Experimental and numerical investigations into torsional-flexural behaviours of railway composite sleepers and bearers

2.1 FFU composite materials

An FFU specimen exposed to service conditions for 30 years was used in a laboratory test by the Technical University of Munich. The test results exhibited residual high strength properties without significant changes in the density [11]. The manufacturers also claimed that the high level of precision and quality involved in the manufacturing process through the pultrusion technique is the contributor for the high strength. However, the study by Askeland et al. [15] suggested that it is the peculiarity of glass fibres that contributes to the stiffness of the polymer resin in the FFU sleeper sample, which prevents variation in the density. Moreover, some studies [9] demonstrated that the matrix system inside the material can harden and form stronger bonds between fibres and matrix during its lifecycle.

Structural integrity of railway sleepers and bearers is crucial for public safety. A train can derail by wider rail gauge and/or broken components caused by impact and fatigue loading [9]. Traditional sleeper materials possess high geological risks since the strength and engineering properties can be impaired. For example, timber when exposed to moisture would soften due to the moisture ingress, which affects the stiffness and leads to excessive deflection. In addition, although FFU bearers have a closed cell structure with a water ingress rate of 3.3 mg/cm² [10], the continuous exposure to moisture can affect the damping behaviours of composites and lead to a reduction in the flexural stiffness of the material [12]. However, it is reported that, when the FFU sleepers experienced impact loads caused by a drop weight of 500 kg from a specific height, little distortion could be observed. Similarly, when it was exposed to 2.5 million load cycle (e.g. dynamic fatigue forces), only a mere elastic deflection can be measured [11]. The superior endurance and impact resistance of FFU composites have thus attracted various adoption in the industry in recent years.

There were some experiments recently done in Finland. FFU sleepers were exposed to a static loading condition at room temperature and at −65°C. The resultant load–deflection curve showed a linear elastic behaviour that was uncommon for other sleeper materials (e.g. concrete or steel) [11]. According to the study by Kaewunruen et al. [10], the resin in the composite sleepers causes a brittle failure at very low temperatures. Hence, it signifies the role of glass fibres present in the resin matrix in contributing to the ductile nature of the composite material. However, the degree of material anisotropy can additionally affect the strength and engineering properties of the composites [16]. The glass fibres that are arranged longitudinally in FFU material can well withstand flexural stresses; however, lesser allocation of fibres in the transverse direction yields inefficient strength and hence, cannot be used in certain applications (e.g. rail bridge transoms) where the interaction due to shear stress is dominant [8].

2.2 Loads induced at turnout crossings

The wheel–rail interaction produces a significant number of complex stresses and strains on sleepers. According to previous studies [7,12], the passage of trains generates high-frequency forces and irreversible plastic deformations on bearers over the wheel transfer zone through the crossing nose, as seen in Figure 2. In addition to vertical loadings, the change in wheel/rail contact tensors is not smooth due to the dip-like geometrical irregularity coupled with the blunt angle of crossing rate. The complex forces are generally exerted onto the bearers at the crossing nose along the path on which the train wheel follows through the trajectory and suddenly changes direction [7,12]. When the wheel and rail are in smooth contact with each other (i.e. free from any sort of undulations), the moving trains produce low-frequency forces. The magnitude of the force depends largely on the dip angle, which measures the angle between the tangents of the wheel trajectories at the turnouts where the direction is changed. It was reported that when the equivalent dip angle was reduced, a significant increase in ride quality was experienced from the reduction of dynamic effects that produce higher frequency loads [5,8]. In particular, many turnout simulations under design track loads also suggested that the maximum deflections tend to occur at the bearers under and adjacent to the crossing nose [3,6,10].

Figure 2

The characteristic of impact forces at the railway crossing.

In addition, previous studies revealed that the FFU sleepers and bearers have high damping and stiffness to withstand dynamic loads [13]. Therefore, the FFU composite material with high damping coefficient will require a thinner layer of ballast support in transferring the induced force and vibration uniformly to the ground [8].

2.3 Load behaviour analysis

The flexural strength of FFU composite sleepers and bearers were investigated previously [2] for a specimen size of 3.2 m × 0.25 m × 0.16 m in accordance with EN 13230 standards combined with a numerical study by finite element approach using STRAND 7. The failure modes were then analysed. The tests identified the cracking on the internal fibres along the longitudinal direction at a load of 34 kN, and further load increments caused the sample to fail at a load of 132 kN with a deflection of 0.164 m (Figure 3). The experimental tests showed that larger fibre delamination can be observed at the breaking point while some minor fibre breaks could be initially noticed. These brittle behaviours suggested that a significant safety factor be required in designing composite sleepers and bearers [2,17].

Figure 3

Load–deflection behaviour of full-scale composite bearers.

When compared with traditional sleeper materials, it was found that the FFU composite’s flexural strength is sufficient against design requirements [11] whereas the composite sleepers with a smaller dimension can withstand an induced load of 240 kN required by the design standard. In the field trials, no permanent deformations could be observed on the composite sleepers. It is noteworthy that a review [18] demonstrated that the test span length makes very huge differences in the flexural strength of the composite materials when subjected to flexural loading conditions.

Based on the critical literature review, it is very clear that the previous studies have placed very little emphasis on the torsional behaviours of composite sleepers. However, the study by Sae Siew et al. [3] had demonstrated that the turnout bearers in the crossing panel can experience torsional deformation (or twist) while enduring the vertical translation. This is because the dip angle at the crossings can be very complex in three-dimensional space, and the wheel-rail trajectory on the complex 3D nose topology can cause torsional forces transferred onto the bearers. On this ground, this study places the focus on the coupling flexural-torsional behaviours of the FFU composites, which have not been investigated before in the past. The new insights will help railway engineers better predict the service life of composite bearers located in the turnout systems with a significant crossing rate.

3.1 Flexural experimental tests

The specimens are subjected to flexural action using 3-point bending approach under room temperature. A static load is applied at the centre of the specimen that is placed in between two roller supports distant at 200 mm centre to centre with a distance 25 (L/10) mm hanging away from each end of the specimen (Figure 4). The load could deform the specimen up to its maximum capacity reaching maximum stress and rupture strain induced on the material. The loading procedures and the support conditions are in accordance with EN 13230 [2].

Figure 4

Test setup for flexural bending test.

The experiments measure only the positive bending capacity because the specimens’ cross-section is symmetrical, and the experiments are performed on an articulated support made of steel following EN 13230. Note that there are no existing standard limits for detecting failure modes of flexible composites [2]. The prepared specimens have been carefully inspected for any uneven surface at the contact area between the specimen and the loading nose to ensure accuracy in the measurements of deflection [16]. Instron 34TM – 30 series (30 kN force capacity) with a high-precision load cell have been used. The equipment has an in-built strain measurement in accordance with the EN 10002-4 standards and has the capability of measuring displacement at a high accuracy [19]. The testing has been initiated under a displacement control method at a rate of 0.05 mm/s. It is assumed that the relationship between the applied force and the resultant deformations is proportional to each other up to an elastic limit, which makes the specimen recover completely when the applied load from the testing machine is removed within this range. At the elastic limit, the material is assumed to demonstrate the similar ratio of stress and strain over the tension and compression zones. Considering the specimens’ rectangular cross section, the maximum fibre stress occurs at top and bottom layer, which is half the overall depth of the specimen from its neutral axis [20]. The stress and strain values of the composite material can be obtained using the following equations using the recorded force-displacement values obtained from the testing machine [18]; the bending moment can be calculated by

The flexural stress from the corresponding bending moment can then be obtained by,

and the flexural strain can be determined using the following relationship,

where F is the applied vertical load, L is the length between two supports, b and d are the width and depth of the test specimen, u is the recorded displacement, and D is the thickness of specimen cross-section.

3.2 Torsional experimental tests

The specimens are tested in two sets in order to induce the coupling loads at minimum and maximum eccentricities using two different setups to produce a torque from twisting. The maximum eccentricity for the torsional tests is 20.5 cm measured from the specimen centre to the point load, which has a displacement rate of 0.05 mm/s. The clamps shown in Figure 5 are used as hinge supports to facilitate the torsional tests. Note that the distance between the two supports is 200 mm. A minimum eccentricity is initiated by applying a point load at 1.25 cm away from the centre of the specimen onto the metal lever arm (Figure 6). The specimen is pinned at the supports at a span of 200 mm centre-to-centre (c-c) using clamps.

Figure 5

Experimental setup for a torsional test at maximum eccentricity, including its detailed sketch. (a) Testing machine. (b) Specimen. (c) Testing diagram.

Figure 6

Setup for a torsional test at minimum eccentricity.

The torsional tests are later performed on a basis of superposition method [18], where the load acting at a point away from the centre of the specimen (or an eccentric load) is equal to the combined effect produced by the coupling of torque and vertical force at the centre of the specimen. The shear stresses and shear strain due to the torque reach maximum on the edges of the specimen [21] and can be calculated using the following equations [22] on a basis of the recorded experimental results at a particular eccentricity. The torque can be obtained by

The shear stress due to torsion can then be determined using the equation,

or

and the shear strain induced on the specimen is found by

The modulus of rigidity to measure shear strain can be obtained from

where F is the applied load, e is the eccentric distance from the centre of the specimen to the applied load, μ is a dimensionless coefficient for varying b/d ratio, and v is the poison’s ratio.

3.3 Numerical development of finite element model

The non-linear finite element simulation has been established using ABAQUS CAE 2022. The simulation model will be based on the displacement control method. The specimen has been modelled as a deformable brick type in the same size as the experimental dimensions. For the flexural loading (Figure 7), the loading part and roller supports are modelled as an analytical rigid brick type at the centre and each end spanning 200 mm c-c from the supports. The end supports are pinned, which prevents movement along U1(x), U2(y), and U3(z) directions. The middle support is restricted in U2(y) direction. The point of reference at the centre of the specimen is defined by restraining all directions except along the axis in the U2(y) direction.

Figure 7

FEM for flexural simulation.

Different mesh sizes have been taken into full consideration for checking the convergence of the ultimate flexural results from finite element modeling (FEM) and the experimental value. The model is in very good agreement with the experiments; and the outcome converges at a mesh size of 10 mm, which divides the model into 390 elements for the generalized analysis neglecting the effects of inertia [23]. The specimen properties as demonstrated in the validation section are then used for all simulations to obtain excellent agreements with the experimental load–displacement curves.

For torsional simulations (Figure 8), the validated finite element model is adopted and fixed at both ends. The load head is modelled as a discrete rigid block type where the reference point is in tie constraint with the surface of the model allowing to displace along the U2(y) direction under a controlled displacement at an increment size of 0.1. The load transfer block is shifted to capture the ultimate load for different eccentricity values. The flexural-torsional interaction diagram and the relationship between force and displacement can thus be fully obtained.

Figure 8

FEM for torsional simulation at 20 mm eccentricity from the centre.

4.1 Model validation of FFU railway sleepers and bearers

Non-linear stress–strain behaviours can be obtained from the experimental load–displacement curves as shown in Figure 9 (i.e. EXP line) through the applications of Eqs. (1)–(3) for flexural stress. The calculated stress and strain values are incorporated into the specimen’s plastic properties to initiate the damage plasticity behaviour concrete damage plasticity. The model input properties are tabulated in Table 1 for the numerical validation [2,24].

Figure 9

Experimental load displacement curve of flexural bending for three specimens with their average curve (purple) and simulated curve (green).

The non-linear load–displacement behaviour obtained from the simulation is found to be in excellent agreement with the experimental data with a proximal discrepancy of lesser than 1% at the ultimate load values (as illustrated by the discrepancy between FEM and EXP lines in Figure 9). The numerical result is also found to be within the upper and lower bounds of the experiments. In this study, the non-linear FE model adopts identical damage behaviour properties of the railway sleeper models subjected to three-point bending previously performed in the study by Rezaie and Farnam [24]. The dilation angle, which denotes the angle of internal friction of the material, is considered as 35; and the ratio of biaxial stress to uniaxial compressive yield stress on an element is considered as 1.16. The viscosity and damage parameter are taken as 0; and the damage parameter is obtained by subtracting one from the ratio of flexural stress to the yield stress [14].

4.2 Failure modes of FFU railway sleepers and bearers

4.2.1 Flexural results

The load–displacement curves obtained from the experiments have been averaged and illustrated in Figure 10 to display the flexural behaviours of the composite material. Observably, the specimens initially exhibit a linear behaviour, but as the load is increased at a given displacement rate, the curve tends to behave non-linearly. The FFU specimens suddenly fail, and their averaged ultimate load-displacement values are presented in Table 2. Similar trend of failure was also reported on prestressed concrete [24] under a three-point bending test in which specimen ruptures after experiencing a little deformation after reaching a certain ultimate point. However, for FFU composite materials, it can be surprisingly observed that the failed specimens can recover their shape nearly back to their original condition.

Figure 10

Validation curve between experiment (Red) and simulation (Black).

Table 2

Average values at the ultimate point for flexural loading

Force (kN)	Displacement (mm)	Flexural stress (MPa)	Flexural strain
10.065	17.2	96.631	0.0645

As shown earlier in Figure 9, the percentage difference between the numerical and experimental results is found to vary between 5.46, 4.06, and 1.52% for trial nos 1, 2, and 3, respectively. Although the discrepancy is relatively small and acceptable in engineering field, it is important to note that these variations can be attributed to the versatile arrangement of glass fibres within the FFU composite, which causes some small variations in the resistance against flexural loading conditions. Furthermore, the load–deflection curves portrait distortions that resemble the reduction in flexural strength accompanied by breaking sounds produced from internal fibre cracking. It can be observed that the material fails by the delamination of longitudinal fibres in tension zone of the specimen as shown in Figure 11 where the tensile stresses are significant. Note that the numerical simulations can indicate higher stress concentration (Figure 12) that causes small indentation at the applied load axis.

Figure 11

Failure under three-point bending test.

Figure 12

Flexural simulation by FEM.

Some studies on fibre glasses [25,26] suggested that the damage modes in composites are important especially when the failure due to delamination occurs. This type of failure is caused initially by cracking of the matrix material under the mixed action of shear and bending. Then, fibre breakage is another common failure that can be demonstrated through the fibre bundle theory, which states that, when a proportion of fibre breaks, it causes the tensile failure in the specimen [25]. In fact, the shear stresses induced on the specimen are taken initially by the matrix and then are progressed onto the fibres; hence, the length, orientation, and arrangement of fibres are crucial in resisting shear stresses [26].

4.2.2 Torsional results

The first set of experiments has been conducted at a maximum eccentricity of 20.5 cm, and the second set at a minimum eccentricity of 1.25 cm. Three tests from each set are then averaged and the load–displacement curves from the experiments are displayed in Figures 13 and 14. The load–displacement curves demonstrate an elastic-plastic behaviour (showing an extent of elongation beyond the assumed yield point) representing a ductile failure mode under torsion. Note that the displacement is measured at the centre of the specimens.

Figure 13

Experimental load displacement curve for torsional loading, e = 20.5 cm.

Figure 14

Experimental load displacement curve for torsional loading, e = 1.25 cm.

When the load has been removed after reaching its ultimate point, it is found that the specimen returned to its original form with slight visible deformations at the bottom and load impressions on the surface (Figure 15) due to the plastically deformable nature of the individual materials used in the specimen. Under the torsion imparted by the maximum eccentric loading, the specimen shows no sign of delamination (as clearly illustrated in Figure 16) even though the specimen has reached its ultimate load value relatively early. However, cracking sounds from internal fibres have been heard during the experiments, which resemble the shear failure and the reduction in shear resistance of the specimen.

Figure 15

Deformation at minimum eccentricity during loading and deformation after unloading. (a) Loading. (b) After loading.

Figure 16

Deformation at maximum eccentricity during loading and deformation after unloading. (a) Loading. (b) After loading.

According to Figure 13, the specimen has an ultimate load capacity of 1.19 kN and 8.52 kN producing a torque of 243.95 and 106.375 kN mm at maximum (e = 205 mm) and minimum (e = 12.5 mm) eccentricities respectively compared to the flexural ultimate load value of 10.06 kN without any torque produced. It is apparent that the effect of torsion is relatively significant to the design of FFU sleepers and bearers, especially when the crossing rate is high, and the torsional force can be significantly induced.

The torsion produced from the maximum eccentric loading can cause the specimens to form a progressive diagonal cracking at the supports as observed in Figure 17. This failure pattern is due to the culmination of both shear and flexural loads, which can be derived from the equations for torsional shear stress (described in Section 3.1). At maximum eccentricity, the torsional shear stress is 3.90 N/mm², whereas a lesser torsional shear stress of 1.70 N/mm² is recorded at the minimum eccentricity.

Figure 17

Diagonal cracking observed at maximum eccentric loading.

In addition, the results from the non-linear FEM simulations reveal a reduction in the ultimate load capacity when the loading eccentricity increases as illustrated in Figure 18. The numerical results are later used in developing the flexural and torsional interaction diagram.

Figure 18

Ultimate load values at different eccentricities from the centre of the component.

4.3 Load interaction

The flexural–torsional interaction diagram is shown in Figure 19. Surprisingly, the diagram exhibits an elliptical nature, which is very useful in obtaining the design capacity of FFU rectangular sections under the combined effect of the flexural-torsional moments. Note that the combined effect can be determined using the equation in Section 3.2 (plotted in the x-axis) while the corresponding ultimate load for different eccentricities (plotted in the y-axis) is extracted from Figure 18. The interaction curve projection is later extrapolated for the condition of pure torsion. This interaction diagram also depicts the ultimate load induced on the specimens under the absence of torsion before the failure. Overall, the flexural-torsional interaction from the experimental testing is in excellent agreement with the numerical results obtained from the non-linear FEM.

Figure 19

Interaction between flexure and torsion from non-linear FEM in comparison with the experimental testing.

It is noted that the interaction curve between torsion and shear also produces an elliptical curve for concrete materials. This shows that the nature of interaction curve can vary based on the section shape and complexity of the material properties used in the component manufacturing [22].

By adopting the same modelling methodology and input parameters, a full-scale bearer can be numerically modelled with the real-scale dimension of 3,000 mm × 250 mm × 200 mm as specified in Engineering Specification SPC 231 [27]. The models apply different eccentricities, of which their numerical results also present an elliptical nature. The full-scale specimens yield higher values of the interaction diagram (Figure 20) in comparison with the small-scale laboratory specimens. The comparison infers the significance of sleeper size in resisting early failure due to the coupling load interaction. Note that, due to the scope of this study, the findings obtained from both the simulations and the experiments should be compared with those in similar conditions [28,29,30,31].

Figure 20

Interaction of flexure and torsion from FEM for large-scale size sleeper.

In addition, the elliptical nature of flexural and torsional interactions of the specimens both experimentally and numerically indicates that, as the eccentricity at which load exerts is increased, the composite material reaches its ultimate failure condition earlier than it would under pure bending action since the combined action of load and torsion can cause the specimens to deform and fail more quickly.