Tensile strength, fracture toughness and fracture energy
Tensile strength has wide use in characterising the mechanical properties of paper and board. It is easy to measure and understand. Yet, the results have no direct significance, since paper and board are seldom loaded to tensile failure. In paper webs, flaws at stress levels that are a fraction of tensile strength usually trigger failure. Fracture toughness is a measure of paper performance in such situations. In board products, compressive failure is relevant.
In the past, tensile strength has been the subject of extensive theoretical and experimental research, and the theories and ideas have many connections to other engineering materials. Many models relate fibre and bond properties to the tensile strength of paper, but their validity can be seriously questioned. After all, it is intuitively clear that the tensile failure must start, in some sense, at a local weak spot. One should therefore be suspicious of any microscopic theory that considers the average sheet structure, average fibres and average bonds. Instead, the research in recent years has demonstrated that continuum fracture mechanics can connect the tensile strength of paper to the average properties of its microscopic constituents. Fracture toughness and fracture energy are the key concepts in this respect.
We will begin this section by considering web breaks and the continuum fracture mechanics that explain the breaks. Aside from process disturbances, infrequent web breaks can be triggered by defects in the paper. Such defects are very rare and therefore play no role in the usual testing of paper strength. In that case, the “weak spots” that control the location of paper failure arise from the non-uniformity, including formation, of paper. The formation-related non-uniformity can be so low that it has an insignificant effect on the actual tensile strength values. Indeed, the observed variability in tensile strength measurements is often small, e.g. when compared with the variability of the elastic modulus. It is therefore possible to consider the average tensile strength of paper as a material property. Motivated by this, we will then explain how tensile strength relates through fracture energy to the microscopic properties of the fibres and the fibre network. Different measurement methods of fracture energy and experimental observations on the tensile properties of paper are also discussed. In addition, we ponder furnish and papermaking effects on tensile strength.
