Analysis of length effect dependencies in tensile test for paperboard

• Main Author: Claesson, Filip
• Format: Others
• Language: English
• Published: Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik 2020
• Subjects: paperboard; short span; Applied Mechanics; Teknisk mekanik
• Online Access: http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-80410

Paperboard combined with polymer and aluminium films are widely used in food packages. Paperboard is used for the bulk of the package material, and provides the stiffness. Paperboard is a highly anisotropic material, which is affected by how the fibers are orientated. Most fibers are aligned in the machine direction (MD), which is the stiffest direction, perpendicular is the cross-machine direction (CD) where fewer fibers are aligned, and the thickness direction (ZD) which is considerably weaker than in the MD and CD directions. Continuum models are used to describe the material properties to aid the design of package manufacturing processes. In continuum models there are no inherent length scale effects, and the material behaviour is the same regardless of the geometry. For paperboard there have been experimentally observed effects of the gauge length and width of tensile tests. To calibrate and develop these models it is important to observe which effect is a material property, if there is an inherent length scale, and which properties are from the boundary conditions of the experimental setup. Creasing is a process where the length scale is considerably smaller than at the standard tensile test, where the material deforms plastically to create creasing lines to easier fold the paperboard. The failure properties from standard tensile tests are not a good predictor of failure in creasing, where the length scale is considerably smaller. To investigate if there is an effect of the length scale, as the length gets smaller, tensile tests have been performed at different gauge lengths. The tensile tests were performed with a width of 15mm and the gauge length was varied in the range 3-100mm in MD and CD. The results from the tensile tests were, the failure strain and failure stress increased as the gauge length of the tests specimens decreased, both in MD and in CD. Initial stiffness decreased as the gauge length decrease (more notable in MD), and there was an increase in hardening at large strains with decreasing gauge length (more notable in CD). An analytical calculation of the reduction in measured stiffness as the gauge length get smaller was performed, where the decrease in stiffness deemed to be strongly related to the out-of-plane shear modulus. By fitting the analytical solution the experimental data the shear modulus was approximated to 60MPa. The shear modulus has been measured for the same paperboard to 70±23MPa. Simulations of the tensile tests at 5mm did fit the experimental data when the material model was calibrated from the tensile test at 100mm, except the increase in hardening at large strains in CD. It was noted that it was important to use the shear modulus that was inversely calculated by the analytical calculations to get the right initial slope of the simulations of the 5mm tensile tests. Creasing simulations were performed of a test setup of the creasing procedure. The male die was lowered 0.3mm to perform the creasing, which in the tests setup do not result in failure in the material. From the simulations the stress at the bottom of the paperboard during creasing exceeded the failure stress from the tensile test performed at 100mm. The stress during creasing was biaxial, it has stresses both in MD and CD, with is different compared to the uniaxial tensile tests at 100mm. The stress from the creasing simulation in CD was at a maximum of 40MPa where the 3mm tensile tests in CD resulted in a failure stress at 39MPa. The maximum stress in the MD creasing simulation was 96MPa, where the 3mm tensile test resulted in a failure stress at 69MPa. The properties from a long span tensile test are not good predictors of failure in creasing, where both stress state and length scale are very different. The failure stress at 3mm tensile tests in CD is close to the maximum stress from creasing simulations, and may be a good indication of failure. The 3mm tensile test in MD resulted in a considerably lower failure stress than the maximum stress in the creasing simulations, which indicates that the 3mm long tensile test is not a good predictor of failure in MD for creasing, where the length scale is even smaller.