PSI - Issue 28

Saiaf Bin Rayhan et al. / Procedia Structural Integrity 28 (2020) 1901–1908 Author name / Structural Integrity Procedia 00 (2019) 000–000

1902

2

1. Research Motivation Plates and shells are the fundamental building blocks of aerostructure, which are made of metal alloys and composite materials. One of the main failure types of the plates is buckling. Nowadays, composites are preferred and regularly adopted in structures over metals due to their excellent strength to weight ratio, low part counts, better fatigue life and corrosion resistance. Besides, in recent times, the utilization of woven composites has noticeably increased over unidirectional composites due to the easiness of reinforcing fiber in more than one direction in a single ply and drape ability to form a complex curvature. In this section, we will provide a concise review of critical plate buckling phenomena along with the homogenization and multiscale analysis of woven composite materials. 1.1. Critical plate buckling review To achieve the critical buckling load of a plate, three different approaches are mainly adopted, namely, closed-form solution or analytical method, experimental testing and numerical approximation. Some of the developments of exact analytical solutions of orthotropic plates can be found in earlier literature (Bao et al. (1997); Reddy (1997); Reddy and Khdeir (1989); Senthilnathan et al. (1988); Whitney (1987)). However, one of the main problems associated with these formulations is the limitation of the available equation for a different set of loading and boundary conditions. Besides, solutions are not readily available for orthotropic plates with cutouts, which are regularly found in plate structures to serve various purposes like wiring, maintenance, oil supply lines, weight reduction, etc. The experimental tests play a crucial role to understand the buckling behavior of plates, especially the post-buckling phenomena and nonlinear events (Singer et al. (1998)). Mechanical specimen tests remain a primary step to validate both analytical and numerical solutions (Roberts et al. (1998); Kharghani and Guedes (2020); Madenci (2020)) However, in general, to achieve an average critical buckling load from experiments requires three to five times testing of a single coupon (Rayhan (2019); Tercan and Aktaş (2009)). Besides, it is not feasible to investigate optimization studies like the ply stacking sequence, plate thickness, plate aspect ratio, etc. through experiments (Haftka and Walsh (1992); Hu and Lin (1995); Ho-Huu et al. (2016)). At present, most of the buckling investigations are conducted adopting commercial finite element software like Abaqus, Ansys, Nastran-Patran, etc. due to the availability of powerful computers and faster solution time (M Bash et al. (2020); Atilla et al. (2020); Civalek et al. (2020); Oluwabushi and Toubia (2020)). Besides, geometric nonlinearity and material nonlinearity can be applied to the standard linear solutions to capture the post-buckling load-displacement curve (Muameleci (2014); Quinn et al. (2009)). Moreover, for composite plates, a visualization of the damaged area after buckling can be detected easily by applying different failure modes (Erdem et al. (2019)). However, as stated earlier, experimental data remains a benchmark to evaluate the buckling load accuracy predicted by finite element software and in some cases, the discrepancy of the predicted data and experiments may reach up to an unacceptable limit, as high as 30% (Baba (2007)). 1.2. Micromechanical modeling of woven composites To evaluate the mechanical properties of woven composite materials, a notable amount of research is conducted to develop the homogenization methods (Angioni et al. (2011); Ansar et al. (2011)) based on the Representative Volume Element (RVE) as a unit cell, which is the minimum volume to represent the whole lamina of a composite (Li and Sitnikova (2019)). Back in 1970, a theoretical model was developed to investigate the stiffness of 2D and 3D woven composite materials (Halphin et al. (1971)). Further developments of analytical models are reported by Ishikawa and Chou (1982a); Ishikawa and Chou (1982b); Naik and Ganesh (1992); Naik and Shembekar (1992); Shembekar and Naik (1992), where various parameters like undulation, yarn thickness, the gap between two adjacent layers, slice arrangement (series-parallel and parallel-series) in a unit cell, etc. are considered to calculate the stiffness properties. Later on, semianalytical models were proposed to evaluate the elastic moduli of woven composites assuming that the matrix properties are isotropic and the contact between the fibers and the matrix is perfect (Jiang et al. (2000); Tanov and Tabiei (2001)). In recent times, with the development of multicore computers and commercial software codes, the finite element method has gained popularity to calculate the mechanical properties of woven composite materials. Moreover, the predictions are usually in good agreement with the experimental findings (Aliabadi (2015)). Despite many advantages, the finite element method inherits some drawbacks such as complex geometry modeling,