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Inconsistencies in Plane‐strain Elasto‐plastic Rolling Simulations
Author(s) -
Kainz Alexander,
Krimpelstaetter Konrad,
Zeman Klaus
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610174
Subject(s) - classification of discontinuities , discontinuity (linguistics) , plasticity , versa , von mises yield criterion , plane (geometry) , stress (linguistics) , plane stress , flow (mathematics) , zero (linguistics) , mechanics , mathematics , mathematical analysis , physics , geometry , finite element method , thermodynamics , computer science , linguistics , philosophy , database
Plane strain conditions are frequently used as model assumptions for the approximate calculation of flat rolling processes for sufficiently wide strips. This means that during the entire forming process, the strain rate in strip width direction (z‐direction) remains zero. In the case of elasto‐plastic material, the transitions from elastic to plastic states and vice versa are of particular interest. If we accept the flow rule of Levy‐Mises, the normal stress σ zz equals the average value of the normal stresses σ xx and σ yy inside plastic domains. Using Hooke's law we obtain a different relation for σ zz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for σ zz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of σ zz at the transition points and consequently to discontinuities of the stress σ yy as well as the strains ε zz and ε yy , provided a continuous behaviour of σ xx in rolling direction is postulated. The resulting discontinuity of ε zz indicates therefore an inconsistency of such a plane strain model. Some key aspects of the underlying theory and consequences of such model assumptions will be pointed out. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)