A criterion for the onset of growth of two shear cracks in an elastic body under plane-strain conditions

Kaminsky, A. A.; Kipnis, L. A.; Хазін, Геннадій Анатолійович

doi:10.1007/s10778-006-0100-5

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…The other problem is problem K. Since its solution is well known, it is sufficient to solve the former problem. To find its exact solution, we will use the Wiener-Hopf method in combination with the Mellin transform [5,7,13].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the plastic zone at the corner point of interface

Kipnis

Полищук

2009

Int Appl Mech

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A symmetric problem of elasticity is formulated to analyze the plastic zone at the corner point of the interface between two isotropic media. The piecewise-homogeneous isotropic body with an interface in the form of angle sides consists of different elastic parts joined by a thin elastoplastic layer. The plastic zone is modeled by discontinuity lines of tangential displacement, which are located at the interface. The exact solution of the problem is found using the Wiener-Hopf method and is then used to determine the length of the plastic zone. The stress at the corner point is analyzed Keywords: plastic zone, corner point, interface, displacement discontinuity line, Wiener-Hopf method Introduction. There are a great variety of recent publications on plastic and other fracture process zones at cracks tips in anisotropic and piecewise-homogeneous bodies [1,[10][11][12][14][15][16][17][18]. Of current importance are problems related to fracture process zones at corner points of such bodies. For example, of considerable interest for the fracture mechanics of adhesive joints is analysis of the stress-strain state at singular points of piecewise-homogeneous bodies composed of different elastic parts bonded with each other by a thin elastoplastic layer. Here we will perform such an analysis for a corner point of the interface between media.This stress-strain analysis is reduced to problems of elasticity for piecewise-homogeneous wedge-shaped bodies. The information on the singularities of the stresses at corner points obtained by solving these problems can be used in developing numerical methods for stress-strain analysis of compound piecewise-homogeneous bodies with corner points.1. Problem Formulation. Assuming plane strain, we will formulate a symmetric problem of elasticity for a piecewise-homogeneous isotropic body. It has an interface in the form of angle sides and consists of different elastic parts bonded to each other by a thin elastoplastic layer.As the external load increases, a plastic zone develops at the corner point, which is a peaked stress concentrator. The zone has the form of two narrow bands emerging from the point and located in the interface. We will study only the initial stage of development of the plastic zone and consider that the external load is weak for the zone to be much less than the body.The task is to determine the length of the plastic zone and to analyze the stress state at the corner point.Since the bonding material is elastoplastic, primarily shear deformation occurs in the fracture process zone. Therefore, we will model the zone by a discontinuity line of tangential displacement on which the tangential stress is equal to the shear yield stress of the bonding material t s .Thus, we arrive at a static symmetric plane problem of elasticity for a piecewise-homogeneous isotropic plane having an interface in the form of angle sides and cuts of finite length emerging from the corner point and located in the interface (Fig. 1). At infinity, the solution of this problem is the solution of ...

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Section: Introductionmentioning

confidence: 99%

Analysis of the plastic zone at the corner point of interface

Kipnis

Полищук

2009

Int Appl Mech

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“…Recently, there has been considerable success in the understanding of the deformation and fracture of piecewise-homogeneous cracked bodies under static loading [5,6,8,9,11]. Unfortunately, there are very few problem solutions for compound bodies with cracks under dynamic loading.…”

Section: Introductionmentioning

confidence: 99%

Passages to the limit in the dynamic problem for a crack at the interface between elastic media

2008

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The paper analyzes numerically the passages to the limit in the dynamic problem for a penny-shaped crack at the interface between dissimilar linear elastic, homogeneous, isotropic materials as either the frequency of harmonic load or the difference between the properties of the materials decreases. It is shown that as the frequency decreases, the solution of the dynamic problem tends to that of the static problem, and as the physical and mechanical properties of the materials become less different, the original problem goes into the dynamic problem for a crack in a homogeneous body Keywords: interface crack, harmonic load, boundary integral equations, passage to the limit Introduction.Recently, there has been considerable success in the understanding of the deformation and fracture of piecewise-homogeneous cracked bodies under static loading [5,6,8,9,11]. Unfortunately, there are very few problem solutions for compound bodies with cracks under dynamic loading. This is because of the difficulty of describing dynamic processes. In [7], boundary integral equations were derived to solve a problem for a crack at the interface between two elastic half-spaces under dynamic loading. A numerical solution to a problem of elasticity for a circular crack at the interface under a harmonic load was first obtained in [4,12]. It was shown there that in the dynamic case, the stress-strain state of a compound body with an interfacial crack is greatly different from that of a homogeneous body with a crack.Note that reference solutions that could be used for comparison and validation purposes in solving new problems are usually not available. Therefore, solution reliability is an issue of extreme and current importance. As the frequency of loading tends to zero, dynamic solutions in solid mechanics are known to tend to the corresponding static solutions, which, thus, can be used for the validation of dynamic solutions [1,2]. In our recent publications, we examined the variation of forces at the front of a penny-shaped crack (for several pairs of materials [13,14]) and the displacement-discontinuity vector at the crack edges (for the pair of tungsten and aluminum [13]) with decreasing frequency of load, and compared the dynamic solution with the static one. As the difference in the physical and mechanical properties between the constituent materials decreases, problems for composite bodies go over into similar problems for continuous bodies, whose solutions can also be used as a reference.The present paper involves multiparameter numerical analysis of the passages to the limit in the dynamic problem for a penny-shaped crack at the interface between linear elastic, homogeneous, isotropic materials as either the frequency of harmonic load or the difference between the mechanical properties of the materials decreases. Special attention is focused on the variation in the normal and tangential displacements of the crack edges with decreasing difference between the mechanical properties of the materials.1. Problem Formulation. Consider, in...

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“…3, K C »700 kg/mm 3/2 is maximum and K IC »300 kg/mm 3/2 is minimum. Thus, their ratio is 2.3, which is the middle of the intervals (14) and (15).…”

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“…Primarily, it was necessary to correct and estimate the stress state near a crack tip by retaining the subsequent regular terms of the stress field. The results obtained within the framework of the K T I - [6,16], J Q - [18,20,22], and J A -2 [17,21] concepts and other approaches [5,14,15] made it possible to estimate the effect of the regular terms of the stress field on the classical fracture strength characteristics. However, these two-parameter approaches failed to formulate a failure criterion that would relate these parameters.…”

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confidence: 99%

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

Galatenko

2007

Int Appl Mech

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The generalized Dugdale crack model is used to formulate two-parameter failure criteria for the cases of quasibrittle state and developed plastic zones at a mode I crack tip. The failure criteria relate the fracture strength characteristics and the stress mode at the crack tip through the plastic constraint factor. The critical state of bodies with cracks under uni-and biaxial loading is analyzed in the cases of plane stress and plane strain using the Tresca and von Mises yield criteria. A small-scale yield criterion, which is an analytic relation between the critical stress intensity factor and T-stresses, is established

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A criterion for the onset of growth of two shear cracks in an elastic body under plane-strain conditions

Cited by 8 publications

References 11 publications

Analysis of the plastic zone at the corner point of interface

Analysis of the plastic zone at the corner point of interface

Passages to the limit in the dynamic problem for a crack at the interface between elastic media

Two-parameter failure criterion for elastoplastic bodies with mode I cracks

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