Взаємодія кільцевого штампа із попередньо напруженим ізотропним шаром, що зчіплений із жорсткою основою

Abstract

Отримано формули для визначення контактних напружень у шарі, в який втискується абсолютно гладкий штамп за наявності в шарі залишкових деформацій, що зумовлені зосередженим нагрівом при зварюванні. Наведено числовий приклад і показано, що наявність у шарі залишкових деформацій суттєво впливає на величину і характер розподілу контактних напружень.

Increase of reliability and durability of structures and mechanisms is one of the most actual tasks of modern construction and engineering. Residual deformation is known to occur almost always in the structural elements and machine parts. The nature of their appearance can be very different: irreversible deformation (plasticity, creep), structural changes in the material, changes of the aggregate state in some areas, mechanical, chemical and technological processes, etc. Taking into account the residual deformation while calculating welded structures is of special importance. Resulted stress can cause fracture and accelerate some phase transitions, corrosion. When the residual strains under development of the important structural elements of machines and installations is taken into account, the material strength life can be estimated more accurately which can result in reduce of its costs, while maintaining the necessary functional characteristics of the elements in general. That is why the study of the contact interaction of the elastic bodies with residual deformations is up to date and will remain in the future. The isotropic layer has thickness and is fused with rigid base. The perfectly smooth hard annular punch is pressed forward (without rotation) in the layer (Fig. 1). Smoothness means that the interface tangential stresses are equal to zero. Absence of rotation means that the efforts which are applied to the punch can be reduced to the resultant force, which is directed along the axis of the punch. In the contact area the punch is limited by the surface of rotation, which consists of three parts: planes for and parabolas with tips at points and . On the upper surface of the layer heating caused by welding was concentrated which resulted in the field of residual deformations. The problem is treated as the construction of the solution of the integral equations with kernels involving the Bessel functions. The author has developed a method of approximate solutions of this type. The main idea of this method is to represent the unknown distribution function of the contact stresses as the Fourier series with unknown coefficients and to construct a system of the linear equations to find them. To demonstrate the proposed methods the numerical example of the construction of the contact stresses distribution function is presented in the paper. Formulae for finding contact stresses in the layer, in which perfectly smooth punch is pressed, when residual deformations are available in the layer caused by the localized heating under welding, are obtained.