A Kinetic Approach to Fracture of Solids I. General Theorie

Abstract

Abstract It is shown that the fracture of a solid is a kinetical process which starts immediately after applying the load and proceeds during the whole time till the rupture of the specimen. This process begins with the opening of microcracks and proceeds by their growth and coalescence until a macroscopic crack arises. A general kinetic equation is derived governing the distribution function ϱ( q,t ) of cracks depending on their dimensions and on other parameters q and on the time t . Together with the equation for the probability of crack coalescence and some auxiliary conditions it forms a system of equations from which ϱ( q,t ) can be determined. A method for solving this system is proposed based on a division of all cracks into three groups and on an iteration technique. The method is illustrated in a simple special case. More complicated problems will be considered in future papers.