Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle

The problem of physically incorrect results due to neglecting the interaction of the crack edges in fracture mechanics is discussed. The cases of dynamic loading, interface cracks, and thermal loading in fracture mechanics are analyzed. The main conclusion is that the majority of results obtained in these areas of fracture mechanics are physically incorrect Keywords: fracture mechanics, physically incorrect results, interaction of crack edges Introduction. By physically incorrect results in fracture mechanics, we will mean results of mathematical modeling that disregards certain physical factors of fracture phenomena studied within the framework of fracture mechanics. In this connection, physically correct results in fracture mechanics will be meant results of mathematical modeling that takes into account all physical factors of fracture phenomena studied within the framework of fracture mechanics.A number of such factors are quite obvious a priori and should be taken into account in formulating problems of fracture mechanics. At least, neglecting them should be analyzed and commented. However, there are situations where the necessity of allowing for some factors becomes clear a posteriori, after solving a specific problem of fracture mechanics. Examples of such situations will be given below.The present paper analyzes the physical correctness of results in fracture mechanics that are united by the phenomenon of interaction of the edges of crack near its tips or throughout its length. Making consistent and rigorous allowance for the interaction of crack edges is possible only within the framework of nonlinear fracture mechanics where the linear equations of motion and constitutive equations can be used with nonlinear boundary conditions that change during deformation. As termed in [18], these problems of fracture mechanics are nonclassical because Condition 3 [18] that the boundary conditions do not change during deformation is not satisfied.Nowadays, the overwhelming majority of researchers neglect the interaction of crack edges and solve problems of fracture mechanics in a linear formulation. Such an approach assumes, making no clear provision and no comments, that the crack edges as if penetrate each other during deformation, which obviously leads to physically incorrect results. The sole exception is the approach [1-3, 17, 20-22, 30] for dynamic fracture mechanics that is based on a nonlinear formulation and accounts for the interaction of crack edges. As termed above, the results in dynamic fracture mechanics obtained with this approach are physically correct.In what follows, we will analyze, in a brief and simple manner, the physical correctness of results in fracture mechanics in the cases of dynamic loading, interface cracks between two materials, and thermal loading. We will avoid detailing mathematical methods for a wider range of experts to perceive the matter. The list of references does not cover all well-known publications on the research areas being discussed and includes only typical publications.

Section: Physical Incorrectness Of Results In Dynamic Linear Fracturementioning

confidence: 93%

On physically incorrect results in fracture mechanics

Guz

2009

“…This is equally true for both homogeneous and inhomogeneous materials. In laminated composites, both inter-and intralaminar cracks can contribute to the initiation of fracture process [4,8,9,11]. Let us consider a crack with the following initial opening, which frequently occurs in such cases (Fig.…”

Section: Boundary Integral Equationsmentioning

confidence: 99%

Effect of contact interaction of the crack faces for a crack under harmonic loading

Menshykov

Guz

2007

This paper is concerned with dynamic problems in fracture mechanics for elastic solids having cracks with contacting faces. The contact problem for a penny-shaped crack with a nonzero initial opening under normally incident harmonic wave is solved by the method of boundary integral equations. The solutions are compared with those that neglect the contact interaction of the crack faces. Results are presented for different values of the initial crack opening Keywords: fracture mechanics, harmonic loading, contact interaction of crack faces, boundary integral equations 1. Introduction. The achievements of material science such as the new high-tech materials (both homogeneous and heterogeneous) make it possible to increase significantly the strength and stiffness of structures designed. The level of safety requirements increases consequently because the cost of unpredictable fracture is always enormously high. Therefore, the ultimate goal of modern engineering fracture mechanics is fracture control, in order to predict the behavior of structures and avoid sudden collapse [1, 2, 5, 12].All existing structural materials contain different inter-and intra-component defects (cracks, delaminations, etc). The presence of cracks and delaminations considerably decreases the strength and the lifetime of structures as well as significantly increases the cost of maintenance. Unfortunately, the micro-defects cannot be fully avoided. Therefore, it is necessary to ensure that the residual strength of the structure will not fall below an acceptable level over the required service life.The opposite faces of existing cracks interact with each other under deformation, altering significantly the stress and strain distribution near crack tips [5]. The nature of the contact interaction between two surfaces is very complex. The shape of the contact region is unknown beforehand and must be determined as a part of the solution. The difficulties of the problem are further compounded by the fact that the contact behavior is very sensitive to the materials of the two contacting surfaces, their texture and topology, frequency, magnitude and direction of the external loading in relation to the contact region. Such dependences make the contact crack problem highly nonlinear. It is only possible to solve these problems using advanced numerical methods, since analytical solutions are limited to a relatively small number of idealized model situations corresponding to very special geometrical configurations and loading conditions. This means that the majority of contact crack problems ignore the real distribution of stresses and strains due to the above-mentioned difficulties of finding the appropriate numerical solution.The present paper is devoted to the solution of the three-dimensional fracture dynamics problem for a penny-shaped crack under a normally incident harmonic wave. The problem is solved with allowance for the contact interaction of the crack faces.

“…The contact interaction of crack edges under the action of a harmonic loading was studied in numerous publications by Guz and Zozulya. It was shown that it is very important to take into account the contact interaction of crack edges in a cracked body (see [6,7] for more details and bibliography). Some similar problems were considered in [4,5,[11][12][13]. In some situations, harmonic loading may induce antiplane deformation in the vicinity of a crack.…”

mentioning

confidence: 99%

Contact problem for a plane crack under a normally incident antiplane shear wave

Zozulya

2007

The contact-interaction problem for a stationary plane crack with friction between its edges under the action of a normal (to the crack plane) harmonic shear wave is addressed. Antiplane deformation conditions are considered. The distribution of contact forces and displacement discontinuity of crack edges are studied Keywords: contact interaction, stationary plane crack, friction of sides, harmonic shear wave, antiplane deformationWe will study the frictional contact interaction of the edges of a finite plane crack subject to a normally incident harmonic shear wave, which produces antiplane deformation. The contact forces and displacement discontinuity will be analyzed.