复杂循环加载多轴疲劳寿命预测

doi:10.7527/S1000-6893.2026.32947

Abstract

Abstract:

Multiaxial fatigue in structural components of aircraft engines is one of the critical challenges limiting the improvement of engine reliability and structural integrity. The presence of non-zero mean stress and non-proportional multiaxial cyclic loading further complicates the fatigue life assessment. To accurately predict the life under complex multiaxial cyclic loading， the peak， valley， and mean points of the loading path are first defined. Based on this， a definition of the multiaxial stress ratio is proposed. Subsequently， the Walker correction method for uniaxial fatigue with non-zero mean stress is extended to multiaxial fatigue using the proposed multiaxial stress ratio. In conjunction with existing multiaxial fatigue models， a multiaxial fatigue life model suitable for non-zero mean cyclic loading is developed. To address the characteristics of non-proportional loading paths under non-zero mean loading conditions， a method for characterizing non-proportional paths under non-zero mean loading is proposed， which further extends the applicability of the non-zero mean cyclic loading multiaxial fatigue model. Finally， experimental data on non-zero mean， non-proportional path multiaxial fatigue for three materials are used to validate the proposed model. The results show that， without introducing additional parameters， most predicted life values fall within a scatter band of 3^±1 times the experimental data， and the prediction accuracy surpasses that of three commonly used models. This demonstrates that the proposed model can accurately capture the influence of non-zero mean loading and non-proportional paths on multiaxial fatigue life.

Key words: multiaxial fatigue, non-zero mean, non-proportional path, multiaxial stress ratio, fatigue life model

CLC Number:

V231.95

Yanrong WANG, Tonghui WANG, Bo ZHONG. Multiaxial fatigue life prediction under complex cyclic loading[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(19): 232974.

Figures/Tables 23

Fig.1

Fig.2

Table 1

Fig.3

Fig. 4

Fig.5

Table 2

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 3

Fig.11

Fig.12

Fig.13

Table 4

Fatigue parameters of different materials

材料牌号	E/GPa	$σ f'$ /MPa	$ε f'$	b	c	γ
TC4^［40］	108.4	1 116.9	0.579	-0.049	-0.679	0.52
In718^［41］	209	1 640	2.67	-0.06	-0.82	0.48
S460N^［42］	208.5	834	0.157	-0.079	-0.493	0.48

Table 4

Table 5

Multiaxial fatigue test data for TC4［40］

$δ x y, x /$ （°）	$ε x, a$	$ε x, m$	$γ x y, a$	$γ x y, m$	N_f /循环
0	0.382	0	0.714	1.17	19 750
0	0.556	0	0.889	1.495	5 126
90	0.417	0	0.704	1.213	62 435
90	0.485	0	0.828	1.409	4 772
0	0.438	0.754	0.719	0	5 225
0	0.565	1.042	0.911	0	4 422
90	0.420	0.428	0.698	0	6 878
90	0.502	0.974	0.822	0	2 394
0	0.466	0.978	0.726	1.386	8 867
0	0.614	1.016	0.916	1.697	4 364
90	0.423	0.826	0.705	1.253	5 357
90	0.510	1.019	0.825	1.521	6 035

Table 5

Fig.14

Table 6

Multiaxial fatigue test data for In718［41］

$δ x y, x /$ （°）	$ε x, a$	$ε x, m$	$γ x y, a$	$γ x y, m$	N_f/循环
0	0.007 1	0.007 1	0.012 3	0.012 3	1 050
0	0.007 1	0.007 1	0.012 3	0.012 3	1 000
0	0.007 0	0.007 0	0.012 0	0.012 0	1 050
0	0.007 0	0.007 0	0.012 0	0.012 0	1 000
0	0.003 5	0.003 5	0.006 3	0.006 3	4 800
0	0.003 5	0.003 5	0.006 3	0.006 3	7 500
0	0.003 5	0	0.006 3	0.006 3	5 000
0	0.003 5	0	0.006 3	0.006 3	4 000
0	0.003 5	0.003 5	0.006 3	0	3 000
90	0.003 5	0.003 5	0.006 2	0	3 550
90	0.003 5	0.003 5	0.006 2	0	3 330

Table 6

Fig.15

Table 7

Multiaxial fatigue test data for S460N［42］

$δ x y, x /$ （°）	$ε x, a$	$ε x, m$	$γ x y, a$	$γ x y, m$	N_f/循环
0	0.001 4	0.001 4	0.002 5	0	106 300
0	0.001 4	0.001 4	0.002 5	0	76 600
0	0.001 7	0.001 7	0.003	0	20 000
0	0.001 7	0.001 7	0.003	0	22 700
0	0.001 7	0	0.003	0.003	17 000
0	0.001 4	0.001 4	0.002 5	0.002 5	67 100
90	0.001 4	0.001 4	0.002 5	0	43 300
90	0.001 4	0.001 4	0.002 5	0	48 500
90	0.001 2	0.001 2	0.002	0	386 800
90	0.001 2	0.001 2	0.002	0	325 100

Table 7

Fig.16

References 44

[1]	李其汉，王延荣. 航空发动机结构强度设计问题［M］. 上海：上海交通大学出版社， 2014： 14-20.
	LI Q H， WANG Y R. The design problem of aero-engine structure strength［M］. Shanghai： Shanghai Jiao Tong University Press， 2014： 14-20 （in Chinese）.
[2]	王延荣，张小伟，袁善虎，等. 航空发动机零件可靠性安全性设计［M］. 北京：航空工业出版社， 2018： 33-37.
	WANG Y R， ZHANG X W， YUAN S H，et al. Reliability and safety design of aero engine components［M］. Beijing： Aviation Industry Press， 2018： 33-37 （in Chinese）.
[3]	FATEMI A， SHAMSAEI N. Multiaxial fatigue： An overview and some approximation models for life estimation［J］. International Journal of Fatigue， 2011， 33（8）： 948-958.
[4]	PAGLIARI L， CONCLI F. A review of multiaxial low-cycle fatigue criteria for life prediction of metals［J］. International Journal of Damage Mechanics， 2025， 34（3）： 377-414.
[5]	钟波. 粉末材料及构件的多轴疲劳试验与寿命预测［D］. 北京：北京航空航天大学， 2018： 54-62.
	ZHONG B. Multiaxial fatigue experiment and life prediction of a P/M superalloy and its structures［D］. Beijing： Beihang University， 2018： 54-62 （in Chinese）.
[6]	王彤晖. 榫连结构高应力梯度多轴疲劳模型及试验研究［D］. 北京：北京航空航天大学， 2025： 38-55.
	WANG T H. Multiaxial fatigue model and experimental investigation on dovetail joints with high stress gradient［D］. Beijing： Beihang University， 2025： 38-55 （in Chinese）.
[7]	FASH J W， SOCIE D F， MCDOWELL D L. Multiaxial fatigue［M］. West Conshohocken： ASTM International， 1985： 497-513.
[8]	PASCOE K J， DE VILLIERS J R. Low cycle fatigue of steels under biaxial straining［J］. Journal of Strain Analysis， 1967， 2（2）： 117-126.
[9]	ITOH T， YANG T. Material dependence of multiaxial low cycle fatigue lives under non-proportional loading［J］. International Journal of Fatigue， 2011， 33（8）： 1025-1031.
[10]	ZHONG B， WANG Y R， WEI D S， et al. A new life prediction model for multiaxial fatigue under proportional and non-proportional loading paths based on the pi-plane projection［J］. International Journal of Fatigue， 2017， 102： 241-251.
[11]	BROWN M W， MILLER K J. A theory for fatigue failure under multiaxial stress-strain conditions［J］. Proceedings of the Institution of Mechanical Engineers， 1973， 187（1）： 745-755.
[12]	尚德广，王德俊. 多轴疲劳强度［M］. 北京：科学出版社， 2007： 118-127.
	SHANG D G， WANG D J. Multiaxial fatigue strength［M］. Beijing： Science Press， 2007： 118-127 （in Chinese）.
[13]	KANDIL F A， BROWN M W， MILLER K J. Biaxial low-cycle fatigue fracture of 316 stainless steel at elevated temperature［C］∥International Conference on Mechanical Behaviour and Nuclear Applications of Stainless Steel at Elevated Temperatures. London： The Metal Society， 1982：203-209.
[14]	LIU K C. Advances in multiaxial fatigue［M］. West Conshohocken： ASTM International， 1993： 67-84.
[15]	CHEN X， XU S， HUANG D. A critical plane-strain energy density criterion for multiaxial low-cycle fatigue life under non-proportional loading［J］. Fatigue & Fracture of Engineering Materials & Structures， 1999， 22（8）： 679-686.
[16]	SOCIE D. Multiaxial fatigue damage models［J］. Journal of Engineering Materials and Technology， 1987， 109（4）： 293-298.
[17]	SMITH R H， WATSON P， TOPPER T H. A stress-strain function for the fatigue of metals［J］. Journal of Materials， 1970，5（4）：767-778.
[18]	FATEMI A， SOCIE D F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading［J］. Fatigue & Fracture of Engineering Materials & Structures， 1988， 11（3）： 149-165.
[19]	CHU C C， CONLE F A， BONNEN J. Multiaxial stress-strain modeling and fatigue life prediction of SAE axle shafts［M］∥Advances in multiaxial fatigue. West Conshohocken： ASTM International， 1993：37-54.
[20]	CHU C C. Fatigue damage calculation using the critical plane approach［J］. Journal of Engineering Materials and Technology， 1995， 117（1）： 41-49.
[21]	GOODMAN J. Mechanics applied to engineering［M］. 3rd ed. London： Longmans， Green， 1903： 631-636.
[22]	MORROW J. Fatigue design handbook： Section 3.2. Fatigue properties of metals［M］. Warrendale： Society of Automotive Engineers， 1968.
[23]	WALKER K. Effects of environment and complex load history on fatigue life［M］. West Conshohocken： ASTM International， 1970： 1-14.
[24]	VANTADORI S， CARPINTERI A， LUCIANO R， et al. Mean stress effect on fatigue life estimation for Inconel 718 alloy［J］. International Journal of Fatigue， 2020， 133： 105391.
[25]	ITOH T， NAKAMURA H， TAKANASHI M， et al. Multiaxial low cycle fatigue life of Ti-6Al-4V under non-proportional loading with mean strain［J］. Theoretical and Applied Fracture Mechanics， 2017， 90： 165-173.
[26]	LI J， SHAO F S， HE Z W， et al. Multiaxial fatigue life prediction using an improved Smith-Watson-Topper model［J］. Fatigue & Fracture of Engineering Materials & Structures， 2024， 47（6）： 1944-1961.
[27]	ŁAGODA T， VANTADORI S， GŁOWACKA K， et al. Using the Smith-Watson-topper parameter and its modifications to calculate the fatigue life of metals： The state-of-the-art［J］. Materials， 2022， 15（10）： 3481.
[28]	INCE A， GLINKA G. A generalized fatigue damage parameter for multiaxial fatigue life prediction under proportional and non-proportional loadings［J］. International Journal of Fatigue， 2014， 62： 34-41.
[29]	FATEMI A， KURATH P. Multiaxial fatigue life predictions under the influence of mean-stresses［J］. Journal of Engineering Materials and Technology， 1988， 110（4）： 380-388.
[30]	GLINKA G， WANG G， PLUMTREE A. Mean stress effects in multiaxial fatigue［J］. Fatigue & Fracture of Engineering Materials & Structures， 1995， 18（7-8）： 755-764.
[31]	SHANG D G， WANG D J. A new multiaxial fatigue damage model based on the critical plane approach［J］. International Journal of Fatigue， 1998， 20（3）： 241-245.
[32]	吴志荣，胡绪腾，宋迎东. 基于最大切应变幅和修正SWT参数的多轴疲劳寿命预测模型［J］. 机械工程学报， 2013， 49（2）： 59-66.
	WU Z R， HU X T， SONG Y D. Multi-axial fatigue life prediction model based on maximum shear strain amplitude and modified SWT parameter［J］. Journal of Mechanical Engineering， 2013， 49（2）： 59-66 （in Chinese）.
[33]	陈家权，陈国军，温洁明. 考虑应变路径的多轴低周疲劳寿命预测模型［J］. 工程力学， 2012， 29（4）： 84-89.
	CHEN J Q， CHEN G J， WEN J M. Multi-axial low cycle fatigue life prediction model based on strain path［J］. Engineering Mechanics， 2012， 29（4）： 84-89 （in Chinese）.
[34]	孙国芹，尚德广，王杨. 金属多轴疲劳行为与寿命预测研究进展［J］. 机械工程学报， 2021， 57（16）： 153-172.
	SUN G Q， SHANG D G， WANG Y. Research progress on fatigue behavior and life prediction under multiaxial loading for metals［J］. Journal of Mechanical Engineering， 2021， 57（16）： 153-172 （in Chinese）.
[35]	BORODII M V， STRIZHALO V A. Analysis of the experimental data on a low cycle fatigue under nonproportional straining［J］. International Journal of Fatigue， 2000， 22（4）： 275-282.
[36]	钟波，王延荣，魏大盛，等. 基于应变路径非比例度的多轴疲劳寿命预测［J］. 航空动力学报， 2016， 31（2）： 317-322.
	ZHONG B， WANG Y R， WEI D S， et al. Multiaxial fatigue life prediction based on non-proportionality of strain path［J］. Journal of Aerospace Power， 2016， 31（2）： 317-322 （in Chinese）.
[37]	何国求，陈成澍，高庆，等. 基于微结构分析定义应变路径非比例度［J］. 金属学报， 2003， 39（7）： 715-720.
	HE G Q， CHEN C S， GAO Q， et al. Definition of non-proportionality of strain path based on microstructures analysis［J］. Acta Metallurgica Sinica， 2003， 39（7）： 715-720 （in Chinese）.
[38]	于海生，谢·尼·舒卡耶夫，王兴国，等. 一种多轴非比例载荷低周疲劳寿命预测方法［J］. 机械强度， 2004， 26（S1）： 250-253.
	YU H S， SHUKAYEV S N， WANG X G， et al. Lcf life prediction method for multiaxial non-proportional loadings［J］. Journal of Mechanical Strength， 2004， 26（S1）： 250-253 （in Chinese）.
[39]	BORODII M， SHUKAEV S. Additional cyclic strain hardening and its relation to material structure， mechanical characteristics， and lifetime［J］. International Journal of Fatigue， 2007， 29（6）： 1184-1191.
[40]	吴志荣. 钛合金多轴疲劳寿命预测方法研究［D］. 南京：南京航空航天大学， 2014： 20-26.
	WU Z R. Research on multi-axial fatigue life prediction method for titanium alloy［D］. Nanjing： Nanjing University of Aeronautics and Astronautics， 2014： 20-26 （in Chinese）.
[41]	SOCIE D F， KURATH P， KOCH J. A multiaxial fatigue damage parameter［C］∥Biaxial and Multiaxial Fatigue-EGF3. London： Mechanical Engineering Publications， 1989： 535-550.
[42]	JIANG Y Y， HERTEL O， VORMWALD M. An experimental evaluation of three critical plane multiaxial fatigue criteria［J］. International Journal of Fatigue， 2007， 29（8）： 1490-1502.
[43]	《航空发动机设计用材料数据手册》编委会. 航空发动机设计用材料数据手册-第三册［M］. 北京：航空工业出版社， 2008： 439-465， 979-997.
	Editorial Committee of the Materials Data Handbook for Aero Engine Design. Materials data handbook for aero engine design， Vol. 3［M］. Beijing： Aviation Industry Press， 2008： 439-465， 979-997 （in Chinese）.
[44]	DOWLING N E. Mean stress effects in strain-life fatigue［J］. Fatigue & Fracture of Engineering Materials & Structures， 2009， 32（12）： 1004-1019.

路径名	加载路径示意图	对应π平面投影路径
Path 1
Path 2
Path 3
Path 4
Path 5

疲劳类别	图形类别	非零平均载荷	忽略非零平均应力后相应的零平均载荷
单轴疲劳	载荷波形
多轴疲劳	载荷波形
	载荷路径
	对应的π平面投影路径

载荷类型	时序加载波形	路径图
比例、零平均加载
比例、非零平均加载
非比例、非零平均加载

Multiaxial fatigue life prediction under complex cyclic loading

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