MATHEMATICAL AND MECHANICAL RELATIONSHIP OF CRACKS GRIFFITH AND A NEW TYPE IN SOME NANOTECHNOLOGIY

Abstract

In this paper, for the first time, mathematically strictly, models of Griffiths cracks and cracks of a new type are constructed simultaneously. Accurate models are constructed as a result of the convergence of the ends of two semi-infinite deformable stamps located on a deformable multilayer base. The mechanism of destruction of the medium by cracks of a new type is radically different from the mechanism of destruction of the medium by Griffiths cracks, and has so far been poorly studied. Griffiths formed his cracks with a smooth border as a result of compression from the sides of an elliptical cavity in the plate. Cracks of a new type have a piecewise smooth border, resulting from the replacement of an ellipse with a rectangle compressed from the sides. The construction of models in the work is based precisely on these descriptions of the origin of cracks formed by the ends of approaching deformable stamps. When creating models, the results of previously performed studies on the construction of exact solutions to a number of integral equations of contact problems, published in this journal, are used. The paper found that the destruction of the medium, in the case of cracks of a new type, occurs earlier than in the case of Griffith cracks, which, according to the authors, explains the reason for the destruction of Griffith cracks in the experiment earlier than the theory predicts. Griffiths explained this by the presence of microcracks on the border of the main crack. The authors tend to believe that the cause is the transformation of one type of crack into another, under certain conditions. The results obtained make it possible to compare and quantify the behavior of the medium in the presence of both one and another type of cracks. It is applicable both for the study of mutual transitions of Griffith cracks and cracks of a new type, and for the construction of models of adhesion of wetted nanoparticles.