Behavior Of Closed-cell Aluminum Foam Research Articles

Fatigue analysis of closed-cell aluminium foam using different material models

The fatigue analyses of AlSi7 closed-cell aluminium foam were performed using a real porous model and three different homogenised material models: crushable foam model, isotropic hardening model and kinematic hardening model. The numerical analysis using all three homogenised material models is based on the available experimental results previously determined from fatigue tests under oscillating tensile loading with the stress ratio R=0.1. The obtained computational results have shown that both isotropic and kinematic hardening models are suitable to analyse the fatigue behaviour of closed-cell aluminium foam. Besides, the kinematic hardening material model has demonstrated significantly shorter simulation time if compared to the isotropic hardening material model. On the other hand, the crushable foam model is recognized as an inappropriate approach for the fatigue analyses under tension loading conditions.

Micro-mechanical and X-Ray micro-computed tomographical analysis of quasi-static three-point loading behaviour of closed-cell aluminium foam with and without epoxy-bonded aluminium face-sheet

Abstract A quasi-static three-point loading experiment of closed-cell aluminium foam without face sheet (CCA) and closed-cell aluminium foam with face sheet (CCAF) was performed. During the experiment, load-deformation curves of CCA and CCAF foams were monitored for varying span length and crosshead velocity. CCA and CCAF foam maximum loading capacity were around 283.41 N and 1633.76 N, respectively. The effect of facesheet on the morphological and elemental inhomogeneity was analysed and related to understand the foam failure behaviour. It was observed that the presence of high strength epoxy-bonded face sheet prevented the tensile zone fracture in CCAF foams as compared to CCA foams. Micro Computed Tomographical analysis showed adjacent undeformed cells of the fractured region of CCA foams. CCA foams showed ductile-brittle mode with brittle dominating failure mode. In contrast, CCAF foams showed the gradual pore deformation and mixed deformation mode with initial indentation followed by the core shear process. Microstructural, elemental, and phase analysis of the failed zone showed micro-cracks, micro dimples, and ridges present in the foam core's cell wall. Ca–Ti–Al precipitates and intermetallics were present in plateau and cell wall regions. These precipitates act as reinforcement to the cell wall's strength during compression (as in CCAF foams). However, in tensile loading zone, they acted as a centre of crack initiation (as in CCA foams).

Correction to: Experimental and Numerical Study of Compressive Deformation Behavior of Closed-Cell Aluminum Foam

K. S. Verma, D. Muchhala, S. Panthi, and D. P. Mondal, “Experimental and numerical study of compressive deformation behavior of closed-cell aluminum foam,” Strength Mater., 52, 451–457 (2020), https://doi.org/10.1007/s11223-020-00197-4 the authors’ affiliations should read:

Initial yield behaviour of closed-cell aluminium foams in biaxial loading

This study investigates the initial yield characteristics of closed-cell aluminium foam (Alporas) in multiaxial stress states using experimental and numerical approaches. The mechanical responses of foams with two relative densities (11.7% and 17.2%) are presented in uniaxial compression, uniaxial tension, biaxial compression, biaxial tension and combined tension-compression loading conditions. Cubic and dog-bone specimens are fabricated for uniaxial compression and tension tests respectively. A Modified Maltese Cross Specimen (MMCS) geometry is custom designed for testing closed-cell foams in biaxial stress states. The experimental investigations reveal a consistently stiffer response of closed-cell foams in tensile dominated stress states. This is attributed to the stretching mode of deformation observed in the cell walls in tensile loading conditions, in contrast to the bending/buckling dominant deformation in compressive loading conditions. To complement the experimental data, a wide range of multiaxial stress states is simulated using irregular 3D Voronoi models. An initial yield surface normalized with respect to the uniaxial compressive yield strengths is constructed in the mean-effective stress space using both experimental and numerical data. The normalized initial yield surfaces appear considerably shifted towards the positive mean stress axis. An yield criterion for closed-cell aluminium foams that adequately captures this asymmetric nature of the yield surface about the effective stress axis is proposed, which requires only uniaxial compressive yield strength as a parameter. An empirical relation function estimating the uniaxial compressive yield strength based on the density of the foam material is proposed to facilitate direct application of the yield criterion in early stages of the design.

Experimental and Numerical Study of Compressive Deformation Behavior of Closed-Cell Aluminum Foam

In the present study, closed-cell aluminum foams of varying porosities (65–75%) were produced through the stir casting technique using TiH2 (1 wt.%) as a foaming agent. Under the uniaxial compressive loading, the compressive stress-strain responses of these foams were examined. The finite element (FE) models of the foam were elaborated using the ABAQUS FE simulation software and realized via the ABAQUS Explicit solver. Within the test domain, the experimental results were compared with the FE-predicted ones for the same porosities and both yielded similar stress-strain responses. The energy absorption capacity, yield stress, and densification strain values of AFs obtained through FE simulation were in good agreement with the experimental results, while the predicted plateau stress values differed from the latter by no more than 4–5%.

Biaxial mechanical behavior of closed-cell aluminum foam under combined shear—compression loading

Abstract Combined shear—compression tests and simulations were performed on a closed-cell aluminum foam over a wide range of loading angles in order to probe their yield behaviors under biaxial loading conditions. Combined shear—compression tests were carried out by using a pair of cylindrical bars with beveled ends. The yield surfaces were experimentally measured and compared with various theoretical yield surface models. The cellular structures of closed-cell aluminum foams were modeled as tetrakaidecahedrons and their biaxial crushing behaviors were simulated by the finite element method. The results show that, yield initiates from the stress-concentrated corners in the specimens under combined shear—compression loading and the stress distribution is no longer uniform at the specimen/bar interfaces. In the range of cell sizes studied, the larger the foam cell size is, the higher the yield stress is. Aluminum foam density is found to be the dominant factor on its mechanical properties compared with the cell size and is much more significant in engineering practice.

Compressive Behaviour of Closed-Cell Aluminium Foam at Different Strain Rates.

Closed-cell aluminium foams were fabricated and characterised at different strain rates. Quasi-static and high strain rate experimental compression testing was performed using a universal servo-hydraulic testing machine and powder gun. The experimental results show a large influence of strain rate hardening on mechanical properties, which contributes to significant quasi-linear enhancement of energy absorption capabilities at high strain rates. The results of experimental testing were further used for the determination of critical deformation velocities and validation of the proposed computational model. A simple computational model with homogenised crushable foam material model shows good correlation between the experimental and computational results at analysed strain rates. The computational model offers efficient (simple, fast and accurate) analysis of high strain rate deformation behaviour of a closed-cell aluminium foam at different loading velocities.

Numerical Modeling and Experimental Behavior of Closed-Cell Aluminum Foam Fabricated by the Gas Blowing Method under Compressive Loading.

This paper deals with the experimental and numerical study of closed-cell aluminum-based foam under compressive loading. Experimental samples were produced by the gas blowing method. Foam samples had an average cell size of around 1 mm, with sizes in the range 0.5–5 mm, and foam density of 0.6 g/cm3. Foam samples were subjected to a uniaxial compression test, at a displacement rate of 0.001 mm/s. Load and stress were monitored as the functions of extension and strain, respectively. For numerical modeling, CT scan images of experimental samples were used to create a volume model. Solid 3D quadratic tetrahedron mesh with TETRA 10-node elements was applied, with isotropic material behavior. A nonlinear static test with an elasto-plastic model was used in the numerical simulation, with von Mises criteria, and strain was kept below 10% by the software. Uniform compressive loading was set up over the top sample surface, in the y-axis direction only. Experimental tests showed that a 90 kN load produced complete failure of the sample, and three zones were exhibited: an elastic region, a rather uniform plateau region (around 23 MPa) and a densification region that started around 35 MPa. Yielding, or collapse stress, was achieved around 20 MPa. The densification region and a rapid rise in stress began at around 52% of sample deformation. The numerical model showed both compressive and tensile stresses within the complex stress field, indicating that shear also had a prominent role. Mainly compressive stresses were exhibited in the zones of the larger cells, whereas tensile stresses occurred in zones with an increased number of small cells and thin cell walls.

Low cycle fatigue behaviour of closed-cell aluminium foam

The computational and experimental investigation of the fatigue behaviour of AlSi7 aluminium foam is presented in this study. The internal structure of a highly porous specimen was recorded using CT images to enable the subsequent detailed numerical modelling using the finite element method. A new approach for determination of the fatigue life of foam materials was developed, where the standardised approach is very difficult or even not possible to be used. In the proposed approach, several numerical models with different porosity were built and analysed instead of the numerical model, with real porosity of an actual porous structure. Stress-strain results obtained by the numerical analyses of these models were then used in the subsequent fatigue analysis to determine the fatigue lives of the treated porous specimens. Numerical results were compared with the experimental results, which were performed using low cycle fatigue testing under oscillating tensile loading with stress ratio R = 0.1. The developed approach enables the fatigue analyses and prediction of the fatigue lives of various porous structures where a real numerical model is very difficult to build because of its very complicated internal structure.

The Effect of Shot-Peening Treatment on Microstructure and Corrosion Behavior of Closed-Cell Aluminum Foam

Closed-cell aluminum foam was shot peened at different processing time (0 s, 5 s, 10 s, and 20 s), the intensity was the 0.12 mmA. The X-ray diffraction results showed that the reflections became weakened obviously with the shot peened time increased. Combined with Popa model and lognormal distribute model, the surface microstructure of closed-cell aluminum foam was inves-tigated by using the Rietveld whole pattern fitting analysis method. The results revealed that domain size and microstrain fluctuated along different reflection directions after shot peened, which attributed to the random and anisotropic deformation direction. With the shot peened processing time prolonged, a decrease in domain size and an increase in microstrain were also observed. Moreover, the corrosion behavior of closed-cell aluminum foam was studied by weight-loss test. The results indicated that corrosion properties of specimen subjected to shot peened processing was better than the unpeened specimens.

Numerical Investigation on Mechanical Behaviour of Closed-cell Aluminium Foams Using a Representative Volume Element Method

In this study, a representative volume element (RVE) method is developed to capture the mechanical behaviour of aluminum foams under compressive loadings. Octadecahedrons are selected for forming cells of a microstructured RVE model to simulate mechanical behaviour of the aluminium foams under quasi-static compressive loadings. A convergence test is conducted to determine an appropriate mesh density. The stress-strain relationship obtained from the numerical simulations is compared to that from experimental study and agreements between these results demonstrate the efficiency of the proposed RVE model. Thereafter failure modes during a compressive loading process of the aluminum foams are also identified and discussed using this RVE model.

Investigation of strain-rate effect on the compressive behaviour of closed-cell aluminium foam by 3D image-based modelling

Three-dimensional (3D) finite element models based on computed tomography (CT) images are developed to investigate the strain-rate effect on the compressive behaviour of closed-cell aluminium foam (Alporas). It is found that at strain-rates below shock conditions the rate dependence of the cell–wall material is the main cause of the strain-rate hardening of the compressive strength of Alporas foam. The foam exhibits slightly higher strain-rate sensitivity than that of the cell–wall material due to localised strain-rate amplification in some critical load-bearing elements. By contrast, the micro inertia of individual cell walls associated with the nonuniform deformation of Alporas foam has a negligible contribution. Under shock conditions the stress measured at the loading end is always enhanced, but the stress measured at the supporting end is complicated, depending on the characteristics of the contiguous cells. In general, shock leads to a concentrated large deformation in the cells at the loading end, but a restrained small deformation in the cells at the supporting end. Consequently, the hardening effect of the rate dependence of cell–wall material on the supporting stress becomes constrained with further increasing strain-rate, and the supporting compressive strength is limited to the quasi-static level when the cell–wall material is rate-independent.

Research on Dynamic Compression-Shear Behavior of Closed-Cell Aluminum Foam

In this paper, the dynamic compression-shear experiments on the closed-cell aluminum foam with porosity of 72%-92% are carried out by using improved split Hopkinson pressure bar. A high speed camera is used to observe the dynamic deformation behavior of the samples on the compression-shear loading. A finite element software ABAQUS is employed to simulate the dynamic compression-shear process of closed-cell aluminum foam. The results demonstrate that there is a compression-shear band on the samples during the compression-shear loading. The most severely damaged area of the material is on the compression-shear band; Low-porosity closed-cell aluminum foam has significant strain rate effect, however high-porosity closed-cell aluminum foam can ignore the strain rate effect. The yield stress of samples decreases with increasing samples angle, whereas shear stress increase with increasing samples angle, and also the corresponding time when the samples just begin to yield decreases with increasing samples angle.

X-ray and finite element analysis of deformation response of closed-cell metal foam subjected to compressive loading

Time-lapse X-ray computed microtomography was employed to quantify the deformation behaviour of closed-cell aluminium foam. The specimen was incrementally loaded and tomographically scanned using a custom X-ray tomographic device to capture the deforming microstructure. Because of the very small thickness of the cell walls and the high ratio between pore size and cell wall thickness cone-beam reconstruction procedure was applied. A finite element (FE) model was developed based on the reconstructed three-dimensional data. The FE model was used for two purposes: i) the nodal points were used for tracking the displacements of the deforming structure, ii) verification of the material model for description of the foam's deformational behaviour. Digital volumetric correlation (DVC) algorithm was used on data obtained from the time-lapse tomography to provide a detailed description of the evolution of deformation in the complex structure of aluminium foam. The results from DVC demonstrate the possibility to use the complex microstructure of the aluminium foam as a random pattern for the correlation algorithm. The underlying FE model enables easy comparison between experimental results and results obtained from numerical simulations used for evaluation of proposed constitutive models.

Effect of temperature on the indentation behavior of closed-cell aluminum foam

Abstract Deep indentation response of closed-cell aluminum foam under different temperatures was experimentally investigated by using flat-ended and hemispherical-ended punches and compared with that under uniaxial compression. Cross-sectional views show that the deformation is roughly confined to the material directly underneath the indenter though has slight lateral spread. The plastic collapse strength, tear energy and energy absorption are found to be temperature dependent. An empirical formula incorporating indentation depth effect and test temperature effect is presented for the tear energy.

Compressive behaviour of closed-cell aluminium foams at high strain rates

It has been well established that ALPORAS® foams is a strain rate sensitive material. However, the strain rate effect is not well quantified as it is not unusual for strain rate to vary during high speed compression. Moreover, according to previous research, aluminium foams, especially ALPORAS® foams, behave differently at low and high strain rates. Therefore, different plastic deformation mechanisms are expected for low and high strain rate loadings as a result of micro-inertia of cell walls. In this paper, the strain rate effect on the energy dissipation capacity of ALPORAS® foam was investigated experimentally by using a High Rate Instron Test System, with cross-head speed up to 10 m/s. The compressive tests were conducted over strain rates in the range of 1 × 10 −3 to 2.2 × 10 2 s −1, with each test being at a fairly constant strain rate. An energy efficiency method was adopted to obtain the densification strain and plateau stress. The effect of strain rate and the foam density was well presented by empirical constitutive models. The experimental data were also discussed with reference to the recent results by other researchers but with different range of strain rates. An attempt has been made to qualitatively explain the observed decrease of densification strain with strain rate.

Comparison of quasi-static and dynamic compression behavior of closed-cell aluminum foam

Aluminum foams have the potential to be used as structural material for impact energy absorption applications due to their extended constant stress region during compression. The compressive behavior of closed-cell aluminum foams synthesized by liquid melt route using TiH2 as a blowing agent is studied in the present work. Both quasi-static (ε˙=1×10−3 s−1) and dynamic (ε˙∼750 s−1) compression tests were carried out on foam specimens having relative density ranging from 0.062 to 0.373 and average pore diameter in the range of 2.2mm to 4.5mm. The dynamic tests were conducted using a split Hopkinson pressure bar (SHPB) apparatus with a hollow aluminum transmitter bar. The results of the study indicated that the plateau stress of aluminum foam increases with relative density and strain rate. Additionally, at high strain rates, an increase in the energy absorption capacity was observed. Such higher energy absorption capability during dynamic compression is beneficial when the material is used for impact energy absorption applications.

Anisotropic damping behavior of closed-cell aluminum foam

Closed-cell aluminum foams were prepared by molten body transitional foaming process. The anisotropic damping property of closed-cell aluminum foam was measured in two directions using the forced vibration method. The measured results show that the loss factors of the TD specimens are higher than that of the LD specimens. The loss factors ratio β L / β T depends linearly on the shape-anisotropy ratio R. Anisotropic damping behavior is due to the variation of Young’s modulus resulting from anisotropic cell morphology.

Fatigue of a laterally constrained closed cell aluminum foam

An experimental investigation into the constant stress amplitude compression–compression fatigue behavior of closed-cell aluminum foam, both with and without lateral constraint, was conducted. Results show that while the early stages of strain accumulation due to fatigue loading are independent of constraint, the rapid strain accumulation stage behaviors are sensitive to the constraint. This was ascribed to the noticeable hardening with plastic deformation observed under constraint during quasi-static loading, which in turn reduces the effective maximum stress experienced by the foam specimen during fatigue loading. This was demonstrated through a simple empirical model that connects fatigue strain accumulation without constraint to that under constraint. Complementary X-ray tomography experiments suggest that the fatigue behavior of the foams is relatively less sensitive to morphological defects such as missing walls than the quasi-static mechanical properties such as plastic strength. Evaluation of the energy absorption behavior suggests that the damage that accumulates during fatigue does not affect the energy-absorbing ability of the foam adversely.

In situ observations of compressive behaviour of aluminium foams by local tomography using high-resolution X-rays

We have investigated the compressive behaviour of closed-cell aluminium foams using a high-resolution X-ray CT. The microstructures of cell walls or Plateau borders in the foams were visualized in 3D using the local tomography technique which is a high-resolution CT method to reconstruct a region of interest within a large sample. The shapes and the 3D distribution of micropores, particles, and regions of solute segregation in the foams are evaluated, comparing the cell walls with the Plateau borders. Under compressive loads, the damage behaviour of such microstructures has been observed using an in situ test rig. It is found that the microcracks were mainly initiated from the cell walls and the micropores with large diameters were also damaged. The crack initiation sites are classified from the results. In addition, a method for non-destructive characterization of elastic and plastic deformation in the foams, which is called a 3D microstructure gauge (MG) method, is presented. Thousands of micropores as markers on each load were automatically matched by the information of those volumes and surface areas. The local strain mapping by the MG indicates that the edges of the micropores with large diameters have large strain under compression and this is consistent with the crack analyses.