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Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)13656-0
10.1016/j.heliyon.2024.e37625
e37625
Research Article
Flow softening and recrystallization accompanied flow in AZ61 magnesium alloy during thermomechanical processing
Abbasi-Bani A.R. a
Zarei-Hanzaki A. zareih@ut.ac.ir
a⁎⁎
G. Shabestari M. b
Abedi H.R. habedi@iust.ac.ir
b⁎
a Hot Deformation & Thermomechanical Processing Laboratory of High-Performance Engineering Materials, School of Metallurgy and Materials Engineering, College of Engineering, University of Tehran, Tehran, Iran
b School of Metallurgy & Materials Engineering, Iran University of Science and Technology (IUST), Tehran, Iran
⁎ Corresponding author. habedi@iust.ac.ir
⁎⁎ Corresponding author. zareih@ut.ac.ir
07 9 2024
30 9 2024
07 9 2024
10 18 e3762530 3 2024
5 9 2024
6 9 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
The present work deals with characterizing the recrystallization accompanied flow and high temperature softening behavior of an extruded AZ61 magnesium alloy. This was supported by conducting a set of hot compression tests at temperatures in the range of 250–450 °C under the strain rate ranging from 0.001 to 0.1s−1. The flow curves at all thermomechanical conditions indicated high fractional softening representing the domination of dynamic recrystallization mechanism. Through a new quantitative approach, “Arrhenius type model”, “modified Avrami equations” and Poliak and Jonas method were simultaneously employed to investigate the kinetic of dynamic recrystallization. It was revealed that the strain required for the same amount of recrystallization fraction increased with decreasing deformation temperature, and at a specified temperature, the required strain increases with increasing strain rate. Interestingly, an anomaly was found at 400 °C under the strain rate of 0.001s−1, where the recrystallization kinetic was faster than that of what was recorded at 450 °C. This anomaly was discussed relying on the nanoprecipitation of γ-phase at the prior boundaries and sub-boundaries which prohibited the grain boundary migration and also the rotation and coalescence of adjacent sub-grains.

Keywords

Magnesium alloy
Thermomechanical processing
Recrystallization kinetics
Microstructure
Avrami equation
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pmc1 Introduction

The empirical approach, which has long been used, is now recognized as being of limited value, because the cost of industrial scale parametric experimental investigations is prohibitively expensive in many cases. In contrast, the phenomenological and physical quantitative methods have drawn much attention due to their capability to predict the material's deformation behavior [[1], [2], [3]]. However, the accuracy of the proposed models is one of the most significant issues, which has been discussed in the majority of involved researches [4,5]. It has been widely demonstrated that the precision of quantitative models is microstructural dependent, in particular for the case of high temperature industrial forming processes, where the dynamic recrystallization and dynamic recovery operates as the main restoration phenomenon [6,7]. Accordingly, in designing any processing scheme, the detailed knowledge of recrystallization characteristics is of paramount importance, particularly those related to the kinetics. Thus, the modelling of dynamic recrystallization behavior is considered valuable issue.

The Avrami relationship [8] has been originally developed to study the kinetic of static recrystallization. However, in view of physically observed similarities between static and dynamic recrystallization, this relation is being increasingly adopted by researchers to model the progress of dynamic recrystallization in a wide variety of metals and alloys [[9], [10], [11]]. The application of this relation was originally proposed as a so-called ﬂow curve analysis method by Medina and Hernandez [12] and then modiﬁed by Najafizadeh and Jonas [13] using a different functional form to evaluate the work hardening/softening characteristics. In the modified Avrami equation, the dynamic recrystallization volume fraction (XDRX) is considered as a function of applied strain, and can be quantified through metallographic investigations or flow curve analysis. The latter estimation requires the profound knowledge of flow stress-strain and work hardening behavior. In this regard, Stewart et al. [14] has employed the critical strain (εc), and the strain at which the rate of softening was at its maximum (ε*) to plot the XDRX vs. ε. The accuracy of their mechanical description was confirmed through their experiments to measure the volume fraction of dynamically recrystallized grains.

In the case of magnesium alloys, many efforts have been directed towards characterizing the recrystallization behavior from the qualitative point of view. It has been found that the AZ series, as the most common wrought and cast magnesium alloys, are prone to be dynamically recrystallized in wide range of temperature and strain rate through continuous [15], discontinuous [16], and/or geometrical [17,18] mechanisms. In spite of the comprehensive researches conducted in this regard, there are limited ones which investigate the kinetic of recrystallization quantitatively. As a consequence, the object of the present work is the recrystallization behavior modelling of as-extruded AZ61 Mg alloy through applying the Arrhenius type and modified Avrami equation. The effects of thermomechanical parameters including strain rate, strain and temperature are properly addressed through the manuscript. In addition, it is speculated that the presence of various microstructural features (the presence of γ nano-precipitates distributing either along grain boundaries or sub-boundaries) may possibly introduce a significant effect on the recrystallization kinetics of AZ61 alloy.

2 Experimental procedure

The experimental AZ61 Mg alloy was received in as-extruded rods holding the approximate composition of (Mg- 6.53 Al- 0.74 Zn %wt.). The cylindrical compression specimens, 12 mm in height and 8 mm in diameter (according to ASTM E209 [19]), were machined from the rods in a way that the deformation axis to be parallel to the extrusion direction. The hot compression tests were carried out using a GOTECH AI-7000 L A 30-servo controlled electronic universal testing machine equipped with an electrical resistance furnace. The tests were performed at predetermined temperatures in the range of 250–450 °C under the strain rates of 0.001, 0.01 and 0.1 s−1. Prior to the tests, the specimens were preheated at deformation temperature for 7min and then the specimens were deformed up to the true strain of 0.6. Finally, at the end of straining the specimens were immediately quenched in water. To examine the microstructural evolution, the specimens were sectioned along the deformation axis and then mechanically grinded and polished. This was followed by etching the specimens by Acetic Picral solution (10 ml Acetic acid, 4 g Picric acid, 5 ml water, 50 ml ethanol). The initial starting microstructure and deformed ones were revealed through optical and scanning electron microscopy analysis.

3 Result and discussion

From the quantitative viewpoint, the compressive true stress-true strain curves of the experimental alloy at different thermomechanical conditions are given in Fig. 1(a–c). The experimental curves indicate a typical recrystallization-accompanied plastic flow, where a single peak is followed by work softening down to the steady state regime at higher imposed strain. In the early deformation stage, the dislocation generation, multiplication and their intersects are significant, where the cross-slip is not enough to overcome the effect of work hardening, so the flow stress shows a rapid increase. Once the critical strain is exceeded, the dynamic recrystallization may take place due to the adequate accumulation of the strain energy. Thus, the flow curve drops continuously to achieve the steady state which is the dynamic balance between work hardening and dynamic softening. The sigmoidal S-shape of the flow curves at the early stage of deformation at 250 °C (specially at higher strain rates) is attributed to the possible activity of deformation twinning which substantially decreases at higher temperature. The contribution of prismatic and pyramidal slip systems at the temperatures higher that 250 °C [15] is substantially increased and not only decreases the twinning activity but also influence the softening behavior of the experimented alloy and the involved recrystallization mechanisms.Fig. 1 The hot compression flow behavior of the experimental material at various temperatures under the strain rates of (a) 0.001, (b) 0.01 and (c) 0.1s−1.

Fig. 1

Many attempts have been conducted up to date to develop mathematical models to identify the critical strain for initiation of dynamic recrystallization. According to Jonal and Poliak model [20], it is postulated that the inflection point of the work hardening vs. stress curves (θ–σ), which would be plotted up to the peak point reveals the critical stress. This is detected by ﬁtting a proper third order polynomial Eq. (1):(1) θ=α1σ3+α2σ2+α3σ+α4

where α1, α2, α3 and α4 are constants for a given set of thermomechanical conditions. The best third order curves were fitted to the experimental θ-σ curves as are shown in Fig. 2(a–c). At critical stress (σc) point, the second derivative of Eq. (2) would be equal to zero:(2) 3α1σc+α2=0

Fig. 2 The variations of strain hardening rate (dσ/dε) with true stress, which are plotted up to the peak points under the strain rates of (a) 0.001, (b) 0.01 and (c) 0.1s−1.

Fig. 2

Accordingly, the critical stress and critical strain values are calculated, and the variation of which have been plotted vs. Zener-Holloman parameter (Z = ε˙ exp(Q/RT)) in Fig. 3(a and b). As is expected the critical stress (critical strain) has been decreased at higher deformation temperature and lower strain rates i.e. by decreasing the Zenner-Holloman parameter.Fig. 3 The relationship between (a) the critical stress and ln Z, and (b) the critical strain and ln Z.

Fig. 3

The typical microstructures of the specimens which have been deformed at temperatures of 250, 300, 350, 400 °C under the strain rate of 0.1s−1 are shown in Fig. 4. The microstructure of the as-extruded material is also included (Fig. 4(a)). The occurrence of partial dynamic recrystallization at all thermomechanical condition is clearly recognized, where the nucleation of the new grains mainly occurs at the prior grain boundaries. Since the dislocation tangles are much denser at the vicinity of grain boundaries, those are the preferred sites for the formation of recrystallized grains particularly at lower temperatures as is seen in Fig. 4b, c, d and e (follow the white arrows).Fig. 4 The microstructures of (a) as-received material and the specimens deformed under the strain rate of 0.1 s−1 at (b) 250 °C, (c) 300 °C, (d) 350 °C, and (e) 400 °C up to the true strain of 0.6.

Fig. 4

The higher the deformation temperature, the higher volume fraction of the recrystallized grains is achieved. This may be rationalized considering the fact that the activation energy to trigger the restoration processes is lower at higher deformation temperatures.

In order to assess the recrystallization kinetics, the recrystallized volume fraction is expressed as a function of time as normal S-curves [21], similar to those observed in classical recrystallization. Under the constant strain rates, time can be replaced by strain and the recrystallized fraction can be described by the modified Avrami equation. So, the materials’ capability to recrystallize at specified deformation condition may be represented utilizing Eq. (3) [4],:(3) XDRX=1−exp[−(ε−εcε*)m]

where XDRX is the volume fraction of dynamic recrystallized grain, ε is the experimental strain, εc is the critical strain for onset of recrystallization, ε* is the strain for maximum softening rate, and m is the Avrami's constant.

The strain for maximum softening rate, ε*, is attained where the value of work hardening (θ=dσ/dε) reaches the negative peak corresponding to a minimum point of θ versus σ plotted after the peak point, Fig. 5(a–c). The Avrami constant (m-value) is also obtained from the mean slopes of ln(ln(1∕(1−X)))1∕(1−X)))ln vs. ln((ε−εc)/ε*), which are plotted for all the deformation conditions. In this regard, Eq. (4) is used to calculate the amount of X:(4) X=σp−σσp−σss

where σp is the peak stress, σ is the experimental stress after peak and σss is the steady state stress (which corresponds to the XDRX ≈ 1) and the mean grain size remains constant. In order to calculate X, as is shown in Eq. (4), two terms are used: the σp−σ term indicates the flow softening from peak to the stress of σ and the σp−σss term represents the maximum achievable softening. Therefore, Eq. (4) gives the magnitude of fractional softening at a given stress (σ).Fig. 5 The θ versus σ plots after the peak points under strain rates of (a) 0.001, (b) 0.01 and (c) 0.1s−1.

Fig. 5

The predicted volume fractions of dynamic recrystallization obtained through Avrami's equation under the different deformation temperatures and strain rates are given in Fig. 6(a–c). The recrystallization kinetics is described as the variation of recrystallized volume fraction vs. true strain. The corresponding sigmoidal behavior (S-curve) indicates that the recrystallization volume fraction increases with the imposed true strain and nearly reaches the constant value of unity, which refers to the completion of the restoration process.Fig. 6 The predicted volume fractions of dynamic recrystallization obtained at different deformation temperatures under the strain rates of (a) 0.001, (b) 0.01, and (c) 0.1s−1.

Fig. 6

As is seen, under the specific strain rate, the strain required for the same amount of recrystallization volume fraction increases with decreasing deformation temperature. In contrast, at a particular temperature, the required strain increases with increasing strain rate; this means that the recrystallization is delayed to a longer time. This finding can be justified considering the fact that the thermally activated processes have been decelerated by increasing the strain rate and decreasing temperature. Thus, under higher strain rates and at lower temperatures, the deformed materials tend to have an incomplete or partial recrystallization; that is to say, the recrystallization volume fraction tends to be less than 1.

According to Fig. 6, the coupled effect of temperature and imposed strain on the recrystallization behavior of the experimented alloy is more pronounced under the lower strain rate. Under the higher strain rates, the “recrystallized fraction vs. strain” S-curves are closer to each other and under lower strain rates, they are further apart. At the strain rate of 0.001 s−1, the recrystallization kinetic at 400 °C is higher than that of what has developed at 450 °C. This anomaly would be rationalized considering the changes occurred in the related microstructures by increasing the temperature up to 450 °C. In this regard, the following procedure has been employed to calculate the activation energy through the Arrhenius type equation (Eq. (5)) which correlates the flow stress to the strain, temperature and strain rate:(5) ε˙=AF(σ)exp(−QRT)

(6) F(σ)={σmασ<0.8exp(βσ)ασ<1.2[sinh(ασ)]nforallσ}

where ε∙ is the strain rate (s−1), R is the universal gas constant (8:31 kJ mol-1), T is the absolute temperature (K), and Q is the activation energy (KJmol−1); σ is the flow stress (MPa) for a given strain, the range of which is defined in Eq. (6), and A, α, n, m are the material constants which are experimentally determined. The true stress-true strain results obtained from the compression tests at various processing conditions were employed to calculate the materials constants of the aforementioned constitutive equations. The values of m and β are obtained from the mean slope of ln(σ) vs. ln(ε˙) plot and σ vs. ln(ε˙) plot, respectively (Fig. 7(a and b)) and α = β/m. Moreover, at a given strain (the true strain of 0.3), a set of parallel lines would be obtained by plotting ln[sinh(ασ)] vs. lnε˙ at different temperatures (Fig. 7(c)). Thus, the average slope of the lines would give the value of n.Fig. 7 Evaluating of (a) m by plotting ln σ vs. ln ε˙, (b) β by plotting σ vs. ln ε˙, (c) n by plotting ln [sinh (ασ)] vs. ln ε˙ and (d) Q by plotting ln [sinh (ασ)] vs. 1000/T.

Fig. 7

Finally, under a constants strain rate, the partial differentiation of Eq. (5) would lead to the following equation:(7) QRn=dln[sinh(ασ)]d(1/T)

The activation energy Q can be determined by plotting the ln [sinh (ασ)] in Eq. (7d) against the reciprocal of absolute temperature. The Q-value of approximately 223 KJ mol−1 was obtained at the true strain of 0.3 through the whole temperature range of 250–450 °C. However, in order to explore the reason behind the observed anomaly in recrystallization kinetics (Fig. 6), the investigated temperature range has been classified into the two specified regions and ln [sinh (ασ)] has been replotted against the reciprocal temperature (Fig. 8(a)). The slope of the line is obviously changed at 400 °C and the corresponding activation energy is considerably increased. The Q-value at the true strain of 0.3, in the region I (250–400 °C), was calculated to be approximately 169 KJ mol−1 and in the region II (400–450 °C) was about 260 KJ mol−1. In addition, through plotting the stress as a function of temperature (Fig. 8(b)) a radical change in the stress is also recognized at 400 °C. In fact, a substantial decrease in stress level is expected to occur by increasing the deformation temperature from 400 °C to 450 °C, however, owing to activation of a specified mechanism the flow stress experiences minimal changes. These clearly indicate the variation in deformation mechanism by increasing the temperature from 400 °C to 450 °C.Fig. 8 (a) The variation of ln [sinh (ασ)] vs. 1000/RT, and (b) The stress as a function of temperature.

Fig. 8

All in all, the observed variations are in accord with the predicted anomaly in recrystallization kinetic at 400 °C (Fig. 6), and can be justified considering the transition in deformation mechanisms controlling the softening behavior of the alloy. Increasing the activation energy by increasing deformation temperature proposed occurrence of dynamic precipitation accelerating under the lower strain rates. In this respect, the deformed microstructure at 450 °C and strain rate of 0.001s−1 has been investigated in details and compared with the starting microstructure (Fig. 9(a, b)). The deformed microstructures clearly verify the dynamic precipitation of γ-M17Al12 phase at the prior grain boundaries (Fig. 9(c, d)). The precipitation of nano-sized γ-phase, not only consumes the provided stored energy during thermomechanical processing but also decreased the grain boundary mobility and the capability for boundary migration. The presence of nano-precipitates at the developed sub-boundaries could also prevent the subgrain rotation and coalescence. Accordingly, owing to the effective Zener pinning effect of the γ-nanoprecipitates, deceleration of the dynamic recrystallization and the observed anomaly in corresponding kinetic is logically expected.Fig. 9 The starting microstructure (a, b) and the microstructure of the specimen which has been deformed at 450 °C under the strain rate of 0.001s–1 (c, d).

Fig. 9

4 Conclusion

High temperature flow curve analysis and microstructure characterization were employed to investigate the recrystallization kinetics of extruded AZ61 Mg alloy. Toward this end, the hot compression tests were conducted in the temperature range of 250–450 °C under the strain rates of 0.001, 0.01 and 0.1s−1. The critical strain of dynamic recrystallization, and the strain of maximum softening rate were determined utilizing Poliak and Ponas analysis. The correlated activation energy, and strain rate sensitivity values were also determined through development of Arrhenius type constitutive equations. Calculating all materials constants, the modified Avrami equation was constructed and the recrystallization kinetics was described in terms of sigmoidal type behavior of the recrystallized volume fraction vs. true strain. Under higher strain rates and lower temperatures, the deformed microstructure tended to have an incomplete or partial recrystallization. Under the strain rate of 0.001s−1, the recrystallization kinetic at 400 °C was found to be faster than that of obtained at 450 °C one. The observed anomaly was attributed to the precipitation of nanosized γ-precipitates at the prior grain boundaries and sub-boundaries. This decelerated dynamic recrystallization through prohibition of grain boundary migration, and rotation/coalescence of the adjacent subgrains.

Data and code availability statement

Data will be made available on request.

CRediT authorship contribution statement

A.R. Abbasi-Bani: Writing – original draft, Validation, Methodology, Investigation, Conceptualization. A. Zarei-Hanzaki: Writing – review & editing, Supervision, Conceptualization. M. G. Shabestari: Writing – review & editing, Software, Data curation. H.R. Abedi: Writing – review & editing, Project administration, Investigation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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