scholarly journals Distribution of Bending Stiffness of Orthotropic Fibrous Material Based on an Example of Corrugated Board

2020 ◽  
Vol 28 (3(141)) ◽  
pp. 50-54
Author(s):  
Zbigniew Kołakowski ◽  
Włodzimierz Szewczyk ◽  
Maria Bieńkowska
Keyword(s):  
Fibrous Material ◽  
Bending Stiffness ◽  
Cross Direction ◽  
Corrugated Board ◽  
Practical Usefulness

Commonly known methods for calculating the bending stiffness of corrugated board allow to calculate values related to the machine and cross direction of corrugated board but do not allow to calculate bending stiffness in any intermediate direction. The article presents a method for calculating bending stiffness in any direction in the plane of corrugated board, on the basis of the bending stiffness values in the machine and cross direction. Comparing the results of measurements of bending stiffness in selected directions with those of their calculations, the method proposed was verified and its practical usefulness confirmed.

Prediction of box failure from paper data for asymmetric corrugated board

TAPPI Journal ◽  
2018 ◽  
Vol 17 (08) ◽  
pp. 429-434 ◽  
Author(s):  
Heinz Joachim Schaffrath ◽  
Felix Reichenbach ◽  
Samuel Schabel
Keyword(s):  
Compression Test ◽  
Elastic Moduli ◽  
Bending Stiffness ◽  
Machine Direction ◽  
Paper Properties ◽  
Cross Direction ◽  
Corrugated Board ◽  
Influencing Parameters ◽  
Theoretical Considerations

The well-known McKee formula was derived in 1963 for symmetric fluting constructions. This paper presents investigations showing the influence of asymmetric properties, either geometric or concerning the elastic moduli. Paper properties of the base papers used are taken to calculate the panel properties of corrugated boards. From these results, the box failure is predicted. To do this, a model approximating the corrugated medium by triangles is presented. With this assumption, the bending stiffness of corrugated board, no matter how many flutes, can be predicted from paper data. Machine direction and cross direction are treated separately. The theoretical considerations are verified by measuring paper parameters such as short compression test (SCT), thickness, and bending stiffness, as well as edge compression test (ECT) and bending stiffness of corrugated board and box compression test (BCT) of the boxes. It can be stated that the prediction of using paper data instead of corrugated board data may lead to even better prediction results, as the measuring of bending stiffness at the board may sometimes be influenced by sampling inconveniences. Finally, thickness of the used base papers, as well as thickness of the manufactured board, appear to be the main influencing parameters. The McKee formula is robust enough to be applied for asymmetric corrugated board as well.

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.

Relating bending stiffness measurements across various free span lengths

TAPPI Journal ◽  
2020 ◽  
Vol 19 (8) ◽  
pp. 419-424
Author(s):  
DOUGLAS CASH ◽  
BENJAMIN FRANK
Keyword(s):  
Intrinsic Property ◽  
Standard Test ◽  
Bending Stiffness ◽  
Test Method ◽  
Corrugated Board ◽  
Different Types ◽  
Practical Tool ◽  
Bending Behavior ◽  
The Relationship ◽  
Corrugated Fiberboard

Bending stiffness should be an intrinsic property of a material, so it is puzzling that the TAPPI Standard Test Method T 836 “Bending stiffness, four point method” specifies span lengths when testing different types of corrugated fiberboard. These specified spans often limit the samples that can be measured with this method. To better understand the relationship between bending stiffness and span length, we performed measurements on a range of materials at different spans. The results provide a practical tool enabling comparison of bending stiff-ness measurements made at various span lengths. Additionally, this note discusses several areas that could serve as the foundation for more fundamental work exploring the bending behavior of corrugated board.

Multiple recycling of paperboard: Paperboard characteristics and maximum number of recycling cycles— Part I: Multiple recycling of corrugated base paper

TAPPI Journal ◽  
2019 ◽  
Vol 18 (11) ◽  
pp. 631-638
Author(s):  
FREDERIC KREPLIN ◽  
HANS-JOACHIM PUTZ ◽  
SAMUEL SCHABEL
Keyword(s):  
Compression Test ◽  
Production Capacity ◽  
Strength Properties ◽  
Paper Properties ◽  
Corrugated Board ◽  
Laboratory Conditions ◽  
Base Paper ◽  
Study Results ◽  
Short Span ◽  
Multiple Recycling

Paper for recycling is an important fiber source for the production of corrugated base paper. The change in production capacity toward more and more packaging papers affects the composition of paper for recycling and influences the paper quality. This research project investigated the influence of the multiple recycling of five different corrugated base papers (kraftliner, neutral sulfite semichemical [NSSC] fluting, corrugating medium, testliner 2, and testliner 3) on suspension and strength properties under laboratory conditions. The corrugated board base papers were repulped in a low consistency pulper and processed into Rapid-Köthen laboratory sheets. The sheets were then recycled up to 15 times in the same process. In each cycle, the suspension and the paper properties were recorded. In particular, the focus was on corrugated board-specific parameters, such as short-span compression test, ring crush test, corrugating medium test, and burst. The study results indicate how multiple recycling under laboratory conditions affects fiber and paper properties.

CALCULATION-EXPERIMENTAL METHOD FOR DEFINITION OF LOWEST FREQUENCY IN BENDING VIBRATIONS OF COACH CAR BODY IN VERTICAL PLANE BASED ON IDENTIFICATION OF ITS BENDING STIFFNESS

2020 ◽  
Vol 2020 (9) ◽  
pp. 35-46
Author(s):  
Aleksandr Skachkov ◽  
Viktor Vasilevskiy ◽  
Aleksey Yuhnevskiy
Keyword(s):  
Least Squares Method ◽  
Vertical Plane ◽  
Bending Stiffness ◽  
Dimensional Problem ◽  
Euler Beam ◽  
Bending Vibrations ◽  
Car Body ◽  
Variable Function ◽  
Experimental Values ◽  
Definition Of

The consideration of existing methods for a modal analysis has shown a possibility for the lowest frequency definition of bending vibrations in a coach car body in a vertical plane based on an indirect method reduced to the assessment of the bending stiffness of the one-dimensional model as a Bernoulli-Euler beam with fragment-constant parameters. The assessment mentioned can be obtained by means of the comparison of model deflections (rated) and a prototype (measured experimentally upon a natural body) with the use of the least-squares method that results in the necessity of the solution of the multi-dimensional problem with the reverse coefficient. The introduction of the hypothesis on ratability of real bending stiffness of the prototype and easily calculated geometrical stiffness of a model reduces a multi-dimensional problem incorrect according to Adamar to the simplest search of the extremum of one variable function. The procedure offered for the indirect assessment of bending stiffness was checked through the solution of model problems. The values obtained are offered to use for the assessment of the lowest frequency of bending vibrations with the aid of Ritz and Grammel methods. In case of rigid poles it results in formulae for frequencies into which there are included directly the experimental values of deflections.

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