Two-Parameter Model of a Mode I Crack in an Elastoplastic Body under Plane-Strain conditions

Abstract

The Dugdale crack model is generalized to the case of plane strain. The governing equations are set up to determine the stresses in the plastic zone. Numerical results from specific problems are analyzed and compared with those for plane stress state and other cases. A relationship between the crack model and K I -T theory is established in the case of small-scale yielding at the crack tip Keywords: Dugdale crack model, generalized model, plane strain, fracture toughness, T-stresses, plastic zone, plane stress state, small-scale yielding Introduction. Classical fracture mechanics, either linear or nonlinear, is based on a one-parameter estimate of the limiting state of a body with a mode I crack. For example, Griffith-Irwin-Orowan theory [31,33,40] considers an asymptotic field of elastic stresses at the crack tip and describes the limiting state by only the stress intensity factor (SIF) K I or energy release rate G I . Nonlinear fracture mechanics based on the Cherepanov-Rice J-integral proceeds from the singularity of the asymptotic stress field in a nonlinearly elastic material [19,32,41].The intensive experimental investigations initiated almost immediately after the above concepts had been put forward revealed that the fracture characteristics depend on specimen geometry and loading conditions, as shown by the dependence of the maximum SIF on the thickness of the specimen, the ratio of the crack length to its width, etc. [16,17]. In this connection, much effort went to the development of standards for determining fracture toughness K IC in the case of plane strain. The weaknesses of the one-parameter approach made themselves evident later, in analyzing the influence of two-axis loading on the limiting state of a cracked body [13,20]: this theoretical approach did not confirmed the experimentally revealed effect of the homogeneous normal stresses along the crack on the maximum SIF.The above-mentioned and other facts are indicative of the limitation of the one-parameter approach to the description of quasibrittle fracture. Two factors influencing the limiting state of cracked bodies attracted the attention of researchers: constrained plastic strains in different stress-strain states (SSSs) at the crack front and regular (according to the elastic solution) terms of the stress field. However small the plastic zone at the crack tip, the stresses at the boundary of the elastic and plastic zones are always finite, and the effect of regular terms may be significant. Obviously, a closed-form elastoplastic solution for a mode I crack would account for these factors. Such analytical solutions are as yet unavailable, however; and researchers have to use crack models to simplify the distribution of stresses and strains and the form of the plastic zone.Recently, the following nonclassical approaches have been developed: -the criteria of plasticity theory and various numerical methods of analyzing the plastic zone at the crack periphery [16,27];-criteria of local buckling near cracks [2, 13]; -more complete description of ...

On the direction of development of a thin fracture process zone at the tip of an interfacial crack between dissimilar media

“…In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].Most theoretical studies in the field of the mechanics of interfacial cracks supposed that the fracture process zone is a surface on which the normal or tangential displacements discontinue. This surface is located on the continuation of the crack and does not go beyond the crack plane [2,4,11,12,15].…”

“…In recent years, there has been intensive development of studues in the field of the fracture mechanics of various deformable bodies, including composite materials, welded and adhesive joints, fractured rocks, and concrete and polymers. That was owing to new models of fracture mesomechanics that account, more fully than in the classical models, for the features of fracture process zones at crack tips [2][3][4][10][11][12][13][14][15].…”

Applied Problems in the Mechanics of Strain Hardening of Structural Metallic Materials

“…The papers [14,15] address approximate approaches to estimate the length of the plastic zone (or the fracture process zone in composites [81,84]), which is a part of the effective crack length, in the direction of crack propagation. It is assumed that when operating under extreme conditions, structural members may be subjected to overloads, in particular, those accompanied by plastic strains.…”

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

“…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.…”