Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression

In the present study, crashworthiness characteristics of thin-walled steel tubes containing annular grooves are studied. For this purpose, the grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are controlling the buckling mode and predicting energy absorption capacity of the tubes. To do so, circumferential grooves are cut alternately inside and outside of the tubes at predetermined intervals. Quasi-static axial crushing tests are performed and the load-displacement curves are studied. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. It is found a good agreement between the theoretical results and experimental findings. The results indicate that the load-displacement curve and energy absorbed by the axial crushing of tubes could be controlled by the introduction of grooves with different distances. Also, grooves can stabilize the deformation behavior and thus, the proposed method could be a good candidate as a controllable energy absorption element.     

Energy absorption of axially compressed thin-walled square tubes with patterns

The paper suggests the introduction of patterns to the surface of conventional thin-walled square tubes to improve the energy absorption capacity under axial compressive loads. A quasi-static axial crushing analysis has been conducted numerically by the nonlinear explicit finite element code LS-DYNA. Two types of patterns constructed using the basic pyramid elements were introduced. Type A pattern was aimed at triggering the extensional mode for relatively thin square tubes whereas type B pattern was intended to develop new collapse mode capable of absorbing more energy during collapse. A total of 30 tubes with a length of 120 mm, thickness 1.2 mm and widths of 40 or 60 mm were simulated. Numerical results showed that all tubes with type A patterns developed the extensional collapse mode instead of the symmetric collapse mode and absorbed about 15–32.5% more energy than conventional thin-walled square tubes with a mass increase less than 5%. Meanwhile, a new collapse mode named octagonal collapse mode was observed for tubes with type B pattern and the energy absorption of tubes developing this mode increased by 54–93% compared with the conventional tube. The influence of various configurations of the patterns on the deformation and energy absorption of the tubes was also discussed. The paper opens up a new avenue in design of high energy absorption components.     

Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption

The axial crushing of hollow multi-cell columns were studied analytically and numerically. A theoretical solution for the mean crushing force of multi-cell sections were derived, and the solution was shown to compare very well with the numerical predictions. Numerical studies were also carried out on foam-filled double-cell and triple-cell columns. Based upon the numerical results, closed-form solutions were derived to calculate the mean crushing strength of these sections. It was found that the interaction effects between the foam core and the column wall contribute to the total crushing resistance by the amounts equal to 140% and 180% of the direct foam resistance for double cell and triple cell respectively. Finally, the relative merits of single-cell, multi-cell and foam-filled sections were discussed.     

Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes

Foam-filled thin-wall structures exhibit significant advantages in light weight and high energy absorption. They have been widely applied in automotive, aerospace, transportation and defense industries. Quasi-static tests were done to investigate the crash behavior of the empty and polyurethane foam-filled end-capped conical tubes. Non-linear dynamic finite element analyses were carried out to simulate the quasi-static tests. The predicted numerical crushing force and fold pattern were found to be in good agreement with the experimental results. The energy absorption capacities of the filled tubes were compared with the empty end-capped conical tubes. The results showed that the energy absorption capability of foam-filled tube is somewhat higher than that of the combined effect of the empty tube and the foam alone. Finally, the crash performance of the empty and foam filled conical and cylindrical tubes were compared. Results from this study can assist aerospace industry to design sounding rocket carrier payload based on foam-filled conical tubes.     

Attempts to improve energy absorption characteristics of circular metal tubes subjected to axial loading

In this paper, experimental investigation of two new structural design solutions with the aim of improving crashworthiness characteristics of cylindrical metal tubes is performed. In the first design method, a rigid steel ring is press-fitted on top of circular aluminum tubes. When this arrangement of dissipating energy is subjected to axial compression, the rigid ring is driven into the cylindrical tube and expands its top area; then, plastic folds start shaping along the rest of the tube length as the compression of the structure continues. In the second design method, wide grooves are cut from the outer surface of steel thick-walled circular tubes. In fact, this method converts thick-walled tubes into several thin-walled tubes of shorter length, being assembled together coaxially. When this energy absorbing device is subjected to axial compression, plastic deformation occurs within the space of each wide groove, and thick portions control and stabilize collapsing of the whole structure. In the present study, several specimens of each developed design methods with various geometric parameters are prepared and compressed quasi-statistically. Also, some ordinary tubes of the same size of these specimens are compressed axially to investigate efficiency of the presented structural solutions in energy absorption applications. Experimental results show the significant efficiency of the presented design methods in improving crashworthiness characteristics and collapse modes of circular tubes under axial loading.     

Quasi-static axial and lateral crushing of radial corrugated composite tubes

This paper presents the effect of corrugation geometry on the crushing behavior, energy absorption, failure mechanism, and failure mode of woven roving glass fibre/epoxy laminated composite tube. Experimental investigations were carried out on three geometrical different types of composite tubes subjected to axial and lateral compressive loadings. On the addition to a radial corrugated composite tube, cylindrical composite tube, and corrugated surrounded by cylindrical tube were fabricated and tested under the same condition in order to know the effect of corrugation geometry. The results showed that the loading carrying capability is significantly influenced by corrugation geometry in axial crushing. However, no affect of corrugation geometry was observed for lateral crushing. Load–displacement curve was plotted for all conducted tests, thus clear comparison between different specimen's geometry was achieved. It is also found that radial corrugation could significantly applicable as a stable and effective energy absorber.     

Theoretical prediction and numerical simulation of multi-cell square thin-walled structures

The axial crushing of square multi-cell columns were studied analytically and numerically. Based on the Super Folding Element theory, a theoretical solution for the mean crushing force of multi-cell sections were derived by dividing the profile into 3 parts: corner, crisscross, and T-shape. Numerical simulations of square multi-cell sections subjected to dynamic axial crushing were conducted and an enhancement coefficient was introduced to account for the inertia effects for aluminum alloy AA6060 T4. The analytical solutions show an excellent agreement with the numerical results. It was found that the crisscross part was the most efficient component for energy absorption and the energy absorption efficiency of a single-cell column can be increased by 50% when the section was divided into 3×3 cells. Finally, the proposed method was extended to analyze the plateau stress of square cell honeycomb subjected to out-plane axial crushing and to some extent validate the mechanical insensitivity of honeycomb to cell size.     

A numerical study of the influence of bump type triggers on the axial crushing of top hat thin-walled sections

This paper deals with the issue of a trigger design and its performance. In this respect, a numerical investigation is carried out to study the effects of the geometrical features of a bump type trigger on the crush behavior of an energy absorbing member subjected to axial impact loading. The member was constructed by joining a top hat profile with a flat lid. The trigger was considered to be a bump with a semi-circular cross section on the hat profile. The finite element solver, LS-DYNA was used in all crush simulations. As a result, the introduction of the trigger was found to be effective on the peak crush force and the energy absorption capability of the member under axial impact loading. It was also shown that the crush response could be controlled by varying the location and the geometry of the trigger.     

Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces

This paper describes a computationally aided design process of a thin wall structure subject to dynamic compression in both axial and oblique directions. Several different cross sectional shapes of thin walled structures subjected to direct and oblique loads were compared initially to obtain the cross section that fulfills the performance criteria. The selection was based on multi-criteria decision making (MCDM) process. The performance parameters used are the absorbed crash energy, crush force efficiency, ease of manufacture and cost. Once the cross section was selected, the design was further enhanced for better crash performances by investigating the effect of foam filling, increasing the wall thickness and by introducing a trigger mechanism. The outcome of the design process was very encouraging as the new design was able to improve the crash performance by an average of 10%.     

Quasi-static axial compression of concentric expanded metal tubes

Previous studies have demonstrated that the failure mechanism and energy absorption capacity of expanded metal tubes strongly depends on the orientation of the cells. This paper presents an experimental investigation on the collapse of concentric expanded metal tubes subjected to quasi-static axial compression. Square tubes with two different cell orientations are tested to failure, and the energy absorption characteristics are calculated. The results show that the combination of cell geometries lead to a complex buckling mode interaction, which enhances the energy absorption capacity of expanded metal tubes.     

The strengthening effect of polystyrene foam filling in aluminum thin-walled cylindrical tubes

The strengthening effect of foam filling in thin-walled circular tubes, deforming in diamond and concertina modes, was investigated in polystyrene foam filled aluminum tubes. Empty tubes of two different diameters (16 and 25 mm) deformed in diamond mode, while foam filling changed the deformation mode into concertina in 25 mm tube due to thickening effect of foam filling. The strengthening coefficient in concertina mode was found around unity, while in diamond mode it was greater than unity. In concertina mode, foam and tube were observed to deform independently. However, in diamond mode, foam was compressed in between the folds, leading to a higher strengthening coefficient. The effects of deformation rate and the use adhesive on the average crushing loads of the filled tubes were also determined.     

空心和泡沫填充且端部封闭锥形筒的耐撞性试验和数值分析

泡沫填充的薄壁结构的优点是质量轻和高吸能性能,广泛地应用于汽车、航空、运输和防护等行业。采用拟静力试验,分析空心和泡沫填充的端部封闭的锥形筒的耐撞性能,采用非线性动力有限元模拟拟静力试验,数值分析的抗冲撞力与试验数据很吻合。对未填充的锥形筒和填充的锥形筒的耗能能力进行对比,结果显示,泡沫填充的锥形筒的耗能能力比较好。最后,比较了空心、泡沫填充端部封闭的锥形筒和圆筒的耐撞性。     

Analysis and optimization of externally stiffened crush tubes

Nonlinear finite element analysis is used to investigate the quasi-static axial collapse response of cylindrical tubes which are externally stiffened by multiple identical rings. The rings divide the long tube into a series of short thin-walled tubes. It is assumed that the size and shape of integral stiffeners are controlled through a machining process. The effects of various geometric parameters such as wall thickness, ring spacing, ring thickness and width on the collapse response, crush force and energy absorption of monolithic, integrally stiffened steel tubes are studied and used as a general framework for a design optimization study. Through design and analysis of computer experiments, global metamodels are developed for the mean crush force and energy absorption, using the radial basis function approximation technique. Using both single- and multi-objective design optimization formulations, optimum designs for different response characteristics are found. The crush mode in the form of progressive collapse or buckling is found to heavily depend on the ratio of stiffener spacing to stiffener height as well as the ratio of wall thickness to stiffener thickness. The optimization results show the viability of externally stiffened tubes as efficient energy absorbers.     

Multi-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentations

In this paper, the effects of tapering and introducing axisymmetric indentations on the crash performances of thin-walled tubes are investigated. The crash performances of the tubes are evaluated using two metrics: the crush force efficiency (CFE, the ratio of the average crushing load to the peak load), and the specific energy absorption (SEA, absorbed energy per unit mass). The optimum values of the number of the axisymmetric indentations, the radius of the indentations, the taper angle and the tube thickness are sought for maximum CFE and maximum SEA using surrogate based optimization. In addition, multi-objective optimization of the tubes is performed by maximizing a composite objective function that provides a compromise between CFE and SEA. The CFE and SEA values at the training points of surrogate models (metamodels) are computed using the finite element analysis code LS-DYNA. Polynomial response surfaces, radial basis functions, and Kriging are the different surrogate models used in this study. Surrogate based optimization of the tubes showed that the tubes with indentations have better crush performance than tubes without indentations. It is found that maximum CFE requires large number of indentations with high radius, small thickness, and medium taper angle, while maximum SEA requires small number of indentations with low radius, large thickness and small taper angle. It is also found that the globally most accurate surrogate model does not necessarily lead to the optimum.     

准静态轴向和侧向挤压下对径向波纹管的分析

介绍了波纹几何形状对破坏性能、能量吸收、失效机理和玻璃纤维方格布／环氧复合材料管失效模式的影响。对承受轴向和侧向压力的3个具有不同几何形状的复合材料管进行试验研究。同时对相同受力条件下的径向波纹复合管、圆柱型复合管、圆柱管环绕的波纹管进行试验,以了解波纹几何形状的影响。结果表明,轴向挤压中波纹几何形状会显著影响管的承载能力。然而,侧向挤压中并没有发现波纹几何形状的影响。试验中绘制了荷载一位移曲线,因此可以对各种不同几何形状的构件进行清晰的对比。研究同时发现,径向波纹可以稳定并有效地吸收能量。     

Dynamic effects on buckling and energy absorption of cylindrical shells under axial impact

The crushing behaviour of aluminium and steel cylindrical shells, when subjected to an axial impact, is examined using a numerical simulation. The influence of the material properties, shell geometry, boundary conditions and loading techniques on the energy absorbed and the buckling shapes is explored. Various shell response characteristics, such as the peak load, fold lengths, axial compression and energy absorption are studied. An examination is also made of the influence of filtering on the accuracy of data obtained usually in dynamic tests.     

A study of lateral collapse of square and rectangular metallic tubes

The paper presents an experimental and computational study of rectangular and square tubes made of aluminium and mild steel and subjected to quasi-static transverse loading. Deformed shapes at different stages, load–compression and energy–compression curves have been obtained experimentally. The deformation process was numerically simulated using finite element code FORGE2. The contours of different components of stress and strain rate tensors and nodal velocity have been plotted. Mechanics of deformation process, comparison of experimental and computed results and effect of process parameters on the mode of deformation are presented and discussed.     

Axial crushing analysis of end-capped circular tubes

The paper investigates collapse mechanisms and energy absorption capacity during the axial compression of the end-capped thin-walled circular aluminum tubes which are hollow or filled with polyurethane foam. An experimental technique is used to evaluate the crushing behavior of the circular tubes under compressive quasi-static strain rate. A numerical model is presented based on finite element analysis to simulate the crushing of circular tubes considering nonlinear response due to material behavior, contact boundary conditions and large deformation. The validated model using existing experimental results is used to evaluate the dynamic response in order to determine the dynamic amplification factor relating the quasi-static results to dynamic response. The experimental and numerical results are used to determine energy absorption capacity due to the plastic deformation of thin-wall tube and crushable foam. The performance of end-capped tubes is compared with non-capped tubes and it is found that maximum initial peak load can be controlled and convenient crash protection systems can be obtained using end-capped circular tubes.