scholarly journals Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Perforations

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 1095
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Jakub Krzysztof Grabski
Keyword(s):  
Compressive Strength ◽  
Estimation Error ◽  
Analytical Formula ◽  
Shear Stiffness ◽  
Element Model ◽  
Numerical Approach ◽  
Analytical Framework ◽  
Width Ratio ◽  
Corrugated Board ◽  
Corrugated Cardboard

This paper presents a modified analytical formula for estimating the static top-to-bottom compressive strength of corrugated board packaging with different perforations. The analytical framework is based here on Heimerl’s assumption with an extension from a single panel to a full box, enhanced with a numerically calculated critical load. In the proposed method, the torsional and shear stiffness of corrugated cardboard, as well as the panel depth-to-width ratio is implemented in the finite element model used for buckling analysis. The new approach is compared with the successful though the simplified McKee formula and is also verified with the experimental results of various packaging designs made of corrugated cardboard. The obtained results indicate that for boxes containing specific perforations, simplified methods give much larger estimation error than the analytical–numerical approach proposed in the article. To the best knowledge of the authors, the influence of the perforations has never been considered before in the analytical or analytical–numerical approach for estimation of the compressive strength of boxes made of corrugated paperboard. The novelty of this paper is to adopt the method presented to include perforation influence on the box compressive strength estimation.

scholarly journals Estimation of the Compressive Strength of Corrugated Cardboard Boxes with Various Openings

Energies ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 155
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Jakub Krzysztof Grabski
Keyword(s):  
Compressive Strength ◽  
Numerical Method ◽  
Analytical Approach ◽  
Estimation Error ◽  
Shear Stiffness ◽  
Analytical Framework ◽  
Critical Force ◽  
Width Ratio ◽  
Corrugated Cardboard ◽  
Hole Dimensions

This paper presents mixed analytical/numerical method for estimating the static top-to-bottom compressive strength of corrugated packaging with different ventilation openings and holes, in which the torsional and shear stiffness of corrugated cardboard as well as the panel depth-to-width ratio are included. Analytical framework bases on Heimerls assumption with a modification to a critical force, which is here computed by a numerical algorithm. The proposed method is compared herein with the successful McKee formula and is verified with the large number of experiment results of various packaging designs made of different qualities of corrugated cardboard. The results show that, for various hole dimensions or location of openings in no-flap and flap boxes, the estimation error may be reduced up to three times than in the simple analytical approach.

scholarly journals The Role of Buckling in the Estimation of Compressive Strength of Corrugated Cardboard Boxes

Materials ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 4578 ◽  
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Jakub Krzysztof Grabski
Keyword(s):  
Compressive Strength ◽  
Analytical Approach ◽  
Estimation Error ◽  
Full Range ◽  
Shear Stiffness ◽  
Width Ratio ◽  
Force Estimation ◽  
Corrugated Cardboard ◽  
Precise Prediction

This paper presents analytical methods for estimating the static top-to-bottom compressive strength of simple corrugated packaging, in which the torsional and shear stiffness of corrugated cardboard as well as the panel depth-to-width ratio are included. The methods are compared herein with a basic and more detailed buckling description with the successful McKee formula, which is over fifty years old but still widely used among packaging designers and quality control departments. Additionally, the assumptions and applied simplifications used in the literature are analyzed, and the limits of applicability of different versions of the selected methods are checked. Finally, all approaches are verified with the experiment results of various packaging designs made of corrugated cardboard. The results show that, for certain proportions of dimensions of simple flap boxes, simplified methods give an even two times larger estimation error than the analytical approach proposed in the paper. Furthermore, it is evidenced that including all flexural, torsional and shear stiffnesses in the buckling force estimation gives a very precise prediction of the box compressive strength for the full range of package dimensions.

Corrugated Board Flute-Shaped Finite Element Analysis and Optimization

2013 ◽  
Vol 477-478 ◽  
pp. 1205-1209 ◽  
Author(s):  
Wei Yuan ◽  
Gai Mei Zhang ◽  
Da Zhi Liao ◽  
Jing Liu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compressive Strength ◽  
Gradual Transition ◽  
Radius Of Curvature ◽  
Element Analysis ◽  
Corrugated Board ◽  
Key Points ◽  
Corrugated Cardboard ◽  
Corrugated Structure

UV-shaped corrugated cardboard Fusion V-shaped and U-shaped structure the advantages made, to make up for the lack of V-type and two U-shaped corrugated cardboard, the higher the compressive strength, good elasticity, is widely used UV type corrugated manufacturing corrugated board. But no strict standards for UV-shaped concrete structure of corrugated board size parameter corresponding corrugating roll no uniform size of the corrugated shape, in order to achieve the best elasticity and compressive strength. First, by mathematical methods, the corrugated structure is analyzed, and analysis to facilitate research, to select the 1/4 cycle corrugated. Create multiple vertical auxiliary line level is divided into 10 equal parts, to identify key points in shape between the V-shaped and U-shaped curve, connecting into multiple segments curve. Studied the actual thickness of the corrugated board of 3.8mm, a smaller thickness and therefore a straight line can be connected to each group of the resultant key points simplify the corrugated curve, model 1/4 of a cycle of UV-shaped corrugated first determined, using the symmetry of the model to establish a cycle, 300mm side length of the square created by one cycle of replication, about 38 of the corrugated board corrugated cycle. Use of finite element analysis in ANSYS corrugated structure, including a gradual transition to a simplified model of the 11 U-shaped flute-shaped corrugated cardboard from the V-shaped set of material properties, loads are cloth pressure, research corrugated cardboard stress and strain, i.e., the smaller the radius of curvature of the curve can be obtained along corrugated, the closer the U-shaped, corrugated board having a larger strain, i.e. has good flexibility, consistent with the empirical data to prove the feasibility of this analysis method.

scholarly journals Analytical Determination of the Bending Stiffness of a Five-Layer Corrugated Cardboard with Imperfections

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 663
Author(s):  
Tomasz Garbowski ◽  
Anna Knitter-Piątkowska
Keyword(s):  
Load Capacity ◽  
Element Model ◽  
Critical Discussion ◽  
Bending Stiffness ◽  
Analytical Determination ◽  
Published Data ◽  
Corrugated Board ◽  
Correct Determination ◽  
Corrugated Cardboard

Bending stiffness (BS) is one of the two most important mechanical parameters of corrugated board. The second is edge crush resistance (ECT). Both are used in many analytical formulas to assess the load capacity of corrugated cardboard packaging. Therefore, the correct determination of bending stiffness is crucial in the design of corrugated board structures. This paper focuses on the analytical determination of BS based on the known parameters of the constituent papers and the geometry of the corrugated layers. The work analyzes in detail the dependence of the bending stiffness of an asymmetric, five-layer corrugated cardboard on the sample arrangement. A specimen bent so that the layers on the lower wave side are compressed has approximately 10% higher stiffness value. This is due to imperfections, which are particularly important in the case of compression of very thin liners. The study showed that imperfection at the level of a few microns causes noticeable drops in bending stiffness. The method has also been validated by means of experimental data from the literature and simple numerical finite element model (FEM). The obtained compliance of the computational model with the experimental model is very satisfactory. The work also included a critical discussion of the already published data and observations of other scientists in the field.

The Finite Element Study of the Compressive Strength of Typical Waveform Corrugated Box

2012 ◽  
Vol 262 ◽  
pp. 390-394 ◽  
Author(s):  
Wei Yuan ◽  
Wen Cai Xu ◽  
Gai Mei Zhang ◽  
Li Hua Xie
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Compressive Strength ◽  
Optimization Design ◽  
Element Model ◽  
Element Analysis ◽  
Corrugated Board ◽  
The Finite Element Analysis ◽  
The Finite Element Model ◽  
Element Study

The finite element model of a 0201 V-shaped, U-shaped, and UV-shaped single corrugated board corrugated boxes are established. The stress distribution and strain of the three types of waveform corrugated box to withstand the pressure of the top surface stacking are calculated. Three kinds of corrugated board compression are analyzed. Analysis of the structure shows that the V-shaped corrugated board has good rigidity, U-type corrugated box has good cushioning properties, and the range during which the UV type is a better choice. This is consistent with the experimental results, prove the validity of the finite element analysis, and provide data basis for optimization design of the shape of the corrugated board corrugated waveform.

scholarly journals Crushing of Double-Walled Corrugated Board and Its Influence on the Load Capacity of Various Boxes

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4321
Author(s):  
Tomasz Gajewski ◽  
Tomasz Garbowski ◽  
Natalia Staszak ◽  
Małgorzata Kuca
Keyword(s):  
Load Capacity ◽  
Analytical Techniques ◽  
Shear Stiffness ◽  
Mechanical Tests ◽  
Torsional Stiffness ◽  
Bending Test ◽  
Corrugated Board ◽  
Four Point Bending ◽  
Residual Thickness ◽  
Corrugated Cardboard

As long as non-contact digital printing remains an uncommon standard in the corrugated packaging industry, corrugated board crushing remains a real issue that affects the load capacity of boxes. Crushing mainly occurs during the converting of corrugated board (e.g., analog flexographic printing or laminating) and is a process that cannot be avoided. However, as this study shows, it can be controlled. In this work, extended laboratory tests were carried out on the crushing of double-walled corrugated board. The influence of fully controlled crushing (with a precision of ±10 μm) in the range from 10 to 70% on different laboratory measurements was checked. The typical mechanical tests—i.e., edge crush test, four-point bending test, shear stiffness test, torsional stiffness test, etc.—were performed on reference and crushed specimens. The residual thickness reduction of the crushed samples was also controlled. All empirical observations and performed measurements were the basis for building an analytical model of crushed corrugated board. The proven and verified model was then used to study the crushing effect of the selected corrugated board on the efficiency of simple packages with various dimensions. The proposed measurement technique was successfully used to precisely estimate and thus control the crushing of corrugated board, while the proposed numerical and analytical techniques was used to estimate the load capacity of corrugated board packaging. A good correlation between the measured reduced stiffness of the corrugated cardboard and the proposed analytical predictive models was obtained.

scholarly journals Crushing of Single-Walled Corrugated Board During Converting: Experimental and Numerical Study

2021 ◽  
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Damian Mrówczyński ◽  
Radosław Jędrzejczak
Keyword(s):  
Numerical Study ◽  
Shear Stiffness ◽  
Calculation Model ◽  
Basic Material ◽  
Corrugated Board ◽  
Material Stiffness ◽  
Residual Thickness ◽  
Corrugated Cardboard ◽  
Recycled Fibers ◽  
The Impact

Corrugated cardboard is an ecological material, mainly because, in addition to virgin cellulose fibers also the fibers recovered during recycling process are used in its production. However, the use of recycled fibers causes slight deterioration of the mechanical properties of the corrugated board. In addition, converting processes such as printing, die-cutting, lamination, etc. cause micro-damage in the corrugated cardboard layers. In this work, the focus is precisely on the crushing of corrugated cardboard. A series of laboratory experiments were conducted, in which the different types of single-walled corrugated cardboards were pressed in a fully controlled manner to check the impact of the crush on the basic material parameters. The amount of crushing (with a precision of 10 micrometers) was controlled by a precise FEMat device, for crushing the corrugated board in the range from 10 to 70 % of its original thickness. In this study, the influence of crushing on bending, twisting and shear stiffness as well as a residual thickness and edge crush resistance of corrugated board was investigated. Then, a procedure based on a numerical homogenization, taking into account a partial delamination in the corrugated layers to determine the degraded material stiffness was proposed. Finally, using the empirical-numerical method, a simplified calculation model of corrugated cardboard was derived, which satisfactorily reflects the experimental results.

Optimization of the Effective Shear Properties of a Bidirectionally Corrugated Sandwich Core Structure

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Camille C. Besse ◽  
Dirk Mohr
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
Element Model ◽  
Core Structure ◽  
Tool Geometry ◽  
Width Ratio ◽  
Four Point Bending ◽  
Representative Unit Cell ◽  
Sandwich Core ◽  
Dome Shape

The transverse shear stiffness of a newly-developed all-metal sandwich core structure is determined experimentally and numerically. The core structure is composed of a periodic array of domes which are introduced into an initially flat sheet through stamping. A finite element model of the stamping process is built and validated experimentally. A parametric study is performed to choose the stamping tool geometry such that the resulting core structure provides maximum shear stiffness for a given relative density. It is found that the optimal geometries for relative densities ranging from 0.2 to 0.35 all feature the same dome shape with the same height-to-width ratio. The simulation results also show that the estimated transverse shear strength of the proposed core structure is the same as that of hexagonal honeycombs of the same weight for high relative densities (greater than 0.35), but up to 30% smaller for low relative densities (lower than 0.2). In addition to numerical simulations of a representative unit cell, four-point bending experiments are performed on brazed prototype sandwich beams to validate the computational model.

Corrugated Board UV Flute-Shaped Structure Size Optimization Design Based on the Finite Element

2013 ◽  
Vol 469 ◽  
pp. 213-216
Author(s):  
Wei Yuan ◽  
Jin Xin Sun ◽  
Gai Mei Zhang ◽  
Da Zhi Liao ◽  
Ya Jun Wang
Keyword(s):  
Finite Element ◽  
Compressive Strength ◽  
Optimization Design ◽  
Gradual Transition ◽  
Radius Of Curvature ◽  
Element Analysis ◽  
Corrugated Board ◽  
Key Points ◽  
Corrugated Cardboard ◽  
Corrugated Structure

UV-shaped corrugated cardboard Fusion V-shaped and U-shaped structure the advantages made, to make up for the lack of V-type and two U-shaped corrugated cardboard, the higher the compressive strength, good elasticity, is widely used UV type corrugated manufacturing corrugated board. But no strict standards for UV-shaped concrete structure of corrugated board size parameter corresponding corrugating roll no uniform size of the corrugated shape, in order to achieve the best elasticity and compressive strength. First, by mathematical methods, the corrugated structure is analyzed, and analysis to facilitate research, to select the 1/4 cycle corrugated. Create multiple vertical auxiliary line level is divided into 10 equal parts, to identify key points in shape between the V-shaped and U-shaped curve, connecting into multiple segments curve. Studied the actual thickness of the corrugated board of 3.8mm, a smaller thickness and therefore a straight line can be connected to each group of the resultant key points simplify the corrugated curve, model 1/4 of a cycle of UV-shaped corrugated first determined, using the symmetry of the model to establish a cycle, 300mm side length of the square created by one cycle of replication, about 38 of the corrugated board corrugated cycle. Use of finite element analysis in ANSYS corrugated structure, including a gradual transition to a simplified model of the 11 U-shaped flute-shaped corrugated cardboard from the V-shaped set of material properties, loads are cloth pressure, research corrugated cardboard stress and strain, i.e., the smaller the radius of curvature of the curve can be obtained along corrugated, the closer the U-shaped, corrugated board having a larger strain, i.e. has good flexibility, consistent with the empirical data to prove the feasibility of this analysis method.

scholarly journals Crushing of Single-Walled Corrugated Board during Converting: Experimental and Numerical Study

Energies ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 3203
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski ◽  
Damian Mrówczyński ◽  
Radosław Jędrzejczak
Keyword(s):  
Numerical Study ◽  
Shear Stiffness ◽  
Calculation Model ◽  
Basic Material ◽  
Corrugated Board ◽  
Material Stiffness ◽  
Residual Thickness ◽  
Corrugated Cardboard ◽  
Recycled Fibers ◽  
The Impact

Corrugated cardboard is an ecological material, mainly because, in addition to virgin cellulose fibers also the fibers recovered during recycling process are used in its production. However, the use of recycled fibers causes slight deterioration of the mechanical properties of the corrugated board. In addition, converting processes such as printing, die-cutting, lamination, etc. cause micro-damage in the corrugated cardboard layers. In this work, the focus is precisely on the crushing of corrugated cardboard. A series of laboratory experiments were conducted, in which the different types of single-walled corrugated cardboards were pressed in a fully controlled manner to check the impact of the crush on the basic material parameters. The amount of crushing (with a precision of 10 micrometers) was controlled by a precise FEMat device, for crushing the corrugated board in the range from 10 to 70% of its original thickness. In this study, the influence of crushing on bending, twisting and shear stiffness as well as a residual thickness and edge crush resistance of corrugated board was investigated. Then, a procedure based on a numerical homogenization, taking into account a partial delamination in the corrugated layers to determine the degraded material stiffness was proposed. Finally, using the empirical-numerical method, a simplified calculation model of corrugated cardboard was derived, which satisfactorily reflects the experimental results.

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