Three-point bending test has been performed on a Zwick Z 020 tensile test machine (Figure 3). The composite hose has been placed between cylindrical bend fixtures. Diameter of the upper support is 30 mm, diameter of the lower supports, whose vertical midplanes are situated 500 mm from each other symmetrically to the vertical midplane of the upper support, is 18 mm (Figure 4). In the course of the bending test, the upper support has descended 80 mm.

Standard bending test of the hose onto a disc is utilized in practice as a means of quality control (Figure 5). Standard bending test has been carried out manually by bending the composite hose onto a disc, being 30 mm thick, having a diameter of 180 mm. Radial reaction forces have been measured by a force gauge. Mean reaction force calculated based on 10 experimental values measured in the position depicted in Figure 5 is 121.0 N.

Material of reinforcement plies is transversely isotropic, which is a special case of

linear orthotropy. Orthotropic materials have three mutually perpendicular planes of symmetry, filament-wound composite hoses, with their fibres aligned uniaxially, are usually regarded as transversely isotropic because the plane perpendicular to the fibre direction is a plane of isotropy (E₂ = E₃, G₁₂ = G₁₃, υ₁₂ = υ₁₃). Transversely isotropic materials have five independent elastic constants (E₁, E₂, G₁₂, G₂₃, υ₁₂) [10] .

Material properties of components of reinforcement plies are as follows: modulus of elasticity of fibre is E_f = 2961 MPa, Poisson’s ratio of fibre is supposed to be υ_f = 0.2, modulus of elasticity of rubber matrix is E_m = E_r = 6.14 MPa, Poisson’s ratio of rubber matrix is supposed to be υ_r = 0.5 [4] .

With the use of the aforementioned parameters, material properties of reinforcement plies are as follows:

E₁ = 1338 MPa, E₂ = E₃ = 19 MPa, G₁₂ = G₁₃ = G₂₃ = 6 MPa, υ₁₂ = υ₁₃ = 0.37, υ₂₃ = 0.498 [4] .

Rubber liners are described by a 2 parameter Mooney-Rivlin model [4] , whose parameters are: C₁₀ = −0.4982 MPa, C₀₁ = 1.523 MPa, D = 0 [1/MPa], therefore the liners are considered as incompressible.

There are bonded contacts between the reinforcement plies and the outer rubber liner and the reinforcement plies and the inner rubber liner respectively because rubber, being the material of the matrix and also material of inner and outer liners, is vulcanized around yarns. The contacts between the outer rubber liner and upper and lower supports are frictional with a frictional coefficient µ = 0.8 based on [11] and formulation “Augmented Lagrange”.

Upper and lower supports are modelled as rigid bodies (Figure 6).

The current FE simulation is incremental with large strains, consisting of one time step and several substeps. In the course of FE simulation, upper support descends 80 mm in global Y direction, meanwhile lower supports are fixed.

Force-displacement curves of FE simulation and experiment of three-point bending show fairly good agreement (Figure 7) the biggest difference in forces being 10% of experimental results.

Material properties of the hose are in accordance with Chapter 3.1, the geometry of the hose is presented in Chapter 2.1. Standard disc is modelled as a rigid body

with a diameter of 180 mm and a thickness of 30 mm. Positioning pins utilized for the bending process, placed inside the hose, are also rigid bodies, whose diameters equal the inner diameter of the hose. 70 mm long sections of the pins lay inside the hose. The aforementioned pins have holes, whose centers serve as a remote point for positioning the hose during the bending process, the centers of the holes are 50 mm from the base of the hose.

Connection of inner and outer rubber liners to reinforcement plies is bonded, which is intended to model that rubber, being material of matrix and liners, is vulcanized around yarns.

Frictional contact is defined between the outer lateral surface of the hose and the disc with a coefficient of friction µ = 0.8 based on [11] . There are bonded contacts between the inner lateral surface of the hose and pins utilized for positioning the hose.

Disposition of the FE simulation along with mesh can be observed in Figure 8.

The hose is in connection with the disc continuously during the bending process, therefore, its centreline is transformed gradually into a circle, whose radius equals the sum of the radii of the hose and the disc. In the bending process, centreline of the hose is coincident with the tangent of the above-mentioned circle (Figure 9). Therefore, the length of the hose segment not in connection with the disc decreases step by step.

Positioning of the hose is carried out by the two remote points placed at each center of hole as presented in Figure 8. Positions of the right half of the hose in each time step are shown in Figure 9, while positions of the right remote point represented by global X and Y coordinates can be seen in Figure 10. The prescribed trajectory ensures that there is no reaction force in the tangential direction at the current point of tangency on the disc, therefore the finite element

bending process is smooth enough. Positions of the left remote point are symmetric to the positions of the right remote point in every time step, the plane of symmetry is the global YZ plane. Translation of remote points in direction Z is not allowed, rotation around axes X and Y is not allowed either, however, rotation around axis Z is possible.

In the current FE model, the disc is completely fixed.

Mean radial reaction force disclosed in Chapter 2 is 121.0 N in the position depicted in Figure 5, in this position in the FE simulation, the radial reaction force at the connection of the inner rubber liner and the positioning pin is 122.5 N. Hence, experimental and simulation results show good agreement. Position of the hose while measuring radial reaction force in simulation and during the experiment is apparently the same (Figure 11 and Figure 5 respectively).

Figures 12-14 show the strain state in the outermost reinforcement ply (ply1) at the end of the standard bending test. The strains in material direction 1 are not significant due to the high modulus of elasticity in that direction (Figure 12).

Modulus of elasticity is lower in material direction 2, so Figure 13 shows higher strain values in material direction 2. The strain component having the highest values is shear strain, shown in Figure 14, which is a result of shear-extension coupling [12] , being a typical feature of composite layers.

Table 1 shows maximal strains for each reinforcement ply. It can be seen that approximately equal strains are present in plies. Shear strains have opposite signs in adjacent plies, this can be attributed to the balanced layup of the hose (orientation angle of adjacent plies are ±ω).

Figures 15-17 show stress state in ply1 at the end of the standard bending test. Maximal stresses are present in material direction 1 according to Figure 15, because mostly yarns bear the load exerted from bending. Normal stress in material

direction 2 and shear stress in plane 12 are shown in Figure 16 and Figure 17 respectively. Although these components are not negligible either, they have a magnitude considerably lower compared to normal stress in fibre direction.

Load is distributed nearly equally among reinforcement plies (Table 2), pre

dominant role of normal stress in material direction 1 is confirmed. Shear stresses, like shear strains, are approximately equal in adjacent plies although having opposite signs. This is realized due to adjacent plies having opposite orientation angles (±ω).