The influence of strain rate and pulp properties on the stress relaxation of wet paper — modeling of relaxation

The time-dependent stress (tension) relaxation behavior of wet paper plays a key role in web transfer from the press to the dryer section of a paper machine. In this study, three linear viscoelastic models were used to predict the short time range tension relaxation of wet paper. Over longer time periods, all three models gave relaxation moduli that were apparently linear on a logarithmic timeline. However, the results showed that the tension relaxation of wet paper had more than one characteristic time constant, meaning that the initial tension relaxation phase had a different constant than the later phase or phases. In practical applications, the most relevant time range for runnability of the wet paper web is from milliseconds to a few seconds. The obtained results suggest that the strain rate and initial tension of the relaxation dictate the shape of the tension relaxation curve of wet paper: the higher the strain rate, the greater the tension loss during the first second of relaxation. The tension relaxation behavior of wet paper did not generally depend on pulp type, refining level of pulp, or solids content. However, there can be significant differences between furnishes and solids content in the amount of draw that leads to a sufficient web tension. The results indicated that the tension relaxation behavior of wet paper may be based on a general viscoelastic mechanism that is independent of fiber network properties but depends on the fiber wall material. The findings suggest that the redistribution mechanism of stresses in the wet fiber network has a high level of regularity. The Prony series was capable of predicting tension relaxation behavior of wet paper over a wide time range. Therefore, it can be a very useful simulation tool not only for wet webs, but for any viscoelastic material that shows stress (tension) relaxation.