A mechanical model of damage and delamination in corrugated board during folding

The mechanical behavior of a layered paper structure subjected to a combined load of bending and tension is studied. A finite element analysis is performed to include a gradient enhanced continuum damage theory since a non-local theory has to be used when stress gradients are present. Despite the anisotropic nature of paper materials, each layer is modeled as isotropic and homogenous where material parameters are estimated from the in-plane properties of the paper sheet. The two failure modes, material failure and delamination between top and base layer is analyzed within the frameworks of fracture and continuum damage mechanics. Delamination is assumed to be in shearing mode since the crack surfaces are predominantly sliding and crack opening is vanishing. An analytic solution for the fracture energy release rate is derived utilizing engineering beam theory assuming small deformations. Different combinations of stiffness and thickness ratios between the top and base layer are examined in order to judge the risk for having material failure or delamination failure of the multi-ply linerboard. Having a thick and weak top layer, compared to the base layer, increases the probability to obtain through-thickness damage failure in favor of delamination. On the other hand, having a stiff and thin top layer, compared to the base layer, increases the probability to obtain delamination prior to rupture of the top layer. Experiments performed on two-ply linerboards consisting of one ply of mainly virgin fibers and one ply of recycled fibers confirm the predictions made by the model.