Peak Crushing Force Research Articles

Crushing analysis for novel bio-inspired hierarchical circular structures subjected to axial load

Hierarchical structures are widely observed in nature, and used in engineering due to superior mechanical properties. In this paper, a novel hierarchical circular tube (HCT) by iteratively adding self-similar sub-circle at the junctions of the primary ribs is proposed to enhance structural crashworthiness performance. The finite element model of HCT is firstly established through LS-DYNA and validated via experiment testing. The energy absorption performance of different hierarchical HCTs is investigated under dynamic load. The hierarchical organization has remarkable potential to improve the crashworthiness behavior of thin-walled structure, especially, the 2nd order HCT exhibits significant advantages for energy absorption efficiency. Then, parametric designs are performed to explore the crashworthiness effect on main geometrical parameters of 2nd order HCT. Furthermore, theoretical model of 2nd order HCT is derived based on super folding element method, and obtain the good prediction accuracy for energy absorption and mean crushing force. To further obtain the optimal design of the 2nd order HCT, multi-objective optimization is performed by employing radial basis function (RBF) neural networks and multi-objective particle swarm optimization (MOPSO) algorithm. The several optimal structures are obtained under different peak crushing force (PCF). The findings of this research offer a new route of designing novel crashworthiness structure with high energy absorption capacity.

Crashworthiness optimization of combined straight-tapered tubes using genetic algorithm and neural networks

This paper was aimed to evaluate crashworthiness capability of new designed multi-cell structures with different cross-sectional shapes (i.e. square, hexagonal, octagonal, decagonal and circular) to dissipate collision energy. The multi-cell structures included outer and inner tubes connected together by four stiffening plates. Two dimensional parameters (i.e. S1 and S2) were defined to describe cross sectional configuration of the structures. Indeed, S1 and S2 were ratios of the inner tube side length to the outer tube side length at the ends of the structures. Values of both S1 and S2 were assumed as 0, 0.25, 0.5, 0.75 and 1. Longitudinal geometry of the outer tube was straight; while, both the straight or tapered geometry could be generated for the inner tube depending on the values of S1 and S2. An experimentally validated model generated in finite element code LS-DYNA was utilized to study crushing behavior of these structures under axial impact. Geometrical dimensions of these structures were optimized using ANNs (artificial neural networks) and GA (genetic algorithm) by considering three different scenarios. The optimal structures were compared together from the crashworthiness point of view by considering two conflicting crashworthiness indicators namely SEA (specific energy absorption) and PCF (peak crush force) using a decision making method called TOPSIS (technique for ordering preferences by similarity to ideal solution). Ranking of the studied cross sections was obtained as Octagonal-Circular-Decagonal-Hexagonal-Square for all the mentioned scenarios. Consequently, octagonal multi-cell structure was selected as the best cross sectional configuration among the studied cross sections. In addition, the proposed octagonal multi-cell structure was found to have higher crashworthiness capacity than conventional single-cell and simple multi-cell ones.

Experimental investigation of the quasi-static axial crushing behavior of filament-wound CFRP and aluminum/CFRP hybrid tubes

This study aims to investigate the effects of winding angles (25°, 50°, 75°, 90°; the 0° winding angle is along the axial direction of the tube) and thicknesses (3-ply, 6-ply, 9-ply) on crashworthiness characteristics of carbon fiber reinforced plastics (CFRP) tube and aluminum/CFRP hybrid tube molded by the filament winding technique through quasi-static crushing tests. The interaction between the outer CFRP tube and inner aluminum tube in a hybrid configuration was explored by comparing the sum of energy absorption of individual components with the hybrid form. It was found that both winding angle and wall thickness had significant influence on failure modes and crushing characteristics of both CFRP and hybrid tubes. With the same laminate thickness, increasing the winding angle decreased the specific energy absorption (SEA), energy absorption (EA) and peak crushing force (PCF) of pure CFRP and hybrid tubes. With the same winding angle of CFRP tube, increasing the thickness of CFRP tube increased the SEA, EA and PCF of both the CFRP and hybrid tubes. The SEA of 9-ply CFRP tube with winding angle of 25° and 9-ply CFRP/aluminum hybrid tube with winding angle of 25° were the highest of all the CFRP and hybrid tubes (48.74 J/g and 79.05 J/g), respectively. Moreover, EA of the hybrid tube exceeded the sum of that of the individual components thanks to the positive interaction between these components; making the hybrid tubes better crashworthiness than individual components.

Multi-objective crashworthiness optimization for an auxetic cylindrical structure under axial impact loading

There is an increasing interest in designing lightweight automobile parts to enhance the passive safety of automobiles and reduce the fuel cost consumption. Variable kinds of novel smart structures/materials have been studied to apply in the field of the crashworthiness of the automobile. In this paper, a novel crash box based on the cylindrical cellular structure with negative Poisson's ratio (NPR) is proposed. The unit cell for the NPR structure is the double-V configuration. The structure can contract in the radial direction when compressed to enhance the stiffness. Then the parametric finite element (FE) model is constructed with MATLAB scripts to study the influence of the geometrical parameters on the crashworthiness. During the analysis, the Rescaled Range Analysis (RRA) is utilized. Then the specific energy absorption (SEA) and peak crushing force (PCF) are chosen as the optimization objective, and the Pareto fronts are attained by employing the multi-objective particle swarm optimization (MOPSO) algorithm. Also, the optimal results are compared with the initial model to verify the effectiveness of the approach. It is found that the SEA increases from 4.33KJ/Kg to 6.06KJ/kg by 39.3% and PCF decreases to 78.89KN by 10.3% when the geometry parameters are optimized. Compared with the thin-walled circle structure, the cylindrical NPR structure has lower peak crushing force and higher energy absorption. Also, the crushing force is more stable under the impact loading. Therefore, the cylindrical NPR structure has a great prospect in the application of the energy absorber of the automobile.

Multi-objective optimization of tapered tubes for crashworthiness by surrogate methodologies

In this paper, the single and multi-objective optimization of thin-walled conical tubes with different types of indentations under axial impact has been investigated using surrogate models called metamodels. The geometry of tapered thin-walled tubes has been studied in order to achieve maximum specific energy absorption (SEA) and minimum peak crushing force (PCF). The height, radius, thickness, tapered angle of the tube, and the radius of indentation have been considered as design variables. Based on the design of experiments (DOE) method, the generated sample points are computed using the explicit finite element code. Different surrogate models including Kriging, Feed Forward Neural Network (FNN), Radial Basis Neural Network (RNN), and Response Surface Modelling (RSM) comprised to evaluate the appropriation of such models. The comparison study between surrogate models and the exploration of indentation shapes have been provided. The obtained results show that the RNN method has the minimum mean squared error (MSE) in training points compared to the other methods. Meanwhile, optimization based on surrogate models with lower values of MSE does not provide optimum results. The RNN method demonstrates a lower crashworthiness performance (with a lower value of 125.7% for SEA and a higher value of 56.8% for PCF) in comparison to RSM with an error order of 10-3. The SEA values can be increased by 17.6% and PCF values can be decreased by 24.63% by different types of indentation. In a specific geometry, higher SEA and lower PCF require triangular and circular shapes of indentation, respectively.

On crashworthiness design of double conical structures under oblique load

A novel multi-cell tube with non-collinear outer and inner conical angles (MBCT) is proposed to enhance structural performance under different load conditions. The finite element models (FEMs) are developed and validated by experimental tests. The comparative analysis is carried out to investigate the crashworthiness of different conical structures. The results indicate that MBCT has the most desirable load characteristics and highest energy absorption capacity. Furthermore, parametric studies reveal that large outer conical angle facilitates energy absorption and desirable load characteristics. Large wall thickness, on the other hand, has conflicting effects on crashworthiness since it increases peak crushing force (PCF) but cannot improve special energy absorption (SEA). Crashworthiness assessment of a MBCT crush box in a full vehicle further indicates the merits of energy absorption of double conical structures. The study offers insights on designing energy absorbers that are both weight efficient and reliable under uncertain load conditions.

Crushing analysis and multi-objective optimization of a cutting aluminium tube absorber for railway vehicles under quasi-static loading

To explore a diverse number of energy absorption methods, this paper presents an investigation of a cutting aluminium tube absorber for railway vehicles. A quasi-static cutting experiment on an aluminium tube is conducted. The finite element models presented in this study are based on experimental tests, and good agreement is achieved between the experimental and finite element results. It is shown that the cutting aluminium tube absorber presents a stable deformation mode. The chip morphologies of the numerical simulation and experimental test results are coincident, demonstrating that failure criteria defined under the material model are effective. Moreover, a parametric study is performed using finite element models under quasi-static loading. It is found that the cutting depth t, cutting depth w and cutting angle α have a distinct effect on the energy absorption (EA), mean crushing force (MCF) and peak crushing force (PCF) of the absorber. Sobol’ sensitivity analysis is employed to analyze the effects of the design parameters (t, w, and α) on the objective responses (EA and PCF) based on a polynomial response surface model. It is found that at a larger cutting depth, the increases in EA and PCF are larger. Additionally, to optimize the crushing performance of the absorber, a multi-objective optimization is applied to achieve the maximum EA and minimum PCF values. The results show that EA increases with increasing PCF and at the optimal point B (EA = 78.29kJ, PCF = 341.88kN), and thus, a balance between EA and PCF is obtained.

Evaluation of axially-crushed cellular truss structures for crashworthiness

ABSTRACTThin-walled tubes have long been used as energy absorbing structures, owing to their high specific energy absorption (SEA) capacity. But, they are associated with substantial high values of peak crush force (PCF). A high PCF results in a high deceleration pulse on the critical components and/or the passengers. This poses serious safety concerns. Even the use of triggers and grooves do not reduce the PCF considerably. To achieve improvement on the safety aspect, the research on the crashworthiness of the cellular truss structures was conducted in this paper. Finite element simulation model was developed by using ABAQUS/Explicit software and validated experimentally with structures fabricated through additive manufacturing. The truss structures were compared to the thin-walled tubes on the basis of their mass, SEA and PCF values. For an equal amount of energy absorption, while the truss structures had a higher mass, the PCFs were lowered significantly. The PCFs decreased at a rate 1.5 to 4.5 times faster than the corresponding decrease in SEAs. The example of the crash box showed that the drop in PCF due to the use of truss structure resulted in a reduction of around 5g deceleration at the cost of 1 kg of additional mass.

A numerical study on the energy absorption of a bending-straightening energy absorber with large stroke

This paper presents a novel energy absorber that can generate a larger deformation stroke than its free length. The effective crushing distance rate (ECDR) of this structure can exceed 1. During collision, the impact kinetic energy is dissipated by the elastic-plastic deformation of a steel plate and aluminium honeycomb. The bending theory of the steel plate is analysed to estimate the energy absorption (EA) and the mean crushing force (MCF). Then, a finite element (FE) model of the energy absorber is established, and its accuracy is validated by the theory of plate blending. When the plate thickness is 2mm and 5mm, the error between the simulation and theoretical results are 1.93% and 3.05%, respectively. The FE model is used to investigate the crashworthy performance. When the new absorber is deformed, the influence of the type of aluminium honeycomb, steel plate thickness and width, guide wheel radius, and number of guide wheels on energy absorption are analysed. Aluminium honeycomb with appropriate parameters can significantly reduce the peak crushing force (PCF) by up to 60.8%. The crushing force (CF) and EA increase as the plate thickness, plate width, and number of guide wheels increase but decreases as the guide wheel radius decreases.

Evaluation of the Performance of Initiator on Energy Absorption of Foam-Filled Rectangular Tubes: Experimental and Numerical Assessment

In this paper, the effect of initiator on axial crushing response of partially foam-filled and foam-filled rectangular tubes was investigated. For this purpose, an initiator was placed at the top of the filling rectangular tube with rigid polyurethane foam to prevent a suddenly applied force to the main part of the structure when the accident occurs. In this new idea, the process of axial crushing was carried out in two steps. In the first step, the initiator crushed the foam core as much as the initiator length, and, the second step, the initiator simultaneously crushed the thin-walled rectangular tube and the foam core. In this research, a number of numerical simulations were performed to study the dissipated energy of the rectangular tubes with initiator. To verify these numerical findings, some quasi-static experimental tests were conducted to explain energy absorption, initial peak load and crush force efficiency. Moreover, load-displacement curves and deformation mechanism of this shock absorber with different length of initiators were described. The results showed that, in the considered material and geometry, the design with an initiator on partially foam-filled and foam filled rectangular tube have superior performance rather than the specimen without an initiator. In addition, selecting the appropriate length of initiator for the specimens of partially foam-filled and foam-filled resulted in an increase in the energy absorption. Besides, the results showed that the increase in the absorbed energy in the foam-filled specimen was more than that of the partially foam-filled specimens. Therefore, by applying the initiator on the top of the tube, it would be help to reduce the occupant injury and main structure in a collision.

Dynamic axial crushing of bitubular tubes with curvy polygonal inner-tube sections

Bitubular structural configurations, where the outer tube is circular, square and curvy square in shape while the inner-tube section is curvy triangular, square and hexagonal in different proposed configurations, are numerically crushed under dynamic axial loading. The crashworthiness effectiveness for changing inner-tube polygonal cross-section for each of the outer tube sections is studied and compared with changing outer tube shape. The deformation plots and energy absorption (EA) parameters such as peak crushing force (PCF) mean crushing force (MCF), energy absorption and crush force efficiency for each case are evaluated. Most of the configurations showed ovalization with low PCF and MCF and moderate crush force efficiency. Afterwards, effects of [Formula: see text] and [Formula: see text] on deformation modes and EA are demonstrated by selecting one of the configurations from each group using published experimental results.

Enhance crashworthiness of composite structures using gradient honeycomb material

ABSTRACTLightweight cellular materials can effectively improve the crashworthiness of thin-walled structures. To further investigate the potential of honeycomb-filled thin-walled structures, this paper proposed a novel functionally graded honeycomb (FGH) as filler. First, the finite element model of the functionally graded honeycomb-filled tube (FGHT) is established and validated via experimental results. Then, the key factors of FGHT for crashworthiness are identified. The results show that gradient pattern is critical to the crushing response. As for the overall energy absorption capability, we thoroughly examined the effects of gradient exponent n and the thickness range of honeycomb shells. Next, we conducted single and multi-objective optimisation, adopting genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II), to seek the parameters that deliver overall crashworthiness performance. The Kriging surrogate metamodel was established to formulate specific energy absorption (SEA) and peak crushing force (PCF) in relation to the key parameters. The single objective optimisation revealed that, provided the same PCF, the SEA of FGHT is always higher than uniform honeycomb filled tube (UHFT); the Pareto front obtained from multi-objective optimisation also indicate that FGHT is generally more efficient than UHFT. This paper gives insights on the honeycomb-filled materials to achieve maximum crashworthiness performance.

Experimental and numerical investigation on the deformation and energy dissipation of AA6061-T6 circular extrusion subjected to blast loading

The study detailed in this manuscript focuses on the numerical and experimental testing of circular AA6061-T6 aluminum alloy extrusions subjected to cutting deformation modes under blast loading conditions, as energy dissipation devices. The experimental investigation was completed utilizing a specially designed cutter with the presence of a deflector mounted on a ballistic pendulum. Plastic explosives (PE4) where charge masses varied from 20g to 40g were used to initiate blast loads. Experimental results revealed that the cutting deformation mode was repeatable and controllable having a stable and clean curling cut. Numerical simulations of the detonation as well as the axial cutting deformation process employing an Eulerian finite element formulation were performed. Numerical detonation models were in good agreement with experimental results having an average standard error less than 3% for impulse predictions. Good predictive capabilities of the numerical model for the axial cutting behaviour and large scale deformation response were observed. An almost constant force during cutting was observed, which eliminated the initial high peak crush force associated with a dynamic plastic collapse deformation mode. The average mean cutting force, measured at the load cell for both experimental and numerical testing methods as a result of cutting deformation was observed to be 33.5kN for the specific specimen geometry and material. Finally, a force analysis was conducted using theoretical and numerical models to study the steady-state cutting condition.

Multiobjective Optimization of Functionally Corrugated Tubes for Improved Crashworthiness under Axial Impact

This study aims to analyze the effectiveness of introducing sinusoidal corrugations with varying wavelength and amplitude along the length of cylindrical tubes in order to improve their energy absorption characteristics. Different sinusoidal functions are used to obtain the generatrix of corrugated profiles. Non-linear finite element code LS-DYNA is used in order to carry out the numerical analyses of these corrugated tubes under axial loading conditions. The results obtained from the analyses are then used to obtain functions using MATLAB's native non-linear regression tool fitnlm. Two objectives are to maximize the Energy Absorbed (EA) by the tube and to minimize the Peak Crushing Force (PCF). The degrees of graded corrugation functions (Amplitude and Wavelength function) are chosen as the two design variables in this study. Unconstrained multiobjective Genetic Algorithm is the optimization algorithm used in this study using MATLAB to produce the Pareto frontier which gives an optimal set of tube configurations.

Crashworthiness efficiency optimisation for two-directional functionally graded foam-filled tubes under axial crushing impacts

ABSTRACTRecent advancements in crashworthiness analysis of functionally graded foam-filled tubes are achieved by studying the energy absorption characteristics in lateral or axial directions, separately. In this paper, for the first time, two-directional (lateral and axial directions together) functionally graded foams (TDFGFs) under axial crushing loads are considered. The effect of variations of foam density on the specific energy absorption (SEA) and peak crushing force (PCF) is studied by controlling the gradient exponential parameters which give rise to significant effects on the crashworthiness of TDFGFs. Also, it is further analysed that how the mass of the TDFGF tube changes values of SEA in crushing process. In addition, as the result of performing multi-objective particle swarm optimisations, it is seen that the energy absorption characteristics of TDFGFs for higher values of gradient exponential parameters are improved significantly. The crashworthiness properties of optimum configurations for TDFGF are compared with the extreme cases of minimum, maximum densities and uniform foam-filled tubes with the same weight as the corresponding TDFGF tubes. Finally, a global sensitivity analysis is carried out. The results of this analysis reveal that the SEA and PCF functions are generally sensitive to the variations of the gradient exponential parameters.

Energy absorption characteristics of diamond core columns under axial crushing loads

The energy absorption characteristics of diamond core sandwich cylindrical columns under axial crushing process depend greatly on the amount of material which participates in the plastic deformation. Both the single-objective and multi-objective optimizations are performed for columns under axial crushing load with core thickness and helix pitch of the honeycomb core as design variables. Models are optimized by multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). Results show that optimization improves the energy absorption characteristics with constrained and unconstrained peak crashing load. Also, it is concluded that the aluminum tube has a better energy absorption capability rather than steel tube at a certain peak crushing force. The results justify that the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. A ranking technique for order preference (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a multi-criteria decision which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. Furthermore, local and global sensitivity analyses are performed to assess the effect of design variable values on the SEA and PCF functions in design domain. Based on the sensitivity analysis results, it is concluded that for both models, the helix pitch of the honeycomb core has greater effect on the sensitivity of SEA, while, the core thickness has greater effect on the sensitivity of PCF.

Numerical modeling of TRIP steel in axial crashworthiness

With their high strain rate hardening capacity and good combination of strength and ductility, transformation induced plasticity (TRIP) steels offer lightweight solutions for reinforcement components undergoing crash events. The TRIP effect correlates with stress-stimulated martensitic transformation from austenite, which depends on a myriad of kinematic ingredients, including three-dimensional plastic deformation, temperature change, strain-rate, and stress state. The complex interdependency of these kinematic ingredients requires stepwise and time iterative numerical analyses, especially when boundary-value problems are imposed. Typically engineering desired boundary value problems involve simulations designed to control energy absorption under complex crash scenarios. In this paper, we demonstrate a new phenomenological framework for thermo-mechanical modeling of multi-phase TRIP steel that captures the evolution of phase transformation. The model was implemented into the user-defined subroutine of the explicit dynamic version of the commercial finite element software LS-DYNA. Simulations were performed on a top-hat crush tube made of an industrial multiphase TRIP 800 steel. The results were utilized within an optimization simulation framework to pinpoint composition windows, which maximize the energy absorption capacity. When not concerned about peak crush force, larger compositions of austenite (typically ∼70%) will outperform all other compositions. However, lowering the austenite volume fraction with higher volume fractions of bainite (∼80%) with balanced ferrite could produce a top-hat crush rail with a superior crush force and efficiency compared to TRIP 800 steel without increasing the peak crush force.

Optimization of foam-filled double ellipse tubes under multiple loading cases

In this paper, a novel foam-filled double ellipse tube (F-DET) is proposed. First, the circle and ellipse tubes with three different configurations(hollow, foam-filled, double foam-filled) are investigated under axial and oblique impact by using the nonlinear finite element code LS-DYNA. The numerical results showed that the F-DET tube has the best crashworthiness performance than tubes with other configurations. Then to optimize the F-DET tube, the Kriging model about the radial rate f, thickness of wall t and foam density ρf is constructed. Based on the Kriging model, the multiobjective particle swarm optimization (MOPSO) algorithm is utilized to achieve the optimized F-DET tube, foam-filled ellipse(F-ET) tube and foam-filled double circle(F-DCT) tube on the maximizing specific energy absorption (SEA) and minimizing peak crush force (PCF) under multiple loading angles. It can be found that the F-DET tube has better crashworthiness performance than F-ET tube and F-DCT tube. This indicates F-DET tube can be a potential energy absorber under the multiple loading cases.

Crushing analysis and multiobjective crashworthiness optimization of foam-filled ellipse tubes under oblique impact loading

In this paper, a novel foam-filled ellipse tube (FET) is proposed and compared with other hollow and foam-filled tubes with different cross-sections under multiple loading angles, which include square, circle and rectangle. First, finite element analyses of these tubes reveal that the FET tube has the best crashworthiness under multiple loading angles. Second, design of experiments (DOE) was used to analyze the parameters that radial rate f, thickness of wall t and foam density ρf. Third, the Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to optimize the FET tube, in which the optimal parameter variation is sought for maximizing specific energy absorption (SEA) and minimizing peak crush force (PCF) under multiple loading angles. The optimized FET tube exhibits better crashworthiness than the origin FET tube and other tubes with different cross-section, indicating that the FET tube can be a potential energy absorber especially under oblique impact loading.

On design of multi-cell thin-wall structures for crashworthiness

Multi-cell thin-wall structures have drawn increasing attention and been widely applied in automotive and aerospace industries for their significant advantages in high energy absorption and lightweight. The number of cells and the topological configurations of the multi-cell thin-wall structures have a significant effect on the crashworthiness. In order to investigate the effect of the number of cells and the topological configurations of multi-cell structures on their crashworthiness characteristics, this paper first sets up the simulation models of multi-cell tubes and verifies their accuracy with the quasi-static and dynamic impact experiments. Second, it compares the energy absorption characteristics of the multi-cell structures with different numbers of cells and topological configurations under dynamic impact condition using finite element analysis (FEA). The results show that the mean crushing force (MFC) and specific energy absorption (SEA) increase with the increase in the number of cells of the multi-cell tubes, among which the five-cell tube has the best energy absorption characteristics. Third, a parametric study is carried out to investigate the effects of wall thickness and topology configurations on the crashworthiness of five-cell tubes. Finally, the multiobjective Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to further optimize the five-cell tube for maximizing specific energy absorption and minimizing peak crushing force (PCF). The optimal five-cell tube has excellent crashworthiness and is a potential energy absorber.