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Digital Volume Correlation (DVC) Analysis of Aluminium Foam

Cellular materials are widespread in nature; wood, cork, bamboo, trabecular bone and sponge are some examples. Their peculiar structure leads to a unique combination of properties, which has inspired the manufacturing of synthetic cellular materials using polymers, metals, glasses, ceramics and carbon with the aim to mimic their behaviour.

 Multifunctional materials with properties such as low weight, low thermal conductivity, high specific surface area, ability to undergo large deformations at relatively low and constant stresses without rebounding, are particularly attractive nowadays for lightweight structures, fluid flow control, porous electrodes, energy absorption, thermal insulation, acoustic damping, and vibration damping.

X-ray computed tomography (CT) has been successfully exploited in different fields as a non-destructive testing (NDT) technique to qualitatively and quantitatively inspect components. Intricate structures, such as cellular solids, require a three-dimensional characterisation, therefore X-ray CT can provide insights of the behaviour for this class of materials.

Previous studies have explored the use of X-ray CT to characterise cell and ligaments morphology in Aluminium (Al) foam providing information on cross-section shape, cell size, and ligament area distribution [i]. Similarly, the meso-scale geometry was obtained to create a more realistic mesh for numerical simulations [ii],[iii]. In these studies the Al foam was in the undeformed state; however, in-situ experiments can be conducted to assess the Al foam behaviour under mechanical or thermal load, which is the aim of TWI’s latest project.

VIDEO: NDT Digital Volume Correlation Analysis

Objectives

  • To show the feasibility of using X-ray CT in-situ mechanical (or thermal experiments) and digital volume correlation (DVC) analysis to achieve insights of Al open-cell foam behaviour, such as the internal deformation of the foam structure.
Figure 1. Compressive response for the Al open-cell foam. Experimental observations are represented by dots, while the curve is obtained by interpolation of the experimental data.
Figure 1. Compressive response for the Al open-cell foam. Experimental observations are represented by dots, while the curve is obtained by interpolation of the experimental data.

Materials and Methodology

The material used is an Al open-cell foam, manufactured by directional solidification, with 10 pore per inch (ppi) and 8% density. A cylindrical specimen with a diameter of 9mm and height of 11mm was obtained by waterjet cutting. In-situ quasi-static compression experiments, carried out using the Deben loading device, were conducted under a constant displacement rate of 0.1mm/min. The displacement was interrupted at intermediate levels (Figure 1), allowing the examination of the specimen by the use of X-ray CT. The specimen was held under compressive load during the image acquisition.

X-ray experiments were performed at TWI with the Zeiss Xradia Versa 520. The energy used was of 70 keV, number of projections 1601, exposure time 4 s, and a voxel size of 11.12 µm. Acquired datasets have been analysed to identify damage micro-mechanisms, and to perform a digital volume correlation (DVC) study using Avizo 9.7. Two DVC methods were investigated, the local digital volume correlation analysis (LADVC) and the global digital volume correlation analysis (GADVC), both of which were implemented in Avizo.

Results and Conclusions

X-ray CT images provide information on the cell wall microstructure, which in turn depends on the manufacturing process. Non-homogeneous cell wall material microstructure can be revealed by virtually sliding across the full volume under investigation. In addition, the presence of microscopic features such as foreign particles, precipitates and of micro-pores can be detected (Figure 2).

This is of particular importance because it might result in a non-homogeneous stress/strain distribution. Three-dimensional analysis is required for investigating cell morphology, spatial distribution of micro-pores and other features inside the cell walls. Figure 3 shows the 3D rendering of the Al foam during the in-situ compression experiment. Intermediate loading conditions considered are highlighted in the curve in Figure 1. The compressive load was applied upwards from the bottom sample end.

The in-situ results revealed four main stages in the material behaviour:

  • First stage, nearly linear regime in the load/displacement curve up to the peak load, characterised by relatively small translations along the loading direction up to the peak load. However, no relevant deformations were visible. The volume A in Figure 3 is representative of this stage.
  • Second stage, the cell deformation and collapse start along an inclined band with respect to the load direction (at around 60˚) corresponding to the point D reported in Figure 1. The deformation band appears approximately at one third of the high of the specimen with respects to the loading and supporting end, as shown in Figure 4. The overlapping of the volumes between D and E (Figure 1), shows that displacements are mostly associated with the lower sub-volume defined by the deformation band, while the sub-volume on the top of the deformation band is matching, see Figure 4. The main deformation modes along the deformation band are bending and buckling.
  • Third stage, characterised by the plateau region. This represents a typical behaviour of Al foam structures, making them excellent candidates for energy absorption applications. Results showed that the volume does not undergo to large deformations during this stage, see comparison between volume E and F in Figure 3.
  • Fourth stage, associated with the steep increase of displacement (last regime of the curve in Figure 1). A correspondent increase of deformation with failure of the cell branches along the deformation band is observed, see volume F in Figure 3. The sub-volume in the upper side of the deformation band also starts exhibiting displacements, and the band of crushed cells spreads downwards defining the collapsing zone, see volume G in Figure 3.

 

Time-lapse datasets acquired at intermediate stages of deformation, as shown in Figure 3, were used to perform DVC analysis. DVC analysis uses specific features inside registered volumes of interest to compute displacements (discontinuous displacement fields in the local approach and continuous displacement fields in the global approach) and volumetric strain map. In this specific case the whole volume was considered for the DVC analysis, but the analysis can be also performed on sub-volumes. Figure 5 shows the axial displacement along the direction of the load (uz) obtained corresponding to the first stage, between the unloaded condition and points A and B respectively in Figure 1.

The displacement map associated with the first stage of the material behaviour, Figure 5, highlights:

  • The displacement vector field has an axial component (uz) but also a radial component
  • The foam structure exhibits different displacements from loading end to supporting end. In particular, higher displacements are associated with the loading end; see Figure 5(b).

 

The volumetric strain map obtained applying a global DVC analysis for the first stage of the material behaviour is shown in Figure 6. Results highlight:

  • Almost uniform and very low strain corresponding to a displacement of 0.12 mm, Figure 6(a)
  • Gradient of strain distribution along the structure for the magnitude displacement of 0.24 mm, Figure 6(b). Specifically, loading and supporting ends do not show any strain changes respect to the previous loading stage, Figure 6(a); while the strain increases in the intermediate region of the structure. This provides an indication of the location of the deformation band and damage initiation.

 

The current study exploits the use of complementary methods, such as time-lapse imaging by X-ray CT, in-situ experiments and DVC analyses to provide insights into the Al foam behaviour subjected to compression. The same approach can be used to study different cellular structures.

 

References

[i.] W.-Y. Jang and S. Kyriakides, “On the crushing of aluminum open-cell foams: Part I. Experiments,” International Journal of Solids and Structures, vol. 46, pp. 617-634, 2009

[ii.] Y. Sun, Q. M. Li, T. Lowe, S. A. McDonald and P. J. Withers, “Investigation of strain-rate effect on the compressive behaviour of closed-cell aluminium foam by 3D image-based modelling,” Materials & Design, vol. 89, pp. 215-224, 2016

[iii.] M. A. Kader, M. A. Islam, M. Saadatfar, P. J. Hazell, A. D. Brown, S. Ahmed and J. P. Escobedo, “Macro and micro collapse mechanisms of closed-cell aluminium foams during quasi-static compression,” Materials & Design, vol. 118, pp. 11-21, 2017

 

Acknowledgements

This work was carried out by past and present members of the TWI NDT team, in particular Serafina Garcea aided by Giorgos Asfis and Muntasir Hashim.

Figure 2. 2D cross-section perpendicular to the load direction of the Al open-cell foam in the undeformed condition.
Figure 2. 2D cross-section perpendicular to the load direction of the Al open-cell foam in the undeformed condition.
Figure 3. 3D rendering of the Al open-cell foam under compressive loading. With reference to the loading curve in Figure 1, incremental stages refer to a displacement of: 0.12 mm (A), 1.14 mm (E), 1.74 mm (F), and 2.94 mm (G).
Figure 3. 3D rendering of the Al open-cell foam under compressive loading. With reference to the loading curve in Figure 1, incremental stages refer to a displacement of: 0.12 mm (A), 1.14 mm (E), 1.74 mm (F), and 2.94 mm (G).
Figure 4. Overlapped volumes for the displacement levels of 0.54 mm (in blue) and 1.14 mm (in green), correspondingly with point D and E in Figure 1 respectively.
Figure 4. Overlapped volumes for the displacement levels of 0.54 mm (in blue) and 1.14 mm (in green), correspondingly with point D and E in Figure 1 respectively.
Figure 5. Axial displacement (uz) obtained by global DVC analysis for the magnitude displacement of 0.12 mm (a), and 0.24 mm (b).
Figure 5. Axial displacement (uz) obtained by global DVC analysis for the magnitude displacement of 0.12 mm (a), and 0.24 mm (b).
Figure 6. Axial strain map (εzz) obtained by global DVC analysis for the magnitude displacement of 0.12 mm (a), and 0.24 mm (b).
Figure 6. Axial strain map (εzz) obtained by global DVC analysis for the magnitude displacement of 0.12 mm (a), and 0.24 mm (b).
Avatar Giorgos Asfis Project Leader, Non-Destructive Testing

Giorgos Asfis joined TWI in September 2012. He holds a degree in Mechanical Engineering (BSc and MSc) from the National Technical University of Athens (NTUA), where he focused on structural and machine dynamics, vibration analysis, predictive maintenance and modal analysis. Working in TWI’s NDT department, Giorgos has experience in ultrasonics, guided waves, radiography, computed tomography, finite element modelling and high performance computing and, since joining TWI, he has become increasingly involved in electronics and programming. He is certified as a Level II inspector in a number of NDT methods and Level III in PAUT.

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