Initial Development of the Prefracture Zone Near the Tip of a Crack Reaching the Interface Between Dissimilar Media

Kaminskii, A. A.; Kipnis, L. A.; Dudyk, М. V.

doi:10.1023/b:inam.0000028596.95084.ce

Cited by 19 publications

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“…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].…”

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

2006

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The Wiener-Hopf method is used to study, under the conditions of plane strain, the direction of development of a thin fracture process zone at the tip of an interfacial crack in a piecewise homogeneous isotropic elastoplastic body. The zone is modeled by a straight line of tangential displacement discontinuity that emerges from the crack tip at an angle to the interface. The dependences of the zone length and the angle on the load and other parameters of the problem are investigated Keywords: piecewise homogeneous isotropic elastoplastic body, interfacial crack, process zone Introduction. 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].The present paper addresses a piecewise-homogeneous body consisting of elastic and elastoplastic half-spaces. There is a rectilinear crack in the interface between the half-spaces. The body is under the conditions of plane strain. We examine the asymmetric case where a thin fracture process zone modeled by a line of discontinuity of tangential displacements develops in the body. The condition at infinity is formulated so as to account for the influence of the external field on the stress-strain state of the body. The integral Mellin transform is used to derive the functional Wiener-Hopf equation. Its exact solution is expressed in terms of Cauchy integrals and gamma functions. This solution is used to derive an equation for the determination of the length of the zone and to analyze the dependences of its length and angle on the external load and other parameters of the problem.1. Problem Statement. Consider the following plane-strain problem for a piecewise-homogeneous isotropic body: Determine the direction of development of a thin fracture process zone at the tip of a crack located in the interface between two dissimilar homogeneous half-planes with Young's moduli E 1 and E 2 and Poisson's ratios ν 1 and ν 2 . The material of the upper half plane is assumed elastoplastic; therefore, the preferential strains in the process zone, which is a thin layer, follow the shear mechanism. Because of this, we will simulate the thin process zone by a straight line that emanates from the crack tip at an angle α to the interface and on which the tangential displacement discontinues and the tangential stress is equal to a predefined material constant τ. The constant τ is the tangential stress averaged over the length...

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

2006

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“…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 the plastic zone using a discrete system of slip bands [1,15,34,35] or domains of simple configuration [16][17][18];-more complete description of the stress distribution at the crack periphery, and not just its singular part [22, 36-39, 42, 46, 47]; …”

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“…-criteria of local buckling near cracks [2, 13]; -more complete description of the plastic zone using a discrete system of slip bands [1,15,34,35] or domains of simple configuration [16][17][18];…”

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

Kaminskii

Galatenko

2005

Int Appl Mech

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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 ...

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“…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.…”

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

2010

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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]:

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Initial Development of the Prefracture Zone Near the Tip of a Crack Reaching the Interface Between Dissimilar Media

Cited by 19 publications

References 7 publications

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

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

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

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

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