On the modeling of hardening in metals during non-proportional loading

The purpose of the current work is the formulation and initial application of a phenomenological model for hardening effects in metals subject to non-proportional loading histories characterized by one or more loading-path changes. This model is closely related to the incremental model of Teodosiu and Hu [Teodosiu, C., Hu, Z., 1995. Evolution of the intragranular microstructure at moderate and large strains: modelling and computational significance. In: Shen, S.F., Dawson, P.R. (Eds.), Simulation of Materials Processing: Theory, Methods and Applications. Balkema, Rotterdam, pp. 173–182; Teodosiu, C., Hu, Z., 1998. Microstructure in the continuum modelling of plastic anisotropy. In: Proceedings of 19th Risø International Symposium on Material’s Science: Modelling of Structure and Mechanics of Materials from Microscale to Product. Risø National Laboratory, Roskilde, Denmark, pp. 149–168]. Like their model, the current model captures in particular hardening stagnation after a load reversal as well as cross-hardening after orthogonal loading-path changes. On the other hand, the two models predict qualitatively different behavior during loading-path changes which take place purely in the inelastic range. Such is the case for example during orthogonal loading-path changes from uniaxial tension to simple shear without release, or during monotonic simple shear, or during deep-drawing. As shown by the experimental results reported on in the current work for the mild steel DC06, significant cross-hardening can occur during continuous orthogonal loading-path changes. Beyond this, the current model accounts in an approximate way for the possible effects of texture development on the material behavior with the help of the plastic spin. After investigating the behavior of the current model for various ideal two-stage loading histories (e.g., tension-shear), the current work ends with a comparison of standard combined hardening and current approaches in the context of the simulation of internal stress development and residual stresses during deep-drawing and the resultant springback after ring-splitting.