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Application of the upper bound theorem for metal forming processes considering an arbitrary isotropic pressure-independent yield criterion with no strength differential effect

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Abstract

The present paper concerns the application of the upper bound theorem based on the work function to analyze metal forming processes. An advantage of this theorem formulation is that it provides a unified method for finding solutions for any yield criterion. In particular, any available kinematically admissible velocity field used in conjunction with the von Mises yield criterion can be utilized with no modification. On the other hand, an explicit function representing the work function associated with a given yield criterion cannot readily be expressed except for some particular cases. The approach proposed in the present paper is to assume a work function instead of a yield criterion. The paper is restricted to the work functions represented by first-order homogeneous functions. Moreover, the material is supposed to be isotropic and incompressible. The strength differential effect is neglected. Illustrative examples reveal the effect of the yield criterion on the limit load for axisymmetric extrusion and ring compression processes. These solutions utilize kinematically admissible velocity fields available in the literature.

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Acknowledgements

This work was made possible by the NCKU 90 and AAAA-A20-120011690136-2 programs. It was financially supported by the Ministry of Science and Technology of Taiwan (MOST 108-2221-E-006-228-MY3, 1 109-2923-E-006-005-MY3, 110-2124-M-006-005 and 111-2221-E-006-214) and Air Force Office of Science Research (AFOSR) under contract no. FA4869- 06-1-0056 AOARD 064053. Professor Yeau-Ren Jeng would like to acknowledge Medical Device Innovation Center (MDIC) and Intelligent Manufacturing Research Center (iMRC) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and AC2T research GmbH (AC2T) in Austria (COMET InTribology, FFG-No.872176).

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Authors and Affiliations

  1. Laboratory for Technological Processes, Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, Moscow, 119526, Russia

    Sergei Alexandrov & Elena Lyamina

  2. Department of Biomedical Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Yeau-Ren Jeng

  3. Academy of Innovative Semiconductor and Sustainable Manufacturing, National Cheng Kung University, Tainan70101, Taiwan

    Yeau-Ren Jeng

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  1. Sergei Alexandrov
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Contributions

Sergei Alexandrov: Conceptualization, Methodology, Software, Validation, Investigation, Data curation, Writing – original draft. Elena Lyamina: Supervision, Writing – review & editing. Yeau-Ren Jeng: Conceptualization, Funding acquisition, supervision, Writing – review & editing.

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Correspondence to Yeau-Ren Jeng.

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Alexandrov, S., Lyamina, E. & Jeng, YR. Application of the upper bound theorem for metal forming processes considering an arbitrary isotropic pressure-independent yield criterion with no strength differential effect. Int J Adv Manuf Technol 126, 3311–3321 (2023). https://doi.org/10.1007/s00170-023-11312-5

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