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T. Wahlström and P. Mäkelä. Predictions of anisotropic multiply board properties based on isotropic ply properties and drying restraints. In Advances in Paper Science and Technology, Trans. of the XIIIth Fund. Res. Symp. Cambridge, 2005, (S.J. I’Anson, ed.), pp 241–281, FRC, Manchester, 2018.


There is a link missing between pulp properties and machine-made paper properties. The aim of this paper is to close a part of this gap by proposing an engineering model which, based on pulp or stock properties, makes it possible to predict the resulting anisotropic material behaviour of a multiply paper or board based on any given fibre anisotropy and drying restraint.

An anisotropic model for the shrinkage and stiffness inter-action between the individual plies in a multiply structure is formulated. The input data to the model is the isotropic restrained dried and free dried stiffness, the free shrinkage strain and the density of each ply in the multiply structure. The basis weight, fibre anisotropy and total strain after drying are variables in the model. This means that besides the standard handsheet procedure only measurement of shrinkage and stiffness for one extra free dried handsheet is needed for the calibration of the model.

The proposed model is validated with a series of anisotropic handsheet trials. Various combinations of single ply anisotropic handsheets were couched together into seven different multiply
boards, which were dried freely and restrained. The isotropic input data of the individual plies were used to predict the free and restrained dried tensile stiffness index and bending stiffness of the multiply boards. The agreement between the experimental and predicted results showed good agreement. The model constitutes a useful tool in engineering predictions and parametric investigations of the mechanical behaviour of multiply boards. As a demonstration of the use of the model, the relation for tensile and bending stiffness versus total strain accumulated during drying was predicted for different board compositions. The basis weight and fibre anisotropy were varied in one of its plies.

As another example the MD and CD stiffness profiles of a multiply board were simulated based on a given MD stretch and CD shrinkage profile.

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