Thermomechanical properties and stress analysis of 3-D textile composites by asymptotic expansion homogenization method

Abstract

This paper formulates asymptotic expansion homogenization method for the analysis of 3-D composites whereby thermomechanical effects are considered. The equivalent thermomechanical properties, viz. elastic constants and coefficient of thermal expansion, of 3-D orthogonal interlock composites are obtained based on a unit-cell derived from the optical microscopy observation. The Young’s modulus and Poisson’s ratio obtained from the analysis are compared with those obtained by experiments. The results show a good agreement especially for the Young’s modulus. Localization analysis based on the present formulation is also presented to assess the stresses within the constituents of 3-D composites (fiber tows and resin region) due to mechanical loading and temperature difference. In order to facilitate the localization analysis, the unit-cell of 3-D composites is first subjected to temperature difference in order to obtain thermal residual stresses. Subsequently, a beam model utilizing homogenized thermomechanical properties of 3-D composites is built to obtain stresses due to mechanical loading. Two loading cases are considered: beam under uniaxial tension (Case 1) and beam under bending load (Case 2). The thermal residual stresses and stresses due to mechanical loading in each case are then superposed to obtain total stresses. The total stresses are then used to understand the complete response of composite constituents under mechanical and thermal loadings.

Introduction

Composite materials have been widely used in aerospace structures due to their excellent properties as compared to the metallic materials, e.g. high strength-to-weight ratio, good corrosion resistance. The recent development of composite materials aims to obtain better characteristics, such as enhanced damage tolerance and delamination resistance. However, the complexity and heterogeneity of composites often come with costly computational efforts. A modeling approach whereby all composite constituents (fibers and matrix) are explicitly built renders cumbersome meshing techniques, and requires high computational resources. An excellent technique to cope with this problem is to idealize the composite as a unit-cell representing the whole constituents and the corresponding responses, while the equivalent properties and other detailed stresses can be obtained. Representative unit-cell approach has been commonly used in the analysis of 3-D textile composites. Several studies employing this approach in order to predict the failure strength and ballistic impact damage behavior of 3-D orthogonal woven composites were performed by Tan et al. [1] and Sun et al. [2], respectively.

Dealing with the so-called unit-cell, asymptotic expansion homogenization (AEH) method is often employed. This method assumes that the unit-cell can be repeated in specific directions to represent periodicity. AEH regards the composite structure as a homogeneous macrostructure, which is formed by a large number of periodic and heterogeneous microstructure. AEH incorporates asymptotic expansion analysis to couple between microscopic and macroscopic behavior of a system [3]. Generally, AEH is often formulated to obtain thermomechanical properties of heterogeneous structures. Guedes and Kikuchi [4] derived a rigorous formulation of AEH method, and applied the formulation to analyze sandwich honeycomb plate. AEH is also used to analyze textile composites [5], [6], [7], [8] and metal-matrix composites [9]. Francfort [10] developed asymptotic expansion technique for the case of linear thermoelasticity. The incorporation of thermal effects into the heterogeneous unit-cell was performed by several authors to obtain mechanical properties as well as the coefficient of thermal expansions (CTE) [11], [12], [13].

In order to investigate the response of a unit-cell, localization analysis is usually performed in the framework of AEH. The localization analysis can be seen as a reverse scheme of the homogenization method that aims to obtain the local stresses of a unit-cell in a microscopic scale due to the external loads applied onto the homogeneous macrostructure [5], [14]. However, in the studies described in Refs. [5], [14], thermal residual stresses were not considered. In fact, thermal residual stresses may affect the damage behavior of composites [15], [16].

In this paper, a detailed mathematical and finite element formulation of AEH method is proposed to study the thermomechanical response of 3-D textile composite. The textile composite under consideration is 3-D orthogonal interlocked composites. The numerical analysis includes the calculation of equivalent thermomechanical properties, and the localization analysis whereby the critical regions in the constituents of 3-D orthogonal interlock composites are identified based on the maximum stresses. Two load cases, namely uniaxial tension and bending, are studied to determine the critical loading condition by which the damage may initiate in 3-D orthogonal interlock composites. The method developed in this paper may potentially aid the material selection processes, damage analysis of composites, design of textile composites and other engineering steps in various industries (aerospace, automotive, marine, electronic devices [17], medical [18], etc.). Apparently, the composite material selected for present analysis, i.e. 3-D orthogonal interlock composites, has a limited commercial application due to high cost pertaining to the manufacturing processes. This specific type of 3-D composites has been applied only for a few specific areas where 2-D laminates and metallic materials cannot satisfy the desired properties [19]. Nevertheless, the type of 3-D composites selected herein is deemed appropriate to test the capability of homogenization method because of their microstructural complexities.