Introduction

Every vehicle is designed with the prime objective of safe transportation of its occupants. But when we deal with high speed in lightweight structures specifically in open-wheel-type race cars, generally known a formula type car, the importance of these structures is immense. These structures of the chassis are known as the crash attenuator, and they are involved in absorption of the impact energy during an event of a crash (Fig. 1). Over the years, the design of these structures has evolved based on the outer aerodynamic shape of the formula type cars but the engineering underneath that skin defies its limit whenever a crash takes place. Improving its specific energy absorption (SEA) is always the prime target of any composite engineer within the bounds of regulation since that plays a crucial role in the safety of the driver. The application of numerical analysis with the base of extended finite element methods (XFEM) have made this easier but still, the prediction and approximation in the behavior of these carbon fiber composite laminates remain a challenge. This project tries to work more toward solving this challenge by modeling and simulating a rear crash attenuator of an IndyCar and validating the results with the experiment to develop a better prototype structure for the future.

Fig. 1
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Deceleration–displacement diagram for frontal impact

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IndyCar is the most premium level of open-wheel-type racing in North America. This is a spec-level racing series with Dallara Automobili being the prime constructor. Unlike its European counterpart Formula1, all the teams are required to race on the same chassis with governed restriction to the aero bits changes on the car. The current model of IndyCar uses DW12/UAK18 chassis which was a complete lightweight carbon fiber honeycomb sandwich structure and is the focus of the research. This chassis has four crucial crash absorption structures—front nose cone, rear crash attenuator, side impact structures and roll hoop (Fig. 2).

Fig. 2
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Crash safety structures of 2018 season IndyCar

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A previous study [1,2,3] conducted on crashworthiness and impact damage of carbon fiber composites via numerical analysis has been following the procedure of using finite element methods and later validating them with experimentation. Every research talk on a different aspect of carbon fiber properties which is crucial from the fact that certain constraints must be established, while we numerically model them using the concepts of continuum damage mechanics. Also, different software is utilized to create such models but the prime focus for such explicit dynamics and nonlinear finite element analysis takes place utilizing the software LS-DYNA.

Feraboli [4] talks about how the variation in shape affects the energy absorption of carbon fiber structures during a crash and formulates it based on the curvatures present in the structure through his experimental setup as well as numerical methods. In his research he concludes that in delamination, “little energy is absorbed in splitting the material along an interlaminar crack front” [4]. High energy is absorbed during the fragmentation failure mode and curved geometries suppress delamination fronts and initiates fragmentation, thereby causing higher energy absorption.

Agreeing to this concept, Anghileri [5] conducts experiments and find out the deceleration curves using the LS-DYNA where he very well explains the importance and modeling of various parameters in software. He uses MAT 58 card to model the material and provides a sensitivity study on the mesh so that the overall simulation time can be reduced.

Research shows that the energy absorption can be modeled efficiently by utilizing chamfer triggers which acts as an intrinsic part of the simulation since it allows a gradual application of force. The use of innovative triggers outperforms the conventional triggers for efficient initiating longitudinal cracking, fragmentation, and delamination [6]. The research agrees on the effects of geometrical shape and curvatures as mentioned by Feraboli [4] and discusses the contribution of geometric parameters for effective design.

Cherniav [7] details the important elements of LS-DYNA specifically to model the carbon fiber composites and discusses the shortcomings of three specific material modules and their accuracy with the experiments. He also explains the parameters affecting a simulation and ways to accommodate these in a simulation to get desired results. Wentao [8] explains his investigation on the carbon fiber–aluminum sandwich structures by numerically modeling them predicting their energy absorption and improvements by changing the ply direction and thicknesses. While the research focusses on the static drop tests and impact loading, a significant discussion is made on the influence of face sheet thickness on impact resistance and energy absorption in the honeycomb structures. Also, a significant analysis shows that the variation in honeycomb core thickness and cell wall density is an independent factor in the energy absorption during crash [8].

Modeling delamination in a composite structure is tough to achieve and is generally neglected since the amount of energy absorbed in this process is less as compared to splaying and fragmentation. Research by Belingardi [9] shows ways to model this phenomenon of delamination in LS-DYNA using a different material module and doing a comparative study of modeling techniques. Performing this analysis on small specimens and validating it by experiments, he then applicates it to large carbon fiber crash structures. Also, he comments on the “detailed reproduction of the physical phenomenon” [9] at the expense of very high computational time.

Although every author has some specific detail to talk about based on their research and experimentation, they unanimously agree on the future scope and development of carbon fiber structures exploiting its energy absorbing properties which will help in creating safe and crashworthy structures for application in motorsports and aerospace. The results produced by Feraboli [4] are validated and approved by the Federal Aviation Administration (FAA) utilized in the design of modern-day aerospace structures. The results produced by Anghileri [5] are utilized by Fédération Internationale de l’Automobile (FIA) for validating their motorsports structures, numerically analyzing them, and further developing it for improved results and designing prototypes.

Problems and Objectives

The rear impact attenuator of IndyCar broke off from its bulkhead at the time of an oblique impact over a series of 3 seasons and three similar crash scenarios taking place at Texas in 2018, and at Iowa in 2017 and 2016 (Fig. 3). The investigation conducted by the regulatory body of IndyCar found that the attenuator breaks off when impact takes place at a 30° axis or more. Also, in case of a straight impact, the structure does not deform much, causing reduction in energy absorption and car deceleration. This violates the safety of the driver as well as that of other cars during a race.

Fig. 3
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Deceleration–time plots of the three crash scenarios from the accident data recorder (ADR) in the cars. (a) Texas 2018 crash, (b) Iowa 2017 crash, (c) Iowa 2016

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The objective of this paper is to increase the specific energy absorption of the structure with an optimization analysis on the structural weight by result validation and composite ply optimization. Also, reasonable modification as per the regulation body’s requirement specifically the deceleration values of 20 g will be made to the crash attenuator and improving its performance by redesigning a prototype for the IndyCar-2021 season (Fig. 4).

Fig. 4
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Deceleration vs. time plot of the experimental crash test conducted by FIA for IndyCar

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The other objectives include developing a better correlation of the modeled structure numerically and understand the working of a composite structure. This will ensure ease in designing and help in reducing the experimental cost analysis.

Model Formulation and Experimental Comparison

Material and Experimental Detail

The material specifications and the design of the attenuator were provided by the OEM Dallara Automobili. The structural construction of the attenuator includes a carbon fiber–aluminum honeycomb sandwich structure. The skin composed of RC245T 40% 3 K T300 2 × 2 twill carbon fiber and the aluminum honeycomb 5052 1/8 4.5 pcf for the core. Standard tests as per the FIA guidelines [10] were performed on the attenuator which was accepted by the IndyCar for overall design. This includes

  • An impactor mass of 900 kg impacting at a speed of 11.9 m/s.

  • The peak deceleration over the first 225 mm of deformation does not exceed 20 g.

  • The maximum deceleration does not exceed 20 g for more than a cumulative 15 ms, this being measured only in the direction of impact.

  • All the structural damage must be contained within the area behind the rear wheel center line [10].

The impact test was performed, and the deceleration graphs were plotted which certainly shows the need for remodeling of the structure since the peaks overshoot the design limits (Fig. 4) causing hindrance to safety.

Experimental Correlation and Calibration

To understand the working of this specific carbon fiber prepreg and its equivalent mesh modeling in LS-DYNA, square tube specimens were tested under axial compression load with this material (Fig. 5). A 45° chamfer was given to the tube so that it acts like a trigger and the progressive failure mode is achieved. The layup for the testing was chosen to be [0,45]s with a ply thickness of 0.25 mm. The tests were conducted on MTS-858 Mini Bionix II and the samples were crushed to over 60%. The data output was plotted as force vs. displacement curves which were later used for the result validation in LS-DYNA. Following previous research [7], the non-physical parameters along with the material properties from the datasheet were utilized for conducting simulations on the square tube test specimen of length 171.45 mm.

Fig. 5
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Specimen model simulation for calibration of the LS-DYNA software

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A significant overshoot in the initial peak was observed in every simulation run which got suppressed as the crushing progressed. A total of 4 significant runs were made in order to configure the final SLIMi parameters that closely resembles the experimental force–displacement graph. These data were then filtered using a low-pass SAE1000 filter to clear out the unmodulated peeks and get an accurate representation close to the experimental data (Fig. 6). It was observed that varying the parameter SLIMC1 and SLIMC2 which is a factor to determine the minimum stress limit after the maximum stress in fiber compression and matrix compression [11], respectively, affected the correlation the most while other SLIMi parameters (SLIMT1, SLIMT2, SLIMTS, SOFT, ERODS) were kept constant based on the literature [2, 3] and iterative simulations conducted in accordance for the correlation. The calibrated values to the RC245T carbon fiber in Fig. 8 were further utilized to conduct simulations on the attenuator structure (Fig. 7).

Fig. 6
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Experimental correlation and dependence on the SLIMi parameters. (a) Correlation with RAW experimental data, (b) correlation with low-pass-filtered data

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Fig. 7
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Calibrated MAT_058 properties utilized for simulation

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Finite Element Material Modeling

MAT058_LAMINATED_COMPOSITE_FABRIC module in LS-DYNA was utilized to model for the numerical simulation. This is a Matzenmiller’s damage mechanics-based model accounting for nonlinear peak softening of the composite plies [12]. This is inferred as two sets of parametric properties Ei and SLIMi which consists of the physically defined material properties and individual non-physical parameters which needs to be calibrated as per the experimental data. The table illustrates the parametric data that was used for calibration of the software to establish an experimental correlation and baseline for the development simulation runs. The MAT058 material model consists of two parts to determine the element erosion- the first being the damage mechanics model that involves modulus reduction using three nonnegative parameters which vary from 0 to 1 [6]. The other part is the complete removal of element layer after maximum effective strain is achieved using ERODS.

The specimen model was meshed with Belytschko–Tsay thin shell elements, and the trigger was modeled as an element wide consisting of half the number of plies in the overall structure. The impactor was designed as a rigid body and the structural force was measured using the RC_FORCE card. The parametric properties of SLIMi were adjusted to calibrate the software for the further runs. The validation with the experiments ensured these values to be within the limits for effective simulation.

The rear attenuator CFRP outer skin was meshed using the quality optimization tool included in the HyperMesh software. This tool is a Quality Index-based tool, which optimizes the mesh following a chosen algorithm and a variety of parameters as per designer’s choice. The crash analysis algorithm was utilized here which performs the geometric simplifications and places the elements in a fashion that the crashworthiness analysis is optimized. This CFRP skin was assigned with the Belytschko–Tsay thin shell elements [12, 13] for analysis and the number of integration points increase with the increase in addition of layers using the PART_COMPOSITE module of LS-DYNA (Fig. 8). A total of 28,673 elements were identified and the boundary constrains similar to that of the experimental setup was designed using BOUNDARY_SPC. The impactor was modeled as a rigid body [8] with a weight of 900 kg and was constrained to move in only x-direction with other motion fixed at a velocity of 11.9 m/s. The simulation was run on 16 core 3.3 GHz AMD Ryzen computer, and the total time for simulation was about 8 h and 43 min. The graphs of deceleration, forces and displacement were obtained in the form of Binary D3 plots.

Fig. 8
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Finite element model for the crash simulation as per the FIA regulation at (a) 0°, (b) 30° off-axis

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Parametric Analysis on Failure Criteria

Deformation and Failure Mechanics

The energy dissipation in metallic materials takes place through “plastic folding, work hardening and adiabatic losses due to heating” [14]. Contrastingly, carbon fibers “dissipate energy through external and internal frictions, fiber bending and kinematic dissipation through fragmentation” [14]. In addition, one of its properties of high specific energy absorption has been exploited to achieve vehicle deceleration during crash. During a brittle fracture in composites, 4 of the energy absorbing phenomena could take place- global buckling, progressive folding, progressive splaying, and progressive fragmentation. The damage mechanism may occur in four different ways in a fiber reinforced plastic. This includes fiber failure, matrix failure, fiber–matrix shear failure and delamination [15].

Fragmentation dominated the energy absorption mechanism resulting in energy absorption of over 50 kJ. Also, Mode-1a failure which is failing of the structure by micro-cracks was observed as the failure mode in the rear attenuator structure. Delamination was not modeled specifically due to very high simulation times and its comparatively less involvement in energy absorption over the other failure model. Since matrix failure is the dominant cause of delamination, the amount of energy absorbed by the matrix over the fibers is usually 10%. Also, since the structure has high amount of curvatures, the delamination failure is suppressed [4].

Effect of Ply Thickness

Thinner unidirectional plies are usually used in aerospace grade manufacturing but the trend in motorsports has been a bit different. Though a material with a specified thickness was provided by the manufacturer, a study was conducted to understand the effect of ply thickness on the deceleration values which is one of the prime objectives of the research. Four different plies of thicknesses ranging from 0.135 to 1.08 mm were simulated on the test specimen with the experimentally determined parametric properties of the material. It is to be noted that the overall thickness of the structure was kept same while simulating the results which can be inferred as the variation in the number of plies involved in the structure (Table 1).

Table 1 Study of ply thickness and its effect on peak deceleration
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Effect of Impact Angles

The impacts taking place during a race is rarely head-on, and the attenuator has to be designed in a way so that it sufficiently absorbs the torque produced in case of an oblique impact rather than shearing off from its attachment. Deceleration and energy absorption at two different impact angles of 15° and 30° of axis were measured to study its effects. In both the simulations performed using the calibrated LS-DYNA, we found the peak deceleration to be 30 g and 25 g lasting for less than 2 ms which is under the norms of FIA regulations [10]. While the 15° impact represented a deceleration curve close to 0° head-on impact but lasted for over 50% more and reflected higher SEA. The impact at 30° also lasted for 50% more than the 0° head-on impact but reflected a trough which can be evaluated as the failure of bulkhead taking place at that time. This can be adjusted to get better values since the amount of energy absorbed closely matches to the 0° head-on impact and can be justified for the bulkhead failure.

Results and Discussion

The specific energy absorption was determined at different configurations of impact of the rear attenuator. This was achieved by evaluating the force over a crushed displacement of the reinforced sandwich structure. The layup was adjusted, the sensitive points were stiffened, and the core thickness was varied throughout the structure to improve the overall SEA by 41.8% with a gradual deceleration value to that of the prescribed (Fig. 9). This overall design worked well for both the head-on impacts and angular impacts as required by the governing body of IndyCar and are well under the regulations (Fig. 10). The redesigned rear attenuator is capable of absorbing 58% more energy and is optimized for minimum weight improving it by 12.8%. The further modification of the structure for changing its overall external design was limited to the prototype phase since this may influence the aerodynamics of the car. The validation of the redesigned attenuator awaits experimental correlation, but since the baseline results have a 90% match with the experimental data, the improved results obtained via numerical modeling and simulations are precise (Fig. 11).

Fig. 9
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Deceleration (× 100 g) vs. time (s) plot of the simulated deceleration over the crushed length of the attenuator at 30° impact angle. (a) Current attenuator, (b) redesigned prototype

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Fig. 10
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Deceleration (g) vs. displacement (mm) plot to find the deceleration over the crushed length of the attenuator at 0° impact angle. (a) Current attenuator, (b) redesigned prototype

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Fig. 11
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Parametric comparison of the improved result from the redesigned prototype structure

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