Modeling of the dynamic recrystallization behavior of Csf/AZ91D magnesium matrix composites during hot compression process

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Zhenjun Wang, Biao Huang, Lehua Qi, Gui Wang, Matthew S. Dargusch PII: S0925-8388(17)30779-X

DOI: 10.1016/j.jallcom.2017.03.010

Reference: JALCOM 41048

To appear in: Journal of Alloys and Compounds

Received Date: 14 November 2016 Revised Date: 21 February 2017 Accepted Date: 2 March 2017

Please cite this article as: Z. Wang, B. Huang, L. Qi, G. Wang, M.S. Dargusch, Modeling of the dynamic recrystallization behavior of Csf/AZ91D magnesium matrix composites during hot compression process, Journal of Alloys and Compounds (2017), doi: 10.1016/j.jallcom.2017.03.010.

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Modeling of the dynamic recrystallization behavior of Csf/AZ91D magnesium

matrix composites during hot compression process

Zhenjun Wang a, b, c∗, Biao Huang a , Lehua Qi b , Gui Wang c, Matthew S. Dargusch c a

National Defense Key Discipline Laboratory of Light Alloy Processing Science and Technology, Nanchang Hangkong University, Nanchang 330063, China b

State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, China

c

Centre of Advanced Materials Processing and Manufacturing, The University of Queensland, St Lucia, QLD 4072, Australia

Abstract The deformation and microstructure evolution behavior of 15 vol. % short

carbon fiber reinforced AZ91D composites (Csf/AZ91D) were investigated by hot compression test. An obvious dynamic recrystallization (DRX) was found in the matrix alloy, and the recrystallized grains around the fibers were finer than those in the alloy. The average grain size and volume fraction of the recrystallized grain increases with the increase of deformation temperature or the decrease of strain rate. The volume fraction of the recrystallized grain increases with increasing strain in a rapid–slow manner. By regression analysis on these results, a constitutive model was developed for the first time in attempt to quantitatively evaluate the effect of temperature, strain and strain rate on the DRX behaviors. The calculated average grain size and volume fraction of the recrystallized grains are in good agreement with the experimental ones, thereby validating the accuracy of the developed model.

Keywords magnesium matrix composites; hot compression; constitutive model;

dynamic recrystallization

1 Introduction

Over the past decades, discontinuously reinforced magnesium matrix composites (DRMMCs) have attracted increasing attention due to their excellent mechanical properties, such as high specific strength and modulus, low preparation cost, and good isotropic property [1–3]. Compared with traditional light alloys, applying DRMMCs in

∗_{Corresponding author. Tel: +86-791-86453167; Fax: +86-791-86453167.}

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aerospace and automotive engineering remain limited. A proper secondary processing technique is thus required for improving the microstructure and properties of DRMMCs and direct manufacturing of components from the as-cast DRMMCs so as to extend the application of these composites in lightweight structures. DRMMCs can hardly be deformed at ambient temperature because of the hexagonal close-packed crystal structure of magnesium alloy and the addition of brittle reinforcement [4, 5]. Therefore, scholars have developed a series of hot forming methods and extensively investigated the hot deformation behavior of DRMMCs.

The processing map of DRMMCs can be obtained using power dissipation efficiency with functions of temperature and strain rate, where the workability and instability domains can be observed visually [6–8]. Several constitutive models were established to describe the hot deformation behavior of DRMMCs and quantitatively formulate the dependence of flow stress on deformation temperature, strain rate, and strain [9-12]. Meanwhile, the stress exponent (n) and activation energy (Q) can be calculated by constitutive equations, which are key parameters for investigating the deformation mechanisms of DRMMCs. A large number of researches have shown that the plastic deformation at elevated temperature usually leads to the dynamic recrystallization (DRX) of DRMMCs. For example, Zhu et al. [13] reported that DRX occurs in Mg2B2O5w/AZ31 composites during hot compression, and DRX grains grew larger when the strain rate decreases and temperature rises. Zhong et al. [14] reported that the variation of average DRX grain size in nano-alumina reinforced AZ31 magnesium composite subjected to hot extrusion can be described as a linear function of the Zener–Hollomon parameter on the double logarithmic scale. In the hot extruded nano-particle/AZ80 composites, the particles significantly affect grain refinement. The size of the DRX grains in the composites was lower than that in the monolithic AZ80 alloy, which presents a typical necklace structure with a limited DRX grain [15]. These metallurgical transformations significant influence the mechanical properties of the DRMMC product [16]. However, few quantitative researches on the dependence of microstructure characteristic on hot deformation parameters have been carried out so far. Specifically, the DRX behavior of magnesium matrix composites has not been

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modeled as a function of deformation temperature and strain rate.

In this work, the deformation behavior and microstructure evolution of magnesium matrix composites (AZ91D alloy reinforced with 15 vol. % short carbon fibers) were investigated through hot compression test. The influence of deformation temperature, strain, and strain rate on grain morphology in matrix alloy was evaluated according to metallographic observation results. A constitutive model describing the DRX behavior of the composites was established for the first time through multiple nonlinear regression analysis. The model was validated by comparing the calculated and experimental average grain size and volume fraction of the recrystallized grains.

2 Experimental materials and methods

The material used in this study was AZ91D alloy reinforced with 15 vol. % chopped carbon fibers, namely, the Csf/AZ91D composites. The chemical composition of the magnesium alloy provided by Shanghai Regal Magnesium Industry Co. Ltd is presented in Table 1. The properties of the chopped T300 carbon fiber produced by Toray Co. Ltd are displayed in Table 2. The Csf/AZ91D composite ingot was prepared through the vacuum-assisted liquid metal infiltration method [9]. The as-cast composite ingot was cut into cylindrical specimens with a diameter of 10 mm and a height of 15 mm through the electrical discharge machining method. The specimens for the hot compression testing were treated by the T6 procedure to relax the residual stress aroused during the preparation and machining process.

The hot compression testing was performed on a Gleeble-3500 thermo-mechanical simulator with the deformation temperatures ranging from 400 °C to 460 °C and the strain rate ranging from 0.001s−1 to 0.1s−1. The reduction in height is 50% at the end of the hot compression test. All the specimens were first heated to the desired deformation temperatures with a heating rate of 30 K/s, followed by an isothermal holding time of 120 s to acquire a uniform temperature field in specimens. A thermocouple element inserted at the middle section of the specimen was used to control the temperature of the specimens during the heating and the hot compression process. The load–displacement data of the specimens was automatically collected by the microcomputer processing system from the thermo-mechanical simulator. The

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appearance of the specimens before and after compression is illustrated in Fig. 1. The specimens were quenched by water immediately after being hot compressed to preserve the deformed microstructure. Then, the compressed specimens were cut along the longitudinal section. The cutting surface was ground, polished, and corroded with 5 wt.% citric acid. The microstructure of the compressed specimen was examined through quantitative metallography method.

3 Results and discussion 3.1 Microstructure observation

The microstructure of the Csf/AZ91D composites before and after being hot compressed is depicted in Fig. 2. The grains in the hot compressed composites (Figs. 2b–d) are finer than those in the as-cast composites (Fig. 2a), which indicate that an obvious DRX process has occurred in the matrix alloy. At the strain rate of 0.001s−1, the average grain size in the compressed composites at 460 °C (Fig. 2d) is larger than that at 430 °C (Fig. 2b). The ability of the grain boundary migration and the dislocation sliding is enhanced with the increase of deformation temperature; this condition can contribute to the growth and coarsening of the recrystallized grains. At the deformation temperature of 430 °C, the grain size in the compressed composites at a high strain rate (Fig. 2c) is smaller than that compressed at a low strain rate (Fig. 2b). The accumulated dislocations near the carbon fiber can hardly annihilate in time at the high strain rate, which may accelerate the nucleation of DRX grains. This activity can be supported by the presence of a dislocation pile-up group in the region between the two carbon fibers as revealed by the TEM micrograph as presented in Fig. 3. Moreover, not enough time is available for the new recrystallized grains to grow up sufficiently. Therefore, the high strain rate can promote the refinement of the recrystallized grains in the composites.

In addition, the dynamically recrystallized grains near the fibers, especially those in the local fiber-rich region, are finer than those far away from fibers. A similar phenomenon has also been observed in SiC nanoparticle reinforced magnesium composite processed by hot extrusion. Nie[16] and Wang[17] reported that large-scale dynamic recrystallization produced finer grains within the SiC nanoparticle bands

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than those between SiC nanoparticle bands. The pinning effect of carbon fibers on dislocation slipping causes a high dislocation density in the fiber-rich regions during the hot compression process. The stored energy and the large driving force for nucleation in these regions can stimulate the nucleation of a new grain in the matrix alloy. In addition, the existence of fiber can effectively hinder the growth of the new recrystallized grain. Consequently, the size of the recrystallized grains around the fibers is smaller than those in the matrix alloy.

3.2 Constitutive modeling

1) Critical strain

According to classic DRX theory for metal materials [18], the critical condition for DRX is generally determined as ε βε_c= _p, where ε_p is the peak strain on a true stress–strain curve, and β is a coefficient less than 1.0. However, the DRX behavior of the matrix alloy in the Csf/AZ91D composites was more complicated and different from that of the AZ91D magnesium alloy because of adding the short fiber. The simple linear relationship between the critical strain

ε

_c and the peak strain

ε

_p is not applicable for describing the critical conditions of the DRX process in the Csf/AZ91D composites. In this study, the critical strain for the DRX of the matrix alloy was determined through the method based on the irreversible thermodynamic principle introduced by Poliak and Jonas [19, 20]. The true stress–strain curves of the Csf/AZ91D compressed at an elevated temperature are illustrated in Fig. 4. After the flow stress increases rapidly to the peak value at a small strain, the flow stress declines continuously to a steady-state stress with the growth of the true strain. The deformation behavior is a result of the interaction between the DRX softening and the work hardening. The DRX is considered to have occurred before the peak value appears on the true stress–strain curve. For the uniaxial compression with constant deformation temperature and strain rate, the critical condition for the DRX can be derived through the incremental power balance method of a thermodynamic system as the following:

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=0 θ σ σ ∂  ∂  −   ∂  ∂  , (1)

where θ is the strain hardening rate,

,T ε

σ

θ

ε

∂   =_∂   _& .

Based on the true stress–strain data measured from Fig. 4, the typical θ σ− and

(

θ σ

)

σ

− ∂ ∂ − plots at the strain rate of 0.001s−1 and at the temperature of 400 °C, 430 °C, and 460 °C are presented in Figs. 5 and 6, respectively. According to Eq. (1), the critical condition for the DRX in the Csf/AZ91D composites is corresponding to the minimum point of the − ∂ ∂

(

θ σ σ

)

− curves in Fig. 6. In this figure, the critical stress

σ

_c corresponding to the onset of the DRX was 46.2043, 34.1001, and 22.4081 MPa; these values correspond to the deformation temperatures of 400 °C, 430 °C, and 460 °C. The critical stress

σ

_c corresponding to the onset of the DRX at other deformation temperature and strain rate can be calculated by repeating the above procedure. Then, the corresponding values of the critical strain

ε

_c would be obtained based on the true stress–strain data (Fig. 4).

The critical strain

ε

_c and the peak strain ε_p on the true strain–stress curves can be described as the functions of the Zener–Hollomon parameter synthetically, which can be expressed as follows:

exp( / )

Z =ε& Q RT , (2) where ε& is the strain rate (s−1), R is the universal gas constant (8.31 J·mol−1·K−1),

T is the absolute temperature (K), and Q is the apparent activation energy of hot deformation. According to the previous work [21], the average value of Q was 262.84 KJ/mol for the Csf/AZ91D composites. The relationship of εc−Z and εp−Z was obtained by the linear fit of critical strain lnε_c and the peak strain lnε_p with lnZ as Fig. 7 depicts. These relationships can be formulated by Eqs. (3) and (4) as follows:

-4 0.1005

=2.5001 10

c Z

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and -4 0.0845 p=6.0499 10 Z

ε

× . (4) 2) Kinetic equation

The DRX depends on the evolution of dislocation density in the matrix alloy during the hot deformation process. Therefore, the DRX process is characterized according to the strain hardening and softening behaviors at the different deformation conditions. At the critical strain, the dislocation density in grain boundary and interface is high enough to motivate the nucleation of grains, indicating the onset of DRX process. When the flow stress reaches the steady state, the DRX is fully completed and the recrystallized grains would keep constant shape and size. In this study, the modified Avrami equation was used to describe the volume fraction of the DRX grain as the function of the true strain as follows [22–24]:

m 1 exp c DRX p X k

ε ε

ε

 _ ₋ _    = − − _ _  _ _    , (5)

where X_DRX is the volume fraction of the DRX grain,

ε

is the true strain,

ε

_c is the critical strain of DRX, ε_p is the peak strain, and k and m are the material constants.

Fig. 8 illustrates the dynamic softening of flow stress for the Csf/AZ91D compressed at elevated temperature. The flow stress reaching the peak value σp decreased continuously to the steady state stress σss rather than increasing to the state recovery stressσ_sat, which can be attributed to the softening mechanism of the DRX. The deviation extent of σ_drx from σ_re_cov reflects the extent of the DRX softening effect on flow stress. Therefore, the volume fraction of the DRX grains (X_DRX) can be expressed as a function of the flow stress [23, 25]. Given the minute difference between σ_sat, σrecov, and σp, the XDRX can also be calculated using the following equation:

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cov p drx re drx DRX sat ss p ss X

σ

− − = ≈ − − . (6)

According to Eq. 6, the value of X_DRX at the different flow stresses can be calculated, and the corresponding true strain

ε

was measured from the true stress–strain curves (Fig. 4). The relationship of

(

)

(

)

ln_−ln 1−X_DRX _−ln_ ε ε ε− _c _p_{ can be calculated at a specific temperature and} strain rate by substituting the value of XDRX and

ε

into Eq. 5. The linear fitting of

(

)

(

D CZ− , (7) where C and n are the dimensionless material constants.

Fig. 10 presents the position for microstructure observation in the vertical section of the compressed specimens. The metallograph of one point in zones (I) and (II) and three points in zone (III) was observed, in which five lines passing through 10–20 grains are drawn by the image processing software Image-Pro Plus. Then, the average diameter of the recrystallized grains at various deformation conditions was calculated

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according to the length of each line segment and the number of grains on the line segment. In Fig. 11, the relationship between D_DRX and Z in the dual logarithmic coordinate by substituting the value of DDRX at a given deformation condition and the corresponding parameter Z into Eq. (7) is depicted. The slope of the fitting line of lnZ−lnD_DRX provides the value of n at 0.0375, while the intercept results in the value of C to be 62.0320.

3.3 Validation of the constitutive equation

The microstructure observation experiment was conducted to verify the developed constitutive equation for the Csf/AZ91D composites. Fig. 12 shows the evolution of the DRX grains in the composites with the increase of the true strain at the deformation condition of 430 °C and 0.01s−1. At the strain of 0.05, multiple initial recrystallized grains with small size occurred near the fiber and the original grain boundary (Fig. 12a). At the strain of 0.2, more recrystallized grains were found to form inside initial grain as well as in fiber-rich region (Fig. 12b). At the strain of 0.4, most of the coarse grains have translated into the DRX grains as Fig. 12c illustrates. When the strain reached 0.7 (Fig. 12d), the original grains were fully replaced by the new DRX grains, indicating that the DRX process has been completed. At the strain of 0.05, 0.2, 0.4, and 0.7, the acquired metallographs of the three points in the deformation zone III (Fig. 10) were first digitally processed. Then, the total area of the matrix alloy and the area of the DRX grains were calculated using the Image-Pro Plus software, and the ratio of the area was defined as XDRX for each point. Thereafter, the measured XDRX at the various strains was estimated statistically by averaging the XDRX value of the three points. The comparison of the calculated

DRX

X (Eqs. 3–5) with the measured XDRX is depicted in Fig. 13. The calculated result can match the measured ones on the whole, indicating that the established kinetic model can describe the DRX process of the Csf/AZ91D composites during the hot compression.

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The calculated values of XDRX varying with the strain at the different temperatures and strain rates are presented in Fig. 14. The increase of XDRX with the true strain increases in a rapid–slow manner, which was different from the DRX behavior for the magnesium alloy. When AZ31[25] and AZ91D[26] were hot compressed, the volume fraction of the DRX grains increases as the strain increases and evolution exhibits slow–rapid–slow growth trends in terms of S-curves. In the initial deformation stage, the DRX process of the Csf/AZ91D composites is more active than that of the magnesium alloy, indicating that adding the short carbon fiber greatly promoted the onset of the DRX process in the matrix alloy. Fig. 14a shows that the XDRX value increases with the decrease of the strain rate at a given strain. This result can be due to sufficient time for the newly nucleated grain to grow up considering the low strain rate. At a given strain, the XDRX value increases with the increase of temperature as shown in Figs. 14(b–d). The high temperature is conducive to the grain boundary migration and the dislocation slipping, which facilitate the nucleation and growth of the new grain during the DRX process.

The recrystallized grains in the Csf/AZ91D composites after being hot compressed at 400 °C and 460 °C are presented in Fig. 15. Given the same strain rate, it can be seen that the recrystallized grain size obtained at 460 °C (Figs. 15c and d) is larger than that at 400 °C (Figs. 15a and b) respectively. At the same deformation temperature, the recrystallized grain size obtained at the high strain rate (Figs. 15b and d) is smaller than that at the low strain rate (Figs. 15a and c). The comparison of the calculated DDRX (Eq. 7) with the measured ones are illustrated in Fig. 16. The calculated values agree with the experimental data. The maximum and the average relative error are 6.97% and 2.68%, respectively. These results indicate that the established equation is reliable for predicting the average size of the recrystallized grains in the composites during the current hot deformation process.

4 Conclusion

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investigated utilizing the hot compression test. A finer DRX microstructure around the fibers was found compared with those in the matrix alloy, which indicates that the existence of fiber stimulates the nucleation and inhibits the growth of the recrystallized grains. The volume fraction of the recrystallized grain increases in a rapid–slow manner with the increase of strain. The increase of the strain rate or the decrease of the temperature leads to the reduction of the average grain size and the volume fraction of the recrystallized grains.

A set of constitutive equations were developed to characterize the effect of temperature, strain, and strain rate on the DRX behavior of the composites. The average grain size and the volume fraction of the recrystallized grains predicted by the equation agree with the experimental ones on the whole. These results suggested that the developed equations are feasible for describing the DRX process of the Csf/AZ91D composites in the current experimental domain.

Acknowledgement

The authors thank the financial supports from the National Nature Science Foundation of China (No.51365043), the Nature Science Foundation of Jiangxi Province (No.20151BAB206004), the fund of the State Key Laboratory of Solidification Processing in Northwestern Polytechnical University (No. SKLSP201228), and the fund of the National Defense Key Discipline Laboratory of Light Alloy Processing Science and Technology in Nanchang Hangkong University (No. GF201301007). We also thank for the financial support to visiting scholar from the China Scholarship Council (No. 201608360034).

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Table legend:

Table 1 Chemical composition of the AZ91D magnesium alloy (wt.%) Table 2 Properties of the chopped carbon fiber

Figure legend:

Fig. 1 Appearance of the specimens before and after compression

Fig. 2 Microstructure of the Csf/AZ91D composites before and after hot compression (a) as-cast (b) 430 °C, 0.001s−1 (c) 430 °C, 0.1s−1 (d) 460 °C, 0.001s−1

Fig. 3 Dislocation patterns in the region near the carbon fibers (TEM micrograph) Fig. 4 True stress–strain curves of the Csf/AZ91D composites

(a)ε& =0.001s−1 (b)ε& =0.01s−1 (c)ε& =0.1s−1

Fig. 5 Strain hardening rate θ when _ε_{& =0.001s}−1 Fig. 6 Curves of− ∂

(

θ σ

∂ −

)

σ

when _ε_{& =0.001s}−1

Fig. 7 Double logarithmic relationships of parameter Z with

ε

_c (a) and ε_p(b) Fig. 8 Dynamic softening in the true strain–stress curve of the Csf/AZ91D composites

during hot compression

Fig. 9 Linear fitting curve of ln_−ln 1

(

−X_DRX

)

_−ln_

(

ε ε ε− _c

)

_p_{ at} 1

0.1s

ε ₌ −

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Fig. 10 Position for the microstructure observation in the compressed specimen Fig. 11 Relationship between the D_DRX and parameter Z

Fig. 12 Microstructure of the Csf/AZ91D composites at the different true strains (430 °C and 0.01s−1)

(a) 0.05 (b) 0.2 (c) 0.4 (d) 0.7

Fig. 13 Comparison between the calculated XDRX and the measured ones at the different true strains

Fig. 14 Calculated XDRX versus true strain at the different hot deformation parameters

(a) temperature of 430 °C (b) strain rate of 0.001s−1 (c) strain rate of 0.01s−1 (d) strain rate of 0.1s−1

Fig. 15 Microstructure of the Csf/AZ91D composites compressed at the different deformation conditions

CE

PT

ED

Highlights

•The DRX grains near the fibers were finer than those in the alloy of the C_sf/AZ91D. •The average D_DRX and X_DRX increase with increasing temperature or decreasing

strain rate.

•The X_DRX increases with the increase of true strain in a rapid–slow manner.