Modeling the fracture process zone near a crack tip in a nonlinear elastic body

Abstract

The model of a fracture process zone near the tip of a mode I crack in a nonlinear elastic body is proposed. Using the numerical solution of an appropriate boundary-value problem, the effect of the fracture process zone on a crack opening displacement is examined Keywords: nonlinear elastic body, crack, fracture process zone 1. Introduction. As experiments [1,3,8,12] show, fracture occurs in a local area near a crack tip (fracture process zone) where extremely high stresses give rise to submicrocracks that grow and coalesce. The shape and structure of this zone depend on the material properties and loading conditions.The strains in the fracture process zone are very high (more than 50% in an elastoplastic body [4]). This is why many attempts to describe the deformation process in this zone using the small-strain deformation theory of plasticity led to physically incorrect results that disagree with experimental data [1].A great many theoretical studies of the stress-strain behavior near a crack tip in nonlinear bodies disregarding the fracture process zone were published in the 1960-70s [1,7,8]. Researchers presumed that by solving nonlinear boundary-value problems, it was possible to eliminate the singularity of the stresses and strains at the crack tip, which would be consistent with reality.However, the singularity was still there, but of different type. Thus, stresses and strains at the crack tip remained infinitely high.The lack of information on fracture mechanisms is compensated for by modeling the fracture process zone [1, 3, 10-13] based on experimental data [1, 8] on the localization of nonlinear deformation in narrow zones (slipbands) at the crack tip. This phenomenon is especially typical for the early stage of loading. Since the fracture process zone is usually located on the continuation of the crack and is much shorter than the crack, it is modeled, expanding upon the Leonov-Panasyuk model [6], by a slit with faces subject to certain stresses.The experiments [4] indicate that the fracture process zone occurs inside the zone of nonlinear deformation near the crack tip. We will study the effect of the fracture process zone on the opening displacement of a mode I crack. Use will be made of the model proposed in [3,11,12]. In this model, the length of the fracture process zone and, hence, the length of the slit remain constant with increase in the external load. What do change are the stresses applied to the faces of the slit. They are determined by solving a boundary-value problem and satisfying the continuity and limitation conditions for the stresses at the slit tip.We will analyze the role of the fracture process zone near a crack tip in a nonlinear elastic body in the case of a generalized plane stress state assuming small strains. The boundary-value problem will be formulated in terms of the displacement components. By solving the problem, we will ascertain how the fracture process zone influences the crack opening displacement.1. Preliminaries. To formulate the boundary-value problem, we need th...