Equilibrium state of the internal crack in the infinite elastic wedge with thin coating

Abstract

We studied the stress concentration in the neighborhood of the vertices of the internal crack located on the bisector of an infinite elastic wedge. Normal forces are applied to the edges of the crack. The edges of the wedge are supported by a thin flexible covering, free from stresses from the outside. The effect of the coating on the stress-strain state of the wedge is modeled by a special boundary condition. The correctness of which is confirmed by numerical simulations. The integral Mellin transform made it possible to reduce the problem to the solution of a singular integral equation of the first kind with a Cauchy kernel with respect to the derivative of the crack opening function. Solutions of the integral equation are constructed by the collocation method for various combinations of geometric and physical parameters of the problem.

Determination of the stress concentration in the corner point of the wedge-shaped region reinforced by a more rigid thin coating

“…Given the mechanical properties of the wedge and lining materials, Equations (10), (12), (14), (16) and (18) It should be noted that in problems V-V and V-I the voltages become singular when the angle of the wedge solution becomes larger than p, and the index l reaches 0.5 at 2 p: Figure 4 shows the solution to problem V-IV. Figure 5 shows the solution to problem V-III.…”

“…A general approach to constructing an asymptotic series was proposed by Belokon [10]. In our work [11,12] we considered a series of problems on the equilibrium state of elastic bodies, which were supported by a thin flexible coating and contained internal cracks. These publications present the results of a study of plane problems of the theory of elasticity, respectively, for a strip and a wedge impaired by the internal cracks and reinforced by a thin coating at the boundaries.…”

Features of Stresses at the Apex of an Elastic Wedge, Supported by a Thin Flexible Coating on the Sides

“…Методы исследования. Математическая модель тонкого гибкого покрытия на границе упругого тела, содержащего внутренние трещины, рассмотрена в работах авторов данной статьи [6,7]. Она сформулирована на основе асимптотического анализа решения задачи для упругой полосы [8] и представляет собой специальное граничное условие.…”