Irregular Winding of Pre-preg Fibres Aimed at the Local Improvement of Flexural Properties Neenakomerno navijanje predhodno impregniranih vlaken za lokalno izboljšanje upogibnih lastnosti

The main undisputed benefi t of using long fi bre composite materials, whose properties could be targeted for a particular application, lies in the effi cient utilisation of material. Using a method of pre-impregnated fi bre winding, a rod with a reinforced middle part was created through the local adjustment of the winding angle in order to increase the local bending stiff ness. The aim of our work was to describe, experimentally and subsequently using appropriate numerical models, the behaviour of two composite rods, one with a locally variable winding angle and the other with a constant winding angle. The diff erence in the mechanical behaviour of both structures was clearly evident during the experiment. By using a suitable composite pre-processor and by choosing some multiple element sets, it was also possible to accurately simulate the real behaviour of such components, which actually have several regions, each with diff erent mechanical parameters. Together with the expected diff erent fl exural strength, a traditional three-point bending test also explored the diff erent shape of the resulting deformation in the two compared parts. Diff erences in the maximum strength and the mode of fi nal deformations were also identifi ed.


Introduction
High-strength constructions based on long bre composite frames are becoming increasingly important across all industrial sectors.Plastic materials reinforced by long bres are widely used because of their high strength and excellent Young's modulus to density ratio.While conventional materials show one Izvleček Največja korist kompozitnih materialov, ojačenih s fi lamenti, so široke možnosti za učinkovito izrabo materiala, tako da bi bile te lastnosti usmerjene v uporabo za posebne namene.Z uporabo metode navijanja predhodno impregniranih fi lamentov je bila izdelana palica z ojačenim srednjim delom, kjer je bila za povečanje lokalne upogibne togosti uporabljena možnost lokalne nastavitve kota navijanja.Namen raziskave je bil opisati in preizkusiti primerne numerične modele obnašanja dveh kompozitnih paličastih elementov, enega izdelanega z lokalno spremenljivim kotom navijanja in drugega s stalnim kotom navijanja.Eksperimentalno je bila dokazana razlika v mehanskem obnašanju obeh struktur.Z uporabo ustreznega predprocesorja za defi nicijo strukture kompozitov in z izbiro večelementnih nizov je bilo mogoče natančno simulirati realno obnašanje komponent z več predeli, od katerih ima vsak drugačne mehanske parametre.Skupaj s pričakovano različno upogibno trdnostjo so bile s tradicionalnim tritočkovnim testom upogibanja proučene tudi različne oblike nastalih deformacij v dveh primerjanih predelih.Ugotovljene so bile tudi razlike v maksimalni trdnosti in obliki končnih deformacij.Ključne besede: kompozit, predhodno impregnirana vlakna, navijanje, upogibna togost, lokalna ojačitev failure mode (i.e.cracking), composites may exhibit one or a combination of failure modes, includingbre rupture, matrix cracking, delamination, interface de-bonding and void growth [1,2].Compared to conventional materials, composite laminates o er some unique engineering properties, while presenting interesting and challenging problems for analysts and designers [3].e aim of this presented work was to study composite rods with local reinforcement achieved through the local varying of the winding angle in chosen layers during manufacturing, and compare it with a constant winding angle.e winding methods were based on the layering of carbon bres from several spools spinning around a non-bearing core.Information about the optimisation of surfaces created in this way and the associated cross-sections can be found in other works [4,5].Zu [4] studied the strain energy criterion in order to create the most appropriate shape of toroidal vessels, achieved through a signi cantly lower weight and aspect ratio (i.e. the height to width ratio).It was concluded that the structural e ciency of lament-wound material can be determined through a condition of equal shell strains.Blazejewski [5] studied several possible combinations of surface textures and the associated properties that derive from individual plies and the combination of angles.Mertiny [6] studied the dependency of ply angles on the global strength of composite structures, and observed that appropriate structures created using this method are commonly subjected to complex loading conditions.Modern design so ware and computer controlled machines allow us to create almost any winding angle (i.e. the angle between the bre direction and the axis of the mandrel).Fibres may be wound in directions ranging from 0° (axial layering) to 90° (hoop -practically impossible).Computer-controlled winding machines also facilitate the adjustment of the winding angle during an operation.is facilitates the production of multi-angle lamentwound structures.Lea [7] described the bene ts of multi-angle winding (e.g.improved tension and bending characteristics) compared with winding at the traditional angle of 54°. is led to signi cantly higher functional and structural strength under loadings with hoop-to-axial ratios of less than one.However, all of the above mentioned works addressed the idea of a constant angle in each ply.In the presented work, a method based solely on local angle adjustment is introduced.

Materials and methods
e used manufacturing method, referred to as winding, is the simultaneous deposition of several laments, described in the works of Chen [8] or Petru [9].In our case, carbon pre-preg tapes were used instead of wet bre laments. is method of manufacturing parts with rotational shapes from pre-pregs is usually limited only to the straight tubes.e presented method could handle the problem, and through the segmentation of the primary material (i.e. the simultaneously wrapping of up to 20 thin laments instead of wrapping one wide), we were able to create curved shapes and even parts with uently changed crosssections, or to locally change the angles in any place of the part.
e material used was an epoxy UD carbon pre-preg.According to measurements taken, the nal thickness a er polymerisation was approximately 85% of the original thickness.Pre-preg was produced from reinforced high-strength carbon bres with a unidirectional orientation (nominal area weight of 150 g/cm 2 and nominal bre density 180 g/m 3 ) and epoxy resin.Nominal resin content was 38%, while nominal area weight was 242 g/m 2 , using a cure cycle of 60 minutes at 120 °C.
e created tubes were wound from 16 thin tapes and had four plies with a total thickness of 0.84 mm. e bre layout in the case of the regular rod was 55/-55/55/-55, with a weight of 158 g.In the case of the locally thickened rod, the global layout of the rst and fourth plies was also 55/-55/55/-55, while the global layout of the second and third plies in the middle part was locally 55/-70/70/-55, with a weight of 165 g (Figure 1).e prediction of mechanical properties of transversely isotropic composites has been the subject of many studies and research in the past, and is also the subject of current research [10][11][12].It should be noted that elastic constants are generally di erent for each type of composite, making it di cult to determine all the constants using analytical models.e sti ness matrix C of one ply in the laminate could be described by equation 1 in the form of expressed engineering constants, where the E i represents the Young modulus of elasticity in the i-th directions, G ij represents the shear modulus in the ij-plane and µ ij represents Poisson's ratio in the speci ed planes.
Because there were several plies with various angles, it was necessary to transform the sti ness matrix of each ply to the nal matrix of the entire composite by using equation 2 for individual elements: where the line in the upper index represents the element of the transformed matrix and θ represents the angle of direction of individual plies.e theoretical values of the basic engineering constant a er the mutual summing of the individual transformed sti ness matrix for the two concepts of layered rods are presented in polar graphs in Figure 2, one with a constant regular winding angle and the other for the irregular winding angle, reinforced in the centre.attached force-meter and a cylindrical indenter were used as the source of the loading force.e use of a hydraulic system is particularly advantageous with regard to constant speed regulation, shock absorption and the smoothness of movement without "jumps" that are typical, for example, for pneumatic systems due to the compressibility of the used medium.Devices based on electric power are usually limited by their size and the range of the operating values.e applied quasi static loading was increased in increments of 0.5 mm/s until it caused the nal displacement of the used indenter of 40 mm or until total failure of the tested samples occurred.It is evident from the pictures in Figure 3

Model
e prediction of the behaviour of composite materials is a very complex problem because the process induces the orientation of bres, the interface of plies, etc. e nite-element method (FEM) is a powerful tool, without which it is impossible to eciently design composite parts today.Numerical analysis allows us to derive the di erent strain energies stored in the material directions of the constituents of composite materials [13].In our case, the models of the shell composite plate of the two tubes were created using an ANSYS ACP pre-post processor.e model was solved as a fully contact task.
e pure penalty formulation with the nodal-normal detection of integration points was used for the combination of solid and shell elements.Frictional support with asymmetric behaviour was also set.
e simplest way of handling an initially unconstrained model (i.e. a rod simply lying on solid supports) was to add weak springs as mentioned by Gruber or Whitney [14,15].e spring constant was dependent on the loading parameter, thus the e ect could only be seen in the beginning of the simulation.e scheme of the created model with boundary conditions is shown in Figure 4, which also presents the results of equivalent stress in the simulation of the regularly wound tube (±55°).e irregular winding (local reinforcement) in the middle third of the modelled rod was created using a combination of several local coordinate rosettes and oriented elements sets.In order to double the density of the central laminate, the de ection of the inner rosette BETA is equal to equation 4: where alpha represents the global winding angle relative to the actual central axis.e computed values for both cases are illustrated in Figure 5, while the reference vectors in the second ply of the model can be seen in Figure 6. e eventual drop-o places in the boundaries between the various sectors was lled by material with the same properties as the primary composite in order to simplify the model solution.e equivalent stress in the entire locally reinforced rod can be seen in Figure 7.

Results and discussion
Behaviour in terms of the exural loading of both types of rods was experimentally measured and simultaneously modelled.Experimental results are shown in Figure 8.Even if the values of the maximum forces are almost the same, the distinctly di erent course of displacement could be seen.While the ruptures and delamination were uent in the case of the regular rod, the reinforced rod was extremely durable until the nal moment of sudden total collapse.Basic statistics from the resultant bending stress and absolute deformation in the direction of the acting load are presented in Table 1 below for several created samples.e results obtained in the created model (Figure 9) showed similar trends for approximately the rst 10 mm of deformation.is is also the point where the results of our experiment start to di er signi cantly.One of the chosen criteria was Tsai-Hill.Capela, for example, studied this criterion in bending and torsion loading in his work [16].He claimed that the Tsai-Hill criterion could su ciently predict the loading e ect on the static strength of specimens.e second criterion used was the Puck criterion, which is probably the most frequently used criterion today because of its universal application.Quite interesting research was conducted in this eld by Francis [17] who stated that the matrix shear or tension cracking modes were always observed in the rst ply for carbon/epoxy thin-walled tubes with [0/90] s and [±45] s .It is evident from Figure 10 that the modes of the layer failure are slightly di erent.In Figure 10b, the "undamaged" green elements are precisely in the location of the supports and all other elements of the composite rod are fully loaded.In the case of ultimate loading, this means that the stress will be still transferred through the entire part, not just locally, as could be seen in Figure 3a. is is the right way to create composite parts because there is no reason to use reinforced composite materials when the concentration of acting stresses is not high.

Conclusion
e unconventional method of pre-preg winding was introduced in the rst part of this study.Even if there are numerous bene ts (compared to traditional "wet" methods), the main problem lies in the fact that the stickiness of material causes a signi cant increase of forces in the entire mechanism and the occurrence of the imperfect alignment of bres and their mutual storage in several places.e aim of this study was to use this method to create and subsequently compare the behaviour of two rods, one with a regular winding angle in all plies and the other locally reinforced by local adjustments to the angle in two of the four total plies.During our experiment, we identi ed a signi cantly di erent behaviour between the two types of rods tested, particularly at the moment of part rupture.
e experimental results were evaluated using a numerical model, applying an advanced composite pre-post processor.Based on the work performed, we can conclude that local changes in the winding angle may not only locally increase (or decrease) exural strength, but may also change the shape of part deformation and the resulting material failure process (Figure 11).rough the targeted local adjustment of the winding angle, it is possible to save the material and concentrate it solely in places that actually require reinforcement. is could be seen, for example, in Figure 10, which illustrates a mutual comparison of failure criteria.
is is one of the most important ndings of our work, as one of the basic principles of designing composite structures is to provide bres only where are they need.
e presented work introduced a topically important area in the eld of advanced high-strength materials.Future work will concentrate not only on straight tubes, but also on certain curved and closed composite frames.e question of how to adequately describe imperfections in layered plies, such as the wrapping and twisting of the bres, remains unanswered.

Figure 1 :
Figure 1: CAD model of bre layout with visible: a) constant and b) various winding angle

Figure 2 :
Figure 2: Engineering properties of the a) regular and b) irregular rod2.2Experimente exural strength of a material is the maximum stress that a material subjected to bending load is able to resist before failure.A traditional three-point bending test was used to compare the homogenous and locally variable tube.A hydraulic circuit with an that the two types of rods showed signi cantly di erent shapes of deformation during loading.e distance between the supports was 380 mm in this case.It is possible to determine exural stress based on the measured deformation and force response (equation 3, where D and d [m] represent the outer and inner tube diameters, F [N] represents the maximal bending force and l [m] represents the distance between supports).It should be emphasised that it is not possible to use the additive law for the cross section module W o , simply using the di erence of values of individual diameters.

Figure 3 :
Figure 3: Shape of deformation during the bending test for: a) homogenous and b) locally reinforced rod

Figure 4 :
Figure 4: Layout of the solved shell/solid model (results of stress distribution for regular winding)

Figure 5 :Figure 6 :
Figure 5: Scheme of ply orientation with an irregular centre part

Figure 7 :
Figure 7: Equivalent stress distribution in the irregularly wound rod

Figure 8 :
Figure 8: Graph of experimental results of the bending test for: a) regular and b) reinforced rods

Figure 9 :
Figure 9: Graph of the model results of the bending test for: a) regular and b) reinforced rods

Figure 10 :
Figure 10: Tsai-Hill and Puck failure criteria in a) regular and b) irregular rods

Table 1 :
Experimental results of the three-point bending test