Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

Abstract

Stress-strain state of isotropic plate with rectilinear through-crack at combined action of bending and tension, realized by applying distributed forces and bending moments at infinity, the vectors of which are parallel and perpendicular to the crack, is investigated. Under the influence of the internal stress the crack faces contacts on area of constant width near the upper base of plate, and plastic zones forms in its tips. Using methods of the theory of complex variables, complex potentials plane problem of elasticity theory and the classical theory of plates bending, solving of the problem is reduced to the set of linear conjugation problems and their analytical solution is built in a class of functions of limited plastic zones in the crack tips. The conditions of existence of the solution of the problem in these terms are determined. Using Treska plasticity conditions in the form of surface layer or the plastic hinge, the length of plastic zone and crack opening displacement are found analytically. Their numerical analysis for various parameters of the problem is conducted.

Tribology Characteristics of Heatproof Alloys at a Dynamic Pin Ladening in the Variable Temperature Field

“…Researchers [27][28][29], based on the model of contact along the line, considered the issue of the mechanics of the destruction of plate parts, taking into account the partial closure of crack-like defects during bending. Similar problems about the behaviour of contact cracks in plates under the action of simultaneous stretching and bending were studied in publications [30][31][32].…”

Pure Bending of Strip (BEAM) with Crack in Strip of Tensile Stress with Allowance for Plastic Strips Near Crack Tips

“…An analysis of stress-strain state under combined bending and tension of an isotropic plate with crack is represented by Sulym et al (2018) in the assumption of line and constant width area contact between crack faces but with no plastic zones near the crack tips. In the articles by Nykolyshyn et al (2010Nykolyshyn et al ( , 2015, the tension of homogeneous isotropic plate weakened by two through cracks with plastic zones is considered.…”