1. Introduction
Due to the extensive usage of polymer composites in various structural applications, promoting green composites that are based on natural fibers and bio derived polymers helps to create a sustainable green environment for our next generation. Due to the green materials used in the green composite, it emits no or nil carbon emissions during its destruction than that of a synthetic composite. This, in turn, reduces environmental pollution and provides a sustainable green environment. The evolution of natural fiber composites in loadbearing applications such as the automotive, construction and other sectors encourages the researchers to focus on the natural fiber composites subjected to static and dynamic loads. Due to the structural instability of composite structures, the structure will attain a failure in various ways such as fatigue failure and buckling failure. The possibility of the occurrence of a buckling failure of composite structures due to the axial compression load or thermal load happens often. As the natural fiber polymer composite structures are used in various loadbearing applications, it may be under an axial compression load all along their service. During the entire life cycle of a natural fiber reinforced polymer (NFRP) composite, it must withstand loads and remain stable. However, the structure might be subjected to large compressive loads, which in turn cause a buckling failure. When a failure is due to buckling, an NFRP composite structure fails at a load equal to several times lesser than the material’s yield strength. It is well known that the buckling on a structure depends on the slenderness ratio of the structure. Several research works have addressed the mechanical properties and more physical characteristics of NFRP composites. In addition to the characterization of new materials, it is essential to study their structural performance during the service. Hence it is important to examine the buckling behavior of NFRP composite structures to enhance their usage in various applications.
Leissa [
1] presented a brief overview about the buckling characteristics of laminated composite plates and concentrated on various studies such as a plate with interior holes, shear deformation, local effects, nonlinear stress-strain behavior, sandwich construction involving other materials, hygro-thermal effects, external stiffeners, post buckling behavior and the effects of early imperfections. Biggers and Srinivasan [
2] addressed the buckling characteristics of a composite plate and identified the improvements achieved during compression/buckling loads of a rectangular composite plate. The authors also discussed the effects of tailoring the laminated composite plates with different boundary conditions, thicknesses, aspect ratios and membrane stiffnesses on the buckling loads.
Kim and Hoa [
3] carried out experimental and numerical investigations to study the buckling performance of composite plates subjected to bi-axial loading and proposed the modified rectangular plate specimen. Peining et al. [
4] explored the buckling performance of a thin-walled carbon/epoxy laminated circular cylindrical composite shell under combined axial and torsional loading both analytically and experimentally. It was found that the stiffness eccentricity played a major role on the amount of axial buckling load than that of the combined load. Tafreshi [
5] presented a buckling and post buckling analysis of a laminated composite cylinder with cut outs when it was subjected to the combined effect of internal pressure and compression and found that the buckling load of a compression loaded cylinder was highly influenced by internal pressure, cut out and orientation.
Zhong and Gu [
6] developed an exact solution using the first-order shear deformation theory to investigate the buckling performance of simply supported rectangular plates with a symmetrical cross ply subjected to unidirectional linearly changing in-plane loads. A parametric study was also conducted to probe the buckling load factor due to the effects of the thickness-to-width ratio, the aspect ratio and the modulus ratio.
Priyadarsini and Kalyanaraman [
7] addressed the buckling and post buckling characteristics of thin carbon fiber reinforced polymer laminated composite cylindrical shells under load and displacement controlled static and dynamic axial compression both experimentally and numerically. Parametric studies were also carried out by performing a numerical simulation to discover the effect of the different types of loadings, lamina lay-up and amplitudes of imperfection and geometric properties on the ultimate strength of the cylinder under compression. Prabhakaran et al. [
8] explored the sound absorption and vibration damping properties of woven flax/epoxy composites and made a comparison with woven glass/epoxy composites. It was found that the sound absorption coefficient and vibration damping capability of flax fiber reinforced composites were higher than that of glass fiber reinforced composites.
Sayer [
9] carried out an experimental and numerical investigation to study the ramifications of different ceramic particles such as aluminum oxide (Al
2O
3), silicon carbide and boron carbide (B
4C) on the elastic properties and load carrying capabilities of ceramic particle filled E-glass/epoxy composite plates and found that the critical buckling load of a 10 wt% boron carbide (B
4C) particle filled composite increased by 42%. Abdellaoui et al. [
10] investigated the effects of the number of layers, fiber directions and mechanical properties of a jute fiber reinforced polymer laminated composite both experimentally and numerically. The authors found that the difference between the experimental and calculated results were due to the assumption of a perfect adhesion between the fibers and the matrix. Triki et al. [
11] examined the influence of an alkali treatment on the dielectric characteristics of a woven flax fiber reinforced epoxy composite and found that the adhesion of the fibers/matrix highly depended on the cleaning process of the fabric, which affected the dielectric characteristics of the composite. Bensadoun et al. [
12] investigated the fatigue behavior of various flax fiber composites (under tension–tension mode) where the flax fiber in the form of textile architectures, a random mat and two laminate configurations were used. It was found that the fiber architecture had a major impact on the fatigue performance of the flax fiber composites where the superior static strength and modulus combinations delivered the best fatigue characteristics.
Rajesh and Pitchaimani [
13] investigated the influence of the weaving pattern of plant fiber yarns such as a conventional twisted straight yarn and braided yarn and also the fiber yarn orientation on the mechanical behavior such as tensile, flexural and impact properties. The results revealed that the composite made of the woven fabric with braided jute yarn showed better mechanical properties than that of the composite made with the other fabric having a conventional weaving pattern. It was also found that the composite made of the woven braided fabric exhibited better mechanical properties than that of a random oriented short fiber reinforced composite. Rajesh and Pitchaimani [
14] explored the buckling and free vibration behaviors of a natural fiber reinforced composite beam subjected to axial compression experimentally. An experimentally computed critical buckling load was verified with a numerical analysis based on the finite element method. It was found that the buckling strength of the composite laminate was enhanced with the number of layers and it was also observed that the weaving style of a woven fabric affected the critical buckling load in which the basket type weaving model gave a better buckling strength. Suthenthiraveerappa and Gopalan [
15] investigated the effect of porosity associated with natural, i.e., plant fiber, composites along with the transversely isotropic characteristics of plant fibers on the elastic constants of both jute and aloe fiber composites. A new methodology was also developed to estimate the elastic constants of uniform and taper polymer laminated composites reinforced with natural fiber.
Rozylo et al. [
16] performed a numerical and experimental investigation on the buckling of thin-walled carbon/epoxy laminate composite profiles with top-hat sections under an axial compression and focused mainly on the critical and post critical states. Gopalan et al. [
17] carried out experimental and numerical investigations on the dynamic characteristics of uniform plant fiber reinforced polymer laminated composite plates wherein the experimentally determined elastic constants of the composite lamina were used for the numerical simulation based on the hierarchical finite element method. Suthenthiraveerappa et al. [
18] addressed the dynamic characteristics of thickness tapered plant fiber reinforced polymer laminated composite plates both numerically and experimentally. A variable size (h) and polynomial degree (p) [h-p] finite element model using the higher-order shear deformation theory was proposed in a numerical simulation. Various parametric studies were also performed using the proposed finite element model by considering the different parameters such as the ply orientation, the aspect ratio and the number of layers. For the numerical simulation, the elastic constants were determined using a new theoretical approach especially for the NFRP laminated composites.
Xu et al. [
19] presented a new symplectic analytical approach embedded with the finite element method to investigate the buckling and vibration characteristics of a partially or internally cracked natural fiber reinforced composite plate with corner point supports. The authors stated that a plate with an internal crack would decrease the critical buckling load and the natural frequency more than that of a plate with a surface crack. Chew et al. [
20] explored the mechanical performance of a flax epoxy composite, which was made in the form of a helicoidal laminate stacking configuration under out-of-plane and impact loads and found that this kind of stacking configuration absorbed more energy under an impact load than that of cross ply and quasi-isotropic natural fiber reinforced polymer composite laminates. Ebrahimi et al. [
21] investigated the buckling behavior of a graphene oxide powder reinforced (GOPR) nanocomposite shell using the mathematical model based on the first-order shear deformation theory and explored that the critical buckling load of GOPR nanocomposite shells increased significantly with the increase of the weight fraction of the graphene oxide powder. Vallala et al. [
22] addressed the structural characteristics of natural fiber reinforced composite plates and pressure vessels such as bending, buckling and vibration responses using the developed mathematical model.
Tuni et al. [
23] examined in detail which categories of the supply chain were actually associated in a green performance assessment and discussed the various quantitative methods that are suitable for assessing the environmental performance of supply chains. Goh [
24] presented a case study and investigated the barriers on adopting low-carbon warehousing in the Asia-Pacific through an elastic net regression analysis. This work also suggested a low-carbon warehousing technique or procedure to control the carbon emissions in warehouses for providing a sustainable green environment. Carbone et al. [
25] discussed the development of environmental dynamic capabilities (DCs) in the field of green supply chain management based on the regression analysis performed to enhance the profitability of the companies and to obtain a sustainable supply chain.
Although many research works have discussed the various research aspects of natural fiber composites, the buckling behavior of natural fiber composites have not been explored well either experimentally or numerically. Optimization tools such as the response surface methodology in the determination of the optimum critical buckling load of natural fiber composites are also not often attempted. Very few works have reported the elastic constants of natural fiber composites but the elastic constants of flax fiber composites are not exposed much. To enhance environmental sustainability, the evolution of green composites in all applications is a must. In order to accomplish that evolution, the development of green composites with a high stiffness and strength is essential.
In this work, experimental and numerical analyses on the buckling behavior of woven flax/bio epoxy composites under an axial compression were carried out. The response surface methodology (RSM) was used to frame the various combinations by considering three different factors that were the number of layers, the width of the plate and the ply orientation and in each parameter three levels were followed. Using the RSM approach, twenty samples each having different combinations were framed for the buckling analysis. The critical buckling load and compressive strength of a woven flax/bio epoxy (WFBE) laminated composite was obtained experimentally for three out of the twenty samples, which were framed using the RSM approach. The numerical simulation was then carried out for the same samples using the finite element software ANSYS. The elastic constants needed for the numerical simulation were determined experimentally. The finite element model used in ANSYS was endorsed by comparing the critical buckling loads of the three samples obtained numerically with the experimentally obtained results. The regression equation was then obtained from MINITAB© software. In addition to the comparison of the experimental and numerical results, the results obtained from the regression equation were compared with both the experimental and numerical results. The authors concentrated on the development of a green composite for buckling loadbearing structural applications to enhance environmental sustainability. This work focused on the composite production industries and researchers in the field of composite structures who are keenly looking to shift from synthetic composites to green composites.