Modulus Of Composites Research Articles

Evaluation and prediction of tensile properties of 3D‐printed continuous carbon/Kevlar fiber‐filled composites by coaxial hybrid process

AbstractContinuous hybrid fiber‐reinforced composites (CHFRCs) have excellent mechanical properties, and strong designability, and are widely used in aerospace and other fields. The development of 3D printing technology offers novel directions in the design and manufacture of complicated CHFRC components in aerospace. For this purpose, this study focused on the design and characterization of hybrid continuous fiber‐reinforced composites prepared by 3D printing. The rapid mold‐free integrated manufacturing of hybrid continuous Kevlar/carbon fiber‐reinforced composites was realized by coaxial hybrid 3D printing technology. The regulation and mechanism of tensile properties of 3D‐printed CHFRCs were elucidated. The tensile strengths of 3D‐printed CHFRCs were enhanced by up to 15.3% and 92.4%, respectively, compared to single continuous carbon and Kevlar fiber composites produced by the same process parameter. A new tensile modulus predicting method for 3D‐printed CHFRCs was proposed. It mitigated the influence of complex interfacial characteristics on mechanical property prediction and achieved precise estimation of the tensile modulus of 3D‐printed CHFRCs. This will provide the theoretical support for the application and development of 3D‐printed CHFRCs.Highlights Mouldless rapid manufacturing of coaxial hybrid fiber composites achieved. The tensile strength and modulus of the fiber composites are greatly improved. A new prediction method for the tensile modulus of 3D‐printed composites is proposed.

Effect of stable-structural 3D woven preform on tensile and flexural properties of carbon fiber/epoxy composites

The geometry of yarns effect the structural stability of 3D woven preform, which influence the mechanical properties of carbon fiber/epoxy composites. To investigate the effect of stable-structural preform on the elastic properties of 3D woven composites, the factors that caused the unstable structure of preform were discussed, and comparative study was conducted. The geometric models of yarn cross-section and preform were established to discuss the stability. The results showed that increasing the opening angle of warp yarns and the elongation of yarn outer contour can improve the stability of preform. The tensile and bending tests of 3DLAC and 3DBAC with stable and unstable structural preform were conducted. The results showed that the tensile and flexural elastic moduli were inversely proportional to the curvature of load-bearing yarns, and the elastic modulus of composites with stable-structural preform can increase by 9%–13%. The redistribution of internal stress in composites was macroscopically manifested as stable changes in experimental process. 3D woven composites with stable-structural preform showed the regular fracture cross-section, and fiber fracture and interface adhesion effect were the main failure mode in tensile tests, and fiber fracture on the compression surface and matrix cracking were the main failure modes in bending tests.

Indentation of sandwich beams: Comparison of Vlasov, Winkler, and shear theories with composite surfaces reinforced by CNTs and ANN model

The use of sandwich structures has spread to a wide range of fields today. As a result of their thin top and low stiffness, sandwich beams are very susceptible to local loads. One practical solution to increase the sandwich structure's indentation resistance is to add bending strength to the top. The structural properties of carbon nanotubes make them well-suited for use in polymer matrixes; their addition improves the attributes of polymers. Experimental and theoretical investigations of the sandwich structure's indentation behavior are presented in this article. As well, simulations of sandwich structures are conducted using Abaqus software. A tensile test of composite samples and Mori Tanaka's theory were used to determine the elastic modulus of epoxy resin reinforced with carbon nanotubes at different mass percentages. The elastic modulus of composites can be improved by adding carbon nanotubes up to 0.3 % by mass while the mechanical properties are reduced when more than 0.3 % of carbon nanotubes were added. Finally, the analytical solution and Abaqus modeling results for the indentation of the sandwich structure were compared with the results obtained from the experimental tests. A machine learning model is proposed for prediction of sandwich beams deflection. The results of the predictions were phenomenal, with MAE of less than 2 %. The computational costs have been compared with the experimental results, and the machine learning method is very efficient.

PVA-TiO2 Nanocomposite Hydrogel as Immobilization Carrier for Gas-to-Liquid Wastewater Treatment

This study investigates the development of polyvinyl alcohol (PVA) gel matrices for biomass immobilization in wastewater treatment. The PVA hydrogels were prepared through a freezing–thawing (F-T) cross-linking process and reinforced with high surface area nanoparticles to improve their mechanical stability and porosity. The PVA/nanocomposite hydrogels were prepared using two different nanoparticle materials: iron oxide (Fe3O2) and titanium oxide (TiO2). The effects of the metal oxide nanoparticle type and content on the pore structure, hydrogel bonding, and mechanical and viscoelastic properties of the cross-linked hydrogel composites were investigated. The most durable PVA/nanoparticles matrix was then tested in the bioreactor for the biological treatment of wastewater. Morphological analysis showed that the reinforcement of PVA gel with Fe2O3 and TiO2 nanoparticles resulted in a compact nanocomposite hydrogel with regular pore distribution. The FTIR analysis highlighted the formation of bonds between nanoparticles and hydrogel, which caused more interaction within the polymeric matrix. Furthermore, the mechanical strength and Young’s modulus of the hydrogel composites were found to depend on the type and content of the nanoparticles. The most remarkable improvement in the mechanical strength of the PVA/nanoparticles composites was obtained by incorporating 0.1 wt% TiO2 and 1.0 wt% Fe2O3 nanoparticles. However, TiO2 showed more influence on the mechanical strength, with more than 900% improvement in Young’s modulus for TiO2-reinforced PVA hydrogel. Furthermore, incorporating TiO2 nanoparticles enhanced hydrogel stability but did not affect the biodegradation of organic pollutants in wastewater. These results suggest that the PVA-TiO2 hydrogel has the potential to be used as an effective carrier for biomass immobilization and wastewater treatment.

Field stiffening: A way to break the bounds on the properties of composites

It is common practice for humans to enhance the stiffness of a material by adding stiffer ingredients into it, which leads to the development of various composites of wide applications. However, irrespective of the configuration of the constituents of a multiphase composite, its compression elastic moduli are always between some bounds which are determined by the volume fractions and elastic moduli of the constituents inherently. Here, we report a magnetic composite material that is composed of a soft matrix material and two magnetic thin plates with small volume fraction. The compressive elastic modulus of the composite material is 25 times higher than the Halpin-Tsai upper bound due to the effect of the internal magnetic field. The measured maximum initial tangent modulus of the magnetic composite is ca. 40 times and 54 times higher than that of the nonmagnetic composite and PDMS matrix, respectively. This work provides a new direction for improving the performance of materials by fields.

A bound for twists of $${\textrm{GL}}_3\times GL_2$$ L-functions with composite modulus

A bound for twists of $${\textrm{GL}}_3\times GL_2$$ L-functions with composite modulus

Dynamic mechanical properties of graphene and carbon fabric‐reinforced epoxy nanocomposites

AbstractThe present work attempts to estimate the impact of graphene and carbon fabric on the dynamic‐mechanical properties of epoxy nanocomposites with different weight percentages. By applying an oscillatory force to a composite, its response is measured, and by calculating the viscosity and the stiffness in relation to the temperature, time, or frequency, valuable information can be realized. It helps to identify “thermal transitions” occurring in polymers. The complex modulus shows the resistance of the composites to deformation caused by viscous and elastic effects. Though dynamic mechanical analysis (DMA) is used for the depiction of temperature‐dependent viscoelastic properties, in this investigation, the objectives were multi‐fold. It is aimed at understanding the role of carbon fabric and the incorporation of 1 wt% of graphene nanoplatelet (GNP) in the epoxy matrix, and the effect of 0.5 to 5 wt% of GNP. The dynamic mechanical properties, including storage modulus, loss modulus, and damping factor, are examined across a temperature range of 25–250°C. Based on the findings, the storage modulus of the composites exhibits a range between 2000 and 9000 MPa. Notably, the epoxy composite containing 1 wt% GNP filler demonstrates the highest storage modulus. The details of mechanisms involved in DMA measurement are schematically summarized.Highlights Epoxy‐GNP and Epoxy‐GNP‐carbon fabric composites were fabricated. Storage modulus of composites does not show much dependence on the GNP. An increase in storage modulus by 05 times is observed in the ECG1 composite. The loss modulus of EC and EG1 composite is much higher.

Investigation on the mechanical properties and damage mechanisms of plain-woven composites at elevated temperatures through a newly-designed testing system

In this paper, the mechanical properties and damage mechanisms of T800/epoxy plain-woven composites at elevated temperatures are investigated by using a newly-designed testing system, including improved digital image correlation (DIC) equipment, modified fixture and dedicated environmental chamber. The molecular structure, glass transition temperature (Tg) and thermal stability of the composites and epoxy resin are separately characterized. The tensile and compressive experiments of plain-woven composites are conducted at 20 °C, 60 °C, 100 °C and 150 °C. The full-field strain distributions of plain-woven composites at elevated temperatures can be accurately measured by the newly-designed testing system. The experimental results indicate that the modulus, failure strengths and damage mechanisms of plain-woven composites are highly temperature dependent. In general, the tensile and compressive moduli decrease slightly with increasing temperature, and the temperature exhibits a more pronounced weakening effect on compressive strength. When the temperature exceeds Tg, the resin attached to fiber yarns is gelatinous. High temperatures severely degrade the interlayer performance of plain-woven composites, resulting in severe delamination accumulation. Particularly, a modified Gibson model is proposed to predict the failure strengths of plain-woven composites at elevated temperatures, which is in high agreement with the experimental results.

Effect of silanization of poly (urea-formaldehyde) microcapsules on the flexural strength and self-healing efficiency of an experimental self-healing dental resin composite (An in-vitro study)

ObjectivesThis study investigated the impact of using γ-methacryloxypropyl trimethoxy silane (MPS) for surface silanization of poly (urea-formaldehyde) (PUF) microcapsules which enclose a healing liquid of “triethylene glycol dimethacrylate (TEGDMA) and N,N dihydroxyethyl-p-toluidine (DHEPT)” on some mechanical properties of an experimental dental composite as well as its self-healing efficiency. MethodsSynthesis of PUF microcapsules was done via in situ polymerization, followed by silanization with MPS silane. Silanized and non-silanized microcapsules were incorporated into a composite containing 30% polymer matrix and 70% fillers at different weight percentages (0%, 5%, 7.5% and 10%). The composite strength and elastic modulus were evaluated by Flexural testing. Fracture toughness KIc and self-healing efficiency were assessed by utilizing the “single edge notched beam” method. ResultsFlexural strength of all groups containing silanized microcapsules was non-significantly different from control group without microcapsules. However, in contrast to control group, all groups containing non-silanized microcapsules displayed considerably decreased flexural strength. Adding silanized and non-silanized microcapsules didn't show a significant change in the KIc-virgin. The silanized microcapsules' groups achieved a self-healing efficiency of about 49–77% recovery in KIc-virgin compared to 38–69% for their non-silanized counterparts. SignificanceIn order to increase the interfacial adhesion with the polymer matrix, improve the mechanical properties, and increase the efficiency of self-healing of dental resin composite, PUF microcapsules were silanized for the first time in the dental field using MPS silane. This innovative silanized microcapsule-containing self-healing composite may hold promise for repairing the damage caused by restorative cracks and extending their service life.

Study on micromolecular mechanical properties of C-atom reinforced SBR polymer composites

A three-layer microscopic model with Fe atoms as the top and bottom layer and SBR polymer composites as the middle layer and SBR polymer composite was established and studied. By adding C atoms as reinforcement, the stability and elastic modulus and frictional coefficient changes of SBR polymer composites before and after adding C atoms were studied. In this study, the molecular dynamics method was used to change of elastic modulus was observed by stretching, compression and shear of the SBR polymer composite; The simulation shows that after adding C atom the elastic modulus of SBR polymer composite increased, the friction coefficient of polymer composite upper and lower decreases and the relative atomsic concentration, temperature, velocity, overall temperature average, kinetic energy, total energy and MSD in the thickness direction are reduced after adding C atoms. The stability of SBR polymer composites is enhanced, and the deformation under shear is weakened. In addition, it is found that the binding energy between SBR polymer composites and Fe atoms is reduced after adding C atoms.The stability of SBR polymer composites is improved during use. This work provides a method for studying the properties of rubber composites by studying the enhancement of the stability of SBR polymer composites from the microscopic point of view.

Определение модуля деформации бинарного композита с помощью искусственной нейронной сети

Using of existing methods of determining the characteristics of soils which are part of current regulatory documents and which are based on the hypothesis of normal character of distribution require considerable time and material costs. According to the results of conducted laboratory researches the hypothesis wasn’t confirmed. In the paper it proposes to use trained artificial neural network for determination of the deformation modulus of binary composite «sand — granules of expanded polystyrene». Thus, it has been proven efficiency proposing method using trained artificial neural network in compare classical regression equation for determination of the deformation modulus of the binary composite. With a confidence probability of P = 95 % the absolute value of the relative error is equal to 11,8 % the proposing learning artificial neural network in 11 times less than the absolute value of the relative error of classical regression equation. Also with a confidence probability of P = 95 % the coefficient of determination is equal to 0,5641 and in 6,6 times less than it of regression equation. Further research will be directed to the selection of the values of the parameters of the artificial neural network program for increase the accuracy of determining the deformation modulus of the binary composite.

Characterization and Industrial Applications of Wushishi Clay Deposit

The Wushishi clay deposit in Niger State, Nigeria, was examined to understand its possible industrial uses. The clay samples were randomly selected from different locations. They Clay samples appeared dry and had a dark gray color. The research focused on properties like drying and firing behavior, apparent porosity, bulk density, water absorption capacity, plasticity, modulus of rupture, shrinkage, and chemical composition. The Chemical screening revealed a composition of 59.8% SiO2, 17.08% Al2O3, 2.54% Fe2O3, 0.3% MgO, 4.39% Na2O, 2.54% K2O, and 1.5% CaO. The clay exhibited moderate plasticity of approximately 2.83 kgf/cm2, moderate shrinkage of 10.5%, and a modulus of rupture (strength) ranging from 22.56 to 34.86kgf/cm2 at different temperatures. The clay deposit equally demonstrated strong positive significant correlation (r=0.993, p=0.007) between apparent porosity and water absorption capacity of clay. The higher the apparent porosity of the clay deposit the greater the clay's ability to absorb water. Additionally, the clay's color changed from gray to red upon firing. These properties indicate that Wushishi clay can be classified as stoneware clay. It has potential applications in the production of flowerpots, as a silica source for floor tiles and brickmaking, and as a binder in the absence of standard binders like phosphoric acid.

Enhanced mechanical properties of multi-scaled carbon reinforcements in ternary epoxy composites materials

Carbon nanotubes (CNT) and graphene have widely used as reinforcements in epoxy for various aims and applications since their ‘discovery’. For example, in the area of aviation and aerospace materials, carbon reinforcements are desirable as they offer solutions for light weight yet mechanically enhanced materials. The objective of this work is to investigate the effects of adding combination of carbon fillers of different aspect ratios on the thermal mechanical, Young’s Modulus and Fracture Toughness properties of the resultant epoxy composites. The carbon fillers include carbon nanotubes (CNT), graphene, and carbon black (CB) and their combined loading will be varied from 0.5 wt. % until 7 wt. % to form sets of binary epoxy composites and a ternary epoxy composites. All of the fillers are kept at the 1:1 weight ratio for CB + CNT, CB + Graphene, CNT + Graphene, and CB + CNT + Graphene. Among these combinations, the system with ternary fillers at 7 wt.% demonstrated the highest value of glass transition temperature (Tg) and KIC, and Young’s Modulus. The percent improvement for glass transition temperature (Tg) and KIC, and Young’s Modulus compared to neat epoxy are 9.5 %, 571%, and 58.3%, respectively. This work clearly demonstrated the effectiveness of employing various carbon fillers with different aspect ratio and morphology in enhancing the values of mechanical properties of epoxy system.

Effect of fiber content on mechanical properties of carbon fiber-reinforced polyether-ether-ketone composites prepared using screw extrusion-based online mixing 3D printing

The mechanical properties of carbon fiber-reinforced polyether-ether-ketone (CF/PEEK) composites are closely related to the fiber content. However, the low fiber content (typically below 20 wt%) that can be prepared by current material extrusion limits the application of the composites. In this work, CF/PEEK composites with up to 50 wt% carbon fiber content were manufactured using a custom-made screw extrusion-based online mixing 3D printhead. The impact of fiber loading on the rheological and flow characteristics of the composites was thoroughly examined initially. Subsequently, the influence of fiber content on the crystallinity and mechanical behavior of 3D-printed parts before and after annealing was further explored. The results indicated that adding CF and annealing significantly enhanced the strength and modulus of the 3D-printed composites within a fiber content range of 10 wt% to 40 wt%, compared to those of pure PEEK. At 40 wt% CF, the tensile and flexural strengths of the samples reached their maximum values at 135.9 MPa and 251.2 MPa, respectively, which were enhanced by 94% and 111% compared to those of the unannealed pure PEEK specimens. Also, these properties are the highest values achieved in 3D-printed short CF/PEEK composites. The mechanical properties of composites are affected by various factors such as fiber content, crystallinity, and internal pore defects when the fiber content is less than 20 wt%. However, when the fiber content exceeds 20 wt%, the influence of crystallinity on the mechanical properties becomes less significant. This study further explores the potential application of CF/PEEK composites and provides a novel approach for composite preparation.

Retracted: Predicting the Elastic Modulus of Nanoparticle-Reinforced Polymer Matrix Composites Based on Digital Image Processing and Finite Elements

Retracted: Predicting the Elastic Modulus of Nanoparticle-Reinforced Polymer Matrix Composites Based on Digital Image Processing and Finite Elements

Multi-scale experimental studies on mechanical properties of three-dimensional porous graphene cementitious composite

This study aimed to reveal the influence of 3D porous graphene on the cementitious composites from multiple scales. At the macro level, the 3D porous graphene could greatly improve the strength, elastic modulus, and crack resistance of the cementitious composite. At the micro level, the nanoindentation test indicated that the thickness of the interfacial transition zone (ITZ) could be reduced by adding 3D porous graphene, and the microcracks and pores could be lowered as well, which led to mechanical enhancement. Besides, statistical nanoindentation technique (SNT), X-ray diffraction (XRD), isothermal calorimetry, energy dispersive spectroscopy (EDS), and scanning electron microscope (SEM) evidenced that the 3D porous graphene could promote cement hydration and strengthen the elastic modulus and hardness of hydration products. Embedded in the hydration products, the 3D porous graphene could fill the cracks and pores and anchor the cement matrix at the micro-scale, which exhibited the reason for the positive effect caused by the 3D porous graphene at the macro-scale.

Modeling Electrical Conductivity of Injection-Molded Polymer Composite Bipolar Plates

Bipolar plates can be responsible for up to 40% of the total stack cost and 80% of the weight of a polymer electrolyte membrane fuel cell [1]. To reduce these cost and weight limitations, this work explores injection molding of polymer composites. Injection molding is well-suited for mass production and polymeric materials can significantly reduce the weight of traditional metallic bipolar plates. While polymers lack electrical conductivity, fillers can be added to fabricate conductive polymer composites. The main objective of this research is to model and injection mold polymer composites that will meet the United States Department of Energy technical target for bipolar plate electrical conductivity (> 100 S/cm).A fiber contact model was developed to predict electrical conductivity based upon direction in the material, fiber alignment, fiber length and diameter, fiber concentration, and fiber conductivity [2]. Fiber alignment was measured experimentally by imaging cross sections of injection-molded nylon/carbon fiber composites. Imaging was performed on samples with different weight percentages of carbon fiber and from different mold designs to compare how fiber angles change based on mold geometry. To reduce the significant time required to measure fiber angles experimentally, computer recognition and processing of fiber alignment was developed. Nylon composites were injection molded with carbon fiber loadings ranging from 10 to 40 wt%. Modeling predictions show good correlation within 20% of experimental conductivity measurements. Samples with at least 20 wt% carbon fiber exceeded the US DOE technical target for bipolar plate conductivity, reaching 250 S/cm. In addition to modeling electrical conductivity, the Halpin-Tsai equations are used to model the elastic modulus and ultimate strain of the polymer composite. Tensile testing showed that the modulus of elasticity increases with carbon fiber loadings up to 30 wt%, reaching 7.3 GPa. At loadings above 30 wt%, the higher filler content can create voids which decrease the modulus of elasticity. De Las Heras, A.; Vivas, F. J.; Segura, F.; Andujar, J. M., From the cell to the stack. A chronological walk through the techniques to manufacture the PEFCs core. Renewable & Sustainable Energy Reviews 2018, 96, 29-45.Weber, M.; Kamal, M. R., Estimation of the volume resistivity of electrically conductive composites. Polymer Composites 1997, 18 (6), 711-725. Figure 1

Computer homogenization of porous piezoceramics of different ferrohardness with random porous structure and inhomogeneous polarization field

The article is concerned with the homogenization problems, in which the effective moduli of porous piezoceramic composites are determined taking into account the inhomogeneity of the polarization field. The homogenization problems are solved by the finite element method in the framework of the theory of effective moduli and the Hill energy principle using the ANSYS package. To this end, in static problems of electroelasticity, the displacements and electric potential, which are linear in spatial variables, are specified on the boundary of a representative volume to provide constant stress and electric induction fields for a homogeneous reference medium. After solving a set of boundary value problems under different boundary conditions and determining the volume-averaged stress components and the electric induction vector, a complete set of effective moduli for the piezoelectric composite is calculated. A representative volume of the piezocomposite is created in the form of a regular finite element mesh consisting of cubic elements. Pores in the representative volume are assumed to be filled with a piezoelectric material with extremely small moduli. Finite elements with pore properties are selected according to a simple random algorithm. The inhomogeneous polarization field is found by solving an electrostatic problem, in which the polarization process in the representative volume is modeled based on a simplified linear formulation. The local coordinate systems for individual finite elements of the composite matrix are specified by the directions of the polarization vectors. In the following, when solving the problems of electroelasticity, these local coordinate systems associated with the elements of the piezoelectric matrix allow recalculating the material properties according to the formulas of transformation of the tensor components as the coordinate systems rotate. In addition, consideration is given to different models describing the change in the moduli of the material from an unpolarized state to a polarized one as a function of the polarization vector. Computational experiments were carried out for three types of piezoceramics: soft ferroelectric piezoceramics PZT-5H, piezoceramics PZT-4 of medium ferrohardness, and piezoceramics PZT-8 with higher degree of ferrohardness. The dependences of the effective moduli on porosity are compared for different laws of polarization inhomogeneity and different kinds of piezoceramic material of the composite matrix.

Effective modulus of 3D-printable curvilinear fiber reinforced composites

This paper presents the coupling between curvilinearity and effective modulus for a set of mathematically admissible high-symmetry and low-symmetry fiber architectures. The contour of the fiber is decomposed into a series of unidirectional short segments, and its effective modulus is determined using an integration scheme that combines theoretical analysis and finite element simulations. Results show that the modulus of low-symmetry sinusoidal and hyperbolic tangent fibers varies nonlinearly with orientation and controlled by the segments forming the smallest direction cosine with the loading direction. Both the orientation of the midline and amplitude of the fibers strongly influence the effective behavior. For unidirectional fiber reinforced composites, results reveal the existence of a critical fiber-orientation angle of 60° where the modulus is minimum. Fibers are the majority stress carrier below 60°, and above this angle, the matrix carries the load. The integration scheme can be applied to determine effective modulus of composites comprising fibers of arbitrary geometries and orientations, and the findings are expected to advance the design of additively manufactured complex composite structures.

Calculation method for composite modulus of flexible pile composite foundation for high-speed railway under post-work settlement source

The flexible pile composite foundation (FPCF) in deep soft soil regions often experiences post-work settlement, leading to rail irregularities in the high-speed railway (HSR). However, few studies have identified the characteristics of post-work settlement sources (PWSS) for FPCF. Hence, a calculation method for the composite modulus under the PWSS has yet to be established. Based on a full-scale field test of the FPCF for a high-speed railway (HSR), this study analysed the time-varying characteristics of the settlement and location of the PWSS. By analysing the properties of soft soil materials and the additional stress on FPCF, the formation mechanisms of PWSS were revealed. A 3D finite element model (FEM) of the FPCF-subgrade-ballastless track system was established, and the settlement curve was input at the location of the PWSS. The rationality of the numerical results was first verified through a scale-model experiment. Subsequently, based on the computational results of typical settlement transfer processes, it was found that settlement undergoes fast settlement, transitional following settlement, and following settlement during its transfer from the underlying layer to the rail. During the settlement transfer process, the reinforcement zone and embankment significantly reduced the settlement irregularities, which made the settlement of the ballastless track follow that of the subgrade bed. The pile compression modulus primarily regulated the rail amplitude, whereas the area replacement ratio primarily regulated the rail wavelength. Finally, based on the settlement transfer results, a method for determining the composite modulus was proposed, and a formula for calculating the composite modulus was derived. This formula contributes to a faster analysis of the influence of the PWSS of the FPCF on rail smoothness.