PSI - Issue 28

Saiaf Bin Rayhan et al. / Procedia Structural Integrity 28 (2020) 1892–1900 Author name / Structural Integrity Procedia 00 (2019) 000–000

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composites is weight reduction, corrosion resistance, part-count reduction, enhanced fatigue life, and wear resistance, to name a few. In composite micromechanics, homogenization is the first step towards the design and analysis of composite structures (Yan (2003)). The main aim of homogenization is to establish the macroscopic behavior of composites which are microscopically heterogeneous (Cioranescu and Donato (2010)) in order to describe the stiffness presented by five elastic properties namely E 11 (modulus of elasticity in the fiber direction), E 22 (modulus of elasticity in the direction transverse to the fibers), G 12 (in-plane shear modulus), G 23 (out of plane shear modulus) and υ 12 (in-plane Poisson’s ratio) (Barbero (2011)). Dating back from the 19th century, many researchers have proposed analytical, semi-analytical and computational homogenization models based on representative volume element (RVE) to evaluate the elastic properties of unidirectional composite materials (Saeb et al. (2016)). The simplest law to quickly estimate the four elastic constants (E 11 , E 22 , υ 12 , and G 12 ) is the rule of mixture (ROM), which is mainly established by Voigt (1889) and Reuss (1929). However, since the predicted values of E 22 and G 12 adopting ROM disaccord with the experiments, the modified rule of mixture (MROM) can be an alternative for better estimation (Younes et al. (2012)). A similar attempt to correct the values of E 22 and G 12 is found by Halpin-Tsai equations (Affdl and Kardos (1976)). However, the main limitation of using ROM, MROM and Halpin-Tsai models is that they cannot predict the value of G 23 . To formulate all five independent elastic properties, a well-accepted micromechanical model is the Chamis model which uses the same formulation of ROM to estimate E 11 and υ 12 ; however, different approaches for other elastic moduli E 22 , G 12 and G 23 (Sendeckyj et al. (1989)). Other widely used constitutive laws are elasticity approach model (EAM) (Hashin and Rosen (1964); Christensen (1990)), self-consistent model (S-C) (Hershey (1954); Budiansky and Wu (1962); Hill (1965)) and Mori-Tanaka model (M-T) (Mori and Tanaka (1973); Benveniste (1987); Luo and Weng (1987)). More recently, a new analytical approach, termed as bridging micromechanics model was established based on bridging matrix to predict both the stiffness (Huang (2001a)) and strength (Huang (2001b)) of unidirectional composite materials. Since the development of computer simulation programs, the finite element method (FEM) has been widely used by researchers to estimate the elastic properties of composite materials (Alexander and Tzeng (1997); Michel et al. (1999); Sun et al. (2001); Andreassen and Andreassen (2014); Otero et al. (2015)). FEM can be an effective tool to predict macroscopic properties of pultruded composite lamina (Xin et al. (2019)). For more complex problems, like the determination of effective properties of nonlinear composite materials reinforced with particles of different shapes, a hybrid M-T/FEM method can be used with simplified geometry (Ogierman (2019)). In recent times, the virtual element method (VEM) has gained popularity for computational materials homogenization, which is a powerful generalization of FEM, capable of solving polygonal mesh elements including non-convex or highly distorted elements (Lo et al. (2020)). Other than FEM, meshless methods such as Natural Neighbour Radial Point Interpolation Method (NNRPIM) can be used efficiently to predict better results than FEM with an expense of high computation time (Rodrigues et al. (2018)). Even though the numerical methods are widely used to predict the mechanical properties of composite materials, defining the geometry of RVE and boundary conditions can be a challenging and time-consuming task [Saeb et al. (2016); Younes et al. (2012)). To overcome these problems, a preloaded geometric definition of RVEs and boundary conditions can be employed via Ansys Material Designer to estimate the stiffness of composite lamina (Ansys Inc. (2018)). The main objective of this current research paper is to compute the elastic moduli of the unidirectional composite lamina (carbon/epoxy and polyethylene/epoxy) and compare them with available predictions of analytical/semi-analytical models, namely, I. Chamis Model, II. EAM Model, III. Bridging Model, IV. M-T Model and V. S-C Model; Computational model, namely, VI. Comsol Multiphysics FEA & VII. Experimental data found in the literature (Younes et al. (2012)) to evaluate the efficiency and reliability of the FEM technique adopted by Ansys Material Designer. To the best of the authors’ knowledge, there is no previously published work presenting the modeling of elastic properties based on Ansys Material Designer.