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Competing damage mechanisms in the thermo-mechanical fatigue of AISI 304L stainless steel
Materials Science and Engineering A 529 (2011) 417–424
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Competing damage mechanisms in the thermo-mechanical fatigue of AISI 304L stainless steel Keun-Ho Bae, Hyun-Ho Kim, Soon-Bok Lee ∗ Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 January 2011 Received in revised form 28 June 2011 Accepted 7 September 2011 Available online 17 September 2011 Keywords: Thermo-mechanical fatigue Phase difference Creep Dynamic strain aging
a b s t r a c t Thermo-mechanical fatigue (TMF) in AISI 304L stainless steel is investigated in two temperature ranges using four phase differences between the mechanical loading and the temperature. In the temperature range from 450 ◦ C to 700 ◦ C, the fatigue life was lowest in the in-phase condition. However, in the temperature range from 400 ◦ C to 650 ◦ C, the minimum fatigue life occurs in the counter-clockwise-diamond condition. Estimation of creep strains occurring in the TMF cycle based on the monotonic creep tests predicts the highest creep strains in the in-phase conditions in the two temperature ranges, but cannot explain the minimum life in the counter-clockwise-diamond condition in the lower temperature range. This phenomenon is explained qualitatively by the operation ranges of dynamic strain aging and the creep of this material and their competition in the TMF cycle. This explanation predicts the highest influence of the creep in the counter-clockwise-diamond condition in the temperature range of 400–650 ◦ C. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Austenitic stainless steels are commonly used for applications at elevated temperatures, such as those of nuclear power plants, automobiles and gas turbine systems, because they have good oxidation resistance in addition to high ductility and toughness. AISI 304 is one of the most widely used stainless steels as a construction material in nuclear reactor systems. Many researchers have investigated AISI 304 and AISI 304L at elevated temperatures, studying factors such as the behavior under monotonic loading [1], under low-cycle fatigue (LCF) conditions [1–3], under creep conditions [4,5] and under thermo-mechanical fatigue conditions [6–8]. In thermo-mechanical fatigue environments, materials experience various damaging mechanisms, such as fatigue, creep, dynamic strain aging, and oxidation, simultaneously or independently depending on the testing conditions. Dynamic strain aging is caused by the interaction between the moving dislocations and obstacles such as solute atoms, which hinders the movement of dislocations. In austenitic stainless steels it has been suggested that carbon-vacancy pairs and clusters of carbon atoms interact with gliding dislocations [9,10] at temperatures below 400 ◦ C. When the temperature exceeds 400 ◦ C, chromium atoms become more active and interfere with moving dislocations [1,11,12]. It is well known from low-cycle fatigue tests of AISI 304 that dynamic strain aging (DSA) induces the maximum stress
amplitude [1–3,11]. The temperature at which the peak of the stress amplitude occurs due to DSA is reportedly 400 ◦ C [1], 470 ◦ C [2], 525 ◦ C [13], and 550 ◦ C [14] depending on the heat treatment of the AISI 304L. The creep behavior of this steel is also known to be greatly influenced by the heat treatment under investigation [15,16]. This is reportedly due to the different degrees of microporosity or inclusions caused by differences in the production conditions, as well as deviations in the concentrations of the composition and any additional elements. Due to these variations very different creep curves are observed. In some works a steady state creep behavior (secondary creep) has been reported [15–17], whereas in other studies no region with a constant creep rate was noted. In the latter case, a steady state creep rate is frequently approximated by the minimum creep rate [18]. The stress exponent n is usually employed to characterize the dependence of the creep rate on the stress. Zauter et al. [4] reported a value of 10.4 (±0.9) from stress change experiments conducted at a temperature of 650 ◦ C and the value of 7.7 from constant stress tests in a stress range of 150–250 MPa. In this research, thermo-mechanical fatigue tests of AISI 304L are performed using two different temperature intervals with four different phase differences between the mechanical loading and the temperature. In addition, dynamic strain aging and creep behaviors are investigated to explain the behavior of the TMF results. 2. Experimental procedure
∗ Corresponding author. Tel.: +82 42 350 3029; fax: +82 42 350 5028. E-mail address: [email protected] (S.-B. Lee). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.09.054
AISI 304L stainless steel is used in this research. In addition to thermo-mechanical fatigue tests, tensile, low-cycle fatigue and
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K.-H. Bae et al. / Materials Science and Engineering A 529 (2011) 417–424
Fig. 1. Specimen for the thermo-mechanical fatigue test (dimensions in mm).
creep tests are performed to obtain the basic properties of the material. A tensile specimen with a gauge length of 36 mm and a diameter of 6 mm as well as a low-cycle fatigue specimen with a gauge length of 20 mm and a diameter of 8 mm were designed as smooth
cylindrical specimens according to the ASTM E606-92 specifications. The tensile specimen was also used in the creep tests. A specimen for the thermo-mechanical fatigue test was designed as a hollow specimen with a gauge length of 20 mm, an outer diameter of
Fig. 2. Schematic illustration of the variety of phase differences between the temperature and mechanical strain.
K.-H. Bae et al. / Materials Science and Engineering A 529 (2011) 417–424
419
Fig. 4. Relationship between the thermo-mechanical fatigue life and the phase difference in the temperature range of 450–700 ◦ C (a) at εme /2 = 0.6% and (b) at εme /2 = 0.8%.
Fig. 3. Relationship between the thermo-mechanical fatigue life and the phase difference in the temperature range of 400–650 ◦ C (a) at εme /2 = 0.6% (b) at εme /2 = 0.8% and (c) at εme /2 = 1.0%.
8 mm, and an inner diameter of 4 mm to improve the uniformity of the temperature distribution. The TMF specimen is shown in Fig. 1. A closed loop servo hydraulic system with a 10 ton capacity was used in all of the tests. An induction heater and a K-type thermocouple were used to control the temperature. The strain was measured by a spring-loaded high-temperature extensometer. The tensile tests were performed under a displacement control of 4.8 mm/min, which is translated approximately as 0.2%/s in terms
of the strain rate at from room temperature to 700 ◦ C with 100 ◦ C intervals. The low-cycle fatigue tests were performed under strain control of 2 × 10−3 /s at temperatures ranging from room temperature to 800 ◦ C with 100 ◦ C intervals, except for at 100 ◦ C. The total strain was controlled to strain settings of ±0.6, 0.8, 1.0, and 1.2%. Thermo-mechanical fatigue tests were performed in two temperature ranges; from 400 ◦ C to 650 ◦ C and from 450 ◦ C to 700 ◦ C, with a heating and cooling rate of 5 ◦ C/s. The total strain range, which is the summation of the mechanical strain range and thermal expansion strain range, was controlled. Three different mechanical strain ranges (εme /2 = 0.6%, 0.8%, 1.2%) were then tested in the 400–650 ◦ C temperature range while two mechanical strain ranges (εme /2 = 0.6%, 0.8%) were tested in the 450–700 ◦ C temperature range. Four different phase differences with given temperatures and the mechanical strains were investigated to determine the effects of the phase difference on the thermo-mechanical fatigue behavior and the lifespan. The four phase differences were in-phase (IP, 0◦ phase difference), out-of-phase (OP, 180◦ phase difference), clockwise-diamond-phase (CD, 90◦ phase difference), counterclockwise-diamond-phase (CCD, 270◦ phase difference) as shown in Fig. 2. More than 20 thermal cycles were run under zero-load control and the last three cycles were averaged to create the thermal strain expansion data file. The accuracy of the expansion file was checked via a zero-stress test. Both the TMF life and the lowcycle fatigue life were determined at the point where a drop in the stress of 10% of the maximum load was measured.
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Fig. 6. Variation of the cyclic hardening exponent as a function of the temperature.
Fig. 5. Characteristics of the tensile behavior as a function of the temperature: (a) stress–strain curves, (b) elongations, and (c) ultimate tensile strengths.
3. Results and discussion 3.1. Thermo-mechanical fatigue Figs. 3 and 4 show the relationships between the thermomechanical fatigue life and the phase difference under different testing conditions. Fig. 3 shows the results for the temperature range of 400–650 ◦ C. The minimum fatigue life was observed at
Fig. 7. TEM micrographs at εt /2 = 0.8% and 400 ◦ C.
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Fig. 8. Relationship between the temperature-compensated minimum creep rate (Zener–Hollomen parameter) and the applied stress.
the phase difference of 270◦ in all cases. Fig. 4 shows the results for the temperature range of 450–700 ◦ C. Here, in contrast to the 400–650 ◦ C range, the in-phase cases show the minimum fatigue life. It is clear that there is a difference in the damage mechanisms between the temperature ranges of 400–650 ◦ C and 450–700 ◦ C; this will be exploited further in terms of creep and dynamic strain aging later in this paper. 3.2. Dynamic strain aging The occurrence of DSA can be manifested by anomalous features of material behavior. While serrated yielding is the most commonly observed manifestation of DSA, there are various types of concurrent phenomena. Other anomalies associated with DSA have been described by Rodriguez [19]; during monotonic tensile deformation, DSA is manifested by a serrated flow in the stress–strain curve, a peak or plateau in the variation of the material strength with the temperature, the minima in the variation of the ductility with the temperature, a peak in the variation of the work hardening value, a peak in the variation of the Hall–Petch slope with the temperature, and finally negative strain-rate sensitivity (SRS). Hong et al. [20,21] investigated the effects of DSA on the fatigue behavior and life. Fig. 5 shows the characteristics of the tensile behavior. In Fig. 5(b) and (c) which depicts the variations of the elongation and the ultimate tensile strength as a function of the temperature, anomalies induced by DSA are clearly shown. Fig. 5(b) shows the minimum value, while Fig. 5(c) shows a plateau around 400 ◦ C. Fig. 6 shows another anomaly associated with DSA. The value of the cyclic hardening exponent (n ) reaches a maximum at 400 ◦ C. These are typical manifestations of DSA. From these observations it is reasonable to assume that the influence of DSA is strongest at 400 ◦ C and that its operation range is from 300 ◦ C to 500 ◦ C. It is important to note that this material does not show any clear serration in the tensile stress–strain curves. Though serration was not observed, the planar structures of the dislocations were observed, as shown in Fig. 7. Fig. 7 shows transmission electron microscopy (TEM) images from the low-cycle fatigue test at εt /2 = 0.8% and 400 ◦ C. The planar arrangements of the dislocations are clear evidence of DSA. Similar layer/wall structures of dislocations in the DSA regime were reported [22,23]. 3.3. Creep Hostinsky´ et al. [24] investigated the creep and creep fracture behavior of AISI 304L at temperatures ranging from 773 K to 1073 K
Fig. 9. Estimated creep strains when (a) 450–700 ◦ C, εme /2 = 0.6%, (b) 450–700 ◦ C, εme /2 = 0.8%, and (c) 400–650 ◦ C, εme /2 = 1.0%.
and applied stresses ranging from 73 MPa to 490 MPa. The relationship between the minimum creep rate and the applied stress was found to be curved in a double logarithmic plot. The apparent activation energy of creep, Qc = [∂ ln ε˙ m /∂(−1/RT )] (T is the temperature and R is the gas constant) was found to decrease as the stress increases: Qc (kJ mol−1 ) = (459 ± 82) − (0.021 ± 0.010). The applied stress sensitivity parameter of the minimum creep rate,
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Fig. 10. Schematic diagrams showing the DSA region (dotted lines) at (a) 400–650 ◦ C and (b) 450–700 ◦ C.
Table 1 Experimental results of the constant stress creep tests. Temperature (◦ C)
Stress (MPa)
Steady or minimum strain rate (%/s)
700 700 700 700 600 600 500 400
281 211 140 70 282 353 388 424
0.0958 0.0053 2.18E−4 9.61E−7 9.34E−5 0.00341 7.31E−7 1.8E−6
Z = ε˙ m exp
m = (∂ ln ε˙ m /∂ ln )T was found to decrease as the temperature increases: m = (9.5 ± 2.2) − (0.003 ± 0.002)T. Table 1 shows the experimental results of the constant stress creep tests of this material. The temperature-compensated minimum creep rate, so known as Zener–Hollomen parameter, was used to correlate the creep rate to the applied stress. Z = ε˙ m exp
Q av c
RT
Here R is the gas constant and Qcav is the average weighted value of Qc , which is assumed to be 366 kJ mol−1 , as in an earlier study [5]. The Zener–Hollomen parameter is plotted as a function of the applied stress in Fig. 8 and its fitting curve is shown as a solid line. Because d ln Z/d ln = (∂ ln ε˙ m /∂ ln )T , it follows from Fig. 8 ˇ et al. [5] also that m increases as the stress increases. Sustek reported a linear relationship between m and the applied stress. From the experimental results, it was found that
(1)
Q av c
RT
= A × (m0 +c)
where A is 100 s−1 MPa−1 , m0 is 4.81, and c is 0.0038 MPa−1 . Using this formula, the creep strain during the TMF cycle can be estimated. The estimated creep strains occurring during the TMF cycle are plotted in Fig. 9. In all conditions, in-phase (0◦ phase difference) cases produce the highest estimated creep strains. In comparison with Figs. 3 and 4, the estimated creep strains fittingly explain the TMF fatigue life when the temperature range is from 450 ◦ C to 700 ◦ C. The fatigue life is in inverse proportion to the creep strain and the minimum life in the in-phase case is explained by the highest creep strain. However, when the temperature range is from 400 ◦ C to 650 ◦ C, the estimated creep strains from the
Fig. 11. Schematic diagrams showing the DSA region (dotted lines) and creep region (solid lines) at 400–650 ◦ C.
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Fig. 12. Dislocation arrangements in the temperature range of 400–650 ◦ C (a) in-phase (0◦ phase difference), (b) clockwise-diamond phase (90◦ phase difference), (c) out-of-phase (180◦ phase difference), and (d) counter-clockwise-diamond phase (270◦ phase difference).
monotonic creep tests cannot explain the fatigue life. Here, the minimum fatigue life occurs in the counter-clockwise-diamond case (CCD, 270◦ phase difference), but the maximum creep strain estimated by the monotonic creep tests develops in the in-phase case. When the temperature range is from 450 ◦ C to 700 ◦ C, the creep is the most dominant damaging mechanism and explains the fatigue life, but when the temperature range is lowered by 50 ◦ C, the creep damage is not the only dominant mechanism; thus, more explanation is required. 3.4. Competition between DSA and creep In the temperature range from 400 to 650 ◦ C, DSA and creep are believed to be operating together because the DSA operation range of this material was 300–500 ◦ C and for austenitic stainless steels creep usually occurs above 550 ◦ C [25]. Although much research has been done on DSA and creep independently, less is known about the interaction between the two mechanisms. Here, qualitative modeling of the effect of the interaction between creep and DSA on the TMF life is attempted and verified by TEM micrographs.
Fig. 10 shows schematically the DSA operating regime based on the assumption that DSA occurs from 300 ◦ C to 500 ◦ C. The dotted lines indicate the region in the hysteresis loop where DSA is believed to be operating. Given that sufficient quantitative modeling of the DSA in non-isothermal conditions has not been done, it is not perfectly safe to assume that DSA occurs only in these designated regions. However, from the tensile and low-cycle fatigue results mentioned earlier, it is reasonable that these DSA regions have high probabilities of the occurrence of DSA. As shown in Fig. 10, when the temperature range is from 450 ◦ C to 700 ◦ C, the region of DSA is small and it is difficult to imagine that DSA has a large influence on the material behavior and lifespan. However, the region of DSA when the temperature range is 400–650 ◦ C is large and covers almost half of the hysteresis loop, thus affecting the material behavior and lifespan. In Fig. 11, creep regions are superimposed on the DSA region in Fig. 10(a) based on the assumption that creep occurs above 550 ◦ C. In the counter-clockwise-diamond case (CCD, 270◦ phase difference) most of the tensile part is the creep region and most of the compressive part is the DSA region. In the clockwise-diamond case (CD, 90◦ phase difference), the
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opposite holds true; the tensile part is the DSA region and the compressive part is the creep region. In the in-phase (IP, 0◦ phase difference) and the out-of-phase (OP, 180◦ phase difference) cases, the DSA and creep regions cover both the tensile and compressive parts. The difference in the IP and OP cases is that in the IP case, the creep region covers the tensile peak point, whereas in the OP case the DSA region covers the tensile peak point. The relative dominance between the DSA and creep can be assessed based on Fig. 11. The creep in the compressive part is well known to negate the creep effects in the tensile part, closing the cavities produced in the tensile part. By the same token, the CCD case is favorable for creep effects, as the compressive part is governed by the DSA, which hinders the movement of the dislocations, thus enhancing the irreversibility. In contrast, in the CD case, the compressive part is ruled by creep, erasing all creep effects, if any exist. In the IP and OP cases, creep regions exist in the tensile part, but the associated creep effects are partially negated by the creep region in the compressive parts. As the stress magnitude in the creep region is higher in the IP case than in the OP case, it is reasonable to assume that the creep dominance is greater in the IP than in the OP case, but this is also true for the recovery effects of the compressive part in the IP case. Therefore, an exact comparison is difficult to obtain. The relative dominance of creep over DSA is estimated as CCD IP ≥ OP CD. This estimation of the relative dominance of creep over DSA was verified by TEM micrographs, as shown in Fig. 12. A clear difference between the CCD and the other cases is observed. The CCD case shows equiaxed structures, whereas the other cases show more planar structures. Elongated or equiaxed dislocation arrangements are usually observed in the creep regime, whereas planar dislocation arrangements are observed in the DSA regime [20]. Though it is difficult to assess and compare the magnitudes of the influence of DSA or creep from Fig. 12(a), (c), and (d), these TEM micrographs are consistent with the previous qualitative prediction of the CCD case having the highest dominance of creep over DSA, also explaining the minimum fatigue life, in the CCD case shown in Fig. 3. 4. Conclusion This investigation of thermo-mechanical fatigue (TMF) tests of AISI 304L stainless steel at two temperature ranges, 400–650 ◦ C and 450–700 ◦ C, in addition to low-cycle fatigue, tensile, and creep tests, leads to the following conclusions: 1. Dynamic strain aging (DSA) occurs from 300 to 500 ◦ C based on the observations of the ultimate tensile strength, elongation, and cyclic hardening exponent. Serration, which is a typical
indication of DSA is not a good indicator here. The occurrence of DSA is verified by TEM micrographs. 2. In the temperature range from 450 ◦ C to 700 ◦ C, creep is the most dominant damaging mechanism; the TMF lifespan can be explained by the estimated creep strains from monotonic creep tests. 3. In the temperature range from 400 ◦ C to 650 ◦ C, the counterclockwise-diamond (CCD) case was found to be the most damaging, and TEM observations prove that only the counterclockwise-diamond condition induces creep-like dislocation arrangements, instead of the DSA-like dislocation arrangements observed in other conditions. 4. A simple qualitative explanation of the competition between creep and DSA is given comparing the operation ranges of creep and DSA based on assumptions that DSA occurs in the temperature interval from 300 ◦ C to 500 ◦ C and that creep occurs above 550 ◦ C; this predicts the highest creep effect in the CCD condition and, thus explains the minimum thermo-mechanical fatigue lifetime in this condition. References [1] [2] [3] [4] [5] [6] [7] [8]
[9] [10] [11] [12] [13]
[14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
K. Tsuzaki, T. Hori, T. Maki, I. Tamura, Mater. Sci. Eng. 61 (1983) 247–260. H. Abdel-Raouf, A. Plumtree, T.H. Topper, Metall. Trans. 5 (1974) 267–277. R. Koterazawa, T. Nosho, Fatigue Fract. Eng. Mater. Struct. 14 (1991) 1–9. R. Zauter, F. Petry, H.-J. Christ, H. Mughrabi, Mater. Sci. Eng. A 124 (1990) 125–132. ˇ V. Sustek, M. Pahutová, J. Cadek, Mater. Sci. Eng. A 177 (1994) 75–81. K. Kuwabara, A. Nitta, Fatigue Fract. Eng. Mater. Struct. 2 (1979) 293–304. S. Taira, M. Fujino, R. Ohtani, Fatigue Fract. Eng. Mater. Struct. 1 (1979) 495–508. G.R. Halford, M.A. McGraw, R.C. Bill, P.D. Fanti, in: H.D. Solomon, G.R. Halford, L.R. Kaisand, B.N. Lies (Eds.), Low Cycle Fatigue: Future Directions, ASTM STP 942, 1988, pp. 625–637. K.S.B. Rose, S.G. Glover, Acta Metall. 14 (1966) 1505–1516. C.F. Jenkins, G.V. Smith, TMS-AIME 245 (1969) 2149–2156. R. Zauter, F. Petry, H.-J. Christ, H. Mughrabi, in: H. Sehitoglu (Ed.), Thermomechanical Fatigue Behavior of Materials, ASTM STP 1186, 1993, pp. 70–90. K. Ohnishi, J. Ishizaka, J. Iron Steel Inst. Jpn. 63 (1977) 2362–2371. F. Petry, H.-J. Christ, H. Mughrabi, in: Microstructure and Mechanical Properties of Materials, Proc. DGM Symp., Bad Nauheim FRG, 1990, DGM Informations gesellschaft mbH, Oberursel, Germany, 1991, pp. 79–90. K.B.S. Rao, M. Valsan, R. Sandhya, S.L. Mannan, P. Rodriguez, Met. Mater. Process 2 (1990) 17–35. V.K. Sikka, H.E. McCoy Jr., M.K. Booker, C.R. Brinkman, ASME J. Press. Vessel Technol. 97 (1975) 243–252. R.W. Swindeman, K. Farrell, M.H. Yoo, Res. Mech. Lett. 1 (1981) 67–71. I.W. Chen, A.S. Argon, Acta Metall. 29 (1981) 1321–1333. P.J. Wray, O. Richmond, J. Appl. Phys. 39 (1968) 5754–5761. P. Rodriguez, Bull. Mater. Sci. 6 (1984) 653–663. S.G. Hong, K.O. Lee, S.B. Lee, Int. J. Fatigue 27 (2005) 1420–1424. S.G. Hong, S.B. Lee, Int. J. Fatigue 26 (2004) 899–910. R. Zauter, H.-J. Christ, H. Mughrabi, Metall. Trans. A 25A (1994) 407–413. S.-G. Hong, S.-B. Lee, J. Nucl. Mater. 340 (2005) 307–314. ˇ ´ J. Komurka, J. Cadek, T. Hostinsky, Met. Mater. 15 (1977) 445–460. A. Nitta, K. Kuwabara, in: R. Ohtani, M. Ohnami, T. Inoue (Eds.), Hightemperature Creep-fatigue, Elsevier Applied Science, 1988, pp. 203–222.
Contents lists available at SciVerse ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Competing damage mechanisms in the thermo-mechanical fatigue of AISI 304L stainless steel Keun-Ho Bae, Hyun-Ho Kim, Soon-Bok Lee ∗ Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 7 January 2011 Received in revised form 28 June 2011 Accepted 7 September 2011 Available online 17 September 2011 Keywords: Thermo-mechanical fatigue Phase difference Creep Dynamic strain aging
a b s t r a c t Thermo-mechanical fatigue (TMF) in AISI 304L stainless steel is investigated in two temperature ranges using four phase differences between the mechanical loading and the temperature. In the temperature range from 450 ◦ C to 700 ◦ C, the fatigue life was lowest in the in-phase condition. However, in the temperature range from 400 ◦ C to 650 ◦ C, the minimum fatigue life occurs in the counter-clockwise-diamond condition. Estimation of creep strains occurring in the TMF cycle based on the monotonic creep tests predicts the highest creep strains in the in-phase conditions in the two temperature ranges, but cannot explain the minimum life in the counter-clockwise-diamond condition in the lower temperature range. This phenomenon is explained qualitatively by the operation ranges of dynamic strain aging and the creep of this material and their competition in the TMF cycle. This explanation predicts the highest influence of the creep in the counter-clockwise-diamond condition in the temperature range of 400–650 ◦ C. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Austenitic stainless steels are commonly used for applications at elevated temperatures, such as those of nuclear power plants, automobiles and gas turbine systems, because they have good oxidation resistance in addition to high ductility and toughness. AISI 304 is one of the most widely used stainless steels as a construction material in nuclear reactor systems. Many researchers have investigated AISI 304 and AISI 304L at elevated temperatures, studying factors such as the behavior under monotonic loading [1], under low-cycle fatigue (LCF) conditions [1–3], under creep conditions [4,5] and under thermo-mechanical fatigue conditions [6–8]. In thermo-mechanical fatigue environments, materials experience various damaging mechanisms, such as fatigue, creep, dynamic strain aging, and oxidation, simultaneously or independently depending on the testing conditions. Dynamic strain aging is caused by the interaction between the moving dislocations and obstacles such as solute atoms, which hinders the movement of dislocations. In austenitic stainless steels it has been suggested that carbon-vacancy pairs and clusters of carbon atoms interact with gliding dislocations [9,10] at temperatures below 400 ◦ C. When the temperature exceeds 400 ◦ C, chromium atoms become more active and interfere with moving dislocations [1,11,12]. It is well known from low-cycle fatigue tests of AISI 304 that dynamic strain aging (DSA) induces the maximum stress
amplitude [1–3,11]. The temperature at which the peak of the stress amplitude occurs due to DSA is reportedly 400 ◦ C [1], 470 ◦ C [2], 525 ◦ C [13], and 550 ◦ C [14] depending on the heat treatment of the AISI 304L. The creep behavior of this steel is also known to be greatly influenced by the heat treatment under investigation [15,16]. This is reportedly due to the different degrees of microporosity or inclusions caused by differences in the production conditions, as well as deviations in the concentrations of the composition and any additional elements. Due to these variations very different creep curves are observed. In some works a steady state creep behavior (secondary creep) has been reported [15–17], whereas in other studies no region with a constant creep rate was noted. In the latter case, a steady state creep rate is frequently approximated by the minimum creep rate [18]. The stress exponent n is usually employed to characterize the dependence of the creep rate on the stress. Zauter et al. [4] reported a value of 10.4 (±0.9) from stress change experiments conducted at a temperature of 650 ◦ C and the value of 7.7 from constant stress tests in a stress range of 150–250 MPa. In this research, thermo-mechanical fatigue tests of AISI 304L are performed using two different temperature intervals with four different phase differences between the mechanical loading and the temperature. In addition, dynamic strain aging and creep behaviors are investigated to explain the behavior of the TMF results. 2. Experimental procedure
∗ Corresponding author. Tel.: +82 42 350 3029; fax: +82 42 350 5028. E-mail address: [email protected] (S.-B. Lee). 0921-5093/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2011.09.054
AISI 304L stainless steel is used in this research. In addition to thermo-mechanical fatigue tests, tensile, low-cycle fatigue and
418
K.-H. Bae et al. / Materials Science and Engineering A 529 (2011) 417–424
Fig. 1. Specimen for the thermo-mechanical fatigue test (dimensions in mm).
creep tests are performed to obtain the basic properties of the material. A tensile specimen with a gauge length of 36 mm and a diameter of 6 mm as well as a low-cycle fatigue specimen with a gauge length of 20 mm and a diameter of 8 mm were designed as smooth
cylindrical specimens according to the ASTM E606-92 specifications. The tensile specimen was also used in the creep tests. A specimen for the thermo-mechanical fatigue test was designed as a hollow specimen with a gauge length of 20 mm, an outer diameter of
Fig. 2. Schematic illustration of the variety of phase differences between the temperature and mechanical strain.
K.-H. Bae et al. / Materials Science and Engineering A 529 (2011) 417–424
419
Fig. 4. Relationship between the thermo-mechanical fatigue life and the phase difference in the temperature range of 450–700 ◦ C (a) at εme /2 = 0.6% and (b) at εme /2 = 0.8%.
Fig. 3. Relationship between the thermo-mechanical fatigue life and the phase difference in the temperature range of 400–650 ◦ C (a) at εme /2 = 0.6% (b) at εme /2 = 0.8% and (c) at εme /2 = 1.0%.
8 mm, and an inner diameter of 4 mm to improve the uniformity of the temperature distribution. The TMF specimen is shown in Fig. 1. A closed loop servo hydraulic system with a 10 ton capacity was used in all of the tests. An induction heater and a K-type thermocouple were used to control the temperature. The strain was measured by a spring-loaded high-temperature extensometer. The tensile tests were performed under a displacement control of 4.8 mm/min, which is translated approximately as 0.2%/s in terms
of the strain rate at from room temperature to 700 ◦ C with 100 ◦ C intervals. The low-cycle fatigue tests were performed under strain control of 2 × 10−3 /s at temperatures ranging from room temperature to 800 ◦ C with 100 ◦ C intervals, except for at 100 ◦ C. The total strain was controlled to strain settings of ±0.6, 0.8, 1.0, and 1.2%. Thermo-mechanical fatigue tests were performed in two temperature ranges; from 400 ◦ C to 650 ◦ C and from 450 ◦ C to 700 ◦ C, with a heating and cooling rate of 5 ◦ C/s. The total strain range, which is the summation of the mechanical strain range and thermal expansion strain range, was controlled. Three different mechanical strain ranges (εme /2 = 0.6%, 0.8%, 1.2%) were then tested in the 400–650 ◦ C temperature range while two mechanical strain ranges (εme /2 = 0.6%, 0.8%) were tested in the 450–700 ◦ C temperature range. Four different phase differences with given temperatures and the mechanical strains were investigated to determine the effects of the phase difference on the thermo-mechanical fatigue behavior and the lifespan. The four phase differences were in-phase (IP, 0◦ phase difference), out-of-phase (OP, 180◦ phase difference), clockwise-diamond-phase (CD, 90◦ phase difference), counterclockwise-diamond-phase (CCD, 270◦ phase difference) as shown in Fig. 2. More than 20 thermal cycles were run under zero-load control and the last three cycles were averaged to create the thermal strain expansion data file. The accuracy of the expansion file was checked via a zero-stress test. Both the TMF life and the lowcycle fatigue life were determined at the point where a drop in the stress of 10% of the maximum load was measured.
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Fig. 6. Variation of the cyclic hardening exponent as a function of the temperature.
Fig. 5. Characteristics of the tensile behavior as a function of the temperature: (a) stress–strain curves, (b) elongations, and (c) ultimate tensile strengths.
3. Results and discussion 3.1. Thermo-mechanical fatigue Figs. 3 and 4 show the relationships between the thermomechanical fatigue life and the phase difference under different testing conditions. Fig. 3 shows the results for the temperature range of 400–650 ◦ C. The minimum fatigue life was observed at
Fig. 7. TEM micrographs at εt /2 = 0.8% and 400 ◦ C.
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Fig. 8. Relationship between the temperature-compensated minimum creep rate (Zener–Hollomen parameter) and the applied stress.
the phase difference of 270◦ in all cases. Fig. 4 shows the results for the temperature range of 450–700 ◦ C. Here, in contrast to the 400–650 ◦ C range, the in-phase cases show the minimum fatigue life. It is clear that there is a difference in the damage mechanisms between the temperature ranges of 400–650 ◦ C and 450–700 ◦ C; this will be exploited further in terms of creep and dynamic strain aging later in this paper. 3.2. Dynamic strain aging The occurrence of DSA can be manifested by anomalous features of material behavior. While serrated yielding is the most commonly observed manifestation of DSA, there are various types of concurrent phenomena. Other anomalies associated with DSA have been described by Rodriguez [19]; during monotonic tensile deformation, DSA is manifested by a serrated flow in the stress–strain curve, a peak or plateau in the variation of the material strength with the temperature, the minima in the variation of the ductility with the temperature, a peak in the variation of the work hardening value, a peak in the variation of the Hall–Petch slope with the temperature, and finally negative strain-rate sensitivity (SRS). Hong et al. [20,21] investigated the effects of DSA on the fatigue behavior and life. Fig. 5 shows the characteristics of the tensile behavior. In Fig. 5(b) and (c) which depicts the variations of the elongation and the ultimate tensile strength as a function of the temperature, anomalies induced by DSA are clearly shown. Fig. 5(b) shows the minimum value, while Fig. 5(c) shows a plateau around 400 ◦ C. Fig. 6 shows another anomaly associated with DSA. The value of the cyclic hardening exponent (n ) reaches a maximum at 400 ◦ C. These are typical manifestations of DSA. From these observations it is reasonable to assume that the influence of DSA is strongest at 400 ◦ C and that its operation range is from 300 ◦ C to 500 ◦ C. It is important to note that this material does not show any clear serration in the tensile stress–strain curves. Though serration was not observed, the planar structures of the dislocations were observed, as shown in Fig. 7. Fig. 7 shows transmission electron microscopy (TEM) images from the low-cycle fatigue test at εt /2 = 0.8% and 400 ◦ C. The planar arrangements of the dislocations are clear evidence of DSA. Similar layer/wall structures of dislocations in the DSA regime were reported [22,23]. 3.3. Creep Hostinsky´ et al. [24] investigated the creep and creep fracture behavior of AISI 304L at temperatures ranging from 773 K to 1073 K
Fig. 9. Estimated creep strains when (a) 450–700 ◦ C, εme /2 = 0.6%, (b) 450–700 ◦ C, εme /2 = 0.8%, and (c) 400–650 ◦ C, εme /2 = 1.0%.
and applied stresses ranging from 73 MPa to 490 MPa. The relationship between the minimum creep rate and the applied stress was found to be curved in a double logarithmic plot. The apparent activation energy of creep, Qc = [∂ ln ε˙ m /∂(−1/RT )] (T is the temperature and R is the gas constant) was found to decrease as the stress increases: Qc (kJ mol−1 ) = (459 ± 82) − (0.021 ± 0.010). The applied stress sensitivity parameter of the minimum creep rate,
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Fig. 10. Schematic diagrams showing the DSA region (dotted lines) at (a) 400–650 ◦ C and (b) 450–700 ◦ C.
Table 1 Experimental results of the constant stress creep tests. Temperature (◦ C)
Stress (MPa)
Steady or minimum strain rate (%/s)
700 700 700 700 600 600 500 400
281 211 140 70 282 353 388 424
0.0958 0.0053 2.18E−4 9.61E−7 9.34E−5 0.00341 7.31E−7 1.8E−6
Z = ε˙ m exp
m = (∂ ln ε˙ m /∂ ln )T was found to decrease as the temperature increases: m = (9.5 ± 2.2) − (0.003 ± 0.002)T. Table 1 shows the experimental results of the constant stress creep tests of this material. The temperature-compensated minimum creep rate, so known as Zener–Hollomen parameter, was used to correlate the creep rate to the applied stress. Z = ε˙ m exp
Q av c
RT
Here R is the gas constant and Qcav is the average weighted value of Qc , which is assumed to be 366 kJ mol−1 , as in an earlier study [5]. The Zener–Hollomen parameter is plotted as a function of the applied stress in Fig. 8 and its fitting curve is shown as a solid line. Because d ln Z/d ln = (∂ ln ε˙ m /∂ ln )T , it follows from Fig. 8 ˇ et al. [5] also that m increases as the stress increases. Sustek reported a linear relationship between m and the applied stress. From the experimental results, it was found that
(1)
Q av c
RT
= A × (m0 +c)
where A is 100 s−1 MPa−1 , m0 is 4.81, and c is 0.0038 MPa−1 . Using this formula, the creep strain during the TMF cycle can be estimated. The estimated creep strains occurring during the TMF cycle are plotted in Fig. 9. In all conditions, in-phase (0◦ phase difference) cases produce the highest estimated creep strains. In comparison with Figs. 3 and 4, the estimated creep strains fittingly explain the TMF fatigue life when the temperature range is from 450 ◦ C to 700 ◦ C. The fatigue life is in inverse proportion to the creep strain and the minimum life in the in-phase case is explained by the highest creep strain. However, when the temperature range is from 400 ◦ C to 650 ◦ C, the estimated creep strains from the
Fig. 11. Schematic diagrams showing the DSA region (dotted lines) and creep region (solid lines) at 400–650 ◦ C.
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Fig. 12. Dislocation arrangements in the temperature range of 400–650 ◦ C (a) in-phase (0◦ phase difference), (b) clockwise-diamond phase (90◦ phase difference), (c) out-of-phase (180◦ phase difference), and (d) counter-clockwise-diamond phase (270◦ phase difference).
monotonic creep tests cannot explain the fatigue life. Here, the minimum fatigue life occurs in the counter-clockwise-diamond case (CCD, 270◦ phase difference), but the maximum creep strain estimated by the monotonic creep tests develops in the in-phase case. When the temperature range is from 450 ◦ C to 700 ◦ C, the creep is the most dominant damaging mechanism and explains the fatigue life, but when the temperature range is lowered by 50 ◦ C, the creep damage is not the only dominant mechanism; thus, more explanation is required. 3.4. Competition between DSA and creep In the temperature range from 400 to 650 ◦ C, DSA and creep are believed to be operating together because the DSA operation range of this material was 300–500 ◦ C and for austenitic stainless steels creep usually occurs above 550 ◦ C [25]. Although much research has been done on DSA and creep independently, less is known about the interaction between the two mechanisms. Here, qualitative modeling of the effect of the interaction between creep and DSA on the TMF life is attempted and verified by TEM micrographs.
Fig. 10 shows schematically the DSA operating regime based on the assumption that DSA occurs from 300 ◦ C to 500 ◦ C. The dotted lines indicate the region in the hysteresis loop where DSA is believed to be operating. Given that sufficient quantitative modeling of the DSA in non-isothermal conditions has not been done, it is not perfectly safe to assume that DSA occurs only in these designated regions. However, from the tensile and low-cycle fatigue results mentioned earlier, it is reasonable that these DSA regions have high probabilities of the occurrence of DSA. As shown in Fig. 10, when the temperature range is from 450 ◦ C to 700 ◦ C, the region of DSA is small and it is difficult to imagine that DSA has a large influence on the material behavior and lifespan. However, the region of DSA when the temperature range is 400–650 ◦ C is large and covers almost half of the hysteresis loop, thus affecting the material behavior and lifespan. In Fig. 11, creep regions are superimposed on the DSA region in Fig. 10(a) based on the assumption that creep occurs above 550 ◦ C. In the counter-clockwise-diamond case (CCD, 270◦ phase difference) most of the tensile part is the creep region and most of the compressive part is the DSA region. In the clockwise-diamond case (CD, 90◦ phase difference), the
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opposite holds true; the tensile part is the DSA region and the compressive part is the creep region. In the in-phase (IP, 0◦ phase difference) and the out-of-phase (OP, 180◦ phase difference) cases, the DSA and creep regions cover both the tensile and compressive parts. The difference in the IP and OP cases is that in the IP case, the creep region covers the tensile peak point, whereas in the OP case the DSA region covers the tensile peak point. The relative dominance between the DSA and creep can be assessed based on Fig. 11. The creep in the compressive part is well known to negate the creep effects in the tensile part, closing the cavities produced in the tensile part. By the same token, the CCD case is favorable for creep effects, as the compressive part is governed by the DSA, which hinders the movement of the dislocations, thus enhancing the irreversibility. In contrast, in the CD case, the compressive part is ruled by creep, erasing all creep effects, if any exist. In the IP and OP cases, creep regions exist in the tensile part, but the associated creep effects are partially negated by the creep region in the compressive parts. As the stress magnitude in the creep region is higher in the IP case than in the OP case, it is reasonable to assume that the creep dominance is greater in the IP than in the OP case, but this is also true for the recovery effects of the compressive part in the IP case. Therefore, an exact comparison is difficult to obtain. The relative dominance of creep over DSA is estimated as CCD IP ≥ OP CD. This estimation of the relative dominance of creep over DSA was verified by TEM micrographs, as shown in Fig. 12. A clear difference between the CCD and the other cases is observed. The CCD case shows equiaxed structures, whereas the other cases show more planar structures. Elongated or equiaxed dislocation arrangements are usually observed in the creep regime, whereas planar dislocation arrangements are observed in the DSA regime [20]. Though it is difficult to assess and compare the magnitudes of the influence of DSA or creep from Fig. 12(a), (c), and (d), these TEM micrographs are consistent with the previous qualitative prediction of the CCD case having the highest dominance of creep over DSA, also explaining the minimum fatigue life, in the CCD case shown in Fig. 3. 4. Conclusion This investigation of thermo-mechanical fatigue (TMF) tests of AISI 304L stainless steel at two temperature ranges, 400–650 ◦ C and 450–700 ◦ C, in addition to low-cycle fatigue, tensile, and creep tests, leads to the following conclusions: 1. Dynamic strain aging (DSA) occurs from 300 to 500 ◦ C based on the observations of the ultimate tensile strength, elongation, and cyclic hardening exponent. Serration, which is a typical
indication of DSA is not a good indicator here. The occurrence of DSA is verified by TEM micrographs. 2. In the temperature range from 450 ◦ C to 700 ◦ C, creep is the most dominant damaging mechanism; the TMF lifespan can be explained by the estimated creep strains from monotonic creep tests. 3. In the temperature range from 400 ◦ C to 650 ◦ C, the counterclockwise-diamond (CCD) case was found to be the most damaging, and TEM observations prove that only the counterclockwise-diamond condition induces creep-like dislocation arrangements, instead of the DSA-like dislocation arrangements observed in other conditions. 4. A simple qualitative explanation of the competition between creep and DSA is given comparing the operation ranges of creep and DSA based on assumptions that DSA occurs in the temperature interval from 300 ◦ C to 500 ◦ C and that creep occurs above 550 ◦ C; this predicts the highest creep effect in the CCD condition and, thus explains the minimum thermo-mechanical fatigue lifetime in this condition. References [1] [2] [3] [4] [5] [6] [7] [8]
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