Inconsistencies in Plane-strain Elasto-plastic Rolling Simulations

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)