Tomasz Wierzbicki

Experimental and numerical studies of foam-filled sections

A comprehensive experimental and numerical studies of the crush behavior of aluminum foam-filled sections undergoing axial compressive loading is performed. Non-linear dynamic finite element analyses are carried out to simulate quasi-static test conditions. The predicted crushing force and fold formation are found to be in good agreement with the experimental results. Based on the numerical simulations, simple closed-form solution is developed to calculate the mean crushing force of the foam-filled sections. It is found that the increase of mean crushing force of a filled column has a linear dependence with the foam compressive resistance and cross-sectional area of the column. The proposed solution is within 8% of the experimental data for wide range of column geometries, materials and foam strengths.

Crushing analysis of metal honeycombs

Abstract A method for determining the crushing strength of hexagonal cell structures subjected to axial loading is given. The method is based on energy considerations in conjunction with a minimum principle in plasticity. The problem is shown to be equivalent to the analysis of a system of collapsing angle elements undergoing bending and extensional deformations. The theory is first developed for an arbitrary angle between panels and then is specified for the 120° angle, appropriate for the hexagonal cell structures. Simple formulas are derived relating the crushing force and the wavelength of the local folding wave to the wall thickness and diameter of the cell. The theoretical solution has been compared with experimental results published in the literature and an excellent correlation has been obtained for the wide range of geometrical parameters involved. This solution replaces the less accurate earlier analysis of the same problem due to McFarland. The purpose of this study was to provide a simple and rational means by which hexagonal cell structures can be designed for use as energy absorbers in impact or impulsive loading situations.

A Comparative Study on Various Ductile Crack Formation Criteria

Various fracture criteria, based on different assumptions and different mechanical models, have been proposed in the past to predict ductile fracture. The objective of this study is to assess their effectiveness and accuracy in a wide range of process parameters. A series of tests on 2024-T351 aluminum alloy, including upsetting tests and tensile tests is carried out. It is found that none of the existing fracture criteria give consistent results. Two totally different fracture mechanisms are clearly observed from microfractographs of upsetting and tensile specimens. This observation confirms that it is impossible to capture all features of ductile crack formation in different stress states with a single criterion. It is shown that different functions are necessary to predict crack formation for different ranges of stress triaxiality. Weighting functions in a wide range of stress states can be obtained by determining the fracture locus in the space of equivalent strain to fracture and stress triaxiality.

Crash behavior of box columns filled with aluminum honeycomb or foam

Abstract The effect of low density filler material, such as aluminum honeycomb or foam, on the axial crushing resistance of a square box column under quasi-static loading conditions is studied. Numerical simulation shows that in terms of achieving maximum energy absorption, filling the box column with aluminum honeycomb can be preferable to thickening the column wall. Superior specific energy absorption is also obtained by filling the column with moderate or high strength aluminum foam. Simple formulas for the relationship between mean crushing force and the strength of filler are developed. Moreover, the presence of adhesive increases energy absorption significantly compared to unbonded filling.

Relative merits of single-cell, multi-cell and foam-filled thin-walled structures in energy absorption

The axial crushing of hollow multi-cell columns were studied analytically and numerically. A theoretical solution for the mean crushing force of multi-cell sections were derived, and the solution was shown to compare very well with the numerical predictions. Numerical studies were also carried out on foam-filled double-cell and triple-cell columns. Based upon the numerical results, closed-form solutions were derived to calculate the mean crushing strength of these sections. It was found that the interaction effects between the foam core and the column wall contribute to the total crushing resistance by the amounts equal to 140% and 180% of the direct foam resistance for double cell and triple cell respectively. Finally, the relative merits of single-cell, multi-cell and foam-filled sections were discussed.

Alexander revisited—A two folding elements model of progressive crushing of tubes

Abstract A new model of the progressive crushing of circular tubes is developed in which an active zone of plastic deformations contains two folds or buckles. The model captures, with great realism, several features of the crushing process which were unaccounted for in all previous computational models of progressive folding. These include : finite values of the load peaks, alternating heights of the peaks, unequal distances between peaks, reduced crush distance, realistic final shape of crushed tubes and a longer distance between the two first peaks. Closed-form solutions, derived for the length of the plastic folding wave and the mean crushing force, show very good agreement with experimental results. The history of the crushing force is shown to depend on the eccentricity parameter, i.e. on the way the lube material folds with respect to the original tube radius. However, the mean crushing force is found to be independent of the eccentricity parameter.

On the modeling of crush behavior of a closed-cell aluminum foam structure

Crush behavior of a closed-cell aluminum foam is studied analytically and numerically. A new model of a truncated cube, which captures the basic folding mechanism of an array of cells, is developed. The model consists of a system of collapsing cruciform and pyramidal sections. Theoretical analysis is based on energy consideration in conjunction with the minimum principle in plasticity. The assumed kinematic model for the crushing mechanism of the truncated cube cell gives a good agreement with the deformation mechanism obtained from the numerical simulation. Analytical formulation for the crushing resistance of the truncated cube cell is shown to correlate very accurately with the numerical results. Closed form solutions for crushing resistance of closed-cell aluminum foam in terms of relative density are developed. The formulas are compared with the experimental results and give an excellent agreement.

Indentation of tubes under combined loading

Abstract 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.

Effect of an ultralight metal filler on the bending collapse behavior of thin-walled prismatic columns

Abstract The effect of low-density metal filler, such as aluminum foam or honeycomb, is studied on the bending collapse resistance of thin–walled prismatic columns. A combination of analytical and numerical results is used to predict the initial and post collapse response of empty and filled columns. Closed-formed solutions for the bending-rotation characteristics are constructed in terms of the geometrical parameters and the filler strength. The low-density metal core retards sectional collapse of the thin-wall column, and increases bending resistance for the same rotation angle. Numerical simulations show that, in terms of achieving the highest energy absorption to weight ratio, columns with aluminum honeycomb or foam core are preferable to thickening the column wall. Moreover, the presence of adhesive improved the specific energy absorption significantly.

Stress profiles in thin-walled prismatic columns subjected to crush loading II. Compression

This paper extends the concept of a superfolding element, developed originally for axially loaded columns to the case of bending and combined bending/compression loading. A simple kinematic model of a column was constructed with four free parameters. Closed-form solutions were derived for the moment-rotation characteristics of square columns in the post-failure range and stress profiles in the most general case of a floating neutral axis. Considerable simplifications were obtained by assuming that the neutral axis stays within the tensile flange. It was shown that, in this case, the bending characteristics of a column, can in fact, be derived from the known characteristics of an identical column subjected to axial crush. High accuracy numerical calculations were run on a square column with three different width-to-thickness ratios to check the validity of various approximating assumptions. For all three cases considered, the simplified analytical solution was shown to predict the moment-rotation relationship with an absolute error not greater than 7%. Finally, the present method was generalized to arbitrarily shaped multi-cornered sheet metal columns.