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Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy
Accepted Manuscript Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy H. Matsunaga, M. Makizaki, D.F. Socie, K. Yanase, M. Endo PII: DOI: Reference:
S0013-7944(14)00119-2 http://dx.doi.org/10.1016/j.engfracmech.2014.04.015 EFM 4268
To appear in:
Engineering Fracture Mechanics
Please cite this article as: Matsunaga, H., Makizaki, M., Socie, D.F., Yanase, K., Endo, M., Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy, Engineering Fracture Mechanics (2014), doi: http://dx.doi.org/10.1016/j.engfracmech.2014.04.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy H. Matsunaga1, 2, 3, M. Makizaki4, D.F. Socie5, K. Yanase3, 6 and M. Endo3, 6 1
Department of Mechanical Engineering, Kyushu University, Fukuoka, Japan
2
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Fukuoka, Japan
3
Institute of Materials Science and Technology, Fukuoka University, Fukuoka, Japan
4
Graduate School of Fukuoka University, Fukuoka, Japan
5
Department of Mechanical Science and Engineering, University of Illinois at UrbanaChampaign, Illinois, United States
6
Department of Mechanical Engineering, Fukuoka University, Fukuoka, Japan Corresponding author: H. Matsunaga. Email: [email protected]
ABSTRACT The effect of an occasional mode II loading on the subsequent mode I fatigue crack growth was investigated in a thin-walled 7075-T6511 aluminum alloy tube. Careful observation of crack growth behavior revealed that an occasional mode II loading has two contrasting effects on the subsequent crack growth. First is a retardation effect that is associated with a crack closure development due to the mode II loading. However, this effect was insignificant with respect to the crack growth life as a whole. Second is an acceleration effect that is associated with an accelerated crack growth rate in mode II. It was found that, in a relatively high ΔK regime, mode II crack growth was from one to two orders of magnitude faster than mode I crack growth. This study shows that mode II crack growth should be considered as a predominant factor in evaluating the effect of an occasional mode II loading for a mode I crack in 7075 aluminum alloy.
Keywords: Fatigue crack growth, Occasional shear loading, Shear-mode growth, 7075 aluminum alloy, Crack closure
Submitted to Engineering Fracture Mechanics
1
1. Introduction In practical service conditions for various machine components and structures in aircrafts, automobiles and power generators etc., shear loadings are occasionally mixed with cyclic tensioncompression loadings (e.g. bending and twisting of an aircraft wing). Thus, the effect of occasional mode II loading upon mode I fatigue crack growth has been a matter of concern for various materials [1-7]. With respect to the underlying issues, Nayeb-Hashemi and Taslim [1] studied the effect of a single mode II cycle on subsequent mode I growth in a quenched and tempered AISI 4340 steel. They reported that the mode II loading causes crack growth acceleration for a very short distance, much smaller than the transient plastic zone size. Further, Decreuse et al. [2] obtained similar results for S355NL steel. Sander and Richard [3] carried out a series of fatigue tests to investigate the effect of mixed mode overloading in 7075-T651 aluminum alloy. They found that a pure mode II overloading had a negligible influence on the subsequent mode I growth. In contrast, Dahlin and Olsson [4-6] demonstrated a marked reduction of subsequent mode I growth due to a single mode II loading in AISI 01 steel. Retardation of crack growth was also observed by Hua and Fernando [7] in a quenched and tempered low alloy steel. Acceleration or retardation due to occasional mode II loading, if any, has been attributed to the following crack closure mechanisms [1, 5]: (i) roughness induced fatigue crack closure (RIFCC) caused by a mismatch between crack faces due to relative tangential displacement, and (ii) plasticity-induced fatigue crack closure (PIFCC) caused by a large stretch of material in the vicinity of the crack tip. In the literature, Dahlin and Olsson [5] analyzed the RIFCC caused by a single mode II loading by using a theoretical model by Budiansky and Hutchinson [8]. They successfully simulated the experimental results for AISI 01 steel and showed that the recovery distance (i.e. distance for the crack growth rate to revert to its original level) is much larger than the size of the mode II induced plastic zone. On the other hand, Nayeb-Hashemi and Taslim [1] discussed the PIFCC due to mode II overloading. It is well known that mode II loading can produce a much larger plastic zone compared to mode I loading. Correspondingly, Fig. 1 illustrates the shapes and dimensions of the respective plastic zones formed by modes I and II loadings based on the von Mises yield condition [9]. Nayeb-Hashemi and Taslim [1] point out that mode II overloading can cause a small amount of crack acceleration while mode I overloading causes a significant retardation, both of which are closely related to the amount of plastic stretch near the crack tip as
2
well as the crack face interference. The above studies by two research groups [1, 4-6] infer that RIFCC can play more dominant role than PIFCC in determining the behavior of subsequent mode I growth after occasional mode II loading. Nonetheless, it is not a straightforward task to justify whether occasional mode II loading causes acceleration or retardation for the subsequent crack growth for other loading conditions and materials. To understand such a complicated phenomenon, the effects of these factors need to be quantified based on the experimental observations and adequate mechanistic modeling. In this study, our focus is on 7075 aluminum alloy that has been widely used for aircraft structures. Based on a series of observations of fatigue crack growth behaviors, dominating factors on the effect of the mode II loading are discussed.
2. Experimental 2.1. Material The study was carried out by using a commercial grade 7075-T6511 aluminum alloy. The chemical composition in mass % was 0.1 Si, 0.25 Fe, 1.6 Cu, 0.06 Mn, 2.6 Mg, 0.2 Cr, 5.6 Zn, 0.01 Ti and bal. Al. The 0.2 % offset yield and tensile strength of the alloy was found to be 600 and 634 MPa, respectively. The average Vickers hardness, HV, measured with a load of 9.8 N was 184.
2.2. Specimen Thin-walled tubular specimens were machined from a 16 mm-diameter round bar. Fig. 2 shows the shape and dimensions of the specimen: 12 mm outer-diameter and 1 mm wall-thickness at the test section. The specimen surface was finished by polishing with an emery paper and then by buffing with an alumina paste. In the middle of specimen, a through hole (1 mm diameter) was introduced as a crack starter.
2.3. Fatigue tests Two types of servo-hydraulic fatigue testing machines, uniaxial tension-compression and combined tension-torsion, were used to apply the mode I and mode II loadings, respectively. The machines were operated at a test frequency of 0.1~10 Hz. A stress ratio R of −1 was selected both for the mode I and mode II loadings. Fatigue crack growth behavior was investigated by applying two series of loading sequences:
3
(i) Sequence A: A single mode II loading in the middle of mode I fatigue test (cf. Fig. 3(a)) At first, fatigue crack was initiated and propagated in mode I from the 1-mm drill hole under a constant amplitude tension-compression loading. After the total crack length including hole, 2a reached 2 mm, 1-cycle of torsion was applied. Thereafter, the tension-compression fatigue test was resumed. (ii) Sequence B: Mode II fatigue test after mode I fatigue test (cf. Fig. 3(b)) Similar to Sequence A, a crack was grown to a length 2a of 2 mm under a constant amplitude tension-compression loading. Then, the loading type was switched to cyclic torsion, and the crack was propagated under mode II loading.
The fatigue tests were periodically halted for microscopic observation of crack growth processes, and the crack length at specimen surface was measured by using the plastic replica method. Stress intensity factors, KI and KII, were caluculated by considering a cylindrical shell with a circumferential crack subjected to tension and torsion, respectively [10, 11].
3. Results and discussion 3.1. Effect of a single mode II loading on mode I fatigue crack growth (Sequence A) Fig. 4 shows the crack growth curves obtained for Sequence A. The value of ΔKI in the figure indicates the mode I stress intensity factor range when a single mode II cycle is applied, and the value of ΔKII single indicates the stress intensity factor range for the single mode II loading. Fig. 5 shows the fatigue cracks just before and after applying the single mode II loading. As the figures show (cf. Figs. 5(c) and 5(d)), even a single mode II cycle causes some amount of crack growth. Such mode II growth will be discussed in detail in the following sections. In all the experiments performed in this study, the crack path in mode I growth was macroscopically perpendicular to the specimen axis even after the mode II loading. This is in contrast to the crack path in steels, in which a single mode II loading results in a slight kink of subseqent mode I growth [6]. Fig. 6 shows the crack growth rate da/dN as a function of ΔKI, which was obtained from the crack growth curves shown in Fig. 4. In the case of (ΔKI, ΔKII single) = (20, 20) in MPa m , the
single mode II cycle had little influence on the subsequent growth (cf. Fig. 6(a)). On the other hand, when ΔKII single is greater than ΔKI (e.g. (ΔKI, ΔKII single) = (15, 25) and (10, 25) in MPa m ), a slight retardation, if any, was observed just after the single mode II loading (cf. Figs. 6(b) and 6(c)). 4
It is noted that the crack length was measured at specimen surface using the plastic replica method. The crack growth at specimen surface was microstructurally irregular, which resulted in a large scatter in da/dN data, as exhibited by Fig. 6. Due to the irregularity, it is difficult to accurately determine the recovery distance within which the growth rate reverts to its original level. However, the recovery distance observed in this study is estimated to be less than a few hundred microns, which is much smaller than the recovery distance in AISI 01 steel reported by Dahlin and Olsson [4-6] (e.g. ≈ 6 mm for (ΔKI, ΔKII single) = (20, 20) in MPa m ). In their experiment, the recovery distance was a order of magnitude larger than the mode II induced plastic zone. Accordingly, they concluded that a primary reason for crack retardation due to a single mode II loading is not PIFCC but RIFCC. In contrast, in this study, the recovery distance is smaller than the size of mode II induced plastic zone. The PZS ahead of mode II crack, rpII, can be approximated by the following equation [12] 3 ⎛ K II ⎞ ⎜ ⎟ rpII = 2π ⎜⎝ σ YS ⎟⎠
2
(1)
where σYS is the yield stress. Note that rpII is the same in plane stress and plane strain, as shown in
Fig. 1. For example, from Eq. (1), rp II is calculated to be 829 μm for the combination of ΔKII =25 MPa m and σYS = 600 MPa. As indicated above, crack growth retardation due to occasional mode II loading is strongly dependent on material type, loading level etc., which can influence the crack closure behavior after the mode II loading. The material dependence of crack closure behavior has been discussed for mode I fatigue crack growth by Ishihara et al. [13]. They point out that PIFCC is favored in alloys of low elastic modulus and relatively low yield strength. In addition, materials with a low strainhardening rate (e.g. 6061 aluminum alloy) favor PIFCC. On the other hand, steels having a higher elastic modulus and a higher strain-hardening rate, in general, exhibit RIFCC, even though they have a comparable yield strength level to aluminum alloys. For example, in ferritic steels, the roughness of fracture surface is larger and the crack-opening level is higher than those in aluminum alloys because of the larger grain size of the microstructure [13]. Also in the crack closure associated with occasional mode II loading, it can be deduced that the mechanical properties and microstructures plays a key role in determining the crack retardation behavior, though the detailed mechanism is unclear at present.
5
As already mentioned, Dahlin and Olsson [4-6] showed that in AISI 01 steel, RIFCC is much more dominant than PIFCC in determining the retardation due to occasional mode II loading. In addition, Nayeb-hashemi and Taslim [1] also point out the insignficance of PIFCC in a quenched and tempered AISI 4340 steel for similar problem. They concluded that residual plastic stretch is missing at the crack front after the mode II overloading, whereas in the case of mode I overloading, the existence of residual plastic stretch at crack front can definitely cause crack retardation [1]. Both of above two series of studies suggest that PIFCC due to a single mode II loading plays a minor role on the subsequent crack growth. In order to clarify those phenomenon in more detail, we performed a crack growth simulation to quantify the change in PIFCC due to a single mode II loading in a twodimensional middle-crack tension geometry by using the finite element analysis. The detail of the method is illustrated in a separate paper [14]. Fig. 7 shows the examples of the results; the relationship between the range of crack tip opening displacement, ΔCTOD, and crack length under plane strain and plane stress conditions [14]. It is noted that in the analyses, the crack faces were modeled as a horizontal straight line, i.e. the RIFCC was not taken into account but only the PIFCC was simulated. For example, in the case of ΔKI = ΔKII single, ΔCTOD was decreased by 15 ~ 25 % compared to the original level, and the recovery distance was nearly the same as the plastic zone formed by the mode II loading. The results indicate that PIFCC can slightly be enhanced by a single mode II loading, but it can play a minor role in the crack growth life as a whole.
3.2 Fatigue crack growth under cyclic mode II loading (Sequence B) Fig. 8 shows the crack growth curves obtained for Sequence B. Fig. 9 shows the fatigue cracks before and after switching the loading type. For ΔKII larger than 7 MPa m , no crack branching occurred and the crack grew macroscopically straight in the mode II direction. In steels, it has been observed that a crack under cyclic shear loading can easily branch and grow in diagonal directions [15-19]. On the other hand, in aluminum alloys, the fatigue crack can propagate in the mode II direction by cyclic shear loading in a wider range of ΔKII [20-22]. In this respect, the aluminum alloy has a unique fatigue characteristic different from steels. Fig. 10 shows the crack growth rate da/dN as a function of ΔK, which was obtained from the crack growth curve shown in Fig. 8. In the figures, the open symbols represent the mode I crack growth and the closed symbols represent the mode II crack growth. After switching the loading type from mode I to mode II, the crack growth rate was significantly increased (cf. Figs. 10(a) and 10(b)), and this is in strong contrast to the results for
6
Sequence A (cf. Fig. 6). Corresponding to Fig. 8(c), Fig. 10(c) shows the crack growth rate as a function of ΔKII for a ΔKII-decreasing test, where ΔKII was decreased from 15 to 7 MPa m . The mode II growth gradually decelerated with a decrease in ΔKII, and the crack finally branched to propagate in the mode I direction at ΔKII of ≈ 7 MPa m , as shown in Fig. 11.
3.3 Effect of occasional mode II loading on the mode I fatigue crack growth Fig. 12 summarizes all of the da/dN data in Figs. 6 and 10. At higher ΔK level (e.g. ΔK = 15 ~ 30 MPa m ), the mode II crack growth was about an order of magnitude faster than the mode I crack growth. Similar phenomenon of 7075-T6 aluminum alloy was also reported by Otsuka et al. for a different stress ratio [22]. In Fig. 12, both of the two series of da/dN for modes I and II decrease gradually with a decrease in ΔK level, and they merged at ΔK ≈ 10 MPa m .
Fig. 12 also includes the increment of crack length due to the single mode II loading in Sequence A, which were measured at specimen surface (cf. Figs. 5(c) and 5(d)). The increment due to the single mode II loading (■) is even larger than da/dN values in the stable mode II growth ( ). The reason for such a remarkable growth due to the single mode II loading can be explained as follows. It is known that the crack front edge of a stably propagating crack should terminate at the surface obliquely. Fig. 13 schematically illustrates the fronts of propagating cracks in a plate under modes I and II loadings [23]. In a stable mode I growth, the crack prefers to grow at the middle of thickness (cf. Fig. 13(a)) [13, 23], whereas in a stable mode II growth, the crack prefers to grow at the surface (cf. Fig. 13(b)) [24, 25]. Owing to this difference in crack front shape between stable mode I growth and stable mode II growth, an occasional mode II loading mixed with a stable mode I growth can generate more severe stress state near the surface, which causes the non-uniform growth preferentially near the surface. As seen above, in 7075 aluminum alloy, the mode II loading has a greater driving force to grow the crack than mode I loading. Therefore, in evaluating the effect of occasional mode II loading, the mode II crack growth should be considered as a predominant factor.
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Conclusions Effect of occasional mode II loading on subsequent mode I fatigue crack growth was studied by using a thin-walled tube made of 7075-T6511 aluminum alloy. According to the present study, the following conclusions were obtained. (1) Fatigue crack closure due to a single mode II loading had negligible influence for the subsequent mode I crack growth. (2) Under relatively high ΔK level, the mode II growth was an order of magnitude faster than the mode I growth. Moreover, the occasional mode II loading can further accelerate the crack growth near the surface due to a mechanistic reason related to the crack front shape. Therefore, in evaluating the effect of occasional mode II loading on the crack growth life, it is essential to consider the accelerated mode II growth.
Acknowledgements This research was in part sponsored by Japanese Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C) (Fund number 22560092, 2010-2012) and in part by Shiraisi Research Fund (Fukuoka University). The first author gratefully acknowledges the support of the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology.
References 1. Nayeb-Hashemi H, Taslim ME. Effects of the transient mode II on the steady state crack growth in mode I. Engineering Fracture Mechanics 1987; 26: 789-807. 2. Decreuse PY, Pommier S, Gentot L, Pattofatto S. History effect in fatigue crack growth under mixed-mode loading conditions. International Journal of Fatigue 2009; 31: 1733-41. 3. Sander M, Richard HA. Lifetime predictions for real loading situations—concepts and experimental results of fatigue crack growth. International Journal of Fatigue 2003; 25: 9991005. 4. Dahlin P, Olsson M. Reduction of mode I fatigue crack growth rate due to occasional mode II loading. International Journal of Fatigue 2004; 26: 1083-93. 5. Dahlin P, Olsson M. Mode I fatigue crack growth reduction mechanisms after a single mode II load cycle. Engineering Fracture Mechanics 2006; 73: 1833-48. 6. Dahlin P, Olsson M. Fatigue crack growth − mode I cycles with periodic mode II loading. International Journal of Fatigue 2008; 30: 931-41. 8
7. Hua G, Fernando US. Effect of non-proportional overloading on fatigue life. Fatigue & Fracture of Engineering Materials & Structures 1996; 19: 1197-1206. 8. Budiansky B, Hutchinson JW. Analysis of closure in fatigue crack growth. Journal of Applied Mechanics 1978; 45: 267-76. 9. Jing P, Khraishi T, Gorbatikh L. Closed-form solutions for the mode II crack tip plastic zone shape. International Journal of Fracture 2003; 122: L137-42. 10. Murakami Y, Editor-in-chief. Stress Intensity Factors Handbook. Vol. 2, 1359-60. Oxford: Pergamon press; 1987. 11. Murakami Y, Editor-in-chief. Stress Intensity Factors Handbook. Vol. 3, 916-18. Oxford: Pergamon press; 1992. 12. Hua G, Brown MW, Miller KJ. Mixed-mode fatigue thresholds. Fatigue & Fracture of Engineering Materials & Structures 1982; 5: 1-17. 13. Ishihara S, Sugai Y, McEvily AJ. On the distinction between plasticity- and roughness-induced fatigue crack closure. Metallurgical and Materials Transactions 2012; A43: 3086-96. 14. Matsunaga H, Makizaki M, Yanase K. Finite element modeling of plasticity-induced crack closure due to occasional mode II loading on mode I fatigue crack growth. Engineering Fracture Mechanics, in press. 15. Murakami Y, Hamada S. A new method for the measurement of mode II fatigue threshold stress intensity factor range ΔKτth. Fatigue & Fracture of Engineering Materials & Structures 1997; 20: 863-70. 16. Takahashi K, Murakami Y. Torsional fatigue strength of specimens containing an initial small crack introduced by tension-compression fatigue. Transactions of the Japan Society of Mechanical Engineers A 2002; 68: 645-52. 17. Matsunaga H, Muramoto S, Shomura N, Endo M. Shear mode growth and threshold of small fatigue cracks in SUJ2 bearing steel. Journal of the Society of Materials Science, Japan 2009; 58: 773-80. 18. Zhang H, Fatemi A. Short fatigue crack growth behavior under mixed-mode loading. International Journal of Fracture 2010; 165: 1-19. 19. Matsunaga H, Muramoto S, Shomura N, Endo M. Shear mode threshold for a small fatigue crack in a bearing steel. Fatigue & Fracture of Engineering Materials & Structures 2010; 34: 7282. 20. Otsuka A, Tohgo K, Matsuyama H. Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6. Engineering Fracture Mechanics 1987; 28: 721-32. 21. Qian J, Fatemi A. Mixed mode fatigue crack growth: A literature survey. Engineering Fracture Mechanics 1996; 55: 969-90. 22. Otsuka A, Mori K, Ohshima T, Tsuyama S. Fatigue crack growth of steel and aluminum alloy specimens under mode II loading. Journal of the Society of Materials Science, Japan 1980; 29: 9
1042-48. 23. Bažant ZP, Estenssoro L.F. Surface singularity and crack propagation. International Journal of Solids and Structures 1979; 15: 405-26. 24. Otsuka A, Tohgo K, Yoshida M. Fatigue crack growth of a mixed mode three-dimensional crack (2nd report, fatigue crack growth behavior from a semi-elliptical surface crack under shear loading). Journal of the Society of Materials Science, Japan 1988; 58: 1735-44. 25. Murakami Y, Takahashi K, Kusumoto R. Threshold and growth mechanism of fatigue cracks under mode II and III loadings. Fatigue & Fracture of Engineering Materials & Structures 2003; 26: 523-31.
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Fig.1 Shapes and dimensions of the plastic zone formed by the modes I and II loadings
Fig.2 Shape and dimensions of the specimen
11
(a) Loading sequence A ((ΔKI, ΔKII single) = (20, 20), (15, 25) and (10, 25) in MPa
(b) Loading sequence B ((ΔKI, ΔKII) = (15, 15), (20, 20) and (15, 15 7) in MPa Fig.3 Loading sequences
12
at 2a = 2mm)
at 2a = 2mm)
(a) (ΔKI, ΔKII single) = (20, 20) in MPa
(b) (ΔKI, ΔKII single) = (15, 25) in MPa
(c) (ΔKI, ΔKII single) = (10, 25) in MPa Fig.4 Crack growth curves in Sequence A
13
(a) Just before single mode II loading (2a = 2 mm, ΔKI = 20 MPa
(b) Just after single mode II loading (ΔKII single = 20 MPa
)
(c) Just before single mode II loading (2a = 2 mm, ΔKI = 10 MPa
(d) Just after single mode II loading (ΔKII single = 25 MPa
)
Fig.5 Fatigue cracks before and after a single mode II loading
14
)
)
(a) (ΔKI, ΔKII single) = (20, 20) in MPa
(b) (ΔKI, ΔKII single) = (15, 25) in MPa
(c) (ΔKI, ΔKII single) = (10, 25) in MPa Fig.6 Relationships between da/dN and ΔKI in Sequence A
15
(a) (ΔKI, ΔKII single) = (20, 20) in MPa
under plane strain condition
(b) (ΔKI, ΔKII single) = (20, 20) in MPa
under plane stress condition
Fig.7 Results of FEM analysis for PIFCC [14]
16
(a) (ΔKI, ΔKII) = (15, 15) in MPa
(b) (ΔKI, ΔKII) = (20, 20) in MPa
(c) (ΔKI, ΔKII) = (15, 15 7) in MPa Fig.8 Crack growth curves in Sequence B
17
(a) Just before mode II loading (2a = 2 mm, ΔKI = 15 MPa
(b) After 100-cycle mode II loading (ΔKII ≈ 15 MPa
)
)
(c) Just before mode II loading (2a = 2 mm, ΔKI = 20 MPa
(d) After 100-cycle mode II loading (ΔKII ≈ 20 MPa
)
)
Fig.9 Fatigue cracks before and after 100-cycle mode II loading
18
(a) (ΔKI, ΔKII) = (15, 15) in MPa
(b) (ΔKI, ΔKII) = (20, 20) in MPa
(c) (ΔKI, ΔKII) = (15, 15 7) in MPa Fig.10 Relationships between da/dN and ΔK in Sequence B
19
Fig.11 Branched crack
Fig.12 Summary of the da/dN data
20
(a) Stable mode I growth
(b) Stable mode II growth Fig.13 Crack front shapes on the stable growth under modes I and II loadings
Highlights •
We study the effect of occasional mode II loading on mode I fatigue crack growth.
•
A thin-walled 7075-T6511 aluminum alloy tube is used.
•
Retardation effect by crack closure is negligible.
•
Mode II growth is much faster than mode I growth in this alloy.
•
The accelerated mode II growth should be considered as a predominant factor.
21
Nomenclature a
half crack length
CTODmax
maximum crack tip opening displacement
CTODmin
minimum crack tip opening displacement
da/dN
crack growth rate
KI, KII
stress intensity factors in modes I and II
Kmax
maximum stress intensity factor
Kmin
minimum stress intensity factor
N
number of cycles
R
stress ratio (= Kmin/Kmax)
RI, RII
stress ratio in modes I and II
ΔCTOD
range of crack tip opening displacement
ΔK
stress intensity factor range
ΔKI, ΔKII
stress intensity factor ranges in modes I and II
ΔKII single
stress intensity factor range in mode II for a single shear loading
rpII
size of forward plastic zone in mode II
σa
normal stress amplitude
σYS
yield stress
τa
shear stress amplitude
22
S0013-7944(14)00119-2 http://dx.doi.org/10.1016/j.engfracmech.2014.04.015 EFM 4268
To appear in:
Engineering Fracture Mechanics
Please cite this article as: Matsunaga, H., Makizaki, M., Socie, D.F., Yanase, K., Endo, M., Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy, Engineering Fracture Mechanics (2014), doi: http://dx.doi.org/10.1016/j.engfracmech.2014.04.015
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Acceleration of fatigue crack growth due to occasional mode II loading in 7075 aluminum alloy H. Matsunaga1, 2, 3, M. Makizaki4, D.F. Socie5, K. Yanase3, 6 and M. Endo3, 6 1
Department of Mechanical Engineering, Kyushu University, Fukuoka, Japan
2
International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Fukuoka, Japan
3
Institute of Materials Science and Technology, Fukuoka University, Fukuoka, Japan
4
Graduate School of Fukuoka University, Fukuoka, Japan
5
Department of Mechanical Science and Engineering, University of Illinois at UrbanaChampaign, Illinois, United States
6
Department of Mechanical Engineering, Fukuoka University, Fukuoka, Japan Corresponding author: H. Matsunaga. Email: [email protected]
ABSTRACT The effect of an occasional mode II loading on the subsequent mode I fatigue crack growth was investigated in a thin-walled 7075-T6511 aluminum alloy tube. Careful observation of crack growth behavior revealed that an occasional mode II loading has two contrasting effects on the subsequent crack growth. First is a retardation effect that is associated with a crack closure development due to the mode II loading. However, this effect was insignificant with respect to the crack growth life as a whole. Second is an acceleration effect that is associated with an accelerated crack growth rate in mode II. It was found that, in a relatively high ΔK regime, mode II crack growth was from one to two orders of magnitude faster than mode I crack growth. This study shows that mode II crack growth should be considered as a predominant factor in evaluating the effect of an occasional mode II loading for a mode I crack in 7075 aluminum alloy.
Keywords: Fatigue crack growth, Occasional shear loading, Shear-mode growth, 7075 aluminum alloy, Crack closure
Submitted to Engineering Fracture Mechanics
1
1. Introduction In practical service conditions for various machine components and structures in aircrafts, automobiles and power generators etc., shear loadings are occasionally mixed with cyclic tensioncompression loadings (e.g. bending and twisting of an aircraft wing). Thus, the effect of occasional mode II loading upon mode I fatigue crack growth has been a matter of concern for various materials [1-7]. With respect to the underlying issues, Nayeb-Hashemi and Taslim [1] studied the effect of a single mode II cycle on subsequent mode I growth in a quenched and tempered AISI 4340 steel. They reported that the mode II loading causes crack growth acceleration for a very short distance, much smaller than the transient plastic zone size. Further, Decreuse et al. [2] obtained similar results for S355NL steel. Sander and Richard [3] carried out a series of fatigue tests to investigate the effect of mixed mode overloading in 7075-T651 aluminum alloy. They found that a pure mode II overloading had a negligible influence on the subsequent mode I growth. In contrast, Dahlin and Olsson [4-6] demonstrated a marked reduction of subsequent mode I growth due to a single mode II loading in AISI 01 steel. Retardation of crack growth was also observed by Hua and Fernando [7] in a quenched and tempered low alloy steel. Acceleration or retardation due to occasional mode II loading, if any, has been attributed to the following crack closure mechanisms [1, 5]: (i) roughness induced fatigue crack closure (RIFCC) caused by a mismatch between crack faces due to relative tangential displacement, and (ii) plasticity-induced fatigue crack closure (PIFCC) caused by a large stretch of material in the vicinity of the crack tip. In the literature, Dahlin and Olsson [5] analyzed the RIFCC caused by a single mode II loading by using a theoretical model by Budiansky and Hutchinson [8]. They successfully simulated the experimental results for AISI 01 steel and showed that the recovery distance (i.e. distance for the crack growth rate to revert to its original level) is much larger than the size of the mode II induced plastic zone. On the other hand, Nayeb-Hashemi and Taslim [1] discussed the PIFCC due to mode II overloading. It is well known that mode II loading can produce a much larger plastic zone compared to mode I loading. Correspondingly, Fig. 1 illustrates the shapes and dimensions of the respective plastic zones formed by modes I and II loadings based on the von Mises yield condition [9]. Nayeb-Hashemi and Taslim [1] point out that mode II overloading can cause a small amount of crack acceleration while mode I overloading causes a significant retardation, both of which are closely related to the amount of plastic stretch near the crack tip as
2
well as the crack face interference. The above studies by two research groups [1, 4-6] infer that RIFCC can play more dominant role than PIFCC in determining the behavior of subsequent mode I growth after occasional mode II loading. Nonetheless, it is not a straightforward task to justify whether occasional mode II loading causes acceleration or retardation for the subsequent crack growth for other loading conditions and materials. To understand such a complicated phenomenon, the effects of these factors need to be quantified based on the experimental observations and adequate mechanistic modeling. In this study, our focus is on 7075 aluminum alloy that has been widely used for aircraft structures. Based on a series of observations of fatigue crack growth behaviors, dominating factors on the effect of the mode II loading are discussed.
2. Experimental 2.1. Material The study was carried out by using a commercial grade 7075-T6511 aluminum alloy. The chemical composition in mass % was 0.1 Si, 0.25 Fe, 1.6 Cu, 0.06 Mn, 2.6 Mg, 0.2 Cr, 5.6 Zn, 0.01 Ti and bal. Al. The 0.2 % offset yield and tensile strength of the alloy was found to be 600 and 634 MPa, respectively. The average Vickers hardness, HV, measured with a load of 9.8 N was 184.
2.2. Specimen Thin-walled tubular specimens were machined from a 16 mm-diameter round bar. Fig. 2 shows the shape and dimensions of the specimen: 12 mm outer-diameter and 1 mm wall-thickness at the test section. The specimen surface was finished by polishing with an emery paper and then by buffing with an alumina paste. In the middle of specimen, a through hole (1 mm diameter) was introduced as a crack starter.
2.3. Fatigue tests Two types of servo-hydraulic fatigue testing machines, uniaxial tension-compression and combined tension-torsion, were used to apply the mode I and mode II loadings, respectively. The machines were operated at a test frequency of 0.1~10 Hz. A stress ratio R of −1 was selected both for the mode I and mode II loadings. Fatigue crack growth behavior was investigated by applying two series of loading sequences:
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(i) Sequence A: A single mode II loading in the middle of mode I fatigue test (cf. Fig. 3(a)) At first, fatigue crack was initiated and propagated in mode I from the 1-mm drill hole under a constant amplitude tension-compression loading. After the total crack length including hole, 2a reached 2 mm, 1-cycle of torsion was applied. Thereafter, the tension-compression fatigue test was resumed. (ii) Sequence B: Mode II fatigue test after mode I fatigue test (cf. Fig. 3(b)) Similar to Sequence A, a crack was grown to a length 2a of 2 mm under a constant amplitude tension-compression loading. Then, the loading type was switched to cyclic torsion, and the crack was propagated under mode II loading.
The fatigue tests were periodically halted for microscopic observation of crack growth processes, and the crack length at specimen surface was measured by using the plastic replica method. Stress intensity factors, KI and KII, were caluculated by considering a cylindrical shell with a circumferential crack subjected to tension and torsion, respectively [10, 11].
3. Results and discussion 3.1. Effect of a single mode II loading on mode I fatigue crack growth (Sequence A) Fig. 4 shows the crack growth curves obtained for Sequence A. The value of ΔKI in the figure indicates the mode I stress intensity factor range when a single mode II cycle is applied, and the value of ΔKII single indicates the stress intensity factor range for the single mode II loading. Fig. 5 shows the fatigue cracks just before and after applying the single mode II loading. As the figures show (cf. Figs. 5(c) and 5(d)), even a single mode II cycle causes some amount of crack growth. Such mode II growth will be discussed in detail in the following sections. In all the experiments performed in this study, the crack path in mode I growth was macroscopically perpendicular to the specimen axis even after the mode II loading. This is in contrast to the crack path in steels, in which a single mode II loading results in a slight kink of subseqent mode I growth [6]. Fig. 6 shows the crack growth rate da/dN as a function of ΔKI, which was obtained from the crack growth curves shown in Fig. 4. In the case of (ΔKI, ΔKII single) = (20, 20) in MPa m , the
single mode II cycle had little influence on the subsequent growth (cf. Fig. 6(a)). On the other hand, when ΔKII single is greater than ΔKI (e.g. (ΔKI, ΔKII single) = (15, 25) and (10, 25) in MPa m ), a slight retardation, if any, was observed just after the single mode II loading (cf. Figs. 6(b) and 6(c)). 4
It is noted that the crack length was measured at specimen surface using the plastic replica method. The crack growth at specimen surface was microstructurally irregular, which resulted in a large scatter in da/dN data, as exhibited by Fig. 6. Due to the irregularity, it is difficult to accurately determine the recovery distance within which the growth rate reverts to its original level. However, the recovery distance observed in this study is estimated to be less than a few hundred microns, which is much smaller than the recovery distance in AISI 01 steel reported by Dahlin and Olsson [4-6] (e.g. ≈ 6 mm for (ΔKI, ΔKII single) = (20, 20) in MPa m ). In their experiment, the recovery distance was a order of magnitude larger than the mode II induced plastic zone. Accordingly, they concluded that a primary reason for crack retardation due to a single mode II loading is not PIFCC but RIFCC. In contrast, in this study, the recovery distance is smaller than the size of mode II induced plastic zone. The PZS ahead of mode II crack, rpII, can be approximated by the following equation [12] 3 ⎛ K II ⎞ ⎜ ⎟ rpII = 2π ⎜⎝ σ YS ⎟⎠
2
(1)
where σYS is the yield stress. Note that rpII is the same in plane stress and plane strain, as shown in
Fig. 1. For example, from Eq. (1), rp II is calculated to be 829 μm for the combination of ΔKII =25 MPa m and σYS = 600 MPa. As indicated above, crack growth retardation due to occasional mode II loading is strongly dependent on material type, loading level etc., which can influence the crack closure behavior after the mode II loading. The material dependence of crack closure behavior has been discussed for mode I fatigue crack growth by Ishihara et al. [13]. They point out that PIFCC is favored in alloys of low elastic modulus and relatively low yield strength. In addition, materials with a low strainhardening rate (e.g. 6061 aluminum alloy) favor PIFCC. On the other hand, steels having a higher elastic modulus and a higher strain-hardening rate, in general, exhibit RIFCC, even though they have a comparable yield strength level to aluminum alloys. For example, in ferritic steels, the roughness of fracture surface is larger and the crack-opening level is higher than those in aluminum alloys because of the larger grain size of the microstructure [13]. Also in the crack closure associated with occasional mode II loading, it can be deduced that the mechanical properties and microstructures plays a key role in determining the crack retardation behavior, though the detailed mechanism is unclear at present.
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As already mentioned, Dahlin and Olsson [4-6] showed that in AISI 01 steel, RIFCC is much more dominant than PIFCC in determining the retardation due to occasional mode II loading. In addition, Nayeb-hashemi and Taslim [1] also point out the insignficance of PIFCC in a quenched and tempered AISI 4340 steel for similar problem. They concluded that residual plastic stretch is missing at the crack front after the mode II overloading, whereas in the case of mode I overloading, the existence of residual plastic stretch at crack front can definitely cause crack retardation [1]. Both of above two series of studies suggest that PIFCC due to a single mode II loading plays a minor role on the subsequent crack growth. In order to clarify those phenomenon in more detail, we performed a crack growth simulation to quantify the change in PIFCC due to a single mode II loading in a twodimensional middle-crack tension geometry by using the finite element analysis. The detail of the method is illustrated in a separate paper [14]. Fig. 7 shows the examples of the results; the relationship between the range of crack tip opening displacement, ΔCTOD, and crack length under plane strain and plane stress conditions [14]. It is noted that in the analyses, the crack faces were modeled as a horizontal straight line, i.e. the RIFCC was not taken into account but only the PIFCC was simulated. For example, in the case of ΔKI = ΔKII single, ΔCTOD was decreased by 15 ~ 25 % compared to the original level, and the recovery distance was nearly the same as the plastic zone formed by the mode II loading. The results indicate that PIFCC can slightly be enhanced by a single mode II loading, but it can play a minor role in the crack growth life as a whole.
3.2 Fatigue crack growth under cyclic mode II loading (Sequence B) Fig. 8 shows the crack growth curves obtained for Sequence B. Fig. 9 shows the fatigue cracks before and after switching the loading type. For ΔKII larger than 7 MPa m , no crack branching occurred and the crack grew macroscopically straight in the mode II direction. In steels, it has been observed that a crack under cyclic shear loading can easily branch and grow in diagonal directions [15-19]. On the other hand, in aluminum alloys, the fatigue crack can propagate in the mode II direction by cyclic shear loading in a wider range of ΔKII [20-22]. In this respect, the aluminum alloy has a unique fatigue characteristic different from steels. Fig. 10 shows the crack growth rate da/dN as a function of ΔK, which was obtained from the crack growth curve shown in Fig. 8. In the figures, the open symbols represent the mode I crack growth and the closed symbols represent the mode II crack growth. After switching the loading type from mode I to mode II, the crack growth rate was significantly increased (cf. Figs. 10(a) and 10(b)), and this is in strong contrast to the results for
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Sequence A (cf. Fig. 6). Corresponding to Fig. 8(c), Fig. 10(c) shows the crack growth rate as a function of ΔKII for a ΔKII-decreasing test, where ΔKII was decreased from 15 to 7 MPa m . The mode II growth gradually decelerated with a decrease in ΔKII, and the crack finally branched to propagate in the mode I direction at ΔKII of ≈ 7 MPa m , as shown in Fig. 11.
3.3 Effect of occasional mode II loading on the mode I fatigue crack growth Fig. 12 summarizes all of the da/dN data in Figs. 6 and 10. At higher ΔK level (e.g. ΔK = 15 ~ 30 MPa m ), the mode II crack growth was about an order of magnitude faster than the mode I crack growth. Similar phenomenon of 7075-T6 aluminum alloy was also reported by Otsuka et al. for a different stress ratio [22]. In Fig. 12, both of the two series of da/dN for modes I and II decrease gradually with a decrease in ΔK level, and they merged at ΔK ≈ 10 MPa m .
Fig. 12 also includes the increment of crack length due to the single mode II loading in Sequence A, which were measured at specimen surface (cf. Figs. 5(c) and 5(d)). The increment due to the single mode II loading (■) is even larger than da/dN values in the stable mode II growth ( ). The reason for such a remarkable growth due to the single mode II loading can be explained as follows. It is known that the crack front edge of a stably propagating crack should terminate at the surface obliquely. Fig. 13 schematically illustrates the fronts of propagating cracks in a plate under modes I and II loadings [23]. In a stable mode I growth, the crack prefers to grow at the middle of thickness (cf. Fig. 13(a)) [13, 23], whereas in a stable mode II growth, the crack prefers to grow at the surface (cf. Fig. 13(b)) [24, 25]. Owing to this difference in crack front shape between stable mode I growth and stable mode II growth, an occasional mode II loading mixed with a stable mode I growth can generate more severe stress state near the surface, which causes the non-uniform growth preferentially near the surface. As seen above, in 7075 aluminum alloy, the mode II loading has a greater driving force to grow the crack than mode I loading. Therefore, in evaluating the effect of occasional mode II loading, the mode II crack growth should be considered as a predominant factor.
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Conclusions Effect of occasional mode II loading on subsequent mode I fatigue crack growth was studied by using a thin-walled tube made of 7075-T6511 aluminum alloy. According to the present study, the following conclusions were obtained. (1) Fatigue crack closure due to a single mode II loading had negligible influence for the subsequent mode I crack growth. (2) Under relatively high ΔK level, the mode II growth was an order of magnitude faster than the mode I growth. Moreover, the occasional mode II loading can further accelerate the crack growth near the surface due to a mechanistic reason related to the crack front shape. Therefore, in evaluating the effect of occasional mode II loading on the crack growth life, it is essential to consider the accelerated mode II growth.
Acknowledgements This research was in part sponsored by Japanese Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C) (Fund number 22560092, 2010-2012) and in part by Shiraisi Research Fund (Fukuoka University). The first author gratefully acknowledges the support of the International Institute for Carbon Neutral Energy Research (WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology.
References 1. Nayeb-Hashemi H, Taslim ME. Effects of the transient mode II on the steady state crack growth in mode I. Engineering Fracture Mechanics 1987; 26: 789-807. 2. Decreuse PY, Pommier S, Gentot L, Pattofatto S. History effect in fatigue crack growth under mixed-mode loading conditions. International Journal of Fatigue 2009; 31: 1733-41. 3. Sander M, Richard HA. Lifetime predictions for real loading situations—concepts and experimental results of fatigue crack growth. International Journal of Fatigue 2003; 25: 9991005. 4. Dahlin P, Olsson M. Reduction of mode I fatigue crack growth rate due to occasional mode II loading. International Journal of Fatigue 2004; 26: 1083-93. 5. Dahlin P, Olsson M. Mode I fatigue crack growth reduction mechanisms after a single mode II load cycle. Engineering Fracture Mechanics 2006; 73: 1833-48. 6. Dahlin P, Olsson M. Fatigue crack growth − mode I cycles with periodic mode II loading. International Journal of Fatigue 2008; 30: 931-41. 8
7. Hua G, Fernando US. Effect of non-proportional overloading on fatigue life. Fatigue & Fracture of Engineering Materials & Structures 1996; 19: 1197-1206. 8. Budiansky B, Hutchinson JW. Analysis of closure in fatigue crack growth. Journal of Applied Mechanics 1978; 45: 267-76. 9. Jing P, Khraishi T, Gorbatikh L. Closed-form solutions for the mode II crack tip plastic zone shape. International Journal of Fracture 2003; 122: L137-42. 10. Murakami Y, Editor-in-chief. Stress Intensity Factors Handbook. Vol. 2, 1359-60. Oxford: Pergamon press; 1987. 11. Murakami Y, Editor-in-chief. Stress Intensity Factors Handbook. Vol. 3, 916-18. Oxford: Pergamon press; 1992. 12. Hua G, Brown MW, Miller KJ. Mixed-mode fatigue thresholds. Fatigue & Fracture of Engineering Materials & Structures 1982; 5: 1-17. 13. Ishihara S, Sugai Y, McEvily AJ. On the distinction between plasticity- and roughness-induced fatigue crack closure. Metallurgical and Materials Transactions 2012; A43: 3086-96. 14. Matsunaga H, Makizaki M, Yanase K. Finite element modeling of plasticity-induced crack closure due to occasional mode II loading on mode I fatigue crack growth. Engineering Fracture Mechanics, in press. 15. Murakami Y, Hamada S. A new method for the measurement of mode II fatigue threshold stress intensity factor range ΔKτth. Fatigue & Fracture of Engineering Materials & Structures 1997; 20: 863-70. 16. Takahashi K, Murakami Y. Torsional fatigue strength of specimens containing an initial small crack introduced by tension-compression fatigue. Transactions of the Japan Society of Mechanical Engineers A 2002; 68: 645-52. 17. Matsunaga H, Muramoto S, Shomura N, Endo M. Shear mode growth and threshold of small fatigue cracks in SUJ2 bearing steel. Journal of the Society of Materials Science, Japan 2009; 58: 773-80. 18. Zhang H, Fatemi A. Short fatigue crack growth behavior under mixed-mode loading. International Journal of Fracture 2010; 165: 1-19. 19. Matsunaga H, Muramoto S, Shomura N, Endo M. Shear mode threshold for a small fatigue crack in a bearing steel. Fatigue & Fracture of Engineering Materials & Structures 2010; 34: 7282. 20. Otsuka A, Tohgo K, Matsuyama H. Fatigue crack initiation and growth under mixed mode loading in aluminum alloys 2017-T3 and 7075-T6. Engineering Fracture Mechanics 1987; 28: 721-32. 21. Qian J, Fatemi A. Mixed mode fatigue crack growth: A literature survey. Engineering Fracture Mechanics 1996; 55: 969-90. 22. Otsuka A, Mori K, Ohshima T, Tsuyama S. Fatigue crack growth of steel and aluminum alloy specimens under mode II loading. Journal of the Society of Materials Science, Japan 1980; 29: 9
1042-48. 23. Bažant ZP, Estenssoro L.F. Surface singularity and crack propagation. International Journal of Solids and Structures 1979; 15: 405-26. 24. Otsuka A, Tohgo K, Yoshida M. Fatigue crack growth of a mixed mode three-dimensional crack (2nd report, fatigue crack growth behavior from a semi-elliptical surface crack under shear loading). Journal of the Society of Materials Science, Japan 1988; 58: 1735-44. 25. Murakami Y, Takahashi K, Kusumoto R. Threshold and growth mechanism of fatigue cracks under mode II and III loadings. Fatigue & Fracture of Engineering Materials & Structures 2003; 26: 523-31.
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Fig.1 Shapes and dimensions of the plastic zone formed by the modes I and II loadings
Fig.2 Shape and dimensions of the specimen
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(a) Loading sequence A ((ΔKI, ΔKII single) = (20, 20), (15, 25) and (10, 25) in MPa
(b) Loading sequence B ((ΔKI, ΔKII) = (15, 15), (20, 20) and (15, 15 7) in MPa Fig.3 Loading sequences
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at 2a = 2mm)
at 2a = 2mm)
(a) (ΔKI, ΔKII single) = (20, 20) in MPa
(b) (ΔKI, ΔKII single) = (15, 25) in MPa
(c) (ΔKI, ΔKII single) = (10, 25) in MPa Fig.4 Crack growth curves in Sequence A
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(a) Just before single mode II loading (2a = 2 mm, ΔKI = 20 MPa
(b) Just after single mode II loading (ΔKII single = 20 MPa
)
(c) Just before single mode II loading (2a = 2 mm, ΔKI = 10 MPa
(d) Just after single mode II loading (ΔKII single = 25 MPa
)
Fig.5 Fatigue cracks before and after a single mode II loading
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)
)
(a) (ΔKI, ΔKII single) = (20, 20) in MPa
(b) (ΔKI, ΔKII single) = (15, 25) in MPa
(c) (ΔKI, ΔKII single) = (10, 25) in MPa Fig.6 Relationships between da/dN and ΔKI in Sequence A
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(a) (ΔKI, ΔKII single) = (20, 20) in MPa
under plane strain condition
(b) (ΔKI, ΔKII single) = (20, 20) in MPa
under plane stress condition
Fig.7 Results of FEM analysis for PIFCC [14]
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(a) (ΔKI, ΔKII) = (15, 15) in MPa
(b) (ΔKI, ΔKII) = (20, 20) in MPa
(c) (ΔKI, ΔKII) = (15, 15 7) in MPa Fig.8 Crack growth curves in Sequence B
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(a) Just before mode II loading (2a = 2 mm, ΔKI = 15 MPa
(b) After 100-cycle mode II loading (ΔKII ≈ 15 MPa
)
)
(c) Just before mode II loading (2a = 2 mm, ΔKI = 20 MPa
(d) After 100-cycle mode II loading (ΔKII ≈ 20 MPa
)
)
Fig.9 Fatigue cracks before and after 100-cycle mode II loading
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(a) (ΔKI, ΔKII) = (15, 15) in MPa
(b) (ΔKI, ΔKII) = (20, 20) in MPa
(c) (ΔKI, ΔKII) = (15, 15 7) in MPa Fig.10 Relationships between da/dN and ΔK in Sequence B
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Fig.11 Branched crack
Fig.12 Summary of the da/dN data
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(a) Stable mode I growth
(b) Stable mode II growth Fig.13 Crack front shapes on the stable growth under modes I and II loadings
Highlights •
We study the effect of occasional mode II loading on mode I fatigue crack growth.
•
A thin-walled 7075-T6511 aluminum alloy tube is used.
•
Retardation effect by crack closure is negligible.
•
Mode II growth is much faster than mode I growth in this alloy.
•
The accelerated mode II growth should be considered as a predominant factor.
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Nomenclature a
half crack length
CTODmax
maximum crack tip opening displacement
CTODmin
minimum crack tip opening displacement
da/dN
crack growth rate
KI, KII
stress intensity factors in modes I and II
Kmax
maximum stress intensity factor
Kmin
minimum stress intensity factor
N
number of cycles
R
stress ratio (= Kmin/Kmax)
RI, RII
stress ratio in modes I and II
ΔCTOD
range of crack tip opening displacement
ΔK
stress intensity factor range
ΔKI, ΔKII
stress intensity factor ranges in modes I and II
ΔKII single
stress intensity factor range in mode II for a single shear loading
rpII
size of forward plastic zone in mode II
σa
normal stress amplitude
σYS
yield stress
τa
shear stress amplitude
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