Mathematical modeling of fracture conditions of thin-walled cylindrical shells under external pressure and axial tension

T. V. Karpeta

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 11 (2019) no. 4, pp. 47-55

Résumé

The stability loss conditions under plastic deformation of a thin-walled cylindrical shell, including large-diameter pipes, under tensile (positive) axial stresses and compressive (negative) ring stresses are considered. The purpose of the article is to specify the dependences of critical deformations, stresses, pressures, and axis loads on the shell on the parameters and loading conditions. The research method is based on the application of Swift–Marciniak criterion on the loss in stability of the plastic deformation process. The material of the shell is assumed to be isotropic with exponential-power deformation diagram. Explicit analytical expressions for the target values were obtained. Considering the given parameters of the shell and loading conditions, the results allow to determine critical pressures, critical axial loads and wall thickness at a given working pressure.

Détail

Keywords: thin-walled cylindrical shell, large-diameter pipe, plastic stability, Swift criterion, critical deformations, critical stresses, critical pressures, localization of plastic deformation.

Bibliographie

[1] V. D. Chernyaev, K. V. Chernyaev, V. L. Berezin et al., System reliability of hydrocarbon pipeline transport, Nauka, M., 1997, 516 pp. (in Russ.)

[2] P. P. Borodavkin, V. L. Berezin, Main Pipeline Construction, Nedra, M., 1987, 471 pp. (in Russ.)

[3] S.S. Hector, S.C. Carlos, “Deformation of steel pipes with internal pressure under axial compression and bending load under seismic action”, The 14-th World Conference on Earthquake Engineering (October 12–17, 2008, Beijing, China)

[4] P. J. Eiber, “Outside Force Causes Most Natural Gas Pipeline Failures”, Oil and Gas J., 85:11 (1987), 52–57

[5] N. N. Malinin, “Biaxial Plastic Extension Stability of Anisotropic Sheets and Cylindrical Shells”, Izv. AN SSSR. Mekhanika tverdogo tela, 1971, no. 2, 115–118 (in Russ.)

[6] A. N. Monoshkov, S. I. Pykhov, I. A. Pustin, “Plastic Stability and its Role in Assessing Pipes Strength”, Coated Pipe Manufacturing, Pipe Finishing and Quality Control, Metallurgiya, M., 1972, 77–81 (in Russ.)

[7] S. A. Kurkin, Strength of Welded Thin-Walled Pressure Vessels, Mashinostroenie, M., 1976, 183 pp. (in Russ.)

[8] V. L. Dil'man, A. A. Ostsemin, “On the Effect of Biaxial Loading on the Bearing Capacity of the Main Gas and Oil Pipelines”, Izv. RAN. Mekhanika tverdogo tela, 2000, no. 5, 179–185 (in Russ.)

[9] V. L. Dil'man, A. A. Ostsemin, “On the Loss of Plastic Stability of Thin-Walled Cylindrical Shells”, Problemy mashinostroyeniya i nadezhnosti mashin, 2002, no. 5, 50–57 | MR

[10] V. L. Dil'man, “Plastic Instability of Thin-Walled Cylindrical Shells”, Mech. Solids, 40:4 (2005), 113–121

[11] V. L. Dil'man, Mathematical Models of the Stress State of Inhomogeneous Thin-Walled Cylindrical Shells, Izd-vo YuUrGU Publ., Chelyabinsk, 2007, 201 pp. (in Russ.)

[12] V. L. Dil'man, T. V. Eroshkina, Mathematical Modeling of Soft Layers Critical State in Inhomogeneous Compounds, Izdatel'skiy Tsentr YuUrGU Publ., Chelyabinsk, 2011, 275 pp. (in Russ.)

[13] V. L. Dilman, T. V. Karpeta, “Critical State of a Thin-Walled Cylindrical Shell Containing an Interlayer Fabricated from a Material of Lesser Strength”, Chemical and Petroleum Engineering, 49:9–10 (2014), 668–674 | DOI

[14] H.W. Swift, “Plastic Instability under Plane Stress”, Journal of the Mechanics and Physics of Solids, 1:1 (1952), 1–18 | DOI | MR

[15] Z. Marciniak, “Utrata stateczności rozciaganych powlok plastycznych”, Mech. teoretyzna i stosowona, 4:3 (1966), 209–220

[16] G. I. Koval'chuk, “On the Issue of Plastic Deformation Stability Loss of the Shells”, Problemy prochnosti, 1983, no. 5, 11–16 (in Russ.)

[17] G. S. Pisarenko, Deformation and Strength of Materials under Complex Stress State, Naukova dumka, Kiev, 1976, 415 pp. (in Russ.)

[18] A. N. Diyab, “Critical States of Homogeneous Thin-Walled Cylindrical Shells under Internal Pressure and Axial Compression”, Proceedings of the International Scientific and Practical Conference “Fundamental Problems of the Main Directions of Scientific and Technical Research” (Volgograd, March 17, 2018), AMI Publ., Sterlitamak, 2018, 35–39 (in Russ.)

[19] V. L. Dilman, T. V. Karpeta, A. N. Dheyab, “Modelling of Critical Conditions Thin-Walled Cylindrical Shells with a Negative Coefficient Biaxial Loading”, Proc. Int. conference «Modern problems of innovative technologies in oil and gas production and apply mathematics» (Baku, December 13–14, 2018), 45–47

[20] V. L. Dil'man, A. A. Ostsemin, “Strength of Straight-Seam and Spiral-Seam Pipes in Transmission Gas and Oil Pipelines”, Welding International, 15:7 (2001), 557–562 | DOI

[21] V. L. Dilman, A. A. Ostsemin, A. A. Voronin, “Static Strength of Welded Joints in Spiral-Seam Pipes”, Welding International, 15:10 (2001), 812–815 | DOI

[22] V. L. Dilman, A. A. Ostsemin, “Evaluation of the Effect of Defects and Service Reliability of Welded Joints in Straight-Seam and Spiral-Seam Pipes”, Welding International, 16:2 (2002), 139–144 | DOI | MR

[23] V. L. Dilman, A. A. Ostsemin, “Load-Carrying Capacity of Straight-Seam Large Diameter Pipes with Defects at the Fusion Boundary of the Welded Joint”, Welding International, 17:5 (2003), 376–380 | DOI

[24] V. L. Dilman, A. A. Ostsemin, “Static Strength of a Welded Joint with Hard Interlayers and Defect at the Fusion line of the Weld”, Welding International, 18:10 (2004), 805–808 | DOI

[25] V. L. Dilman, A. A. Ostsemin, “Analysis of the Ductile Strength of Welds Weakened by Notches in Longitudinally Welded Pipes of large Diameter by the Method of Slip Lines”, Strength of Materials, 36:3 (2004), 274–281 | DOI

[26] V. L. Dilman, A. A. Ostsemin, “Bearing Capacity of Large-Diameter Helical-Seam Pipes”, Chemical and Petroleum Engineering, 38:5–6 (2002), 326–333 | DOI

[27] A. A. Ostsemin, V. L. Dil'man, “Calculating Wall Thickness for Major Oil Product Pipelines: Analysis of Regulation Documents”, Chemical and Petroleum Engineering, 38:1–2 (2002), 58–63 | DOI

[28] V. L. Dilman, A. A. Ostsemin, “Effects of Surface Defects on the Static Strength of Welds in Spiral-Seam Tubes”, Chemical and Petroleum Engineering, 40:1–2 (2004), 87–93 | DOI

[29] A. A. Ostsemin, V. L. Dil'man, “Calculation of Test Pressure for Arterial Pipelines”, Chemical and Petroleum Engineering, 39:1–2 (2003), 16–22 | DOI

[30] A. L. Vorontsov, “On the Approximation of Hardening Curves”, Vestnik mashinostroeniya, 2002, no. 1, 51–54 (in Russ.)

[31] V. A. Krokha, “On the Approximation of Hardening Curves Dependence of the Strain Hardening Index on the Degree of Deformation and the Fulfillment of the Power Hardening Law”, Problemy prochnosti, 1981, no. 8, 72–77 (in Russ.)

[32] V. L. Dil'man, A. A. Ebel', “On the Dependence of the Strain Hardening Index on the Degree of Deformation and the Implementation of the Power Law of Hardening”, Obozrenie prikladnoy i promyshlennoy matematiki, 13:4 (2006), 638–639 (in Russ.)