Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China
Cite this article:
Zhefeng ZHANG, Rui LIU, Zhenjun ZHANG, Yanzhong TIAN, Peng ZHANG. Exploration on the Unified Model for Fatigue Properties Prediction of Metallic Materials. Acta Metall Sin, 2018, 54(11): 1693-1704.
The fatigue of metallic materials can be divided into high-cycle fatigue (HCF) and low-cycle fatigue (LCF); the damage of these two types of fatigue is commonly evaluated through stress amplitude and strain amplitude of cyclic loading, respectively. The mismatch of the evaluation standards between HCF and LCF leads to difficulties in the design and selection of anti-fatigue materials. Under this condition, systematic researches on fatigue properties and microscopic damage mechanisms of HCF, LCF and extra-low-cycle fatigue (ELCF) for pure Cu and Cu-Al alloys were summarized in this work. On the bases of the experimental results, a three-dimensional fatigue model is proposed, which is simultaneously applicable to both the HCF and LCF properties. The model is built up in a three-dimensional coordinate system of stress amplitude-strain amplitude-fatigue life; it could be associated with the cyclic stress-strain (CSS) curve, S-N curve and E-N curve through the projection method, or be transformed into the Basquin equation, Coffin-Manson equation and hysteretic energy model under specific conditions. In this way, this generally applicable fatigue model helps provide a new viewpoint for the evaluation and optimization of fatigue properties based on the classical fatigue theories.
Fund: Supported by National Natural Science Foundation of China (Nos.51331007, 51501198 and 51771208) and the Strategic Priority Research Program of Chinese Academy of Sciences (No.XDB22020202)
Fig.1 S-N curves of high-cycle fatigue (HCF) of coarse-grain (CG) materials (a), fine-grain (FG) materials (b), ultra-fine-grain (UFG) materials (c) and nano-grain (NG) materials (d) in pure Cu and Cu-Al alloys (ECAP—equal-channel angular pressing, HPT—high-pressure torsion, CR—cold-rolling, FSP—friction stir processing, Δσ/2—stress amplitude, Nf—cycles to failure)[12]
Fig.2 Low-cycle fatigue (LCF) properties of E-N curves (a) and S-N curves (b) for pure Cu and Cu-Al alloys (Δε/2—strain amplitude)[12]
Fig.3 Extra-low-cycle fatigue (ELCF) properties of pure Cu and Cu-Al alloys including stabilized cyclic stress-strain (CSS) hysteresis loops with Δε/2=6.0% (a), stabilized CSS hysteresis loops of Cu-8%Al alloy with various strain amplitudes (b), CSS curves (c), E-N curves (d), S-N curves (e) and W-N curves (f) (Wa—hysteresis energy)[12]
Fig.4 Microstructure evolution of pure Cu and Cu-Al alloys during fatigue tests[12] (a1~a3) original states of CG, UFG and NG materials, respectively (b1~b3) microstructures of Cu-5%Al, Cu-11%Al and Cu-15%Al after HCF tests, respectively (c1~c3) microstructures of pure Cu, Cu-5%Al and Cu-11%Al after LCF tests, respectively (d1~d3) microstructures of Cu-5%Al, Cu-8%Al and Cu-11%Al after ELCF tests, respectively
Fig.5 Construction and projection of the three-dimensional fatigue model including hysteresis loop planes, space curve and projected CSS curve (a), space curve and projected S-N curve (b), space curve and projected E-N curve (c) and space plane of the three-dimensional fatigue model, as well as the definition of energy-based evaluation criterion Wf (d)
Microstructure
Material
lg(σ0 / MPa)
lg(ε0 / 106)
lgNf0
lg(Wf / (MJm-3))
CG
Cu
10.56
4.56
25.96
35.09
5Al
9.80
4.21
46.26
54.26
11Al
10.20
4.52
41.88
50.61
15Al
10.40
4.63
39.91
48.95
FG
5Al
9.94
4.69
44.70
53.33
11Al
9.89
4.85
57.12
65.87
15Al
10.61
5.02
56.96
66.60
UFG
Cu
10.30
4.93
37.08
46.30
5Al
9.16
5.08
41.63
49.86
11Al
10.16
5.31
39.72
49.19
15Al
11.23
5.37
42.59
53.19
NG-CR
5Al-CR
11.43
5.48
32.64
43.54
NG-ECAP
Cu-ECAP
11.94
5.60
22.31
33.86
5Al-ECAP
11.79
5.66
25.59
37.04
11Al-ECAP
11.69
5.81
27.15
38.65
NG-HPT
Cu-HPT
12.27
5.76
20.76
32.79
5Al-HPT
12.48
5.97
22.82
35.26
15Al-HPT
12.28
6.08
23.86
36.22
Table 1 Typical values of parameters in the three-dimensional fatigue model for pure Cu and Cu-Al alloys
Fig.6 Validation and plane fitting of the three-dimensional fatigue model for pure Cu (a1, a2), Cu-5%Al (b1, b2) and Cu-11%Al (c1, c2) produced by ECAP from overall view (a1~c1) and partial view (a2~c2) (Data points in black for HCF properties, and data points in red for LCF properties)
Fig.7 Evaluation of fatigue properties based on the three-dimensional fatigue model including plots of Wf against Al contents (a), plots of Wf against grain sizes (b), plots of Wf against Al contents, with materials under different processes (c) and three-dimensional plots of Wf against Al contents and grain sizes (d)
Fig.8 Optimization of fatigue properties based on the three-dimensional fatigue model
[1]
Ashby M F.Materials Selection in Mechanical Design[M]. 4th Ed., Burlington: Butterworth-Heinemann, 2010: 1
[2]
Meyers M A, Chawla K K.Mechanical Behavior of Materials [M]. 2nd Ed., New York: Cambridge University Press, 2005: 1
[3]
Suresh S.Fatigue of Materials [M]. 2nd Ed., Cambridge: Cambridge University Press, 1998: 1
[4]
Forrest P G.Fatigue of Metals [M]. Oxford: Pergamon Press, 1962: 1
[5]
Zhao S B, Manual of Anti-Fatigue Design [M]. 2nd Ed., Beijing: China Machine Press, 2015: 1(赵少汴. 抗疲劳设计手册 [M]. 第2版. 北京: 机械工业出版社, 2015: 1)
[6]
Basquin O H.The exponential law of endurance tests[J]. Am. Soc. Test. Mater., 1910, 10: 625
[7]
Coffin L F Jr. A study of the effects of cyclic thermal stresses on a ductile metal[J]. Trans. ASTM, 1954, 76: 931
[8]
Manson S S.Behavior of materials under conditions of thermal stress [R]. USA: National Advisory Committee for Aeronautics, 1953
[9]
Callister W D Jr, Rethwisch D G. Materials Science and Engineering: An Introduction[M]. 8th Ed., John Wiley and Sons, Inc, 2010: 1
[10]
Shao C W, Zhang P, Liu R, et al.Low-cycle and extremely-low-cycle fatigue behaviors of high-Mn austenitic TRIP/TWIP alloys: Property evaluation, damage mechanisms and life prediction[J]. Acta Mater., 2016, 103: 781
[11]
Kim Y W, Kim G, Hong S G, et al.Energy-based approach to predict the fatigue life behavior of pre-strained Fe-18Mn TWIP steel[J]. Mater. Sci. Eng., 2011, A528: 4696
[12]
Liu R.Investigations on Tensile and Fatigue Properties of Cu-Al alloys [D]. Beijing: University of Chinese Academy of Sciences, 2018(刘睿. 铜铝合金拉伸与疲劳性能研究 [D]. 北京: 中国科学院大学, 2018)
[13]
Liu R, Zhang Z J, Zhang P, et al.Extremely-low-cycle fatigue behaviors of Cu and Cu-Al alloys: Damage mechanisms and life prediction[J]. Acta Mater., 2015, 83: 341
[14]
Shimada K, Komotori J, Shimizu M.The applicability of the Manson-Coffin law and Miner's law to extremely low cycle fatigue[J]. Trans. Jpn. Soc. Mech. Eng., 1987, 53A: 1178
[15]
Shao C W, Zhang P, Liu R, et al.A remarkable improvement of low-cycle fatigue resistance of high-Mn austenitic TWIP alloys with similar tensile properties: Importance of slip mode[J]. Acta Mater., 2016, 118: 196
[16]
An X H, Wu S D, Wang Z G, et al.Enhanced cyclic deformation responses of ultrafine-grained Cu and nanocrystalline Cu-Al alloys[J]. Acta Mater., 2014, 74: 200
[17]
An X H, Lin Q Y, Wu S D, et al.Improved fatigue strengths of nanocrystalline Cu and Cu-Al alloys[J]. Mater. Res. Lett., 2015, 3: 135
[18]
Xue P, Huang Z Y, Wang B B, et al.Intrinsic high cycle fatigue behavior of ultrafine grained pure Cu with stable structure[J]. Sci. China Mater., 2016, 59: 531
[19]
Liu R, Tian Y Z, Zhang Z J, et al.Exploring the fatigue strength improvement of Cu-Al alloys[J]. Acta Mater., 2018, 144: 613
[20]
Liu R, Tian Y Z, Zhang Z J, et al.Fatigue strength plateau induced by microstructure inhomogeneity[J]. Mater. Sci. Eng., 2017, A702: 259
[21]
Liu R, Zhang Z J, Zhang Z F.The criteria for microstructure evolution of Cu and Cu-Al alloys induced by cyclic loading[J]. Mater. Sci. Eng., 2016, A666: 123
[22]
Valiev R Z, Islamgaliev R K, Alexandrov I V.Bulk nanostructured materials from severe plastic deformation[J]. Prog. Mater. Sci., 2000, 45: 103
[23]
Valiev R.Nanostructuring of metals by severe plastic deformation for advanced properties[J]. Nat. Mater., 2004, 3: 511
[24]
H?ppel H W, Zhou Z M, Mughrabi H, et al.Microstructural study of the parameters governing coarsening and cyclic softening in fatigued ultrafine-grained copper[J]. Philos. Mag., 2002, 82A: 1781
[25]
Argon A S.Strengthening Mechanisms in Crystal Plasticity [M]. New York: Oxford University Press, 2008: 1
[26]
Agnew S R, Vinogradov A Y, Hashimoto S, et al.Overview of fatigue performance of Cu processed by severe plastic deformation[J]. J. Electron. Mater., 1999, 28: 1038
[27]
Kocks U F, Mecking H.Physics and phenomenology of strain hardening: The FCC case[J]. Prog. Mater. Sci., 2003, 48: 171
[28]
Qu S, An X H, Yang H J, et al.Microstructural evolution and mechanical properties of Cu-Al alloys subjected to equal channel angular pressing[J]. Acta Mater., 2009, 57: 1586
[29]
Liu R, Zhang Z J, Li L L, et al.Microscopic mechanisms contributing to the synchronous improvement of strength and plasticity (SISP) for TWIP copper alloys[J]. Sci. Rep., 2015, 5: 9550
[30]
Li X Y, Lu K.Playing with defects in metals[J]. Nat. Mater., 2017, 16: 700
[31]
Murr L E.Interfacial Phenomena in Metals and Alloys[M]. London: Addison-Wesley Educational Publishers Inc., 1975: 1
[32]
An X H, Lin Q Y, Wu S D, et al.Significance of stacking fault energy on microstructural evolution in Cu and Cu-Al alloys processed by high-pressure torsion[J]. Philos. Mag., 2011, 91: 3307
