Enhancement by Metallic Tube Filling of the Mechanical Properties of Electromagnetic Wave Absorbent Polymethacrylimide Foam

By the addition of a carbon-based electromagnetic absorbing agent during the foaming process, a novel electromagnetic absorbent polymethacrylimide (PMI) foam was obtained. The proposed foam exhibits excellent electromagnetic wave-absorbing properties, with absorptivity exceeding 85% at a large frequency range of 4.9–18 GHz. However, its poor mechanical properties would limit its application in load-carrying structures. In the present study, a novel enhancement approach is proposed by inserting metallic tubes into pre-perforated holes of PMI foam blocks. The mechanical properties of the tube-enhanced PMI foams were studied experimentally under compressive loading conditions. The elastic modulus, compressive strength, energy absorption per unit volume, and energy absorption per unit mass were increased by 127.9%, 133.8%, 54.2%, and 46.4%, respectively, by the metallic tube filling, and the density increased only by 5.3%. The failure mechanism of the foams was also explored. We found that the weaker interfaces between the foam and the electromagnetic absorbing agent induced crack initiation and subsequent collapses, which destroyed the structural integrity. The excellent mechanical and electromagnetic absorbing properties make the novel structure much more competitive in electromagnetic wave stealth applications, while acting simultaneously as load-carrying structures.


Introduction
Multi-functional designs of materials and structures, such as collaborative design of mechanical and electromagnetic (EM) wave absorption, which is critical in aircraft and aerospace applications, are more and more attractive and have been widely studied. Metamaterial absorber (MMA) is a kind of composite material, which usually consists of periodic artificial structures and dielectric substrates [1,2]. By transforming the electromagnetic wave energy into other forms (e.g., as thermal energy), MMA can exhibit electromagnetic wave absorption [3][4][5]. A frequency-selective surface (FSS) absorber consists of lossy resistive patches, and the performance of broadband absorbing can be easily obtained by reasonable design of the planar patterns [6][7][8]. Three-dimensional structures [9][10][11] were also developed for wide-band and wide-angle electromagnetic wave absorption, such as folded resistive patches [9] and honeycombs [12]. Such structures have excellent electromagnetic (EM) wave absorption

Measurement of Electromagnetic Wave Absorbtion
The electromagnetic wave absorption of the absorbent PMI foam was characterized by the measurement of reflection. As shown in Figure 2a, the measurement was carried out at the frequency of 2-18 GHz by using the free-space method in a microwave anechoic chamber at ambient temperature, through the test system based on an Agilent E8363B Network Analyzer. The electromagnetic wave reflection property of normal and absorbent PMI foams with the dimensions of 600 mm × 600 mm × 20 mm were measured. A metal plate with the same size of the specimen was employed as the back plate to avoid wave transmission. It is noted that the reflection from a metal plate used as a prototype should be firstly measured, for the sake of normalization.

Compressive Tests
The detailed parameters of normal and absorbent PMI foam specimens for compressive tests are listed in Table. 1. Quasi-static compression was carried out by an electronic universal testing machine (INSTRON-3382) at room temperature. The loading rate was fixed at 2 mm/min, with a nominal strain rate less than 10 −3 s −1 . The compressive strain of at least 75% was achieved for each specimen to ensure complete deformation and energy absorption. Digital images of each specimen were acquired to capture the deformation modes and explore the failure mechanisms. No less than three specimens in each case were measured in the tests to acquire the averaged mechanical properties.

Measurement of Electromagnetic Wave Absorbtion
The electromagnetic wave absorption of the absorbent PMI foam was characterized by the measurement of reflection. As shown in Figure 2a, the measurement was carried out at the frequency of 2-18 GHz by using the free-space method in a microwave anechoic chamber at ambient temperature, through the test system based on an Agilent E8363B Network Analyzer. The electromagnetic wave reflection property of normal and absorbent PMI foams with the dimensions of 600 mm × 600 mm × 20 mm were measured. A metal plate with the same size of the specimen was employed as the back plate to avoid wave transmission. It is noted that the reflection from a metal plate used as a prototype should be firstly measured, for the sake of normalization.

Compressive Tests
The detailed parameters of normal and absorbent PMI foam specimens for compressive tests are listed in Table 1. Quasi-static compression was carried out by an electronic universal testing machine (INSTRON-3382) at room temperature. The loading rate was fixed at 2 mm/min, with a nominal strain rate less than 10 −3 s −1 . The compressive strain of at least 75% was achieved for each specimen to ensure complete deformation and energy absorption. Digital images of each specimen were acquired to capture the deformation modes and explore the failure mechanisms. No less than three specimens in each case were measured in the tests to acquire the averaged mechanical properties.

Electromagnetic Wave Absorbtion
The electromagnetic wave absorptivity can be expressed as [11,26]: where A represents the electromagnetic wave absorptivity, while

Electromagnetic Wave Absorbtion
The electromagnetic wave absorptivity can be expressed as [11,26]: where A represents the electromagnetic wave absorptivity, while |S 11 | 2 and |S 21 | 2 represent the reflectivity and the transmissivity, respectively. Note that, in this calculation, S 11 and S 21 are linear values. Here, |S 21 | 2 is equal to 0, due to the employment of the metal backboard in the present measurement. Figure 2b shows the reflectivity of the vertical incident waves (S 11 ) at the frequency of 2-18 GHz. The average reflectivity of the absorbent PMI foam at the frequency of 4.9-18 GHz was less than −8 dB, which implies that the electromagnetic wave absorptivity A, calculated by Equation (1), can be larger than 85%. At the frequency of 5.2-7.3 GHz, 9.9-12.85 GHz, and 14.5-18 GHz, the reflectivity was even less than −10 dB, with the absorptivity larger than 90%. At the specific range of 6.25-6.55 GHz, the reflectivity decreased to less than −15 dB. In contrast, the electromagnetic waves were completely reflected by the normal PMI foam (see Figure 2b). This implies that the present absorbent PMI foam possessed good electromagnetic wave-absorbing properties.  Figure 3a compares the compressive stress versus strain curves of normal and absorbent PMI foams. All specimens exhibited foam-like features, i.e., the three typical regions including linear, plateau, and densification regions [34]. The absorbent PMI foam had similar density to the normal one, but the compressive strength σ peak (the first peak stress) and plateau strength were even less than half of those of the normal foam. It can be seen from Figure 4 that during the compressive process, cracks could be obviously observed in the absorbent PMI foam specimen, which caused subsequent collapses, while for the normal foam, only compaction occurred leading to densification. dB, which implies that the electromagnetic wave absorptivity A, calculated by Equation (1), can be larger than 85%. At the frequency of 5.2-7.3 GHz, 9.9-12.85 GHz, and 14.5-18 GHz, the reflectivity was even less than −10 dB, with the absorptivity larger than 90%. At the specific range of 6.25-6.55 GHz, the reflectivity decreased to less than −15 dB. In contrast, the electromagnetic waves were completely reflected by the normal PMI foam (see Figure 2b). This implies that the present absorbent PMI foam possessed good electromagnetic wave-absorbing properties. Figure 3a compares the compressive stress versus strain curves of normal and absorbent PMI foams. All specimens exhibited foam-like features, i.e., the three typical regions including linear, plateau, and densification regions [34]. The absorbent PMI foam had similar density to the normal one, but the compressive strength peak σ (the first peak stress) and plateau strength were even less than half of those of the normal foam. It can be seen from Figure 4 that during the compressive process, cracks could be obviously observed in the absorbent PMI foam specimen, which caused subsequent collapses, while for the normal foam, only compaction occurred leading to densification.

Enhancement of Compressive Strength
(a) (b)   dB, which implies that the electromagnetic wave absorptivity A, calculated by Equation (1), can be larger than 85%. At the frequency of 5.2-7.3 GHz, 9.9-12.85 GHz, and 14.5-18 GHz, the reflectivity was even less than −10 dB, with the absorptivity larger than 90%. At the specific range of 6.25-6.55 GHz, the reflectivity decreased to less than −15 dB. In contrast, the electromagnetic waves were completely reflected by the normal PMI foam (see Figure 2b). This implies that the present absorbent PMI foam possessed good electromagnetic wave-absorbing properties. Figure 3a compares the compressive stress versus strain curves of normal and absorbent PMI foams. All specimens exhibited foam-like features, i.e., the three typical regions including linear, plateau, and densification regions [34]. The absorbent PMI foam had similar density to the normal one, but the compressive strength peak σ (the first peak stress) and plateau strength were even less than half of those of the normal foam. It can be seen from Figure 4 that during the compressive process, cracks could be obviously observed in the absorbent PMI foam specimen, which caused subsequent collapses, while for the normal foam, only compaction occurred leading to densification.

Enhancement of Compressive Strength
(a) (b)   A metallic tube was employed as a filler to improve the poor compressive performance of the absorbent PMI foam. Figures 5a and 6a present the typical stress-versus-strain curves of the tube-enhanced normal and absorbent PMI foams, respectively. It is shown that filling of both aluminum and 304 stainless steel tubes led to significant enhancement of the compressive performances of both normal and absorbent PMI foams. The tube-enhanced PMI foams still underwent foam-like features but exhibited some obvious fluctuations in the plateau region. The jagged stress-versus-strain curves presented multiple peaks and valleys before densification. Each stress peak and valley were related to one folding (i.e., progressive buckling deformation [23,35]), which could be demonstrated through the buckling deformation mode layer by layer, as shown in Figure 7d. Moreover, internal filling of the PMI foam into 304 stainless steel tube (specimen 9) led to a significant increase of the compressive strength of the tube-enhanced absorbent PMI foam, while no obvious improvement could be seen in the case of the aluminum tube-enhanced foam (specimen 7). This may be attributed to the fact that the wall thickness of the 304 stainless steel tube (0.2 mm) was smaller than that of the aluminum tube (0.5 mm), and the buckling mode of the tube with the thinner wall could be more easily affected by the internal filling of foam. Therefore, the internal filling of foam changed the buckling mode of the 304 stainless steel tube and led to the increase of compressive strength.
A metallic tube was employed as a filler to improve the poor compressive performance of the absorbent PMI foam. Figure 5a,6a present the typical stress-versus-strain curves of the tube-enhanced normal and absorbent PMI foams, respectively. It is shown that filling of both aluminum and 304 stainless steel tubes led to significant enhancement of the compressive performances of both normal and absorbent PMI foams. The tube-enhanced PMI foams still underwent foam-like features but exhibited some obvious fluctuations in the plateau region. The jagged stress-versus-strain curves presented multiple peaks and valleys before densification. Each stress peak and valley were related to one folding (i.e., progressive buckling deformation [23,35]), which could be demonstrated through the buckling deformation mode layer by layer, as shown in Figure 7d. Moreover, internal filling of the PMI foam into 304 stainless steel tube (specimen 9) led to a significant increase of the compressive strength of the tube-enhanced absorbent PMI foam, while no obvious improvement could be seen in the case of the aluminum tube-enhanced foam (specimen 7). This may be attributed to the fact that the wall thickness of the 304 stainless steel tube (0.2 mm) was smaller than that of the aluminum tube (0.5 mm), and the buckling mode of the tube with the thinner wall could be more easily affected by the internal filling of foam. Therefore, the internal filling of foam changed the buckling mode of the 304 stainless steel tube and led to the increase of compressive strength.  absorbent PMI foam. Figure 5a,6a present the typical stress-versus-strain curves of the tube-enhanced normal and absorbent PMI foams, respectively. It is shown that filling of both aluminum and 304 stainless steel tubes led to significant enhancement of the compressive performances of both normal and absorbent PMI foams. The tube-enhanced PMI foams still underwent foam-like features but exhibited some obvious fluctuations in the plateau region. The jagged stress-versus-strain curves presented multiple peaks and valleys before densification. Each stress peak and valley were related to one folding (i.e., progressive buckling deformation [23,35]), which could be demonstrated through the buckling deformation mode layer by layer, as shown in Figure 7d. Moreover, internal filling of the PMI foam into 304 stainless steel tube (specimen 9) led to a significant increase of the compressive strength of the tube-enhanced absorbent PMI foam, while no obvious improvement could be seen in the case of the aluminum tube-enhanced foam (specimen 7). This may be attributed to the fact that the wall thickness of the 304 stainless steel tube (0.2 mm) was smaller than that of the aluminum tube (0.5 mm), and the buckling mode of the tube with the thinner wall could be more easily affected by the internal filling of foam. Therefore, the internal filling of foam changed the buckling mode of the 304 stainless steel tube and led to the increase of compressive strength.
(a) (b)  The averaged elastic modulus E and the compressive strength σ peak are summarized in Table 2. For the absorbent PMI foam, filling with the metallic tube only contributed a little to the increase of density (less than 5.3%) but increased the elastic modulus E of the normal PMI foam by 77.7% (specimen 3), and that of the absorbent PMI foam by 128% (specimen 9). Moreover, the peak compressive strength σ peak was increased by 18.3% (specimen 4) for the normal PMI foam, and surprisingly by 133.8% (specimen 9) for the absorbent PMI foam. The averaged elastic modulus E and the compressive strength peak σ are summarized in Table 2. For the absorbent PMI foam, filling with the metallic tube only contributed a little to the increase of density (less than 5.3%) but increased the elastic modulus E of the normal PMI foam by 77.7% (specimen 3), and that of the absorbent PMI foam by 128% (specimen 9) . Moreover, the peak compressive strength peak σ was increased by 18.3% (specimen 4) for the normal PMI foam, and surprisingly by 133.8% (specimen 9) for the absorbent PMI foam.

Enhancement of Energy Absorption
The energy absorption capacity is commonly characterized by energy absorption per unit volume W v : The energy absorption per unit volume W v as a function of compressive strain of the PMI foam, tube-enhanced PMI foam, and tube-enhanced absorbent PMI foam, is shown in Figure 3, Figure 5b, and Figure 6, respectively, and the calculated W v at ε = 0.5 are summarized in Table 2. As shown in Figure 3b, the absorbent PMI foams were not as effective as the normal ones in energy absorption, for the electromagnetic absorbing agent addition in PMI foam caused an increase of brittle features, which decreased the compressive strength. It was found that the tube filling influenced the energy absorption of both normal and absorbent PMI foams.
In addition, the specific energy absorption (SEA) was another important parameter in weight-sensitive applications, which could be defined as averaged energy absorption per unit mass [34]: The W m of the specimens are also shown in Table 2. For normal PMI foams (specimens 1-4), the energy absorption per unit volume W v and per unit mass W m by filling the metallic tube was increased by 18% (specimens 3 and 4) and 6.7% (specimen 4), respectively. A much more obvious enhancement was found for the tube-enhanced absorbent PMI foams (specimens 5-9): W v and W m of tube-enhanced absorbent PMI foams were increased by 54.2% (specimen 9) and 46.4% (specimen 9), respectively. Figure 7 presents the specimen images of the normal PMI foam, tube enhanced, and foam-filled tube-enhanced PMI foams after compression. For all three kinds of specimens, the structural integrity could be well ensured. During the compressive process, the normal PMI foam underwent compaction and densification, showing ductile collapse. In contrast, the absorbent PMI foam exhibited brittle collapse, with cracking and delamination occurring due to the addition of the electromagnetic absorbing agent. As shown in Figure 8, the specimens were all damaged completely after compression (with compressive strain over 75%) and broken into small pieces of different sizes. In local fractography in Figure 8d, the interfaces between the foam and the absorbing agent of the absorbent PMI foam can be seen clearly. The poor interfaces with weak bonding strength were more prone to initiate a crack, leading to delamination and subsequent collapse of the specimen. Figure 8e,f show the fracture surfaces of the absorbent PMI foam with different magnifications.

Failure Mechanism
Adding the absorbing agent improved the electromagnetic wave absorption of the absorbent PMI foam. Meanwhile, the weaker interfaces between the foam and the absorbing agent also decreased its mechanical properties. Therefore, the present effective enhancement approach by metallic tube filling is of great significance for engineering applications.

Comparison
The specific compressive strength peak c Y σ ρ σ (here, Y σ refers to the yielding strength of the metallic tubes) and energy absorption per unit mass m W (SEA) of the present tube-enhanced normal and absorbent PMI foams were compared with those of other competing metallic sandwich cores [36]. As shown in Figure 9, the present tube-enhanced PMI foams were quite competitive especially in energy absorption. Compared with other metallic lattice cores, which have shown significant advantages in load-carrying applications [37,38], the present tube-enhanced PMI foam seemed more effective. By optimizing the design of the geometric parameters in the future, the present tubereinforced structure will be more competitive.

Comparison
The specific compressive strength σ peak /ρ c σ Y (here, σ Y refers to the yielding strength of the metallic tubes) and energy absorption per unit mass W m (SEA) of the present tube-enhanced normal and absorbent PMI foams were compared with those of other competing metallic sandwich cores [36]. As shown in Figure 9, the present tube-enhanced PMI foams were quite competitive especially in energy absorption. Compared with other metallic lattice cores, which have shown significant advantages in load-carrying applications [37,38], the present tube-enhanced PMI foam seemed more effective. By optimizing the design of the geometric parameters in the future, the present tube-reinforced structure will be more competitive.

Conclusions
In conclusion, a PMI foam was endowed with the property of electromagnetic wave absorption by adding an electromagnetic absorbing agent during the foaming process, to form a novel absorbent PMI foam. Metallic circular tubes, made of 6061 aluminum alloy and 304 stainless steel, were chosen as the fillers to enhance the mechanical performance of the normal and absorbent PMI foams. The properties of electromagnetic wave absorption, as well as compressive strength and energy absorption, were experimentally investigated. The main findings are summarized as follows: (1) The absorbent PMI foam exhibited good electromagnetic wave absorption, with electromagnetic wave absorptivity larger than 85% at a large frequency range of 4.9-18 GHz. The absorptivity even exceeded 90% at a specific range of frequency.
(2) During the compressive process, the normal PMI foam underwent compaction and densification, showing ductile collapse. In contrast, the absorbent PMI foam exhibited brittle collapse, with cracking and delamination occurring due to the addition of the electromagnetic absorbing agent.
(3) A filling of metallic tubes increased the mechanical properties of both normal and absorbent PMI foams, and the enhancement was greater for the absorbent PMI foam. The elastic modulus E , compressive strength peak σ , and energy absorption per unit volume v W and per unit mass m W of the tube-enhanced absorbent PMI foam could be increased by 127.9%, 133.8%, 54.2%, and 46.4%, respectively, with the density increasing only by 5.3%. Filling with a 304 stainless steel tube was more effective than filling with an aluminum tube.
(4) With their outstanding performances in electromagnetic wave absorption, compressive strength, and energy absorption, the proposed tube-enhanced absorbent PMI foam is quite competitive in applications such as simultaneous electromagnetic wave stealth, load carrying, and impact resistance.  Acknowledgments: Special thanks should be given to Hunan Zihard Material Technology Co. Ltd for the supply of the PMI foams.

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

Conclusions
In conclusion, a PMI foam was endowed with the property of electromagnetic wave absorption by adding an electromagnetic absorbing agent during the foaming process, to form a novel absorbent PMI foam. Metallic circular tubes, made of 6061 aluminum alloy and 304 stainless steel, were chosen as the fillers to enhance the mechanical performance of the normal and absorbent PMI foams. The properties of electromagnetic wave absorption, as well as compressive strength and energy absorption, were experimentally investigated. The main findings are summarized as follows: (1) The absorbent PMI foam exhibited good electromagnetic wave absorption, with electromagnetic wave absorptivity larger than 85% at a large frequency range of 4.9-18 GHz. The absorptivity even exceeded 90% at a specific range of frequency.
(2) During the compressive process, the normal PMI foam underwent compaction and densification, showing ductile collapse. In contrast, the absorbent PMI foam exhibited brittle collapse, with cracking and delamination occurring due to the addition of the electromagnetic absorbing agent.
(3) A filling of metallic tubes increased the mechanical properties of both normal and absorbent PMI foams, and the enhancement was greater for the absorbent PMI foam. The elastic modulus E, compressive strength σ peak , and energy absorption per unit volume W v and per unit mass W m of the tube-enhanced absorbent PMI foam could be increased by 127.9%, 133.8%, 54.2%, and 46.4%, respectively, with the density increasing only by 5.3%. Filling with a 304 stainless steel tube was more effective than filling with an aluminum tube.
(4) With their outstanding performances in electromagnetic wave absorption, compressive strength, and energy absorption, the proposed tube-enhanced absorbent PMI foam is quite competitive in applications such as simultaneous electromagnetic wave stealth, load carrying, and impact resistance.