Identifying the weak spots in\xa0packaging paper: local variations in grammage, fiber orientation and density and the resulting local strain and failure under load

Abstract

Measured local paper structure—i.e. local basis weight, local thickness, local density and local fiber orientation—has been linked to local strain and local material failure (local temperature increase due to energy dissipation upon fiber–fiber bond failure) measured during tensile testing. The data has been spatially linked through data map registration delivering several thousand 1times 1,hbox{mm}^2 paper regions, each containing all measured properties. The relation between local paper structure and resulting local deformation and failure is studied with regression models. Multiple linear regression modeling was used to identify the paper structure related drivers for local concentrations of strain under load and local concentrations of material failure, which are both starting to occur considerably before rupture of the paper. Analyzing the development of local strain in paper we found that regions with higher basis weight and higher fiber orientation in load direction tend to exhibit considerably lower strain during tensile testing. Furthermore, the relation between local strain and local grammage can be predicted with the statistical theory of elasticity. Also regions with higher density have lower local strain, but not as pronounced. The findings for local fiber–fiber bond failure of paper are similar but not equivalent. The strongest correlation exists with local grammage. Local density and local fiber orientation show in turn weaker correlation with local bond failure. Local variations in paper thickness were not relevant in any case. These findings are highlighting the relevance of local fiber orientation and local density variations as structural mechanisms governing paper failure. In the past the focus has been mostly on paper formation. Together with local grammage (formation) they are responsible for the weak spots in paper, and thus cause local concentrations of paper strain and the initiation of failure under tensile load.