Experimental Mechanics

, Volume 11, Issue 12, pp 540–547 | Cite as

On the modality of fatigue-endurance distributions

In this investigation, the log-normal, extreme value, combinations of two truncated log-normal or truncated log-normal and extreme-value-distribution functions were fitted to the experimental endurance distributions
  • G. K. Korbacher


Altogether, 884 OFHC copper specimens were fatigued under axial load at 5 different stress levels and zero mean stress. Log-normal, extreme value, combinations of two truncated log-normal or truncated log-normal and extreme-value-distribution functions were fitted to the experimental endurance distributions. The main results of this statistical fatigue study are that (1) the two endurance distributions observed with, e.g., alloyed steel and aluminum could not be verified for polycrystalline (OFHC) copper; (2) at stress levels around the lower knee, the existence of two modes (bimodality) was apparent; (3) at stress levels well above the knee, endurance distributions seem to become single log-normal, below the knee, extremal; (4) the bimodality seems to be caused by a transition of predominance from one (e.g Wood'sH) to another (Wood'sF) fatigue mechanism.


Copper Aluminum Fatigue Mechanical Engineer Fluid Dynamics 
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Weibull shape parameter


long-term fatigue-designating the high-endurance component in a bimodal distribution


total number of specimens in the sample of a population


number of observations, the endurance, values of which are known in a truncated sample


endurance of a specimen in cycles


the ith ordered endurance when the endurance values of a sample are arranged in ascending sequence


the minimum-life parameter,N o is defined by probabilityF (N≤N o )=0


correlation coefficient


short-term fatigue—designating the low-endurance component in a bimodal distribution


Estimate of σ 2 obtained from a sample, sample variance


sample standard deviation estimate of σ


characteristic life parameter in Weibull distribution defined byF(V)=1/e


log10 (N)

\(\overline X \)

mean ofX i , given by\(\overline X = 1/n \mathop \Sigma \limits_{i = 1}^n X_i \)


theith ordered value ofX


variance of a population


population standard deviation


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Copyright information

© Society for Experimental Mechanics, Inc. 1971

Authors and Affiliations

  • G. K. Korbacher
    • 1
  1. 1.Institute for Aerospace StudiesUniversity of ToronioCanada

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