Elsevier

Composite Structures

Volume 204, 15 November 2018, Pages 882-895
Composite Structures

A design algorithm to model fibre paths for manufacturing of structurally optimised composite laminates

https://doi.org/10.1016/j.compstruct.2018.07.088Get rights and content

Abstract

Fibre steering is involved in the development of non-conventional variable stiffness laminates (VSL) with curvilinear paths as well as in the lay-up of conventional laminates with complex shapes. Manufacturability is generally overlooked in design and, as a result, industrial applications do not take advantage of the potential of composite materials. This work develops a design for manufacturing (DFM) tool for the introduction in design of the manufacturing requirements and limitations derived from the fibre placement technology. This tool enables the automatic generation of continuous fibre paths for manufacturing. Results from its application to a plate with a central hole and an aircraft structure – a windshield front fairing – are presented, showing good correlation of resulting manufacturable paths to initial fibre trajectories. The effect of manufacturing constraints is assessed to elucidate the extent to which the structurally optimal design can be reached while conforming to existing manufacturing specifications.

Introduction

Fibre-reinforced composites are traditionally designed by stacking plies built with a discrete set of constant fibre orientation angles: 0°, ±45° and 90° [1]. These designs do not take full advantage of the potential of composite materials [1], [2], [3]. Performance improvements can be driven by the lay-up of curvilinear fibres [4], [5], which benefits from a better stress distribution and an expanded design space [6], [7]. Automated Fibre Placement (AFP) offers the capability of steering individual fibre tows over the surface of a laminate [1], [5], [8], [9], [10]. Due to the variation of stiffness properties associated with the continuous change in fibre orientation of a layer, these structures were termed as variable stiffness laminates (VSL) [11].

Design and manufacturing of composite structures are interdependent [12]. AFP presents a set of limitations that will affect the manufacturability and quality of designed variable stiffness laminates, such as minimum steering radius (smallest radius of the fibres that can be laid without significant defects, like local fibre buckling or ply wrinkling), minimum cut length (shortest length a tow can be laid in a controlled manner), and gaps and overlaps (defects introduced when a course, set of tows laid up in one machine pass, is not laid parallel to an adjacent one). For instance, tow kinking and wrinkling is noticed in the cylinders manufactured by Blom et al. [13] and Wu et al. [14]. Gaps and overlaps are observed in the cylindrical shells manufactured by Wu et al. [14] and the flat plates manufactured by Tatting and Gürdal [15]. Recently, a new manufacturing technology called continuous tow shearing (CTS) has been developed, avoiding gaps and overlaps at the expense of thickness variation [16], [17].

This type of non-conventional laminates shows an increasing interest from the specialised literature. An extensive review on design optimisation methods can be found in Ghiasi et al. [18] and Sabido et al. [19]. Design approaches include aligning the fibres with the principal stress trajectories and load paths [4], [20], [21], [22], [23], [24] and using lamination parameters to find the optimal stiffness distribution [6], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], which is followed by a retrieval of fibre orientations step [6], [31], [32]. These methods result in an optimal fibre angle distribution, where continuity of the distribution is not guaranteed and manufacturing constraints are difficult to impose. Discontinuities between neighbouring elements are noticed in the optimal fibre orientations in the work of [6], [41], [42]. The manufacturing of such designs with curvilinear fibres is not possible [42], and post-processing would be required [43]. For instance, introducing constraints to ensure continuity of fibre orientations could alleviate this issue [28], [42], [44], [45].

In addition, to overcome this issue, many authors have employed a functional parametrisation to represent the fibre paths. This approach typically consists of optimising a reference path, and then, a ply is created by replicating this path, either by shifting the reference path in a specified direction (usually x- or y- axis) or by placing adjacent courses parallel to one another. The former leads to the occurrence of gaps and overlaps between adjacent courses, which may affect the performance of the laminate [46]; while the latter will likely result in kinks as the radius of the tows decreases to remain parallel to the reference path. Linearly varying fibre angles, introduced in [47], has been widely used in the research [5], [9], [15], [46], [48], [49], [50], [51], [52], [53], [54], [55]. To overcome the reduced design space of a linear fibre path representation, non-linear variations of fibre angles have also been proposed, for example by means of Lagrangian polynomials [56], [57], [58], Lobatto-Legendre polynomials [59], [60], Bezier curves [17], [61], [62], splines [63], [64], B-splines surfaces [41], NURBS (Non-Uniform Rational B-Splines) [65], and Lagrangian interpolation functions applied to a manufacturing mesh [66], [67]. This method reduces the number of design variables and ease the consideration of manufacturing constraints while modelling continuous paths. However, the design space is limited due to the pre-specified set of possibilities [68]. A streamline analogy, also known as a fluid flow analogy, has been employed to compute continuous fibre paths from discrete fibre angles [4], [21], [23], [31], [59], [69], [70].

Other manufacturing features are considered in design, such as minimum curvature radius [12], [32], [66], [67], [68], [71], [72], [73], [74], [75] and minimum cut length [13]. For laminate analysis, studies have been conducted on capturing the influence of as-manufactured geometry and features such as gaps, overlaps, tow-drops and variable thickness for the analysis of VSL, by means of 3D FE models [48], [76], [77], [78], [79], [80], [81], [82], [83], analytical methods [84] and experimental tests [13], [81], [85], [86], [87]. A review focused on analysis methods for buckling, failure and vibration was published by Ribeiro et al. [88] and on design for manufacturing by [89].

However, structural optimisation has been the subject of a larger body of research works, where manufacturability is usually neglected. As a result, few examples exist of practical applications of curvilinear fibre laminates. Besides the design of variable stiffness laminates, fibre steering becomes necessary in high-complexity structures. Frequently, fibre paths cannot follow the designed constant fibre orientation in a layer due to the part geometry (e.g. double curvature), which is dealt with manually on a case-by-case basis. Hence, generic capabilities for the design of fibre-steered laminates and analysis of manufacturing features are required [89].

A design for manufacturing (DFM) software tool is described in this work that enables the automatic modelling of fibre paths considering manufacturing constraints of fibre placement technologies. It provides a novel approach to consider manufacturability of laminates requiring fibre steering. Also, each fibre path is modelled explicitly and controlled independently, providing higher flexibility than existing methods. Thus, it contributes to improve the applicability of advanced laminate designs with curvilinear fibres in industry. Algorithms to generate continuous paths from discrete angles and to adapt fibre paths to manufacturing specifications are presented in Section 2.1 and 2.2, respectively. The procedures to analyse manufacturing features, such as curvature radius and gaps and overlaps are explained in Section 3. This tool is applied to a flat plate with a hole designed with curvilinear fibres and to an aircraft component – a windshield front fairing – with conventional fibre in Section 4. The paper is concluded in Section 5.

Section snippets

Tool to design variable stiffness laminates for manufacturing

A software tool for manufacturing analysis and optimisation of fibre steering named FIPAM (Fibre Paths for Manufacturing) has been developed. It provides a post-processing of the design configurations from structural optimisation prior to manufacturing. This tool enables the automatic generation of fibre paths (i.e., machine trajectories), imposing manufacturing requirements. It is integrated in CATIA V5, where each path is modelled individually considering constraints to ensure

Analysis of manufacturing features of variable stiffness laminates

For the implementation of manufacturing constraints in the algorithms discussed in Section 2, tools to analyse these manufacturing features are required. Specifically, methods to compute the gaps and overlaps of a particular fibre path design and to calculate the minimum curvature radius are presented.

Design of flat square plate with a hole

The variable stiffness design of a plate with a circular cut-out loaded in tension and optimised for strength has been undertaken. The details of the structural optimisation are found in Peeters et al. [68]. The laminate is composed of 6 independent plies. The laminate is assumed to be balanced and symmetric, leading to a total of 24 layers (thickness of 4.6 mm). The manufacturing constraints and design of the case study is described in Fig. 8.

The optimal fibre angle distribution is converted

Conclusions

The potential of fibre steering is limited by current manufacturing constraints of fibre placement technologies and design specifications. A novel approach to automatically model fibre paths based on structurally optimised fibre angle distributions and considering manufacturing requirements is proposed. This approach enables to design variable stiffness laminates with curvilinear paths as well as conventional complex structures that require fibre steering. Algorithms are described that create

Acknowledgements

This work was supported by Airbus Group Innovations UK, EPSRC (funding ref. 1247822) and the CANAL (CreAting Non-conventionAl Laminates) Project, part of the European Union Seventh Framework Program (grant agreement no: 605583).

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