Identifying the weak spots in packaging 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 $$1\times 1\,\hbox{mm}^2$$ 1 × 1 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.

How Different Carryover Pitch Extractive Components are Affecting Kraft Paper Strength

“…Slightly lower tensile stiffness occurred only in the case of the weakest paper with docosanol. After reaching the plastic region, i.e., the onset of fiber−fiber bond failure, 36 differences in the specific stress−strain curves started to occur. Papers with weaker internal bonding strength reached the plastic region sooner and eventually ruptured at lower specific stress and strain values.…”

Finding globally optimal arrangements of multiple point loads in structural design using a single FEA

“…Knowing the optimal arrangement of point loads thus can best utilize the given structure and avoid structural failure. Besides, the structure can exhibit the highest and lowest performance if the loads are arranged on the 'sweet spots' (Cross 1998) and 'weak spots' (Lahti et al 2020), respectively. However, finding such extremal (i.e., globally optimal) arrangements of point loads in a complex structure is very challenging.…”

Identifying microstructural properties of paper

“…The fiber orientation distribution within a microstructure can be determined in different ways. Established methods are, for example, sheet splitting [3][4][5] or tracing of previously dyed fibers [6,7]. Increasingly, microcomputed tomography (CT) scanning [6][7][8] is also being used, as it is a nondestructive analysis method with high resolution.…”

“…On the microscale, component properties such as geometry, density, or strength have a massive influence on the material and thus on product properties at the macroscale. When analyzing the material paper and paperboard, the distribution of the cellulose‐based paper fibers plays a prominent role for the structural properties such as tensile stiffness [2] or breaking strength [3].…”