Rolling at Small Scales

Abstract

The rolling process is widely used in the metal forming industry, and has been so for many years. However, the process has attracted renewed interest as it recently has been adapted to very small scales where conventional plasticity theory cannot accurately predict the material response. It is well-established that gradient effects play a role at the micron scale, and the objective of this study is to demonstrate how strain gradient hardening affects the rolling process. Specifically, the paper addresses how the applied roll torque, roll forces, and the contact conditions are modified by strain gradient plasticity. Metals are known to be stronger when large strain gradients appear over a few microns; hence the forces involved in the rolling process are expected to increase relatively at these smaller scales. In the present numerical analysis, a steady-state modeling technique that enables convergence without dealing with the transient response period is employed. This allows for a comprehensive parameter study. Coulomb friction, including a stick-slip condition, is used as a first approximation. It is found that length scale effects increase both the forces applied to the roll, the roll torque, and thus the power input to the process. The contact traction is also affected, particularly for sheet thicknesses on the order of 10µm and below. The influences of the length parameter and the friction coefficient are emphasized, and results are presented for multiple sheet reductions and roll sizes.

Rolling induced size effects in elastic–viscoplastic sheet metals

“…It has been shown by Nielsen et al (2015) that the roller radius plays an important role in relation to size effects. Thus, rate-sensitive results will be presented for various roller sizes in the following, while keeping the punch displacement, ∆/H, fixed.…”

“…Thus, no additional pull force will be added to the sheet (see e.g. Nielsen et al, 2015, for details on the procedure). Moreover, no force acts on the sheet in front of the roller.…”

“…At micron scale, GNDs can become a substantial portion of the total dislocation density, and thus dominate the amount of energy required to deform the material. Nielsen et al (2015) recently demonstrated rolling related size effects in the rateindependent limit of an elastic-viscoplastic solid (cold rolling), employing a steady-state numerical framework. By accounting for a dissipative length scale, it has been shown that the forces (punch force, roll torque, power input etc.…”

“…The steady-state formulation put forward by Dean and Hutchinson (1980) is well suitable for history dependent material deformation processes and it readily accounts for elastic unloading. Their method has been adapted to rolling in the study by Nielsen et al (2015), and it will be further exploited in the present investigation. The objective of the present study is to gain insight into, and quantify, the combined effect of strain ratesensitivity and strain gradient hardening during flat sheet rolling; essentially studying rate effects as the characteristic length scale reaches into the range where size effects become important.…”

“…The numerical framework is, however, unstable in the limit when L D → 0, and thus a conventional material model has been independently developed and coded for comparison in Nielsen et al (2015). The material properties considered in the present study are summarized in Tab.…”