A fatigue life approach model of automotive parts based on stress equivalence relation

Xuewen Zhang^{¹^,²}, Wei Zhou^{¹^,²}, Lu Zhang^{¹^,²}()

1Research Institute of Highway, Ministry of Transport, Beijing 100088, China

2Key Laboratory of Operation Safety Technology on Transport Vehicles, Beijing 100088, China

Show Author Information

Abstract

Fatigue failure under alternating loads represents a significant failure mode for automotive components. This study focuses on predicting the fatigue life of automotive parts subjected to multi-level stress loading. Current nonlinear models often require extensive test data or face challenges in selecting appropriate reference values, which imposes limitations on automotive reliability assessments. By analyzing the process of fatigue damage transformation between two levels of stress, the relationship, i.e., $S_{i}^{2} \times Δ S_{i} = S_{i + 1}^{2} \times Δ S_{i + 1}$ , considering the equivalent transformation of adjacent stresses based on the S-N characteristic curve of materials. The equivalent formula for cumulative fatigue damage and the expression for residual fatigue life between adjacent stresses acress two, three, and higher stress levels are derived. Then a fatigue life prediction model based on the stress equivalence relation is proposed. The calculation process of this model relies solely on the fatigue life of the materials subjected to at least two stress levels to determine the S-N characteristic curve. The experimental data utilized include existing test results for two-, three-, four-, and five-level stress loading, as reported by relevant scholars. Specifically, the two-level stress materials analyzed are AL-2024 and 30CrMnSiA, the three-level stress material is LY12CZ, and the four- and five-level stress material is an aluminum alloy. The average and maximum relative errors of the Miner model, Manson model, Subramanyan model, Hashin model, and the proposed model are all calculated and compared. Additionally, the statistical values of cumulative fatigue damage, cumulative fatigue life, and the discrepancies between cumulative fatigue damage and test cumulative fatigue damage predicted by each model are summarized. The results show that the proposed model, which is based on the equivalent transformation of adjacent loads, demonstrates superior overall performance in predicting fatigue life and damage compared to the Miner model, Manson model, Subramanyan model, and Hashin model, thereby offering a more accurate application for fatigue life and damage prediction under multi-level loading conditions.

Keywords

automotive engineering equivalent transformation fatigue damage fatigue life multi-levels load

References

[1]

Liu, J.; Wang, Y.; Li, W. Simplified fatigue durability assessment for rear suspension structure[J]. International Journal of Automotive Technology, 2010, 11(5): 659-664.

Materials	AL-2024	30CrMnSiA
$K$	5 189.39	1 366
$b$	−0.273	−0.095 4

Stress amplitude (MPa)	482（Maximum stress 732, reference stress 250）	586（Maximum stress 836, reference stress 250）
Lifetime (time)	55 757	7 186

Stress amplitude (MPa)	Experimental result		Miner model		Manson model		Subramanyan model		Hashin model		Proposed model
Stress amplitude (MPa)	d₁	d₂	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)
150−200	0.2	0.96	0.80	13.79	0.91	3.97	0.93	2.30	0.90	5.19	0.91	4.43
	0.4	0.89	0.60	22.48	0.75	10.66	0.79	8.06	0.73	12.40	0.80	7.05
	0.6	0.54	0.40	12.28	0.54	0.08	0.58	3.21	0.52	1.92	0.66	10.57
	0.2	0.67	0.80	14.94	0.65	2.05	0.62	6.23	0.68	0.65	0.60	7.88
200−150	0.4	0.24	0.60	56.25	0.45	33.11	0.42	28.11	0.47	36.45	0.33	13.89
	0.6	0.18	0.40	28.21	0.28	13.44	0.26	10.49	0.30	15.45	0.15	3.64
	0.2	0.96	0.80	13.79	0.91	3.97	0.93	2.30	0.90	5.19	0.91	4.43
Mean relative error (%)			24.66		10.55		9.73		12.01		7.91
Maximum relative error (%)			56.25		33.10		28.11		36.45		13.89

Stress level	S₁	S₂	S₃	S₄
Stress amplitude (MPa)	224.20	246.49	359.87	503.18
Lifetime (time)	719 424	312 500	12 098	524

Loading sequence	Experimental result			Miner model		Manson model		Subramanyan model		Hashin model		Proposed model
Loading sequence	d₁	d₂	d₃	d₃	E_r (%)	d₃	E_r (%)	d₃	E_r (%)	d₃	E_r (%)	d₃	E_r (%)
S₁, S₃, S₄	0.556	0.248	0.646	0.196	13.52	0.986	23.44	0.939	20.18	0.908	18.05	0.838	13.23
S₁, S₄, S₃	0.556	0.191	0.517	0.253	20.02	0.376	11.16	0.563	3.62	0.620	8.15	0.383	10.61
S₄, S₃, S₂	0.191	0.248	0.159	0.561	93.81	0.037	20.47	0.076	13.95	0.115	7.30	0.028	21.91
Mean relative error (%)				42.45		18.35		12.58		11.17		15.25
Maximum relative error (%)				93.81		23.44		20.18		18.05		21.91

Loading sequence	Loading A, S₁-S₂-S₃-S₄-S₁			Loading B, S₁-S₂-S₃-S₄			Loading C, S₄-S₃-S₂-S₁
Evaluation index	Sum of lifetime (time)	Cumulative fatigue damage	E_r (%)	Sum of lifetime (time)	Cumulative fatigue damage	E_r (%)	Sum of lifetime (time)	Cumulative fatigue damage	E_r (%)
Experimental result	531 000	1.139	-	434 500	1.151	-	236 500	-	-
Miner model	414 250	1.000	12.20	414 250	1.000	13.12	414 250	1.000	26.58
Manson model	522 670	1.129	0.87	447 940	1.250	8.57	266 780	0.824	4.36
Subramanyan model	465 610	1.061	6.84	487 720	1.544	34.17	200 030	0.745	5.70
Hashin model	467 740	1.064	6.61	485 840	1.530	32.95	202 040	0.747	5.40
Proposed model	453 310	1.047	1.73	432 610	1.137	5.22	301 800	0.866	9.65

	Minimum value	Maximum value	Standard deviation
Miner model	−0.45	0.40	0.25
Manson model	−0.23	0.34	0.12
Subramanyan model	−0.13	0.39	0.13
Hashin model	−0.16	0.38	0.14
Proposed model	−0.13	0.19	0.09

Stress amplitude (MPa)	Experimental result		Miner model		Manson model		Subramanyan model		Hashin model		Proposed model
Stress amplitude (MPa)	d₁	d₂	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)	d₂	E_r (%)
586−482	0.167	0.662	0.833	20.63	0.546	14.05	0.611	6.177	0.649	1.58	0.722	7.20
	0.208	0.582	0.792	26.58	0.499	10.46	0.563	2.401	0.601	2.38	0.660	9.88
	0.417	0.287	0.583	42.05	0.320	4.66	0.369	11.712	0.400	16.12	0.387	12.64
	0.694	0.125	0.306	22.10	0.149	2.89	0.175	6.127	0.192	8.23	0.130	0.60
482−586	0.223	0.917	0.777	12.28	0.967	4.37	0.942	2.187	0.923	0.54	0.868	4.27
	0.269	0.903	0.731	14.68	0.949	3.94	0.917	1.205	0.894	0.76	0.839	5.46
	0.448	0.750	0.552	16.53	0.838	7.37	0.782	2.665	0.747	0.28	0.715	2.88
	0.628	0.615	0.372	19.55	0.652	2.98	0.586	2.318	0.549	5.34	0.570	3.60
	0.807	0.425	0.193	18.83	0.385	3.22	0.334	7.374	0.307	9.58	0.388	3.01
Mean relative error (%)			21.47		5.99		4.68		4.98		5.67
Maximum relative error (%)			42.05		14.05		11.71		16.12		12.64