The Strain Dependence of Postdynamic Recrystallization in 304 H Stainless Steel A. NAJAFIZADEH, J.J. JONAS, G.R. STEWART, and E.I. POLIAK Using double-hit hot compression tests, the softening behavior of 304 H stainless steel was studied during unloading. The prestrains used were associated with the initiation of dynamic recrystallization (DRX) (ec), the peak strain (ep), ½ (ec 1 ep), the strain at maximum softening rate (ei), and the onset of steady state flow (es). The following conditions of deformation were used: T 5 1000 °C, 1050 °C, and 1100 °C, e_ ¼ 0:01 and 0.1 s"1, and delay times of 0.3 to 1000 seconds. To define the above important strains, single-hit hot compression tests were performed over a wider range of deformation conditions than the double-hit ones—i.e., 900 °C to 1100 °C and e_ ¼ 0:01 to 1 s"1. The results show that a transition strain (e*) separates the strain-dependent range of postdynamic softening from the strainindependent range. At strains between ec and e*, both metadynamic and static recrystallization contribute to interhit softening. The value of e* obtained in this work was e* 5 4/3 ep. It was also found that the strain hardening rate was identical at all the critical strains (e*) and took the value "22 MPa. I. INTRODUCTION
THE high-quality production of 304 stainless steel requires a detailed understanding of the softening kinetics during interpass times; this can help to ensure accurate thickness and microstructure control. Both dynamic and static recrystallization can occur during and after deformation, respectively. Once the strain exceeds a certain critical value (ec), dynamic recrystallization (DRX) is initiated, which is subsequently followed by both static recrystallization (SRX) and metadynamic recrystallization (MDRX).[1–7] The observations by Djaic and Jonas on high carbon steel[8] as well as by Cho et al. on Nb microalloyed steel[9] indicate that abrupt changes in recrystallization time can take place at strains of about ep (the peak strain) that involve a transition from strain dependence to strain independence. These abrupt changes are associated with MDRX becoming the dominant softening process. Uranga et al.[10] have studied this transition strain and reported that the strainindependent range begins at about e* 5 1.7ep in a Nb microalloyed steel. Zahiri et al.[11] have noted that the critical strain e* in IF steels is just greater than ep and that the value depends on that of the Zener-Hollomon parameter Z. They showed that the critical strain e* fell in the range 0.6 to 1.5 when 9 3 1012 # Z # 1014 s"1. There is no currently available information regarding the value of e* in 304 stainless steels. The objective of this study was therefore to analyze the interpass softening behavior of 304 H stainless steel in the DRX 1 MDRX range and then to identify the critical strains at which the rate of MDRX becomes strain-independent. In this way, characteristics associated with e* could also be clarified. A. NAJAFIZADEH, Professor, is with the Department of Materials Engineering, Isfahan University of Technology, Isfahan, Iran. Contact e-mail: abbas.najafi
[email protected] J.J. JONAS, Professor, and G.R. STEWART, Postdoctoral Fellow, are with the Department of Metallurgical Engineering, McGill University, 3610 University Street, Montre´al, Canada H3A 2B2. E.I. POLIAK, Senior Researcher, is with Research Laboratories, Mittal Steel Co., East Chicago, IN, U.S.A. Manuscript submitted August 30, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
II.
MATERIALS AND EXPERIMENTAL PROCEDURE
The chemical composition of the 304 H stainless steel used in this work is given in Table I. This material was supplied in the form of a hot-rolled bar with a diameter of 7.94 mm. Cylindrical samples 7.9 mm in diameter and 11.5 mm in height were prepared with their axes aligned along the rolling direction. One- and two-hit hot compression tests were carried out on a computer-controlled servohydraulic MTS machine equipped with a radiant furnace. The MTS hot compression machine was programmed to operate at constant true strain rate by incremental calculation of the current true strain. The samples were deformed in an argon atmosphere after the specimens were preheated at 1200 °C for 15 minutes. They were then cooled to the test temperature at 1 °C/second and held for 5 minutes prior to deformation for temperature homogenization purposes. To minimize the coefficient of friction during hot compression testing, mica plates covered with boron nitride powder were used for lubrication. Two types of hot compression tests were carried out: (1) One-hit isothermal compression tests to a strain of 1. These tests were performed at 900 °C, 950 °C, 1000 °C, 1050 °C, and 1100 °C and at strain rates of 0.01, 0.1, 0.5, and 1 s"1. The objective of these tests was to determine the continuous stress–strain curves and so to define the DRX behavior, including the values of important strains such as the critical strain for the initiation of DRX (ec), the peak strain (ep), the inflection strain (ei), and the strain corresponding to the onset of steady-state flow (es). These tests also permitted the apparent activation energy for deformation to be derived and (2) Double-hit isothermal compression tests to strains below 1. The primary objective of these tests was to study the kinetics of interpass softening. For this purpose, interrupted compression tests were conducted at strain rates of 0.01 and 0.1 s"1 to initial strains ranging from that corresponding to the initiation of DRX (ec) to the onset of steady-state flow (es). Test temperatures of 1000 °C, 1050 °C, and 1100 °C (inclusive) were used. Interpass times were varied from 0.3 to 1000 seconds. These times were selected to characterize the softening behavior and also to determine the transition VOLUME 37A, JUNE 2006—1899
Table I. Chemical Composition of the Experimental 304 H Stainless Steel Cr 17.65
Ni
Mn
Mo
Cu
C
Si
P
S
Fe
7.91
1.74
0.57
0.32
0.067
0.71
0.026
0.022
Balance
Data are given as wt pct.
Fig. 1—EBSD map of the microstructure prior to deformation; average grain size is about 24 mm.
preload at which the kinetics of softening change from being strain-dependent to strain-independent. The fractional softening was determined using the 0.2 pct offset method, for which the generalized equation is:[12] X5
sm " sy2 sm " sy1
[1]
Here sy1 and sm 5 the initial 0.2 pct offset yield stress and the flow stress just before first-hit unloading, respectively, and sy2 5 the offset yield stress for the second hit. The initial austenite grain size was determined by electron back-scatter diffraction (EBSD) analysis on a sample that had been water quenched after soaking at 1200 °C for 15 minutes. The average grain size was measured by the mean linear intercept method, and the twins that were present were omitted from the measurements. This led to a mean grain size of about 24 mm (Figure 1). III.
RESULTS
A. Continuous Stress–Strain Curves 1. Identification of the critical strains The first step in this study was to identify the important points along the continuous stress–strain curves pertaining to each of the deformation conditions. Some representative flow curves are presented in Figure 2. These curves exhibit peaks and softening to a steady state, which indicate DRX 1900—VOLUME 37A, JUNE 2006
Fig. 2—Representative flow curves determined at (a) 0.01 s"1 and (b) 1100 °C.
behavior. The peak stresses and strains increased with decreasing temperature (Figure 2(a)), as well as with increasing strain rate (Figure 2(b)). One of the objectives was to identify the strains ec, ep, ei, and es. The critical point for the initiation of DRX was determined using the method of Poliak and Jonas[13–17] as modified by Najafizadeh and Jonas.[18] In their approach, METALLURGICAL AND MATERIALS TRANSACTIONS A
the initiation of DRX is associated with a point of inflection in the strain hardening rate (u) vs flow stress (s) plot. According to the latter method, the strain hardening rate was plotted against flow stress, and the third-order equation that best fit the experimental u–s data from zero to the peak stress was found for each set of the deformation conditions. Then the value of ec was obtained numerically from the coefficients of the third-order equation.[18] The values of ei were identified from the inflection points on the s–e curves located between the peak and steady-state stresses. For this purpose, the stress–strain curves were once again fitted using a third-order equation and ei was calculated by setting the second derivative of this equation to zero. 2. Calculation of the activation energy The activation energy for deformation was derived with the aid of the following relation between the ZenerHollomon parameter (Z) and the peak stress (sp).[5] " # Qdef [2] Z 5 e_ exp 5 A sinhðasp Þn RT Therefore, Qdef
" # @ ln sinhðasp Þ ¼ Rn @ lnð1=TÞ e_
[3]
where A, a, and n 5 empirical constants, e_ is the true strain rate, T 5 the absolute temperature, Qdef 5 the apparent activation energy for deformation, and R 5 the gas constant.[19–22] The application of Eqs. [2] and [3] to the present data resulted in a mean value of 370 (kJ/mol) for the peak stress. This was obtained by regression analysis and is consistent with values measured previously by other workers.[5,19] B. Double-Hit Stress–Strain Curves 3. Softening behavior during unloading The objectives of these tests were (1) to clarify the static and metadynamic softening behavior during unloading, (2) to determine the strain (e*) at which the kinetics of interpass softening become strain-independent, and (3) to identify the properties of this point. For this purpose, the data obtained from the single-hit hot compression tests were used to identify the values of the important prestrains (i.e., ec, ep, ei, and es). Then, double-hit hot compression tests were conducted at strain rates of 0.01 and 0.1 s"1 and test temperatures of 1000 °C, 1050 °C, and 1100 °C to prestrains ranging from the initiation of DRX (ec) to the onset of steady-state flow (es), as shown in Figure 3. Interpass times were varied from 0.3 to 1000 seconds. Some of the double-hit stress–strain curves obtained at 1100 °C and a strain rate of 0.1 s"1 are presented in Figure 4. Here, delay times of 1 to 100 seconds were used after prestrains of 0.11 (Figure 4(a)) and 0.31 (Figure 4(b)). These strains correspond to the initiation of DRX and the peak stress, respectively. The second-hit strain used was relatively low (e2 5 0.03) so that the microstructure evolution after quenching could be studied. The clear difference between the amounts of softening taking place after a specific delay time can be seen by comparing Figure 4(a) with METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 3—Schematic stress–strain curve associated with the occurrence of DRX during deformation. Arrows indicate the strains used in this research to study the kinetics of softening after unloading.
Figure 4(b). Applying a strain of 0.31, softening was essentially complete after 100 seconds of delay time, whereas after a strain of 0.11, softening was far from complete after the same time. As can be seen in Figure 4(b), the second-hit yield stress (sy2) decreases sharply with delay time increasing from 1 to 10 seconds. By contrast, after a prestrain of 0.11 (see Figure 4(a)), there were no significant changes in sy2 until 10 seconds had elapsed. These contrasting behaviors indicate that MDRX plays an important role under the deformation conditions of Figure 4(b), whereas after a prestrain of 0.11 (Figure 4(a)), only SRX takes place during unloading. The dependence of the second-hit yield stress (sy2) on delay time is presented in Figure 5 for the following strains: (1) the onset of DRX (ec), (2) the average of the peak and critical strains, ½ (ec 1 ep), (3) the peak strain (ep), and (4) the inflection strain (ei). Up to a strain of 0.11, SRX is the only recrystallization mechanism that takes place during unloading. By contrast, at the much larger strain of ei, MDRX controls the rate of softening. At a strain of 0.21, both recrystallization mechanisms are activated. It is evident that the ep and ei curves are still separate, indicating that the kinetics of softening still depend on the amount of the prestrain at ep. The dependence of the fractional softening on temperature and prestrain is illustrated in Figure 6 for a strain rate of 0.01 s"1 and in Figure 7 for 0.1 s"1. The effects of the process variables (i.e., the temperature, strain rate, and strain) can be readily seen. IV.
DISCUSSION
Softening during interpass times at high temperatures is usually described by the Johnson-Mehl-AvramiKolmogorov (JMAK) equation as follows: $ " #n % t [4] X ðtÞ ¼ 1 " exp "0:693 t50 VOLUME 37A, JUNE 2006—1901
Fig. 5—Effect of delay time and preload strain on the decrease in yield stress.
Fig. 4—Double-hit compression flow curves determined at 1100 °C and 0.1 s"1. The preloading strains of (a) 0.11 and (b) 0.31 correspond to the critical strain for the onset of DRX and the peak strain, respectively.
Here X 5 the fractional softening, n 5 the Avrami exponent, and t50 5 the time corresponding to a softening fraction of 50 pct. The latter depends on the conditions before and during deformation and can be described by an expression of the type:[12,23] " # Qs t50 ¼ ADb0 e p Zq exp [5] RT s Here D0 5 the grain size prior to preloading; e 5 the prestrain; Z 5 the Zener-Hollomon parameter pertaining 1902—VOLUME 37A, JUNE 2006
to the preceding deformation, Z 5 e_ exp ðQdef =RT def Þ, e_ is the strain rate; Qdef 5 the activation energy for deformation; Tdef and Ts 5 the absolute temperatures of deformation and softening, respectively; and the coefficient A and the exponents b, p, and q are constants. These depend on _ and e), and the the material, deformation conditions (T, e, predominant softening mechanism. As can be seen from Figures 6 and 7, all of the curves are S-shaped and do not display any plateaus. The fractional softening increases with increasing temperature, strain rate, and strain. It is known[10,11] that if the prestrain reaches a certain value, usually referred to as e*, the kinetics of softening becomes independent of strain. Under such conditions, the mechanism that dominates the softening is MDRX. In Figures 6 and 7 (especially in Figures 6(a), 7(a), (b), and (c)), the time for 50 pct softening decreases with increasing prestrain from ec to ei. Afterward, it becomes independent of the prestrain. This behavior indicates that there is a prestrain between the peak (ep) and maximum rate of softening prestrain (ei) at which the kinetics of softening during unloading do not depend on the prestrain. Some workers[8,9] have reported that the peak strain has such properties. These researchers worked on carbon or microalloyed steels. In 304 H stainless steel, the total percentage of alloying elements is relatively high. Thus, the e* value may be higher in such materials. To determine this prestrain, it is convenient to use the temperature-compensated time for 50 pct softening (t 50) proposed by Sellars and Whiteman.[24] This term can be extracted from Eq. [5] by writing: " # Qs t 50 ¼ t50 exp " [6] 5 ADb8 e p Zq RT s The term for the peak strain ðt 850 Þ becomes: " # Q t 850 5 t850 exp " s 5ADb8 epp Z q RT s
[7]
METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 6—Dependence of fractional softening on time and prestrain: (a) 1000 °C, (b) 1050 °C, and (c) 1100 °C. 8 where t50 is the time for 50 pct softening when the prestrain is ep. Dividing Eq. [6] by [7] results in: " #p t 50 t50 e 5 5 ¼ wp [8] 8 8 ep t 50 t50
The dependence of t 50 =t 850 on the normalized strain (w 5 e/ep), within the present range of deformation conditions, METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 7—Dependence of fractional softening on time and prestrain: (a) 1000 °C, (b) 1050 °C, and (c) 1100 °C.
is presented in Figure 8, where t 50 =t 850 is the normalized temperature-compensated time for 50 pct softening. This figure shows that a power law relationship applies between t 50 =t 850 and w as far as w 5 4/3 5 1.33. Beyond this value, the normalized temperature-compensated time for 50 pct softening becomes strain-independent. Here t50 becomes strain-independent after prestrains greater than e*. VOLUME 37A, JUNE 2006—1903
Fig. 8—Dependence of the normalized time for 50 pct softening on normalized strain within the range of deformation conditions studied in this work.
In Figure 8, the equation of the best-fit line to the relationship displayed can be written: " # t 50 log 8 5p log w 1 c t 50 At t 50 ¼
t 850 ;
" #p t 50 e p 0 w 5 1 0c 5 0 so 0 8 5 w 5 ep t 50 [9]
where ec # e # e*. At e 5 e*, 0 t 5 t*, so " # #p " #p t #50 e 4 ¼ 5 8 3 e t 50 p The value of
t #50 t 850
[10]
in Figure 8 is about 0.63. Inserting this
quantity into Eq. [10] results in p 5 "1.6. Thus, Eq. [9] can be rewritten as follows: t 50 ¼
t 850
" #"1:6 e ep
[11]
where again ec # e # e*. The"dependence of the normalized " time#for 50 pct soft# t50 s ening 8 is presented in on normalized stress u5 sp t50 Figures 9(a) and (b) for strain rates of 0.01 and 0.1 s"1 and temperatures of 1000 °C, 1050 °C, and 1100 °C. These figures show that the normalized time for 50 pct softening decreases when the normalized stress is gradually increased to 1. Beyond the stress peak, the normalized time for 50 pct softening decreases and tends toward a steady-state value. 1904—VOLUME 37A, JUNE 2006
Fig. 9—Dependence of the normalized time for 50 pct softening on normalized preloading stress within the range of deformation conditions studied in this work: (a) 0.01 s"1 and (b) 0.1 s"1.
The value of e* can also be obtained as shown in Figures 10(a) and (b). These figures illustrate the effect of strain on the fractional softening when the delay time is held constant at 3 seconds. As can be seen, the fractional softening does not change until e 5 ½ (ec 1 ep) is attained. Beyond this value of the strain, it increases approximately linearly up to e*. Above e*, increasing the strain has only a minor effect on the fractional softening. These observations can be interpreted as follows. During unloading, three softening mechanisms are involved: (1) static recovery (SRV), (2) SRX, and (3) MDRX. SRX involves the nucleation of new grains followed by their growth. Such nucleation requires an incubation time that depends on the material, predeformation conditions, and annealing temperature. By contrast, MDRX uses the dynamic nuclei formed during the predeformation stage. This mechanism does not METALLURGICAL AND MATERIALS TRANSACTIONS A
Fig. 11—Lack of dependence of the critical strain hardening rate (u*) on deformation temperature and strain rate.
A. Identification of e* on the Stress–Strain Curves As discussed above, e* is the strain at which MDRX converts from strain dependence to strain independence. It is well known that ec, ep, ei, and es have specific properties that are valid for all stress–strain curves associated with DRX behavior. The question thus arises: are specific properties associated with e*? " In #this work, it was found that the strain hardening rate ds had such properties. The strain hardening rate at e* de is presented in Figure 11, from which it can be seen that it is independent of temperature and strain rate within the range of deformation conditions studied in this work. Here, the points that corresponded to a strain of e* 5 4/3 ep in the one-hit tests (see Section III–A) have also been added. This figure clearly shows that the strain hardening rate at e* is independent of the deformation conditions and takes a constant value. Fig. 10—Effect of strain on the fractional softening at (a) 1050 °C and (b) 1100 °C. Here a strain rate of 0.1 s"1 and a constant delay time of 3 seconds were used.
require an incubation time for nucleation, so the kinetics of MDRX follows the grain growth rule. DRX begins when the prestrain attains ec; beyond this value, the volume fraction of DRX grains depends on the material and the deformation conditions, particularly on the strain. In 304 H stainless steel, perhaps because of the relatively high alloying element content, even after applying a prestrain of ½ (ec 1 ep), MDRX did not significantly increase the amount of fractional softening (Figures 10(a) and (b)). At the stress peak, especially at 1050 °C, MDRX was still far from becoming the dominant softening mechanism. Finally, at a prestrain of e* 5 4/3 ep, DRX and MDRX determine the softening rate and the kinetics of interpass softening becomes independent of strain. METALLURGICAL AND MATERIALS TRANSACTIONS A
V.
SUMMARY AND CONCLUSIONS
The principal conclusions that can be drawn from the present work are the following: 1. The critical strains along the stress–strain curve, such as ec, ep, ei, and es, have been determined under the deformation conditions studied in this work. The results show that these critical strains decrease when the deformation temperature is increased or the strain rate is decreased. _ 2. Under each set of deformation conditions (i.e., T and e), increasing the prestrain from ec to a specific value, referred to here as e*, increases the contribution of MDRX to the overall softening. Above e*, SRX no longer affects the softening behavior. 3. The kinetics of softening during unloading begins to be strain-independent at a prestrain of e* 5 4/3 ep. 4. The ‘‘strain-independent’’ prestrain e* can be specified in terms of the strain hardening rate at this point of the stress–strain curve. This strain hardening rate, referred VOLUME 37A, JUNE 2006—1905
to here as u*, has the same value (u* 5 "22 MPa) under all the deformation conditions studied in this work. ACKNOWLEDGMENT A. Najafizadeh expresses his thanks to the Isfahan University of Technology for granting a period of sabbatical leave during which this work was carried out. REFERENCES 1. A. Belyakov, H. Miura, and T. Sakai: Scripta Mater., 2000, vol. 43, p. 21. 2. M. El Wahabi, J.M. Cabrera, and J.M. Prado: Mater. Sci. Eng., 2003, vol. A343, p. 116. 3. H.J. McQueen, N. Jin, and N.D. Ryan: Mater. Sci. Eng. A, 1995, vol. 190, p. 43. 4. A. Dehghan-Manshadi, H. Beladi, M.R. Barnett, and P.D. Hodgson: Mater. Sci. Forum, 2004, vol. 467–470, p. 1163. 5. G.R. Stewart, J.J. Jonas, and F. Montheillet: ISIJ Int., 2004, vol. 44 (7), p. 1263. 6. H.J. McQueen, S. Yue, N.D. Ryan, and E. Fry: Mater. Process. Technol., 1995, vol. 53, p. 293.
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7. G.R. Stewart and J.J. Jonas: ISIJ Int., 2004, vol. 44 (7), p. 1581. 8. R.A.P. Djaic and J.J. Jonas: Metall. Trans., 1973, vol. 4, p. 621. 9. S.H. Cho, K.B. Kang, and J.J. Jonas: ISIJ Int., 2001, vol. 41 (7), p. 766. 10. P. Uranga, A.I. Fernandez, B. Lopez, and J.M. Rodriguez-Ibabe: Mater. Sci. Eng. A, 2003, vol. 345, p. 319. 11. S. Matthies and G.W. Vinel: Phys. Stat. Sol. (b), 1982, vol. 112, pp. K111-K114. 12. S. Matthies and G.W. Vinel: Phys. Stat. Sol. (b), 1982, vol. 112, pp. K115-K120. 13. E.I. Poliak and J.J. Jonas: Acta Mater., 1996, vol. 44 (1), p. 127. 14. E.I. Poliak and J.J. Jonas: ISIJ Int., 2003, vol. 43 (5), p. 684. 15. E.I. Poliak and J.J. Jonas: ISIJ Int., 2003, vol. 43 (5), p. 692. 16. J.J. Jonas and E.I. Poliak: Mater. Sci. Forum, 2003, vol. 426–432, p. 57. 17. E.I. Poliak and J.J. Jonas: ISIJ Int., 2004, vol. 44 (11), p. 1874. 18. A. Najafizadeh and J.J. Jonas: ISIJ Int. 2006, in press. 19. S.F. Medina and C.A. Hernandez: Acta Mater., 1996, vol. 44, p. 147. 20. S.F. Medina and C.A. Hernandez: Acta Mater., 1996, vol. 44, p. 149. 21. C.A. Hernandez, S.F. Medina, and J. Ruiz: Acta Mater., 1996, vol. 44, p. 155. 22. S.F. Medina and C.A. Hernandez: Acta Mater., 1996, vol. 44, p. 165. 23. C.M. Sellars: Mater. Sci. Technol., 1990, vol. 6, p. 1072. 24. C.M. Sellars and J. Perttula: ISIJ Int., 1996, vol. 36, p. 729.
METALLURGICAL AND MATERIALS TRANSACTIONS A
