REFERENCE
1 Schütz W. A history of fatigue. Eng Fract Mech . 1996;54:
263–300.
2 Belattar A, Taleb L, Hauet A, Taheri S. Dependence of the cyclic
stress–strain curve on loading history and its interaction with fatigue
of 304L stainless steel. Mater Sci Eng A . 2012;536: 170–180.
3 Kamaya M, Kawakubo M. Loading sequence effect on fatigue life of Type
316 stainless steel. Int J Fatigue . 2015;81: 10–20.
4 Giancane S, Nobile R, Panella FW, Dattoma V. Fatigue life prediction
of notched components based on a new nonlinear continuum damage
mechanics model. Procedia Eng . 2010;2: 1317–1325.
5 Anes V, Caxias J, Freitas M, Reis L. Fatigue damage assessment under
random and variable amplitude multiaxial loading conditions in
structural steels. Int J Fatigue . 2017;100: 591–601.
6 Calderon-Uriszar-Aldaca I, Biezma MV. A plain linear rule for fatigue
analysis under natural loading considering the sequence effect.Int J Fatigue . 2017;103: 386–394.
7 Zheng X, Engler-Pinto CC, Su X, Cui H, Wen W. Modeling of fatigue
damage under superimposed high-cycle and low-cycle fatigue loading for a
cast aluminum alloy. Mater Sci Eng A . 2013;560: 792–801.
8 Fatemi A, Yang L. Cumulative fatigue damage and life prediction
theories: a survey of the state of the art for homogeneous materials.Int J Fatigue . 1998;20: 9–34.
9 Liu X, Wu Q, Su S, Wang Y. Evaluation and prediction of material
fatigue characteristics under impact loads: review and prospects.Int J Struct Integr . 2022;13: 251–277.
10 Liao D, Zhu S-P, Keshtegar B, Qian G, Wang Q. Probabilistic framework
for fatigue life assessment of notched components under size effects.Int J Mech Sci . 2020;181: 105685.
11 Miner M. Cumulative damage in Fatigue. J Appl Mech . 1945;3.
12 Hectors K, De Waele W. Cumulative Damage and Life Prediction Models
for High-Cycle Fatigue of Metals: A Review. Metals . 2021;11: 204.
13 Corten HT, Dolan TJ. Cumulative Fatigue Damage. In: Vol 1. London,
UK: Institution of Mechanical Engineering and American Society of
Mechanical Engineers; 1956:235–242.
14 Freudenthal AM, Heller RA. On Stress Interaction in Fatigue and a
Cumulative Damage Rule. J Aerosp Sci . 1959;26: 431–442.
15 Subramanyan S. A Cumulative Damage Rule Based on the Knee Point of
the S-N Curve. J Eng Mater Technol . 1976;98: 316–321.
16 Remadi A, Bahloul A, Bouraoui C. Prediction of fatigue crack growth
life under variable-amplitude loading using finite element analysis.Comptes Rendus Mécanique . 2019;347: 576–587.
17 Manson SS, Halford GR. Practical implementation of the double linear
damage rule and damage curve approach for treating cumulative fatigue
damage. Int J Fract . 1981;17: 169–192.
18 Chaboche JL, Lesne PM. A Non-linear Continuous Fatigue Damage Model.Fatigue Fract Eng Mater Struct . 1988;11: 1–17.
19 Lv Z, Huang H-Z, Zhu S-P, Gao H, Zuo F. A modified nonlinear fatigue
damage accumulation model. Int J Damage Mech . 2015;24: 168–181.
20 Shang D. A nonlinear damage cumulative model for uniaxial fatigue.Int J Fatigue . 1999;21: 187–194.
21 Golos K, Ellyin F. Generalization of cumulative damage criterion to
multilevel cyclic loading. Theor Appl Fract Mech . 1987;7:
169–176.
22 Golos K, Ellyin F. A Total Strain Energy Density Theory for
Cumulative Fatigue Damage. J Press Vessel Technol . 1988;110:
36–41.
23 Peng Z, Huang H-Z, Zhu S-P, Gao H, Lv Z. A fatigue driving energy
approach to high-cycle fatigue life estimation under variable amplitude
loading: A Fatigue Driving Energy Approach to High-cycle Fatigue Life
Estimation. Fatigue Fract Eng Mater Struct . 2016;39: 180–193.
24 Jiang C, Liu X, Zhang M, Wang X, Wang Y. An improved nonlinear
cumulative damage model for strength degradation considering loading
sequence. Int J Damage Mech . 2021;30: 415–430.
25 Ye D, Wang Z. A new approach to low-cycle fatigue damage based on
exhaustion of static toughness and dissipation of cyclic plastic strain
energy during fatigue. Int J Fatigue . 2001;23: 679–687.
26 Chaboche J-L. Continuous damage mechanics — A tool to describe
phenomena before crack initiation. Nucl Eng Des . 1981;64:
233–247.
27 Gough H. The Fatigue of Metals . London: Scott, Green- wood and
Son; 1924.
28 Akita M, Nakajima M, Uematsu Y, Tokaji K, Jung J-W. Some factors
exerting an influence on the coaxing effect of austenitic stainless
steels. Fatigue Fract Eng Mater Struct . 2012;35: 1095–1104.
29 Zhao LH, Li JX, Yu WY, Ma J, Zheng SL. Experimental Study on the
Coaxing Effect of Multi-Level Stresses with Different Sequences.Strength Mater . 2017;49: 55–60.
30 Nakajima M, Jung JW, Uematsu Y, Tokaji K. Coaxing Effect in Stainless
Steels and High-Strength Steels. Key Eng Mater . 2007;345–346:
235–238.
31 Nakajima M, Akita M, Uematsu Y, Tokaji K. Effect of strain-induced
martensitic transformation on fatigue behavior of type 304 stainless
steel. Procedia Eng . 2010;2: 323–330.
32 Sinclair G. An Investigation of the Coaxing Effect in Fatigue of
Metals. In: Vol 52. ; 1952:743–758.
33 Nakagawa T, Ikai Y. Strain ageing and the fatigue limit in carbon
steel. Fatigue Fract Eng Mater Struct . 1979;2: 13–21.
34 Zhao LH, Feng JZ, Zheng SL. Effect of Cyclic Stresses Below the
Endurance Limit on the Fatigue Life of 40Cr Steel. Strength
Mater . 2018;50: 2–10.
35 Lu X, Zheng S. Changes in mechanical properties of vehicle components
after strengthening under low-amplitude loads below the fatigue limit.Fatigue Fract Eng Mater Struct . 2009;32: 847–855.
36 Hironobu N, Ken-Ichi T. Significance of initiation, propagation and
closure of microcracks in high cycle fatigue of ductile metals.Eng Fract Mech . 1981;15: 445–456.
37 Scott-Emuakpor O, Schwartz J, George T, Cross C, Holycross C, Shen
MHH. In-Situ Study on Coaxing During Vibration-Based Bending Fatigue of
Inconel 625 and 718. In: Volume 7A: Structures and Dynamics . San
Antonio, Texas, USA: American Society of Mechanical Engineers;
2013:V07AT27A003.
38 Lu X, Zheng S. Strengthening of transmission gear under low-amplitude
loads. Mater Sci Eng A . 2008;488: 55–63.
39 Lu X, Zheng S. Strengthening and damaging under low-amplitude loads
below the fatigue limit. Int J Fatigue . 2009;31: 341–345.
40 Zhu S-P, Huang H-Z, Wang Z-L. Fatigue Life Estimation Considering
Damaging and Strengthening of Low amplitude Loads under Different Load
Sequences Using Fuzzy Sets Approach. Int J Damage Mech . 2011;20:
876–899.
41 Zhang J, Fu X, Lin J, Liu Z, Liu N, Wu B. Study on Damage
Accumulation and Life Prediction with Loads below Fatigue Limit Based on
a Modified Nonlinear Model. Materials . 2018;11: 2298.
42 Zheng S, Lu X. Lightweight design of vehicle components based on
strengthening effects of low-amplitude loads below fatigue limit.Fatigue Fract Eng Mater Struct . 2012;35: 269–277.
43 Mahtabi MJ, Stone TW, Shamsaei N. Load sequence effects and variable
amplitude fatigue of superelastic NiTi. Int J Mech Sci . 2018;148:
307–315.
44 Li Z, Shi D, Li S, Yang X. Residual fatigue life prediction based on
a novel damage accumulation model considering loading history.Fatigue Fract Eng Mater Struct . 2020;43: 1005–1021.
45 Ishihara S, McEvily AJ. A coaxing effect in the small fatigue crack
growth regime. Scr Mater . 1999;40: 617–622.
46 Dattoma V, Giancane S, Nobile R, Panella F. Fatigue life prediction
under variable loading based on a new non-linear continuum damage
mechanics model. Int J Fatigue . 2006;28: 89–95.
47 Jin O, Lee H, Mall S. Investigation Into Cumulative Damage Rules to
Predict Fretting Fatigue Life of Ti-6Al-4V Under Two-Level Block Loading
Condition1. J Eng Mater Technol . 2003;125: 315–323.
48 Pavlou DG. A phenomenological fatigue damage accumulation rule based
on hardness increasing, for the 2024-T42 aluminum. Eng Struct .
2002;24: 1363–1368.
49 Manson S, Freche J, Ensign C. Application of a double linear damage
rule to cumulative fatigue. In: Fatigue Crack Propagation .
Philadelphia,PA: ASTM International; 1967:384–412.
50 Zhu S, Hao Y, Oliveira Correia JAF, Lesiuk G, Jesus AMP. Nonlinear
fatigue damage accumulation and life prediction of metals: A comparative
study. Fatigue Fract Eng Mater Struct . 2019;42: 1271–1282.
51 Tian J, Liu Z, He R. Nonlinear fatigue-cumulative damage model for
welded aluminum alloy joint of EMU. J China Railw Soc . 2012;34:
40–43.
52 Fang Y, Hu M, Luo Y. New continuous fatigue damage model based on
whole damage filed measurement. J Mech Strength . 2006;28:
582–586.
53 Aid A, Amrouche A, Bouiadjra BB, Benguediab M, Mesmacque G. Fatigue
life prediction under variable loading based on a new damage model.Mater Des . 2011;32: 183–191.
54 Zheng S, Lu X. Microscopic Mechanism of Strengthening Under
Low-Amplitude Loads Below the Fatigue Limit. J Mater Eng Perform .
2012;21: 1526–1533.
55 Zhang X, Wu Y, Xie L, Zhang Y, Zhang K. The effects of pre-cyclic
stress on fracture properties and fatigue crack propagation life of 7N01
aluminum alloy. Eng Fract Mech . 2018;191: 1–12.
56 Lados D, Apelian D. Fatigue crack growth characteristics in cast
Al–Si–Mg alloysPart I. Effect of processing conditions and
microstructure. Mater Sci Eng A . 2004;385: 200–211.
57 Wu Z, Lu W. Study on Fatigue Damage Below the Fatigue Limit and the
Coaxing Effects. Acta Meta . 1996;3: 5.
58 Zheng S, Lu X, Ma X. Microscopic Mechanism of Automobile Structure
Strengthening under Low Amplitude Load. Mater Mech Eng . 2006;30:
29–32.
59 Wang J, Yao Y. An Entropy Based Low-Cycle Fatigue Life Prediction
Model for Solder Materials. Entropy . 2017;19: 503.
60 Shi Y, Yang X, Yang D, Shi D, Miao G, Wang Z. Evaluation of the
influence of surface crack-like defects on fatigue life for a P/M
nickel-based superalloy FGH96. Int J Fatigue . 2020;137: 105639.
61 Miao G, Yang X, Shi D. Competing fatigue failure behaviors of
Ni-based superalloy FGH96 at elevated temperature. Mater Sci Eng
A . 2016;668: 66–72.
62 Stinville JC, Martin E, Karadge M, et al. Fatigue deformation in a
polycrystalline nickel base superalloy at intermediate and high
temperature: Competing failure modes. Acta Mater . 2018;152:
16–33.
63 Introduction. In: Fatigue Design of Steel and Composite
Structures . Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KGaA;
2018:13–15.
64 Si-Jian L, Wei L, Da-Qing T, Jun-Bi L. A new fatigue damage
accumulation model considering loading history and loading sequence
based on damage equivalence. Int J Damage Mech . 2018;27:
707–728.
65 Sarkar A, Nagesha A, Parameswaran P, Sandhya R, Laha K, Okazaki M.
Investigation of Cumulative Fatigue Damage Through Sequential Low Cycle
Fatigue and High Cycle Fatigue Cycling at High Temperature for a Type
316LN Stainless Steel: Life-Prediction Techniques and Associated
Mechanisms. Metall Mater Trans A . 2017;48: 953–964.
66 Kwofie S, Rahbar N. A fatigue driving stress approach to damage and
life prediction under variable amplitude loading. Int J Damage
Mech . 2013;22: 393–404.
67 Peng Z, Huang H-Z, Zhou J, Li Y-F. A New Cumulative Fatigue Damage
Rule Based on Dynamic Residual S-N Curve and Material Memory Concept.Metals . 2018;8: 456.
68 Zhu S-P, Liao D, Liu Q, Correia JAFO, De Jesus AMP. Nonlinear fatigue
damage accumulation: Isodamage curve-based model and life prediction
aspects. Int J Fatigue . 2019;128: 105185.