Plastic and creep deformations of thick-walled cylinder with a rigid casing under internal pressure

S. V. Firsov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 4, pp. 696-715.

Résumé

The creep and plastic flow of cylindrical pressurized vessel with rigid casing was considered. To combine creep and plastic deformations the vessel was heated and subjected to the high inner pressure. The semi-analytical solution for plain strain problem of a thick-walled cylinder with rigid casing in the frame of small strain theory was obtained in this paper. This solution consists of analytical formula for displacement distribution with asking values of pressure and irreversible strains (plastic and creep) and a numerical solution for irreversible strain values. The Norton power law and advanced Mises condition for viscoplasticity, associated with flow rules have been used to describe creep and plastic behavior of medium. Four stages of the deformation process were considered: pressure increasing, pressure fixed on maximum value for a long time, pressure decreasing and relaxing stage with zero pressure. Two cases of maximum pressure values of 200 MPa and 320 MPa were studied. An additional case of elastoplastic deformation was considered to investigate the influence of creep on the deformational process. It has been observed that creep has a significant influence on stress and strain evolution in medium, especially on stages with maximum and zero pressure. Also, because of the creep plastic flow evolves slower and stoppes earlier on the loading stage. In the unloading stage, the plastic flow starts earlier and affects greater area due to greater irreversible strains. Creep leads to sufficient stress relaxation and stresses for two pressure cases get similar values at the end of the stage with maximum pressure value. At the end of the relaxing stage besides stresses displacement and deformation also became similar for the two cases.

Détail

Keywords: cylinder, thick-walled tube, tube with a rigid casing, creep and plastic flow, viscoplasticity, internal pressure, plain strain, small strain.

Bibliographie

[1] Nadai A., Plasticity, McGraw Hill Book Comp., New York, London, 1931, 392 pp.

[2] Hill R., Lee E. H., Tupper S. J., “The theory of combined plastic and elastic deformation with particular reference to a thick tube under internal pressure”, Proc. R. Soc. Lond., Ser. A, 191:1026 (1947), 278–303 | DOI | Zbl

[3] Cook G., “The stresses in thick-walled cylinders of mild steel overstrained by internal pressure”, Proc. Inst. Mech. Eng., 126:1 (1934), 407–455 | DOI

[4] Allen D. N., Sopwith D. G., “The stresses and strains in a partly plastic thick tube under internal pressure and end-load”, Proc. R. Soc. Lond., Ser. A, 205:1080 (1951), 69–83 | DOI | Zbl

[5] Steele M. C., “Partially plastic thick-walled cylinder theory”, J. Appl. Mech., 19:2 (1952), 133–140 | DOI | Zbl

[6] Sokolovsky V. V., Teoriia plastichnosti [Theory of Plasticity], Vyssh. Shkola, Moscow, 1969, 608 pp. (In Russian)

[7] Chu S. C., Vasilakis J. D., “Inelastic behavior of thick-walled cylinders subjected to nonproportionate loading”, Exp. Mech., 13:3 (1973), 113–119 | DOI

[8] Gao X.-L., “An exact elasto-plastic solution for an open-ended thick-walled cylinder of a strain-hardening material”, Int. J. Pres. Ves. Pip., 52:1 (1992), 129–144 | DOI

[9] Chu S.-C., “A more rational approach to the problem of an elastoplastic thick-walled cylinder”, J. Franklin Inst., 294:1 (1972), 57–65 | DOI

[10] Gao X.-L., “An exact elasto-plastic solution for a closed-end thick-walled cylinder of elastic linear-hardening material with large strains”, Int. J. Pres. Ves. Pip., 56:3 (1993), 331–350 | DOI

[11] Durban D., “Large strain solution for pressurized elasto/plastic tubes”, J. Appl. Mech., 46:1 (1979), 228–330 | DOI

[12] Bonn R., Haupt P., “Exact solutions for large elastoplastic deformations of a thick-walled tube under internal pressure”, Int. J. Plast., 11:1 (1995), 99–118 | DOI | Zbl

[13] MacGregor C. W., Coffin L. F., Fisher J. C., “The plastic flow of thick-walled tubes with large strains”, J. Appl. Phys., 19:3 (1948), 291–297 | DOI

[14] Durban D., “Finite straining of pressurized compressible elasto-plastic tubes”, Int. J. Eng. Sci., 26:9 (1988), 939–950 | DOI | Zbl

[15] Durban D., Kubi M., “A general solution for the pressurized elastoplastic tube”, J. Appl. Mech., 59:1 (1992), 20–26 | DOI | Zbl

[16] Gao X.-L., “Elasto-plastic analysis of an internally pressurized thick-walled cylinder using a strain gradient plasticity theory”, Int. J. Solids Struct., 40:23 (2003), 6445–6455 | DOI | Zbl

[17] Darijani H., Kargarnovin M. H., Naghdabadi R., “Design of thick-walled cylindrical vessels under internal pressure based on elasto-plastic approach”, Mat. Des., 30:9 (2009), 3537–3544 | DOI

[18] Nejad M. Z., Alamzadeh N., Hadi A., “Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition”, Compos. B. Eng., 154 (2018), 410–422 | DOI

[19] Coffin L. F., Jr., Shepler P. R., Cherniak G. S., “Primary creep in the design of internal-pressure vessels”, J. Appl. Mech., 16:3 (1949), 229–241 | DOI

[20] Weir C. D., “The creep of thick tubes under internal pressure”, J. Appl. Mech., 24:3 (1957), 464–466 | DOI | Zbl

[21] Sankaranarayanan R., “Steady creep of circular cylindrical shells under combined lateral and axial pressures”, Int. J. Solids Struct., 5:1 (1969), 17–32 | DOI | Zbl

[22] Murakami S., Iwatsuki S., “Transient creep of circular cylindrical shells”, Int. J. Solids Struct., 11:11 (1969), 897–912 | DOI

[23] Murakami S., Iwatsuki S., “Steady-state creep of circular cylindrical shells”, Bull. JSME, 14:73 (1971), 615–623 | DOI

[24] Murakami S., Suzuki K., “On the creep analysis of pressurized circular cylindrical shells”, Int. J. Non-Linear Mech., 6:3 (1971), 377–392 | DOI | Zbl

[25] Murakami S., Tanaka E., “On the creep buckling of circular cylindrical shells”, Int. J. Mech. Sci., 18:4 (1976), 185–194 | DOI

[26] Pai D. H., “Steady-state creep analysis of thick-walled orthotropic cylinders”, Int. J. Mech. Sci., 9:6 (1967), 335–348 | DOI

[27] Bhatnagar N. S., Gupta S. K., “Analysis of thick-walled orthotropic cylinder in the theory of creep”, J. Phys. Soc. Japan, 27:6 (1969), 1655–1661 | DOI

[28] Bhatnagar N. S., Arya V. K., “Large strain creep analysis of thick-walled cylinders”, Int. J. Non-Linear Mech., 9:2 (1974), 127–140 | DOI | Zbl

[29] Sharma S., Sahni M., Kumar R., “Thermo creep transition of transversely isotropic thick-walled rotating cylinder under internal pressure”, Int. J. Contemp. Math. Sci., 5:11 (2010), 517–527 | Zbl

[30] Singh T., Gupta V. K., “Effect of anisotropy on steady state creep in functionally graded cylinder”, Compos. Struct., 93:2 (2011), 747–758 | DOI

[31] Altenbach H., Gorash Y., Naumenko K., “Steady-state creep of a pressurized thick cylinder in both the linear and the power law ranges”, Acta Mech., 195:1 (2008), 263–274 | DOI | Zbl

[32] Chen J. J., Tu S. T., Xuan F. Z., Wang Z. D., “Creep analysis for a functionally graded cylinder subjected to internal and external pressure”, J. Strain Anal. Eng. Des., 42:2 (2007), 69–77 | DOI

[33] You L. H., Ou H., Zheng Z. Y., “Creep deformations and stresses in thick-walled cylindrical vessels of functionally graded materials subjected to internal pressure”, Compos. Struct., 78:2 (2007), 285–291 | DOI

[34] Jamian S., Sato H., Tsukamoto H., Watanabe Y., “Creep analysis of functionally graded material thick-walled cylinder”, Appl. Mech. Mater., 315 (2013), 867–871 | DOI

[35] Loghman A., Ghorbanpour Arani A., Amir S., Vajedi A., “Magnetothermoelastic creep analysis of functionally graded cylinders”, Int. J. Pres. Ves. Pip., 87:7 (2010), 389–395 | DOI

[36] Singh T., Gupta V. K., “Analysis of steady state creep in Whisker reinforced functionally graded thick cylinder subjected to internal pressure by considering residual stress”, Mech. Adv. Mater. Struct., 21:5 (2014), 384–392 | DOI

[37] Gupta S. K., Pathak S., “Thermo creep transition in a thick-walled circular cylinder under internal pressure”, Indian J. Pure Appl. Math., 32:2 (2001), 237–253 | Zbl

[38] Sharma S., Sahay I., Kumar R., “Creep transition in non homogeneous thick-walled circular cylinder under internal and external pressure”, Appl. Math. Sci., 6:122 (2012), 6075–6080 | Zbl

[39] Kovtanyuk L. V., Panchenko G. L., “On the changing mechanisms of the production of large irreversible deformations in the conditions of rectilinear motion in a cylindrical layer”, Mech. Solids, 55:2 (2020), 162–171 | DOI | DOI

[40] Galimzyanova K. N., Kovtanyuk L. V., Panchenko G. L., “Creep and plastic flow of a spherical viscoelastic layer material at its loading and unloading”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 270–283 (In Russian) | DOI | Zbl

[41] Begun A. S., Kovtanyuk L. V., Lemza A. O., “Creep and stress relaxation in the case of loading and unloading of a cylindrical layer with allowance for the development and deceleration of a viscoplastic flow”, J. Appl. Mech. Tech. Phys., 60:4 (2019), 748–757 | DOI | DOI | Zbl

[42] Burenin A. A., Kovtanyuk L. V., Panchenko G. L., “Creep and plastic flow of a material of a thick-walled cylindrical pipe under the action of uniform internal pressure”, Bulletin of the Yakovlev Chuvash State Pedagogical University, Ser. Mechanics of Limit State, 2020, no. 3 (45), 72–79 (In Russian) | DOI

[43] Firsov S. V., “Irreversible deformations of a rotating cylinder”, Izv. Altai State Univ., 102:4 (2018), 114–117 (In Russian) | DOI

[44] Firsov S. V., Prokudin A. N., “Creep and plastic flow in rotating hollow cylinder”, Bulletin of the Yakovlev Chuvash State Pedagogical University, Ser. Mechanics of Limit State, 2019, no. 4 (42), 45–55 (In Russian) | DOI

[45] Firsov S. V., Prokudin A. N., Burenin A. A., “Creep and plastic flow in a rotating cylinder with a rigid inclusion”, J. Appl. Ind. Math., 13:4 (2019), 642–652 | DOI | DOI

[46] Banshchikova I. A., Gorev B. V., Sukhorukov I. V., “Two-dimensional problems of beam forming under conditions of creep”, J. Appl. Mech. Tech. Phys., 43:3 (2002), 448–456 | DOI | Zbl

[47] Kuznetsov E. B., Leonov S. S., “Technique for selecting the functions of the constitutive equations of creep and long-term strength with one scalar damage parameter”, J. Appl. Mech. Tech. Phys., 57:2 (2016), 369–377 | DOI | DOI

[48] Burenin A. A., Tkacheva V. E., “Assembly of a two-layered metal pipe by using shrink fit”, Mech. Solids, 54:4 (2019), 559–569 | DOI | DOI

[49] Rabotnov Yu. N., Creep Problems in Structural Members, North-Holland Publ. Co., Amsterdam, London, 1969, xiv+822 pp. | Zbl

[50] Norton F. H., The Creep of Steel at High Temperatures, Classic Reprint Series, Forgotten Books, London, 2017, 102 pp.