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
Article

Abstract

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.

Keywords

Copper Aluminum Fatigue Mechanical Engineer Fluid Dynamics 

Notation

b

Weibull shape parameter

LTF

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

n

total number of specimens in the sample of a population

ntr

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

N

endurance of a specimen in cycles

Ni

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

No

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

r

correlation coefficient

STF

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

s2

Estimate of σ 2 obtained from a sample, sample variance

s

sample standard deviation estimate of σ

V

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

X

log10 (N)

\(\overline X \)

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

Xi

theith ordered value ofX

σ2

variance of a population

σ

population standard deviation

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Swanson, S. R., “A Two-Distribution Interpretation of Fatigue S-N Data,” Can. Aero. Jnl.,6 (6) (June 1960).Google Scholar
  2. 2.
    Cicci, F., “An Investigation of the Statistical Distribution of Constant Amplitude Fatigue Endurance for Maraging Steel,” UTIAS Tech. Note No. 73 (July, 1964).Google Scholar
  3. 3.
    Swanson, S. R., “Systematic Axial Load Fatigue Tests Using Unnotched Aluminum Alloy 2024-Tr Extruded Bar Specimens,” UTIAS Tech. Note No. 35 (May, 1960).Google Scholar
  4. 4.
    Swanson, S. R., “An Investigation of the Fatigue of Aluminum Alloy Due to Random Loading,” UTIAS Report No. 84 (Feb. 1963).Google Scholar
  5. 5.
    Freundenthal, A. M., “Fatigue of Materials and Structures Under Random Loading,” WADC TR-676, 129 (March, 1961).Google Scholar
  6. 6.
    Lazan, B. J., “Damping and Resonant Fatigue Behaviour of Materials,” Internatl. Conf. on Fatigue of Metals, New York and London, 90 (1956).Google Scholar
  7. 7.
    Wood W. A., “Some Basic Studies of Fatigue in Metals,” Published Jointly by Technology Press and John Wiley & Sons (1959).Google Scholar
  8. 8.
    Wild, M., “Joint International Conference on Creep,” New York, August 25–29, 1963,2,discussions Arising from Papers, published in Vol. 1.Google Scholar
  9. 9.
    Finney, J. M., “A Review of the Discontinuity or Hump Phenomenon in Fatigue S/N Curves; Theories and Further Results,” Report SM 314 (March, 1967).Google Scholar
  10. 10.
    Dolan, T. J., “Basic Research in Fatigue of Metals,” ASTM Bulletin 240, Research Sub-Committee, Committee E-9 (Sept. 1959).Google Scholar
  11. 11.
    Gumbel, E. S. and Freudenthal, A. M., “Distribution Functions for the Prediction of Fatigue Life and Fatigue Strength”, Internatl. Conf. on Fatigue of Metals, New York and London, 262, 1956.Google Scholar
  12. 12.
    International Conference on Fatigue of Metals, New York and London, 1956.Google Scholar
  13. 13.
    Keys, R. D. and Schwarzberg, F. R., “Techniques from Axial Fatigue Testing of Sheet Materials Down to −423 °F,” Paper presented at the 66th Ann. Mtg., ASTM (June, 1963).Google Scholar
  14. 14.
    Haagensen, P. J., “Statistical Aspects of Coexisting Fatigue Failure Mechanisms in OFHC Copper,” UTIAS Tech. Note No. 112 (June, 1967).Google Scholar
  15. 15.
    Muggeridge, D. B., “An Attempt to Correlate Bimodal Fatigue Endurance Distributions in OFHC Copper with Wood's H, F and S Ranges,” UTIAS Tech. Note No. 111 (June, 1967).Google Scholar
  16. 16.
    Ravindran, R., “Statistical and Metallographic Aspects of Fatigue Failure Mechanisms in Metals,” UTIAS Tech. Note No. 123 (Feb., 1968).Google Scholar
  17. 17.
    Nine, H. D. and Bendler, H. M., “Effect of Strain Amplitude on Fatigue in Copper Single Crystals,” ACTA Metallurgical,12 (Aug., 1964).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1971

Authors and Affiliations

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

Personalised recommendations