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.     

Energy absorption of aluminium alloy circular and square tubes under an axial explosive load

The energy absorption of circular and square aluminium alloy tubes subjected to an axial explosive load, which is transmitted to a tube by a small attached mass, is discussed. Particular attention is paid to the interaction between the inertia of the attached mass and a tube when the importance of the initial compression phase is revealed. The effect of this phase on the mean load, which is characteristic of the energy absorption capacity of structural elements, is demonstrated. The influence of the material models on the prediction of the response of aluminium alloy circular and square tubes is also discussed in relation with the temperature effects caused by the high strain rates. The analysis shows that the material properties play an important role for the formation of the buckling pattern due to the finite duration of the initial compression phase when plastic stress waves at different speeds propagate along a shell.     

Collision performance of square tubes with diaphragms

The energy absorption responses of conventional tubes and tubes with diaphragms are analysed here by means of finite element simulation. Numerical results show that tubes with diaphragms exhibit a relatively stable crushing process. The effect of imperfect energy absorption responses is also analysed, including the top shape of tubes and oblique loading. The strain rate affects the dynamic response of tubes with diaphragms. Four prototypes of these tubes were constructed and tested; however, sizeable differences were obtained between experimental results and the results of numerical simulation of the ideal structure in terms of process errors.     

Axial crushing of flattened expanded metal tubes

This paper presents an investigation on the structural behavior of flattened expanded metal tubes subjected to axial crushing. At first, the study is carried out experimentally to investigate the effect of the angle formed between the expanded metal cell and the applied load. Secondly, the results are compared with experimental results for standard expanded metal sheets. Thereafter, numerical analyses are conducted by means of nonlinear finite element models, to investigate the enhancement in the energy absorption characteristics due to flattening of the expanded metal. Both results, experimental and numerical show a significant increase in energy absorbing capacity and mean force for the flattened tubes.     

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 and optimal design of square tubes with graded thickness

Introducing thickness gradient in cross-section is a quite promising approach to increase the energy absorption efficiency and crashworthiness performance of thin-walled structures. This paper addresses the deformation mode and energy absorption of square tubes with graded thickness during axial loading. Experimental study is firstly carried out for square tubes with two types of thickness distributions and numerical analyses are then conducted to simulate the experiment. Both experimental and numerical results show that the introduction of graded thickness in cross-section can lead to up to 30–35% increase in energy absorption efficiency (specific energy absorption) without the increase of the initial peak force. In addition, structural optimization of the cross-section of a square tube with graded thickness is solved by response surface method and the optimization results validate that increasing the material in the corner regions can indeed increase the energy absorption efficiency of a square tube.     

Computer simulation and energy absorption of tapered thin-walled rectangular tubes

Tapered thin-walled tubes have been considered desirable energy absorbers under axial loading due to their relatively stable crush load and deformation response compared with straight tubes. This paper compares the energy absorption response of straight and tapered thin-walled rectangular tubes under quasi-static axial loading, for variations in their wall thickness, taper angle and number of tapered sides. Overall the study highlights the advantages of using tapered tubes as energy absorbers. In particular, the peak load required to crush the tubes decreases with the introduction of a taper, and as the taper angle increases. This is desirable for minimising the impact loads transmitted to the protected structure. The practical outcome of the study is design information for the use of tapered thin-walled rectangular tubes as energy absorbers in impact loading applications. Analysis has been undertaken using a finite element model, validated using existing theoretical and numerical models.     

Comparative analysis of energy absorption and deformations of thin walled tubes with various section geometries

In this paper, deformations and energy absorption capacity of thin walled tubes with various section shapes (circular, square, rectangular, hexagonal, triangular, pyramidal and conical) are investigated both experimentally and numerically. The tubes have the same volume, height, average section area, thickness and material and are subjected under axial quasi static loading. The results of simulations are in good agreement with the experimental data and show that the section geometry has considerable effect on the energy absorption. The circular tube has the most energy absorption capacity and the most average force among all investigated sections. Since the maximum force is concerned in impact events, pyramidal and conical tubes are recommended, due to their uniform load–displacement curves and therefore, less difference between the maximum and the average forces.     

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.     

Load-carrying capacity and energy absorption of thin-walled profiles with edge stiffeners

The paper presents results of the study into plastic mechanisms (collapse behaviour) of short stub thin-walled profiles with edge stiffeners under compression. The aim of the study was to investigate an applicability of such profiles as energy absorbers. Solutions of other researchers and the author are presented. The new plastic mechanism solution for hat-section column is derived.     

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.     

Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular,square, hexagonal and octagonal sections

Energy must dissipate during a collision to prevent damage and injury. To reduce loss from collision, energy absorbers are used that dissipate energy upon deformation and folding to prevent damage to critical parts of a structure. In this paper, simple and multi-cell thin-walled tubes made from aluminum with triangular, square, hexagonal and octagonal sections were subjected to quasi-static loading. The experimental results were then compared with numerical simulations. The results showed that the energy absorption capacity of multi-cell sections is greater than for that of simple sections. Also, hexagonal and octagonal sections in a multi-cell configuration absorbed the greatest amounts of energy per unit of mass.     

Effects of boundary conditions on the energy absorption of thin-walled polymer composite tubes under axial crushing

Polymer composite tubes can be designed to absorb high levels of impact energy by progressive crushing. When a tube is crushed onto a flat platen, energy is absorbed by bending failure of the plies, delamination and friction mechanisms. In the present work, significant increases in energy absorption are shown when a shear mode of failure is initiated by crushing the tube onto a radiused plug (or initiator). A study of plug radius, R, normalised with respect to the tube wall thickness, t, in the range of 0R/t5 for circular tube diameter/thickness ratios of 10<D/t<33 was undertaken with continuous filament random mat glass/polyester composite. Different radii plugs lead to significantly different deformed shapes and crush zone morphologies. Large radius initiators (R/t>2) cause the tubes to split and energy is absorbed primarily through friction and axial splitting. As the initiator radius decreases, the amount of through-thickness shear damage in the fronds increases along with specific energy absorption (SEA). When the plug radius becomes small compared to the wall thickness (R/t<0.75) a debris wedge forms between the initiator and the tube and acts like a larger radius initiator. The highest energy absorption was seen to occur at R/t1 when through-thickness shear damage was induced. In this range, under static loading conditions, SEA was seen to be higher than that for tubes crushed onto a flat platen.     

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.     

Analysis of nested tube type energy absorbers with different indenters and exterior constraints

The present work presents both numerically and experimentally the quasi-static lateral compression of nested systems with vertical and inclined side constraints. The force–deflection response of mild steel short tubes compressed using two types of indenters is examined. The variation in response due to these indenters and external constraints and how these can contribute to an increase in the energy absorbing capacity of such systems are illustrated. The implicit version of the Finite Element code via ANSYS is used to simulate these nested systems and comparison of results is made with those obtained in experiments and were found to be in good agreement.     

Experimental investigations on the crush behaviour of AA6061-T6 aluminum square tubes with different types of through-hole discontinuities

An experimental investigation was conducted to compare the crush characteristics and energy absorption capacity of AA6061-T6 aluminum alloy extrusions with centrally located through-hole discontinuities. Three different types of geometrical discontinuities, namely, circular, slotted and elliptical holes were fabricated into AA6061-T6 extrusions which had a length of 200 mm, nominal side width of 38.1 mm and wall thickness of 3.15 mm. Furthermore, three different major axis lengths (7.14, 10.72, and 14.29 mm) and three different aspect ratios (1.33, 2.0, and 3.0) of the slotted and elliptical discontinuities were considered. It was found that by introducing crush initiators into the structural members, a splitting and cutting deformation mode was generated rather than global bending deformation which was observed for specimens without any discontinuities. The peak crush load was reduced by incorporating the through-hole crush initiators within a range of 5.2–18.7%, and total energy absorption was increased within a range of 26.6–74.6%. The most significant improvement was noted in the crush force efficiency, which was increased within the range of 54.5–95.8%. For specimens with discontinuities which had a major axis length of 7.14 mm the peak crush load and total energy absorption was independent of initiator geometry and aspect ratio. However, for specimens which had discontinuities with a major axis length of 10.72 and 14.29 mm and an aspect ratio of 3, a geometrical influence on the peak crush load and total energy absorption was apparent.     

Degradation and collapse of square tubes under cyclic bending

This paper presents the results of an experimental investigation of the elastic–plastic degradation and collapse of steel tubes with square cross-section under cyclic pure bending in a curvature symmetric fashion. The results indicate that the structural performance of the tubes degrades due to the growth of periodic, transverse deflections in their flanges. The wavelength of these deflections is equal to the wavelength of the buckling mode of the tubes under monotonic pure bending. Persistent cycling induces localization of the amplitude of these deflections and leads to the formation of a kink in one of the flanges. This causes collapse of the tube.     

Study of lateral compression of round metallic tubes

A detailed experimental and computational investigation of round metallic tubes subjected to quasi-static loading is presented. Experiments were conducted wherein round aluminium and mild steel tubes of different diameter to thickness ratios were subjected to lateral compression in an Instron machine. Their deformation histories and load–compression curves were obtained. The deformation of the tubes has also been studied and analysed with the help of the finite element code FORGE2. Contours of nodal velocity, equivalent strain rate and equivalent strain at different stages of compression are presented and discussed. Experimental and computed results are compared. Basic mechanism of their deformation and the effects of process parameters on deformation behaviour of the tubes are presented and discussed.     

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.     

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.