Conditions Of Antiplane Deformation Research Articles

On one method of constructing the cauchy kernel of the singular integral equation for clarifie the stress-strain state of the wedge system under anti-plane deformation

An analytical approach to the construction of a singular integral equation (SIE) with Cauchy kernel is proposed, which makes it possible to clarify the stress-strain state of multi-wedge system with loaded radial cracks. This approach is based on the use of the theory of residues and the clarification of the solutions periodicity of the multi-wedge system characteristic equation. It is illustrated on the example of the construction of a SIE with Cauchy kernel for a two-wedge system with a loaded interfacial crack under the conditions of anti-plane deformation. For particular cases of geometric and mechanical parameters of the two-wedge system, the values necessary for constructing such an equation were calculated.

Distribution of Stresses Near Angular Notches on an Orthotropic Elastic Plane Under Conditions of Antiplane Deformation

By using a solution of the antiplane eigenvalue problem of the theory of elasticity for an elastic orthotropic wedge, we construct the distribution of singular stresses and displacements in a neighborhood of the tip of the corresponding angular notch under the conditions of antiplane deformation. By the method of singular integral equations, we solve the corresponding problem for an orthotropic plane with semiinfinite angular rounded notch and establish the relationship between the stress intensity and stress concentration factors at the sharp and rounded tips of angular notches.

Harmonic Vibration and Resonance Effects in the Case of Longitudinal Shear of a Hollow Cylinder with Crack

We propose an efficient analytic-numerical method for the evaluation of dynamic stresses in a hollow cylindrical body of arbitrary cross section with a through crack under the conditions of antiplane deformation. This method enables us to separately solve the integral equations on the surface of the defect and satisfy the conditions of harmonic loading on the boundary of the body. We deduce the formulas for the dynamic stress intensity factors in the vicinity of the crack and study the influence of its geometric parameters and the frequency of vibration on the indicated factors, in particular, with the evaluation of resonance frequencies.

Simulation of fracture of elasto-platic solids with cracks under conditions of out-of plane deformation

The paper considers a tearing mode crack (mode III fracture) propagation in elasto-plastic materials having ultimate strain. The fracture process of such material has been described in the modified Leonov-Panasyuk-Dugdale model with using an extra parameter such as the plastic zone width (the pre-fracture zone width. The two-parameter criterion of quasi-brittle fracture for mode III cracks in elasto-plastic material has been derived for conditions of the low-scale yielding in the presence of a stress field singularity of the field in the vicinity of a crack. The deformation fracture criterion has been deduced for the initial crack tip, whereas the force criterion has been deduced for tangential stresses with account for their averaging at the tip of a model crack. The lengths of initial and model cracks differ by the length of the pre-fracture zone. The sequential analysis of application possibility of the proposed strength criterion has been performed when determining fracture loads for solids with tearing mode cracks. Fracture diagrams of quasi-brittle fracture under conditions of antiplane deformation have been plotted for a band with an edge crack.

Periodic System of Closely Located Holes in an Elastic Plane Under the Conditions of Antiplane Deformation

We construct a singular integral equation of an antiplane periodic problem of the theory of elasticity for an isotropic plane weakened by smooth curvilinear holes. A numerical solution of the problem is obtained in the case of closely located holes with rounded V-shaped vertices made in the elastic plane under the conditions of uniform shear at infinity. On this basis, we determine the stress concentration factors at the rounded vertices of a bilateral V-shaped semiinfinite notch. By using the well-known relation between the stress intensity and stress concentration factors for sharp and rounded V-shaped notches, we perform the limit transition to a bilateral sharp V-shaped notch. The dependence of the stress intensity factor at the sharp vertices of a bilateral V-notch on its apex angle is determined.

Development of plastic zones in a body with rectangular slot under the conditions of antiplane deformation

We study the quasistatic development of plastic zones in a perfectly elastoplastic body with rectangular slot caused by the action constant shear forces applied at infinity. The exact analytic solution of the problem is obtained, and it is shown that the plastic zones can be studied in the initial stage of development on the basis of the elastic solution of the problem. The shapes of the plastic zones are analyzed depending on the loads for the cases of cracklike, wide, and square slots.

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

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

Linear model of a plastic zone in the vicinity of a sharp notch under the conditions of longitudinal shear

A procedure is proposed for the evaluation of the load in the case where the plastic zone in the vicinity of a stress concentrator increases almost self-similarly (homothetically). The notion of measure of nonself-similarity of the development of the shape of the zone determined on the basis of its simulation by a single plastic strip is introduced. For some types of stress concentrators, under the conditions of antiplane deformation, we determine the levels of loading for which the plastic zone develops self-similarly (with required accuracy).

Modeling of Plastic Zones in the Process of Shear Deformation of a Half Layer Containing a Crack

We study the evolution of plastic zones in a perfectly elastoplastic half layer containing a crack in its median plane under the conditions of antiplane deformation caused by displacements of the rigid faces of the half layer, deduce equations for the boundary of the continual plastic zone and its length in the plane of the crack as functions of the load, and perform the approximate analysis of the stress intensity factors of the elastic solution for the zones (the so-called linear model of the plastic zone).

The optimal control of fracture and stress parameters in a piezoceramic halfspace with cracks

An approach to the determination of the optimal control of fracture and strength parameters in a piezoceramic halfspace with cracks under antiplane deformation conditions is proposed. The distribution over certain part of the halfspace boundary, harmonically changing with time under the influence of axial forces or electric charges is analyzed as a control interaction. The solution of the inverse problem in fracture mechanics is obtained from the solution of the corresponding direct boundary value problem; in this case, the optimization problem is reduced to the momentum problem. The solution of the direct electroelastic problem using the method of the boundary integral equations is obtained. Various control functions permitting to realize the optimal process of control, i.e. the minimal energetic expenses, are given.

Plastic zones near the tip of a unilaterally exfoliated rigid inclusion under the conditions of antiplane deformation

We obtained the analytic solutions of the problem of initial stage of the ramified plasticity zone appearing in the vicinity of the tip of a unilaterally exfoliated rigid plate-like inclusion subjected to longitudinal shear. If the zone consists of a single band, it makes an angle of 150° with the nonexfoliated side of the inclusion. The zone of continuous plastic strains is a special case corresponding to the infinite number of plasticity bands. We determined the boundary between the regions of plastic and elastic strains.

Strength of a body with stochastic distribution of thin defects under the conditions of antiplane deformation

Strength of a body with stochastic distribution of thin defects under the conditions of antiplane deformation

Partially-bonded rigid inhomogeneities in antiplane deformation

A partially-bonded rigid inhomogeneity embedded in an infinite elastic matrix under conditions of antiplane deformation is examined. The modeling is based upon the complex variable method and utilizes conformal mapping and continuation techniques in developing the solution. Closed form solutions of the specific case of a uniform shear stress and a screw dislocation in the matrix are provided. The singular form of the stress field at the singular interface points is examined and their interaction is discussed.

Two approaches to the investigation of antiplane deformation of an isotropic solid with a thin elastic inclusion

An approach is proposed to the investigation of the state of stress and strain of a piecewise-homogeneous plane consisting of a matrix and a thin tunnel-like rectangular inclusion with rounded-off corners under the assumption that such a composite body is under antiplane deformation conditions. A numerical comparison is made of the results obtained in this paper and on the basis of an approximate model /1/. It is shown that they agree satisfactorily at sufficiently large distances from the vertices of the inclusion, when the inclusion is more pliable than the matrix.

Interaction of stress waves with curvilinear tunnel cracks of longitudinal shear in a half-space

A steady wave process is considered in the half-space with tunnel-like curvilinear cracks under conditions of antiplane deformation. The ensuing boundary value problems are reduced to singular integro-differential equations which are realized numerically. If the crack tip reaches the half-space boundary, the kernel of the integrodifferential equation contains, besides a moving singularity of the Cauchy type, a fixed singularity, and this singificantly affects the pattern of longitudinal shear stress wave fields. This case is the subject of detailed investigation below. Certain singularities of such wave processes are pointed out, and the results of calculations of the dynamic stress intensity coefficient are presented.

Dynamics of a rectilinear isolated crack growing at a constant rate under conditions of antiplane deformation

Article [i] discusses the problem of the development of a rectilinear crack under the conditions of antiplane deformation with its arbitrary loading and an arbitrary law of the motion of its ends. The difficulty in the practical application of the solution obtained consists in the need for a consecutive calculation of all the wave diffractions running along the crack from one of its edges to the other. Under these circumstances, for large times (in comparison with the time of the passage of a wave over the length of the crack) it is practically impossible to find a solution. With this aspect, the best properties are those of self-similar solutions, obtained in the problem of the development of a rectilinear isolated crack from zero at a constant rate under the action of the corresponding load. Here the arbitrary law of the loading can be approximated [2] by the sum of self-similar loads. For the case of plane and axisymmetric deformation, several such self-similar problems have been solved [3-9]. In the present article, analogs of these problems for antiplane deformation are considered as a partial case. The consideration of antiplane deformation is explained, on the one hand, by the great mathematical simplicity of this case in comparison with plane deformation and, on the other hand, by the fact that many of the qualitative aspects of the solutions in the cases of plane and antip!ane deformation are common.

Dynamic interaction of systems of cracks under antiplane deformation conditions

Dynamic interaction of systems of cracks under antiplane deformation conditions

Some self-similar problems of star crack development under antiplane deformation conditions

The formulation under investigation can be considered as a model for the mathematically more complex problem of plane deformation. In an unloaded x, y plane let a system of 2n radial slits start to be developed from the origin at a constant speed at the initial instant. The slit edges are loaded in such a way that the whole elastic space is subjected to antiplane deformation along the z axis. Hence, only w =w(x, y, t) - the z axis component of the displacement vector - is not zero. In this case the nonzero components of the stress tensor have the following form: z~z = ~Ow/Oy; T= = ~taw/Ox. The function w satisfies the wave equation O~w/Ox 2 ~- 02w/Og s : b-~a2w(Ot~.