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.     

泡沫填充薄壁结构的抗弯性分析及多目标优化设计*

泡沫铝填充薄壁结构具有轻质、较大承载能力以及高效吸能特性,越来越多地应用于各种工程结构。提出一种新颖的轴向梯度泡沫填充薄壁结构,采用试验与数值分析的方法,系统地分析空管、均匀泡沫填充及梯度泡沫填充薄壁圆管在弯曲工况下的力学响应及能量吸收特性。研究发现,泡沫填充薄壁结构比空管具有更好的抗弯性能。与均匀泡沫填充结构相比,梯度泡沫不仅使得填充薄壁结构的变形模式从单褶皱模式变为多褶皱模式,截面扁化量和抗弯刚度损失显著减小,而且有效地提高了填充结构的承载力及吸能特性。为了进一步探索填充结构的最优耐撞性,结合Kriging近似技术与粒子群数值优化方法,对均匀泡沫和功能梯度填充泡沫薄壁结构进行多目标优化设计,得到了泡沫填充薄壁结构耐撞性的最佳参数匹配设计,并有效提高了结构的抗弯性能,为泡沫填充薄壁结构抗弯性设计提供了参考依据。     

Torsional crushing of foam-filled thin-walled square columns

Torsional crushing behavior of foam-filled thin-walled square columns were investigated analytically, numerically and experimentally. The lower and upper bounds on the torsional resistance of foam-filled columns were established analytically. Numerical simulations were carried out and showed that the presence of the filler changes the torsional collapse mechanism and gives rise to higher order sectional collapse modes, which results in a higher torsional resistance. Torsional experiments were performed and results were compared to the analytical and numerical solutions with reasonably good agreement. It was found that bonding of the foam to the walls changes the deformation mode by spreading deformation over the whole length. The corresponding torsional resistance is also larger for the first 40° of rotation. It is concluded that fitting prismatic members with the aluminum foam of a density ranging from 0.14 to 0.28 g/cm³ can double the energy absorption of a given member.     

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.     

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.     

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.     

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.     

Influence of spot-weld failure on crushing of thin-walled structural sections

Structural effectiveness differences have been observed in a recent study on the progressive axial collapse of thin-walled structural sections when made from different classes of steels (mild steel, interstitial-free rephosphorized high-strength steel and high-strength low-alloyed steel). A higher effectiveness was observed for spot-welded top-hat sections made from a mild steel than for similar sections made from a high-strength steel. For square sections, the structural effectiveness was not affected by the steel classes. It is anticipated that this observation applies not only for spot-welded top-hat and square sections, but for other joined and unjoined thin-walled structures as well.

The part and full failure of spot-welds, during the axial collapse of the thin-walled structural sections, is one possible explanation for the above inconsistency. This is investigated experimentally in this article using peel tests on spot-weld samples under quasi-static and dynamic conditions. Despite having a lower material strength, the mild steel spot-weld samples exhibited a higher peak force and similar energy absorption during failure when compared with a high-strength steel, both under quasi-static and dynamic loadings.

The potential contribution to the mean crushing force during progressive axial collapse is estimated from the experimental results and comparisons are made with deformed thin-walled structural sections from a recent experimental study. Possible implications for the determination of the mean crushing force from analytical and numerical models are identified and discussed.     

Theoretical analysis for axial crushing behaviour of aluminium foam-filled hat sections

A theoretical analysis was performed to predict the crushing behaviour of aluminium foam-filled single hat and double hat sections subjected to axial compression. The experimental results and superfolding element theory were used to create deformation models for the aluminium foam contained in the hat sections, and several assumptions were made for the theoretical analysis. According to the energy method and superfolding elements theory, the mean crushing force and the interactive effect were theoretically predicted for the axial compression of the aluminium foam-filled hat sections. The final formula specified the relationship between the mechanical characteristics of the aluminum foam and the height of the superfolding element. The mean crush forces and the interactive effect predicted by the theoretical analysis were in good agreement with the experimental results. The theoretical prediction results showed that the interactive effect was mainly from the aluminium foam.     

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.     

Determination of flow stress of thin-walled tube based on digital speckle correlation method for hydroforming applications

The flow stress, used to describe the plastic deformation behavior of thin-walled tube, is one of the most important parameters to ensure reliable finite element simulation in the tube hydroforming process. In this study, a novel approach of on-line measurement based on digital speckle correlation method is put forward to determine flow stress of thin-walled tube. A simple experimental tooling is developed and free-bulged tests are performed for 304 stainless steel and H62 brass alloy tubes. An analytical approach is proposed according to the membrane theory and the force equilibrium equation. The developed method is validated by means of FE simulations. The results indicate that the present method is acceptable to define the flow stress in the tube hydroforming process.     

A new hardening rule for metallic foam plasticity

Metallic foams are a class of porous materials widely used in the industry because of their advantages. In recent years, extensive studies on the behavior of these materials have been conducted. Several constitutive equations have also been presented and applied. This study proposes a new constitutive equation that predicts metallic foam behavior using the stress–strain curve in uniaxial compression. The proposed model offers a new functionality for work hardening and is evaluated for both isotropic and combined hardening. The constitutive equations are implemented in MATLAB and integrated using return mapping algorithm. The material parameters are identified using genetic algorithm and through a comparison of the experimental and numerical results. The aluminum foams discussed in this paper are the commercially available types, Foaminal and Alporas. The comparison of numerical and experimental results indicate that this new constitutive equation predicts foam behavior in a reasonable manner. Moreover, a good agreement is observed between the experimental and computational curves.     

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)     

Study on the crushing and hydroforming processes of tubes in a trapezoid-sectional die

A study on the bulging processes of tubes in a trapezoid-sectional die has been carried out through finite-element (FE) analysis. A FE model of the single-step hydroforming process and several FE models of crushing combined with subsequent hydroforming processes in a trapezoid-sectional die with different die closing seams are proposed. The simulations are performed using the FE code LS-DYNA. For the single-step hydroforming process, the effects of loading paths on the formability of the trapezoid-sectional part are investigated. In the case of the crushing combined with subsequent hydroforming processes, the effects of die closing seams, tube diameters, and preforming loading paths on the forming process and the final parts are analyzed. A comparison between the parts formed through single-step hydroforming process and through crushing combined with subsequent hydroforming processes is performed. Finally, an experiment of tube hydroforming in a trapezoid-sectional die is carried out on the hydroforming machine developed by Shanghai Jiaotong University. The simulation results show good agreement with the experimental results.     

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.     

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.     

Numerical study of welding simulation and residual stress on butt welding of dissimilar thickness of austenitic stainless steel

It has been well documented in the literature the importance of strict surface integrity checks upon performance and quality of machined components, especially for the safety critical components (e.g., aerospace) that work at cyclic high mechanical loads and elevated temperatures. In this field, Waspaloy, within the commercially available nickel-based superalloys, is extensively applied in different industries such as aircraft, chemical plant equipment, and petrochemical equipment. The main objective of this paper is to implement a reliable FE model, for dry orthogonal machining of Waspaloy, capable to predict microstructural changes and dynamic recrystallization during the cutting process. A user subroutine was implemented in FE code to simulate the dynamic recrystallization and consequently grain refinement and hardness variation on the machined surface and below it. Zener–Hollomon (Z-H) and Hall–Petch (H-P) equations were employed to, respectively, predict grain size and microhardness. In addition, depth of the affected layer was controlled using the critical strain equation. FE numerical model was properly calibrated using an iterative procedure based on the comparison between simulated and experimental results. Finally, very good agreement was found between experimental and simulated results of grain size, microhardness, depth of the affected layer, and other fundamental variables such as cutting forces, temperature, and chip morphology.     

Plate assembly effect and cross-section distortion of rectangular tube in rotary draw bending

Rotary draw bending is nowadays the most universal approach to produce thin-walled bent tubes. Cross-section distortion is inevitably avoided, and the plate assembly effect is a key influencing factor. To study the relevance, a 3D finite element (FE) simulation model for the rotary draw bending process of rectangular tube is established, and the cross-section distortion characters are investigated combined with experiment and FE simulation. And then, the plate assembly effect is carried out by different test schemes based on FE model. Finally, the effects of geometrical dimensions on the maximum concave distance of outer flange are derived, and the analytical function is validated to be credible and efficient. It is of significance to design process parameters and to control defects in bending process.     

Dynamic crushing of a ductile cellular array

A range of deformation mechanisms occur during dynamic crushing of a tightly-packed array of thin-walled metal tubes. Within the array, both stable and unstable modes of deformation for individual tubes are observed; these depend on the packing arrangement, the deformation of surrounding tubes and the rate-of-crushing. Unstable deformation within narrow bands of cells accounts for most of the crushing in these systems. After unstable deformation is initiated, the average crushing force is insensitive to the rate-of-crushing; this feature makes cellular systems attractive for damage mitigation applications. Despite the highly localized nature of this deformation, the final extent of crushing is almost proportional to the ratio of the impact energy to an idealized energy dissipation capacity for a layer of cells.     

Static crushing of square aluminium extrusions with aluminium foam filler

An experimental investigation was carried out to study the behaviour of square aluminium extrusions filled with aluminium foam under quasi-static loading conditions. Based on the experimental work, simple relations between dimensionless numbers governing the influence of the foam on the characteristics of the crush problem were identified. Furthermore, a simplified set of equations applicable for design of foam-filled components was proposed.