Вплив залишкових деформацій на контактну взаємодію жорсткого штампа та пружного півпростору

Abstract

Наведено розв’язок осесиметричної контактної задачі про тиск штампа складної конфігурації на пружний ізотропний півпростір з урахуванням попередніх напружень. Побудовано функції розподілу контактних напружень для граничної площини. Проаналізовано вплив поля залишкових деформацій на розподіл контактних напружень та форму площадки контакту.

Calculating the strength of structural elements and mechanisms is one of the most important stages in the process of their design. As it is known [2], residual deformation is almost always available 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. Resultant stress can cause fracture and accelerate some phase transitions, corrosion in particular. To improve the accuracy of calculations the residual must be taken into account, which directly affect the state of bodies. Taking into account all the factors that affect the interaction of the body is one of the key problems to determine the stability, reliability and other characteristics. Therefore, consideration of residual stress in the study of contact interaction of elastic bodies is an important task. Research problems of the contact interaction investigations of the preliminary stressed bodies in our country and abroad had appeared in the sufficient quantity only by the end of the last century. First of all it is due to the fact, that the linear elasticity theory does not consider the residual stresses in bodies. In general, strict proper statement of such problems requires the use of system of the nonlinear elasticity theory, however, for the sufficiently large values of the initial stresses its linearized version can be referred to. In the article the solution of axisymmetric contact problem of pressure a punch of complex shape for an elastic isotropic half-space, taking into account preliminary stresses is described. Besides distribution function of contact stresses and displacements for the plane boundary of semi-space was created. Besides, the residual deformation field characteristics effect on the amount and nature of the contact stresses under punch has been analyzed.