that is continuous and defined along the entire working range. Substituting this equation into Eq. (6), the following relation is obtained:

1

gJ ¼ _ re

Z r 0

  Q sinh ðarÞn dr A exp  RT

ð7Þ

This parameter and its variation with temperature and strain rate form the basis for construction of maps of constant forming efficiency contours of gJ. Fig. 9 shows a two-dimensional map of constant forming efficiency contours. Every constant efficiency value gJ is determined by a set of strain rates and temperatures. A smooth variation of the contour lines is observed due to the use of a single equation for the entire working range with a unique hyperbolic sine stress exponent. Fig. 9 shows values of gJ between 0.05 and 0.17 increasing the efficiency for decreasing strain rates at constant temperature. The possible zone for forming, 490–560 °C, is close to a maximum of efficiency at 8.7 s1 (ln e_ ¼ 2:16). It is to be noted that the efficiency increases continuously above 823 K. However, the material cannot be formed at much higher temperatures since local melting at grain boundaries could occur. At 8.7 s1 and 823 K (560 °C) a low loss of deformation energy (85%) is predicted. In contrast, at 490 °C the loss is 87%. That is, there is a small difference of 2%. It should be noted that the maximum efficiency is presented at high temperature and low strain rates. However, the stability is not optimal at low strain rates. The intersection region for maximum stability defined by the Lyapunov criterion (Fig. 8) together with the maximum efficiency region (Fig. 9) should give the best conditions for the forming process. In the case of the WE54 magnesium alloy, the analysis of these figures indicates that, for a strain rate of 8.7 s1, the optimum forming temperatures with minimum risk of defect formation are in the range 490–560 °C. This is in agreement with the ductility curves showing a maximum at about 520 °C. Furthermore, the efficiency at this temperature is close to the optimal as shown in Fig. 9. It is, therefore, concluded that 520 °C is the ideal forming temperature at 8.7 s1 having the alloy a high efficiency/stability relation in the forging operation. However, 490 °C is a temperature where the forming process may take place with little risk of failure and with important savings in energy.

Fig. 9. Strain rate as a function of temperature and contours of forming efficiency according to Eq. (7).

M. Carsi et al. / Materials and Design 58 (2014) 30–35

4. Conclusions A heterogeneous microstructure was revealed at the various regions of the compression samples that has been proven to be related to the amount of deformation in these regions. The high temperature data of WE54 alloy can be predicted by a Garofalo equation using a stress exponent of 4.4 and an activation energy of 237 kJ/mol. A maximum in ductility was reached at 520 °C in a tension test conducted at 0.9 s1. According to the first Lyapunov criteria, hot rolling could be carried out with minimum risk of defect formation between 490 and 560 °C. At these temperatures the forming efficiency is also good. As a result, a hot forming temperature of about 520 °C is recommended. Acknowledgments This work is financially supported by CICYT, Spain, under program MAT2012-38962. References [1] Aghion E, Bronfin B. Magnesium alloys development towards the 21st Century. Mater Sci Forum 2000;350–351:19–30. [2] Spigarelli S, Regev M, Evangelista E, Rosen A. A review of the creep behavior of AZ91 mg alloy produced by different technologies. Mater Sci Technol 2001;17:627–38. [3] Blum W, Zhang P, Watzinger B, Grossmann BV, Haldenwanger HG. Comparative study of creep of the die-cast Mg-alloys AZ91, AS21, AS41, AM60 and AE42. Mater Sci Eng A 2001;319–321:735–40. [4] Anyanwu IA, Kamado S, Kojima Y. Creep properties of Mg–Gd–Y–Zr alloys. Mater Trans 2001;42:1212–8. [5] Mordike BL. Creep-resistant magnesium alloys. Mater Sci Eng A 2002;324:103–12. [6] Polmear IJ. Magnesium alloys and applications. Mater Sci Technol 1994;10:1–16. [7] Chen Q, Shu D, Zhao Z, Zhao Z, Wanga Y, Yuan B. Microstructure development and tensile mechanical properties of Mg–Zn–RE–Zr magnesium alloy. Mater Des 2012;40:488–96. [8] He SM, Zeng XQ, Peng LM, Gao X, Nie JF, Ding WJ. Microstructure and strengthening mechanism of high strength Mg–10Gd–2Y–0.5Zr alloy. J Alloys Compd 2007;427:316. [9] Pekguleryuz MO, Avedesian MM. Magnesium alloying-some metallurgical aspects. In: Mordike BL, Hehmann F, editors. Magnesium alloys and their applications. Garmish (Germany): DGM, Oberursel; 1992. p. 213–20. [10] Suzuki M, Sato H, Maruyama K, Oikawa H. Creep behavior and deformation microstructures of Mg–Y alloys at 550 K. Mater Sci Eng A 1998;252:248–55. [11] Morgan JE, Mordike BL. Investigation into creep-resistant, as-cast magnesium alloys containing yttrium, zinc, neodymium and zirconium. Metall Trans A 1981;12:1581–5. [12] Wang JG, Hsiung LM, Nieh TG, Mabuchi M. Creep of a heat treated Mg–4Y–3RE alloy. Mater Sci Eng A 2001;315:81–8. [13] Peng QM, Hou XL, Wang LD, Wu YM, Cao ZY, Wang LM. Microstructure and mechanical properties of high performance Mg–Gd based alloys. Mater Des 2009;30:292–6.

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