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The influence of grain boundary angle on the hot cracking of single crystal superalloy DD6
Journal of Alloys and Compounds 676 (2016) 181e186
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
The influence of grain boundary angle on the hot cracking of single crystal superalloy DD6 P. Rong a, N. Wang a, *, L. Wang a, R.N. Yang b, W.J. Yao a a The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, School of Science, Northwestern Polytechnical University, Xi'an 710072, China b Guiyang AVIC Power Investment Casting Co., Ltd., Guiyang 550014, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 October 2015 Received in revised form 2 March 2016 Accepted 22 March 2016 Available online 23 March 2016
Grain boundary is found to be the most vulnerable place to produce hot cracking during casting and welding processes. Understanding the underlying mechanism of it is helpful to prevent the crack for the repair of aerospace and automotive parts. By producing bi-crystal with pure tilt grain boundary, the effect of boundary misorientation on hot cracking susceptibility was studied for Ni-based superalloy DD6. It is found that the crack takes place when the grain boundary angle is larger than 16 under the present processing conditions. The experimental results are discussed by the theory of coalescence at the last stage of solidification. Furthermore, the calculated temperature interval corresponding to the vulnerable regime in the intradendritic region is much smaller than the coalescence undercooling for the residual liquid film at the boundary, indicating that if the grain boundary exists, the key factor to the hot cracking is the liquid film but not those in the intradendritic region. © 2016 Elsevier B.V. All rights reserved.
Keywords: Grain boundary angle Hot cracking Laser welding Superalloys
1. Introduction Nickel-base single crystal (SX) superalloys have been extensively applied to manufacture the turbine blades because of its outstanding performance in the high temperature and high pressure environment [1]. However, under terrible working conditions for certain time, the tip defections, such as tip-cracking and tip deformations, could form. The blade will be abandoned in most situations when the defects appear. Due to high cost of the SX materials, effective repair techniques on the SX blade, such as the laser metal forming, have been developed [2e6]. One normal defect in the repair processes is the occurrence of solidification cracking, which is produced at the last stage of solidification and makes the repair invalid [7e9]. Experimentally, it was found that hot cracks, if appear, locate usually at grain boundaries (GBs). This indicates that GBs have an effect on solidification crack behaviors. Therefore, the study on that how the grain boundary influences the hot cracking is necessary. Some works have been performed on this aspect and a major theoretical breakthrough was made by Rappaz et al. [10]. In their
* Corresponding author. E-mail address: [email protected] (N. Wang). http://dx.doi.org/10.1016/j.jallcom.2016.03.164 0925-8388/© 2016 Elsevier B.V. All rights reserved.
theory, the situations of the coalescence of different dendrite grains changes with the mutual crystal orientation, which will lead to “attractive” or “repulsive” forces when the liquid film becomes very thin and dendrite branches join at a grain boundary [11,12]. A critical coalescence undercooling, DTb, for the liquid film for a pure material can be defined as [13]:
DTb ¼
ggb 2gsl 1 DSf d
(1)
where ggb is the grain boundary energy, gsl is the solid/liquid interfacial energy, DSf is the entropy of fusion per unit volume, and d is the thickness of diffuse interface. If ggb < 2gsl, DTb < 0. This corresponds to the case that dendrite arrays join as soon as their interfaces reach the interaction distance, d, and the boundary is referred to as “attractive”. When ggb ¼ 2gsl, coalescence occurs at zero undercooling. The boundary for this situation is referred to as “neutral”. If ggb > 2gsl, DTb > 0. The liquid film remains stable with respect to this coalescence undercooling which could result in the hot cracking. The boundary in this case is referred to as “repulsive”. It can be seen from Eq. (1) that, the key factor to control the remaining liquid film to appear or not at the last stage of solidification is the difference in the GB energy, ggb, and the solid/liquid interfacial energy, gsl. It is known that gsl varies slightly within a
182
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temperature range and is nearly constant. However, ggb is grain boundary misorientation dependent. The variation in the grain boundary angle, therefore, could influence the formation of hot cracking. This was proved experimentally by Wang et al. [14]. They changed the grain boundary energy by varying the misorientation angle and found that hot cracks appear once the angle exceeds a critical value. According to Eq. (1), if one knows the exact values of the GB energy and the solid/liquid interfacial energy at the fusion point for the coalescence of single crystal superalloy, the critical GB angle beyond which the boundary experiences “attractive to repulsive” could be predicted [13], and its effect on the hot cracking could be examined. However, this is not easy since the thermophysical parameters for the superalloys are rare. Therefore, the experimental investigations are necessary for the concerned materials to determine the limit of misorientation angle for hot cracking susceptibility. In this work, we intend to investigate the misorientationdependent hot cracking susceptibility of DD6 superalloy, which is one second-generation superalloy developed in China and contains high fraction of Re [15]. The composition of DD6 is given in Table 1. The critical GB angle for producing the crack was determined. The coalescence undercooling was further calculated to compare with the temperature interval corresponding to the vulnerable region where the liquid is difficult to feed. It is found that the coalescence undercooling is much larger than the latter temperature interval, suggesting that the key factor to the hot cracking is the liquid films at GBs but not those in the intradendritic region. 2. Experiments To study the effect of the GB misorientation on the hot cracking susceptibility, bi-crystals with symmetrical tilt boundaries were prepared by laser welding two single crystal plates, as shown in Fig. 1. The half-round plate specimens with thickness of 0.5 mm were cut from a single crystal ingot, which has a diameter of 15 mm. They are machined with their [100] crystallographic orientation having a desired angle a in (001) plane with the welding edge, as shown in Fig. 1(a). Two such plates were welded together to produce symmetrical tilt grain boundaries with a misorientation angle of q ¼ a þ a, Fig. 1(b). The convergent dendritic growth was selected in the experiments since the divergent growth always leads to the forming of equiaxed grains in the boundary region. Fig. 2 gives the schematic illustration of the laser welding
Table 1 Nominal composition of SX alloys DD6 in wt% [15]. Element
Cr
Co
Mo
W
Ta
Re
Nb
Al
Hf
Ni
DD6
4.3
9.0
2.0
8.0
7.5
2.0
0.5
5.6
0.1
Bal.
(001)
(001)
(001)
Fig. 2. Schematic illustration of laser welding configuration.
experiment, which shows the laser scanning direction on the single crystal specimens. The welding was performed using a 1 kW continuous wave Nd: YAG laser with the processing conditions: laser power is 300 W and scanning speed is 2.5 mm/s. To ensure epitactic columnar growth of the single crystal welds, welding was initiated in the gap at some distance (2 mm) from the edge. The samples were polished and then etched with a diluent royal solution (50% HCL, 25% HNO3, and 25% H2O in volume ratio). The microstructures and hot cracks were observed with optical and electron microscopes. The length of the solidification cracks, if any, was measured and used to evaluate the hot-cracking susceptibility. 3. Results and discussion 3.1. Misorientation-dependent hot cracking susceptibility Fig. 3 presents a series of experimental microstructures with misorientation angle from 0 to 28 . The thickness of specimens is small enough thus full penetration welds were obtained in the experiments after a short distance. It can be seen that bi-crystals with desired tilt boundaries were produced. Although a few stray grains appear at the two sides of the weld pool for certain GB angle, they do not grow to touch the boundary. Therefore, this does not influence our concern on the effect of misorientation on hot cracking susceptibility. In the case of q ¼ a ¼ 0 , no crack forms. With the increase of a, tilt grain boundaries with angle q ¼ 2a are produced. Over the range of 0 < q < 16 , there is still no crack, Figs. 3(b) and (b). It should be noted that a small crack appears at the initial part of weld. This kind of small crack, however, is caused by the very thin gap between the two single plates rather than the grain boundary. Once q exceeds a critical value of qc ¼ 16 , well-developed macroscopic crack formed. Two examples with misorientation angles of q ¼ 22 and 28 are given in Figs. 3(c) and (d). The crack developed and grew along the grain boundary to a certain length. The crack length was measured and plotted as a function of misorientation angle in Fig. 4. In the case of low angels (q ¼ a þ a < 16 ), short initial cracks with an average length of about 100 mm are produced due to the presence of the initial unwelded gap between two plates. When the misorientation angle reaches 16 , hot cracking appears steadily and the average length is around 600 um. With further increase of the grain boundary misorientation, the crack length has nearly no change. 3.2. Hot cracking mechanism
Fig. 1. Schematic illustrations of (a) the orientation of as machined half round plate and (b) bi-crystal configuration with angle q ¼ a þ a.
According to the coalescence theory proposed by the Rappaz et al. [10], with the increase of the misorientation angle, the increasing grain boundary energy leads to a transition of the boundary from an attractive (ggb < 2gsl) to a repulsive one (ggb > 2gsl). The transition occurs at an angle q corresponding to ggb ¼ 2gsl. Once the boundary becomes repulsive, a stable liquid film appears at the grain boundary. In this case, the solidification
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183
Fig. 3. Microstructure of the welded bicrystals.
For an anisotropic material with cubic symmetry and elastic constants C11, C12 and C44, the item G/(1 n) in the Eq. (2) is expressed as follows [17]:
1=2 G C44 1 2ð1 s100 Þ ¼ 1 n 1 s100 a 1 þ að1 2s100 Þ
Fig. 4. Crack length versus misorientation angles q.
crack could be produced at a critical misorientation angle since only one liquid film is residual and the strain is concentrated there. In order to show this underlying mechanism clearly, the undercooling of the liquid film should be determined. For this purpose, the GB energy, ggb, should be calculated firstly. Based on dislocation theory [16], the GB energy for a tilt grain boundary with small misorientation angle q can be expressed as:
ggb ¼
Gbq q 1 ln qm 4pð1 nÞ
(2)
where G is the shear modulus, b is the Burgers vector of the edge dislocations, n is the Poisson ratio, qm is the angle at which the GB energy reaches its maximum. Beyond qm, Eq. (2) does not apply, so that the maximum of the GB energy is assumed to stay constant at its maximum value if the grain angle exceeds qm.
(3)
where s100 is equal to C12/(C11 þ C12) and a ¼ 2C44/(C11 C12) is an anisotropy factor. Due to the lack of the data for the elastic constants for DD6 at high temperatures, the values at 973 K were used in the calculation [15]. qm is assumed to be 18 [18]. In this case, the maximum value of the grain boundary energy is determined to be 0.781 J/m2. Since there is no data of gsl for DD6, we use that for pure nickle, 0.307 J/m2 [19]. The parameters used in the calculations are listed in Table 2. The calculated relationships between the GB energy and undercooling versus the misorientation angle are presented in Fig. 5. With the increasing misorientation angle, ggb increases, as shown in Fig. 5(a). This leads to a transition of grain boundary from “attractive” to “repulsive” at a critical value q* ¼ 7.6 . For the attractive boundary in a pure material without microstructure and no microsegregation in a positive thermal gradient, it should solidify as soon as the two interfaces impinge. For the repulsive grain boundary, the coalescence will happen at an undercooling DTb(q). The larger the misorientation angle, the higher the value of DTb(q) and the lower the temperature for the coalescence. For an alloy, determining this temperature is more complex since the solid is formed of dendrite with complex morphology. In order to exploit the coalescence temperature in a qualitatively way, we assume the dendrites for attractive boundary become fully coherent at a temperature TaL which corresponds to a volume fraction fs ¼ 0.94 [20]. Taking this value as a reference for the repulsive grain boundary, the liquid film remains stable to a temperature at TaL DTb(q), and then the coalescence takes place. By the data for the misorientation angle dependent grain boundary energy, the value of DTb(q) for DD6 is calculated and given in Fig. 5(b). Corresponding to the value of qc ¼ 16 for the occurrence of the hot carcking, DTb(16 ) is 139 K. This indicates that at the position
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changed.
Table 2 The parameters used to calculate the undercooling. Physical parameters
Unit
Value
Solid/Liquid interfacial energy gsl Burgers vector b Elastic constants C11 at 700 C Elastic constants C12 at 700 C Elastic constants C44 at 700 C
J/m2 m Pa Pa Pa
0.307 [19] 3.578 1010 [17] 164 109 [15] 113 109 [15] 245 109 [15]
3.3. Hot cracking susceptibility in intradendritic region According to the liquid feeding theory, inside a single dendrite grain, hot cracking forms in the vulnerable region between the point where the liquid feeding becomes difficult (fs ~ 0.90) and the point where the continuous liquid films transforms into separated liquid drops (fs ~ 0.94) [20]. In this vulnerable region, since the solidification shrinkage cannot be compensated by the liquid feeding, hot cracking takes place. If grain boundary exists and when it becomes repulsive, the liquid film extends to a deeper position at lower temperature at the boundary region, where the strain is localized strongly since the solid skeleton has formed inside the grain. The only film staying in between the grains cannot resist the strain there and the boundary is thus more vulnerable to the hot cracking. If the liquid film in the intradendritic region inside the grain is longer, that means the liquid film in the grain boundary will be extended further, which will make the alloy more susceptible to the cracks. Therefore, the comparison of the temperature interval corresponding to the vulnerable length between fs ~0.90 and fs ~0.94 in the grain with the coalescence undercooling at the grain boundary is also helpful to understand the hot cracking susceptibility. Recently, Kou et al. considered the contribution of the vulnerable length of the intradendritic region1 to hot cracking inside the grain and proposed a simple criterion [21] on the basispof ffiffiffiffi RDG model [20]. Based on their criterion, the maximum dT=d fs was proposed as an for cracking susceptibility. The higher the ffi pffiffiffiindex value of dT=d fs , the less resistance to the cracking. The variation in fs with T characterizes the rate of the approaching velocity of the dendrite second arms to each other, namely, the distance pffiffiffibetween ffi the second arms of two adjacent dendrites. High dT=d fs results in a small distance for a certain volume fraction. This produces long liquid film along the interdendritic region. According to the HagenPoiseuille law [22], the volumetric flow rate of a liquid through a channel decreases with the channel length due to the resistance to flow caused by the viscosity pffiffiffiffi of liquid. Therefore, a superalloy with higher value of dT=d fs will pffiffiffiffibe more susceptible to hot cracking than one with lower dT=d fs . Kou's model has applied to analyze the cracking susceptibilities of different alloys and it is reliable [23]. In order to determine the temperature interval corresponding to the vulnerable length in intradendritic region of DD6, Kou's criterion was used for calculation. Assuming that there is no diffusion in solid phase, the relationship between T and fs can be determined by the Scheil equation [24]:
T ¼ Tm ðTm TL Þð1 fs Þk1 Fig. 5. The representations of the effect of misorientation angle on the coalescence temperature. (a) Grain boundary energy versus grain boundary angle, When q>q*, the grain boundary changes from an attractive to a repulsive one. (b) the coalescence temperature versus misorientation angle.
DTb(16 ),
corresponding to the strain rate or stress cannot be resisted due to the existence of the liquid film, and thus the hot cracking forms. One point which should be emphasized is that for the case of q* < q < qc, although the liquid film exists at the grain boundary, there is no hot crack. This suggests that the stress localized at the boundary region is not strong. Until the stress is strong enough at a low temperature when q is larger than qc, the crack appears. Note that if the stress distribution varies, the value of qc could also be
(4)
where Tm is the melting point of pure Ni, TL is the liquidus temperature, and k is the equilibrium coefficient. By differffi pffiffiffipartition entiating Eq. (4) with respect to fs , one obtains:
pffiffiffiffi dT pffiffiffiffi ¼ 2ð1 kÞðTm TL Þð1 fs Þk2 fs d fs
(5)
Within the vulnerable region of 0.9 < fs < 0.94, the temperature interval can be determined. This temperature interval can be
1 Although the author said he dealt with the situation at grain boundary, it is not the case. The liquid film he considered is in the intradendritic region since all the dendrites grow in the same orientation and they belong to a single grain.
P. Rong et al. / Journal of Alloys and Compounds 676 (2016) 181e186
compared with the coalescence undercooling to show which is more important for hot cracking: the intradendritic liquid film in the vulnerable region or the residual atpthe ffi pffiffiffifilm ffiffiffiffi grain boundary. The ffi pffiffiffirelationship pffiffiffiffi between dT=d fs and fs and that between T and fs dT=d fs for DD6 are calculated by Eqs. (4) and (5) and the results are given in Fig. 6, in which the calculated date for CMSX-4 and MC2 are also presented for comparison. The parameters used in the calculations are listed in Table 3. From Fig. 6(a), p one ffiffiffiffi can see that over the range of 0.90 < fs < 0.94, namely 0.949 < fs < 0.970, the ffiffiffi ffi p values of dT=d fs for the superalloys increases in sequence of DD6, MC2, and CMSX-4. Correspondingly, as marked in Fig. 6(b), the temperature intervals of these three alloys are: 10, 12, and 27 K, which also increase in the same sequence. This indicates that if there is no grain boundary, DD6 is the strongest one whereas CMSX4 is the weakest one to resist hot cracking. Although the difference in the temperature intervals for different alloys in interdendritic region exists, the coalescence undercooling at the grain boundary, as shown in Fig. 5(b), is much larger for DD6. For MC2, this trend is similar [14]. It indicates that the liquid film remaining in the boundary extends to a relatively lower temperature than the position where the solid skeleton forms inside dendrite grains. The localization of the strain at low
185
Table 3 The parameters used to calculate the hot cracking susceptibilities [25].
DD6 CMSX-4 MC2
T m, K
TL, K
T S, K
k
1726 1726 1726
1672 1669 1632
1615 1619 1596
0.81 0.64 0.845
temperature thus has a stronger effect on the cracking formation at grain boundary than inside the grains. This has been proved frequently in casting and laser welded procedures. The coalescence undercooling is relatively larger than the temperature interval corresponding to the vulnerable regime 0.9 < fs < 0.94, suggesting that once the grain boundary exists, the key factor to the hot cracking is the liquid film residual at the boundary, but not those in the intradendritic region. 4. Conclusions The grain boundary angle is a key factor to control the occurrence of hot-cracking at the last stage of solidification since a high misorientation angle results in the formation of stable liquid film at the boundary region. The higher the misorientation angle, the lower the temperature at which the liquid film extends. At a position with a critical temperature where the strain localizes, the hot cracking forms. This kind of misorientation angle dependent solidification cracking susceptibility was studied and the critical angle was found to be 16 for DD6. The coalescence undercooling of the dendritic grains are determined, which is much larger than the temperature interval corresponding to the vulnerable region inside the grain. This indicates that if the grain boundary exists, the key factor to the hot cracking is the liquid film at the boundary but not those in the intradendritic region. Acknowledgements This work was supported by the Aviation Science Foundation (Grant No. 2013ZF53080), the National Natural Science Foundation of China (Grant No. 51271149), and the Fund of the Innovation Base of Graduate Students of NPU. References
pffiffiffiffi pffiffiffiffi pffiffiffiffi Fig. 6.pThe ffiffiffiffi relationship pffiffiffiffi between dT=dpffiffiffifsffi and fs and that between T and fs . (a) dT=d fs versus fs and (b) T versus fs .
[1] R.C. Reed, The Superalloys: Fundamentals and Applications, 2006. Cambridge, New York. [2] M.B. Henderson, D. Arrell, R. Larsson, M. Heobel, G. Marchant, Nickel based superalloy welding practices for industrial gas turbine applications, Sci. Technol. Weld. Join. 9 (2004) 13e21. [3] S.S. Babu, S.A. David, J.W. Park, J.M. Vitek, Joining of nickel base superalloy single crystals, Sci. Technol. Weld. Join. 9 (2004) 1e12. [4] C. Churchman, E.A. Bonifaz, N.L. Richards, Comparison of single crystal ni based superalloy repair by gas tungsten arc and electron beam processes, Mater. Sci. Technol. 27 (2011) 811e817. [5] H.S. Wang, H.G. Chen, J.S.C. Jang, Microstructure evolution in Nd:YAG laserwelded (Zr53Cu30Ni9Al8)Si0.5 bulk metallic glass alloy, J. Alloys Compd. 495 (2010) 224e228. [6] H. Yan, A.H. Wang, K.D. Xu, W.Y. Wang, Z.W. Huang, Microstructure and interfacial evaluation of Co-based alloy coating on copper by pulsed Nd:YAG multilayer laser cladding, J. Alloys Compd. 505 (2010) 645e653. [7] S. Kou, Welding Metallurgy, Wiley, Toronto, 1987. [8] S.A. David, T. Debroy, Current Issues and problems in welding science, Science 257 (1992) 497e502. [9] J. Campbell, Castings, Butterworth-Heinemann, Oxford, 1991. [10] M. Rappaz, J.M. Drezet, M. Gremaud, A new hot-tearing criterion, Metall. Mater. Trans. A 30 (1999) 449e455. [11] D.P. Woodruff, The Solid-Liquid Interface, 1973. Cambridge London. [12] G.F. Bolling, On the average large-angle grain boundary, Acta Metall. 16 (1968) 1147e1157. [13] M. Rappaz, A. Jacot, W.J. Boettinger, Last stage solidification of alloys: a theoretical study of dendrite arm and grain coalescence, Metall. Mater. Trans. A 34 (2003) 467e479.
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[14] N. Wang, S. Mokadem, M. Rappaz, W. Kurz, Solidification cracking of superalloy single- and bi-crystals, Acta Mater 52 (2004) 3173e3182. [15] X.L. Yuan, China aeronautical Materials Handbook: Wrought Superalloy and Cast Superalloy, second ed., Standards Press of China, Beijing, 2001 (in Chinese). [16] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley/Interscience, New York, 1982. [17] W.T. Read, W. Shockley, Dislocation models of crystal grain boundaries, Phys. Rev. 78 (1950) 275e289. [18] G. Hasso, C. Goux, Interfacial energies of tilt boundaries in aluminium: experimental and theoretical determination, Scripta Met. 5 (1972) 889e894. [19] N. Eustathopoulos, Energetics of solid/liquid interfaces of metals and alloys, Int. Met. Rev. 28 (1983) 189e210.
[20] M. Rappaz, J.M. Drezet, M. Gremaud, A new hot-tearing criterion, Metall. Mater. Trans. A 30 (1999) 449e455. [21] S. Kou, A criterion for cracking during solidification, Acta Mater 88 (2015) 366e374. [22] S. Kou, Transport Phenomena and Materials Processing, Wiley, Hoboken, 1996. [23] J.W. Liu, S. Kou, Effect of diffusion on susceptibility to cracking during solidification, Acta Mater 100 (2015) 359e368. [24] W. Kurz, D.J. Fisher, Fundamentals of Solidification, Trans. Tech. Publications, Switzerland, 1981. [25] S. Mokadem, Epitaxial Laser Treatment of Single Crystal Nickel-base Superalloys (Ph D thesis (No. 3127)), EPFL, 2004.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
The influence of grain boundary angle on the hot cracking of single crystal superalloy DD6 P. Rong a, N. Wang a, *, L. Wang a, R.N. Yang b, W.J. Yao a a The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education, School of Science, Northwestern Polytechnical University, Xi'an 710072, China b Guiyang AVIC Power Investment Casting Co., Ltd., Guiyang 550014, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 25 October 2015 Received in revised form 2 March 2016 Accepted 22 March 2016 Available online 23 March 2016
Grain boundary is found to be the most vulnerable place to produce hot cracking during casting and welding processes. Understanding the underlying mechanism of it is helpful to prevent the crack for the repair of aerospace and automotive parts. By producing bi-crystal with pure tilt grain boundary, the effect of boundary misorientation on hot cracking susceptibility was studied for Ni-based superalloy DD6. It is found that the crack takes place when the grain boundary angle is larger than 16 under the present processing conditions. The experimental results are discussed by the theory of coalescence at the last stage of solidification. Furthermore, the calculated temperature interval corresponding to the vulnerable regime in the intradendritic region is much smaller than the coalescence undercooling for the residual liquid film at the boundary, indicating that if the grain boundary exists, the key factor to the hot cracking is the liquid film but not those in the intradendritic region. © 2016 Elsevier B.V. All rights reserved.
Keywords: Grain boundary angle Hot cracking Laser welding Superalloys
1. Introduction Nickel-base single crystal (SX) superalloys have been extensively applied to manufacture the turbine blades because of its outstanding performance in the high temperature and high pressure environment [1]. However, under terrible working conditions for certain time, the tip defections, such as tip-cracking and tip deformations, could form. The blade will be abandoned in most situations when the defects appear. Due to high cost of the SX materials, effective repair techniques on the SX blade, such as the laser metal forming, have been developed [2e6]. One normal defect in the repair processes is the occurrence of solidification cracking, which is produced at the last stage of solidification and makes the repair invalid [7e9]. Experimentally, it was found that hot cracks, if appear, locate usually at grain boundaries (GBs). This indicates that GBs have an effect on solidification crack behaviors. Therefore, the study on that how the grain boundary influences the hot cracking is necessary. Some works have been performed on this aspect and a major theoretical breakthrough was made by Rappaz et al. [10]. In their
* Corresponding author. E-mail address: [email protected] (N. Wang). http://dx.doi.org/10.1016/j.jallcom.2016.03.164 0925-8388/© 2016 Elsevier B.V. All rights reserved.
theory, the situations of the coalescence of different dendrite grains changes with the mutual crystal orientation, which will lead to “attractive” or “repulsive” forces when the liquid film becomes very thin and dendrite branches join at a grain boundary [11,12]. A critical coalescence undercooling, DTb, for the liquid film for a pure material can be defined as [13]:
DTb ¼
ggb 2gsl 1 DSf d
(1)
where ggb is the grain boundary energy, gsl is the solid/liquid interfacial energy, DSf is the entropy of fusion per unit volume, and d is the thickness of diffuse interface. If ggb < 2gsl, DTb < 0. This corresponds to the case that dendrite arrays join as soon as their interfaces reach the interaction distance, d, and the boundary is referred to as “attractive”. When ggb ¼ 2gsl, coalescence occurs at zero undercooling. The boundary for this situation is referred to as “neutral”. If ggb > 2gsl, DTb > 0. The liquid film remains stable with respect to this coalescence undercooling which could result in the hot cracking. The boundary in this case is referred to as “repulsive”. It can be seen from Eq. (1) that, the key factor to control the remaining liquid film to appear or not at the last stage of solidification is the difference in the GB energy, ggb, and the solid/liquid interfacial energy, gsl. It is known that gsl varies slightly within a
182
P. Rong et al. / Journal of Alloys and Compounds 676 (2016) 181e186
temperature range and is nearly constant. However, ggb is grain boundary misorientation dependent. The variation in the grain boundary angle, therefore, could influence the formation of hot cracking. This was proved experimentally by Wang et al. [14]. They changed the grain boundary energy by varying the misorientation angle and found that hot cracks appear once the angle exceeds a critical value. According to Eq. (1), if one knows the exact values of the GB energy and the solid/liquid interfacial energy at the fusion point for the coalescence of single crystal superalloy, the critical GB angle beyond which the boundary experiences “attractive to repulsive” could be predicted [13], and its effect on the hot cracking could be examined. However, this is not easy since the thermophysical parameters for the superalloys are rare. Therefore, the experimental investigations are necessary for the concerned materials to determine the limit of misorientation angle for hot cracking susceptibility. In this work, we intend to investigate the misorientationdependent hot cracking susceptibility of DD6 superalloy, which is one second-generation superalloy developed in China and contains high fraction of Re [15]. The composition of DD6 is given in Table 1. The critical GB angle for producing the crack was determined. The coalescence undercooling was further calculated to compare with the temperature interval corresponding to the vulnerable region where the liquid is difficult to feed. It is found that the coalescence undercooling is much larger than the latter temperature interval, suggesting that the key factor to the hot cracking is the liquid films at GBs but not those in the intradendritic region. 2. Experiments To study the effect of the GB misorientation on the hot cracking susceptibility, bi-crystals with symmetrical tilt boundaries were prepared by laser welding two single crystal plates, as shown in Fig. 1. The half-round plate specimens with thickness of 0.5 mm were cut from a single crystal ingot, which has a diameter of 15 mm. They are machined with their [100] crystallographic orientation having a desired angle a in (001) plane with the welding edge, as shown in Fig. 1(a). Two such plates were welded together to produce symmetrical tilt grain boundaries with a misorientation angle of q ¼ a þ a, Fig. 1(b). The convergent dendritic growth was selected in the experiments since the divergent growth always leads to the forming of equiaxed grains in the boundary region. Fig. 2 gives the schematic illustration of the laser welding
Table 1 Nominal composition of SX alloys DD6 in wt% [15]. Element
Cr
Co
Mo
W
Ta
Re
Nb
Al
Hf
Ni
DD6
4.3
9.0
2.0
8.0
7.5
2.0
0.5
5.6
0.1
Bal.
(001)
(001)
(001)
Fig. 2. Schematic illustration of laser welding configuration.
experiment, which shows the laser scanning direction on the single crystal specimens. The welding was performed using a 1 kW continuous wave Nd: YAG laser with the processing conditions: laser power is 300 W and scanning speed is 2.5 mm/s. To ensure epitactic columnar growth of the single crystal welds, welding was initiated in the gap at some distance (2 mm) from the edge. The samples were polished and then etched with a diluent royal solution (50% HCL, 25% HNO3, and 25% H2O in volume ratio). The microstructures and hot cracks were observed with optical and electron microscopes. The length of the solidification cracks, if any, was measured and used to evaluate the hot-cracking susceptibility. 3. Results and discussion 3.1. Misorientation-dependent hot cracking susceptibility Fig. 3 presents a series of experimental microstructures with misorientation angle from 0 to 28 . The thickness of specimens is small enough thus full penetration welds were obtained in the experiments after a short distance. It can be seen that bi-crystals with desired tilt boundaries were produced. Although a few stray grains appear at the two sides of the weld pool for certain GB angle, they do not grow to touch the boundary. Therefore, this does not influence our concern on the effect of misorientation on hot cracking susceptibility. In the case of q ¼ a ¼ 0 , no crack forms. With the increase of a, tilt grain boundaries with angle q ¼ 2a are produced. Over the range of 0 < q < 16 , there is still no crack, Figs. 3(b) and (b). It should be noted that a small crack appears at the initial part of weld. This kind of small crack, however, is caused by the very thin gap between the two single plates rather than the grain boundary. Once q exceeds a critical value of qc ¼ 16 , well-developed macroscopic crack formed. Two examples with misorientation angles of q ¼ 22 and 28 are given in Figs. 3(c) and (d). The crack developed and grew along the grain boundary to a certain length. The crack length was measured and plotted as a function of misorientation angle in Fig. 4. In the case of low angels (q ¼ a þ a < 16 ), short initial cracks with an average length of about 100 mm are produced due to the presence of the initial unwelded gap between two plates. When the misorientation angle reaches 16 , hot cracking appears steadily and the average length is around 600 um. With further increase of the grain boundary misorientation, the crack length has nearly no change. 3.2. Hot cracking mechanism
Fig. 1. Schematic illustrations of (a) the orientation of as machined half round plate and (b) bi-crystal configuration with angle q ¼ a þ a.
According to the coalescence theory proposed by the Rappaz et al. [10], with the increase of the misorientation angle, the increasing grain boundary energy leads to a transition of the boundary from an attractive (ggb < 2gsl) to a repulsive one (ggb > 2gsl). The transition occurs at an angle q corresponding to ggb ¼ 2gsl. Once the boundary becomes repulsive, a stable liquid film appears at the grain boundary. In this case, the solidification
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183
Fig. 3. Microstructure of the welded bicrystals.
For an anisotropic material with cubic symmetry and elastic constants C11, C12 and C44, the item G/(1 n) in the Eq. (2) is expressed as follows [17]:
1=2 G C44 1 2ð1 s100 Þ ¼ 1 n 1 s100 a 1 þ að1 2s100 Þ
Fig. 4. Crack length versus misorientation angles q.
crack could be produced at a critical misorientation angle since only one liquid film is residual and the strain is concentrated there. In order to show this underlying mechanism clearly, the undercooling of the liquid film should be determined. For this purpose, the GB energy, ggb, should be calculated firstly. Based on dislocation theory [16], the GB energy for a tilt grain boundary with small misorientation angle q can be expressed as:
ggb ¼
Gbq q 1 ln qm 4pð1 nÞ
(2)
where G is the shear modulus, b is the Burgers vector of the edge dislocations, n is the Poisson ratio, qm is the angle at which the GB energy reaches its maximum. Beyond qm, Eq. (2) does not apply, so that the maximum of the GB energy is assumed to stay constant at its maximum value if the grain angle exceeds qm.
(3)
where s100 is equal to C12/(C11 þ C12) and a ¼ 2C44/(C11 C12) is an anisotropy factor. Due to the lack of the data for the elastic constants for DD6 at high temperatures, the values at 973 K were used in the calculation [15]. qm is assumed to be 18 [18]. In this case, the maximum value of the grain boundary energy is determined to be 0.781 J/m2. Since there is no data of gsl for DD6, we use that for pure nickle, 0.307 J/m2 [19]. The parameters used in the calculations are listed in Table 2. The calculated relationships between the GB energy and undercooling versus the misorientation angle are presented in Fig. 5. With the increasing misorientation angle, ggb increases, as shown in Fig. 5(a). This leads to a transition of grain boundary from “attractive” to “repulsive” at a critical value q* ¼ 7.6 . For the attractive boundary in a pure material without microstructure and no microsegregation in a positive thermal gradient, it should solidify as soon as the two interfaces impinge. For the repulsive grain boundary, the coalescence will happen at an undercooling DTb(q). The larger the misorientation angle, the higher the value of DTb(q) and the lower the temperature for the coalescence. For an alloy, determining this temperature is more complex since the solid is formed of dendrite with complex morphology. In order to exploit the coalescence temperature in a qualitatively way, we assume the dendrites for attractive boundary become fully coherent at a temperature TaL which corresponds to a volume fraction fs ¼ 0.94 [20]. Taking this value as a reference for the repulsive grain boundary, the liquid film remains stable to a temperature at TaL DTb(q), and then the coalescence takes place. By the data for the misorientation angle dependent grain boundary energy, the value of DTb(q) for DD6 is calculated and given in Fig. 5(b). Corresponding to the value of qc ¼ 16 for the occurrence of the hot carcking, DTb(16 ) is 139 K. This indicates that at the position
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changed.
Table 2 The parameters used to calculate the undercooling. Physical parameters
Unit
Value
Solid/Liquid interfacial energy gsl Burgers vector b Elastic constants C11 at 700 C Elastic constants C12 at 700 C Elastic constants C44 at 700 C
J/m2 m Pa Pa Pa
0.307 [19] 3.578 1010 [17] 164 109 [15] 113 109 [15] 245 109 [15]
3.3. Hot cracking susceptibility in intradendritic region According to the liquid feeding theory, inside a single dendrite grain, hot cracking forms in the vulnerable region between the point where the liquid feeding becomes difficult (fs ~ 0.90) and the point where the continuous liquid films transforms into separated liquid drops (fs ~ 0.94) [20]. In this vulnerable region, since the solidification shrinkage cannot be compensated by the liquid feeding, hot cracking takes place. If grain boundary exists and when it becomes repulsive, the liquid film extends to a deeper position at lower temperature at the boundary region, where the strain is localized strongly since the solid skeleton has formed inside the grain. The only film staying in between the grains cannot resist the strain there and the boundary is thus more vulnerable to the hot cracking. If the liquid film in the intradendritic region inside the grain is longer, that means the liquid film in the grain boundary will be extended further, which will make the alloy more susceptible to the cracks. Therefore, the comparison of the temperature interval corresponding to the vulnerable length between fs ~0.90 and fs ~0.94 in the grain with the coalescence undercooling at the grain boundary is also helpful to understand the hot cracking susceptibility. Recently, Kou et al. considered the contribution of the vulnerable length of the intradendritic region1 to hot cracking inside the grain and proposed a simple criterion [21] on the basispof ffiffiffiffi RDG model [20]. Based on their criterion, the maximum dT=d fs was proposed as an for cracking susceptibility. The higher the ffi pffiffiffiindex value of dT=d fs , the less resistance to the cracking. The variation in fs with T characterizes the rate of the approaching velocity of the dendrite second arms to each other, namely, the distance pffiffiffibetween ffi the second arms of two adjacent dendrites. High dT=d fs results in a small distance for a certain volume fraction. This produces long liquid film along the interdendritic region. According to the HagenPoiseuille law [22], the volumetric flow rate of a liquid through a channel decreases with the channel length due to the resistance to flow caused by the viscosity pffiffiffiffi of liquid. Therefore, a superalloy with higher value of dT=d fs will pffiffiffiffibe more susceptible to hot cracking than one with lower dT=d fs . Kou's model has applied to analyze the cracking susceptibilities of different alloys and it is reliable [23]. In order to determine the temperature interval corresponding to the vulnerable length in intradendritic region of DD6, Kou's criterion was used for calculation. Assuming that there is no diffusion in solid phase, the relationship between T and fs can be determined by the Scheil equation [24]:
T ¼ Tm ðTm TL Þð1 fs Þk1 Fig. 5. The representations of the effect of misorientation angle on the coalescence temperature. (a) Grain boundary energy versus grain boundary angle, When q>q*, the grain boundary changes from an attractive to a repulsive one. (b) the coalescence temperature versus misorientation angle.
DTb(16 ),
corresponding to the strain rate or stress cannot be resisted due to the existence of the liquid film, and thus the hot cracking forms. One point which should be emphasized is that for the case of q* < q < qc, although the liquid film exists at the grain boundary, there is no hot crack. This suggests that the stress localized at the boundary region is not strong. Until the stress is strong enough at a low temperature when q is larger than qc, the crack appears. Note that if the stress distribution varies, the value of qc could also be
(4)
where Tm is the melting point of pure Ni, TL is the liquidus temperature, and k is the equilibrium coefficient. By differffi pffiffiffipartition entiating Eq. (4) with respect to fs , one obtains:
pffiffiffiffi dT pffiffiffiffi ¼ 2ð1 kÞðTm TL Þð1 fs Þk2 fs d fs
(5)
Within the vulnerable region of 0.9 < fs < 0.94, the temperature interval can be determined. This temperature interval can be
1 Although the author said he dealt with the situation at grain boundary, it is not the case. The liquid film he considered is in the intradendritic region since all the dendrites grow in the same orientation and they belong to a single grain.
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compared with the coalescence undercooling to show which is more important for hot cracking: the intradendritic liquid film in the vulnerable region or the residual atpthe ffi pffiffiffifilm ffiffiffiffi grain boundary. The ffi pffiffiffirelationship pffiffiffiffi between dT=d fs and fs and that between T and fs dT=d fs for DD6 are calculated by Eqs. (4) and (5) and the results are given in Fig. 6, in which the calculated date for CMSX-4 and MC2 are also presented for comparison. The parameters used in the calculations are listed in Table 3. From Fig. 6(a), p one ffiffiffiffi can see that over the range of 0.90 < fs < 0.94, namely 0.949 < fs < 0.970, the ffiffiffi ffi p values of dT=d fs for the superalloys increases in sequence of DD6, MC2, and CMSX-4. Correspondingly, as marked in Fig. 6(b), the temperature intervals of these three alloys are: 10, 12, and 27 K, which also increase in the same sequence. This indicates that if there is no grain boundary, DD6 is the strongest one whereas CMSX4 is the weakest one to resist hot cracking. Although the difference in the temperature intervals for different alloys in interdendritic region exists, the coalescence undercooling at the grain boundary, as shown in Fig. 5(b), is much larger for DD6. For MC2, this trend is similar [14]. It indicates that the liquid film remaining in the boundary extends to a relatively lower temperature than the position where the solid skeleton forms inside dendrite grains. The localization of the strain at low
185
Table 3 The parameters used to calculate the hot cracking susceptibilities [25].
DD6 CMSX-4 MC2
T m, K
TL, K
T S, K
k
1726 1726 1726
1672 1669 1632
1615 1619 1596
0.81 0.64 0.845
temperature thus has a stronger effect on the cracking formation at grain boundary than inside the grains. This has been proved frequently in casting and laser welded procedures. The coalescence undercooling is relatively larger than the temperature interval corresponding to the vulnerable regime 0.9 < fs < 0.94, suggesting that once the grain boundary exists, the key factor to the hot cracking is the liquid film residual at the boundary, but not those in the intradendritic region. 4. Conclusions The grain boundary angle is a key factor to control the occurrence of hot-cracking at the last stage of solidification since a high misorientation angle results in the formation of stable liquid film at the boundary region. The higher the misorientation angle, the lower the temperature at which the liquid film extends. At a position with a critical temperature where the strain localizes, the hot cracking forms. This kind of misorientation angle dependent solidification cracking susceptibility was studied and the critical angle was found to be 16 for DD6. The coalescence undercooling of the dendritic grains are determined, which is much larger than the temperature interval corresponding to the vulnerable region inside the grain. This indicates that if the grain boundary exists, the key factor to the hot cracking is the liquid film at the boundary but not those in the intradendritic region. Acknowledgements This work was supported by the Aviation Science Foundation (Grant No. 2013ZF53080), the National Natural Science Foundation of China (Grant No. 51271149), and the Fund of the Innovation Base of Graduate Students of NPU. References
pffiffiffiffi pffiffiffiffi pffiffiffiffi Fig. 6.pThe ffiffiffiffi relationship pffiffiffiffi between dT=dpffiffiffifsffi and fs and that between T and fs . (a) dT=d fs versus fs and (b) T versus fs .
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