Calculation of stresses in a spherical shell with internal surface defects
Pressure vessels, in particular cylindrical and spherical thin-walled vessels, are widely used in the industry. The aggressive impact of the environment during operation, as well as workloads, lead to the gradual accumulation of defects in structures. Since local defects act as stress concentrators, to ensure the strength and reliability of a structure, it is necessary to take into account the stress concentration near the defects. The paper considers a thin-walled sphere under pressure with the damages on its inner surface. The author modeled the defects as spherical notches immersed to the depth equal to half of their radius. Defects are evenly spaced along one of the circumferences of a large sphere. To estimate the stress state, the author built 3-D models of a spherical vessel with defects. The study considers the different number of defects and various sizes of defects; each parameter value corresponds to its geometry model. With the ANSYS Workbench package of finite element analysis, for each model, the author carried out the application of loads (pressure acts on the inner surface of a vessel), model decomposition into finite elements, and builds the field of maximum normal stresses distribution in a body. Calculations are made in the framework of the linear theory of elasticity. The author carried out a numerical experiment to study the influence of the number of surface defects on the stress state within their neighborhood. The paper studies the dependence of calculated stresses in the body on the depth of defects. The study showed that with an increase in the number of defects, as well as with an increase in their depth, the maximum normal stress increases.
Brighenti R., Carpinteri A. Surface cracks in fatigued structural components: A review. Fatigue and Fracture of Engineering Materials and Structures, 2013, vol. 36, no. 12, pp.1209–1222.
Glushkov S.V., Skvortsov Yu.V., Perov S.N. Comparison of the results of solving the problem of fracture mechanics for pipe with non-through crack. Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2014, no. 3, pp. 36–49.
Afshar R., Berto F. Stress concentration factors of periodic notches determined from the strain energy density. Theoretical and Applied Fracture Mechanics, 2011, vol. 56, no. 3, pp.127–139.
Shuvalov G.M., Kostyrko S.A. Second-order perturbation method for elastic solid with slightly curved boundary. Protsessy upravleniya i ustoychivost’, 2017, vol. 4, no. 1, pp. 256–260.
Shuvalov G.M., Kostyrko S.A. Effect of surface elasticity on reconstruction of stressed solid surface. Protsessy upravleniya i ustoychivost’, 2018, vol. 5, no. 1. 224–228.
Kostyrko S.A., Shuvalov G.M. Surface elasticity effect on diffusional growth of surface defects in strained solids. Continuum Mechanics and Thermodynamics, 2019, no. 31, pp. 1795–1803.
Vakaeva A.B. Effect of surface stresses and the shape of nanometer surface relief of a hole in an elastic body. Protsessy upravleniya i ustoychivost’, 2016, vol. 3, no. 1, pp. 154–158.
Grekov M.A., Vakaeva A.B. The perturbation method in the problem on a nearly circular inclusion in an elastic body. Proceedings of the 7th International Conference on Coupled Problems in Science and Engineering (Coupled Problems 2017). Rhodes, 2017, pp. 963–971.
Vakaeva A.B., Grekov M.A. Effect of interfacial stresses in an elastic body with a nanoinclusion. AIP Conference Proceedings, 2018, vol. 1959, pp. 070036. DOI: 10.1063/1.5034711.
Abakarov A.M., Nikulina M.M. Computation of stress state for stretched plate with spherical surface defects. Protsessy upravleniya i ustoychivost’, 2019, vol. 6, no. 1, pp. 63–67.
Gasratova N.A., Stareva I.A. Investigation of the stress-strain state of a reinforced concrete beam in the presence of a crack. Molodoy ucheniy, 2016, no. 9, pp. 10–15.
Ostsemin A.A., Utkin P.B. Stress-strain state and stress intensity factor in the vicinity of crack-like defects under biaxial tension of a plate. Journal of Applied Mechanics and Technical Physics, 2014, vol. 55, no. 6, pp. 1045–1054.
Nakai T., Matsushita H., Yamamoto N., Arai H. Effect of pitting corrosion on local strength of hold frames of bulk carriers (1st report). Marine Structures, 2004, vol. 17, no. 5, pp. 403–432.
Obeyesekere N.U. Pitting corrosion. Trends in Oil and Gas Corrosion Research and Technologies: Production and Transmission. Elsevier, 2017, pp. 215–248.
Tarasenko A.A., Chepur P.V., Kuzovnikov E.V., Tarasenko D.A. Calculation of stress-strain receiving pipe dispensers with defects in order to justify its further exploitation. Fundamentalnye issledovaniya, 2014, no. 9-7, pp. 1471–1476.
Korobkov G.E., Yanchushka A.P., Zakiryanov M.V. Numerical modeling of a stress-strain state of a gas pipeline with cold bending offsets according to in-line inspection. Journal of Mining Institute, 2018, vol. 234, pp. 643–646.
Sedova O.S., Khaknazarova L.A. Stress analysis of a notched thick spherical member. Protsessy upravleniya i ustoychivost’, 2014, vol. 1, no. 1, pp. 212–217.
Okulova D.D., Vakaeva A.B., Sedova O.S. Stress calculation in sphere with surface defects. Protsessy upravleniya i ustoychivost’, 2019, vol. 6, no. 1, pp. 112–116.
Carpinteri A., Ronchei C., Vantadori S. Stress intensity factors and fatigue growth of surface cracks in notched shells and round bars: two decades of research work. Fatigue and Fracture of Engineering Materials and Structures, 2013, vol. 36, no. 11, pp. 1164–1177.
Arumugam T., Karuppanan S., Ovinis M. Finite element analyses of corroded pipeline with single defect subjected to internal pressure and axial compressive stress. Marine Structures, 2020, vol. 72, pp. 102746.
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