An exact rigid/plastic solution for a thick-walled tube subject to internal pressure and axial load considering a general isotropic hardening law and its application
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https://doi.org/10.15625/2525-2518/18665Keywords:
combined elongation (or shortening) and expansion, rigid plastic material, general hardening law, tube hydroforming, analytical solutionAbstract
The paper presents a new exact rigid/plastic solution that describes the combined elongation (or shortening) and expansion of a tube. The von Mises yield criterion and its associated flow rule are adopted. No restriction is imposed on the isotropic hardening behavior of the material. The solution is facilitated using a Lagrangian coordinate. A numerical technique is only required for evaluating ordinary integrals. The solution applies to the preliminary design of tube hydroforming. In particular, the variation of the inner pressure with the current tube’s length that ensures a prescribed change in the tube’s radii is determined. Moreover, the modified Cockroft-Latham fracture criterion applies to predict ductile fracture initiation.
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References
Hill R. - The mathematical theory of plasticity, Oxford, Clarendon Press, 1950.
Collins I. F., Meguid S. A. - On the influence of hardening and anisotropy on the plane-strain compression of thin metal strip, Transactions ASME is J. Appl. Mech. Trans. 44 (1977) 271-278.
Durban D., Budiansky B. - Plane-strain radial flow of plastic materials, J. Mech. Phys. Solids 26 (5 - 6) (1978) 303-324. doi.org/10.1016/0022-5096(78)90002-9.
Durban D. - Axially symmetric radial flow of rigid/linear-hardening materials, ASME. J. Appl. Mech. 46 (2) (1979) 322-328. doi.org/10.1115/1.3424549.
Shufen R., Dixit U. S. - A review of theoretical and experimental research on various autofrettage processes, Transactions of the ASME is J. Press. Vessel Technol. 140 (5) (2018) 050802. doi.org/10.1115/1.4039206.
Durban D., Baruch M. - Analysis of an elasto-plastic thick walled sphere loaded by internal and external pressure, Int. J. Non-Linear Mech. 12 (1) (1977) 9-22. doi.org/10.1016/0020-7462(77)90012-9.
Alexandrov S., Pirumov A., Jeng Y. R. - Expansion/contraction of a spherical elastic/plastic shell revisited, Continuum Mech. Thermodyn. 27 (2015) 483-494. doi.org/10.1007/s00161-014-0365-6.
Gamer U. - The elastic-plastic shrink fit with supercritical interference, Acta Mechanica 61 (1986) 1-14. doi.org/10.1007/BF01176358.
Parmaksizogˇlu C., Güven U. - Plastic stress distribution in a rotating disk with rigid inclusion under a radial temperature gradient, Mech. Based Des. Struct. Mach. 26 (1) (1998) 9-20. doi.org/10.1080/08905459808945417.
Alexandrov S., Manabe Ki., Furushima T. - A general analytic solution for plane strain bending under tension for strain-hardening material at large strains, Arch. Appl. Mech. 81 (2011) 1935-1952. doi.org/10.1007/s00419-011-0529-9.
Alexandrov S., Lyamina E., Hwang Y.-M. - Plastic bending at large strain: A review, Processes 9 (3) (2021) 406. doi.org/10.3390/pr9030406.
Brooks D.S. - The elasto-plastic behaviour of a circular bar loaded by axial force and torque in the strain hardening range. Int. J. Mech. Sci. 11(1) (1969) 75-85. doi.org/10.1016/0020-7403(69)90081-2.
Hünlich R. - On simultaneous torsion and tension of a circular cylindrical bar consisting of an elastoplastic material with linear hardening, Z. Angew. Math. Mech. 59 (1979) 509-516. doi.org/10.1002/zamm.19790591003.
Crossland B., Hill R. - On the plastic behaviour of thick tubes under combined torsion and internal pressure, J. Mech. Phys. Solids 2 (1) (1953) 27-38. doi.org/10.1016/0022-5096(53)90024-6.
Hwang Y. M., Manabe K. I. - Latest hydroforming technology of metallic tubes and sheets, Metals 11 (2021) 1360. doi.org/10.3390/met11091360.
Lin C., Chu G., Sun L. - An investigation into the effect of pre-bending on the tube hydro-forging technology, Int. J. Adv. Manuf. Technol. 121 (2022) 2343-2363. doi.org/ 10.1007/s00170-022-09483-8.
Yasui H., Miyagawa T., Yoshihara S., Furushima T., Yamada R., Ito Y. - Influence of internal pressure and axial compressive displacement on the formability of small-diameter ZM21 magnesium alloy tubes in warm tube hydroforming, Metals 10 (2020) 674. doi.org/10.3390/met10050674.
Ghorbani-Menghari H., Kahhal P., Jung J., Mohammadhosseinzadeh M., Hoon Moon Y., Hoon Kim J. - Multi-objective evolutionary neural network optimization of process parameters for double-stepped tube hydroforming, Int. J. Precis. Eng. Manuf. 24 (2023) 915–929. doi.org/10.1007/s12541-023-00802-x.
Vu Q. D., Nguyen T. D., Dang H. V., Phan D. T. - Effect of loading paths on hydroforming ability of stepped hollow shaft components from double layer pipes, EUREKA Phys. Eng. 4 (2023) 143-154. doi.org/10.21303/2461-4262.2023.002797.
Alexandrov S., Lyamina E., Lang L. - Description of the expansion of a two-layer tube: an analytic plane-strain solution for arbitrary pressure-independent yield criterion and hardening law, Metals 11 (5) (2021) 793. doi.org/10.3390/met11050793.
Strashnov S., Alexandrov S., Lang L. - A new semi-analytical solution for an arbitrary hardening law and its application to tube hydroforming, Materials 15 (17) (2022) 5888. doi.org/10.3390/ma15175888.
Luege M., Luccioni B.M. - Numerical simulation of the lubricant performance in tube hydroforming. J. Mater. Process. Technol. 198 (1 - 3) (2008) 372-380. doi.org/10.1016/ j.jmatprotec.2007.07.040.
Zhu H. L., Xu Y., Chen W. J., Zhang S. H., Banabic D., Lăzărescu L., Pokrovsky A. I. - Research on hydroforming through combination of internal and external pressures for manufacturing the structure of double-layer tube with gap, Int. J. Mater. Form. 15 (2022) 55. doi.org/10.1007/s12289-022-01699-z.
Marlapalle B. G., Hingole R. S. - Numerical and experimental predictions of formability parameters in tube hydroforming process, Aust. J. Mech. Eng. 21 (3) (2023) 991-1007. 10.1080/14484846.2021.1938952.
Ribas L. M., Gipiela M. L., Lajarin S. F., Filho R. A. C., Marcondes P. V. P. - Comparative study of six failure criteria via numerical simulation of stamped DP600 steel, Int. J. Adv Manuf. Technol. 121 (2022) 2427-2435. doi.org/10.1007/s00170-022-09440-5.
Oh S. I., Chen C. C., Kobayashi S. - Ductile fracture in axisymmetric extrusion and drawing, Part 2: Workability in extrusion and drawing, ASME. J. Eng. Ind. 101 (1) (1979) 36-44. doi.org/10.1115/1.3439471.
Alexandrov S., Vilotic D. - A theoretical - experimental method for the identification of the modified Cockroft-Latham ductile fracture criterion, Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 222 (9) (2008) 1869-1872. doi:10.1243/09544062JMES1055
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