Cohesive Model Application in the Assessment of Plastic Zone Magnitude for One Particular Case of Crack Loading

Abstract

The answer of the thin, infinite, central cracked plate, subjected to in-plane loading, is investigated. The plate is made from a ductile metallic material. The two pairs of the concentrate forces, F, act on the crack surface in the direction perpendicular to it. The other edges of the plate, at infinity, are free of loading. The forces, F, open the crack and they are monotonously increased. The small plastic zones around crack tips will appear. It is assumed an isotropic and non-linear strain hardening of a plate material which can be good described by the Ramberg-Osgood´s equation. The investigations were carried out for the several different values of the strain hardening exponent n which is changed among the discrete values n = 2, 3, 4, 5, 7, 10, 15, 25, 50 and 1000. One well-known cohesive model (Dugdale´s model) was applied in the crack tip plasticity investigating. It was assumed that the cohesive stresses within the plastic zone are changed according to non-linear law. Also, a new algorithm was established which enables direct calculation of plastic zone magnitude depending on the magnitude of external loads. The contemporary mathematical tools, like the software package Wolfram Mathematica, were used. The solutions are presented through the special, Gamma and the Hypergeometric functions.