Tear, Tensile or Fracture Toughness
Fracture toughness describes the ability of the material to resist the propagation of a pre-existing crack. It is an important material property since the occurrence of flaws (cracks) is not completely avoidable in the processing, fabrication, or service of a material/component. Fracture toughness is often determined as the critical stress intensity factor, and sometimes in material mechanics it is referred to as “tenacity”. In paper physics, fracture toughness has been conventionally measured as “fracture energy index” (Jm/kg), which equals the critical fracture energy release rate divided by the paper grammage. It is the critical point beyond which if the fracture energy release rate increases, the crack will start to propagate.
Fracture toughness of paper is difficult to measure due to the elastic, visco-elastic and plastic properties of paper. The conventional linear elastic fracture mechanics (LEFM) approach is not directly applicable to paper fracture toughness. Different methods have been developed for measuring paper fracture toughness. The most commonly used measuring methods are “J-integral”, which has been incorporated into the SCAN-test standard; “In-plane tear energy”, which shows a good agreement with the “J-integral”; and “EWF-essential work of fracture”. In some cases, paper fracture toughness is directly calculated with tensile strength index and stretch of the paper.1 The fracture toughness applied in material mechanics equals the geometric mean value of paper fracture toughness (fracture energy index) times specific elastic modulus.
Despite being difficult to measure, fracture toughness has attracted more and more attention from the paper industry in recent years since the conventional strength properties have often proved inadequate for evaluating the paper web breaks in its manufacturing and end-use processes. The most commonly used strength properties for the evaluation of pulp and paper strength in industry have been tensile strength and Elemendorf or Brecht-Imset tearing (out-of-plane) resistance.
Tensile strength gives the maximum tension-carrying capacity of paper. It is known that tensile strength only measures the weakest point in a test strip while the weakest point is a random event. It is hard to relate the random strength to the web resistance to breaks. It has been shown that web breaks normally occur at web tensions that are much lower than the tensile strength of paper. No reports have shown that there is a good correlation between web break frequency and tensile strength directly. (Web breaks have been shown to correlate with other morphological properties such as length and coarseness however, which do in turn affect tensile strength.) To reach high in-plane strength properties, the sheet generally requires a high degree of bonding. This requirement is invariably negatively correlated with “out-of-plane” tearing resistance since the tearing resistance decreases with increased bonding after a maximum, usually corresponding to a very low in-plane strength, is reached. What is more is that the out-of-plane tearing mode makes the tearing resistance less relevant for many end-use applications.
When paper fails by crack propagation initiated by defects in a web, the mechanism underlying the failing process is clearly more likely to being understood using a fracture toughness approach than simply a tensile strength approach. It is never likely to be understood using an out-of-plane tearing resistance approach. Unlike tensile strength, paper fracture toughness is a fundamental material property, which always measures the resistance against the crack propagation along the crack line and almost not affected by the weak point in the test specimen. In fact, it has been shown that the paper fracture toughness either measured directly or calculated from tensile strength and stretch is the only strength property that correlates to the paper runnability in press-house.
equation derived by Seth, Fracture toughness = 0.6 (Tensile (N)0.74 + Stretch(%)0.58)