Curl in Paper

(3) Numerical Simulation of History-Dependent Curl

Abstract

Numerical simulation of history-dependent curl has been made on the basis of the viscoelastic laminate model [5]. Curl behavior of paper under varying humidity conditions depends not only on the present value of moisture content but also on the moisture history that paper has experienced in the past, such as typically seen in Figs. 1 to 3. In order to predict such complex curl behavior, a computer simulation model was developed by using the classical lamination theory and the general linear theory of viscoelasticity which was proposed by Coleman [4]. Drying stress effects were incorporated by assuming presence of stresses in the reference state, which was taken in the final drying stage [5].
Simulation results for curvature response to repeated humidity cycling showed that the paper curl can be separated into two components, i. e., reversible and irreversible componets. The reversible component is essentially determined by difference in hygroexpansion coefficients between top and bottom sides of the sheet, whereas the irreversible curl is governed mainly by mechanical causes, i. e., asymmetric distribution of drying stresses and two-sidedness in relaxation moduli. When the top and bottom sides of the sheet are subjected to different moisture histories and returned to the original uniform moisture distribution, such as often seen in printing and xerography processes, paper shows residual curl after the process in the absence of non-uniformity in paper properties in the thickness direction. This phenomenon is caused by viscoelastic relaxation of hygro-stress gradient which is produced during the process. In this case it is, therefore, important to control the “average” values of hygroexpansion coefficients and relaxation moduli through the thickness, as well as the two-sidedness of these properties.
Since paper curl is a complex manifestation of different effects of non-uniformity, a measure for curl control varies with practical situations. The computer simulation model developed in this study provides a rational design tool for various paper products by clarifying each contribution of the different curl mechanisms.