On the axial splitting and curling of circular metal tubes

The present paper investigates the axial splitting and curling behaviour of circular metal tubes. Mild steel and aluminum circular tubes were pressed axially onto a series of conical dies each with different semi-angle. By pre-cutting eight 5 mm slits which were distributed evenly at the lower end of each tube, the tube split axially and the strips curled outward. Experiments showed that this mechanism results in a long stroke and a steady load. An approximate analysis is presented which successfully predicts the number of propagated cracks, the curling radius and the force applied. This analysis takes into account ductile tearing of the cracks, plastic bending/stretching and friction. Effects of tube dimensions, semi-angle of the die and friction are discussed in detail.     

Axial crushing of wood-filled square metal tubes

The behaviour of thin tubes made of sheet metal and not so thin extruded tubes filled with wood and subjected to axial crushing is studied. Experiments show that the mode of elastic buckling is changed by the presence of the wood filler. The plastic crushing of thin tubes resulted in Euler-type buckling, while a considerable enhancement in the load carrying capacity and energy absorption was seen in the case of thicker walled tubes which were examined both under quasi-static and dynamic loading conditions. A new idealized deformation mechanism for the progressive crushing of the wood-filled tube is suggested and analysed. The results obtained for the mean loads agree reasonably with experimental observations. An alternative method employed to predict the mean crushing load of empty tubes and using a thickness that provides an equivalent stiffness to that of a filled tube is also seen to produce reasonable agreement with the experiment.     

Axial crushing of foam-filled tapered sheet metal tubes

Following earlier work on the axial crushing of foam-filled sheet metal tubes of square and rectangular cross-section and empty tapered tubes the behaviour of foam-filled tapered tubes is considered. Theoretical estimates of the variation in the mean crushing loads for both quasi-static and dynamic loading conditions are provided and compared with experimental data.     

An experimental study on tearing energy in splitting square metal tubes

An experiment was performed to study the tearing energy in splitting square aluminium and mild steel tubes of thicknesses ranging from 0.47 to 1.67 mm. It was carried out by driving four rollers each attached to the side wall of the tube, leading to the bending of the wall to a constant curvature and, at the same time, the tearing along the four corners. By pre-cutting some corners to a different length, the tearing energy involved was determined. It was found that the tearing energy per unit torn area (R) may be related to the ultimate stress of the material (σ_u) and the fracture strain (_f) as R = 8.8σ_uf for mild steel and R = 37.2σ_uf for aluminium tubes; here the two coefficients have length dimensions in mm.     

On the number of cracks in the axial splitting of ductile metal tubes

An analysis is given for the number of cracks which propagate in experiments on the splitting of ductile metal tubes when the ends are flared out. The number of cracks depends on the diameter of the tube (2r₀), the strength-to-toughness ratio of the metal ( ) and its hoop fracture strain _θ∫ (which may be related to microstructure via models of microvoid growth and coalescence). Since the expression for the number of cracks contains the product of ( ) and _θ∫, approximately the same number of cracks is predicted whether the tubes are annealed or work-hardened. Experiments by Reddy and Reid [Int. J. Mech. Sci. 28, 111 (1986)] give support to the predictions.     

Axial crushing of square tubes

The mechanics of the large deformation of a square tube under axial load is discussed. Theoretical results are substantiated by experimental results. The elastic buckling load is predicted by assuming the tube to be comprised of four plates simply supported at their edges. The highest load the tube can sustain is predicted by allowing for the development of plasticity near the corners. The mean crushing load is predicted from an incremental plasticity analysis which allows for travelling plastic hinges. Comparison with circular tube behaviour is considered and an attempt to explain some of the peculiarities is made.     

Long stroke energy dissipation in splitting tubes

A passive crashworthy system that dissipates impact energy by fracture and plastic deformation of metal tubes is analysed. The energy dissipating component is a square tube that is pressed axially against a die where it splits at the corners and curls outward. Experiments on the effect of die radius have shown that a remarkably constant force causes this rate-independent deformation in a dural tube. Tubes which both split and curl can be designed for energy absorbing systems requiring large stroke to length ratio and good specific energy absorption.     

Axial crushing behavior of the intermittent tack-welded cylindrical tubes

The objective of this paper is to evaluate the effect of intermittent weldment of cylindrical tubes on the energy absorbing behavior under axial crushing. This paper describes the test results for cylindrical empty and foam-filled tubes and discussions of the improvement of energy absorbing efficiency by the sequential rupture of intermittent weldment. The weldment rupture of a cylindrical foam-filled tube reduces the peak values of crush load and increases the valley values, while the mean crush load is maintained at a similar level as in the fully welded tube. The weldment rupture of a cylindrical foam-filled tube improves the energy-absorbing efficiency by reducing the crush load amplitude without a loss of total energy absorption.     

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.     

Axial crushing analysis of tubes deforming in the multi-lobe mode

Similar to the concertina mode, the wall of axially crushed tubes deforming in multi-lobe or diamond mode, will be laid down partly to the inside and partly to the outside of the tube generator with the latter part being smaller than the former. Such proportion of the folding length is known as the eccentricity factor, in both the concertina and multi-lobe modes. The present work examines the collapse of tubes in the multi-lobe in an attempt to evaluate the crushing load using this unique factor. The analysis produced a distinctive value for the eccentricity factor that simplifies the expression for the mean collapse load, which is a function of tube geometry and number of lobes. The analytical outcome for the mean crushing load, the total deflection is in a reasonable agreement with those obtained from experiment. Furthermore, the measured values of the eccentricity factor and the critical folding angles obtained for tubes of different materials and geometric ratios are also in good agreement with those produced by the analysis which postulates that the distinctive value of m is independent of the tube’s material and geometric ratios.     

Plastic mechanism analysis of circular tubes under pure bending

There are a number of solutions available to predict the response of a circular steel tube under pure bending. However, most of these solutions are based on an elasto-plastic treatment, which is complex and difficult to use in any routine design. This paper describes a theoretical treatment to predict the moment-rotation response of circular hollow steel tubes of varying D/t ratios under pure bending. The Mamalis et al. (J. Mech. Sci. 1989;203:411–7) kinematics model for a circular tube under a controlled moment gradient was modified to include the effect of ovalisation along the length of the tube. Inextensional deformation and rigid plastic material behaviour were assumed in the derivation of the deformation energy. The plasticity observed in the tests was assumed to spread linearly along the length of the tube. Two local plastic mechanisms (Star and Diamond shapes) were studied to model the behaviour observed in the tests especially during the unloading stage. The theoretical predictions are compared with the experimental results recently obtained by Elchalakani et al. (Quartral. J. Struct. Eng. 2000;3(3):1–16). Good agreement was found between the theoretical predictions and experimental moment-rotation responses, particularly for the Star shape mechanism. A closed-form solution is presented suitable for spreadsheet programming commonly used in routine design.     

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.     

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.     

复合导布辊胀形技术

介绍了复合导布辊胀形技术,分析了其理论依据,计算了胀形后内、外层之间的贴合力和胀形所需的成型压力,并简要介绍了模具的结构以及液压系统。     

On the quasi-static piercing of square metal tubes

This paper investigates the energy absorption properties of square tubes pierced by pointed punches under quasi-static conditions. In a series of tests, square section pyramidal punches and conically headed cylindrical punches were pierced slowly into square steel tubes having 40×40 mm² outside dimensions. Wall thicknesses of 1.6 and 2.5 mm were tested, and the length of tubes was varied. Some typical loads were plotted against deflection, and a number of interesting conclusions were drawn from the tests. Based on the test results and observations, preliminary theoretical considerations are presented. The theoretical results agree fairly with the experiments.     

Mean moment effect on sharp-notched circular tubes under cyclic bending

This study discusses an experimental investigation of the effect of the mean moment on the response and collapse of sharp-notched circular tubes subjected to cyclic bending. To highlight the influence of the mean moment effect, five different moment ratios r (minimum moment / maximum moment) were experimentally investigated. We found that the moment-curvature loop gradually shrinks, and stabilizes after a few cycles for r = ?1. However, the moment-curvature loop exhibits ratcheting and increases with the number of cycles for r ≠ ?1. In addition, the ovalization-curvature curve shows unsymmetrical, ratcheting and increasing manner with the number of cycles for any r. Finally, the empirical formulation proposed by Chang et al. [1] was modified to simulate the relationship between the controlled moment range and the number of cycles necessary to produce buckling. The results of the experimental investigation and the simulation were in good agreement with each other.     

Investigation of single phase frictional pressure loss in circular micro tubes

Single phase pressure drops in micro tubes were investigated through an experimental measurement and a numerical simulation. Experimental Po was obtained in circular micro tubes with 87 and 118 μm diameter with distilled water. Experiments were carried out in laminar flow region with varying the Re 15–450 for the 87 μm diameter tubes and 60–1300 for the 118 μm diameter tube. No early transition from laminar to turbulent flow was detected for the experimental range. The computational estimation of pressure drop in the 87 μm diameter tube was performed with the aid of CFD software. Boundary conditions from experiments were used for the numerical simulation. The results of experimental and numerical studies showed a good agreement with the conventional macro theory.     

An analysis of the nosing process of metal tubes

In this paper, the finite element method is used to investigate the cold nosing process of partially laterally constrained metal tubes with a conical die from a tube billet. A series of simulations on the tube nosing using the FEM program ANSYS/LS-DYNA was carried out. The influences of the process parameters such as tube length, tube thickness, die fillet radius, die angle, friction factor, strength coefficient and strain hardening exponent of the billet material on the critical nosing ratio of the tube are analysed. Experiments were carried out with stainless steel SUS304 tube billets at room temperature, and the results of experiments were compared with the FEM calculations.     

Large deformations of thin-walled circular tubes under transverse loading—II: Experimental study of the crushing of circular tubes by centrally applied opposed wedge-shaped indenters

The behaviour of aluminium and mild steel tubes of 2 in. dia., 0.064 in. thickness and of lengths ranging from 2–24 in. loaded centrally by opposed wedge-shaped indenters is examined. Three modes of deformation are identified and analysed on the basis of plastic work considerations. Reference is also made to the behaviour of a very thin-walled tube of diameter to thickness ratio equal to 190.     

Non-axisymmetric buckling behaviour of elastic-plastic circular tubes subjected to a nosing operation

Theoretical investigations have been carried out to predict the non-axisymmetric buckling seen in the throat of circular elastic-plastic tubes subjected to a nosing operation along a frictionless conically shaped die. The buckling points and associated modes are determined by Hill's bifurcation theory in conjunction with a non-axisymmetric buckling mode. The results show that increasing the die semi-angle and the tube thickness or decreasing the material work-hardening rate are always beneficial to improve the buckling limit. The associated critical buckling mode number generally decreases as the tube thickness increases and does not depend drastically on the die semiangle nor on the hardening rate. The effect of the average r value is substantial and the buckling limit is improved when the r value reduces. Part of the present results predict well the results observed in existing experimental work.