Numerical analysis of paperboard delamination using cohesive elements

Abstract: A new test method for measuring the shear strength associated with mode III delamination of paperboard is studied with the purpose of reducing the size of the test configuration. The method, which uses a split cantilever beam (SCB) specimen, measures the shear strength indirectly through the fracture resistance. The methodology is based on the double cantilever beam (DCB) specimen, used for measuring the normal delamination strength of paperboard. The study is based on finite element analyses, where cohesive elements are implemented for predicting the fracture response. An experimental evaluation of the test method was carried out in a pre-study conducted between Karlstad, Skövde and Lund University together with Tetra Pak. The experiments considered both the SCB-specimen and the standardised DCB-specimen, and for determination of the fracture behaviour the cohesive law presented by Tryding & Ristinmaa (2017) were considered. The result obtained from the experiments is used as a basis for evaluating the analyses. To model the fracture development, the relation presented by Tryding & Ristinmaa (2017) is implemented in the commercial finite element software Abaqus through a user-specified element. From the analyses of the DCB-specimen it is shown that through implementation of a specified cohesive law, it is possible to simulate mode I fracture development of paperboard in an accurate manner. The results for the DCB analyses correlate well with the experimental results. The result for the SCBspecimen shows a deviating behaviour from the experimental result by underestimating the shear strength. It is noted that the specimen is subjected to notable deformations in both the first shear direction and the normal direction, preventing pure shear loading from being obtained. Based on the analyses, it is indicated that the current test configuration does not obtain pure shear separation in mode III, and thereby underestimates the actual shear strength of the paperboard. It is also shown that reducing the specimen length with 400 mm has no significant impact on the properties related to the cohesive law. By altering the initial crack length, it is possible to further reduce the length of the specimen. However, to prevent development of unstable fracture, the length of the paperboard should exceed 300 mm. Alternating the crack length and the width of the paperboard also seems to contribute to lower displacements in the normal direction and provides a better fit with the experiments. Tryding, J. & Ristinmaa, M. (2017). Normalization of cohesive laws for quasi-brittle materials. Engineering Fracture Mechanics, 178, 333-345. doi:10.1016/j.engfracmech.2017.03.020