high-temperature tensile-hold crack-growth behavior x alloy...

Mech Time-Depend Mater (2008) 12: 31–44DOI 10.1007/s11043-008-9049-6

High-temperature tensile-hold crack-growth behaviorof HASTELLOY® X alloy compared to HAYNES® 188and HAYNES® 230® alloys

S.Y. Lee · Y.L. Lu · P.K. Liaw · H. Choo · S.A. Thompson · J.W. Blust · P.F. Browning ·A.K. Bhattacharya · J.M. Aurrecoechea · D.L. Klarstrom

Received: 14 June 2007 / Accepted: 8 January 2008 / Published online: 16 February 2008© Springer Science+Business Media B.V. 2008

Abstract The creep–fatigue crack-growth tests of HASTELLOY® X alloy were carried outat the temperatures of 649°C, 816°C, and 927°C in laboratory air. The experiments wereconducted under a constant stress-intensity-factor-range (�K) control mode with a R-ratioof 0.05. In the constant �K tests, a �K of 27.5 MPa

√m and a triangular waveform with

a frequency of 0.333 Hz were used. Various tensile hold times at the maximum load wereimposed to study fatigue and creep–fatigue interactions. Crack lengths were measured bya direct current potential drop method. In this paper, effects of hold time and tempera-ture on the crack-growth rates are discussed. Furthermore, the crack-growth rates of theHASTELLOY® X alloy are compared to those of the HAYNES® 188 and HAYNES® 230®

superalloys.

Keywords Nickel-based superalloy · Creep-fatigue crack-growth · Hold time

1 Introduction

The HASTELLOY X (47Ni–22Cr–18Fe–9Mo, in weight percent) alloy (Haynes online lit-erature, No. H-3009) is a high-temperature nickel-based superalloy that possesses an ex-ceptional combination of oxidation resistance, fabricability, and high-temperature strength.It has a wide use in gas turbine engines for combustion zone components, such as transitionducts, combustor cans, spray bars, and flame holders as well as in afterburners, tailpipes andcabin heaters. It is also used in the chemical process industry for retorts, muffles, catalyst

S.Y. Lee · Y.L. Lu · P.K. Liaw (�) · H. ChooDepartment of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996,USAe-mail: [email protected]

S.A. Thompson · J.W. Blust · P.F. Browning · A.K. Bhattacharya · J.M. AurrecoecheaSolar Turbines, Inc., 2200 Pacific Hwy., PO Box 85376, MZ R-1, San Diego, CA 92186, USA

D.L. KlarstromHaynes International, Inc., 1020 W. Park Ave., PO Box 9013, Kokomo, IN 46904, USA

32 Mech Time-Depend Mater (2008) 12: 31–44

support grids, furnace baffles, tubing for pyrolysis operations and flash drier components.It shares many applications in gas-turbine engines with the HAYNES 188 (Haynes online lit-erature, No. H-3001) and HAYNES 230 (Haynes online literature, No. H-3000) superalloysdue to comparable excellent high-temperature properties. These high-temperature compo-nents are often subjected to creep–fatigue loading conditions during service time. Thus, theinvestigation of creep–fatigue crack growth properties is of great importance for the safe andreliable design of these components.

Several studies have investigated the low-cycle fatigue properties of HASTELLOY Xalloy. Tsuji and Kondo (1987) studied the effects of cyclic frequency, strain waveform,and hold time on low-cycle fatigue behavior of HASTELLOY X and its modified version,HASTELLOY XR, at 900◦C in a helium environment. These authors found that the decreaseof cyclic frequency would lead to a considerable reduction in the fatigue life. Furthermore,the reduction in the fatigue life was found to be the most significant for the tests with ten-sile hold times, and more effective than for the tests with symmetric hold times, while noappreciable fatigue life reduction was recognized for the tests with compressive hold times.Klarstrom and Lai (1988) examined the effects of thermal aging on the low-cycle fatiguebehavior of HASTELLOY X and found that the fatigue life was degraded by the aging treat-ment at 760◦C for 1,000 hours. They suggested that the cause of the fatigue-life degradationwas the precipitation of the sigma-phase and M23C6 carbides after long-term aging. Minerand Castelli (1992) studied the cyclic-hardening mechanism of HASTELLOY X duringisothermal and thermomechanical cyclic deformation, and observed that the alloy exhibiteda broad peak in cyclic hardening between about 200◦C and 700◦C, with a maximum in-crease in the cyclic stress amplitude around 500◦C. However, there are few studies of thefatigue-crack-growth behavior with tensile hold time on HASTELLOY X alloy (Hour andStubbins 1990; Lu et al. 2006).

In this investigation, the crack-growth experiments with different hold times and temper-atures were performed under a constant �K control to study the effects of creep–fatigueinteractions on the crack-growth rates of HASTELLOY X alloy. Moreover, the effects ofgrain size on tensile-hold crack-growth behavior are discussed by the comparison of threeHASTELLOY X, HAYNES 188, and HAYNES 230 superalloys.

2 Experimental procedures

The HASTELLOY X alloy was supplied by the Haynes International, Inc. and receivedin solution heat-treated condition. The average grain diameter was found to be about95 µm. The compact-tension (CT) geometry selected for the crack-growth tests is shownin Fig. 1. The specimens were prepared according to the American Society for Testingand Materials (ASTM) Standard E647-99 (ASTM Standard E 647-99 2000). The crack-growth tests were conducted using an Instron servo-controlled, hydraulically-actuated, andclosed-loop test machine. A high-frequency induction generator was used to heat the spec-imen. The fluctuation of the test temperature was maintained within a range of ±2◦C.A direct-current-potential-drop (DCPD) method was used to measure the crack length.The crack length is related to the electric potential by Johnson’s equation (Johnson 1965;Ritchie and Bathe 1979),

Vm

Vo

= cosh−1[ cosh(πy/W)

cos(πa/W)]

cosh−1[ cosh(πy/W)

cos(πao/W)] (1)

Mech Time-Depend Mater (2008) 12: 31–44 33

Fig. 1 The geometry of acompact-tension specimen

Table 1 Summary ofcrack-propagation tests forHASTELLOY X alloy

Temperature (◦C) Control mode Hold time

649 Constant �K 0, 0.05, 0.167, 0.5, 2, 10, 60,300 min., and infinite



where Vo and ao are the initial crack-mouth potential and crack length, respectively, Vm anda are the instantaneous crack-mouth potential and crack length, respectively, y is half ofthe distance between the two points for which the crack-mouth potential is measured, andW is the specimen width. The stress-intensity factor, K , was obtained (Tada et al. 1985;Rooke and Cartwright 1976),

K = P (2 + α)

B√

W(1 − α)3/2(0.886 + 4.64α − 13.32α2 + 14.72α3 − 5.6α4) (2)

where P = applied load, B = thickness, and a = crack size for a CT specimen, and�K = Kmax. − Kmin.(Kmax. and Kmin. are the maximum and minimum stress-intensity fac-tors, respectively).

The tests were conducted under a constant �K-control (Lu et al. 2002; Liaw et al. 1987).The crack-growth tests are summarized in Table 1. A �K value of 27.5 MPa

√m was se-

lected. In the fatigue-crack-growth (FCG) experiment, the triangular waveform with a fre-quency of 0.333 Hz and a R-ratio of 0.05 were employed (R = Kmin./Kmax., where Kmin.

and Kmax. are the minimum and maximum stress-intensity factors, respectively, during afatigue cycle). The creep-crack-growth (CCG) test was conducted with a constant Kmax.

The creep–fatigue crack-growth tests (CFCG) were performed by superimposing differenthold times on the triangular waveform at the maximum stress-intensity factor. Various holdtimes ranging from 0, 0.05, 0.167, 0.5, 2, 10, 60, 300 minutes to infinite were introduced tostudy creep–fatigue interactions on the crack-propagation behavior. The crack-growth rateswere compared to those of the HAYNES 188 and HAYNES 230 alloys performed under a


constant �K mode (Lee et al. 2007; Lu et al. 2006). Furthermore, the fracture surfaces ofspecimens were examined using a LEO scanning-electron microscope (SEM) to determinefracture mode.

3 Results and discussion

3.1 Effects of hold time and temperature

The crack-propagation tests with various hold times under a constant �K-control modewere conducted at 649◦C, 816◦C, and 927◦C, which are typical application temperatures.The cyclic-crack-growth rate, da/dN , and unit time-crack-growth rate, da/dt , versus thehold time are shown, respectively, in Figs. 2(a) and 2(b). The cyclic-crack-growth rate isthe change of the crack length per cycle, and the unit time-crack-growth rate is the changeof crack length per time. As the temperature and hold time increased, the cyclic-crack-growth rate increased, as presented in Fig. 2(a). It can be noted that the difference of the

Fig. 2 The effects of hold timeand temperature on(a) cyclic-crack-growth rate and(b) unit time-crack-growth rate at�K of 27.5 MPa

√m for the

HASTELLOY X alloy


Fig. 3 The influence offrequency on (a) da/dN and(b) da/dt at �K of 27.5MPa

√m for the HASTELLOY X

alloy

crack-growth rate increases with increasing the hold time. In Fig. 2(b), the crack-growthrate reduced gradually at both 649◦C and 816◦C. However, the crack-growth rate remainedalmost constant with increasing the hold time at 927◦C. These results show that the crack-growth rates are irrelevant to the duration of hold time, as the temperature increases from649◦C to 927◦C. The test frequency was obtained from the hold time using (3) to study theeffect of frequency on the crack-growth rates.

ν = 1/(tc + th) (3)

ν is the cyclic frequency, tc is the time for fatigue cycle, and th is the hold time introducedat the maximum tensile stress. The cyclic-crack-growth rates, da/dN , and unit time-crack-growth rates, da/dt , are plotted as a function of the test frequency, respectively, in Figs. 3(a)and 3(b). The cycle-dependent and time-dependent cracking regions are also shown in Fig. 3.

The cycle-dependent cracking and time-dependent cracking are direct function of cycleand time, respectively, irrespective of the test frequency. da/dN for cycle-dependent crack-


Fig. 4 The effect of temperatureon da/dt , at �K of27.5 MPa

√m for the

HASTELLOY X alloy

ing line and da/dt for time-dependent cracking line were measured by the tests with zerohold time and infinite hold time, respectively.

At 927◦C, the slope of the log–log plot in Fig. 3(a) is −1 for all frequencies, showingthat the cyclic-crack-growth rate is inversely proportional to the frequency. It indicates thatlonger hold times resulted in larger increase of crack length per cycle. In Fig. 3(b), the unittime-crack-growth rate maintained constant irrespective of the frequency. Consequently, thecrack-growth behaviors at 927◦C are totally dependent on time for all frequencies.

At 816◦C, the crack-growth rates show the time-dependent cracking at frequencies be-low about 0.0016 Hz, indicating that the unit-time crack-growth rates are independent onfrequencies. At frequencies above about 0.164 Hz, the crack-growth rates exhibit cycle-dependent cracking because the cyclic-crack-growth rates remained constant regardless ofthe frequency. At frequencies between 0.0016 Hz and 0.164 Hz, the crack-growth rates canbe thought as a function of both cycle and time.

At 649◦C, the crack-growth behaviors are cycle-dependent at frequencies above about0.074 Hz. The cycle-dependent regions at 649◦C were larger than those at 816◦C. At fre-quencies below about 0.00028 Hz, the time-dependent cracking was observed. The time-dependent regions at 649◦C were smaller than those at 816◦C. At frequencies between0.00028 Hz and 0.074 Hz, the crack-growth behaviors rely on both the cycle and time.

The unit time-crack-growth rates, da/dt , as a function of the test temperature are shownin Fig. 4. As the temperature increased, all of the crack-growth rates increased. As the holdtime increased from 3 sec. to 10 min. at 649◦C and 816◦C, the crack growth rates decreased.More specifically, the unit time-crack growth rate with a 3 sec.-hold time was about fourtimes larger than that with a 30 sec.-hold at 649◦C, while thirty-seven times larger than thatwith a 10 min.-hold at 649◦C. However, the crack-growth rates at 927◦C were comparable.These observations confirm that time-dependent cracking becomes dominant gradually withincreasing the temperature.

The fracture surfaces after the crack-growth tests are examined to observe the fracturemode under various creep–fatigue loading conditions using scanning electron microscope.Figure 5(a) shows that the crack propagated in a typical transgranular fracture mode forthe test without hold time at 816◦C. Well-defined fatigue striation was found in all fracturesurfaces. The secondary crack was often observed, suggesting that the grain boundary cavi-tation would be developed by creep deformation although alloy is subjected to only fatigueloading. When 2 min.-hold time was imposed at Kmax., the fracture appearance changed


Fig. 5 SEM micrographs offracture surface at 816◦C:(a) zero hold time; (b) 2 min.hold time; (c) 1 hr. hold time


from transgranular to intergranular feature, as indicated Fig. 5(b). The fatigue striationswere hardly discovered in the 2 min.-hold time test. As the hold time increased to 1 hour,the fracture mode was completely intergranular, as shown in Fig. 5(c). The crack-growthtest without hold time at 927◦C is presented in Fig. 6(a). Most of the fracture surfaces hadan intergranular fracture mode. It is obvious that the dominant creep damage during tensilehold resulted in the intergranular fracture path. When the hold time of 2 min. and 1 hour wasintroduced, the typical intergranular appearances for HASTELLOY X were demonstrated inFigs. 6(b) and 6(c). It is noted that the fracture appearances examined are correlated wellwith the crack-growth results. As the hold time was introduced from 2 min. to 5 hr. at816◦C, the intergranular fracture appearances were observed for all tests, which were in agood agreement with a frequency range of the time-dependent cracking line, as shown inFig. 3(b). In addition, an intergranular cracking path was investigated for all tests at 927◦C,which exactly corresponds to the time-dependent cracking range, as indicated in Fig. 3(b).Consequently, as the test temperature and hold time increase, a change of the fracture ap-pearances occurred from transgranular to intergranular and it resulted in higher crack growthrate following time-dependent cracking.

The time-dependent and cycle-dependent cracking characterizations are relevant to thesize of the creep-damage zone and the fatigue-damage zone (Lu et al. 2006). The creep-damage zone size at the crack tip is dependent on the temperature and the duration of holdtime. Higher temperatures and longer hold times will result in larger creep-zone sizes. How-ever, the fatigue-zone size as a function of �K would not change much under a constant�K-control test. Therefore, as the hold time and temperature increased, the creep-zone sizegrew larger than the fatigue-zone size, resulting in the time-dependent cracking.

3.2 Comparison of crack-growth rates among three superalloys

Figures 7 and 8 show the comparisons of the cyclic and unit time-crack-growth rates mea-sured from constant �K-control tests, respectively, for HAYNES 188, HAYNES 230, andHASTELLOY X alloys. The cyclic-crack-growth rates of three alloys increased with in-creasing hold time for all temperatures. The unit time-crack-growth rates of three alloysdecreased with increasing the hold time at 649◦C and 816◦C, while those of three alloyswere comparable at 927◦C. At 649◦C, the cyclic-crack-growth rates of these three alloysare similar when hold times are lower than 2 minutes. When hold times are greater than 10minutes, the HASTELLOY X alloy possesses the lowest crack-growth rates, followed bythe HAYNES 230 alloy, and then, the HAYNES 188 alloy. At 816◦C, the crack-growth ratesof the HASTELLOY X alloy are the highest among these three alloys during all hold times.When the hold time is lower than 10 minutes, the crack-growth rates of the HAYNES 188and HAYNES 230 alloys are similar. When the hold time is greater than 30 minutes, theHAYNES 230 alloy has lower crack-growth rates than the HAYNES 188 alloy. At 927◦C,the HAYNES 188 alloy has the lowest crack-growth rates for all hold times, followed by theHAYNES 230 alloy and then the HASTELLOY X alloy.

The comparison of crack-growth rates of three alloys become more interesting if ini-tial grain sizes of three superalloys are considered. There have been very few studies ofthe grain-size effects on the creep–fatigue interaction (Yamaguchi and Kanazawa 1980;Maiya and Majumdar 1977). These studies showed that the grain-size effect would bepronounced if intergranular features were considerable. Yamaguchi and Kanazawa (1980)pointed out that the fatigue lives of a stainless steel with various tensile hold times decreasedas the grain size increased at about 600◦C. The decrease of fatigue lives was attributed tothe ease of the formation of wedge cracks and cavities at the grain boundaries in coarse-grain materials. Maiya and Majumdar (1977) observed similar results in Type 304 SS. They


Fig. 6 SEM micrographs offracture surface at 927◦C:(a) zero hold time; (b) 2 min.hold time; (c) 1 hr. hold time


Fig. 7 The comparison ofcyclic-crack-growth ratesobtained from the constant�K-controlled tests(�K = 27.5 MPa

√m) among

HAYNES 188, HAYNES 230,and HASTELLOY X alloys at(a) 649◦C, (b) 816◦C, and(c) 927◦C


Fig. 8 The comparison of unittime-crack-growth rates obtainedfrom the constant �K-controlledtests (�K = 27.5 MPa

√m)

among HAYNES 188, HAYNES230, and HASTELLOY X alloysat (a) 649◦C, (b) 816◦C, and(c) 927◦C


found that grain-size effects were more pronounced under tensile hold times. The decreaseof fatigue lives could be thought of as the increase of crack-propagation rates, because thecrack-propagation period consists of a large part of component lives at high temperatures.

In this study, the measurements of the grain size showed that the HAYNES 188 (Leeet al. 2007), HAYNES 230 (Lu et al. 2006), and HASTELLOY X alloys have initial grainsizes of about 45 µm, 70 µm, and 95 µm, respectively, as shown in Fig. 9. At 649◦C, thecrack-propagation rate of the HASTELLOY X alloy with the largest grain size was the low-est, followed by the HAYNES 230 alloy and HAYNES 188 alloys, as indicated Fig. 7(a). Itis suspected that the order of the creep–fatigue resistance of the alloys was a reflection ofthe difference in the grain size. Under the creep–fatigue loading condition, the creep resis-tance of the alloy will have an influence not only on crack-propagation rates but also on thefatigue lives. A material with a fine grain size is unfavorable for the creep resistance becauselots of grain boundaries could effectively facilitate the formation of cavities and cracks. Itcould be pronounced from the comparison of crack growth results in Fig. 3 with those ofLu et al. (2006) and Lee et al. (2007). The time-dependent cracking range of HAYNES188 with the smallest grain size at 649◦C is the largest and the cycle-dependent crackingrange is the smallest among three alloys, which support that an intergranular fracture couldoccur with the shortest hold time for HAYNES 188 alloy. As a result, it results in highercrack-propagation rates. However, as the temperature is higher, the crack-growth rate of theHASTELLOY X alloy with the largest grain size is the highest. Especially at 927◦C, theHASTELLOY X alloy had the highest crack-growth rates for all hold times, followed bythe HAYNES 230 alloy and the HAYNES 188 alloy, corresponding to the order of decreaseof grain size. It might be thought that the grain size has some influences on the kinetics ofthe formation of intergranular fracture. As shown in Fig. 3(b), the time-dependent crack-ing range of HASTELLOY X at 816◦C is the largest among three alloys (Lu et al. 2006;Lee et al. 2007), which means that the time-dependent cracking was developed at shorterhold time for HASTELLOY X alloy. When the hold times greater than 2 minutes are applied,Fig. 8(b) presents that unit time-crack-growth rate of HASTELLOY X maintains constant,while longer hold times greater than 1 hour are required for the time-dependent crackingfor HAYNES 188 and HAYNES 230 alloys. It could be also supported by the fractogra-phy analyses for 2 min.-hold tests. As shown in Fig. 5(b), 2 min.-hold test resulted in anintergranular fracture mode for HASTELLOY X with the largest grain size. However, thefracture path was a mixed transgranular/intergranular for HAYNES 188 and HAYNES 230,as illustrated in Lu et al. (2006) and Lee et al. (2008). It is concluded that an intergranularfracture for HASTELLOY X with the largest grain size is occurred at shorter hold time.Therefore, the crack-growth rate of the HASTELLOY X alloy with the largest grain size isthe highest among three alloys.

4 Summary

The crack-growth experiments of HASTELLOY X with various hold times were performedunder a constant �K-control mode at the temperatures of 649◦C, 816◦C, and 927◦C. Thecyclic-crack-growth rate increased as the hold time and temperature increased. The unittime-crack-growth rate decreased with increasing the hold time at 649◦C and 816◦C. How-ever, the unit time-crack-growth rate maintained approximately constant with increasing thehold time at 927◦C. As a result, the crack-growth rates are dependent on time. Moreover,the effects of grain size on the crack-growth rate are studied by the comparison of three su-peralloys. At 649◦C, the crack-propagation rate of the HAYNES 188 alloy with the smallest


Fig. 9 The microstructure ofthree superalloys (a) HAYNES188; (b) HAYNES 230;(c) HASTELLOY X


grain size was the highest, followed by the HAYNES 230 alloy and HASTELLOY X alloys.At 927◦C, the HASTELLOY X alloy had the highest crack-growth rates for all hold times,followed by the HAYNES 230 alloy and the HAYNES 188 alloy, corresponding to the orderof decrease of grain size.

Acknowledgements This work is supported by the Solar Turbines, Inc., Haynes International, Inc., theCenter for Materials Processing (CMP) at the University of Tennessee (UT), the U.S. Department of En-ergy’s Advanced Turbine Systems Program, the National Science Foundation (NSF), under Grant No. DMI-9724476, the NSF Combined Research-Curriculum Development (CRCD) Programs, under EEC-9527527and EEC-0203415, the Integrative Graduate Education and Research Training (IGERT) Program, under DGE-9987548, and the International Materials Institutes (IMI) Program under DMR-0231320, with Dr. D. Durham,Ms. M. Poats, Dr. C.J. Van Hartesveldt, Dr. D. Dutta, Dr. W. Jennings, Dr. L. Goldberg, and Dr. C. Huber ofNSF as program directors.

References

ASTM Standard E 647-99: Standard Test Method for Measurement of Fatigue Crack-Growth Rates, 2000Annual Book of ASTM Standards, vol. 03.01, pp. 591–630

Haynes online literature, No. H-3009, HASTELLOY X alloy brochure: http://www.haynesintl.comHaynes online literature, No. H-3001, HAYNES 188 alloy brochure: http://www.haynesintl.comHaynes online literature, No. H-3000, HAYNES 230 alloy brochure: http://www.haynesintl.comHour, K.Y., Stubbins, J.F.: Acta Metallurgica Materialia 38, 1463–1474 (1990)Johnson, H.H.: Mater. Res. Stand. 5, 442–445 (1965)Klarstrom, D.L., Lai, G.Y.: Superalloys 1988, pp. 585–594. Reichman, S., Duhl, D.N., Maurer, G., An-

tolovich, S., Lund, C.: The Metallurgical Society/AIME, Champion (1988)Lee, S.Y., Lu, Y.L., Liaw, P.K., Chen, L.J., Benson, M.L., Thompson, S.A., Blust, J.W., Browning, P.F.,

Bhattacharya, A.K., Aurrecoechea, J.M., Klarstrom, D.L.: Eng. Fract. Mech. (2008, to be published)Lee, S.Y., Lu, Y.L., Liaw, P.K., Choo, H., Thompson, S.A., Blust, J.W., Browning, P.F., Bhattacharya, A.K.,

Aurrecoechea, J.M., Klarstrom, D.L.: Key. Eng. Mater. 345–346, 287–290 (2007)Liaw, P.K., Leax, T.R., Fabis, T.R., Donald, J.K.: Eng. Fract. Mech. 26, 1–13 (1987)Lu, Y.L., Chen, L.J., Liaw, P.K., Wang, G.Y., Brooks, C.R., Thompson, S.A., Blust, J.W., Browning, P.F.,

Bhattacharya, A.K., Aurrecoechea, J.M., Klarstrom, D.L.: Mater. Sci. Eng. A 429, 1–10 (2006)Lu, Y.L., Chen, L.J., Liaw, P.K., Wang, G.Y., McDaniels, R.L., Thompson, S.A., Blust, J.W., Browning, P.F.,

Bhattacharya, A.K., Aurrecoechea, J.M., Klarstrom, D.L.: Modeling the Performance of EngineeringStructural Materials III. TMS Fall Meeting, Columbus, Ohio, Oct. 6–9, pp. 123–133 (2002)

Lu, Y.L., Liaw, P.K., Chen, L.J., Wang, G.Y., Benson, M.L., Thompson, S.A., Blust, J.W., Browning, P.F.,Bhattacharya, A.K., Aurrecoechea, J.M., Klarstrom, D.L.: Mater. Sci. Eng. A 433, 114–120 (2006)

Maiya, P.S., Majumdar, S.: Mater. Trans. 8A, 1651–1660 (1977)Miner, R.V., Castelli, M.G.: Metall. Trans. 23A, 551–561 (1992)Ritchie, R.O., Bathe, K.J.: Inter. J. Fract. 15, 47–55 (1979)Rooke, D.P., Cartwright, D.J.: Compendium of Stress Intensity Factors. Her Majesty’s Stationery Office,

London (1976)Tada, H., Paris, P.C., Irwin, G.R.: Stress Analysis of Cracks Handbook. Del Research Co., St. Louis (1985)Tsuji, H., Kondo, T.: J. Nucl. Mater. 150, 259–265 (1987)Yamaguchi, K., Kanazawa, K.: Metall. Mater. Trans. 11A, 1691–1699 (1980)

本文献由“学霸图书馆-文献云下载”收集自网络，仅供学习交流使用。

学霸图书馆（www.xuebalib.com）是一个“整合众多图书馆数据库资源，

提供一站式文献检索和下载服务”的24 小时在线不限IP

图书馆。

图书馆致力于便利、促进学习与科研，提供最强文献下载服务。

图书馆导航：

图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具

http://www.xuebalib.com/cloud/

http://www.xuebalib.com/

http://www.xuebalib.com/cloud/


http://www.xuebalib.com/vip.html

http://www.xuebalib.com/db.php

http://www.xuebalib.com/zixun/2014-08-15/44.html


high-temperature tensile-hold crack-growth behavior x alloy...

Documents