NC State
B.C. Donner. A heuristic model of paper rupture. In The Fundamentals of Papermaking Materials, Trans. of the XIth Fund. Res. Symp. Cambridge, 1997, (C.F. Baker, ed.), pp 1215–1247, FRC, Manchester, 2018.


In-plane (Mode I) fracture of paper is tested at both cryogenic and standard temperatures . It is shown that newsprint tested at cryogenic temperatures is very nearly linear elastic but does not obey classical linear elastic fracture mechanics (LEFM). The discrepancy is traced to changes in the crack tip stress
field due to the sheet’s fibrous structure.

A new fracture model is proposed which integrates the Griffith energy method, Irwin’s correction for nonlinear material behavior, and a similar correction for the fibrous structure. The statistical distribution of mass and local fibre orientation (structural formation) are explicitly considered, and the model thereby links fracture and tensile strength of paper. This approach is consistent with Bazant’s
theoretical treatment of quasi-brittle fracture.

The separation of material nonlinearity and structural formation permits :

  • computing the Essential Work, linking the model to an established approach
  • estimating the fast fracture response that might occur in practice
  • normalizing strength for the paper machine dependent structural formation

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