Tow Path Research Articles

A parametric modeling method for 3D woven composites considering realistic meso-structural characteristics

The precision of mesoscale simulation for three-dimensional woven composites (3DWCs) is intricately linked to the fidelity of the geometric representation. This paper aims to present a novel parametric modeling approach for generating representative volume element (RVE) of the 3DWCs while considering its realistic meso-structural characteristics. The real architecture of 3DWCs is defined to consider the squeezed surface warp tow. Tow geometry is specified, accounting for torsion of tow cross-section and crimp of weft tow path. The RVEs of the composites are geometrically assembled via a specific translational symmetry. The tensile response of the composites with the novel geometry is scrutinized utilizing a progressive damage model, compared with that of the ideal geometry. Additionally, the impact of weft tow size on the tensile response of the composites is explored.

Uncertainty quantification for natural frequency and mode of variable angle tow composite plates with random and interval uncertainties

Variable angle tow (VAT) composite laminated structures are produced by automated tow-placement technology which can take advantage of the designability of composites to meet the aerospace industry’s need for dynamic properties. Complex production techniques inevitably lead to uncertainties in material properties due to manufacturing defects. The aim of this work is to present an efficient computational method for estimating the dynamical properties of VAT composite laminated plates due to multiscale hybrid uncertainties. This method consists of perturbation stochastic finite element method and particle swarm optimization combined with Mori-Tanaka homogenization. The degree of influence of the multiscale parameters on the dynamic properties of VAT composites with different structural forms has been obtained by sensitivity analyses of the frequency and mode. The method is applied to investigate variations in natural frequency and mode of a variety of VAT composite laminated plates with different fiber tow paths, layers, and boundary conditions. The results indicate that variations in natural frequencies and mode shapes are strongly linked to fiber tow paths and boundary conditions. The frequency and modes of the VAT show a nonlinear variation with angle. This method can quickly obtain the probability distribution intervals of the frequency, which is of great significance for assessing the reliability of VAT composites laminated plates dynamic designs.

Design optimization of advanced tow-steered composites with manufacturing constraints

Tow steering technologies, such as automated fiber placement, enable the fabrication of composite laminates with curvilinear fiber, tow, or tape paths. Designers may therefore tailor tow orientations locally according to the expected local stress state within a structure, such that strong and stiff orientations of the tow are (for example) optimized to provide maximal mechanical benefit. Tow path optimization can be an effective tool in automating this design process, yet has a tendency to create complex designs that may be challenging to manufacture. In the context of tow steering, these complexities can manifest in defects such as tow wrinkling, gaps, overlaps. In this work, we implement manufacturing constraints within the tow path optimization formulation to restrict the minimum tow turning radius and the maximum density of gaps between and overlaps of tows. This is achieved by bounding the local value of the curl and divergence of the vector field associated with the tow orientations. The resulting local constraints are effectively enforced in the optimization framework through the Augmented Lagrangian method. The resulting optimization methodology is demonstrated by designing 2D and 3D structures with optimized tow orientation paths that maximize stiffness (minimize compliance) considering various levels of manufacturing restrictions. The optimized tow paths are shown to be structurally efficient and to respect imposed manufacturing constraints. As expected, the more geometrical complexity that can be achieved by the feedstock tow and placement technology, the higher the stiffness of the resulting optimized design.

Generation of Tow Paths on a Curved Shell in Three-Dimensional Space for Fiber Steering

A multimesh framework to optimize two-dimensional, flat-steered fiber laminates for a given loading condition is extended to include complex curved laminates in three-dimensional (3D) space. The optimal fiber angle distribution solution is used by a tow path planner to generate (steered) tow paths in curved laminates in 3D space. The framework utilizes two meshes in the optimization step: i) a coarse quadrilateral element-based manufacturing mesh (MM) used to discretize the fiber angle distributions with nodal values; and ii) a fine triangular element-based stress mesh used in the finite-element-based stress analysis to ensure a converged solution. Lagrangian interpolation functions are used to determine the fiber angles at the centroid of each finite element analysis (FEA) mesh element within a given MM. The number of design variables is minimized without jeopardizing the accuracy of the FEA solution. A third mesh, the tessellation mesh, is used to project the generated tow paths onto the curved laminates in 3D space accurately. This paper presents all the steps needed to go from optimized fiber angles to tow paths. In conclusion, a methodology is proposed and implemented to optimize variable-stiffness laminates on complex curved structures.

Utility of a modified lightweight recreational scallop dredge for surveys of estuarine ark clams (cockles)

Arcid cockles support extensive subsistence, recreational and commercial fisheries across the world. In south-eastern Australia, there is minimal published research and a lack of quantitative surveys for the primary harvested species, Sydney Cockle Anadara trapezia, with which to inform management of the resource. Here, we describe the modification and application of an off-the-shelf lightweight recreational scallop dredge for conducting scientific surveys of arcid clams in estuarine soft sediment habitats. Specifically, we look at performance of the gear for sampling medium-large (>45 mm shell length) cockles, and report on the outcomes of preliminary trials of the gear for surveying Sydney Cockle. Efficiency trials showed that the gear captured and retained ∼95% of the cockles in the tow path, however efficiency decreased in compacted sediments (∼66%). Trial surveys captured cockles between 33 and 78 mm shell length, at densities as high as 186 individuals 100 m−2. The modified scallop dredge provides a robust and portable (∼10 kg weight) fishing gear for sampling estuarine soft sediment habitats from small vessels. Both the sampling gear, and the methodology presented here, are broadly applicable for surveying arcid cockles and other bivalve species from similar soft sediment habitats elsewhere.

3D winding path modeling on truncated conical shell with proposed outer-contour expanding and convex helix algorithms

A novel filament winding virtual tool is proposed to develop the 3D winding paths on the workpiece contour in real-time. The semi-geodesic and constant-wall-thickness (CWT) trajectories are used to generate the centerline of the 3D path. A tow overlaps processing method and the outer-contour expanding algorithm (OEA) are developed to eliminate the tow interference. The convex helix algorithm (CHA) is proposed to smooth the cliff generated in the interference elimination. The OEA and CHA algorithms are considered due to their high computational efficiency as compared to the traditional algorithms, such as the Backward Search algorithm (BSA) and L-BFGS Algorithm. The prospective virtual tool develops a stable winding path, and experimental results have shown that the 3D path does have advantages over the traditional 2D path in terms of high preservation of the tow path and the prevention of the tow slippage.

Automated fibre placement path generation for complex surfaces via digital image deconvolution algorithm

Automated fibre placement (AFP) potentiates the fabrication of fibre-reinforced composite with high efficiency and quality. Complex surface design on aircraft components leads to irregular reference directions for tow layup. Path aligned with such direction would inevitably generate excessive gap/overlaps over the ply to cause quality degradation, and vice versa. Existing methods mostly generate tow paths via geometric offset from an initial guide curve, making it hard to compromise the contradiction. This paper resolves this trade-off issue by developing a digital image deconvolution algorithm. The problem is formulated as a linear partial differential equation and rasterized into digital image domain to be solved by proposed image deconvolution algorithm, which is proved to be computationally efficient and accurate. Compared with exiting path planning strategy, the proposed method finds global optimal tow paths achieve enhanced fibre alignment and acceptable ply thickness variation, providing new paradigm for AFP path planning on complex surface laminates.

Prediction of mechanical properties for three-dimensional woven composites considering interference between tows

The mechanical performance of three-dimensional woven composites is usually modeled by an ideal model with straight tow paths and constant cross-sectional areas. This ideal model predicts inaccurate properties due to oversimplification of tow shapes. In this paper, we present a more accurate method to predict properties of the 3D woven composite considering waviness and contraction of tows due to interference between them. The tow waviness is defined by elliptic and trigonometric functions. The shrinkage of the tow cross-sectional area is modeled using a cubic polynomial. The elastic moduli are predicted using the modeled tows and the weighted average model. The predicted properties are compared with test results to verify the accuracy. In addition, the usefulness of the present method is verified by comparing the calculated moduli using the ideal model. We conclude that the present method is useful for the design of structures to which 3D woven composites are applied.

Tow Path Planning Strategies for Fiber Steered Laminates

Fiber steering leads to gaps and overlaps in plies and laminates. The position of these gaps and overlaps as well as their total volume/area is very much influenced by the seeding strategy when transforming from a theoretical to a manufacturing design. The theoretical designs obtained from a steered fiber laminate optimization routine are the starting point of a tow path planning step. The seed points together with the theoretical fiber angle determine the path of a tow. Normally, seed points are determined by a manufacturing engineer. In this paper, two different strategies to automate the selection of initial seed points and subsequent points based on the calculation of previous tow paths are proposed and evaluated. For two-dimensional plate problems both proposed methods reduce the gaps and overlaps. The method based on the median tow path is spreading gaps and overlaps more uniformly and yields fewer gaps and overlaps. A cut and restart procedure is discussed and implemented, which can be used to manually or automatically prevent/limit overlaps and fill large gaps.

Effect of intra-tow flow on plain woven fabric permeability using virtual fiber-voxel element method

A geometric modeling platform based on the virtual fiber-voxel element is proposed to characterize textile reinforcement in a cost-effective way, which could reflect the systemic local changes of the tow path and tow cross-section. The finite volume method is used to solve the governing equation of the boundary value problem, and the permeability of the fabric is calculated by using the flow field data obtained from the model. The flow field analysis and pressure drop in flow direction of different thickness unit cells suggest that the size of inter-tow channels play a vital role in determining the overall in-plane permeability values. The flow channels of the inter tow in warp direction were found to be greater than in the weft direction, which causes the overall permeability to be anisotropic.

Consolidation and Tow Spreading of Digitally Manufactured Continuous Fiber Reinforced Composites from Thermoplastic Commingled Tow Using a Five-Axis Extrusion System

During the development of digitally manufactured, commingled tow continuous fiber reinforced composites, consolidation force was controlled using a controlled spring force that yielded a repeatable tow width. However, the use of the extruder face to consolidate the material requires that the extruder remain perpendicular to the placement surface throughout the process. When considering more complex tool contours including sloped surfaces, more than three axes of motion are necessary to maintain the perpendicularity of the extruder tip to the surface. In this effort, a five-axis system is developed and used to demonstrate the ability to consolidate over complex contours. In addition, the nozzle face temperatures required for good consolidation and wetout result in poor tow path fidelity when complex paths are introduced. The implementation of an automated, computer-controlled localized cooling system enables both good wetout and consolidation while also enabling more accurate changes in tow path due to improvements in local tow tack. With the development of the five-axis system it is also shown that the tow width can be adjusted by rotating the existing placement nozzle to angles not equal to 90°. Thus, through a combination of controlled localized cooling and real-time control of the nozzle angle, a possible approach to control of tow width, independent of the tow placement angle and radius of curvature during tow steering, is described.

Curved fibre path optimisation for improved shape adaptive composite propeller blade design

The propulsive efficiency of a shape adaptive composite propeller increases with passive pitch (twist) change under a hydrodynamic load. These adaptive marine propellers are usually designed using straight fibre tows to obtain optimised layup with such bend-twist character. This paper aims to present an alternative optimisation approach for such composite propellers using a curved fibre path method where tow paths are allowed to vary spatially within individual plies. In this work, three optimisation studies were performed to highlight that employing curved tows produce better results, including increased twist change for efficiency or, lowered deflection for structural improvements. Laminate plates were first optimised and manufactured using an automated fibre placement robot for experimental validation. Cantilevered loading test results show that optimised curved fibre plates generated >10% more twist compared to their straight fibre counterparts. In the following optimisation on a hydrofoil model, the curved fibre design produced the same tip angle change as the optimised straight fibre layup, yet it reduced the tip deflection by 15%. Finally, the optimisation was performed on a Wageningen B-series marine propeller, in which the optimised blade design with curved fibre layup achieved a 20% reduction in the Tsai-Hill failure index under the same pitch change.

Reliability-based buckling optimization with an accelerated Kriging metamodel for filament-wound variable angle tow composite cylinders

A reliability-based optimization framework is introduced and used to design filament-wound cylindrical shells with variable angle tow. Seven design cases are investigated to enable a comparison between constant-stiffness and variable angle tow designs, also considering effects of thickness variation created due to overlapping tow paths, determined using the kinematics of the filament winding manufacturing process. The uncertainty in the winding angle is considered in the optimization by means of metamodels constructed using the Kriging method. Moving search windows are incorporated into the Kriging metamodel to accelerate its convergence by reducing the number of training iterations. The results prove the efficacy of the proposed framework and clearly demonstrate the advantage of variable-stiffness designs over conventional ones for achieving a maximum load carrying capacity, while keeping the robustness of the design towards manufacturing uncertainties.

Continuous curvilinear variable stiffness design for improved strength of a panel with a cutout

Continuous curvilinear variable stiffness (CCVS) is presented as a novel solution to improve the load carrying capacity of a fuselage panel with a cutout. The CCVS technique allows for the tow paths to curve around cutouts of arbitrary geometry with initial fiber angle and geometry as design inputs. An optimum CCVS design is generated using a genetic algorithm method coupled with a finite element model in NASTRAN and the results are compared with those obtained using a quasi-isotropic laminate. The optimized CCVS laminate is found to improve the load carrying capacity compared with the quasi-isotropic design by 57%.

Geometrical modeling of tow wrinkles in automated fiber placement

This paper presents a thorough investigation of wrinkling within a path on a general surface for a composite tow constructed using the AFP process. Governing equations and assumptions for the presented model are derived based on geometrical considerations. A simple form of the wrinkled shape is assumed and applied to the inner edge of the tow path. For a given wavelength, the amplitude of the wrinkles can be approximated based on a worst-case scenario where all the difference in length between the edges of the path is absorbed through an out-of-plane wrinkle. The wrinkle wavelength can be obtained either from existing mechanics models in the literature or experimental measurements, otherwise an adequate wavelength can be assumed. A numerical solution is implemented to visualize wrinkles on the curved paths and to indicate potential regions for wrinkling on the surface. Several examples are presented to demonstrate the model, including constant angle paths on a double-curved surface and curved paths on a flat surface. From a geometrical standpoint, increasing the tow width or the path curvature results in an increase in the wrinkles’ amplitude. Calculation of the wrinkles’ amplitude for a steered path on flat surface shows good agreement with experimental measurements.

Analysis of tow architecture variability in biaxially braided composite tubes

Spatial deviations in composite braid unit cell dimensions limit mechanical performance and are challenging to model. Full-field measurements of the irregular tow placement in biaxially braided composite tubes were obtained by digital image correlation. Analysis of the reconstructed tow paths showed long-range defects along the hoop direction with short-range defects dominating the biased tow direction. A route toward numerical simulation of the composite response is established by developing a 3D model of the composite using the measured tow trajectories. Finally, a comparison to previously-published triaxial braid results indicates axial tows work to constrain unit cells dimensions along the hoop direction.

Stiffness and buckling analysis of variable stiffness laminates including the effect of automated fibre placement defects

Composite materials are finding increasing application, for example in commercial aircraft. Traditionally fiber angles are constant in a single layer. Currently, so called variable stiffness panels with steered fibres, where the angle is changing within a layer are investigated. These panels are usually manufactured using automated fibre placement machines. Since the fibre angle is changing, and the tow paths are shifted as a whole in a single direction, gaps and/or overlaps between consecutive tows are created. This paper explores the effect of these gaps on the stiffness and buckling load of variable stiffness panels. A methodology is presented using homogenization to account for the gaps in a computational efficient way. The result shows that the stiffness results are on conservative side and are within 5% accuracy. However, the buckling results are on the unconservative side. The computational cost of the pre-processing of the proposed method is 45 times lower than the cost of the defect-ply method presented in the literature.

Robust design optimization of variable angle tow composite plates for maximum buckling load in the presence of uncertainties

A robust design optimization algorithm is proposed for variable angle tow composite structures in the presence of uncertainties in the constituent material properties and applied loads. The proposed algorithm uses a stochastic perturbation method to propagate these uncertainties through to the simulated structural response, measured in terms of buckling load. The expected value plus a selected number of standard deviations of the response in the form of a bi-criteria problem. To describe the curvilinear fibres, two types of fibre path function, namely linear- and nonlinear-variation formulae, are adopted to illustrate the proposed methodology. A comparison between the resulting robust designs and deterministic designs is made, and changes to the final designs of fibre tow paths arising from the inclusion of uncertainty are discussed. It is shown that the robust designs out-perform the deterministic designs under real-world situations that include uncertainties.

Thermal buckling optimization of variable angle tow fibre composite plates with gap/overlap free design

Composite structures in a thermal environment may suffer from buckling failures due to thermally induced compressive forces, leading to concerns over their application in environmentally aggressive conditions. This issue is addressed by proposing a novel approach to the design of tow paths for enhancing thermal buckling performance, and it can also overcome the problems of tow gaps and overlapping. A level set function, such as defined by signed distance function, for representing a series of equidistant tows throughout the laminate, is adopted here to formulate an optimization problem that seeks to maximize the buckling load under thermal loading, and the level set values are thus the design variables. Sensitivities of thermal buckling eigenvalues with respect to tow paths, i.e. level set values, are derived through the adjoint method, and they are used to solve the optimization problem through the Hamilton-Jacobi equation. In this study, numerical examples are presented to demonstrate the effectiveness of the proposed method, where laminated plates made of various materials under different boundary conditions are considered. Results show that the proposed approach can provide efficient solutions with enhanced buckling performance.

Stress analysis of a plain orthogonally woven textile composite under tension along the warp direction

A non-idealized finite element model of a plain orthogonally woven textile composite was subjected to tension along the warp direction, and the predicted stress state was investigated. The effect of refining the geometry and mesh on the volume average stresses and the percentage of each constituent at different stress levels was explored. For the particular textile architecture considered, which consisted of large reinforcement tows and complex tow cross sections, it was shown that the typical mesh refinement in the literature might suffice for volume average stresses, but a higher mesh refinement is needed to accurately capture stress concentrations. The locations of stress concentrations within each constituent were identified. For the three types of tows, [Formula: see text], transverse normal stress in the local coordinate system, in the wefts was predicted to be the most severe component of stress. For the layers of wefts that are crossed over or under by a binder, stress concentrations developed where the warps were the most distorted. Whereas, for the interior layer of wefts, stress concentrations developed where a binder came closest to the weft. In the matrix, [Formula: see text], the normal stress in the direction of the load, concentrations developed where a binder came close to a warp or weft. The locations of peak cross-sectionally averaged stresses along the tow paths were shown to match the locations of local stress concentrations. However, it was observed that many of the stress concentrations might be sensitive to the method used to create the finite element model, boundary conditions, or accounting for the variation of local fiber-volume fraction that results from a variation of cross-sectional area.