Analysing fluctuation of material properties of non-circular profile filament wound composite pipes along perimeter of cross-section

Introduction

Polymer composites made of thermosetting polymer matrix (mainly epoxy, vinylester or unsaturated polyester resins) and reinforcing fibres (glass, carbon or aramide fibres) show high strength, acceptable elastic modulus, low density and high chemical resistance. These special properties have made fibre reinforced polymer composites suitable for the underground piping industry, where the low maintenance need of these materials is an additional benefit.1 Glass fibre reinforced unsaturated polyester pipes and vessels have been manufactured for more than four decades and applied successfully in chemical and food industries and in underground water and sewerage piping.2 Major advantages of polymer composite pipes compared to steel ones are low weight, which decreases construction and transportation costs, and corrosion and chemical resistance, which reduces maintenance costs and lengthens the lifetime of the pipes. Compared to thermoplastic polymer pipes (polyethylene, polypropylene and polyvinyl chloride), composite pipes have higher strength, which gives higher pressure resistance and load bearing capacity3 and finally allows the designer to use lower wall thicknesses. Besides their advantageous special properties, polymer composites often show uncommon behaviours, such as time and temperature dependent properties,4^–6 degradation7 and water absorption,8 owing to the macromolecular structure of the polymer matrix material. Composites also show uncommon damage modes in comparison with homogeneous materials, such as interlaminar fracture types, 9 , 10 owing to their fibre reinforced laminated structure.

Composite pipes are manufactured mainly by filament winding and centrifugal spraying, and they can be operated under gravity or as pressure pipes. The filament winding manufacturing technology is more common for high performance pipes mainly because the anisotropic mechanical properties of the pipe material can be fitted to the loads by changing the winding angle. 11 , 12 It is also more capable of manufacturing non-circular profile pipes, because a wooden mandrel with non-conventional geometry can be fabricated economically even for smaller series of production.

In the early stage of sewerage piping, various cross-sections were used for pipe construction from stones or bricks with masonry technique.13 The so called regular egg shaped (or normal ovoid) profile was one of the most widespread non-circular cross-sections from the end of the eighteenth century because of its good flow and ergonomic properties14 (Fig. 1). The first egg shaped sewers were constructed in London in 1846, and later, in the 1870s, they were also used in Germany. Up to now, one can find hundreds of kilometres of egg shaped sewers in the main cities of Europe, such as London, Paris, Brussels, Berlin, Dresden, Hamburg, Vienna, Budapest, etc. In the case of a combined (communal wastewater and rainwater) sewer, the egg shape profile provides deeper flow during dry periods, owing to the narrow lower part of the section, than an equivalent circular profile, and this way, it prevents sedimentation. In case of wet weather, the section has enough spare capacity to transport stormwater. On the other hand, egg shape is very similar to the figure of the human body (e.g. on all fours); this is why a 1200×700 mm section or even smaller can be man accessible. An egg shaped profile is ‘anatomic’ because of the vertical alignment and the wider crown region that lets shoulders in the sewers. An additional benefit of egg shaped sewers was, during the construction works, that a narrower trench was suitable for laying them than the one for an equivalent circular pipe (with equal cross-sectional area). Nowadays, egg shaped profile pipes are mainly used for the repair and recovery of deteriorated pipelines, because manufacturing various non-circular profiles for new construction is not cost effective enough, and sizes cannot be easily standardised.

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Figure 1

Regular egg shaped profile, α₁ = 180°, α₂ = 36·87° and α₃ = 53·13° (1: resin impregnated fibreglass filaments, wound under +θ angle; 2: resin impregnated fibreglass filaments, wound under −θ angle)

A notable amount of the non-circular profile pipes are older than a hundred years and need to be rehabilitated in order to provide safe and environmentally friendly operation. Effective ways of repairing underground pipes are the trenchless lining technologies, since the surface traffic is only slightly affected by the construction works. One of the most common trenchless sewer pipe lining technologies is ‘cured in place pipe’ lining,15 where a preformed reinforcement hose preimpregnated or wetted in situ by uncured resin is pulled into the section to be repaired and then filled and cured with pressurised steam. Another well known relining technology is the ‘short pipe process’, where prefabricated (cured) liner pipe sections are pulled or pushed (jacked) into the old deteriorated pipe. Both technologies are capable of lining non-circular profile pipes. Liner pipes for the short pipe process are mainly manufactured with filament winding of the fibreglass reinforced polyester. In the case of filament winding of non-circular pipes, owing to the uneven forces acting on the fibre filaments around the perimeter of the winding mandrel, varying wall thicknesses can occur.

The aims of this study were to analyse the wall thickness and material property variations observed during the filament winding of egg shaped profile composite pipes and finally to find the reasons for these variations. This is important because the wall thickness and material properties of the pipe material are crucial input parameters of every modelling, scaling and stress analysing method, such as finite element modelling.

Experimental

Test methods

Three pipes were tested to check the reproducibility of the manufacturing technology and the variations in density and fibre volume fraction around the perimeter of the section. Specimens were taken from each end of the three test pipes. First rings were cut from the ends of the pipes (altogether six rings), and then square (20×20 mm) pieces were cut from particular areas of the rings. Five pieces from the upper, four pieces from each lateral and three pieces from the lower regions of the rings were taken, as can be seen in Fig. 2. Altogether, 96 square specimens were fabricated, in which the tests were executed. The pipe ends were numbered and referred as ‘end 1’ and ‘end 2’ in the tables.

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Figure 2

Ring and square specimens cut from test pipes

The density of the composite material was examined according to ISO 1183-1 using the immersion method. The fibreglass weight fraction was determined with the burning method according to ISO 3451-1. As the density of reinforcement fibres is almost two times higher than that of the matrix material, the fibre content was calculated into volume fraction with the help of equation (1) to give more proper information about the material composition (1) where v_f (%) is the fibre volume fraction, w_f (%) is the fibre weight fraction, ρ_c (g cm⁻³) is the density of the composite and ρ_f (g cm⁻³) is the density of the reinforcing fibres.

Results and discussion

Table 1 shows the results of the executed density measurements. Each cell contains the average and standard deviation values of the examined specimen series. The average and standard deviation values were calculated for the same type series under the relevant rows using all the raw data obtained during the tests to show the differences between specific regions of the test pipes.

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Table 1

Density values measured on specimens taken from different parts of examined pipes (pipe 1 end 1 refers to first end of pipe 1)

Density/g cm−3	Upper	Lateral left	Lateral right	Lower
Pipe 1 end 1	1·917±0·005	1·877±0·018	1·887±0·019	1·965±0·019
Pipe 1 end 2	1·940±0·011	1·892±0·013	1·920±0·013	1·964±0·012
Pipe 2 end 1	1·940±0·008	1·899±0·019	1·900±0·015	1·956±0·015
Pipe 2 end 2	1·959±0·014	1·912±0·014	1·926±0·008	1·969±0·010
Pipe 3 end 1	1·949±0·014	1·897±0·005	1·909±0·005	1·960±0·018
Pipe 3 end 2	1·940±0·007	1·900±0·023	1·894±0·013	1·937±0·009
Average	1·941	1·900	1·900	1·958
Standard deviation	0·016	0·019	0·019	0·016

Table 2 shows the determined fibre volume fractions of the test pipes in the same order as in Table 1. Analysing the results, it is obvious that both density and fibre volume fraction are the highest in the lower region of the section (smallest local radius of curvature) and the lowest in the lateral regions (biggest local radius of curvature). The differences between the values are quite small, but concerning the very low deviations (under 2%), it is worth analysing the data statistically. Student t tests were applied to verify if the small differences are significant or are due to the accidental scattering of results. q (%) values in Table 3 show the probability of invalidity of the hypothesis that the pairs of data series are scattering around the same average values. Student t test results show that the differences between the average values of densities and the fibre volume fractions of the pipe material in different regions are significant. After analysing the validity of the results, the graphs in Fig. 3 were constructed showing the examined properties as a function of the radii of curvatures of the place of origin of the specimen series.

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Figure 3

a density and b fibre volume fraction of egg shaped profile composite pipes as function of local radius of curvature of profile

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Table 2

Fibre volume fraction values measured on specimens taken from different parts of examined pipes

Fibre volume fraction/%	Upper	Lateral left	Lateral right	Lower
Pipe 1 end 1	53·57±0·53	50·55±0·96	50·54±1·03	56·54±0·69
Pipe 1 end 2	55·04±0·50	50·75±0·67	53·30±0·80	56·38±0·69
Pipe 2 end 1	55·75±0·53	51·85±0·91	51·69±0·57	56·24±0·73
Pipe 2 end 2	56·28±0·49	52·62±0·60	53·58±0·34	57·26±0·34
Pipe 3 end 1	56·13±0·53	52·07±0·17	52·50±0·26	56·60±0·74
Pipe 3 end 2	55·79±0·25	52·10±0·78	51·95±0·60	55·76±0·59
Average	55·43	51·96	51·96	56·46
Standard deviation	1·03	1·13	1·13	0·71

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Table 3

Student t test results for densities and fibre volume fractions measured on specimens taken from different regions of test pipes

	Upper–lower	Upper–lateral	Lower–lateral
t values for densities	3·73	9·80	11·61
q/%	>99·9	>99·9	>99·9
t values for fibre volume fractions	3·76	13·62	15·74
q/%	>99·9	>99·9	>99·9

The strong linear relationships in Fig. 3 can be written with the help of equations (2) and (3) (2) (3) where ρ_l (g cm⁻³) is the local density of the material of specimens, v_fl (%) is the local fibre volume fraction of the specimens, R_gl (mm) is the local radius of curvature of the profile and R² is the correlation coefficient. The high values of correlation coefficients were probably due to the strong physical relationship among the material properties and the radii of curvatures and the high amount of examined specimens. The density and fibre fraction variations can be caused by uneven fibre force distribution during filament winding. The fibre bundles stretched stronger to the surface of the winding mandrel can compress more resin out of themselves, increasing the fibre fraction and the density of the final structure. Deeper analysis of forces acting in the fibre direction and perpendicular to the fibres (from the mandrel surface) was carried out earlier in the textile industry, where winding is a common step of technologies.16

Figure 4 shows the universal geometrical and mechanical models of the filament winding process in case of a cylindrical mandrel. The fibre bundles are placed on the cylindrical mandrel under helical alignment so that they include the θ angle (winding angle) with the axis of rotation. Tensile forces F and F+dF act at the ends of a small line element ds of the helix in the tangential directions, perpendicular to the constant radius of curvature R_g in the endpoints owing to the fibre fastening system of the winding machine. Resultant force coming from the tensile forces acting on the selected line element with dβ central angle (estimated with straight section in case of small angle) is the so called packing force dN, which acts in the direction of the centre of curvature of the winding mandrel. Assuming that the difference between the tensile forces acting on the ends of ds is only caused by friction, equation (4) can be written on the basis of the simple formula for rope friction forces (4) where μ is the coefficient of friction.

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Figure 4

a geometrical and b mechanical model of filament winding of circular profile pipe

As fibres are impregnated with liquid resin during filament winding, ‘lubricated’ friction occurs instead of dry friction, as originally assumed in equation (4). This effect lowered the friction forces between the fibres and the winding mandrel significantly, so the effect of friction was neglected. Considering that dF = 0, equations (5) and (6) can be written using proper triangles of Fig. 4b (5) (6) Equation (7) can be written with reducing equations (5) and (6), which gives the packing force for a unit line element (7) where R_g is the constant radius of curvature of the helix and can be written with the Euler curvature formula17 using the winding angle θ, as in equation (8) (8) where R_{g mandrel} is the cross-sectional radius of the winding mandrel. As the winding angle was high (θ = 83·5°), the difference between R_g and R_{g mandrel} was only 1·3%, so the latter was applied for further calculations. Using the general equations written for the circular mandrel, the authors switched to the local analysis of the winding process on a regular egg shaped profile mandrel, which has constant radii of curvatures for each region of the cross-section. It can be stated according to equation (9) that the packing force in a selected point of the profile for a unit line element (dN/ds), which is perpendicular to the surface of the winding mandrel, is inversely proportional to the local radius of curvature of the profile R_gl, while the fibre fastening force F is constant (9) This statement is capable of describing the reason for the variations in density, fibre volume fraction and finally wall thickness of the tested non-circular pipes around the profile. As the packing force varies around the perimeter of the section, various amounts of resin is compressed out of the continuous fibre bundles, and the resultant properties are influenced by this effect.

Conclusions

According to the presented geometrical and mechanical models and calculations, the following conclusions can be drawn.