Тернопiльський національний технiчний унiверситет iменi Iвана Пулюя
Abstract
Побудовано точний розв’язок антиплоскої задачі для біматеріалу з міжфазною тріщиною, навантаженого неоднорідним нормальним стиском та циклічним навантаженням у поздовжньому напрямку. Методом функцій стрибка задача зведена до системи сингулярних інтегральних рівнянь для стрибків зміщень і напружень у зонах проковзування з тертям. Проаналізовано вплив параметрів навантажування і тертя на розміри цих зон та дисипацію енергії.The present paper investigates the anti-plane problem for a semi-homogeneous bi-material with the closed interface crack considering sliding friction. Solid is exposed to the combined cyclic loading in the longitudinal direction and arbitrary normal load required to prevent loss of contact between the sliding surfaces of the cracks. It is assumed that the load on each step of loading increases from zero to its maximum monotonically and slowly enough not to consider the effect of inertia.
Using jump function method the problem is reduced to the solution of singular integral equations with a Cauchy-type kernel for the jumps of displacements and stresses in areas with sliding friction. This solution allows us to obtain explicit expressions for displacements, stress intensity factors and energy dissipation.
Analyzing of the elasticity problem involving friction under the variable (cyclic) loading requires consideration of the history of loading. No incremental formulation is necessary for solving of this problem on each local step because of quasi-statically way of the step loading. To take account of cyclical loading multistep method of solution is proposed. The basis of this technique is the idea of consideration at every step of loading previous step stresses and displacements as the residual. Correctness of the obtained solution is justified. Evolution of the slip zone in matrix is considered at different stages of loading. Critical load values for determining the onset of slip are investigated. Available size of slip zone with an increase in loading is determined from the condition of equality to zero the stress intensity factor. Upon reaching the second critical value of the load, when the slip zone size matches the size of the crack, there are singular stresses in the crack threshold and non-zero values of stress intensity factors.
We numerically analyze the effect of friction and loading parameters on the size of slip zone and stress intensity factors. It is discovered that the slip zone appears and grows fastest when it pressing normal stresses are minimal. Growth rate of slip zone also promotes increasing the distance of application points of concentrated power factors from her. The growth coefficient of friction significantly reduces the intensity of the stresses in the vicinity of the ends of the crack. Energy dissipation for all examined cases of loading was calculated
