An Alternative Method of Investigating the Thermal Stability of Shoe-Braked Railway Wheel Steels Based on Strain Hardening Analysis

: During service, shoe-braked railway wheel steels are often subjected to a severe thermal cycle. Therefore, understanding the evolution of the microstructure and the resulting changes in mechanical properties during service is fundamental in the choice of steel. In previous research, the effects of the thermal loading on the microstructure and mechanical properties of five different steels for railway wheels (ER7, HYPERLOS ® , Class B, SANDLOS ® and Class C) were investigated by hardness, tensile and toughness tests, in the as-supplied condition and after different heat treatments designed to replicate the modification of the microstructure due to braking. In this paper, the tensile work hardening behavior was studied by interpolating the tensile flow curves with the constitutive equation related to the dislocation density proposed by Voce, which correlates the Voce equation parameters with the microstructural features of metallic materials. The work hardening analysis revealed that there is a good correlation between the Voce parameters and the microstructure of the five steels in as-supplied condition and after heat treatments. An interesting correlation was found between Voce parameters and apparent fracture toughness. After heat treatments at 700 ◦ C and 750 ◦ C the properties of the steels decreased, which was consistent with the evolution of the microstructure. However, after exposure at 970 ◦ C with subsequent cooling in air, Class C steel appears to have a microstructure similar to the original microstructure, with tensile and toughness properties very similar to the as-supplied condition, demonstrating better microstructural stability compared to steels ER7, HYPERLOS ® , Class B and SANDLOS ® .


Introduction
During operation, railway wheels experience microstructural changes in their surface layers, which have a significant impact on their performance and longevity.The material integrity is particularly challenged by the thermal cycle that wheel treads undergo during block braking, which alternates between heating from friction with the brake shoe and cooling from rail contact and is extremely accentuated by the formation of hot spots that have even higher temperatures [1][2][3].This cyclic loading can cause significant tensile stresses [4,5], microstructural alterations such as pearlite spheroidization [6][7][8][9] or the production of white etching layers [10][11][12], roughness caused by wear processes on the tread leading to undesirable tread profiles [13][14][15][16][17][18][19] or cracks [20][21][22], possibly degrading until the failure of the component.Therefore, choosing and optimizing the right steel compositions for the production of railway wheels requires a deep understanding of the evolution of microstructure and its subsequent impacts on mechanical behavior.
Mechanical properties, like tensile, fatigue, thermal-fatigue, wear resistance and fracture toughness are paramount information to design the safe applications of metallic mate-rials.Knowing the correlations between mechanical properties, microstructure and production route makes it possible to establish manufacturing parameters for a cost-effective high-quality industrial production.However, the microstructure characterization can be a time-and energy-effective procedure and quite often the gathered information is qualitative and can barely achieve some quantitative relationship with mechanical properties, unless one uses expensive and unpractical techniques for industrial purposes, like electron microscopy or micro-tomography, for instance.These microanalytical techniques have high resolution power, so they need a lot of statistics and the identification of the relevant aspects of their results is not always straightforward.On the other side, the acquirement of mechanical properties involves high material volumes, like the gauge of tensile specimens, for instance, so they represent reliable integral information according to the international standards.
Tensile testing gives the fundamental information for designing the applications of materials, like railway wheels' steel, and is the simplest test.So, a procedure based on tensile properties for assessing the quality of steels and metallic materials should be desirable and give solid relationships between the relevant microstructure features and the tensile information.At the same time, a relationship between this assessment and other mechanical properties, like fatigue resistance or fracture toughness, for instance, should be hopefully established, being very useful for industrial production valuation and designing potential applications of steels.Indeed, besides the tensile mechanical properties, like Yield Stress (YS), Ultimate Tensile Stress (UTS) and ductility (A5), other information can be gathered by the analysis of the tensile strain hardening, analysis that is based on the determination of the strain hardening rate, that is, dσ/dε p where σ is the true stress and ε p is the true plastic strain.Some constitutive equations that fit the tensile flow curves have physical base, like the Voce equation, for instance, and their fitting procedure is based on strain hardening analysis [23].Furthermore, the best fitting equation parameters relate to the relevant microstructure features of the metallic materials, which could give rise to a quality-assessment procedure that is successfully used in foundry alloys [24,25].In the present investigation, the quality assessment procedure based on strain hardening and the Voce equation was used to analyze and to relate the results of microstructure (grain size and phases) taken through conventional metallography, experimental hardness, tensile and toughness tests.These tests, conducted by Faccoli et al. [26,27], involved five railway wheel steels in the as-supplied condition and three different heat treatments designed to replicate the modification of the microstructure due to braking.The large amount of microstructure and mechanical data reported in [26,27] is not here reported to avoid redundance of information, while focus on the results of the new assessment procedure of material quality applied to the railway steels is the subject of this work.The novel procedure based on strain hardening analysis and the Voce constitutive equation has been here used for the first time on wrought steels rather than foundry materials for which it was designed.Only the summaries of the relevant microstructure and mechanical properties found in [26,27] are reported in the present work, for clarity's sake.The correlation between microstructure features of the steels and the best fitting Voce parameters is reported, as well as the relation with Brinell hardness measurements (HB) and apparent fracture toughness (K Q ) in controlled conditions.The quality-assessment procedure based on strain hardening and the Voce equation supported the evidence that investigated steels have a different microstructure and mechanical stability when undergoing severe thermal cycles.

Materials and Methods
A summary of the experimental tests previously conducted (see [26,27] for more details), as well as the analyses performed to derive the parameters of interest, is presented below.

Steels and Heat Treatments
ER7, HYPERLOS ® , Class B, SANDLOS ® and Class C forged railway wheel steels, supplied by Lucchini RS (Lovere, Bergamo, Italy), were investigated in the as-supplied condition and after heat treatment.The as-supplied condition of the wheel refers to the industrial process involving rim chilling followed by tempering heat treatments (for details, see [26]).The heat treatment involves heating to a pre-selected temperature at a rate of 40 • C per hour, maintaining this temperature for 45 min, and then cooling to room temperature in still air.The maintaining temperatures for the heat treatments-700 • C, 750 • C and 970 • C-were determined based on simulation results [26] and represent the regions of the iron-iron carbide phase diagram below the eutectoid temperature A 1 , between critical temperatures A 1 and A 3 , and above A 3 , respectively which are reached in the wheel rim during drag braking.The chemical compositions of the steels are reported in Table 1.

Hardness Testing
In [26,27], Brinell hardness measurements (HB) were carried out on the radial section of the rim at a depth of 35 mm under the running surface (corresponding to the limit of wear or last turning diameter) complying with the EN 13262 Standard [28].The tests were conducted using a 5 mm diameter ball, under a load of 7355 N, and with a dwell time of 15 s.

Tensile Testing and Tensile Data Treatment
Tensile tests were conducted in accordance with the EN 13262 Standard [28] using round tensile specimens.These specimens were extracted from a depth of 15 mm below the wheel running surface, with their axes aligned parallel to the tread.The strain gauge was 50 mm with a 10 mm wide diameter.The engineering stress S and engineering strain e of the tensile flow curves were transformed into true stress σ = S•(1 + ε) and true strain ε = ln(1 + e), respectively, by using engineering data up to UTS, as beyond UTS localized deformation at necking occurred, and the true stress and strain are not representative of the strain gauge plastic deformation.Finally, the true plastic strain ε p was calculated by subtracting the elastic strains from the strains, according to the equation ε p = ε − σ/E, where E is the experimental Young modulus.So, the plastic flow curves were fitted through the Voce equation that is defined as follows: The Voce equation is an exponential decay equation, where σ V is the saturation stress and ε c is the critical strain that defines the rate with which the σ V is achieved.σ o is the back extrapolated stress at zero plastic strain, ε p = 0.In order to fit Equation (1) to the experimental flow curves, that is, find the Voce parameters σ V , σ o and ε c , the strain hardening analysis was investigated.In fact, the differential form of Equation ( 1) is given by: Θ o is a constant, equal to σ V /ε c , while ε c has the usual meaning.So, if Equation ( 1) is the proper constitutive equation describing the experimental flow curve, through plotting the experimental strain hardening rate ( dσ dε p ) vs. the true stress σ, a linear data region should be found, and through fitting this linear region with Equation (2), the parameters Θ o and ε c are found according to the procedure reported in [24,25].Finally, σ V = Θ o •ε c , while σ o is found through minimizing the difference between Equation (1) and the experimental flow curve.
According to a wide body of literature [23], the Voce parameters Θ o and ε c have physical meaning.Θ o is athermal by nature, and describes the dislocation multiplication that is related to the mean distance λ between obstacles to dislocation motion; λ is related to the coarseness of the microstructure: the finer the microstructure (short λ), the bigger the Θ o .So, bainitic structure has a smaller λ and bigger Θ o than a pearlitic structure, for instance, while finer pearlite grain size is described by a bigger Θ o .The final value of Θ o depends on the statistical contribution of all the obstacles to dislocation motion according to a qualitative equation like where V i and λ i represent the volume fractions and the mean distance of the i-th obstacle of the microstructure, respectively, and α i are multiplicative factors.The contribution from every single obstacle (α i ) cannot be easily found, and Equation (3) represents a qualitative relationship: different microstructures could have similar Θ o , and so Θ o is a parameter describing the effective microstructure.1/ε c is thermal by nature and is related to a set of micro mechanisms that soften the deformed materials via reducing the dislocation density, like dislocation annihilation and formation of a low-energy dislocation structure, which depends on the dislocation motion: different crystallographic matrices and different chemical compositions have different values of 1/ε c .
In foundry products, it was found that by plotting the Voce parameters 1/ε c vs. Θ o of a set of significant tensile tests of the same material, they lie alongside a single line.The distribution of these Voce parameters on a line depends on the natural scattering of microstructure features, that is, the scattering of the characteristic lengths λ i , while the dislocation activity of dislocation multiplication and dynamic recovery is the same for all tensile flow curves as the matrix is unchanged.The plot 1/ε c vs. Θ o is called Matrix Assessment Diagram (MAD), and on it metallic materials with different chemical compositions and/or different crystallographic structures lie on distinct lines that are like fingerprints [24].For sound materials like wrought steels the intercept is positive, while in defective materials like some foundry products the best fitting lines of the Voce parameters in MAD have negative intercepts.The more defective the material, the more negative the intercept is, and this consistent behavior is called Defects-Driven Plasticity [29,30].

Toughness Testing and Metallographic Observations
The EN 13262 Standard mandates a minimum toughness for ER7 tread-braked wheels to prevent any type of undesired brittle fracture and ensure safety in service.The current standards do not specify requirements for fracture toughness for wheels made from the other steels investigated.The toughness tests were performed in accordance with the ASTM E399 Standard [31].Compact Tension specimens with a thickness of 30 mm (CT30) and a width of 60 mm were machined from the wheel rim.Six samples were extracted from each wheel in the as-supplied condition, spaced every 60 degrees along the tangential direction (for more details, see [26,27]).For each heat-treated condition, three samples were tested, each extracted from positions 120 degrees apart.At the conclusion of the test, the specimen was sectioned along the mid-plane orthogonal to the fracture surface, parallel to the wheel tread.The resulting section was prepared using standard metallographic techniques and was chemically etched with 2% Nital to reveal the microstructure.Microstructural observations and pearlite grain size measurements, complying with ASTM E112 [32], were Metals 2024, 14, 814 5 of 18 conducted using an optical microscope.All the results in [26,27] are summarized in Table 2 for the steels in as-supplied condition, while for the steels after heat treatments the results in [26,27] are summarized in Table 3.

Steels in the As-Supplied Condition
The microstructural observation results, HB measurements, tensile properties, fracture toughness taken from [26,27] and the calculated best fitting Voce parameters of the steels in the as-supplied condition are reported in Table 2.
In Figure 1, the best fitting Voce parameters of the steels in the as-supplied condition are reported as 1/ε c vs. Θ o in the MAD.The data lay close to a single line, suggesting that the different chemical compositions and production routes had significant effects on the different microstructural constituents of the steels, observed in [26,27] and summarized in Table 2, like the presence of ferrite (F), lamellar pearlite (P), bainite (B) and pearlite grain size (G), but there were no significant effects on the dislocation activity, i.e., on the soft ferrite where dislocation multiplication and dynamic recovery occurred, even if the chemical compositions of the steels were different.Besides Class B which had only ferrite and pearlite, the other steels also had traces of bainite and similar pearlite grain size, as reported in Table 2.The main alloying elements of the five investigated steels were C, Mn and Si; in addition, some of them were micro-alloyed with V.While C and Mn have the main effects on volume fractions and fineness of pearlite and bainite, Si partitions mainly in ferrite, strengthening it through the solid solution mechanism.In HYPERLOS ® , V is added since it has been reported [32,33] that V forms carbides, strengthening the ferritic matrix, but preserving ductility and toughness.So, the different chemical compositions of the steels did not affect significantly the ferrite where dislocations move, multiply and dynamically recover, resulting in Voce parameters lying alongside the same linearity in MAD.
Metals 2024, 14, 814 6 of 18 main effects on volume fractions and fineness of pearlite and bainite, Si partitions mainly in ferrite, strengthening it through the solid solution mechanism.In HYPERLOS ® , V is added since it has been reported [32,33] that V forms carbides, strengthening the ferritic matrix, but preserving ductility and toughness.So, the different chemical compositions of the steels did not affect significantly the ferrite where dislocations move, multiply and dynamically recover, resulting in Voce parameters lying alongside the same linearity in MAD.In Figure 2, selected mechanical properties were plotted vs. the best fitting Voce parameter o.Linear relationships were found, proving that the Voce parameter o was really related to the coarseness of the microstructure.In fact, the finer the microstructure, the higher the hardness and the YS, and so the inverse linear trend between o and the values of HB and YS confirmed the validity of Equation (3).In Figure 2, selected mechanical properties were plotted vs. the best fitting Voce parameter Θ o .Linear relationships were found, proving that the Voce parameter Θ o was really related to the coarseness of the microstructure.In fact, the finer the microstructure, the higher the hardness and the YS, and so the inverse linear trend between Θ o and the values of HB and YS confirmed the validity of Equation (3).In Figure 3, the apparent fracture toughness KQ values are reported vs. the Voce parameter o of the steels in the as-supplied condition.A good linearity was found between KQ and o for the steels.The apparent fracture toughness KQ was reported vs. HB hardness and YS in Figure 4a-c, respectively, where for KQ vs. HB, KQ vs. YS and KQ vs. UTS good linear trends were also found.In Figure 3, the apparent fracture toughness K Q values are reported vs. the Voce parameter Θ o of the steels in the as-supplied condition.A good linearity was found between K Q and Θ o for the steels.The apparent fracture toughness K Q was reported vs. HB hardness and YS in Figure 4a-c, respectively, where for K Q vs. HB, K Q vs. YS and K Q vs. UTS good linear trends were also found.

Steels after Heat Treatments
In Table 3, the calculated best fitting Voce parameters of the five steels after heat treatments are reported, with the microstructure, the pearlite grain size, HB measurements, tensile properties and fracture toughness taken from [26,27].After heat treatments at 700 and 750 • C, the microstructure and tensile properties had significant variations, with the appearance of globular pearlite (Pg in Table 3) because of exposure at high temperatures and a moderate increase in grain size.Consequently, there was a decrease in HB, YS and UTS, and consistently the Θ o also decreased.After heat treatment at a temperature of 970 • C, the microstructures seemed to restore partially to the original microstructure (summarized in Table 2), which has been reported in [26,27], besides the pearlite grain size that increased significantly after every heat treatment, particularly at a temperature of 970 • C. Consistently, the HB, YS and UTS after austenitizing at a temperature of 970 • C increased significantly with respect to the heat treatments at temperatures of 700 • C and 750 • C, but did not achieve the original values of the as-supplied condition, see Table 2.The apparent fracture toughness decreased for ER7 after heat treatments at temperatures of 700 • C and 750 • C, remained unchanged for HYPERLOS ® and Class C, and improved slightly for Class B and SANDLOS ® .After heat treatment at a temperature of 970 • C for the steels ER7 and HYPERLOS ® K Q decreased significantly, while it was unchanged for Class B, Class C and SANDLOS ® which presented the worst K Q in the as-supplied condition, showing a certain stability of the apparent fracture toughness.The Voce parameter Θ o which was inversely related to the fineness of the microstructure (Equation (3)) reduced dramatically after heat treatments at a temperature of 700 • C and 750 • C for all the steels, supporting the microstructure observations in Table 3, and after heat treatment at a temperature of 970 • C seemed to restore the original values of the steels ER7, HYPERLOS ® and Class C in the as-supplied condition, while for Class B and SANDLOS ® Θ o was significantly lower than the as-supplied steels, see Table 2.
In Figure 5, the best fitting Voce parameters of the steels in the as-supplied condition (black open circle data) and after heat treatments (red data) were reported as 1/ε c vs. Θ o in the MAD (Figure 5).In Figure 5, the best fitting red dotted line comes from fitting only the data after heat treatments (red data), and the as-supplied condition data (black open circle data) lay quite close to the best fitting line.Thus, all the data lay close to a single line, confirming the hypothesis suggested in Figure 1 for the steels in the as-supplied condition: the different chemical compositions, production routes and heat treatments had significant effects on the different microstructural constituents of the steels, like the volume fraction of ferrite, pearlite (lamellar or globular), bainite, martensite and pearlite grain size, but there were no significant effects on the dislocation activity.So, the soft ferrite where dislocation motion, multiplication and dynamic recovery occurred was similar in all the steels in the as-supplied condition and after heat treatments, even if the chemical compositions of the steels were different.The applied heat treatment routine increased the presence of soft ferrite and globular pearlite and coarsened the grain size after annealing at temperatures of 700 • C and 750 • C, see Table 3, lowering the values of Θ o , as reported in Table 3 and Figure 5 (open red square data and open red triangle data, respectively).However, after the heat treatment at a temperature of 970 • C (solid red circle data), the Voce parameter Θ o was restored similarly to the as-supplied condition for the steels HYPERLOS ® and Class C, even if apparently the microstructure reported in Table 3 did not match the as-supplied microstructure reported in Table 2.In the other steels, namely, ER7, Class B and SANDLOS ® , Θ o turned out to be smaller than the values from the as-supplied steels, even if apparently the microstructures were restored.In Figure 6, the apparent fracture toughness KQ values were reported vs. the Voce parameter o of the steels (Figure 6) after the heat treatments at temperatures of 700 °C, 750 °C and 970 °C; the data of the steels in the as-supplied condition are reported for comparison's sake.In Figure 6a,b, after annealing at temperatures of 700 °C and 750 °C there were significant reductions in the values of o, consistently with the coarsening of the microstructures, as supported by microstructure observations reported in Table 3.After annealing at temperatures of 700 °C and 750 °C , the reduction of the apparent fracture toughness was significant for ER7, while KQ was unchanged for steels HYPERLOS ® and Class C with respect to the as-supplied condition, and it even improved slightly for steels Class B and SANDLOS ® .After heat treatment at a temperature of 970 °C the microstructures had microstructures similar to the original conditions of the as-supplied steels HY-PERLOS ® and Class C having some traces of martensite, see Tables 2 and 3, so for these steels the Voce parameter o went back to similar values of the as-supplied condition, as reported in Table 3 and Figure 6c, while, in contrast, the steels ER7, Class B and SAND-LOS ® did not go back to the original conditions.However, after austenitizing at a temperature of 970 °C the apparent fracture toughness of HYPERLOS ® and ER7 degraded further in respect to the original values, while the KQ values of Class B, Class C and SANDLOS ® kept similar values to the as-supplied condition.In conclusion, after the heat treatment at a temperature of 970 °C only the steel Class C restored both microstructure and apparent fracture toughness that were like the values of the steel in the as-supplied condition.In Figure 6, the apparent fracture toughness K Q values were reported vs. the Voce parameter Θ o of the steels (Figure 6) after the heat treatments at temperatures of 700 • C, 750 • C and 970 • C; the data of the steels in the as-supplied condition are reported for comparison's sake.In Figure 6a,b, after annealing at temperatures of 700 • C and 750 • C there were significant reductions in the values of Θ o , consistently with the coarsening of the microstructures, as supported by microstructure observations reported in Table 3.After annealing at temperatures of 700 • C and 750 • C, the reduction of the apparent fracture toughness was significant for ER7, while K Q was unchanged for steels HYPERLOS ® and Class C with respect to the as-supplied condition, and it even improved slightly for steels Class B and SANDLOS ® .After heat treatment at a temperature of 970 • C the microstructures had microstructures similar to the original conditions of the as-supplied steels HYPERLOS ® and Class C having some traces of martensite, see Tables 2 and 3, so for these steels the Voce parameter Θ o went back to similar values of the as-supplied condition, as reported in Table 3 and Figure 6c, while, in contrast, the steels ER7, Class B and SANDLOS ® did not go back to the original conditions.However, after austenitizing at a temperature of 970 • C the apparent fracture toughness of HYPERLOS ® and ER7 degraded further in respect to the original values, while the K Q values of Class B, Class C and SANDLOS ® kept similar values to the as-supplied condition.In conclusion, after the heat treatment at a temperature of 970 • C only the steel Class C restored both microstructure and apparent fracture toughness that were like the values of the steel in the as-supplied condition.

Steels in the As-Supplied Condition
Microstructure-properties-production relationships are paramount to assess the production route, the potential applications of metallic materials and the material evolution during service.Five railway wheel steels were investigated in the as-supplied condition and after various heat treatments to simulate the microstructural alterations during braking.Besides the conventional mechanical properties, like HB Brinell hardness, YS UTS and A5 presented in [26,27], in the present paper the strain hardening behavior of the steels was investigated, through fitting the true stress and true strain data with the Voce equation, that is, a dislocation-density-related constitutive equation with physical bases.The fitting procedure was based on dealing with the experimental differential tensile data, namely, d/dεp vs. , and by fitting these data with the linear differential Voce equation (Equation ( 2)) to find the best fitting Voce parameters.It has been reported in [24,25] that, plotting the best fitting Voce parameters 1/εc vs. o in a diagram called Matrix Assessment Diagram (MAD) for different metallic alloys with different chemical compositions and production routes, the Voce parameters lay alongside unique lines that identify unambiguously the materials.The procedure was tuned with foundry products, like spheroidal cast irons, austempered ductile irons (ADIs) and isothermed ductile irons (IDIs).Furthermore, the procedure has been capable of identifying defectiveness in foundry products,

Steels in the As-Supplied Condition
Microstructure-properties-production relationships are paramount to assess the production route, the potential applications of metallic materials and the material evolution during service.Five railway wheel steels were investigated in the as-supplied condition and after various heat treatments to simulate the microstructural alterations during braking.Besides the conventional mechanical properties, like HB Brinell hardness, YS UTS and A5 presented in [26,27], in the present paper the strain hardening behavior of the steels was investigated, through fitting the true stress and true strain data with the Voce equation, that is, a dislocation-density-related constitutive equation with physical bases.The fitting procedure was based on dealing with the experimental differential tensile data, namely, dσ/dε p vs. σ, and by fitting these data with the linear differential Voce equation (Equation ( 2)) to find the best fitting Voce parameters.It has been reported in [24,25] that, plotting the best fitting Voce parameters 1/ε c vs. Θ o in a diagram called Matrix Assessment Diagram (MAD) for different metallic alloys with different chemical compositions and production routes, the Voce parameters lay alongside unique lines that identify unambiguously the materials.The procedure was tuned with foundry products, like spheroidal cast irons, austempered ductile irons (ADIs) and isothermed ductile irons (IDIs).Furthermore, the procedure has been capable of identifying defectiveness in foundry products, where metallurgical discontinuities and defects are particularly copious [28].The success of using the Voce equation relies on solid physical bases, and the Voce parameters are related to the dislocation dynamics [23].In Figure 2, the mechanical properties HB, YS and UTS of the steels in the as-supplied condition are plotted vs. the best fitting Voce parameter Θ o .Linear trends were found, confirming that the Voce parameter Θ o was genuinely related to the coarseness of the microstructure, as stated in Equation (3).In fact, the finer the microstructure, the higher the hardness HB, the YS and UTS.So, in Figure 1 in the MAD the best fitting Voce parameters of the five steels in the as-supplied condition are reported, namely, 1/ε c vs. Θ o .
The data lay alongside a line, which suggested that the different chemical compositions and production routes had significant effects on the different microstructural constituents that strengthen or soften the steels, but there was no significant effect on the dislocation activity, i.e., on how in the soft ferrite dislocation motion, multiplication and dynamic recovery occurred, even if the chemical compositions of the ferrite were different.The investigated steels are low-alloyed hypoeutectoid steels, where the main alloying elements were C, Mn and Si.Their microstructures came into proeutectoid ferrite and pearlite colonies.Ferrite consisted of BCC crystallographic structure, while pearlite was a eutectoid product coming into alternating lamellar cementite (Fe 3 C, orthorhombic crystallographic structure) and lamellar ferrite.Cementite was hard and brittle, while ferrite was soft and tough, and dislocation motion and activity occurred in ferrite.Bainite is also a eutectoid product of austenite transition resulting from faster cooling rates, it consists of fine platelike cementite in ferrite matrix and it is harder than pearlite.Martensite is extremely hard and brittle, is body-centered tetragonal and results from extremely fast cooling rates.The microstructural constituents like pearlite, bainite and martensite depend mainly on production route that determines the pre-transforming state of the austenite, like austenite grain size, C contents in austenite and cooling rates.So, as the investigated steels had similar production routes [26,27] and heat treatments, C was expected to be relevant in determining the different microstructure, so the Voce parameters Θ o that are related to the microstructure, as stated in Equation (3), are plotted vs. the C content in Figure 7.It is evident that with lower C content (ER7 and HYPERLOS ® ) the microstructure was softer (lower Θ o ), because it was richer in ferrite, while with increasing C content the microstructure was harder (higher Θ o ) with increasing pearlite content.Similar trends could be found with the other mechanical properties, that is, HB, YS and UTS.ER7 presented the lowest C content (0.49%wt., see Table 1), resulting in the highest ferrite phase fraction: therefore, o was low (23,549 MPa) and HB, YS and UTS were low.
HYPERLOS ® had C, Mn and Si contents quite similar to ER7, while the main difference was the higher V content that formed stable carbides, reducing the pearlite content, and increasing significantly ductility (28%, see  ER7 presented the lowest C content (0.49%wt., see Table 1), resulting in the highest ferrite phase fraction: therefore, Θ o was low (23,549 MPa) and HB, YS and UTS were low.HYPERLOS ® had C, Mn and Si contents quite similar to ER7, while the main difference was the higher V content that formed stable carbides, reducing the pearlite content, and increasing significantly ductility (28%, see Table 2) and apparent toughness (102.2 ± 14 MPa•m 1/2 ) with respect to ER7 (14% and 89 ± 6 MPa•m 1/2 ).Θ o seemed to represent properly this difference by far more than HB, YS and UTS, assuming values of 23,549 MPa and 35,273 MPa for HYPERLOS ® and ER7, respectively.Steels Class B and SANDLOS ® had intermediate C content (0.65 and 0.63%wt., respectively), producing a volume fraction of ferrite that was intermediate between ER7, HYPERLOS ® and Class C that had the highest C content (0.74 wt.%), which produced a pearlitic microstructure with little ferrite.So, in Class C steel HB, YS and UTS were higher, and the Voce parameter Θ o assumed a higher value of 55,046 MPa, while, consistently, the apparent fracture toughness decreased to 48 ± 4 MPa•m 1/2 .SANDLOS ® is an upgraded Class B modified [26,27] with a higher content of Mn and Si.Mn is a pearlite refiner, reducing the pearlite channels' dimension, and, as a consequence, increasing the HB hardness, YS, UTS and the work-hardening behavior [26,27,34].Si partitions into the ferrite, strengthening it by a solid solution mechanism, and improving HB and cyclic YS [24,26,34].So higher Mn and Si contents caused the increase in mechanical properties, like HB, YS and UTS, and the increase in the Voce parameter Θ o (55,910 MPa) with respect to Class B, achieving values like steel Class C. Consistently, the apparent fracture toughness was 49 ± 3 MPa•m 1/2 , similar to Class C. In Figure 3, the apparent fracture toughness K Q values vs. the Voce parameter Θ o are reported for the steels in the as-supplied condition.A good linearity was found between K Q and Θ o for the steels, suggesting that the Voce parameter might be a good parameter to index the fracture properties of these steels in the as-supplied condition.Indeed, K Q was reported also vs. HB hardness, YS and UTS in Figure 4a-c, respectively, where the data shown poorer linear relationships.Furthermore, though also in Figure 4 good linear trends were found, it was noteworthy that the data points for SANDLOS ® and Class C did not match, even if fracture toughness was the same, see Tables 2 and 3.In fact, in Figure 3, where K Q vs. Θ o was plotted, the data points of SANDLOS ® and Class C overlap perfectly.Indeed, the Voce parameter Θ o might be a more reliable parameter than HB, YS and UTS to represent the microstructure and to be related to the apparent fracture toughness.In cases of HB, this could be rationalized by the fact that hardness measurements concern mainly compressive loading, as eventual microstructure features that might nucleate and propagate cracks and fracture were not active during compression.In cases of YS and UTS measurements that presented the best linearities in Figure 4b and Figure 4c, respectively, YS concerns dislocation motion through obstacles (inversely proportional to mean obstacle distance) but also concerned dislocation unlocking because of anchor phenomena of C atoms, which is known as static strain ageing and is described by the Bilby-Cottrell atmosphere theory.UTS comes from the balance between athermal dislocation multiplication hardening and dynamic recovery softening.So, from the strain hardening theory of Kocks and Mecking, the parameter Θ o that is related only to the athermal dislocation multiplication phenomenon [23] seemed to be the mechanical parameter related to the microstructure features more relevant for the apparent fracture toughness.

Steels after Heat Treatments
After heat treatments at temperatures of 700 • C and 750 • C, the microstructure and mechanical properties had significant variations, with the partial dissolution of lamellar pearlite to form into globular pearlite and a moderate increase in grain size, see Table 3 and references [26,27] for more details.Consequently, a decrease in HB, YS, UTS and Θ o occurred, as reported in Table 3.After austenitizing at a temperature of 970 • C the microstructures seemed to restore partially to the original microstructures, which was found in [26,27] and is summarized and reported in Table 3, besides grain size which increased considerably.Consistently, the HB, YS and UTS after 970 • C increased significantly with respect to the heat treatments after 700 and 750 • C, without achieving, however, the original values of the as-supplied condition, see Tables 2 and 3 for comparison, and reference [26,27] for detailed microstructure observations.Indeed, only HYPERLOS ® and Class C steels had mechanical properties comparable to the as-supplied condition, while for the other steels the properties were slightly lower.The apparent fracture toughness K Q decreased significantly for ER7 after heat treatments at temperatures of 700 • C and 750 • C, was unchanged for HYPERLOS ® and Class C, and increased slightly for steels Class B and SANDLOS ® .After the heat treatment at a temperature of 970 • C, the microstructure was similar to the original condition of the as-supplied HYPERLOS ® and Class C steels, see Tables 2 and 3, so for these steels the Voce parameter Θ o went back to similar values of the as-supplied condition, as reported in Table 3.In contrast, the ER7, Class B and SANDLOS ® steels did not go back to the original conditions.However, after 970 • C heat treatment the apparent fracture toughness of HYPERLOS ® and ER7 degraded further with respect to the original values, while the K Q values of Class B, Class C and SANDLOS ® kept similar values to the as-supplied condition.In conclusion, after the heat treatment at 970 • C only the steel Class C had both similar microstructure and apparent fracture toughness to the values of the steel in the as-supplied condition.Figure 5 shows the best fitting Voce parameters for steels in both the as-supplied condition (black open circles) and after heat treatments (red data) in a 1/ε c vs. Θ o plot.The red dotted line, fitted from the heat-treated data, also aligns closely with the as-supplied data, indicating that despite differences in chemical composition, production methods and heat treatments, all data align on a single line.This suggests significant effects on the microstructure components such as ferrite, pearlite, bainite, martensite and pearlite grain size.Conversely, the soft ferrite where dislocation multiplication and dynamic recovery occurred was not substantially affected after heat treatments, even if chemical compositions were different.After heat treatments at temperatures of 700 • C and 750 • C, the Voce parameters 1/ε c and Θ o lowered because of the coarsening of the microstructure, while after austenitizing at a temperature of 970 • C they increased assuming values similar to the as-supplied ones, because of refining of the matrix microstructure, while the pearlite grain size was finally coarser.In Figure 6, the apparent fracture toughness K Q values are plotted vs. the Voce parameter Θ o of the steels after the heat treatments at temperatures of 700 • C, 750 • C and 970 • C, and the data of the steels for all heat treatment routines and material in as-delivered condition (Figure 6).After high temperature treatments, the data seemed to have good linearity, and in Figure 6c it is evident that the steel Class C was the only one to have a microstructure similar to the original assupplied condition (microstructure and K Q ), while for the other steels either microstructure (Θ o ) or apparent fracture toughness K Q were lower after austenitizing at a temperature of 970 • C without any full recovery to the as-supplied condition.Microstructure and K Q evolution can be rationalized on the critical temperatures of the Fe-Fe 3 C state diagram and different chemical compositions of the steels.The temperature of 700 • C was slightly below the eutectoid temperature A 1 , so the heat treatment changed the original lamellar pearlite morphology, resulting in ferrite with lamellar and new globular pearlite, and a bigger grain size compared to the as-supplied steels.At a temperature of 750 • C, the steels were heated between the critical temperatures A 1 and A 3 , causing a partial austenitization and resulting in a final microstructure also consisting of ferrite with lamellar and new globular pearlite.At a temperature of 970 • C, the steels were heated above A 3 , fully austenitizing and resulting after cooling in a microstructure of lamellar pearlite and ferrite for all steels, with bainite and martensite traces for SANDLOS ® and Class C steels.Though Si between 400 and 600 • C, and particularly Mn at temperature higher than 600 • C, has stabilizing properties for pearlite, the values of Θ o in Figure 6a,b were significantly reduced with respect to the as-supplied condition.The reduction was more significant for the harder steels, like SANDLOS ® and Class C. Furthermore, after heat treatments at temperatures of 700 • C and 750 • C the apparent fracture toughness K Q reduced significantly for ER7, but kept quite constant for the other steels, besides Class B and SANDLOS ® where K Q even improved.This finding could be attributed to the appearance of globular pearlite that can positively affect toughness [26,27,34].Conversely, ER7 that had the lowest content of C, had the highest volume fraction of ferrite, resulting in less influence by the globular pearlite, while HYPERLOS ® with similar content of C had vanadium carbides that are stable at low temperatures.After full austenitizing at a temperature of 970 • C the full annealing and cooling restored microstructural constituents with high strength and strain hardening capability, like lamellar pearlite, bainite and martensite, while globular pearlite was not present.The heat treatment at temperatures of 970 • C heat treatment could restore the low K Q of steels Class B and SANDLOS ® of the as-supplied condition, but the apparent fracture toughness of the softer steels ER7 and HYPERLOS ® were degraded.The poor K Q properties of Class C were indeed maintained constant after any heat treatment.So, as reported in Figure 6c, only Class C restored fully the original microstructure and toughness conditions of the as-supplied condition.In Figure 2, the mechanical properties HB, YS and UTS were plotted vs. Θ o , showing good linearities that supported Equation (3), where Θ o was stated to be proportional to the microstructure coarseness.So, the apparent fracture toughness K Q could be plotted vs. HB, YS and UTS with good linearities, as indeed was found in Figure 4 for the steels in the as-supplied condition.As mentioned in Section 3.1, HB hardness was related to compressive loading, and this explained the worst relationship with K Q .However, YS and UTS that involve tensile loading had better linear relationships with K Q .So, in Figure 8 the apparent fracture toughness K Q vs. YS and UTS of the steels after the heat treatments at temperatures of 700 • C, 750 • C and 970 • C are reported (red solid circle data) to investigate the capability of different tensile parameters to be related to the apparent fracture toughness; in all plots, as-supplied data (open black circle data) were presented for comparison's sake.The information that can be gathered from YS and UTS in Figure 8 was quite equivalent to what was reported in Figure 3 for K Q vs. Θ o .The square correlation coefficients appear to be slightly better for K Q vs. Θ o , and between YS and UTS the values of R 2 seem to be slightly better for the latter.In Figure 9, a comparison is shown between YS and UTS and the best fitting Voce parameter Θ o of the steels in the as-supplied condition (black open circle data) and after heat treatments (red data).
After high temperature heat treatments, good linear relationships between YS, UTS and Θ o were found, proving that the Voce parameter Θ o was really related to the coarseness of the microstructure (Figure 9).However, it was noteworthy that in the plot YS vs. Θ o there was a step between some discontinuities in the trend.The red dotted best fitting lines were calculated on the steel data after heat treatments (red data): in Figure 9a for YS vs. Θ o , the as-supplied steels data were quite far away from the best fitting line, while in Figure 9b, UTS vs. Θ o , the as-supplied steels data lay about the red dotted best fitting line.This finding could be rationalized by the fact that, even if YS and UTS concern tensile loading, yielding dealt with dislocation motion and also unlocking of dislocations from a C atoms atmosphere that anchors dislocations, a phenomenon known as strain ageing and described by the Bilby-Cottrell atmosphere theory [35].When unlocking occurred at yield showing a sharp yield point, plastic deformation began and the C atoms did not interact any more with dislocation motion and activity, unless tensile tests were at intermediate temperatures where the interaction between dislocations and solute atoms might be dynamic, giving rise to dynamic strain ageing, also known as the Portevin-Le Chatelier effect [34].So, the sharp yield point was a static phenomenon, that was dependent on the initial solute atoms' distribution, but does not affect strain hardening or eventually fracture behavior.Strain ageing with sharp yield point occurred for steels at room temperature depending on the chemical compositions and production routes, and the investigated steels in the as-supplied condition and after heat treatments did not always present sharp yield points, as is summarized in Table 4.This finding should explain the data in Figure 9, and at the same time, it suggests that UTS and Θ o should be the best parameters to describe the effective microstructure of the investigated steels.So, the use of diagram K Q vs. Θ o or K Q vs. UTS should be encouraged, even if the results coming from using K Q vs. YS also appeared meaningful, since they present good linearities.After high temperature heat treatments, good linear relationships between YS, UTS and o were found, proving that the Voce parameter o was really related to the coarseness of the microstructure (Figure 9).However, it was noteworthy that in the plot YS vs. o there was a step between some discontinuities in the trend.The red dotted best fitting lines were calculated on the steel data after heat treatments (red data): in Figure 9a for YS in the as-supplied condition and after heat treatments did not always present sharp yield points, as is summarized in Table 4.This finding should explain the data in Figure 9, and at the same time, it suggests that UTS and o should be the best parameters to describe the effective microstructure of the investigated steels.So, the use of diagram KQ vs. o or KQ vs. UTS should be encouraged, even if the results coming from using KQ vs. YS also appeared meaningful, since they present good linearities.

Conclusions
The quality-assessment procedure based on strain hardening and the Voce equation was used to analyze the results of experimental hardness, tensile and toughness tests.These tests involved five railway wheel steels in the as-supplied condition and after three

Conclusions
The quality-assessment procedure based on strain hardening and the Voce equation was used to analyze the results of experimental hardness, tensile and toughness tests.These tests involved five railway wheel steels in the as-supplied condition and after three different heat treatments designed to replicate the modification of the microstructure due to braking.The correlation between microstructure features of the steels and the best fitting Voce parameters was reported, as well as the relation with Brinell hardness measurements (HB) and apparent fracture toughness (K Q ) in controlled conditions.The quality-assessment procedure based on strain hardening and the Voce equation supported the evidence that investigated steels had a different microstructure and mechanical stability when undergoing severe thermal cycles.The following conclusions could be drawn: • The Voce parameter Θ o was genuinely related to the coarseness of the microstructure, and linear relationships with HB, YS and UTS were found; • In the Matrix Assessment Diagram MAD (1/ε c vs. Θ o ), the as-supplied steel data lay alongside a line, which suggested that the different chemical compositions and production routes had significant effects on the different microstructural constituents, but ferrite where dislocation activity occurred was the same for the five steels; • The apparent fracture toughness K Q vs. the Voce parameter Θ o presented good lin- earities for the steels in the as-supplied condition, suggesting that the Voce parameter might be a good parameter to indicate the fracture properties of these steels in the as-supplied conditions; • The apparent fracture toughness K Q vs. the Voce parameter Θ o presented good linearities for the steels after heat treatments, indicating the fracture properties of these steels also after working conditions; • Also, K Q vs. YS and K Q vs. UTS could give valuable information, equivalent to the use of the Voce analysis approach (K Q vs. YS); however, the physical bases of the Voce parameter can give some additional information.
After heat treatments at temperatures of 700 • C and 750 • C, the properties of the steels decreased, which was consistent with the evolution of the microstructure, while after exposure at a temperature of 970 • C with subsequent cooling in air, Class C steel appeared to have a microstructure similar to the original microstructure, with tensile and toughness properties very similar to the as-supplied conditions, demonstrating better microstructural stability compared to steels ER7, HYPERLOS ® , Class B and SANDLOS ® .

Figure 1 .
Figure 1.Matrix Assessment Diagram (MAD) of the five steels tensile-tested in the as-supplied condition.

Figure 1 .
Figure 1.Matrix Assessment Diagram (MAD) of the five steels tensile-tested in the as-supplied condition.

Figure 2 .
Figure 2. Comparison between selected mechanical properties and the best fitting Voce parameter o of the steels in the as-supplied condition: (a) Brinell Hardness (HB) vs. o; (b) yield stress (YS) vs. o; (c) ultimate tensile stress (UTS) vs. o.

Figure 2 .
Figure 2. Comparison between selected mechanical properties and the best fitting Voce parameter Θ o of the steels in the as-supplied condition: (a) Brinell Hardness (HB) vs. Θ o ; (b) yield stress (YS) vs. Θ o ; (c) ultimate tensile stress (UTS) vs. Θ o .

20 Figure 3 .
Figure 3. Apparent fracture toughness KQ vs. best fitting Voce parameter o of the steels in as-supplied condition.

Figure 4 .
Figure 4. Apparent fracture toughness KQ vs. selected mechanical properties of the investigated steels in the as-supplied condition: (a) KQ vs. HB; (b) KQ vs. YS; (c) KQ vs. UTS.

Figure 3 . 20 Figure 3 .
Figure 3. Apparent fracture toughness K Q vs. best fitting Voce parameter Θ o of the steels in assupplied condition.

Figure 4 .
Figure 4. Apparent fracture toughness KQ vs. selected mechanical properties of the investigated steels in the as-supplied condition: (a) KQ vs. HB; (b) KQ vs. YS; (c) KQ vs. UTS.

Figure 4 .
Figure 4. Apparent fracture toughness K Q vs. selected mechanical properties of the investigated steels in the as-supplied condition: (a) K Q vs. HB; (b) K Q vs. YS; (c) K Q vs. UTS.

Figure 5 .
Figure 5. Matrix Assessment Diagram (MAD) of the five steels tensile-tested in the as-supplied condition (open black circle data) and after heat treatments (red data).

Figure 5 .
Figure 5. Matrix Assessment Diagram (MAD) of the five steels tensile-tested in the as-supplied condition (open black circle data) and after heat treatments (red data).

Figure 6 .
Figure 6.Apparent fracture toughness KQ vs. best fitting Voce parameter o of the steels in the assupplied condition (open black circle data) and after heat treatments (solid red circle data): (a) at a temperature of 700 °C; (b) at a temperature of 750 °C; (c) at a temperature of 970 °C.In all plots, the as-supplied data (open black circle data) are reported for comparison's sake.

Figure 6 .
Figure 6.Apparent fracture toughness K Q vs. best fitting Voce parameter Θ o of the steels in the as-supplied condition (open black circle data) and after heat treatments (solid red circle data): (a) at a temperature of 700 • C; (b) at a temperature of 750 • C; (c) at a temperature of 970 • C. In all plots, the as-supplied data (open black circle data) are reported for comparison's sake.

Figure 7 .
Figure 7. Θ o Voce parameter vs. C content (%wt.) for the five steels in as-supplied condition.

4. 3 .
Considerations on the Use of Θ o and the Other Mechanical Properties to Relate to K Q

Figure 8 .
Figure 8. Apparent fracture toughness KQ vs. yield stress (YS) of the steels in the as-supplied condition (open black circle data) and after heat treatments (solid red circle data): (a) at a temperature of 700 °C; (c) at a temperature of 750 °C; (e) at a temperature of 970 °C.Apparent fracture toughness KQ vs. ultimate tensile stress (UTS) of the steels in the as-supplied condition (open black circle data) and after heat treatments (solid red circle data): (b) at a temperature of 700 °C; (d) at a temperature of 750 °C; (f) at a temperature of 970 °C .In all plots, the as-supplied data (open black circle data) are reported for comparison's sake.

Figure 8 .
Figure 8. Apparent fracture toughness K Q vs. yield stress (YS) of the steels in the as-supplied condition (open black circle data) and after heat treatments (solid red circle data): (a) at a temperature of 700 • C; (c) at a temperature of 750 • C; (e) at a temperature of 970 • C. Apparent fracture toughness K Q vs. ultimate tensile stress (UTS) of the steels in the as-supplied condition (open black circle data) and after heat treatments (solid red circle data): (b) at a temperature of 700 • C; (d) at a temperature of 750 • C; (f) at a temperature of 970 • C. In all plots, the as-supplied data (open black circle data) are reported for comparison's sake.

Figure 9 .
Figure 9.Comparison between selected mechanical properties and the best fitting Voce parameter o of the steels in the as-supplied condition and after heat treatments: (a) yield stress YS vs. o; (b) ultimate tensile stress UTS vs. o.

Figure 9 .
Figure 9.Comparison between selected mechanical properties and the best fitting Voce parameter Θ o of the steels in the as-supplied condition and after heat treatments: (a) yield stress YS vs. Θ o ; (b) ultimate tensile stress UTS vs. Θ o .

Table 1 .
Chemical composition wt.% of the investigated steels.

Table 4 .
Sharp yield point appearance in the tensile curves of the investigated steels in the as-supplied condition and after heat treatments.

Table 4 .
Sharp yield point appearance in the tensile curves of the investigated steels in the as-supplied condition and after heat treatments.