Experimental Mechanics

, Volume 7, Issue 10, pp 409–418 | Cite as

Random-load fatigue tests on a fail-safe structural model

Testing of redundant structural models under constant- and variable-amplitude loading consistently shows the existence of a fail-safe capacity after failure of the weakest member
  • R. A. Heller
  • R. C. Donat


Experiments performed on a ten-member redundant “fail-safe” structural model subjected to randomized load sequences confirm predictions of fatigue life and reliability based on a probabilistic approach.

The statistical variation in ultimate strength of 2024-T4 aluminum alloy combined with an exponentially distributed, Markovian, bending load-amplitude sequence with a constant-amplitude S-N relation for single specimens, is utilized in the analysis.

Experimental results are presented for the statistical distribution of ultimate bending strength of 2024-T4 aluminum alloy. Constant load-amplitude flat-bending fatigue tests on single specimens and on multimember structures, and variable-amplitude flat-bending tests on fail-safe structures are reported. Life to failure of the weakest member, as well as the remaining “fail-safe” life in the parallel structure, are examined.


Aluminum Fatigue Mechanical Engineer Aluminum Alloy Fluid Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of Symbols


normalizing factor


width of specimen






base of exponential logarithms


energy loss due to plastic bending, statistical minimum and characteristic energy loss


probability density function


probability distribution function

h, hx

parameters of exponential load distribution


thickness of specimen


subscript forith stress level


initial number of members in the structure

K, Ksi,KR,Kx

linear strength-reduction parameters


number of load levels in the spectrum

Mi, ΔM

bending-moment level and difference


plastic moment


number of applied load cycles

N, Nm,Nx

number of load cycles in general, minimum safe life, and to failure of thexth member


down-transition probability


frequency of occurrence ofith stress level



\(\bar P\)

transition probability matrix


relative resistance of a member, statistical minimum, and characteristic resistance


reliability function, probability of exceedance

S, Sx,i, ΔSx

random-applied stress amplitude,ith stress level, afterx failures, stress difference


initial ultimate bending strength, statistical minimum and characteristic bending strength

s, sx, i, ΔSx,Su,Sum

respective stress or strength divided byS uc

V, Vi

characteristic, single specimen, constant-amplitude fatigue life


number of failed members


section modulus


parameter of extreme value (weibull) distribution


angle of bend in impact test


strength-reduction parameter


strength-reduction parameter

λ, λx

probability rate of failure


number of cycles between successive failure


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  1. 1.
    Heller, A. S., Heller, R. A., and Freudenthal, A. M., “Random Fatigue Failure of a Multiple Load Path Redundant Structure,” Proc. Tenth Sagamore Army Materials Conference, 187 (1964); also Air Force Systems Command, ML-TDR-64-160.Google Scholar
  2. 2.
    Heller, R. A., and Heller, A. S., “Fatigue Life and Reliability of a Redundant Structure,” Annals of Reliability and Maintainability,4,881–895; also Institute for the Study of Fatigue and Reliability, TR No. 17, Columbia University (1965).Google Scholar
  3. 3.
    Heller, R. A., and Donat, R. C., “Experiments on the Fatigue Failure of a Redundant Structure,” Amer. Soc. Test. Mats. Special Tech. Publication STP 404 (1966); also Institute for the Study of Fatigue and Reliability, TR No. 26, Columbia University (1965).Google Scholar
  4. 4.
    Thompson, N., “Fatigue in Aircraft Structures,”Academic Press, 43,New York (1956).Google Scholar
  5. 5.
    Bazovsky, I., “Reliability: Theory and Practice,” Prentice-Hall (1961).Google Scholar
  6. 6.
    Gumbel, E. J., “Statistics of Extremes,”Columbia Univ. Press, New York (1958);also “A Guide for Fatigue Testing and Statistical Analysis of Fatigue Data,” ASTM Spec. Tech. Publ. No. 91-A, Second ed. (1963).Google Scholar
  7. 7.
    Parkes, E. W., “The Permanent Deformation of a Cantilever Struck Transversely at Its Tip,”Proc. Royal Soc., London, A228, 462 (1955).Google Scholar
  8. 8.
    Hodge, P. G., Jr., “Plastic Analysis of Structures,” McGraw-Hill, 13 (1959).Google Scholar
  9. 9.
    Donat, R. C., and Heller, R. A., “Experiments on a Fail-Safe Structural Model,” Institute for the Study of Fatigue and Reliability, TR No. 38, Columbia University (1966).Google Scholar
  10. 10.
    Schijve, J., “The Endurance under Program-Fatigue Testing,” Proc. Symposium Full-Scale Fatigue Testing of Aircraft Structures, Amsterdam, 1959, Pergamon Press, 41 (1961).Google Scholar
  11. 11.
    Heller, R. A., andShinozuka, M., “Development of Randomized Load Sequences with Transition Probabilities Based on a Markov Process,”Technometrics,8,1 (1966);also Institute for the Study of Fatigue and Reliability, TR No. 4, Columbia University (1964).Google Scholar
  12. 12.
    Freudenthal, A. M., “Expected Time to First Failure,” Air Force Systems Command AF-ML 66-37 (1966).Google Scholar
  13. 13.
    Heller, R. A., andHeller, A. S., “The Relationship of Earliest Failures to Fleet Size and Parent Population,”Annals of Reliability and Maintainability,5,722 (1966);also Air Porce Systems Command AF-ML 66–168 (1966).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1967

Authors and Affiliations

  • R. A. Heller
    • 1
  • R. C. Donat
    • 2
  1. 1.Institute for the Study of Fatigue and ReliabilityColumbia UniversityNew York
  2. 2.Air Force Materials LaboratoryDayton

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