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In conventional manufacturing processes of composites, Carbon Fibre Reinforced Plastic (CFRP) laminates have been made by stacking unidirectional or woven prepreg sheets. Recently, as a manufacturing process of CFRP, 3D printing of CFRP composites has been developed. The 3D printing process of CFRP composites enables us to fabricate CFRP laminates with arbitrary curvilinear fibre plies. This indicates that the optimization of the in-plane curved carbon fibre placement in a planar ply is strongly required to realize superior 3D printed composites. In the present paper, in-plane curved carbon fibre alignment of a ply with an open hole is optimized in terms of maximization of the fracture strength. For the optimization process, a genetic algorithm is adopted. To describe curved carbon fibre alignments in a planar ply, stream lines of perfect flow is employed. By using the stream lines of the perfect flow, number of optimization parameters is significantly reduced. After the optimization, the fracture strength of CFRP laminate is compared with the results of unidirectional CFRP ply. The curved fibre placement in a planar ply shows superior fracture improvement.

Carbon Fibre Reinforced Polymer (CFRP) composites are applied in aerospace and automobile industry because of the high specific strength and the high specific modulus of the CFRP composites. The mechanical properties of the CFRP composites significantly depend on the direction of the carbon fibre. This gives us an additional chance to optimize the fibre direction of CFRP composite structures.

Conventional CFRP laminates are manufactured by stacking prepreg plies. The optimizations of the stacking sequence of the CFRP laminates are, therefore, the most important issue for the conventional CFRP laminates. Many researchers have proposed the stacking sequence optimization methods [

Recently, a brand new manufacturing method of 3D printed CFRP composites has been developed [

To make distributed different fibre angles in a ply, researches [

In the present study, therefore, continuous curved carbon fibre placement in a ply is optimized with a stream line method used for analyses of perfect fluid. The stream lines of the perfect fluid are intrinsically continuous and do not have an intersection with each other. The new optimizing method using the fibre stream line is, therefore, adopted as a suitable method for the manufacturing of 3D printed CFRP composites. The newly developed optimization method using the stream lines reduces number of design parameters significantly, and the method realizes continuous results of fibre direction without an intersection of fibre bundles. The objective function of the present

paper is to improve the fracture strength of a ply with an open hole. The present study deals with a fibre placement in a ply, and stacking optimizations of plies are our future projects.

The optimization target domain is an open-hole-single-ply plate as shown in

Modulus of elasticity in fibre direction | 134 GPa |
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Modulus of elasticity in transverse to fibre direction | 8.62 GPa |

Modulus of elasticity in out of plane direction | 8.20 GPa |

In plane share modulus | 4.68 GPa |

Out of plane shear modulus in fibre direction | 3.78 GPa |

Out of plane shear modulus in transverse to fibre direction | 2.36 GPa |

In plane Poisson’s ratio | 0.338 |

Out of plane Poisson’s ratio in fibre direction | 0.318 |

Out of plane Poisson’s ratio in transverse to fibre direction | 0.571 |

Tensile strength in carbon fibre direction | 3060 MPa |

Compressive strength in carbon fibre direction | 1600 MPa |

Tensile strength in transverse to carbon fibre direction | 84 MPa |

Compressive strength in transverse to carbon fibre direction | 248 MPa |

Shearing strength | 98 MPa |

Modulus of elasticity | 8.62 GPa |
---|---|

Share modulus | 3.19 GPa |

Poisson’s ratio | 0.35 |

Tensile strength | 84 MPa |

Compressive strength | 248 MPa |

Shearing strength | 90 MPa |

where S_{1} is stress in carbon fibre direction, S_{2} is stress in transverse direction to the carbon fibre, t_{12} is shearing stress, F_{Lt} is tensile strength in carbon fibre direction, F_{Lc} is compressive strength in carbon fibre direction, F_{Tt} tensile strength in transverse to carbon fibre direction, F_{Tc} is compressive strength in transverse to carbon fibre direction, F_{LT} is shearing strength.

Fracture of the each element is judged when the Tsai-Wu fracture index λ exceeds 1. The objective function of the present study is to minimize the maximum value of the Tsai-Wu fracture index λ.

Two types of fibre placement optimizations are conducted in the present study: non-symmetric and symmetric as shown in

To calculate the Tsai-Wu fracture index of at the various elements, FEM analysis is indispensable. The FEM analysis requires the fibre angle for each element to obtain the stiffness. Fibre angle of each element is defined from the continuous curves of the fibre stream lines in the present study. Carbon fibre direction of the each FEM element is decided by using the direction of the fibre stream line at the center of each element, as shown in

these fibre placement of the extremely large curvature. To remove these large curvature points, the property of the matrix is given to the elements where the element center locates within the distance of 10mm from the center of the fibre vortex. This means the fibre bundle is not placed at the element. The gray circle shown in

The objective function of the present study is to maximize fracture stress, which is equal to the minimization of the maximum value of the Tsai-Wu fracture index. For the optimization process, a well-known genetic algorithm is employed. The design variables are shown in

In the present study, a MATLAB Genetic Algorithm (GA) optimization toolbox is used for the optimizations. As a first procedure of the GA, the initial individuals are made by Latin Hypercube Sampling. For example, in the case of the non-symmetric optimization, each individual has 34 variables that satisfy the maximum limit and the minimum limit value requirements shown in ^{−6}, the GA process is terminated. The parameters of the GA in the present study are shown in

Parameter | What the parameter denotes in the flow field | Lower limit | Upper Limit |
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1 | Length between a source point and a sink point. | 1.2 | 20 |

2 | Length between a source point and a source point or sink point and sink point. | 0.6 | 20 |

3 | Tilt of the rectangular consists of source points and sink points. | -90° | 90° |

4 | Diameter of the column. | 0 | 0.2 |

5 | X coordinate of the fibre vortex1. | -0.6 | 0.6 |

6 | Y coordinate of the fibre vortex1. | -0.3 | 0.3 |

7 | Vorticity of the fibre vortex1. | -0.3 | 0.3 |

8 | X coordinate of the fibre vortex2. | -0.6 | 0.6 |

… | … | … | … |

34 | Vorticity of the fibre vortex10. | -0.3 | 0.3 |

Parameter | What the parameter denotes in the flow field | Lower limit | Upper Limit | |
---|---|---|---|---|

1 | Length between a source point and a sink point. | 1.2 | 20 | |

2 | Length between a source point and a source point or sink point and sink point. | 0.6 | 20 | |

3 | Diameter of the column. | 0 | 0.2 | |

4 | X direction length between fibre vortexes. | 0 | 0.6 | |

5 | Y direction length between fibre vortexes. | 0 | 0.3 | |

6 | Vorticity | -0.3 | 0.3 | |

Number of the population in one generation | 200 |
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Maximum generation | 250 |

Initial population selection style | Latin Hypercube Sampling |

Selection style | Roulette selection |

Cross over style | Uniform cross over |

Number of cross over | 152 |

Number of mutation | 38 |

Number of elite preservation | 10 |

Before the optimization of the fibre placement, an optimization of the fibre angle of unidirectional ply of the specimen shown in

unidirectional ply is λ = 1.81. This means that the fracture occurs approximately 55% of the reference applied load. The results of the GA are compared with the result of 0˚ unidirectional ply in the present study.

As the GA is one of the stochastic optimization methods, five runs of optimizations are performed for both types by changing random seed, and the best value is searched in the present study. The best Tsai-Wu fracture index of the non-symmetric type is λ = 0.64, and that of the symmetric type is λ = 0.61. The fracture index λ = 0.64 means that the fracture occurs at 128% of the applied reference load. Compared to the result of the 0° unidirectional ply, the fracture index obtained by the GA with flow stream lines is significantly improved in both types.

Obtained optimized fibre placement of the non-symmetric type is shown in

Although there is slight difference of the Tsai-Wu index values between the non- symmetric specimen and symmetric specimen, the difference is very small. As the Tsai-Wu index value is calculated using the approximation of the fiber direction of each FEM element as described before, the difference seems negligible. This result shows that the symmetric and non-symmetric placement of fibre vortexes have small effect on the increase of Tsai-Wu index value. The Tsai-Wu fracture index value surely increased using the fibre vortexes. This means that the curved fibre placement has possibility to increase the fracture strength of CFRP composites. Fracture of laminated CFRP is our future work.

In the present paper, a new optimization method to provide continuous curved fibre placement without inter-section of fibre bundles in a ply is proposed for the 3D printed continuous fibre composites. The new method adopts stream lines of perfect fluid using sources, sinks and vortexes. The method automatically provides curved fibre lines without an intersection, which is indispensable for actual processing of 3D printed composites. The optimization method is applied to an open-hole single ply under tensile stress and the fracture stress of the ply is maximized by changing fibre placement. As a result, the fracture stress increases up to 173% compared with the unidirectional ply. This indicates that there is possibility to increase composite performance by changing fibre placement in a ply.

The present research was performed with the found of “Development of Numerical Simulation Methods for Cost-Effective Aircraft Design Development of Structure Design Simulation Technologies for Aircrafts, Development of Technologies for Next- Generation Structure Component: Creation and Processing” by New Energy and Industrial Technology, Development Organization of the Japanese government in 2015 and 2016. I would like to express sincerely thanks to them.

Yamanaka, Y., Todoroki, A., Ueda, M., Hirano, Y. and Matsuzaki, R. (2016) Fiber Line Optimization in Single Ply for 3D Printed Composites. Open Journal of Composite Materials, 6, 121-131. http://dx.doi.org/10.4236/ojcm.2016.64012