Comparison Studies on Dynamic Packaging Properties of Corrugated Paperboard Pads

Transcription

1 Engineering, 2010, 2, doi: /eng Published Online May 2010 ( Coparison Studies on Dynaic Packaging Properties of Corrugated Paperboard Pads Abstract Yanfeng Guo 1, Wencai Xu 2, Yungang Fu 1, Wei Zhang 1 1 Departent of Packaging Engineering, Xi an University of Technology, Xi an, China 2 Departent of Packaging Engineering, Beijing Institute of Graphic Counication, Beijing, China E-ail: {guoyf, fygpack, zhang_wei}@xaut.edu.cn, xuwencai@263.net Received Deceber 17, 2009; revised February 23, 2010; accepted February 26, 2010 Corrugated paperboard is a kind of inexpensive and environental-friendly packaging aterial, and ay be ade into pads of package cushioning to protect products fro shock and vibration daage by isolation during distribution. This article deals with the characterization of dynaic packaging properties of corrugated paperboard pads, such as dynaic cushioning curves, vibration transissibility and frequency curves. The ain feature of article is the evaluation on the dynaic shock cushioning property and vibration transissibility of corrugated paperboard pads by a series of experiental studies on the drop shock tester and vibration tester, the establishent of experiental forulas of dynaic cushioning curves, and the analysis of resonance frequencies and vibration transissibility. By using the fitting polynoial of curve and ethod of the least ean square, the experiental forulas with third order polynoial function of dynaic cushioning curves for corrugated paperboard pads are obtained. By using linear vibration theory with single degree of freedo, the resonance frequencies, vibration transissibility and daping ratios of corrugated paperboard pads at different static loads are acquired. All results show the dynaic properties relevant to design applications of corrugated paperboard pads for protective packaging. Keywords: Corrugated Paperboard Pads, Dynaic Shock Cushioning Property, Dynaic Cushioning Curve, Vibration Transissibility, Resonance Frequency 1. Introduction Corrugated paperboard is a kind of inexpensive and environental-friendly packaging aterial with corrugated sandwich structure, holds lightweight, high strength-toweight and stiffness-to-weight ratios, and has econoic and environental advantages over plastic foas [1,2]. It also has excellent achining technology of packaging, and ay be ade into pads of package cushioning to protect products fro shock and vibration daage by isolation during distribution. The usual technology is to interpose the corrugated paperboard pad between the product and the container to provide the necessary isolation [3-5]. So, there is an increasing interest in utilizing corrugated paperboard pads for protective packaging of products (e.g. precise equipent and instruent, household appliance and fragile goods etc). For corrugated paperboard, the copressive strength, crush strength, bending defection and flexural stiffness, creep property and recoverability were investigated by Hahn, Lee, Urbanik, Guo et al. [6-9]. By using soe finite eleent odels and coercial finite eleent code ABAQUS or ANSYS, the echanical behaviors of corrugated paperboard such as buckling, transverse shear, elasticity, stability, collapse and ultiate failure were studied by Gilchrist, Nordstrand, Aboura, Rai, Talbi et al. [10-14]. Within the finite eleent odels (e.g. thin shell eleent, siplified hoogenization odel), both geoetric nonlinearity (large deforation) and aterial nonlinearity (anisotropy or orthotropy) effects were considered. The cushioning property and its predictive odel, the vibration transissibility and frequency response of single-wall corrugated paperboard were analyzed by Sek et al. [15,16]. But for the corrugated paperboard pads (e.g. single layer pad, two layers pad, three layers pad), the lack of dynaic packaging properties such as dynaic cushioning curves and vibration transissibility hapers its application for protective packaging of products [4-5]. Therefore the ais of this research work are as follows: Firstly, evaluate the dy-

2 Y. F. GUO ET AL. 379 naic shock cushioning property of corrugated paperboard pads by drop shock tests, and establish the experiental forulas of dynaic cushioning curves. Secondly, study the vibration transissibility of corrugated paperboard pads at different static loads by vibration tests, and analyze the resonance frequencies, vibration transissibility and daping ratios. 2. Structure of Corrugated Paperboard Pads The structure of corrugated paperboard pads usually covers single layer corrugated paperboard pad in Figure 1(a), two layers corrugated paperboard pad in Figure 1(b), and three layers corrugated paperboard pad in Figure 1(c). The difference of these pads is the layer quantity (or thickness of pad). The thicknesses of single layer pad, two layers pad, three layers pad are 7.81, and 23.43, respectively. The top surface of all test speciens is square, and the diension is 15 c 15 c. They would be respectively called single layer pad, two layers pad, three layers pad for short. These corrugated paperboard pads are also ade of double-wall corrugated paperboard with A and B flutes by achining technology of cutting, folding and pasting. The single layer pad is directly ade of the double-wall corrugated paperboard, the structure of two layers pad coprises two layers of the double-wall corrugated paperboard, and the structure of three layers pad consists of three layers of the double-wall corrugated paperboard. The thickness of double-wall corrugated paperboard with A and B flutes is 7.81, the corrugated cores and inner sheet are corrugated paper with graage of 150 g/ 2, and the face sheets are kraft linerboard with graage of 250 g/ 2. Before each of tests, all test (a) (b) (c) Figure 1. Photograph of corrugated paperboard pads. speciens of corrugated paperboard pads should be preconditioned to equilibriu in air uniforly aintained for at least 24 hours at abient teperature 23 and relative huidity 60%. 3. Description of Dynaic Packaging Properties 3.1. Description of Dynaic Shock Cushioning Property The dynaic shock cushioning property describes the capability of absorbing drop shock energy of corrugated paperboard pads, and reflects the relationship between peak acceleration and static stress during drop shock. The peak acceleration is a non-diension ratio of peak acceleration of the packaged ite to gravity acceleration. It is usually presented as a faily of dynaic cushioning curves (or peak acceleration and static stress curve), which shows peak acceleration during drop shock for a range of static loads and is constructed for several drop heights [3]. The test syste for dynaic shock cushioning property (Figure 2) shall consist of a drop shock tester, a signal acquisition & processing device, a set of Data Acquisition & Signal Processing Engineering Technology (DASP-ET) software. The drop shock tester has a drop block and weight (to represent the packaged ite) and ipact base for dynaic loading of a test specien to siulate drop shock in handling. The weight is ounted on the drop block. The ass of weight and drop height of the drop block are adjustable. An acceleration sensor is ounted on the drop block, and the signal output fro the acceleration sensor is firstly fed into the signal acquisition & processing device, then the drop shock acceleration and tie curve ay be read and displayed by DASP-ET. While the drop block with the weight ipacts the test specien of corrugated paperboard pad fro a predeterined drop height by eans of area contact, according to the law of conservation of energy, the potential energy of weight and drop block shall be transferred as the kinetic energy of weight and drop block and the deforation energy of test specien [3]. The relationship ay be described as the following expression 1 2 ( ) ( ) (1) 2 V AT d g h T 0 where stands for ass of drop block and weight, V is ipact velocity of weight and drop block, A is contact area between test specien and drop block, T is thickness of test specien, σ and ε are copression stress and strain of test specien, and h is a predeterined drop height. When the ipact velocity of weight and drop block becoes zero (V = 0), the axiu deforation

3 380 Y. F. GUO ET AL. Figure 2. Test syste of dynaic shock cushioning property: 1.Weight; 2.Drop block; 3.Guide colun; 4.Test specien 5. Acceleration sensor. of test specien is reached, and the axiu stress of test specien and peak acceleration G would be occurred, and Equation (1) ay be rewritten as g h h ( ) d ( ) ( ) (2) 0 s A T T where s is static stress exerted on test specien. In addition, according to the Newton s law of otion, the axiu force exerted on weight and drop block equals to its inertial force plus its own weight [3], and the relationship ay be written as ( G 1) (3) where G is peak acceleration divided by gravity acceleration g. Then substituting Equation (3) into Equation (2), the following expression ay be derived where 0 G 0 s h ( ) 1 (4) ( ) d T is the ratio of axiu stress to unit ( ) d volue stored energy. It is obvious that peak acceleration ay directly indicate the capability of absorbing drop shock energy of corrugated paperboard pad, and ay express the dynaic shock cushioning property of corrugated paperboard pad. So the dynaic cushioning curve has proved to be the ost practical basis for describing the dynaic shock cushioning property, the lower the dynaic cushioning curve swings, and the better protection the package cushioning provides [4,5]. transissibility (Figure 3) shall consist of a dynaoelectric vibration tester, a signal acquisition & processing device, a set of DASP-ET software. Two test speciens cobination under investigation are placed in the test fixture, and the ass block is placed on the botto test specien. The two test speciens, ass block (to represent the packaged ite) and fixture are ounted on the vibration tester. The weight of ass block is changeable, and the static load exerted on the botto test specien ay be adjusted by changing the weight of ass block. One acceleration sensor is attached to the platfor of vibration table to onitor the excitation acceleration, and the other is located in the ass block to easure the response acceleration. The signal outputs fro the sensor located in the ass block and on the platfor of vibration table are siultaneously fed into the signal acquisition & processing device, then the experiental data shall be analyzed and presented in the for of vibration transissibility and frequency curve by DASP-ET. Although ost package cushioning aterials exhibit nonlinear property, a brief discussion of linear syste with single degree of freedo will aid in understanding soe of the fundaental aspects of vibration as related to packaging considerations [4,5]. For the vibration test syste in Figure 3, the ass block cushioned on the test specien ay be idealized as the linear single degree of freedo syste with viscous daping, and the vibration transissibility T r of package cushioning syste with corrugated paperboard pads would be described as T r 2 1 (2 ) (1 ) (2 ) (5) f where λ stands for frequency ratio ( ), f is excitation frequency of vibration table, f r is resonance fre- fr quency of the package cushioning syste, and ζ represents daping ratio. It is evident that vibration transissibility has a close relationship with frequency ratio and daping ratio. When the resonance takes place (λ = 1), the daping ratio ζ ay be derived fro Equation (5) and written as 3.2. Description of Vibration Transissibility The vibration transissibility is usually described as the relationship between vibration transissibility and resonance frequency of corrugated paperboard pads at different static loads. Vibration transissibility is a non-diension ratio of response acceleration aplitude of the packaged ite in steady-state forced vibration to excitation acceleration aplitude [3]. The test syste for vibration Figure 3. Test syste of vibration transissibility: 1) Clap device; 2) Test speciens; 3) Mass block; 4) Acceleration sensors.

4 Y. F. GUO ET AL T r 1 So, after obtaining the vibration transissibility and frequency curves of corrugated paperboard pads by vibration tests with slow sine sweep, resonance frequencies, vibration transissibility and daping ratios ay be analyzed, and the vibration transissibility of corrugated paperboard pads shall be coprehensively evaluated. 4. Experiental Methods of Dynaic Packaging properties (6) The ost coprehensive ethod for deterining dynaic shock cushioning property is described in the standard ASTM D 1596 Standard test ethod for dynaic shock cushioning characteristics of packaging aterials. The test procedure is as follows: Firstly, position the test specien on the ipact base and prepare the drop block to ipact the test specien. Secondly, ipact the test specien at the predeterined drop block weight (static load) and drop height, then repeat the sae test procedure with the other two test speciens. The drop shock acceleration and tie curve should be recorded for each test. The average value of peak accelerations for these three drop shock tests is taken as the peak acceleration at the predeterined static load. Thirdly, repeat the drop shock procedure with several ore increents of weight until sufficient data are derived to establish the dynaic cushioning curve. Lastly, the sae procedure shall be eployed for different drop heights. For a drop height, a piece of dynaic cushioning curve ay be obtained by aking drop shock tests for a range of static loads. Then adjusting the drop height and aking siilar drop shock tests, another piece of dynaic cushioning curve ay be also obtained. Therefore by aking a series of drop shock tests for different drop heights, a faily of dynaic cushioning curves should be obtained. On the basis of the faily of dynaic cushioning curves, the dynaic shock cushioning property of corrugated paperboard pads shall be thoroughly evaluated. The ost coprehensive ethod for deterining vibration transissibility is described in the standard ASTM D 4168 Standard test ethod for vibration transissibility of package cushioning aterial. The test procedure is as follows: Firstly, place two speciens cobination under investigation in the test fixture, one below and the other above the ass block. The ass block weighted for the desired static load is placed on the botto test specien, and the top test specien is placed above the ass block, then the fixture is claped in place. Secondly, start the vibration test with slow sine sweep, and present experiental data in the for of vibration transissibility and frequency curve. In order to thoroughly evaluate the vibration transissibility of corrugated paperboard pads, the range of frequency sweep is selected fro 3 Hz to 600 Hz in order to wholly investigate on the vibration propery of corrugated paperboard pads. The frequency sweep rate is one octave per inute, and sine excitation acceleration is held constant aplitude at 0.5 g. Thirdly, the sae procedure shall be used for different static loads. These different static loads would be selected fro the faily of dynaic cushioning curves of corrugated paperboard pads. On the basis of vibration transissibility and frequency curves at different static loads, the vibration transissibility of corrugated paperboard pads would be investigated. 5. Results and Discussions 5.1. Dynaic Shock Cushioning Property of Corrugated Paperboard Pads According to the test ethod ASTM D 1596, the drop shock tests of corrugated paperboard pads are ade for drop heights 30 c, 60 c and 90 c respectively. The waves of drop shock acceleration are siilar to half-sine pulses at different static loads for different drop height, e.g. the wave in Figure 4 is that of single layer pad for drop height (DH) 30 c and static load kpa, the peak acceleration is g (gravity acceleration). In addition Figure 5 provides the wave of two layers pad for drop height 60 c and static load kpa, the peak acceleration is g. Figure 6 is the wave of three layers pad while drop height 90 c and static load kpa, the peak acceleration is g. Due to the liited space other drop shock acceleration and tie curves are oitted. By coparison studies on the drop shock tests for corrugated paperboard pads, seven pieces of dynaic cushioning curve shall be obtained, which are shown in Figures 7 to 9. For single layer pad, while the drop height is 60 c or 90 c, the test speciens would be wholly crushed and lose dynaic shock cushioning property, so it has only one piece of dynaic cushioning curve for drop height 30 c (Figure 7). The curves in Figure 8 are for two layers pad, and that of Figure 9 are for three layers pad. These dynaic cushioning curves are the ost practical basis for the package cushioning design procedure of corrugated paperboard pads [4-5], so it is necessary to develop experiental forulas of these curves. Fro the characterization of dynaic cushioning curves suarized above, these curves have a close relationship with the drop height and static stress. When the drop height is constant, the peak acceleration ay be described as a function of static stress, and the experiental forulas of dynaic cushioning curves ay be established by using the fitting polynoial of curve [17-18]. By coparing

5 Y. F. GUO ET AL. 382 Figure 4. Drop shock acceleration and tie curve of single layer pad. Figure 7. Dynaic cushioning curve of single layer pad. Figure 5. Drop shock acceleration and tie curve of two layers pad. Figure 6. Drop shock acceleration and tie curve of three layers pad. the test data of average peak acceleration with its theoretical data derived fro the fitting polynoial of curve, the third order polynoial function of static stress has proved to be the best expression, and the experiental forulas of dynaic cushioning curves of corrugated paperboard pads is written as G a0 a1 s a2 s2 a3 s3 (7) where G is average peak acceleration, s represents static stress, a0, a1, a2, a3 are four characteristic factors. For exaple, Figure 10 gives the dynaic cushioning curve of three layers pad at drop height 60 c, and the circle dots stand for test data of average peak acceleration. The dynaic cushioning curve is obtained by using the fitting polynoial with third order polynoial function of the curve. So, on the basis of test data of average peak acceleration and static stress obtained fro the drop shock tests of corrugated paperboard pads for drop heights 30 c, 60 c and 90 c respectively, using Equation (7) and Method of the Least Mean Square, the characteristic factors of dynaic cushioning curves are solved and shown in Table 1. Figure 8. Dynaic cushioning curves of two layers pad. Figure 9. Dynaic cushioning curves of three layers pad.

6 Y. F. GUO ET AL. 383 Figure 10. Dynaic cushioning curves of three layers pad (DH = 60 c). By coparing and analyzing these dynaic cushioning curves of corrugated paperboard pads, soe conclusions ay be drawn as follows: 1) Each piece of dynaic cushioning curves of corrugated paperboard pads (Figures 7-9) is always concave and upward, and has only one iniu value point. This rule can be understood as follows [5]. If the ass of weight and drop block is light, the drop shock would result in very little copressive deforation, and the corrugated paperboard pad absorbs and stores a little echanical energy per unit volue, so the acceleration peak is relatively large. This represents the left hand side of dynaic cushioning curve. In the iddle area, the corrugated paperboard pad is properly copressed and absorbs and stores uch echanical energy per unit volue, so the iniu peak acceleration shall be reached. After passing through a certain point, the greater ass of weight and drop block copresses the corrugated paperboard pad too uch, so the corrugated paperboad pad shall be bottoed out, then the iniu peak acceler- Table 1. Characteristic factors of dynaic cushioning curves. Pad type Drop height /c a 0, a 1, a 2, a 3 Single layer pad , , , 3325 Two layers pad Three layers pad , , , , , , , -8067, 48250, , , , , , , , , , ation increases. This is the right hand side of the curve. So the iddle area of the curve is the optiu perforance range. 2) For the sae corrugated paperboard pad, with the increent of drop height, the concave point of dynaic cushioning curves (Figures 8 and 9) has a trend to rise along leftward and upward direction. Therefore the drop height is an iportant factor to influence on the dynaic shock cushioning property, and the selection of dynaic cushioning curve should be coincided with the predeterined drop height in package cushioning design of corrugated paperboard pads. 3) For the sae drop height, with the increent of layer quantity of corrugated paperboard pads, the iniu peak acceleration declines. The iniu peak acceleration of three layers pad is least. So three layers pad holds better dynaic shock cushioning property than single layer pad and two layers pad Vibration Transissibility of Corrugated Paperboard Pads On the basis of the faily of dynaic cushioning curves of corrugated paperboard pads (Figures 7 to 9), these different static loads exerted on the botto test specien are respectively selected as follows: 1) For single layer pad, four kinds of different static loads, kpa, kpa, kpa and kpa; 2) For two layers pad, fourteen kinds of different static loads, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa and kpa; 3) For three layers pad, eleven kinds of different static loads, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa, kpa and kpa. According to the test ethod ASTM D 4168, the vibration tests with slow sine sweep for corrugated paperboard pads at different static loads are ade, and the vibration transissibility and frequency curves are obtained. For exaple, Figure 11 is the vibration transissibility and frequency curve of single layer pad at static load kpa, Figure 12 gives that of two layers pad at static load kpa, and Figure 13 provides that of three layers pad at static load kpa. Due to the liited space, other vibration transissibility and frequency curves are oitted. On the basis of these vibration transissibility and frequency curves, resonance frequencies, vibration transissibility and daping ratios are analyzed by using linear vibration theory with single degree of freedo, and the daping ratios (saller than one) are estiated by using Equation (6). For exaple, Table 2 gives the experiental results of single layer pad at static loads of kpa and kpa. Table 3 provides that of two layers pad at static loads of kpa, kpa, kpa, kpa,

7 384 Y. F. GUO ET AL. Figure 11. Vibration transissibility and frequency curve of single layer pad. Figure 12. Vibration transissibility and frequency curve of two layers pad. Figure 13. Vibration transissibility and frequency curve of three layers pad kpa and kpa. Table 4 reflects that of three layers pad at static loads of kpa, kpa, kpa, kpa and kpa. Due to the liited space, other experiental results are oitted. By coparing and analyzing the experiental results and curves of vibration transissibility of corrugated paperboard pads at different static loads, soe conclusions ay be reached as follows: 1) The package cushioning syste of corrugated paperboard pads has different resonance frequencies, yet only several resonance frequencies are priary and other resonance frequencies have a little effect on the packaged ite during distribution. For instance, while static load kpa is exerted on two layers pad, the vibration

8 Y. F. GUO ET AL. 385 Table 2. Vibration transissibility of single layer corrugated paperboard pad. Static load /kpa Resonance Frequency /Hz Vibration transissibility Daping ratio Table 3. Vibration transissibility of two layers corrugated paperboard pad. Static load /kpa Resonance Frequency /Hz Vibration transissibility Daping ratio transissibility and frequency curve (Table 3 and Figure 12) has six resonance frequencies such as 12 Hz, 45 Hz, 74 Hz, 114 Hz, 138 Hz and 156 Hz, their vibration transissibility are 1.038, 1.416, 7.926, 2.941, and 0.873, respectively. The vibration transissibility at 74 Hz is about 9.08 ties as uch as that of 156 Hz, the vibration transissibility at 138 Hz is about 3.58 ties as uch as that of 156 Hz, so the resonance frequency 74 Hz should be taken as the first principle ode of vibration, resonance frequency 138 Hz as the second ode, etc. The result indicates an iportant guidance that the priary resonance frequencies ust be avoided in package cushioning design of corrugated paperboard pads. 2) For the package cushioning syste with corrugated paperboard pad, there is critical frequency at which the vibration transissibility is high, and above the critical frequency the vibration transissibility drops and is saller than one. For exaple, the critical frequency of single layer pad is 191 Hz (Table 2). When the excitation frequency is higher than 191 Hz, the vibration transissibility is very low, and the corrugated paperboard pad shall efficiently decrease vibration. In addition, for two layers pad, the critical frequency is 208 Hz (Table 3), and for three layers pad, the critical frequency is 185 Hz (Table 4). So the package cushioning syste of corrugated paperboard pad ay efficiently attenuate vibration with higher excitation frequency during distribution. 3) The static load exerted on the corrugated paperboard pad has an evident influence on vibration transissibility. The influence relates to the echanical behavior of corrugated paperboard, especially viscoelasticity. The result suggests another iportant guidance that the Table 4. Vibration transissibility of three layers corrugated paperboard pad. Static load /kpa Resonance Frequency /Hz Vibration transissibility Daping ratio

9 386 Y. F. GUO ET AL. vibration transissibility and frequency curve ust be selected according to the static load exerted on it in package cushioning design of corrugated paperboard pads. 6. Conclusions This research work obtains dynaic cushioning curves, vibration transissibility and frequency curves of corrugated paperboard pads by a series of experiental studies, and evaluates its dynaic packaging properties relevant to its application for protective packaging such as dynaic shock cushioning property and vibration transissibility. The waves of drop shock acceleration are siilar to half-sine pulses, the shapes of dynaic cushioning curves are always concave and upward, and each piece of dynaic cushioning curves has only one iniu value point. The package cushioning syste of corrugated paperboard pads has different resonance frequencies, and only several resonance frequencies are priary. The results show that corrugated paperboard pads possess dynaic shock cushioning property for drop shock, and the three layers pad has better dynaic shock cushioning property than single layer pad and two layers pad. For the package cushioning syste with corrugated paperboard pads, there is critical frequency at which the vibration transissibility is high, and above the critical frequency the vibration transissibility drops and is saller than one. The critical frequency of single layer pad is 191 Hz, that of two layers pad is 208 Hz, and that of three layers pad is 185 Hz. The package cushioning syste of corrugated paperboard pad ay efficiently attenuate vibration with higher excitation frequency during distribution. 7. Acknowledgeents This research work is supported by the Scientific Research Foundation of Science and Technology Departent of Shaanxi Province under the Grant 2007K07-21 and the Scientific Research Foundation of Printing & Packaging Material and Technology Beijing Area Major Laboratory under the Grant KF We would like to thank Northwest Corrugated Paperboard Liited Copany for providing test speciens of corrugated paperboard pads. 8. References [1] G. W. Kooistra, V. Deshpande and H. N. G. Wadley, Hierarchical Corrugated Core Sandwich Panel Concepts, Journal of Applied Mechanics, Vol. 74, No. 1, 2007, pp [2] J. Kirkpatrick and M. Sek, Replaceent of Polyeric Cushioning with Corrugated Fiberboard-Case Study, Proceedings of 10th IAPRI World Conference on Packaging, Melbourne, Australia, 1997, pp [3] R. D. Mindlin, Dynaics of Package Cushioning, Bell Syste Technical Journal, Vol. 24, No. 7-10, 1945, pp [4] G. S. Mustin, Theory and Practice of Cushion Design, The Shock and Vibration Inforation Center, U.S. Departent of Defense, [5] U. S. Departent of Defense, Military Standardization Handbook, Package Cushioning Design (MIL-HDBK- 304B), [6] E. K. Hahn, A. D. Rudo, B. S. Westerlind and L. A. Carlsson, Copressive Strength of Edge-Loaded Corrugated Board Panels, Experiental Mechanics, Vol. 32, No. 3, 1992, pp [7] M. H. Lee and J. M. Park, Flexural Stiffness of Selected Corrugated Structures, Packaging Technology and Science, Vol. 17, No. 5, 2004, pp [8] T. J. Urbanik, Effect of Corrugated Flute Shape on Fiberboard Edgewise Crush Strength and Bending Stiffness, Journal of Pulp and Paper Science, Vol. 27, No. 10, 2001, pp [9] Y. F. Guo, Y. G. Fu and W. Zhang, Creep Properties and Recoverability of Double-Wall Corrugated Paperboard, Experiental Mechanics, Vol. 48, No. 3, 2008, pp [10] A. C. Gilchrist, J. C. Suhling and T. J. Urbanik, Nonlinear Finite Eleent Modeling of Corrugated Board, Proceedings of International Conference on Mechanics of Cellulosic Materials, Virginia, USA, 1999, pp [11] T. Nordstrand and A. Allansson, Stability and Collapse of Corrugated Board Panels, Nuerical and Experiental Analysis, Proceedings of 6th International Conference on Sandwich Structures, Florida, USA, 2003, pp [12] Z. Aboura, N. Talbi, S. Allaoui and M. L. Benzeggaph, Elastic Behavior of Corrugated Cardboard: Experients and Modeling, Coposite Structures, Vol. 63, No. 1, 2004, pp [13] H. A. Rai, J. Choi, B. S. Wei, R. Popil and M. Schaepe, Refined Nonlinear Finite Eleent Models for Corrugated Fiberboards, Coposite Structures, Vol. 87, No. 4, 2009, pp [14] N. Talbi, A. Batti, R. Ayad and Y. Q. Guo, An Analytical Hoogenization Model for Finite Eleent Modeling of Corrugated Cardboard, Coposite Structures, Vol. 88, No. 2, 2009, pp [15] M. Sek and J. Kirkpatrick, Characteristics of Corrugated Fiberboard as a Cushioning Material in Protective Packaging, Proceedings of 10th IAPRI World Conference on Packaging, Melbourne, Australia, 1997, pp [16] M. Sek and J. Kirkpatrick, Prediction of the Cushioning Properties of Corrugated Fiberboard fro Static and Quasidynaic Copression Data, Packaging Technology and Science, Vol. 10, No. 2, 1997, pp [17] G. Burgess, Generation of Cushion Curves fro One Shock Pulse, Packaging Technology and Science, Vol. 7, No. 2, 1994, pp [18] Y. F. Guo and J. H. Zhang, Shock Absorbing Characteristics and Vibration Transissibility of Honeycob Pa perboard, Shock and Vibration, Vol. 11, No. 5-6, 2004, pp