Optimization of the mechanical and vibrational damping properties of a hybrid rubber particle and glass fibre railway sleeper composite

In the locomotive industry, the railway structural material is frequently subjected to harsh loads and vibration, and the current durability and vibration-resilience capabilities of the sleepers are insufficient. The aim of this paper is to fabricate a railway sleeper composites with enhanced mechanical and vibrational properties. A full factorial experimental design was followed in the composite fabrication with the rubber particles and fibreglass volume fraction ratio varied between 5 and 20% and 5 to 8% respectively. Modelling and optimisation of the mix design was then carried out using numerical modelling techniques. ANOVA tests were carried out to show the model’s accuracy in predicting tensile strength, compression strength, flexural strength, and vibrational damping, as shown by R2 values of 60.69%, 86.60%, 60.05% and 81.41%, respectively. However, the model was not reliable for the composite hardness which had an R2 value of 37.87%. The optimisation model developed in the study indicated that rubber particles of size of 150 μm at volume fraction of 7.48% and fibreglass volume fraction of 8% gave the optimum mechanical and vibrational properties.


Introduction
A railway sleeper is a critical structural component of the railway track system [1].The railway sleeper is a supporting, and damping beam located beneath the railway track and can be made up of various materials such as timber, steel, concrete, and composite materials [2].The durability of concrete and steel sleepers over wooden sleepers made them popular in the late 1990s [3].Nevertheless, the vibration of the steel and concrete sleepers in the railway track system resulted in several issues, including concrete fracture, rail fastener failure, flexural cracking, and rail seat abrasion [4].Trains are getting heavier and faster, thus there is need of a railway structure that can sustain much larger static and dynamic stresses Ballasts are incoporated into railway track system to assist in dampening as part of numerous strategies to alleviate the vibration problem [5].However, the vibration on the ballasts causes them to deteriorate over time [5].In addition, excessive abrasion can cause the rail to tip, lose the clip toe load, and widen the gauge size.The culmination of all these problems might be a catastrophic train derailment [6].Carrascal (2007) and Connolly (2015(2007) [7] presented a novel technique for improving the dampening of the railway track system by installing railway sleeper pads underneath the railway's structural material.However, when heavily loaded trains are using the railway line, the sleeper pad material tends to loosen and gradually separate from the railway framework.Meesit et al (2017) [1] introduced a novel technique for producing a composite railroad sleeper that combines cement and rubber particles from used tires [8][9][10].The effectiveness of this hybrid cement composite was attributed to the rubber particle's ability to dampen vibrations in the railway line.However, it was noted that the compression strength of the sleeper was compromised when waste tyre rubber particles are blended with concrete [1,11].The use of concrete containing fly ash and blast furnace slag as filler has been developed to mitigate on the lower strength of the concrete [12].Prestressed concrete sleepers are also used extensively however, the cost and the heavy weight of the sleeper makes its use prohibitive [13,14].Steel sleepers have also been used but, their susceptibility to corrosion makes them to lack the necessary durability [15].
Waste tyre disposal is a global environmental challenge, with approximately 1.5 billion tyre waste generated annually [16].These tyres are normally disposed of through incineration and landfills in an environmentally unfriendly manner.The development of a composite railway sleeper containing rubber particles could enhance vibration damping properties and alleviate the challenge of disposal of the waste tyres [17][18][19].
This study will focus on the use of waste tyre rubber particles, fibreglass, and polyester resin in the development of a composite railway sleeper with improved mechanical and vibrational properties.

Materials
The properties of the raw materials used in this research including fiberglass and rubber particles are outlined in the following subsections.General purpose NC901 polyester resin was used in this study.

Fibre glass
The properties of the fibre glass used in the study are as shown in table 1.

Rubber particles
The rubber particle used were of particle size of 150 μm and 300 μm.The chemical composition of the rubber particles was analyzed using an EDS and the results are as shown in table 2.
The rubber particles constituted of largely carbon and trace amounts of potassium.

Experimental designs
A full factorial 3 level and 4 factor experimental design was used to fabricate the composite material specimens.From this experimental design the relationship between the volume fraction of the rubber particles and fibreglass on the vibration damping and mechanical properties was deduced.

Vibration test analysis
A vibrational shaker table was used to perform the composite vibration test.ASTM E756 standard was followed in conducting this test [23].This test method is accurate over a frequency range of 50 to 5000 Hz over the practical temperature range of the materials, and it assesses the loss factor, young modulus or shear modulus, and vibration properties of materials.The vibration tests were conducted using vibration specimens with the measurements 140 mm × 14 mm × 5 mm.

Numerical modelling
Numerical modelling was carried out to optimize the response parameters to determine the specific composite composition.The numerical optimization was carried out after inputting the target response outputs.Overlaid contour plot graphs were plotted to identify the optimum regions on the plot.The responses were then selected, and the contours defined.The optimization process was carried out using Minitab software version 17.1.0.All the mechanical and vibration damping parameters were set at maximum as shown in table 3, for the optimisation process.

Model validation
The Model validation process was carried out by running experimental tests on the optimum composite composition computed by the numeric model and measuring deviation in responses between experimental and theoretical.The experiment characterization results, which included the mechanical and vibrational results, were then statically compared with those obtained from the model to validate the model's fit to experimental data.

Results and discussion
The results obtain from the full experimental design in the study are as shown in table 4. The parameters considered in carrying out the optimisation are the tensile, flexural, compressive strength and vibrational damping.

Optimum composite regions
This section discusses the regression analysis of mechanical characterization results for tensile strength, compression strength, flexural strength, and vibrational damping properties.

Tensile strength
The ANOVA analysis of tensile strength is reported in table 5.
From table 5, it was observed that fibre volume fraction was statistically insignificant for the linear terms, according to the t-test having a p-value of less than 0.05.However, the rubber particle fibre fraction was  From table 6, it was observed that fibre volume fraction and rubber particle volume were statistically insignificant for the linear terms, according to the t-test having a p-value of less than 0.05.However, rubber particle size was statistically significant, having a p-value of 0.596.The effects of the interaction between the square of ABC were statistically insignificant and significant.Rubber particles volume fraction and rubber particles volume fraction interaction were statistically significant, giving a p value of 0.065.The interaction between the square of adj R 2 was 50.58%, and The R 2 value shows that the model explains 86.60%, indicating that the model accurately represents the data.
By applying multiple regression analysis, the following compression strength regression equation was obtained.From table 7, it was observed that fibre volume fraction was statistically insignificant for the linear terms, according to the t-test having a p-value of less than 0.05.Furthermore, rubber particle, fibre fraction and particle size were statistically significant, having a p-value of 0.009, 0.001 and 0.455, respectively.The effects of the interaction between the square of ABC were statistically significant, and insignificant rubber particles and rubber particles gave a value of 0.131, which is statistically significant.Fibreglass gave 0.675, which is statically insignificant, giving a p-value greater than 0.05.However, the interaction between the square of adj R 2 was 50.58, and The R 2 value shows that the model explains 65.05%, indicating that the model accurately represents the data.

=
By applying multiple regression analysis, the following flexural strength regression equations were obtained.

Vibrational damping
The ANOVA analysis of vibrational damping is reported in table 8.
From table 8, it was observed that fibre mass fraction and fibreglass were statistically insignificant for the linear terms, according to the t-test having a p-value of less than 0.05.However, the rubber particle size fraction was statistically significant, having a p-value of 0.974.The interaction effects between the square of AB and C were statistically significant.However, the interaction between the square of adj R 2 was 50.58, and The R 2 value shows that the model explains 81.41%, indicating that the model accurately represents fits the data.
By applying multiple regression analysis, the following vibrational damping regression equation was obtained.

Hardness
The ANOVA analysis of hardness is reported in table 9.
From table 9, it was observed that particle size was statistically insignificant for the linear terms, according to the t-test having a p-value of less than 0.05.However, rubber particles were statistically significant and gave a value of 0.938, and fibre fraction was statistically significant, with a p-value of 0.292.The effects of the interaction between the square of ABC were statistically significant.However, the 2-way interaction indicates that rubber particles and fibreglass and the particle size were statistically significant.However, the rubber particles' volume fraction and particle size were statically insignificant.The R2 value shows that the model explains 37.87%, indicating that the model inaccurately represents fits the data.

Overlaid contour plot
This section discusses the optimum regions for the various mechanical properties, which include tensile strength, compression strength, flexural strength, and hardness in the form of contour plots.Furthermore, there is a plot for the optimum regions for vibrational damping.

Tensile strength
The contour plot figure 1 shows the tensile strength of a hybrid composite that is fabricated from rubber particles size 150 μm, polyester resin and fibreglass.
The highest values of rating for tensile strength, which gave the strength of greater than 13.5 MPa, are in the upper centre of the plot between 5% and 16% rubber particle volume fraction and limited to 6.8-8% fibreglass loading.The lowest values of rating tensile strength are in the lowest left and right corners of the plot, which corresponds with low values of both fibreglass (0-2.5%) and rubber particles volume fraction of between 0%-0.5% and 19%-20%.

Compression strength
The contour plot figure 2 shows compression strength of hybrid composite that is fabricated from rubber particles size 150 μm, polyester resin and fibreglass.
The highest ratings for the hybrid composite's compression strength gave greater than 40 MPa in the plot's upper right corner between 0% and 5% rubber particle volume fraction and limited to 4-8% fibreglass loading, which are also the highest percentage values for both fibreglass volume fractions.The low values of both fibreglass between (0-8%) and rubber particles volume fraction of between 17%-20%.

Flexural strength
The contour plot figure 3 shows a flexural strength of hybrid composite that is fabricated from rubber particles size 150 μm, polyester resin and fibreglass.
In the upper left corner of the plot, which corresponds to the high values of both fibreglass volume fractions in %, are the highest ratings for flexural strength of the hybrid composite, giving flexural strength greater than 40 MPa.The lowest rating values are in the lower left corner of the plot, giving flexural strength less than 15 MPa, that is, between 17%-20% volume fractions of rubber particles at the lowest values of fibreglass of 0%-2%.

Hardness
The contour plot figure 4 shows the hardness of a hybrid composite that is fabricated from rubber particles size 150 μm, polyester resin and fibreglass.The highest values of rating for the hardness of hybrid composite are in the upper right corner of the plot between 0%-4% of volume fraction of rubber particles and between fibreglass volume fraction of 7.2-8%, which correspond with the high values of both fibreglass volume fractions in percentage.The lowest hardness values are in the lowest left corner of the plot and gave hardness of less than600 between volume fraction of 0%-17%, at a volume fraction of fibreglass between 0%-5.2% which corresponds with low values of both fibreglass and rubber particles volume fraction.

Vibrational damping
The contour plot figure 5 shows the damping of hybrid composite fabricated from rubber particles size 150 μm, polyester resin and fibreglass.
The highest values of rating in the plot gave damping of greater than 0.2 in the upper right corner of the plot in between 17% and 20% rubber particle volume fraction and limited to 7-8% fibreglass loading.The lowest values of rating damping are in the lowest right corners of the plot, which corresponds with low values of both fibreglass (0-1.7%) and rubber particles volume fraction of between 0%-1%.

Numerical optimization
The optimization plot, as shown in figure 6, displays the fitted values for the predictor settings.
The composite desirability in the model was recorded as 0.6764, which was greater than 0.5, indicating that the model accurately optimises the overall responses.The optimum mix design from the model is 7.4747% of 150 um rubber particles at an 8% fibreglass volume fraction.From figure 6, increasing the rubber particle content steadily increases vibrational damping.However, an increase in rubber particles lowers the composite's hardness, flexural strength, and compressive strength.An incremental amount of rubber particles increases the tensile strength to an optimum point, and beyond that, the tensile strength is reduced.The addition of fibres to the composite increased all the mechanical strength properties and vibrational properties, as shown in figure 6. Increasing rubber particle size has different responses.Increasing rubber particle size increases damping value but decreases hardness, compression flexural and tensile strength.Therefore, the optimal setting is in the range of (150 μm), which is a compromise between conflicting goals.This result suggests that rubber particles less than 150 μm should be considered to maximize mechanical strength.The graphs show that when rubber particle size is increased, damping increases and mechanical strength decreases.

Response prediction
The standard error of fit estimates the variation in the estimated mean responses for the specified variable settings.Vibrational damping, flexural strength, compressive strength, and tensile strength had a low standard  error of fit, indicating that with 95% confidence, the mean is within range, as shown in table 10.However, hardness had a high standard error due to the unpredictability of its results.
The 95% confidence interval for all the responses is within range for all the experimental The confidence intervals for all responses are relatively narrow, implying strong confidence in the mean of future values.
The 95% prediction interval assesses the prediction precision.The prediction intervals are all within acceptable boundaries for the responses except for hardness.The low prediction interval for hardness could be attributed to the lack of composite homogeneity giving variable results due to the nature of random laying.The prediction interval has a wider range than the confidence interval due to uncertainty in predicting a single response compared to a mean response.The mean damping is 0.14160, and the range of likely values for a single future value is 0.08941 to 0.19378.The mean hardness is 647.8, and the range of likely values for a single future value is 492.8 to 802.7.

Model validation
The model validation was done by fabricating the composite using optimum values obtained from the model.The rubber particles of size 150 μm at a volume fraction of 7.476% reinforced with 8% fibreglass was used to fabricate the composite.Table 11 shows the deviation of experimental results from the model.
The standard deviation of the results was low for all the parameters except hardness.This low standard deviation showed a good fit between the experimental and predicted optimum results.The higher standard deviation for hardness was of concern; however, it was within acceptable limits.The standard deviation for hardness should be between 4% and 95%.

Conclusion
The study investigated the effect of varying the volume fraction of rubber particles and fibreglass on the mechanical and vibrational properties of a composite railway sleeper.The following conclusions were drawn from the study.
• The ANOVA test showed the model's accuracy in predicting tensile strength, compression strength, flexural strength, and vibrational damping, as shown by R 2 values of 60.69%, 86.60%, 60.05% and 81.41%, respectively.However, the model was not reliable for hardness which had an R 2 value of 37.87%.

Figure 6 .
Figure 6.Optimization plot for mechanical and damping properties.

Table 2 .
EDS report on elements of the rubber particles.

Table 3 .
The target response outputs.The particle size was statistically significant, having a p-value of 0.073.The effects of the interaction between the squares of ABC were statistically significant.The R 2 value shows that the model explains 60.69%, indicating that the model accurately represents fits the data.By applying multiple regression analysis, the following tensile strength regression equation was obtained.

Table 4 .
Mechanical and damping results.

Table 5 .
ANOVA for composite tensile strength.

Table 6 .
ANOVA for composite compression strength.
A-Rubber particle volume fraction; B-Fibre volume fraction; C-Rubber particle size MS-Mean square; DF-Degree of freedom; SS-the sum of squares; R 2 -Coefficient of determination; Adj R 2 -Adjusted coefficient of determination

Table 7 .
ANOVA for composite flexural strength.

Table 8 .
ANOVA for composite vibrational damping.A-Rubber particle volume fraction; B-Fibre volume fraction; C-Rubber particle size MS-Mean square; DF -Degree of freedom; SS-the sum of squares; R 2 -Coefficient of determination; Adj R 2 -Adjusted coefficient of determination *
* A-Rubber particle volume fraction; B-Fibre volume fraction; C-Rubber particle size MS-Mean square; DF-Degree of freedom; SS-the sum of squares; R 2 -Coefficient of determination; Adj R 2 -Adjusted coefficient of determination

•
The optimum composite mix design obtained from the developed model was 7.4747% of 150 um rubber particles and 8% fibreglass volume fraction.These factors correspond to responses 13.385 MPa, 36.027MPa, 36.587MPa, 647.751Leeb and 0.142 for tensile, compressive, flexural strength, hardness, and vibrational damping.