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Online First
A Kinetic Model of the Evolution of Cracks
Volume: 262
Series: A-22
The paper presents a kinetic approach to the problem of evolution of numerous cracks. The ensemble of microcracks is described by the size distribution function of cracks. Using the methods of the kinetic theory of gases, we derive the nonlinear, integro-differential equation of evolution of the size distribution function. We assume that cracks can nucleate with some nucleation rate, propagate with probability P and velocity v, and that they can coalesce with other cracks. The probability of crack fusion is defined by fusion cross-section.
CONTENTS
Abstract, ...3
1. Introduction, ...4
2. Derivation of the kinetic equation, ...9
3. Analytical solutions, ...13
4. Exponential and long-tail distributions, ...16
5. Numerical solutions, ...20
6. The crack populations, ...23
7. Spatial dependence of the distribution function, ...30
8. Conclusions, ...34
References, ...42
Streszczenie, ...45