F.G. Rammerstorfer

Experimental studies on the quasi-static axial crushing of steel columns filled with aluminium foam

Abstract Experimental investigations are carried out in order to study the effects of different tube and filler arrangements on the crushing behaviour of axially compressed tubular crush elements. To this end quasistatic experiments are performed on monotubal and bitubal, empty and filled steel profiles with different materials, dimensions and cross-sectional shapes. Aluminium foam, produced by a powder metallurgical production process, is applied as filler material. The test results confirm that considerable mass efficiency improvements with respect to energy absorption may be obtained, even if reduced stroke lengths, caused by the presence of foam, are taken into account. Distinct differences are pointed out between the different cross-sectional shapes. Bitubal arrangements, consisting of outer and inner profiles with foam in between, are shown to be particularly efficient crush elements, as long as global failure can be avoided. Explanations for the experimental observations are obtained by a simplified analysis of interaction effects. Constraints concerning the appropriate choice of Al-foam densities are summarized, too, in order to provide an aid for the future design of ‘optimally tuned’ crush elements composed of tubular members and Al-foam.

Crushing of axially compressed steel tubes filled with aluminium foam

SummaryThis study, with the emphasis on experiments, investigates the applicability of aluminium foam as filler material in tubes made of mild steel having square or circular cross sections, which are crushed axially at low loading velocities. In addition to the experiments finite element studies are performed to simulate the crushing behaviour of the tested square tubes, were a crushable foam material model is shown to be suitable for describing the inelastic response of aluminium foam with respect to the considered problems. The experimental results for the square tubes reveal efficiency improvements with respect to energy absorption of up to 60%, resulting from changed buckling modes of the tubes and energy dissipation during the compression of the foam material itself. The principal features as well as the changes of the crushing process due to filling can also be studied by the numerical simulations. A global failure mechanism due to a high foam density can be observed for filled circular tubes. Aluminium foam is shown to be a suitable material for filling thin-walled tubular steel structures, holding the potential of enhancing the energy absorption capacity considerably, provided the plastic buckling remains characterized by local modes.

Buckling of stretched strips

Abstract Flat plates subjected to tensile loads may buckle locally in the presence of geometric discontinuities such as cracks, holes or varying dimensions [Shaw D, Huang YH. Buckling behavior of a central cracked thin plate under tension. Engng Fract Mech 1990;35(6):1019–27; Gilabert A, et al. Buckling instability and pattern around holes or cracks in thin plates under tensile load. Eur J Mech A Solids 1992;11(1):65–89; Shimizu S, Yoshida S. Buckling of plates with a hole under tension. Thin-Walled Struct 1991;12:35–49; Tomita Y, Shindo A. Onset and growth of wrinkels in thin square plates subjected to diagonal tension. Int J Mech Sci 1988;30(12):921–31]. However, it appears to be surprising that even in the absence of any geometric discontinuity, buckling due to global tension occurs as a result of special boundary conditions. This effect can be observed during the stretching of thin strips, where high wave number buckling modes can affect large areas. In order to study this phenomenon and to find explanations, computational and analytical investigations were performed. A novel diagram for buckling coefficients is presented, enabling the determination of critical longitudinal stresses.

On thermo-elastic-plastic analysis of heat-treatment processes including creep and phase changes

Abstract A method is described for calculating the stresses in a body during heat-treatment and for calculating the remaining residual stress distribution. Special attention is given to the thermo-elastic-plastic material behaviour which is highly temperature-dependent. A pseudo-plasticity effect due to microstresses appearing during phase transformations is taken into account. The stress analysis of a cylinder is performed using ADINA. Calculated results are compared with results obtained experimentally.

Micromechanical investigations of arrangement effects in particle reinforced metal matrix composites

Abstract The influence of inclusion arrangements and shapes on the mechanical and thermomechanical behavior predicted by unit cell descriptions of particle reinforced metal matrix composites is investigated. Three-dimensional cubic geometries, axisymmetric models and plane geometries are compared, and all periodic arrangements of inclusions are shown to display at least some degree of three-dimensional anisotropy under mechanical loading. Deviations from isotropy are more marked for simple cubic than for body centered and face centered cubic arrangements in both the elastic and inelastic ranges, and the overall linear and nonlinear responses predicted by axisymmetric models are found to be in good agreement with the three-dimensional cubic descriptions. The thermal expansion behavior of cubic models is isotropic provided cube-shaped or spherical inclusions are used. However, both axisymmetric descriptions and cylindrical inclusions in three-dimensional models give rise to noticeable anisotropies in the predicted overall response to a thermal load.

A thermo-elasto-plastic constitutive law for inhomogeneous materials based on an incremental Mori–Tanaka approach

Abstract The behavior of a composite consisting of aligned thermo-elastic reinforcements embedded in a thermo-elasto-plastic matrix is described by an incremental Mori–Tanaka mean field approach. The matrix phase behavior is described by incremental J2 plasticity and the breakdown of isotropy of the matrix phase upon yielding is accounted for. The proposed method is implemented as a constitutive material model for a finite element code incorporating temperature dependent material data. An implicit solution strategy is introduced and special emphasis is put on the appropriate handling of the thermal expansion behavior. The applicability of the method is shown by both material characterization and a structural analysis of a hybrid component.

Computational simulation of internal bone remodeling

SummaryA review of the state of the art in computational modeling and analysis of the mechanical behavior of living bone is given. Particular attention is placed on algorithms for the simulation of the stress or strain induced remodeling processes. A special remodeling algorithm is presented which allow the simulation of internal bone remodeling taking into account not only adaptation of the spatial distribution of the effective mass density, but also the adaptation of the orientation of the material axes and of the orientation dependent stiffness parameters. Such remodeling algorithms require a sound formulation of the constitutive relations of bony material. For this purpose some micro-macro mechanical descriptions of bone in its different microstructural configurations are discussed. In conjunction with the above mentioned remodeling algorithm a new unified material model is derived for describing the linear elastic, orthotropic behavior of bone in the full range of micro-structures of cancellous and cortical bone. The application of the novel remodeling algorithm is demonstrated in an example.

Some simple models for micromechanical investigations of fiber arrangement effects in MMCs

Abstract The influence of the fiber arrangement on the microscale stress and strain fields and on the overall thermoelastoplastic properties of two classes of unidirectional metal matrix composites (MMCs) is investigated. A micromechanical approach employing the Finite Element (FE) method is used, which is based on analyzing the nonlinear response of periodically repeating unit cells. By applying suitable boundary conditions, microgeometries which are modified from regular fiber arrays are modeled at relatively low computational cost. When applied to discontinuously reinforced composites, this strategy allows the investigation of materials containing regular arrangements of two or more different types of aligned short fibers. In the case of continuously reinforced composites, periodic hexagonal arrays as well as regular, modified and clustered square arrangements of parallel fibers are considered. The influence of the fiber arrangement on the overall thermomechanical properties of the damage-free composites is generally found to be small, the main exception being the overall response to transverse mechanical loading. The computed microfields, however, are predicted to depend noticeably on the microgeometry, and consequently, damage-related parameters such as the hydrostatic microstresses, the interfacial stress distributions and the shakedown limits show a marked sensitivity to the fiber arrangement.

Some direction-dependent properties of matrix-inclusion type composites with given reinforcement orientation distributions

A Mori-Tanaka mean-field approach for predicting the overall thermoelastic properties of multi-phase composites with given orientation distributions of the inclusion phases is used to study the influence of the inclusion orientation distribution on the effective material properties. The aim of this study is primarily to understand the effects of the inclusion orientations in short-fiber-reinforced composites and to identify the basic mechanisms of interaction between the phases which govern the overall thermoelastic behavior. Perfectly aligned discontinuous fibers, various orientation distributions as well as two-dimensional and three-dimensional random orientations of the inclusions are studied. The overall Youngs moduli, shear moduli and coefficients of thermal expansion, as well as the onset of yielding of the matrix phase under thermal and mechanical loading conditions, are calculated. The results are evaluated both in terms of the orientation distributions of the inclusions and in terms of the direction dependences of the predicted overall moduli. From these findings useful information on the appropriate requirements for the design of composite materials and composite structures can be obtained.

Buckling phenomena related to rolling and levelling of sheet metal

Abstract The paper deals with analytical and numerical considerations of buckling phenomena in thin plates or strips under in-plane loads which typically appear during rolling and levelling, i.e. straightening by stretching, of sheet metal. Buckling due to self-equilibrating residual stresses, caused by the rolling process, in eventual conjunction with global tensile stresses (denoted as “rolling buckling”) as well as buckling during the levelling process (denoted as “stretching buckling” or “towel buckling”) are considered. Analytical estimates are derived and compared against results of numerical simulations and field observations. Mode jumping by varying the global strip tension is explained on the basis of the derived analytical solutions. It is shown how from the waves, i.e. height and length, observed on the strip sliding over or lying on a rigid plane one can provide information about the distribution of the differences in the plastic strains over the width of the strip which lead to the buckled configuration. And, vice versa, knowledge of the plastic strain distribution can be used for estimating the expected wave heights representing a measure for the geometrical quality of the rolled product. The influence of the dead weight of the strip on the post-buckling pattern is also discussed on the basis of non-linear analyses.