3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

Background

Experimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.

Objective

The main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.

Methods

X-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.

Results

The results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.

Conclusions

In-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

     

Crack-growth-rate estimation on a three-point bend specimen during low-cycle fatigue

The ratio of the change of the clip-gage measured crack-opening displacement of a three-point bend specimen to the change of the displacement at the point of application of the cyclic load is shown to vary linearly with the ratio of the crack length to the specimen height. With the aid of this relation, the crack-growth rate is obtained by numerical differentiation of the crack length with respect to the number of load cycles. A clip-gage correction factor is introduced in order to compensate for the use of external edges to position the clip-gage during the experiment.     

Distortional hardening plasticity model for paperboard

A distortional hardening elasto-plastic model at finite strains suitable for modeling of orthotropic materials is presented. As a prototype material, paperboard is considered. An in-plane model is established. The model developed is motivated from non-proportional loading tests on paperboard where the paperboard is pre-strained in one direction and then loaded in the perpendicular direction. A softening effect is revealed in the pre-strained samples. The observed experimental findings cannot be accurately predicted by current models for paperboard. To be able to model the softening effects, a yield surface based on multiple hardening variables is introduced. It is shown that the model parameters can be obtained from simple uniaxial experiments. The model is implemented in a finite element framework which is used to illustrate the behavior of the model at some specific loading situations and is compared with strain fields obtained from Digital Image Correlation experiments.     

Experimental and numerical studies of creasing of paperboard

A laboratory creasing device to capture the most important properties of a commercial rotary creasing tool was designed. Finite element analysis of the creasing of a multiply paperboard in the laboratory crease device was presented. The multiply paperboard was modeled as a multilayered structure with cohesive softening interface model connecting the paperboard plies. The paperboard plies were modeled by an anisotropic elastic–plastic material model. The purpose of the analysis of the laboratory creasing device was to present material models that represent paperboard, and to investigate how well the analysis captured the multiply paperboard behavior during laboratory creasing. And to increase the understanding of what multiply paperboard properties that influence the laboratory crease operation. The result of the simulations showed very good correlations with the experimental obtained results. The results indicated that the paperboard properties that have the most influence is the out-of-plane shear, out-of-plane compression and the friction between the laboratory creasing device and the paperboard.