The effect of retained austenite stability on impact-abrasion wear resistance in carbide-free bainitic steels

The effect of retained austenite stability on impact-abrasion wear resistance in carbide-free bainitic steels

Wear 428–429 (2019) 127–136 Contents lists available at ScienceDirect Wear journal homepage: www.elsevier.com/locate/wear The effect of retained aus...

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Wear 428–429 (2019) 127–136

Contents lists available at ScienceDirect

Wear journal homepage: www.elsevier.com/locate/wear

The effect of retained austenite stability on impact-abrasion wear resistance in carbide-free bainitic steels ⁎

Binggang Liu, Wei Li, Xianwen Lu, Xiaoshuai Jia , Xuejun Jin

T



Institute of Advanced Steels and Materials, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Retained austenite Mechanical stability Cutting and cracking Impact

The effect of retained austenite stability on impact-abrasion wear resistance was investigated. Using an impactabrasion wear testing machine, it was demonstrated that a high mechanical stability of retained austenite brought about improved wear resistance in bainite steels. However, the wear resistance worsened when the retained austenite stabilization was sufficient to suppress the transformation of retained austenite to martensite. The retained austenite not only enhanced the hardness of the contact surface, but also resisted crack opening and propagation by deformation and transformation. Furthermore, material removal by microcutting and microcracking were the dominant contributions to mass loss during impact-abrasive wear. Therefore, a wear model was developed based on cutting and fracture mechanisms, and the hardness and fracture toughness were the key factors that dominated the impact-abrasion wear resistance.

1. Introduction

[13]. The blocky RA is mainly located between the prior austenite boundaries, block boundaries and packet boundaries, whereas the filmlike RA is embedded between bainitic ferrite lathes [14]. Commonly, the stability of blocky RA is lower than that of filmy RA, and the new coarse martensite formed by blocky RA during abrasion wear is more prone to crack nucleation and propagation. Furthermore, the austenite with nanoscale twins dominates the plastic strain, which could resist crack propagation during impact-abrasion wear [15]. It has been demonstrated that bainitic ferrite also plays an important role during wear. A decrease in the bainitic ferrite lath thickness leads to an increase in hardness [16]. Furthermore, in bainitic steels, the strength of bainite ferrite is considered higher than that of RA; thus, the bainitic ferrite could carry more stress and bring about a shield effect for the RA during plastic deformation, which could reduce the austenite transformation rate [17]. This means that a strong matrix could lead to an increase in the mechanical stability of RA. Thus, sometimes the transformation of RA to martensite does not occur even under the actions of stress or strain. Impact-abrasion wear, as a severe wear condition, includes abrasive extrusion, abrasive cutting and rolling, and fatigue crack opening and propagation. It has been reported that the impact abrasive wear resistance increases with increasing hardness [18]. In addition, microcracking can occur during abrasion where flaking of materials occurs. Thus, a fracture model is introduced to describe the removal of material by cracking, and the results show that the wear resistance first increases

Bainite steel combines high strength and ductility, shows better wear resistance than pearlitic or martensite steels and is already used in the rail industry [1–3]. In particularly, the wear resistance of nanocrystalline bainite structures transformed at low temperature has been found to be greatly enhanced over standard lower bainite or other structures in terms of the sliding/rolling wear process [2,4,5]. Under sliding, abrasive or three-body wear conditions, the wear resistance has a linear relationship with the worn surface hardness, which means that a higher hardness brings about a higher wear resistance. The RA (retained austenite) beneath the worn surface undergoes martensitic transformation, which results in a dramatic increase in hardness compared with materials containing no RA [2,6,7]. In addition, the martensitic transformation of RA induces the compressive residual stress fields due to the volume expansion from the fcc to bcc structure along the crack path, which could suppress crack initiation and propagation [8,9]. However, the effect of RA on wear resistance is still controversial. In carbide-free bainite steels, the volume percent of RA could be 14–50%, which brings about different wear behaviors during sliding [10]. The wear coefficient increases when the volume percent of RA is approximately 100% in the sample. However, Fe-Mn austenitic steel [11,12], composed of 100% austenite, shows a high wear resistance, which accounts for the high work hardening rate of austenite. Furthermore, there are two types of RA morphology: blocky and film-like



Corresponding authors. E-mail addresses: [email protected] (X. Jia), [email protected] (X. Jin).

https://doi.org/10.1016/j.wear.2019.02.032 Received 23 November 2018; Received in revised form 24 February 2019; Accepted 27 February 2019 Available online 28 February 2019 0043-1648/ © 2019 Published by Elsevier B.V.

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Table 1 Chemical composition of steel, wt%. C

Si

Mn

Cr

Mo

Nb

Ti

0.95

2.90

0.75

0.52

0.25

0.03

0.012

and then decreases with increasing fracture toughness [19–21]. The RA behavior during wear in steels is complicated by the effects of its size, volume fraction, morphology and surrounding microstructures. However, RA behavior can be described by its mechanical stability. However, few studies have investigated the effects of the stability of RA on wear resistance or determined the relationship between the wear resistance and RA stability. In this paper, carbide-free bainitic steels were used to study the RA behavior during the impact abrasive wear process. Furthermore, an impact-abrasion wear model was developed based on cutting and fracture mechanisms.

Fig. 1. (a) Photograph of the MLD-10 wear machine and (b) schematic of the MLD-10 wear machine [15].

2. Materials and methods

3. Results

The chemical composition of steel is listed in Table 1, and its melt process was reported in a previous study [15]. The samples were austenitized at 1253 K (980 °C) for 20 min, followed by austempering in a salt bath furnace at 623 K (350 °C) for 3 h, 573 K (300 °C) for 7 h, 523 K (250 °C) for 24 h, and 493 K (220 °C) for 72 h before quenching in water. The carbides were inhibited due to the high silicon content, and it was assumed that the alloying elements did not diffuse during austempering. The microstructures of the tested steels were mechanically polished to 1 µm and etched in 4% nital solution, followed by scanning electron microscopy (SEM; TESCAN, Czech Republic) and metallographic analysis with optical microscopy (OM; ZEISS, Germany). The retained austenite content was measured by X-ray diffraction with monochromatic Co-Kα radiation (XRD; BRUKER, Germany), and the diffractometer operated at 40 kV and 40 mA with a scanning speed of 1°/ min. To study the volume fraction changes of RA in the subsurface region, the RA content was measured from 0 µm of worn surface to a 350 µm depth. Each 25 μm-thick section of material was ground off, and then the surface was polished to 1 µm, followed by electropolishing in 7% perchloric acid solution at 30 V at 253 K (– 20 °C). In addition, the carbon content in the RA was calculated by Eq. (1) [22]:

3.1. Wear resistance of bainite steels

a γ = 3.5780 + 0.033wC + 0.00095wMn + 0.0006wCr + 0.0031wMo

As shown in Fig. 2, there is a nonlinear relation between wear loss and hardness. This shows that the wear loss decreased with increasing hardness and reached its lowest point at 590 HV for B250, and then increased to 650 HV for B220. The thickness of bainite ferrite became finer when the isothermal temperature decreased, which brought about a higher hardness. Clearly, the wear loss variation went against the rule that wear loss has a linear relation with the hardness. 3.2. Microstructure of the bainite steels Fig. 3 shows that the microstructure of the bainite steels consists of bainitic ferrite and RA, but their morphology is completely different. As shown in Fig. 3(a), the bainite ferrite formed at 350 °C is coarse and feather-like, and the retained austenite is mainly coarse and blocky. The size of the bainite ferrite and RA decreased with decreasing isothermal temperature. The morphology of bainitic ferrite in B250 is needle-like, and its thickness is approximately 70–100 nm, so it is referred to as nanostructured bainite steel in Fig. 3(c). The retained austenite formed at lower austempering temperatures is mainly film-like (Fig. 3(c) and (d)). The mechanical properties of bainite steels are shown in Fig. 4 and listed in Table 2. Both the ultimate strength and yield strength were improved by decreasing the austempering temperature. In contrast, the elongation decreased significantly from 19% to 3.1%. The impact toughness is also reduced from 32.9 J/cm2 to 11.5 J/cm2 with the vnotch sample, but it remains high and no fracture occurred in the nonotch samples of B350, B300 and B250 in Table 2. Thus, it can be concluded that these steels had a high crack sensitivity under a stress concentration. The ratio of blocky RA and filmy RA could be estimated by Eq. (2) [14]:

(1)

°

where a γ is the lattice parameter of austenite in A , and wi is the content of element i in wt%. The relative error of measurement was ± 0.05%. Micro-Vickers hardness along the subsurface microstructure was measured using a hardness tester (Zwick/Roell, Germany) at a load of 25 g. The tensile samples had a gauge length of 16 mm and were tested by a Zwicks universal testing machine (Zwick/Roell, Germany). The impact tests were conducted with 10 × 10 × 55 mm samples with a Vnotch and no-notch geometry on an impact testing machine with a maximum impact energy of 300 J (PTM2000, Suns, China) at room temperature. The fracture toughness was measured by a standard compact tension sample (BISS, India) in accordance with ASTM E-399 at a constant speed of 1 mm/min at room temperature. The impactabrasive wear tests were conducted on a MLD-10 machine (MLD, China), as shown in Fig. 1(a) and (b) [15]. The working process was discussed in a previous study [15], and at least three samples were prepared for each condition. The impact energy was set at 4 J, and the size of the quartz abrasive particle was approximately 3 mm at 360 g/ min during wear.

Vfγ Vbγ

=

0.15VBF Vγ − 0.15VBF

(2)

where Vfγ and Vbγ are the volume fraction of filmy RA and blocky RA, respectively. The VBF is the bainitic ferrite content, and Vγ is the volume fraction of RA. The volume percent of RA is nearly 47% in B350, and the ratio of Vfγ/Vbγ is lower than that in the others, as shown in Fig. 5(a). The volume fraction of RA decreases, but the ratio of Vfγ/Vbγ increases when the temperature decreases, as shown in Fig. 5(a). Both B350 and B300 have a low ratio of Vfγ/Vbγ, but the carbon content in RA of B300 is much higher than that in B350. B250 and B220 also show almost the same RA content, but B220 has higher carbon content in the 128

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Fig. 2. (a) The hardness of B350 (bainite formed at 350 °C), B300 (bainite formed at 300 °C), B250 (bainite formed at 250 °C), B220 (bainite formed at 220 °C) and (b) the wear loss as a function of hardness.

3.3. Worn surface and subsurface microstructure

RA, as shown in Fig. 5(a). The mechanical stability of retained austenite was estimated by the change in the RA content at different strains, which is shown in Fig. 5(b). The mechanical stability of RA was evaluated by the exponent decay law by Eq. (3) [23]:

f = f0 exp(−kε )

Figs. 6 and 7 show the morphology of the worn surface and cross sections of bainite steels. All the worn surfaces of the tested steels were rough due to the multiple impacts and abrasive particles, and the fragments of the abrasive particles could be easily found in the pits. Abundant wear flakes are observed in B350, and abrasive pits are exposed on the worn surface, as shown in Fig. 6(a) and (e). Furthermore, the number of flakes gradually decreases from B350 to B220, the large flakes disappear and only small cracks are left in the worn surface in B220, as shown in Fig. 6(d) and (h). The microcutting caused by the abrasive were also found on these bainite steels. The microstructure of the subsurface layer was highly deformed by the abrasive particles, and the cracks mainly formed in the vicinity of the pits in Fig. 7. Then, the crack propagated parallel to the wear direction in the subsurface layer until the debris detached from the surface, as shown in Fig. 7. The deformed area beneath the worn surface in

(3)

where f is the volume fraction of RA as a function of ε, ε is the true strain, f0 is the initial volume fraction of RA, and k represents the stability of RA during tensile deformation, where a large k value means a low stability. The k value declined from B350 to B220, which meant that the RA stabilization improved, as shown in Fig. 5(b). In addition, the RA content remained unchanged during plastic deformation in B220, which indicates that no RA transformed into martensite until fracture during tensile testing in Fig. 5(b). Thus, the k value of B220 was set to 0.

Fig. 3. SEM microstructure: (a) B350, (b) B300, (c) B250, and (d) B220. 129

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12–33 J/cm2 with the a V-notch, which indicated that cracks easily propagated under pre-existing concentrations in these bainite steels. Therefore, the deformed area caused by the abrasive particle determines the wear loss during the impact-abrasive wear process. The crack nucleation and propagation played an important role during the wear process. The abrasive particles are sliding and rolling between the test sample and counter sample under a load in Fig. 9(c). Thus, microcutting or microplowing would be generated during the movements of abrasive particles.

4.2. The role of RA during wear The volume fraction of bainitic ferrite increased and its thickness decreased when the austempering temperature decreased, which was due to an increase in the driving force. The mechanical stability of the RA was enhanced due to the geometrical restrictions imposed by the surrounding refined bainitic ferrite. Furthermore, the size of the RA embedded into the bainitic ferrite became fine, and the ratio of Vfγ/Vbγ increased as the isothermal temperature decreased. In addition, the carbon content in RA also increased due to the carbon partitioning from bainitic ferrite to surrounded austenite, which increased the RA stability. The decrease in the austempering temperature led to an improvement in RA stabilization, which resulted from a strong bainitic ferrite, finer morphology and high carbon content. During plastic deformation, the retained austenite deformed and then transformed into hard martensite, as shown in Fig. 10(a). It formed a hardening layer in the subsurface where the volume fraction of induced martensite decreased with subsurface depth. The martensitic transformation of the RA could alleviate defects, such as cracks or voids, formed under the worn surface by absorbing the energy from repeated impact. The induced martensite not only enhanced the hardness of the worn surface but also the hardness in the subsurface. Furthermore, the hardness of the worn surface increased as the RA stability, as shown in Fig. 10(b). It is shown that the abrasive wear resistance increased linearly with the worn surface hardness because the high hardness could resist the abrasive particles extruding into the worn surface [25,26]. Therefore, a higher RA stability resulted in a higher abrasive wear resistance in bainitic steels. The stability of blocky RA was typically considered lower than that of filmy RA in steels due to its morphology and lower carbon content [27]. It is clear that the size of the RA decreased at 6% strain in B350 and B250 after tensile deformation, which proves that the large RA was unstable and prone to transformation into martensite during deformation, as shown in Fig. 11. Furthermore, the martensite formed within the blocky RA and caused the strain/stress to be inhomogeneous and concentrations to form at the phase boundaries during plastic deformation around it, as shown in Fig. 11(e). It was proven that the carbon atoms could form the Cottrell atmosphere; thus, there was a partial RA transformation during deformation in the carbon depleted area in the blocky RA region [28]. The cracks preferred to nucleate at the strain concentrations and then propagate and coalesce with the defects around the martensite boundaries in the wear direction. Finally, a flake was generated and detached from the surface. Although the surface hardness was increased by the RA transformation into a hard martensite in B350, the new irregular martensite could act as the origin of defects, such as cracks or voids. Furthermore, the blocky RA content

Fig. 4. The mechanical properties of bainitic steels.

B300 is smaller than that in B350, and only the microstructure around the pit is obviously deformed in Fig. 7(c) and (d). In B250 and B200, the pits in the worn surface are relatively smaller compared with those in B350 and B300. Furthermore, the crack tip is blunt in the B250 steel, as shown in Fig. 7(f). 3.4. The deformation area in steels The changes in the RA are consistent with the hardness in the hardening layers in Fig. 8. The depths of the plastic deformation area were approximately 160 µm in B350, 160 µm in B300, 200 µm in B250, and 80 µm in B220 by the variation of hardness and RA. The hardness of the worn surface was substantially improved compared with that of the bulk materials in those steels. The RA at the top surface all transformed into martensite in B350, B300 and B250, and was triggered by the strains. However, only a small part of RA in B220 underwent the RA transformation during wear. 4. Discussion 4.1. The impact-abrasive wear process The impact-abrasive wear process could also be seen as a three-body wear process plus multiple impacts, which is shown in Fig. 9. The material removal accumulated in two ways: microcutting and microcracking. The microstructure beneath the worn surface was highly deformed due to the multiple impacts as shown in Fig. 9(a). The abrasive particles may have been extruded into the worn surface during the impact process, which resulted in severe plastic deformation around the abrasive particles in Fig. 9(b). Cracks and voids were most likely located in the loading contact zone, high stress locations, or other subsurface defects during sliding/rolling wear conditions [24]. In the impact-abrasive wear process, the highly local concentrated stress caused by the abrasive particles would easily become the origins of the cracks. Once the crack nucleated, the crack would propagate along the wear direction until the wear debris was generated and detached from the worn surface. The impact toughness of these bainite steels was higher than 300 J/cm2 without a notch. However, it suddenly decreased to Table 2 Mechanical properties of bainitic steels. Sample

Rm (MPa)

Rp0.2 (MPa)

Uniform elongation (%)

Total elongation (%)

Impact toughness with notch (J/cm2)

Impact toughness without notch (J/cm2)

B350 B300 B250 B220

1773 1845 2052 2174

734 1414 1689 1931

18.0 ± 1.5 22.0 ± 2.0 14.0 ± 2.5 1.33 ± 2.0

19.0 23.0 15.0 3.1

32.9 33.5 19.4 11.5

> 375 > 375 > 375 342 ± 5.0

± ± ± ±

10 9 12 10

± ± ± ±

10 9 12 10

± ± ± ±

1.5 2.0 2.5 2.0

130

± ± ± ±

2.0 1.5 2.0 2.0

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Fig. 5. (a) The volume fraction of RA and its carbon content in bainitic steels and (b) the mechanical stability of RA.

Fig. 6. Morphology of the worn surface: (a) and (e) B350, (b) and (f) B300, (c) and (g) B250, and (d) and (h) B220.

131

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Fig. 7. Morphology of the cross section: (a) and (b) B350, (c) and (d) B300, (e) and (f)[15] B250, and (g) and (h) B220.

when the crack grew along the RA boundaries [15]. The volume expansion due to martensitic transformation could enhance the crack closer effect, which is referred to as transformation-induced crack closure [8]. Therefore, B250 had a better crack resistance than B350 during the impact-abrasion wear process. In addition, the size of the RA or bainite ferrite was coarser in B350 than in the others. Thus, there were fewer boundaries to deflect the crack effectively to retard its propagation. In contrast, fewer flakes were generated at its worn surface due to its finer microstructure in B250. B250 and B220 had approximately the same volume fraction of RA

was the highest, and its size was the largest in B350 among the bainite steels considered here, which led to more flakes on its worn surface and worse wear resistance than that of the other samples. The RA in B350 had a lower mechanical stability than B250. Thus, a greater volume fraction of RA resulted in a martensitic transformation at 6% strain in B350 compared with that in B250, as shown in Fig. 11(a), (b), (c) and (d). This meant that less RA was left to arrest the crack propagation in B350 than in B250 under the same strain. It has been reported that the transformation of RA into martensite beneath the worn surface could reduce the stress concentration at the crack tip 132

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Fig. 8. Hardness and volume faction of RA distribution in the subsurface: (a) B350, (b) B300, (c) B250, and (d) B220.

and Vfγ/Vbγ ratio, but the wear behaviors were different. In B220, the fine bainite ferrite lath structure and RA should be more effective in deflecting the crack growth path to reduce the wear loss. However, the wear loss was higher than that in B250 because the higher carbon content of RA in B220 led to a higher mechanical stability compared to that in B250. The results showed that B220 had nearly 18% RA, and only a small amount of RA transformed into the martensite during wear. Thus, the RA could not substantially effect on the crack propagation resistance if it was sufficiently stable; it would then not trigger the martensitic transformation during wear.

particles and large debris were detached from the wear surface owing to crack nucleation and propagation [20]. Thus, during the impact-abrasion wear process, the abrasive cutting mechanism and fracture mechanics were used to describe the removal of materials. There was an elastic and plastic contact between the abrasive particles and wear surface, which is shown in Fig. 12. Thus, the applied surface pressure during the impact and cutting wear process could be estimated by the Eqs. (4)–(6) [29]:

4.3. Impact-abrasion wear model

S ≈ 2πR1⋅

P=

The material removal due to microcutting and microcracking was the main mass loss during impact-abrasion wear. Microcutting resulted in a volume loss by abrasive sliding equal to the volume of wear grooves. The microstructure at the near-worn surface was highly hardened by the multiple impacts; thus, the microplowing caused by the abrasives on the worn surface was neglected. Furthermore, microcracking occurred when concentrated stress was imposed by abrasive

l′ =

F S

(4)

l′ tan α

F ⋅ tan α πσm

(5)

(6)

where the contact area S was regarded as a spherical cap. l` is the width of the pit for plastic contact, and σm is the tensile ultimate strength, which considers the working hardening effect. Parameter α is the angle of pit, which is related to the abrasive particles. Here, α is

Fig. 9. The impact abrasive wear process. 133

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Fig. 10. (a) The volume fraction of induced martensite and (b) the hardness enhancement with RA stabilization.

approximately 45°, which is estimated from the experimental results in Fig. 7. The size of abrasive R1 = 1.5 mm, and the infinite size of steel sample R2 = ∞. Parameter F is the applied force during impact and sliding. The applied force during the cutting process can be obtained by Eq. (7):

F1 ≈ mg

(7)

where m was the mass of the hammer, 10 kg and g was 9.8 N/kg. The momentary contact peak force during impact could be obtained by Eqs. (8)–(10) [30,31]: Fig. 12. The pit and microstructure beneath the worn surface.

1/5

F2 ≈ 0.814⋅⎛ ⎝ ⎜

V 6m3R1 E 2 ⎞ 1+δ ⎠

1 − v12 1 − v22 1 = + E E1 E2



(8)

δ=

R1 R2

(10)

where V is the impact speed, which was estimated to be 0.89 m/s; m is the mass of 10 kg. The elastic modulus of bainite steel is E1 ≈ 195 GPa

(9)

Fig. 11. EBSD maps, where the red is bainite ferrite and the blue is the RA: (a) B350, (b) B250, (c) B350 + 6% strain, (d) B250 + 6% strain, and (e) the KAM of blocky RA + 6% strain. 134

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The wear resistance increased with increasing worn surface hardness because the hardness of the worn surface could effectively resist cutting by abrasive particles. However, the fracture toughness dominates the wear resistance when the worn surface hardness is high enough, at which the RA stability is high enough that martensitic transformation could not occur the during wear. It is shown that a higher RA stability brings about a higher worn surface hardness in Fig. 14. The retained austenite transformation-induced hardness could greatly improve the abrasive wear resistance. However, the fracture toughness decreased with increasing RA stability. Thus, the relationship between RA stability and wear resistance is developed, as shown in Fig. 14. The results showed that the wear resistance improved with increasing RA stability, which was due to the hardness enhancement by RA transformation. However, it became worse when the RA hardly triggered a martensitic transformation to resist crack propagation due to high mechanical stability.

Table 3 The data in the wear prediction model. Samples

B350 B300 B250 B220

P1 (MPa)

20.4 20.8 21.9 22.5

P2 (MPa)

308.2 314.4 331.6 341.3

H (HV)

380 520 590 650

Hworn (HV)

2

KIC (MPa·m1/ )

W−1 (g−1)

630 670 760 770

124.3 83.2 65.5 30.2

13.6 16.4 17.2 16.4

5. Conclusion The effect of retained austenite stability on the impact-abrasion wear resistance of carbide-free bainitic steels was studied. It was demonstrated that RA stability has a close relationship with wear resistance. Furthermore, the wear mechanism of impact-abrasion wear was discussed. The major findings were as follows:

Fig. 13. The fitting curve of wear resistance.

(1) The RA stability increased with decreasing austempering temperature in bainitic steels. The improved mechanical stability of RA resulted in a high wear resistance. However, it became worse when the mechanical stability of RA was sufficient to retard the transformation of RA to martensite. (2) Microcutting and microcracking were the main mechanisms during wear. The microcutting was generated by the abrasive particles and related to the hardness of the worn surface. The flakes were detached from the worn surface due to crack nucleation and propagation. (3) The hardness and fracture toughness were the key factors that dominated the wear resistance. A higher RA stability led to a higher worn surface hardness, but a lower fracture toughness. Acknowledgements

Fig. 14. The wear resistance with RA stability.

The authors are grateful to the financial support of the National Basic Research Program of China (No. 2016YFB0300601), National Natural Science Foundation of China (U1564203, Nos. 51571141 and 51201105), the Interdisciplinary Program of Shanghai Jiao Tong University (No. YG2014MS23), National Natural Science Foundation of China (Grant No. 51601113) and Key Basic Scientific Research Projects of the National Defense Science and Technology Commission (JCKY2017208B003).

[32], and for the quartz abrasive particle E2 ≈ 50 GPa. Poisson's ratio of sample v1 ≈ 0.25 [29] and for the abrasive v2 ≈ 0.25. The wear rate dominated by microcutting and microcracking for the highly hardened steels containing strain/stress concentrations could be estimated by the modified Eqs. (11) and (12) [19,21,25,29,33]:

W = ΔWCutting + ΔWCracking W ∝ b⋅

P1 d1/2⋅P 5/4 + c⋅ 3/4 2 1/2 Hworn KIC ⋅H

(11)

(12)

References

where b and c are wear coefficients related to the impact and sliding wear process, respectively. Here, b and c were approximately 2.5 and 0.1 in the predicted model, respectively. P1 and P2 were the applied pressures of cutting and impact, respectively, by Eqs. (4), (7) and (8). P The first part W1 ∝ b⋅ H 1 was the wear loss of microcutting, and the worn Hworn was the surface hardness after it was worn. The second part

W2 ∝ c⋅

d1/2 ⋅ P25/4 3/4 ⋅ H1/2 KIC

[1] S.M. Hasan, D. Chakrabarti, S.B. Singh, Dry rolling/sliding wear behaviour of pearlitic rail and newly developed carbide-free bainitic rail steels, Wear 408 (2018) 151–159. [2] T. Sourmail, F.G. Caballero, C. García-Mateo, V. Smanio, C. Ziegler, M. Kuntz, R. Elvira, A. Leiro, E. Vuorinen, T. Teeri, Evaluation of potential of high Si high C steel nanostructured bainite for wear and fatigue applications, Mater. Sci. Technol. 29 (2013) 1166–1173. [3] M. Shah, S.D. Bakshi, Three-body abrasive wear of carbide-free bainite, martensite and bainite-martensite structure of similar hardness, Wear 402 (2018) 207–215. [4] K. Singh, A. Singh, Tribological response and microstructural evolution of nanostructured bainitic steel under repeated frictional sliding, Wear 410 (2018) 63–71. [5] R. Rementería, I. García, M. Aranda, F. Caballero, Reciprocating-sliding wear behavior of nanostructured and ultra-fine high-silicon bainitic steels, Wear 338 (2015) 202–209. [6] S.D. Bakshi, A. Leiro, B. Prakash, H. Bhadeshia, Dry rolling/sliding wear of nanostructured bainite, Wear 316 (2014) 70–78. [7] A. Leiro, E. Vuorinen, K.-G. Sundin, B. Prakash, T. Sourmail, V. Smanio, F. Caballero, C. Garcia-Mateo, R. Elvira, Wear of nano-structured carbide-free

was the fracture wear model, which is related to the

removal of material by cracking. Parameter d is the effective size of the abrasive particles. H is the hardness of the bulk material. KIC is the fracture toughness of these steels. The data used in the wear model are listed in Table 3. The model shows that the hardness and fracture toughness are the main factors during the whole wear process, and the calculated wear resistance fits well with the experimental results, as shown in Fig. 13. 135

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