Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

In this paper, an analytical solution is developed for the problem of an infinite 1D hexagonal piezoelectric quasi-crystal medium weakened by an elliptical crack and subjected to mixed loads on the crack surfaces. The mixed loads comprise the phonon pressure, phason pressure, electric displacement, and temperature increment, and the crack surfaces can be electrically permeable or impermeable. Based on a general solution, combined with the generalized potential theory, the steady-state 3D thermo-electro-elastic field variables in the quasi-crystal are obtained in terms of elliptic integral functions and elementary functions. Several important physical quantities on the cracked plane, such as the generalized crack surface displacements, normal stresses, and stress intensity factors, are derived in closed forms. An illustrative numerical calculation verifies the presented analytical solution and shows the distribution of the 3D thermo-electro-elastic field. It is indicated that the influence of the phason field on the result is pronounced, especially for the electric field variables, and the electric permeability of crack surfaces has a significant effect on the electric displacement intensity factor at the crack tip.

Determination of crack resistance of a tank with elliptical crack

The occurrence of crack-like defects is a common phenomenon in the operation of vertical steel tanks (VST). Such defects can occur both at the beginning of the operation of the tanks, which may be associated with a violation of the manufacture conditions or the installation procedures of the tank elements and during operation. Over time, such defects increase significantly and turn into cracks. Existing regulations prohibit the operation of VST with cracks. At the same time, the organization that operates the tank does not always have the opportunity to perform repairs immediately. There are cases of trouble-free operation of tanks with non-through surface cracks at the stage of sustainable growth, which are confirmed by model calculations are known from practical experience. The analysis of crack resistance of the VST-5000 tank with a semi-elliptical crack under the action of hydrostatic pressure is carried out in the work. The level of filling the tank with petroleum products is 95% of its height. The semi-elliptical crack is located on outside surface of the wall panel in lower row of cladding. Determination of crack resistance of a tank with a crack is performed on the basis of stress intensity factors (SIF). Direct and energy methods were used to SIF calculation. Determination of the stress-strain state is performed on the basis of the semi-analytical finite element method (SFEM). The SIF distribution along the crack front obtained using SFEM by both direct and energy methods almost coincides and agrees well with the values of SIF calculated by the direct method when using three-dimensional FEM. The obtained values of SIF differ along the crack front by 50%: the minimum value of SIF acquires at the point of the front, which is located on the outer surface of the tank, the maximum one - at the point of the front inside the wall that is furthest from the outer surface. The obtained results show the quite uneven SIF distribution along the crack front, so that the calculation of such problems requires the spatial setting of problem.

Study of stress-strain state of plate with semi-elliptical and through cracks

The study of the elastic and elastoplastic stress-strain state of a plate with a semi-elliptical crack when changing its geometry has been carried out. The process of transition of a semi-elliptical crack into a through one was considered. Options of the stress-strain state were determined by means of the FEA method. An approximating dependence of the stress intensity factor on geometry of the plate is suggested. Keywords: strength, semi-elliptical crack, K-calibration, stress intensity factor, elastoplastic deformation, stress state intensity.

Analysis of Crack Growth in the Wall of an Electrolyser Compartment

Electrolysis units are widely used in different branches of industry. They are high-pressure tanks, each having a chamber and electrodes placed therein, which are arranged in assemblies, a cover as well as an inlet and outlet pipes. High requirements are imposed on their technical characteristics, confirming the urgency of the problem of improving calculation methods. To simulate the kinetics of the thermally stressed state in elements of power plants with complex rheological characteristics of the material and taking into account its damageability, a special technique and software complex have been developed on the basis of the finite element method, which allow solving a wide class of nonlinear nonstationary problems in a three-dimensional formulation with simultaneous consideration of all operating factors. The kinetics of the crack was studied using the method of calculating the survivability of structural elements, which is based on the principles of brittle fracture mechanics, while the plastic zone at the crack tip is assumed to be small compared to the crack size, and the crack kinetics is determined by the stress intensity factors at crack tips. The technique is based on calculating the kinetics of the crack to its critical dimensions, when an avalanche-like destruction of a structural element occurs, or a crack grows through the thickness of the element. The kinetics of a semi-elliptical crack emerging on the inner surface of the cell wall was studied under the action of static and cyclic loading. With the use of the developed technique, computational studies of the thermal stress state of the upper part of the electrolyser cell were carried out. The results obtained show that the cylindrical part of the cover is the most loaded. There have been carried out studies of the development of an internal surface semi-elliptical crack, which originated in this zone. It was found that with a small number of cycles per year, the crack will grow for a long time to a certain depth, then the rate of its growth from static loading will increase so quickly that the growth of the crack from cyclic loading can be neglected.