Modelling dispersion effects in paper-effective thickness estimates

Abstract

The structural properties of paper and cardboard are important for the design of containers and of packaging. Amcor, a Melbourne-based producer of packaging, pulp and paper products, proposed the initial problem of explaining the large discrepancies which were sometimes observed between the nominal thickness, as determined by hard platen measurements, and the effective thickness which would account for the experimentally measured values of bending stiffness. The question was also raised as to whether or not ultrasonic waves could be used to measure directly, and on-line, the effective thickness.

Paper can be regarded as a fibre-composite material, with a pronounced anisotropy due to the preferential alignment of fibres in the machine direction as a consequence of the manufacturing process. The salient features of elastic (ultrasonic) wave propagation in an anisotropic plate will be presented, with an emphasis on addressing the questions raised above. In particular, it will be noted that the characterization of the first anti-symmetric (flexural) mode should provide a convenient on-line measurement of the flexural stiffness, which is the more relevant property for quality control and structural design than the effective thickness.