Оцінювання впливу залишкових напружень на втомне руйнування і залишковий ресурс оболонкових конструкцій з кільцевими зварними з’єднаннями

Abstract

У рамках концепції ефективного розмаху КІН з урахуванням величини закриття тріщини оцінено вплив залишкових напружень на довговічність ділянки трубопроводу із зовнішньою поверхневою тріщиною у зварному шві. Отримано систему двох нелінійних диференціальних рівнянь для визначення зміни геометричних параметрів тріщини в процесі зміни числа циклів навантаження з урахуванням дії залишкових напружень. На цій основі для конкретного зварного з’єднання досліджено величину глибини тріщини і відношення її довжини до глибини для різного числа циклів і різних рівнів залишкових напружень. Побудовано діаграми для визначення критичного числа циклів навантаження внутрішнім тиском для довільних рівнів усереднених по поверхні тріщини кільцевих залишкових напружень.

Geometric inhomogeneities, especially in the firm of pointed crack-like type defects can influence essentially the strength and durability of metal structures. Therefore, detection and measurement of such defects without violation the structures integrity, identification of their shape and sizes is one of the basic problems. The procedure of schematization the detected defects by defects of canonic shape, which are convenient to describe in corresponding mathematical models, is important in identification of defects for subsequent utilization of its results to estimate the resource of secure operation of shell machine-building structures. For pointe defects the cracks of semi-elliptical and throng cracks are the most conservative schematization. The work studies a linear part of the shell under internal pressure p with welded joint with internal surface defect in a ring field joint, which, according to the normative documents, is modeled by a longitudinal surface semi-elliptical cracks with semi-axes a and c in a circular cylinder. The location of arbitrary point on the crack contour is given by the angle φ ( 0 ≤ φ ≤ π ). The durability (residual resource) of operation of welded shell structures depends on the fatigue crack growth rate caused by external loads and residual stresses, which, in turn induce the stress intensity factors. Therefore, the work studies the fatigue surface crack growth in a welded joint under pulsing load by internal pressure p and residual stresses. We assumed that a crack in the welded joint in the shape of semi-ellipse with semi-axes a and c developed from the internal surface of the pipe. To determine the stress intensity factor caused by the internal pressure p we used the expression [2]. The fatigue crack growth rate under cyclic load was determined by Paris equation [7] with regard for efficient range of stress intensity factor. The solutions of a system of nonlinear equations to determine the crack growth were found by numerical method. For particular geometric sizes of the pipe with semi-elliptical crack we calculated the number of cycles N from initial state in the defect till such for which the condition of static strength is not satisfied. Numerical analysis was carried out for the pipe part of compressor station made of steel X-70 with diameter D = 219 mm and wall thickness t = 7 mm under pulse internal pressure of maximal value pmax = 4,5 MPa, and the sizes of initial crack in the welded joint were chosen as a0 = 1 mm, c0 = 1, 2a0 . It was determined that when the value of parameter increased ξ res the number of cycles N, for which critical crack depth is reached, decreases. And, besides, it was determined that when the parameter value ξ res increases the relation of semi-axes c/a decreases, and the shape of semi-elliptical crack approaches is circular one. If ξ res = 0 , then with an error which does not exceed 1%, it can be assured that relation c/a with increase of the cyclic number does not range, that c/a = const.