Kinetics equations and microstructural evolution during metadynamic recrystallization in a nickel-based superalloy with δ phase

Accepted Manuscript Kinetics equations and microstructural evolution during metadynamic recrystallization in a nickel-based superalloy with δ phase Dao-Guang He, Y.C. Lin, Ming-Song Chen, Ling Li PII:

S0925-8388(16)32474-4

DOI:

10.1016/j.jallcom.2016.08.096

Reference:

JALCOM 38598

To appear in:

Journal of Alloys and Compounds

Received Date: 4 July 2016 Revised Date:

9 August 2016

Accepted Date: 12 August 2016

Please cite this article as: D.-G. He, Y.C. Lin, M.-S. Chen, L. Li, Kinetics equations and microstructural evolution during metadynamic recrystallization in a nickel-based superalloy with δ phase, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.08.096. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Kinetics equations and microstructural evolution during metadynamic recrystallization in a nickel-based superalloy with δ phase Dao-Guang Heb, Y.C. Lina,b,c,∗, Ming-Song Chena,c, Ling Lia,b School of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China b c

Light Alloy Research Institute of Central South University, Changsha 410083, China

State Key Laboratory of High Performance Complex Manufacturing, Changsha 410083, China

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a

Abstract

The metadynamic recrystallization (MDRX) characteristics of a nickel-based superalloy with δ phase

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are studied by isothermal two-pass hot compressive experiments. The kinetic equations are developed to evaluate the softening fractions caused by MDRX. The microstructural changes induced by MDRX are

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investigated using interrupt experiments and quantitatively characterized by microscopic observations. It is found that the softening fraction significantly increases with increasing the pre-strain, strain rate and deformation temperature. The evaluated softening fractions well agree with the tested ones, which demonstrates that the developed kinetic equations can accurately evaluate the MDRX fractions for the investigated superalloy. Additionally, the MDRX grain size sharply increases when the pre-strain and

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deformation temperature are increased, while obviously decreases with increasing the strain rate. Keywords: Hot compression; Superalloy; Metadynamic recrystallization; Dynamic softening

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1. Introduction

Generally, metals or alloys often experience complicated plastic deformation during hot working [1].

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For most metal forming processes, there are several successive deformation passes. When the deformation degree surpasses the critical strain ( ε c ) for initiating dynamic recrystallization [2-5], the metals or alloys often experience metadynamic recrystallization (MDRX) during inter-pass. Recently, the deformation characteristics and microstructural changes during MDRX have attracted some attentions. For instance, the metadynamic recrystallization (MDRX) behaviors of 42CrMo steel [6], 2124 aluminum alloy [7], Nimonic 80A superalloy [8], and 30Cr2Ni4MoV ultra-super-critical rotor steel [9] were studied using two-pass hot deformation, and the corresponding kinetic models of MDRX were established for these alloys. Previous

∗

Corresponding author. Tel.: +86-013469071208. E-mail address: [email protected], [email protected] (Y.C. Lin) 1

ACCEPTED MANUSCRIPT studies indicate that the deformation characteristics and microstructural changes of alloys during MDRX are very complex, which should be well understood to optimize deformation parameters. Nickel-based superalloys are widely applied in manufacturing the high-temperature components, e.g., turbine disk and engine blades [10]. In past, several accurate constitutive equations were developed to

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forecast the flow characteristics of some typical nickel-based superalloys, including GH4169 nickel-based superalloys [ 11 , 12 ], Ni-20.0Cr-2.5Ti- 1.5Nb-1.0Al superalloy [ 13 ], and hot isostatically processed nickel-based superalloy [14], etc. Moreover, suitable processing maps were developed to optimize the hot forming parameters of some typical nickel-based superalloys [ 15 - 18 ]. In addition, the dynamic

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recrystallization (DRX) characteristics [19-22], and microstructural evolution [23-28] of some nickel-based superalloys during hot forming were studied. According to these previous studies, it was found that the flow

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characteristics and microstructural evolution were often complicated for nickel-based superalloys during hot forming. Also, the influences of forming parameters on the flow behaviors and microstructures of nickel-based superalloys are significant.

Despite several investigations focusing on high-temperature deformation characteristic and microstructural changes of some nickel-based superalloys during one-pass hot forming, there are limited

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literatures reporting the kinetics and microstructural changes induced by MDRX for a nickel-based superalloy with δ phase. Additionally, previous studies [29] illustrate that a combination of DRX and MDRX can supply a novel way to optimize material microstructures and properties. In present study, the MDRX behaviors of a nickel-based superalloy with δ phase are investigated by two-pass hot compressive

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experiments. The influences of deformation parameters on microstructural changes induced by MDRX are

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discussed. The kinetic equations are established to predict the softening fractions caused by MDRX.

2. Material and experiments The chemical composition ( wt. % ) of a commercial superalloy applied in present paper is

52.82Ni-18.96Cr- 5.23Nb-3.01Mo-1.00Ti-0.59Al-0.03C-0.01Co-(Bal) Fe . Cylindrical specimens (Φ8 mm x 12 mm ) were mechanically prepared from a wrought billet. The tested samples were solute at 1045 o C for 0.75 h , then quenched by cold water, and finally aged at 900 o C for 12 h . Two-pass hot compressive experiments were performed on a Gleeble-3500 thermo-mechanical simulator, and the detailed procedures are indicated in Fig. 1. Firstly, the specimen was progressively heated to tested temperature at 10 o C /s, holding for 5 min to eliminate temperature gradients. Three deformation temperatures (950, 980 and 2

ACCEPTED MANUSCRIPT 1010 o C ), and three strain rates (0.001, 0.01 and 0.1 s -1 ) were applied in the first and second hot forming stages. According to authors’ previous work [25], the critical strain ( ε c ) for initiating dynamic recrystallization is smaller than 0.2. To study the influences of pre-strains on deformation behaviors and microstructural changes during MDRX, the true strain of the first deformation stage should be larger than ε c .

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So, three pre-strains (the true strain of the first deformation stage) were selected as 0.22, 0.36 and 0.51. To study the microstructural changes induced by MDRX of the investigated superalloy, the microstructures before the beginning of the second pass (at the point of M indicated in Fig. 1) were retained using interrupt experiments and quantitatively analyzed by Scanning electron microscopy (SEM) and electron backscattered

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diffraction (EBSD) techniques. The sections for SEM analysis were first polished, and then etched in a chemically solution of (20 ml HCl , 20 ml CH 3 CH 2 OH and 1 g CuCl2 ). Meanwhile, the samples for

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EBSD analysis were machined from the compressed specimens, and punched into the disks (Φ3 mm). Then, the disks were electro-polishing in a solution (30 ml

HClO 4 and 270 ml CH 3 CH 2 OH ). The

microstructures before hot compressive deformation were observed in Fig. 2. Distinctly, the initial microstructures compose of δ phases, coarse grains, and twins.

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3. Results and discussion

3.1. Influences of deformation parameters on softening behaviors and microstructures during MDRX

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Generally, the flow softening fractions caused by MDRX of metals or alloys can be determined using peak stress method [7], maximum stress method [29], 0.2% offset yield strength method [30], average stress

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method [31], and back extrapolation method [32]. In present study, the softening fractions are determined by 0.2% offset yield strength method, i.e., Xmdrex =

σm − σ2 σm −σ1

(1)

where σ m represents the flow stress at the interruption point, σ 1 and σ 2 are the offset yield stresses at the first-pass and second-pass hot forming, respectively.

3.1.1. Influences of deformation temperature Fig. 3 indicates the representative two-pass hot compressed curves of the investigated superalloy at various deformation temperatures. Here, the pre-strain, inter-pass time, and strain rate are 0.36, 60 s, and 3

ACCEPTED MANUSCRIPT 0.01 s -1 , respectively. From Fig. 3, it can be seen that the true stresses in both deformation stages are abruptly affected by deformation temperature. With the increased deformation temperature, the true stresses sharply decrease. This is because that the work hardening effects induced by dislocations accumulations and pile-up become weak, while the dynamic softening behavior resulting from the vacancy migration and

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dislocation annihilation is enhanced, when the deformation temperature is increased [10]. Fig. 4 displays the influences of deformation temperature on MDRX softening fraction. Here, the pre-strain and strain rate are 0.36 and 0.01s-1, respectively. From Fig. 4, it is distinctly found that the MDRX softening fraction abruptly increases with increasing deformation temperature. It implies that the softening behavior induced by MDRX

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becomes more and more obvious with increasing deformation temperature. This phenomenon is mainly attributed to the following aspects. On one hand, the generation and movement of both vacancies and

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dislocations increase with increasing deformation temperature, which leads to the increase of mobility of grain boundaries [11]. The influences of deformation temperature on the MDRX grain diameter distribution during inter-pass are illustrated in Fig. 5. Here, the pre-strain, inter-pass time and strain rate are 0.36, 60 s and 0.01 s -1 , respectively. From Fig. 5, it is observed that the degree of MDRX increases with increasing the deformation temperature. Meanwhile, the MDRX grains gradually grow up with increasing the deformation

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temperature. On the other hand, the solute atoms diffusion and dislocations motion can also be sped up as the temperature is increased, which promotes the diffusion and reduction of δ phases [28]. In order to quantitatively characterize the evolution characteristics of δ phases during inter-pass, SEM technique is

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used. Fig. 6 indicates the SEM micrographs of the deformed superalloy at different deformation temperatures during inter-pass. Obviously, there are a large content of δ phases, and most of them experience

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the distortion and deformation at 950 o C , as illustrated in Fig. 6a. Furthermore, it is observed that the contrast between δ phases and the matrix is different in Fig. 6. So, the content percentage of unsolved

δ phases under a given tested condition can be quantitatively evaluated using the Image-pro software. Meanwhile, in order to have an accurate content percentage of unsolved δ phases, over ten SEM pictures under a given tested condition were used to evaluate the average content percentage of unsolved δ phases. The content percentage of unsolved δ phases of the deformed superalloy at 950 o C , can be statistically estimated as 8.39%. However, most of δ phases dissolved and the percentage content of the unsolved is significantly decreased to 3.2%, when the deformation temperature is increased to 1010 o C , as shown in Fig. 6b. Generally, δ phases act as the geometric barriers for the motion of grain boundaries. So, the reduction of 4

ACCEPTED MANUSCRIPT δ phases may result in the rapid growth of MDRX grains. Then, the softening fraction caused by MDRX increases.

3.1.2. Influences of pre-strain Fig. 7 displays the representative two-pass hot compressed curves of the investigated superalloy at

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different pre-strains. Here, the deformation temperature, strain rate, and inter-pass time are 950 o C , 0.01 s -1 , and 60s, respectively. From Fig. 7, it can be seen that the yield stress of the second-pass deformation stage obviously decreases with the increased pre-strain. This implies that the dynamic softening behavior induced

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by MDRX becomes obvious with the increased pre-strain. Fig. 8 illustrates the changes of MDRX softening fraction with pre-strain. Distinctly, the MDRX softening fraction is raised with the increased pre-strain. It is mainly attributed to that the deformation storage energy in deformed blocks significantly increases with

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increasing the pre-strain. Large deformation storage energy can offer larger driving force for the migration of grain boundaries [33]. Fig. 9 indicates the MDRX grain diameter distribution at different pre-strains. From Figs. 5a, 9a and 9c, it is distinctly found that the degree of MDRX increases as increasing the pre-strains. Meanwhile, the growth of MDRX grains is abruptly accelerated at high pre-strain during inter-pass, as illustrated in Figs. 5b, 9b and 9d. In addition, the variations of δ phases with pre-strain during inter-pass are

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investigated through SEM analysis, and corresponding micrographs are indicated in Fig. 10. Obviously, a large content of the unsolved δ phases can be observed, and most of them undergo the distortion and deformation at the true strain of 0.22, as indicated in Fig. 10a. By the statistical analysis, it can be observed

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that the content percentage of the unsolved δ phases at true strain of 0.22 is 10.52%. When the pre-strain is increased to 0.51, the δ phases obviously dissolve and the content percentage is decreased to 5.36%, as

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illustrated in Fig. 10b. As discussed in section 3.1.1, the reduction of δ phases can decrease the resistance for the growth of MDRX grains. So, the growth of MDRX grains in inter-pass period becomes easy, when the pre-strain is increased. In addition, the substructures, such as high density dislocations network, dislocation cells and subgrains, increase with the increased pre-strain. It leads to the increase of DRX nuclei in the first hot deformation stage, when the pre-strain is increased. Therefore, the MDRX softening fraction increases with the increased pre-strain.

3.1.3. Influences of strain rate The representative two-pass hot compressed curves of the studied superalloy at different strain rates are

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ACCEPTED MANUSCRIPT displayed in Fig. 11. Here, the deformation temperature, inter-pass time, and pre-strain are 950 o C , 60 s, and 0.36, respectively. From Fig. 11, it is understood that the true stresses in both deformation stages increase with the increased strain rate. This characteristic result from the fact that low stain rate ensures the sufficient deformation time for the growth of DRX grains, which enhances the dynamic softening behavior. Fig. 12

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illustrates the influences of strain rates on MDRX softening fraction. Obviously, the MDRX softening fraction drastically increases with the increased strain rate. This implies that the MDRX softening is enhanced as the strain rate is increased. This is because the high strain rates allow less time for the progress of dynamic recovery, i.e., dislocations annihilation and rearrangement in the first-pass hot deformation. This

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results in the increased substructures in deformed block, when the strain rate is high. On one hand, the increase of substructures results in the increased DRX grains nuclei in the first hot compression stage. On

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the other hand, high density of substructures retards the growth of MDRX grains. The orientations imaging microscopy maps and MDRX grain diameter distribution at various pre-strains are shown in Fig. 13. Here, the pre-strain, inter-pass time and deformation temperature are 0.36, 60 s and 950 o C , respectively. As illustrated in Figs. 13a, 13c and 5a, the MDRX degree distinctly increases with decreasing the strain rate. Meanwhile, the MDRX grains during inter-pass become more and more refined with the increased strain rate,

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as illustrated in Figs. 5b, 13b and 13d. In addition, the growth of MDRX grains can be greatly affected by grains boundary mobility. The δ phase, a metallurgical barrier to pin the motion of grains boundary, has a significant influence on the evolution of MDRX grains for the studied superalloy. Fig. 14 indicates the SEM

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micrographs of the investigated superalloy at different strain rates during inter-pass. When the strain rate is 0.1 s -1 , a large content of distorted and deformed δ phases can be found, as illustrated in Fig. 14a.

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Furthermore, the content of the unsolved δ phases can be statistically estimated as 10.15%. However, the content of the unsolved δ phases drastically decreases to 5.54% when the strain rate is decreased to 0.001 s -1 , as illustrated in Fig.14b. In general, the reduction of δ phases can result in the pinning effects on the growth of MDRX grains become weaken. So, the growth of MDRX grains is accelerated.

3.2. Kinetic equations of metadynamic recrystallization Generally, the kinetics of MDRX can be predicted by [7,32],

X mdrex = 1 − exp(−0.693(

t n ) ) t0.5

(2)

where n and t are the material constant and inter-pass time, respectively, t0.5 represents the time for 50% 6

ACCEPTED MANUSCRIPT MDRX fraction [30], X mdrex indicates the MDRX fraction. For the investigated superalloy, the stacking fault energy is low [19,22]. It is commonly known that the effects of static recovery on the deformation resistance of the alloys with low stacking fault energy are very small during hot forming, and can be reasonably neglected. So, the softening behaviors of the studied superalloy during two-pass deformation are

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mainly induced by MDRX. Furthermore, the MDRX fraction in left side of Eq. (2) can be simply substituted by MDRX softening fraction (as indicated in Eq. (1)).

t0.5 = Aε& q exp(

Qmdrex ) RT

(3)

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where A and q are the material constants. Qmdrex is the apparent activation energy of MDRX ( J ⋅ mol−1 ). T is the deformation temperature (K). R illustrates the gas constant (8.314 J ⋅ mol −1 ⋅ K −1 ).

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However, Fig. 8 indicates that the influences of pre-strain on MDRX softening behaviors are significant. So, t0.5 for the studied superalloy should be modified as,

t0.5 = Aε p ε& q exp(

3.2.1. Calculation of n

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where p is the material constant.

Qmdrex ) RT

(4)

Taking a natural logarithm on both sides of Eq. (2) gives, (5)

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  1 ln  ln( )  = ln 0.693 + n ln t − n ln t0.5  1 − X mdrex 

Substituting the values of X mdrex and t at various tested conditions into Eq. (5), the average values

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  1 of n can be obtained from the relationships between ln  ln( )  and ln t . The detailed procedures to  1 − X mdrex  identify the values of n were illustrated in authors’ previous investigations [7,30]. Then, based on the linear regression method, the mean value of n can be assessed as 0.947, which is similar to the previous reports [9].

3.2.2. Determination of t0.5 As indicated in Eq. (4), four parameters ( A , p , Qmdrex and q ) are needed to be determined. Taking a natural logarithm of Eq. (4) gives,

ln t0.5 = ln A + p ln ε + q ln ε& + 7

Qmdrex RT

(6)

ACCEPTED MANUSCRIPT Substituting n into Eq. (5), the values of t0.5 under various experimental conditions can be identified from the relationship between X mdrex and corresponding inter-pass time. Then, taking the values of t0.5 , ε , T and ε& into Eq. (6), the plots of ln t0.5 − 1 T , ln t0.5 − ln ε , and ln t0.5 − ln ε& are developed using the similar method indicating in the author previous investigations [7,30]. Then, the values of Qmdrex , p and q can

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be evaluated as 145.33 kJ/mol−1, -1.31, and -0.158, respectively. Furthermore, the values of Qmdrex , p , and q are substituted into Eq. (5), and the value of A can be obtained as 2.31×10-6. So, the kinetic equations of MDRX for the studied superalloys can be expressed as,

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X mdrex = 1 − exp[−0.693( t0.5t )0.947 ]

(8)

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t0.5 = 2.31× 10−6 ε −1.31ε& −0.158 exp(145330 / RT )

(7)

3.2.3. Verification of the developed MDRX kinetic equations

In this section, comparisons between the tested and forecasted MDRX fractions are carried out to verify the established kinetic equations (Eqs. 7 and 8). Meanwhile, in order to evaluate the accuracy of the developed kinetic equations, the correlation coefficient ( R ) and average absolute error ( AARE ) are

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determined,

N

R=

∑ (M i =1

N

∑ (M i =1

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AARE (%) =

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where N is the number of tested data.

i

i

− M )( Pi − P )

−M)

1 N

∑ (P − P) i =1

N

∑ i =1

(9)

N

2

2

i

M i − Pi Mi

(10)

M i and Pi are the tested and predicted results,

respectively. M and P are the average values of M i and Pi , respectively. Fig. 15 compares the tested and predicted t0.5 . Obviously, the predicted t0.5 well agrees with the tested t0.5 . The relationships between the tested and predicted MDRX fractions at various experimental conditions are illustrated in Fig. 16. Distinctly, the experimental results well agree with the calculated ones. So, it can be concluded that the developed kinetic equations can reasonably predict the MDRX softening characteristics of the investigated superalloy.

4. Conclusions 8

ACCEPTED MANUSCRIPT The metadynamic recrystallization (MDRX) behaviors in a nickel-based superalloy with δ phase are investigated. It is observed that the MDRX behaviors are greatly affected by deformation parameters. With the increase of the pre-strains, strain rates and deformation temperatures, the softening fractions caused by MDRX obviously increase. The metadynamic recrystallization kinetic equations are developed to describe

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the MDRX softening behaviors. The predicted MDRX volume fractions are well consistent with the tested ones, which illustrates the developed equations can reasonably describe the MDRX behaviors. It is found that the growth of metadynamic recrystallization grains and the dissolution of δ phases become more and more obvious with increasing the deformation temperature and pre-strain. However, when the strain rate is

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increased, the metadynamic recrystallization grains can be obviously refined, while the dissolution of

δ phases becomes weaken.

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Acknowledgements

This work was supported by the National Natural Science Foundation Council of China (Grant No. 51375502), the Project of Innovation-driven Plan in Central South University (Grant No. 2016CX008),

the National Key Basic Research Program (Grant No. 2013CB035801), the Natural Science Foundation for Distinguished Young Scholars of Hunan Province (Grant No. 2016JJ1017), Program of Chang Jiang

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Scholars of Ministry of Education (No. Q2015140), and the Graduate Innovation Foundation of Central South University (Grant No. 2016zzts047), China.

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Captions of Tables and Figure Fig. 1. Experimental procedures for two-pass hot compression Fig. 2. The initial microstructures of the studied superalloy before hot compressive deformation

Fig. 4. Effects of deformation temperature on the MDRX softening fraction.

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Fig.3. Typical two-pass true stress-true strain curves indicating the MDRX occurrence at different deformation temperatures.

Fig. 5. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at: (a-b) 950 o C ; (c-d) 980 o C ; (e-f) 1010 o C (Pre-strain, inter-pass time, and strain rate are 0.36, 60 s, and 0.01 s-1, respectively.)

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Fig. 6. SEM micrographs at the center area of the deformed samples during inter-pass at: (a) 950 o C ; (b) 1010 o C (Pre-strain, inter-pass time, and strain rate are 0.36, 60 s, and 0.01 s-1, respectively.)

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Fig. 7. Typical two-pass true stress-true strain curves indicating the occurrence of MDRX at different pre-strains. Fig. 8. Effects of pre-strain on the MDRX softening fractions.

Fig. 9. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at the pre-strains of: (a-b) 0.22; (c-d) 0.51 (Deformation temperature, inter-pass time, and strain rate are 950 o C , 60 s, and 0.01 s-1, respectively).

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Fig. 10. SEM micrographs at the center area of the deformed samples during inter-pass at the pre-strains of: (a-b) 0.22; (c-d) 0.51 (Deformation temperature, inter-pass time, and strain rate are 950 o C , 60 s, and 0.01 s-1, respectively). Fig. 11. Typical two-pass true stress-true strain curves indicating the occurrence of MDRX at different strain rates. Fig. 12. Effects of strain rate on the MDRX softening fraction.

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Fig. 13. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at the strain rates of: (a-b) 0.1s-1; (c-d) 0.001s-1 (Pre-strain, inter-pass time and deformation temperature are 0.36, 60 s and 950 o C , respectively.).

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Fig. 14. SEM micrographs at the center area of the deformed samples during inter-pass at the strain rates of: (a-b) 0.1s-1; (c-d) 0.001s-1 (Pre-strain, inter-pass time and deformation temperature are 0.36, 60 s and 950 o C , respectively.). Fig. 15. Comparisons between the tested and predicted t0.5 . Fig. 16. Comparisons between the tested and predicted MDRX fractions at: (a) strain rate of 0.01s-1and pre-strain of 0.36; (b) deformation temperature of 950 o C and pre-strain of 0.36; (c) all tested conditions (solid plots is the predicted results; symbols is the experimental results).

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Temperature (oC)

5 min holding

First compression

Second compression

M Test temperatures: 950 oC, 980 oC, 1010 oC -1 -1 -1 Strain rates: 0.001s , 0.01s , 0.1s Inter-pass times: 10s, 30s, 45s, 60s Pre-strains: 0.22, 0.36, 0.51

Water quencing

Heating rate (10 oC/s)

RI PT

Time

M AN U

SC

Fig. 1. Experimental procedures for two-pass hot compression

Fig. 2. The initial microstructures of the studied superalloy before hot compressive deformation

Pre-strain: 0.36 Inter-pass time: 60s Strain rate: 0.01s-1

250 200

950 oC

TE D

Ture Stress (Mpa)

350 300

150

980 oC

100

1010 oC

50

0 0.0

0.2

0.4 0.6 Ture Strain

0.8

1.0

EP

Fig. 3. Typical two-pass true stress-true strain curves indicating the MDRX occurrence at different deformation temperatures.

Softening fractions

AC C

1.0 0.8 0.6 Strain rate: 0.01s-1 Pre-strain: 0.36 Deformation temperature: 950 oC 980 oC 1010 oC

0.4 0.2 0.0

0

10

20

30 40 Time (s)

50

60

70

Fig. 4. Effects of deformation temperature on the MDRX softening fraction.

12

ACCEPTED MANUSCRIPT 40 30 20 10 0

(a)

0

5 10 15 20 25 MDRX grain diameter (µm)

(b)

Daverage = 5.12 (µm) 30 20 10 0

5 10 15 20 25 MDRX grain diameter (µm)

30

(d)

M AN U

(c)

0

SC

Volume fraction (%)

40

30

RI PT

Volume fraction (%)

Daverage = 4.04 (µm)

Volume fraction (%)

40

Daverage = 5.44 (µm)

30 20 10

TE D

0

0

5 10 15 20 25 MDRX grain diameter (µm)

30

AC C

EP

(e) (f) Fig. 5. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at: (a-b) 950 o C ; (c-d) 980 o C ; (e-f) 1010 o C (Pre-strain, inter-pass time, and strain rate are 0.36, 60 s, and 0.01 s-1, respectively.)

δ

(a) (b) Fig. 6. SEM micrographs at the center area of the deformed samples during inter-pass at: (a) 950 o C ; (b) 1010 o C (Pre-strain, inter-pass time, and strain rate are 0.36, 60 s, and 0.01 s-1, respectively.)

13

ACCEPTED MANUSCRIPT Deformation temperature: 950 oC Inter-pass time: 60s Strain rate: 0.01s-1

200

100 0.22

0.36 0.51

0 0.0

0.2

0.4 0.6 Ture Strain

0.8

RI PT

Ture Stress (Mpa)

300

Strain rate: 0.01s-1 Deformation temperature: 950 oC Pre-strains: 0.22 0.36 0.51

0.8 0.6 0.4 0.2 0.0

0

M AN U

Softening fractions

1.0

SC

Fig. 7. Typical two-pass true stress-true strain curves indicating the occurrence of MDRX at different pre-strains.

10

20

30 40 Time (s)

50

60

70

Fig. 8. Effects of pre-strain on the MDRX softening fractions.

TE D

Volume fraction (%)

40

Daverage = 3.82 (µm)

30 20 10

0

0

Volume fraction (%)

AC C

EP

(a)

5 10 15 20 25 MDRX grain diameter (µm)

30

(b) 40 Daverage = 4.55 (µm) 30 20 10 0

(c)

0

5 10 15 20 25 MDRX grain diameter (µm)

30

(d)

Fig. 9. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at the pre-strains of: (a-b) 0.22; (c-d) 0.51 (Deformation temperature, inter-pass time, and strain rate are 950 o C , 60 s, and 0.01 s-1, respectively).

14

RI PT

ACCEPTED MANUSCRIPT

(a) (b) Fig. 10. SEM micrographs at the center area of the deformed samples during inter-pass at the pre-strains of: (a-b) 0.22; (c-d) 0.51 (Deformation temperature, inter-pass time, and strain rate are 950 o C , 60 s, and 0.01 s-1, respectively).

SC

Deformation temperature: 950 oC Inter-pass time: 60s pre-strain:0.36

400

0.1s-1

300 200

M AN U

Ture Stress (Mpa)

500

0.01s-1

100

0.001s-1

0 0.0

0.2

0.4 0.6 Ture Strain

0.8

1.0

TE D

Fig. 11. Typical two-pass true stress-true strain curves indicating the occurrence of MDRX at different strain rates.

EP

Softening fractions

1.0

Deformation temperature: 950 oC Inter-pass time: 60s pre-strain: 0.36

0.8 0.6 0.4

Strain rates: 0.1 s-1 0.01 s-1 0.001 s-1

0.2 0.0

0

10

20

30 40 Time (s)

50

60

70

AC C

Fig. 12. Effects of strain rate on the MDRX softening fraction.

Volume fraction (%)

40 Daverage = 3.72 (µm) 30 20 10 0

(a)

0

5 10 15 20 25 MDRX grain diameter (µm)

(b)

15

30

ACCEPTED MANUSCRIPT

Volume fraction (%)

40 Daverage = 4.81 (µm) 30 20 10

0

5 10 15 20 25 MDRX grain diameter (µm)

30

RI PT

0

M AN U

SC

(c) (d) Fig. 13. Orientation imaging microscopy maps and MDRX grain diameter distribution at the center area of the deformed samples at the strain rates of: (a-b) 0.1s-1; (c-d) 0.001s-1 (Pre-strain, inter-pass time and deformation temperature are 0.36, 60 s and 950 o C , respectively.).

TE D

(a) (b) Fig. 14. SEM micrographs at the center area of the deformed samples during inter-pass at the strain rates of: (a-b) 0.1s-1; (c-d) 0.001s-1 (Pre-strain, inter-pass time and deformation temperature are 0.36, 60 s and 950 o C , respectively.).

EP

60

Predicted t0.5

AC C

50

AARE=0.11% R=0.9958

40 30 20 10 10

20

30

40

50

60

Tested t0.5

Fig. 15. Comparisons between the tested and predicted t0.5 .

16

ACCEPTED MANUSCRIPT

0.6

1010 oC

0.4

980 oC o

950 C

0.2 0.0

-2

0

2

4

0.8 0.6

0.1s-1

0.4

0.01s-1

0.2 0.0

6

Temperature: 950 oC Pre-strain: 0.36

0.001s-1 -2

0

(a)

(b) 1.0

4

6

0.8

AARE= 4.1% R= 0.995

0.6 0.4 0.2 0.0 0.0

0.2

SC

Predicted Xmdrex

2 lnt

lnt

0.4 0.6 0.8 Tested Xmdrex

1.0

M AN U

(c)

RI PT

0.8

1.0

Strain rate: 0.01s-1 Pre-strain: 0.36

MDRX fractions

MDRX fractions

1.0

AC C

EP

TE D

Fig. 16. Comparisons between the tested and predicted MDRX fractions at: (a) strain rate of 0.01s-1and pre-strain of 0.36; (b) deformation temperature of 950 o C and pre-strain of 0.36; (c) all tested conditions (solid plots is the predicted results; symbols is the experimental results).

17

ACCEPTED MANUSCRIPT

Research highlights: Metadynamic recrystallization (MDRX) behaviors of a Ni-based superalloy with δ phase are studied. Softening fraction significantly increases with increasing pre-strain, strain rate and temperature.

RI PT

The developed kinetic equations can accurately evaluate the softening fractions caused by MDRX. MDRX grain size sharply increases when the pre-strain and deformation temperature are increased.

AC C

EP

TE D

M AN U

SC

MDRX grain size obviously decreases with increasing the strain rate.