Inconsistencies in Plane‐strain Elasto‐plastic Rolling Simulations

Abstract

AbstractPlane 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 σzz equals the average value of the normal stresses σxx and σyy inside plastic domains. Using Hooke's law we obtain a different relation for σzz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for σzz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of σzz at the transition points and consequently to discontinuities of the stress σyy as well as the strains εzz and εyy, provided a continuous behaviour of σxx in rolling direction is postulated. The resulting discontinuity of εzz 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)