Application of mean-field approximation to elastic-plastic behavior for closed-cell metal foams

Kitazono, Koichi; Satô, Eiichi; Kuribayashi, Kazuhiko

doi:10.1016/s1359-6454(03)00322-7

Cited by 48 publications

(33 citation statements)

References 28 publications

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“…1) with different relative densities and different yield behaviour of the matrix material have been investigated in order to clarify the influence of the internal pore pressure on the macroscopic mechanical behaviour. The numerical results obtained will be discussed in the context of the analytical findings given in [14].…”

Section: Introductionmentioning

confidence: 97%

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Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure

Öchsner

Mishuris

2009

Finite Elements in Analysis and Design

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Section: Introductionmentioning

confidence: 97%

“…[12,13]. A comprehensive study of the elastic-plastic properties of metal foams under consideration of internal gas pressure can be found in [14]. Kitazono et al applied in this paper the equivalent inclusion method and the mean-field approximation to derive analytical formulae for the effective properties, i.e.…”

Section: Introductionmentioning

confidence: 99%

Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure

Öchsner

Mishuris

2009

Finite Elements in Analysis and Design

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“…[6] Descriptions based on continuum approaches have been proposed as well. [7,8,9] Obviously, for an experimental validation an accurate experimental determination is important. In fact, X-ray tomography can be used to measure a large number of cells with high precision.…”

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confidence: 99%

The Influence of Cell Shape Anisotropy on the Tensile Behavior of Open Cell Aluminum Foam

et al. 2008

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There are numerous processes for the fabrication of openand closed cell metal foams and some of these methods result in a strong anisotropy in cell shape. The mechanical properties of these specific foams, such as the stiffness, yield stress and ultimate tensile strength (UTS) (see Fig. 1), also show anisotropy which is often linked to the cell shape. [1,2,3,4,5] Gibson and Ashby (G&A) constructed an analytical beam bending model to calculate the influence of the cell aspect ratio, i.e. the long cell axis divided by the short cell axis, on the stiffness and plastic strength. [6] Descriptions based on continuum approaches have been proposed as well. [7,8,9] Obviously, for an experimental validation an accurate experimental determination is important. In fact, X-ray tomography can be used to measure a large number of cells with high precision. [10,11,12] From the measured aspect ratio in the cell shape the anisotropy in the stiffness in tension was calculated in agreement with experiments. [11] In addition, by accounting for the anisotropy in plastic behavior the peak stress and strain have been predicted based on a critical strain criterion. [9] In these studies, however, the role of damage accumulation during straining has not been incorporated in the modeling, nor has it been quantitatively measured as a function of density.In a previous study we have shown that damage accumulation starts well before the peak stress has been reached and that the onset and rate of damage evolution depends critically on the base material properties and the relative density of the foam. [13] The ability of the foam to accommodate the applied strain by strut bending and reorientation was identified as an important mechanism responsible for the large peak strain at small densities. The objective of this paper is to study the effect of cell shape anisotropy looked upon in the light of these mechanisms. We start by relating the yield stress to the cell orientation at small strains, followed by a study of the damage evolution at large strain by measuring the electrical resistance in-situ.The material used is ERG Duocel open cell aluminum foam (20 PPI, alloy AA6101). The relative densities of the samples are grouped according to the following three ranges: 3-5 % (low), 6-7 % (medium) and 10-13 % (high). The relative density of each sample was calculated by measuring the mass and dividing it by the volume and the mass of pure Al (2.7 g/cm 3 ). The samples were received in the annealed (AN) condition (3 hrs at 412°C, followed by slow cooling to 260°C and maintaining that temperature for 0.5 hr followed by slow cooling to RT). Some of the samples were subjected to an additional precipitation hardening heat treatment (HT) to increase the yield stress. First the samples were exposed to a solid solution heat treatment (527°C for 8 hrs) followed by quenching in RT water. After 16 hrs at RT the samples were artificially aged for 8 hrs at 177°C, followed by cooling inside the furnace. Table 1 shows the mechanical properties in tension of the Al a...

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“…5. Assuming the pore shape as spheroid, the authors 16) calculated the thermal conductivity as a function of the aspect ratio and the porosity. Experimental data agreed well with the broken line of ¼ 0:1.…”

Section: Discussionmentioning

confidence: 99%

Superplastic Forming and Foaming of Cellular Aluminum Components

Kitazono

2006

Mater. Trans.

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Liquid and semi-solid state foaming processes have been widely used as a manufacturing method of closed-cell metal foams. These metal foams usually have large pores as well as high porosity. Large pores and inhomogeneous pore distribution often cause a decrease in mechanical properties. Therefore, microcellular foams are desirable for engineering applications. In the present study, solid-state foaming process under superplastic conditions is examined in order to manufacture microcellular aluminum foams. The superplastic flow during the high temperature foaming accelerates the foaming rate and increases the porosity. Commercial SP5083 aluminum alloy sheets were used as a starting material because they are typical superplastic material. Preform sheet containing titanium hydride particles was produced through accumulative rollbonding (ARB) processing. Heating the preform sheet under superplastic conditions, we obtained aluminum foam with small oblate pores. The thermal conductivity was quite small because of the oblate pore shape. Superplastic flow enabled to produce a thin sandwich panel and porous bulge structures. These panel and bulge with oblate spheroidal pores parallel to the surface are industrially important because of their excellent thermal insulation. Present experimental results of superplastic forming and foaming (SPFF) processing has potential for near net-shape forming of microcellular aluminum foams.

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Application of mean-field approximation to elastic-plastic behavior for closed-cell metal foams

Cited by 48 publications

References 28 publications

Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure

Modelling of the multiaxial elasto-plastic behaviour of porous metals with internal gas pressure

The Influence of Cell Shape Anisotropy on the Tensile Behavior of Open Cell Aluminum Foam

Superplastic Forming and Foaming of Cellular Aluminum Components

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