Design optimization of infill pattern structure and continuous fiber path for CFRP-AM: Simultaneous optimization of topology and fiber arrangement for minimum material cost
Introduction
Additive manufacturing (AM), also known as three-dimensional (3D) printing, allows for easily fabricating a microstructure inside an object. A lightweight machine part with high strength and stiffness can be fabricated by processing the complex spatial structure inside. Meanwhile, the weight reduction achieved through reducing the required materials leads to shorter fabrication times, lower costs, and less environmental impact. In addition, integrating multiple mechanisms into a single part reduces the assembly cost [1]. Recently, the merits of the design for AM (DfAM) method have been widely researched [2,3].
Among the various AM types, the material extrusion type allows for using a wide variety of materials, including various plastics [4,5], metals [6], and ceramics [7]. Fused filament fabrication (FFF), which mainly involves thermoplastic materials, is a typical material extrusion method. When fabricating an object via FFF, the fabrication conditions, such as the extrusion paths and the extrusion temperature, affect the fabrication accuracy and the mechanical properties after the fabrication [8,9]. For these reasons, numerous studies have been conducted about the design method for FFF. For their part, Jin et al. [10] proposed a full-filling path generation method to improve the fabrication accuracy and reduce the fabrication time, while Gupta et al. [11] proposed a continuous path generation method for fabricating a lightweight infill structure.
In addition, design optimization aimed at achieving the desired mechanical properties while considering the FFF conditions has become a topic of interest. Here both Mass and Amir [12] and Ven et al. [13] proposed topology optimization methods that involve controlling the overhangs of the structure to reduce the support structure required in the fabrication process.
Meanwhile, various other design methods target the cellular structures to realize the applications with desired properties [14]. For periodic cellular structures, there are topology optimization for 3D lattice structures based on the homogenization method [15], and an optimization method for graded metamaterial structures [16]. In addition, design method combining solid and lattice structures obtained with topology optimization are researched [17]. Some researches proposed methods for directly designing non-periodic cellular structures. In these methods, the characteristics of microstructure in the homogenization-based optimization are projected to the topological optimized geometry [[18], [19], [20]]. Wu et al. [21] proposed an optimization method for the internal cellular structure to achieve the desired mechanical stiffness while considering the overhangs during the FFF process. When fabricating lightweight structures such as lattice structures via FFF, the anisotropy of the structure's strength will be extremely large since the adhesion strength between the layers is low. Wang et al. [22] proposed an optimization method while taking this anisotropy of strength into account. In short, when fabricating mechanical parts via FFF, it is important to consider the anisotropic mechanical properties in the design process.
Material extrusion type AM also has an advantage in that multiple materials can be used simultaneously [23]. Li et al. [24] proposed a density-based topology optimization method for infill structures composed of multiple materials.
Recently, using continuous carbon fiber, or carbon-fiber-reinforced plastics, with this type of AM method (CFRP-AM) has attracted a great deal of attention since it potentially allows for improving the strength and stiffness of an object without changing its shape [25,26]. There exist several CFRP-AM methods, with the multi-nozzle method currently the most popular. Here, the base material determines the structure's shape, and continuous carbon fibers are placed inside the structure to improve the strength and stiffness in the fiber directions.
Fernandez et al. [27] have proposed a toolpath optimization method to strengthen objects by filling them with a short carbon fiber composite resin material. Papapetrou et al. [28] proposed a topology optimization method for structures fabricated using CFRP-AM. In the method, first, a geometry of a base structure is optimized by energy-based or level-set optimization. Next, continuous carbon fibers are placed considering the path continuity and orientation for fabrication. The fiber direction is not taken into account in the topology optimization phase. Elsewhere, Li et al. [29] proposed a topology optimization method to simultaneously design the structure and the continuous arrangement of the carbon fibers. However, since AM fabrication is not assumed in this method, various problems emerge, such as the carbon fiber path having branches or not being closed, which leads to difficulties in fabrication using CFRP-AM.
With all this in mind, the purpose of this study was to propose a method for simultaneously optimizing the infill pattern structure and the carbon fiber arrangement for reducing the material and fabrication cost. The infill structure is repetitive structure of a unit cell and easy to fabricate using CFRP-AM. First, the proposed optimization method using a genetic algorithm (GA) is described before we outline the two types of optimization performed for a simple cantilever, which involved optimizing the carbon fiber arrangement only. To compare the optimization results, all patterns of carbon fiber arrangement were sought. Meanwhile, the second optimization involved the simultaneous optimization of the infill structure and the carbon fiber arrangement, with the optimization parameters evaluated in terms of the results. Following this, 3-point bending structure was optimized to find the influence of the characteristics of a base infill structure. In addition, a bicycle brake lever was designed using the two types of optimization. The obtained structures were fabricated using CFRP-AM.
Section snippets
Purpose of optimization on inner structure using carbon-fiber-reinforced plastics
Fig. 1 presents a schematic of the design optimization for CFRP-AM, where the horizontal axis is the weight and volume of the structure and vertical axis is the strength and stiffness. The black dashed lines in Fig. 1 represent the material costs and the cost is equal on the same dashed line and becomes higher toward the right. When the base plastic structure is given by the yellow point, the blue area shows the properties that can be achieved by reducing materials. The structural optimization
Settings and finite element simulation on the target structure
First, to evaluate the proposed encoding method for carbon fiber arrangement, optimizations were performed on a simple cantilever. In the same time, a full search for all carbon fiber arrangement patterns was performed to evaluate the optimization results. The algorithms were implemented in Python 3.8.
Fig. 8 shows the target structure and boundary conditions. Here, one end of the structure was fixed, and a 300 N load was applied to the other end. Fig. 9 shows the target structure with no carbon
Settings and finite element simulation on the target structure
Next, we optimized a 3-point bending structure. As Fig. 16 shows, the structure was supported at both ends of the bottom edge and a 400 N load was applied on the center of the top edge.
Two types of optimization were performed, the first of which involved optimizing the carbon fiber arrangement without changing the structure, while the second involved optimizing the infill structure and the carbon fiber arrangement simultaneously. The thickness and height of the infill wall, the setting of the
Application to a brake lever
Assuming that the fabrication would involve the use of CFRP-AM, a bicycle brake lever was designed using the proposed method. Here, we performed two types of optimization, the first of which involved optimizing the carbon fiber arrangement without changing the structure, while the second involved optimizing the infill structure and the carbon fiber arrangement simultaneously. The structure was too large in terms of the number of walls to apply a full search. The designed structures were
Conclusions
The above study indicates the following conclusions.
- (1)
The design approaches to CFRP-AM fabrication can be divided into two types: the design of the carbon fiber arrangement for reinforcing the base structure and the design of the infill structure for reducing the materials. In this paper, the authors proposed a simultaneous optimization method for the structure and the carbon fiber related to the CFRP infill structure while taking the continuous and closed carbon fiber arrangements into account.
- (2)
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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