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Investigation of microstructure and fracture toughness of Fe-Zr welded joints
Materials Letters 231 (2018) 134–136
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Investigation of microstructure and fracture toughness of Fe-Zr welded joints Qiaoling Chu a,b,⇑, Min Zhang a,⇑, Jihong Li a, Fuxue Yan a, Cheng Yan b a b
School of Materials and Engineering, Xi’an University of Technology, Xi’an 710048, China School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, QLD 4001, Australia
a r t i c l e
i n f o
Article history: Received 17 July 2018 Received in revised form 4 August 2018 Accepted 7 August 2018 Available online 7 August 2018 Keywords: Fracture toughness Intermetallics Nanoindentation Microstructure, Welding
a b s t r a c t In this work, the mechanical properties of Fe-Zr welded joints and its dependence with the microstructures were investigated using nanoindentation. In the weld metal, Fe2Zr intermetallic phase was observed and its average hardness and fracture toughness are 19.3 GPa and 2.52 MPam1/2, respectively. It was noticed that radial cracks initiated from the corners of the impressions. Fine lamellar structure (aFe + Fe2Zr) with an average hardness of 7.5 GPa were observed but no cracks were observed when subjected to a peak load of 300 mN. A simple model was developed to explain possible phase formation mechanism in the Fe-Zr system. Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction Zirconium (Zr) alloys possess excellent corrosion resistance, mechanical properties and creep resistance [1]. Joining Zr with Fe to form dissimilar joints has both technical and economic advantages. According to Fe-Zr phase diagram, several intermetallics can be formed, including Fe2Zr, FeZr2 and FeZr3 [2,3]. These compounds may play a critical role in controlling the overall mechanical behavior of the welds. However, the fracture behavior of such Fe-Zr intermetallics has not been well understood, and a quantitative relationship between the microstructure and mechanical properties has yet been built. Recently, nanoindentation technique has been increasingly used to evaluate the mechanical behavior at nanoscale [4,5]. For the brittle materials, the indentation loads may cause cracks under the impressions, which can be used to evaluate the facture toughness [6,7]. In this work, phase formation and associated mechanical properties were investigated. A simplified model was also developed to explain possible phase formation mechanism in the Fe-Zr binary system.
pure Zr filler (0.05 wt% C, 0.2 wt% Fe). The joints were single pass welded using Tungsten inert gas method. SEM (JEOL-7001F) was used to examine the microstructures in weld metal. X-ray diffraction (XRD) patterns were collected using a Rigaku-binary diffractometer (Rigaku SmartLab) with a Cu target. Hardness (H) and elastic modulus (E), were determined by Hysitron Triboindenter TL-950 with Berkovich tip. A peak load of 8 mN with total 120 points were set. Fracture toughness (KC) was determined by MTS-G200 with Berkovich tip (peak load = 300 mN). KC was calculated by Eq. (1), which is most suitable for superficial cracks [5,8–11].
a1=2 E 2=3 P K C ¼ vv l H c3=2
ð1Þ
2. Experimental procedures
where P is the indentation load, a is the length from the center of the indentation to the corner, l is the length of crack from the indentation corner, c is the average crack length from the centre of the indent to the crack tip (c = l + a), and vD is an empirical constant which depends on the indenter geometry. For a Berkovich indenter, vD is found to be 0.016 [5]. This equation is most accurate for short cracks (c/a < 2.5).
A commercial low alloy steel plate (0.2 wt% C, 0.5 wt% Si, 1.2 wt % Mn, 0.35 wt% Cu) with the thickness of 2 mm was butt welded by
3. Results and discussion
⇑ Corresponding authors at: School of Materials and Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail addresses: [email protected] (Q. Chu), [email protected] (M. Zhang). https://doi.org/10.1016/j.matlet.2018.08.038 0167-577X/Ó 2018 Elsevier B.V. All rights reserved.
A global view of microstructure at Fe/Zr interface is shown in Fig. 1a. The resultant weld metal is consisted of three regions, marked as I, II and III in Fig. 1b-c. The chemical compositions are listed in Table 1. The coarse dendrite (region II) is primary
Q. Chu et al. / Materials Letters 231 (2018) 134–136
135
Fig. 1. (a)–(d) Microstructure at Fe/Zr interface; (e) Hardness distribution across Fe/Zr interface; (f) P-h curves; (g) XRD results. BM: base metal; WM: weld metal.
Table 1 Chemical compositions of typical phases in Zr weld metal (at%). Regions
Fe
Zr
Possible phases
Hardness/ GPa
Elastic modulus/ GPa
I II III
90.52 68.01 33.84
9.48 31.99 66.16
aFe + Fe2Zr
7.5 19.3 8.0
210.2 223.9 212.3
Fe2Zr FeZr2
consisted of Fe2Zr phase, while region I distributed among the dendrite structure is featured by fine lamellar structure (aFe + Fe2Zr, rich in Fe). The corresponding EBSD phase mapping confirms this characteristic distribution (Fig. 1d). The white dashed rectangle indicates the location of indentations in Fig. 1b. Fig. 1c shows the microstructure near the centre of the weld, where bright region (region III) is distributed among region II (Fe2Zr). Region III is
mainly consisted of FeZr2. The XRD pattern in Fig. 1g confirms the above phase constitutions. The global hardness distribution is presented in Fig. 1e. Fe2Zr intermetallics show higher hardness values (averaged hardness 19.3GPa). aFe + Fe2Zr and FeZr2 phases have an average hardness of 7.5 GPa and 8.0 GPa, respectively. The load-displacement (P-h) curve in aFe + Fe2Zr region is smooth whereas that in Fe2Zr region exhibits a significantly discontinuity at a load slightly below 3 mN during loading. Such feature is often referred as the ‘‘pop-in” event, signaling the onset of plasticity in the indented materials [12–14]. The inset in Fig. 1f reveals some pile-up around Fe2Zr impression. aFe+Fe2Zr compounds show no obvious ‘‘pop-in” events. The maximal indenter displacement (hmax) upon the peak load is much larger for aFe + Fe2Zr compounds (241 nm) and FeZr2 (225 nm) compared to that of Fe2Zr phase (168 nm). Fig. 2 shows the backscattered electron (BSE) micrograph of representative indentations with a peak load of 300 mN in Zr weld
Fig. 2. BSE images of indentations in (a)-(b) Fe2Zr region and (c) aFe + Fe2Zr region.
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Q. Chu et al. / Materials Letters 231 (2018) 134–136
Fig. 3. Schematic diagrams showing the progression of phase transformation in Zr weld.
metal. No obvious pip-up around the impression edges is observed. In this study, only indentations showing well-developed cracks and without chipping are used to calculate KC. Radial cracks which are the most common crack configuration for brittle materials are observed in Fe2Zr phase. These cracks initiate from one or two indentation corners and propagate along a straight-line path (indicated by white arrows), as presented in Fig. 2a and b. The crack length (c) is systematically recorded for every indentation. According to H, E, and c obtained by the nanoindentation experiments, KC is calculated by Eq. (1). A mean value and standard deviation of 2.52 ± 0.76 MPam1/2 is obtained for Fe2Zr intermetallics. The variation is probably due to residual stresses induced by welding thermal cycles. The averaged E/H ratio of Fe2Zr intermetallic phase is 11.5, which is in good agreement with the ones expected for ceramic-like materials (E/H 10 [15]). aFe + Fe2Zr region shows no obvious cracks under a peak load of 300 mN, shown in Fig. 2c. The mechanical properties are highly related to the microstructure type and distribution. Transformation of the microstructure in the molten varies over time. In order to further build the link between microstructure and mechanical properties in Zr weld metal, a schematic illustrating the phase transformation is developed in Fig. 3. Zr weld metal is composed of Zr filler and partial Fe BM. GB (grain boundary) wetting occurs between Fe BM (S, solid) and molten (L, liquid). The property of GBs in S + L region determines Fe BM/Zr WM interface strength. The contact angle (h) increases gradually with decreasing temperature [16,17]. Based on Fe-Zr phase diagram [2,3], proeutectoid Fe2Zr phase starts to precipitate in the liquid at the temperature below 1673 °C. The upper limit of Fe in Fe2Zr phase is around 73 at%. It is pointed out by Cahn [18] that, when the critical consolution point of two phases (Fe2Zr and L in this paper) is approached, GBs of one critical phase should be wetted by a layer of another critical phase. In the Fe2Zr + L twophase region, the GB transformation for the Fe2Zr GBs wetting by Fe-containing melt occurs. When the temperature drops below 1337 °C, fine lamellar structure forms by eutectic reaction (L M cFe + Fe2Zr). This characteristic morphology (also see Fig. 1b) is similar to that presented in [17]. Introduction of Fe2Zr phase into the soft metallic matrix (Fe) is an effective method to design high performance materials. Ultrafine eutectic-dendrite composites containing of Fe2Zr and aFe phases show a good combination of strength and ductility at room temperature [19]. The above hypothesis is further confirmed by nanoindentation tests, where no cracks are initiated in aFe + Fe2Zr region under the peak load. Fe2Zr has three polymorphs, e.g. cubic (C15), dihexagonal (C36) and hexagonal (C14). Among these, C15-Fe2Zr phase is the most stable structure under ambient conditions, while the others are stable at high temperatures [20,21]. The residual liquid is then rich in Zr element. The GB transformation for the Fe2Zr GBs wetting by Zr-containing melt also occurs.
At the temperature around 951 °C, FeZr2 forms by the peritectic reaction (Fe2Zr + L M FeZr2). FeZr2 remains stable at room temperature due to the high cooling rate during fusion welding. Similarly, FeZr2 also has two polymorphs (tetragonal C16 and cubic structure) and C16-FeZr2 phase has been confirmed as the most stable structure [22]. 4. Conclusions In this study, the correlation between microstructure and mechanical properties in Fe-Zr weld metal was investigated. The resultant weld metal was primary composed of Fe2Zr, aFe + Fe2Zr and FeZr2 phases. The fracture toughness was evaluated by nanoindentation at different zones of the Zr weld metal. For the Fe2Zr intermetallic phase, the estimated average hardness and fracture toughness are 19.3 GPa and 2.52 MPam1/2, respectively. No obvious cracks initiated from the fine eutectic compounds (aFe + Fe2Zr), implying a good combination of strength and ductility. Acknowledgements This work was supported by Key Laboratory Project of Shaanxi Provincial Education Department (15JS082) and Australian Research Council Discovery Project (DP180102003). The data reported in this paper were obtained at the CARF in QUT. References [1] J.Y. Chen, A. Khalifa, L.J. Xue, M. King, J. Mater. Process. Technol. 255 (2018) 184–194. [2] H. Okamoto, J. Phase Equilib. Diffus. 27 (5) (2006) 543–544. [3] C. Servant, C. Gueneau, I. Ansara, J. Alloy. Compd. 220 (1995) 19–26. [4] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. [5] N. Cuadrado, D. Casellas, M. Anglada, E. Jiménez-Piqué, Scr. Mater. 66 (2012) 670–673. [6] S.R. Jian, J.S. Jang, J. Alloys Compd. 482 (2009) 498–501. [7] C.Y. Yen, S.R. Jian, Y.S. Lai, P.F. Yang, Y.Y. Liao, J.S. Jang, T.H. Lin, J.Y. Juang, J. Alloy. Compd. 508 (2010) 523–527. [8] M.T. Laugier, J. Mater. Sci. Lett. 6 (1987) 897–900. [9] K. Niihara, J. Mater. Sci. Lett. 2 (1983) 221–223. [10] J.H. Lee, Y.F. Gao, K.E. Johanns, G.M. Pharr, Acta Mater. 60 (2012) 5448–5467. [11] J.I. Jang, G.M. Pharr, Acta Mater. 56 (2008) 4458–4469. [12] J.E. Bradby, J.S. Williams, J.W. Leung, J. Mater. Res. 16 (2001) 1500–1507. [13] R. Rao, J.E. Bradby, S. Ruffell, J.S. Williams, Microelectron. J. 38 (2007) 722–726. [14] S.R. Jian, Y.C. Tseng, I.J. Teng, J.Y. Juang, Materials 6 (2013) 4259–4267. [15] K.E. Johanns, J.H. Lee, Y.F. Gao, G.M. Pharr, Model. Simul. Mater. Sci. Eng. 22 (2014) 1–21. [16] B.B. Straumal, P. Zie˛ba, W. Gust, Grain boundary phase transitions and phase diagrams, Int. J. Inorg. Mater. 3 (2001) 1113–1115. [17] B.B. Straumal, A.S. Gornakova, O.A. Kogtenkova, S.G. Protasova, V.G. Sursaeva, B. Baretzky, Phys. Rev. B 78 (2008) 054202. [18] J.W. Cahn, J. Chem. Phys. 66 (1977) 3667–3672. [19] X.J. Jin, S.H. Chen, L.J. Rong, Mater. Sci. Eng. A 722 (2018) 173–181. [20] F. Stein, G. Sauthoff, M. Palm, J. Phase Equilib. 23 (2002) 480–494. [21] L.N. Guseva, T.O. Malakhova, Metallofiz. Kiev. 46 (1973) 111–113. [22] K. Ali, P.S. Ghosh, A. Arya, J. Alloys Compd. 723 (2017) 611–619.
Contents lists available at ScienceDirect
Materials Letters journal homepage: www.elsevier.com/locate/mlblue
Investigation of microstructure and fracture toughness of Fe-Zr welded joints Qiaoling Chu a,b,⇑, Min Zhang a,⇑, Jihong Li a, Fuxue Yan a, Cheng Yan b a b
School of Materials and Engineering, Xi’an University of Technology, Xi’an 710048, China School of Chemistry, Physics and Mechanical Engineering, Science and Engineering Faculty, Queensland University of Technology (QUT), Brisbane, QLD 4001, Australia
a r t i c l e
i n f o
Article history: Received 17 July 2018 Received in revised form 4 August 2018 Accepted 7 August 2018 Available online 7 August 2018 Keywords: Fracture toughness Intermetallics Nanoindentation Microstructure, Welding
a b s t r a c t In this work, the mechanical properties of Fe-Zr welded joints and its dependence with the microstructures were investigated using nanoindentation. In the weld metal, Fe2Zr intermetallic phase was observed and its average hardness and fracture toughness are 19.3 GPa and 2.52 MPam1/2, respectively. It was noticed that radial cracks initiated from the corners of the impressions. Fine lamellar structure (aFe + Fe2Zr) with an average hardness of 7.5 GPa were observed but no cracks were observed when subjected to a peak load of 300 mN. A simple model was developed to explain possible phase formation mechanism in the Fe-Zr system. Ó 2018 Elsevier B.V. All rights reserved.
1. Introduction Zirconium (Zr) alloys possess excellent corrosion resistance, mechanical properties and creep resistance [1]. Joining Zr with Fe to form dissimilar joints has both technical and economic advantages. According to Fe-Zr phase diagram, several intermetallics can be formed, including Fe2Zr, FeZr2 and FeZr3 [2,3]. These compounds may play a critical role in controlling the overall mechanical behavior of the welds. However, the fracture behavior of such Fe-Zr intermetallics has not been well understood, and a quantitative relationship between the microstructure and mechanical properties has yet been built. Recently, nanoindentation technique has been increasingly used to evaluate the mechanical behavior at nanoscale [4,5]. For the brittle materials, the indentation loads may cause cracks under the impressions, which can be used to evaluate the facture toughness [6,7]. In this work, phase formation and associated mechanical properties were investigated. A simplified model was also developed to explain possible phase formation mechanism in the Fe-Zr binary system.
pure Zr filler (0.05 wt% C, 0.2 wt% Fe). The joints were single pass welded using Tungsten inert gas method. SEM (JEOL-7001F) was used to examine the microstructures in weld metal. X-ray diffraction (XRD) patterns were collected using a Rigaku-binary diffractometer (Rigaku SmartLab) with a Cu target. Hardness (H) and elastic modulus (E), were determined by Hysitron Triboindenter TL-950 with Berkovich tip. A peak load of 8 mN with total 120 points were set. Fracture toughness (KC) was determined by MTS-G200 with Berkovich tip (peak load = 300 mN). KC was calculated by Eq. (1), which is most suitable for superficial cracks [5,8–11].
a1=2 E 2=3 P K C ¼ vv l H c3=2
ð1Þ
2. Experimental procedures
where P is the indentation load, a is the length from the center of the indentation to the corner, l is the length of crack from the indentation corner, c is the average crack length from the centre of the indent to the crack tip (c = l + a), and vD is an empirical constant which depends on the indenter geometry. For a Berkovich indenter, vD is found to be 0.016 [5]. This equation is most accurate for short cracks (c/a < 2.5).
A commercial low alloy steel plate (0.2 wt% C, 0.5 wt% Si, 1.2 wt % Mn, 0.35 wt% Cu) with the thickness of 2 mm was butt welded by
3. Results and discussion
⇑ Corresponding authors at: School of Materials and Engineering, Xi’an University of Technology, Xi’an 710048, China. E-mail addresses: [email protected] (Q. Chu), [email protected] (M. Zhang). https://doi.org/10.1016/j.matlet.2018.08.038 0167-577X/Ó 2018 Elsevier B.V. All rights reserved.
A global view of microstructure at Fe/Zr interface is shown in Fig. 1a. The resultant weld metal is consisted of three regions, marked as I, II and III in Fig. 1b-c. The chemical compositions are listed in Table 1. The coarse dendrite (region II) is primary
Q. Chu et al. / Materials Letters 231 (2018) 134–136
135
Fig. 1. (a)–(d) Microstructure at Fe/Zr interface; (e) Hardness distribution across Fe/Zr interface; (f) P-h curves; (g) XRD results. BM: base metal; WM: weld metal.
Table 1 Chemical compositions of typical phases in Zr weld metal (at%). Regions
Fe
Zr
Possible phases
Hardness/ GPa
Elastic modulus/ GPa
I II III
90.52 68.01 33.84
9.48 31.99 66.16
aFe + Fe2Zr
7.5 19.3 8.0
210.2 223.9 212.3
Fe2Zr FeZr2
consisted of Fe2Zr phase, while region I distributed among the dendrite structure is featured by fine lamellar structure (aFe + Fe2Zr, rich in Fe). The corresponding EBSD phase mapping confirms this characteristic distribution (Fig. 1d). The white dashed rectangle indicates the location of indentations in Fig. 1b. Fig. 1c shows the microstructure near the centre of the weld, where bright region (region III) is distributed among region II (Fe2Zr). Region III is
mainly consisted of FeZr2. The XRD pattern in Fig. 1g confirms the above phase constitutions. The global hardness distribution is presented in Fig. 1e. Fe2Zr intermetallics show higher hardness values (averaged hardness 19.3GPa). aFe + Fe2Zr and FeZr2 phases have an average hardness of 7.5 GPa and 8.0 GPa, respectively. The load-displacement (P-h) curve in aFe + Fe2Zr region is smooth whereas that in Fe2Zr region exhibits a significantly discontinuity at a load slightly below 3 mN during loading. Such feature is often referred as the ‘‘pop-in” event, signaling the onset of plasticity in the indented materials [12–14]. The inset in Fig. 1f reveals some pile-up around Fe2Zr impression. aFe+Fe2Zr compounds show no obvious ‘‘pop-in” events. The maximal indenter displacement (hmax) upon the peak load is much larger for aFe + Fe2Zr compounds (241 nm) and FeZr2 (225 nm) compared to that of Fe2Zr phase (168 nm). Fig. 2 shows the backscattered electron (BSE) micrograph of representative indentations with a peak load of 300 mN in Zr weld
Fig. 2. BSE images of indentations in (a)-(b) Fe2Zr region and (c) aFe + Fe2Zr region.
136
Q. Chu et al. / Materials Letters 231 (2018) 134–136
Fig. 3. Schematic diagrams showing the progression of phase transformation in Zr weld.
metal. No obvious pip-up around the impression edges is observed. In this study, only indentations showing well-developed cracks and without chipping are used to calculate KC. Radial cracks which are the most common crack configuration for brittle materials are observed in Fe2Zr phase. These cracks initiate from one or two indentation corners and propagate along a straight-line path (indicated by white arrows), as presented in Fig. 2a and b. The crack length (c) is systematically recorded for every indentation. According to H, E, and c obtained by the nanoindentation experiments, KC is calculated by Eq. (1). A mean value and standard deviation of 2.52 ± 0.76 MPam1/2 is obtained for Fe2Zr intermetallics. The variation is probably due to residual stresses induced by welding thermal cycles. The averaged E/H ratio of Fe2Zr intermetallic phase is 11.5, which is in good agreement with the ones expected for ceramic-like materials (E/H 10 [15]). aFe + Fe2Zr region shows no obvious cracks under a peak load of 300 mN, shown in Fig. 2c. The mechanical properties are highly related to the microstructure type and distribution. Transformation of the microstructure in the molten varies over time. In order to further build the link between microstructure and mechanical properties in Zr weld metal, a schematic illustrating the phase transformation is developed in Fig. 3. Zr weld metal is composed of Zr filler and partial Fe BM. GB (grain boundary) wetting occurs between Fe BM (S, solid) and molten (L, liquid). The property of GBs in S + L region determines Fe BM/Zr WM interface strength. The contact angle (h) increases gradually with decreasing temperature [16,17]. Based on Fe-Zr phase diagram [2,3], proeutectoid Fe2Zr phase starts to precipitate in the liquid at the temperature below 1673 °C. The upper limit of Fe in Fe2Zr phase is around 73 at%. It is pointed out by Cahn [18] that, when the critical consolution point of two phases (Fe2Zr and L in this paper) is approached, GBs of one critical phase should be wetted by a layer of another critical phase. In the Fe2Zr + L twophase region, the GB transformation for the Fe2Zr GBs wetting by Fe-containing melt occurs. When the temperature drops below 1337 °C, fine lamellar structure forms by eutectic reaction (L M cFe + Fe2Zr). This characteristic morphology (also see Fig. 1b) is similar to that presented in [17]. Introduction of Fe2Zr phase into the soft metallic matrix (Fe) is an effective method to design high performance materials. Ultrafine eutectic-dendrite composites containing of Fe2Zr and aFe phases show a good combination of strength and ductility at room temperature [19]. The above hypothesis is further confirmed by nanoindentation tests, where no cracks are initiated in aFe + Fe2Zr region under the peak load. Fe2Zr has three polymorphs, e.g. cubic (C15), dihexagonal (C36) and hexagonal (C14). Among these, C15-Fe2Zr phase is the most stable structure under ambient conditions, while the others are stable at high temperatures [20,21]. The residual liquid is then rich in Zr element. The GB transformation for the Fe2Zr GBs wetting by Zr-containing melt also occurs.
At the temperature around 951 °C, FeZr2 forms by the peritectic reaction (Fe2Zr + L M FeZr2). FeZr2 remains stable at room temperature due to the high cooling rate during fusion welding. Similarly, FeZr2 also has two polymorphs (tetragonal C16 and cubic structure) and C16-FeZr2 phase has been confirmed as the most stable structure [22]. 4. Conclusions In this study, the correlation between microstructure and mechanical properties in Fe-Zr weld metal was investigated. The resultant weld metal was primary composed of Fe2Zr, aFe + Fe2Zr and FeZr2 phases. The fracture toughness was evaluated by nanoindentation at different zones of the Zr weld metal. For the Fe2Zr intermetallic phase, the estimated average hardness and fracture toughness are 19.3 GPa and 2.52 MPam1/2, respectively. No obvious cracks initiated from the fine eutectic compounds (aFe + Fe2Zr), implying a good combination of strength and ductility. Acknowledgements This work was supported by Key Laboratory Project of Shaanxi Provincial Education Department (15JS082) and Australian Research Council Discovery Project (DP180102003). The data reported in this paper were obtained at the CARF in QUT. References [1] J.Y. Chen, A. Khalifa, L.J. Xue, M. King, J. Mater. Process. Technol. 255 (2018) 184–194. [2] H. Okamoto, J. Phase Equilib. Diffus. 27 (5) (2006) 543–544. [3] C. Servant, C. Gueneau, I. Ansara, J. Alloy. Compd. 220 (1995) 19–26. [4] W.C. Oliver, G.M. Pharr, J. Mater. Res. 7 (1992) 1564–1583. [5] N. Cuadrado, D. Casellas, M. Anglada, E. Jiménez-Piqué, Scr. Mater. 66 (2012) 670–673. [6] S.R. Jian, J.S. Jang, J. Alloys Compd. 482 (2009) 498–501. [7] C.Y. Yen, S.R. Jian, Y.S. Lai, P.F. Yang, Y.Y. Liao, J.S. Jang, T.H. Lin, J.Y. Juang, J. Alloy. Compd. 508 (2010) 523–527. [8] M.T. Laugier, J. Mater. Sci. Lett. 6 (1987) 897–900. [9] K. Niihara, J. Mater. Sci. Lett. 2 (1983) 221–223. [10] J.H. Lee, Y.F. Gao, K.E. Johanns, G.M. Pharr, Acta Mater. 60 (2012) 5448–5467. [11] J.I. Jang, G.M. Pharr, Acta Mater. 56 (2008) 4458–4469. [12] J.E. Bradby, J.S. Williams, J.W. Leung, J. Mater. Res. 16 (2001) 1500–1507. [13] R. Rao, J.E. Bradby, S. Ruffell, J.S. Williams, Microelectron. J. 38 (2007) 722–726. [14] S.R. Jian, Y.C. Tseng, I.J. Teng, J.Y. Juang, Materials 6 (2013) 4259–4267. [15] K.E. Johanns, J.H. Lee, Y.F. Gao, G.M. Pharr, Model. Simul. Mater. Sci. Eng. 22 (2014) 1–21. [16] B.B. Straumal, P. Zie˛ba, W. Gust, Grain boundary phase transitions and phase diagrams, Int. J. Inorg. Mater. 3 (2001) 1113–1115. [17] B.B. Straumal, A.S. Gornakova, O.A. Kogtenkova, S.G. Protasova, V.G. Sursaeva, B. Baretzky, Phys. Rev. B 78 (2008) 054202. [18] J.W. Cahn, J. Chem. Phys. 66 (1977) 3667–3672. [19] X.J. Jin, S.H. Chen, L.J. Rong, Mater. Sci. Eng. A 722 (2018) 173–181. [20] F. Stein, G. Sauthoff, M. Palm, J. Phase Equilib. 23 (2002) 480–494. [21] L.N. Guseva, T.O. Malakhova, Metallofiz. Kiev. 46 (1973) 111–113. [22] K. Ali, P.S. Ghosh, A. Arya, J. Alloys Compd. 723 (2017) 611–619.