Influence Of Relative Humidity And Strain Rate On The Energy Absorption Properties Of Paper-based Cushioning Materials

Paper honeycomb and multi-layered corrugated paperboard are widely used in distribution chains as energy absorbers or cushions to protect products from accidental impacts. These benefited mainly from the surprising long plateau on the compressive load-deflection curves of paper honeycomb and multi-layered corrugated paperboard. It is this long plateau that makes paper honeycomb and multi-layered corrugated paperboard the perfect candidates for use as cushioning materials to resist external loads in the transport process. The energy absorption property of paper honeycomb and multi-layered corrugated paperboard may be sensitive to the ambient humidity and nominal strain rate besides structural parameters. The energy absorption properties of these two kinds of cushioning materials in various ambient humidities and their strain-rate effect received the widest attention in this field; therefore, they were the focus of our dissertation. In this paper, combined with experimental research and theoretical analysis, the energy absorbing capacity in various ambient humidities, deformation mechanism and strain rate sensitivity of paper honeycomb and multi-layered corrugated paperboard were studied systematically. The energy absorption properties of these two typical structures were surveyed and compared.Comprehensive experimental investigations on the crushing behaviours of paper honeycomb and multi-layered corrugated paperboard were carried out. Three types of common used paper honeycomb core and eight kinds of typical corrugated paperboard were compressed quasi-statically in each experimental relative humidity, i.e.,40%,50%,65%,75%, 85% and 95%, at a fixed temperature of 23℃and under six groups of strain rates, that is, 8.3×10-4,5.0×10-3,3.3×10-2,6.1×101,8.6×101 and 1.1×102S-1. The effects of relative humidity and strain rate on the energy absorption characteristics of paper honeycomb and multi-layered corrugated paperboard were concluded as following:the plateau stress and energy absorption per unit volume of these two materials were decrease with the decreasing of the thickness-to-length ratios in different ambient humidities and various nominal strain rates involved in this study. The relationships between the plateau stress and energy absorption capability of paper honeycomb and relative humidity can be divided into two stages demarcated by relative humidity of 75%. They were insensitive to relative humidity in the range from 30% to 75%. However, when relative humidity is higher than 75%, these two indicators of energy absorbing properties decreased significantly with the increasing of relative humidity. The plateau stress and energy absorption properties of multi-layered corrugated paperboard were decreased with the increasing of ambient humidity constantly; Plateau stress and energy absorption capability of two materials were promoted at intermediate nominal strain rates compared to that at quasi-static compression, thus demonstrate strain-rate effect to some extent. All these experimental works provided a solid foundation for further analysis.A mathematically model was developed to predict the plateau stress of axially loaded paper honeycomb in various humidity environments. It is a simple formula relating the plateau stress to the thickness-to-length ratio of honeycomb-core cell, the yielding stress of cell-material tested under the controlled atmosphere [23℃,50% relative humidity (RH)] and the ambient RH. Paper honeycomb with various thickness-to-length ratios were researched-under several levels of RH, and the plateau stress of each kind of paper honeycomb was obtained. The created model was then verified by comparing the predictions with observations. A good agreement between them corroborates the feasibility and accuracy of the model. The present model can be used to chareaterize the energy-absorption properties of paper honeycomb in an actual logistic environment, and so can be used to optimize the structural design of paper honeycomb.A theoretical model was constructed to predict the initial buckling stress of multi-layered corrugated paperboard. It is a simple function characterized by the thickness-to-length ratio of the corrugated-core cell and the yielding strength of corrugated medium. Combining this model with the empirical relationship between the sub-yielding modulus and the flute pitch, we obtained the prediction model of the stress plateau curve of multi-layered corrugated paperboard in a specified humidity environment. Given the influencing of relative humidity upon the yielding strength, a prediction equation was constructed to calculate the initial buckling stress of multi-layered corrugated paperboard used in actual logistical environments.A theoretical model was developed to describe the relationship between the energy absorption properties of paper honeycomb and multi-layered corrugated paperboard and ambient humidity, as well as the structural parameters thereof. The model is a piecewise function modelling the energy absorption of each deformation stage separately (four stages for paper honeycomb, that is, linear-elastic stage, yield stage, plateau stage and densification stage; whilst three sections for multi-layered corrugated paperboard, i.e., linear-elastic section, plateau section and densification section). Function of each stage is a simple formula relating the energy absorption capacity to the thickness-to-length ratio, the mechanical property of a cell-wall material tested under a controlled atmosphere and the RH. Energy absorption curves were thereby obtained for paper honeycombs and multi-layered corrugated paperboard with a wide range of thickness-to-length ratios in arbitrary humidity environments. The created model was then verified by comparing the predicted energy absorption curves with the experimental ones. A good accordance between the predictions and the observations was achieved, indicating that the energy absorption models developed here could be used to practical application for the designing optimisation and material selection of these two cushioning materials.The gas trapped in a confined space of honeycomb cell generated a returning force due to rapid compression. This force helps in promoting of plateau stress of paper honeycomb under dynamic loading conditions. Taking this restoring force into consideration, mathematical models of dynamic plateau stress and dynamic energy absorption of paper honeycomb were established. Dynamic plateau stress increased slightly with the increasing of strain, thus result an obliquity of energy absorption curve in this stage.As typical energy absorbers, paper honeycomb and multi-layered corrugated paperboard are very attractive since they increase the choices in structural optimization, therefore, packaging designers can choose the optimum structural parameters and the best candidate for cell wall material according to actual logistical conditions. Energy absorption diagram can effectively provide the designers with systematically optimization of paper honeycomb and multi-layered corrugated paperboard.Through plentiful experimental work, we constructed the energy absorption diagram of paper honeycomb and multi-layered corrugated paperboard that loaded under a certain nominal strain rate in various ambient humidities and that compressed under various nominal strain rates in a constant relative humidity. These energy absorption diagrams we constructed synthesize the structural parameters, ambient humidity and nominal strain rate, they can be used to characterize the cushioning properties and optimize the structures of two kinds of energy absorber for energy-absorbing application.