Thermo-viscoelastic analysis of the integrated T-shaped composite structures
Introduction
Integrated T-shaped composite structures have been used as an aircraft part for many years, which can minimize the numbers of required fasteners, reduce fit-up and shimming efforts, and yield a highly optimized composite design with both cost and weight savings. Residual stresses play a predominant role in the post-molding behaviors of the integrated T-shaped composite structures such as mechanical performance, curing deformation, dimensional stability or durability. Therefore, it is necessary to study the relationships between the residual stresses and the curing deformation of the integrated composite structure by using a reasonable constitutive model.
There are many factors to influence the process-induced residual stresses and the curing deformation of the integrated composite structure, such as the hygrothermal expansion, the resin exothermic chemical reaction, the coefficients of anisotropic thermal expansion (CTE) for composite materials and so on [1], [2], [3], [4], [5]. Most studies [6], [7], [8], [9] about curing deformation mechanisms of the integrated composite structures are concentrated on the residual stresses and the warpage deformation. In earlier studies, some researchers used purely elastic models to describe the curing deformation behavior of the integrated composite structures [10], [11]. Cure Hardening Instantaneously Linear Elastic (CHILE) model is also used to study the residual stresses and the curing deformation of the composite structures based on the temperature dependence of elastic modulus [1], [12], [13], [14]. However, the fundamental validity and applicability of these models have not been proved [15]. In fact, the elastic model is not sophisticated enough to capture the complexity of the problem or to obtain quantitatively good results for realistic cases. Recently, the viscoelastic model [16], [17], [18], [19], [20], [21] has been developed to study the mechanical behavior of the polymer composites [22], [23] including both linear viscoelastic behavior [21], [24] and nonlinear viscoelastic characterizations [19], [20], [22], [23], [25].
The aim of this paper is to establish a three dimensional (3D) incremental viscoelastic constitutive model and provide a numerical method to predict the residual stresses and the curing deformation of the integrated T-shaped composite structures during the curing process. And the effects of the cooling rate and the curing strategies on warpage deformation of the integrated T-shaped composite structures are also studied.
Section snippets
Heat transfer equations
The thermo-chemical model [6] is described by:where ρ denotes the density of the composite; C is the specific heat of the composite; T is the temperature of the composite; kx, ky and kz are the thermal conductivities of the composite in the x, y, z directions, respectively; represents the instantaneous heat generated by the cross-linking polymerization of the resin, which is determined by the following expression [8], [26]:where α is the
Configuration
A typical integrated T-shaped composite structure is shown in Fig. 1a. The frame 1 consists of six plies of T300/QY8911 prepreg tape with a [−45/0/45/90/−45/0] lay up, the frame 2 consists of six plies of T300/QY8911 prepreg tape with a [−45/0/45/90/−45/0] lay up, and the skin laminate consists of 16 plies of T 300/QY8911 prepreg tape with a [45/0–45/90/45/0/−45/0]s lay up. The thickness of the single ply is 0.25 mm. In the adhesive noodle zone, the material is also T300/QY8911, but the fiber
Discussion
The interlaminar normal stress distributions along x1-axis are studied for the integrated T-shaped composite structures. At the same time, both the residual stresses and the curing deformation of the integrated T-shaped composite structures are analyzed under different cool-down paths and curing strategies.
Conclusions
In this paper, both a reasonable and effective constitutive model and an effective calculation method are established to evaluate the curing residual stresses and the curing deformation for the integrated T-shaped composite structures, some important conclusions are shown as:
- (1)
A three dimensional (3D) incremental viscoelastic constitutive equation is established and implemented into finite element software ABAQUS to predict the deformation and the residual stresses of the integrated T-shaped
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