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Записано сингулярні інтегральні рівняння для системи крайових паралельних нерівних нахилених тріщин у пружній півплощині, береги яких контактують без тертя під час переміщення герцівського навантаження вздовж краю півплощини. Запропоновано алгоритм визначення меж ділянок контактування берегів тріщин та коефіцієнтів інтенсивності напружень у їх вершинах. Числові результати отримано для випадку двох паралельних рівних тріщин.
The surface (edge) parallel cracks system is one of typical contact fatigue damages of elements of wheel-rail technical pair. So, the important task for estimation of a contact strength and durability of such pair is determination of a stress-strain state or stress intensity factors (SIF) at crack tips under operational conditions. In given investigation the model scheme, where in a two-dimensional case damaged bodies are simulated by elastic halfplane with cuts, and counterbody action by forward unidirectional movement of model contact load along halfplane boundary, has been used for simulation of contact rolling interaction. Other parameters have been chosen according to operational conditions for wheel-rail pair and typical features of damages. Singular integral equations of contact problem of elasticity theory for halfplane with the system of parallel inclined cracks, the faces of which are in contact without friction under action of a moving model load (Hertzian pressure with tangential component) have been constructed. The algorithm (iterative procedure) for finding of opened segments of a cracks faces has been developed. Numerical results for the case of two equal parallel cracks, inclined at angle β = 5π/6 to direction of a tangential contact efforts and, respectively, at angle π –β = 30° to direction of a counterbody movement for different values of a friction coefficient (f = 0.1 and f = 0.3) in a contact between rolling bodies and different relative distances between cracks δ = b/a depending on a contact load position in relation to cracks have been obtained. The maps of cracks faces contacting during a contact load movement along halfplane boundary (change of parameter λ = х0/а) have been constructed and stress intensity factors KI, KII and mixed SIF KIθ have been calculated. It was determined that cracks begin to close mainly from the mouth during contact load movement. The value of ∆KII = maxKII(λ) – minKII(λ) parameter, that controls the fracture by shear mechanism significantly depends on a distance between the cracks and a substantial weakening of rolling body nearsurface area (maximum of ∆KII) is achieved under distance, that commensurable with the contact segment length. Maximum and minimum of KII(λ) are realized if both cracks are contacting along all its length. So, partial opening of cracks has little influence on ∆KII range. The analysis of K I∗θ = max K Iθ (λ , θ ) parameter, that controls the fracture by opening mechanism, showed: when the contact load is directly above the crack(s) not only shear fracture can occur, but fracture by opening can occur too. Generally, the presence of a fully closed crack with contacting faces can significantly influence the SIF of another opened crack. Therefore, this influence can not be neglected. |
