Simulation of nonstationary hydrogen diffusion processes near the crack tip in a field of inhomogeneous mechanical stresses

An elastic-plastic isotropic body is investigated, weakened by a rectilinear crack directed along the abscissa axis, under the action of stresses symmetric with respect to its plane. The hydrogen concentration near the crack tip is calculated. An approximate solution of this problem is constructed under the condition that the distribution of hydrostatic stresses along the crack extension is approximated by a parabola. For a numerical solution, a method of the third order of accuracy with a two-sided estimate of the main term of the local error is proposed.

INTERFERENCE OF CLOSABLE CRACKS AND NARROW SLITS IN AN ELASTIC PLATE UNDER BENDING

The problem of bending of an infinite plate containing an array of trough closable cracks and narrow slits is considered in a two-dimensional statement. A crack is treated as a mathematical cut, the edges of which are able to contact along the line on the plate outside. A slit is referred to as a cut with contact stress-free surfaces and the negative jump of normal displacement can occur on this cut. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and previously developed model of the contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions in the form of inequalities on the cuts is formulated. The method of singular integral equations was applied in order to develop approximate analytical and numerical solutions to the problem. The forces and moments intensity factors near the peaks of defects and contact reaction on the closed edges of the cracks are calculated. A detailed analysis was carried out for parallel rectilinear crack and slit, depending on their relative location. Presented results demonstrate qualitative differences in the stress concentration near the defects of different nature.

Mathematical modeling of elastic state in a three-component plate containing a crack due to the action of unidirectional tension

Purpose. A two-dimensional mathematical model for the problem of elasticity theory in a three-component plate containing rectilinear crack due to the action of mechanical efforts is examined. As a consequence, the intensity of stresses in the vicinity of tops of the crack increases, which significantly affects strength of the body. This may lead to the growth of a crack and to the local destruction of a structure. Such a model represents to some extent a mechanism of destruction of the elements of engineering structures with cracks, we determined stress intensity factors (SIFs) at the tops of the crack, which are subsequently used to determine critical values of the tension. Therefore, the aim of present work is to determine the two-dimensional elastic state in plate containing an elastic two-component circular inclusion and crack under conditions of power load in the case of unidirectional tension of the plate perpendicular for the crack line. This makes it possible to determine the critical values of unidirectional tension in order to prevent crack growth, which will not allow the local destruction of the body. Methodology. The methods of studying two-dimensional elastic state body with crack as stress concentrators based on the function of complex variable method by which the problem of elasticity theory is reduced to singular integral equations (SIE) of the first and second kind, the numerical solution by the method of mechanical quadratures was obtained. Findings. In this paper two-dimensional mathematical model in the form of the system of two singular integral equations on closed contour (boundary of inclusion) and unclosed contour (crack) are obtained; numerical solutions of these integral equations were received by the method of mechanical quadratures; stress intensity factors at the tops of a crack are identify and explored to detect the effects of mechanical character. Graphical dependencies of SIFs, which characterize distribution of the intensity of stresses at the tops of a crack as function of elastic properties of inclusion and also as function of the distance between crack and inclusion are obtained. This makes it possible to analyze the intensity of stresses in the vicinity of a crack's tops depending on the geometrical and mechanical factors, as well as to determine the limit of permissible values of unidirectional tension of the plate perpendicular to the crack line at which the crack begins to grow and the body being locally destroyed. It is shown that the proper selection of elastic characteristics of the components of three-component plate can help achieve an improvement in the strength of the body in terms of the mechanics of destruction by reducing SIFs at the crack's tops. Originality. Scientific novelty lies in the fact that the solutions of the new two-dimensional problems of elasticity for a specified region (plate containing an elastic two- component circular inclusion and a rectilinear crack) under the action of unidirectional tension of the plate perpendicular to the crack line are obtained. Practical value. Practical value of the present work lies in the possibility of a more complete accounting of actual stressed-strained state in the piecewise-homogeneous elements of a structure with cracks that work under conditions of different mechanical loads. The results of specific studies that are given in the form of graphs could be used when designing rational operational modes of structural elements. In this case, the possibility for preventing the growth of a crack through the appropriate selection of composite's components with the corresponding mechanical characteristics is obtained.

Pure bending of strip (beam) with the arbitrarily oriented cross-cutting crack

The problem of pure bending of strip (beam) with transverse rectilinear crack, edges of which are free from acuter load, is investigated in this paper. Under bending moment its edges may not contact or smoothly contact throughout its area length or part. Dependently on where it is located.Using methods of theory of functions of complex variable and complex potentials the problem at issue has been reduced to the problems of linear conjugation, their analytical solution is found. Explicit expressions on complex potentials is written. Based on the energy criterion of destruction stress intensity factors are determined. Limit value of moment when the crack begins to propagate is found. For the case when crack edges partially contact, area length of contact of her edges is determined. Numerical analysis of critical moment of failure of strip (beams) is performed under various parameters of the problem, which are related to the mechanical state of crack. The corresponding graphic dependencies are constructed.

Inverse problem of contact fracture mechanics for a hub of friction pair taking into account thermal stresses

Methods of fracture mechanics enable a new approach to the design of structures, ensuring prevention of crack development. The plane problem of mechanics of contact fracture for the hub of a friction pair during operation is studied. It is accepted that near the rough friction surface, the hub has a rectilinear crack. A criterion and a method for solving the inverse problem of the mechanics of contact fracture on definition of the function of displacements of external contour points of the hub of a friction pair with regard to temperature drop and inequalities of the contact surface in friction pair components is given. The found function of displacements of the external contour points of the hub provides an increase of the load-bearing capacity of the hub of a friction pair. The problem of prevention of the fracture of the hub of a friction pair with allowance for the real friction surface was first posed and then solved.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.

ENERGY INVARIANTS IN THEORY OF ELASTOPLASTIC CRACKS

The paper considers a problem on a rectilinear crack in hardening elastoplastic material with load which is applied at infinity under plane-strain deformation conditions. While distributing J-integral in this case it is necessary to take into account specific characteristics associated with strain potential for environments with nonholonomic state equations. While considering a problem on a crack in elastoplastic material a principal term of asymptotic expansion in crack tip vicinity has an unknown singularity index in addition to an indefinite multiplier. It has been shown for steel 12X18H9T that while having invariance of energy integral it is possible to trace a singularity index for a principal term of stresses. The paper presents dependences of crack length compared to permissible Griffith’s length in accordance with the applied load which is associated with yield strength. Conceptions of J-integrals have been described for solution of a quasi-static problem. The developed approach can be used to formulate a criterion for destruction of elastoplastic material containing a rectilinear crack. The obtained theoretical dependences pertaining to determination of structure limit state characteristics have permitted to make a motivated selection of geometric parameters with due account of material strength properties. Results of the investigations can be used while preparing recommendations for development of structures with prescribed properties. The given approach makes most sense to be applied for determination of critical forces and critical value of crack length for elastoplastic material.