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.     

Partial Al foam filling of commercial 1050H14 Al crash boxes: The effect of box column thickness and foam relative density on energy absorption

The crushing behavior of partially Al closed-cell foam filled commercial 1050H14 Al crash boxes was determined at quasi-static and dynamic deformation velocities. The quasi-static and dynamic crushing of the boxes were simulated using the LS-DYNA. The results showed that partial foam filling tended to change the deformation mode of empty boxes from a non-sequential to a sequential folding mode. In general, the experimental and simulation results showed similar mean load values and deformation modes. The SEA values of empty, partially and fully foam filled boxes were predicted as function of box wall thickness between 1 and 3 mm and foam filler relative density between 0 and 0.2, using the analytical equations developed for the mean crushing loads. The analysis indicated that both fully and partially foam filled boxes were energetically more efficient than empty boxes above a critical foam filler relative density. Partial foam filling, however, decreases the critical foam filler density at increasing box wall thicknesses.     

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.     

Simply supported empty and filled thin-square-tubular beams under central wedge loading

Experiments were performed whereby thin-walled square tubes of different span lengths were simply supported and laterally loaded by a wedge indenter in an Instron machine and under the impact of a drop hammer. The tubes were empty as well as filled with polyurethane foam or wood. The span length seems to greatly influence the mode of deformation. Typical histories of deformation and load–compression curves of empty and filled tubes are presented and the effect of infill material and the rate of loading on energy absorbing characteristics of the tubes is discussed. Based on the mechanics of deformation observed experimentally, an analysis is presented to compute the collapse load as well as the post collapse load–compression curve for the simply supported tubes. The analysis considers the formation of stationary and rolling plastic hinges. The results thus obtained compare well with the experiments.     

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.     

Frusta structure designing to improve quasi-static axial crushing performances of triangular tubes

To improve quasi-static axial crushing performances of thin-wallled triangular tubes, frusta structures were designed and fabricated. Quasi-static axial compression experiments were carried out to reveal the collapse mode and energy absorption characteristic of the triangular frusta tube. Peak loads and mean crushing forces (MCFs) of tubes with different taper angles were compared. In-extensible and extensible collapse modes were suggested to predict the MCF of the triangular frusta tube with small and great taper angles, respectively. A new collapse mode, inward folding, was observed in the experiments. An energy absorption stability factor was defined to evaluate the anti-crushing efficiency of the triangular frusta tube. With greater taper angles, the energy absorption stability factor is much closer to 1, denoting more stable deformation style. It is concluded that frusta structures with taper angles effectively enhance the anti-crushing efficiency and stability of thin-walled triangular tubes.     

Optimization of the foam-filled aluminum tubes for crush box application

Axial impact crush tests on empty and foam-filled square aluminum tubes have been performed. Furthermore, in order to find more details about the crush processes, finite element simulations of the experiments have been done. In terms of finding more efficient and lighter crush absorber and achieving maximum energy absorption, multidesign optimization (MDO) technique has been applied for optimizing the square rectangular tubes. Based on practical requirements the optimum tube geometry, which absorbs maximum energy and has a minimum weight, has been determined. Results of previous work indicated that using high density honeycomb for filling the tubes will results more energy absorption but the weight efficiency has been lost [Zarei HR, Kröger M. Optimum honeycomb filled crash absorber design. Mater Des 2007;29:193–204]. Therefore, a comprehensive study has been performed in order to find out the crush behavior of tube filled with foam with different densities. The MDO procedure has been implemented to find an optimum filled tube that absorbed the same energy as an optimum empty tube can absorb.     

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.     

泡沫填充的薄壁圆柱壳体轴向压碎的分析模型

由于填充轻型泡沫的薄壁钢管有良好的耗能能力而被广泛地应用于工程中。当结构轴心受压时,钢管与泡沫芯之间的作用对吸收能量起到关键作用。已有理论研究的大部分对象为完全填充的钢管。本文提出了一个理论模型,用于分析部分填充的钢管的轴向对称压碎性能。采用改进的模型分析壳体,并考虑了泡沫芯的作用。由能量平衡原理得到极限压力的平均值。建议公式得到的结果与先前文献中的结果吻合。参数分析用于研究泡沫芯稳定时期的压力值(σf),以及填充的比例和壳体的径厚比对结构轴向受压性能的影响。为薄壁结构的吸能性能方面的设计提供指导。     

Crashworthiness investigation of kagome honeycomb sandwich cylindrical column under axial crushing loads

For the classic thin-walled energy absorber, the energy dissipation during a collision is concentrated over relatively narrow zones. This means that a great deal of materials of the columns do not participate in the plastic deformation or not enter into the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, a new type of kagome honeycomb sandwich bitubal circular column is presented in this paper. This innovative impact energy absorber is made of two circular aluminum tubes filled with core shaped as a large-cell kagome lattice. The interaction effect, deformation mode and energy absorption characteristics of the composite structure are investigated numerically. Observing the collapsing process, it is found that the kagome lattices buckle first, which triggers the outer and inner skin tubes to fold locally. This behavior increases the plastic deformation areas. Moreover, the presence of the outer and inner tubes strengthens the buckling capacity of kagome cell. Furthermore, the folded tube walls intrude into the gap of the honeycomb cell, which further retards the collapse of the honeycomb cell. So the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. In addition, the effects of geometrical parameters of the kagome honeycomb on the structural crashworthiness are studied. It is found that the cell wall thickness and cell distribution (cell number in the circumferential direction) have distinct effects on the specific energy absorption. Besides, we also studied the foam-filled column with the same foam density as the kagome honeycomb and compared it with the kagome sandwich structure. It is found that the kagome sandwich column has higher mean crash force and better energy absorption characteristics.     

Instability behavior and application of prismatic multi-tube latticed steel column

Multi-tube latticed steel columns without diagonal tubes and the ones with diagonal tubes are two common types of prismatic latticed columns used nowadays. Instability behavior of prismatic multi-tube latticed steel columns is studied in this paper. The focus on the problem is based on the derivation of shear stiffness for multi-tube latticed steel columns. Formulas are established to express the elastic buckling loads as well as the modified slenderness ratios, in which the effect of shear deformation is taken into account. Cases are analyzed via finite element method ANSYS to calculate the ultimate load-carrying capacity of the latticed columns for comparison with the design method in different design codes for compressive members. Formulas to estimate the design resistance for axial compressive prismatic multi-tube latticed steel columns are proposed and detailed design suggestions for the component steel tubes are presented as well.     

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.     

Quasi-static and dynamic crushing behaviors of aluminum and steel tubes with a cutout

Tubular members are commonly used as an energy absorber in engineering structures and many such members have a cutout. In this study, the crushing behaviors of tubes with a cutout are characterized and the effects of cutout on the energy absorption capabilities of these tubes are quantified. Systematic parametric studies were carried out to study the effect of material properties, including yield and ultimate strength of material, strain rate effect, location of cutout, tube length and impact speed on the crushing behaviors and energy absorption capacity of aluminum and steel tubes. First, a numerical model was constructed with a commercial explicit finite element code. It will be first proven that the numerical simulation can produce sufficiently accurate results in an economic manner. Subsequently, the crushing behavior of aluminum and steel tubes with a cutout was experimentally characterized and their energy absorption capacity was evaluated in terms of mean crushing force, peak crushing force and specific energy absorption (SEA). Tubes of various lengths with a cutout located at different locations, subject to both quasi-static and dynamic impact loadings were considered. For steel tubes, the numerical simulation investigated the influence of the strain rate effect and variation in strain hardening ratio of the material. Empirical equations describing the mean and peak crushing forces of aluminum and steel tubes with a cutout were developed using linear and nonlinear regression methods applied to the results obtained from the numerical and experimental studies.     

Collapse behaviour of plastic tubes filled with wood sawdust

The influence of foam-like wood filler on the mode of collapse and energy absorption performance of polyvinylchloride (PVC) tubes has been investigated under quasi-static loading conditions. The mode of collapse of axially crushed PVC tubes has been found to revert from regular three-lobe diamond mode to axisymmetric concertina mode at a certain wood-filling density. The energy absorption capacity of the PVC tubes is enhanced by wood compression as well as by extra stretching in the tube circumference due to shifting from multi-lobe to axisymmetric mode. The collapse of the PVC tubes has been analyzed considering multi-lobe mode, concertina mode and mixed mode. In these models, the interaction of the wood sawdust filler on the final mode of collapse of the PVC tubes has been incorporated. The mean crushing load of the PVC tubes collapsing into the mixed mode is considered as the average mean of that of the concertina mode, the multi-lobe mode and that causing crushing of wood sawdust. Compression tests on wood sawdust were used to extract its mechanical properties and the results have been used in the validation of the analytical model. The analytical results obtained for the mean crushing load agree reasonably well with those from experimental observations.     

An analytical model for axial crushing of a thin-walled cylindrical shell with a hollow foam core

A thin-walled tube filled with light-weighted foam has wide engineering applications because of its excellent energy absorption capacity. When the structure is axially crushed, the interaction between the tube and foam core plays an important role in its energy absorption performance. Previous theoretical studies so far have largely been concerned with fully in-filled tubes. In this paper, a theoretical model is proposed to predict the axi-symmetric crushing behaviour of such structures but with a partial infill. Using a modified model for shell and considering the volume reduction for the foam core, the mean crushing force is predicted by the energy balance. The proposed formula agrees well with previous results reported in literature. A parametric study is carried out to examine the contribution of foam core plateau stress (σ_f), amount of filling and shell's radius-to-thickness ratio (R/h) on the axial crushing behaviour of the structure. This study can give valuable design guidelines in using thin-walled structures as an energy absorber.     

Design of protective structures with aluminum foam panels

Design of protective structures requires multiple functions and reasonable safety criteria according to target structures. Hardening is one of the common concept to protect facilities and people. A general concept of blast pressure mitigation by metal foams was proposed. In this paper, a composite panel with aluminum foams and steel skins is introduced. Aluminum foams have low density and are attractive materials to mitigate high-speed pressure by blast loads due to high-energy absorption capabilities. A steel skin with high energy absorption capacity can be effectively used to resist penetration at front surface of the barrier and debris risk at rear surface. Mechanical properties of the aluminum foam according to different densities were obtained by material tests. Three material models for concrete, steel and aluminum foam were utilized considering strain-rate effects. Using the derived material models, explicit analyses of the composite panels were performed and their performance was evaluated. The newly developed high strength foam showed higher yield strength and better energy absorption capacity resulting in lightweight protective panels. For high blast pressure, the combination of energy absorbing steel skin and relatively dense foam or thicker foam is more effective.     

对钢管材料在液压膨胀试验中的应力—应变关系的测定

基于塑性膜理论和力平衡方程等,对试验数据进行曲线拟合,来确定在液压成形过程（THF）中薄壁管的应力一应变关系。由此提出一种简单实用的液压膨胀试验方法,并对不锈钢和低碳钢管进行自由膨胀试验,以得到所需的试验变形数据。而自由膨胀的有限元模拟同时也验证了该方法的有效性。结果表明：目前的做法是正确的,可用于对钢管材料的应力一应变性能进行界定,此外,由此法也可得到扩展的大应变流动应力曲线。     

Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes

A comprehensive experimental and numerical study of the crash behavior of circular aluminum tubes undergoing axial compressive loading is performed. Non-linear finite element analyses are carried out to simulate quasi-static and dynamic test conditions. The numerical predicted crushing force and fold formation are found to be in good agreement with the experimental results. A summary of available analytical solutions is presented in order to estimate the mean crushing load and establish a comparison between these analytical loads and the experimental one. Some observations are made on the influence of geometrical imperfections and material strain rate effect.     

Lateral compression behaviors of thin-walled equilateral triangular tubes

The paper deals with one important topic in impact engineering - the lateral compression behavior of thin-walled tubes. To study the lateral collapse modes and energy absorption behaviors of equilateral triangular tubes, quasi-static compression experiments were carried out. Crushing modes were revealed by the experiments. Three typical crushing stages characterize the lateral deformation plateaus of equilateral triangular tubes. In simulation, perfect tubes have symmetrical crushing modes. Strengths of the tubes were correctly predicted by the competition between yielding and buckling. Based on the observed crushing modes, plastic models were proposed for each stage to predict the lateral crushing behaviors theoretically. Equilateral triangular tubes have unified energy absorbing mechanisms, including five plastic hinges and one traveling plastic hinge. Plastic models have been constructed to predict the mean crushing forces and evaluate the energy absorption efficiency of the equilateral triangular tubes.