3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

Abstract

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.

Three‐dimensional forming of plastic‐coated fibre‐based materials using a thermoforming process

“…This could be attributed to the curved shape of side walls compared to the flat bottom found on paperboard samples (Figure 12). Other studies have also found an increase in the thickness of paper‐type materials under tensile deformation 29,30 . Verma et al 27 further demonstrated that the rate of this auxetic behaviour can vary depending on the structure of fibre networks and the method of preparing paper materials.…”

“…Other studies have also found an increase in the thickness of paper-type materials under tensile deformation. 29,30 Verma et al 27 further demonstrated that the rate of this auxetic behaviour can vary depending on the structure of fibre networks and the method of preparing paper materials. Similarly, the rate of thickness increase between Paperboards 2 and 4 is different in the current study, as shown by Figure 12.…”

Microscale deformation mechanisms in paperboard during continuous tensile loading and 4D synchrotron X‐ray tomography

“…The specially designed grips are described in Tryding et al [ 21 ] and consist of a cylinder (3 mm in diameter), and a flat surface between which the sample is clamped. Photograph of the grips can be found in Johansson et al [ 18 ]…”

“…For this purpose, the full‐resolution reconstructed image stacks were first cropped to an ROI as described above, after which Gaussian filtering was applied to decrease the amount of noise in the images. The spatial variation in sample thickness was then calculated for each pixel in the in‐plane direction following Johansson et al [ 18 ] Examples of resulting thickness maps are shown in Figure 2, where the visible fibre structure is mainly caused by the surface fibres on the non‐coated side of the paperboard. The data in Figure 2 represent initial sample properties, as they are calculated from the images acquired before loading (Load Step 1).…”

“…The analysis of the strain field evolution in paperboard by Johansson et al [ 18 ] was limited by the temporal resolution due to the image acquisition time with the laboratory X‐ray microtomography. A detailed analysis of rapid changes in the material, for example, close to peak load, was therefore not achievable.…”