*Article* **Aluminum Foam-Filled Steel Tube Fabricated from Aluminum Burrs of Die-Castings by Friction Stir Back Extrusion**

**Yoshihiko Hangai 1,\*, Ryusei Kobayashi 1, Ryosuke Suzuki 1, Masaaki Matsubara <sup>1</sup> and Nobuhiro Yoshikawa <sup>2</sup>**


Received: 30 December 2018; Accepted: 18 January 2019; Published: 24 January 2019

**Abstract:** A mixture of Al burrs of Al high-pressure die-castings and a blowing agent powder was used to fabricate Al foam-filled steel tubes by friction stir back extrusion (FSBE). It was shown that the mixture can be sufficiently consolidated to form an Al precursor that is coated on the inner surface of a steel tube by the plastic flow generated during FSBE. Namely, a precursor coated steel tube can be fabricated from Al burrs by FSBE. By heat treatment of the precursor coated steel tube, an Al foam-filled steel tube can be fabricated. Al foam was sufficiently filled in the steel tube, and the porosity was almost homogeneously distributed in the entire sample. In compression tests of the samples, the Al foam-filled steel tube fabricated from Al burrs exhibited similar compression properties to an Al foam-filled steel tube fabricated from the bulk Al precursor. Consequently, it was shown that an Al foam-filled steel tube cost-effectively fabricated from Al burrs by FSBE compares favorably with an Al foam-filled steel tube fabricated from the bulk Al precursor.

**Keywords:** cellular materials; composites; friction welding; foam; recycle

#### **1. Introduction**

Composite structures consisting of a dense metallic tube filled with aluminum (Al) foam have attracted interest in various industrial fields owing to their light-weight and good energy absorption properties [1,2]. Generally, Al foam-filled metallic tubes have been fabricated by simply placing Al foam into a metallic tube with a gap between the Al foam and the metallic tube, which adversely affects the mechanical properties of the tube [3,4]. Hamada et al. and Toksoy et al. demonstrated that bonding between the Al foam and Al tube with adhesives resulted in superior absorption properties to those without any bonding [3,5]. Bonaccorsi et al. fabricated an Al foam-filled steel tube with metal bonding between the Al foam and steel tube by foaming a precursor in the steel tube [6]. The precursor was a solid Al homogeneously containing blowing agent [7,8]. Duarte et al. fabricated an Al foam-filled Al tube with metal bonding between the Al foam and Al tube by foaming a precursor in the Al tube [9].

Friction stir back extrusion (FSBE) has been developed for coating wear-resistant Al-25%Si on the surface of an Al-Si-Cu alloy AC2B engine cylinder [10], and for fabricating Al tubes and copper tubes with a fine grain structure from bulk starting materials [11,12]. Hangai et al. developed a fabrication process for Al foam-filled steel tubes [13,14] and Al foam-filled Al tubes [15,16] by FSBE. In this process, a bulk Al precursor was placed into a metal tube; then a rotating tool was plunged onto the precursor. The generated friction heat between the rotating tool and precursor softened the precursor, then the plastic flow of the precursor occurred, causing it to fill the space between the rotating tool and the metal tube, resulting in the coating of the precursor on the surface of the metal tube. The plastic

flow induced the exposure of the new surface of the precursor and metal tube, realizing strict contact between them. Heat treatment of the precursor resulted in the foaming of the precursor, which filled the tube and bonded to the tube with metallic bonding. A bilayer tube consisting of an outer Al foam and an inner Al tube can also be fabricated by a similar process [17].

A reduction in cost and the high recyclability of Al foam-filled metal tubes can be expected by using Al chip waste from industrial production [18,19]. Consolidation of Al chips has been attempted by hot extrusion [18,19], compression torsion processing [20,21], friction extrusion [22], friction consolidation [23–25], screw extrusion [26], and FSBE [27]. Among these processes, FSBE can fabricate an Al tube directly from Al chips and realize strict contact with an outer metal tube.

In this study, a mixture of Al burrs of Al high-pressure die-castings and a blowing agent powder was used to fabricate Al foam-filled steel tubes by FSBE. It was expected that a foamable precursor would be fabricated by consolidating the mixture by the plastic flow generated during FSBE, along with the coating of the precursor on the inner surface of the steel tube. By heat treatment of the precursor coated steel tubes, Al foam-filled steel tubes were obtained. The pore structures of the inner Al foam were nondestructively observed to determine whether sufficient foaming occurred, and the pores were found to be homogeneously distributed in the whole specimen. Thereafter, compression tests of the obtained Al foam-filled steel tubes were conducted to determine whether similar mechanical properties to those of an Al foam-filled tube fabricated from the bulk Al precursor could be obtained.

#### **2. Materials and Methods**

#### *2.1. Fabrication of Al Foam-Filled Steel Tube*

Figure 1 shows Al burrs used to fabricate the Al foam of the Al foam-filled steel tube. The Al burrs were from Al-Si-Cu alloy ADC12 (equivalent to A383.0 Al alloy) die-castings. Figure 1a shows a scanning electron microscope (JEOL Ltd., Tokyo, Japan) image of the ADC12 burrs in powder form. As received ADC12 burrs were sieved with a mesh size of 180 μm to remove the impurities and for easy mixing with the blowing agent powder. Figure 1b shows the ADC12 burrs in round-plate form. Relatively thick (approximately 0.2 mm thickness) ADC12 burrs were cut into a circular shape with a diameter of 18 mm.

**Figure 1.** ADC12 burrs (**a**) in powder form and (**b**) in round-plate form.

Figure 2 shows the fabrication process of the Al foam-filled steel tube by FSBE. First, as shown in Figure 2a, ADC12 burrs in powder form and a blowing agent powder were mixed. TiH2 powder (<45 μm) was used as the blowing agent. The amount of TiH2 was one mass% relative to the mass of ADC12 burrs in accordance with reference [13]. As shown in Figure 2b, the mixture was placed in a SUS304 stainless-steel tube fixed by a steel jig. The steel tube had a diameter of 20 mm, a thickness of 0.2 mm, and 40 mm height. Then, five ADC12 burrs in round-plate form were laminated on top of the mixture in the steel tube to prevent the mixture from scattering during FSBE. As shown in Figure 2c, a rotating tool was plunged from above until the tip of the tool reached 3 mm above the bottom of the steel tube using friction stir welding machine (Hitachi Setsubi Engineering Co., Ltd., Hitachi, Japan). The rotation speed and plunging rates were 1500 rpm and 4 mm/min, respectively. The tool was made of tool steel with a diameter of 16 mm and had a flat bottom. The mixture was consolidated by loading

the tool and the plastic flow of the mixture, resulting in the formation of a precursor and the coating on the inner surface of the steel tube. The temperature during the plunging of the tool was obtained by a K-type thermocouple placed at half the height of the steel tube and 2 mm from its surface. As shown in Figure 2d, the upper and lower parts of the obtained precursor coated steel tube were machined by wire electrical discharge machining, then the entire tube was foamed by heat treatment in an electric furnace previously held at 675 ◦C for 6.5–7.0 min. Then, as shown in Figure 2e, an Al foam-filled steel tube was obtained. The upper and lower parts of the obtained Al foam-filled steel tube were machined by wire electrical discharge machining to obtain a compression test specimen with 20 mm diameter and 20 mm height. Fourteen compression test specimens were obtained. In addition, similar compression test specimens were fabricated from a bulk Al precursor, which was fabricated by the friction stir welding route [28,29], by the same process as above using FSBE.

**Figure 2.** Schematic illustration of fabrication process of Al foam-filled steel tube by FSBE.

#### *2.2. Evaluation of Pore Structures*

The pore structures of the compression test specimens were nondestructively observed by a microfocus X-ray CT system (Shimadzu Corporation, Kyoto, Japan) at room temperature in accordance with reference [30]. The X-ray source was tungsten. A cone-beam CT system, where only one rotation of the specimen is required to obtain a set of cross-sectional X-ray CT images with the slice pitch equal to the length of one pixel in the CT image, was employed. The number of slices was about 450. The voltage and current of the X-ray tube were 80 kV and 30 μA, respectively. The equivalent length of a pixel was approximately 74 μm.

The porosity (volume fraction of pores) *p* (%) of the Al foam part of each compression test specimen was evaluated as follows. First, the density of the Al foam part *ρ<sup>f</sup>* was evaluated as

$$\rho\_f = \frac{m\_{\rm FFT} - m\_{\rm tube}}{V\_{\rm FFT} - V\_{\rm tube}},$$

where *m*FFT and *V*FFT are the mass and volume of the compression test specimen, respectively, which were obtained from the measured weight and dimensions of the specimen. *m*tube and *V*tube are the mass and volume of the steel tube part of the compression test specimen, respectively. Then, *p* was evaluated as

$$p = \frac{\rho\_i - \rho\_f}{\rho\_i} \times 100\text{\AA}$$

where *ρ<sup>i</sup>* is the density of the precursor without the tube before foaming, for which the density of ADC12 Al alloy [31] was used.

#### *2.3. Compression Tests*

Compression tests of the obtained Al foam-filled steel tubes were conducted using a universal testing machine (Shimadzu Corporation, Kyoto, Japan). The compression rate was 4 mm/min in accordance with reference [32]. The compression stress was obtained by dividing the compression load by the area of the circle equivalent to the outer diameter of the Al foam-filled steel tube.

#### **3. Results and Discussion**

#### *3.1. Time–Temperature Relationship during FSBE*

Figure 3 shows typical relationships obtained between torque *N* and time *t* and between temperature *T* and time *t*. *t* = 0 was defined as the time when the tool first came in contact with the ADC12 burrs in the round-plate form. As the indentation of the tool increased, the ADC12 burrs were densified, and plastic flow occurred. It has been reported that the filling of the Al between the rotating tool and tube occurs from the upper part, which is softened by the friction heat generated between the rotating tool and the Al precursor [15]. It is considered that plastic flow occurred in the vicinity of the tool where friction heat was generated. The torque and temperature gradually increased in this stage. At around *t* = 5 min, the torque increased rapidly. The temperature exhibited a similar tendency except with a small delay due to the time for the generated heat to be transferred to the thermocouple. In this stage, densification of the ADC12 burrs had finished, and only plastic flow occurred, resulting in a rapid increase in the resistance force and temperature. Similar tendencies were observed for all other samples, and the maximum temperatures of all the samples were between 350 and 415 ◦C. Also, similar tendencies were observed for the samples using the bulk Al precursor. These temperatures are much lower than the solidus temperature of ADC12 (515 ◦C [31]), at which the foaming of the precursor begins [33,34]. It has been demonstrated that the decomposition of TiH2 gradually occurs between 390 and 920 ◦C [35], 427 and 850 ◦C [36], and 440 and 800 ◦C [37]. In the FSBE process, it is assumed that little decomposition of TiH2 occurred because the temperature of the precursor reached these reported decomposition temperatures for only a limited time. Therefore, almost all the TiH2 remained without decomposition.

**Figure 3.** Torque *N*– indentation time *t* and temperature *T*–*t* relationships during FSBE.

#### *3.2. Obtained Al Foam-Filled Steel Tube*

Figure 4a shows the as-fabricated precursor coated tube. It was shown that the ADC12 burrs were sufficiently consolidated except in the upper part of the tube. The upper part of the tube was subjected to a less plastic flow during FSBE, resulting in insufficient consolidation of the ADC12 burrs. These parts were machined before foaming as shown in Figure 4b. Figure 4c shows a cross-section of the machined precursor before foaming, and Figure 4d shows an enlarged image of the bonding region of Figure 4c. It was shown that the ADC12 burrs were sufficiently consolidated to form the precursor and were coated on the surface of the tube without a gap between the tube and precursor by the load of the tool and the intense plastic flow during the FSBE.

**Figure 4.** (**a**) As-fabricated precursor-coated steel tube. (**b**) machined precursor-coated steel tube before foaming and (**c**) its cross section. (**d**) enlarged image of bonding region of (**c**).

Figure 5a,b show the as-foamed Al foam-filled steel tubes after foaming for 6.5 min and 7.0 min, Figure 5c,d show the Al foam-filled steel tube compression test specimens obtained by machining the samples shown in Figure 5a,b, and Figure 5e,f show their cross-sectional X-ray CT images, respectively. Black and white regions in the X-ray CT images indicate pores and Al, respectively. Although a few large pores were observed, it was shown that the coated precursor was sufficiently foamed and filled the tubes. The porosities of the Al foam part of the compression test specimens shown in Figure 5c,d were *p* = 79.3% and *p* = 90.2%, respectively.

**Figure 5.** (**a**,**b**) As-foamed Al foam-filled steel tubes after foaming for 6.5 min and 7.0 min, respectively. (**c**,**d**) Al foam-filled steel tube compression test specimens machined from (**a**,**b**), respectively. (**e**,**f**) Their cross-sectional X-ray CT images.

Figure 6 shows the relationship between the porosity and foaming time of all the compression test specimens. The figure indicates that vigorous foaming occurred between 6.5 min and 7.0 min. In previous studies on the foaming of ADC12 precursor [33,34], it was demonstrated that the precursor started to foam once the precursor temperature exceeded the solidus temperature and gradually foamed between the solidus and liquidus temperatures. Then, vigorous foaming occurred once the precursor temperature exceeded the liquidus temperature. Although some variation among the porosities appeared at a foaming time of 6.5 min owing to the difficulty of obtaining the same foaming behavior for each specimen using an electric furnace, a foaming time of around 7.0 min induced sufficient foaming for the precursor temperature of all the samples to exceed the liquidus temperature.

Figure 7 shows the porosity distributions of the compression test specimens shown in Figure 5c,d in the height direction for foaming times of 6.5 min (*p* = 79.3%) and 7.0 min (*p* = 90.2%), respectively, which were evaluated using X-ray CT images such as shown in Figure 5e,f by image processing software. Although there were a few large pores, the Al foam sufficiently filled the tube with an almost homogeneous porosity distribution throughout the entire specimen, especially for the sample foamed for 7.0 min, which exhibited sufficient foaming of the precursor. The variation of the porosity and the existence of large pores are considered to be due to the insufficient distribution of the foaming agent compared with that in the bulk precursor because it was difficult to homogeneously mix the ADC12 burr and TiH2 powders with different particle sizes. Also, slight segregation occurred during the insertion of the mixture into the tube and during the FSBE. This may be prevented by using ADC12 burr particles with a similar size to that of TiH2.

**Figure 6.** Relationship between porosity and foaming time of obtained Al foam-filled steel tube compression test specimens.

**Figure 7.** Porosity distributions in the height direction of Al foam-filled steel tube compression test specimens with (**a**) *p* = 79.3% and (**b**) *p* = 90.2% corresponding to Figure 5c,d, respectively.

#### *3.3. Compression Properties*

Figure 8 shows the deformation behavior of the fabricated Al foam-filled steel tubes with *p* = 79.3% and *p* = 90.2%, respectively, which are shown in Figure 5c,d during the compression test, along with that of the tube fabricated from the bulk Al precursor with *p* = 84.5% by FSBE in accordance with Ref. [13]. The three black lines on the surface of the samples perpendicular to the compression direction were marks made to easily observe the deformation behavior. It was found that the deformation occurred layer by layer. Little difference was observed in the deformation behavior between the Al foams with different porosities, although the number of buckling folds were different. This difference is because the lower-porosity Al foam expanded in the width direction as the deformation increased. In contrast, the higher-porosity Al foam deformed with little expansion in the width direction. The deformation behavior was similar for the other specimens fabricated in this study, including those fabricated from the bulk Al precursor.

**Figure 8.** Deformation behavior during compression test of the fabricated Al foam-filled steel tube with (**a**) *p* = 79.3%, corresponding to Figure 5b,c. (**b**) *p* = 90.2%, corresponding to Figure 5d,c Al foam-filled steel tube fabricated using bulk Al precursor with (**c**) *p* = 84.5%.

Figure 9 shows the stress *σ* – strain *ε* curves of the fabricated Al foam-filled steel tubes with *p* = 79.3% and *p* = 90.2%; along with that of the tube fabricated from the bulk Al precursor with *p* = 84.5%, whose deformation behavior is shown in Figure 8. An elastic region in the early stage of the *σ*–*ε* curves, where *σ* rapidly increased to an initial maximum stress was observed. Then, a plateau region exhibiting an appropriately constant or slightly increasing *σ* was observed as *ε* increased. Then, a densification region where *σ* rapidly increased was observed. The increases and decreases in *σ* in the plateau region were observed when the folds were generated. These *σ*–*ε* curves were also observed for other specimens fabricated in this study regardless of the porosity.

**Figure 9.** Stress–strain curves for the specimens in Figure 8.

Figure 10 shows the plateau stress *σ*pl– porosity *p* and energy absorption per unit volume *E*V– porosity *p* relationships for all the samples including those fabricated from the bulk Al precursor. *σ*pl was defined as the average *σ* for *ε* = 0.2–0.3 in the *σ*–*ε* curves and *E*<sup>V</sup> was defined as the area under the *σ*-*ε* curves for *ε* = 0–0.5 in accordance with Ref. 32. It was found that *σ*pl and *E*<sup>V</sup> decreased as *p* increased. This tendency was also observed for the samples fabricated from the bulk Al precursor. Consequently, it was shown that Al foam-filled steel tubes can be fabricated from ADC12 burrs that exhibit almost the same compression properties as Al foam-filled steel tubes fabricated from the bulk Al precursor when the porosity of the Al foam part is the same.

**Figure 10.** Relationship between (**a**) plateau stress *σ*pl and (**b**) energy absorption per unit volume *E*<sup>V</sup> and porosity *p* for the obtained Al foam-filled steel tubes fabricated from ADC12 burrs along with those fabricated from the bulk Al precursor.

#### **4. Conclusions**

In this study, a mixture of ADC12 burrs of Al high-pressure die-castings and a blowing agent powder was used to fabricate Al foam-filled steel tubes by FSBE. The experimental results led to the following conclusions.

(1) A mixture of ADC12 burrs and a blowing agent can be sufficiently consolidated to form a precursor that is coated on the inner surface of a steel tube by FSBE. Namely, a precursor-coated steel tube can be fabricated from ADC12 burrs by FSBE.

(2) An Al foam-filled steel tube can be fabricated by heat treatment of the precursor coated steel tube. Al foam was sufficiently filled in the steel tube, and the porosity was almost homogeneously distributed in the entire sample.

(3) The Al foam-filled steel tube fabricated from ADC12 burrs exhibited similar compression properties to an Al foam-filled steel tube fabricated from the bulk Al precursor.

Consequently, it was shown that an Al foam-filled steel tube can be cost-effectively fabricated from Al burrs by FSBE and compares favorably with an Al foam-filled steel tube fabricated from the bulk Al precursor.

**Author Contributions:** Y.H. elaborated the research idea and wrote this manuscript. R.K. and R.S. performed the experimental work and contributed to the discussion of the experimental results. M.M. and N.Y. performed literature review and contributed to the discussion of the experimental results.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## *Review* **Brief Review on Experimental and Computational Techniques for Characterization of Cellular Metals**

#### **Isabel Duarte 1,\*, Thomas Fiedler 2, Lovre Krstulovi´c-Opara 3and Matej Vesenjak <sup>4</sup>**


Received: 23 April 2020; Accepted: 26 May 2020; Published: 30 May 2020

**Abstract:** The paper presents a brief review of the main experimental and numerical techniques and standards to investigate and quantify the structural, mechanical, thermal, and acoustic properties of cellular metals. The potential of non-destructive techniques, such as X-ray computed tomography and infrared thermography are also presented.

**Keywords:** cellular metals; X-ray computed tomography; infrared thermography; mechanical characterization; thermal characterization; acoustic characterization

#### **1. Introduction**

Cellular metals are considered to be one of the world's most versatile lightweight multifunctional materials for a wide range of commercial, industrial, and military applications [1–4]. Cellular metals are non-flammable and recyclable, extremely tough, and can plastically deform and absorb energy. They can survive high temperatures in comparison to cellular polymers (e.g., polyurethane foams), which are widely used as crash/impact energy absorbers for vehicles due to their high strength-to-weight and stiffness-to-weight ratios and high energy absorption capacity [4].

Over recent decades, many products and solutions based on cellular metals [5–18] have been developed combined with other light materials like advanced high strength steels, light metals [19,20], polymers [21–27] and carbon nanostructures (e.g., carbon fibers) [28]. For example, cellular solids are used and/or tested as filler [29–32] and cores [33,34] of thin-walled structures and sandwich panels for buildings, industrial machines, cars, trains, and aircrafts. Their use contributes to an immediate weight reduction and material savings of the components, but also to perform multiple functions due to their 3D porous cellular structures (open-or-closed-cells) [35]. The open- and closed-cell structures are used as functional materials (e.g., electrodes, heat exchangers, and biomedical implants) and structural materials (e.g., impact/crash energy absorbers in vehicles, antivibration dampers), respectively [1,2]. The field of cellular materials has significantly increased over the last decades, which is reflected in the growth of published literature (Figure 1). Several cellular metals have been emerging due to two main reasons. The first reason is the need to create cellular structures with high structural efficiency and capacity to absorb both impact and damping noise and vibration. The second reason is the need to create periodic cellular structures with an easily reproducible unit cell to achieve predefined performances, establishing the process–structure–property relationships. Recent developments include composite and nanocomposite metal foams [28], lattices [36,37], 3D printed structures [38], syntactic foams [26,29,39], hollow sphere structures [27], auxetic materials [40–42], and hybrid structures [22–25,43] (e.g., filled hollow structures

and sandwich panels). The latter often leads to the introduction of new technologies (e.g., 3D additive manufacturing) and products.

**Figure 1.** Number of published documents per year in the field of cellular materials (Source: Scopus).

Given the importance and diversity of these cellular materials, it is essential that the researchers use the same measurement science tools and techniques to assess their performance for comparing the different cellular materials. Most of the experimental tests are based on standards. Nevertheless, there is the need to improve and upgrade current testing techniques and methods in some cases.

#### **2. Geometrical and Structural Characterization**

Cellular metals are complex materials, formed by two or more phases (Figure 2). For example, two phases are observed in the open- and closed-cell metal foams, a discontinuous or continuous gaseous phase (cells or pores) and a continuous solid phase (base material or matrix). The base material can also have micro and nano reinforcement elements (e.g., alumina and carbon nanotubes) [28]. Other cellular materials like some syntactic foams can be formed by two solid phases (material from the porous particles/hollow spheres and interstitial material) and a discontinuous or continuous gaseous phase (e.g., pores from filler particle) [39].

**Figure 2.** Closed-cell foam (cross section: 20 mm × 20 mm) (**a**) and syntactic foam (diameter: 30 mm) (**b**).

Several material characterization techniques are normally used to characterize them. Microstructure, morphology formed phases/precipitates within matrix are usually analyzed by optical microscopy, scanning electron microscopy (SEM), X-ray diffraction (XRD), energy-dispersive x-ray spectroscopy (EDS), and atomic force microscopy (AFM). Formed phases, precipitates, fibers, and particles can also be investigated to some extent with nanotomography [44].

AFM is used to achieve a correlation between the surface roughness with the precipitated phase density in metallic matrix. Nano and micro indentation testers are used to determine the parameters like the stiffness and Vickers hardness of the matrix. XRD is used to identify and determine the various crystalline forms.

The morphometric parameters of the cellular metals such as a mean cell size and cell size distribution, fraction of solid, connectivity between cells, cell orientation, and porosity can be measured by a non-destructive technique, X-ray microcomputed tomography (μCT). This technique has revealed a power tool to characterize the cellular structure of these materials [45–47], but also to study their deformation behavior [48–50] and to develop numerical models to predict the mechanical, thermal and acoustic behavior. There are many different μCT scanners on the market, each having different capabilities, namely the resolution, maximum energy level, different filter options, stage set up and internal chamber area.

The equipment is composed of an X-ray source, a motor controlling rotating stage (where the specimen is mounted) and a detector (Figure 3a). The specimen is mounted between the X-ray source and the detector panel and projections are taken after each degree of rotation. Flat panel is an example of a commercial detector which is composed by an array of discrete sensors arranged as a matrix. The response of each sensor is proportional to the radiation energy that reaches its surface and is captured. The capture of data from each discrete part produces a 2D projection/scanned image (Figure 3a) that is converted into a digital image and, thus, is immediately visualized on a computer.

**Figure 3.** Scheme of the X-ray microcomputed tomography (μCT) equipment and an open-cell aluminum foam (height: 20.4 mm; diameter: 18.9 mm) (**a**) and showing and showing raw scans/projections, segmented images, reconstructed structure, and real photo (**b**).

The μCT principles are based on an X-ray source, which produces the X-ray emission that passes across the specimen and is projected on a digital detector, measuring the attenuation of the X-rays and producing a radiograph (known as scanned or projection image, Figure 3). The quality of the images mainly depends on the partial absorption and differential absorption that occurs during the scanning step. The partial absorption is associated to the absorption of some X-rays by the specimen and the transmission of others to the detector. The differential absorption refers to the absorption characteristics of the different materials to be scanned. For example, in the case that there is no differential absorption, the specimen result comes out as a uniform gray level (no contrast). Usually, it is difficult to distinguish the different materials within the specimen. Both (partial and differential) absorptions are influenced by several aspects, such as the size of the specimen and the chemical composition of the materials that are made which the X-rays have to pass. The projection images are taken incrementally over a total rotation (180◦ or 360◦). The projection images (Figure 3a) are then processed using a computer software, producing a series of reconstructed images (2D slices) that allow to observe the internal structure of the object. Basically, the μCT data analysis is divided in four main steps, which are scanning, segmentation, reconstruction and visualization, as shown in Figure 3b. To optimize the image quality during these steps, it is necessary to adjust several parameters like magnification, incident X-ray intensity, filter type (e.g., no filter, copper, and aluminum), rotation step and acquisition time, and threshold.

There are many commercial software tools (e.g., NRecon v.1.7.3.1, Bruker, Kontich, Belgium; Octopus 8.6, Inside Matters BVBA, Aalst, Belgium and Phoenix datos, GE Sensing & Inspection Technologies GmbH, Wunstorf, Germany) that include the filtering (artefacts) and smoothing of the μCT data to enhance the quality of the images. Threshold segmentation converts a grey value image into a binary one. The resulting image then comprises two sets: one represents the background (e.g., black), the other one the object (e.g., white). This image binarization/segmentation procedure is an essential step in which the different phases/constituents using thresholding algorithms to measure the grayscale values in the μCT images are distinguished.

The reconstructed μCT images can be used for volume rendering of tomographic data, creating 3D models (Figure 4) using numerous available software tools, e.g., CTAn, CTvox, CTVol, VGStudio, and Avizo. The data visualization includes the mapping and the rendering of the results.

**Figure 4.** Volume rendering showing the cellular structure and the dense metal skin covered a closed-cell foam (width: 20 mm) with color by local structure separation, a measure of pore size.

The μCT can also be used to study the deformation and failure mode of these materials using ex-situ and in-situ tests. Ex-situ tests use specimens previously subjected to a mechanical test in a universal testing machine. In-situ imaging is performed inside μCT scanner using a material testing stage that allows the study of the deformation and failure behavior. The specimen is placed into the material testing stage (MTS) chamber and an accurate force, measured by a load cell, is applied to the specimen. The resulting deformation is measured by a precision displacement sensor. During scanning, the loading curve is displayed on the screen in real time.

Figure 5 shows a force–displacement curve of a closed-cell foam compressed with MTS up to 1540 N and 11 mm displacement, showing the collapse of pores of cellular structure.

**Figure 5.** Force–displacement curve, showing the three orthogonal reconstructed slices (from Bruker's Data Viewer software [51]) of a closed-cell foam (cross section: 15 mm × 15 mm).

The μCT is also used together with finite element modelling [52,53] to develop the numerical models to describe and predict different process parameters and the mechanical, acoustic, and thermal behavior of the cellular materials, studying the different geometrical parameters. Finite element method (FEM) models can help to select the best microstructure for a given property (then for a given application) without the traditional, complex, time consuming, and labor-intensive experimental tests. The μCT scanned images are reconstructed using algorithms (e.g., filtering and smoothing) and software like NRecon (Bruker, Belgium). The μCT scanned images are used to create FEM meshes (Figure 6).

**Figure 6.** Finite element method (FEM) meshes of aluminum closed-cell foam (cross section: 10mm ×10mm). Courtesy of Diogo Heitor, Universidade de Aveiro, Portugal.

After segmentation, geometry cleanup, and refinement the model can be discretized and analyzed in a software (e.g., Abaqus, ANSYS). The geometrical properties of the mesh elements are based on the actual structure of the solid phase measured in the μCT image [54,55].

#### **3. Mechanical Characterization**

Mechanical characterization provides an insight into the mechanical response of cellular metals when subjected to various loading conditions. For this purpose, mechanical tests are being used. They allow to determine the deformation mechanics and mechanical properties of various types of cellular materials and structures. The tests can vary with respect to loading conditions (e.g., type, direction, and velocity), tested materials and expected results. Most commonly, mechanical tests are carried out by experimental or numerical (computational) methods, as the complexity of the cellular structure usually exceeds the efficiency and applicability of the analytical approach.

#### *3.1. Experimental Methods*

The most frequently applied experimental method for cellular metals is the uniaxial compressive test [56–59] because: (i) cellular metals are in applications often subjected to compressive loading and (ii) this type of test is straightforward, cost-effective and has minimum time requirements (short preparation time). From the compressive tests, the force-displacement (engineering/true stress–strain) diagrams can be obtained via load cells (or additional sensors) and the deformation behavior by visual capturing. Regardless of the type of the cellular metal, porosity or relative density (influences the elastic modulus, plastic strength, and energy absorption [60], base material, topology, and morphology (e.g., cell size effect [61], graded porosity [62]), a characteristic compressive behavior can be observed (Figure 7), which can be distributed in four main sections. Quasi-linear response (i) represents the initial stiffness of the cellular metal and is followed by transition zone (ii), where the cellular structure constituents (cell walls and struts) start to compress, bend, or stretch, resulting in local yielding. After additional loading, the stress–strain curve flattens into the stress plateau (iii). The stress is kept almost constant due to bending, buckling, stretching, and crushing of the cellular structure up to densification (iv), where the stiffness increases and approaches the base material properties at full compaction. The most important mechanical properties are initial stiffness, stress plateau σ*pl* (in cellular metal literature also sometimes referred to as yield stress, yield strength), densification strain ε*d*, and energy absorption capacity (grey area under the stress–strain curve).

**Figure 7.** Characteristic compressive behavior of cellular materials.

The other types of mechanical tests involve bending [43,63], tensile [59,64], shear [59] and torsion load. The described loading types can be also combined into multiaxial loading conditions (to define e.g., multiaxial loading/stress states [59], yield surfaces [65]). For these tests, longer preparation time for specimen preparation and setting up the experimental device is usually needed.

The cellular specimens can be during the tests subjected to quasi-static or dynamic (monotonic or cyclic [66–68]) loading. According to [69], the quasi-static loading is considered for strain rates up to approx. 5 s<sup>−</sup>1. During compressive loading, three different deformation modes (in respect to critical velocities) can occur [70]: homogeneous, transitional, or shock mode. For the homogeneous mode at low loading velocities, it is common that the material starts to deform at its weakest point (negligible effect of inertia), while at the shock mode the main deformation takes place at the loading surface, regardless to the position of the weakest point in the material (substantial effect of inertia and strain rate sensitivity). In addition to dynamic servo-hydraulic testing machines other testing methods are also being used to achieve higher strain rates, e.g., drop towers, Taylor tests, Split–Hopkinson Pressure Bar (SPHB) tests [71].

The deformation mechanics and collapse mechanisms can be monitored by recording the visual data. For this purpose, cameras with a sufficient frame rate must be used, especially for the high-velocity testing. The deformation behavior can additionally be monitored and analyzed by e.g., digital image correlation (DIC) techniques (e.g., ARAMIS and GOM Correlate [72]), ex- and in-situ μCT (see Section 2), infrared thermography (see Section 4).

#### *3.2. Numerical Methods*

In the last two decades, numerical methods became a useful tool to supplement the mechanical characterization of various types of cellular metals. They can be used before experimental testing to reduce the number of specimens and experimental tests by predicting the mechanical response or after to validate computer models and reduce the number of further experimental tests. In some cases, computer simulations provide additional insight into the deformation behavior of cellular metals since they also provide data for material points inside the specimens. In solid mechanics, the finite element method (FEM) is the most used tool for analyzing the mechanical behavior of materials and structures subjected to different types of loading conditions [73]. Advanced quasi-static and dynamic numerical models of cellular structures allow to simultaneously account for material (e.g., strain rate dependent elasto-plasticity with damage and failure), geometrical (e.g., large deformation) and structural (e.g., contact and changing boundary conditions) nonlinearities. There are several ways how to model and discretize a cellular metal. The structure can be discretized in a detail (using beam [74], shell [75], or solid [76] finite elements, usually resulting in longer computational times) or as a homogenized material (most commonly as solid finite elements, resulting in shorter computational times). The geometry of the detailed computer models is either -based on computer aided design (for regular and simple cellular geometries) or μCT-based (for irregular and complex cellular structures [55]), as described in Section 2. In the case of homogenized models, the volume of the complex foam structure is simply fully discretized with solid finite elements (structured mesh) with proper constitutive relation, e.g., crushable foam [77]. If a regularity or periodicity can be found in the cellular structure, a part of the structure can be represented with a unit cell (representative volume element—RVE [78]) and proper boundary conditions, which drastically decreases the computational time. In addition to the finite element method, also some other numerical methods can be used to study the mechanical properties with highly effective accuracy and time consumption ratio, e.g., discrete element method (DEM) [79]. Numerical methods are also a very efficient tool for performing parametric studies (varying topology and morphology of the cellular structure). Furthermore, specific effects in the mechanical behavior can be easily isolated and studied. Their influence can be analyzed by changing one single or several material or geometric parameters. Additional possibilities and applicability of numerical methods represent topological optimization and current trends and development of additive manufacturing and other production techniques allowing fabrication of pre-designed cellular metals targeted for specific applications in various industries [80–84]. Although it is usually easier to predict the behavior of pre-designed structures (performing numerical simulations before the fabrication), special care should be taken to account for the additive manufacturing effects, e.g., surface roughness [85,86] (crucial also for studying the osseointegration [87]) and balling [88–90].

#### **4. Infrared Thermography**

Infrared (IR) thermography is a non-destructive testing method and already part of engineering norms and standard procedures [91–93] applicable in evaluation of dynamic deformation process of cellular materials. As cellular materials are often used as energy absorption structural elements, such components are mostly loaded in compression, where a compression yield plateau is characterizing the force-displacement, i.e., energy absorption response. It is common to use compression tests and evaluation at loading rates starting from quasi-static to dynamic and impact velocities. To understand the deformation scenario and what locally happens with cellular specimen, the strain at the specimen's surface is relevant. The passive IR thermography [91,94] is similar to the digital image correlation (DIC), both applicable to such testing as these methods are providing strain distribution during loading process. In references [95–99], it is shown how thermal image is comparable to effective strain obtained by DIC. In [95], we have shown for the first time the similarity of strain pattern and thermal image on a simple tension example, while in [96], more profound evaluation including tension and three-point bending is provided. Both methods provide strain pattern (field) on specimen surface and deformation of energy absorbing material, energy is mostly converted to the heat, thermal image reveals, where the energy is locally transformed, where yielding occurs, where plastic strain is created and how plastification zones spread through the specimen [96,97]. The thermographic approach, where DIC is combined with IR thermography has been adopted also by other authors [98,99]. IR thermography is not applicable at quasi-static to low-rate dynamic loading velocities as the heat dissipates trough material, what makes the DIC a more appropriate method. For higher loading rates DIC is requiring faster CCD cameras, where the available hardware limits the ability to obtain clear images relevant for surface pattern recognition, as reported in [96–99]. Contrary to DIC, higher heat generation with less dissipation enables better IR images with lower integration time. Importantly, IR hardware has specific acquisition rate characteristics. Most appropriate are middle-wave IR focal point array detectors (e.g., InSb detector) cooled to cryogenic temperatures [92]. Such detector enables approximately 150 fps of clear images for full resolution (when data from all detector's pixels are acquired) up to 1000 fps for reduced size image resolution (when reduced number of data from detector are used, so called window). Focal Point Array detectors of cooled middle wave (MW) IR cameras are capable to acquire data for high frame rate. To transfer all data from detector to computer, windowing (reducing active pixels) enables higher frame rates, with a drawback of recording just a portion of full frame image. For the FLIR SC 5000 MW camera (FLIR Systems Inc., Portland, OR, USA) with InSb, Focal Point Array detector was used in this research, with full size of 320 × 265 pixels, while minimum window size enabling faster frame rates with 160 × 128 pixels and 64 × 120 pixels. Although, there are MW cameras capable of acquiring 35,112 fps for a strip for reduced window size (64 × 4 pixels), it has been proven that the above mentioned camera provides for reliable observation of cellular metals dynamic deformation behavior. The method based on IR thermography is not limited to any particular type of cellular material. Various types of cellular metals can be evaluated, e.g., open- and closed-cell foams, advanced pore morphology (APM) foam elements, syntactic foams, pre-designed cellular structures [25,100]. Typical conclusions that can be drawn are, e.g., where yielding is initialized, how plastification fronts propagate, where densification occurs. This was shown in the previous research [25,100] related to thermography in experimental testing of porous materials.

It is a full field method and the temperature image can be processed as a thermal gradient image [97], giving information about direction of thermal change. Thus, from a single thermal image it can be concluded what is happening with a specimen (Figure 8). The example in Figure 8 shows the case of dynamical compression of a syntactic aluminum specimen (diameter: 26.9 mm; height: 43.2 mm). Infrared images are showing the specimen's surface, where generated heat is representing energy dissipated during compression process and, thus, the source of plastic deformation and collapse. IR camera acquisition rate was 489 Hz. IR images present specimen's deformation at a strain increment of approximately 10%.

**Figure 8.** Photo and Infrared (IR) image of aluminum syntactic specimen compressed at the rate of 284 mm/s.

#### **5. Thermal Characterization**

Thermal characterization methods of cellular metals predominantly address their thermal conductivity and heat capacity. The heat capacity is readily determined based on foam density and the heat capacity of the metallic matrix. Hence, this overview concentrates on commonly used measurement techniques for the effective thermal conductivity of cellular metals. All methods are summarized in Table 1. Techniques can be differentiated into transient and steady-state methods. In general, transient methods are faster, permit simpler setups, and can operate within a narrow temperature band. Steady-state methods are highly accurate and permit directional measurements (thermal anisotropy) yet often require complex equipment and significant temperature gradients. A challenge that affects all experimental techniques is thermal contact resistance. Cellular metals are particularly susceptible to thermal contact resistance due to their porous surfaces and resulting small contact areas. Failure to minimize and/or consider thermal contact resistance will result in an underestimation of the effective thermal conductivity. Mitigation strategies include the application of compressive force, thermal paste, and soft metallic foils at the interphases of samples, sensors, heaters, and cooling elements.

#### *5.1. Transient Methods*

The well-established hot wire method [101,102] is not commonly used for cellular metals. In order to measure the effective thermal conductivity of cellular metals, a representative volume element (RVE) must be considered. The relatively small sample volume that is affected by hot wire measurements often does not meet this requirement. Instead, transient hot strip (THS), transient hot disc (THD), or transient hot plane (THP) methods with larger planar sensors are utilized [103–109]. In all cases, a wire is attached to a carrier material and acts simultaneously as the sensor (measuring the variation of electrical resistance) and the heat source. The planar sensor must be positioned between two samples and the measured thermal diffusivity is an average value of both samples. The evaluation of these methods is relatively complex and requires the solution of Fourier's differential equation [110]. The intermediate result is the effective thermal diffusivity, which can be converted into an effective thermal conductivity using the foam's density and specific heat capacity. Benefits of these transient methods are a minor temperature increase of only 1–5 K and the ability to measure thermal conductivities between 0.01–200 W/mK [111]. The maximum measurement temperature is limited by the carrier material and is currently about 800 ◦C [111].



Another commonly used transient method is laser flash measurement [112]. However, the complex geometry of the foam surface does not ensure a controlled energy transfer to the sample. In addition, sample sizes are often too small to achieve RVEs. Hence, this method is not usually applied for the characterization of cellular metals.

#### *5.2. Steady-State Methods*

Steady-state measurements impose a time-independent temperature gradient on a sample. Key benefits are a high accuracy, simple test evaluation and the ability to measure directional conductivities. In addition, heat flux passes through the entire sample facilitating measurements on RVEs. As a negative, a significant temperature gradient is required that complicates the measurement of the variation of thermal conductivity with temperature. Another disadvantage are the long measurement times required to ensure thermal steady-state, in particular for materials with low thermal diffusivities.

In absolute steady-state methods, the effective thermal conductivity is measured directly [113]. A commonly used method is the guarded hot plate [114–116]. The sample is positioned between a heating and a cooling element to generate a thermal gradient within the sample. After reaching steady-state, Fourier's law is used for the evaluation, i.e., . *Q* = *k*·*A*·Δ*T*/Δ*x*, where *k* is the effective thermal conductivity of the cellular metal, *A* is the sample cross section, and Δ*T*/Δ*x* the temperature gradient. In the guarded hot plate method, the heat flux . *Q* is determined as the energy input into the heating element at steady state. The term "guarded" describes the thermal isolation of the measurement setup to prevent convective and radiation heat losses. The Heat-Flow-Meter [115,117] resembles the guarded hot plate, however, instead of directly measuring the energy input into the heating element a heat flux sensor is positioned between the sample and the cooling element. The panel test technique [104,118–120] is another variation, where the heat flux is measured using a calorimeter that simultaneously acts as the cooling element. Compared to the guarded hot plate method, higher measurement temperatures can be achieved.

In relative steady-state methods, the thermal conductivity is measured relative to a reference material [121–124]. For increased accuracy, the thermal conductivities of the sample and the reference should be similar. In the cut bar method, the sample and either one or two reference bodies are stacked on a heating (cooling) element. The upper surface of the stack is brought into contact with a cooling (heating) element and usually a compressive force is applied to minimize thermal contact resistances within the stack. After reaching steady state, the reference bodies act as the heat flux sensors (similar to a heat-flow-meter) and Fourier's equation can be used for the evaluation.

#### *5.3. Numerical Methods*

In addition to the experimental methods outlined above, numerical analysis can be used to predict the effective thermal conductivity of metallic foams. An important step is the discretization of the typically complex cellular geometries. Unit cell models [125] and simplified model structures [126] suffice in some cases, however, improved accuracy can be obtained by deriving the numerical models from microcomputed tomography data [127,128]. Analogous to the experimental methods, transient or steady-state calculations can be performed. Due to the significantly higher computational cost of transient methods, almost exclusively steady-state analysis is selected. The two predominant numerical methods are the Finite Element Method (FEM) [125–128] and the Lattice Monte Carlo (LMC) method [129]. The result of the numerical analyses is typically a relative conductivity, i.e., the effective thermal conductivity is determined as a fraction of the matrix material. These numbers can readily be scaled for different type of matrices and temperatures. Comparison of effective thermal conductivities obtained by numerical analysis and experimental studies usually results in good agreement [129,130].

#### **6. Acoustic Characterization**

The acoustic characterization of the cellular metals is essential, since they are subjected to the noise and vibration applications (e.g., high resonance response). However, the knowledge and data are lacking for this type of materials. Few works have been published in this research topic [131–140]. The natural cork (100%) is an example of a natural cellular material widely used to minimize noise and vibration problems in mechanical systems, including industrial machines, appliances, vehicles, and buildings. The noise, vibration, and harshness (NVH) are one of the most fundamental issues for automotive industry. The NVH analysis has commonly two targets, which are to reduce and control noise and vibration for the benefits of users (occupants' comfort and environmental noise emission) and to minimize the effects of harsh forces and vibration on equipment (e.g., loosen joints and material fatigue). The vibrations are measured in two ways (frequency and amplitude) and expressed as waves per second (Hz). Vibrations that are felt are under 200 Hz, while vibrations between 20–20,000 Hz are audible by humans. Vibrations over 20,000 Hz are ultrasonic and not audible by humans.

The sound absorption coefficient (α), noise reduction coefficient (NRC), sound transmission loss, impact sound transmission and damping behavior (e.g., vibration frequencies, modes, and damping ratios) are examples of the parameters measured to characterize the acoustic properties of cellular metals.

The ability of a material to reduce sound reflections, reverberation, and echo within an enclosed space are determined based on the sound absorption coefficient and noise reduction coefficient. These are the parameters used to evaluate the sound absorption characteristics of the cellular materials and are assessed using an impedance tube according to the ASTM E1050 standard [141]. The cylindrical specimen is placed into the impedance tube (e.g., inner diameter: 37 mm) at one end, while a sound source consisting of a loudspeaker emitting a random noise is introduced at the other end of the tube [22,23]. Two microphones are placed into the tube between the sound source and the studied specimen to detect the sound pressure wave transmitted through the specimen and the wave portion that was reflected. The acoustic absorption coefficient is defined as a ratio of absorbed sound intensity in a given material and the incident sound intensity that is imposed on that material. The acoustic absorption coefficient varies from 0 (0% sound absorption) to 1 (100% sound absorption). The value 0 means no sound is absorbed, while the value 1 means the opposite. The noise reduction coefficient is calculated by defining an average of the sound absorption coefficients at the frequencies 250, 500, 1000, and 2000 Hz and rounding off the result to the nearest multiple of 0.05. The absorption and noise reduction values are also measured in a small echo chamber, either in sound transmission test or echo chamber.

The vibroacoustic behavior is measured by microphones (to measure sound pressure), accelerometers (to measure acceleration), and force/displacement/velocity transducers (to measure forces), in which the measurements are made by setting the instrument for a certain bandwidth and center frequency vibration analyzer, covering the values over that range. The ability to act as a barrier preventing airborne sound transmission from one space to another, sound transmission loss coefficient at 1/3 octave bands, will be performed according to the ASTM E90. The modal analyses are usually performed by vibration of specimens, exciting by a shaker or an impact hammer, measuring the response using a laser scanning vibrometer [140]. The time domain response and loss factor from their damped wave decay is determined using a spectral analyzer. The damping ratio of the resonance mode is determined using the half-power bandwidth method.

#### **7. Conclusions**

Different experimental and numerical characterization methods of the cellular metals are presented, i.e., different techniques to determine their structural, mechanical, thermal, and acoustic properties. The methodology, the experimental set-up, the equipment, and its principles and standards were summarized. The potential of non-destructive methods like X-ray computed tomography and infrared thermography are also presented.

X-ray microcomputed tomography is a powerful tool to characterize the complex cellular structure of cellular metals in terms of their structural morphometric parameters, to study their deformation and failure behavior and to develop numerical models to predict the mechanical, thermal, and acoustic behavior. Infrared thermography is a versatile tool well suited for the study of dynamic deformation processes of cellular metals (e.g., closed-cell foams, syntactic foams and metal hollow spheres structures) and filled profiles and sandwich panels based on cellular materials.

In general, there is a huge demand for experimental and computational characterization of physical properties of novel cellular metals. Thus, new opportunities for advances in new experimental techniques and computational modelling arise. Furthermore, computational modelling can help in designing new cellular materials (in combination with additive manufacturing) with desired properties and behavior demanded by an application.

**Author Contributions:** Conceptualization, I.D., T.F., L.K.-O., and M.V.; methodology, I.D., T.F., L.K.-O., and M.V.; software, I.D., T.F., L.K.-O., and M.V.; validation, I.D., T.F., L.K.-O., and M.V.; formal analysis, I.D., T.F., L.K.-O., and M.V.; investigation, I.D., T.F., L.K.-O., and M.V.; resources, I.D., T.F., L.K.-O., and M.V.; data curation, I.D., T.F., L.K.-O., and M.V.; writing—original draft preparation, I.D., T.F., L.K.-O., and M.V.; writing—review and editing, I.D., T.F., L.K.-O., and M.V.; visualization, I.D., T.F., L.K.-O., and M.V.; supervision, I.D., T.F., L.K.-O., and M.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by Portuguese Science Foundation (FCT): UIDB/00481/2020 and UIDP/ 00481/2020-FCT and CENTRO-01–0145-FEDER-022083 (Centro 2020 program-Portugal 2020).

**Acknowledgments:** Supports given by the Portuguese Science Foundation (FCT), UIDB/00481/2020 and UIDP/00481/2020-FCT and CENTRO-01–0145-FEDER-022083 (Centro 2020 program-Portugal 2020, Centro Portugal Regional Operational Partnership Agreement through the European Regional Development Fund).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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