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JMEPEG (2013) 22:2168–2175 DOI: 10.1007/s11665-013-0496-0

Dynamic Recrystallization during Hot Deformation of 304 Austenitic Stainless Steel A. Marchattiwar, A. Sarkar, J.K. Chakravartty, and B.P. Kashyap (Submitted October 15, 2012; in revised form December 24, 2012; published online February 13, 2013) The kinetics of dynamic recrystallization (DRX) during hot compression of 304 austenitic stainless steel was studied over the temperature range of 900-1200 °C and strain rate range of 0.002-0.1 s21. The initiation and evolution of DRX were investigated using the process variables derived from flow curves. By the regression analysis for conventional hyperbolic sine equation, the activation energy for DRX was determined as Q = 475 kJ mol21. The temperature and strain rate domain where DRX occurred were identified from the strain rate sensitivity contour map. The critical stress (and strain) for the initiation of DRX was determined from the inflection point on the work hardening rate (h = dr/de) versus flow stress (r) curve. The saturation stress of the dynamic recovery (DRV) curve was calculated from the h-r plot at the same condition at which DRX occurred. Progress of fraction recrystallization was determined from the difference between the generated DRV curve and the experimental DRX curve. In addition, the microstructural evolution at different strain levels during DRX was characterized and compared with the calculated fraction recrystallization.

Keywords

austenitic Stainless Steel, compression test, dynamic recrystallization, recrystallization kinetics

1. Introduction Austenitic stainless steels, primarily SS304 and SS316, are used as structural materials in various engineering applications owing to their excellent elevated temperature mechanical properties. Generally, these steels are processed through various thermo-mechanical treatments before they are fabricated into final components. Determination of the load to carry out these operations is of paramount importance. Load depends on the flow stress characteristic of the materials besides the geometry of the die and friction at the tool-workpiece interface. Therefore, prediction of hot deformation behavior linking process variables such as strain, strain rate, and temperature to the flow stress of the deforming materials is necessary (Ref 1). Moreover, several interconnected metallurgical phenomena such as work hardening, dynamic recovery (DRV), dynamic recrystallization (DRX), etc., occur during high temperature deformation of materials. In light alloys such as magnesium alloy and aluminum alloy, DRV can balance work hardening, and a plateau is achieved in stress (Ref 2, 3). However, in

A. Marchattiwar and B.P. Kashyap, Department of Metallurgical Engineering and Materials Science, IIT Bombay, Mumbai 400076, India; and A. Sarkar and J.K. Chakravartty, Mechanical Metallurgy Division, Bhabha Atomic Research Centre, Mumbai 400085, India. Contact e-mail: [email protected].

2168—Volume 22(8) August 2013

austenitic steels with higher deformation resistance, the kinetics of DRV is lower, and DRX can be initiated at a critical condition of stress accumulation (Ref 4). The occurrence of DRX brings about grain refinement and reduction in deformation resistance due to which the evaluation of the rate and progress of DRX, in terms of deformation conditions, is important (Ref 5). The general descriptive model for DRX is that the nucleation of DRX grains can start at a critical strain which is a function of initial microstructure and deformation conditions. Then, the evolution of DRX microstructure can proceed further by increasing deformation and through the formation of a necklace structure (Ref 6). Considerable research on DRX kinetics has focused on measuring by metallographic images or EBSD maps of the frozen microstructures at different deformation conditions such as temperature, strain rate, and amount of plastic deformation. Meanwhile, the relationships between microstructure variations and deformation parameter are analyzed at different levels. However, little attention has been paid to model microstructure evolution by analyzing flow curves collected by hot compression tests (Ref 1-6). For austenitic steels such as SS304, during a plastic forming process, a pronounced interaction between DRX evolution and mechanical property is implicit in flow behavior. Thus, it is realizable to model DRX evolution by analyzing the true stress-true strain curves. The objective of this study is to establish the relationship between the flow stress, strain, strain rate, and temperature to predict the high temperature flow behavior of SS304. Toward this end, isothermal hot compression tests were conducted in a wide range of strain rates and temperatures. The experimental stressstrain data were then employed to derive a constitutive equation relating flow stress, strain rate, and temperature. In the present study, the kinetics of DRX was determined through a flow curve analysis directly by comparing generated dynamic recovery curves with those obtained from the experiments. Finally, the progress in DRX is investigated through a metallographic study.

Journal of Materials Engineering and Performance

2. Experimental Procedures Compression samples of SS304 (70.8%Fe, 18.4%Cr, 8.3%Ni, 0.73%C, 0.03%P, 0.004%S, 0.6%Si, 1.09%Mn) steel with 8 mm height and 5 mm diameter were machined from the as-received rod. Samples were annealed at 700 C for 1 h before the compression test. Figure 1 shows the optical micrograph of an annealed sample. Hot compression tests were conducted at DIL805 deformation dilatometer. These tests were performed isothermally in the temperature range of 11731473 K (900-1200 C) (in steps of 100 K) at various constant strain rates from 0.002 to 0.1 s1 in vacuum of 5 9 105 mbar. To freeze the hot deformed microstructure, the specimens were quenched with argon gas as soon as the specified amounts of strains were imparted. The hot deformed samples were cut along the longitudinal direction using a precision cut-off machine. One half of the sample was taken to prepare specimens for the electron backscattered diffraction (EBSD) investigation. The microstructures were examined in the maximum deformation zone of the specimens. EBSD scans were performed on all processed samples using a TSLOrientation Imaging Microscopy (OIM) system attached to an FEI Quanta 200 scanning electron microscope (FEI, Eindhoven, Netherlands) operating at 30 kV. Samples for EBSD were polished up to 0.25-lm grit diamond paste using the standard metallographic polishing procedure. Finally, samples were electro polished to insure removal of any residual surface deformation. EBSD maps were collected from the processed samples using a step size of 0.5 lm using a hexagonal grid.

3. Analysis and Results 3.1 Constitutive Equations Approach The correlation between the flow stress (r), temperature (T), and strain rate ( e_ ), particularly at high temperatures, could be expressed by an Arrhenius-type equation (Ref 7). Further, the

effects of temperature and strain rate on deformation behavior could be represented by the Zener-Holloman parameter (Z) in an exponent-type equation (Ref 8). These are mathematically expressed as Z ¼ e_ exp

Q RT

¼ Aðsin hðarÞÞn

Q e_ ¼ AFðrÞ exp RT

ðEq 1Þ

ðEq 2Þ

where F ðrÞ ¼rn ¼expðbrÞ ¼½sinhðarÞn

for ar < 0:8 for ar > 1:2 for all r

Here, R is the universal gas constant (8.31 J mol1 K1); T is the absolute temperature in K; Q is the activation energy (kJ mol1); and A, a, b, and n are the materials constants, a = b/n. True stress-true strain curves were obtained at three strain rates of 0.1, 0.01, and 0.002 s1 and at temperatures 900, 1000, 1100, and 1200 C. True stress versus true strain data from the compression tests (Fig. 2) at various deformation conditions were used to evaluate the material constants of the constitutive equations. The following are the evaluation procedures of material constants at a true strain of 0.5. For low and high stress levels, substituting the value of F(r) in Eq 2, at constant temperature, gives the following corresponding relationships: e_ ¼ Brn

ðEq 3Þ

e_ ¼ C expðbrÞ

ðEq 4Þ

where B and C are the material constants, depending on temperature. A logarithm of both sides of Eq 3 and 4 yields, respectively, 1 1 lnðrÞ ¼ lnð_eÞ lnðBÞ n n

ðEq 5Þ

1 1 r ¼ lnð_eÞ lnðCÞ b b

ðEq 6Þ

The values of n and b can be obtained from the slope of the lines in the lnr versus ln e_ plot (Fig. 3a) and r versus ln e_ plot (Fig. 3b), respectively. It is apparent that the lines are almost parallel, leading us to observe that the slope of the lines consequently varies in a very small range. The slight variation in the slope of the lines could be attributed to scattering in the experimental data points. The inverse of mean value of the slopes was taken as the value of n and b, which was found to be 5.055 and 0.0533 MPa1, respectively. This gives the value of a = b/n = 0.0105 MPa1. For low as well as high stress levels, Eq 2 can be written as Q e_ ¼ A½sin hðarÞn exp RT

ðEq 7Þ

Taking the logarithm of both sides of the above Eq 7 gives ln½sin hðarÞ ¼ Fig. 1 Optical microstructure of the starting annealed SS304 sample


ln e_ Q ln A þ n nRT n

ðEq 8Þ

For a particular strain rate, differentiating Eq 8 gives

Volume 22(8) August 2013—2169

6.0

300

Strain Rate 0.1 s -1 250

1000oC

200

5.0

1000oC 150

1100oC

100

ln (σ /MPa)

True Stress σ (MPa)

900 C

4.5

1200oC

1200oC

0 0.0

3.5

0.1

0.2

(a)

0.3

0.4

0.5

0.6

3.0 -7

0.7

True Strain ε 200

-6

(a)

900oC

150

-5

-4

-3

-2

-1

-1

ln (Strain rate/s ) 250

Strain Rate 0.01 s-1

900oC

200

1000oC σ (MPa)

True stress σ (MPa)

1100oC

4.0

50

1000oC

100

1100oC

150

1100oC

100

50

1200oC 0 0.0

0.1

0.2

(b)

0.3

0.4

0.5

0.6

0.7

Strain Rate 0.002 s-1

900oC 1000oC

1100oC 1200oC

0.1

0.2

(c)

0.3

0.4

0.5

0.6

0.7

True Strain ε

Fig. 2 True stress-true strain curves at various temperatures and strain rates (a) 0.1 s1, (b) 0.01 s1, (c) 0.002 s1

Q ¼ Rn

d fln½sin harg dð1=T Þ

ðEq 9Þ

The value of Q can be derived from the slopes in a plot of ln [sinh(ar)] versus 1/T (Fig. 4a). The value of Q was determined


-6

-5

-4

-3

-2

-1

ln (Strain rate/s-1)

Fig. 3 Plots of (a) ln (stress) against ln (strain rate) and (b) stress against ln (strain rate) to evaluate the value of n and b, respectively

100

0 0.0

0 -7

(b)

50

1200oC

50

True Strain ε 150


900oC

5.5

o

by averaging the values of Q under different strain rates. At 0.5 true strain, the value of Q was found to be 475 kJ/mol. The value of A at a particular strain could be obtained by plotting the relationship between ln Z versus ln [sinh(ar)]. As shown in Fig. 4(b), the value of A at 0.5 strain was found to be 1.05103 9 1017. Once the material constants are evaluated, the flow stress at a particular strain can be predicted. Considering Eq 1 and 7, the constitutive equation relating the flow stress and ZenerHolloman parameter can be written as 1=n 1 Z ðEq 10Þ r ¼ sin h1 a A Figure 5 shows the plot of the predicted stress versus experimentally measured stress at the strain of 0.5. It can be seen that the prediction is better for low stress values corresponding to a higher temperature and lower strain rate deformation conditions.

3.2 Strain Rate Sensitivity Map In this study, the strain rate sensitivity (m) was calculated from the r, T, e_ data which are converted to a contour map in a


2

-1.0

0.1s-1 0.01s-1

0.23

0.002s-1

1

0.28 0.26

-1.5

0.21

-1

log (ε, s )

ln(sinh(σα))

0.19

0

0.19 -2.0

0.17 0.15

-2.5

-1

0.10

0.12 900 -4

7.0x10

-4

1200

-4

7.7x10

8.4x10

T (°C) Fig. 6 Contour map of strain rate sensitivity m in a frame of T and e_

50

45

ln (Z/s-1)

1100

1/T (K-1)

(a)

40

35

30 -2

-1

(b)

0

1

2

ln(sinh(α σ ))

250

200

150

100

50

0

0

50

100

150

200

250

σ experimental(MPa)

Fig. 5 Correlation between the experimental and predicted flow stress data from the constitutive Eq 10 at a strain of 0.5


frame of T and e_ as shown in Fig. 6 for a strain of 0.5. The contour numbers in Fig. 6 represent the value of m. It can be seen that the value of m is positive for entire temperature and strain rate range of this study. m value is maximum (0.28) at a strain rate of 0.1 s1 and temperature range 1000-1200 C. This high value of m usually corresponds to the occurrence of DRX (Ref 9). It is pertinent to mention here that Venugopal et al. (Ref 10, 11) have constructed the processing map for SS304. Their processing map also exhibited a DRX domain at similar deformation conditions (Ref 10, 11). The detailed investigation of DRX in this deformation condition is dealt with in the next section.

3.3 Kinetics of DRX from Flow Curve Analysis

Fig. 4 Plots of (a) ln[sinh(ar)] vs. 1/T and (b) ln z vs. ln [sinh(ar)] to estimate the values of Q and A, respectively

σ predicted(MPa)

1000

Some representative flow curves of SS304 at different strain rates and at different deformation temperatures are shown in Fig. 2. The flow behavior exhibits features typical of a material undergoing DRX and reveals a single peak prior to steady state (Ref 12). It is seen that both the peak and the steady state stress increase with increasing strain rate and decreasing temperature. The initial grain morphology of the annealed material was essentially equiaxed with an average grain diameter of about 50 lm (Fig. 1). Microstructures of the samples deformed at 900 and 1000 C at a strain rate of 0.01 s1 are shown in Fig. 7(a) and (b), respectively. It is seen that the initial structure is completely modified and the deformed microstructures consist of fine uniform grains. This is the typical characteristic of DRX. DRX in austenitic stainless steel has been investigated by several researchers (Ref 6, 13-15). There is now a reasonable understanding of the micromechanism of DRX in steels. DRX is considered to be the most important restoration mechanism during thermo-mechanical processing of a wide variety of materials (Ref 16-23). In view of this, extensive research work has been carried out during the past few decades not only for academic interest but also for its immense consequence in industrial processing. In designing the processing steps, detailed knowledge of the DRX characteristics is of paramount importance particularly those related to kinetics. The Avrami relation (Ref 24-26),


Fig. 7

EBSD images of deformed samples at strain rate of 0.01 s1(a) 900 C, (b) 1000 C

Fig. 8 Schematic representation of flow curves during dynamic recovery and dynamic recrystallization defining various stress and strain parameters involved in Avrami analysis

originally developed to study static recrystallization (SRX) in metallic systems, is being increasingly adopted by researchers to model the progress of DRX in a wide variety of metals and alloys (Ref 27-30). The general form of the Avrami equation is retained to study the progress of DRX and the relation is expressed as 0

X ¼ 1 expðktn Þ

ðEq 11Þ

Here, X represents the recrystallized volume fraction, t is the time, k is the Avrami constant, and n¢ is termed as the Avrami time exponent.


The application of the Avrami relation to DRX kinetics was originally proposed as a so-called flow curve analysis method by Medina and Hernandez (Ref 30) and was modified recently by Jonas et al. (Ref 14) using a different functional form to evaluate the work hardening characteristics. In the following, we briefly describe the underlying concept of the study of DRX kinetics from flow curve analysis. The study of DRX kinetics in terms of the Avrami equation is not straightforward. During hot deformation, the restoration processes that occur dynamically tend to cancel out the effects of work hardening. In dynamic recovery, the generation and accumulation of dislocations due to work hardening are continuously offset by dislocation rearrangement and annihilation, resulting in a steady state (rsat) value as shown in Fig. 8 (marked DRV). When DRX is the restoration process, the flow curve (marked DRX) rises initially as a result of work hardening and recovery processes to a peak value (rp), beyond which the flow stress drops with increasing strain to a steady state value (rss) at large strain. This flow behavior is typical of DRX and has been reported for a wide variety of metals and alloys (Ref 15, 31, 32). It has been shown that a critical value of strain (ec) is required for the nucleation of relatively dislocation-free regions initiating the DRX process and this occurs before the strain (ep) at rp (Ref 33). The softening (exhibited by the decrease of flow stress) beyond peak stress results from the large-scale removal of dislocations by the growth of dislocation-free regions. In general, the strain required for arriving at the steady state (ess) in DRV is much higher than ec for DRX. Intuitively then, the effect of time on structural changes in SRX is similar to that of strain in DRX (Ref 34). Equation 11 can be modified to be consistent with the DRX mechanism by replacing ‘‘t’’ (time from the start of DRX) with strain (ex) at a given rate. The modified form of the equation is


1.0

700

40

X=1-exp(-16.7(ε-εc)2.19)

600

-dθ /dσ

500

20 0.6

400

X

θ (MPa)

0.8

30

10 30

40

300

50 σ (MPa)

60 0.4

200 0.2

100 0

0.0

25

30

35

40

(a)

45

50

55

60

65


0.4

0.6

Fig. 10 Variation of fraction recrystallization w.r.t. (e-ec) DRV

70 60

DRX

50

12000C, SR 0.1s-1

40 30 20 10 0.0

0.2

ε - εc

σ (MPa) 80

(b)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

True Strain ε

Fig. 9 (a) h vs. r plot, (b) reconstructed dynamic recovery (DRV) curve plotted along with the experimental dynamic recrystallization (DRX) curve for SS304 deformed at 1200 C, 0.1 s1

0 X ¼ 1 exp kðe ec Þn

ðEq 12Þ

Note that the strain under consideration is beyond the critical strain associated with the DRX process and is represented accordingly as (e-ec). Since X (fraction recrystallized) is related to the ‘‘loss of dislocations,’’ in principle, it can be estimated from the difference between the DRX flow curve (obtained by experiment) and the corresponding DRV flow curve (expected stress-strain behavior if recovery was the only operative restoration process) predicted under similar conditions of deformation of DRX. In this modeling technique, an important consideration is the construction of the DRV flow curve. The necessary inputs for this are stress parameters like rc (corresponding to ec), rp, rsat, associated strain parameters, and work hardening. A key assumption in this modeling technique is that the DRV work hardening behavior represents the behavior of the unrecrystallized volume and it is similar to that before the initiation of DRX. In this sense, the work hardening behavior of DRV is expected to be similar to that of the experimental DRX curve prior to rc. In this work, we


study the DRX kinetics of SS304 using the method developed by Jonas et al. (Ref 14). The first step toward DRX analysis is the identification of ec and the corresponding rc. Conventionally, ec is determined from a plot of work hardening rate, i.e., h = dr/de (calculated from the experimental r-e data) versus r. A typical plot of work hardening rate (h = dr/de) versus r for the SS304 sample deformed at 1200 C and 0.1 s1 is presented in Fig. 9(a), which shows that h decreases with increasing r. The onset of DRX corresponds to a deviation from linearity in this work hardening curve. Since it is difficult to discern the exact location of this deviation in such plots, we adopt the suggestion of Poliak and Jonas (Ref 35) to determine rc from a plot of the derivative of the work hardening rate (dh/dr) against r. A minimum in the plot of (dh/dr) versus r shown in the inset of Fig. 9(a) delineates the point of inflection of the work hardening plot. The stress value corresponding to this minimum is rc (the associated ec is noted from the r-e curve). The initial rapid decrease of h with r is considered to be associated with dynamic recovery (Ref 14, 32) and a linear extrapolation of the part just before the critical point to h = 0 establishes rsat. Locating rp and ep is straightforward from r-e plot as it is related to h = dr/de = 0. The next step is to generate the DRV curve. In the approach of Jonas et al. (Ref 14), the description of work hardening is based on the Estrin-Mecking (Ref 36) equation for the development of dislocation density with strain: dq ¼ h rq de

ðEq 13Þ

where h is the athermal work hardening rate and r is the rate of dynamic recovery. Using this equation, Jonas et al. (Ref 14) derived the equation for flow stress for dynamic recovery as r ¼ ðr2sat ðr2sat r20 Þ expðreÞÞ1=2

ðEq 14Þ

where r0 is the yield stress and can be determined from the experimental flow curve. Using some simple algebraic substitutions, the following relationship was established: r

dr ¼ r h ¼ 0:5rr2sat 0:5rr2 de

ðEq 15Þ

It is seen from Eq 15 that r and rsat can be obtained from the slope and intercept of the r. h versus r2 curve, respectively.


Fig. 11 Image quality map showing microstructure evolution at different strain levels (a) 0.1, (b) 0.2, (c) 0.5, (d) 0.7 strain during deformation at 1200 C and 0.1 s1

Grain Average Misorientation (°)

0.8 40 0.7 35

0.6 0.5

30 0.4 0.3

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Average Grain Size (μ m)

45

0.9

25

Strain Fig. 12 Variation of GAM value and grain size with strain for sample deformed at 1200 C, 0.1 s1

Figure 9(b) shows the corresponding work hardening or recovery curve obtained using the r and rsat values along with the experimental DRX curve. The recrystallized volume fraction is considered to be responsible for the difference between the rDRV and rDRX curves. The difference between these two curves (Drs) is the net softening and is directly attributed to DRX. The maximum value of Drs is (rsat rss), where rss is the steady state stress under DRX conditions. The evolution of fractional softening with strain is expressed as X = Drs/ (rsat rss). Thus, once the recovery curve is derived for a particular deformation condition, the evolution of X with (e-ec) can be obtained in a straightforward way. Figure 10 shows the variation of X with (e-ec) for the sample deformed at 1200 C at a strain rate of 0.1 s1. The Avrami exponents n¢ and k have been determined by nonlinear regression fit of the calculated X versus (e-ec) data with Eq 12. The n¢ values obtained for different deformation conditions have been found to be nearly equal to 2. The n¢ values are indicative of the nature of nucleation sites which may be the prior grain boundaries or twin edges, etc. Nearly similar n¢ values have been reported by Andiawanto et al. (Ref 37) and El Wahabi et al. (Ref 27) during DRX of other materials (Ref 29). The


results of this section clearly establish the efficacy of the flow curve analysis method to characterize the progress of DRX in SS304. Progress of DRX during hot deformation can also be investigated by a metallographic study of the deformed samples. To study the evolution of DRX from the metallographic investigation, samples were deformed at 1200 C and 0.1 s1 to different strain levels and quenched. Figure 11 shows the EBSD maps of these samples. It can be seen that at lower strain, the sample consists of larger grains. Beyond critical strain, a small recrystallized grain appeared in the microstructure and its number density increased with increasing strain. Thus, the microstructures support the increase in recrystallization with progressive deformation as obtained from the flow curve analysis. Figure 12 shows the variation of the average grain size and average grain average misorientation (GAM) (determined from the EBSD map) with strain. It can be seen that the grain size and GAM value decreased with increasing strain. These further support the increase in DRX with strain.

4. Conclusion The DRX behavior of SS304 austenitic stainless steel is investigated under different deformation conditions through hot compression tests. The results of these tests are summarized as follows: (1)

(2)

(3)

(4)

The stress-strain curves of SS304 exhibited typical DRX behavior with a single peak stress followed by a gradual fall toward a steady state stress. The progress of DRX in SS304 during hot deformation can be well predicted on the basis of the Avrami relation in conjunction with features of the flow curve and work hardening data. The values of the Avrami exponent for different conditions (n 2) signify that prior grain boundaries or twin edges are the nucleation sites for DRX in SS304. Flow stress for SS304 during hot working can be predicted well based on the sine hyperbolic type of constitutive equation relating stress and strain.


Acknowledgments The authors would like to thank Prof. I. Samajdar of IIT Bombay for providing the EBSD facility and Dr. Rajeev Kapoor of MMD, BARC, for careful reading of the manuscript. AM wishes to thank Materials Group, BARC, for providing necessary support to complete this work.

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