3D printed functionally graded foams response under transverse load

The applications of 3D printing are rapidly increasing in aerospace and naval applications. Nonetheless, 3D printing (3DP) of graded foams exhibiting property variation along the thickness direction is yet to be explored. In the current work, the different volume fractions of hollow glass micro balloon (GMB) reinforced high-density polyethylene (HDPE) composite based graded foams are 3D printed using the fused deposition modelling (FDM) technique. The bonding between successive layers and porosity distribution of these graded configurations are studied using micro-CT scan. Further, the 3D Printed functionally graded foams (FGFs) are tested for flexural response, and results are compared with numerical values. The micro-CT results showed delamination absence between the layers. In neat HDPE layers, porosity is not evident, while minor porosity creeps in the layers having the highest GMB content. Experimental results of the flexural test showed that the graded sandwiches exhibited better strength than the graded core alone. Compared to neat HDPE, the modulus of FGF-2 (H20 – H40 – H60) increased by 33.83%, implying better mechanical stiffness. Among all the FGFs, FGF-2 exhibited a better specific modulus. A comparative study of experimental and numerical results showed a slight deviation due to neglecting the induced porosity.


Introduction
Material developed by combining two or more materials is called composite.Based on the selection of matrix material, they are classified into metal, ceramic and polymer composites.Based on the reinforcement size (filler/fibre) they are further classified into micro and nanocomposites.Metal matrix composites (MMC) are used in tribological and electronic industries [1][2][3].Polymer composite is used in various weight sensitive applications [4,5].Sandwich structures are widely used in structural applications.Sandwich structures comprise top and bottom face sheets and a lightweight core.The main aim of the lightweight core is to enhance flexural stiffness while keeping the overall weight lower.These sandwiches are used in many applications of aerospace industries, building panels, refrigerators, and automobile industries [6][7][8][9][10].Their properties are governed by the skin/core material and their interface.Comprehensive material options for the skin and core increased the scope of research on these sandwiches and their failure characteristics.The primary failure, most frequently observed in these structures, is delamination between skin and core [11,12].This might be due to sharp material property transition at the skin and core interface.The aim of minimizing this sudden property transition at the skin and core interface is to replace the plain core with functionally graded materials (FGMs), wherein the material composition is varied spatially.The Japanese introduced these FGMs in 1984 for their space plane project [13].These graded structures are named non-homogeneous, where the material property is a function of thickness f(x) (x -thickness), i.e., varying material properties along the thickness direction.The introduction of FGMs made researchers develop different processing methods for fabricating them and studying the FGM behavior concerning loading conditions, failure mechanisms, etc.Besides all the research done so far, analysis of 3D printed FGMs is still fancy due to its wide range of applications in aeronautics, naval, and space regimes [14].Numerous studies on FGMs have been carried out using analytical and numerical methods in addition to limited experimental investigations [15][16][17].FGMs have been realized using powder metallurgy, gas-based, liquid, and solid processes [18,19].Metal based FGMs utilize processes like physical, chemical vapour deposition and additive manufacturing [20][21][22][23].Comprehensive material options for this skin and core increased the scope of research on FGMs and their failure characteristics.The interface strength of the skin and lightweight core can be further improved by opting for all-at-once or one-go/in-situ processing methods like 3D printing and prompted towards the present effort in developing all at once printed sandwiches with a graded lightweight core leading to the lower lead time, minimized human effort/interventions, and minimum failure probability of skin-core interfaces.
Additive manufacturing (AM) is a layered deposition process wherein three-dimensional object/part/component is realized without tooling [24].It can potentially develop a physical component from a digitally encoded design by depositing material through a deposition head/nozzle.AM is divided into several types according to the energy source and material flexibility.Direct energy deposition method (DED), powder bed fusion (PBF), VAT polymerization, and material extrusion is classified based on the form of material feed and energy.DED and PBF processes are mostly used in processing metal composites.Fused deposition modelling is extrusion based AM technique used predominantly for polymers [21].In this method, the filament fed through the heated nozzle gets melted in the thermal heater block (extrusion head) and deposited on the build platform per nozzle motion to develop a desired part in 3D [25].It is a fusion process wherein one material layer is fused with another.Hence, properly bonding between the skin and core interface can be established, avoiding delamination and enhancing part quality.Moreover, the entire part (sandwich composite) can be printed in a single stretch without expensive bonding methods.Thermoplastic materials like polycarbonate [26], polylactic acid (PLA) [27], acrylonitrile butadiene styrene (ABS) [28], and polymethylmethacrylate [29] are being processed using FDM for 3DP.In comparison, the works on thermoplastic materials like HDPE and polypropylene (PP) [30][31][32] are limited due to their warpage issues [33][34][35].The embedment of fillers lowers warpage in addition to imparting better mechanical properties.Different fillers like nano clay [36], bioactive glass (BAG) [37], and fly ash cenosphere [38,39] are used in composite development, which can be processed using FDM.Developing lightweight components necessitated incorporating hollow fillers like GMB and cenosphere in a matrix (syntactic/closed cell foams) for structural applications wherein the weight is a crucial parameter.These foams' main advantage is their weight reduction potential [40][41][42][43].
Gupta et al. [44] studied the flexural response of functionally graded plates using non-polynomial higher-order shear theory.They worked on investigating the effect of boundary conditions and geometry conditions on their properties.Results show that central deflection increases with a decrease in the side-to-thickness ratio (a/h) ratio and decrease with an increase in foundation parameters.Kim et al. [45] worked on the flexural response of FGM-based sandwich, I beamed, using shear deformation theory, and investigated the effect of gradation index and material ratio on the flexural-torsion response of beams.Results reveal a strong influence of the gradation law from 0 to 5. Atta et al. [46] worked on the flexural response of functionally graded polymer composite beams developed using the hand layup technique.Results show that delamination between the layers is dominant.From numerical analysis, they also mentioned that the gradation pattern of FGM is a significant parameter in enhancing flexural strength.Bharath et al. [47] worked on the flexural response of 3D-printed hollow GMB-reinforced plain foams, revealing they have good specific properties.Balu et al. [48] worked on the mechanical characterization of cenosphere-reinforced plain foams, indicating increased moduli with filler percentage.The literature studies show that the behavior of graded FGM foams through FDM can enhance the existing functionalities.This necessitated the present work to focus on 3DP of functionally graded foams (FGF) and functionally graded sandwich foams (FGSFs) using the FDM method, and their flexural responses and failure analysis.

Constituent materials and composite development
In the present work, HDPE granules of HD50MA180 grade (Fig. 1) in as received conditions having MFI, density, Vicat softening point, yield strength, and flexural modulus values respectively as 20 g/10 min, 0.950 gm/cm 3 , 124 • C, 22 MPa, and 750 MPa are used as matrix material.The hollow GMB of im30 k (Fig. 1), having wall thickness and average diameter of 1.4 and 15.3 μm is used as filler.As received properties of GMB, i.e., crushing strength and density, respectively, are 27,000 psi and 0.6 gm/cm 3 [49].In developing the composite material using Brabender, 20, 40, and 60 vol % GMB filler is mixed with HDPE matrix (Fig. 1).The suitable process parameters like screw speed and blending temperatures are maintained at 10 rpm and 160 • C to eliminate the filler breakage due to extra shear forces creeping in during blending [50,51].The developed composites are H20, H40, and H60, where H represents the HDPE matrix and 20, 40, and 60 represent filler volume percentage.Above 60%, particle agglomeration, higher filament roughness, and increased brittleness is observed.3D printing of composite with higher filler % may be possible by adopting pallet based 3D printer rather than a filament-based one as it eliminates the filament extrusion stage.

Filament extrusion and 3D printing
The composite blends are required to be converted into filaments to be fed to the 3D printer.The filaments are processed using a single screw extruder.Initially, the composite blends (pellets) are preheated for 24 h at 80 • C to eliminate past thermal history and moisture traces.The set points of the thermal heaters in between the feed-to-die segment of the extruder are adjusted to 145-150-155-145 • C. Once the temperatures of heaters are stabilized to a set point, pre-heated composite pellets are placed in the hopper of a single screw extruder, and filament extrusion is initiated.The diameter of the extruded filament is finalized concerning 3D printer specification, which is 2.85 ± 0.05 mm in the present work.This required diameter can be acquired by adjusting the screw and takeoff speeds, which are 25 rpm and 11.5 rpm, respectively [52].The FDM-based 3D printer is used in the current work to develop FGFs and FGSFs.This 3D printer contains two nozzles of 0.5 mm diameter, each named primary (N1) and secondary nozzle (N2).The temperatures of these nozzles are adjusted according to the material's melt flow index and melting point.The respective nozzle temperatures while printing H,  [31,52].The 3D printed part quality depends upon the printing parameters like extrusion multiplier, infill percentage, layer height, raster angle, and printing speed.These are chosen appropriately for respective filament compositions.The extrusion multiplier for processing H, H20, and H40 is 1, while H60 is processed at 1.2.A comparatively higher extrusion multiplier for H60 is due to its highly viscous nature and lower MFI.The remaining parameters, like infill percentage, layer height, raster angle, and printing speed, are constant for all configurations, as 100%, 0.5 mm, ±45 • , and 35 mm/s [52].Total 6 FG compositions are printed, namely, FGF-1 (H-H20-H40; H is the bottom/lower region), FGF-2 (H20-H40-H60), FGF-3 (H-H20-H40-H60), FGSF-1 (H-H-H20-H40-H), FGSF-2 (H-H20-H40-H60-H) and FGSF-3 (H-H-H20-H40-H60-H).G-code generated using Simplify 3D slicing software with all desirable printing parameters is given as input to the 3D printer.Once the nozzles reach the set temperatures, the H filament is inserted in the primary nozzle and H20 in the secondary nozzle.Before starting the print, both nozzles are purged to check filament continuity.Subsequently, N1 starts depositing H following the path as per G-code until the desired thickness of 1 mm (skin) gets deposited.Once the desired thickness of H is reached, N2 having H20 filament, comes into the position and initiates the deposition of H20 layers until it reaches 6 mm (core).Once again, as the desired thickness is reached, the machine is paused, and the nozzle is lifted by 5 mm in the Z direction.Further, filaments in the N1 and N2 are replaced by H40 and H60, respectively, and both nozzles are purged again (removal of any traces of previously loaded filament) before resuming the print.This process is continued until the entire sandwich is completed all at once/in one go/in situ.Once the print is completed, the sample is allowed to cool on the printer platform to minimize the residual thermal stresses, if any.Following the similar procedure as outlined earlier, all the FGFs with l × b × h of 180 × 18 × 6 mm and FGSFs of 180 × 18 × 8 mm are 3D printed all at once (180 mm is the sample length -span length + supporting length).The span length for FGF (96 mm) and FGSFs (128 mm) are considered sixteen times the total thickness [47].The process flow diagram of the 3D printing process is presented in Fig. 2. 3DP of FGF-2, FGSF-2, and FGSF-3 are shown in Fig. 3.The main advantage of developing FGF and FGSFs using 3DP over traditional methods is establishing the near-perfect bonding between the layers due to the proper fusion of layers.Moreover, most probable defects like delamination in a sandwich at the skin and core interface can be eliminated by the 3D printing process due to possibly a very good bonding at the skin and core interfaces.

Phoenix vtome x s scanner, by General Electric Measurement and
Control Solutions, is used for the Micro-CT scan.Scanning parameters like tube voltage, current, resolution, and exposure time are maintained at 80 kV, 200 μ amps, 50 μm, and 333 ms respectively.

Flexural response of functionally graded beams
3D printed FGF and FGSFs with dimensions of 180 × 18 × 6 and 180 × 18 × 8 mm are tested for their flexural response at a strain rate of 0.01 s − 1 (ASTM-D790) with crosshead displacement velocity of 2.54 mm/ min for FGFs and 3.41 mm/min for FGSFs.Zwick-Roell Z020 universal testing machine with 0.1 MPa pre-load is used for experimental investigation of flexural response.Equation (1) and equation ( 2) are used for evaluating the modulus and strength of the 3D printed FGF and FGSFs.Five samples of each composition are tested, and average values of the obtained results with standard deviation are mentioned in the current work.
'S' indicates span length, m resembles slope, w resembles width, t resembles thickness, E f indicates flexural modulus, σ fm resembles flexural strength, and P indicates load.An extensive micrographic analysis is performed on 3D printed pre-and post-tested FGF and FGSFs.To observe the bonding at cross-sections, all samples are freeze fractured post liquid nitrogen treatment for 24 h.

Micro-CT and density
The micro-CT is carried out on 3D-printed graded foams to reconstruct porosity distribution in foams and bonding between the different composite layers.The results of the micro-CT are presented in Fig. 4. Three different cross sections (CS) along the thickness direction of the FGF-1 (H-H20-H40), FGF-2 (H20-H40-H60), and FGSF-2 (H-H20-H40-H60-H) are represented in Fig. 4a, b and c respectively.There is no delamination between the 3D printed layers of HDPE and foam interfaces, as evident from the CT scan images.From the micro-CT imaging, it is observed that the HDPE zone is porous-free.Among foams, minimum micro-porosities are observed in H20, possibly due to the lower filler restriction towards matrix movements at lower GMB loadings.Though such porosities might compensate for few mechanical properties, these in-situ voids enhance weight-saving potential, which might not be possible alone with GMBs.Physical property like density plays a crucial role in deciding the weight reduction potential of the foams.In accordance with ASTM D792-20, the densities of 3D printed FGF and FGSF beams are computed experimentally using the Contech analytical balance.The theoretical densities of FGF and FGSFs are measured using the rule of mixtures as mentioned in equations ( 3) and ( 4).The experimental and theoretical densities of H and FGFs are estimated to be 927 ± 12 (H), 841.56 ± 11 (FGF-1), 746.89 ± 14 (FGF-2), 792.24 ± 10 (FGF-3) kg/m 3 and 950, 880, 810, 845 kg/m 3 respectively whereas for FGSF-1, FGSF-2, FGSF-3 it is estimated respectively as 850 ± 09, 794 ± 13, 810 ± 07 kg/m 3 and 897.5, 845, 871.25 kg/m 3 .The results reveal a difference between theoretical and experimental densities due to the voids transfer from the filament processed through a non-vented type extruder to the 3D prints in addition to the raster gaps creeping in during printing.Equation ( 5) is used to estimate the void %.This void percentage is noted to be 4.43 (FGF-1), 7.92 (FGF-2), and 6.27 (FGF-3) % respectively, whereas 5.29, 6 and 7% are noted for FGSF-1, FGSF-2, and FGSF-3.These voids help enhance the weight saving potential of FGF and FGSF beams for weight-sensitive structural applications.The difference between H and graded foams density is considered the weights saving potential of foams.For FGFs, it is observed to be 9.22-19.42%,whereas, for FGSFs, it is in the range of 8.3-14.43%.Among all 3D printed beams, FGF-2 exhibited the highest weight reduction potential of 19.42%.

Micrographic analysis
Filler sustainability and interface bonding are observed using SEM analysis on freeze-fractured 3D-printed graded foams (Fig. 5).It's evident from the micrographs that no filler breakage implies the suitability of the chosen processing parameters at all three stages of blending, extrusion, and 3DP (Fig. 5a).Fig. 5b presents the voids that might help in enhancing weight-saving potential.Yellow arrows in Fig. 5b represents improper interface bonding between filler and matrix.Surface treatments on fillers and associated matrix modifications can improve the poor filler matrix interface.The seamless interface between the HDPE skin and foamed core (H60) and within the core (H60/H40) is shown in Fig. 5c and d.This is due to the proper fusion of one layer with another, which signifies the appropriate deposition rate and the suitably chosen printing parameters.This seamless bonding helps in effective load transfer between material layers.Moreover, adequate bonding signifies bond strength.Inter-laminar delamination is absent, which might creep in, owing to the higher stresses caused due to the applied load at the interface of layers than the bond strength.Lower bonding strength results in delamination or crack propagation along the longitudinal direction at the interfaces, which is not seen for the proposed methodology of 3DP of FGSFs.Only type-2 of FGF and FGSFs underwent fracture among all the printed samples.SEM analysis at the fractured cross-section showed that due to induced tensile and compressive stresses in the layers below and above the neutral axis, one layer is diffused into the other more firmly, exhibiting the yielding phenomenon of HDPE during crack propagation resulting in the polymer fibre elongation (Fig. 5e).Furthermore, due to the induced compressive stress in the layers above the neutral axis, one layer is forced into the other, Fig. 4. Micro-CT of 3D printed graded foams.('CS'represents cross section along thickness direction of sample).
D. Bonthu et al. leading to the voids' collapse and resulting in densification.Filler failure is not observed.Nevertheless, GMBs are observed to be de-bonded from the HDPE matrix (Fig. 5f), which is very much anticipated as both, the HDPE and GMBs are used without any surface modifications.EDX is performed on the sample to find the elements present in the developed syntactic foams (Fig. 6a).EDX results showed that GMB contains 6.89% carbon, 51.91% oxygen, 3.29% sodium, 31.48%silicon, and 6.42% calcium (Table 3).EDX of the H60, as shown in Fig. 6b reveals the presence of 62.50% carbon, 27.60% oxygen, 8.26% silicon, and 1.63% calcium (Table 4).

FTIR spectroscopy
FTIR analysis is performed on neat HDPE and HDPE/GMB composites (Fig. 7).Sharp peaks at 2914 and 2848 cm-1 represent the asymmetric and symmetric stretching of C-H bond.The peak observed at 1471 cm − 1 signifies the asymmetric deformation (bending) of CH 2 .The wagging of CH 2 group and stretching of C-C bond results in the formation of peak at 1368 and 1045 cm − 1 .Sharp peaks at 794 and 717 cm − 1 are due to the rocking vibration of CH 2 [53].All the peaks and their corresponding vibration band assignments are listed in Table 5.

Flexural responses of 3D printed FGF and FGSFs
These functionally graded foam beams are developed for weightsensitive applications in aeronautical and naval sectors, where these structures are subjected to transverse loading conditions.Thereby, investigating the flexural response and failure mechanisms of 3Dprinted FGF and FGSF beams is of utmost importance.Three-point bending test is performed on all 3D printed FGF and FGSFs to study      their response toward transverse loading conditions.The initial mounting position of the FGF-3 sample is presented in Fig. 8a.All the samples did not undergo fracture phenomenon.The bending test is performed until 10% strain.Upon gradual increase in load, initial elastic behavior is prominently observed and continues to reach its yield zone.
A pictorial representation of FGF-3 at its yield position is shown in Fig. 8b.FGF-3 did not exhibit any crack initiation even as the higher deformation is caused due to an increase in the applied load (Fig. 8c).Similar behavior is observed in FGSF-3 (Fig. 8d).Among all types of the tested sample, only FGF-2 and FGSF-2 exhibited fracture.A fractured sample of FGSF-2 under applied load is shown in Fig. 8e.The semicrystalline HDPE gets melted and cools slowly onto the build platform during printing.During the process of cooling, HDPE undergoes the phenomenon of contraction well within limits, leading to the tight packing of GMBs.Further, cooling naturally on the build platform induces circumferential compressive stresses.These induced stresses increase the HDPE matrix's yield phenomenon and arrest crack propagation.The current work tests all the FGFs at 2.54 mm/min.Representative stress versus strain graphs of FGFs are depicted in Fig. 9a, and experimentally obtained modulus and strength are listed in Table 1.
The results show that FGF-2 showed higher modulus and lower strength.
The combined effect of gradation and the presence of a higher volume fraction of reinforced GMB in FGF-2 made it stiffer than other FGFs, exhibiting a higher modulus.This higher stiffness is the primary reason which leads FGF-2 to exhibit brittle fracture.The modulus of FGF-2 is 1.03 and 1.11 times that of FGF-3 and FGF-1.Across all FGFs, FGF-1 exhibited better strength due to lower in-situ micro porosity embedment during different processing stages.The experimental results show that with an increase in the GMB volume percentage, the modulus of the graded foams increased with comparable strength.There are two reasons for observing the decreasing trend of strength with an increase in the filler, (1) a weaker interface between the filler and matrix leading to a non-effective load transfer from matrix to filler, minimizing the strength, and (2) an increase in void percentage with an increase in the filler volume fraction.Once the sample reaches the yield zone, crossing its elastic limit, the porosity formed between raster due to layered printing acts as the catalyst for stress drop and subsequent sample failure.As the effect of these two phenomena is comparatively less in FGF-1, it exhibits better strength than the others with compromise in rigidity and weight-saving potential.The flexural strengths of FGF-1 are 1.26 and 1.40 times that of FGF-3 and FGF-2.FGSFs are 3D printed all at once to control the stress drop rate and delay the failure probability of crack initiation from the bottom most tensile layers under transverse load.These FGSFs are realized by sandwiching FGF core in 3D printed HDPE skin.A three-point bending test for FGSFs is performed at a 3.41 mm/min loading rate.Results acquired through experimental investigation are presented in Table 2.The results show that FGSFs exhibited superior strength compared to their respective FGFs, which shows sandwiches' significance in improving the beams' strength.Experimental responses of stress versus strain for respective FGSFs are depicted in Fig. 9b.This plot shows that FGSFs' exhibited similar behavior to the core with comparatively higher yield strength.FGSF-2 exhibited rigid behavior compared to FGSF-1 and FGSF-3.FGSF-2 exhibited a higher flexural modulus of 1.23 and 1.19 times, respectively, than FGSF-1 and FGSF-3.FGSF-1 exhibited higher strength of 1.15 and 1.06 times than FGSF-2 and FGSF-3.Even at higher deformation conditions, no macroscopic crack initiation exists in FGSF-1 and FGSF-3 (Fig. 8d).Fig. 8d also exhibits the absence of delamination failure at the skin and core interface, even at the higher deformation stages.These observations indicate that developing sandwich structures all at once through the 3D printing process and with the gradual variation of properties along the core helps overcome the most probable delamination defects in sandwiches processed through traditional methods.Further, specific properties are crucial in showing their significance in weight-sensitive applications.Hence, the specific properties of FGF and FGSFs are listed in Table 6 and Table 7.The results show that FGF-2 and FGSF-2 exhibited higher specific modulus than their other configurations.Among the FGFs and FGSFs, FGFs exhibited higher specific modulus than their corresponding sandwiches (Fig. 10a).From the specific strength perspective, FGSFs show superior behavior compared to their respective FGFs as seen in Fig. 10b.Nonetheless, in future investigations, the combination of reinforced skins with CNTs/ CNFs and higher skin thickness will be explored to enhance the modulus and strength of FGSFs substantially.

Comparison of the flexural response of graded foams with plain foams
The driving force for developing the graded foam cored sandwiches over plain cored sandwich composites is eliminating the sharp transition of stiffness and thermal properties at the skin and core interface.The capability of sandwiches to enhance mechanical stability and stiffness made the current work 3D print the sandwiches of the respective graded foams.These developed sandwiches are further investigated for their flexural response.The properties of the plain core and their corresponding sandwiches are referred from the previously published works on foams for comparing graded foams with plain foams [47].The respective stress versus strain graphs of the plain core and sandwiches are represented in Fig. 9c and d.The modulus and strength values of H, H20, H40, and H60 are obtained as 990 ± 11.28, 1210 ± 19.56, 1280 ± 11.87, 1360 ± 11.23 MPa, and 25.4 ± 0.12, 21.0 ± 0.58, 17.1 ± 0.47, 15.1 ± 0.72 MPa respectively.H60 exhibited better modulus among all plain core foams due to the higher filler percentage.The modulus and strength values of SH20, SH40, SH60 are obtained as 927 ± 18.46, 1000 ± 13.58, 1050 ± 12.86 MPa and 21.80 ± 0.45, 20.53 ± 0.52, 19.72 ± 0.80 MPa respectively (Fig. 9d) [47].The comparison among the plain core with their respective sandwiches showed that the modulus values of the sandwich are comparatively lesser concerning their respective foams.Specific properties of core and sandwich samples are compared in Fig. 10c and d.H60 exhibited better specific modulus among all plain core and sandwich samples, which made it more suitable for weight-sensitive applications.A comparative study shows that the flexural modulus of FGFs increased in the range of 19.6-33.83%higher than pure HDPE.The flexural strength of FGF-1 is comparable with HDPE, whereas it is 49.66% higher than H60.Compared to plain sandwiches, graded compositions exhibited 10.5-22.1% higher strength.Smooth variation of properties helps eliminate the deleterious effects like thermal expansion mismatch while processing and sharp stiffness transition at the interface of skin and core when subjected to mechanical loadings.The two aforementioned phenomena significantly affect the shear stresses and enhance the strength of the 3D-printed graded foams.GMB % per unit cross-sectional area is more in core when compared with their respective sandwiches.This made the FGF samples exhibit better modulus when compared with their respective sandwiches.

Failure mechanism of FGSFs
The most probable failure mechanisms observed in sandwich structures are delamination at the skin and core interface, core shear, indentation, and face wrinkling/dimpling (inter-cell micro buckling),  facing failure [56,57].The type of failure depends on the core structure, skin strength, processing method, and core materials composition [58].Generally, delamination defect is observed due to improper binding force between skin and core (Fig. 11a).Indentation is based on the relative compressive strength of the core and applied force, as seen in Fig. 11b.Face wrinkling/dimpling is mostly observed in sandwich structures where honeycomb cellular structures are used as cores (Fig. 11c).Face failure occurs due to insufficient face or core thickness, causing a tensile or compressive face, as depicted in Fig. 11d.Fig. 11e shows the core shear failure that is most common in sandwiches.Even at higher loading conditions, delamination at the skin and core interface is not observed in the present work, as seen in Fig. 11g, which resembles the advantage of opting for 3D printing methods for fabricating sandwich structures.This is due to the formation of seamless bonding and properly fused skin and core layers, owing to the suitability of the printing parameters.An indentation on the top skin at the point of contact with the wedge is observed in Fig. 11b.This might be due to the applied load on the sample reaching beyond the compressive yield strength of the skin.Among all the tested samples, face and shear failure (Fig. 11d and e) are observed only in FGF-2 and FGSF-2.The fractured specimen of FGSF-2 is shown in Fig. 11f and g.

Finite element analysis (FEA) of FGF and FGSFs
The graded foam finite element analysis is performed to analyze the stress distribution and deflection occurrence in FGF and FGSFs along their length and thickness direction under transverse loading conditions.FEA analysis is carried out using a commercially available Ansys package.In FGF and FGSF beams, 180 mm lengths are modeled layer-wise.Out of total length, 96 and 128 mm are considered span lengths, respectively, and subsequently activated ADD FROZEN command for restricting the relative motion between the layers.These beams are meshed using SOLID 186 elements, leading to 19,238 nodes, 2418 elements, and 21,844 nodes, 2854 elements, respectively, for FGF and FGSF (Fig. 12).Boundary conditions applied while performing numerical analysis are shown in Fig. 12c.Experimental material properties like young's modulus, Poisson's ratio, and density are taken from previous works, while finite element analysis [47,59] and load data are taken from experimental results.Fig. 13a and b show the stress distribution of FGF and FGSFs in the X direction.Stress on the top layer subjected to compressive force is observed to be higher than the bottom layer under tensile force.The one possibility for such an unsymmetrical stress distribution along the thickness direction is the presence of a neutral axis near the top layer.The position of the neutral axis of different FGFs and FGSFs is evaluated using Equation ( 6), and the computed results are mentioned in Table 8.

Neutral axis position
E i represents the modulus of the material, A i represents the area of cross-section, z i is the distance of the centroid of an i th layer from the bottom, and n represents the number of layers.In the present work, material property gradation increases from the bottom-most layers to the top layer.Fig. 14a and b exhibit the Von-misses stress distribution of FGF and FGSFs.Among graded core and sandwiches, FGSFs' exhibited higher stress than FGFs.Fig. 15a and b show the total deformation of FGF and FGSFs'.Due to the higher stiffness, the FGF-2 and FGSF-2 exhibited lower deformation magnitudes.Some deviation between FEA and experimental values is observed (Table 9).This deviation might be due to geometric in-homogeneities like interface de-bonding between the constituent materials and the isometric material property assumptions.Moreover, the porosity formed in the sample while 3D printing, which is clearly shown in the micro-CT scan, is also neglected while performing analysis, which might be the root cause for the observed deviations in the results [60].The deformation values mentioned in the current paper are the average values of a complete set of samples tested for each configuration.If the comparisons are estimated corresponding to the highest deformation sample, this deviation is noted to be 5-15%.

Property chart
The property chart compares flexural properties as a function of the density of the developed composite.From the literature survey, it is observed that the experimental investigation on 3D printed graded foams and their sandwiches is yet to be explored.FGF and FGSFs' properties are compared with plain composites of similar and dissimilar materials developed using 3D printing [36,47].Comparative results showed that, apart from the H60, FGF-2 exhibited a better modulus   value than others and is nearer to H40 values (Fig. 16a).The strengths of the FGF-2 are higher than H60 and H40.From the strength point of view, FGSFs' exhibited superior response compared to other materials, as seen in Fig. 16b.With comparable modulus and density, better strength is observed in the graded foams.Among all 3D Printed foams, FGSF-1 exhibited higher strength.From the comparative study carried through the property chart, it is observed that the mechanical stability of the beams can be enhanced by adopting the graded sandwich foams in place of plain foams.The properties of the FGF and FGSFs can be further enhanced by adopting symmetric gradation with respect to the neutral axis and adopting much finer material property variation along the thickness direction.

Conclusion
The current work uses experimental and FEA to study functionally graded 3D printed core and sandwich syntactic foams under transverse loading conditions.The results are summarized below.
• All FGFs and FGSFs are 3D printed without any warpage issues.
• Micro-CT scan analysis showed a proper bonding between the skin and the graded core.• FGSFs exhibited better strength compared to FGFs.Among all samples, FGF-2 exhibited the highest modulus.• The modulus of FGF-2 enhanced by 33.83% compared to pure HDPE.
• All at once 3D printed FGSFs exhibited better strength compared to non-graded foams.• Due to material property gradation, the asymmetric stress distribution is observed along the thickness direction.
FGSF and FGFs have the potential to replace plain foams in weightsensitive structural applications.

Fig. 5 .
Fig. 5. SEM of graded foams (a) GMB sustainability (b) Interface of filler and matrix (c) HDPE and core interface (d) interface among core (e) Layer diffusion at fractured cross section and (f) De-bonding.

Table 1
Density and flexural properties of FGFs.

Table 2
Density and Flexural properties of FGSFs.

Table 3
Elemental composition of GMB.

Table 6
Specific properties of FGFs.

Table 7
Specific properties of FGSFs.

Table 8
Position of Neutral axis.

Table 9
Experimental and FEA comparison of graded foams.