Development of Fracture Mechanics to Study End Use of Paper Webs
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This thesis deals with the application of fracture mechanics to study the strength of paper webs. The main aim of fracture mechanics is to predict the critical combination of defect size, structure geometry and external loading that will lead to a catastrophic failure. To serve as a practical tool, the fracture testing must be carried out on lab-scale structures, and the predictions must be made for an arbitrary size of the structure and defect geometry. That is, transferability must prevail. As a starting point for this thesis, we found (in Paper II) that for a range of different paper materials (SC, newsprint, MWC, liner board, uting and sack paper), the static strength of large paper webs with an edge notch was excellently predicted using the J-integral failure criterion and isotropic deformation theory of plasticity as a material model. Fracture toughness testing was done on small lab-scale specimens. The web failure predictions were made using the Finite Element Method (FEM), and the verification was done using a custom-built static tensile tester - able to test 1.8 m long a 1 m wide paper webs. The tools of fracture mechanics are rarely used by the paper industry. There are several reasons for this. For many paper materials and printing press situations, there exist no clear evidence that defects - such as holes, cuts and shives - are responsible for the majority of web breaks. Another reason, which is an important topic in this thesis, is that for a given notch length and web size, the web failure conditions predicted by the standard fracture mechanics theory, is a factor 2-3 times higher than that experienced in a printing press for the same notch length. Skew web-tension profiles (caused by baggy webs or non-aligned rollers), moisture induced effects during printing, out-of-plane deformation such a buckling (amplified by a pressurized turner bar) and low basis weight areas around a defect are all examples of factors that are not accounted for in the standard laboratory fracture testing and predictions of web strength - and at the same time are present in a printing press situation. These factors are all believed to reduce the strength of a paper web. This thesis has addressed how all these factors can be taken into account when estimating the web strength. In the first article we wanted to test the hypothesis that some of the variation seen in the strength of notched paper samples is caused by variation in the basis weight close to the notch tip(s). By mapping the basis weight using a β-formation apparatus, and correlating the basis weight in the notch-tip region to the individual strengths, a relation between the local basis weight and the applied peak load was found. The distribution of floc-size and floc-orientation was found to be of importance to whether or not a correlation was found. For the SC and newsprint paper grades, ocs and anti-ocs were oriented more strongly in the MD, as well as having a smaller average size, than what was observed in the copy paper grade. This explained why a much stronger correlation was found between the notch tip basis weight properties and the individual critical strengts of the copy paper grade than for the news and SC paper grades. Out-of-plane deformations will take place at the free notch edges in a notched paper loaded in tension. This is known as buckling, and will - compared to a sample that is prevented from buckling - drastically reduce its critical strength. In standard fracture toughness testing of paper, buckling is prevented. This will cause a situation quite different than in a printing press - where paper is free to buckle. From experiments on small paper samples, we found in Paper III that this buckling caused a strength reduction of 10-35 % depending on the notch length and paper grade. Through FEM simulations and by using the J-integral failure criterion, the strength reducing effect of buckling was successfully described (except for the smallest notch lengths). The degree of anisotropy and paper thickness were found to be important for the strength reducing effect of buckling. The strength reducing effect of buckling was found to decrease with both increasing anisotropy and material thickness. In Paper IV, buckling is further investigated - using a 3D cohesive zone model. The model satisfyingly describes the experimental result from paper III. For small notches, the interaction between the process zone close to the notch tip and the buckle is found necessary to fully describe the observed strength reducing effect of buckling. A phenomenologically defined effective notch length - based on the shape of the damaged region - was defined from the simulations. In Paper V, three different loading situations - suspected of being detrimental to the runnability in a printing press - are investigated through numerical simulations of large paper webs. The factors investigated were buckling edge and center notches, skew web tension and a notch placed in a pressurized turner bar situation. Both buckling center and edge notches were shown to reduce the web strength compared to a web prevented from buckling. A skew web tension was also shown to decrease the web strength from 10-30 % depending on the notch length and applied web skewness. To investigate the possibility of simulating the turner bar pressure situation, experiments where an air pressure was applied to small center notched specimens were done. The experiments showed a reduction in critical strength (compared to no applied pressure) of 15-20 % depending on the amount of applied pressure and notch length. This was found to be in good agreement with the numerical results. The effect of an air pressure applied to center notched paper webs was, using FEM, shown to drastically reduce the critical web strength. When taking into account both free buckling and a 2 kPa surface pressure applied to the notched region, a ~45 % reduction in web strength (compared to a web kept in plane) was found.