Crashworthiness of aluminum extrusions subjected to oblique loading: experiments and numerical analyses

Oblique loading was studied through quasi-static experiments and numerical simulations. The behavior of square aluminum columns in alloy AA6060 subjected to quasi-static oblique loading was investigated experimentally for three different load angles. The square columns were clamped at one end and oblique load conditions were realized by applying a force with different angles to the centerline of the column. These tests were used to validate a numerical model. Numerical studies of oblique impact were carried out using the validated model, and the mean crush load was investigated through factorial analysis with parameters as load angle, thickness, length, and heat treatment of the alloy and impact velocity.     

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.     

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.     

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.     

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.     

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.     

Static and dynamic axial crushing of foam-filled sheet metal tubes

Experimental results are provided for the quasi-static and dynamic axial crushing of thin-walled square and rectangular tubes manufactured from sheet metal. The tubes were tested both empty and filled with polyurethane foam of various densities. Both the stability and the energy absorbing characteristics of the tubes are described and discussed. Simple theoretical models are proposed to explain and quantify the interaction between the foam and the sheet metal tubes.     

An experimental study of the ratchetting and creep of thick flanged tubes subjected to steady axial mechanical loading and transient thermal loading

The aims of the investigation were to obtain experimental data against which finite element predictions can be assessed and to see whether the lead alloy used was suitable as a “ratchetting” model material. Thermal ratchetting tests were performed on lead alloy flanged tube components. In some of the tests, dwell periods were allowed between successive thermal shocks. Electrical resistance strain gauges were used to measure the ratchet and creep strains in plain tube and stress concentration regions.It was found that both the plain tube and peak fillet ratchet strains increased with increasing mechanical and thermal load for short dwell periods. However, the ratio of the peak fillet to plain tube ratchet strains reduced with increasing mechanical and thermal load. Also, the ratio of the peak fillet to plain tube ratchet strains increased with increasing dwell period.The data obtained from the lead alloy model component tests were found to correlate with data from a number of different components made from various materials, indicating that the material may be useful as a “ratchetting” model material.     

Stress distributions in energy generating two-layer tubes subjected to free and radially constrained boundary conditions

Analytical solutions are obtained for thermally induced axisymmetric elastic and elastic–plastic deformations in heat generating composite tubes having a free inner and a radially constrained outer boundaries. Tresca's yield condition and its associated flow rule are used to determine the elastic–plastic response of the assembly. Depending on the physical properties of the materials used, eight different plastic regions with different mathematical forms of the yield condition may occur in the assembly. The closed form solutions for these plastic regions are obtained by assuming linearly hardening material behavior. Various numerical examples are handled using thermal and mechanical properties of real engineering materials.     

Experimental studies on the axial crash behavior of aluminum foam-filled hat sections

Drop hammer tests were carried out to study the axial crash behavior of aluminum foam-filled hat sections. First, the axial crash tests of the empty hat sections, aluminum foam and the aluminum foam-filled hat sections were carried out; then, based upon the test results, the axial crash behavior of the aluminum foam-filled hat sections were analyzed. It was found that aluminum foam filling can increase the energy absorption capacities of the hat sections. Compared with the non-filled structures, aluminum foam-filled structures were much more stable and needed less mass to absorb the specified energy. __________ Translated from Chinese Journal of Mechanical Engineering, 2006, 42(4) (in Chinese)     

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.     

Parametric study and numerical analysis of empty and foam-filled thin-walled tubes under static and dynamic loadings

In this paper the crushing behavior of thin-walled tubes under static and dynamic loading is investigated. First, a finite element (FE) model for empty thin-walled tube was constructed and validated by available experimental and numerical data. The comparison between the FE results and the existing numerical solutions as well as the available experimental results showed good agreements. Next, a model for the foam was adopted and implemented in an in-house FE code. The implemented isotropic foam model was then used to simulate the behavior of foam-filled tubes under both static and dynamic loadings. Good agreement was observed between the results from the model with those obtained by analytical relations and experimental test data. The validated FE model was then used to conduct a series of parametric studies on foam-filled tapered tubes under static and dynamic loadings. The parametric studies were carried out to determine the effect of different parameters such as the number of oblique sides, foam density and boundary conditions on crushing behavior of rectangular tubes. The characteristic included deformed shapes, load–displacement, fold length and specific energy absorptions.     

Buckling and vibration of stiffened plates subjected to partial edge loading

The buckling and vibration characteristics of stiffened plates subjected to in-plane partial and concentrated edge loadings are studied using finite element method. The initial stresses are obtained considering the pre-buckling conditions. Buckling loads and vibration frequencies are determined for different plate aspect ratios, edge conditions and different partial non-uniform edge loading cases. The non-uniform loading may also be caused due to the supports on the edges. The analysis presented determines the stresses all over the region for different kinds of loading and edge conditions. In the structural modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. The vibration characteristics are discussed and the results are compared with those available in the literature. Buckling results show that the stiffened plate is less susceptible to buckling for position of loading near the supported edges and near the position of stiffeners as well.     

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.     

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.     

On thin rings and short tubes subjected to centrally opposed concentrated loads

The deformation behaviour of mild steel rings and short tubes of various diameters, thicknesses and lengths loaded centrally by opposed conically-headed cylindrical punches is examined. The test equipment and procedure are briefly described and typical histories of deformation, punch load—displacement diagrams and the increase in the horizontal ring or tube radius for increasing punch travel are presented. A comparison is made between the latter and those predicted by use of a simple expression based on the assumption of rigid-plastic material deformation. Good correlation is obtained with rings of different diameter to thickness ratio.     

Indentation of tubes under combined loading

A theoretical analysis is presented of the problem of large plastic deformations of tubes subjected to combined loading in the form of lateral indentation, bending moment and axial force. A model of the shell is proposed, describing local damage of tubes subjected to large strain, rotation and shape distortion. The model is effectively decoupling the 2-D problem into a set of 1-D problems. The force-deflection characteristics of tubes were shown to depend strongly on the magnitude of the bending moment and/or axial force applied to the tube ends. The calculations revealed that the resistance of the tube to lateral indentation and thereby the energy that the tube can absorb sharply diminishes as the direction of axial force changes from pre-tension to pre-compression. The present results were shown to give good correlation with existing experimental data.     

Computer simulation of the human leg subjected to impact loading

One of the most important tasks in clinical practice is to determine accurately the forces and displacements of the various anatomical structural components of the human leg, especially when subjected to impact loading. This paper therefore develops a computer simulation which describes the biodynamic response of the human lower extremity for realistic activities such as kicking by foot etc. Firstly, the paper derives the nonlinear equations of motion and nonlinear constraint equation governing the sagittal plane response of the human leg subjected to impact loading. The equations are then solved using numerical techniques and the results are presented. Special attention is given to the ligament, contact and muscle group forces, the location of contact points, anterior-posterior displacements and the motion trajectories of the femur and the tibia.     

Analytical and experimental investigations into the controlled energy absorption characteristics of thick-walled tubes with circumferential grooves

In this paper, the energy absorption characteristics of grooved circular tubes are investigated under quasi-static loading condition. For experiments, thick-walled tubes with circumferential grooves are prepared. The grooves divide the thick-walled tube into several shorter thin-walled portions. Specimens are subjected to axial crushing load to observe the effect of distribution of circular grooves on the deformation mechanism and energy absorption capacity. Geometrical parameters of the specimens are designed utilizing the Taguchi method to cover a reasonably wide range of groove length-to-wall thickness ratios. An analytical approach based on the concept of energy dissipation through the plastic hinges is applied. Taking the effect of strain hardening into account, the obtained analytical results are in good agreement with the experimental ones. The agreement between analytical and experimental results may indicate the validity of the proposed analytical approach. Desirable mechanism of deformation observed justifies the pre-forming method for obtaining favorable energy absorption characteristics.