Influence of tension along a crack on the plastic zone in an anisotropic body

Abstract

The influence of longitudinal loading on the size and shape of the plastic zone near a crack in an anisotropic body is analyzed. A generalized plane stress state is considered. A relevant boundary-value problem is solved numerically to study the behavior of the main plastic zone at the crack tip, a new plastic zone above the crack, and an additional plastic zone on the lateral surface, which merge to form a single plastic zone Keywords: anisotropic body, crack, plastic zone, merging of two plastic zones Introduction. Various crack models are widely used in elastoplastic fracture mechanics [5,[8][9][10][11][12][13][14][15]. These models can be justified only if the size and shape of plastic zones near cracks are known. In this connection, it is extremely important to solve the relevant boundary-value problems. Many boundary-value problems for plane and antiplane strain as well as generalized plane stress state were solved (by analytic and numerical methods) in [3, 4, 6, etc.]. However, all of them deal with plastic zones in isotropic bodies. Plastic zones in anisotropic bodies are still poorly understood. They were studied in few publications [16][17][18], where several boundary-value problems for plane strain and generalized plane stress state were solved numerically and the influence of anisotropy and crack length on the size and shape of plastic zones was analyzed.Note that elastoplastic fracture under loads acting along a crack is studied by nonclassical fracture mechanics because the classical Griffith-Irwin-Barenblatt and Leonov-Panasyuk-Dugdale approaches fail to describe such processes [11,17]. It is therefore of current importance to thoroughly study this anomalous case to complete the overall picture of elastoplastic fracture.The present paper deals with a plastic zone near a crack in an anisotropic body. A generalized plane stress state is considered. The body is subject to tensile loads acting along and transversely to the crack. Strains are assumed small. The boundary-value problem is formulated in terms of the displacement components. By solving this problem numerically, we study the influence of longitudinal load on the size and shape of the plastic zone.1. Preliminaries. Assume that deformation involves no Pointing effect. Therefore, we can use tensor-linear constitutive equations to describe the deformation of the body.1.1. Tensor-Linear Constitutive Equations. The components of the stress tensor S and the components of the strain tensor D are related by the following tensor-linear equations [18]:

Influence of the anisotropy of the material on the limit state of an orthotropic plate weakened by a periodic system of collinear cracks

“…Relation (11) determines the distance between the cracks at which the coalescence of the process zones of two neighboring cracks occurs under the given load. …”

A Methodology to Determine the Effective Plastic Zone Size Around Blunt V-Notches under Mixed Mode I/II Loading and Plane-Stress Conditions

“…Many factors can influence the shape and size of the plastic zone. For example, the influence of deformation anisotropy, the elastic mismatch, and the tension along a crack on the plastic zone in an anisotropic body have been reported in [35][36][37], respectively. Alongside analytical and numerical methods for determination of the size and shape of the plastic zone, experimental studies have also been performed.…”

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

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