Quasi-static axial compression of thin-walled circular aluminium tubes

This paper presents further experimental investigations into axial compression of thin-walled circular tubes, a classical problem studied for several decades. A total of 70 quasi-static tests were conducted on circular 6060 aluminium tubes in the T5, as-received condition. The range of D/t considered was expanded over previous studies to D/t=10–450. Collapse modes were observed for L/D10 and a mode classification chart developed. The average crush force, F_AV, was non-dimensionalised and an empirical formula established as F_AV/M_P=72.3(D/t)^0.32. It was found that test results for both axi-symmetric and non-symmetric modes lie on a single curve. Comprehensive comparisons have been made between existing theories and our test results for F_AV. This has revealed some shortcomings, suggesting that further theoretical work may be required. It was found that the ratio of F_MAX/F_AV increased substantially with an increase in the D/t ratio. The effect of filling aluminium tubes with different density polyurethane foam was also briefly examined.     

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.     

Experimental quasi-static axial crushing of top-hat and double-hat thin-walled sections

Quasi-static axial crushing tests have been carried out on thin-walled top-hat and double-hat mild steel spot-welded sections. Several post-test collapse modes were identified for the structures and the associated energy-absorbing characteristics have been examined and compared with previous tests. A new empirical equation is suggested for relating the structural effectiveness to the structural density of top-hat and double-hat sections.     

Plastic collapse of thin-walled frusta and egg-box material under shear and normal loading

The quasi-static plastic collapse of thin-walled frusta is determined for combined shear and out-of-plane compression. Experiments and finite element calculations are conducted on conical metallic frusta with semi-included cone angles of 30^ο and 45° to determine the shear collapse response. Additional finite element predictions are given for compressive loading, and for combined shear-compressive loading. The dependence of strength and energy absorption upon geometry is explored. The predicted response of an array of conical frusta is used to give the overall response of an egg-box material sandwiched between rigid face sheets. Scaling laws are determined for the stiffness and strength as a function of relative density of the egg-box material.     

A theoretical analysis for the quasi-static axial crushing of top-hat and double-hat thin-walled sections

A theoretical analysis, using superfolding elements (SE), has been carried out to determine the mean crushing loads for the quasi-static axial loading of top-hat and double-hat, spot-welded mild steel sections. The theoretical predictions compare favourably with experimental results reported in a companion article and with the experimental and numerical predictions of other authors.     

The static axial compression of tall hollow cylinders with high interfacial friction

Hollow cylinders of initial height to diameter ratios between 1:1 and 2:1, with central holes of various diameters, were compressed axially under dry, quasi-static conditions. In the initial phase of compression three modes of flow could be identified, distinguished by single (I), double (II) or triple (III) barrels on the free surface.During continued compression, mode III degenerated into an unstable process similar to the collapse of thin-walled cans, whilst specimens initially displaying mode II changed to mode I or retained their initial form. Those cylinders that initially displayed mode I were found to retain this form throughout their subsequent compression.The deformation characteristics outlined above are shown to be dependent on the initial height to diameter ratio and the size of the bore.A preliminary axi-symmetric upper bound analysis is presented, but the simple models used are shown to be insufficient to represent accurately the complex phenomena observed. It is suggested that finite-element elastic-plastic analysis may be more appropriate.     

Stability of confined thin-walled steel cylinders under external pressure

The present paper investigates the structural stability of thin-walled steel cylinders surrounded by an elastic medium, subjected to uniform external pressure. A two-dimensional model is developed, assuming no variation of load and deformation along the cylinder axis. The cylinder and the surrounding medium are simulated with nonlinear finite elements that account for both geometric and material nonlinearities. Cylinders of elastic material within a rigid boundary are considered first, and the numerical results are compared successfully with available closed-form analytical predictions. Subsequently, the external pressure response of confined thin-walled steel cylinders is examined, in terms of the initial out-of-roundness of the cylinder, the initial gap between the cylinder and the medium, and the stiffness of the surrounding medium. Numerical results are presented in the form of pressure-deformation equilibrium paths, and show a rapid drop of pressure after reaching the maximum pressure level, as well as a significant imperfection sensitivity. A plastic-hinge mechanism is developed that results in a closed-form expression and illustrates the post-buckling response of the cylinder in an approximate manner. The distributions of plastic deformation, as well as the variation of cylinder-medium contact pressure around the cylinder cross-section are also depicted and discussed. Furthermore, the effects of uniform vertical preloading on the maximum pressure sustained by the cylinder are examined. Finally, the numerical results show good comparison with a simplified closed-form expression, proposed elsewhere, which could be used for design purposes.     

Experimental research on local buckling of BS700 high-strength steel thin-walled box-section members under axial compression

In this study, the ultimate bearing capacity and local buckling failure mode of members were investigated, and the results were compared to the predicted values of the existing steel structures design code. The results indicated that the failure mode of the specimen was local buckling. Finite element model is verified using experimental results. FE model is capable of predicting the behaviour of specimens and it is used for further numerical analyses. Experimental results are compared with recommendations of the steel structures design code of GB50017-2017, ANSI/AISC 360-16 and Eurocode 3. It is observed that the 83.3 % of the test bearing capacity are slightly higher than the predictions of existing codes with a variance of 5 %. It is concluded that the provisions of existing codes can meet the design requirements. However, the number of tests is limited and further related experimental and FE numerical studies are required.

     

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.     

Modes of axial collapse of unconstrained capped frusta

Efforts are made to classify the modes of deformation of unconstrained capped end frusta when crushed axially between two parallel plates. Tens of aluminum spun capped end frusta of different semi-apex angles (15–60°) and thicknesses (1–3 mm) are crushed at quasi-static loading conditions using a universal instron machine. The resulting modes of deformation can be classified into: (1) outward inversion, (2) limited inward inversion followed by outward inversion, (3) full inward inversion followed by outward inversion, (4) limited extensible crumpling followed by outward inversion, and (5) full extensible crumpling. Samples of frusta made of low carbon steel sheets and nylon plastic were tested statically and gave similar results. An explicit version of ABAQUS 5.8 finite element (FE) program is used to model the crushing modes. Good agreement is obtained between the FE predictions and the experimental work.     

Plastic analysis of pressurized cylinders under axial load

A theoretical stress analysis of fully plastic states in a cylindrical tube is given for axial load combined with external or internal pressure. The material is rigid-plastic, non-hardening, and either isotropic or transversely isotropic. New general results are found by judicious choice of the mechanical and kinematical variables. Solutions in simple closed terms are also derived for the yield criteria of Tresca and Hill, respectively, and a previous partial solution for von Mises's criterion is completed.     

Classification of the axial collapse of cylindrical tubes under quasi-static loading

The results of an experimental investigation of the axial crushing modes and energy absorption properties of quasi-statically compressed aluminium alloy tubes are presented. In particular, the influence of tube length on these properties is discussed and quantified and a classification chart presented. This chart together with other experimental data, enables a designer to predict the energy absorbing properties of a given tube as well as its mode of crushing.     

Flat-topped conical shell under axial compression

Based on experimental observations of a grid-domed textile composite under axial compression, the large deformation mechanisms of a flat-topped conical shell are identified. Accordingly, both elastic model and rigid-plastic model are proposed to describe the collapse process and predict the load–displacement characteristics. In the rigid-plastic analysis, the energies dissipated in bending along plastic hinge lines and in stretching of the thin-wall segments between the plastic hinge lines are taken into account. Analytical expressions describing the load–displacement and energy–displacement relationships during the large deformation process are derived. Illustrated by typical numerical examples, the effects of apical angle of a flat-topped conical shell on its energy absorption capacity are revealed. The respective strain distributions on the conical shell resulted from bending deformation and membrane deformation are presented. A good agreement is shown between the theoretical predictions and experimental results.     

Partial slip between contacting cylinders under transverse and axial shear

The interfacial stick-slip system present between two infinitely long cylinders, pressed together by a normal force, is considered. The shearing traction distribution is represented in a piecewise-linear sense, using overlapping triangles of shear, which may have both transverse and axial components. Several external force histories are modelled, starting off with a monotonically increasing transverse force (the Cattaneo–Mindlin problem). Subsequently, an axial force is applied, again within the partial slip regime, and finally a complete closed cycle of transverse and axial forces is studied. The stick-slip regime and distribution of shearing traction is displayed at several points within the cycle, and it is shown that a steady state is almost achieved within one cycle of loading.     

Energy absorption of aluminum alloy thin-walled tubes under axial impact

Aluminum alloys are important technological materials for achieving the lightweight design of automotive structures. Many works have reported on the deformation and energy absorption of thin-walled tubes. Multicorner tubes with extra concave corners in the cross section were presented in this study to improve the energy absorption efficiency of aluminum alloy thin-walled tubes. The axial crushing of square and multicorner thin-walled tubes was simulated with the same cross-sectional perimeter. The method of folding element was applied to predict the crushing behavior of the thin-walled tubes under axial impact. The corners on the cross section were discussed to determine their effect on the energy absorption performance of thin-walled tubes. Results showed that the increasing performance of energy absorption of aluminum alloy thin-walled tubes was caused by the increasing number of corners on the cross section of multicorner tubes. Both the number and size of corners had an important effect on the crushing force efficiency of multicorner tubes. The maximum crushing force efficiency of multicorner tubes was 11.6% higher than that of square tubes with the same material consumption of thin-walled tubes. The multicorner tubes with 12 corners showed better energy absorption performance than the tubes with more than 12 corners; this high number of corners could lead to the small size of corners or unstable deformations. The high energy absorption performance of multicorner tubes prefers increasing the corner number and corner size of adjacent sides at the same time.     

The inhomogeneous deformation of polycarbonate circular honeycombs under in-plane compression

In-plane uniaxial and equi-biaxial compression tests were conducted quasi-statically on polycarbonate circular honeycombs. While the uniaxial compression tests were easy to implement, a special test rig was designed to carry out the in-plane (x–y) equi-biaxial compression tests in a conventional universal testing machine. The deformation characteristics of a honeycomb block under uniaxial compression are quantitatively described by tracking the variations of the cells’ parameters, such as the area strain and the angle of cells, during the deformation process of the honeycomb. As the distribution of the deformation within the honeycomb block under biaxial compression is much more complex, a series of color maps based on the area strain of each cell are produced to demonstrate the inhomogeneous deformation among the cells in the honeycomb block, by which the initiation of deformation inhomogeneity and its evolution in the honeycomb block are characterized. To identify the role of the friction between the honeycomb sample and the test rig, finite element analysis is conducted to simulate the collapse process of the circular honeycomb under equi-biaxial compression. Furthermore, an inhomogeneity index, I_inh, is defined as a function of the overall compression of a sample to quantify the severity of the deformation inhomogeneity of the honeycomb; this index facilitates quantitative comparisons among the results under various loading conditions. It is found that the value of I_inh of a sample is closely related to some internal factors, such as the localization band of deformation and the deformation pattern of cells.     

Plastic buckling of conical shells under axial compression

Analysis and experimental results are presented on the plastic axisymmetric buckling of steep, truncated conical shells under axial compression. Specimens of 6061-T6 aluminum and type 416 stainless steel were tested; in spite of the considerable difference in the stress-strain curves for the two materials, the buckling modes observed in the experiments for geometrically identical cones were the same. Perturbation analysis, which takes account of the continuous change in direction of the plastic strain rate vector during buckling, is found to describe the essential features of the observed buckling deformation.     

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.     

Plastic buckling of tubes under axial compression and internal pressure

The plastic buckling and collapse of long cylinders under combined internal pressure and axial compression was investigated through a combination of experiments and analysis. Stainless-steel cylinders with diameter-to-thickness values of 28.3 and 39.8 were compressed to failure at fixed values of internal pressure up to values 75% of the yield pressure. The first effect of internal pressure is a lowering of the axial stress–strain response. In addition, at some plastic strain level, the cylinder develops uniform axisymmetric wrinkling. Under continued compression, the wrinkles grow stably, gradually reducing the axial rigidity of the structure and eventually lead to a limit load instability. All pressurized cylinders remained axisymmetric until the end of the test past the limit load.The critical stress and wavelength were established using classical plastic bifurcation theory based on the deformation theory of plasticity. The evolution of wrinkling, and the resultant limit state, were established by modeling a periodic domain that is one half of the critical wavelength long. The domain was assigned an initial imperfection corresponding to the axisymmetric buckling mode calculated through the bifurcation check. The inelastic material behavior was modeled through the flow theory of plasticity with isotropic hardening. The variations of the axial response and of the limit strain with pressure observed in the experiments were reproduced well by the model. Inclusion of Hill-type anisotropic yielding in all constitutive models was required for good agreement between predictions and experiments.