Image-based correlation between the meso-scale structure and deformation of closed-cell foam

Abstract

In the correlation between structural parameters and compressive behaviour of cellular materials, previous studies have mostly focused on averaged structural parameters and bulk material properties for different samples. This study focuses on the meso-scale correlation between structure and deformation in a 2D foam sample generated from a computed tomography slice of Alporas TM foam, for which quasi-static compression was simulated using 2D image-based finite element modelling. First, a comprehensive meso-scale structural characterisation of the 2D foam was carried out to determine the size, aspect ratio, orientation and anisotropy of individual cells, as well as the length, straightness, inclination and thickness of individual cell walls. Measurements were then conducted to obtain the axial distributions of local structural parameters averaged laterally to compression axis. Second, the meso-scale deformation was characterised by cell-wall strain, cell area ratio, digital image correlation strain and local compressive engineering strain. According to the results, the through-width sub-regions over an axial length between the average (lower bound) and the maximum (upper bound) of cell size should be used to characterise the meso-scale heterogeneity of the cell structure and deformation. It was found that the first crush band forms in a sub-region where the ratio of cell-wall thickness to cell-wall length is a minimum, in which the collapse deformation is dominated by the plastic bending and buckling of cell walls. Other 2 morphological parameters have secondary effect on the initiation of crush band in the 2D foam.The finding of this study suggests that the measurement of local structural properties is crucial for the identification of the "weakest" region which determines the initiation of collapse and hence the corresponding collapse load of a heterogeneous cellular material.

Cutting-induced end surface effect on compressive behaviour of aluminium foams

“…local density variation) in foam samples is considered. Previous 3D characterisation of Alporas foam using X-ray tomography showed that the axial variation in the local relative density of Alporas foam is less than 3% (Saadatfar et al, 2012), and similar observation was reported by Sun et al (2017) who analysed the local relative density distribution using X-ray tomography slice of Alporas foam. Therefore, the stochastic variation in local relative density cannot be the cause of the observed significant differences in the measured compressive properties shown in Figs.…”

“…In contrast, the peak and plateau of compressive stress are similar between the samples prepared by different cutting methods. Considerable scatter in compressive stress-strain curves is observed, which can be attributed to both the scatter in relative density (Table 1) and the inherent heterogeneity of foam structures (Ramamurty and Paul, 2004;Sun et al, 2017).…”

“…When the yielding (or failure) of end-surface layers occurs immediately after loading (Sun et al, 2016a), the global compressive strain can be expressed as 5-8. Given the explanation offered by a continuum mechanics model, it should be pointed out that the variation in the macroscopic compressive properties actually reflects a series of complicated deformation processes occurring at both micro-and meso-scales (Sun et al, 2016a;Sun and Li, 2018;Sun et al, 2017;Sun et al, 2014).…”

Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling

“…Such a conceptual equivalence between the macroscopic local strain and mesoscopic global strain for cellular materials has been applied in experimental strain mapping using digital image correlation [18,19], and in numerical strain calculations based on the cross-sectional displacement [20,21] and finite element nodal distance in a cell neighbourhood [22,23]. Similarly, the mesoscopic local strain and the microscopic global strain are equivalent, and they are both a measure of the deformation of the base material [21,[24][25][26]. This conceptual equivalence, again, acts as the link between the meso-scale and micro-scale.…”

“…It is evident that, in the quasi-static and transitional dynamic regimes, the first crush band forms in the presumably weakest sites and then more crush bands form in other sites which are separate from or adjacent to the first band. The weakest sites can be identified by examining the mesoscopic structural heterogeneity or imperfection[21,207]. The localised deformation is randomly distributed in the sample.…”