Conference material: "Proceedings of the International Conference on Computer Graphics and Vision “Graphicon”"
Authors:Andreev V.V., Andreeva O.V., Gai V.E.
Computer Modelling Based on the Percolation Theory of the Third Stage of Cracks Formation and Development on the Steel Microstructures Surfaces
The modeling of the process of destruction of structural materials under cyclic loads in the field of high-cycle fatigue was considered. A phenomenological analysis of the main stages of the formation of cracks, mechanisms and schemes of their initiation, formed in the process of destruction of real objects, was carried out. The implementation of these mechanisms using the tools of the percolation theory made it possible to increase the reliability of modeling the processes occurring in real conditions during the destruction of a structure. The parameter of the model of damage accumulation on the images of the microstructure of the surface of metals and alloys was formulated, which makes it possible to detect the moment of completion of the formation of a crack. The fractal dimension of the percolation cluster obtained on the cells belonging to the damage was chosen as a parameter. To calculate the sizes of percolation clusters the Hoshen – Kopelman multiple labeling algorithm was used. The existing algorithm was supplemented with an auxiliary label for open cells belonging to the percolation cluster, which made it possible to get rid of the additional operation of comparing labels and re-marking nodes when combining parts of a single cluster. To confirm the effectiveness of the proposed parameter, simulation the process of damage accumulation on images of the surface microstructure was made. The magnitude of the error did not exceed 6.6% for calculations using the values of the fractal dimension of percolation clusters built on the cells belonging to the crack.
Modeling of fatigue fractures, percolation cluster, fractal dimension, simulation