Rolling induced size effects in elastic–viscoplastic sheet metals

Rolling processes for which the characteristic length scale reaches into the range where size effects become important are receiving increased interest. In particularly, this is owed to the roll-molding process under development for high-throughput of micron-scale surface features. The study presented revolves around the rolling induced effect of visco-plasticity (ranging hot and cold rolling) in combination with strain gradient hardening – including both dissipative and energetic contributions. To bring out first order effects on rolling at small scale, the modeling efforts are limited to flat sheet rolling, where a non-homogeneous material deformation takes place between the rollers. Large strain gradients develop where the rollers first come in contact with the sheet, and a higher order plasticity model is employed to illustrate their influence at small scales. The study reveals that the energetic length parameter has negligible effect on the rolling quantities of interest, while the contribution coming from the dissipative length parameter can be dominant. Considering a slow and a fast moving sheet, respectively, convergence towards the rate independent limit is demonstrated, and a characteristic velocity is identified, for which the torque and punch force applied to the roller becomes independent of the material rate-sensitivity.