Open AccessAnalytical elastic–plastic study on flange wrinkling in deep drawing process
Author(s) -
Mehran Kadkhodayan,
Farzad Moayyedian
Publication year - 2011
Publication title -
scientia iranica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.299
H-Index - 51
eISSN - 2345-3605
pISSN - 1026-3098
DOI - 10.1016/j.scient.2011.03.020
Subject(s) - blank , flange , plasticity , nonlinear system , materials science , uniqueness , plane stress , deformation theory , deep drawing , mechanics , deflection (physics) , yield surface , stress field , structural engineering , geometry , mathematics , mathematical analysis , constitutive equation , classical mechanics , composite material , physics , finite element method , engineering , quantum mechanics
Based on the two-dimensional plane stress wrinkling model of an elastic–plastic annular plate and a bifurcation functional from Hill’s general theory of uniqueness in polar coordinates, the critical conditions for the elastic and plastic wrinkling of the flange of a circular blank during the deep-drawing process are obtained to improve previous results of the literature. The influence of a blank-holder on wrinkling and on the number of waves generated can also be quantitatively predicted. A closed-form solution for the critical drawing stress is developed, based on the Tresca yield criterion, along with the assumption of perfectly plastic material. A nonlinear plastic stress field and the deformation theory of plasticity are used. It is demonstrated that using the large deflection theory for a strain tensor with neglecting nonlinear terms has the same result as the small deflection theory