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Evaluation of fatigue crack growth rate and life prediction of Inconel 718 at room and elevated temperatures
Materials Science and Engineering A277 (2000) 250 – 257 www.elsevier.com/locate/msea
Evaluation of fatigue crack growth rate and life prediction of Inconel 718 at room and elevated temperatures Q. Chen a,*, N. Kawagoishi a, H. Nisitani b a b
Faculty of Engineering, Kagoshima Uni6ersity, Kagoshima 890 -0065, Japan Faculty of Engineering, Kyushu Sangyo Uni6ersity, Fukuoka 813 -8503, Japan Received 16 February 1999; received in revised form 25 June 1999
Abstract The fatigue crack growth behavior of Inconel 718 was investigated under rotating bending fatigue at room temperature, 300, 500, and 600°C in air. It has been found that the small crack growth rate could be evaluated by the small crack growth law at high stress levels, where the small-scale yielding conditions are exceeded and the Paris law is not applicable, irrespective of the temperature. The fatigue strength of plain specimens increased considerably in the long-life region at the elevated temperatures, because the early growth of a small crack in the range of 20 – 30 mm was suppressed. However, a crack grew faster at higher temperature after growing beyond about 50 mm due to the decrease of crack growth resistance. The fatigue life in the stable crack growth period can be predicted by the small crack growth law. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Fatigue; Crack growth rate; Small crack growth law; Elevated temperature; Inconel 718
1. Introduction The significance of a small fatigue crack in the life assessment has been emphasized in much research [1– 6]. That is, the growth behavior of a small fatigue crack has become a vital problem that engineers must be aware of in the fields of machine design, equipment maintenance as well as new material development. Nickel-base superalloys are usually used under severe operating conditions because of their high strength at high temperature and excellent corrosion resistance. However, the effect of temperature on the crack growth behavior of these alloys has not been clarified. For example, it was reported that the crack growth resistance increased, decreased or did not change at high temperature [7–9], and a unified explanation has not yet been achieved. Furthermore, when a crack is small, the crack growth is easily influenced by the microstructure, and the estimation of crack growth rate is more difficult. * Corresponding author. Tel.: +81-99-285-8277; fax: + 81-99-2503181. E-mail address: [email protected] (Q. Chen)
In the present study, the growth behavior of a mechanically small crack [10] of nickel-base superalloy Inconel 718 is investigated under rotating bending fatigue at room and elevated temperatures in air. Evaluations of small crack growth rate based on the Paris law [11] and the small crack growth law [12] are compared in order to determine the parameter which controls the small crack growth rate. Life prediction based on the controlling parameter is performed.
2. Material and experimental procedures The material used was a rolled round bar (13 mm in diameter) of Inconel 718. The chemical composition is shown in Table 1. The alloy was solid-solution treated by heating at 982°C for 1 h and water quenching, aging at 720°C for 8 h, furnace cooling to 621°C and aging at 621°C for another 8 h, and finally by air cooling. Fig. 1 shows the microstructure of Inconel 718. The mechanical properties after the heat treatment are presented in Table 2. Fig. 2 shows the shape and dimensions of a specimen. To localize crack initiation site, the mid-surface of the plain specimen (Fig. 2a) was either partially
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Table 1 Chemical composition (wt.%) C
Si
Mn
P
S
Ni
Cr
Mo
Co
Cu
Al
Ti
Fe
B
Nb+Ta
0.03
0.05
0.06
0.008
0.002
Bal.
18.5
3.08
0.27
0.02
0.55
0.96
19.18
0.004
5.03
notched (Fig. 2b) by emery papers (the average grain size of finish emery papers was less than 20 mm), or blindly holed (0.3 mm in depth and diameter; Fig. 2c). The partially notched specimens were used to examine the initiation and early growth behavior of a small fatigue crack in the alloy. Because the decrease of fatigue strength due to the partial notch was less than 10%, i.e. the strength reduction factor, Kf, was close to unity, the fatigue behavior of a small crack in the partially notched specimens could be used to simulate the fatigue behavior of a small crack in the plain ones. Hence, hereinafter, the partially notched specimens are mentioned as the plain specimens. To evaluate small crack growth rate, the holed specimens were used because the crack initiation site could be localized to the hole rim, and the monitoring of crack growth was easy. However, data in the range below the diameter of the hole were not available. Furthermore, the early propagation of a crack was influenced by the hole shape and the stress concentration induced by the hole. Therefore, in the case of the holed specimens, only the data in the range of crack length beyond approximately 0.5 mm were examined, for which the formation of crack surfaces was independent of the hole, and the aspect ratio was nearly a constant. Prior to fatigue testing, all the specimens were electropolished, removing about 20 mm from the surface to remove worked layers. The removal of worked layers was confirmed by measuring the hardness and residual stress in the surface region of the specimen after electropolishing. The observation of surface damage and the measurement of crack length were conducted directly under a scanning electron microscope or under an optical microscope by using the plastic replica tech-
Fig. 2. Shape and dimensions of a specimen (mm): (a) plain specimen; (b) detail of partial notch; (c) detail of blind hole.
nique (the maximum resolution of the replica films was approximately 100 A, ). For tests performed at the elevated temperatures, the tests were interrupted and the specimens were cooled down at specific intervals of stress repetition to make the replication of specimen surface. However, the influence of repetitious heating and cooling process on the fatigue lives was almost not recognized. The crack length, l, was measured along the circumferential direction around the specimen surface by including the diameter of the hole, 0.3 mm. In the present study, the mechanical evaluation of small crack growth was based on the surface crack observation, while the validity of surface crack observation depends on a good
Fig. 1. Microstructure of Inconel 718: (a) longitudinal section; (b) cross-section.
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Table 2 Mechanical properties at all the temperatures studied Temperature (°C)
0.2% Proof stress (MPa)
Tensile strength (MPa)
True breaking stress (MPa)
Reduction of area (%)
Room 300 500 600
1320 1127 1050 1070
1461 1335 1254 1226
2320 1987 1734 1848
70.0 44.0 38.4 45.0
correspondence of crack growth in the depth with that on the surface, i.e. on a constant aspect ratio. This aspect ratio, b/l (b, crack depth; l, surface crack length), was approximately 0.4. The stress value referred to was the nominal stress amplitude, sa, at the net area of specimens by neglecting the partial notch or the blind hole. The fatigue tests were carried out at room temperature (RT), 300, 500, and 600°C in air by using an Ono-type rotating bending fatigue testing machine with a capacity of 100 N m, operating at about 55 Hz.
Fig. 3. Optical micrographs showing the changes in the surface state of plain specimen due to stress repetition under sa = 800 MPa at (a) room temperature and (b) 500°C ( l, axial direction): (a1) before fatigue cycling; (a2) after cycled for 9 × 103 cycles, l= 15 mm; (a3) after cycled for 1.9 × 104 cycles, l = 57 mm, (b1) before fatigue cycling; (b2) after cycled for 4× 103 cycles, l = 15 mm; (b3) after cycled for 8×103 cycles, l= 61 mm.
3. Results and discussion
3.1. E6aluation of small crack growth rate Fig. 3 shows the changes in surface state of the plain specimens at RT and 500°C, as an example. In the case of the plain specimens, a fatigue crack initiated from transgranular slip bands at both temperatures. Fig. 4 shows the morphologies of surface cracks initiated from the hole rim at RT and 500°C. As reported in the previous study [13], that striation was observed on the fractured surface of both the plain and holed specimens at all the tested temperatures, the influence of tempera-
Fig. 4. Optical micrographs showing the morphology of a crack initiated from the rim of the holed specimen (sa =800 MPa): (a) at room temperature; (b) at 500°C.
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temperatures and stress levels. Therefore, it is reasonable to use the holed specimens in research for a controlling mechanical parameter of small crack growth rate, and the following investigations are mainly based on the results of the holed specimens. Examples of the crack growth curve at all the experimental temperatures are shown in Fig. 6. With the increase of temperature, the crack growth is accelerated. The relation between the logarithm of crack length, log l, and the number of cycles, N, can be approximated linearly at all the temperatures, as long as a crack is small (e.g. in the range below 1–2 mm) and the stress applied is high (e.g. sa \ 0.6ss, where ss is the yield stress or 0.2% proof strength) [14]. That is log l8 N
(1)
By differentiating Eq. (1) with respect to N, the crack growth rate can be expressed as Eq. (2), which holds for all the small cracks growing at high stress levels, irrespective of the temperatures. Fig. 5. Comparison of crack growth rate between plain and holed specimens.
Fig. 6. Crack growth rate of holed specimens at all the temperatures.
ture on the fracture mechanism of Inconel 718 can be ignored in the present study. Fig. 5 shows the relation between crack growth rate and crack length for both the plain and holed specimens at RT and 500°C. In the case of plain specimens, the growth rate of a crack in the range of 0.05–2 mm is approximately proportional to the crack length at each temperature. For cracks smaller than 50 mm, however, it is difficult to evaluate their growth rates by merely a mechanical parameter due to the influences of microstructure [10] and other factors such as surface oxidation at elevated temperature [13]. The linear relation between crack growth rate and crack length exists in the holed specimens as well. Particularly, in the stable crack propagation, the crack growth rates in the holed specimens are almost equal to those in the plain specimens. Similar results were obtained at the other
dl/dN 8l
(2)
The relation between crack growth rate and crack length at RT and 500°C is shown in Fig. 7. For cracks growing from 0.5 to 1–2 mm, crack growth rate can be correlated linearly with crack length at both temperatures. But the stress dependence was recognized in the relation of Eq. (2), i.e. dl/dN 8 l 2 at low stress levels (e.g. sa B 0.5ss) [14] and dl/dN 8l at high stress levels, respectively. In Fig. 8, the crack growth rate is evaluated by the stress intensity factor range, DK (approximated by (2/ p) Ds pl/2; Ds, nominal stress range). Although the Paris law holds at low stress levels (sa B 0.5ss), e.g. dl/dN 8 DK 4 at RT, it fails at high stress levels (sa \ 0.6ss) where the stress dependence is recognized in the relation between dl/dN and DK at both room tempera-
Fig. 7. Relation between crack growth rate and crack length: (a) at room temperature; (b) at 500°C.
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dl/dN 8 DK m
(3)
in which constant m: 4. Fig. 9 shows the stress dependence of the term (dl/dN)/l for cracks which satisfied Eq. (2). From the results in Fig. 9, the small crack growth law [12] can be derived. dl/dN= Cs nal
Fig. 8. Crack growth rate as a function of DK: (a) at room temperature; (b) at 500°C.
ture and 500°C. Similar results were also obtained at 300 and 600°C. Therefore, it can be concluded that the Paris law is not applicable for cracks growing at high stress levels, irrespective of the temperature.
(n: 5)
(4)
in which C and n are constants related to material properties as well as testing conditions [15,16]. Although C and n were basically determined through a series of experiments, with the accumulation of experimental data for each group of materials, C and n can be estimated by using empirical formulae [17]. In the case of Inconel 718, n was about 5 at all the tested temperatures, indicating that the stress dependence of small crack growth rate did not vary with the temperature. Therefore, the temperature dependence of small crack growth rate in the alloy can be represented by the coefficient C. As seen from Table 3, the value of C increased with the increase of temperature, i.e. the crack growth rate increases with the increase of temperature. This means that the crack growth resistance of the alloy decreased with the increase of temperature because the matrix was softened at elevated temperatures (Table 2).
3.2. Life prediction In general, most of the fatigue life in a plain specimen is occupied by the growth life of a small crack, and the small crack growth rate can be determined by the small crack growth law, i.e. Eq. (4). Therefore, it is possible to apply the small crack growth law to predict the fatigue life of a plain specimen. By integrating Eq. (4), the whole fatigue life, Nf, can be estimated by Eq. (5). 1 1 l2 Nf = Nl 1 − l 2 = log n a aCs a l1
(5)
where Nl 1 − l 2 is the crack growth life from the length l1 to l2, and a is the ratio of Nl 1 − l 2 to Nf. In Eq. (5), the temperature dependence of Nf is related to the temperature dependence of coefficient C. Because the value of Table 3 The values of C in Eq. (5) at all the experimental temperatures studied Temperature (°C)
C Fig. 9. Plot of (dl/dN)/l versus sa.
Room
300
500
600
2.95×10−19
5.56×10−19
8.13×10−19
1.09×10−18
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Fig. 10. S – N curves of plain specimens at all the temperatures.
718 and grew to nearly 1 mm in thickness [18], a sufficient thickness for the closure of small cracks in the range of about 20–30 mm, growing at the rate of 10 − 9 to 10 − 8 m/cycle (Fig. 5), so that the crack growth rate was decreased. Moreover, the plasticity-induced crack closure effect becomes pronounced at elevated temperature because the matrix of Inconel 718 is softened (Table 2) and easy to deform, which also promotes the decrease of small crack growth rate. On the other hand, the reason for the regrowth of stagnated crack may be explained as follows. At elevated temperature, the faces of the closed crack near the tips are covered with hard oxide films and subject to a compressive cyclic stress. During the fatigue process, the crack faces near the tips are crushed gradually by the hard oxides and, finally, the closed crack opens and starts propagation.
C increased with the increase of temperature (Table 3), Nf will decrease with the increase of temperature. Fig. 10 shows the S – N curves of plain specimens at all the tested temperatures. In the short-life region, the fatigue strength decreases with the increase of temperature, showing a good correspondence to Eq. (5). In the long-life region, however, the fatigue strength is much higher at elevated temperatures than at room temperature, showing disagreement with the tendency of Eq. (5). In the following, the reasons will be investigated from the viewpoint of the influence of elevated temperature on the crack initiation and its early propagation process. Figs. 11 and 12 show the crack growth curves of l–N and l– N/Nf at the stress levels where the fatigue lives of plain specimens at the tested temperatures are nearly the same, i.e. Nf :4 ×104 and 4×105 cycles, respectively. The shapes of crack growth curves are different depending on the stress level and the temperature, although most of fatigue life is occupied by growth life, irrespective of the stress level and the temperature. That is, in the short-life region, the relation of dl/dN 8 l, i.e. Eq. (5), holds for most of the crack propagation process (Fig. 12). On the other hand, in the long-life region at the elevated temperatures, the crack growth life controlled by Eq. (5) is very limited and a large portion of crack growth life is occupied by the growth life of a small crack in the range of about 20 – 30 mm due to the stagnation of crack growth (Fig. 11). The stagnation of crack growth is more remarked at high temperatures, which contributes to the increase of fatigue strength at the elevated temperatures. The stagnation or the suppression of small crack growth at the elevated temperatures is caused by the decrease in driving force for crack growth due to the crack closure effect. It was reported that oxide films formed rapidly in the early heating process of Inconel
Fig. 11. Crack growth data of plain specimens around the fatigue life Nf =4 × 105 cycles: (a) l– N; (b) l– N/Nf.
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However, the quantitative estimation of crack growth rate in this propagation process is very difficult because a crack is too small to measure the crack opening and closing behavior, and evaluate the mechanical severity accurately. These are main reasons why the dependence of the stress and temperature were recognized in the correlation of S – N curves and Eq. (5). Fig. 13 shows the relation of l versus (N–N0.05)/ (Nf –N0.05) at high stress levels (sa \0.6ss) at all the tested temperatures, in which N0.05 is the fatigue life for a crack to grow up to 50 mm and was determined from the measured crack growth curves by interpolation. There is neither the stress dependence nor the temperature dependence recognized in the relation. Moreover, the relation can be linearly approximated. That is, when a crack grows over 50 mm, the crack growth rate can be evaluated by Eq. (4) and, further,
Fig. 13. Plot of l versus (N – N0.05)/(Nf – N0.05) at all the temperatures studied.
Fig. 14. Fatigue life prediction based on the small crack growth law.
Fig. 12. Crack growth data of plain specimens around the fatigue life Nf = 4 ×104 cycles: (a) l –N; (b) l –N/Nf.
the fatigue life can be predicted by Eq. (5). For example, let l1 = 0.05 mm, l2 = 5 mm, a: 1 by considering the results in Fig. 11, substitute them into Eq. (5) together with the C values (Table 3), and the fatigue crack growth life from 50 mm to final fracture, Nf – N0.05, can be predicted easily. Fig. 14 shows the predicted S–(Nf –N0.05) curves for specimens tested at high stress levels (sa \0.6ss) at all the tested temperatures. In Fig. 14, experimental data of specimens whose crack growth curves were measured are plotted for comparison. It can be seen that the predicted fatigue life (Nf –N0.05) has a excellent agreement with the experimental one at each temperature, although the fatigue life for a crack to grow up to 50 mm is difficult to predict quantitatively.
Q. Chen et al. / Materials Science and Engineering A277 (2000) 250–257
It should be mentioned that the main concern of this work was laid on the mechanical evaluation of small crack growth behavior of Inconel 718 at elevated temperatures. However, even for a material like Inconel 718, which has excellent heat resistance at high temperature, the influences of stress repetition and environmental conditions on its oxidation characteristics also need to be taken into account in the research of fatigue crack growth behavior at elevated temperature. These are the problems to be investigated in the future.
4. Conclusions The crack growth rate of plain specimens can be evaluated by that of holed specimens as long as a crack is beyond 50 mm in length. The crack growth rate of a small crack can be evaluated by the small crack growth law (dl/dN = Cs na l) under high stress levels (sa \0.6ss, where ss is the yield stress or 0.2% proof strength) or by the Paris law (dl/dN = CDK m) under low stress levels (sa B 0.5ss) at each tested temperature. The crack growth is suppressed around the crack length of 20 mm at elevated temperatures. The stagnation of crack growth is more remarkable at lower stress or in the long-life region. Consequently, the fatigue strength is higher at elevated temperatures than at room temperature. The fatigue growth life for a crack exceeding about 50 mm can be predicted by the small crack growth law at each temperature.
.
257
References [1] H. Kitagawa, S. Takahashi, C.M. Suh, S. Miyashita, ASTM STP 675 (1979) 420. [2] K.J. Miller, Fatigue Fract. Eng. Mater. Struct. 5 (1982) 223– 232. [3] H. Nisitani, N. Kawagoishi, Trans. Jpn. Soc. Mech. Eng. 49A (1983) 431 (in Japanese). [4] R.O. Ritchie, J. Lankford (Eds.), Small Fatigue Cracks, The Metallurgical Society Inc., Salt Lake, UT, 1986. [5] Y. Murakami, S. Harada, T. Endo, H. Tani-ishi, Y. Fukushima, Eng. Fract. Mech. 18 (1983) 909. [6] N. Kawagoishi, M. Goto, H. Nisitani, T. Toyohiro, H. Tanaka, Proceedings of the 6th International Fatigue Congress, Pergaman, Berlin, 1996, p. 265. [7] B.A. Leach, S.D. Antolovich, Met. Trans. A 21 (1990) 2169. [8] W. Hoffelner, Mater. Sci. Technol. 3 (1987) 765. [9] J.S. Crompton, J.W. Martin, Met. Trans. A 15 (1984) 1711. [10] K.J. Miller, Fatigue Fract. Eng. Mater. Struct. 10 (1987) 75. [11] P. Paris, F. Erdogan, Trans. ASME J. Basic Eng. 85 (1963) 528. [12] H. Nisitani, in: T. Mura (Ed.), Mechanics of Fatigue, AMD ASME, vol. 47, ASME, OH, USA, 1981, p. 151. [13] N. Kawagoishi, Y. Ozono, Q. Chen, M. Goto, H. Tanaka, E. Kondo, Trans. Jpn. Soc. Mech. Eng. 64A (1998) 839 (in Japanese). [14] H. Nisitani, N. Kawagoishi, JSME Int. J. 351 (1992) 1. [15] N. Kawagoishi, H. Nisitani, M. Goto, Proceedings of the 4th International Conference on Computer-Aided Assessment and Control-Localized Damage 96, Computational Mechanics Publications, Boston, 1996, p. 223. [16] N. Kawagoishi, H. Nisitani, M. Goto, X. Wang, H. Tanaka, Proceedings of Asian – Pacific Conference on Strength of Materials and Structures, International Academic Publishers, Beijing, 1996, p. 49. [17] H. Nisitani, M. Goto, N. Kawagoishi, Eng. Fract. Mech. 41 (1992) 499. [18] M. Lenglet, R. Guillamet, J. Lopitaux, B. Hannoyer, Mater. Res. Bull. 25 (1990) 715.
Evaluation of fatigue crack growth rate and life prediction of Inconel 718 at room and elevated temperatures Q. Chen a,*, N. Kawagoishi a, H. Nisitani b a b
Faculty of Engineering, Kagoshima Uni6ersity, Kagoshima 890 -0065, Japan Faculty of Engineering, Kyushu Sangyo Uni6ersity, Fukuoka 813 -8503, Japan Received 16 February 1999; received in revised form 25 June 1999
Abstract The fatigue crack growth behavior of Inconel 718 was investigated under rotating bending fatigue at room temperature, 300, 500, and 600°C in air. It has been found that the small crack growth rate could be evaluated by the small crack growth law at high stress levels, where the small-scale yielding conditions are exceeded and the Paris law is not applicable, irrespective of the temperature. The fatigue strength of plain specimens increased considerably in the long-life region at the elevated temperatures, because the early growth of a small crack in the range of 20 – 30 mm was suppressed. However, a crack grew faster at higher temperature after growing beyond about 50 mm due to the decrease of crack growth resistance. The fatigue life in the stable crack growth period can be predicted by the small crack growth law. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Fatigue; Crack growth rate; Small crack growth law; Elevated temperature; Inconel 718
1. Introduction The significance of a small fatigue crack in the life assessment has been emphasized in much research [1– 6]. That is, the growth behavior of a small fatigue crack has become a vital problem that engineers must be aware of in the fields of machine design, equipment maintenance as well as new material development. Nickel-base superalloys are usually used under severe operating conditions because of their high strength at high temperature and excellent corrosion resistance. However, the effect of temperature on the crack growth behavior of these alloys has not been clarified. For example, it was reported that the crack growth resistance increased, decreased or did not change at high temperature [7–9], and a unified explanation has not yet been achieved. Furthermore, when a crack is small, the crack growth is easily influenced by the microstructure, and the estimation of crack growth rate is more difficult. * Corresponding author. Tel.: +81-99-285-8277; fax: + 81-99-2503181. E-mail address: [email protected] (Q. Chen)
In the present study, the growth behavior of a mechanically small crack [10] of nickel-base superalloy Inconel 718 is investigated under rotating bending fatigue at room and elevated temperatures in air. Evaluations of small crack growth rate based on the Paris law [11] and the small crack growth law [12] are compared in order to determine the parameter which controls the small crack growth rate. Life prediction based on the controlling parameter is performed.
2. Material and experimental procedures The material used was a rolled round bar (13 mm in diameter) of Inconel 718. The chemical composition is shown in Table 1. The alloy was solid-solution treated by heating at 982°C for 1 h and water quenching, aging at 720°C for 8 h, furnace cooling to 621°C and aging at 621°C for another 8 h, and finally by air cooling. Fig. 1 shows the microstructure of Inconel 718. The mechanical properties after the heat treatment are presented in Table 2. Fig. 2 shows the shape and dimensions of a specimen. To localize crack initiation site, the mid-surface of the plain specimen (Fig. 2a) was either partially
0921-5093/00/$ - see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 1 - 5 0 9 3 ( 9 9 ) 0 0 5 5 5 - 9
Q. Chen et al. / Materials Science and Engineering A277 (2000) 250–257
251
Table 1 Chemical composition (wt.%) C
Si
Mn
P
S
Ni
Cr
Mo
Co
Cu
Al
Ti
Fe
B
Nb+Ta
0.03
0.05
0.06
0.008
0.002
Bal.
18.5
3.08
0.27
0.02
0.55
0.96
19.18
0.004
5.03
notched (Fig. 2b) by emery papers (the average grain size of finish emery papers was less than 20 mm), or blindly holed (0.3 mm in depth and diameter; Fig. 2c). The partially notched specimens were used to examine the initiation and early growth behavior of a small fatigue crack in the alloy. Because the decrease of fatigue strength due to the partial notch was less than 10%, i.e. the strength reduction factor, Kf, was close to unity, the fatigue behavior of a small crack in the partially notched specimens could be used to simulate the fatigue behavior of a small crack in the plain ones. Hence, hereinafter, the partially notched specimens are mentioned as the plain specimens. To evaluate small crack growth rate, the holed specimens were used because the crack initiation site could be localized to the hole rim, and the monitoring of crack growth was easy. However, data in the range below the diameter of the hole were not available. Furthermore, the early propagation of a crack was influenced by the hole shape and the stress concentration induced by the hole. Therefore, in the case of the holed specimens, only the data in the range of crack length beyond approximately 0.5 mm were examined, for which the formation of crack surfaces was independent of the hole, and the aspect ratio was nearly a constant. Prior to fatigue testing, all the specimens were electropolished, removing about 20 mm from the surface to remove worked layers. The removal of worked layers was confirmed by measuring the hardness and residual stress in the surface region of the specimen after electropolishing. The observation of surface damage and the measurement of crack length were conducted directly under a scanning electron microscope or under an optical microscope by using the plastic replica tech-
Fig. 2. Shape and dimensions of a specimen (mm): (a) plain specimen; (b) detail of partial notch; (c) detail of blind hole.
nique (the maximum resolution of the replica films was approximately 100 A, ). For tests performed at the elevated temperatures, the tests were interrupted and the specimens were cooled down at specific intervals of stress repetition to make the replication of specimen surface. However, the influence of repetitious heating and cooling process on the fatigue lives was almost not recognized. The crack length, l, was measured along the circumferential direction around the specimen surface by including the diameter of the hole, 0.3 mm. In the present study, the mechanical evaluation of small crack growth was based on the surface crack observation, while the validity of surface crack observation depends on a good
Fig. 1. Microstructure of Inconel 718: (a) longitudinal section; (b) cross-section.
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Table 2 Mechanical properties at all the temperatures studied Temperature (°C)
0.2% Proof stress (MPa)
Tensile strength (MPa)
True breaking stress (MPa)
Reduction of area (%)
Room 300 500 600
1320 1127 1050 1070
1461 1335 1254 1226
2320 1987 1734 1848
70.0 44.0 38.4 45.0
correspondence of crack growth in the depth with that on the surface, i.e. on a constant aspect ratio. This aspect ratio, b/l (b, crack depth; l, surface crack length), was approximately 0.4. The stress value referred to was the nominal stress amplitude, sa, at the net area of specimens by neglecting the partial notch or the blind hole. The fatigue tests were carried out at room temperature (RT), 300, 500, and 600°C in air by using an Ono-type rotating bending fatigue testing machine with a capacity of 100 N m, operating at about 55 Hz.
Fig. 3. Optical micrographs showing the changes in the surface state of plain specimen due to stress repetition under sa = 800 MPa at (a) room temperature and (b) 500°C ( l, axial direction): (a1) before fatigue cycling; (a2) after cycled for 9 × 103 cycles, l= 15 mm; (a3) after cycled for 1.9 × 104 cycles, l = 57 mm, (b1) before fatigue cycling; (b2) after cycled for 4× 103 cycles, l = 15 mm; (b3) after cycled for 8×103 cycles, l= 61 mm.
3. Results and discussion
3.1. E6aluation of small crack growth rate Fig. 3 shows the changes in surface state of the plain specimens at RT and 500°C, as an example. In the case of the plain specimens, a fatigue crack initiated from transgranular slip bands at both temperatures. Fig. 4 shows the morphologies of surface cracks initiated from the hole rim at RT and 500°C. As reported in the previous study [13], that striation was observed on the fractured surface of both the plain and holed specimens at all the tested temperatures, the influence of tempera-
Fig. 4. Optical micrographs showing the morphology of a crack initiated from the rim of the holed specimen (sa =800 MPa): (a) at room temperature; (b) at 500°C.
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temperatures and stress levels. Therefore, it is reasonable to use the holed specimens in research for a controlling mechanical parameter of small crack growth rate, and the following investigations are mainly based on the results of the holed specimens. Examples of the crack growth curve at all the experimental temperatures are shown in Fig. 6. With the increase of temperature, the crack growth is accelerated. The relation between the logarithm of crack length, log l, and the number of cycles, N, can be approximated linearly at all the temperatures, as long as a crack is small (e.g. in the range below 1–2 mm) and the stress applied is high (e.g. sa \ 0.6ss, where ss is the yield stress or 0.2% proof strength) [14]. That is log l8 N
(1)
By differentiating Eq. (1) with respect to N, the crack growth rate can be expressed as Eq. (2), which holds for all the small cracks growing at high stress levels, irrespective of the temperatures. Fig. 5. Comparison of crack growth rate between plain and holed specimens.
Fig. 6. Crack growth rate of holed specimens at all the temperatures.
ture on the fracture mechanism of Inconel 718 can be ignored in the present study. Fig. 5 shows the relation between crack growth rate and crack length for both the plain and holed specimens at RT and 500°C. In the case of plain specimens, the growth rate of a crack in the range of 0.05–2 mm is approximately proportional to the crack length at each temperature. For cracks smaller than 50 mm, however, it is difficult to evaluate their growth rates by merely a mechanical parameter due to the influences of microstructure [10] and other factors such as surface oxidation at elevated temperature [13]. The linear relation between crack growth rate and crack length exists in the holed specimens as well. Particularly, in the stable crack propagation, the crack growth rates in the holed specimens are almost equal to those in the plain specimens. Similar results were obtained at the other
dl/dN 8l
(2)
The relation between crack growth rate and crack length at RT and 500°C is shown in Fig. 7. For cracks growing from 0.5 to 1–2 mm, crack growth rate can be correlated linearly with crack length at both temperatures. But the stress dependence was recognized in the relation of Eq. (2), i.e. dl/dN 8 l 2 at low stress levels (e.g. sa B 0.5ss) [14] and dl/dN 8l at high stress levels, respectively. In Fig. 8, the crack growth rate is evaluated by the stress intensity factor range, DK (approximated by (2/ p) Ds pl/2; Ds, nominal stress range). Although the Paris law holds at low stress levels (sa B 0.5ss), e.g. dl/dN 8 DK 4 at RT, it fails at high stress levels (sa \ 0.6ss) where the stress dependence is recognized in the relation between dl/dN and DK at both room tempera-
Fig. 7. Relation between crack growth rate and crack length: (a) at room temperature; (b) at 500°C.
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dl/dN 8 DK m
(3)
in which constant m: 4. Fig. 9 shows the stress dependence of the term (dl/dN)/l for cracks which satisfied Eq. (2). From the results in Fig. 9, the small crack growth law [12] can be derived. dl/dN= Cs nal
Fig. 8. Crack growth rate as a function of DK: (a) at room temperature; (b) at 500°C.
ture and 500°C. Similar results were also obtained at 300 and 600°C. Therefore, it can be concluded that the Paris law is not applicable for cracks growing at high stress levels, irrespective of the temperature.
(n: 5)
(4)
in which C and n are constants related to material properties as well as testing conditions [15,16]. Although C and n were basically determined through a series of experiments, with the accumulation of experimental data for each group of materials, C and n can be estimated by using empirical formulae [17]. In the case of Inconel 718, n was about 5 at all the tested temperatures, indicating that the stress dependence of small crack growth rate did not vary with the temperature. Therefore, the temperature dependence of small crack growth rate in the alloy can be represented by the coefficient C. As seen from Table 3, the value of C increased with the increase of temperature, i.e. the crack growth rate increases with the increase of temperature. This means that the crack growth resistance of the alloy decreased with the increase of temperature because the matrix was softened at elevated temperatures (Table 2).
3.2. Life prediction In general, most of the fatigue life in a plain specimen is occupied by the growth life of a small crack, and the small crack growth rate can be determined by the small crack growth law, i.e. Eq. (4). Therefore, it is possible to apply the small crack growth law to predict the fatigue life of a plain specimen. By integrating Eq. (4), the whole fatigue life, Nf, can be estimated by Eq. (5). 1 1 l2 Nf = Nl 1 − l 2 = log n a aCs a l1
(5)
where Nl 1 − l 2 is the crack growth life from the length l1 to l2, and a is the ratio of Nl 1 − l 2 to Nf. In Eq. (5), the temperature dependence of Nf is related to the temperature dependence of coefficient C. Because the value of Table 3 The values of C in Eq. (5) at all the experimental temperatures studied Temperature (°C)
C Fig. 9. Plot of (dl/dN)/l versus sa.
Room
300
500
600
2.95×10−19
5.56×10−19
8.13×10−19
1.09×10−18
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Fig. 10. S – N curves of plain specimens at all the temperatures.
718 and grew to nearly 1 mm in thickness [18], a sufficient thickness for the closure of small cracks in the range of about 20–30 mm, growing at the rate of 10 − 9 to 10 − 8 m/cycle (Fig. 5), so that the crack growth rate was decreased. Moreover, the plasticity-induced crack closure effect becomes pronounced at elevated temperature because the matrix of Inconel 718 is softened (Table 2) and easy to deform, which also promotes the decrease of small crack growth rate. On the other hand, the reason for the regrowth of stagnated crack may be explained as follows. At elevated temperature, the faces of the closed crack near the tips are covered with hard oxide films and subject to a compressive cyclic stress. During the fatigue process, the crack faces near the tips are crushed gradually by the hard oxides and, finally, the closed crack opens and starts propagation.
C increased with the increase of temperature (Table 3), Nf will decrease with the increase of temperature. Fig. 10 shows the S – N curves of plain specimens at all the tested temperatures. In the short-life region, the fatigue strength decreases with the increase of temperature, showing a good correspondence to Eq. (5). In the long-life region, however, the fatigue strength is much higher at elevated temperatures than at room temperature, showing disagreement with the tendency of Eq. (5). In the following, the reasons will be investigated from the viewpoint of the influence of elevated temperature on the crack initiation and its early propagation process. Figs. 11 and 12 show the crack growth curves of l–N and l– N/Nf at the stress levels where the fatigue lives of plain specimens at the tested temperatures are nearly the same, i.e. Nf :4 ×104 and 4×105 cycles, respectively. The shapes of crack growth curves are different depending on the stress level and the temperature, although most of fatigue life is occupied by growth life, irrespective of the stress level and the temperature. That is, in the short-life region, the relation of dl/dN 8 l, i.e. Eq. (5), holds for most of the crack propagation process (Fig. 12). On the other hand, in the long-life region at the elevated temperatures, the crack growth life controlled by Eq. (5) is very limited and a large portion of crack growth life is occupied by the growth life of a small crack in the range of about 20 – 30 mm due to the stagnation of crack growth (Fig. 11). The stagnation of crack growth is more remarked at high temperatures, which contributes to the increase of fatigue strength at the elevated temperatures. The stagnation or the suppression of small crack growth at the elevated temperatures is caused by the decrease in driving force for crack growth due to the crack closure effect. It was reported that oxide films formed rapidly in the early heating process of Inconel
Fig. 11. Crack growth data of plain specimens around the fatigue life Nf =4 × 105 cycles: (a) l– N; (b) l– N/Nf.
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However, the quantitative estimation of crack growth rate in this propagation process is very difficult because a crack is too small to measure the crack opening and closing behavior, and evaluate the mechanical severity accurately. These are main reasons why the dependence of the stress and temperature were recognized in the correlation of S – N curves and Eq. (5). Fig. 13 shows the relation of l versus (N–N0.05)/ (Nf –N0.05) at high stress levels (sa \0.6ss) at all the tested temperatures, in which N0.05 is the fatigue life for a crack to grow up to 50 mm and was determined from the measured crack growth curves by interpolation. There is neither the stress dependence nor the temperature dependence recognized in the relation. Moreover, the relation can be linearly approximated. That is, when a crack grows over 50 mm, the crack growth rate can be evaluated by Eq. (4) and, further,
Fig. 13. Plot of l versus (N – N0.05)/(Nf – N0.05) at all the temperatures studied.
Fig. 14. Fatigue life prediction based on the small crack growth law.
Fig. 12. Crack growth data of plain specimens around the fatigue life Nf = 4 ×104 cycles: (a) l –N; (b) l –N/Nf.
the fatigue life can be predicted by Eq. (5). For example, let l1 = 0.05 mm, l2 = 5 mm, a: 1 by considering the results in Fig. 11, substitute them into Eq. (5) together with the C values (Table 3), and the fatigue crack growth life from 50 mm to final fracture, Nf – N0.05, can be predicted easily. Fig. 14 shows the predicted S–(Nf –N0.05) curves for specimens tested at high stress levels (sa \0.6ss) at all the tested temperatures. In Fig. 14, experimental data of specimens whose crack growth curves were measured are plotted for comparison. It can be seen that the predicted fatigue life (Nf –N0.05) has a excellent agreement with the experimental one at each temperature, although the fatigue life for a crack to grow up to 50 mm is difficult to predict quantitatively.
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It should be mentioned that the main concern of this work was laid on the mechanical evaluation of small crack growth behavior of Inconel 718 at elevated temperatures. However, even for a material like Inconel 718, which has excellent heat resistance at high temperature, the influences of stress repetition and environmental conditions on its oxidation characteristics also need to be taken into account in the research of fatigue crack growth behavior at elevated temperature. These are the problems to be investigated in the future.
4. Conclusions The crack growth rate of plain specimens can be evaluated by that of holed specimens as long as a crack is beyond 50 mm in length. The crack growth rate of a small crack can be evaluated by the small crack growth law (dl/dN = Cs na l) under high stress levels (sa \0.6ss, where ss is the yield stress or 0.2% proof strength) or by the Paris law (dl/dN = CDK m) under low stress levels (sa B 0.5ss) at each tested temperature. The crack growth is suppressed around the crack length of 20 mm at elevated temperatures. The stagnation of crack growth is more remarkable at lower stress or in the long-life region. Consequently, the fatigue strength is higher at elevated temperatures than at room temperature. The fatigue growth life for a crack exceeding about 50 mm can be predicted by the small crack growth law at each temperature.
.
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