The role of flute morphology in mechanical behaviour of corrugated fibreboard : a numerical, analytical and empirical study : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Engineering at Massey University, Palmerston North, New Zealand
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2020
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Massey University
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Abstract
Corrugated fibreboard (CFB) packaging is designed to protect its contents during the shipping and storage of goods – a role threatened by damage to the CFB. Damaged goods will not only make the customers unhappy but also cause significant loss to the suppliers. As different goods require different design of CFB box, there is no one solution fits all to overcome this issue. This thesis was focused on understanding the fundamentals of CFB damage, relating the damage with the strength loss, and including the damage in strength predictive tools such as finite element (FE) and analytical models to allow for faster design of CFB boxes and the possibility of finding optimal solutions for different requirements. The type of CFB damage that the research narrowed down into was changes to the flute profile that could arise. Such flute damage could be unintentional (crushing and indentation at any stage during the shelf life of the packaging) or intentional (accompanying perforation for instance – a design option to provide secondary functionality such as in shelf ready applications). There is currently no systematic way of observing and quantifying the structure of the flute profile to allow for a proper understanding of the morphology of the flute. Typically, this is done either through measuring the change in calliper or direct observation on the profiles at the edge of CFB blanks which suffers additional physical damage due indentation from the cutting process. A new technique was presented to be able to do this by laser cutting the samples and digitalising the flutes. The method also includes a statistical tool that can compare different flutes and quantify the change in morphology through a variable called the ‘Similarity Factor’. The technique was demonstrated for flute profiles with different extents of crushing, and also allowed for transferring the digitalised profile for FE modelling purposes.
Developing a full box compression strength (BCT) FE model with the micro-geometry of the fluting structure can be very time consuming as it will involve a huge number of mesh element and result in a long simulation time. So to overcome this, smaller component models like the bending and crushing tests that have been shown to be the largest factor affecting the BCT were developed with micro-geometry structure that allowed for significantly less computation time and better understanding of the effect of flute profile. A new finding identified through the application of the bending model was that the orientation of the sample can be rotated to find an optimal orientation angle that gives the best bending stiffness and maximum bending force performance. Analytical models were also assembled, and their performance compared with the FE models. These provided accurate outcomes for bending but were limited in cases such as inability to predict the maximum bending force and determining the locus of failure.
Global damage to the CFB was simulated through deliberately crushing samples to different extents experimentally. The effect of different levels of crushing on flute morphology and mechanical performance was measured through image analysis, torsional, compressive and bending tests. These tests showed that the torsional behaviour of CFB had the highest sensitivity to crushing at low levels. Since the flute morphology measurements showed negligible changes (the original flute geometry was recovered after crushing), it is suggested that the crushing could affect other localised damage to CFB components such as to the fibres in the constituent papers. Further investigation of the extent and nature of this damage could be an interesting extension to find out its relation to the BCT. On the other hand, the reduction in bending strength and edge crush test followed a similar tend to change in flute morphology with increasing crush levels. This shows that some of the loss in strength could be attributed to the change in flute geometry as well as the reduction in calliper (beyond a threshold where morphology was recoverable after compression).
By combining the new tool to characterise the flute structure and with models of varying complexity, their ability to predict the strength of CFB at different extents of crushing could be compared (simulating unintentional damage). These models consisted of an actual flute geometry, idealized flute geometry and an equivalent flute geometry FE models along with analytical solution models. This comparison showed that the use of an actual flute geometry was useful to predict mechanical performance but that the dominant effect on bending strength is the calliper and the flute morphology is a secondary influence.
The utility of the FE model was further demonstrated with inclusion of an intentional localised damage through perforation. The model accurately predicted the drop in the experimentally measured apparent bending stiffness. The findings of the localised perforation study also demonstrated that the bending force of the CFB can be significantly improved by avoiding punching through the peaks that rest on the compressive side of the liner.
The key new contribution of this research was the development of new a way to accurately measure and describe the actual flute profile within CFB exposed to pre-test damage. The profile allowed geometric damage to be quantified and for the true profile to be included in detailed finite element modelling of mechanical behavior. The effect of flute damage on the mechanical behavior of CFB could therefore be determined and predicted and allowed the potential effects on the strength of CFB packages to be inferred.