Comparison study of the in-plane crushing failure behavior of traditional and arc-curved hexagonal honeycomb

The honeycomb structures have been widely adopted as the aerospace engineering for the impact dynamic performance. To reveal the in-plane crushing behavior and improve the energy absorption ability, the influence of typical honeycomb structure is studied under different impact velocity and wall thickness. The deformation behavior of arc-curved hexagonal honeycomb with in-plane impact is researched. Results show that three typical deformation model including I, V and X shape are exhibited for traditional and arc-curved types. The deformation model would transfer from X to I shape with the increasing of impact velocity, and the impact load would be more unstable. With the increasing of central angle of arc-curved hexagonal honeycomb, the global deformation occurs instead of local deformation including X and V model, and stronger energy absorption ability is exhibited for the larger angle.


Introduction
The aircraft would be suffered various impact load during the entire service life, and they have a serious threat to the safety of occupant.To improve the impact dynamic performance, the energy absorption structure have been extensively investigated, and many innovative aircraft structures have been proposed [1,2].
The aircraft structure with light weight and high strength has given great attention such as composite and lattice structures.The compression performance after low velocity impact damage of woven flax and basalt fiber reinforced polyester composite is investigated [3].The woven composite has been extensively researched for the excellence interlayer performance [4].To improve the crashworthiness, the CFRP/Al hybrid tube, channel section and sinusoidal structures with controlled failure mechanism are studied [5,6].To improve the energy absorption ability, the additively manufactured cellular structure with two different kinds of materials are conducted with crush test [7].The biomimetic sandwich plate box, truss-like lightweight structure, foam filled hat-stiffened CFRP shell have better performance, and they has great application potential in aircraft [8][9][10][11].
Honeycomb is one of the most important structure to resist impact load with high performance.Inspire by coconut palm, a novel concentric auxetic reentrant honeycomb is given and researched [12].Besides, the dynamic and quasi-static behavior of vertex-based hierarchical auxetic, circular honeycomb are investigated [13,14].The honeycomb has better in-plane performance and it is always adopted as the energy absorption structure [15,16].To improve the in-plane impact dynamic performance, many innovation structures including re-entrant combined-wall, bionic, graded with hierarchical architecture, joint-based hierarchical, negative Poisson's honeycomb have been proposed and investigated [17][18][19][20][21][22][23][24].To improve the structural performance, a new arc-curved hexagonal honeycomb has been given and the out-of-plane energy absorption characteristics are demonstrated [25,26].However, few researches have been conducted on the in-plane crushing behavior.Consequently, the comparison study of traditional and arc-curved hexagonal honeycomb under in-plane impact are investigated here.The failure behavior, impact load and energy absorption ability of honeycomb with different geometrical factors is researched.

Finite element model and validation
The honeycomb with a 2D array of hexagonal cells is given as figure 1, and it has 16 × 15 cells in the two directions.The edge length, thickness of each cell is 4.7 mm and 0.2 mm [26,27].The length and width of entire honeycomb is 130.3 × 108.1 mm.The explicit finite element method is adopted, and shell element is modelled to simulate the impact process.The aluminium material is simplified as ideal perfectly elastic-plastic, the Young's modulus and yield stress are 69 GPa and 76 MPa, respectively.The explicit finite element method is adopted, and the mesh size is chosen as 0.4 mm after the mesh convergence study.The single surface self-contact and surface-to-surface are given as the contact of honeycomb and the contact between honeycomb and rigid wall, and the friction coefficient is 0.3.A rigid wall with a constant impact velocity is crushed with the honeycomb.A rigid wall with a mass of 0.018 kg impact with honeycomb.The impact dynamics have been great influenced by the impact velocity, structural style and thickness etc.
A rigid wall with a constant velocity is crushed with honeycomb.The deformation pattern, impact load and energy absorption characteristics are the three key parameters of the crashworthiness performance.Thereinto, the deformation pattern is the most important factor because it determines the impact load and energy absorption ability.The deformation pattern and impact load are compared with [27].The deformation pattern of honeycomb under the rigid wall with 14 m s −1 constant impact velocity is given as figure 2, and the numerical result in this research is close to that of [27].It could be seen that there are two types of deformation of the honeycomb.One is a localized deformation behavior close to the loading end, and the other one is a similar X shape deformation band for the global deformation.The impact load is compared with that of 3 in figure 3, and the error is within 10%.It could be seen that there is a peak impact load initial stage, and the load is stable in the subsequent stages.
The deformation model of honeycomb under 3.5 m s −1 impact velocity is given as figure 4. The deformation pattern of this research and [3] are demonstrated in the above and bottom of figure 4. It could be seen that the deformation is very similar with that of [3].At the beginning, there is a small local deformation mode of the loading end.Then, X shaped deformation pattern occurs near the loading end.At last, another X shaped deformation pattern is generated from fixed end with the development of global deformation.The two X shaped deformation patterns cross and form a parallelogram in the middle of honeycomb.

Impact dynamics of traditional honeycomb
The impact dynamics of honeycomb is very complicated and it would be great influenced by the impact velocity and wall thickness.The effect of impact velocity on the failure behavior is given as figures 5-6.The failure mode in the initial stage is demonstrated as figure 5.It could be seen that there is a great difference of failure behavior with respect to impact velocity.Three different failure mode are exhibited including I, V and X shape.The X shape failure behavior is demonstrated for the velocity below 20 m s −1 , and the failure zone moves towards to the end under impact.A larger size of X shape becomes smaller as the increasing of impact velocity.The failure near the middle of honeycomb for the 3.5 m s −1 is large than that of larger velocity.The deformation of honeycomb is X shape for the lower impact velocity, and the shape become V and I shape for the higher impact load.The failure area is concentrated at the end when the impact velocity is above 40 m s −1 .
Following with the initial stage, the typical failure stage of honeycomb are exhibited, another X shape failure mode is demonstrated for the 3.5 m s −1 .Different from lower impact velocity, the V shape failure behavior is exhibited for the 10 m s −1 and 20 m s −1 , and the I shape deformation is shown during the entire impact process.Through analyzing the entire failure process, the global deformation mode such as X and V shape would become the local deformation mode with the increasing of impact velocity.The impact load versus displacement curves are exhibited as figure 7. Shown as the figure, the two impact load stages including initial and stable ones are demonstrated.There a small different between three cases including 3.5 m s −1 , 10 m s −1 and 20 m s −1 , and they have the similar stable impact load.There are little influence of impact velocity on the impact load and energy absorption ability for the low impact velocity.Different from the low impact velocity, oscillating load for the 40 m s −1 and 60 m s −1 is shown for the larger impact velocity.Because the global deformation is exhibited for smaller impact velocity, and local deformation is demonstrated for larger impact velocity.As the increasing of impact velocity, the impact load would be more unstable due to the unstable failure process.The deformation model of honeycomb with different wall thickness including 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm are given as figure 8.There are two X shape deformation model shown as this figure, and little difference could be seen from the deformation model.Similar energy absorption efficiency is demonstrated for the different wall thickness.

Arc-curved hexagonal honeycomb
The hexagonal honeycomb with arc-curved edge is proposed by Bauer [25], and it is exhibited as figure 9. Different from conventional honeycomb, the tube wall is replaced with arc-curved line.The arc-curved honeycomb has better impact dynamic performance for the out-of-plane impact [10].This novel honeycomb  also has complicated deformation model.To better understand the impact dynamics, the crush behavior of arccurved honeycomb with 0.2 mm thickness under 3.5 m s −1 is researched.The central angles including 30°, 60°, 90°, 120°, 150°, 180°are considered, and the deformation models are demonstrated as figures 10-15.
Similar with traditional honeycomb, initial deformation like X shape is produced from the end shown as figure 10.Then, another X shape deformation appeared in the another end.Finally, two X shape deformation models for the 0 and 30°central angle are exhibited.A rhombus at the centre of honeycomb is formed between the two X shape deformation model.After that, more localized deformation is formed till the honeycomb is complete crushed.
The arc-curved honeycombs with 60°, 90°and 120°have similar failure behavior given as figures 11-13.It could be seen that X shape deformation is produced on the bottom of honeycomb different from honeycomb with 0°and 30°.With the development of deformation, more localized deformation occurs at the middle of honeycomb.Then, a V shape deformation model occurs close to the up end.With the increasing of central angle, the more material would be accumulated in the middle of deformation zone.
The failure process of arc-curved honeycomb with 150°and 180°are shown as figures 14-15.It could be seen that there are no X shape deformation like small central angle.A small inverted V shape deformation appears in the bottom end.Then, much more layer of cells is localized deformed.A small X shape deformation occurs at the middle.Totally different from the above cases, there are no X and V shape deformation for the 180°.The failure process began from the bottom end, and then the deformation gradually spreads to the other end.The unit cell with larger central angle has great structural gap, the honeycomb with 180°and 150°would

Conclusions
The typical impact parameters including impact velocity and wall thickness have great influence on the impact dynamic performance of honeycomb under in plane impact.Three typical deformation model including I, V and X are exhibited for the different impact conditions.X shape deformation is demonstrated if the impact   velocity is below 20 m s −1 , then the deformation model would transform into V shape with higher impact velocity.Finally, I shape deformation is shown if the impact velocity is higher than 40 m s −1 .The impact load curve would become fluctuation and oscillation with the increasing of impact velocity.The wall thickness has   little effect on the crushing behavior of honeycomb.The totally different deformation model is exhibited for the arc-curved hexagonal honeycomb with different central angle.The deformation model is X shape for the small central angle, and then it becomes V shape.The global deformation instead of local deformation is produced.The SEA is a decreasing function with respect to the central angle if this is smaller than 120°, and it would increase with the increasing of angle with higher value.

Figure 1 .
Figure 1.The finite element model of honeycomb.

Figure 5 .
Figure 5.The initial failure behavior of honeycomb with different velocity.

Figure 6 .
Figure 6.The typical failure behavior of honeycomb with different velocity.

Figure 7 .
Figure 7.The influence of impact velocity on the load versus Displacement curves.

Figure 8 .
Figure 8.The influence of thickness on the failure behavior.