Gradient Deformation Criterion of Brittle Fracture. Analytical Grounds and Experimental Confirmation

Abstract

In the article [1], we propose a new fracture criterion based on the assumption that brittle fracture occurs when the deformation gradient modulus reaches a limit value. We consider in more detail the fact that the modulus of the temperature gradient, and, consequently, that of the deformation, becomes significant in a thin boundary layer where a quick temperature change occurs. We also present the solution of a new thermoelastic problem of a quick temperature change in a circular area. As it turned out, in the case of a curved boundary of the cooled area E2, where E2 is the Euclidean plane, the fracture criterion becomes complicated and gets a form of a limit value of the gradient modulus of the main deformations sum or just of the main stresses sum. Destruction is determined by the criterion the time of which setting in is less. It is also shown in the aticle that in the case of a heated circular area in E2 the criterion for brittle fracture of a continuum medium is the limit value of the gradient modulus of the main deformations sum. The results of the preliminary experiment with organic glass samples during a quick temperature change in the area with a rectilinear boundary are presented. During the experiment, there appeared a crack along the boundary of the temperature leap, although the stresses across this boundary are equal to zero, but there is a significant deformation gradient.