Finite plane strain bending under tension of isotropic and kinematic hardening sheets

The present paper provides a semianalytic solution for finite plane strain bending under tension of an incompressible elastic/plastic sheet using a material model that combines isotropic and kinematic hardening. A numerical treatment is only necessary to solve transcendental equations and evaluate ordinary integrals. An arbitrary function of the equivalent plastic strain controls isotropic hardening, and Prager’s law describes kinematic hardening. In general, the sheet consists of one elastic and two plastic regions. The solution is valid if the size of each plastic region increases. Parameters involved in the constitutive equations determine which of the plastic regions reaches its maximum size. The thickness of the elastic region is quite narrow when the present solution breaks down. Elastic unloading is also considered. A numerical example illustrates the general solution assuming that the tensile force is given, including pure bending as a particular case. This numerical solution demonstrates a significant effect of the parameter involved in Prager’s law on the bending moment and the distribution of stresses at loading, but a small effect on the distribution of residual stresses after unloading. This parameter also affects the range of validity of the solution that predicts purely elastic unloading. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Authors
Strashnov S. 1 , Alexandrov S.2, 3 , Lang L.2
Journal
Publisher
MDPI AG
Number of issue
5
Language
English
Pages
1-21
Status
Published
Number
1166
Volume
14
Year
2021
Organizations
  • 1 General Education Courses Department, Рeoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 2 School of Mechanical Engineering and Automation, Beihang University, 37 Xueyuan Road, Beijing, 100191, China
  • 3 Faculty of Materials Science and Metallurgy Engineering, Federal State Autonomous Educational Institution of Higher Education “South Ural State University (National Research University), 76 Lenin Prospekt, Chelyabinsk, 454080, Russian Federation
Keywords
Bending under tension; Isotropic hardening; Kinematic hardening; Large strain; Semianalytic solution
Date of creation
20.04.2021
Date of change
20.04.2021
Short link
https://repository.rudn.ru/en/records/article/record/72086/
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