Applications of an analytical method to calculate the load distribution along a fibre in a loaded fibre network

摘要

A new analytical solution for the load distribution along a fibre in a network has been used to investigate some aspects of paper tensile strength and elastic modulus. The method uses a similar approximation to the shear-lag formulation but allows stress transfer at individual contacts, rather than specifying a single stress transfer function applying along the entire length of the fibre. Measured elastic modulus data, where the fibres only varied in length and not cross-section, showed only a small effect of fibre length on modulus. This is consistent with a high overall stress transfer coefficient for each fibre-fibre contact, resulting in the contacts at the ends of the fibres being heavily loaded. The maximum force at the middle of the fibre was calculated as a function of the fibre-fibre shear bond strength. The data showed that most literature values are too low to allow the fibre to break during paper fracture. The simulation method was able to explain the reduction in sheet tensile strength with a reduction in density, but was unable to explain the reduction in sheet strength with reduced fibre length. The assumption that a fibre-fibre bond fails completely once its breaking load is exceeded is believed to cause the discrepancy.