V. V. Struzhanov, A. E. Chaikin

DETERMINING THE MOMENT OF DESTRUCTION OF PROTECTIVE COATINGS ON PIPES AND SPHERICAL VESSELS

An analytical method is developed to determine the moment of destruction of thin coatings on pipes and spherical vessels. The coating material works at the stage of elasticity; it has the property of strain softening, that is, destruction with increasing deformation occurs in the process of stress drop. The properties of the coating material are described by convex-concave potentials both under uniaxial tension and in a plane stress state. To determine the moment of destruction, methods of the mathematical theory of catastrophes are applied, which allow one to find all the equilibrium positions of systems and the point of loss of stability of the deformation process.

References:

1. Fedorov Yu.Yu., Popov S.N., Savvina A.V., Vasilyev S.V., Rodionov A.K. Evaluation of the Axial Stresses of a Gas Pipeline Made of Reinforced Polyethylene Pipes under Conditions of Permafrost Soils. Diagnostics, Resource and Mechanics of materials and structures, 2017, iss. 3, pp. 36–41. DOI: 10.17804/2410-9908.2017.3.036-041. URL: http://dream-journal.org/issues/2017-3/2017-3_122.html (assessed: 22.03.2018).
2. Struzhanov V.V., Mironov V.I. Deformatsionnoe razuprochnenie materiala v elementakh konstruktsiy [Strain Softening of Material in Structural Elements]. Ekaterinburg, UrO RAN Publ., 1995, 190 p.
3. Andrasic C.P., Parker A.P. Dimensionless stress intensity factors for cracked thick cylinders under polynomial crack face loadings. Engng. Fract. Mech., 1984, vol. 19, no. 1, pp. 187–193.
4. Shannon R.W.E. Stress intensity factors for thick-walled cylinders. Int. J. Pres. Ves. and Piping, 1974, vol. 2, pp. 19–29.
5. Kachanov L.M. Osnovy teorii plastichnosti [Fundamentals of the Theory of Plasticity]. Мoscow, Nauka Publ., 1969, 420 p. (In Russian).
6. Korkin A.V., Struzhanov V.V., Chaykin A.E. Stability of uniform tension of a disk with a central zone of softening material. In: Proceedings of the Eleventh All-Russian Scientific Conference with International Participation “Mathematical Modeling and Boundary Value Problems” (May, 27–30, 2019, Samara, Russian Federation), vol. 1, Samara State Technical Univ., Samara, 2019, pp. 64–68. (In Russian).
7. Struzhanov V.V., Korkin A.V., Chaykin A. E. One approach to determination of the ultimate load-bearing capacity of mechanical systems with softening elements. Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, vol. 22 (4), pp. 762–773. DOI: 10.14498/vsgtu1624. (In Russian).
8. Struzhanov V.V. The determination of the deformation diagram of a material with a falling branch using the torsion diagram of a cylindrical sample. Sib. Zh. Ind. Mat., 2012, vol. 15 (1), pp. 138–144. (In Russian).
9. Poston Т., Stuart I. Teoriya katastroph i ee prilozheniya [Poston T., Stewart I. Catastrophe Theory and Its Applications, London, San Francisco, Melbourne, Pitman, 1978]. Мoscow, Mir Publ., 1980, 608 p. (In Russian).
10. Gilmore R. Prikladnaya teoriya katastroph. Kn. 1 [Gilmore R. Catastrophe Theory for Scientists and Enqincers, New York, Dover, 1993]. Moscow, Mir Publ., 1984, 350 p. (In Russian).
11. Timoshenko S.P., Gudier D.N. Teoriya uprugosti [Timoshenko S.P., Goodier J.N. Theory of Elasticity, New York, Toronto, London, McGraw Hill Book Company Inc., 1951]. Мoscow, Nauka Publ., 1979, 560 p. (In Russian).
12. Pars L. Analiticheskaya dinamika [Pars L. A Treatise on Analytical Dynamics. Heinemann, London, 1965; reprinted by Ox Bow Press, Woodbridge, CT, USA, 1979]. Мoscow, Nauka Publ., 1971, 636 p.

Article reference