Abstract Introduction

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2018-01-0119

Published 03 Apr 2018

Studies on Impact Performance of Gradient Lattice Structure Applied to Crash Box Xian Wu, Shuxian Zhang, and Jianwang Shao Tongji University Citation: Wu, X., Zhang, S., and Shao, J., “Studies on Impact Performance of Gradient Lattice Structure Applied to Crash Box,” SAE Technical Paper 2018-01-0119, 2018, doi:10.4271/2018-01-0119.

Abstract

T

he conventional crash box with thin-walled column conceals some limitations on pedestrian protection and lightweight. The metallic NPR metamaterials designed in this study are based on re-entrant lattice structures. Re-entrant structures are known to be one main class of axenic structures that display negative Poisson’s ratio (NPR), which can be manufactured by 3D printing technology. This kind of metamaterial has good designability and can be used as the filling structure of the crash box to improve the crashworthiness of the car. This paper starts from the relations between geometric parameters of the metamaterial. Considering the deformation characteristics of the crash box, the structure were designed into some gradient types. The mechanical properties of different gradient structures under

Introduction

C

rash box is an important part of the car bumper system, installed between the longitudinal beam and the front beam. Crash box is one of the main energyabsorbing components mainly through the compression deformation. Also, the impact force is reduced with the help of the crash box. The impact force, which is transformed to the longitudinal, could be dispersed by the crash box [1]. Because the impact force has been distributed to more parts, the acceleration of the crew compartment would be decreased and the less injuries would take place [2]. The impact performance of the crash box is closely related to the safety of the car and can be influenced by some factors, such as the material, the structure and the forming method. Mi Lin et al. [3] studied the impact performance of five kinds of different cross-sectional shapes of the singlechamber crash box. Furthermore, they compared the impact performance between single-chamber structure and the multi-cavity structure under compression. They found that the multi-cavity structure has much better impact performance. Because the crash box is a form of thin-walled tube, there is a large number of studies about the filling structures of the crash box and the foam Aluminum is the most

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the same impact conditions were compared to find the proper gradient structures. Based on the studies, the gradient lattice structure is applied to the automobile crash box. We made some simulation by the finite element software LS-DYNA of vehicle head-on collision. We compared the crashworthiness of the cars which have different crash boxes. The accelerations of some key points in the crew compartment were measured. Also, we compared the energy absorption efficiency of the boxes. We came to the conclusion that the gradient lattice structure can efficiently improve the structural crashworthiness criteria of the thin-walled column and also achieve better pedestrian protection of the vehicle structure. Because the lattice structure has good impact performance, some other vehicle structures which need to have a good impact behavior can also be replaced by it .

common. Gabriel Jiga [4] and A.K. Toksoy [5] found that the deformations of the thin-walled tube and the foam Aluminum filled tube were different, which is the main cause of the improvement. Wang Wei et al. [6] revealed the mechanical behavior of the composite filled structures and the influence factors were given. Cellular material refers to the material that contains a lot of holes but also has a certain cell structure. Single cell was cyclical arranged in the lattice material. So, lattice structure is a special cellular structure. From the eighties of the last century, Professor Evans [7] of Princeton University, Professor Hutchinson of Harvard University, Ashby [8] of Cambridge University firstly proposed a three-dimensional lattice structure. As the lattice structure has excellent mechanical properties and light characteristics, more and more research scholars are engaged in the study. With the maturity of 3D printing technology, lattice structure in the aerospace and other fields have a wider range of uses. In this paper, the lattice structure is applied to the filling of the crash box, changing the deformation process, so as to improve the energy absorption characteristics of the crash box.

Downloaded from SAE International by Jianwang Shao, Wednesday, March 28, 2018 Studies on Impact Performance of Gradient Lattice Structure Applied to Crash Box

Mechanical Properties of the Thin-Walled Crash Box Structural Crashworthiness Criteria

TABLE 1 The related parameters of the material

Material

Density (kg/m3)

Young’s Modules (GPa)

Poisson’s Ratio

Steel

7.9*103

210

0.3

© SAE International

2

FIGURE 1 FE model of the thin-walled column


The design optimization aims to generate a controllable crashing pattern for maximizing energy absorption and minimizing the forces during collapse [9]. There are several key indicators to evaluate crashworthiness of a structure, e.g. the initial force peak (Fmax), energy absorption (EA), specific energy absorption (SEA), average crash force (Favg), and crash force efficiency (CFE), as given in Eqs. (1)-(4) respectively, are widely used in the measurement [10]. The energy absorption (EA) of a structure measures the capacity of absorbing impact energy can be determined mathematically as, δ

∫

EA = F (δ ) dδ (1) 0

Where, F(δ) = the instantaneous crashing force with a function of the displacement δ. The specific energy absorption (SEA) assesses the absorbed energy per unit mass of a structure as, EA (2) m Where m is the total mass of the structure. A higher value indicates a higher energy absorption efficiency of material. The average crashing force Favg for a given deformation also indicates the capacity of energy-absorption of a structure, which is calculated as EA divided by the compressive displacement δ as

SEA =

EA (3) δ The crash force efficiency (CFE) and specific energy absorption can increase simultaneously [11]. The CFE indicates the uniformity of force-displacement curve, meaning that the higher the CFE, the more efficient the structure. CFE can be defined as,

Favg =

CFE =

four-node shell elements with five integration points through thickness and six degrees of freedom at each node. The oblique load exerted to the tube is modeled by the rigid wall. When dealing with contact condition between column and mass block surface, contact automatic surface to surface model is employed with the static and dynamic friction coefficient setting to 0.2. The material used here is the elaso-plastic constitutive model (*MAT_SIMPLIFIED_JOHNSON_COOK) with the constants values A = 600, B = 221, N = 0.6, C = 0.23 is adopted. The numerical results of the crash force are shown in Figure 2. This is a typical force-displacement curve for thin-walled metal structures. When loading the impact, an initial force peak (Fmax) would come along first. After that, a slightly concussion appeared and the force nearly keep unchanged. When the structure is compacted, the force jumped up significantly. The initial force peak would lead to structural failures if it exceeded the maximum yield force. So, we need to make Fmax in an acceptable range. The structural crashworthiness criteria are shown in Table 2. FIGURE 2 The numerical results of the crash force

Favg × 100% (4) Fmax

TABLE 2 The thin-walled structural crashworthiness criteria

Fmax(KN)

EA (KJ)

SEA (KJ/Kg)

Favg(KN)

CFE

392.83

9.43

27.67

81.86

0.208



The thin-walled structure used here is a straight column whose cross-section is a regular hexagon and the length of the side is 60 mm. The total length is 140 mm. The thickness of the column is 0.8 mm. The bottom part is fixed, the top part is impacted by a rigid wall with an initial velocity of 10 m/s. The added impacting mass is 1000 kg in order to imitate the real process in vehicle crash event. The related parameters of the material are shown in Table 1. The thin-walled column subjected to oblique impact loading here is implemented in the finite element (FE) program LS-DYNA. The structure is modeled using Belytschiko-Tsay


rashworthiness Criteria of C the Thin-walled Structure


The crashworthiness criteria are unsatisfactory, especially the high value of the Fmax and the low EA. In order to optimize the energy absorption, the lattice structure was introduced as the filling material to reach better crashworthiness criteria.

The manner in which materials change shape and size when they are subjected to uniaxial stress or pressure is described and quantified by their elastic constants. These elastic constants include the Poisson’s ratio, which characterizes the resultant strain in the y-direction for a material under longitudinal deformation in the x-direction [12]. The Poisson’s ratio is defined by:

ε1 (5) ε2 Where, ε1 is the strain perpendicular to the direction of compression or stretching and ε2 is the strain parallel to the direction of compression or stretching. Most materials get thinner when stretched and the Poisson’s ratio is typically a positive property with values. However, Almgren [13] got the NPR structure by changing the geometrical parameters. The structure with NPR has good mechanical properties.

ρr =

Where: ρt is the density of the cellular structure; ρ is the density of the base material. In the actual calculation, the relative density of the structure is obtained by using the single-cell analysis method:

ρr =

γ =−

he New Metallic NPR T Metamaterial Larsen [14] et al. first adopted the method of topological optimization to design a structure with negative poisson ratio effect, and obtained the two-dimensional structure of concave. A large number of theories and experiments show that the inner concave can cause the negative poisson ratio effect of the structure, and the most typical two-dimensional negative poisson ratio is the internal concave hexagon honeycomb structure. Later Yang [15] extended the two-dimensional concave hexagon structure into three-dimensional structure, and also obtained the structure with negative poisson ratio effect. Based on this conclusion, a variety of three-dimensional hollow structure is put forward [16, 17, 18], these structures all showed negative poisson’s ratio effect. In this paper, a concave structure was put forward. The structure is shown in Figure 3. The metamaterial is composed of 7 beams. Four parameters (Figure 3) are used to define the structure: h1, h2 , l, r. Where r is the radius of the cross section. h And we defined the height coefficient α h = 1 , the length h2 l coefficient α l = to implement normalization. h2 The properties of cellular materials depend on its relative density. The relative density may directly influence the impact performance and the energy absorption properties [19]. It defines as: © 2018 SAE International. All Rights Reserved.

ρt (6) ρ

4 3π  1 + α l2 / 3 + α h2 + α l2 / 3 + (1 − α h ) / 3 r 2   (7) 2 (1 − α h )(α lh2 )

The relative density depends in this case by those geometrical factors. The elastic modulus is the stress required by the material under external force to produce the elastic deformation of the unit. It is an important criteria to evaluate the resistance to elastic deformation. The effective elastic modulus is FIGURE 4 The fitted curve of effective elastic modules



Mathematical Description of the Metallic NPR Metamaterial Introduction of the NPR Metamaterial

3

FIGURE 3 The NPR matematerial

FIGURE 5 The force and the constraint loaded on the

single cell



introduced to study the mechanical properties of lattice structure.

Ee =

F (8) A ( ∆h2 / h2 )

The effective elastic modules is closely related to the relative density. Equ. (9) [13] is used to fit the curve.

f r = a ∗ x b (9)

Where: x is the relative density, which is equal to ρr . a, b are both constants. The value of b can significantly affect the trend of the fitted curve. Because the relative density of the lattice metamaterial is in the range of [0,1], the effective elastic modulus (fr) goes down more slowly with the decrease of the relative density (x) if b equals a smaller value. Thus, when the FIGURE 6 Trend of the mechanical properties when

geometrical parameters are changed

elastic modulus requirement is certain, the smaller relative density can be selected to realize the lightweight design. Rsq is used to evaluate the accuracy of the function which is supposed to be larger than 0.9. The fitted curve could reflect the mechanical properties of the NPR metamaterial to a large extent. For this fitted curve, a = 20590; b = 1.392; Rsq = 0.9908. The accuracy of the function is acceptable. b value is relatively low among the cellular materials (b value of foam Aluminum is about 2.0). Therefore, we can come to the conclusion that the new NPR metamaterial has good mechanical properties. In order to find the exact relationship between the mechanical properties and the geometrical parameters. h2, r remain unchanged, αl and αh varies in a certain range. Single-cell method was adopted to analyze the mechanical properties using the finite element analysis software Hypermesh/Nastran. The outer radius and the inner radius of the beam section were 1 mm and 0.5 mm respectively. The height coefficient αh were 0, 0.1, 0.2, 0.3, 0.4, 0.5 and the length coefficients αl were 0.5, 0.75, 1.0, 1.25 and 1.5 respectively. Constrain the lower vertex and load a static force of 50 N at the upper vertex, as shown in the figure. Figure 6 shows how the Poisson’s ratio and the relative elastic modulus change with the two geometrical parameters. when αh = 0.5; αl = 1.50, the negative Poisson’s ratio effect is the highest and the effective elastic modulus reaches the peak. When applied to the crash box, we choose the structure with αh = 0.5; αl = 1.0.

Mechanical Properties of Homogeneous Lattice Structures Validation of FE Models The impact performance analysis of the lattice structure was carried out by finite element analysis software LS-DYNA. In order to shorten the calculation time, we use the beam element (Belytschko-Schwer beam) instead of the solid element. Belytschko-Schwer beam model can well reflect the bending, extension and torsional properties of the beam. However, the beam element has some distortion in the deformation of the


FIGURE 7 The test model


4



Studies on Impact Performance of Gradient Lattice Structure Applied to Crash Box

FIGURE 8 Comparison between the test and the simulation

5

omparison of the C Homogeneous Structures with Different Geometrical Parameters Mechanical properties and microstructure of the geometric parameters of the lattice structure has the close relation. By controlling the geometrical parameters αh = 0.5; αl = 1.0, changing cross section radius r, we studied the change laws of mechanical properties with the geometric parameters. Select the geometric model as shown in the table, and the axial impact is carried out, and the impact energy is 50KJ. The matrix material is stainless steel. The material is the same as the thin-walled column and fitted by *MAT_SIMPLIFIED_ JOHNSON_COOK. JOHNSON - COOK model is based on the experiments, which can well describe the strain hardening effect of metal materials, strain rate effect and temperature softening effects [20]. It has the characteristics of simple form and easy to use, so JOHNSON - COOK model is used to curve fitting stainless steel structure. Its specific expression is:

(

σ y = A + Bε p


structure. We conducted a quasi-static compression test of the structure to make a verification between the solid sample and the beam model. The sample was produced by 3D printing technology. The contact of the beam element model is adopted by * CONTACT_AUTOMATIC_GENERAL. The quasi-static load was applied along the axial direction, and the force change curves were obtained respectively. From the curves, we can see that the simulation and the test can fit well. Therefore, the beam element can be used to reflect the actual structure stress. The deformation modes of the test and the simulation were similar at some important stages. Both of the models showed an obvious Negative Poisson’s ratio effect. The force-displacement curves of the simulation and the test matched well when the quasi-static force was loaded. We can get the conclusion that the beam model could reflect the real mechanical properties. So, the beam model was used in this study.

TABLE 3 The relevant parameters of the stainless steel

Density (kg/m3)

Young’s Modulus (GPa)

Poisson’s Ratio

A

7.9*103

210

0.3

600 221


B

N

c

0.6

0.23

n

)(1 + c ln ε ) ∗

Where, A,B,C and n are constants; ε p is the effective ε plastic strain; ε∗ = is the strain rate when ε0 = 1s −1 . The ε0 parameters of the stainless steel are shown in the table. The crash force variation curve of different radius homogeneous structure is shown in the Figure 8. Similar to the metal thin-walled structure, the force variation curve of the homogeneous lattice structure also underwent three stages, namely the elastic phase, the platform phase and the compaction phase. It can be seen that the initial force peak of the homogeneous structure is smaller, which reduces the risk of structural damage to a certain extent. It can be seen from the figure that as the radius increases, the platform becomes larger and the platform phase becomes shorter, indicating that the geometrical parameters of the structure have a great influence on the mechanical properties of the structure. As shown in the Figure 9, the initial peak force (Fmax) and the average force (Favg) curve with the radius r of the cross FIGURE 9 Force-Displacement curves of different

honogenous structures




FIGURE 12 The gradient lattice structure and the

homogeneous structure

TABLE 4 The description of the gradient structures

Radius Gradient (mm)

Relative Density

Gradient Distribution (from top to bottom)

0.05

0.3854

0.4 mm-1.05 mm

0.10

0.3608

0.4 mm-1.0 mm

0.15

0.4332

0.45 mm-1.05 mm

0.20

0.4046

0.4 mm-1.0 mm

0.25

0.3828

0.5 mm-1.0 mm

the compression of homogeneous structures. Therefore, the corresponding force is similar to the homogeneous structure. As the relative density increases, the force increases gradually. In this way, the trend of gradual change is formed. © 2018 SAE International. All Rights Reserved.


Functionally gradient Materials (Funetionally Graded Materials, FGM) refers to a kind of heterogeneous material. Its performance or composition gradient distribution along the length and thickness direction. FGM was put forward by a Japanese scholar for the first time in 1984 [21]. A large number of studies have shown that the gradient structure can greatly improve the energy absorption characteristics of the structure, and can improve the initial force peak and the change trend of the structure. It mainly influence the force on the platform stage, which can be transformed into the force changing tendency of the actual conditions. Therefore, the gradient design can break the contradiction between CFE and Fmax. When the crash box is subjected to compression deformation, it is hoped that the initial force is smaller and the end of the structure is stable during compression. According to the deformation characteristics of the crash box, we designed a gradient structure with relative density increasing (from the impact end to the other). The gradient structure and homogeneous structure schematic diagram are shown. The light color indicates that the structure density is smaller and the dark color is larger. It can be seen from the graph that the gradient structure increases gradually from the top to the bottom of the density distribution, and the density distribution of the homogeneous structure is uniform. The characteristics of gradient structure can be closely related to the gradient distribution. In this paper, the energy absorption characteristics of five gradient structures are studied, and the basic parameters are shown in the Table 4. Applying the same loading conditions to the gradient structure, the force - displacement curve is shown in the Figure 11. The initial stress peak of gradient structure is greatly reduced, and there is no platform stage of homogeneous structure. The stress increases with the increase of strain. This phenomenon can be explained by the deformation process of gradient structure. The deformation process of the gradient structure is shown in the Figure 12 (Gradient radius is 0.05 mm). Because the strength of the gradient structure decreases gradually from the lower down, the deformation process is collapsing from top to bottom. The compression of each layer approximates

FIGURE 11 Energy Absorption


Mechanical Properties of Graded Lattice Structures

FIGURE 10 Crash force of different structures


section. With the increase of the radius of the cross section, Fmax and Favg both gradually increase, and the increase of Favg directly affects the energy absorption characteristics of the structure, but too large Favg can also cause unnecessary failure of the structure. CFE is an important index for evaluating the absorbability of the structure. Within the structure force acceptable range, the larger CFE, the better. For this lattice structure, the CFE also increases gradually when the radius of the cross section increases. Homogeneous lattice structure has good mechanical properties. However, in practice, it often requires higher CFE and the smaller initial stress peak (Fmax). And the two factors in the homogeneous structure is often contradictory.


6



FIGURE 13 Force-Displacement curves of different gradient structures

FIGURE 14 The deformation process of the gradient

structure (Gradient radius = 0.05 mm)

7

FIGURE 15 The initial peak force (Fmax) trend and average

force (Favg) trend of different radius gradients


The initial peak force (Fmax) and average force (Favg) of different radius gradients are presented in Figure 13. The gradient structure is different from homogeneous structure, and the average force of gradient structure is greater than that of initial peak, that is, CFE > 1.0, which indicates that the gradient structure is more efficient and the energy absorption increases faster. There are significant differences in relative density of different radius gradient structures. Relative density is an important factor affecting the mechanical properties of structures. SAE reflects the amount of energy absorbed by the unit mass structure, which could effectively reflect the energy absorption of different gradient structures. When the radius gradient is 0.05 mm, the ratio of the structure is greater than that of other gradient structures.

Comparisons between the Traditional Crash Box and the Novel Crash Box he Impact Performance of T the Lattice Structure Filled Crash Box Based on the above analysis, the gradient structure with radius change of 0.05 mm is used to fill the thin-walled column. Figure 15 shows the deformation process of the thin-walled column and the gradient structure filled thin-walled column. The crash box filled with gradient lattice structure has more dense folds during compression. Therefore, the thinwalled column plays a bigger role. It can be seen from the table © 2018 SAE International. All Rights Reserved.



FIGURE 16 The energy absorption of different gradients

that the structural crashworthiness criteria of thin-walled metal structure have obviously improved after filling the gradient lattice structure.

ehicle Crash Performance in V the Head-on Collision The metal cavity without filler metal and the metal cavity with gradient lattice filling structure were applied to the whole vehicle respectively. 100% head-on collision were applied on the two types of car models. Initial velocity of the collision was set to 50 km/h. The two models were shown in the Figure 17. We can see in Figure 18, the left B pillar has two typical stages of peak acceleration during the head-on collision. The two stages of the acceleration were reduced by 5 g in the car model with gradient lattice structure filled crash box, which greatly improved the safety of the car crews. The steering wheel is an important index to measure the amount of invasive cabin safety. The crash box filled with gradient lattice structure could effectively reduce the intrusion of the steering wheel, and the reduction was about 5 mm. Above all, we can come to the conclusion that the gradient lattice structure made a great contribution to the safety of the car. The crashworhiness of the crash box has improved a lot. The crashworthiness of the whole car has also got better. The total mass of the gradient structure was only 2 kg which satisfied the demand of the lightweight design.

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FIGURE 20 The accelerations on the left B-pillar


FIGURE 17 The deformation process of two kind of column

FIGURE 18 Force-Displacement curves of the



FIGURE 21 The intrusions of the steering wheel

Conclusion

TABLE 5 Comparison of the crashworthiness criteria between the two kinds of thin-walled structure

EA (KJ)

SEA (KJ/Kg)

Favg (KN)

Fmax (KN)

CFE

9.43

27.67

81.86

392.83

0.208

13.61

39.91

119

276.56

0.430

FIGURE 19 The two car models with the traditional crash box and the gradient structure filled crash box



thin-walled columns

This work initially presents the mechanical model of architected cellular material with NPR configuration. This kind of lattice structure has an obviously better mechanical properties than the solid materials. Its mechanical properties have a closely relationship with its geometrical parameters. Therefore, different geometric parameters were studied under the same impact condition. We concluded that both the force trend and the energy absorption efficiency of the lattice structure were much better than the thin-walled structure. Because the mechanical properties could be controlled by changing the geometric parameters, the gradient structure can be designed according to some actual conditions. The different gradient distributions were studied, and the gradient lattice structure with gradient radius of 0.05 mm was the best. A novel crash box filled with gradient lattice structure was compared with the initial box. All of the structural crashworthiness criteria were improved. The results are encouraging in the sense that it offers another potential material for engineers to address the issue and the novel crash box filled with gradient lattice structure can be widely promoted and achieve further application in the near future.


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Contact Information

12. Almgren, R.F., “An Isotropic Three-Dimensional Structure with Poisson’s Ratio=-1 [J],” Journal of Elasticity 15(4):427-430, 1985.

Shao Jianwang School of Automobile studies, Tongji University NO.4800, Cao'an Road, Jiading District, Shanghai, China [email protected] Tel:+8613636582992

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Acknowledgement

14. Larsen, U.D., Sigmund, O., and Bouwstra, S., “Design and Fabrication of Compliant Micromechanisms and Structures with Negative Poisson’s Ratio,” In Micro Electro

Funded by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (No. [2015]1098) and Shantou Science and Technology Project 201797.

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