Inconsistencies in plane-strain elasto-plastic rolling simulations
Sprache des Vortragstitels:
77'th Annual Meeting of the Gesellschaft für Angewandte Mathematik und Mechanik e.V.
Sprache des Tagungstitel:
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 sig_zz equals the average value of the normal stresses sig_xx and sig_yy inside plastic domains. Using Hooke's law we obtain a different relation for sig_zz in elastic domains. At transition points from elastic to plastic domains and vice versa, above relations for sig_zz have to be fulfilled simultaneously. Generally, this yields a discontinuous behaviour of sig_zz at the transition points and consequently to discontinuities of the stress sig_yy as well as the strains eps_zz and eps_yy, provided a continuous behaviour of sig_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 in detail.
Key words: Plane strain conditions, Elasto-plasticity, Model inconsistency, Stress and Strain discontinuities.