Abstract
A so-called “local probabilistic Paris relation method” was presented for measuring the random thresholds of long fatigue crack propagation. A check was made to the conventional method, in which the thresholds were measured statistically and directly by the test data. It was revealed that this method was not reasonable because the test data have seldom a unified level of crack growth rates. Differently, in the presented method the Paris-Erdogan equation was applied to model the local test data around the thresholds. Local probabilistic relations with both the survival probability and the confidence were established on a lognormal distribution of the stress density factors. And then, the probabilistic thresholds were derived from the probabilistic factors with a given critical level of growth rate. An analysis on the test data of LZ50 axle steel for the Chinese railway vehicles verifies that the present method is feasible and available.
Similar content being viewed by others
References
Wang Kongtan, Zhang Wenyu, Qin Guangyi. Relationship between threshold value and rate of fatigue crack propagation in TA5 titanium alloy[J].Material Development and Applications, 1995,10(3):8–12, 19 (in Chinese).
Xu Renping, Duan Xiaojiang, Zhan Zhaolin. Investigation on theoretical threshold[J].Structure and Environment Engineering, 1995,22(4):12–16 (in Chinese).
Ding Chuanfu, Yu Hui, Wu Xueren. Investigation of threshold and wide range fatigue crack growth rates in LY12CZ alloy[J].Journal of Aeronautical Materials, 2000,20(1):12–17 (in Chinese).
Xiong Junjiang, Peng Junhua, Gao Zhentong Reliability method to determine fracture toughnessK IC and fracture threshold value ΔK th [J].Journal of Beijing University of Aeronautics and Astronautics, 2000,26(6):694–696 (in Chinese).
Clark T R, Herman W A, Hertzberg R W,et al. The influence of theK gradient andK cmax level on fatigue response during theK cmax threshold testing of Van 80 steel and Astrology[J].Internat J Fatigue, 1997,19(2):177–182.
McEvily A J, Renauld M, Bao H,et al. Fatigue fracture-surface roughness and theK-opening level[J].Internat J Fatigue, 1997,19(8/9):629–633.
Wasén J, Heier E. Fatigue crack growth thresholds—the influence of Young's modulus and fracture surface roughness[J].Internat J Fatigue, 1998,20(10):737–742.
Lang M. Explanation of an apparent abnormality in fatigue crack growth rate curves in Titanium alloys[J].Acta Mater, 1999,47(11):3247–3261.
Sivaprasad S, Tarafder S, Tarafder M,et al. An alternative method of decreasing ΔK FCGR testing[J].Internat J Fatigue, 2000,22(8):593–600.
Meshii T, Watanabe K. Comparison of near threshold fatigue crack growth data byK max-constant method with the post-construction codes[J].Nucl Eng Des, 2003,220(2):285–292.
Zhao Yongxiang, Huang Yuzhong, Gao Qing. Probabilistic mechanical properties of LZ50 axle steel for railway vehicles[J].Journal of Traffic and Transportation Engineering, 2003,3(2): 11–17 (in Chinese).
Zhao Yongxiang, Wang Jinnuo, Gao Qing. Unified approach for determining an appropriate assumed distribution of limited fatigue reliability data[J].China Mechanical Engineering, 2001,12(12):1343–1347 (in Chinese).
Paris P, Erdogan F. A critical analysis of crack growth laws[J].J Basic Eng, 1963,85(2): 528–534.
Zhao Yongxiang, Wang Jinnuo, Gao Qing. Probability-based cyclic stress-strain curves and estimation method[J].Chinese Journal of Mechanical Engineering, 2000,36(8):102–106 (in Chinese).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by YUE-Zhu-feng
Project supported by the National Natural Science Foundation of China (Nos. 50375130 and 50323003); the Special Foundation for the Authors of National Excellent Doctoral Dissertations (No. 200234) and the Outstanding Young Teachers Program of State Education Ministry (No. 2101)
Rights and permissions
About this article
Cite this article
Yong-xiang, Z., Bing, Y., Hong-qin, L. et al. New method for measuring random thresholds of long fatigue crack propagation. Appl Math Mech 26, 761–766 (2005). https://doi.org/10.1007/BF02465427
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02465427