Cushioning energy absorption of regular polygonal paper corrugation tubes under axial drop impact

1 Introduction

In the product packaging protection system, the cushioning energy absorption structure such as paper honeycomb, paper corrugation, plastic foam, and their combination structures are extensively utilized to fulfill the product protection and safe transportation [1, 2, 3, 4, 5]. The paper corrugation laminated structure utilizes the transverse compression deformation to achieve the cushioning energy absorption, and this field research works are rich [6, 7, 8]. For example, Naganathan et al. [6] studied the dynamic response characteristics of pre-compressed multilayer corrugated paperboard under drop impacts, and found that the escape effect of gas within the corrugation framework had an influence on the cushioning performance. Guo et al. [7, 8] investigated the dynamic cushioning characteristics of the X-PLY corrugated paperboard and the elastic-type structures of corrugated paperboard, and verified the attractive packaging protection of these structures. Fu et al. [9] studied the static transverse compression deformation of B-type and C-type single corrugated paperboards, proved that the low compression rate affected nearly the optimum energy absorption point, energy absorption efficiency and specific energy absorption, while the cross-section geometry had a greater impact on the energy absorption. Wang et al. [10] develops a mathematical model to depict the energy absorption properties of multi-layered corrugated paperboard (MLCP) in various ambient humidities which can be applied in the optimum design and material selection of cushioning packaging with multi-layered corrugated paperboard. In addition, the paper corrugation tubular structure, an attractive kind of non-metallic energy absorption system, belongs to an innovative protective packaging model, and can reduce the external load and absorb the drop impact energy through axial compression deformation and dynamic buckling. Therefore, it may play an important role for the general protection and packaging technology of military and civil products, especially the protection packaging of air-dropped materials and equipment and product transportation, moreover it holds remarkable social and economic benefits because of the low cost and the outstanding environmental-friend. At present, there is lack of research report on the axial bearing capacity and energy absorption of paper corrugation tubular structure. But a few engineers and researchers have paid close attention to the potential advantage of the corrugation waveform easier bending and buckling deformations under axial compression, and proposed metal or composite corrugation tubular structures which can effectively improve the bearing capacity and energy absorption characteristics of thin-walled tubular structures [11, 12]. For instance, Xiang and Li et al. [13, 14] evaluated the energy absorbing capacity of polygonal tube, multi-cell square tube, aluminum foam-filled square tubes and circular tubes under axial compression. Hanssen et al. [15] analyzed the axial compression properties of aluminum foam filled square tubes under quasi-static and dynamic conditions by experimental method, and gave an empirical formula of platform force based on experimental results. It has been found that the plate force of the square tube after filling the foam is greater than the superposition of the platform forces under the compression of the square tube and the foam, that is, the interaction between the square tube and the foam can effectively increase the platform force of the square tube. Shahbeyk et al. [16] analyzed the dynamic axial compression properties of aluminum foam filled square tubes by numerical simulation. The results agree well with the experimental data of Hanssen. Liu et al. [17] studied the buckling mode and energy absorption of sinusoidal corrugated aluminum circular tubes under axial impact load, and found that the corrugated aluminum circular tubes had controllable energy absorption, and the impact velocity and the ratio of corrugation diameter to thickness were two main parameters controlling axial compression deformation. Zhang et al. [18] analyzed the energy absorption mechanism of the corrugated metal tube under axial compression by using plastic hinge theory, deduced the analytical formula of average crushing load, and simulated the influence of structural parameters, material performance parameters and impact speed of corrugated metal tube on energy absorption. Hao et al. [19] introduced a folded structure on the basis of square tube, the dynamic progressive buckling deformation mode and energy absorption of the folded tube with different geometric parameters under axial impact load were simulated and analyzed, and the results show that the folded tube can effectively improve the smoothness of crushing load, but the specific energy absorption is lower than the square tube. Xu et al. [20] developed a bionic tube based on the bamboo structure to improve the crashworthiness energy absorption of thin-walled tubular structures.

In view of these research works and the new ideas of energy absorbing tubular structures, we put forward the regular polygonal paper corrugation tubes with the cross-section shapes including triangle, quadrangle, pentagon and hexagon, which not only hold the advantage of corrugation structure such as lightweight, high specific stiffness and strength, but also have better stability, bearing capacity, and energy absorption of the whole tubes. Therefore, the purposes of this paper is to study the compression deformation mode and cushioning energy absorption of four kinds of regular polygon paper corrugated tubes under axial drop impacts, and to evaluate the influence rules of structural parameters (e.g. tube direction, tube cross-section shape, tube length) and loading parameters (e.g. impact block mass, impact energy) on the deformation characteristics and cushioning energy absorption of paper corrugation tubes, so as to provide a fundamental basis for the optimization design and engineering application of regular polygon paper corrugation tubes.

2 Corrugation tubes and test methods

The regular polygonal paper corrugation tubes are made of the double-wall corrugated paperboard with B and C flutes by the packaging technologies of die cutting, indentation, full lapped adhesion. The geometric parameters include the cross-section shape of tube, tube length and tube direction as Table 1. The cross-section shape of paper corrugation tubes embodies the regular triangle, quadrangle, pentagon and hexagon, each of them has two kinds of side lengths (35 and 50mm), moreover each side length corresponds to three kinds of tube lengths, and the ratios of the tube length to the corresponding side length are 1.4, 2.2 and 3.0, respectively. The tube length are 49, 77,105 and 70, 110, 150, respectively. The thickness of corrugation paperboard is 7.0mm, and its edge crush strength is 6771 N/m. The thickness and grammage of face (or inner) sheet are 0.28mm and 180g/m², its transverse and longitudinal tensile strength are 15.5 and 38.5 N/mm², and its transverse and longitudinal ring compressed strength is 1.583 and 1.934 kN/m, respectively. The thickness and grammage of core paper are 0.24 mm and 140g/m², its transverse and longitudinal tensile strength are 11.0 and 20.0 N/mm², its transverse and longitudinal ring compressed strength are 0.904 and 1.098kN/m, respectively. The X-direction paper corrugation tube indicates that the axial direction of the tube is parallel to the wave direction of the corrugation paperboard, meanwhile the Y-direction paper corrugation tube represents that the tube axis is parallel to the flute direction of the corrugation board as Table 1.

Table 1

Geometry of paper corrugation tubes of regular polygon cross-section shape

The drop impact compression characteristics of the regular polygonal corrugation paper tubes were tested with reference to the standard ASTM D 1596 “Standard test method for dynamic shock cushioning characteristics of packaging materials” and the Chinese national standard GB 8167 “Testing method of dynamic compression for package cushioning materials”. The sample is placed in the center of the impact table of the impact testing machine, and the impact load with the free-falling hammer is applied to the sample. The bottom area of the square impact block is 200mm×200mm larger than the upper surface of the sample, which can ensure the sample wholly subjected to the drop impact loading and produce a flat dynamic compression process. Three sets of experiments were performed for each set of samples, and each set of experimental data was recorded and averaged. There are two kinds of drop heights as DH₁ (30cm) and DH₂ (50cm), and four kinds of impact block mass as W₁ (7.0kg), W₂ (9.125kg), W₃ (11.275kg) and W₄ (14.55kg), so the experiments have eight groups of drop impact conditions, which hold the corresponding impact energies as 20.6J, 26.8J, 33.1J, 42.8J, 34.3J, 44.7J, 55.2J and 71.3J, respectively. The sample numbering is arranged as CTnd-l₁/l₂-DH/W, CT indicates the paper corrugation tubes, n is the number of cross-section edges of the tube, d is the direction of the paper corrugation tube (X-, Y-direction), l₁ indicates the cross-section length of the tube. l₂ indicates the length of the tube, and DH and W respectively denote the drop height (or impact speed) and the mass of the weight, respectively. Before the experiments, all the samples should be preconditioned for at least 24 hours at ambient temperature 20^∘C and relative humidity 65%.

3 Analysis of deformation mode

For the axial drop impact conditions with different impact energies, the X-direction paper corrugation tubes occur mainly in the accordion deformation mode as Figure 1(a), which is stable and controllable, and does not change with the drop impact energy and the geometric parameters of the tube. This is due to the fact, that the crests and troughs of the sinusoidal corrugation core layers are the crucial reason to guide easily the plastic hinge of tubular walls. Under the dynamic loading of axial drop impact, the paper corrugation tube is compressed along the waveform direction, and the polygon tubular walls of double-wall corrugated paperboard are uniformly applied load along the direction of tube length, so it is easier for the flutes of the corrugated paperboard to be deformed with the periodic folding units. This deformation mode is similar to the spring deformation mode by compression, and a part of the deformation can be restored after eliminating the compression load. The structural characterization may ensure the stability of the deformation mode of X-direction paper corrugation tube, furthermore be conducive to the stability of energy absorption of the paper corrugation tube under drop impact. However, while the X-direction paper corrugation tube is subjected to a large drop impact loading or the tube length is small, the transverse shear deformation and corner tearing deformation would occur as Figure 1(b) and 1(c).

Figure 1

Deformation modes of X-direction paper corrugation tube: (a) accordion deformation, (b) corner tearing deformation and (c) transverse shear deformation

The deformation modes of Y-direction paper corrugation tube under axial drop impact loading include the steady-state progressive buckling, Euler instability, corner tearing and transverse shear, and the main deformation mode is a mixture of steady-state progressive buckling and one or more other non-ideal deformation modes as Figure 2. When the Y-direction paper corrugation tube is subjected to the axial compression, the steady-state progressive buckling occurs firstly. Due to the different arrangement of the surface paper and the corrugation core paper, the corrugated paperboard of tubular walls may take place the delaminating phenomenon, the corrugation core paper comes into being a periodic folding deformation along the flute direction, yet the surface paper forms the layered folding deformation as Figure 2(a). While the Y-direction paper corrugation tube emerges the Euler instability, the bending part of the tube emerges plastic hinges accompanying with the core paper and the surface paper buckling and folding in unison, but the non-bending part does not appear the compression deformation and plastic hinge as Figure 2(b). With the change of cross-section shape, tube length or drop impact energy, the Y-direction paper corrugation tube would happen more or less corner tearing deformation or transverse shear deformation. The surface of corner tearing deformation along the edge ridge comes into being a travelling plastic hinge, while the rest of the tube does not change, as shown in Figure 2(c) and 2(d), so this deformation mode would greatly decrease the bearing capacity of the paper corrugation tube, moreover the total energy absorption and specific energy absorption are also reduced. In addition, the transverse shear deformation mode arises out of the paper corrugation tube wall subjected to the loading of shear force, the surface paper and corrugation core paper appears the delaminating phenomenon, the surface paper does not occur the periodic folding compression, but the corrugation core layer comes into being plastic hinges at the compression loading along the flute direction. The compression densification of the tube is also inconsistent for the different magnitude of drop impact energy, the X-direction paper corrugation tube is easier to be compressed densification than the Y-direction paper corrugation tube at the same impact energy, so the X-direction paper corrugation tube holds more stable and controllable deformation modes than the Y-direction paper corrugation tube, and is beneficial to regulate the axial compression capacity and cushioning energy absorption.

Figure 2

Deformation modes of Y-direction paper corrugation tube: (a) stable progressive buckling, (b) Euler instability, (c) corner tearing and (d) transverse shear

4 Analysis of influence factors

The parameters including the total energy absorption (TEA), unit area energy absorption (EA), specific energy absorption (SEA), and stroke efficiency (SE) are selected to evaluate the influence rules of tube direction, cross-section shape, tube length, drop impact energy and impact block mass on the cushioning energy absorption of paper corrugation tubes [21, 22]. The total energy absorption (E) is calculated through the direct numerical integration of the load and displacement curve before the densification of structure:

where F denotes the compression load on the composite structure during compression, x represents the total deformation of the composite structure from the beginning of the compression load to the final densification.

The unit area energy absorption (EA) is defined as the ratio of the total energy absorption to the cross-section area of the tube:

And, the specific energy absorption (SEA) is defined as the ratio of the total energy absorption to the mass of structure:

Lastly, the stroke efficiency (SE) is defined as the ratio of the compression displacement before the densification to the tube length:

On the base of the dynamic compression curves by drop impact tests and the Eqs. (1) to (4), the total energy absorption, unit area energy absorption, specific energy absorption, and stroke efficiency of the two kinds of paper corrugation tube with regular polygon cross-section shape should be calculated.

4.1 Influence of tube direction

The tube direction of polygonal paper corrugation tube has a crucial effect on the deformation mode and peak stress and plastic platform stress. Figures 3 and 4 reflect the dynamic compression stress and strain curves and the deformation modes of the X-direction and Y-direction paper corrugation tubes with the regular triangular, quadrangular, pentagonal and hexagonal cross-sections at the same drop impact condition, each of the tubes have the same cross-section side length and tube length. In Figure 4 the former of each photograph is the X-direction paper corrugation tube, and the latter is the Y-direction paper corrugation tube. It is clear that, the X-direction paper corrugation tubes have much lower the peak stress and plastic platform stress than the Y-direction paper corrugation tubes, and the fluctuation degree and amplitude of dynamic compression stress are fine and small, with stable compression resistance and continuous stable deformation. The Y-direction paper corrugation tubes possess large peak stress of large fluctuation amplitude and short plastic platform, and have fewer folds than the X-direction paper corrugation tubes, which may affect the cushioning energy absorption.

Figure 3

Dynamic stress and strain curves for different tube directions: (a) triangle, (b) quadrangle, (c) pentagon and (d) hexagon

Figure 4

Deformation modes for different tube directions: (a) triangle, (b) quadrangle, (c) pentagon and (d) hexagon

The tube direction of the polygonal paper corrugation tube has a remarkable influence on the mechanical properties and energy absorbing characteristics. In Figure 5, the cushioning energy absorption of the X-direction and Y-direction paper corrugation tubes are compared at the same drop impact condition DH₂W₄ (drop height 50cm, impact block mass 14.55kg, impact energy 71.3J), and all regular polygonal tubes have the same the cross-section side length and tube length. The total energy absorbed, unit area energy absorbed, specific energy absorbed and stroke efficiency of the X-direction paper corrugation tubes with different cross-section shapes are all larger than that of the Y-direction paper corrugation tubes. When the Y-direction paper corrugation tube is subjected to the axial dynamic compression by drop impact, the surface paper of the paper corrugation tube comes into being fine wrinkles and stable periodic folding (e.g. plastic progressive buckling), while the corrugation core paper appears many folding deformation elements along the flute direction of each sinusoidal waveform, so it dissipates much drop impact energy besides the folding elements at the edges and corners of the tube. But the X-direction paper corrugation tubes are dynamically compressed along the direction of sinusoidal waveform, and it produce far less resistance force than the Y-direction paper corrugation tube. Moreover, the stroke efficiencies of the X-direction and Y-direction paper corrugation tubes are greatly different, and the ratios of the corresponding stroke efficiency for the X-direction to Y-direction regular triangle, quadrangle, pentagon and hexagon paper corrugation tubes are 3.45, 3.01, 3.27 and 2.94, respectively, so the X-direction paper corrugation tube has higher total energy absorption than the corresponding Y-direction paper corrugation tube. Because of the distinctive differences in the space configuration, arrangement and orientation in the waveform direction (or machining direction, X-direction) and the flute direction (or cross-section direction, Y-direction), the mechanical property of the double-wall corrugated paperboard with B and C flutes takes on anisotropy along the X-direction and the Y-direction, and the cushioning energy absorption of the X-direction and Y-direction paper corrugation tubes has large divergence.

Figure 5

Cushioning energy absorption of different tube directions: (a) total energy absorbed, (b) unit area energy absorption, (c) specific energy absorption and (d) stroke efficiency

4.2 Influence of tube cross-section shape

The cross-section shape of the polygonal paper corrugation tube has an influence on the dynamic compression deformation mode and cushioning energy absorbing properties. According to the dynamic compression stress and strain curves in Figure 3 and the compression diagrams in Figure 6(a) of the X-direction paper corrugation tubes with different cross-section shapes, it is obvious that, the X-direction paper corrugation tubes produce relatively stable accordion deformation mode which does not change with the cross-section shape of paper corrugation tubes, but the number of folds produced by the dynamic compression decreases with the increase of the number of cross-section edge length under the same drop impact loading. In like manner, from the dynamic compression curves in Figure 3 and the compression deformation diagrams in Figure 6(b) of the Y-direction paper corrugation tubes with different cross-section shapes, the Y-direction paper corrugation tubes are mainly characterized by the steady-state progressive deformation, yet they are easy to appear the transverse shear deformation mode under the axial drop impact compression. Moreover, the number of folds of the Y-direction paper corrugation tube does not change nearly, and the occurrence of the folds or wrinkles in the regular triangle, quadrangle and pentagon tubes is at the upper end of the tube, yet the position of the folds or wrinkles of the regular hexagon tube is at the upper and lower ends of the tube. In addition, Figure 7 provides the comparison of the cushioning energy absorption of the paper corrugation tubes with different cross-section shapes under axial drop impact, and shows that the unit area energy absorption, specific energy absorption and stroke efficiency of the X-direction and Y-direction paper corrugation tubes decrease with the increase of the number of cross-section edges of the regular polygonal tubes. The reason is mainly due to the increase of the number of cross-section edges of the tube, the effective bearing area and mass of the tube are also increased, yet the change of the total energy absorption is not very obvious, so the unit area energy absorption and specific energy absorption are decreased. For example, under the condition of axial drop impact DH₂W₄ (drop height 50cm, impact block mass 14.55kg, impact energy 71.3J), the total energy absorption of the X-direction paper corrugation tubes with the regular triangle, quadrangle, pentagon and hexagon are 70.06J, 67.48J, 69.05J, and 66.63J, respectively, but that of the Y-direction paper corrugation tubes are in turn 36.71J, 38.08J, 41.62J, and 45.01J.

Figure 6

Deformation modes for different cross-sections: (a) X- and (b) Y-direction paper corrugation tubes

Figure 7

Cushioning energy absorption for different cross-sections: (a) total energy absorbed, (b) unit area energy absorption, (c) specific energy absorption and (d) stroke efficiency

4.3 Influence of tube length

The tube length of the polygonal paper corrugation tube has also evident effect on the dynamic compression deformation mode and cushioning energy absorption. Figure 8 gives the comparison of the dynamic compression stress and strain curves for the square paper corrugation tube with the side length of 35mm and three kinds of tube lengths such as 49mm, 77mm and 105mm, respectively, and Figure 9 describes the corresponding compression deformation mode under the same axial drop impact in Figure 8. The X-direction paper corrugation tube is stable accordion deformation mode, yet due to the small side length of the paper corrugation tube, the transverse shear deformation occurs easily under the axial drop impact, so the surface paper and the corrugation core paper appear the delaminating phenomenon. The deformation mode of the Y-direction paper corrugation tube is mainly steady-state progressive buckling, and a slight Euler instability occurs near the bottom of the tube, also accompanying with a slight transverse shear. With the increase of the tube length, the position of the folds of the Y-direction paper corrugation tubes moves upward. For the same tube length, the number of folds of the X-direction paper corrugation tube is significantly more than that of the Y-direction paper corrugation tube, so the X-direction paper corrugation tube has better cushioning protection. Furthermore, Figure 10 provides the comparison of cushioning energy absorbing characteristics of a regular quadrangle paper corrugation tube with different tube lengths. As the increase of the tube length, the total energy absorption of the X-direction and Y-direction paper corrugation tubes increases by 26.8% and 70.2%, respectively. Because the effective bearing area of the paper corrugation tubes is unchanged, the unit area energy absorption of them is increased by 32.2% and 63.1%, respectively. However, the mass of the paper corrugation tube increases with the increase of the tube length, and has a large impact on the specific energy absorption, for example, the specific energy absorption of the X-direction and Y-direction paper corrugation tubes decreases by 66.7% and 34.8%, respectively. Under the same drop impact condition, with the increase of tube length, the stroke efficiency of the X-direction and Y-direction paper corrugation tubes decreases by 10.5% and 51.5%, respectively.

Figure 8

Dynamic compression curves for different tube lengths: (a) X- and (b) Y-direction paper corrugation tubes

Figure 9

Deformation modes for different tube lengths: (a) X- and (b) Y-direction paper corrugation tubes

Figure 10

Paper corrugation tubes for different tube lengths: (a) total energy absorbed, (b) unit area energy absorption, (c) specific energy absorption (d) stroke efficiency

4.4 Influence of impact block mass

For the dynamic compression along the axis of paper corrugation tubes at the same drop height (or impact speed), the increase of impact block mass would lead to larger impact force and appear the folds or wrinkles at different positions of the paper corrugation tubes, moreover, the amplitude of impact block mass also affects the transient compression deformation process. For example, Figures 11 and 12 gives the effect of the impact block mass on the dynamic compression stress and strain curves and deformation mode of the regular pentagon paper corrugation tube, with the increase of the impact energy (or the impact block mass) for the same drop height, the axial crushing distance of the paper corrugation tube also raises, meanwhile the number of folds or wrinkles of the dynamic compression deformation becomes more. It can be found that, with the increase of impact block mass, the peak stress and plastic platform stress would rise, and the paper corrugation tubes can absorb more drop impact energy. The X-direction paper corrugation tube mainly occurs accordion deformation, and the initial folding position of the regular triangle and quadrangle tubes appears at the upper end close to the drop impact end, and the folds emerge simultaneously at the upper and lower ends of the tube while the impact block mass increases, and the overall tube is finally compacted to densification. The folds of the regular pentagon and hexagon tubes rise at the upper and lower ends, and the number of folds also increases with the increase of impact block mass. Yet the compression deformation of the Y-direction paper corrugation tube is mainly steady-state progressive buckling accompanied by slight lateral shear phenomenon, the axial collapse displacement is increased, the position of the folds is unstable, and the number of folds is also increased.

Figure 11

Influence of impact block mass on compression curves: (a) X- and (b) Y-direction regular pentagon paper corrugation tubes

Figure 12

Influence of impact block mass on compression deformation: (a) X- and (b) Y-direction regular pentagon paper corrugation tubes

For example, for the X-direction and Y-direction paper corrugation tubes with regular polygon cross-sections having the identical side length of 35cm and tube length of 105cm, with the increase of impact block mass, the characterization of cushioning energy absorption is very similar as Figures 13 and 14, namely the total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency take on nearly linear increasing relationship. The feature is determined by the compression deformation mode of the paper corrugation tubes, while the impact block mass is increased, the axial crushing distance and the folds or wrinkles of the paper corrugation tube is increased. The larger the impact block mass, causes the larger compression strain along the tube length, and would arise the stroke efficiency, so the cushioning energy absorption of the paper corrugation tube is also enhanced.

Figure 13

Cushioning energy absorption of X-direction paper corrugation tubes at different impact block masses: (a) total energy absorbed, (b) unit area energy absorption, (c) specific energy absorption and (d) stroke efficiency

Figure 14

Cushioning energy absorption of Y-direction paper corrugation tubes at different impact block masses: (a) total energy absorption, (b) unit area energy absorption, (c) specific energy absorption, (d) stroke efficiency

4.5 Influence of drop impact energy

The drop impact energy may bring about influences on the dynamic compression deformation mode and cushioning protection. For example, with the increase of drop impact energy exerted on the square tubes, the accordion deformation of the X-direction paper corrugation tube, and the steady-state progressive buckling deformation of the Y-direction paper corrugation tube would be more obvious as Figure 15, the actual tube length after dynamic compression is gradually reduced, the crushing distance is increased, and the stroke efficiency is enhanced. Meanwhile, the Y-direction paper corrugation tube is also accompanied by an axial transverse shear deformation mode with splitting of the corrugation core paper and the surface paper. For the X-direction and Y-direction paper corrugation tubes with regular polygon cross-sections having the identical side length of 50cm and tube length of 150cm, Figure 16 provides the comparison of the total energy absorption curves under different conditions of drop impact energy, it is clear that the cross-section shape of the paper corrugation tube has no obvious effect on the total energy absorption, moreover the changes of total energy absorption for the X-direction and Y-direction paper corrugation tubes are basically coincident. With the increase of drop impact energy, the total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency of X-direction and Y-direction paper corrugation tubes all have increasing trends, yet the total energy absorption, unit area energy absorption and specific energy absorption all have two small downward trends owing to the strain rate effect of paper corrugation tube.

Figure 15

Influence of impact energy on deformation mode: (a) X- and (b) Y-direction square paper corrugation tubes

Figure 16

Influence of impact energy on total energy absorption: (a) X- and (b) Y-direction regular polygon paper corrugation tubes

The two kinds of drop impact conditions for the first descent point at the total energy absorption curve of the square X-direction paper corrugation tube as Figure 16(a) are respectively the DH₁W₃ (drop height 30cm, impact block mass 11.275kg, impact energy 33.1J) and DH₂W₁(drop height 50cm, impact block mass 7.0kg, impact energy 34.3J), and the dynamic compression stress and strain curves are shown as Figure 17. When the drop impact energies are close, the drop impact speed of the drop height 50cm is larger than that of the drop height 30cm, and the area surrounded by the stress and strain curve is less. By comparing the Figures 13, 14 and 16, it is found that the cushioning energy absorbing parameters including the total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency of X-direction and Y-direction paper corrugation tubes basically increase linearly with the increase of impact block mass, but the total energy absorption, unit area energy absorption and specific energy absorption have two small downward trends for the drop impact energies 34.3J and 44.7J.

Figure 17

Influence of impact energy on cushioning energy absorption of X-direction paper corrugation tube

5 Conclusions

The paper corrugation tubes belong to an attractive kind of non-metallic energy absorbing structure for the innovative cushioning protection and packaging technology of military and civil products. This research work aims at the cushioning energy absorbing characteristics of the X-direction and Y-direction paper corrugation tubes with four kinds of regular polygon under the different conditions of axial drop impacts, and the main conclusions are as follows:

1. The X-direction paper corrugation tube exhibits relatively stable and controllable accordion deformation mode at small drop impact loading, but also occurs the transverse shear deformation and corner tearing deformation for large drop impact loading or small tube length. Yet the Y-direction paper corrugation tube includes mainly the mixture of steady-state progressive buckling and one or more other non-ideal deformation modes such as Euler instability, transverse shear and corner tearing. At the same drop impact energy, the X-direction paper corrugation tube is easier to be compressed densification than the Y-direction paper corrugation tube.

2. The peak stress of the X-direction paper corrugation tube is low, the number of folds formed is more, the total energy absorption, unit area energy absorption and specific energy absorption of X-direction paper corrugation tube are more one time than those of the Y-direction paper corrugation tube, and the stroke efficiency is more three times than that of the Y-direction paper corrugation tube. Under the same drop impact loading condition, the number of folds of the X-direction paper corrugation tube increases with the increase of the number of cross-section edges of the tube, and the change of the cross-section shape has no obvious effect to the total energy absorption, the unit area energy absorption, specific energy absorption and stroke efficiency decrease as the number of the cross-section edges increases. There is no significant change in the number of folds of Y-direction corrugation tubes. With the increase in the number of cross-section edges, the total energy absorption of Y-direction paper corrugation tubes increased significantly, while the unit area energy absorption, specific energy absorption and stroke efficiency decreased. The number of folds of X-direction paper corrugation tubes is much more than that of Y-direction paper corrugation tubes for the same tube length. With the increase of tube length, the total energy absorption of X-direction and Y-direction paper corrugation tubes increased by 26.8% and 70.2%, respectively, the unit area energy absorption increased by 32.2% and 63.1%, respectively, but the specific energy absorption decreased by 66.7% and 34.8%, the stroke efficiency decreased by 10.5% and 51.5%, respectively.

3. At the same drop height (or impact speed), with the increase of impact block mass, the axial compression distance and the number of folds increase, and the total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency of the X-direction and Y-direction paper corrugation tubes are basically linear increasing trend. With the increase of the drop impact energy, the deformation becomes more obvious, the residual length of the tube is gradually reduced, the crushing distance is gradually increased, the number of folds is increased, the total energy absorption, unit area energy absorption, specific energy absorption and stroke efficiency of the X-direction and Y-direction paper corrugation tubes are increasing, but the total energy absorption, unit area energy absorption, and specific energy absorption appear two small downward trends.