Application of fracture mechanics in analyzing delamination of cyclically loaded paperboard core

Abstract

<div lang="en" class="abs"><p class="abs_header">Abstract</p><p>The primary objective of this work is to study and model the fracture process and durability of paperboard cores in cyclic loading. The results are utilized in creating analytic model to estimate the life time of cores in printing industry. The life time means here the maximum number of winding-unwinding cycles before the core delaminates. This study serves also as an example of use of board as a constructional engineering material.</p><p>Board is an example of complicated, fibrous, porous, hydroscopic, time dependent and statistic material. Different core board grades are typically made of recycled fibers. The material model in this work is linear-elastic, homogeneous and orthotropic.</p><p>The material characteristics, elastic and strength properties are studied first. Then the material is studied from the points of view of fracture and fatigue mechanics. Some of the analysis and test methods are originally developed for fiber composites but have been applied successfully here also for laminated board specimen. An interesting finding is that Scott Bond correlates well with the sum of mode I and mode II critical strain energy release rates. It was also possible to apply Paris’ law and Miner’s cumulative damage theory in the studied example situations. </p><p>The creation of the life time model starts by FEM-analysis of cracked and non cracked cores in a typical loading situation. The elastic-linear material model is used here. The calculated stresses are utilized in analytic J-integral model. The agreement between analytic and numerical J-integral estimations is good.</p><p>The analytic life time model utilizes the analytic J-integral model, Miner’s cumulative damage theory and analytically formulated Wöhler-curves which were constructed by applying the Paris’ law. The Wöhler-curves were constructed also by testing cores to validate the theoretical results. The testing conditions are validated by FEM-analysis.</p><p>The cores heat up when tested or used with non expanding chucks and a temperature correction was needed in the life time model to consider this. Also, single or multi crack model was used depending on the studied case. The calculated and tested durability prediction curves show good correspondence. The results are finally reduced to correspond to certain confidence level.</p></div>