Numerical analysis of diffuse and localized necking in orthotropic sheet metals

In the present paper the diffuse and localized necking models according to Swift [Swift, H.W., 1952. Plastic instability under plane stress, Journal of the Mechanics and Physics of Solids, 11–18], Hill [Hill, R., 1952. On discontinuous plastic states, with special reference to localized necking in thin sheets. Journal of the Mechanics and Physics of Solids 1, 19–30] and Marciniak and Kuczyński [Marciniak, Z., Kuczyński, K., 1967. Limit strains in the process of stretch-forming sheet metal. International Journal of Mechanical Sciences 9, 609–620], respectively, are considered. A theoretical framework for the mentioned models is proposed that covers rigid–plastic as well as elastic–plastic constitutive modelling using various advanced phenomenological yield functions that are able to account very accurately for plastic anisotropy. The mentioned necking models are applied to different orthotropic sheet metals in order to assess their predictive capabilities and to stress out some potential sources for discrepancies between simulations and experiments. In particular, the impact of the applied hardening curve and the equibiaxial r-value, which was recently introduced by Barlat [Barlat, F., Brem, J.C., Yoon, J.W., Chung, K., Dick, R.E., Choi, S.-H., Pourboghrat, F., Chu, E., Lege, D.J., 2003. Plane stress yield function for aluminium alloy sheets – part 1: theory. International Journal of Plasticity 19, 297–1319], on formability prediction is investigated. Furthermore, the impact of the Portevin–LeChatelier effect on the formability of aluminum sheet metals is discussed.