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.     

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.     

The plastic collapse and energy absorption capacity of egg-box panels

The plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression has been measured and modelled. It is observed that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism. Drop weight tests have been performed at speeds of up to 6 ms⁻¹, and an elevation in strength with impact velocity is noted. A 3D finite element shell model is needed in order to reproduce the observed behaviours. Additional calculations using an axisymmetric finite element model give the correct collapse modes but are less accurate than the more sophisticated 3D model. The finite element simulations suggest that the observed velocity dependence of strength is primarily due to strain-rate sensitivity of the aluminium sheet, with material inertia playing a negligible role. Finally, it is shown that the energy absorption capacity of the egg-box material is comparable to that of metallic foams.     

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.     

一种新型吸能装置的轴向耐撞击性能分析

基于传统吸能元件薄壁圆管的结构形态及其功能型要求,给出了一种端部带翻转模的新型吸能装置。在薄壁圆管直径和长度给定的前提下,通过改变翻转模诱导半径和管壁厚度,诱发了圆管在轴向冲击荷载下的四种变形模式,并对其中翻转变形模式进行了深入分析,考察了应变率、惯性效应和几何参数对其耐撞击性能的影响规律。有限元计算结果表明,发生翻转变形模式的薄壁圆管荷载-位移历程较平稳,总效率较高,具有较优异的轴向耐撞击性能;材料的应变率效应、翻转模半径与管壁厚度之比(r/t)、管壁厚度与圆管直径之比(t/D)对撞击荷载有较大的影响,而圆管自身的惯性效应对撞击荷载的影响较小。数值模拟结果为耐撞击结构部件的设计提供了参考依据。     

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.     

A numerical study on the impact response and energy absorption of tapered thin-walled tubes

Tapered tubes have been considered desirable impact energy absorbers due to their relatively stable mean load–deflection response under dynamic loading. Relatively few studies have been reported on the energy absorption performance of tapered tubes compared with straight tubes. This paper compares the energy absorption response of straight and tapered thin-walled rectangular tubes under both quasi-static and dynamic axial impact loading, for variations in wall thickness, taper angle, impact mass and impact velocity. It is found that the dynamic response of tapered tubes is more sensitive to impact velocity and wall thickness than taper angle for lower impact velocities. Inertia effects influenced the dynamic response for both straight and tapered tubes, yet were less significant for the latter. Overall, the results indicate that the energy absorption response of tapered tubes can be controlled via their wall thickness and taper angle, and this highlights their potential for use as energy absorbers. Analysis has been undertaken using a finite element model, validated using existing theory.     

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.     

Optimised design of nested circular tube energy absorbers under lateral impact loading

Arrangements of mild steel (DIN 2393) nested tubes were laterally crushed by dynamic loading. The tests were performed with impact velocities ranging between 3 and 5 m/s, using a fixed mass impinging onto the specimens under the influence of gravity. Two arrangements of nested tube systems were considered; one standard and one optimised design. Their crushing behaviour and energy absorption capabilities were analysed experimentally and simulated numerically using the explicit code LS-DYNA. Results from the numerical analyses were compared to those obtained from experiments. An over-prediction in force–deflection responses was obtained from the numerical code. An attempt was made to explain this inconsistency on the basis of the validity of strain rate parameters used in the Cowper–Symonds relation. It was shown that the optimised energy absorber exhibited a more desirable force–deflection response than the standard arrangement due to a simple design modification that involved mild steel cylindrical dampers.     

Energy absorption of aluminum foam filled braided stainless steel tubes under quasi-static tensile loading conditions

A theoretical model to predict the energy absorption capabilities of aluminum foam filled braided stainless steel tubes under tensile loading conditions has been developed and is presented. Experimental testing was completed on braided tubes, with a nominal diameter of 64.5 mm and woven from 304 stainless steel wires with a diameter of 0.51 mm, filled with rectangular prisms of closed cell aluminum foam with densities ranging from 248 to 373 kg/m³. Based upon observations from experimental testing and applying a unit cell concept to the braided tube, a theoretical model which incorporates two stages of deformation was developed. Within the first stage of deformation, which occurs prior to tow lockup of the braided tube, energy absorption is primarily due to compression of the aluminum foam core. After tow lockup has occurred the energy absorption behavior of the assembly is a sole result of the deformation of the braided tube. Comparisons between the energy absorption predictions of the analytical model and experimental observations were found to be in good agreement for assembly lengths of approximately 400 mm. For the tensile loading conditions and geometry of aluminum foam filled braided tubes considered in this research energy absorption ranged from approximately 5.2 to 7.9 kJ with corresponding tube elongations of 400 mm.     

An analytical model for plate wrinkling under tri-axial loading and its application

The prediction and prevention of wrinkling have been challenging issues in sheet metal forming processes. In an effort to provide the design and process engineers a reliable and efficient tool in assessing the onset of flange wrinkling, an analytical model, based on the wrinkling criterion proposed by Cao and Boyce [1], is presented here. The critical buckling stress and wavelength as functions of normal pressure are calculated using a combination of energy conservation and plastic bending theory. The present results are in excellent agreement with those obtained from Cao and Boyce’s numerical approach which has demonstrated its excellent predictive capability by comparing the experimental study of a conical cup [1] and a square cup forming [2]. Additionally, the effects of the tension in the plane of sheet and material properties on the initiation of flange wrinkling are investigated.     

The collapse response of sandwich beams with a Y-frame core subjected to distributed and local loading

Sandwich beams comprising a Y-frame core have been manufactured by assembling and brazing together pre-folded sheets made from AISI type 304 stainless steel. The collapse responses of the Y-frame core have been measured in out-of-plane compression, longitudinal shear and transverse shear; and the measurements have been compared with finite element predictions. Experiments and calculations both indicate that the compressive response is governed by bending of the constituent struts of the Y-frame and is sensitive to the choice of lateral boundary conditions: the energy absorption for a no-sliding boundary condition exceeds that for free-sliding. Under longitudinal shear, the leg of the Y-frame undergoes uniform shear prior to the onset of plastic buckling. Consequently, the longitudinal shear strength of the Y-frame much exceeds its compressive strength and transverse shear strength. Sandwich beams were also indented by a flat bottomed punch, and a relatively high indentation strength was observed. It is argued that this is due to the high longitudinal shear strength of the Y-frame. While finite element calculations capture the measurements to reasonable accuracy, a simple analytical model over-predicts the indentation strength. Finally, the finite element method was used to investigate the energy absorption capacity of the sandwich beams under indentation loading. The calculations reveal that for a given tensile failure strain of the face-sheet material, a sandwich beam with Y-frame core has a comparable performance to that of a sandwich beam with a metal foam core. The relative performance is, however, sensitive to the choice of design parameter: when the indentation depth is taken as the design constraint, the sandwich beam with a Y-frame core outperforms the sandwich beam with the metal foam core.     

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.     

Optimization of functionally graded foam-filled conical tubes under axial impact loading

Metallic foams as a filler in thin-walled structures can improve their crashworthiness characteristics. In this article, nonlinear parametric finite element simulations of FGF foam-filled conical tube are developed and the effect of various design parameters such as density grading, number of grading layers and the total mass of FGF tube on resulting mode shapes, specific energy absorption and initial peak load is investigated. Multi design optimization (MDO) technique and the geometrical average method, both are based on FE model are applied to maximize the specific energy absorption and minimize the impact peak force by estimating the best wall thickness and gradient exponential parameter “m” that controls the variation of foam density. The results obtained from the optimizations indicated that functionally graded foam material, with graded density, is a suitable candidate for enhancing the crashworthiness characteristics of the structure compared to uniform density foam.     

Elastic moduli and plastic collapse strength of hexagonal honeycombs with plateau borders

The theoretical analysis for the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders is proposed and presented here. The variation of cell edge thickness in real honeycombs is taken into account in deriving their elastic moduli and plastic collapse strengths. A repeating element, composed of three cell edges connected at a vertex with Plateau borders of constant radius of curvature and width, is employed to calculate the elastic moduli and plastic collapse strength of hexagonal honeycombs. Results suggest that both the elastic moduli and plastic collapse strength of hexagonal honeycombs with Plateau borders depend on their relative density and the volume fraction of solid contained in the Plateau border region. Meanwhile, effects of solid distribution on the elastic moduli and plastic collapse strength of hexagonal honeycombs are investigated, providing a guideline for the optimal microstructure design of honeycombs.     

Energy absorption characteristics of composite tubes with different fibers and matrix under axial quasi-static and impact crushing conditions

The collapse characteristics and energy absorption capability of composite tubes with different fibers and matrix were studied in present article under axial quasi-static and impact crushing conditions. The sensitivity to fibers, matrix and loading conditions were thoroughly discussed for the crushing modes and energy absorption capability. Experimental results showed specimens with different matrix and fibers exhibit three typical types of crushing modes. Specimens G803/3234 and G827/3234 had better energy absorption performance than the specimens with 5224 matrix. Impact loading condition led to lower energy absorption capability as compared to quasi-static loading condition. Moreover, impact loading condition also caused the crushing mode transition from splaying mode to fragmentation mode for G803/3234 and G827/3234.     

The plastic collapse of sandwich beams with a metallic foam core

Plastic collapse modes of sandwich beams have been investigated experimentally and theoretically for the case of an aluminium alloy foam with cold-worked aluminium face sheets. Plastic collapse is by three competing mechanisms: face yield, indentation and core shear, with the active mechanism depending upon the choice of geometry and material properties. The collapse loads, as predicted by simple upper bound solutions for a rigid, ideally plastic beam, and by more refined finite element calculations are generally in good agreement with the measured strengths. However, a thickness effect of the foam core on the collapse strength is observed for collapse by core shear: the shear strength of the core increases with diminishing core thickness in relation to the cell size. Limit load solutions are used to construct collapse maps, with the beam geometrical parameters as axes. Upon displaying the collapse load for each collapse mechanism, the regimes of dominance of each mechanism and the associate mass of the beam are determined. The map is then used in optimal design by minimising the beam weight for a given structural load index.     

Experimental and theoretical studies on buckling of thin spherical shells under axial loads

In this paper we present experiments, simulation as well as analysis of the collapse behaviour of thin spherical shells under quasi-static loading. Various aluminium spherical shells with variation in geometrical parameters were manufactured by spinning. Experiments were performed on these shells in a universal testing machine and their load–compression histories were obtained on the machine chart recorder. Three-dimensional numerical simulations were carried out for all the specimens tested under quasi-static loading using ANSYS^®. All the stages of collapse of the shell including non-symmetrical lobe formation were simulated. Material, geometric and contact nonlinearities were incorporated in the analysis. The stress–strain curves of standard samples made from the material were used as input. Piecewise linearity was taken in the plastic region of the material curve. Results thus obtained compared with the experiments well.An analysis was also carried out to study the behaviour of shells under axial compression based on the formation of rolling and stationary plastic hinges. These hinges were also simulated numerically and results match the experiments well.     

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.