Experimental analyses of collapse behaviors of braced elliptical tubes under lateral compression

A series of experiments were conducted for braced, elliptical tubes with semi-axes ratios, , ranging from 0.5 to 2 to verify the theoretical analysis results presented in a companion paper (Wu and Carney, Int. J. Mech. Sci., 1996). In that paper, mathematical models and finite element analyses (ABAQUS (Hibbitt, Karlsson and Sorensen, Inc. ABAQUS Manual, Version 5.3, [2])) were employed to study the initial collapse behavior of braced elliptical tubes. These mathematical and numerical predictions are compared with experimental results in this paper.     

Energy absorbing capacities of braced metal tubes

The collapse and energy dissipation characteristics of metal tubes braced with tension members are considered experimentally and load bounding techniques are employed to estimate collapse loads of such tubes. The results are applied in the full scale crash testing of a vehicle impact attenuation device composed of clusters of steel tubes and subjected to high speed roadway collisions.     

Plastic collapse and energy absorption of empty circular aluminum tube under transverse quasi-static loading

This paper presents an experimental investigation on plastic collapse and energy absorption of empty circular aluminum tubes under quasi-static transverse loading. Tubular structures being a critical demand as material saving, high energy absorption and good strength characteristics were of major concerns due to its wall thinness, and so, its various diameter-to-thickness (D/t) ratios and span lengths. Studies found that empty circular Al-tube structure subjected to transverse standard three-point bending loading undergone three plastic deformation phases, starting with crumpling phase, crumpling and buckling phase, and lastly the structural collapse. The results found that energy absorption of empty aluminum tubes for a constant D/t ratio decreases as span length. On the contrary, the energy absorption of empty aluminum tubes for a given constant span length increases with the increase in D/t ratio.     

Experimental and numerical crashworthiness investigation of combined circular and square sections

Quasi-static experimental and nonlinear finite element analyses are performed to compare the energy absorption and initial peak load of combined circular and square sections with those of regular circular and square sections. The combined circular and square sections have higher energy absorption and lower initial peak load. These tubes can be widely used to ensure passenger safety in automotive and aerospace landing structures. The predicted numerical crushing load and fold pattern are in good agreement with experimental results. The specific energy absorption capability of the combined tube is significantly higher than that of the square tube and is close to that of the circular tube. The initial peak load of combined tube is significantly lower than that of the circular tube and somewhat lower than that of the square tube. Changing the section dimensions and their length results in higher energy absorption of the combined section than that of circular and square sections. Moreover, the initial peak load in the combined section is lower than that of the circular and square sections in all cases.     

Deformation and energy absorption of aluminum foam-filled tubes subjected to oblique loading

Research to quantify the energy absorption of empty and foam-filled tubes under oblique loading with different loading angles and geometry parameters was carried out. Tests on circular tubes made of aluminum alloy AA6063 under quasi-static axial or oblique loading were performed. The collapse behavior of empty, foam-filled single and double tubes was investigated at loading angles of 0°, 5°, 10° and 15° with respect to the longitudinal direction of the tube. The tubes were fixed at both ends and oblique load was realized by applying a load at the upper end of a pair of specimens. When the foam-filled tubular structures subjected to oblique quasi-static loading, some new deformation modes, such as spiral folding mode, irregular extensional folding mode and irregular axi-symmetric or diamond deformation mode, were identified and ascribed to the bending of tubes and shearing of foam filler, as well as the interaction between the tubes and the foam. The energy absorption characteristics of empty and foam-filled single and double tube structures with respect to the load angle and wall thickness are determined. It is found that the energy-absorbing effectiveness factors of the circular tube structures with aluminum foam core are significant higher than those of the empty tubes and the energy absorption capacity of the foam-filled double tubes is better than that of the empty and foam-filled single tubes.     

Plastic collapse and energy absorption of circular filled tubes under quasi-static loads by computational analysis

This study presents the finite element analysis of plastic collapse and energy absorption of polyurethane-filled aluminium circular tubes under quasi-static transverse loading. Increasing focuses were given to impact damage of structures where energy absorbed during impact could be controlled to avoid total structure collapse of energy absorbers and devices designed to dissipate energy. ABAQUS finite element analysis application was utilized for modelling and simulating the polyurethane-filled aluminium tubes, different set of diameter-to-thickness ratios and span lengths, subjected to transverse three-point-bending load. Different sets of polyurethane-filled aluminium tubes subjected to the transverse loading were modelled and simulated. The failure modes and mechanisms of filled tubes and its capabilities as energy absorbers to further improve and strengthening of empty tube were also identified. The results showed that plastic deformation response was affected by the geometric constraints and parameters of the specimens. The diameter-to-thickness ratio and span lengths had shown to play crucial role in optimizing the PU-filled tube as energy absorber.     

Numerical investigations on a new type of energy-absorbing structure based on free inversion of tubes

A new type of structure, called retractable tube, is introduced in the present work to overcome the drawbacks of two traditional types of invertubes. The inversion processes of the proposed tubes under axial compression are simulated by using the non-linear finite element code LS-DYNA and the features of the force-displacement curves and the deformation modes of the proposed tubes are analyzed. A comparative study is conducted to compare the energy absorption characteristics of the new proposed tubes with the plain circular tubes based on the performance indices used most commonly for energy-absorbing devices. The results show that the whole efficiencies of the new proposed tubes are significantly higher than those of the corresponding plain circular tubes. In addition, a parametric study is carried out to investigate the effects of geometric parameters on the behavior of retractable tubes.     

内压及扭矩载荷下无缺陷弯管的应力分析

分析在内压或扭矩载荷作用下非均匀壁厚椭圆弯管的应力分布，结果表明内压引起的最大应力随着弯管的截面不均匀度而变化，由此解释了工程实际中弯管失效的原因，同时也为求解弯管的塑性极限载荷奠定了基础。     

内压及扭矩载荷下无缺陷弯管的塑性极限载荷

弯管在管线中通常是承受应力较大的元件，极限载荷相应较低。为充分发挥结构的塑性极限承载能力，对弯管的塑性极限载荷进行理论分析，利用von Mises屈服准则，推导出内压和扭矩联合载荷作用下等厚弯管、非均匀壁厚椭圆弯管的塑性极限压力。实验验证了理论分析的正确性。     

椭圆翅片管空冷器在乙烯工业中的应用

通过对圆形翅片管和椭圆翅片管的性能分析比较，选取椭圆翅片管对乙烯工业中的圆形翅片管空冷器进行设计改造，达到提高传热效率、降低流动阻力＼节能降耗、提高效益目的。根据改造的结果以及在实际中应用，采用椭圆翅片管空冷器在压缩气体的冷却上各项参数均优于原圆管翅片管空冷器，达到了要求。证明椭圆翅片管空冷器在乙烯工业中有很好的应用价值，在其它类似的场合中也值得应用推广。     

Collapse simulation of tubular structures using a finite element limit analysis approach and shell elements

This paper describes the collapse simulation of thin-walled tubular structures using a finite element limit analysis approach and degenerated four-node shell elements. The simulation traces the path of sequential deformation of the structure modelled by considering the strain-hardening effect, which is important for the analysis of collapse behaviour and energy absorption efficiency. The collapse analysis of some square tubes was used to verify the simulation method proposed. Numerical results are compared with experimental observations for sequential collapse loads and deformation modes, showing fairly good coincidence. The collapse analysis of an S-rail was then carried out for sequential collapse loads as well as deformation modes and its results are compared with elasto-plastic analysis results obtained from the explicit dynamic code PAM-CRASH. The energy absorption capacity was studied for a variety of rectangular cross-section aspect ratios. The results show that the energy absorption capacity increases as the height-to-width aspect ratio becomes larger. Results also demonstrate that the finite element limit analysis can predict the plastic collapse load and collapse mode of thin-walled structures efficiently and systematically. The present algorithm with a simple formulation has the advantage of stable convergence, computational efficiency and easy access to strain-hardening materials compared to the incremental rigid–plastic finite element analysis.     

Energy absorption of pressurized thin-walled circular tubes under axial crushing

By pressurizing cellular materials, honeycombs, or thin-walled structures, their energy absorption can be greatly enhanced, and this enhancement can be controlled by the applied pressure. This concept shines light on the possibility of achieving adaptive energy absorption. To investigate the effect of internal pressure on energy absorption of thin-walled structures, this paper presents a study of axial crushing of pressurized thin-walled circular tubes. In the experiments, three groups of circular tubes with radius/thickness ratio R/t=120-200 were axially compressed under different pressurizing conditions. The results show that with an increase of internal pressure, the deformation mode switches from diamond mode with sharp corners to that with round corners, and eventually to ring mode. In diamond mode, the mean force of the tubes increases linearly with internal pressure. The enhancement comes from two mechanisms: direct effect of pressure and indirect effect due to interaction between pressure and tube wall. After the deformation switches to ring mode, the enhancement resulting from the second mechanism becomes weaker. Based on experimental observations, the deformation mode, energy dissipation mechanisms as well as interaction between internal pressure and tube wall are analyzed theoretically and the theoretical results are in good agreement with the experimental ones.     

Behaviour of axially crushed corrugated tubes

The energy absorption characteristics of corrugated tubes are experimentally studied. The corrugations are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube generator. The aims are to improve the uniformity of the load—displacement behaviour of axially crushed tubes, predict and control the mode of collapse in each corrugation in order to optimize the energy absorption capacity of the tube. Effect of heat treatment and foam filling of these tubes are also considered. Metal tubes are mostly used throughout this study, however, PVC tubes are also considered for comparison purposes. The experimental results of crushing of the corrugated tubes make these tubes a good candidate for a controllable energy absorption element.     

Lateral crushing of square and rectangular tubes by non-orthogonally placed narrow width indenters

A study of the collapse behaviour of square or rectangular tubes subjected to transverse loading by narrow width indenters, placed in orthogonal and non-orthogonal positions is presented. Experiments were conducted on as-received aluminium tubes, wherein the tubes were compressed in an unsymmetrical and a symmetric arrangement. Typical load-compression curves and histories of the deforming specimens are presented. Based on experimental observations, an analysis which considers the energy absorbed in stationary and rolling plastic hinges is developed for typical cases of the two modes of tube collapse. Computed results of the hinge locations, deforming tube geometry and load-compression curves are presented in each case. These results show good agreement with the experimental observations.     

Impact collapse characteristics of CF/Epoxy composite tubes for light-weights

This paper investigates the collapse characteristics of CF/Epoxy composite tubes subjected to axial loads as changing interlaminar number and outer ply orientation angle. The tubes are aften used for automobiles, aerospace vehicles, trains, ships, and elevators. We have performed static and dynamic impact collapse tests by a way of building impact test machine with vertical air-compression. It is fanad that CF/Epoxy tube of the 6 interlaminar number (C-type) with 90° outer orientation angle and trigger absorbed more energy than the other tubes (A, B and D types). Also collapse mode depended upon outer orientation angle of CF/Epoxy tubes and loading type as well ; typical collapse modes of CF/Epoxy tubes are wedged, splayed and fragmentcl.     

Mode of collapse and energy absorption characteristics of constrained frusta under axial impact loading

The energy absorption performance of right circular frusta subjected to dynamic axial load is studied and compared with the results of quasi-static tests. Frusta of different geometric ratios and end constraints were axially crushed using a drop hammer at initial velocities in the range of 2–5 m/s. The effect of heat treatment on the collapse behaviour and energy absorption is also investigated. The experimental observations indicate that the effects of the end constraints and heat treatment on the energy absorption were qualitatively similar to those observed under quasi-static testing. Due to inertia effects, the absolute values of the energy absorbed by similar frusta were higher under dynamic loads than under quasi-static loads. It has been established that constraining the frusta enhances their energy absorption capacity under static and dynamic loading particularly at the top (smaller diameter). The optimum geometric parameters for maximum energy absorption performance are identified when residual stresses and strain hardening characteristics, arising from spinning the frusta, were removed.     

Collapse mode transitions of thin tubes with wall thickness, end condition and shape eccentricity

Transition of deformation mode shapes of round aluminum tubes from axisymmetric concertina to non-axisymmetric diamond mode have been studied with varying tube wall thickness, boundary conditions and tube shape eccentricities. Quasi-static axial compression experiments were carried out on as received aluminum tubes and tubes with wall thickness eccentricity, incorporated by off center machining. Tubes were of D/t=29 and L/D=1.4. The numerical simulation of the collapse phenomenon has been undertaken using a static non-linear finite element analysis in ANSYS with a fine mesh discretization of the tube domain and small incremental displacements as load steps. Convergence studies for the finite element model with respect to load step size and mesh density have also been established. The numerical results are found to compare well with the experimental load compression and energy absorption responses both for the axisymmetric concertina and non-axisymmetric diamond collapse modes. Having validated the numerical model with experiments, it has been used to undertake a systematic study of the load–deformation characteristics, energy absorption response and collapse mode transition of the tubes in varying configurations of wall thickness, shape and inplane boundary condition eccentricities. Dependence of tube collapse characteristics and collapse mode transitions on such eccentricities have been discussed.     

Investigation of deformation and collapse mechanism for magnesium tube in axial crushing test

This paper demonstrates the quasi-static axial compression and high-speed axial compression tests of extruded magnesium alloy circular tubes for evaluating the crash and fracture behavior of mg parts. To capture the buckling and fracture behavior of Mg tube during the axial compression tests, FE simulation adopts different types of flow curves depending on the deformation mode such as tension and compression with LS-DYNA software. The Mg tube undergoes compressive plastic strain prior to buckling while according to the model based on Hill yield criterion only bulging along the radial direction is predicted. Due to the tension-compression asymmetry of Mg alloys, diameter of Mg tube expands largely at the initial plastic strain before having bulging or folding while only a bulging mode typical for materials with cubic crystal structure can be predicted. Simulation results such as punch load and deformation mode are compared with experimental results in the axial crushing test with AZ61 alloy.     

A DXDR large deflection analysis of uniformly loaded square, circular and elliptical orthotropic plates using non-uniform rectangular finite-differences

A finite-difference analysis of the large deflection response of uniformly loaded square, circular and elliptical clamped and simply-supported orthotropic plates is presented. Several types of non-uniform (graded) mesh are investigated and a mesh suited to the curved boundary of the orthotropic circular and elliptical plate is identified. The DXDR method-a variant of the DR (dynamic relaxation) method-is used to solve the finite-difference forms of the governing orthotropic plate equations. The DXDR method and irregular rectilinear mesh are combined along with the Cartesian coordinates to treat all types of boundaries and to analyze the large deformation of non-isotropic circular/elliptical plates. The results obtained from plate analyses demonstrate the potential of the non-uniform meshes employed and it is shown that they are in good agreement with other results for square, circular and elliptical isotropic and orthotropic clamped and simply-supported plates in both fixed and movable cases subjected to transverse pressure loading.     

Inelastic wrinkling and collapse of tubes under combined bending and internal pressure

The problem of inelastic bending and collapse of tubes in the presence of internal pressure is investigated using experiments and analyses. The experiments involve 1.5-inch diameter, D/t=52 stainless steel tubes bent to failure at fixed values of pressure. The moment-curvature response is governed by the inelastic characteristics of the material. Bending induces some ovalization to the tube cross section while, simultaneously, the internal pressure causes the circumference to grow. Following some inelastic deformation, small amplitude axial wrinkles appear on the compressed side of the tube, and their amplitude grows stably as bending progresses. Eventually, wrinkling localizes, causing catastrophic failure usually in the form of an outward bulge. Internal pressure stabilizes the structure, it increases the wavelength of the wrinkles and can increase significantly the curvature at collapse. The onset of wrinkling is established by a custom bifurcation buckling formulation. The evolution of wrinkling and its eventual localization are simulated successfully using a FE shell model. The material is represented as an anisotropic elastic-plastic solid using the flow theory, while the models are assigned initial geometric imperfections with the wavelength of the wrinkling bifurcation mode. It is demonstrated that successful prediction of collapse requires very accurate representation of the material inelastic properties including yield anisotropies, and that as expected, the collapse curvature is sensitive to the imperfection amplitude and wavelength imposed.