Physics of hardening of the rolling surface of rail head from hypereutectoid steel after operation

Introduction

Rails are predominantly removed from service due to contact fatigue damage and surface wear [1; 2]. In recent years, with increasing railway traffic speeds and axle loads, the operational durability requirements for rails have become more demanding [3 – 5]. From both practical and fundamental perspectives, the development of special-purpose rails with enhanced performance characteristics is of significant importance [6 – 8]. In Russia, home to one of the world’s longest railway networks, this challenge has been addressed since 2018 through the production of long, differentially hardened rails with improved wear resistance and contact fatigue strength, classified as DT400IK [9]. These rails are manufactured from steel containing more than 0.8 wt. % carbon, which ensures the formation of a subgrain structure with a high density of low-angle boundaries in the surface layer. Modern physical materials science techniques, particularly transmission electron microscopy [10 – 12], are employed to monitor changes in structure, phase composition, and defect substructure that lead to the degradation of mechanical properties [13 – 15]. Improving the technology for special-purpose rail production and ensuring high-performance properties requires a deep understanding of the physical nature and evolution trends of the structural-phase states and fine substructure in the surface layers of rails [16 – 18]. Such data are crucial for reliably achieving the target of transporting up to 2 billion tons [19 – 21]. Analysis conducted on rails made of hypoeutectoid steel with carbon content below 0.8 wt. % – as presented in [22 – 25] – has enabled the quantification of physical hardening mechanisms, the establishment of their hierarchy, and the determination of overall yield strength. However, there is a notable lack of studies focused on rails made of hypereutectoid steel.

The objective of this study is to compare the deformation hardening mechanisms of the rolling surface and fillet of special-purpose DH400RK rails after they have been in operation on the Russian Railways (RZD) test circuit at Scherbinka, following a tonnage of 187 million tons (gross).

Materials and methods

The internal structure and phase composition were studied on samples of differentially hardened DH400RK category rails, made from E0.9C–Cr–N–V–Fe grade steel produced by EVRAZ ZSMK, after they had undergone a tonnage of 187 million tons (gross) at the Russian Railways (RZD) test circuit. The chemical composition of E90HAF rail steel, according to GOST 5185 – 2013 and TS 24.10.75111-298-057576.2017, included the following main elements, wt. %: 0.92 С, 0.4 Si, 1.0 Mn, 0.3 Cr, 0.14 V, with iron as the base. The mechanical properties are as follows: yield strength – over 900 MPa, tensile strength – 1350 MPa. relative elongation – 9.0 %, relative reduction – 18 %, impact toughness – 15 J/cm², and hardness on the rolling surface of the rail head – 400 – 450 HB.

The rolling surface and fillet of the rail head were investigated (Fig. 1) using transmission electron microscopy (TEM) on thin foils with a JEM-2100 electron microscope (Jeol, Japan) [26 – 28].

To evaluate the hardening mechanisms that contribute to the yield strength in the studied steel, each sample was analyzed for structural morphological features, phase composition, and fine structure parameters, including the volume fractions of morphological constituents P_v. The localization of the carbide phase (cementite) was identified, and for each specific location, the shape, size (d), particle spacing (r), and volume fraction (δ) of the particles were determined. In each morphological component, as well as in the material as a whole, the scalar ρ and excessive ρ_± dislocation densities were calculated, along with the amplitudes of internal stresses generated by them – namely, shear stresses (σ_f , or “forests” of dislocations) and long-range stresses (σ_l), which arise in regions with an excess dislocation density. All quantitative parameters of the fine structure were measured within each morphological component and statistically processed, with the mean values presented in Table  1 (where D1 represents the fragment or subgrain size; χ, χ_pl and χ_el represent the curvature-torsion amplitude of the crystal lattice and its plastic and elastic components, respectively; \(\sigma _{\rm{l}}^{{\rm{pl}}}\) and \(\sigma _{\rm{l}}^{{\rm{el}}}\) are the amplitudes of internal long-range stresses and their plastic and elastic components.

The technique for determining these quantitative parameters is detailed in [9; 29].

Results and discussion

The studies have shown that regardless of the location on the rail head surface (Fig. 1) the following morphological components are observed in the structure: lamellar (ideal) pearlite with parallel alternating lamellae of ferrite and cementite; fragmented lamellar pearlite, in which dislocation walls across the di-rection of α-phase plates are formed; destroyed lamellar perlite with bent, cut and crushed Fe₃C lamellae; globular pearlite in the form of grains with globular Fe₃C particles, subgrain structure – small equiaxed fragments with cementite particles along the boundaries and in the junctions. The images of these morphological components are consistent with those observed for rails made of hypoeutectoid steel, as shown in [1].

A different type of structure was identified on the fillet surface – a completely destroyed structure. This structure, characterized by completely destroyed pearlite colonies, contains small, chaotically arranged carbide particles (Fe₃C) with an acicular shape and a high scalar dislocation density (Fig. 2, а).

The material on the rolling surface in the head center predominantly consists of a subgrain structure (90 %) (Fig. 2, b), while this structure accounts for only 2 % of the fillet surface. The research demonstrated that, in all morphological components, the dislocation structure type remains consistent: the dislocation substructure is represented by dense dislocation arrays. In all morphological components, there are bend extinction contours, originating from interfaces of pearlite grains and colonies, cementite plates in pearlite grains, fragment and subgrain boundaries, carbide particles (cementite) of lamellar and rounded shapes located on the boundaries and within the dislocation fragments and subgrains, junctions of subgrains, and the dislocation substructure.

Calculations presented in [9] indicate that, in the fillet surface layer, within the ideal, destroyed, and globular pearlite, the scalar density of dislocations ρ is higher than the excess density of dislocations ρ_±, as determined from the width of the bend extinction contours (Table 1), meaning that ρ > ρ_± and, accordingly, σ_l < σ_f. This indicates that the curvature-twist of the crystal lattice in these morphological components is purely plastic in nature. In fragmented pearlite, as well as in completely destroyed and subgrain structures, the value ρ is smaller than the calculated value of ρ_±, meaning ρ < ρ_± and, σ_f < σ_l, which implies that the curvature-twist of the crystal lattice in these components is elastic-plastic in nature. However, in fragmented pearlite and completely destroyed structures χ_pl  \( \gg \) χ_el, whereas in the subgrain structure χ_pl ≈ χ_el (Table 1).

In the surface layer of the rail head center, the value ρ in all morphological components was found to be smaller than the value of ρ_± calculated based on the width of extinction contours [9] (Table 2). This indicates that the curvature-twist of the crystal lattice in all morphological components is elastic-plastic, with χ = χ_pl + χ_el. In the subgrain structure, which occupies the majority of the material, χ_el is nearly three times greater than χ_pl .

In the surface layer of the rail head, elastic-plastic curvature-twist of the crystal lattice is observed across all morphological components. Notably, in the subgrain structure, which makes up 90 % of the material, the values of χ and σ_l are the highest, while the value of σ_pl is more than an order of magnitude smaller than that of σ_el (Table 2). This explains the presence of microcracks in these areas.

The quantitative results presented in Tables 1 and 2 served as the basis for calculating the additive (total) yield strength in each morphological component and for the material as a whole. It is important to note that individual mechanisms contribute differently to overall strengthening, as these are influenced by various factors in each case [30 – 32]. Therefore, when estimating the additive yield strength σ_ad, it is crucial to consider the volume fractions P_v of each morphological component σ_i

\[\sigma  = \sum {{P_i}{\sigma _i}} ,\]

where Р_i and σ_i are volume fractions and yield strength of each morphological component of the structure.

Previously, it was assumed that the additive yield strength could be determined by simply summing the contributions of individual hardening mechanisms [30]. However, it has now been demonstrated that, in some cases, these values should be summed using a quadratic approximation [31; 32]. This approach is particularly relevant for the mechanisms Δσ_f and Δσ_g, which act locally and inhomogeneously within the grains. Thus,

\[{\sigma _{{\rm{ad}}}} = \Delta {\sigma _{\rm{p}}} + \Delta {\sigma _{{\rm{s}}}} + \Delta {\sigma _{\rm{g}}} + \Delta {\sigma _{{\rm{or}}}} + \Delta {\sigma _{{\rm{perl}}}} + \Delta {\sigma _{{\rm{ss}}}} + \sqrt {\Delta \sigma _{\rm{f}}^2 + \Delta \sigma _{\rm{l}}^2} ,\]

where Δσ_n = 35 MPa [9] represents the friction stress of dislocations in the crystal lattice of α-iron; Δσ_s refers to solid solution hardening (the hardening of ferrite solid solution by dissolved alloying elements); Δσ_g denotes grain boundary hardening (due to grain boundaries); Δσ_or is the hardening of material by incoherent particles as dislocations bypass them via the Orowan mechanism; Δσ_perl represents hardening due to pearlitic component (barrier inhibition within pearlitic colonies); Δσ_ss refers to substructural hardening (due to intraphase boundaries) the formula contains no such values); Δσ_f is the hardening by the “forest” of dislocations that cut glide dislocations (internal shear stress); and Δσ_l represents hardening by long-range stress fields (internal moment or local stresses), with Δσ_l = Δσ_el + Δσ_pl; where Δσ_el is the elastic component and Δσ_pl is the plastic component of long-range stresses.

The contributions of these hardening mechanisms were qualitatively assessed using the formulas given in [29; 31; 32], and the results are presented in Tables 3 and 4.

The analysis of data from Tables 3 and 4 shows that the strength of the steel is multifactorial, with physical mechanisms that are cumulative in nature. For the fillet surface, the primary hardening mechanism is Orowan strengthening (Δσ_or). This is primarily because the completely destroyed structure occupies the majority (60 %) of the fillet surface. The contributions from long-range stress fields (Δσ_g) and the stresses from the “forest” of dislocations (Δσ_f )are also significant. The emerging subgrain structure forms numerous grain junctions, leading to an increase in the sources of extinction contours and, consequently, a growth in Δσ_g. However, since the volume fraction of the subgrain structure (P_v) is low (2 %), its contribution to the strengthening of the fillet surface is minimal. The strengthening is primarily due to the fragmented substructure and the completely destroyed structure. The additive yield strength at the fillet surface is 2218 MPa.

For the central part of the rolling surface of the rail head, the additive yield strength is much higher, reaching 7950 MPa. The main hardening mechanisms (Table 4) include strengthening by internal elastic local stresses, substructural strengthening, and strengthening by incoherent particles.

The significant difference in the values of additive yield strength (\(\sigma _{{\rm{ad}}}^{{\rm{fillet}}} < \sigma _{{\rm{ad}}}^{{\rm{centr}}}\)) can be explained by the fact that, in the head center’s rolling surface, the volume fraction of the subgrain structure is 45 times higher than that in the fillet. The subgrains form in the nanometer size range, leading to a high density of sub-boundaries and junctions (primarily triple junctions) of subgrains, which are the sources of extinction contours (mainly elastic). These contours result in high values of internal long-range stresses, with the elastic component being more than an order of magnitude higher than the plastic one. This combination determines the final effect. On the fillet surface, the main morphological components are destroyed pearlite and a completely destroyed structure with low-density boundaries.

Conclusions

Transmission electron microscopy was used to reveal the morphological components of the rolling surface of the rail head made of hypereutectoid steel, both at the center and in the fillet. The identified components include lamellar pearlite, fragmented pearlite, destroyed lamellar pearlite, globular pearlite, completely destroyed pearlite, and subgrain structure. We conducted a quantitative analysis of hardening mechanisms and assessed the contributions from lattice friction, solid solution hardening, pearlite hardening, incoherent cementite particles, grain boundaries and sub-boundaries, dislocation substructure, and internal stress fields. For the fillet surface, we established that the main hardening mechanism is due to incoherent particles, along with mechanisms based on internal long-range (local) stresses, internal shear stresses (“forests” of dislocations), and substructural hardening.

For the central part of the rolling surface, the primary hardening mechanisms are long-range stress fields, incoherent particles, and substructural hardening. We determined the additive yield strength at the rolling surface and explained the difference in its values between the head center and the fillet.