Box Compression Research Articles

Relative Humidity and Absolute Moisture Content Effects on the Compression Strength of Corrugated Boxes

Abstract Corrugated boxes are relatively inexpensive and used extensively to contain and protect consumer products as they move through the distribution system, providing a much-needed function in today’s economy. These boxes are constructed from paper, and therefore the mechanical properties of the boxes vary significantly with moisture content in the paper and available in the atmosphere. Relative humidity regularly varies between 30 to 90 % depending on location and time of year. Above a relative humidity of 30 %, paper fibers are affected, resulting in a decrease in the top-to-bottom compression strength of corrugated boxes. Therefore, understanding the moisture effect on box compression strength is essential for the containment, protection, and safe shipment of products. The goal of this study is to characterize the effect of relative humidity and, subsequently, the effects of moisture content on the compressive resistance of corrugated boxes. A total of 3,000 industry supplied boxes are used to evaluate moisture content and compressive strength at seven relative humidity conditions from 30 to 90 %. Three sets of conditions are repeated to test repeatability for a total of ten batches tested. The moisture content for 3 out of every 10 specimens is recorded using a loss-upon-drying moisture balance. Results indicate a second-order polynomial increase in moisture content as a function of relative humidity. The compression strength of corrugated boxes is found to vary linearly with moisture content for the range tested and follows a second-order polynomial decrease with increasing relative humidity. The data from this study are compiled into a table of corrugated box strength reduction factors for comparison with the results from previous studies.

A Comparative Analysis of Artificial Neural Network (ANN) Architectures for Box Compression Strength Estimation

A Comparative Analysis of Artificial Neural Network (ANN) Architectures for Box Compression Strength Estimation

Creep behaviour of day‐old chicken corrugated paperboard packaging under different uniaxial compression loads—An experimental study

AbstractOne of the most important elements for animal transportation is the packaging that ensures the safety and health of the transit. During the transport of live small animals, such as day‐old chickens, the animals may only stay in the boxes for a very limited period, in this case, 48 h. Therefore, it is important to be able to model the strength behaviour of these boxes concerning packaging material requirements and sustainability. The aim of this study was to determine the short‐ and relatively long‐term strength of day‐old chicken packages to better estimate packaging design and to use these data to establish an analytical creep model with suitable parameters that adequately approximate the measured data. Two types of packages were tested, and two types of creep models were used to model the creep strain‐time graphs. The creep behaviour of the two samples was tested at four different uniaxial load cases, with consistent environmental conditions during the tests (23°C and 50% relative humidity [RH]). At the two highest loads, both samples failed before the 48‐h cycle, indicating a significant difference in box strength between short‐term and long‐term load tests. The secondary creep strain rate increases with the magnitude of the compressive load. When comparing the two creep models for both box types, the Power law provided the best accuracy at the 50% of box compression test (BCT) load case, while at the other three load cases, the Andrade law showed better predictions.

Does flute angle influence box performance?

AbstractIn the production of boxes, it is customary to align the flutes vertically, corresponding to a 0° flute angle. This configuration is widely believed to yield optimal compressive strength, despite existing evidence from corrugated flute boards and boxes that challenge this assumption. The present study investigates the hypothesis that non-vertical flute angles do not significantly compromise box compression strength and may potentially offer enhancements in other performance characteristics. Regular slotted container boxes (385 × 238 × 300 mm) constructed from single wall C-flute board were used in this study. Ten flute angles were selected for box level testing: 0°, 5°, 7.5°, 10°, 12.5°, 15°, 20°, 30°, 45° and 60°. Samples of converted board were subjected to edge crush testing (ECT) following TAPPI T-811 and four-point-bending following TAPPI T-820. Box crush testing (BCT) followed NZS 1301.800 2006 (New Zealand Standard). Component testing results were consistent with previous studies. Outcomes showed a general linear reduction in ECT with increasing flute angle, and nonlinear relationships between flute angle and bending force and stiffness. At the box level, peak load did not decline significantly between 0° and 45°, however 60° flute angles had significantly lower peak loads (α = 0.05). At certain angles, notably 10° and 30°, less variation in peak load was observed. BCT force and stiffness of the box significantly improved in terms of median and variation at 10° and 30°. Therefore, a flute angle of less than 45° does not significantly reduce compression strength.

Predicting the effect of pallet overhang on the box compression strength

AbstractA corrugated box's compression strength can easily be affected by how the box is used, including pallet overhang which reduces a box's effective compression strength (BCT). The specific impact of a given amount of overhang on BCT remains poorly defined. In the current study, a range of box sizes and constructions were examined in over a dozen single‐side overhang configurations and five adjacent‐side overhang scenarios to identify key factors contributing to loss of strength, producing an average reduction in BCT of up to 40%. These results indicated that common safety factors fit well with adjacent overhang scenarios but overestimate single‐side overhang scenarios. We developed a range of multiple linear and nonlinear regression models, estimating the change in a box's compression strength due to overhang compared with a no‐overhang scenario. The impact of overhang on the short and long sides, whether overhang exists on a single side or adjacent side, box size, and board type were all statistically significant. This work also indicates the need for further research refining the first‐order model and extending it to other materials, box sizes, and box aspect ratios.

Efficient numerical and ANN models for optimization of filler gradation of particulate-filled composites

Based on hard-sphere-like truncated Lennard-Jones interactions, a box compression simulation method, which belongs to molecular statics, was proposed to calculate the random close packing density of spherical particles. This method accurately provides the gradation corresponding to the maximum random close packing density with higher efficiency than the discrete element method (DEM). We trained an artificial neural network (ANN) model based on the data generated using this method to predict the packing densities of ternary and quaternary packing systems and discussed the applicability of this model in design of particulate-filled composites for electronic packaging. We found that the negative correlation between viscosity and random close packing density only applies to fillers of sizes greater than several microns. When the average filler size is reduced to submicron level, the specific surface area becomes the dominant factor in determining the upper limit of filler loading and viscosity of composites.

Evaluation of wave configurations in corrugated boards by experimental analysis (EA) and finite element modeling (FEM): the role of the micro-wave in packaging design

The aim of this paper is to study the mechanical behavior of corrugated board boxes, focusing attention on the strength that the boxes are able to offer in compression under stacking conditions. A preliminary design of the corrugated cardboard structures starting from the definition of each individual layer, namely the outer liners and the innermost flute, was carried out. For this purpose, three distinct types of corrugated board structures that include flutes with different characteristics, namely the high wave (C), the medium wave (B), and even the micro-wave (E), were comparatively evaluated. More specifically, the comparison is able to show the potential of the micro-wave which would eventually allow a significant saving of cellulose in the fabrication process of the boxes, thus reducing the manufacturing costs and causing a lower environmental footprint. First, experimental tests were carried out to determine the mechanical properties of the different layers of the corrugated board structures. Tensile tests were performed on samples extracted from the paper reels used as base material for the manufacturing of the liners and flutes. Instead, the edge crush test (ECT) and box compression test (BCT) were directly performed on the corrugated cardboard structures. Secondly, a parametric finite element (FE) model to allow, on a comparative basis, the study of the mechanical response of the three different types of corrugated cardboard structures was developed. Lastly, a comparison between the available experimental results and the outputs of the FE model was carried out, with the same model being also adapted to evaluate additional structures where the E micro-wave was usefully combined with the B or C wave in a double-wave configuration.

Prediction of Deflection Due to Multistage Loading of a Corrugated Package

With the expansion of overseas markets, transportation distance, storage periods in warehouses, and traffic volume of goods are increasing. In this distribution environment, the safety problem due to the decrease in the strength of the multistacked corrugated package is becoming very important. This study aims to develop a CAE prediction technology for the height change of multistacked corrugated packages, and for this study, the FEA simulation method for existing corrugated packages has been investigated and supplemented. The four-point bending FE model and the box compression test FE model were also constructed based on the simplified and homogenized composite model for the target corrugated fiberboard (double wall of EB-flute) itself. Four-point bending, box compression, and creep tests were performed to obtain the material constant required for FEA simulation. Through the comparison of the F–D curve area between the test and the FEA simulation, parameter optimization that minimizes the area difference was performed using HyperStudy. The FEA simulation and stacking test for the multistacked target corrugated package were performed simultaneously on four actual stacking scenarios with different package weights and package sizes. A comparison of height changes after 72 h of stacking for each of the four scenarios showed that the concordance between the test and FEA simulation was more than 80% in all cases. To further expand the scope of this application, it is necessary to secure additional reliability through continuous comparative monitoring using the test data and physical properties of various corrugated fiberboards.

Comprehensive investigation of corrugated fiberboard boxes with edge vents for ambient loading of Chinese cabbage: Part Ⅱ – Quality changes in cellulose paper- and LLDPE film-wrapped Chinese cabbage stored in ventilated corrugated fiberboard boxes

Consumption of fresh produce has increased in recent years, as have the post-harvest losses during produce distribution. This has generated a need for optimum post-harvest treatment to increase the longevity of the produce. In this study, the temperature and relative humidity for the storage test were set as the refrigerated container conditions (ambient loading) and the quality change in Chinese cabbage wrapped with a cellulose paper sheet or linear low-density polyethylene (LLDPE) film in ventilated corrugated fiberboard boxes was evaluated. Weight loss, trimming loss, total soluble solid, pH, firmness, and color were measured every 10 d from 0 to 30 d. The weight loss values of Chinese cabbage wrapped with cellulose paper and LLDPE film at 30 d were approximately 3.7–4.4% and less than 1%, respectively. The trimming loss and firmness of Chinese cabbage wrapped with an LLDPE film were significantly better than those wrapped with a cellulose paper sheet at 30 d. However, the outer leaf surface measured by color meter was more damaged in Chinese cabbage wrapped with the LLDPE film than in those wrapped with the cellulose paper sheet because the wrapping of the former was tighter than that of the latter. In addition, the reduction in the mechanical properties of the boxes with 0%, 2%, and 3% of vent hole area against the horizontal cross section containing Chinese cabbage was measured at 0 and 30 d by performing not only mechanical property tests, such as edge crush test, bursting strength test, and box compression strength test, but also data logging of relative humidity in the headspace of each box. The relative humidity in the headspace of each box was constant at 75 ± 5% after the first increase during 0–24 h. Further, we evaluated the results of the box compression strength test at 30 d, comparing them with the required box compression strengths calculated by the equations provided in the criteria of the Fibre Box Association and American Society for Testing and Materials D4619. Thus, our findings can explain the changes in the quality of Chinese cabbage and the mechanical properties of corrugated fiberboard boxes prepared using two different internal package treatments.

Compressive Strength of Corrugated Paperboard Packages with Low and High Cutout Rates: Numerical Modelling and Experimental Validation

The finite element method is a widely used numerical method to analyze structures in virtual space. This method can be used in the packaging industry to determine the mechanical properties of corrugated boxes. This study aims to create and validate a numerical model to predict the compression force of corrugated cardboard boxes by considering the influence of different cutout configurations of sidewalls. The types of investigated boxes are the following: the width and height of the boxes are 300 mm in each case and the length dimension of the boxes varied from 200 mm to 600 mm with a 100 mm increment. The cutout rates were 0%, 4%, 16%, 36%, and 64% with respect to the total surface area of sidewalls of the boxes. For the finite element analysis, a homogenized linear elastic orthotropic material model with Hill plasticity was used. The results of linear regressions show very good estimations to the numerical and experimental box compression test (BCT) values in each tested box group. Therefore, the numerical model can give a good prediction for the BCT force values from 0% cutout to 64% cutout rates. The accuracy of the numerical model decreases a little when the cutout rates are high. Based on the results, this paper presents a numerical model that can be used in the packaging design to estimate the compression strength of corrugated cardboard boxes.

Modified Compression Test of Corrugated Board Fruit Tray: Numerical Modeling and Global Sensitivity Analysis.

This article presents a modified configuration of the box compression test (BCT), which reflects the actual behavior of the vegetable or fruit trays during transport and storage. In traditional load capacity tests, trays are treated as classic transport boxes, i.e., they are compressed between two rigid plates, which does not take into account the specific geometry of this type of packaging. Both the boundary conditions and the loads acting on the tray were modified. The paper presents the concept of a new test, as well as numerical models and a sensitivity analysis of the modified BCT to the basic geometrical dimensions of the tray. The conducted research clearly shows that the proposed configuration of the load-bearing capacity test of a tray is closer to the actual operation of the packaging. As a result, most of the parameters that are not active under the conditions of the classical BCT become more important in the new configuration, which corresponds to the observations on the real performance of the packaging.

Compression Strength Estimation of Corrugated Board Boxes for a Reduction in Sidewall Surface Cutouts-Experimental and Numerical Approaches.

Corrugated cardboard boxes are generally used in modern supply chains for the handling, storage, and distribution of numerous goods. These packages require suitable strength to maintain adequate protection within the package; however, the presence and configuration of any cutouts on the sidewalls significantly influence the packaging costs and secondary paperboard waste. This study aims to evaluate the performance of CCBs by considering the influence of different cutout configurations of sidewalls. The compression strength of various B-flute CCB dimensions (200 mm, 300 mm, 400 mm, 500 m, and 600 mm in length, with the same width and height of 300 mm), each for five cutout areas (0%, 4%, 16%, 36%, and 64%) were experimentally observed, and the results were compared with the McKee formula for estimation. The boxes with cutout areas of 0%, 4%, 16%, 36%, and 64% showed a linear decreasing tendency in compression force. A linear relationship was found between compression strength and an increase in cutout sizes. Packages with 0% and 4% cutouts did not show significant differences in compression strength (p < 0.05). Furthermore, this study shows a possible way to modify the McKee estimation for such boxes after obtaining empirical test data since the McKee formula works with a relatively high error rate on corrugated cardboard boxes with sidewall cutouts. Utilizing the numerical and experimental results, a favorable estimation map can be drawn up for packaging engineers to better manage material use and waste. The results of the study showed that the McKee formula does not appropriately estimate the box compression strength for various cutout sizes in itself.

Sensitivity Analysis of Open-Top Cartons in Terms of Compressive Strength Capacity.

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their production. Geometric parameters that define the shape of the packaging may also be optimized in the design process. In this work, in order to select the most important parameters that affect the load capacity of a tray, sensitivity analysis was used. A sensitivity analysis is often the first step in the process of building artificial-intelligence-based surrogates. In the present work, using the example of a specific tray's geometry, the selection of starting parameters was carried out in the first step, based on the Latin hypercube sampling method. In the next step, local sensitivity analyses were performed at twenty selected starting points of the seventeen-dimensional space of the selected parameters. Based on the obtained results, it was possible to select the parameters that have a significant impact on the load capacity of the tray in the box compression test and whose influence is negligible or insignificant.

Experimental and Numerical Investigation of the In-Plane Compression of Corrugated Paperboard Panels

Finite element analysis (FEA) has been proven as a useful design tool to model corrugated paperboard boxes, and is capable of accurately predicting load capacity. The in-plane deformation, however, is usually significantly underpredicted. To investigate this discrepancy, a panel compression test jig, that implemented simply supported boundary conditions, was built to test individual panels. The panels were then modelled using non-linear FEA with a linear material model. The results show that the in-plane deformation was still underpredicted, but a general improvement was seen. Three discrepancies were identified. The first was that the panels showed an initial region of low stiffness that was not present in the FEA results. This was attributed to imperfections in the panels and jig. Secondly, the experimental results reported a lower stiffness than the FEA. Applying an initial imperfection in the shape of the first buckling mode shape was found to reduce the FEA stiffness. Thirdly, the panels showed a decrease in stiffness near failure, which was not seen in the FEA. A bi-linear material model was investigated and holds the potential to improve the results. Box compression tests were performed on a Regular Slotted Container (RSC) with the same dimensions as the tested panel. The box displaced 13.1 mm compared to 3.5 mm for the panel. There was an initial region of low stiffness, which accounted for 7 mm of displacement compared to 0.5 mm for the panels. Thus, box complexities such as horizontal creases should be included in finite element (FE) models to accurately predict the in-plane deformation, while a bi-linear (or any other non-linear) material model may be useful for panel compression.

Torsional and compression loading of paperboard packages: Experimental and FE analysis

The present study investigates torsional and compressive loading of a paperboard package. Finite element (FE) analyses simulating the tests were performed to improve understanding of the stresses and deformations in the paperboard during loading. A simple experimental characterization of the necessary material properties could be performed to represent the multi‐ply paperboard as a single‐ply structure. The results from the single‐ply model were compared with a laminate model, and the differences between the models were small. Comparing experimental and FE simulations of box compression and torsion showed that the FE models could accurately predict the response curves. However, in the simulations, there was an overprediction of the maximum compressive force and maximum torque, which was expected since geometrical imperfections and the heterogeneous internal structure of the material were not accounted for in the material model or the FE model. Local yield lines formed at the onset of non‐linearities in the package load–displacement curves. Therefore, the strength of the paperboard affects the maximum compressive strength and maximum torque, and the bending stiffness of the paperboard only had a minor effect. When a first local maximum was reached, the number of FE that reached the failure stress increased exponentially. The simulations also showed that box compression was not an effect of package height, but higher packages had a lower maximum torque.

Edge crush testing methods and box compression modeling

While multiple test procedures have been developed to assess the inherent compressive strength of corrugated materials (edge crush test, ECT), limited work has explored the appropriateness of each in the context of box compression modeling. This study incorporates a variety of real-world samples, highlighting the varying challenges different ECT methods face in measuring the intrinsic compressive resistance of combined corrugated board. We examine each of these methods as inputs for different types of models, as well as discuss the propagation of measurement variation through the modeling effort. By highlighting the cases in which a given ECT method no longer proves to be an optimal parameter in box compression strength modeling, we explore how we might better measure this material property.

The Effect of Side Wall Cutout Sizes on Corrugated Box Compression Strength in the Function of Length-to-Width Ratios—An Experimental Study

Packaging made from corrugated cardboard is a widely used solution in modern supply chains for the handling, storage and distribution of goods. These packages are required to maintain adequate protection conditions; however, in many cases, the cardboard box dimensions, handles and/or ventilation holes, quality and their configuration could compromise its protection strength. This study observes and evaluates the performance of corrugated cardboard boxes made with B-flute boards by considering different cutout sizes from the side walls (0%, 20%, 40%, 60% and 80%) in various box length–width ratios of 200 mm, 300 mm, 400 mm, 500 mm and 600 mm in length and a constant 300 mm width and height. Box compression tests were performed in a laboratory, and results were compared with mathematical statistics. In each cutout case, the maximum compression force was observed with the box with dimensions of 400 × 300 × 300 mm. The measurement results showed that the 1.33 length-to-width ratio has the best maximum compression force result. The statistical tests showed that there is no significant difference between the 0% and 20% cutout groups.

Influence of pallet pattern on top-to-bottom compression performance of unitized loads

Environmental scaling factors estimate a corrugated container’s ability to withstand various conditions it will encounter during the storage and distribution process. In this project, we examined the compressive resistance of unitized loads using differing pallet stacking patterns. To simulate real-world failure scenarios in our laboratory tests, we used two different nominal board grades of single-wall C-flute regular slotted containers loaded with a plywood panel and bagged salt to direct the failure location to the bottom of the stack. Our results showed that the columnar aligned pattern provided the greatest compressive resistance and the interlocked stacking arrangement yielded the lowest of the patterns evaluated. Based on the study results, we calculated box compression retention multipliers for each pattern and compared them to scaling factors published by the Fibre Box Association.

Investigation of the Effect of Pallet Top-Deck Stiffness on Corrugated Box Compression Strength as a Function of Multiple Unit Load Design Variables.

Unit loads consisting of a pallet, packages, and a product securement system are the dominant way of shipping products across the United States. The most common packaging types used in unit loads are corrugated boxes. Due to the great stresses created during unit load stacking, accurately predicting the compression strength of corrugated boxes is critical to preventing unit load failure. Although many variables affect the compression strength of corrugated boxes, recently, it was found that changing the pallet’s top deck stiffness can significantly affect compression strength. However, there is still a lack of understanding of how these different factors influence this phenomenon. This study investigated the effect of pallet’s top-deck stiffness on corrugated box compression strength as a function of initial top deck thickness, pallet wood species, box size, and board grade. The amount of increase in top deck thickness needed to lower the board grade of corrugated boxes by one level from the initial unit load scenario was determined using PDS™. The benefits of increasing top deck thickness diminish as the initial top deck thickness increases due to less severe pallet deflection from the start. The benefits were more pronounced as higher board grade boxes were initially used, and as smaller-sized boxes were used due to the heavier weights of these unit loads. Therefore, supposing that a company uses lower stiffness pallets or heavy corrugated boxes for their unit loads, this study suggests that they will find more opportunities to optimize their unit loads by increasing their pallet’s top deck thickness.

Mechanical Behavior Modeling of Containers and Octabins Made of Corrugated Cardboard Subjected to Vertical Stacking Loads.

The aim of this paper is to characterize the mechanical behavior of corrugated cardboard boxes using simple models that allow an approach to the load capacity and the deformation of the boxes. This is very interesting during a box design stage, in which the box does not exist yet. On the one hand, a mathematical model of strength and deformation of boxes with different geometry is obtained from experiments according to the Box Compression Test and Edge Crush Test standards. On the second hand, a finite element simulation is proposed in which only the material elastic modulus in the compression direction is needed. For that, corrugated cardboard sheets are glued to build billets for testing, and an equivalent elastic modulus is obtained. This idea arises from the fact that the collapse of the box is given by the local bucking of the corrugated cardboard panels, due to the slenderness itself, and the properties in the compression direction are predominant. As a result, the numerical models show satisfactory agreement with experiments, concluding that it is an adequate methodology to simulate in a simple and efficient way this type of boxes built with corrugated cardboard.