Variations in erosive wear of metallic materials with temperature via

Materials Chemistry and Physics 172 (2016) 197e201

Contents lists available at ScienceDirect

Materials Chemistry and Physics journal homepage: www.elsevier.com/locate/matchemphys

Variations in erosive wear of metallic materials with temperature via the electron work function Xiaochen Huang a, Bin Yu a, X.G. Yan b, D.Y. Li a, b, * a b

Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, Shanxi, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

Metallic materials' wear resistance is influenced by temperature. Electron work function (EWF) intrinsically determines materials' wear resistance. An EWF-based temperature-dependent solid-particle erosion model is proposed.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 July 2015 Received in revised form 1 January 2016 Accepted 25 January 2016 Available online 5 February 2016

Mechanical properties of metals are intrinsically determined by their electron behavior, which is largely reflected by the electron work function (EWF or 4). Since the work function varies with temperature, the dependence of material properties on temperature could be predicted via variations in work function with temperature. Combining a hardness e 4 relationship and the dependence of work function on temperature, a temperature-dependent model for predicting solid-particle erosion is proposed. Erosive wear losses of copper, nickel, and carbon steel as sample materials were measured at different temperatures. Results of the tests are consistent with the theoretical prediction. This study demonstrates a promising parameter, electron work function, for looking into fundamental aspects of wear phenomena, which would also help develop alternative methodologies for material design. © 2016 Elsevier B.V. All rights reserved.

Keywords: Metals Alloys Tribology Erosion Fermi surface

1. Introduction Though microstructure is a predominant factor governing the performance of materials, intrinsic mechanical properties of metallic materials, e.g., Young's modulus, yield strength and ductility, are fundamentally determined by their electron behavior

* Corresponding author. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, T6G 2V4, Canada. E-mail address: [email protected] (D.Y. Li). http://dx.doi.org/10.1016/j.matchemphys.2016.01.065 0254-0584/© 2016 Elsevier B.V. All rights reserved.

[1e7]. The electron behavior is reflected by the electron work function (EWF), which is the minimum energy required to move electrons at Fermi level from inside a metal to its surface without kinetic energy [8]. This parameter may provide supplementary clues for material design and modification. For instance, EWF can be used to select appropriate alloying elements for solutionstrengthening and to identify beneficial and detrimental phases in multiphase alloys. These capabilities of EWF have been demonstrated by recent studies [9e11]. It should be indicated that mechanical properties of realistic materials are strongly affected by

198

X. Huang et al. / Materials Chemistry and Physics 172 (2016) 197e201

their microstructure, which complicates the dependence of the properties on the electron behavior. However, the mechanical properties of a material can still be reflected by its overall electron work function to a certain degree, since the overall EWF is linked to EWFs of individual phases and interphase boundaries, which play roles in determining the overall properties. The correlation between the overall EWF and those of individual microstructure constituents has been under active study. Electron work function varies with temperature [11e13]. Thus, the dependence of material properties on temperature could be established via EWF-temperature relationship. In this article, the dependence of material loss on temperature, caused by solidparticle erosion, is proposed by combining a simple erosion model, EWF-hardness and EWF-temperature relationships. Solidparticle erosion tests were performed for three sample materials, Cu, Ni and carbon steel, at various temperatures. The first two are single-phase pure metals and the third is a two-phase material consisting iron and cementite. The objectives of this work are 1) to determine if the effect of temperature on erosion is predictable based on the dependence of work function on temperature, and 2) to have a preliminary look into possible influence of the second phase (cementite) in the steel on the prediction. As reported in the article, the trend of material loss of both the single-phase and two-phase materials with temperature is in agreement with the theoretical prediction. The second phase, cementite, affects the erosion resistance of the steel. Such effect could be included in or reflected by a relevant material coefficient, e.g., KE4 and g in Eq. (7), so that the established model could also be applicable to two-phase or multiphase materials. However, the generality of the model for multi-phase materials need further studies, since influences of metallic and non-metallic phases on the overall work function should be different. The established erosiontemperature relation based on EWF may help develop new approaches for looking into fundamental issues of tribological phenomena. It may need to indicate that the effect of temperature on the erosion resistance can be directly evaluated based on the dependence of hardness on temperature without involving the electron work function. However, the ultimate objective of this study is to reveal the correlation between the electron behavior and mechanical & tribological properties. Such correlation would provide supplementary clues for material design. As a matter of fact, considerable studies have been conducted with a long history to correlate mechanical properties with the electron behavior using quantum mechanics. However, the quantum theory is too complicated to be feasibly used in material development especially for structural materials. Studies have shown that the electron behavior is largely reflected by the work function, a simple but fundamental parameter, which much facilitates the efforts in correlating the tribological properties with the electron behavior. Although in an early stage of study, this work has demonstrated the link between the intrinsic wear resistance of materials and their work functions, and also shown the promise of using work function in development of supplementary approaches or alternative methodologies for material design and modification on a feasible electronic base.

F Ac f H

(1)

During erosion, the impact force comes from the kinetic energy of solid particle associated with its moment change when striking the target surface:

F ¼ m

dvy dt

(2)

where m is the mass of the particle striking the surface, and vy represents the vertical component of the velocity of the particle. Thus we have

m

dvy ¼ HAc dt

dy $dvy ¼ HAc $dy m dt Zd

Z0 mvy dvy ¼

∴ v

Zd HAc dy ¼

0

HAc ðyÞdy 0

If the particle strikes the surface at 90 , the above integration yields

Indention volume; V ¼ Ac $d ¼

mv2y 2H

Ac is the average contact area and d is the depth of indent made by the particle. If the particle strikes the surface at a certain angle, the horizontal velocity needs to be taken into account. Thus, a general relation between the erosion volume loss (V) and material's hardness is expressed as

VL ¼ KE

mv2 H

(3)

where KE is an erosion coefficient, which is related to the impingement angle of the particle and other factors such as the size and angularity of the particle. Hardness of a metal is its resistance to plastic deformation, dependent on the number of slip systems, elastic modulus and Poisson's ratio etc. It has been shown that H is related to the work function in the following form [16]:

H 1 m2 ¼ C46

(4)

where m is the Poisson's ratio, C is a coefficient dependent on the crystal structure, the number of activated slip systems, Burgers vector, and the dislocation width, etc. Combining Eq. (4) and Eq. (3) yields

VL ¼ KE

mv2 1 m2 mv2 ¼ KE4 H 46

(5)

When the hardness is converted to the work function, the coefficient KE is replaced by KE4 Reza and Li [17] derived a relation between the work function and temperature, expressed as: 2. Temperature-dependent erosion model For a ductile material, the contact created by the impingement of particle, Ac, is proportional to the impact contact force (F) and inversely proportional to the hardness of the material (H) as described in [14,15],

4ðtÞ ¼ 40 g

ðkB tÞ2 f0

(6)

where 40 is the work function at room temperature (i.e. 295 K), t ¼ T 295 and T is the absolute temperature (K). g is a material


coefficient related to the crystal structure, atomic interactions and thermal expansion coefficient, etc. For polycrystalline materials, microstructural features also influence this coefficient, including the grain size, crystallographic orientations of grains, second phases, grain boundaries and interphase boundaries. Theoretically including all these factors in the coefficient, g, is a challenging job, but the coefficient can be determined by fitting limited experimental data. With a determined coefficient, g, variations in work function of a specific material in an extended temperature range can be predicted and used to predict variations in material properties with temperature. Incorporation of the relation between work function and temperature, i.e. Eq. (6), the erosion volume loss is expressed as a function of temperature via the effect of temperature on work function,

VL ¼ KE4

mv2 1 m2 mv2 1 m2 ¼ K ! E4 6 46 2 40 g ðk4B tÞ

(7)

0

If using mass loss (ML) to represent erosion damage and let

u ¼ KE4(1 m2), Eq. (7) is changed to ML ¼ u

mv2 40

g ðk4B tÞ 0

!6

(8)

2

3. Experimental observation Cu, Ni and carbon steel (CS: 0.25%C, pearlitic steel) samples with dimensions of 20 10 5 mm were polished with 800 and then 1200 grit grinding papers, cleaned with distilled water and acetone. The former were single-phase Cu and Ni samples, while the steel consisted of ferrite and cementite, as illustrated by a TEM image in Fig. 1. A homemade air-jet erosion tester.was used to perform solidparticle erosion tests at various temperatures from the room temperature (295 K) to 545 K. The impingement angle was set at 90 . AFS 50e70 sand was used for the tests. A mixture of sand and pressed air was delivered through a nozzle of 4 mm in inner diameter and the distance between the nozzle and samples was 20 mm. Three sand particle velocities of 55 m/s (air pressure: 40

Fig. 1. A TEM image (transmission electron microscopy) of the carbon steel showing a typical pearlitic structure consisting alternating layers of ferrite and cementite.

199

psi), 35 m/s (air pressure: 30 psi) and 23 m/s (air pressure: 10 psi) were used for the erosion tests, respectively. The weight loss of samples caused by erosion was determined using a balance with an accuracy of 0.1 mg. Eroded surfaces were examined using a Vega-3 TESCAN Scanning Electron Microscope at 20 kV. Fig. 2 illustrates mass losses of the samples with respect to temperature at three different sand particle velocities. Through data fitting, values of g and u in Eq. (8) were determined for the sample materials and are given in Table 1. Electron work functions of the materials, f0 ¼ f259K, are f0(Cu) ¼ 4.6 eV, f0(Ni) ¼ 5.1 eV, f0(CS) ¼ 4.6 eV. Since cementite is an insulative material with low conductivity [18], electron work function of the steel and its variation with temperature could be dominated by those of iron. As shown in Table 1, the coefficient g obtained by data fitting for each sample material shows some non-systematic fluctuations with the particle velocity. This coefficient is a material constant, which should be seen if more data are collected for better statistic data fitting. The coefficient, u, of each material, however, appears not to be a constant and decreases with increasing the velocity of sand particles. It is not very clear why u changes with the particle velocity in the present stage. Such change could be related to variations in response of the materials to dynamic stresses, which may involve effects of strain rate on stain hardening and failure, thus influencing the coefficient KE4 in Eq. (7). It is known that increasing the strain-hardening rate usually reduces the erosion damage [19]. Lee and Chen observed that under compression condition, AleSc alloy showed increased strainhardening rate with higher dislocation density and smaller dislocation cells as the strain rate was raised [20]. It is also reported that the work hardening ability of austenitic manganese steel increases with increasing the impact energy, ascribed to increases in amounts of dislocations, stacking faults and twins [21]. Thus, as the particle velocity was increased, though the overall erosion damage increased (proportional to v2), the enhanced strain-hardening could more or less reduce the increase in erosion damage. This may explain why u value decreased with increasing the particle velocity. It should be mentioned that converting the mass losses to volume loss, using VL ¼ ML/r and rCu ¼ 8.96 g/cm3, rNi ¼ 8.91 g/cm3 and rCS z 7.85 g/cm3, one may see that the volume loss of the carbon steel is smaller than those of Cu and Ni, although its work function is lower than that of Ni and similar to that of Cu. The higher resistance of the carbon steel to erosion is attributed to the strengthening effect of cementite (Fe3C) in the iron matrix. Such effect should be reflected by the smaller u value of the carbon steel as given in Table 1. This study shows that the overall work function of a two-phase material alone does not well reflect its overall performance, which is determined by both the properties of individual microstructural constituents and their microstructural arrangement. However, Eq. (8) works well when the work function is dominated by a conductive microstructure constituent (e.g., iron in the carbon steel) and the microstructure does not change much as temperature varies in a certain temperature range. It is worth having more discussion for the case of two-phase alloys. For the carbon steel, the change in its overall EWF with temperature should result mainly from change in EWF of the metallic phase i.e. iron, since electrons in cementite are localized because of the covalent bonding between Fe and C atoms, although some degree of electron delocalization may exist [22]. Thus, it is not expected that the iron carbide would affect much the coefficient, g, of the carbon steel. In other words, it is not expected that the trend given by Eq. (8) for the steel would change with temperature. The present study on the carbon steel does give results that agree with the model, and the observed trend is similar to those of pure Cu and Ni. This demonstrates the applicability of the model for pure metals

200


Fig. 2. Variations in mass loss of copper, nickel and steel samples with temperature and sand particle velocity. The curves present the theoretical prediction and the data points were collected from the experimental measurements. t ¼ T 295 K and T is the absolute temperature (K).

Table 1 Values of the coefficient g and b of the materials under different conditions. Particle velocity (m/s)

Coefficient

Ni

Cu

CS

55

g u(103 eV6/m/s) g u(103 eV6/m/s) g u(103 eV6/m/s)

3189 0.81 3075 1.23 3262 1.77

2784 0.80 2175 1.09 2026 1.81

3216 0.25 3825 0.30 3633 0.36

35 23

and carbon steel. The model is also expected to be applicable to some other types of materials such as ceramic-reinforced metal matrix composites. However, the situation would be complicated if the following factors are involved: 1) the second phase is also metallic and its EWF has different response to temperature variations, compared to that of host metallic phase, and 2) phase transformations occur in the metallic phases as temperature varies.

Further studies are needed in order to determine how the overall EWF is integrated from those of individual microstructure constituents in order to make this model more comprehensive and functional. Eq. (7) or Eq. (8) reflects the effect of temperature on intrinsic erosion resistance without influences from other external factors such as oxidation. Fig. 3 illustrates corresponding eroded morphologies (SEM) at different temperatures. No obvious oxidation is observed. Under the current erosion condition with high-speed solid particle striking, no oxide scale could stay on sample surface. Thus, possible effect of oxidation on erosion was excluded or minimized. 4. Conclusions Mechanical properties of metallic materials are intrinsically determined by their electron behavior, which is largely reflected by the electron work function. In this study, a temperature-dependent solid-particle erosion model was proposed based on the correlation


201

Fig. 3. SEM images of the eroded surfaces of copper, nickel, and carbon steel at the room temperature (295 K), 373 K and 573 K, respectively.

between hardness and the electron work function and the dependence of work function on temperature. Wear losses of copper, nickel, and carbon steel as sample materials were measured at different temperatures and different sand velocities. Results of the tests are generally in agreement with the theoretical model. This study demonstrates that although the erosion resistance of the two-phase alloy, carbon steel, is determined by properties of individual microstructural constituents (iron and cementite) and their microstructural arrangement (microstructure), the variation in erosion loss of the steel with temperature via corresponding changes in EWF well follows the trend predicted by Eq. (8), implying that the change in work function is dominated by that of the conductive phase, iron. It appears that the dependence of the erosion loss of a two-phase alloy with temperature could be determined based on the variation in EWF of the metallic phase, providing that the microstructure features and EWF of nonconductive phase do not change much with temperature in a certain temperature range. Acknowledgment The authors are grateful for financial support from the Natural Science and Engineering Research Council of Canada (NSERC), Suncor, GIW, AUTO21, Shell Canada, Magna International, and Volant Products.

References [1] L. Qi, D.C. Chrzan, Phys. Rev. Lett. 112 (2014) 115503. [2] M. Buongiorno Nardelli, J.-L. Fattebert, D. Orlikowski, C. Roland, Q. Zhao, J. Bernholc, Carbon N.Y. 38 (2000) 1703. [3] W. Li, M. Cai, Y. Wang, S. Yu, Scr. Mater. 54 (2006) 921. [4] N. Medvedeva, Y. Gornostyrev, A. Freeman, Phys. Rev. Lett. 94 (2005) 136402. [5] Y. Li, D.Y. Li, J. Appl. Phys. 95 (2004) 7961. [6] W. Li, D.Y. Li, Mater. Sci. Technol 18 (2002) 1057. [7] Z.R. Liu, D.Y. Li, Acta Mater. 89 (2015) 225. [8] N.W. Ashcroft, N.D. Mermin, Solid State Physics, first, Holt, Rinehart and Winston, New York, 1976. [9] H. Lu, G. Hua, D. Li, Appl. Phys. Lett. 103 (2013) 261902. [10] H. Lu, X. Huang, D. Li, J. Appl. Phys. 116 (2014). [11] W. Dolan, W. Dyke, Phys. Rev. 95 (1954) 327. [12] A. Kiejna, K.F. Wojciechowski, J. Zebrowksi, J. Phys. F Met. Phys. 9 (1979) 1361. [13] G. Comsa, A. Gelberg, B. Iosifescu, Phys. Rev. 122 (1961) 1091. [14] I.M. Hutchings, Tribology e Friction and Wear of Engineering Materials, Edward Arnold, London, UK, 1992. [15] Ernest Rabinowicz, Friction and Wear of Materials, second ed., Wiley, Hoboken, NJ, USA, 2013. [16] Guomin Hua, Dongyang Li, Phys. Status Solidi (b) 249 (2012) 1517e1520. [17] R. Rehemi, D.Y. Li, Scr. Mater. 99 (2015) 41. [18] M.C. Lee, G. Simkovich, Metall. Trans. A 18 (1987) 485e486. [19] J.R. Weng, J.T. Chang, K.C. Chen, J.L. He, Wear 255 (2003) 219e224. [20] W.S. Lee, T.H. Chen, Mater. Trans. 47 (2006) 355e363. [21] X.Y. Li, W. Wu, F.Q. Zu, L.J. Liu, X.F. Zhang, China Foundry 9 (2012) 248e251. [22] C. Jiang, S.G. Srinivasan, A. Caro, S.A. Maloy, Structural, elastic, and electronic properties of Fe3C from first principles, J. Appl. Phys. 103 (2008) 043502.