A new type of extreme value distributions

Engineering Fracture Mechanics

Volumn 58, Issue 5-6, 1997, Pages 557-570

  Kunin, B ^a  

^a UNIVERSITY OF ALABAMA IN HUNTSVILLE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRACK PROPAGATION; MATHEMATICAL MODELS; WEIBULL DISTRIBUTION;

EXTREME VALUE DISTRIBUTIONS; SHAPE PARAMETERS;

FRACTURE MECHANICS;

EID: 0031274639     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0013-7944(97)00043-x     Document Type: Article

References (26)

1. Fisher, R. A. and Tippett, L. H. S., Limiting forms of the frequency distribution of the largest or the smallest member of a sample. Proceedings of the Cambridge Philosophical Society, 1928, 24, 180-190.
2. Gumbel, E. J., Statistics of Extremes. Columbia University Press, 1958.
3. Galambos, J., The Asymptotic Theory of Extreme Order Statistics. Wiley, New York, 1978.
4. Leadbetter, M. R., Lindgren, G. and Rootzen, H., Extremes and Related Properties of Random Sequences and Processes. Springer, Berlin, 1983.
5. Chudnovsky, A., Kunin, B. and Gorelik, M., Modeling of brittle fracture based on the concept of crack trajectory ensemble. Engineering Fracture Mechanics, 1997, 58, 437-457.
6. Chudnovsky, A. and Kunin, B., A probabilistic model of brittle crack formation. Journal of Applied Physics, 1987, 62(10), 4124-4129.
7. Kunin, B., A stochastic model for controlled discontinuous crack growth, in Probabilities and Materials. Tests, Models and Applications, ed. D. Breysse, NATO ASI Series, Series E, Vol. 269. Kluwer, Dordrecht, The Netherlands, 1994.
8. Freudenthal, A. M., Statistical approach to brittle fracture. Fracture, Vol. 2, ed. H. Leibowitz. Academic Press, New York, 1969.
9. Branger, J., Life estimation and prediction of fighter aircraft. In International Conference on Structural Safety and Reliability, ed. A. Freudenthal. Pergamon Press, New York, 1972, p. 213.
10. Butler, J. P., Reliability analysis in the estimation of transport-type aircraft fatigue performance. In International Conference on Structural Safety and Reliability, ed. A. Freudenthal. Pergamon Press, New York, 1972, p. 181.
11. Davenport, A. G., Structural safety and reliability under wind action. In International Conference on Structural Safety and Reliability, ed. A. Freudenthal. Pergamon Press, New York, 1972, p. 131.
12. Statistical Analysis of Fatigue Data, eds R. E. Little and J. C. Ekvall. ASTM STP 744, ASTM, 1981.
13. Chou, P. C. and Miller, H., Maximum likelihood estimation of a two-segment Weibull distribution for fatigue life. In Statistical Analysis of Fatigue Data, eds R. E. Little and J. C. Ekvall. ASTM STP 744, ASTM, 1981, p. 114.
14. Little, R. E., Estimating the median fatigue limit for very small up-and-down quantal response tests and for S-N data with runouts. In Probabilistic Aspects of Fatigue, ed. R. A. Heller. ASTM STP 511, ASTM, 1972, p. 29.
15. Eggwertz, S., Investigation of fatigue life and residual strength of wing panel for reliability purposes. In Probabilistic Aspects of Fatigue, ed. R. A. Heller. ASTM STP 511, ASTM, 1972, p. 75.
16. Shimokawa, T. and Hamaguchi, Y., Statistical evaluation of fatigue life and fatigue strength in circular-hole notched specimens of a carbon eight-harness-satin/epoxy laminate. In Statistical Research on Fatigue and Fracture, eds T. Tanaka, S. Nishijima and M. Ichikawa. Elsevier, Amsterdam, 1987, p. 159.
17. Ishikawa, H., Tsurui, A. and Kimura, H., Stochastic fatigue crack growth model and its wide applicability in reliability-based design. In Statistical Research on Fatigue and Fracture, eds T. Tanaka, S. Nishijima and M. Ichikawa. Elsevier, Amsterdam, 1987, p. 45.
18. Krausz, A. S. and Krausz, K., Fracture Kinetics of Crack Growth. Kluwer, Boston, MA, 1988.
19. Phani, K. K., Strength of long optical glass fibers. Journal of Applied Physics, 1987, 62(2), 719-720.
20. Phani, K. K., Maitra, A. K. and De, A. K., A new distribution function for analysis of dynamic fatigue of neutral glass. Indian Journal of Technology, 1988, 26, 95-98.
21. Arnol'd, V. I., Ordinary Differential Equations, MIT Press, Cambridge, 1973.
22. Hermann, R., Lie Groups: History, Frontiers and Applications, Vol. 1. Math Science Press, Brookline, MA, 1975.
23. Kunin, B., A completion of the list of extreme value distributions. Advances in Applied Probability, 1997, (submitted).
24. Mischke, C. R., Stochastic methods in mechanical design: Part 1; property data and Weibull parameters, Proceedings of the 8th Biannual Conference on Failure Prevention and Reliability (ASME), Montreal, Canada, 1989.
25. Kunin, B., A probabilistic model for predicting scatter in brittle fracture. Ph. D. Thesis, University of Illinois, Chicago, IL, 1992.
26. Kunin, B. and Dearth, R., Evaluation of statistical fracture parameters on the basis of crack arrest experiment. Probabilistic Engineering Mechanics, 1997, in press.