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Forming behavior and workability of Hastelloy X superalloy during hot deformation
Materials Science and Engineering A 486 (2008) 641–647
Forming behavior and workability of Hastelloy X superalloy during hot deformation M. Aghaie-Khafri ∗ , N. Golarzi Faculty of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box 19395-1999, Tehran, Iran Received 7 March 2007; received in revised form 19 September 2007; accepted 9 November 2007
Abstract The hot deformation behavior of Hastelloy X superalloy has been characterized using hot compression tests in the temperature range of 900–1150 ◦ C and strain rates varying between 0.001 and 0.5 s−1 . The results showed that both kinds of softening mechanisms, dynamic recovery and dynamic recrystallization, occurred during hot working. Hot workability of this alloy has been analyzed by calculating flow localization parameter and construction of workability map for occurrence of shear band. In addition, on the basis of flow stress data obtained as a function of temperature and strain rate in compression, power dissipation map and instability map for hot working have been developed. © 2007 Elsevier B.V. All rights reserved. Keywords: Hot deformation; Superalloy; Hastelloy X; Workability
1. Introduction The Hastelloy X, a nickel-base superalloy is widely used as a high temperature material in gas turbine engine applications and aerospace industry. The high temperature mechanical properties of this alloy are highly sensitive to flow characteristic and microstructural changes of the material during hot working. Hot deformation behaviors of superalloys have been studied in several research works [1–4]. It has been shown that desired mechanical properties after hot deformation of superalloys, are strongly dependent on deformation parameters such as temperature and strain rate. In hot forming of metals at temperatures above recrystallization temperature, the influence of strain on flow stress is insignificant, and the influence of strain rate becomes increasingly important and the degree of dependency of flow stress on temperature varies considerably among different materials. A few studies have also been carried out on the microstructural characterization and recrystallization behavior of superalloys and various empirical equations for prediction of grain size have been proposed [5–8]. There has been much concern in the metal forming research over a number of years about the introduction of the workability
∗
Corresponding author. Tel.: +98 09123088389; fax: +98 21 886 74748. E-mail address: [email protected] (M. Aghaie-Khafri).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.11.059
as the degree of deformation that can be achieved in a particular forming process without creating an undesirable condition. The ultimate objective is to manufacture components with controlled microstructure and properties, without macro- or microstructural defects. Workability of material is highly dependent on the processing parameters such as strain rate and temperature. For instance, to define the processing conditions in the desired range of strain rates, workability parameters should be optimized in the specified temperature domain. One of the requirements for the evaluating of workability is a knowledge of the material flow behavior for defining deformation maps that delineate ‘safe’ and ‘non-safe’ hot working conditions. These maps show the processing conditions for stable and unstable deformation in the processing space [9]. A processing map is an explicit representation of the response of a material, in terms of microstructural mechanisms, to the imposed process parameters and consists of a superimposition of power dissipation and an instability map. These are developed on the basis of the dynamic material model which is essentially a continuum model using the concepts of systems engineering, extremum principles of irreversible thermodynamics with application to continuum mechanics of large plastic flow and those describing the stability and self-organization of chaotic systems [9]. The input to generate a processing map is the experimental data of flow stress (σ) as a function of temperature (T), strain
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M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
Table 1 Chemical composition of the material used in this study in wt.%
2. Experimental procedures
C
Mn
Si
Cr
Mo
Ti
Al
W
Co
Fe
Ni
0.17
0.7
0.35
22.72
8.12
0.176
0.05
0.43
0.99
17.35
Bal.
The chemical composition of the starting material used in this investigation is listed in Table 1. The raw material was produced by vacuum melting process and it was hot forged to remove the casting structure. Cylindrical specimens of 5 mm diameter and 7.5 mm height were machined out of the as-received stock. Hot compression experiments were conducted under isothermal condition at constant true strain rates of 0.001, 0.01, 0.1 and 0.5 s−1 and at temperatures of 900, 950, 1000, 1050, 1100 and 1l50 ◦ C. All samples were held at deformation temperatures for 5 min to eliminate the thermal gradient, then they deformed to total true strain of 0.7. Samples were quenched in water after hot deformation to capture microstructure of hot deformed material and microstructural studies. 3. Results and discussion 3.1. Flow behavior
Fig. 1. True strain–true stress curves at 950 ◦ C and different strain rates.
rate (˙ε) and strain (ε) [10]. Despite the excellent high temperature properties of Hastelloy X, and its extensive use in hot section parts, its hot deformation behavior has been rarely studied. Therefore, more studies are still demanded to understand flow stress behavior and workability of this alloy under different hot working conditions. In the present study, flow behavior of Hastelloy X has been examined. While hot tensile, hot torsion or hot compression techniques may be used for this purpose, hot compression test has decisive advantages over others. First of all, in a compression test on a cylindrical specimen, it is easy to obtain a constant true strain rate using an exponential decay of the crosshead speed, and the test can be conducted under isothermal conditions. Therefore, hot compression experiments were performed in the temperature range between 900 and 1150 ◦ C and strain rates of 0.001–0.5 s−1 . In addition, microstructural studies were done to investigate the effect of deformation parameters on microstructure.
Fig. 2. True strain–true stress curves at 1000 ◦ C and different strain rates.
Figs. 1–3 show true stress–strain curves of Hastelloy X under various test conditions. The shape of the flow curves depends on the strain rate and temperature. It is clear that at lower temperatures, i.e., 950 ◦ C stress–strain curves are typically strain-hardening type except at strain rate of 0.5 s−1 where stress–strain curves show a peak stress and then the flow curves continuously decreased. The flow softening observed can be attributed to the adiabatic heating at high strain rates. The heat generated due to plastic deformation is not conducted away since the time available is too short. As the flow stress is lower at higher temperatures, further deformation is preferred in the narrow band thereby causing localization. The localized flow causes a microstructural change in the band region which reveals fine grains formed due to recrystallization after dynamic recovery, shown in Fig. 4. It is worth noting that flow localization like shear band has been observed at 900 and 950 ◦ C, shown in Fig. 5. This is further discussed in a subsequent section on the characterization of flow instabilities. Flow curves at strain rate of 0.5 s−1 and higher temperatures are the same as discussed above, however, the decline in curves decreased by increasing temperature and show a tendency to reach a saturation stress at 1150 ◦ C.
Fig. 3. True strain–true stress curves at 1150 ◦ C and different strain rates.
M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
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Fig. 6. Microstructure of the sample deformed at temperature of 950 ◦ C and strain rate of 0.001 s−1 . Fig. 4. Microstructure of the sample deformed at temperature of 1000 ◦ C and strain rate of 0.01 s−1 .
At 1000 ◦ C and strain rate of 0.001 s−1 the strain hardening is still the dominant mechanism and plastic instability like shear band has been observed. A single peak stress has been observed at low strain and strain rate of 0.1 s−1 and a wider peak at 0.5 s−1 . Fig. 6 shows the microstructure of the sample deformed ◦ at 1000 C and strain rate of 0.001 s−1 . The microstructure consists of elongated grains with wavy-shape grain boundaries. The formation of serrated grain boundaries during hot deformation can be attributed to the restriction of the grain boundary migration during dynamic recrystallization. The phenomenon caused by the second phases that are still stable at hot working temperatures around 1000 ◦ C. This also causes stress–strain curve shows no evidence of dynamic recrystallization at lower strain rates. At higher temperatures, i.e., 1150 ◦ C stress–strain curves are softening type which is a result of dynamic recrystallization. Multiple stress peaks are the characteristic of the softening curves at low strain rates which is quite evident at 1150 ◦ C. At higher strain rates a single stress peak has been observed especially at 0.5 s−1 . The variations of flow stress with temperature for different strain rates are shown in Fig. 7. It is clear that flow stress decreased with increasing temperature. However, the slope of the
Fig. 5. Macrostructure of Hastelloy X specimen deformed at 900 ◦ C and strain rate of 0.5 s−1 .
curves reduced by increasing temperature and tends to a constant value at high temperatures. The dependence of the flow stress on temperature can be evaluated by Seeger theory of flow stress [11]. The stress required for deformation can be divided into two parts: σ * , which is dependent on the temperature and σ G , which is the athermal component of the flow stress: σ = σ ∗ + σG .
(1)
It can be seen that the athermal component of stress is σ G ≈ 70 MPa at a strain rate of 0.001 s−1 . 3.2. Workability and flow localization Strain rate sensitivity, SRS, as an important material property can affect workability of metals and can be defined as: d ln σ ε˙ dσ m= = . (2) d ln ε˙ ε,T σ d˙ε ε,T The variations of SRS, (m) with strain at different temperatures are shown in Fig. 8. The m value decreased with strain and
Fig. 7. Variation of flow stress at true strain of 0.6 with temperature at different strain rates.
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M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
Fig. 8. Variation of strain rate sensitivity vs. strain.
increased with temperature. It is worth noting that SRS shows an abrupt increase at 1000 ◦ C as indicated by Fig. 9. As it is observed the mean value of m changes from 0.115 at 900 ◦ C to 0.241 at 1150 ◦ C. The phenomenon can be attributed to the dynamic recrystallization at higher temperatures that produces higher strain rate sensitivity [12]. The other important factor affecting hot deformation behavior is the strain hardening rate, γ, which is defined as: (dσ/dε)ε˙ ,T dε + (dσ/dT )ε,˙ε dT 1 dσ = . (3) γ= σ dε ε˙ σ dε Strain hardening rate has been calculated for different deformation conditions on the basis of the stress–strain curves and numerical differentiation. Figs. 10 and 11 show the variations of the γ values with strain and strain rate for different temperatures. It is clear the γ value decreases as the strain or strain rate increases. Several types of plastic instabilities can be developed in the compression test. The first type is associated with a maximum in the true stress–strain curve. The second type deals with inhomogeneous deformation and shear band formation. In compression the stability analysis is the same as those given by Hart for tension test [13]. Hart developed a general analysis of plastic
Fig. 9. Plot of strain rate sensitivity vs. temperature.
Fig. 10. Variation of γ value at strain rate of 0.001 s−1 with strain at different temperatures.
instability of tension test with special attention to the influence of strain rate sensitivity of the flow stress. On the basis of hart analysis, in compression, deformation is stable as long as: (γ + m) ≤ 1,
(4)
and is unstable when: (γ + m) ≥ 1.
(5)
The non-uniform deformation that is often associated with compression testing sometimes leads to regions of highly localized deformation called shear bands. The basic premise of plastic instability analysis along a direction of pure shear is that there is no change in cross sectional area, dA = 0. Therefore, dσ = 0 is the condition for the onset of shear banding occurs at the point of load instability. In a material whose flow curve is dependent on deformation, deformation rate and temperature, the instability condition can be derived as [14]: σ = σ(ε, ε˙ , T ),
Fig. 11. Variation of γ value at true strain of 0.3 with strain rate at different temperatures.
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Table 2 Flow localization parameter values at different temperatures and strain rates
3.3. Power dissipation and metallurgical instability
Strain rate (s−1 )
Srinivasan and Prasad have characterized the deformation behavior based on the dynamic material model (DMM) [9]. In this model the work-piece under hot working conditions is considered to be a dissipator of power. According to DMM, the power P (per unit volume) absorbed by the work-piece during plastic flow is given by:
Temperature (◦ C) 900
0.001 0.01 0.1 0.5
950
7.400 5.229 5.387 22.930
11.220 9.277 <0 –
1000
1050
1100
1150
6.536 1.249 <0 0.529
3.921 1.249 0.021 0.158
1.873 1.141 0.512 0.592
0.457 0.360 0.569 0.510
P = G + J. dσ =
dσ dε
ε˙ ,T
dε +
dσ d˙ε
ε,T
d˙ε +
dσ dT
dT.
(6)
ε,˙ε
Substituting Eqs. (2) and (3) into Eq. (6): dσ = γσ dε +
σ m d˙ε. ε˙
(7)
1 d˙ε γ =− . ε˙ dε m
The G term represents the power dissipated by plastic work, most of which is converted into viscoplastic heat; the little remaining power is stored as lattice defects. The J term is related to the metallurgical mechanisms such as dynamic recovery, dynamic recrystallization and internal fracture which occur dynamically to dissipate power. The efficiency of power dissipation given in terms of the strain rate sensitivity parameter (m) is [9]: η=
Applying the instability condition, dσ = 0: (8)
The workability of metals and alloys under hot deformation condition can be estimated on the basis of the flow localization parameter, γ/m proposed by the Eq. (8) [14]. The flow localization parameter specify that the rate at which shear strain rate concentrations develop in plane strain is proportional to the ratio of the normalized flow softening rate to the strain rate sensitivity parameter. A considerable amount of research has been conducted to establish a correlation between the occurrence of shear bands in isothermal metalworking operations and the flow localization parameter. The values of calculated flow localization parameter corresponding to strain of 0.1 at different temperatures and strain rates are shown in Table 2. It is clear that at higher strain rates and low temperatures, the higher values of flow localization parameter, the possibility of occurring flow localizations is quite high, leading to a poor workability of the material. Considering the abrupt changes of m in 1000 ◦ C, the dominant parameter controlling flow localization is the strain rate sensitivity of the material. The high values of m at higher temperatures result in lower values of γ/m, and therefore, more stable flow at high temperatures. For the case of low temperature the thermal microstructural mechanisms dominate over the strain rate sensitivity effect and hence the specimens underwent softening which eventually led to flow localization. A workability diagram can be constructed on temperature strain rate maps in which the strain rates and temperatures at which shear bands are generated in the isothermal hot compression tests have been established from metallographic sections of deformed specimens. Fig. 12 shows the workability map for Hastelloy X. Extensive studies on titanium alloys have shown that, when γ/m exceeds about 5, shear band formation is prevalent [15]. It can be seen that, with the exception of one point, the loci corresponding to α ≥ 5 separate regimes in which shear bands are not observed for Hastelloy X.
(9)
J Jmax
=
2m . m+1
(10)
For ideally plastic flow (m = 1), one half of the power is dissipated in material flow and the other half is dissipated in viscous heat. The other extreme occurs for materials which are strain rate insensitive (m = 0), where all the power would be dissipated by heat which leads to plastic instability by a continuum process such as adiabatic shearing. The variation of a dimensionless parameter (η) called the efficiency of power dissipation, with strain (ε), strain rate (˙ε) and temperature (T) constitutes a processing map [16]. In this study the values of the strain rate sensitivity parameter (m) to use the efficiency parameter (η) are determined from the flow stress data of the Hastelloy X. A cubic spline fit for the test data is used to generate a greater number of data points and then the computed data is transformed into logarithmic scale. With this transformation, the first derivative of the spline fit gives directly the strain rate sensitivity parameter (m) at the generated intermediate data points. The power dissipation map generated in the temperature range 900–1150 ◦ C and strain rate
Fig. 12. Workability map for occurrence of shear bands in hot compression of Hastelloy X where experimental data are indicated by solid circles (failed) and hollow circles (safe).
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Fig. 13. Power dissipation map of Hastelloy X at a strain of 0.6. Contour numbers represent percent efficiency of power dissipation.
range 0.001–0.5 s−1 at a strain of 0.5 is given in Fig. 13 in which contour numbers represent percent η. The contours represent the rate of microstructural change occurring in the material during hot deformation and may be termed as microstructural trajectories. Since the work-piece system is dynamic and an irreversible dissipator of power, the trajectories may be directly correlated with specific microstructural mechanisms and give rise to domains with local efficiency maximum. The safe hot deformation mechanisms are dynamic recrystallization, dynamic recovery and superplasticity while wedge cracking and void formation at hard particles are damage processes. The mechanisms in each of these domains may be identified and used for optimizing hot workability if found safe. The power dissipation map for Hastelloy X exhibits two domains. One domain occurs in the strain rate range 0.01–0.1 s−1 and temperature range 1050–1150 ◦ C with a peak efficiency of 36%. DRX is the dominant power dissipation mechanism in this region, the maximum efficiency of power dissipation in the DRX domain is generally about 30–40% for low stacking fault energy materials and the contours are widely spaced [17,18]. Another domain can be observed in the temperature range 1000–1150 ◦ C and strain rates lower than 0.01 s−1 . The efficiency is increasing with decreasing strain rate and increasing temperature in this domain. The superplasticity/wedge cracking processes are characterized by high efficiency of power dissipation and a steep rise in efficiency with decrease in strain rates. The low strain rate sensitivity under these conditions (m ≈ 0.24) confirms that any kind of flow instability and discontinuity like wedge cracking can be expected in this region. Other than these two domains all contours in the temperature range 900–1000 ◦ C and strain rate range 0.001–0.5 s−1 with efficiency values between 21 and 36% do not fall into the specific domains. These contours may be termed chaotic
Fig. 14. Flow instability map for Hastelloy X at a strain of 0.6.
trajectories and indicate a transient behavior where no stable microstructural mechanism occurs. However, in view of the low efficiency (21–27%) and temperature (900–950 ◦ C) inside the region, dynamic recovery is one of the active microstructural mechanisms. Prasad and Kalyan Kumar have developed a criterion for evaluating the regimes of flow instabilities [9]. The criterion is based on the continuum principles as applied to large plastic flow proposed by Ziegler [19] according to which instabilities occur when, ξ(˙ε) =
∂ ln(m/m + 1) + m < 0. ∂ ln ε˙
(11)
The ξ(˙ε)parameter may be evaluated as a function of temperature and strain rate to obtain an instability [10,20]. Material instability during hot deformation occurs in regimes where ξ(˙ε) is negative. The instability map developed using the criterion above is shown in Fig. 14. The map exhibits a regime of flow instability in the temperature range 900–950 ◦ C and strain rates lower than 0.001 s−1 ; the manifestation of which is in the form of adiabatic shear bands. Another narrow regime of flow instability occurs at 900 ◦ C and strain rates higher than 0.01 s−1 which indicate the formation of shear bands. The prediction has a fair agreement with experimental observation presented in Fig. 12. 4. Conclusions Hot compression experiments have been performed on Hastelloy X superalloy in the temperatures between 900 and 1150 ◦ C and strain rates of 0.001, 0.01, 0.1 and 0.5 s−1 . By means of stress–strain curves the flow stress behavior and workability of this alloy has been studied. The following conclusions are drawn from this study.
M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
- Dynamic recovery occurs at low temperatures while dynamic recrystallization mainly occurs at temperature of 1050 ◦ C and strain rates of 0.001–0.5 s−1 . However, adiabatic heating effect caused by hot deformation at high strain rates stimulates DRX at low temperatures. - The power dissipation map for Hastelloy X exhibits two domains. One domain in the strain rate range 0.01–0.1 s−1 and temperature range 1050–1150 ◦ C with a peak efficiency of 36% represents DRX. The second domain in the temperature range 1000–1150 ◦ C and strain rates lower than 0.01 s−1 , can be interpreted as wedge cracking area. - The workability indexes, m and γ values decreased by strain. In addition, the strain rate sensitivity of the alloy is not constant at the employed temperature range and shows an increase by increasing temperature in the range of 900–1150 ◦ C. Therefore, it is expected that at higher temperatures the workability would be improved. - Calculation of flow localization parameter and construction of instability map showed that at temperatures between 900 and 950 ◦ C and different strain rates, the formation of severe flowlocalized region is quite possible. However, the prediction made by flow localization parameter had a better agreement with experimental observations. References [1] N.K. Park, I.S. Kim, J. Mater. Proc. Tech. 111 (2001) 98–102. [2] J. Liu, G. Liul, B. Hu, Y. Song, Z. Qin, Y. Zhang, J. Univ. Sci. Tech. Beijing 13 (2006) 319–323.
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[3] N. Srinivasan, Y.V.R.K. Prasad, Metall. Trans. A25 (1994) 2275–2284. [4] S.L. Semiatin, P.N. Fagin, M.G. Glavicic, D. Raabe, Scripta Mater. 50 (2004) 625–629. [5] J.M. Zhang, Z.Y. Gao, J.Y. Zhuang, Z.Y. Zhong, J. Mater. Proc. Tech. 88 (1999) 244–250. [6] H. Yuan, W.C. Liu, Mater. Sci. Eng. A408 (2005) 281–289. [7] D.R. Nielsen, S.W. Thompson, C.J. VanTyne, M.C. Mataya, in: E.A. Loria (Ed.), Superalloys 718, 625, 706 and Various Derivatives, TMS, Warrendale, PA, 1989, p. 119. [8] S.C. Medeiros, Y.V.R.K. Prasad, W.G. Frazier, R. Srinivasan, Mater. Sci. Eng. A293 (2000) 198–207. [9] Y.V.R.K. Prasad, S. Sasidhara (Eds.), Hot Working Guide: A Compendium of Processing Maps, ASM International, Materials Park, OH, 1997. [10] S.V.S. Narayana Murty, B. Nageswara Rao, B.P. Kashyap, J. Mater. Proc. Tech. 166 (2005) 268–278. [11] A. Seeger, in: TMS-AIME Conference, Work Hardening vol. 46 (1966) 27. [12] F. Moneteillet, J.J. Jonas, Metall. Mater. Trans. 27A (1996) 3346–3348. [13] E.W. Hart, Acta Metall. 15 (1967) 351–355. [14] S.L. Semiatin, J.J. Jonas, Formability and Workability of Metals: Plastic Instability and Flow Localization, American Society for Metals, Metals Park, OH, USA, 1984. [15] S.L. Semiatin, G.D. Lahoti, Met. Trans. 13A (1982) 275–281. [16] T. Seshacharyulu, Y.V.R.K. Prasad, Mater. Sci. Eng. A243 (1998) 82–88. [17] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Mater. Sci. Eng. A284 (2000) 184–194. [18] T. Seshacharyulu, S.C. Medeiros, W.G. Frazier, Y.V.R.K. Prasad, Mater. Sci. Eng. A325 (2002) 112–125. [19] H. Ziegler, Some extremum principles in irreversible thermodynamics, with application to continuum mechanics, in: Progress in Solid Mechanics, vol. 4, Wiley, New York, 1963, pp. 93–193. [20] S.V.S. Narayana Murty, B. Nageswara Rao, Mater. Sci. Eng. A254 (1998) 76–82.
Forming behavior and workability of Hastelloy X superalloy during hot deformation M. Aghaie-Khafri ∗ , N. Golarzi Faculty of Mechanical Engineering, K.N. Toosi University of Technology, P.O. Box 19395-1999, Tehran, Iran Received 7 March 2007; received in revised form 19 September 2007; accepted 9 November 2007
Abstract The hot deformation behavior of Hastelloy X superalloy has been characterized using hot compression tests in the temperature range of 900–1150 ◦ C and strain rates varying between 0.001 and 0.5 s−1 . The results showed that both kinds of softening mechanisms, dynamic recovery and dynamic recrystallization, occurred during hot working. Hot workability of this alloy has been analyzed by calculating flow localization parameter and construction of workability map for occurrence of shear band. In addition, on the basis of flow stress data obtained as a function of temperature and strain rate in compression, power dissipation map and instability map for hot working have been developed. © 2007 Elsevier B.V. All rights reserved. Keywords: Hot deformation; Superalloy; Hastelloy X; Workability
1. Introduction The Hastelloy X, a nickel-base superalloy is widely used as a high temperature material in gas turbine engine applications and aerospace industry. The high temperature mechanical properties of this alloy are highly sensitive to flow characteristic and microstructural changes of the material during hot working. Hot deformation behaviors of superalloys have been studied in several research works [1–4]. It has been shown that desired mechanical properties after hot deformation of superalloys, are strongly dependent on deformation parameters such as temperature and strain rate. In hot forming of metals at temperatures above recrystallization temperature, the influence of strain on flow stress is insignificant, and the influence of strain rate becomes increasingly important and the degree of dependency of flow stress on temperature varies considerably among different materials. A few studies have also been carried out on the microstructural characterization and recrystallization behavior of superalloys and various empirical equations for prediction of grain size have been proposed [5–8]. There has been much concern in the metal forming research over a number of years about the introduction of the workability
∗
Corresponding author. Tel.: +98 09123088389; fax: +98 21 886 74748. E-mail address: [email protected] (M. Aghaie-Khafri).
0921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2007.11.059
as the degree of deformation that can be achieved in a particular forming process without creating an undesirable condition. The ultimate objective is to manufacture components with controlled microstructure and properties, without macro- or microstructural defects. Workability of material is highly dependent on the processing parameters such as strain rate and temperature. For instance, to define the processing conditions in the desired range of strain rates, workability parameters should be optimized in the specified temperature domain. One of the requirements for the evaluating of workability is a knowledge of the material flow behavior for defining deformation maps that delineate ‘safe’ and ‘non-safe’ hot working conditions. These maps show the processing conditions for stable and unstable deformation in the processing space [9]. A processing map is an explicit representation of the response of a material, in terms of microstructural mechanisms, to the imposed process parameters and consists of a superimposition of power dissipation and an instability map. These are developed on the basis of the dynamic material model which is essentially a continuum model using the concepts of systems engineering, extremum principles of irreversible thermodynamics with application to continuum mechanics of large plastic flow and those describing the stability and self-organization of chaotic systems [9]. The input to generate a processing map is the experimental data of flow stress (σ) as a function of temperature (T), strain
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M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
Table 1 Chemical composition of the material used in this study in wt.%
2. Experimental procedures
C
Mn
Si
Cr
Mo
Ti
Al
W
Co
Fe
Ni
0.17
0.7
0.35
22.72
8.12
0.176
0.05
0.43
0.99
17.35
Bal.
The chemical composition of the starting material used in this investigation is listed in Table 1. The raw material was produced by vacuum melting process and it was hot forged to remove the casting structure. Cylindrical specimens of 5 mm diameter and 7.5 mm height were machined out of the as-received stock. Hot compression experiments were conducted under isothermal condition at constant true strain rates of 0.001, 0.01, 0.1 and 0.5 s−1 and at temperatures of 900, 950, 1000, 1050, 1100 and 1l50 ◦ C. All samples were held at deformation temperatures for 5 min to eliminate the thermal gradient, then they deformed to total true strain of 0.7. Samples were quenched in water after hot deformation to capture microstructure of hot deformed material and microstructural studies. 3. Results and discussion 3.1. Flow behavior
Fig. 1. True strain–true stress curves at 950 ◦ C and different strain rates.
rate (˙ε) and strain (ε) [10]. Despite the excellent high temperature properties of Hastelloy X, and its extensive use in hot section parts, its hot deformation behavior has been rarely studied. Therefore, more studies are still demanded to understand flow stress behavior and workability of this alloy under different hot working conditions. In the present study, flow behavior of Hastelloy X has been examined. While hot tensile, hot torsion or hot compression techniques may be used for this purpose, hot compression test has decisive advantages over others. First of all, in a compression test on a cylindrical specimen, it is easy to obtain a constant true strain rate using an exponential decay of the crosshead speed, and the test can be conducted under isothermal conditions. Therefore, hot compression experiments were performed in the temperature range between 900 and 1150 ◦ C and strain rates of 0.001–0.5 s−1 . In addition, microstructural studies were done to investigate the effect of deformation parameters on microstructure.
Fig. 2. True strain–true stress curves at 1000 ◦ C and different strain rates.
Figs. 1–3 show true stress–strain curves of Hastelloy X under various test conditions. The shape of the flow curves depends on the strain rate and temperature. It is clear that at lower temperatures, i.e., 950 ◦ C stress–strain curves are typically strain-hardening type except at strain rate of 0.5 s−1 where stress–strain curves show a peak stress and then the flow curves continuously decreased. The flow softening observed can be attributed to the adiabatic heating at high strain rates. The heat generated due to plastic deformation is not conducted away since the time available is too short. As the flow stress is lower at higher temperatures, further deformation is preferred in the narrow band thereby causing localization. The localized flow causes a microstructural change in the band region which reveals fine grains formed due to recrystallization after dynamic recovery, shown in Fig. 4. It is worth noting that flow localization like shear band has been observed at 900 and 950 ◦ C, shown in Fig. 5. This is further discussed in a subsequent section on the characterization of flow instabilities. Flow curves at strain rate of 0.5 s−1 and higher temperatures are the same as discussed above, however, the decline in curves decreased by increasing temperature and show a tendency to reach a saturation stress at 1150 ◦ C.
Fig. 3. True strain–true stress curves at 1150 ◦ C and different strain rates.
M. Aghaie-Khafri, N. Golarzi / Materials Science and Engineering A 486 (2008) 641–647
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Fig. 6. Microstructure of the sample deformed at temperature of 950 ◦ C and strain rate of 0.001 s−1 . Fig. 4. Microstructure of the sample deformed at temperature of 1000 ◦ C and strain rate of 0.01 s−1 .
At 1000 ◦ C and strain rate of 0.001 s−1 the strain hardening is still the dominant mechanism and plastic instability like shear band has been observed. A single peak stress has been observed at low strain and strain rate of 0.1 s−1 and a wider peak at 0.5 s−1 . Fig. 6 shows the microstructure of the sample deformed ◦ at 1000 C and strain rate of 0.001 s−1 . The microstructure consists of elongated grains with wavy-shape grain boundaries. The formation of serrated grain boundaries during hot deformation can be attributed to the restriction of the grain boundary migration during dynamic recrystallization. The phenomenon caused by the second phases that are still stable at hot working temperatures around 1000 ◦ C. This also causes stress–strain curve shows no evidence of dynamic recrystallization at lower strain rates. At higher temperatures, i.e., 1150 ◦ C stress–strain curves are softening type which is a result of dynamic recrystallization. Multiple stress peaks are the characteristic of the softening curves at low strain rates which is quite evident at 1150 ◦ C. At higher strain rates a single stress peak has been observed especially at 0.5 s−1 . The variations of flow stress with temperature for different strain rates are shown in Fig. 7. It is clear that flow stress decreased with increasing temperature. However, the slope of the
Fig. 5. Macrostructure of Hastelloy X specimen deformed at 900 ◦ C and strain rate of 0.5 s−1 .
curves reduced by increasing temperature and tends to a constant value at high temperatures. The dependence of the flow stress on temperature can be evaluated by Seeger theory of flow stress [11]. The stress required for deformation can be divided into two parts: σ * , which is dependent on the temperature and σ G , which is the athermal component of the flow stress: σ = σ ∗ + σG .
(1)
It can be seen that the athermal component of stress is σ G ≈ 70 MPa at a strain rate of 0.001 s−1 . 3.2. Workability and flow localization Strain rate sensitivity, SRS, as an important material property can affect workability of metals and can be defined as: d ln σ ε˙ dσ m= = . (2) d ln ε˙ ε,T σ d˙ε ε,T The variations of SRS, (m) with strain at different temperatures are shown in Fig. 8. The m value decreased with strain and
Fig. 7. Variation of flow stress at true strain of 0.6 with temperature at different strain rates.
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Fig. 8. Variation of strain rate sensitivity vs. strain.
increased with temperature. It is worth noting that SRS shows an abrupt increase at 1000 ◦ C as indicated by Fig. 9. As it is observed the mean value of m changes from 0.115 at 900 ◦ C to 0.241 at 1150 ◦ C. The phenomenon can be attributed to the dynamic recrystallization at higher temperatures that produces higher strain rate sensitivity [12]. The other important factor affecting hot deformation behavior is the strain hardening rate, γ, which is defined as: (dσ/dε)ε˙ ,T dε + (dσ/dT )ε,˙ε dT 1 dσ = . (3) γ= σ dε ε˙ σ dε Strain hardening rate has been calculated for different deformation conditions on the basis of the stress–strain curves and numerical differentiation. Figs. 10 and 11 show the variations of the γ values with strain and strain rate for different temperatures. It is clear the γ value decreases as the strain or strain rate increases. Several types of plastic instabilities can be developed in the compression test. The first type is associated with a maximum in the true stress–strain curve. The second type deals with inhomogeneous deformation and shear band formation. In compression the stability analysis is the same as those given by Hart for tension test [13]. Hart developed a general analysis of plastic
Fig. 9. Plot of strain rate sensitivity vs. temperature.
Fig. 10. Variation of γ value at strain rate of 0.001 s−1 with strain at different temperatures.
instability of tension test with special attention to the influence of strain rate sensitivity of the flow stress. On the basis of hart analysis, in compression, deformation is stable as long as: (γ + m) ≤ 1,
(4)
and is unstable when: (γ + m) ≥ 1.
(5)
The non-uniform deformation that is often associated with compression testing sometimes leads to regions of highly localized deformation called shear bands. The basic premise of plastic instability analysis along a direction of pure shear is that there is no change in cross sectional area, dA = 0. Therefore, dσ = 0 is the condition for the onset of shear banding occurs at the point of load instability. In a material whose flow curve is dependent on deformation, deformation rate and temperature, the instability condition can be derived as [14]: σ = σ(ε, ε˙ , T ),
Fig. 11. Variation of γ value at true strain of 0.3 with strain rate at different temperatures.
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Table 2 Flow localization parameter values at different temperatures and strain rates
3.3. Power dissipation and metallurgical instability
Strain rate (s−1 )
Srinivasan and Prasad have characterized the deformation behavior based on the dynamic material model (DMM) [9]. In this model the work-piece under hot working conditions is considered to be a dissipator of power. According to DMM, the power P (per unit volume) absorbed by the work-piece during plastic flow is given by:
Temperature (◦ C) 900
0.001 0.01 0.1 0.5
950
7.400 5.229 5.387 22.930
11.220 9.277 <0 –
1000
1050
1100
1150
6.536 1.249 <0 0.529
3.921 1.249 0.021 0.158
1.873 1.141 0.512 0.592
0.457 0.360 0.569 0.510
P = G + J. dσ =
dσ dε
ε˙ ,T
dε +
dσ d˙ε
ε,T
d˙ε +
dσ dT
dT.
(6)
ε,˙ε
Substituting Eqs. (2) and (3) into Eq. (6): dσ = γσ dε +
σ m d˙ε. ε˙
(7)
1 d˙ε γ =− . ε˙ dε m
The G term represents the power dissipated by plastic work, most of which is converted into viscoplastic heat; the little remaining power is stored as lattice defects. The J term is related to the metallurgical mechanisms such as dynamic recovery, dynamic recrystallization and internal fracture which occur dynamically to dissipate power. The efficiency of power dissipation given in terms of the strain rate sensitivity parameter (m) is [9]: η=
Applying the instability condition, dσ = 0: (8)
The workability of metals and alloys under hot deformation condition can be estimated on the basis of the flow localization parameter, γ/m proposed by the Eq. (8) [14]. The flow localization parameter specify that the rate at which shear strain rate concentrations develop in plane strain is proportional to the ratio of the normalized flow softening rate to the strain rate sensitivity parameter. A considerable amount of research has been conducted to establish a correlation between the occurrence of shear bands in isothermal metalworking operations and the flow localization parameter. The values of calculated flow localization parameter corresponding to strain of 0.1 at different temperatures and strain rates are shown in Table 2. It is clear that at higher strain rates and low temperatures, the higher values of flow localization parameter, the possibility of occurring flow localizations is quite high, leading to a poor workability of the material. Considering the abrupt changes of m in 1000 ◦ C, the dominant parameter controlling flow localization is the strain rate sensitivity of the material. The high values of m at higher temperatures result in lower values of γ/m, and therefore, more stable flow at high temperatures. For the case of low temperature the thermal microstructural mechanisms dominate over the strain rate sensitivity effect and hence the specimens underwent softening which eventually led to flow localization. A workability diagram can be constructed on temperature strain rate maps in which the strain rates and temperatures at which shear bands are generated in the isothermal hot compression tests have been established from metallographic sections of deformed specimens. Fig. 12 shows the workability map for Hastelloy X. Extensive studies on titanium alloys have shown that, when γ/m exceeds about 5, shear band formation is prevalent [15]. It can be seen that, with the exception of one point, the loci corresponding to α ≥ 5 separate regimes in which shear bands are not observed for Hastelloy X.
(9)
J Jmax
=
2m . m+1
(10)
For ideally plastic flow (m = 1), one half of the power is dissipated in material flow and the other half is dissipated in viscous heat. The other extreme occurs for materials which are strain rate insensitive (m = 0), where all the power would be dissipated by heat which leads to plastic instability by a continuum process such as adiabatic shearing. The variation of a dimensionless parameter (η) called the efficiency of power dissipation, with strain (ε), strain rate (˙ε) and temperature (T) constitutes a processing map [16]. In this study the values of the strain rate sensitivity parameter (m) to use the efficiency parameter (η) are determined from the flow stress data of the Hastelloy X. A cubic spline fit for the test data is used to generate a greater number of data points and then the computed data is transformed into logarithmic scale. With this transformation, the first derivative of the spline fit gives directly the strain rate sensitivity parameter (m) at the generated intermediate data points. The power dissipation map generated in the temperature range 900–1150 ◦ C and strain rate
Fig. 12. Workability map for occurrence of shear bands in hot compression of Hastelloy X where experimental data are indicated by solid circles (failed) and hollow circles (safe).
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Fig. 13. Power dissipation map of Hastelloy X at a strain of 0.6. Contour numbers represent percent efficiency of power dissipation.
range 0.001–0.5 s−1 at a strain of 0.5 is given in Fig. 13 in which contour numbers represent percent η. The contours represent the rate of microstructural change occurring in the material during hot deformation and may be termed as microstructural trajectories. Since the work-piece system is dynamic and an irreversible dissipator of power, the trajectories may be directly correlated with specific microstructural mechanisms and give rise to domains with local efficiency maximum. The safe hot deformation mechanisms are dynamic recrystallization, dynamic recovery and superplasticity while wedge cracking and void formation at hard particles are damage processes. The mechanisms in each of these domains may be identified and used for optimizing hot workability if found safe. The power dissipation map for Hastelloy X exhibits two domains. One domain occurs in the strain rate range 0.01–0.1 s−1 and temperature range 1050–1150 ◦ C with a peak efficiency of 36%. DRX is the dominant power dissipation mechanism in this region, the maximum efficiency of power dissipation in the DRX domain is generally about 30–40% for low stacking fault energy materials and the contours are widely spaced [17,18]. Another domain can be observed in the temperature range 1000–1150 ◦ C and strain rates lower than 0.01 s−1 . The efficiency is increasing with decreasing strain rate and increasing temperature in this domain. The superplasticity/wedge cracking processes are characterized by high efficiency of power dissipation and a steep rise in efficiency with decrease in strain rates. The low strain rate sensitivity under these conditions (m ≈ 0.24) confirms that any kind of flow instability and discontinuity like wedge cracking can be expected in this region. Other than these two domains all contours in the temperature range 900–1000 ◦ C and strain rate range 0.001–0.5 s−1 with efficiency values between 21 and 36% do not fall into the specific domains. These contours may be termed chaotic
Fig. 14. Flow instability map for Hastelloy X at a strain of 0.6.
trajectories and indicate a transient behavior where no stable microstructural mechanism occurs. However, in view of the low efficiency (21–27%) and temperature (900–950 ◦ C) inside the region, dynamic recovery is one of the active microstructural mechanisms. Prasad and Kalyan Kumar have developed a criterion for evaluating the regimes of flow instabilities [9]. The criterion is based on the continuum principles as applied to large plastic flow proposed by Ziegler [19] according to which instabilities occur when, ξ(˙ε) =
∂ ln(m/m + 1) + m < 0. ∂ ln ε˙
(11)
The ξ(˙ε)parameter may be evaluated as a function of temperature and strain rate to obtain an instability [10,20]. Material instability during hot deformation occurs in regimes where ξ(˙ε) is negative. The instability map developed using the criterion above is shown in Fig. 14. The map exhibits a regime of flow instability in the temperature range 900–950 ◦ C and strain rates lower than 0.001 s−1 ; the manifestation of which is in the form of adiabatic shear bands. Another narrow regime of flow instability occurs at 900 ◦ C and strain rates higher than 0.01 s−1 which indicate the formation of shear bands. The prediction has a fair agreement with experimental observation presented in Fig. 12. 4. Conclusions Hot compression experiments have been performed on Hastelloy X superalloy in the temperatures between 900 and 1150 ◦ C and strain rates of 0.001, 0.01, 0.1 and 0.5 s−1 . By means of stress–strain curves the flow stress behavior and workability of this alloy has been studied. The following conclusions are drawn from this study.
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- Dynamic recovery occurs at low temperatures while dynamic recrystallization mainly occurs at temperature of 1050 ◦ C and strain rates of 0.001–0.5 s−1 . However, adiabatic heating effect caused by hot deformation at high strain rates stimulates DRX at low temperatures. - The power dissipation map for Hastelloy X exhibits two domains. One domain in the strain rate range 0.01–0.1 s−1 and temperature range 1050–1150 ◦ C with a peak efficiency of 36% represents DRX. The second domain in the temperature range 1000–1150 ◦ C and strain rates lower than 0.01 s−1 , can be interpreted as wedge cracking area. - The workability indexes, m and γ values decreased by strain. In addition, the strain rate sensitivity of the alloy is not constant at the employed temperature range and shows an increase by increasing temperature in the range of 900–1150 ◦ C. Therefore, it is expected that at higher temperatures the workability would be improved. - Calculation of flow localization parameter and construction of instability map showed that at temperatures between 900 and 950 ◦ C and different strain rates, the formation of severe flowlocalized region is quite possible. However, the prediction made by flow localization parameter had a better agreement with experimental observations. References [1] N.K. Park, I.S. Kim, J. Mater. Proc. Tech. 111 (2001) 98–102. [2] J. Liu, G. Liul, B. Hu, Y. Song, Z. Qin, Y. Zhang, J. Univ. Sci. Tech. Beijing 13 (2006) 319–323.
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