Bimodal grain-structure formation in a Co–Cr-based superalloy during ultrahigh-homologous-temperature annealing without severe plastic deformation

Bimodal grain-structure formation in a Co–Cr-based superalloy during ultrahigh-homologous-temperature annealing without severe plastic deformation

Journal of Alloys and Compounds 783 (2019) 173e178 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: http:...

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Journal of Alloys and Compounds 783 (2019) 173e178

Contents lists available at ScienceDirect

Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom

Bimodal grain-structure formation in a CoeCr-based superalloy during ultrahigh-homologous-temperature annealing without severe plastic deformation Cheng-Lin Li, Jeong Mok Oh, Jong-Taek Yeom, Chan Hee Park* Advanced Metals Division, Korea Institute of Materials Science, Changwon, 51508, Republic of Korea

a r t i c l e i n f o

a b s t r a c t

Article history: Received 31 October 2018 Received in revised form 12 December 2018 Accepted 27 December 2018 Available online 28 December 2018

Bimodal grain structures are often produced in a metal by employing severe plastic deformation followed by low-homologous-temperature annealing (0.4Tm, where Tm is melting temperature). Here, a bimodal grain structure was achieved in a Coe20Cre15We10NieC superalloy via moderate cold rolling (strain z0.3) and ultrahigh-homologous-temperature annealing (0.8Tm). During annealing, carbide-assisted heterogeneous static-recrystallization played a key role in forming the bimodal grain structure. A 40% increase in combined strength and ductility was observed. © 2018 Elsevier B.V. All rights reserved.

Keywords: Metals and alloys Precipitation Mechanical properties Microstructure

1. Introduction The strengtheductility behavior of a metallic material strongly depends on both the grain size and its distribution. Generally, a fine-grained structure has improved strength (as per the HallePetch relation) but limited ductility, whereas a coarse-grained structure has enhanced ductility (due to the longer dislocation slip) but reduced strength [1]. This strengtheductility trade-off has posed significant challenges, because both properties are typically required to ensure structural safety while reducing the risk of catastrophic failure in major structural applications. One effective solution to overcome this trade-off is to fabricate metals with a bimodal grain-size distribution, i.e., with coexisting fine grains (FGs) and coarse grains (CGs). Wang et al. [2] demonstrated that pure Cu with a bimodal grain structure had six-times higher yield strength than that with only CGs, without a significant loss of elongation, and an elongation 50% larger than that with only FGs, with comparable yield strength. To produce this bimodal grain structure, they first imposed severe strain (ε z 2.7) at cryogenic temperatures to induce a fully FG structure, and then carried out short-term annealing at a low homologous temperature (0.35Tm,

* Corresponding author. E-mail address: [email protected] (C.H. Park). https://doi.org/10.1016/j.jallcom.2018.12.320 0925-8388/© 2018 Elsevier B.V. All rights reserved.

where Tm is the melting temperature) to encourage partial recrystallization [2]. Further similar approaches, i.e., severe plastic deformation followed by low-homologous-temperature annealing, have been applied to obtain a bimodal grain structure in other metals [3e5]. Nevertheless, to enable the rapid mass production of metals with well-balanced strength and ductility, it is necessary to design a simpler approach toward producing the bimodal-grain structure, which does not involve severe plastic deformation. One example is hard plate rolling, which has been applied to produce bimodal grain-structured Mg and Al alloys without severe plastic deformation (0.8  ε  1.9) [6,7]. Note that both the strength and ductility of the alloys were improved. Other approaches are phasetransformation assisted [8,9], different-recrystallization-rate induced [10], and preexisting-precipitation stimulated [11] bimodal grain-structure formation. In these studies, metals were subjected to only moderate deformation (ε  1.0), followed by lowto intermediate-homologous-temperature annealing (0.6Tm). In particular, the particle pinning effect of heterogeneously distributed precipitations promoted a bimodal grain-structure formation in ferrite steels [12,13], ferrite/cementite steels [14,15], and austenitic stainless steel [16]. Recently, for Co-Cr-based superalloys, Favre et al. [17] found that a bimodal grain structure can be formed through a similar process, although both the average FG size df (z30 mm) and the average CG size dc (z100 mm) were too large to

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expect high strength. The present study introduces a new approach that creates a bimodal grain structure with much finer df and dc in an initially single-phase CoeCr-based superalloy, by utilizing moderate cold working (ε z 0.3) and ultrahigh-homologous-temperature annealing (0.8Tm). The mechanisms by which the bimodal grain structure formed were analyzed in detail using backscattered electron (BSE) imaging and electron backscattering diffraction (EBSD) analyses. 2. Materials and methods The material used in this investigation was Coe20Cre15We10Nie0.1C superalloy (also known as Haynes 25, L-605, or ASTM F90). Bars of 12 mm diameter were supplied by HVM company (Ansan, Korea) in a solution treated (1250  C for 1 h) and water quenched condition. The measured chemical composition (in wt.%) was Co (bal.), 20.58 Cr, 14.9 W, 10.81 Ni, 0.09 C; and the melting point was about 1410  C. The solution-treated bar was cold rolled (ε z 0.3) using a groove rolling machine. The cold-rolled bars were annealed at temperatures of 1100 or 1200  C for 0.17e180 min and quenched in water. Two-stage annealing (i.e., 1200  C for 30 min then 1100  C for 5 min) was also carried out. The microstructures were observed along the rolling direction, with BSE images taken using a JSM 6610 scanning electron microscope, and EBSD maps taken using a Hitachi SU6600 field-emission scanning electron microscope. The step size of the EBSD scans was varied from 0.05 to 2 mm depending on the grain size of the samples. The indexing rates were 97.0% and 99.1% for the as-rolled and annealed samples, respectively. TSL OIM 8.0 software was used for post-processing. The quantitative EBSD analyses were made using scans of an area three-times larger than that of the high-resolution images shown in this paper. Tensile specimens with a 10-mm gauge length and 2.5-mm gauge diameter (corresponding to ASTM E8/E8M) were machined along the rolling direction. Tensile tests were carried out at room temperature using an INSTRON 5982 machine with a constant strain rate of 103 s1 controlled by a contact-type extensometer. 3. Results Fig. 1 shows the solution-treated alloy microstructure. It consisted of a single face-centered-cubic (fcc) g phase with an average grain size davg of approximately 100 mm (Fig. 1a). The inverse pole figure (IPF) map (Fig. 1b) shows that some typical annealing twins were formed, as previously reported [17,18]. Fig. 2aec shows The cold-rolled alloy microstructure. The figure reveals the development of a heterogeneous microstructure featuring coexisting severely deformed (SD) regions and weakly

deformed (WD) domains. In particular, the IPF map (Fig. 2a) shows the development of 〈111〉 and 〈001〉 textures along the rolling direction, as well as the bending of the original annealing twins, as indicated by the yellow arrows. An in-grain orientation gradient is also visible, inferring the formation of a subgrain structure. Superimposing the image quality (IQ) map onto the misorientation map (Fig. 2b) revealed that the formation of the subgrain structure is attributable to the multiple {111} slip bands (SBs), which caused local misorientation of up to 5 . The intersections between such SBs gave rise to higher local misorientations of up to 15 near grain boundaries (GBs) and twin boundaries (TBs). The geometrically necessary dislocation (GND) map (Fig. 2c) shows strain inhomogeneity. The WD domains, with a few SBs, had a lower GND density of 1e2  1014 m2 compared to the SD regions, which had a GND density of 10e30  1014 m2 (one order of magnitude higher). Still, no phase other than fcc g was detected (Fig. S1). Fig. 2def shows the microstructure of the alloy after cold-rolling and subsequent annealing at the ultrahigh homologous temperature of 0.82Tm (1100  C) for 10 s. To clarify the early stage mechanisms for the formation of a bimodal grain structure, the examination area was the same as in Fig. 2aec (as-rolled state). The IQ map (Fig. 2d) revealed that static recrystallization (SRX) occurred momentarily. Furthermore, outlines of the prior GBs and TBs are obviously visible. The areas marked E0 and F0 in Fig. 2d (enlarged in Fig. 2e and f, respectively) correspond to the areas marked E and F in Fig. 2c. Hence, comparing area E in Fig. 2cee provides insight into the effect of strain inhomogeneity in the asrolled state on the formation of a bimodal grain structure during annealing. A close look at area E reveals SD regions in the upperright and lower-left corners, with WD domains between them. These SD regions and WD domains transformed into FGs and CGs, respectively (Fig. 2e). A similar conclusion can be reached by comparing area F in Fig. 2cef; the SD regions (on the right-handside) and the WD domains (on the left-hand-side) transform into FGs and CGs, respectively, during the initial 10 s of annealing. Interestingly, nanosized precipitates such as M7C3 and M23C6 carbides were observed to have formed around the FGs (inset in Fig. 2f). Fig. 3 shows the microstructural evolution during further annealing at the same temperature of 1100  C (for convenience, grains finer than 5 mm were defined as FGs, while those coarser than 5 mm were designated as CGs). It revealed two important aspects regarding the change of the bimodal grain structure. First, the area fractions of FGs and CGs (ff and fc, respectively) were affected by annealing time. Fig. 3aed shows that ff gradually decreased from 58% to 14% during short-to-intermediate term (1e60 min) annealing, indicating that the proportion of each grain size could be controllable. However, ff approached zero (0.4%) after long-term annealing (180 min), resulting a uniform CG-structure (Fig. 3e).

Fig. 1. (a) Phase map and (b) IPF map of the present alloy solution-treated at 1250  C for 1 h.

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Fig. 2. Microstructural evolution of the cold-rolled (ε z 0.3) alloy during short-term annealing (10 s) at 1100  C (0.82Tm). (a) IPF map, (b) IQ þ misorientation map, and (c) GND map for as-rolled state. (d) IQ map, and (e, f) BSE images for as-annealed state. (e) and (f) are enlarged views of areas E0 and F0, respectively.

Fig. 3. IPF maps of the alloy after cold-rolling and annealing at 1100  C for (a) 1 min, (b) 15 min, (c) 30 min, (d) 60 min, and (e) 180 min. (f) Grain size change during annealing.

Second, both df and dc were also affected by annealing time. Fig. 3f, which was plotted based on the grain size distribution in Fig. S2, reveals that dc significantly increased from 8.1 to 55.4 mm during annealing, whereas a small df was maintained (2.9 vs. 3.8 mm) even at the ultrahigh homologous temperature used. Thus, the bimodality of the grain size distribution strengthened with increasing annealing time. However, because extended annealing gave rise to the formation of a uniform CG-structure, the most promising bimodal grain structure was developed after intermediate-term (60 min) annealing, as shown in Fig. 3d. It was noted that the FGs in Fig. 3d were still surrounded by fine M7C3 and M23C6 carbides (inset in Fig. 3d), whereas the CGs were free from carbides (Fig. S3). Fig. 4a shows the microstructure of the cold-rolled alloy after

annealing at a higher temperature (1200  C) for 30 min. The structure was observed to be uniform, with CGs and no carbides. Fig. 4b shows that this uniform CG structure was decorated with fine M7C3 and M23C6 carbides along the GBs after a further annealing stage at a lower temperature (1100  C) for 5 min. These two microstructures have a similar davg of about 60 mm, thus the only difference between them is absence or presence of carbides. Fig. 4c shows tensile stressestrain curves for the bimodal grain structure with carbides (Fig. 3d), uniform CG structure without carbides (Fig. 4a), and uniform CG structure with carbides (Fig. 4b). The two CG structures exhibited an identical tensile behavior with a yield strength (YS) of about 449 MPa, an ultimate tensile strength (UTS) of about 1017 MPa, and a uniform elongation (Elu) of about

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Fig. 4. IPF maps of the alloy after cold-rolling and (a) annealing at 1200  C for 30 min, and (b) further subsequent annealing at 1100  C for 5 min. (c) Tensile stressestrain curves for a bimodal grain structure (Fig. 3d), and CG-structures (a, b).

71%, suggesting that the carbides did not significantly affect the tensile properties. Hence, the high strength (YS z 548 MPa; UTS z 1193 MPa) and ductility (Elu z 81%) observed for the bimodal grain structure with carbides is likely to be attributed to the high bimodality in grain size distribution rather than the presence of carbides. 4. Discussion In the present study, it was demonstrated that a bimodal grain structure was achieved by ultrahigh-homologous-temperature annealing (0.8Tm) following moderate cold working. Furthermore, this bimodal grain structure successfully increased the combined strengtheductility performance by over 40% (YS  Elu ¼ 44,662 MPa$%) compared to that for a uniform CG (15 mm  dc  100 mm) structure (31,879 MPa$% in this study; 19,968e26,038 MPa$% in similar studies [19,20]) and a uniform FG (df z 3.5 mm) structure (16,120 MPa$% [21]). The mechanisms underlying this formation of a bimodal grain structure can be described as follows. Generally, solution treatment of a metal induces randomly

oriented grains (as evidenced in Fig. 1b), which exhibit different plastic deformation behaviors under an applied stress. The Taylor model for crystal plasticity [22] describes this in relation to the Taylor factor, i.e., the ratio of applied stress to the critical resolved shear stress for slip. A hard-oriented grain with a high Taylor factor is difficult to deform, resulting in WD domains after cold working. In contrast, a soft oriented grain with a lower Taylor factor can more easily accommodate the external strain by dislocation slip or ingrain rotation, generating SD regions. Hence, a cold-rolled microstructure featuring coexisting SD regions and WD domains is generated (Fig. 2c). This is schematically illustrated in Fig. 5a and b: SD regions and WD domains develop from soft oriented grains and harder oriented grains, respectively. Upon short-term annealing at 1100  C (0.82Tm), because SD regions, with high GND density (10e30  1014 m2), provide more nucleation sites for SRX, large numbers of fine recrystallized grains are likely to be formed within this limited area; whereas the WD domains, with much lower GND density (1e2  1014 m2), have less nucleation sites, resulting a smaller number of coarse recrystallized grains (Fig. 2d). At the same time, carbides such as M23C6 and M7C3 precipitate because the carbon content (0.09 wt%) of the

Fig. 5. Schematic illustration of bimodal grain structure formation developed by carbide-assisted heterogeneous static-recrystallization during ultrahigh-homologous-temperature annealing. Ts is the temperature of the carbide solubility limit of the present alloy (Ts ¼ 1150  C or 0.85Tm).

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present alloy is higher than solubility limit (0.06 wt%) at 1100  C [21]. The selective formation of nanoscale carbides around FGs (in prior SD regions) rather than CGs is of great interest (Fig. 2e and f). Moreover, it could be attributed to the following points. First, it has been reported that carbon atoms readily segregate to internal defects such as SBs in SD regions [23]. Second, such defects provide much faster diffusion paths compared to bulk diffusion [24]. Therefore, during short-term annealing, SD regions and WD domains are transformed into FGs (df z 2.9 mm) with many carbides, and CGs (dc z 8.1 mm) with few carbides, respectively, as illustrated in Fig. 5c. Another interesting phenomenon is selective grain growth during further annealing for 60 min, which promotes a higher bimodality in grain size distribution (Fig. 5d). According to the Zener theory [25], coherent precipitates have a strong pinning effect on GB migration. The nanoscale carbides in the present study are coherent with the fcc g matrix [26] and stable even after annealing for 60 min (inset in Fig. 3d). Hence, the FGs largely maintain their original size (df z 3.8 mm), while the CGs, without carbides, grow steadily (dc z 24.4 mm) (Fig. 3f). It should be noted that extended annealing (i.e., 180 min) at the same temperature gave rise to significant grain growth, as shown in Fig. 3e and previously reported in Ref. [17], due to unpinning of the carbides. Thus, excessive annealing should be avoided to obtain a suitable bimodal grain structure. Consequently, carbide-assisted heterogeneous SRX in the present CoeCr-based alloy is a key mechanism for the formation of the bimodal grain structure during short-to intermediate-term annealing at an ultrahigh homologous temperature. In contrast, upon annealing at 1200  C, new grains without carbides are nucleated (Fig. 5e) because the carbon solubility limit (0.12 wt%) at this temperature is higher than the carbon content (0.09 wt%) of the present alloy [21]. This allows the grains to grow significantly due to the absence of the carbide pinning effect (Figs. 4a and 5f), supporting the importance of nanoscale carbide precipitation on the formation of a bimodal grain structure. 5. Conclusion In conclusion, a bimodal grain structure was achieved in a Coe20Cre15We10Nie0.09C alloy by moderate cold rolling (ε z 0.3) and subsequent intermediate-term (60 min) annealing at 1100  C. Cold rolling induced a microstructure featuring coexisting SD regions and WD domains, which respectively promote the formation of FGs (2.9 mm) with nanoscale carbides and CGs (8.1 mm) without carbides during short-term (1 min) annealing. The FGs exhibited less grain growth (3.8 mm) owing to the carbide pinning effect, whereas the CGs grew considerably (24.4 mm) during intermediate-term (60 min) annealing, resulting in a stronger bimodality of grain size distribution. In comparison to the uniform CG-structure, the bimodal grain structure provided higher YS (548 vs. 449 MPa) and UTS (1193 vs. 1017 MPa) without any loss in Elu (81% vs. 71%), making the alloy more suitable for vascular stent applications where both high strength and high ductility are important to enable thinner wall design and higher fatigue life and to improve stent deliverability and expandability. The approach described in this paper may be applied to other carbon-containing Co-Cr-based superalloys or high entropy alloys to achieve a bimodal grain structure. Funding This work was supported by the R&D Program of the Ministry of Trade, Industry and Energy [grant number 10062485]; and the Fundamental Research Program of the Korea Institute of Materials

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Science, Republic of Korea [grant number PNK5700]. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.jallcom.2018.12.320. References [1] N. Hansen, HallePetch relation and boundary strengthening, Scr. Mater. 51 (2004) 801e806. https://doi.org/10.1016/j.scriptamat.2004.06.002. [2] Y. Wang, M. Chen, F. Zhou, E. Ma, High tensile ductility in a nanostructured metal, Nature 419 (2002) 912e915. https://doi.org/10.1038/nature01133. [3] Y.H. Zhao, X.Z. Liao, S. Cheng, E. Ma, Y.T. Zhu, Simultaneously Increasing the Ductility and Strength of Nanostructured Alloys, Adv. Mater. 18 (2006) 2280e2283. https://doi.org/10.1002/adma.200600310. [4] Y.H. Zhao, T. Topping, J.F. Bingert, J.J. Thornton, A.M. Dangelewicz, Y. Li, W. Liu, Y. Zhu, Y. Zhou, E.J. Lavernia, High Tensile Ductility and Strength in Bulk Nanostructured Nickel, Adv. Mater. 20 (2008) 3028e3033. https://doi.org/10. 1002/adma.200800214. [5] X. Wu, M. Yang, F. Yuan, G. Wu, Y. Wei, X. Huang, Y. Zhou, Heterogeneous lamella structure unites ultrafine-grain strength with coarse-grain ductility, Proc. Natl. Acad. Sci. U.S.A. 112 (2015) 14501e14505. https://doi.org/10.1073/ pnas.1517193112. [6] M. Zha, X.T. Meng, H.M. Zhang, X.H. Zhang, H.L. Jia, Y.J. Li, J.Y. Zhang, H.Y. Wang, Q.C. Jiang, High strength and ductile high solid solution AleMg alloy processed by a novel hard-plate rolling route, J. Alloys Compd. 728 (2017) 872e877. https://doi.org/10.1016/j.jallcom.2017.09.017. [7] M. Zha, X. Zhang, H. Zhang, J. Yao, C. Wang, H. Wang, T. Feng, Q. Jiang, Achieving bimodal microstructure and enhanced tensile properties of Mge9Ale1Zn alloy by tailoring deformation temperature during hard plate rolling (HPR), J. Alloys Compd. 765 (2018) 1228e1236. https://doi.org/10. 1016/j.jallcom.2018.04.328. [8] Y. Okitsu, N. Takata, N. Tsuji, A new route to fabricate ultrafine-grained structures in carbon steels without severe plastic deformation, Scr. Mater. 60 (2009) 76e79. https://doi.org/10.1016/j.scriptamat.2008.09.002. [9] A. Karmakar, A. Karani, S. Patra, D. Chakrabarti, Development of Bimodal Ferrite-Grain Structures in Low-Carbon Steel Using Rapid Intercritical Annealing, Metall. Mater. Trans. A 44 (2013) 2041e2052. https://doi.org/10. 1007/s11661-012-1556-z. [10] H. Azizi-Alizamini, M. Militzer, W.J. Poole, A novel technique for developing bimodal grain size distributions in low carbon steels, Scr. Mater. 57 (2007) 1065e1068. https://doi.org/10.1016/j.scriptamat.2007.08.035. [11] M.C. Zhao, T. Hanamura, H. Qiu, K. Yang, Microstructural evolution of submicron sized ferrite in bimodal structural ultrafine grained ferrite/cementite steels by annealing below austenitized temperature, Metall. Mater. Trans. A 37 (2006) 1657e1664. https://doi.org/10.1007/s11661-006-0107-x. [12] Z. Dapeng, L. Yong, L. Feng, W. Yuren, Z. Liujie, D. Yuhai, ODS ferritic steel engineered with bimodal grain size for high strength and ductility, Mater. Lett. 65 (2011) 1672e1674. https://doi.org/10.1016/j.matlet.2011.02.064. [13] S. Patra, S.M. Hasan, N. Narasaiah, D. Chakrabarti, Effect of bimodal distribution in ferrite grain sizes on the tensile properties of low-carbon steels, Mater. Sci. Eng. A 538 (2012) 145e155. https://doi.org/10.1016/j.msea.2011.12.114. [14] M.C. Zhao, F. Yin, T. Hanamura, K. Nagai, A. Atrens, Relationship between yield strength and grain size for a bimodal structural ultrafine-grained ferrite/ cementite steel, Scr. Mater. 57 (2007) 857e860. https://doi.org/10.1016/j. scriptamat.2007.06.062. [15] M.C. Zhao, T. Hanamura, H. Qiu, K. Nagai, K. Yang, Grain growth and HallePetch relation in dual-sized ferrite/cementite steel with nano-sized cementite particles in a heterogeneous and dense distribution, Scr. Mater. 54 (2006) 1193e1197. https://doi.org/10.1016/j.scriptamat.2005.11.032. [16] H. Wu, G. Niu, J. Cao, M. Yang, Annealing of strain-induced martensite to obtain micro/nanometre grains in austenitic stainless, Mater. Sci. Technol. 33 (2017) 480e483. https://doi.org/10.1080/02670836.2016.1229092. gue, E. Maire, A. Chiba, Grain growth and static recrystalli[17] J. Favre, D. Fabre zation kinetics in Coe20Cre15We10Ni (L-605) cobalt-base superalloy, Philos. Mag. 94 (2014) 1992e2008. https://doi.org/10.1080/14786435.2014.903342. [18] S. Mahajan, C.S. Pande, M.A. Imam, B.B. Rath, Formation of annealing twins in f.c.c. crystals, Acta Mater. 45 (1997) 2633e2638. https://doi.org/10.1016/ S1359-6454(96)00336-9. [19] V.A. Kumar, R.K. Gupta, S.V.S.N. Murty, A.D. Prasad, Hot workability and microstructure control in Co20Cr15W10Ni cobalt-based superalloy, J. Alloys Compd. 676 (2016) 527e541. https://doi.org/10.1016/j.jallcom.2016.03.186. [20] K. Ueki, K. Ueda, T. Narushima, Microstructure and mechanical properties of heat-treated Co-20Cr-15W-10Ni alloy for biomedical application, Metall. Mater. Trans. A 47 (2016) 2773e2782. https://doi.org/10.1007/s11661-0163488-5. [21] J. Favre, Recrystallization of L-605 Cobalt Superalloy during Hot-Working Process, Ph.D. thesis, INSA de Lyon, 2012. [22] W. Mao, On the Taylor principles for plastic deformation of polycrystalline metals, Front. Mater. Sci. 10 (2016) 335e345. https://doi.org/10.1007/s11706016-0358-4.

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[23] M.K. Miller, P.A. Beaven, S.S. Brenner, G.D.W. Smith, An atom probe study of the aging of iron-nickel-carbon martensite, Metall. Trans. A 14 (1983) 1021e1024. https://doi.org/10.1007/BF02670440. [24] Y. Mishin, Chr. Herzig, Grain boundary diffusion: recent progress and future research, Mater. Sci. Eng. A 260 (1999) 55e71. https://doi.org/10.1016/S0921-

5093(98)00978-2. [25] P.A. Manohar, M. Ferry, T. Chandra, Five Decades of the Zener Equation, ISIJ Int. 38 (1998) 913e924. https://doi.org/10.2355/isijinternational.38.913. [26] T. Narushima, S. Mineta, Y. Kurihara, K. Ueda, Precipitates in Biomedical Co-Cr Alloys, JOM 65 (2013) 489e504. https://doi.org/10.1007/s11837-013-0567-6.