By J. Yvon (translated from French by H.S.H. Massey)
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Extra resources for Correlations and Entropy in Classical Statistical Mechanics (International series of monographs in natural philosophy 21)
Example text
The second less fundamental but more practical approach is then illustrated. Based on the assumed knowledge of certain micromechanical distributions, the fatigue initiation and propagation processes respectively, are presented. 2 The foundations of micromechanics The fundamental concepts of micromechanics as they first apply to all structured media and then as they specifically apply to the elastic response of idealized polycrystalline metals are presented in this section. 1 The micromechanic axioms pertaining to fatigue failure Over the years the basic concepts of micromechanics have become more and more refined until today they can be presented, as shown by Axelrad (1979), in a concise 27 Chapter 1 Probabilistic approaches to fracture-sensitive structures axiomatic manner.
With a knowledge of the solution of Eq. 68) and is only dependent on the initiated crack distribution &J,(O) and the transition intensity AC. (b) Interpretation of AC. , the type of idealized material that such an approach could cover is just not applicable to materials that are used in a design situation. 69) and leaving the determination of A to experimentation. 4 The micromechanics approach to fatigue failure associated with this interpretation of AC' instead of being Eq. 70) otherwise. Hence, with the specification of A, and the initial distribution of crack penetrations @I,(O) for Eq.
Lin and Yang (1983), assumed Z(X) to be a normal random variable with zero mean and a standard deviation U z . Since Z is a normal variable, Y is a normal variable and the crack growth rate da/dN follows a log-normal distribution as a result of the equation Y = log (da/dN). The stochastic parameter statistical model is represented by Eq. 51) where C1 , C2 , C 3 , and C4 are considered as stochastic variables. It was found that the two parameter Weibull distribution best describes the distribution of the crack size a(N) at a given number of cycles N.