Design and optimization of automotive energy absorber structure with functionally graded material

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ScienceDirect Materials Today: Proceedings 5 (2018) 25640–25648

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IConAMMA_2017

Design and optimization of automotive energy absorber structure with functionally graded material Rahul Nair, K.I Ramachandran Department of Mechanical Engineering, Amrita School of Engineering, Coimbatore, Amrita Vishwa Vidyapeetham, Amrita University, India Abstract An automotive energy absorber is a major safety component of a vehicle during head – on and rear collisions. The beam-structure should withstand and absorb the impact energy; thus preventing energy transfer. Design and analysis are done to reduce the impact resistance in vehicles like tractors which has low speed. This study includes the selection of functionally graded polyurethane (FGPU) and optimizing design thicknesses. Two grades of polyurethane (PU) material are tested for uniaxial compression using a universal testing machine (UTM), and the stress-strain plots are obtained. A hyperelastic constitutive material model is applied to perform the explicit dynamic analysis on the beam-structure. The objective is to maximize the stresses in the FGPU, until fracture. Dynamic analysis is performed using ANSYSWORKBENCH 15.0, while design optimization is carried out using MINITAB 17 and MATLAB 16. © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials and Manufacturing Applications [IConAMMA 2017].

Keywords: Functionally graded polyurethane, Optimization, Compression test, Hyperelastic constitutive material model, explicit dynamics, energy absorber, vehicle crashworthiness, response surface methodology.

2214-7853 © 2018 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials and Manufacturing Applications [IConAMMA 2017].

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Nomenclature S ti

Stress value of corresponding layer. layer thickness, where i = 1,2.

1. Introduction Automotive energy absorber is the crumple zone of an automobile. It undergoes deformation while impact, thus ensuring vehicle crashworthiness and driver safety. The structure transfers the impact energy uniformly towards the chassis. Designing of automotive energy absorber is a challenging issue. Hence researchers and automobile manufacturers had given more importance in this field. Researchers are still being performed in developing a proper material for bumper beam structure. Ramin Hosseinzade et al. [1] studied a commercially available bumper of glass mat thermoplastic (GMT) material, results displayed good resistance to impact. S.M. Sapuana et al. [2] presented a polymeric-based composite automotive bumper system and found that it is the best material for bumper fascia with advantage of lightweight and good aesthetics. Zhi Xiao et al. [3] explored crashworthiness of bumper with functionally graded foam material. Javad Marzbanrad et al. [4] investigated the bumper placed in front of vehicle by combining some different materials; high-strength sheet moulding compound, glass mat thermoplastic, aluminium, and found it very useful. Do-Hyoung Kim et al. [5] successfully manufactured a hybrid carbon and glass mixed bumper. Giovanni Belingardi et al. [6] in their work they selected and studied an epoxy and glass bumper structure with its capability to absorb energy. In this paper, we are trying to study functionally graded polyurethane material for automotive energy absorber structure and we are trying to optimize the stress computationally. 1.1 Polyurathane The elasticity of rubber combined with the durability of metal and toughness is limited in a unique material called polyurethane. Due to wide hardness range (soft to hard) an engineer is able to replace rubber, plastic and metal with polyurethane. It imposes good impact resistance and tear resistance under heavy loading and has high toughness as compared to plastics and rubber. Polyurethanes are used for aircraft, medical equipment, sprockets, wheels, heavy equipment industry. 1.2 Mechanical behaviour of high-density polyurathane High-density polyurethane is a hyperelastic material and on compressive loading yields a relationship between stress and strain, they are represented in Fig 1.

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Fig.1 Stress-Strain curve of high-density polyurethane [7] This curve has three different regions. In the first region material experiences, linear elastic behaviour is known as Hookian region .In the second region cell walls collapse due to buckling and cell crushing occur hence this phase is called the collapse plateau. The final region is known as densification phase, where a steep rise in the curve is seen due to high compressive loads tending towards a constant slope at a constant strain. 1.3 Functionally Graded Polyurathane (FGPU) Functionally Graded Polyurathane (FGPU) is a result of advanced research in materials science and they are characterized by a continuous variation of properties by changing the structure and composition moderately over volume. After the modification, the mechanical and chemical property of material improves. [8]. FGM can be used to avoid corrosion, fatigue, fracture and cracking. FGM had advanced technologically in fields like aerospace, mechanical and electrical Engineering applications and also in bio-mechanical implants. [9] By functionally grading the polyurethane material some of the mechanical properties can be improved also they have better properties compared with commonly used elastomers. The hard urethane segment and soft polyol differ in existence of a degree of immiscibility, which means that they are not structurally homogeneous. Soft and hard segments are mixed up to some extent and phase separation occurs, which produces a structure which is hard domain dispersed in soft segment matrix. [10]. 2. Material properties Samples of two grades (shore hardness 85A and 90A) of polyurethane were tested for uniaxial compression under ASTM 695 standards [11]. The dimensions of samples were 40mm diameter and 50mm in length. The stress-strain data for both the samples are shown in Fig. 2.

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Fig. 2 Stress-strain curve of polyurethane 2.1 Material model To study the non-linear stress–strain behavior of complex materials such as rubbers, polymers we use Ogden [12] (hyperelastic constitutive material model) given in Eq.1 and Eq.2. U=∑

3

(1)

Where: • N is defined as order of curve fitting. , , are stretches • • and α are material parameters which depends on temperature. It was assumed that Poison’s ratio is zero therefore Stretches =

∑

and

are neglected. (2)

With help of Non-Linear least square optimization procedure, Ansys will automatically fit the parameter. 3. Finite element analysis Dynamic analysis of automotive energy absorber structure was performed using Finite element analysis as shown in Fig.3 [13, 14] .The dimensions were obtained by measuring the

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front bumper of the Mahindra swaraj tractor using proper instruments like vernier calliper, measuring tape. The thicknesses were measured to be 2mm. The model has two, 1mm thick layers of polyurethane with different grades. Stress-strain data were given as input and the material constants were calculated by nonlinear least square optimization procedure. The first layer was assigned the properties of greater density of the material. Explicit dynamics analysis is deformed in Ansys15.0 [15]. A rigid cylindrical structure is allowed to hit the absorber with a velocity of 2.3 ± 0.1 mph according to 5MPh bumper law standards [16] as shown in Fig.4. Rigid Structure Absorber Meshed Absorber

Fig.3 The 3D model of absorber structure

Rigid Structure Velocity Direction Absorber

Fig.4 Impact velocity and direction of force 4. Optimization In order to obtain the minimum volume required to serve the effective purpose of the absorber, optimization is carried out. Stress function expressed in terms of thicknesses is

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generated using response surface methodology. Objective is to maximize the stress from first layer. It was made imperative that the total thickness did not exceed 2mm. The schematic representation is shown in Fig.5. The problem can be represented as: Maxti S1 (ti), where S1 is stress value. Subjected to St {0.1 ≤ ti ≤ 2.0, Where i = 1, 2. Basic Model

Optimized Model

Layer 1: Polyurethane (90A)

1mm

Layer 1: Polyurethane (90A) ?

Layer 2: Polyurethane (85A)

1mm

Layer 2: Polyurethane (85A)

Fig.5 Schematic representation of the optimization problem The generated results of initial design have to be optimised by varying both thicknesses by optimization tools. Table 1 shows thirteen set of design data were obtained through optimization in ANSYS 15.0. Table.1 Optimized data set of automotive energy absorber structure design S. No

t1 [mm]

t2 [mm]

Stress [MPa]

1 2 3 4 5 6 7 8 9 10 11 12 13

0.1 0.1 0.1 0.1 0.1 0.09 0.11 0.11 0.1 0.11 0.1 0.09 0.09

0.9 0.9 0.9 0.9 0.9 0.99 0.99 0.81 0.99 0.9 0.81 0.9 0.81

0.01597 0.01597 0.01597 0.01597 0.01597 0.000469 0.028435 0.018614 0.021994 0.013827 0.018118 0.011436 0.026558

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The objective function formulated by MINITAB given in Eq.3. 1.145

3.67

1

2.122

2

24.7

1

0.612

2

9.98

1

2 3

5. Results and discussion The energy absorber should break or deform under impact. Maximizing the stress will result in deformation of the structure preventing the impact energy to transfer towards chassis. Explicit dynamic analysis on the 3D model of the structure was performed using Ansys 15.0. Initially, the simulation was carried out for the structure with two layers of 1mm each. The maximum stress observed was 0.0091392MP as shown in Fig.6.

0.0091392 MPa

Fig.6 Stress plot for initial design Optimization was carried out using response surface methodology (RSM) optimizer in MINITAB 17 and optimized design datas were found to be t1=0.1 mm t2=0.9 mm as shown in Fig.7 and stress found to be 0.01597 MPa.

Fig.7 Optimized values of thickness calculated by RSM optimizer

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According to the problem defined, the objective was to determine the maxima of the stress function subjected to thickness constraints. In order to find local maxima of the function Lagrangian constrained optimization was carried out in Matlab 16. The results obtained were, t1=1.8 mm t2=0.2 mm the stress obtained was 0.046674 MPa as shown in Fig.8.

Fig.8 Stress plot of optimised design data 6. Conclusion Simulation of absorber structure was performed using Ansys 15.0. The results from initial design and RSM optimized data were obtained and compared. It was observed that thicknesses obtained through RSM optimizer yield 65% maximized stresses. Further on, Lagrangian constrained optimization was executed. The thicknesses obtained a stress value which was 80% of initial design. References [1] Ramin Hosseinzadeh ,Mahmood M. Shokrieh ,Larry B. Lessard, Parametric study of automotive composite bumper beams subjected to low-velocity impacts, composite structures, 68 (2005), 419–427. [2] S.M. Sapuan, M.A. Maleque M. Hameedullah ,M.N. Suddin ,N. Ismail, A note on the conceptual design of polymeric, composite automotive bumper system, Journal of Materials Processing Technology, 159 (2005), 145–151. [3] Zhi Xiao, Jianguang Fang, Guangyong Sun, Qing Li, Crashworthiness design for functionally graded foam-filled bumper beam, Advances in engineering software, 85 (2015), 81–95. [4] Javad Marzbanrad, Masoud Alijanpour, Mahdi Saeid Kiasat, Design and analysis of an automotive bumper beam in low-speed frontal crashes, Thin-walled structures 47 (2009), 902–911.

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[5] Do-Hyoung Kim, Hyun-Gyung Kim, Hak-Sung Kim, Design optimization and manufacture of hybrid glass/carbon fibre reinforced composite bumper beam for automobile vehicle, composite structures, 131 (2015), 742–752. [6] Giovanni Belingardi, Alem Tekalign Beyene, Ermias Gebrekidan Koricho, Geometrical optimization of bumper beam profile made of pultruded composite by numerical simulation, Composite Structures, 102 (2013), 217–225. [7] M. Mohamed, S. Anandan, Z. Huo, V. Birman. J. Volz, K. Chandrashekhara, Manufacturing and characterization of polyurethane based sandwich composite structures, Composite structures ,123 (2015), 169–179. [8] Rasheedat M. Mahamood, Esther T. Akinlabi, Mukul Shukla and Sisa Pityana, Functionally graded material: An Overview, Proceedings of the World Congress on Engineering (WCE), Vol III, July 4 - 6, 2012, London, U.K. [9] Ankit Gupta, Mohammad Talha, Recent development in modelling and analysis of functionally graded materials and structures, progress in aerospace sciences, 79(2015), 1–14. [10] Teerin Kongpun and Mutsuhisa Furukawa, Characterization of functionally graded polyurethane elastomers, Energy Procedia 56 (2014), 157 – 162. [11] ASTM Standard Test Method for Compressive Properties of Rigid Plastics: https://www.astm.org/Standards/D695.htm [12] Z. N o w a k, Constitutive modelling and parameter identification for rubber-like materials, engineering transactions, 117–157, 2008. [13] N Saravanan, VNSK Siddabattuni, KI Ramachandran, Static and dynamic analysis of asymmetric bevel gears using Finite element method, International journal of applied engineering research, 2009, 645-664. [14] GK Vijayaraghavan, MC Majumder, KP Ramachandran, S Sundaravalli, A modelling and analysis of delamination in GRP structure using Finite Element Analysis, Proceedings of the 22nd International conference on CAD/CAM Robotics and Factories of the Future (CARs & FOF 2006), Vellore Institute of Technology, India, 105-112. [15] ANSYS, Inc. “ANSYS® Academic Research”, Canonsburg, Pennsylvania, (2011). [16] U.S. department of transportation national high way traffic safety administration laboratory test procedure for regulation part 581 bumper standards, TP-581-01, April 25, 1990, 33.