10639 FACTA UNIVERSITATIS Series: Mechanical Engineering Vol. 20, No 3, 2022, pp. 589 - 615 https://doi.org/10.22190/FUME220404027S © 2022 by University of Niš, Serbia | Creative Commons License: CC BY-NC-ND Original scientific paper THERMAL BUCKLING AND BENDING ANALYSES OF CARBON FOAM BEAMS SANDWICHED BY COMPOSITE FACES UNDER AXIAL COMPRESSION Babak Safaei1,2, Emmanuel Chukwueloka Onyibo1, Dogus Hurdoganoglu1 1Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, Turkey 2Department of Mechanical Engineering Science, University of Johannesburg, Gauteng, South Africa Abstract. The bending and critical buckling loads of a sandwich beam structure subjected to thermal load and axial compression were simulated and temperature distribution across sandwich layers was investigated by finite element analysis and validated analytically. The sandwich structure was consisted of two face sheets and a core, carbon fiber and carbon foam were used as face sheet and core respectively for more efficient stiffness results. The analysis was repeated with different materials to reduce thermal strain and heat flux of sandwich beams. Applying both ends fixed as temperature boundary conditions, temperature induced stresses were observed, steady- state thermal analysis was performed, and conduction through sandwich layers along with their deformation nature were investigated based on the material properties of the combination of face sheets and core. The best material combination was found for the reduction of heat flux and thermal strain, and addition of aerogel material significantly reduced thermal stresses without adding weight to the sandwich structure. Key words: Sandwich beam, Heat flux, Buckling, Total deformation, Finite element analysis Received: April 04, 2022 / Accepted May 23, 2022 Corresponding author: Babak Safaei Department of Mechanical Engineering, Eastern Mediterranean University, Famagusta, North Cyprus via Mersin 10, Turkey Department of Mechanical Engineering Science, University of Johannesburg, Gauteng 2006, South Africa E-mail: babak.safaei@emu.edu.tr mailto:babak.safaei@emu.edu.tr 590 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU 1. INTRODUCTION Sandwich composite structures are made of two thin, rigid skin layers divided by a thicker, softer core as stated by Darzi et al. [1]. Gay and Suong [2] stated that, sandwich structures were created when two thin facings or skins were bonded or welded together on a lighter core that kept the two skins apart. The core increased the panel's bending stiffness and resistance to buckling loads [3,4]. They also found that sandwich structures had fewer lateral deformations, more buckling resistance, and higher natural frequencies than other types of structures. Douville and Grognec [5] showed that sandwich structures were employed in a wide range of industrial applications due to their desirable combination of light weight and strong mechanical qualities. Therefore, steel is commonly used for the skins [6,7]. Hence, Commonly used materials in the core are metallic foams and polymers [8–10]. Rigid-foam core is commonly used and has moderate strength and stiffness [11]. Moreover, one of the common cores used in sandwich panels is a honeycomb [12–14]. In general, sandwich structures are preferred over traditional materials due to their high corrosion resistance [15] and low thermal and acoustic conductivity [16,17]. The high thermal expansion coefficient of aluminum honeycomb sandwich constructions limits their use in thermal management systems [18]. The behavior and failure modes of sandwich structures in flexure have been observed in a variety of studies [17,19–21]. A sandwich structure can fail due to a variety of damage mechanisms, including tensile failure/skin compressive [22], local skin wrinkling [23,24], and core indentation failure [25,26]. The sensitivity of nap-core sandwich, a unique type of structural composite with different characteristics, was studied by Ha et al. [27]. McCormack et al. [28] studied the failure of sandwich beams with metallic foam cores. Ha et al. [29] studied the behaviors of nap-core sandwiches, with a particular emphasis on the effect of symmetry in nap cores. In thermal applications, heat conduction and heat flux in sandwich beams has been experimented. Non-Fourier heat conduction was investigated in a sandwich panel with a cracked foam core by Fu et al. [30]. Under a high-temperature environment, the vibration properties of a carbon nanotube-reinforced sandwich curved shell panel were explored by Mehar and Kumar Panda [31]. Sun et al. [32] investigated the convective cooling efficiency of a sandwich panel with a hierarchical corrugated core heated from face sheets and cooled actively through the core. Onyibo and Safaei [33] applied finite element analysis to honeycomb sandwich structures. Su et al. [34] investigated the thermal insulation performance of structural insulated panels (SIPs) with glass fiber-reinforced polymer (GFRP) surfaces. Moradi-Dastjerdi and Behdinan [35] presented a smart multifunctional sandwich plate with a central lightweight porous layer, two intermediate polymer/graphene nanocomposite layers, and two piezoceramic active faces. Zhang et al. [36] proposed an energy harvester that used an arc-shaped piezoelectric sheet to scavenge rotational energy from rotating devices. Zhao et al. [37] proposed a multifunctional carbon fiber honeycomb sandwich structure (MCFHS). Safaei et al. [38] presented an analytical solution based on molecular mechanics model to estimate the elastic critical axial buckling strain of chiral multi-walled carbon nanotubes (MWCNTs). Using experimental, theoretical, and numerical simulation methodologies, Chen et al. [39] investigated the heat transmission mechanism and thermal insulation performance of fabricated C/SiC corrugated LCSP. Safaei et al. [40] explored the thermoelastic responses of sandwich plates with porous polymeric core and proposed ultra-lightweight engineering structures of sandwich plates with one porous polymeric core and two carbon nanotube (CNT)/polymer nanocomposite outer layers. Asmael et al. [41] reviewed the ultrasonic machining of carbon fiber–reinforced plastic composites. Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 591 According to the law of vibration, everything (components and structures) is in constant motion, vibrating at a given frequency. Safaei [42] investigated the damped vibrational behavior of a lightweight sandwich plate subjected to a periodic force over a short period of time. Liu et al. [43] examined the nonlinear forced vibrations of functionally graded materials (FGMs). Hadji and Avcar [44] investigated free vibration of a square sandwich plate with functionally graded (FG) porous face sheets and an isotropic homogenous core under different boundary conditions. Li et al. [45] theoretically and experimentally studied the nonlinear vibrations of fiber-reinforced composite cylindrical shells (FRCCSs) with bolted joint boundary conditions. Liu et al. [46] developed a novel method for solving nonlinear forced vibrations of functionally graded (FG) piezoelectric shells in multi- physics fields. However, there have been many studies on nonlinear vibration behaviors of various materials [47-54]. The nonlinear forced vibration behaviors of third-order shear deformable nanobeams in the presence of both surface stress and surface inertia due to high surface to volume ratio were investigated by Sahmani et al. [55]. Yang et al. [56] carried out free vibration evaluations on FG graphene nanoplatelet-reinforced composite (FG- GPLRC) arches in both in-plane and out-of-plane. Katariya et al. [57] used higher-order shear deformation theory to construct a generic mathematical model for evaluating the bending and vibration responses of skew sandwich composite plates. Enhanced donnell nonlinear shell theory and Maxwell static electricity/magnetism equations were used by Liu et al. [58] to construct a coupled nonlinear model for composite cylindrical shells to examine nonlinear forced vibrations in multi-physics fields. Moradi-Dastjerdi and Behdinan [59] used an innovative and reliable approach to investigate the free vibration behaviors of multifunctional smart sandwich plates (MSSPs). Buckling is one of the major failure causes of machine elements; therefore, buckling loads should be considered in designs. Bažant and Beghini [60] showed that sandwich shell failures caused by skin, core, and interface fracturing were often associated with instability and as a result, it was difficult to distinguish among delamination, fracturing, damage, buckling, face wrinkling and scaling. However, based on the type of loading, various buckling forms could occur, which can be global or local [61,62]. Zhao [63] investigated new buckling characteristic equation for sandwich pipelines. Alhijazi et al. [64] analyzed the elastic properties of luffa and palm natural fiber composites (NFCs) with epoxy and ecopoxy matrixes, taking fiber volume fractions into account. Fan et al. [65] investigated the thermal post buckling characteristics of porous composite nanoplates. Grygorowicz et al. [66] studied the elastic buckling of a three-layered beam with a metal foam core using analytical and numerical approaches. Ansari et al. [67] studied the pull-in instability properties of hydrostatically and electrostatically actuated circular nanoplates, taking into account the influence of surface stress. Fattahi and Safaei, [68] studied the buckling properties of nanocomposite beams reinforced with single-walled carbon nanotubes (SWCNTs). Liu et al. [69] used a size-dependent numerical solution methodology to investigate nonlinear buckling and post buckling of cylindrical micro sized shells made of checkerboard. Nonlinear buckling of elastically supported functionally graded graphene platelet-reinforced composite (FG-GPLRC) was analytically predicted by Yang et al. [70]. Under temperature conditions, Yang et al. [71] performed an analytical investigation on the asymmetric static and dynamic buckling of a pinned-fixed FG-GPLRC. Safaei et al. [72] performed high- precision thermal and mechanical buckling analyses on UD porous sandwich plates with FG-CNT cluster-reinforced nanocomposite outer layers resting on elastic foundations. Magnucki and Magnucka-Blandzi [73] developed an analytical model for sandwich 592 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU structures using a rectangular plate as an example. Sahmani and Aghdam [74] studied the size-dependent buckling and post buckling characteristics of microtubules embedded in cytoplasm under axial compressive load using the nonlocal strain gradient theory of elasticity, which included both nonlocality and strain gradient size dependency. This was done within the framework of a refined orthotropic shell theory with hyperbolic distribution of shear deformation. Yunliang and Junping [75] studied bifurcation point buckling and extreme point buckling of sandwich structures. Sahoo et al. [76] investigated the finite element solutions of thermal buckling load values of graded sandwich curved shell structures using a higher-order kinematic model that included shear deformation effect. Avilés and Carlsson [77] developed an elastic foundation model for analysis of the local buckling behavior of foam core sandwich columns containing a through-width face/core debond. Also, there have been numerous investigations on nonlinear buckling [78–80], size- dependent buckling, and bending behaviors [81–84]. Jasion et al. [85] investigated the global and local buckling–wrinkling of the face sheets of sandwich beams and sandwich circular plates using computational and experimental methods. Moreover, Léotoing et al. [86] presented the first implementation of a revolutionary unified sandwich model considering closed-form solutions for both global and local buckling. In the presence of surface stress impact, Fan et al. [87] predicted the shear buckling characteristics of skew nano-plates composed of a FGM. Sahmani and Aghdam [88] investigated the size-dependent buckling and post buckling responses of hybrid FG nanoshells integrated with surface-bonded piezoelectric nanolayers using a refined exponential shear deformation shell theory in conjunction with nonclassical Eringen's nonlocal elasticity theory. Under in-plane hydrostatic and uniaxial compression, elastic buckling of regular hexagonal thin sheets made of homogenous and isotropic materials with internal, translational and rotational elastic edge supports were studied by Ghanati and Safaei [89]. However, bending of a slender structural element characterizes its behavior under an external load applied perpendicularly to a longitudinal axis of element. Furthermore, Yan et al. [90] predicted the bending stiffness, peak load and initial failure load of sandwich structures. Mehar and Panda [91] numerically evaluated the deflection behaviors of carbon nanotube-reinforced composite plates using finite-element method and validated the accuracy of results using three-point experimental bending test data. Barbaros et al. [92] carried out a review on FG porous nanocomposite materials considering manufacturing, application, and mechanical characteristics. Liu et al. [93] investigated the impact responses of shear deformable sandwich cylindrical shells with two face layers and a FG porous core. Aldakheel and Miehe [94,95] investigated coupled thermo-mechanical strain gradient plasticity theory taking into account micro- structure-based size effects. Chen [96] used FEM to investigate the collapse behaviors of corrugated cross section beams subjected to three-point bending. Zhao et al. [97] reviewed the mechanical properties of graphene and graphene composites. Wang et al. [98] proposed a novel multilevel modeling approach for calculating the Young's modulus of polymers reinforced with graphene nanoplatelets. Zhang et al. [99] studied the bending strength, stiffness, and energy absorption of a corrugated sandwich composite structure. Few research works have been carried out on natural fiber composites [100,101]. Mehar and Panda [102] conducted deflection analysis to investigate the effect of MWCNT reinforcement on the rigidity of sandwich curved panels. Sahmani and Aghdam [103] estimated the Young's modulus and Poisson's ratio of nano porous biomaterials with refined truncated cube cells. The effect of adding calcium carbonate nanoparticles (NPs) to cement plast on mechanical characteristics was experimentally explored by Safaei et al. [104]. Li et al. [105] investigated vibro-impact resistant performance of fiber reinforced composite (FRC) Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 593 plates with polyurea coating (PC) under four-edge elastic constraints. Seong et al. [106] applied bending mechanism to determine the control parameters of core shear stress and found that, according to analytic calculations, the shear stress of core could be greatly decreased by increasing clearance. Under the impact of mechanical loading and heat field, the frequency, deflection, and stress values of carbon nanotube-reinforced sandwich plate structures were numerically investigated by Mehar et al. [107]. Fattahi et al. [108] presented an experimental investigation on the effect of nanoparticle volume fraction on the elastic characteristics of a polymer-based nanocomposite and obtained comparable results to other existing theoretical models. Moreover, Sivaram [109] improved the strength and mechanical properties of aluminum materials by the inclusion of polypropylene foam sheets. Hu and Wang [110] created a thermal–mechanical analysis model to characterize thermal shock behaviors of auxetic honeycomb core ceramic sandwich structures (CSSs). Daouas et al. [111] investigated thermal performance of walls under optimal conditions. Wang et al. [112] derived an exact analytical solution for steady-state heat transfer in FG sandwich slabs under convective-radiative boundary conditions. Geoffroy et al. [113] studied 3D printed sandwich materials filled with hydrogels at extremely low heat release rates. Safaei et al. [114] used FEM to examine the effect of static and harmonic loads on honeycomb sandwich beams. In this paper, the flexural strength of sandwich beams was improved, heat flux and temperature at which sandwich structures buckle were determined using finite element analysis (commercial software ANSYS). In a connected linear buckling analysis of sandwich beams, the load factor on the static load causing buckling was assessed, the critical buckling load and bending behavior of carbon fiber strut imbedded in sandwich core was determined. In general, sandwich beam heat transfer and thermal strain at corresponding temperature were investigated and compared with added silica aerogel material. 2. PROBLEM OBJECTIVE In this paper, the analysis of buckling caused by thermal expansion in a sandwich beam was presented for simply supported sandwich beams under axial compression and the critical buckling force and buckling mode shapes were investigated. Furthermore, the bending deformation of cantilever sandwich beams with different imbedded carbon fiber materials was studied and results were compared with analytical calculations. In addition, the rate of heat conduction of the sandwich was analyzed to reduce the heat flux and temperature induced stresses and make it a favorable thermal insulator. 2.1. Geometry and Finite Element Model The geometry of sandwich beam solid model structure was used to investigate bending and critical bucking load, while carbon foam core was applied to analyze heat flux and thermal stresses of a given thickness using finite element analysis. The advantages of sandwich solid model are short computational time, good adhesion properties and more reliable results when compared to analytical solution. Fig. 1(a) shows the Solidworks commercial software design of 8 cylindrical bar struts of 1.5 mm diameter and 10 mm spacing. Fig. 1(b) shows carbon fiber strut imbedded in the core in order to improve sandwich axial compression and Fig. 1(c) depicts rectangle shape strut inserted in the core for absorbing bending stresses in sandwich beams. Furthermore, Fig. 1(d) depicts the sandwich with added aerogel layers. Lastly, Table 1 shows the dimensions of the used sandwich beam. 594 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU (a) (b) (c) (d) Fig. 1 Geometry of sandwich beam (a) Cylindrical bar strut of 1.5 mm diameter and 10 mm spacing; (b) Carbon fiber strut imbedded in core; (c) Rectangle shape strut inserted in core (d) Sandwich with added aerogel layers Table 1 Dimensions of sandwich beam Name Length X Length Y Length Z Volume mm2 Mass Kg Nodes Element Skin mm Length 150 80 9 60000 0.471 12300 8880 1 2.2. Loads and Boundary Conditions Axial load case was considered in sandwich buckling while point load was applied in bending tests of sandwich. However, for the buckling of sandwich beam structures, simply supported (pinned at both ends) conditions were used which could only move laterally, and in bending tests, sandwich structures were treated as cantilever Beams (fixed at one end and point load on the other end), as shown in Fig. 2(a). In buckling, no displacement along z-direction, completely fixed on one side and moving on the other side along the direction of applied force, in this case x-direction, as shown in Fig. 2(b). Fig. 2(c) depicts thermal boundary conditions (high temperature applied on top skin and room temperature set at bottom skin). Finally, Fig. 2(d) shows thermal boundary conditions for the temperature that could buckle the sandwich beam. Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 595 (a) (b) (c) (d) Fig. 2 Boundary conditions (a) cantilever for bending analysis; (b) simply supported, moving along horizontal direction; (c) steady-state temperature boundary condition (higher temperature applied on top skin); (d) Thermal expansion of sandwich beam 2.3. Material Properties There has been extensive research on silica aerogels recently. As the lightest processed solid material on the planet, aerogels have the highest empty volume fraction in their structure. They are made by super critically drying silica gels, which was also the first inorganic aerogel to be developed by Patil et al. [115]. In this analysis aerogel was used for the reduction of heat flux, thermal strain and expansion. Sandwich beam materials consist of carbon fiber-polyimide for skins and carbon foam as core. Ogasawara et al. [116] used the same structure to develop an effective heat- resistant sandwich panel. Table 2 summarizes the depicted material properties, carbon fiber-polyimide was used as face sheet and carbon foam was used as the core to analyze flexural strength in cantilever beam conditions and investigate strength along the axis (buckling). Furthermore, the sandwich beam with the same material was subjected to thermal loads and the results with and without aerogel were evaluated. 596 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU Table 2 Material properties of sandwich beams Material Young’s Modulus E (MPa) Poisson’s Ratio ν Shear Modulus G (MPa) Density ρ (Kg/m3) Thermal conductivity (W/m°C) Carbon fiber-polyimide 70000 0.36 25735 1410 2.16 Carbon foam 123.79 0.33 46538 2267 0.11 Silica Aerogel 5 0.2 20833 105 0.016 3. FEM ANALYSIS ANSYS software was applied to perform numerical analysis on sandwich beams with carbon foam core. A linear buckling model was used in finite element analyses. The conceptual buckling strength of an ideal elastic structure was calculated using linear buckling (also known as eigenvalue buckling) and nonlinear analyses to investigate buckling temperature of sandwich beam. However, in contrast to linear solutions, non- linear solutions were also used in experiments to achieve the most precise results. Thereby, this method gave closer buckling estimation. Hence, critical buckling load (stress) and factors that optimize the sandwich structure were investigated and heat flow rate across sandwich layers was observed. All sandwich beam layers were modelled using solid model and was meshed using eight node solid elements SOLID186 (the total statistics of 8880 elements and 12300 nodes). The details of the sandwich structure were b = 80 mm, L = 150 mm, tf = 1 mm, tc = 4 mm, Ef = 70000 MPa, P = 100 N, and Ec = 5 MPa. The faces of sandwich beam were made of carbon fiber-polyimide and its core was made of carbon foam. Tables 3, 4 and 5 show FEM results and analytical calculations. Table 3 Bending of cantilever sandwich beam structure Deformation (mm) FEM 2.14 Analytical 2.17 Table 4 Buckling of sandwich beam structure Critical buckling load (N) FEM 31097 Analytical 3167.1 Table 5 Heat flow rate of sandwich beam structure Heat flux (W/m2) FEM 2090.85 Analytical 2091.00 3.1. Global buckling of sandwich column When studying sandwich systems, it is generally thought that the core only supports shear and that skins carry tensile and compressive loads under flexure [117]. The Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 597 contributions of core and skin to flexural and shear stiffness were considered in the sandwich beams examined in this analysis. Two modes of elastic buckling are possible: Euler buckling mode with sandwich column bending and a core shear mode. The shear deformation of core was taken into account in a more precise approach [118,119]. Fig. 3 shows the schematic model of buckling setup to find out plane displacement on sandwich beam. Fig. 3 Schematic model of buckling setup For case of a strut with built-in ends (which are constrained against rotation), the Euler buckling load PE is: 𝑃𝐸 = 4𝜋2(𝐸𝐼)𝑒𝑞 𝑙2 (1) The equivalent flexural stiffness EIeq of the sandwich beams was calculated by Eq. (2). 𝐸𝐼𝑒𝑞 = 𝑏𝑡 3 6 𝐸𝑓 + 𝑏𝑡𝑑2 2 𝐸𝑓 + 𝑏𝑐3 12 𝐸𝑐 (2) where Ef and Ec are the Young's moduli of face sheet and core materials, respectively, b is the width of sandwich column, t is the thickness of face sheet, and c is the thickness of core. d ≡ t + c is the distance between the mid-planes of face sheets. The core shear buckling load Ps was set by the shear stiffness of core. 𝑃𝑠 = (𝐴𝐺)𝑒𝑞 (3) where the corresponding shear rigidity of core (AG)eq is: (AG)𝑒𝑞≈bcG𝑐 (4) where PS ≈ AGeq, A = (h + H)2/h, Gc = Ec/(1 + 2νc), Gc is the shear modulus of the core and bc the cross-sectional area of the core. However, at transformation values of strut slenderness ratio, these buckling modes interacted to produce a combined collapse load (Pcr) where: P𝑐𝑟=PE+P𝑠 (5) 598 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU 3.2. Heat transfer equations Local heat flux for one-dimensional steady-state heat transfer across a sandwich, according to the Fourier heat transfer law, could be written as: 𝑞 = −𝑘𝛥𝑇 = −𝑘 𝑑𝑇 𝑑𝑥 (6) where q is local heat flux density (W/m2), K is material thermal conductivity (W/m*k), 𝛥𝑇 = 𝑑𝑇 𝒅𝒙 is temperature gradient (K/m). 3.3. Thermal resistance Thermal resistance is a thermal property and a measurement of how well a material resists a heat flow. 𝑄wall = −𝑘𝐴 𝑇2−𝑇1 𝐿 = − 𝑇2−𝑇1 𝑅thcond (7) Rskin = 𝑡 𝐾𝑠𝐴 (8) Rcore = 𝑡 𝐾𝑐𝐴 (9) 𝑅thcond = 2( Rskin ) + 𝑅 core (10) where 𝛥𝑇 is the amount of heat transited through sandwich beam (T2 - T1), Rthcond represents thermal conductive resistance, L is length, t is thickness, A is area, Ks is the thermal conductivity of skin and Kc is the thermal conductivity of core. Hence, in this analysis, temperature was applied on the bottom and top face sheets of the sandwich beam. Fig. 4 depicts the schematic model of conductive heat distribution on sandwich beam and showed that high heat was transferred from the top skin, distributed through core and down to bottom skin. Fig. 4 Schematic model of conductive heat distribution on sandwich beam. Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 599 4. RESULTS AND OBSERVATION 4.1. Deformation of Sandwich Considering the deformation of sandwich beam shape due to applied forces and change in temperature, in order to investigate total deformation and the state of stresses. This analysis considered the buckling of sandwich beam due to applied forces and elevated temperature, bending of sandwich due to applied loads and heat flow rate across the sandwich beam. 4.2. Buckling Analysis In order to determine the failure mode in which relatively large deflections occurred on sandwich beam, buckling analysis was carried out to investigate what load and temperature level caused buckling and elastic instability on sandwich structures. Moreover, sandwich deformation nature was investigated by determining the temperature that buckled the sandwich, according to the material properties used for sandwich beam. Furthermore, simulation was carried out on two sandwich beams, one with carbon fiber strut in the core and the other without carbon fiber strut. Fig. 5 depicts the buckling nature of the sandwich beam without carbon fiber strut. Furthermore, the same procedure was applied to observe the buckling nature of the sandwich with imbedded strut as shown in Fig. 6. In this case, temperature was not added in static structural analyzer and the results showed improvement in buckling load for the sandwich with carbon fiber circular strut, as shown in Table 6. Table 6 Buckling load Sandwich type Buckling Load (N) Sandwich with circular strut imbedded in core 34413 Sandwich without circular strut 31017 (a) (b) Fig. 5 Buckling of sandwich under axial compression (a) isometric view; (b) side view 600 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU (a) (b) (c) Fig. 6 (a) Cylindrical carbon fiber imbedded in the core (diameter of 1.5 mm); (b) Buckling of sandwich under axial compression (isometric view); (c) Buckling of sandwich under axial compression (side view) 4.3. Buckling Analysis with Thermal Expansion Nonlinear buckling was simulated through a static structural analysis in ANSYS. Temperature was raised and sandwich buckling was observed. To begin with, analytical settings in structural run were set and large deflection was turned on. In addition, boundary was assigned, x movements on both sides were constraint to confine the sandwich beam during thermal expansion in order to observe compressive stresses along x-direction. Furthermore, sandwich vertex were prevented from moving along z-direction and finally the left and right sandwich beam edges were restricted from moving vertically. In general, sandwich beam could not expand thermally along x-direction, and expanded only along y and z directions due to the constraints; it was not free to translate and rotate globally. 4.3.1. Load Environment temperature of 70 °F was assigned to sandwich beam in static structural analysis and the thermal condition of sandwich beam was 100 °F. Hence, in this analysis, there was a 30 °F temperature increase that caused thermal expansion. Therefore, temperature that caused state of stresses on the sandwich beam were noted. Hence, Fig. 7(a) shows the first mode shape, the sandwich beam were quizzed due to thermal load and not allowed to move globally which caused it to buckle in the middle. However, as there was 30 °F difference which was the only load on sandwich beam and was multiplied by load multiplier of the first mode in eigenvalue buckling module and summed with 70°F environmental temperature assigned early which resulted to the buckling temperature of 140.47°F. The Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 601 same analysis was repeated for sandwich structures with aerogel layers, in order to investigate effect of aerogel layers and the corresponding bucking temperature. Fig. 7 shows the 3 modes of sandwich beam without silica aerogel. Moreover, the first mode was considered the most. Fig. 8 shows aerogel position in the sandwich beam and first 2 mode shapes of sandwich beam with silica aerogel material. Table 7 summarizes the temperature causing buckling on both sandwich beams with and without aerogel layers. There was 6% increase in temperature that could buckle the sandwich beam when silica aerogel was used. (a) (b) (c) Fig. 7 Mode shapes of sandwich beam without silica aerogel (a) Mode 1; (b) Mode 2; and (c) Mode 3 602 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU (a) (b) (c) Fig. 8 Mode shapes of sandwich beam with silica aerogel (a) Sandwich beam with silica aerogel addition; (b) Mode 1; (c) Mode 2 Table 7 Buckling Temperature Sandwich type Buckling Temperature (°F) Sandwich with silica aerogel 149.44 Sandwich without silica aerogel 140.47 4.4. Bending of Sandwich To evaluate both the ductility and soundness of a material, sandwich structure was treated as cantilever beam with one end fixed and point load of 100 N at the other end. Hence, deformation occurred and stress was observed and analysis was carried out on the three components of sandwich, top skin, core and bottom skin. Therefore, it was observed that the maximum deformation and stress were on the top face sheet as depicted in Fig. 9(a). Also, Fig. 9(b) shows deformation on sandwich core while Fig. 9(c) depicts the bottom skin deformation where both the stress and deformation are at minimum. Hence, with the same boundary and loading conditions, in order to improve the flexural stiffness, rectangular shaped carbon fiber was added to the core. Moreover, Fig. 10(a) and 10(b) depicts the detailed and overlay views of rectangular carbon fiber on sandwich core, respectively. Fig. 10(c) shows the stresses absorbed by carbon fiber rectangular strut. In addition, Fig. 11 illustrates the total deformation of the sandwich beam under different applied forces. As a results of that, the sandwich beam with imbedded rectangular shaped carbon fiber has less deformation when compared to sandwich beam without carbon fiber. Hence, for sandwich beam deformation, Fig. 12 shows the effect of core thickness on deformation. Core thickness was increased by 0.2 mm which significantly reduced deformation. Therefore, there was a good correlation between core thickness and deformation; as core thickness was increased, deformation was decreased. Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 603 (a) (b) (c) Fig. 9 Deformation of sandwich (a) Deformation at top skin; (b) Deformation at core; (c) Deformation at bottom skin (a) (b) (c) Fig. 10 Deformation of sandwich with reinforced carbon fiber (a) sandwich view 1; (b) Sandwich view 2; (c) Stresses acting on rectangular carbon fiber 604 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU Fig. 11 Applied force vs. total deformation of sandwich beam Fig. 12 Core thickness (mm) vs. total deformation (mm) 4.5. Conduction Thermal Analysis of Sandwich Beam and Stresses In order to investigate heat transfer, Sandwich structure was made of more than one material, thermal loads and effective factors of the sandwich were observed. Moreover, a change in temperature produced thermal strains which could cause sandwich deformation. The analysis was conducted under steady state thermal module in ANSYS and the solution was imported into static structural module for the observation of thermal strain and mechanical stress. Temperature of 427 °C was applied to top skin and 22 °C to bottom skin. It was assumed that the sandwich beam was used as cover structure which emitted high temperature. The effects of temperature increase from bottom face sheet to top face sheet (T = 22°C to 427 °C) for the sandwich of carbon fiber-polyimide face skin and carbon foam core are shown in Fig. 13. At high temperatures, thermal stress was increased from minimum to maximum causing expansion on the top face, as shown in Fig. 14. Hence, there Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 605 was some deformation in bottom skin (contraction), as shown in Fig. 15. Similarly, silica aerogel with the thickness of 0.5 mm was added as shown in Fig. 16. Fig. 17 shows the corresponding thermal strain nature of the sandwich beam. As a result of considering the heat conduction of the sandwich, based on review [116], carbon fiber-polyimide and carbon foam materials were used. Fig. 18(a) shows the deformation of aerogel layer on the hot side while Fig. 18(b) depicts the thermal deformation of aerogel material only bonded between top skin and core. In addition, Fig. 18(c) shows thermal strain on the bottom skin of the sandwich beam. It was found that thermal strain was minimal on the sandwich beam due to the addition of silica aerogel layers and the top skin did not deform so much as compared when silica aerogel was not added. In general, it was observed that there was significant decrease in heat flux when silica aerogel was added, as depicted in Fig. 19. Sandwich beam was subjected to high temperature ranging from 100 °C to 430 °C and the corresponding heat flux was recorded for sandwich beams with and without aerogel material. The results showed that the sandwich beam with silica aerogel had significant heat transfer resistance, as shown in Fig. 19. Similarly, simulation was repeated, in this case thermal deformation was considered and results showed that sandwich beam with aerogel layers had good thermal strain resistance, as depicted in Fig. 20. However, thermal deformation was decreased by 17.6% when silica aerogel was added as layer. In this analysis, 0.5 mm aerogel layer improved thermal strain by about 17.6%. Fig. 13 Temperature distribution across the top and bottom skins, temperature increasing from T = 27 °C to 427 °C Fig. 14 Sandwich structure showing deformation on the top face at 427 °C (carbon foam core used) 606 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU Fig. 15 Sandwich structure showing deformation on the bottom face at 427 °C Fig. 16 Sandwich structure with silica aerogel layer (a) (b) (c) Fig. 17 Thermal strain on (a) top skin; (b) core; and (c) bottom skin (Scale 0.5x auto) Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 607 (a) (b) (c) Fig. 18 Sandwich with aerogel layer. (a) Sandwich structure showing deformation on the top face at 427 °C (carbon foam core and aerogel layer used); (b) Thermal strain on top aerogel layer; (c) thermal strain on bottom skin Fig. 19 Change in temperature Vs. heat flux of sandwich 608 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU Fig. 20 Change in temperature Vs. thermal deformation of sandwich beam 4.6. Analysis and Comparison The experimental approaches developed by Goswami [120] were simulated and modified. Goswami used aramid sheet for skin and aramid hexagonal honeycomb core, filled with silica aerogel. The setup was separated into two parts: heating system (part A) where the heater was installed on the top face sheet of the sandwich with thermocouple arrangements while only the thermocouple was installed on the bottom face sheet (part B). Temperature increase stopped at 350 ºC because the manufacturer specified that the flash point of silica aerogel has to be 395 ºC. Fig. 21 shows heat flux on honeycomb sandwich panel in three cases; 1) Honeycomb filled with silica aerogel. 2) Honeycomb with silica aerogel as auxiliary face sheet. 3) Honeycomb without silica aerogel. The results showed that the honeycomb with silica aerogel as an auxiliary face sheet had lower heat flux, thereby providing good heat insulation in the honeycomb sandwich beam. In ANSYS workbench, a thermal analysis experiment was simulated and the results were validated. Moreover, the honeycomb filled with silica aerogel as shown in Fig. 22(a) has higher temperature difference (The heat will take longer to transfer from one side to the other) than the one without silica aerogel as depicted in Fig. 22(b). Furthermore, the methods used by Goswami in the experiment was by no means the most effective approach towards providing heat insulation in the honeycomb sandwich as there was much heat flow in honeycomb cell walls, as shown in Fig. 22(c). In general, silica aerogel was used as an auxiliary face sheet before the honeycomb hexagonal core as depicted in Fig. 22(d). Therefore, heat flow was minimal and evenly distributed through the honeycomb core, as shown in Fig. 22(e). Critical Buckling Bending Analysis of Sandwich Structure Under Axial Compression and Thermal... 609 Fig. 21 Time vs. heat flux of sandwich panel (a) (b) (c) (d) (e) Fig. 22 Honeycomb sandwich panel: (a) Honeycomb filled with silica aerogel; (b) Honeycomb without silica aerogel; (c) Heat flow in honeycomb cell walls on honeycomb filled with silica aerogel; (d) Silica aerogel as auxiliary face sheet; (e) Reduced heat flow on core cell walls (silica aerogel as auxiliary face sheet) 610 B. SAFAEI, E. CHUKWUELOKA ONYIBO, D. HURDOGANOGLU 5. CONCLUSION The findings of a detailed study and simulation were shown and plotted and important observations were recorded. Thermal stresses and buckling temperature were improved by the addition of silica aerogel material. Steady state condition of the sandwich beam was investigated in commercial software ANSYS and the temperature induced stress and the nature of thermal expansion-induced deformation were noted. Hence, the parameters affecting thermal strain and heat flow were mechanical properties and the most significant one was thermal conductivity, as we considered the heat conduction of the sandwich beam (heat flux). In addition, experimental approach was simulated and modified. Filling hexagonal honeycomb cells with silica aerogel was not the most effective way of heat reduction in the sandwich but it could be used as an auxiliary face sheet. Moreover, carbon foam with lower thermal conductivity was further improved by the addition of silica aerogel layer which was the lightest and hence had the mass of 1.22 g and extreme heat flow resistance. 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