STRAIN CONCENTRATION IN APICES OF RADIAL CRACKS IN A THIN COATED PIPE WALL
https://doi.org/10.21822/2073-6185-2017-44-2-37-45
Abstract
Objectives. The well-known discontinuous solution method, used in the study of infinite and semi-infinite domains, is generalised during the construction of solutions in Fourier series. This makes it possible to reduce the problem of the mechanics of a deformable solid for a limited region containing cuts or inclusions to the solution of an integral equation (or system) with respect to discontinuities of the functions being defined.
Methods. The method was implemented through the application to the solution of the theoretical elasticity problem for a pipe section (plane deformation) weakened by an internal radial crack. The pipe was loaded with hydrostatic pressure and a thin coating is applied on its inner surface, improving its physical and mechanical properties. The applied method, combined with the conventional integral transformation, can be effectively used in the construction of discontinuous solutions of three-dimensional problems of the theory of elasticity.
Results. Specially formulated boundary conditions were used as a coating model. In order to verify the adequacy of the adopted model, a series of numerical experiments was carried out. In some cases, calculations were carried out for the cross-section of a coated pipe in finite-element ANSYS and COMSOL software packages. In others, benefiting from the extensive capabilities of the FlexPDE software package, an uncoated pipe model was constructed, although using special boundary conditions. Comparison of the results obtained made it possible to ascertain the adequacy of the models constructed across a certain range of geometric and physical parameters.
Conclusion. The problem is reduced to the solution of a singular integral equation with a Cauchy kernel with respect to the derivative of the jump in the tangential component of the displacement vector on the crack edges. Its solution is determined by the collocation method with a pre-selected feature. The ultimate goal of the study is to determine the values of the strain intensity coefficient at the apices of the crack.
About the Authors
M. M. Payzulaev
Dagestan State Technical University
Russian Federation
Russian Federation
Cand. Sci. (Technical), Senior lecturer, Department of Resistance of Materials, Theoretical and Building Mechanics,
70 I. Shamil Ave, Makhachkala 367026
E. L. Rashidova
Don State Technical University
Russian Federation
Russian Federation
Cand. Sci. ( Physics and Mathematical), Prof., Department of Information Technologies,
Gagarina square, Rostov-on-Don 344000
B. V. Sobol'
Don State Technical University
Russian Federation
Russian Federation
Dr. Sci. (Technical), Prof., Department of Information Technologies,
Gagarina square, Rostov-on-Don 344000
References
1. Popov G.Ya. Kontsentratsiya uprugikh napryazheniy vozle shtampov, razrezov, tonkikh vklyucheniy i podkrepleniy. M.: Nauka; 1982. 382 s. [Popov G.Ya. Concentration of elastic stresses near the stamps, sections, fine inclusions and reinforcements. Moscow: Nauka; 1982. 382 p. (in Russ.)]
2. Aleksandrov V.M., Smetanin B.I., Sobol' B.V. Tonkie kontsentratory napryazheniy v uprugikh telakh. M.: Nauka; 1993. 224 s. [Aleksandrov V.M., Smetanin B.I., Sobol' B.V. Fine stress concentrators in elastic bodies. Moscow: Nauka; 1993. 224 p. (in Russ.)]
3. Aleksandrov V. M., Mkhitaryan S. M. Kontaktnye zadachi dlya tel s tonkimi pokrytiyami i prosloykami. M.: Nauka; 1979. 486 s. [Aleksandrov V. M., Mkhitaryan S. M. Contact problems for bodies with thin coatings and layers. Moscow: Nauka; 1979. 486 p. (in Russ.)]
4. Vatul'yan A.O., Sobol' B.V. Ob odnom effektivnom metode postroeniya razryvnykh resheniy v zadachakh mekhaniki dlya tel konechnykh razmerov. Izvestiya RAN, Mekhanika tverdogo tela. 1995;6:62–69. [Vatul'yan A.O., Sobol' B.V. About the one effective method of discontinuous solution composition in the problems of mechanics of finite dimentional bodies. Mechanics of Solids. 1995;6:62–69. (in Russ.)]
5. Rashidova E.V., Sobol' B.V. Ravnovesnaya poperechnaya vnutrennyaya treshchina v sostavnoy uprugoy poluploskosti. Prikladnaya matematika i mekhanika. 2017;81(3):348-364. [Rashidova E.V., Sobol' B.V. Equilibrium transversal inner crack in combined elastic semi-plane. Journal of Applied Mathematics and Mechanics. 2017;81(3):348-364. (in Russ.)]
6. Morozov E.M., Muyzemnek A.Yu., Shadskiy A.S. ANSYS v rukakh inzhenera: Mekhanika razrusheniya. M.: LENAND; 2010. 456 s. [Morozov E.M., Muyzemnek A.Yu., Shadskiy A.S. ANSYS in the hands of an engineer: mechanics of destruction. Moscow: LENAND; 2010. 456 p. (in Russ.)]
7. Matvienko Yu.G. Modeli i kriterii mekhaniki razrusheniya. M.: Fizmatlit; 2006. 328 s. [Matvienko Yu.G. Models and criterions of mechanics of destruction. Moscow: Fizmatlit; 2006. 328 p. (in Russ.)]
8. Glushkov S.V., Skvortsov Yu.V., Perov S.N. Sravnenie rezul'tatov resheniya zadachi mekhaniki razrusheniya dlya truby s neskvoznoy treshchinoy. Vestnik Permskogo natsional'nogo issledovatel'skogo politekhnicheskogo universiteta. Mekhanika. 2014;3:36-49. DOI: 10.15593/perm.mech/2014.3.03 [Glushkov S.V., Skvortsov Yu.V., Perov S.N. Comparison of solution results of the problem of mechanics of destruction for a pipe with a blind crack. PNRPU Mechanics Bulletin. 2014;3:36-49. DOI: 10.15593/perm.mech/2014.3.03 (in Russ.)]
9. Li C.Q., Yang S.T. Stress intensity factors for high aspect ratio semi-elliptical internal surface cracks in pipes. Int. J. of Pressure Vessels and Piping. 2012;96-97:13-23. DOI: 10.1016/j.ijpvp.2012.05.005
10. Yang S.T., Ni Y.L., Li C.Q. Weight function method to determine stress intensity factor for semielliptical crack with high aspect ratio in cylindrical vessels. Eng. Fract. Mech. 2013;109:138-149. DOI: 10.1016/j.engfracmech.2013.05.014
11. Zhang Y.M., Yi D.K., Xiao Z.M., Huang Z.H., Kumar S.B. Elastic-plastic fracture analyses for pipeline girth welds with 3D semi-elliptical surface cracks subjected to large plastic bending. Int. J. of Pressure Vessels and Piping. 2013;105-106:90-102. DOI: 10.1016/j.ijpvp.2013.03.009
12. Chiodo M.S.G., Ruggieri C. J and CTOD estimation procedure for circumferential surface cracks in pipes under bending. Eng. Fract. Mech. 2010; 77(3):415-436. DOI: 10.1016/j.engfracmech.2009.10.001
13. Madia M., Arafan D., Zerbst U. Reference load solutions for plates with semi-elliptical surface cracks subjected to biaxial tensile loading. Int. J. of Pressure Vessels and Piping. 2014;119:19-28. DOI: 10.1016/j.ijpvp.2014.02.004
14. Atroshchenko E., Potapenko S., Glinka G. Stress intensity factor for a semi-elliptical crack subjected to an arbitrary mode I loading. Mathematics and Mechanics of Solids. 2014;19(3):289-298. DOI: 10.1177/1081286512463573
15. Predan J., Mocilnik V., Gubeljak N. Stress intensity factors for circumferential semi-elliptical surface cracks in a hollow cylinder subjected to pure torsion. Eng. Fract. Mech. 2013;105:152-168. DOI: 10.1016/j.engfracmech.2013.03.033
16. Mechab B., Serier B., Bouiadjra B.B., Kaddouri K., Feaugas X. Linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending. Int. J. of Pressure Vessels and Piping. 2011;88(1):57-63. DOI: 10.1016/j.ijpvp.2010.11.001
Review
For citations:
Payzulaev M.M., Rashidova E.L., Sobol' B.V. STRAIN CONCENTRATION IN APICES OF RADIAL CRACKS IN A THIN COATED PIPE WALL. Herald of Dagestan State Technical University. Technical Sciences. 2017;44(2):37-45. (In Russ.) https://doi.org/10.21822/2073-6185-2017-44-2-37-45
Views:
705
Email this article 
