Peak Crushing Force Research Articles

Effect of taper angle on crashworthiness performance in hybrid tubes

The present paper dealt with the finite element analysis (FE) analyzing the taper angle design of aluminum/E-glass fiber reinforced polymer hybrid tubes. This study investigated the crushing characteristics involving peak crush force (PCF), crush force efficiency (CFE) and specific energy absorption (SEA) capacity of thirty different configurations of hybrid tubes. Three types of geometries were studied numerically, including circular, square and hexagonal. The structures evaluated included circular hybrid tubes fabricated with aluminum alloy and composite. The hybrid structures were subjected to axial impact loads using a 750-kg rigid impactor with an initial velocity of 15 m/s. It was found that the crashworthiness performance increased with increasing taper angle. The SEA and CFE values of the circular hybrid tube with a 10° taper angle were high in the other square and hexagonal hybrid tubes. That hybrid structure can preferable as impact energy absorber due to the ability to withstand axial impact loads effectively.

Crashworthiness analysis and multi-objective optimization of expanding circular tube energy absorbers with cylindrical anti-clamber under eccentric loading for subway vehicles

This paper presents an investigation of the crashworthiness of expanding circular tube energy absorbers with a cylindrical anti-clamber under eccentric loading for subway vehicles. A finite-element model of energy absorbers is created and validated by two quasi-static experiments, and the strain rate sensitivity is evaluated using standard coefficients of the Cowper-Symonds constitutive model. A parametric study is performed using the validated finite-element models. It is found that the eccentric collision of two energy absorbers has a significant effect on their crashworthiness and leads to a decrease in the specific energy absorption (SEA) and an increase in the peak crushing force (PCF). The structural parameters of the energy absorber, including the wall thickness t, conical angle α, and punch radius rp, have a significant effect on its crashworthiness under different eccentric distances. Sobol sensitivity analysis is employed to analyze the effects of the design parameters (t, α, and rp) on the objective responses (EA and PCF). The results show that the design variables t and α have a greater effect on the sensitivity of the EA and PCF functions for the eccentric distance of h = 0 and 40 mm. The interaction between punch angle α and punch radius rp has significant effect on EA. To improve the crashworthiness of the expanding circular tubes, a multi-objective optimization is applied to achieve the maximum EA and minimum PCF values, and weight factors are introduced to investigate the crashworthiness optimization under single-eccentric loading and multiple-eccentric loading. The optimization solutions of the expanding circular tubes under different single-eccentric loadings have considerable implications. For multiple-eccentric loading, the results show that the crashworthiness of the expanding circular tube energy absorber can be better balanced.

Multi-objective crashworthiness optimization of thin-walled multi-cell tubes with different wall lengths

Thin-walled tubes are extensively used in the automotive industry because of their high energy absorption capacity and lightweight advantages. These structures are expected to have high energy absorption and low peak force during any collision. In this study, to obtain low peak crushing force, different wall lengths have applied to the thin-walled tubes. Different wall lengths have investigated using doubly-walled walled, inner multi-cell walled and multi-cell walled tubes obtained from square, hexagon, octagon and circle cross-sections. To evaluate crashworthiness performance dynamic impact analyses at a constant velocity are carried out using the non-linear explicit Finite Element (FE) code Radioss. According to the FE results, tubes with different wall lengths give lower peak crushing force (PCF) of up to 36% compared to normal tubes. On the other hand, in tubes with different wall lengths, there is a decrease of up to 6% in specific energy absorption (SEA) compared to normal tubes. Thus, considering the decrease of the PCF, the advantage of tubes with different wall lengths is presented. Optimization studies have carried out for the second type octagonal tube with different wall lengths (O2G) and the third type octagonal tube with different wall lengths (O3G) which give better SEA and PCF values between all tubes.

Numerical Study on Axial Crushing of Auxetic Foam-Filled Square Tube

Filling the thin-walled tubes with a foam core is a typical method to enhance the energy absorption performance and stabilize their crushing responses under impact loading. Recently, auxetic foam material with negative Poisson’s ratio has gained remarkable popularity as an effective candidate to enhance the energy absorption capability of structures. In this paper, polyurethane auxetic foam is suggested as a foam core with the negative Poisson’s ratio of-0.31. Numerical simulation was performed to quantify the crush characteristics of auxetic foam-filled square aluminum tubes for variations in initial width of tube under quasi-static axial loading using the nonlinear finite element (FE) code LS-Dyna. Based on the numerical results, the influence of tube width was quantified in terms of energy absorption (EA), specific energy absorption (SEA), initial peak force (Pmax) and crush force efficiency (CFE). It is found that the progressive collapse and deformation modes of auxetic foam-filled tube (AFFT) is pronouncedly affected by varying the tube width. Furthermore, the SEA of AFFT is remarkably sensitive to the tube width variations, yet show low sensitivity to the EA of AFFT. The present study provides new design information on the crush response and energy absorption performance of auxetic foam-filled square tube with varying tube width.

On crashworthiness design of hybrid metal-composite structures

As a class of promising cost-effective lightweight structures, metal-composite hybrid structures has rapidly emerged in automotive industry largely attributable to their outstanding multifunctional and crashworthy characteristics. Recently, continuous efforts have been devoted to the studies on the crashworthiness of various hybrid tubes, which commonly present two typical configurational schemes, namely metal-composite (i.e. a metal outer tube internally filled with an inner carbon fiber reinforced plastic (CFRP) tube) and composite-metal (i.e. an outer composite tube internally filled with an inner metal tube). Nevertheless, rather limited studies have focused on revealing energy absorption mechanisms of hybrid structures; and how to optimize the performance to cost characteristics of hybrid structures still remains an open question in literature to date. This study aimed to maximize the energy absorption of different configurational aluminum/CFRP hybrid tubes. First, the finite element (FE) models were developed and validated by comparing the damage modes and crashworthiness indictors with the dedicated experimental study. Second, the interactive effects of the hybrid tubes were investigated by analyzing the discrepancies in the deformation pattern and internal energy absorption of each material through the validated FE models. For the AL-CF configuration (i.e. CFRP inner tube with aluminum outer tube), changes of deformation mode increased the internal energies of aluminum and CFRP tubes by 43.6% and 17.8% compared to the net aluminum tube and net CFRP tube, respectively; and increased the frictional dissipation energy by 45.6% compared to the sum of that of net aluminum and net CFRP tubes, largely enhancing energy absorption of AL-CF. For the CF-AL configuration (i.e. aluminum inner tube with CFRP outer tube), the internal energy increased by 27.6% for the aluminum tube but decreased 31.9% for the CFRP tube compared to the net aluminum tube and net CFRP tube, respectively; whereas the frictional dissipation energy decreased by 47.6% compared to the sum of that of net aluminum and CFRP tubes, indicating the vital importance of hybrid configuration to energy absorption. Third, the effects of wall thickness, sectional dimension and sectional shape on the energy absorption capacity as well as the performance-cost characteristics of the hybrid tubes were further studied. It was found that from a performance perspective, the hybrid tube with a thicker CFRP tube had higher capacity of energy absorption; whilst from a performance to cost perspective, the hybrid tube with a thinner aluminum tube offered better cost-effective energy absorption characteristics. Moreover, with the same weight, the hybrid tube with a circular sectional shape and a smaller sectional size exhibit a better performance. Finally, a multiobjective discrete optimization was conducted to optimize the AL-CF hybrid tube with various sectional shapes, sizes and wall thicknesses. As a result, the weight, peak crush force (PCF) and cost were finally reduced by 41.3%, 18.0% and 11.2% respectively, while the energy absorption (EA) was enhanced by 48.0% in comparison with the baseline design.

Crashworthiness analysis of foam filled star shape polygon of thin-walled structure

This paper aims to fabricate star polygon thin walled energy absorption structure that tends to relapse the intensity of set in decelerations during impact while escalating the amount of energy absorbed. The crashworthiness topology optimization is used for structural optimization of various foam-filled tubes. The relative advantages of 14 configurations are discussed, and the effects of filling five types of foam into the best configuration of the star-shaped tube over an empty one is investigated. Specific Energy Absorption, Peak Crush Force and response of weight of the members during frontal impact are the main dimensions parameters of the member's performance. Numerical simulation is carried out using the explicit dynamics of Ansys 17.1, and obtained results are compared with experimental results conferring crash behavior and energy absorption characteristics. Based on results, the suited configuration with required performance in crashworthiness is suggested, which shall be incorporated in automobiles for safety consideration of passengers during an impact. The results show an increment of 40% in Specific Energy Absorption suggesting a better choice of a particular type of foam over a hollow tube.

How does bio-inspired graded honeycomb filler affect energy absorption characteristics?

Functionally graded structures are widely observed in nature and have been considered to have excellent mechanical properties. In this paper, a novel bio-inspired graded honeycomb-filled circular tube (BGHCT) is proposed to enhance structural energy absorption characteristics under lateral load. The graded honeycomb fillers are constructed using 3D printing techniques. To systematically explore the crashworthiness of BGHCT, the nonlinear finite element models are first developed in Abaqus (explicit) and validated against the experiments. Then graded honeycomb-filled circular tubes with axial and radial graded directions are compared with uniform honeycomb-filled counterparts (UHT). Parametric studies find that BGHCT exhibits superior capacity of energy absorption. Furthermore, various parameters, like effective filling length, thickness and yield stress of column wall, have a considerable effect on the crashworthiness of this novel structure. Lastly, multi-objective optimizations of BGHCT and UHT are carried out with the aim of simultaneously improving specific energy absorption (SEA) and reducing peak crushing force (PCF), based upon the Kriging modeling technique and non-dominated sorting genetic algorithm II (NSGA-II). The optimal design parameters are obtained for these honeycomb-filled structures. By comparison we find that energy absorption characteristics can be increased by up to 89.73%, and effective length filled structure has the best crashworthiness, followed by full graded honeycomb-filled structure. The study provides new insights into the transformation of natural biological inspiration into engineering applications for crashworthiness.

A new homo-polygonal multi-cell structures under axial and oblique impacts; considering the effect of cell growth in crashworthiness

In this paper, groups of new homo-polygonal multi-cell tubes are introduced and investigated under both axial and oblique loads via studying the effect of cell growth on energy absorption characteristics. Finite element models has been developed and validated by experimental tests as well as a new developed theoretical procedure for multi-cell tubes. The new developed homo-polygonal multi-cell structures are investigated considering the effect of cell growth to find the most efficient topology. Different polygonal cross-sections including pentagonal, hexagonal and octagonal are considered while each cross-section has cells in corners form that have the same shape as their own cross-section. Obtained results point out that there is a distinct connection between cell’s size and absorbed energy and cell growth could affect the energy absorption characteristics in a perceptible manner. When cells start to manifest in tubes the peak crush force increases and then drops to its original value as cells reaches their maximum possible size. Acquiring the numerical data of all the structures, by using the COPRAS multi-criteria decision-making method, the best structure is distinguished. Next, the best thickness in the best impact angle of crash found using the relevant RSM as an optimisation method.

Crashworthiness design and optimisation of windowed tubes under axial impact loading

Thin-walled structures are frequently used as energy absorbers in the automotive, railway and aviation industries. This paper addresses the crashworthiness performance of thin-walled windowed tubes under dynamic impact loading. Different shapes of cut-outs were introduced to thin-walled tubes with different cross-sectional shapes to create windowed tubes. Explicit finite element code, LS-DYNA, was used to simulate the crushing behaviour of the windowed tubes under axial impact loading. The Finite Element (FE) model was validated by conducting experimental tests and showing that the numerical and experimental responses are comparable. The crashworthiness responses of the different windowed tubes were compared and the best performing tube was identified using a multi-criteria decision-making method known as Technique of Order Preference by Similarity to Ideal Solution (TOPSIS). It was found that a circular tube with a square window shape outperforms all other sections and exhibits the best energy absorption characteristics.Subsequently, a multi-objective optimisation analysis was performed to find the optimal configuration of the best tube. Response Surface Methodology (RSM) was used to develop models for the energy absorption responses of the tube. The design variables were selected to describe size, number, and distributions of the windows, while specific energy absorption (SEA) and peak crush force (PCF) were set as design responses. Parametric analysis was conducted to understand the effects of the design variables on the crashworthiness behaviour and the optimal configuration was identified.

Crashworthiness analysis of a straight-tapered shrink tube

This paper proposes a new straight-tapered shrink (STS) circular tube, which is planned to be applied on railway coupler for energy absorbing and overload protection. Quasi-static experiment and finite element (FE) simulation were adopted to investigate the crashworthiness performance of the STS tube. In the FE analysis we found that the compressive material properties were more suitable for accurately modeling the STS tube. The results showed that the STS tube can develop two deformation modes, i.e., shrink mode (S-mode) and buckling mode (B-mode), and the B-mode cannot meet the application requirement. Moreover, the distribution of deformation modes under different geometric parameters, namely, wall thickness (t), slope angle (α) and straight zone length (L1), were obtained. It was found that the B-mode mainly occurs when t, α and L1 are all large. The force-displacement characteristics showed that a plateau force occurred in some STS tubes. A theoretical model for predicting the plateau force was then proposed. Finally, the effects of geometric parameters on the peak crush force (Fmax) and specific energy absorption (SEA) were performed. It was found that the increases in the three parameters all result the increases in SEA and Fmax, and α has the most significant effect on the crashworthiness performance of the STS tube.

Evolution of a new geometric profile for an ideal tube inversion for crash energy absorption

Circular tubes under axial load undergoing deformation through inversion phenamena are referred to as invertubes. Inversion phenomena controls high initial peak crush force which is a fundamental requirement of an energy absorbing structure in road vehicles and helps in achieving nearly 100% stroke and crush force efficiencies. This rare combination of these three features offers a good potential for invertubes to be an ideal choice for impact crash energy absorption. Researchers have always attempted to predict inversion forces in invertubes in terms of geometrical and material parameters through empirical relations; and often ignored the geometric imperfections on plastic deformation and their influence on the inversion process. Limited knowledge exist on inversion using stainless steel SS304 material. In this paper, series of attempts are made to evolve a new invertube profile with SS304 material to achieve desirable inversion charecterisitics for an ideal energy absorption. In this process, the effect of geometric parameters and their imperfections that contribute to effective inversion of invertubes have been studied in detail through FEA and experiments. A new invertube profile has been proposed that addresses anamolies in existing literature and inversion characteristics of this profile have been validated experimentally in a quasi-static environment.

Crashworthiness Optimization Design of Thin-Walled Tube Filled with Re-entrant Triangles Honeycombs

A novel re-entrant triangles-filled tube (RTT) is proposed through decoupling structural stiffness and energy absorption. Inner re-entrant triangles are employed to satisfy energy absorption, and outer thin wall is used to acquire high stiffness. This paper starts from establishment of theoretical models between geometric parameters of re-entrant triangles and relative density, equivalent elastic modulus and energy absorption characteristics, which are validated by experiments. On this basis, the optimal geometric parameters of unit cell are sought to maximize unit volume energy absorption and minimize relative density by adopting NSGA-II method. Subsequently, the cross-section of tube with optimal stiffness is obtained with targets for maximizing axial stiffness and lateral stiffness by employing static topology optimization method. To verify the proposed optimization method, RTT is analyzed and compared with positive Poisson’s ratio foam-filled tube (PFT), non-filled traditionally optimized tube (NTT) and pre-optimized square tube (PST). The results show that the novel RTT can improve stiffness and energy absorption performance simultaneously. Compared with the positive Poisson’s ratio material, re-entrant triangles honeycomb shows superior advantages in energy absorption. In comparison with the PFT, energy absorption of the RTT increases by 17.23%, and the peak crush force reduces by 5.04%. Therefore, the proposed decoupling design method demonstrates superiority in satisfying various performance requirements simultaneously.

Theoretical and numerical crush analysis of multi-stage nested aluminium alloy tubular structures under axial impact loading

In this paper, the crush behaviour and energy absorption performance of nested tubular thin-walled structures made of aluminium alloy AA6061-O under dynamic axial loading are investigated. Theoretical solutions for Average Crush Force (Pacf) of these structures are proposed by combining the energy method, simple superposition principle, and interaction among the various components of the structures. The derived theoretical models are verified by comparing their predictions with numerical and experimental values. The energy absorption indicators of the various structures are calculated and used to compare the various structures and to determine the best performing one. It is found that the nested structure with a higher number of tubes exhibits the best crashworthiness performance due to energy absorption enhancements resulted from the interaction effects between its components as well as its capability to reduce the peak crush force.

Design of bionic-bamboo thin-walled structures for energy absorption

Bio-inspired engineering design has drawn considerable attention in the recent years for its great structural and mechanical features. This study aimed to explore the energy absorption characteristics of a novel bionic-bamboo tube (BBT) structure subjected to axial crushing. The tubes with six different cross-sectional configurations were devised with inspiration of bamboo microstructure. The effects of rib shape and rib number were analyzed by using the finite element code LS-DYNA. The numerical results indicated that the BBT structures with the rib shape of “X” and the rib number of six exhibited the best crashworthiness. To further improve the energy absorption capabilities of these BBT structures, the multiobjective optimization was employed with respect to design variables of configurational structure, such as the rib angle of the “X” shaped cross-section, center distance and rib thickness. The response surface method (RSM) and multiobjective particle swarm optimization (MOPSO) algorithm were adopted to maximize specific energy absorption (SEA) while minimizing peak crushing force (PCF). The optimization results demonstrated that compared to the baseline design, the SEA value of the optimized BBT structure was further increased by 6.84% without sacrificing in peak crushing force.

Skeleton-Section Template Parameterization for Shape Optimization

A technique based on a skeleton-section template for parameterizing finite element (FE) models is reported and applied to shape optimization of thin-walled beam components. The template consists of a skeletal curve and a set of cross-sectional profiles. The skeletal curve can be used to derive global model variations, while the cross section is designed to obtain local deformations of the given shape. A mesh deformation method based on the radial basis functions (RBF) interpolation is employed to derive the shape variations. Specifically, the skeleton-embedding space and an anisotropic distance metric are introduced to improve the RBF deformation method. To validate the applicability of the proposed template-based parameterization technique to general shape optimization frameworks, two proof-of-concept numerical studies pertaining to crashworthiness design of an S-shaped frame were implemented. The first case study focused on global deformations with the skeletal curve, and the second treated the cross-sectional profiles as design parameters to derive local reinforcements on the model. Both studies showed the efficiency of the proposed method in generation of quality shape variants for optimization. From the numerical results, considerable amount of improvements in crashworthiness performances of the S-shaped frame were observed as measured by the peak crushing force (PCF) and the energy absorption. We conclude that the proposed template-based parameterization technique is suitable for shape optimization tasks.

Energy absorption of foam-filled multi-cell composite panels under quasi-static compression

This paper reports on the energy absorption characteristics of four types of innovative foam-filled multi-cell composite panels (FMCPs) composed of glass fiber reinforced polymer (GFRP) face sheets, GFRP lattice webs, and polyurethane (PU) foam. Quasi-static compression experiments on the FMCPs manufactured by a vacuum assisted resin infusion process (VARIP) were performed to demonstrate the feasibility of the proposed panels. Compared with the traditional FMCP with double-layer orthogonal foam cells, a maximum decrease in the peak crushing force (PCF) of approximately 148% was obtained for the FMCP with trapezoidal cells. Moreover, the enormous decrease in bearing load has been overcome by the proposed FMCPs. Among the four proposed FMCPs, the FMCP with double-layer dislocation cells exhibited the greatest specific energy absorption (SEA) capacity and the highest mean crushing load (MCL). Several numerical simulations using ANSYS/LS-DYNA were conducted on the FMCP with double-layer dislocation cells to parametrically investigate the effects of the face-sheet and lattice-web thickness, the foam-cell height, the foam-cell width, and the foam density. The effectiveness and feasibility of the numerical model were verified by the experimental results. The numerical results demonstrated that thicker face sheets and lattice webs, higher foam densities, and narrower foam cells can significantly increase the PCF and bearing load decrease. Moreover, the PCF and bearing load decrease were hardly affected by the foam-cell height.

Crashworthiness multi-objective optimization of the thin-walled tubes under probabilistic 3D oblique load

In a real-world loading case (e.g., car crash accidents), energy-absorbing components are subject to oblique loads at various uncertain angles. This paper aims to investigate the behavior of such components under three-dimensional (3D) oblique loads in deterministic and probabilistic loading conditions. In this way, some square tubes are tested experimentally, and results are utilized to validate numerical models. To apply the 3D oblique load, a special test setup is designed, constructed, and installed on a universal tensile testing machine. Hammersley method is employed to design sample points. ABAQUS software is used for the finite element modeling and analysis. GEvoM software is implemented for mapping design variables onto crashworthiness characteristics including energy absorption (EA) and peak crush force (PCF). Both deterministic and reliability-based robust design (RBRD) optimizations are performed, and their results are compared with each other. The primary outcome of this research is the effect of incidence angles on the energy-absorbing characteristics, as well as some remarkable trade-off design points obtained from various multiple-criteria decision-making (MCDM) methods. It was discovered that the obtained design points of probabilistic study, which satisfied the reliability constraint, were roughly 60% more robust than deterministic points.

An experimental and numerical investigation of the effects of geometry and spot welds on the crashworthiness of vehicle thin-walled structures

Abstract This paper aims to develop a new crash box with improved crashworthiness at reduced cost and weight as a base design for use in the automotive industry. Firstly, a baseline crash box model as presently used by the automotive industry was comprehensively examined by numerical crash analysis using Ls-Dyna software. Considering the initial design geometry, forty-five different crash box designs were developed by making changes in the geometry and wall thickness of the thin walled structures. The effects of the changes in wall thickness and geometry in alternative crash box designs on crash performances such as total energy absorption, peak crush force, mean crush force, specific energy absorption and crush force efficiency were investigated. The optimum crash box design obtained numerically was validated experimentally by means of the drop tower impact system. The numerical crash analysis results clearly agree with the experimental test results. In this study, a new crash box design at a lower cost and performing better in crashes compared with the other forty-six designs has been obtained and can be used in the automotive industry as an energy absorber. The results have revealed that crash box geometry, as well as the number and position of the spot welds and sheet-metal thickness have an important effect on crash performance, weight and cost of the crash boxes.

Mechanical properties of spider-web hierarchical honeycombs subjected to out-of-plane impact loading

Spider-web hierarchy can be introduced by adding smaller hexagons at the centers of original cells in an underlying hexagonal network and connecting the adjacent vertices by straight beams. To examine the out-of-plane crashworthiness of this new type of hierarchical honeycomb concept, a finite element model is established and validated by existing theoretical and experimental results. Then, a parametric study on structural variables [Formula: see text] and [Formula: see text] was carried out with three different densities. The mechanical properties of hierarchical honeycombs are also compared with that of regular honeycombs. The research results show that the deformation patterns of hierarchical honeycombs can be divided into three categories. The energy absorption capability can be controlled effectively by proper adjustment of the hierarchical structural parameters. The specific energy absorption per unit mass ([Formula: see text]) of first-order spider-web hierarchical honeycomb with [Formula: see text] and second-order spider-web hierarchical honeycomb with [Formula: see text] and [Formula: see text] increases by 62.1% and 82.4%, respectively. Meanwhile, the spider-web hierarchical characteristics have less influence on the corresponding Peak Crushing Force ( PCF). Further, the mean crushing force is derived by dividing the profile into basic angle elements based on the Simplified Super Folding Element (SSFE) method. The theoretical calculation is in good agreement with the simulation results as the spider-web hierarchical honeycombs deform in Mode I. These results can provide valuable suggestions in the study and design of the new type hierarchical honeycombs.

Crashworthiness design of novel hierarchical hexagonal columns

Self-similar hierarchical structures are widely observed in nature, and have been credited with superior mechanical properties. In this paper, a novel self-similar hierarchical hexagonal columns (HHC) is proposed to improve structural crashworthiness performance. The self-similar hierarchical hexagonal columns are constructed by iteratively adding sub-hexagons at the corners of primary hexagon. To investigate the crashworthiness of HHC, the nonlinear finite element model is first developed and validated against experimental data obtained from 1st order HHC. Numerical investigations of 1st and 2nd order hierarchical hexagonal columns with different hierarchical levels are performed to compare with 0th order HHC, the results show that 1st and 2nd order hierarchical hexagonal columns improve the energy absorption and crush force efficiency by governing the material distribution, especially, 2nd order HHC exhibits significant advantage for energy absorption. In addition, parametric designs of 2nd order HHC are carried out to explore crashworthiness effect on hierarchical size ratio, cell wall thickness and impact velocity. The significant effects on both specific energy absorption (SEA) and the peak crushing force (PCF) are observed. The findings of this study offer a new route of designing novel crashworthiness structure with highly energy absorption capacity.