Elsevier

Composite Structures

Volume 107, January 2014, Pages 160-166
Composite Structures

Optimization of variable stiffness composites with embedded defects induced by Automated Fiber Placement

https://doi.org/10.1016/j.compstruct.2013.07.059Get rights and content

Abstract

Variable stiffness composite laminates can be manufactured using Automated Fiber Placement (AFP) technology. An improvement in structural performance can be achieved by tailoring their material properties in directions that are more favorable to carry loads. During AFP manufacturing, however, the formation of defects, mainly gaps and overlaps, is inevitable. The extent of a defected zone is generally controlled by two sets of parameters: design parameters; and manufacturing parameters. In this work, we investigate how the parameters governing the formation of defects impact the set of optimal solutions for a multi-objective optimization problem, where in-plane stiffness and buckling load are simultaneously maximized. It is found that increasing the number of tows within a course reduces the amount of defected areas, where the course width is kept constant. Furthermore, the amount of defect areas significantly reduces by using a wide course, which has the effect of both increasing the deviation from the designed fiber path and reducing the number of manufacturable designs. The results show that a complete gap strategy shifts the defect-free Pareto front, obtained without considering the effect of defects, towards lower in-plane stiffness and buckling load; on the other hand, a complete overlap strategy shifts the Pareto front towards higher structural properties.

Introduction

Automated Fiber Placement (AFP) is a manufacturing technology that offers great flexibility to build composite laminates with a variety of structural geometries and laminate layups. In particular, complex geometries, such as double curvature surfaces, and non-conventional composites with variable stiffness can be produced by laying down fibers along preferred curvilinear paths within the ply. The structural benefits of variable stiffness laminates are achieved by tailoring the material properties in directions that are more favorable to carry loads within the laminates.

The advantage of using curvilinear fibers to improve the structural performance of a composite laminate has been extensively demonstrated [1], [2], [3], [4], [5], [6]. Several studies proposed the optimum fiber path that minimizes the compliance of a cantilever beam [7], maximizes the buckling load of a plate [8], maximizes the buckling load of a hybrid composite shell [9], simultaneously maximizes the buckling load and in-plane stiffness [10]. These works are promising because they demonstrate the structural improvement that tailored curvilinear fiber paths can potentially generate. However, these results are only theoretically optimum, as they do not consider the manufacturing constraints, e.g. the minimum turning radius of the fiber path imposed by an AFP machine. As a result, some of the optimum solutions might not be manufacturable. Alhajahmad et al. [11] accounted for the minimum turning radius in the search for the optimal fiber path that maximizes the buckling load of a plate subjected to pressure and in-plane loads. Furthermore, Blom et al. [12] obtained a fiber path that maximizes load-carrying capability of a cylinder under pure bending load.

The above works assume the laminates to be defect-free (ignoring the presence of defects). In practice, however, the method used by an AFP machine to manufacture a laminate with curvilinear fibers generally leads to the formation of defects in the form of gaps and/or overlaps. During the manufacturing process, the first course (a band of tows) is laid down along the designed fiber path. Subsequently, the first course is repeatedly shifted to cover the whole laminate. If the course width could change continuously, there would not be any defects in the laminate. Since an AFP machine can change the course width only by a discrete value via either adding or dropping tows, small defect areas form within the laminate. Triangular gaps and/or overlaps generally appear between adjacent courses, an AFP process outcome that affects the structural performance of the final laminate. There are several strategies to drop the tows. 0% coverage (complete gap) is a strategy that involves dropping a tow as soon as one edge of the tow reaches a course boundary; it creates small triangular areas without fibers, i.e. gaps. Another method is 100% coverage (complete overlap); here, a tow is dropped when both edges of the tow cross the course boundary, thereby creating small areas of triangular overlaps. An intermediate scenario is when the coverage is between 0% and 100% [13]. The strategies explained above can be also followed to add a tow. Another strategy to manufacture a laminate without any gap is to avoid dropping the tows, which results in large overlap areas within the manufactured laminate. This strategy is referred to as the tow-overlapping method.

In the literature, the study of the effect of defects, mainly overlaps, on the mechanical properties of variable stiffness laminates manufactured by AFP has attracted the attention of several researchers. Wu et al. [14] conducted experiments that showed the prebuckling stiffness of a 20-layered variable stiffness panel with tow-overlapping is 27% higher than a [±45]5S cross-ply laminate, while it is only 4% higher for the panel with gaps. Lopes et al. [15] investigated the first-ply failure load of a variable stiffness laminate. They found that the optimum variable stiffness design obtained by Tatting and Gürdal [13], [16] increased the first-ply failure load by 24.8% and 33.9% for a complete gap and tow-overlapping strategies, respectively. In another attempt, Lopes et al. [17] further extended the previous results to account for the progressive damage behavior and final structural failure. It was shown that for a flat plate without a central hole, the optimum variable stiffness design can increase the strength by 25.2% and 41.2% for a complete gap and tow-overlapping strategies, respectively. The increase in strength for the plate with a central hole is 13.4% for a complete gap and 55.5% for a tow-overlapping strategy. It should be noted that in the previously mentioned works gaps are not considered in the analysis of the variable stiffness laminates. Blom et al. [18] first investigated the influence of gaps on strength and stiffness of variable stiffness laminates using the Finite Element Method (FEM). They found that increasing the gap areas in the laminate deteriorates both strength and stiffness properties. They also investigated the effect of tow width on the stiffness and strength of a variable stiffness laminate and concluded that in addition to the size of the gap areas, their distribution also has an effect on the structural properties of the laminate.

The area percentage of gaps and overlaps depends on two sets of parameters: manufacturing parameters, such as the tow width, the number of tows in a course, and the tow drop strategy; and design parameters, which define a curvilinear fiber path. In the past, these parameters were not considered in the optimization of a variable stiffness laminate. On the other hand, one expects that optimum fiber paths for an ideal defect-free laminate deviate from those for real manufactured laminates with embedded defects. Hence the aim of this paper is to factor in the effect of gaps and overlaps in the optimization of variable stiffness laminates. In this work, MATLAB subroutines are first developed to calculate the area and extent of gaps and overlaps in a variable stiffness laminate considering both manufacturing and design parameters. Then, the effects of these defects are considered in the calculation of the laminate in-plane stiffness and buckling load. Finally, the optimization problem of maximizing simultaneously in-plane stiffness and buckling load for laminates with embedded defects is formulated and the set of optimal solutions is obtained. A discussion on the effect of design and manufacturing parameters on the optimized variable stiffness designs is presented before the concluding remarks.

Section snippets

Fiber path definition

A variable stiffness laminate can be designed by defining a reference fiber path along which the AFP machine places the first course. The entire laminate can be manufactured by shifting the reference fiber path perpendicular to the direction of the fiber angle variation. As a reference fiber path, we consider here a constant curvature path presented by Blom et al. [18]. Along this reference path, the fiber orientation can be obtained ascosθ=cosT0+|x|ρ,where θ is the fiber orientation along the

Design parameters

In Section 2, the reference fiber path for manufacturing a variable stiffness laminate is defined. During manufacturing, the AFP machine head follows the reference fiber path and places the first course, whose centerline exactly matches the reference fiber path. Then, the machine head is shifted to place the subsequent courses. The shift distance is generally chosen to avoid the formation of major gaps or overlaps within the laminate [18]. MATLAB subroutines are developed here to calculate the

Manufacturing parameters

The tow width and the number of tows in a course are manufacturing parameters that have also a significant effect on the gap and overlap area percentages. Tows are a thin bundle of fibers and resin that typically have a width of 3.175 mm (1/8 in.), 6.35 mm (1/4 in.), or 12.7 mm (1/2 in.). Each tow can be fed at its own rate to allow steering for that tow. In addition, each tow can be cut and restarted independently from the other ones, thereby increasing AFP machine’s manufacturing flexibility.

Optimization of composite laminates with embedded defects

Section 3 has shown that the design and manufacturing parameters of a variable stiffness laminate have a significant effect on the gap and overlap area percentages, as well as on its buckling load and in-plane stiffness. To investigate the maximum influence of gaps and overlaps on the optimization results, we examine here manufacturing parameters that produce the maximum amount of defects, i.e. 8 tows with a width of 3.175 mm (1/8 in.). The goal is to find the optimum fiber path parameters

Conclusions

The effect of design and manufacturing parameters on the gap and overlap area percentages within variable stiffness laminates has been investigated. The buckling load and in-plane stiffness of defected laminates have been calculated and the impact of gaps and overlaps has been depicted on the Pareto solutions of variable stiffness laminate maximizing both buckling load and in-plane stiffness.

From this study, it is seen that the largest number of tows with the smallest width yields the minimum

Acknowledgements

The authors would like to acknowledge the financial support provided by the Natural Sciences and Engineering Research Council of Canada (NSERC) and Consortium for Research and Innovation in Aerospace in Québec (CRIAQ). We also thank the support of the National Research Council of Canada, Bombardier Aerospace and Composites Atlantic.

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