Input Parameter Analysis for Low-Cycle Multiaxial Fatigue Models Using Artificial Neural Network

Abstract:

This study investigates the optimization of input parameters for artificial neural networks (ANNs) to enhance the accuracy of fatigue life prediction under multiaxial loading conditions. Three models were developed using input features derived from the Fatemi–Socie and Ito et al. approaches, as well as a combined set of parameters. The dataset, consisting of 226 experimental results for 10 different materials and various loading paths, was extended to 427 data points through interpolation and normalized using min–max scaling. SHAP (SHapley Additive exPlanations) analysis was applied to assess the contribution of each parameter to fatigue life prediction. The results identified the shear strain range on the maximum shear plane, the normal strain range on the maximum tensile plane, and the non-proportionality parameter as the most influential features, along with Coffin–Manson equation coefficients characterizing material fatigue behavior. The material non-proportional hardening parameter, treated as a constant, was not found to be significant, indicating the potential need for its functional adaptation based on strain amplitude. Retraining the ANN using only the most relevant parameters maintained prediction accuracy, emphasizing their critical role.

• Periodical: Key Engineering Materials (Volume 1035)
• Pages: 59-69
• DOI: https://doi.org/10.4028/p-YA35mB
• Online since: December 2025
• Authors: Yevhenii Savchuk*, Pavlo Yakovhuk, Sergiy Shukayev
• Keywords: Artificial Neural Network, Coefficient of Nonproportionality, Critical Plane Model, Low Cycle Multiaxial Fatigue, Nonproportional Loading

References

[1] Yu, Zheng-Yong, et al. "Multiaxial fatigue damage parameter and life prediction without any additional material constants." Materials 10.8 (2017): 923.

DOI: 10.3390/ma10080923

[2] Carpinteri, Andrea, Andrea Spagnoli, and Sabrina Vantadori. "A review of multiaxial fatigue criteria for random variable amplitude loads." Fatigue & Fracture of Engineering Materials & Structures 40.7 (2017): 1007-1036.

DOI: 10.1111/ffe.12619

[3] Doong, Shiing-Hwa, D. F. Socie, and I. M. Robertson. "Dislocation substructures and nonproportional hardening." (1990): 456-464.

DOI: 10.1115/1.2903357

[4] Ding, Xiang-qun, Guo-qiu He, and Cheng-shu Chen. "Study on the dislocation sub-structures of Al–Mg–Si alloys fatigued under non-proportional loadings." Journal of materials science 45 (2010): 4046-4053.

DOI: 10.1007/s10853-010-4487-3

[5] Chen, Xu, Qin Gao, and X‐F. Sun. "Low‐cycle fatigue under non‐proportional loading." Fatigue & Fracture of Engineering Materials & Structures 19.7 (1996): 839-854.

DOI: 10.1111/j.1460-2695.1996.tb01020.x

[6] Bentachfine, S., et al. "Biaxial low cycle fatigue under non-proportional loading of a magnesium-lithium alloy." Engineering fracture mechanics 54.4 (1996): 513-522.

DOI: 10.1016/0013-7944(95)00223-5

[7] Fatemi, Ali, and Darrell F. Socie. "A critical plane approach to multiaxial fatigue damage including out‐of‐phase loading." Fatigue & Fracture of Engineering materials & structures 11.3 (1988): 149-165.

DOI: 10.1111/j.1460-2695.1988.tb01169.x

[8] Itoh, Takamoto, et al. "Nonproportional low cycle fatigue criterion for type 304 stainless steel." (1995): 285-292.

DOI: 10.1115/1.2804541

[9] Chen, Jie, and Yongming Liu. "Fatigue modeling using neural networks: A comprehensive review." Fatigue & Fracture of Engineering Materials & Structures 45.4 (2022): 945-979.

DOI: 10.1111/ffe.13640

[10] Bock, Frederic E., et al. "A review of the application of machine learning and data mining approaches in continuum materials mechanics." Frontiers in Materials 6 (2019): 110.

[11] Salifu, Smith, and Peter Apata Olubambi. "A Review of Fatigue Failure and Life Estimation Models: From Classical Methods to Innovative Approaches." Science, Engineering and Technology 4.2 (2024): 123-151.

DOI: 10.54327/set2024/v4.i2.140

[12] Li, Xin, Haoran Yang, and Jianwei Yang. "Fretting Fatigue Life Prediction for Aluminum Alloy Based on Particle-Swarm-Optimized Back Propagation Neural Network." Metals 14.4 (2024): 381.

DOI: 10.3390/met14040381

[13] Yang, Jingye, et al. "A novel method of multiaxial fatigue life prediction based on deep learning." International Journal of Fatigue 151 (2021): 106356.

DOI: 10.1016/j.ijfatigue.2021.106356

[14] Wang, Yantian, et al. "Two fatigue life prediction models based on the critical plane theory and artificial neural networks." Metals 14.8 (2024): 938.

DOI: 10.3390/met14080938

[15] Zhu, Yifeng, et al. "A real-time remaining fatigue life prediction approach based on a hybrid deep learning network." Processes 11.11 (2023): 3220.

DOI: 10.3390/pr11113220

[16] Zhang, Peng, et al. "Neural network integrated with symbolic regression for multiaxial fatigue life prediction." International Journal of Fatigue 188 (2024): 108535.

DOI: 10.1016/j.ijfatigue.2024.108535

[17] Yakovchuk, P. V., E. V. Savchuk, and S. M. Shukayev. "Critical Plane Approach-Based Fatigue Life Prediction for Multiaxial Loading: A New Model and its Verification." Strength of Materials 56.2 (2024): 281-291.

DOI: 10.1007/s11223-024-00647-3

[18] You, Bong-Ryul, and Soon-Bok Lee. "A critical review on multiaxial fatigue assessments of metals." International Journal of Fatigue 18.4 (1996): 235-244.

DOI: 10.1016/0142-1123(96)00002-3

[19] Troshchenko, V.T., and L.A. Sosnovskii. Soprotivlenie ustalosti metallov i splavov. Spravochnik. Chast' 1. Kyiv: Naukova Dumka, (1987): 512 pp

[20] Savchuk, Y., and S. Shukayev. "Comparison of critical plane models for multiaxial fatigue life prediction." Mechanics and Advanced Technologies 7.3 (2023): 99.

DOI: 10.20535/2521-1943.2023.7.3.287522

[21] Karolczuk, Aleksander, and Ewald Macha. "A review of critical plane orientations in multiaxial fatigue failure criteria of metallic materials." International Journal of Fracture 134 (2005): 267-304.

DOI: 10.1007/s10704-005-1088-2

[22] Wang, C. H., and M. W. Brown. "A path‐independent parameter for fatigue under proportional and non‐proportional loading." Fatigue & fracture of engineering materials & structures 16.12 (1993): 1285-1297.

DOI: 10.1111/j.1460-2695.1993.tb00739.x

[23] Wu, Zhirong, Xuteng Hu, and Yingdong Song. "Multi-axial fatigue life prediction model based on maximum shear strain amplitude and modified SWT parameter." Jixie Gongcheng Xuebao (Chinese Journal of Mechanical Engineering) 49.2 (2013): 59-66.

DOI: 10.3901/jme.2013.02.059

[24] Wu, Zhi-Rong, Xu-Teng Hu, and Ying-Dong Song. "Multiaxial fatigue life prediction for titanium alloy TC4 under proportional and nonproportional loading." International Journal of Fatigue 59 (2014): 170-175.

DOI: 10.1016/j.ijfatigue.2013.08.028

[25] Zhu, Shun-Peng, et al. "Evaluation and comparison of critical plane criteria for multiaxial fatigue analysis of ductile and brittle materials." International Journal of Fatigue 112 (2018): 279-288.

DOI: 10.1016/j.ijfatigue.2018.03.028

[26] Skibicki, Dariusz. Phenomena and computational models of non-proportional fatigue of materials. Springer, (2014).

[27] Itoh, Takamoto, et al. "A design procedure for assessing low cycle fatigue life under proportional and non-proportional loading." International Journal of Fatigue 28.5-6 (2006): 459-466.

DOI: 10.1016/j.ijfatigue.2005.08.007

[28] Wu, Min, et al. "Low cycle fatigue life of Ti–6Al–4V alloy under non-proportional loading. "International journal of fatigue 44 (2012): 14-20.

DOI: 10.1016/j.ijfatigue.2012.06.006

[29] Borodii, M. V. "Determination of cycle nonproportionality coefficient." Strength of Materials 27.5 (1995): 265-272.

DOI: 10.1007/bf02208497

[30] Borodii, M. V., and V. A. Strizhalo. "Analysis of the experimental data on a low cycle fatigue under nonproportional straining." International Journal of Fatigue 22.4 (2000): 275-282.

DOI: 10.1016/s0142-1123(00)00005-0

[31] Borodii, M. V., and M. P. Adamchuk. "Life assessment for metallic materials with the use of the strain criterion for low-cycle fatigue." International Journal of Fatigue 31.10 (2009): 1579-1587.

DOI: 10.1016/j.ijfatigue.2009.04.011

[32] Zhong, Bo, et al. "A new life prediction model for multiaxial fatigue under proportional and non-proportional loading paths based on the pi-plane projection." International Journal of Fatigue 102 (2017): 241-251.

DOI: 10.1016/j.ijfatigue.2017.04.013

[33] Ellyin, F., K. Golos, and Z. Xia. "In-phase and out-of-phase multiaxial fatigue." Journal of Engineering Materials and Technology, 113(1), (1991): 112

DOI: 10.1115/1.2903365

[34] Shukaev, S., Panasovskii, K., and Gladskii, M. "Fatigue life assessment for metal alloys under nonproportional low-cycle loading. " Strength of materials, 39, (2007): 358-364.

DOI: 10.1007/s11223-007-0040-2

[35] Fatemi, Ali, and Nima Shamsaei. "Multiaxial fatigue: An overview and some approximation models for life estimation." International Journal of Fatigue 33.8 (2011): 948-958.

DOI: 10.1016/j.ijfatigue.2011.01.003

[36] Borodii, M.V., and S. M. Shukaev. "Additional cyclic strain hardening and its relation to material structure, mechanical characteristics, and lifetime." International Journal of Fatigue 29.6 (2007): 1184-1191.

DOI: 10.1016/j.ijfatigue.2006.06.014

[37] Skibicki, Dariusz, and Łukasz Pejkowski. "The relationship between additional non-proportional hardening coefficient and fatigue life." International Journal of Fatigue 123 (2019): 66-78.

DOI: 10.1016/j.ijfatigue.2019.02.011

[38] Scott, M., & Su-In, L. A unified approach to interpreting model predictions. Advances in neural information processing systems, 30 (2017): 4765-4774.