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FOD was introduced on surface-strengthened axle specimens to generate surface defects, and finite element analysis was subsequently performed to evaluate the stress fields in the damaged regions. Fatigue tests were conducted on prefabricated defective specimens to characterize their fatigue behavior. Based on test results, an improved backward statistical inference method was used to fit the fatigue\n                    <jats:italic>P-S-N<\/jats:italic>\n                    curves for each specimen group and derive corresponding fatigue limits. The fatigue limit of full-size damaged axles was estimated by extrapolating from small-scale test results, with due consideration of geometric scale effects on mechanical performance. Considering the stochastic distribution of impact defect depths, an exponential fitting was performed to establish the quantitative relationship between defect depth and full-size axle fatigue limit. Finally, a multivariate fatigue limit prediction model was developed for surface-strengthened full-size EA4T axles based on the El-Haddad formula framework. This model enables comprehensive assessment of fatigue performance under multi-parameter coupling conditions, providing a robust theoretical basis for safety evaluation and maintenance strategies of high-speed train axles subjected to foreign object impacts.\n                  <\/jats:p>","DOI":"10.1038\/s41598-025-34892-6","type":"journal-article","created":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T08:36:08Z","timestamp":1767861368000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Assessment model for multivariable fatigue performance of EA4T axles containing defects"],"prefix":"10.1038","volume":"16","author":[{"given":"Yan","family":"Luo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuanqi","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cunhai","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yongxu","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,8]]},"reference":[{"key":"34892_CR1","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/j.jmatprotec.2016.09.001","volume":"239","author":"YM Huo","year":"2017","unstructured":"Huo, Y. 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