^{1}

^{*}

^{1}

^{1}

The aim of this paper is to present finite element model of a filament-wound composite tube subjected to three-point bending and bending in accordance with standard EN 15807:2011 (railway applications-pneumatic half couplings) along with its experimental verification. In the finite element model, composite reinforcement plies have been characterized by linear orthotropic material model, while rubber liners have been described by a two - parameter MooneyRivlin model. Force-displacement curves of three-point bending show fairly good agreement between simulation results and experimental data. Reaction forces of FE simulation and experiment of standard bending test are in good agreement.

Composite tubes are utilized in a variety of engineering fields due to their high specific strength and high specific stiffness [

General structure of composite tubes can be seen in

ω. Orientation angles of adjacent plies (α_{1}, α_{2}) are opposite in most cases (α_{1}= −α_{2}).

In fibre coordinate system, material direction 1 denotes direction of yarns or grainline (x_{1}(1) for ply 1, x_{1}(2) for ply 2 in _{2}(1) for ply 1, x_{2}(2) for ply 2 in

Geometry of the filament-wound composite hose can be observed in

Since composite tubes are frequently subjected to bending loads during their lifetime, bending tests are an integral part of experiments related to composite tubes. Three-point bending and four-point bending are among the most generally performed bending experiments. Firstly Lehnitskii [

The current article is a verification of the material model of the composite hose, described thoroughly in [

Three-point bending test has been performed on a Zwick Z 020 tensile test machine (

Standard bending test of the hose onto a disc is utilized in practice as a means of quality control (

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 (E_{2} = E_{3}, G_{12} = G_{13}, υ_{12} = υ_{13}). Transversely isotropic materials have five independent elastic constants (E_{1}, E_{2}, G_{12}, G_{23}, υ_{12}) [

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 [

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

E_{1} = 1338 MPa, E_{2} = E_{3} = 19 MPa, G_{12} = G_{13} = G_{23} = 6 MPa, υ_{12} = υ_{13} = 0.37, υ_{23} = 0.498 [

Rubber liners are described by a 2 parameter Mooney-Rivlin model [_{10} = −0.4982 MPa, C_{01} = 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 [

Upper and lower supports are modelled as rigid bodies (

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 (

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 [

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

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 (

Positioning of the hose is carried out by the two remote points placed at each center of hole as presented in

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

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 (

Modulus of elasticity is lower in material direction 2, so

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

Ply no. | ε_{1} [−] | ε_{2} [−] | γ_{12} [−] |
---|---|---|---|

1 | 0.0035 | 0.075 | −0.2452 |

2 | 0.0035 | 0.076 | 0.2313 |

3 | 0.0027 | 0.072 | −0.221 |

4 | 0.0029 | 0.073 | 0.206 |

direction 2 and shear stress in plane 12 are shown in

Load is distributed nearly equally among reinforcement plies (

Ply no. | σ_{1} [−] | σ_{2} [−] | τ_{12} [−] |
---|---|---|---|

1 | 4.77 | 1.42 | −1.535 |

2 | 4.75 | 1.47 | 1.45 |

3 | 5.62 | 1.43 | −1.38 |

4 | 5.31 | 1.42 | 1.29 |

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).

Experimental data series and FE simulation results of three-point bending show good agreement regarding force-displacement curves.

In case of standard bending test, reaction forces acquired from the simulation are in good agreement with experimental reaction forces. Mechanical behavior of composite tube subjected to standard bending test has been demonstrated based on stress and strain states of the FE model.

Authors show gratitude to Department of Polymer Engineering, Budapest University of Technology and Economics, namely to Gábor Szebényi for providing them with the testing environment. The recent study and publication was realized within the Knorr-Bremse Scholarship Program supported by the KnorrBremse Rail Systems Budapest.

Szabó, G., Váradi, K. and Felhős, D. (2018) Bending Analysis of a Filament-Wound Composite Tube. Modern Mechanical Engineering, 8, 66-77. https://doi.org/10.4236/mme.2018.81005