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Hot workability of as-cast Fe3Al–2.5%Cr intermetallic alloy
Materials Science and Engineering A347 (2003) 86 /92 www.elsevier.com/locate/msea
Hot workability of as-cast Fe3Al 2.5%Cr intermetallic alloy /
R.S. Sundar *, D.H. Sastry, Y.V.R.K. Prasad Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India Received 28 May 2002; received in revised form 22 July 2002
Abstract Processing characteristics of as-cast Fe3Al /2.5%Cr alloy have been studied using constant strain rate isothermal compression tests in the temperature range 1023 /1323 K and strain rate range 0.001 /10 s 1. At strain rates 5/0.1 s 1, the stress /strain curves are of steady-state type while at higher strain rates the flow stress reaches a peak before falling into either a steady-state or continuous flow softening with strain. The processing map of the alloy revealed a domain of dynamic recrystallization (DRX) at temperatures greater than 1123 K and the optimum conditions for processing occur at 1273 K and at strain rate of 0.001 s 1. However, at higher temperatures, due to dynamic grain growth, the optimum condition for processing has moved to higher strain rates. Flow instabilities occur in the form of adiabatic shear bands when deformed at strain rates greater than 0.1 s 1 and at temperatures 5/1123 K. A constitutive relationship for hot working is developed to describe the relationship between flow stress, strain rate and temperature. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Intermetallics; Iron aluminides; Flow stress; High temperature deformation; Deformation mechanisms; Dynamic recrystallization; Constitutive relationship; Hot workability
1. Introduction Good oxidation and sulfidation resistance of Fe3Al motivated many researchers to develop alloys based on this intermetallic compound to replace stainless steels for intermediate temperature applications [1 /3]. Compared to stainless steels, Fe3Al alloys are made up of less expensive raw materials and have lower density. In the past two decades, many compositions were developed with the aim of improving overall properties of Fe3Al. Chromium is one of the main alloying elements added to overcome the room temperature brittleness [4]. The effect of chromium on the mechanical properties of Fe3Al, especially strength, ductility [4] and creep resistance [5,6] is well documented. However, its effect on the hot workability of Fe3Al is not clear. Further, it is well known that the intrinsic workability of intermetallic alloys is sensitive to the chemistry, the initial micro-
* Corresponding author. Present address: Research Center, Philip Morris USA, Richmond, VA 23261, USA. Tel.: /1-804-274-2262; fax: /1-804-274-2468 E-mail address: [email protected] (R.S. Sundar).
structure and the prior processing history of the material [7,8]. For successful application of these alloys, it is necessary to develop suitable and economical processing techniques to produce the material with the desired shape without losing the low cost advantage. For designing a suitable processing route and for optimizing the hot workability, it is essential to characterize the constitutive flow behavior of these intermetallic alloys. Such a study will also help in evaluating the mechanisms of hot deformation and achieving microstructural control in processing. Different approaches available for optimizing the hot workability and evaluating the hot working mechanisms have been reviewed recently [9] and these include examination of shapes of stress-strain curves, evaluating kinetic parameters and developing processing maps. The present study aims at assessing the hot workability of a cast Fe3Al /Cr alloy using the approach of processing maps [9] and compare it with that of the binary alloy, the results on which were published elsewhere [10]. The above approach is successful in optimizing the processing conditions of a number of commercial as well as advanced materials [11]. A processing map for a given alloy is developed by superimposing two maps, namely
0921-5093/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 5 8 5 - 3
R.S. Sundar et al. / Materials Science and Engineering A347 (2003) 86 /92
power dissipation map and instability map. The power dissipation map represents the manner in which the power is dissipated by the material through metallurgical processes and is constructed by plotting iso-contours of dissipation efficiency (h ) on a two-dimensional plot with log strain rate (/o) ˙ and temperature (T ) as the axes. The parameter h represents the constitutive response of the material in terms of various microstructural mechanisms that operate under given temperature and strain rate and is given by h
2m m1
(1)
where m is the strain rate sensitivity of the material. The various domains in the power dissipation map may be correlated with specific microstructural mechanisms. Prasad [12] has developed an instability parameter (/j(o)); ˙ based on extremum principles of irreversible thermodynamics, to predict unstable flow regime under processing conditions. This parameter is given by j(o)[@lnfm=(m1)g=@ln ˙ o]m ˙
(2)
Unstable flow is predicted when j(o) ˙ / B/0. The variation of j(o) ˙ with temperature and strain rate constitutes the instability map which is superimposed over the power dissipation map to delineate the unstable flow regime.
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were removed from the furnace and air-cooled to room temperature. The deformed specimens were sectioned parallel to the compression axis using a low speed diamond cutting wheel. The cut surfaces were polished and etched with a solution containing 8 /12 vol.% HNO3/4 vol.% HCl/2 /5 vol.% CH3COOH/4% glycol for optical metallographic observation. Grain size was measured by the linear intercept method. The load /stroke curves from the compression tests were converted into true stress /true plastic strain curves using standard procedures. The flow stress (s) data were corrected for adiabatic temperature rise using a procedure described elsewhere [13]. At a given temperature, a cubic spline fit between log flow stress and log strain rate was used to calculate m as a function of strain rate. This procedure was repeated for different temperatures. Using Eq. (1), h was evaluated from a set of m values as a function of strain rate and temperature, and was plotted as an iso-efficiency contour map. Similarly, j(o) ˙ was calculated, using Eq. (2), as a function of temperature and strain rate to develop an instability map. For a given strain, the above two maps are superimposed to generate the processing map.
3. Results and discussion 3.1. True stress /true strain behavior
2. Experimental The alloy used in the present investigation contained 28.7 at.% Al, 2.5 at.% Cr and balance Fe and was prepared through vacuum induction melting. The ingot was homogenized at 1323 K for 4 h and furnace cooled. The grain size of the alloy after homogenization was about 680 mm. Cylindrical compression samples of 10 mm diameter and 15 mm length were prepared from the homogenized ingot. The details of specimen geometry and preparation methods were given elsewhere [13]. Compression tests were conducted over the temperature range of 1023/1323 K at 50 K intervals and a constant true strain rate range of 0.001 /10 s 1 at intervals of an order of magnitude. The test temperatures and strain rates were selected based on the actual processing conditions of Fe3Al alloys [8]. Isothermal compression tests were conducted on a DARTEC computer controlled servo hydraulic testing machine. The actual specimen temperature and the adiabatic temperature rise during deformation were measured using a thermocouple inserted into the specimen, in a 0.8 mm hole drilled to a depth of 5 mm at half its height. Before the test, the specimen was coated with borosilicate glass paste for lubrication and to minimize oxidation. All the specimens were deformed to half of their original height. Immediately after completion of the tests, the specimens
Typical true stress /true plastic strain curves obtained at two representative temperatures, namely 1073 and 1273 K, and at different strain rates are shown in Fig. 1. At strain rates 5/0.1 s1, the flow curves exhibit gradual strain hardening at strains less than 0.05, followed by a steady-state flow behavior at higher strain levels. At higher strain rates, the flow curves reach a peak in flow stress, followed by either continuous flow softening or drop to a minimum in flow stress and then rise to reach a steady-state. Similar trends are observed at other temperatures. It is not possible to predict the mechanisms of hot deformation from the shape of the stress /strain behavior alone, since different mechanisms may lead to similar behavior [9]. For example, either DRX or unstable flow may lead to flow softening or oscillations. It is necessary to apply other models to evaluate the hot deformation mechanisms. 3.2. Effect of temperature and strain rate The effect of temperature on the flow stress of Fe3Al / Cr alloy is brought out in Fig. 2 for a strain of 0.5. At a given strain rate, the flow stress decreases with increasing temperature in a normal manner. Similarly, at a given temperature, the flow stress increases with increasing strain rate. The above trends indicate that the deformation is thermally activated. Fig. 3 compares the
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conditions, the flow stress of the Cr containing alloy is nearly the same as that of the binary alloy. The kinetic parameters of deformation are evaluated based on the kinetic rate equation of the form o˙Asn exp(Q=RT)
Fig. 1. True stress /true strain curves obtained at different strain rates in Fe3Al /Cr alloy at (a) 1073 K and (b) 1273 K.
temperature dependence of the flow stress in Fe3Al /Cr with that of the binary alloy at a strain of 0.4. It was shown by McKamey et al. [4] that addition of chromium lowered the room temperature yield stress of Fe3Al. Similarly, Cr addition was found to decrease the creep resistance of Fe3Al [5,6]. However, under processing
(3)
where o˙ is the strain rate, n is stress exponent (inverse of strain rate sensitivity), Q is the activation energy, R is gas constant and A is a constant. The parameter n is estimated from the slope of the plot between log strain rate and log flow stress (Fig. 4). The values of n estimated at different true strain levels are presented in Table 1. The n value varies between 3.5 and 8 and decreases with increasing temperature. However, it is nearly independent of strain in the range of 0.1 /0.5. The variation of strain rate at a constant stress is plotted against 1/RT and the apparent activation energy (Q ) for hot deformation is calculated from the slope of this plot. Based on the Q value, the present flow stress data can be divided into two regions. At high temperatures and low stresses (Fig. 5), Q value is about 340 kJ mol 1 and is independent of stress level. This value is in good agreement with those reported in the literature [14] but is higher than that reported for binary Fe3Al [10]. At low temperatures and high stress levels, Q ranges between 250 and 450 kJ mol 1 and decreases with increasing stress (Fig. 6). Since the estimated apparent activation energy values are not in agreement with those for any particular atomic diffusion mechanisms, the evaluation of hot deformation mechanisms is difficult on the basis of the kinetic analysis. 3.3. Processing map The processing map at a true strain of 0.4, obtained by superimposing the power dissipation map and the
Fig. 2. Temperature and strain rate dependence of flow stress of Fe3Al /Cr alloy at a true strain of 0.5.
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Fig. 3. Comparison of flow stress vs. temperature of binary Fe3Al and Fe3Al /Cr alloy at a strain of 0.4.
Table 1 Stress exponent for plastic flow of Fe3Al /Cr alloy as a function of temperature and true strain Temperature (K)
1023 1073 1123 1173 1223 1273 1323
Fig. 4. Strain rate vs. flow stress at different test temperatures typically shown at a true strain of 0.4.
instability map, is shown in Fig. 7. The general features exhibited by the maps at other strains are essentially similar, indicating that the influence of strain on the hot deformation is not significant. The map exhibits a single domain in the range of 1173 /1323 K and 0.001 /1.0 s 1 and is identified to represent the process of dynamic recrystallization (DRX). Within the domain, the peak efficiency value is around 46% and occurs at 1273 K and 0.001 s 1. This temperature/strain rate combination can be regarded as optimum for processing the alloy within the DRX domain [11]. Typical microstructure of the deformed sample corresponding to the peak h is
‘n ’ at a true strain of 0.1
0.3
0.5
6.8 5.0 4.6 4.4 3.9 3.3 3.4
7.4 5.9 4.8 4.9 4.1 3.5 3.6
7.8 5.7 5.0 4.9 4.0 3.6 3.6
shown in Fig. 8. This microstructure exhibits fine newly formed recrystallized grains with irregular grain boundaries typical of dynamic recrystallization. Voyzelle and Boyd [14] have reported deformation maps for Fe / 28Al /5.0Cr /0.5Nb/0.2C under two different starting microstructural conditions. Under both conditions, they have reported the occurrence of DRX in the temperature range of 1173 /1473K. However, in the above study, the optimum conditions within the DRX region are not identified. Though their alloy is stronger than the present ternary Fe3Al /2Cr alloy, the characteristics of deformation processing maps of the two alloys are similar. The characteristics of the DRX domain of the present alloy are similar to those in the binary alloy [10]. However, when compared to the binary alloy, the DRX domain in the Fe3Al /2Cr alloy has moved to lower temperatures and strain rates. At higher temperatures (/1298 K), the peak efficiency has moved to higher strain rate (0.1 s 1). As discussed below, the shift
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Fig. 5. Arrhenius plot showing temperature dependence of flow behavior at high temperatures and low stresses.
Fig. 7. Processing map of Fe3Al /Cr alloy obtained at a true strain of 0.4. Contour numbers represent efficiency of power dissipation as a fraction. Shaded region corresponds to flow instability.
Fig. 8. Microstructure of Fe3Al /Cr alloy deformed in the DRX domain at 1273 K and 0.001 s 1. Fig. 6. Arrhenius plot showing temperature dependence of flow behavior at low temperatures and high stresses.
in peak efficiency or optimum condition of processing at higher temperature is caused by dynamic grain growth at these high temperatures. The variation of average grain size within the domain as a function of temperature is shown in Fig. 9. In general, a sigmoidal variation in the grain size with temperature is observed under DRX conditions [11], i.e. the grain size increases with increasing temperature and at higher temperatures, the grain size levels off. However, in the present alloy, due to the occurrence of concurrent grain growth during deformation at 1323 K, the grain size has increased continuously with deformation temperature, i.e. without leveling off at higher temperatures. Voyzelle and Boyd
Fig. 9. Variation of DRX grain size with temperature in the DRX domain of Fe3Al /Cr alloy.
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[14] have also reported dynamic grain growth during deformation of their Cr containing Fe3Al alloy at temperatures ]/1323 K and at lower strain rates. However, dynamic grain growth was not observed during the deformation of the binary alloy [10] under similar deformation conditions. Although the reason for dynamic grain growth in Cr containing Fe3Al is not clear, it is possible that Cr enhances the diffusivity in Fe3Al at higher processing temperatures. The shape of the flow curve during DRX can give a clue to the process that controls DRX. According to a model proposed by Prasad and Ravichandran [15], on the lines suggested by Derby and Ashby [16], DRX is considered to be consisting of two competing processes namely, formation of interfaces (nucleation) and migration of interfaces (growth). The above two processes are sequential in nature; in which case, the slower of the two will control the deformation. Under constant strain rate condition, the relative value of the two rates decides the shape of the stress /strain curves. If the rate of interface formation is slower than the rate of migration, as in the case of low stacking fault energy (SFE) materials [15,17], a certain strain has to elapse before a critical interface configuration is achieved for migration. At the critical strain, the migration of a large number of interfaces leads to flow softening. On the other hand, if migration rates are slow or if the two rates lead to comparable changes in the interface area as in the case of high SFE materials [17], a steady-state stress /strain curve results. As mentioned in the previous section, steady-state flow curves were observed within the DRX domain. Similarly, steady-state flow behavior was observed during DRX in binary Fe3Al [10] as well as in more complex alloys of Fe3Al [14]. The above observation indicates that DRX in Fe3Al is controlled by migration process. Another interesting feature of the DRX microstructure shown in Fig. 8 is the presence of some as cast grain boundaries (marked by arrows in the micrograph). In general, DRX nucleation starts near grain boundaries. Due to lesser grain boundary area in coarse grained material, there are not enough sites for DRX nucleation to occur near the grain boundaries. Hence, nucleation also occurs inside the grains. In such a case, some of the grain boundaries in the as-cast microstructure may not be eliminated fully during DRX. It is possible that much higher strains are required for the complete conversion of the as-cast microstructure to a wrought microstructure. In addition to DRX, a region of flow instability, (shaded region in Fig. 7) is exhibited in the processing map, at temperatures B/1123 K and at strain rates / 0.1 s1. The manifestation of the flow instabilities is in the form of adiabatic shear bands (Fig. 10). In the flow localization region, cracks (marked A) and fine recrystallized grains (marked B) are observed. While at lower strain rates ( B/0.1 s 1) and at temperatures B/1173 K,
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Fig. 10. Microstructure of Fe3Al /Cr alloy deformed at 1123 K and 10 s 1 revealing adiabatic shear bands.
the microstructure of the deformed sample shows elongated grains perpendicular to the compression axis. The h value in this region is around 20 /30%, which is lower than that in the DRX region. Elongated grain structure and lower efficiency of power dissipation [11] indicate that the material undergoes dynamic recovery (DRV) in this region. In general, DRV involves the occurrence of mechanisms such as cross-slip, climb and nodal unzipping, etc. In the present alloy, under the DRV conditions, the activation energy for deformation decreases with increasing stress (Fig. 6). Similar variation of Q with stress is reported during deformation of Fe3Al alloys at temperatures B/1223 K [14]. The stress dependence of Q suggests that cross slip may be the operating mechanism under DRV.
3.4. Constitutive equation To describe the relationship between flow stress and strain rate and temperature, the following two equations are widely used [18]: o˙ exp (Q=RT)Asn o˙ exp(Q=RT) A0 exp(bs)
(4) (5)
where b , A and A ? are constants. Eq. (4) is arrived by rearranging the terms of Eq. (3) and is obeyed normally at high temperature and low stress conditions, while Eq. (5) is suitable to describe the relationship between the flow stress, temperature and strain rate at low temperatures and high stress conditions. The above two equations are combined to yield a single constitutive equation in the following form, to describe the relationship between the different variables over a wide range of processing conditions [18]: Z o˙ exp(Q=RT )K[Sinh(as)]n
(6)
where Z is the temperature compensated strain rate
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occurrence of which are identified to be 1273 K and 0.001 s 1. 2. The addition of Cr to Fe3Al does not significantly influence the hot workability or the mechanisms of hot deformation. However, when compared to binary Fe3Al, the DRX domain has shifted to lower strain rate at 1223 K, while at higher temperatures, the domain has moved to higher strain rate due to dynamic grain growth. 3. At temperatures less than 1123 K and at high strain rate regions, flow instabilities occur in the form of adiabatic shear bands. Initial processing of the alloy in this temperature should be avoided. 4. A constitutive equation given by Z o˙ exp(340 000=RT)8:951014 [sinh(as)]3:5 describes the relationship between the flow stress and the process variables under hot working conditions. Fig. 11. Plot between sinh (as ) and Zener /Hollomon parameter (Z ).
parameter, popularly known as the Zener/Hollomon parameter, and a and K are constants. The flow stress data obtained at temperatures greater than 1123 K (i.e. within the DRX domain) are utilized to develop a constitutive relation for processing the present alloy. The constants in Eq. (6) are evaluated following the procedure given in Refs. [19,20]. The constant b (0.0275 MPa 1) is calculated from Eq. (5) using the slope of the flow stress versus log strain rate plot at low temperatures and high strain rates. The constant a is in turn calculated from b , through the following relationship a /(b /n). The value of n is taken as 3.6 (from the high temperature range) for calculating a . The constitutive equation is given by Z o˙ exp(340 000=RT) 8:951014 [sinh(0:0076s)]3:5
(7)
The ability of the above equation to correlate test data at different temperatures and strain rates is shown in Fig. 11. The above equation gives a better fit for the experimental data than Eq. (4). Recently Pu et al. [21] modified Eq. (6), to introduce the effect of strain on the deformation parameters. As discussed earlier, in the preset alloy, the flow stress varies very little with the strain at strains greater than 0.05. Similarly, the features of the processing map also did not vary with strain. Hence, it may be concluded that Eq. (7) accurately predicts the variation of flow stress of the alloy with temperature and strain rate under processing conditions.
4. Conclusions 1. As-cast Fe3Al /Cr alloy can be ‘safely’ processed at temperatures greater than 1123 K, where the alloy undergoes DRX, the optimum conditions for the
References [1] C.G. McKamey, J.H. De Van, P.F. Tortorelli, V.K. Sikka, J. Mater. Res. 6 (1991) 1779. [2] S.C. Deevi, V.K. Sikka, C.T. Liu, Prog. Mater. Sci. 42 (1997) 177. [3] N.S. Stoloff, C.T. Liu, S.C. Deevi, Intermetallics 8 (2000) 1313. [4] C.G. McKamey, J.A. Horton, C.T. Liu, J. Mater. Res. 4 (1989) 1156. [5] Y. Sun, Z. Zhang, F. Xue, X. Yu, Mater. Sci. Eng. A258 (1998) 167. [6] R.S. Sundar, T.R.G. Kutty, D.H. Sastry, Intermetallics 8 (2000) 427. [7] P.L. Martin, D.A. Hardwick, in: J.H. Westbrook, R.L. Fleischer (Eds.), Intermetallic Compounds */Principles and Practice, vol. 1, Wiley, New York, 1994, p. 637. [8] V.K. Sikka, B.G. Giesek, R.H. Baldwin, in: K. Natesan, D.J. Tillack (Eds.), Heat Resistance Materials, ASM International, Materials Park, OH, 1991, p. 363. [9] Y.V.R.K. Prasad, T. Seshacharyulu, Int. Mater. Rev. 44 (1998) 243. [10] R.S. Sundar, R.G. Baligidad, Y.V.R.K. Prasad, D.H. Sastry, Mater. Sci. Eng. A258 (1998) 219. [11] Y.V.R.K. Prasad, S. Sasidhara, Hot Working Guide: a Compendium of Processing Maps, ASM International, Materials Park, OH, 1997. [12] Y.V.R.K. Prasad, Indian J. Tech. 28 (1990) 435. [13] R.S. Sundar, PhD thesis, Indian Institute of Science, Bangalore, India, 1998. [14] B. Voyzelle, J.D. Boyd, Mater. Sci. Eng. A258 (1998) 243. [15] Y.V.R.K. Prasad, N. Ravichandran, Bull. Mater. Sci. 14 (1991) 1241. [16] B. Derby, M.F. Ashby, Scripta Metall. 21 (1987) 879. [17] N. Ravichandran, Y.V.R.K. Prasad, Metall. Trans. 22A (1991) 2339. [18] J.J. Jonas, C.M. Sellars, W.J.M.cG. Tegart, Met. Rev. 14 (1969) 1. [19] V. Seetharaman, C.L. Lombard, in: Y.W. Kin, R.R. Boyer (Eds.), Microstructure/Property relationships in Titanium Aluminides and Alloys, TMS, Pittsburgh, PA, 1991, p. 237. [20] D.G. Robertson, H.B. Mc Shane, Mater. Sci. Technol. 14 (1998) 339. [21] Z.J. Pu, K.H. Wu, J. Shi, D. Zou, Mater. Sci. Eng. A192/193 (1995) 780.
Hot workability of as-cast Fe3Al 2.5%Cr intermetallic alloy /
R.S. Sundar *, D.H. Sastry, Y.V.R.K. Prasad Department of Metallurgy, Indian Institute of Science, Bangalore 560 012, India Received 28 May 2002; received in revised form 22 July 2002
Abstract Processing characteristics of as-cast Fe3Al /2.5%Cr alloy have been studied using constant strain rate isothermal compression tests in the temperature range 1023 /1323 K and strain rate range 0.001 /10 s 1. At strain rates 5/0.1 s 1, the stress /strain curves are of steady-state type while at higher strain rates the flow stress reaches a peak before falling into either a steady-state or continuous flow softening with strain. The processing map of the alloy revealed a domain of dynamic recrystallization (DRX) at temperatures greater than 1123 K and the optimum conditions for processing occur at 1273 K and at strain rate of 0.001 s 1. However, at higher temperatures, due to dynamic grain growth, the optimum condition for processing has moved to higher strain rates. Flow instabilities occur in the form of adiabatic shear bands when deformed at strain rates greater than 0.1 s 1 and at temperatures 5/1123 K. A constitutive relationship for hot working is developed to describe the relationship between flow stress, strain rate and temperature. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Intermetallics; Iron aluminides; Flow stress; High temperature deformation; Deformation mechanisms; Dynamic recrystallization; Constitutive relationship; Hot workability
1. Introduction Good oxidation and sulfidation resistance of Fe3Al motivated many researchers to develop alloys based on this intermetallic compound to replace stainless steels for intermediate temperature applications [1 /3]. Compared to stainless steels, Fe3Al alloys are made up of less expensive raw materials and have lower density. In the past two decades, many compositions were developed with the aim of improving overall properties of Fe3Al. Chromium is one of the main alloying elements added to overcome the room temperature brittleness [4]. The effect of chromium on the mechanical properties of Fe3Al, especially strength, ductility [4] and creep resistance [5,6] is well documented. However, its effect on the hot workability of Fe3Al is not clear. Further, it is well known that the intrinsic workability of intermetallic alloys is sensitive to the chemistry, the initial micro-
* Corresponding author. Present address: Research Center, Philip Morris USA, Richmond, VA 23261, USA. Tel.: /1-804-274-2262; fax: /1-804-274-2468 E-mail address: [email protected] (R.S. Sundar).
structure and the prior processing history of the material [7,8]. For successful application of these alloys, it is necessary to develop suitable and economical processing techniques to produce the material with the desired shape without losing the low cost advantage. For designing a suitable processing route and for optimizing the hot workability, it is essential to characterize the constitutive flow behavior of these intermetallic alloys. Such a study will also help in evaluating the mechanisms of hot deformation and achieving microstructural control in processing. Different approaches available for optimizing the hot workability and evaluating the hot working mechanisms have been reviewed recently [9] and these include examination of shapes of stress-strain curves, evaluating kinetic parameters and developing processing maps. The present study aims at assessing the hot workability of a cast Fe3Al /Cr alloy using the approach of processing maps [9] and compare it with that of the binary alloy, the results on which were published elsewhere [10]. The above approach is successful in optimizing the processing conditions of a number of commercial as well as advanced materials [11]. A processing map for a given alloy is developed by superimposing two maps, namely
0921-5093/02/$ - see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 0 2 ) 0 0 5 8 5 - 3
R.S. Sundar et al. / Materials Science and Engineering A347 (2003) 86 /92
power dissipation map and instability map. The power dissipation map represents the manner in which the power is dissipated by the material through metallurgical processes and is constructed by plotting iso-contours of dissipation efficiency (h ) on a two-dimensional plot with log strain rate (/o) ˙ and temperature (T ) as the axes. The parameter h represents the constitutive response of the material in terms of various microstructural mechanisms that operate under given temperature and strain rate and is given by h
2m m1
(1)
where m is the strain rate sensitivity of the material. The various domains in the power dissipation map may be correlated with specific microstructural mechanisms. Prasad [12] has developed an instability parameter (/j(o)); ˙ based on extremum principles of irreversible thermodynamics, to predict unstable flow regime under processing conditions. This parameter is given by j(o)[@lnfm=(m1)g=@ln ˙ o]m ˙
(2)
Unstable flow is predicted when j(o) ˙ / B/0. The variation of j(o) ˙ with temperature and strain rate constitutes the instability map which is superimposed over the power dissipation map to delineate the unstable flow regime.
87
were removed from the furnace and air-cooled to room temperature. The deformed specimens were sectioned parallel to the compression axis using a low speed diamond cutting wheel. The cut surfaces were polished and etched with a solution containing 8 /12 vol.% HNO3/4 vol.% HCl/2 /5 vol.% CH3COOH/4% glycol for optical metallographic observation. Grain size was measured by the linear intercept method. The load /stroke curves from the compression tests were converted into true stress /true plastic strain curves using standard procedures. The flow stress (s) data were corrected for adiabatic temperature rise using a procedure described elsewhere [13]. At a given temperature, a cubic spline fit between log flow stress and log strain rate was used to calculate m as a function of strain rate. This procedure was repeated for different temperatures. Using Eq. (1), h was evaluated from a set of m values as a function of strain rate and temperature, and was plotted as an iso-efficiency contour map. Similarly, j(o) ˙ was calculated, using Eq. (2), as a function of temperature and strain rate to develop an instability map. For a given strain, the above two maps are superimposed to generate the processing map.
3. Results and discussion 3.1. True stress /true strain behavior
2. Experimental The alloy used in the present investigation contained 28.7 at.% Al, 2.5 at.% Cr and balance Fe and was prepared through vacuum induction melting. The ingot was homogenized at 1323 K for 4 h and furnace cooled. The grain size of the alloy after homogenization was about 680 mm. Cylindrical compression samples of 10 mm diameter and 15 mm length were prepared from the homogenized ingot. The details of specimen geometry and preparation methods were given elsewhere [13]. Compression tests were conducted over the temperature range of 1023/1323 K at 50 K intervals and a constant true strain rate range of 0.001 /10 s 1 at intervals of an order of magnitude. The test temperatures and strain rates were selected based on the actual processing conditions of Fe3Al alloys [8]. Isothermal compression tests were conducted on a DARTEC computer controlled servo hydraulic testing machine. The actual specimen temperature and the adiabatic temperature rise during deformation were measured using a thermocouple inserted into the specimen, in a 0.8 mm hole drilled to a depth of 5 mm at half its height. Before the test, the specimen was coated with borosilicate glass paste for lubrication and to minimize oxidation. All the specimens were deformed to half of their original height. Immediately after completion of the tests, the specimens
Typical true stress /true plastic strain curves obtained at two representative temperatures, namely 1073 and 1273 K, and at different strain rates are shown in Fig. 1. At strain rates 5/0.1 s1, the flow curves exhibit gradual strain hardening at strains less than 0.05, followed by a steady-state flow behavior at higher strain levels. At higher strain rates, the flow curves reach a peak in flow stress, followed by either continuous flow softening or drop to a minimum in flow stress and then rise to reach a steady-state. Similar trends are observed at other temperatures. It is not possible to predict the mechanisms of hot deformation from the shape of the stress /strain behavior alone, since different mechanisms may lead to similar behavior [9]. For example, either DRX or unstable flow may lead to flow softening or oscillations. It is necessary to apply other models to evaluate the hot deformation mechanisms. 3.2. Effect of temperature and strain rate The effect of temperature on the flow stress of Fe3Al / Cr alloy is brought out in Fig. 2 for a strain of 0.5. At a given strain rate, the flow stress decreases with increasing temperature in a normal manner. Similarly, at a given temperature, the flow stress increases with increasing strain rate. The above trends indicate that the deformation is thermally activated. Fig. 3 compares the
88
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conditions, the flow stress of the Cr containing alloy is nearly the same as that of the binary alloy. The kinetic parameters of deformation are evaluated based on the kinetic rate equation of the form o˙Asn exp(Q=RT)
Fig. 1. True stress /true strain curves obtained at different strain rates in Fe3Al /Cr alloy at (a) 1073 K and (b) 1273 K.
temperature dependence of the flow stress in Fe3Al /Cr with that of the binary alloy at a strain of 0.4. It was shown by McKamey et al. [4] that addition of chromium lowered the room temperature yield stress of Fe3Al. Similarly, Cr addition was found to decrease the creep resistance of Fe3Al [5,6]. However, under processing
(3)
where o˙ is the strain rate, n is stress exponent (inverse of strain rate sensitivity), Q is the activation energy, R is gas constant and A is a constant. The parameter n is estimated from the slope of the plot between log strain rate and log flow stress (Fig. 4). The values of n estimated at different true strain levels are presented in Table 1. The n value varies between 3.5 and 8 and decreases with increasing temperature. However, it is nearly independent of strain in the range of 0.1 /0.5. The variation of strain rate at a constant stress is plotted against 1/RT and the apparent activation energy (Q ) for hot deformation is calculated from the slope of this plot. Based on the Q value, the present flow stress data can be divided into two regions. At high temperatures and low stresses (Fig. 5), Q value is about 340 kJ mol 1 and is independent of stress level. This value is in good agreement with those reported in the literature [14] but is higher than that reported for binary Fe3Al [10]. At low temperatures and high stress levels, Q ranges between 250 and 450 kJ mol 1 and decreases with increasing stress (Fig. 6). Since the estimated apparent activation energy values are not in agreement with those for any particular atomic diffusion mechanisms, the evaluation of hot deformation mechanisms is difficult on the basis of the kinetic analysis. 3.3. Processing map The processing map at a true strain of 0.4, obtained by superimposing the power dissipation map and the
Fig. 2. Temperature and strain rate dependence of flow stress of Fe3Al /Cr alloy at a true strain of 0.5.
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Fig. 3. Comparison of flow stress vs. temperature of binary Fe3Al and Fe3Al /Cr alloy at a strain of 0.4.
Table 1 Stress exponent for plastic flow of Fe3Al /Cr alloy as a function of temperature and true strain Temperature (K)
1023 1073 1123 1173 1223 1273 1323
Fig. 4. Strain rate vs. flow stress at different test temperatures typically shown at a true strain of 0.4.
instability map, is shown in Fig. 7. The general features exhibited by the maps at other strains are essentially similar, indicating that the influence of strain on the hot deformation is not significant. The map exhibits a single domain in the range of 1173 /1323 K and 0.001 /1.0 s 1 and is identified to represent the process of dynamic recrystallization (DRX). Within the domain, the peak efficiency value is around 46% and occurs at 1273 K and 0.001 s 1. This temperature/strain rate combination can be regarded as optimum for processing the alloy within the DRX domain [11]. Typical microstructure of the deformed sample corresponding to the peak h is
‘n ’ at a true strain of 0.1
0.3
0.5
6.8 5.0 4.6 4.4 3.9 3.3 3.4
7.4 5.9 4.8 4.9 4.1 3.5 3.6
7.8 5.7 5.0 4.9 4.0 3.6 3.6
shown in Fig. 8. This microstructure exhibits fine newly formed recrystallized grains with irregular grain boundaries typical of dynamic recrystallization. Voyzelle and Boyd [14] have reported deformation maps for Fe / 28Al /5.0Cr /0.5Nb/0.2C under two different starting microstructural conditions. Under both conditions, they have reported the occurrence of DRX in the temperature range of 1173 /1473K. However, in the above study, the optimum conditions within the DRX region are not identified. Though their alloy is stronger than the present ternary Fe3Al /2Cr alloy, the characteristics of deformation processing maps of the two alloys are similar. The characteristics of the DRX domain of the present alloy are similar to those in the binary alloy [10]. However, when compared to the binary alloy, the DRX domain in the Fe3Al /2Cr alloy has moved to lower temperatures and strain rates. At higher temperatures (/1298 K), the peak efficiency has moved to higher strain rate (0.1 s 1). As discussed below, the shift
90
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Fig. 5. Arrhenius plot showing temperature dependence of flow behavior at high temperatures and low stresses.
Fig. 7. Processing map of Fe3Al /Cr alloy obtained at a true strain of 0.4. Contour numbers represent efficiency of power dissipation as a fraction. Shaded region corresponds to flow instability.
Fig. 8. Microstructure of Fe3Al /Cr alloy deformed in the DRX domain at 1273 K and 0.001 s 1. Fig. 6. Arrhenius plot showing temperature dependence of flow behavior at low temperatures and high stresses.
in peak efficiency or optimum condition of processing at higher temperature is caused by dynamic grain growth at these high temperatures. The variation of average grain size within the domain as a function of temperature is shown in Fig. 9. In general, a sigmoidal variation in the grain size with temperature is observed under DRX conditions [11], i.e. the grain size increases with increasing temperature and at higher temperatures, the grain size levels off. However, in the present alloy, due to the occurrence of concurrent grain growth during deformation at 1323 K, the grain size has increased continuously with deformation temperature, i.e. without leveling off at higher temperatures. Voyzelle and Boyd
Fig. 9. Variation of DRX grain size with temperature in the DRX domain of Fe3Al /Cr alloy.
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[14] have also reported dynamic grain growth during deformation of their Cr containing Fe3Al alloy at temperatures ]/1323 K and at lower strain rates. However, dynamic grain growth was not observed during the deformation of the binary alloy [10] under similar deformation conditions. Although the reason for dynamic grain growth in Cr containing Fe3Al is not clear, it is possible that Cr enhances the diffusivity in Fe3Al at higher processing temperatures. The shape of the flow curve during DRX can give a clue to the process that controls DRX. According to a model proposed by Prasad and Ravichandran [15], on the lines suggested by Derby and Ashby [16], DRX is considered to be consisting of two competing processes namely, formation of interfaces (nucleation) and migration of interfaces (growth). The above two processes are sequential in nature; in which case, the slower of the two will control the deformation. Under constant strain rate condition, the relative value of the two rates decides the shape of the stress /strain curves. If the rate of interface formation is slower than the rate of migration, as in the case of low stacking fault energy (SFE) materials [15,17], a certain strain has to elapse before a critical interface configuration is achieved for migration. At the critical strain, the migration of a large number of interfaces leads to flow softening. On the other hand, if migration rates are slow or if the two rates lead to comparable changes in the interface area as in the case of high SFE materials [17], a steady-state stress /strain curve results. As mentioned in the previous section, steady-state flow curves were observed within the DRX domain. Similarly, steady-state flow behavior was observed during DRX in binary Fe3Al [10] as well as in more complex alloys of Fe3Al [14]. The above observation indicates that DRX in Fe3Al is controlled by migration process. Another interesting feature of the DRX microstructure shown in Fig. 8 is the presence of some as cast grain boundaries (marked by arrows in the micrograph). In general, DRX nucleation starts near grain boundaries. Due to lesser grain boundary area in coarse grained material, there are not enough sites for DRX nucleation to occur near the grain boundaries. Hence, nucleation also occurs inside the grains. In such a case, some of the grain boundaries in the as-cast microstructure may not be eliminated fully during DRX. It is possible that much higher strains are required for the complete conversion of the as-cast microstructure to a wrought microstructure. In addition to DRX, a region of flow instability, (shaded region in Fig. 7) is exhibited in the processing map, at temperatures B/1123 K and at strain rates / 0.1 s1. The manifestation of the flow instabilities is in the form of adiabatic shear bands (Fig. 10). In the flow localization region, cracks (marked A) and fine recrystallized grains (marked B) are observed. While at lower strain rates ( B/0.1 s 1) and at temperatures B/1173 K,
91
Fig. 10. Microstructure of Fe3Al /Cr alloy deformed at 1123 K and 10 s 1 revealing adiabatic shear bands.
the microstructure of the deformed sample shows elongated grains perpendicular to the compression axis. The h value in this region is around 20 /30%, which is lower than that in the DRX region. Elongated grain structure and lower efficiency of power dissipation [11] indicate that the material undergoes dynamic recovery (DRV) in this region. In general, DRV involves the occurrence of mechanisms such as cross-slip, climb and nodal unzipping, etc. In the present alloy, under the DRV conditions, the activation energy for deformation decreases with increasing stress (Fig. 6). Similar variation of Q with stress is reported during deformation of Fe3Al alloys at temperatures B/1223 K [14]. The stress dependence of Q suggests that cross slip may be the operating mechanism under DRV.
3.4. Constitutive equation To describe the relationship between flow stress and strain rate and temperature, the following two equations are widely used [18]: o˙ exp (Q=RT)Asn o˙ exp(Q=RT) A0 exp(bs)
(4) (5)
where b , A and A ? are constants. Eq. (4) is arrived by rearranging the terms of Eq. (3) and is obeyed normally at high temperature and low stress conditions, while Eq. (5) is suitable to describe the relationship between the flow stress, temperature and strain rate at low temperatures and high stress conditions. The above two equations are combined to yield a single constitutive equation in the following form, to describe the relationship between the different variables over a wide range of processing conditions [18]: Z o˙ exp(Q=RT )K[Sinh(as)]n
(6)
where Z is the temperature compensated strain rate
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occurrence of which are identified to be 1273 K and 0.001 s 1. 2. The addition of Cr to Fe3Al does not significantly influence the hot workability or the mechanisms of hot deformation. However, when compared to binary Fe3Al, the DRX domain has shifted to lower strain rate at 1223 K, while at higher temperatures, the domain has moved to higher strain rate due to dynamic grain growth. 3. At temperatures less than 1123 K and at high strain rate regions, flow instabilities occur in the form of adiabatic shear bands. Initial processing of the alloy in this temperature should be avoided. 4. A constitutive equation given by Z o˙ exp(340 000=RT)8:951014 [sinh(as)]3:5 describes the relationship between the flow stress and the process variables under hot working conditions. Fig. 11. Plot between sinh (as ) and Zener /Hollomon parameter (Z ).
parameter, popularly known as the Zener/Hollomon parameter, and a and K are constants. The flow stress data obtained at temperatures greater than 1123 K (i.e. within the DRX domain) are utilized to develop a constitutive relation for processing the present alloy. The constants in Eq. (6) are evaluated following the procedure given in Refs. [19,20]. The constant b (0.0275 MPa 1) is calculated from Eq. (5) using the slope of the flow stress versus log strain rate plot at low temperatures and high strain rates. The constant a is in turn calculated from b , through the following relationship a /(b /n). The value of n is taken as 3.6 (from the high temperature range) for calculating a . The constitutive equation is given by Z o˙ exp(340 000=RT) 8:951014 [sinh(0:0076s)]3:5
(7)
The ability of the above equation to correlate test data at different temperatures and strain rates is shown in Fig. 11. The above equation gives a better fit for the experimental data than Eq. (4). Recently Pu et al. [21] modified Eq. (6), to introduce the effect of strain on the deformation parameters. As discussed earlier, in the preset alloy, the flow stress varies very little with the strain at strains greater than 0.05. Similarly, the features of the processing map also did not vary with strain. Hence, it may be concluded that Eq. (7) accurately predicts the variation of flow stress of the alloy with temperature and strain rate under processing conditions.
4. Conclusions 1. As-cast Fe3Al /Cr alloy can be ‘safely’ processed at temperatures greater than 1123 K, where the alloy undergoes DRX, the optimum conditions for the
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