A Mathematical Model for Upper-Bound Analysis of Backward Extrusion in Ultra-Thin-Walled Tube Forming

Pahlevani, Zahra; Ebrahimi, RAMIN

doi:10.22068/ijmse.4600

Volume 23, Issue 2 (June 2026 2026) IJMSE 2026, 23(2): 97-114 | Back to browse issues page

‎ 10.22068/ijmse.4600

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Pahlevani Z, Ebrahimi R. A Mathematical Model for Upper-Bound Analysis of Backward Extrusion in Ultra-Thin-Walled Tube Forming. IJMSE 2026; 23 (2) :97-114
URL: http://ijmse.iust.ac.ir/article-1-4600-en.html

A Mathematical Model for Upper-Bound Analysis of Backward Extrusion in Ultra-Thin-Walled Tube Forming

Zahra Pahlevani

, RAMIN Ebrahimi

Abstract: (2958 Views)

This study presents an analytical model based on the upper-bound method to investigate the backward extrusion of ultra-thin-walled tubes (wall thickness 100–400 µm). The deformation zone is divided into distinct regions with kinematically admissible velocity fields and defined discontinuities, allowing accurate estimation of strain rate field. The model incorporates effects of friction, wall thickness variation, and velocity discontinuities to predict extrusion force, deformation zone depth, and strain localization. Validation through both experimental measurements and finite element simulations demonstrates strong agreement with the analytical predictions. The proposed model offers an efficient and reliable framework for understanding deformation mechanics in precision tube extrusion and serves as a practical design tool in metal forming processes.

Keywords: Backward extrusion, ultra-thin-walled tubes, Upper-bound theory, Deformation mechanics, Strain localization