Alexander Kainz, Klaus Zeman, Konrad Krimpelstätter,
"Inconsistencies in Plane-strain Elasto-plastic Rolling Simulations"
, in WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim: PAMM 2006 (GAMM Annual Meeting 2006 - Berlin), Serie PAMM 2006, Vol. 6, Nummer 1, Wiley InterScience, Seite(n) 387-388, 12-2006
Inconsistencies in Plane-strain Elasto-plastic Rolling Simulations
Sprache des Titels:
PAMM 2006 (GAMM Annual Meeting 2006 - Berlin)
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 sigma_zz equals the average value of the normal stresses sigma_xx and sigma_yy inside plastic domains. Using Hooke's law we obtain a different relation for zz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for sigma_zz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of sigma_zz at the transition points and consequently to discontinuities of the stress sigma_yy as well as the strains eps_zz and eps_yy, provided a continuous behaviour of sigma_xx in rolling direction is postulated. The resulting discontinuity of eps_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.