Abstract
A series of uniaxial tensile tests were carried out at different strain rate and different temperatures to investigate the effects of temperature and strain rate on tensile deformation behavior of P92 steel. In the temperature range of 30–700 °C, the variations of flow stress, average work-hardening rate, tensile strength and ductility with temperature all show three temperature regimes. At intermediate temperature, the material exhibited the serrated flow behavior, the peak in flow stress, the maximum in average work-hardening rate, and the abnormal variations in tensile strength and ductility indicates the occurrence of DSA, whereas the sharp decrease in flow stress, average work-hardening rate as well as strength values, and the remarkable increase in ductility values with increasing temperature from 450 to 700 °C imply that dynamic recovery plays a dominant role in this regime. Additionally, for the temperature ranging from 550 to 650 °C, a significant decrease in flow stress values is observed with decreasing in strain rate. This phenomenon suggests the strain rate has a strong influence on flow stress. Based on the experimental results above, an Arrhenius-type constitutive equation is proposed to predict the flow stress.
Introduction
Recently, the growing demand of energy conservation and environmental protection has driven the development of the new generation nuclear power technology. As one of the most promising fission nuclear reactors in generation Ⅳ nuclear power plant, super-critical water-cooled reactor (SCWR) is proposed by several countries [1, 2]. For this next generation nuclear reactor, the structural material operating at high temperature under service stress needs to have excellent mechanical properties, oxidation resistance and irradiation resistance [3]. ASME grade 92 steel (9Cr-0.5Mo-1.8W-VNb) previously developed for ultra-supercritical power plants has been recognized as one of the candidates for the structural components of the new generation nuclear reactors, such as reactor vessels and pipes [4, 5].
In the past decades, a series of studies have been carried out to investigate the effect of temperature and stress on the mechanical properties, creep, low-cycle fatigue, and creep-fatigue behavior of T/P92 steel [6, 7, 8, 9, 10, 11, 12, 13, 14], and large amounts of data are available. Compared with the service temperature of ultra-supercritical power plants, this material used for SCWR exposes to lower temperature, but the service environment is more complex due to the irradiation. Meanwhile, several studies have found that T/P91 steel exhibits serrated flow behavior at intermediate temperature (250–450 °C) which indicates the occurrence of Portevin-Le Chatelier (PLC) effect [15, 16]. As is well-known, this effect gives rise to the degradation of mechanical properties, such as reduction in fracture toughness, the loss of ductility and decrease in fatigue life. Because T/P92 steel is developed from T/P91 steel by a reduction of Mo from 1 to 0.5 % and an addition of 1.8 %W, it is necessary to study the PLC effect of T/P92 steel due to plastic instability during the plastic deformation at intermediate temperature. At present, few attempts have been concentrated on the effect of temperature and strain rate on the tensile deformation behavior of P92 steel. Additionally, the PLC effect of P92 steel has not been fully understood.
Therefore, a series of uniaxial tensile tests were carried out to systematically investigate the influence of temperature and strain rate on the tensile properties of P92 steel. Moreover, the micro-mechanism of the occurrence of PLC effect was discussed in the following section. Based on the experimental results above, an Arrhenius-type constitutive equation was proposed.
Experimental procedures
The P92 steel, 390 mm diameter, 70 mm wall thickness pipe, was investigated in the study. The pipe was normalized at 1,070 °C, followed by tempering at 760 °C. The chemical composition of the material is shown in Table 1. The tensile specimens were machined from the pipe along longitudinal axial direction. The gauge length and diameter of the standard push-pull cylindrical specimens were 30 mm and 5 mm.
Chemical composition (wt%) of the steel studied.
| C | Mn | P | S | Si | Cr | W | Mo | V | Nb | N | B | Ni | Al |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0.114 | 0.392 | 0.011 | 0.004 | 0.315 | 9.21 | 1.93 | 0.475 | 0.189 | 0.073 | 0.037 | 0.003 | 0.275 | 0.011 |
All the tensile tests were performed with an INSTRON 5869 vertical tensile testing machine equipped with a three-zone temperature control furnace. The temperatures in all the tests were controlled within ± 1 °C. In order to investigate the effect of temperature on the tensile properties of P92 steel, a series of tensile tests were performed over a temperature range of 30–700 °C at the strain rate of 5×10−5 s−1. Furthermore, some tensile tests were carried out at high temperature (550–650 °C) in the strain rate range of 1×10−5 s−1 to 1×10−3 s−1. During the tests, 0.2 % proof stress (σys) and Young’s modulus value (E) were measured when the specimens were pulled to the strain level of 1 % in the first phase controlled by strain mode. This initial strain rate was controlled by an extensometer. In the second phase, these specimens controlled by displacement mode were pulled up to fracture to determine the ultimate tensile strength (σult) and the elongation (δ). Meanwhile, the stress–strain plots were recorded continuously in a computer.
A transmission electron microscopy (TEM) sample was examined to reveal the typical microstructure in the initial state using JEOL JEM-2010. This sample was first mechanically thinned to 0.1 mm, and then thinned down to 60 μm or less using emery paper before further thinning using GATAN PIPS-691.
Results and discussion
Microstructure of as-received material
Figure 1 shows TEM images of the initial state of P92 steel. It can be seen in Figure 1(a) that the steel exhibits a pronounced tempered martensitic matrix which is composed of some elements at several scales: prior austenite grains, packet of blocks, block of laths, martensitic laths and subgrains. In addition, these boundaries and subgrain boundaries are decorated by M23C6 carbide precipitated mainly along prior austenite grain boundaries and subgrain boundaries and MX carbonitrides distributed in grain interior; the initial dislocation density inside the subgrains is very high, as shown in Figure 1(b).
TEM micrographs of the initial state of P92 steel: (a) the pronounced tempered martensitic matrix and (b) high density of dislocation.
Effect of temperature on tensile stress–strain behavior
The engineering stress–strain curves
The engineering stress–strain curves of P92 steel at the strain rate of 5×10−5 s−1 at the temperature in the range of 30–700 °C are investigated in the present study, and some serrations are observed on the stress–strain plot. Figure 2 represents the typical segments of stress–strain curves exhibited in arbitrary unit at the strain rate of 5×10−5 s−1 for the temperature ranging from 200 to 400 °C. As one of the most important characteristics, the emergence of serrated flow indicates the occurrence of PLC effect. At present, it is widely accepted that the physical origin of this effect is attributed to dynamic strain aging (DSA). Given the scattering of the force measurement, stress oscillations under 5 MPa are not regarded as DSA serrations. Based on the criterion, the critical temperature for the onset of DSA is identified to be around 250 °C, whereas DSA serrations are not noticed at 30 °C and 200 °C. Moreover, the intensity of serrations increases with increasing temperature ranging from 250 to 450 °C. For this temperature range, it is obvious that the intensity of serrations is found to be strongly dependent on temperature which is manifested by the height of serrations, as seen in Figure 2. The magnitude of the stress drop increases with increasing temperature. This phenomenon could be explained by DSA. As reported by many researchers [17, 18, 19], DSA is governed by the dragging of solute atoms at the mobile dislocation which is arrested by the obstacles, such as forest dislocation and grain boundaries. Due to the increase of the friction stress caused by the dragging of solute atoms, the mobile dislocation is pinned by the solute atoms. However, when the tensile stress increases, owing to the increase of the velocity of mobile dislocation, the atmosphere of solute atoms is peeled off from mobile dislocation. Then, the tensile stress is decreased because of the reduction of the friction stress. Meanwhile, the dislocation velocity is decreased by the reduction of the tensile stress. So the solute atmosphere is formed again around dislocation which is pinned by the solute atoms. This cyclically dragging of solute atoms process induces the serration on the stress–strain curves. It is well-known that the diffusion of solute atoms can be accelerated by the increase of the temperature which leads to larger numbers of solute atoms to diffuse to the dislocation. It increases the strength of solute locking with increasing temperature. So the intensity of serrations increases with increase of the temperature ranging from 250 to 450 °C. When the temperature exceeds 450 °C, the serration amplitude reduces gradually. This indicates the progressive disappearance of the DSA, and the occurrence of dynamic recovery at high temperature.
Segments of engineering stress–strain curves of P92 steel obtained from tensile tests at three different temperatures at the strain rate of 5×10−5 s−1.
The variation of flow stress with temperature
Figure 3 shows the typical true stress (σt) – true plastic strain (εp) curves of P92 steel at strain rate of 5×10−5 s−1 in the temperature range of 30–700 °C, which is expressed in the double logarithmic plots. From all the curves above, it is worth noting that σt−εp curves fall into a very narrow band at low and intermediate temperature in the range of 30–450 °C, and then a rapid decrease in stress values is observed with increase of the temperature over 500 °C. This result is similar to the findings investigated by Kimura et al. [20].
True stress–true plastic strain curves of P92 steel at strain rate of 5×10−5 s−1.
In order to understand the variation of flow stress with temperature, normalized flow stress versus temperature plot at different plastic strain, such as 0.001, 0.002, 0.005, 0.01, 0.02 and 0.05, is presented in Figure 4, where temperature-dependent Young’s modulus value (E) is used in this normalized procedure. It is visible from Figure 4 that there are three pronounced temperature regimes. For the temperature ranging from 30 to 200 °C, the normalized flow stress displays a slight decrease in regime I. As is well-known, the plastic deformation of the steel is linked to the motion of the dislocation. At low temperature, the motion of the dislocation is quite difficult, due to a large friction stress by reason of the Peierls valley. However, this friction stress can be overcome by increasing temperature. Thus, a marginal decrease in flow stress is observed for this temperature range. In regime II, a stress peak is observed at intermediate temperature, and this abnormal phenomenon could be explained by DSA. It has been demonstrated above the dragging of solute atoms hinders the motion of the mobile dislocation which is temporarily arrested by the obstacles. In this regime, the increasing temperature promotes faster diffusion of solute atoms, so the additional pinning effect is produced. This results in a larger solute atmosphere around the dislocation which delays in the recovery of dislocation. Meanwhile, owing to the dislocation pile-up and tangling, dislocation annihilation rate decreases with increasing temperature from 250 to 450 °C. Therefore, the increase of flow stress is observed in this regime. In regime III, a rapid decrease in flow stress is observed with increasing temperature in the range of 500–700 °C. It indicates the dynamic recovery taking place at high temperature. This dynamic recovery is associated with the decrease in dislocation density, and formation of well-defined dislocation subgrain with increasing temperature [21].
Variations of normalized flow stress at different true plastic strain with temperature at strain rate of 5×10−5 s−1.
The effect of temperature on average work-hardening rate
Figure 5 shows the variation of normalized average work-hardening rate (θa) with respect to temperature at strain rate of 5×10−5 s−1. Here, the average work-hardening rate is calculated as:
where σ0.002 and σ0.02 are true plastic stress at true plastic strain of 0.002 and 0.02, respectively. Just as the variation of flow stress with respect to temperature, the effect of temperature on the average work-hardening rate also exhibits three temperature regimes. A slight decrease in the normalized average work-hardening rate is observed in regime I followed by the continuous rise with increasing temperature from 250 to 450 °C. Then, the normalized average work-hardening rate values decrease significantly when the temperature exceeds 500 °C. Generally speaking, the normalized average work-hardening rate decreases with the increase of the temperature due to the increase of the recovery with increasing temperature. So θa – T data show a marginal decrease at low temperature. At intermediate temperature, because of the occurrence of DSA, or more precisely, the interaction between the solute atoms and the dislocation, it enhances the average work-hardening rate of the material. Therefore, the upward trend in the normalized average work-hardening rate occurs within the DSA regime, and the value of the average work-hardening rate reaches the maximum. At high temperature, θa – T curve shows a significant decrease with increasing temperature from 500 °C, and it implies that the dynamic recovery plays a dominant role in this regime.
Variations of normalized average work-hardening rate with temperature at strain rate of 5×10−5 s−1.
The variation of tensile properties with temperature
The influence of temperature on normalized yield strength and ultimate tensile strength is shown in Figure 6(a). It can be seen that the variations of yield strength and ultimate tensile strength with temperature are also composed of three temperature regimes. A decrease in normalized yield strength and ultimate tensile strength is observed with increase of the temperature in the range of 30–200 °C in regime I followed by a continuous increase at intermediate temperature in regime Ⅱ (250–450 °C). In regime II, it gives rise to a peak value with increase of the temperature, which confirms the occurrence of DSA in this material. At intermediate temperature, the observed normalized yield strength and ultimate tensile strength increase with increasing temperature from 250 to 450 °C, which reflects an increase in the deformation resistance in the DSA temperature regimes. The increase is attributed to enhancing of the diffusion of solute atoms with increasing temperature in the DSA regime. So the solute atoms have sufficient mobility to pin the dislocation, and it results in the trend of the increase of DSA and the reduction of dynamic recovery. However, the normalized yield strength and ultimate tensile strength decrease rapidly at high temperature in regime Ⅲ (500–700 °C), it suggests that dynamic recovery plays a vital role in this regime.
Variations of tensile properties with temperature: (a) normalized yield stress and normalized ultimate tensile stress; (b) elongation; (c) reduction in area.
Compared with the regular variation of yield strength and ultimate tensile strength with temperature, the variation of elongation to fracture (δ) and reduction of area (φ) do not exhibit a good consistency, as shown in Figure 6(b) and (c). The experimental data of both parameters have a certain degree of fluctuation, which may be due to the experimental measurement errors. A general δ−T curve or φ−T curve is comprised of three temperature regimes, where the literature data is also exhibited in order to compare with each other [20, 21]. The variation of elongation to fracture with temperature exhibits a significant decrease with increasing temperature in the range of 30–200 °C in regime Ⅰ, whereas reduction of area shows a small decrease in this regime. In regime Ⅱ, there is a slight decrease in elongation to fracture and reduction of area with increase of the temperature in the range of 250–450 °C, and a pronounced increase is noticed at high temperature (500–700 °C) in regime Ⅲ. It is worth noting that this material shows lower ductility in regime Ⅱ, compared with regime Ⅰ(low temperature) and regime Ⅲ (high temperature). At intermediate temperature, the ductility decreases to the minimum.
The strain sensitivity of P92 steel at high temperature
Figure 7 shows the typical true stress (σt) – true plastic strain (εp) curves of P92 steel at different strain rate (1×10−5 s−1 to 1×10−3 s−1) in the temperature range of 550–650 °C. It can be seen from Figure 7 the flow stress of P92 steel exhibits strong sensitivity to temperature, strain rate and strain, which can be attributed to the thermal softening, strain rate hardening and strain hardening. It is worth noting that the strain rate sensitivity of P92 steel is obvious at all the temperatures. Moreover, a significant decrease in flow stress values is observed with decreasing in strain rate.
True stress–true plastic strain curves of P92 steel obtained from tensile tests at different strain rate and temperatures of (a) 550 °C; (b) 600 °C; (c) 650 °C.
The constitutive equation
In order to understand the effects of temperature and strain rate on flow stress in P92 steel, the constitutive equation is used to define the flow stress as a function of temperature and strain rate. The most widely used constitutive equation can be expressed as:
where
Taking logarithms on both sides of eq. (2) gives
From eq. (3), the stress exponent n is defined by
Hence, the stress exponent n is determined by the slope coefficients of ln
Plots used for calculation of (a) n, (b) and (c) α, (d) Q values.
The activation energy Q can be expressed as:
Thus, the activation energy Q can be determined by slope of ln[sinh(ασ)] versus (1/T) plot, as exhibited in Figure 8(d). Meanwhile, lnA is 0.41 by calculation through the linear extrapolation method. Therefore, the constitutive equation can be written as:
In this constitutive equation, it is worth noting that the value of stress exponent (n) and activation energy (Q) may be relatively small compared with that in other investigations [7, 22]. This result may result from the different manufacturing technology between the thick-walled pipe with large diameter and thin-walled tube with small diameter. In the present study, a pipe with the diameter of 390 mm and the thickness of 70 mm was used for the tests, whereas other investigations commonly used thin-walled tubes. Due to the difficulty of manufacturing technology of thick-walled pipes, there are some differences between the experimental results. In addition, because the experimental material comes from different manufacturers with various chemical compositions and heat treatment procedures, all the factors may also result in these differences between the experimental parameters.
Figure 9 shows the comparison of the predicted and experimental values of
Comparison of the predicted values and the experimental values of σε = 0.1 % at different strain rate.
Conclusions
A series of tensile tests were carried out at different strain rate and different temperatures to investigate the effects of temperature and strain rate on tensile deformation behavior of P92 steel. Additionally, an Arrhenius-type constitutive equation is proposed to understand the influence of temperature and strain rate on flow stress in P92 steel. Based on the experimental results above, the main conclusions are as follows:
In the temperature range of 30–700 °C, the variations of flow stress, average work-hardening rate, tensile strength and ductility with temperature all exhibit three temperature regimes.
At intermediate temperature, the material exhibited the serrated flow behavior, the peak in flow stress, the maximum in average work-hardening rate, and the abnormal variations in tensile strength and ductility indicates the occurrence of DSA. These phenomena are attributed to the interaction between the solute atoms and the dislocation in the DSA regime. At high temperature, the sharp decrease in flow stress, the average work-hardening rate and strength values, and the remarkable increase in ductility values with increasing temperature from 450 to 700 °C imply that dynamic recovery plays a dominant role in this regime.
The strain rate sensitivity of P92 steel is obvious in the temperature range of 550–650 °C. Moreover, a significant decrease in flow stress values is observed with decreasing in strain rate.
An Arrhenius-type constitutive equation is proposed to predict the flow stress as a function of temperature and strain rate. The result shows that the predicted values are consistent with the experimental values.
Funding statement: The authors gratefully acknowledge the support provided by the innovation program for graduate students in JiangSu Province of China (No. KYLX15_0800) and the innovation foundation of Inner Mongolia University of Science and Technology (No. 2014QDL023).
References
[1] P. Saha, N. Aksan, J. Andersen, J. Yan, J.P. Simoneau, L. Leung, F. Bertrand, K. Aoto and H. Kamide, Nucl. Eng. Des., 264 (2013) 3–23.10.1016/j.nucengdes.2012.07.023Search in Google Scholar
[2] S.E. Langton, A. Buijs and J. Pencer, Ann. Nucl. Energy, 75 (2015) 635–644.10.1016/j.anucene.2014.09.017Search in Google Scholar
[3] R.W. Grimes, R.J.M. Konings and L. Edwards, Nature Mater., 7 (2008) 683–685.10.1038/nmat2266Search in Google Scholar PubMed
[4] S.X. Jin, L.P. Guo, T.C. Li, J.H. Chen, Z. Yang, F.F. Lu, R. Tang, Y.X. Qiao and F.H. Liu, Mater. Charact., 68 (2012) 63–70.10.1016/j.matchar.2012.03.009Search in Google Scholar
[5] T. Abram and S. Ion, Energy Policy, 36 (2008) 4323–4330.10.1016/j.enpol.2008.09.059Search in Google Scholar
[6] P.F. Giroux, F. Dalle, M. Sauzay, J. Malaplate, B. Fournier and A.F.G. Lorenzon, Mater. Sci. Eng. A, 527 (2010) 3984–3993.10.1016/j.msea.2010.03.001Search in Google Scholar
[7] S. Alsagabi, T. Shrestha and I. Charit, J. Nucl. Mater., 453 (2014) 151–157.10.1016/j.jnucmat.2014.06.033Search in Google Scholar
[8] J.S. Lee, H.G. Armaki and K. Maruyama, Mater. Sci. Eng. A, 428 (2006) 270–275.10.1016/j.msea.2006.05.010Search in Google Scholar
[9] F. Abe, Curr. Opin. Solid State Mater. Sci., 8 (2004) 305–311.10.1016/j.cossms.2004.12.001Search in Google Scholar
[10] F. Abe, T. Horiuchi, M. Taneike and K. Sawada, Mater. Sci. Eng. A, 378 (2004) 299–303.10.1016/j.msea.2003.11.073Search in Google Scholar
[11] V. Sklenicka, K. Kucharova, M. Svoboda, L. Kloc, J. Bursik and A. Kroupa, Mater. Charact., 51 (2003) 35–48.10.1016/j.matchar.2003.09.012Search in Google Scholar
[12] B. Fournier, F. Dalle, M. Sauzay, J. Longour, M. Salvi, C. Caës, I. Tournié, P.F. Giroux and S.H. Kim, Mater. Sci. Eng. A, 528 (2011) 6934–6945.10.1016/j.msea.2011.05.046Search in Google Scholar
[13] K.X. Shi, F.S. Lin, H.B. Wan and Y.F. Wang, Mater. High Temp., 31 (2014) 343–347.10.1179/0960340914Z.00000000050Search in Google Scholar
[14] B. Fournier, M. Salvi, F. Dalle, Y.D. Carlan, C. Caës, M. Sauzay and A. Pineau, Int. J. Fatigue, 32 (2010) 971–978.10.1016/j.ijfatigue.2009.10.017Search in Google Scholar
[15] C. Keller, M.M. Margulies, Z.H. Hamouche and I. Guillot, Mater. Sci. Eng. A, 527 (2010) 6758–6764.10.1016/j.msea.2010.07.021Search in Google Scholar
[16] T. Sakthivel, K. Laha, M. Nandagopal and M.D. Mathew, Mater. High Temp., 31 (2014) 60–68.10.1179/0960340913Z.0000000008Search in Google Scholar
[17] M.A. Lebyodkin, N.P. Kobelev, Y. Bougherira, D. Entemeyer, C. Fressengeas, V.S. Gornakov, T.A. Lebedkina and I.V. Shashkov, Acta Mater., 60 (2012) 3729–3740.10.1016/j.actamat.2012.03.026Search in Google Scholar
[18] H. Aboulfadl, J. Deges, P. Choi and D. Raabe, Acta Mater., 86 (2015) 34–42.10.1016/j.actamat.2014.12.028Search in Google Scholar
[19] Q.C. Zhang, Z.Y. Jiang, H.F. Jiang, Z.J. Chen and X.P. Wu, Int. J. Plast., 21 (2005) 2150–2173.10.1016/j.ijplas.2005.03.017Search in Google Scholar
[20] K. Kimura, K. Sawada, H. Kushima and K. Kubo, Int. J. Mater. Res., 99 (2008) 395–401.10.3139/146.101651Search in Google Scholar
[21] B.K. Choudhary, E.I. Samuel, G. Sainath, J. Christopher and M.D. Mathew, Metall. Mater. Trans. A, 44 (2013) 4979–4992.10.1007/s11661-013-1869-6Search in Google Scholar
[22] K. Kimura, H. Kushima and K. Sawada, Mater. Sci. Eng. A, 510–511 (2009) 58–63.10.1016/j.msea.2008.04.095Search in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
