1. Introduction
Composite laminates are susceptible to manufacture defects due to their inherent anisotropic characteristics of composite materials and complex manufacturing processes. Fiber waviness defects are the most commonly observed manufacturing defects in the composite laminates, which are introduced unintentionally during the manufacturing process. The presence of fiber waviness defects is well-known to reduce the compressive strength of composite laminates. Therefore, the investigations of fiber waviness defects are important both to evaluate the structural integrity of composite components and to improve manufacturing techniques to reduce the defects.
Many studies have been carried out on the formation of fiber waviness defects and the influence of fiber waviness defects on the mechanical performance of fiber-reinforced composites. Recent studies were summarized in Alves et al. [
1] and Kulkarni et al. [
2]. The formation of fiber waviness is mainly caused by the selected processing methods and the geometry features of composite structures [
3,
4,
5]. The investigation of the processing parameters by Kugler and Moon showed that the major reason for the formation of fiber waviness in thin laminates was the mismatch of the coefficient of thermal expansion between the tool plate and part [
3]. The various sources of in-plane and out-of-plane fiber waviness in the composite structures that occurred at the fabrication stage were detailed by Potter et al. [
4]. The tool geometry, such as the inner or external corners, is also a major cause of the out-of-plane fiber waviness [
5]. In the filament-winding process, the local buckling of prepreg or wet hoop-wound filament strands is a result of the pressure exerted by the overwrapped layers [
6]. Layer waviness occurs in thick cross-ply or multidirectional laminates as a consequence of lamination residual stresses built up during curing [
6]. In the molding process of hot drape-forming technology, in-plane slip deformation of fiber layers might be limited in a multilayer prepreg, resulting in in-plane fiber buckling and out-of-plane wrinkling [
7]. In the process of automated fiber placement, the laying heads turning on small radii will cause fibers to buckle out-of-plane [
8]. The unexpected ply gaps and overlaps due to a contoured mold surface also induce out-of-plane waviness during manual/automated prepreg lamination [
9,
10]. Based on its direction, fiber waviness can be categorized as in-plane waviness or out-of-plane waviness [
11,
12]. In-plane waviness, also known as in-plane buckling, involves the cooperative undulation of fibers within the plane of composite laminates [
3,
13]. Out-of-plane waviness, also known as ply waviness or wrinkling, is identified by the fiber-misalignment through-the-thickness of laminate, resulting in localized wavy regions. Out-of-plane waviness is very commonly observed in thick-section components or curved composite parts [
13]. The geometry of out-of-plane waviness is usually characterized with the amplitude, wavelength and waviness angle [
14], and simplified with a sine/cosine function or the Gaussian function [
15]. The out-of-plane waviness is the focus of the current study because they occur in the hat-shaped composite stringers in an aircraft wing, which is of our interest to design.
Fiber waviness defects were demonstrated by experiments and numerical simulations for reducing the mechanical performance of composite laminates and structures, such as compressive strength, tensile strength, fatigue life. In the open literature, the stiffness and natural frequency of a composite beam had a reduction due to the in-plane fiber waviness [
13]. The pristine compressive strength of the laminates also presented a drop due to the out-of-plane fiber waviness defects [
16]. It has been reported that the degradation in terms of the tensile stiffness and the failure load of the laminates grew with the increasing height of the out-of-plane fiber waviness [
15,
17]. The strength of the curved laminates was weakened by the out-of-plane fiber waviness due to the premature failure caused by the local stress concentration around the fiber waviness [
18,
19]. The ultimate open-hole compressive strength of the CFRP laminates was also reduced by the containing concave waviness defects [
20]. Both the in-plane waviness and the out-of-plane waviness reduced the tensile and compressive mechanical properties of composite laminates [
21]. Nartey et al. presented a maximum of 21% and 37% drop in the tensile and compressive strength of the composite laminates containing fiber waviness induced by the most severe combination of gaps and overlaps [
22]. Wisnom and Atkinson carried out a finite element (FE) analysis of the compressive failure of unidirectional laminates with artificially induced waviness [
23]. Garnich and Karami proposed a linear elastic finite element micromechanics model for wavy fiber composite to determine the average stress and strain components [
24] and performed a failure study for various types of localized fiber waviness [
25]. Lemanski et al. performed the FE analysis on the compressive behavior of the unidirectional composites with a region of misaligned reinforcement [
26,
27]. Mukhopadhyay et al. built up three-dimensional FE models to predict the tensile, compressive and fatigue failure of quasi-isotropic composite laminates with embedded ply waviness [
16,
28,
29]. Davidson and Waas developed an FE model to study the interaction and influence of defect dimensions on the compressive strength, which allowed the kinking and splitting of composite layers [
30]. Ning et al. established an elastic-plastic damage model of composite laminates and simulated the compressive behavior of the composite laminates with out-of-plane waviness subjected to axial compressive loading [
31]. Overall, the current investigation of fiber waviness defects shows a trend from unidirectional composite to engineering applications.
In this paper, four configurations of test specimens with different severities of fiber waviness defects were manufactured and tested. The severity of fiber waviness on the specimens was controlled by the customized molds, which were cured together with the specimens. The compression tests were performed following the instructions of ASTM D6641/D6641M-16 [
32]. An FE model was developed based on the specimen information. The continuum damage mechanics and cohesive zone models were incorporated in the developed FE model to simulate the failure process caused by waviness defects. Then, the experimental results were used to validate the developed FE model. On this basis, the influence of two proposed waviness parameters on compressive strength is studied by FE simulations.
The purpose of this study is to build up relationships between waviness parameters and compressive failure load drop and provide further insight into the influence of out-of-plane waviness defects on the failure of composite stringers in an aircraft. The organization of the paper is as follows. The manufacturing process of the hat-shaped composite stringer is briefly described in
Section 2.
Section 3 presents the artificially induced waviness of controlled severity in testing specimens and experimental results. The three-dimensional FE models with the damage formulations are presented in
Section 4. A comparison between the testing results and simulated ones is also shown in
Section 4.
Section 5 discusses the relationship between waviness parameters and compressive failure load drop. Finally, conclusions are drawn based on the above studies in
Section 6.
6. Conclusions
Aiming at the hat-shaped composite stringers in a civil aircraft, experimental testing and numerical simulations have been carried out to investigate the influence of out-of-plane waviness defects, which are commonly observed during their manufacturing process. The waviness-free laminated specimen and the specimens with pre-defined waviness defects have been carefully produced with the designed lay-up as in the composite stringers. Mechanical tests show that the specimens with waviness defects exhibited two principal failure modes in the wrinkle region, which may result in a significant reduction in the compressive capacity of the stringers. Additionally, the inter-ply failure mode was observed for all severity cases, while the fiber fracture failure mode seems to dominate the worst severity case (i.e., A/H = −20%).
A dedicated FE model was developed with a special element mesh methodology to accommodate the waviness profiles. A significant drop of about 37–58% of the compressive failure load was observed for the specimens with waviness defects in both the numerical simulation and experimental results. The FE model was also used to predict the compressive failure load for a large range of severity levels, which generated relationships between the compressive failure load and the waviness parameters.
Several conclusions can be drawn from the current study:
- (1)
Experiments and FE simulations were carried out with the fiber waviness ratio A/H of −20%, −10%, 10%, 20% and waviness-free specimens. The numerical results and failure modes have a good agreement with those from testing. Therefore, the 3D FE model in this paper can be used to predict the compressive failure load and failure mode of composite laminates with out-of-plane waviness defects.
- (2)
With the increase of the fiber waviness ratio A/H (absolute value), the compressive failure load of both convex and concave fiber waviness decreases. It also shows a nonlinear relationship between them. For the current lay-up, the fiber waviness ratio A/H has little influence on the compressive failure load when it is less than 5%. Therefore, this value may be identified as an acceptance criterion during the manufacturing process of the composite stringers, beyond which a significant reduction of compressive failure load may occur.
- (3)
It seems that the effect of the number of plies with fiber waviness n varies under different A/H conditions for convex fiber waviness. We investigated a low, moderate and high level of A/H (i.e., A/H = 7.5%, 15.0% and 25.0%). When it is 7.5%, the compressive failure load only has a slight reduction as n increases. In addition, the curve tends to be flat when n >= 6.
Further work will involve applying the developed FE model for the prediction of the failure mechanism and mode of the aircraft stringers with random fiber waviness defects from a statistical perspective.