FRACTAL MODEL OF DAMAGE ACCUMULATION IN SOLID BODES

Abstract

The paper considers a model of damage accumulation in parts of machines and structures which is based on a theory of fractals. Hidden process of destruction prior to the formation of macroscopic cracks is usually associated with the accumulation of micro-damages. Various models of damage accumulation and crack growth under the influence of power and thermal loads. However, models describing the accumulation process of micro-damages and their outgrowth into macro-crack are practically non-existent. Fractal structures with self-similarity are an adequate model of the fracture process. The MacDonald correlation function describing the medium structure allows to present the self-similarity of structures within a certain range of scales.The paper reviews models of damage accumulation near an opening in a composite medium and at layer boundaries. The Cantor model in a forward algorithm and a backward algorithm have been used in order to describe the model of damage accumulation. As it is known, the Cantor fractal (Cantor dust) is obtained by using a recursive algorithm being applied to fracture mechanics can be regarded as a model of stepwise formation of dispersed micro-damages. The process of damage accumulation (latent destruction phase) and its transition in the formation process of macro-cracks and their unification in a through-thickness crack can be described, for example, by the Paris' law.

Keywords

• structure damage
• macdonald function
• cantor model
• damage accumulation