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Stage I and II behaviors of delayed hydride cracking velocity in zirconium alloys
Journal of Alloys and Compounds 453 (2008) 210–214
Stage I and II behaviors of delayed hydride cracking velocity in zirconium alloys Young Suk Kim ∗ , Soon Sam Park 1 Zirconium Team, Korea Atomic Energy Research Institute, 150 Dukjin-dong, Yuseong, Daejeon 305-353, Republic of Korea Received 4 November 2006; received in revised form 29 November 2006; accepted 29 November 2006 Available online 2 January 2007
Abstract Delayed hydride cracking (DHC) tests were conducted on Zr–2.5Nb compact tension (CT) specimens with 60–80 ppm H at temperatures ranging from 160 to 280 ◦ C in the load increasing mode where the applied stress intensity factor, KI was increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 until a crack grew. Critical hydride lengths, lc , corresponding to the spacing of the striation lines, were determined with the applied stress intensity factor, KI from the fracture surfaces of the Zr–2.5Nb CT specimens. The lc was the largest at as low a KI as just above KIH in Stage I and leveled off to 30 m at a larger KI of above 9 MPa m−1/2 especially at 250 ◦ C, corresponding to Stage II. This finding was also observed at all the investigated temperatures. Since DHCV is inversely governed by lc according to Kim’s DHC model, it is concluded that the KI dependency of DHCV is caused by the KI dependency of lc . The increased lc in Stage I is suggested to arise from the creep effect on the increased KIH that is experimentally supported by Sagat’s results. The rationale for this suggestion is provided using Kim’s hypothesis that cracking of hydrides occurs by their interaction with twins. © 2006 Elsevier B.V. All rights reserved. Keywords: Zirconium; Delayed hydride cracking; Hydride; Striation
1. Introduction One of the unique features of cracking of zirconium alloys by delayed hydride cracking (DHC) is that there are three stages of a crack growth rate with the applied stress intensity factor or KI . For Stage I, the crack growth rate or DHC velocity (DHCV) sensitively changes at a small KI just above KIH under which the crack cannot grow. For Stage II, DHCV becomes constant independent of KI when it becomes considerably larger than KIH and for Stage III, it abruptly increases, leading to an unstable fracture when KI exceeds KIC as shown in Fig. 1. It should be noted that this cracking mechanism applies to stress corrosion cracking and hydrogen induced cracking of steels and other metals [1]. Dutton et al. suggested that at low KI as with Stage I, the hydride could grow in excess of a small plastic zone [2,3]. According to Dutton’s hypothesis [2], part of the hydride would be exposed to the elastic stress field of a crack ahead of the plastic ∗
Tel.: +82 42 868 2359; fax: +82 42 868 8346. E-mail address: [email protected] (Y.S. Kim). 1 Present address: InterPower Engineering & Consulting Co. Ltd., Zip code 137-130, 4th floor, Namgoong Bldg. 90-8, Yangjae-Dong, Seocho-ku, Seoul, Korea. 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.197
zone, causing the local hydrostatic stress at the hydride tip to sensitively change with KI . Since a hydrostatic stress is assumed to be a driving force for diffusion growth of the hydride, it accounts for a rapid increase in the crack growth rate with KI . Dutton et al. also suggested that at large KI as with Stage II, a large hydride could grow within a larger plastic zone with a lesser dependency of the hydrostatic stress with KI , leading the crack growth rate to have a lesser dependency on KI when compared to that in Stage I. It should be noted that Dutton’s DHC model [2,3] has made two unrealistic assumptions: a hydride growth in an elastic field of the zirconium matrix and an autocatalytic precipitation of hydrides upon hydrogen entering into the plastic zone even in an isothermal condition. The hydride growth in the elastic zone as assumed by Dutton et al [2,3] contradicts Westlake’s observation [4] where an applied stress less than the yield strength had no effect on the cooling soluvs but a 5% plastic strain only raised the cooling solvus temperature by 10 K in NbH. Contrary to Dutton’s assumption, precipitation of hydrides cannot occur in an isothermal condition [5] but it can do in a thermal cycle with some undercooling [6–8]. Yan and Eadie [9] also suggested a hypothesis to explain the Stage I and II behaviors of DHCV with KI under the same assumption as Dutton’s. Using the experimentally measured
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Fig. 1. Schematic diagram illustrating the three stages of delayed hydride cracking velocity when plotted as a function of the applied stress intensity factors.
critical hydride length, lc over which hydrides fractured at different KI , they calculated the time, tc for a hydride to grow to that critical hydride length at a fixed KI with Dutton’s assumption that the hydrostatic stress is the driving force for diffusion growth of a hydride. Then, the DHCV dependency of KI was obtained by plotting the velocity defined as lc over tc at different KI . However, this model has some imperfections because, first, hydrides cannot precipitate in an isothermal condition by a difference in the hydrostatic stress [10,11], second, the velocity defined as lc over tc by their definition is an instantaneous DHCV, corresponding to the first stage where the DHCV sensitively changes with KI , not the DHCV in the second stage. The weakest point of all the previous DHC models is that they failed to provide a feasible explanation for the flat crack growth rate in zirconium alloys independent of KI at the second stage. This failure results from their assumption that the hydrostatic stress is the driving force for diffusion of hydrogen towards the crack with a higher tensile stress. With Kim’s DHC model [12–14] that a difference in hydrogen concentration or C due to stress-induced precipitation of hydrides at the crack tip is the driving force for DHC, a constant DHCV in zirconium alloys independent of KI can be understood. When the applied KI is large enough to cause stress-induced precipitation [12,15–17], the crack tip has a decreased hydrogen concentration to the terminal solid solubility for dissolution of hydrogen (TSSD) (point C in Fig. 2) when compared to the bulk region of the supersaturated hydrogen concentration (point B in Fig. 2). Thus, C corresponding to the distance BC as shown in Fig. 2 is created between the crack tip and the bulk region, which is the driving force for DHC. This leads DHCV to depend, not on KI but on C between the crack tip and the bulk region as suggested by Kim’s DHC model [12–14]. Though Kim’s DHC model can account for the flat DHCV independent of KI in the second stage as shown in Fig. 1, it has yet to explain a KI dependency of DHCV and lc in the first stage. In essence, all the DHC models proposed to date failed to provide a feasible rationale of why the critical hydride length, lc and DHCV in zirconium alloys are affected by an applied KI , which is the aim of this study. To this end, we conducted DHC tests to determine the threshold stress intensity factor, KIH for the onset of delayed hydride cracking in a cold-worked Zr–2.5Nb tube in the load increasing mode.
Fig. 2. (a) The solvus lines of hydrogen during a thermal cycle to which the Zr–2.5Nb with 60 ppm H is subjected in the DHC tests. The driving force for DHC is a difference in the hydrogen concentration or C accompanied by nucleation of the hydrides at the crack tip under a tensile stress, which corresponds to 29 ppm H at 250 ◦ C, equal to the distance BC.
2. Experimental procedures 2.1. Specimen preparation Seventeen millimeter compact tension specimens shown in Fig. 3a were used to determine the KIH in the axial direction of a cold worked and stress relieved Zr–2.5Nb pressure tube with a strong tangential texture with most of
Fig. 3. (a) Schematic drawing of the curved compact tension specimens and (b) thermal cycle treatments applied for determining the threshold stress intensity factor, KIH for the onset of delayed hydride cracking in CANDU Zr–2.5Nb tube.
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the (0 0 0 1) basal poles oriented towards the tangential direction [18]. Hydrogen of 60–100 ppm was charged electrolytically into the specimen to form a thick hydride layer on the surface followed by an annealing in a salt bath which can control the specimen temperature to within ±0.5 ◦ C. More details of the hydrogen charging procedure are reported elsewhere [19]. The hydrogen content of the specimen was obtained by averaging five different values measured with a LECO RH 404 analyzer. A pre-fatigue crack of 1.7 mm was introduced using an Instron 8501 to have a ratio of the fatigue length and the CT length (=a0 /W) equal to 0.5. The applied stress intensity factor or KI was 15 MPa m−1/2 at the initiating stage of the pre-fatigue crack and it decreased to 7 MPa m−1/2 after the fatigue crack grew to 1.7 mm.
2.2. Delayed hydride cracking tests Compact tension (CT) specimens were subjected to a constant load in a creep machine while the initiation of a crack was monitored by a dc potential drop method. Fig. 3b shows a typical thermal cycle to which the CT specimens were subjected in the DHC tests. The CT specimens were heated to a peak temperature by 0.5–1 ◦ C/min, held there for 1 h and cooled down to the test temperature followed by applying a load from 30 min after reaching the test temperature. The peak temperature was set at 10 ◦ C higher than the terminal solid solubility for dissolution (TSSD) temperature to dissolve all the charged hydrogen in the zirconium matrix. At the test temperatures ranging from 160 to 280 ◦ C, the initial applied load was increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 in the load increasing mode when the crack did not grow within 24 h. The KIH was defined as the maximum stress intensity factor to cause a crack to grow within 24 h. More than two measured data sets were obtained at each test temperature for the reliability of the KIH data. The crack length was determined on the fractured surface by dividing the area of the DHC crack calculated by an image analyzer by the width.
3. Results Since DHC is a discontinuous process of crack growth, the critical hydride length, lc should correspond to the spacing of the striation lines that can be determined from the fracture surfaces of the Zr–2.5Nb CT specimens [12,20,21]. To identify a correlation of lc and KI , we determined the striation spacing on the fracture surfaces with the striation line sequences. Fig. 4 shows the striation spacing with the striation line sequence for the Zr–2.5Nb CT specimens that were determined from the fracture surfaces after DHC tests at 250 ◦ C in the load increasing mode. The striation spacing was the largest at the first striation line and then it decreased rapidly to around 25–30 m at the ninth striation line despite some scattering of the striation spacing with the line sequence. Similar patterns were observed not only at 250 ◦ C but also at 200 and 280 ◦ C, as shown in Fig. 5, where the striation spacing rapidly decreased for the first few striation line sequences and then leveled off to a constant. Since the striation spacing corresponds to lc over which the hydrides can crack at an applied KI , based on the striation spacing data shown in Figs. 4 and 5, the lc was represented as a function of an instantaneous KI as shown in Fig. 6. Here, the instantaneous KI was obtained using a KI correlation for the CT specimens in accordance with ASTM E399 [22]. The lc was the largest at as
Fig. 4. (a) Striation lines and (b) striation spacing with the striation line sequence for the fracture surfaces of the Zr–2.5Nb CT specimen that was subjected to the DHC tests at 250 ◦ C in the load increasing mode.
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over 9 MPa m−1/2 where an instantaneous plastic zone, γ p , as expressed according to Eq. (1), exceeds lc : KI 2 γp = 0.23 (1) σYS
Fig. 5. Change of the striation spacing with the striation line sequence for the Zr–2.5Nb CT specimens that were subjected to the DHC tests at temperatures ranging from 200 to 280 ◦ C in the load increasing mode.
Fig. 6. Critical hydride length (or lc ) and the plastic zone size formed at the crack tip with an applied stress intensity factor, KI for the Zr–2.5Nb tube that was subjected to DHC tests in the load increasing mode. Here, the lc corresponds to the striation spacing.
low a KI as just above KIH with its drastic decrease to a constant or 30 m above 9 MPa m−1/2 , especially at 250 ◦ C. Here, all the crack fronts must have a sharp DHC crack except for the crack front at the first striation line. Despite the same crack front, the hydride did not fracture at a low KI until it grew to a larger lc (corresponding to point A) but it fractured upon growing to a smaller lc of 30 m at a higher KI , as shown in Fig. 6. It should be noted that the KI dependency of lc shown in Figs. 5 and 6 agrees with that in the Zr–2.5Nb tubes reported by Shek et al. [21] though the striation spacing data in Stage II shown in Fig. 5 are much closer to those of the CANDU Zr–2.5Nb tube determined by a round robin test on delayed hydride cracking velocity of Zr–2.5Nb tubes [23] when compared to those given by Shek et al. [21]. 4. Discussion 4.1. Constant lc in the second stage of DHCV in Zr–2.5Nb tube The results shown in Figs. 4 and 6 showed that in the load increasing mode, lc became constant at a larger KI of
where γ p is a plastic zone at the crack tip formed by an instantaneous deformation, KI an applied stress intensity factor (MPa m−1/2 ) and σ YS the yield strength (MPa) in the tangential direction of the Zr–2.5Nb tube. This finding demonstrates that it is not until hydrides precipitating at the crack tip grow to a constant lc that they fracture, leading the DHC crack to advance, and that cracking of the hydrides is not governed by the applied KI as long as it becomes much larger than KIH . In other words, a critical condition for cracking of the hydrides is not an applied stress but their size. Hence, as cracking of the hydrides is assumed to occur in accordance with Kim’s hypothesis that hydrides fracture by an interaction of the hydrides and dislocation twins at the crack tip, the hydrides will fracture by twins upon their reaching the lc in the plastic zone, γ p which is larger than the lc . This can account for a constant lc and, hence a constant DHCV when the applied KI is large enough to exceed KIH . It should be noted that DHCV is inversely dependent on the lc which governs the hydrogen concentration gradient at the crack tip [12–15]. Consequently, the KI dependency of DHCV in Stages I and II as shown in Fig. 1 is concluded to be caused by a KI dependency of the lc as shown in Fig. 6. The plausibility of our argument that hydrides fracture by their interaction with twins is provided by correlating a rapid increase of KIH in CANDU Zr–2.5Nb pressure tubes at temperatures over 300 ◦ C with the temperature dependency of the twins [24]. The rapid increase in the KIH at temperatures over 300 ◦ C contributes to a decreased DHC velocity, according to Kim’s DHC model [12–15,24], thus leading to a cessation of DHC at 350 ◦ C as observed by Sagat and Puls [25]. 4.2. Change of lc with KI in the first stage of DHCV At a low KI just above KIH , corresponding to Stage I of DHCV, the lc was larger than that in Stage II with the applied KI over 9 MPa m−1/2 as shown in Fig. 6. This increased lc is the cause of the reduced DHCV in the first stage when compared to that in the second stage. When compared to the plastic zone, γ p due to an instantaneous plastic deformation, according to Eq. (1), however, the lc in the first stage is much larger as illustrated in Fig. 6. When an instantaneous deformation only occurs at the crack tip without creep as with the second stage of DHCV, the hydrides precipitated in the plastic zone are too small to fracture even by their interaction with twins. Thus, the fact that the measured lc is much larger than the instantaneous plastic zone, γ p as with Stage I demonstrate that the plastic zone where the hydrides can precipitate must have grown to the lc by a time dependent deformation such as creep. As the increased plastic zone of lc is fully covered with hydrides, the hydrides grow to the lc over the instantaneous plastic zone, γ p . Then, the enlarged hydrides to the lc in length would have fractured easily by their interaction with twins if the twins were still working at the crack
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tip. However, since the creep promotes dislocation slips and suppresses twins, cracking of the hydrides by their interaction with twins will be restrained. This causes the hydrides to become resistant to cracking, thus leading to a larger lc in Stage I when compared to that in Stage II. Evidence for this argument is provided by Sagat’s experiment where the crept Zr–2.5Nb specimens had a higher KIH than that of the Zr–2.5Nb with no creep [26]. This can account for why the hydrides do not fracture until they grow to a larger lc , leading to a lower DHCV in the first stage and why, in the second stage, hydrides fracture at a reduced lc , leading to a higher and constant DHCV. The amount of creep required for γ p to grow to the critical hydride length lc will be inversely proportional to the applied KI . The creep effect on an increased KIH or lc becomes greater at a smaller KI but it becomes zero at a larger KI where a larger instantaneous plastic zone over the critical hydride length is produced without creep. Thus, a rapid drop of lc at a low KI as shown in Fig. 6 is likely to be due to a change in the amount of creep with KI by which γ p can grow to lc . The transition between Stages I and II of DHCV with KI may occur at the KI by which γ p increases to over lc (corresponding to point C as shown in Fig. 6). 5. Conclusions DHC in a Zr–2.5Nb tube occurred discontinuously where the hydrides fractured upon their growth to over the lc . In the load increasing mode where the applied KI increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 using Zr–2.5Nb compact tension specimens, the lc was the largest at as low a KI as just above KIH with its drastic decrease to a constant and reduced value at a larger KI as with Stage II. This finding was observed independent of the test temperatures ranging from 200 to 280 ◦ C. Since DHCV is inversely governed by the lc according to Kim’s DHC model, it is concluded that the KI dependency of DHCV is caused by a KI dependency of the lc . In the second stage where a larger KI is applied to create a larger instantaneous plastic zone at the crack tip without creep, the hydrides growing in the plastic zone fractured upon their growth to over the lc , likely due to an interaction of the hydrides and twins. In the first stage where a smaller γ p is instantaneously formed at a lower KI , creep must occur to extend the plastic zone to the measured lc from a smaller γ p . Hence, a larger lc in the first stage is suggested to be due to a creep effect on the increased KIH which is experimentally supported by Sagat’s results. The rationale why the creep deformation increases the KIH or lc as with the first stage is provided using Kim’s hypothesis that cracking of the hydrides occurs by their interaction with twins.
Acknowledgement This work has been carried out under the auspices of the Nuclear R & D program of Ministry of Science and Technology. References [1] Y.S. Kim, Y.M. Cheong, K.S. Im, Trans. Korean Hydrogen New Energy Society 15 (2004) 266–273. [2] R. Dutton, K. Nuttall, M.P. Puls, L.A. Simpson, Met. Trans. A 8 (1977) 1553–1562. [3] M.P. Puls, L.A. Simpson, R. Dutton, in: L.A. Simpson (Ed.), Fracture Problems and Solutions in the Energy Industry, Pergamon Press, Oxford, 1982, p. 13. [4] D.G. Westlake, Trans. Metall. Soc. A. I. M. E. 245 (1969) 287. [5] J.J. Kearns, C.R. Woods, J. Nucl. Mater. 20 (1966) 241–261. [6] R.L. Eadie, C.E. Coleman, Scripta Metall. 23 (1989) 1865–1870. [7] R.L. Eadie, D.R. Metzger, M. Leger, Scripta Metall. 29 (1993) 335. [8] J.S. Schofield, E.C. Darby, C.F. Gee, Zirconium in the Nuclear Industry: 13th International Symposium, ASTM STP 1423, ASTM, 2002, p. 339. [9] D. Yan, R.L. Eadie, Scripta Mater. 43 (2000) 89–94. [10] S.Q. Shi, G.K. Shek, M.P. Puls, J. Nucl. Mater. 218 (1995) 189–201. [11] M.P. Puls, Acta Metall. 32 (1984) 1259–1269. [12] Y.S. Kim, S.S. Kim, S.B. Ahn, et al., Abstract booklet for 14th Symposium on Zirconium in the Nuclear Industry, ASTM, Stockholm, 2004, p. 81. [13] Y.S. Kim, Met. Mater. Int. 11 (2005) 29–38. [14] Y.S. Kim, K.S. Kim, Y.M. Cheong, J. Nucl. Sci. Technol. 43 (2006) 1120–1127. [15] Y.S. Kim, S.B. Ahn, Y.M. Cheong, J. Alloys Compd. 429 (2007) 221–226. [16] J.C.M. Li, Trans. ASM 60 (1967) 226–227. [17] D.S. Shih, I.M. Robertson, H.K. Birnbaum, Acta Metall. 36 (1988) 111–124. [18] Y.S. Kim, Y. Perlovich, M. Isaenkova, S.S. Kim, Y.M. Cheong, J. Nucl. Mater. 297 (2001) 292–302. [19] Y.S. Kim, Characterization test procedures for Zr–2.5Nb tubes; Korea Atomic Energy Research Report, KAERI/TR-1329/99 (1999). [20] M.T. Jovanovic, G.K. Shek, H. Seahra, R.L. Eadie, Met. Character. 40 (1998) 15–25. [21] G.K. Shek, M.T. Jovanovic, H. Seahra, Y. Ma, D. Li, R.L. Eadie, J. Nucl. Mater. 231 (1996) 221–230. [22] S.S. Park, Dependence of threshold stress intensity factor, KIH on temperature and hydrogen concentration for delayed hydride cracking in Zr–2.5Nb pressure tube, M.S. Thesis, Korea University, 2001. [23] IAEA-TECDOC-1410, Delayed Hydride Cracking in Zirconium Alloys in Pressure Tube Nuclear Reactors, International Atomic Energy Agency, Vienna, 2004. [24] Y.S. Kim, S.B. Ahn, K.S. Kim, Y.M. Cheong, Key Eng. Mater. 326–328 (2006) 919–922. [25] S. Sagat, M.P. Puls, Trans. the 17th International Conference on Structural Mechanics in Reactor Technology (SMiRT 17), 2003, G06-4. [26] S. Sagat, G.W. Newman, D.A. Sagat, in: N.R. Moody, et al. (Eds.), Hydrogen Effects on Material Behavior and Corrosion Deformation Interactions, TMS, 2003, p. 289.
Stage I and II behaviors of delayed hydride cracking velocity in zirconium alloys Young Suk Kim ∗ , Soon Sam Park 1 Zirconium Team, Korea Atomic Energy Research Institute, 150 Dukjin-dong, Yuseong, Daejeon 305-353, Republic of Korea Received 4 November 2006; received in revised form 29 November 2006; accepted 29 November 2006 Available online 2 January 2007
Abstract Delayed hydride cracking (DHC) tests were conducted on Zr–2.5Nb compact tension (CT) specimens with 60–80 ppm H at temperatures ranging from 160 to 280 ◦ C in the load increasing mode where the applied stress intensity factor, KI was increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 until a crack grew. Critical hydride lengths, lc , corresponding to the spacing of the striation lines, were determined with the applied stress intensity factor, KI from the fracture surfaces of the Zr–2.5Nb CT specimens. The lc was the largest at as low a KI as just above KIH in Stage I and leveled off to 30 m at a larger KI of above 9 MPa m−1/2 especially at 250 ◦ C, corresponding to Stage II. This finding was also observed at all the investigated temperatures. Since DHCV is inversely governed by lc according to Kim’s DHC model, it is concluded that the KI dependency of DHCV is caused by the KI dependency of lc . The increased lc in Stage I is suggested to arise from the creep effect on the increased KIH that is experimentally supported by Sagat’s results. The rationale for this suggestion is provided using Kim’s hypothesis that cracking of hydrides occurs by their interaction with twins. © 2006 Elsevier B.V. All rights reserved. Keywords: Zirconium; Delayed hydride cracking; Hydride; Striation
1. Introduction One of the unique features of cracking of zirconium alloys by delayed hydride cracking (DHC) is that there are three stages of a crack growth rate with the applied stress intensity factor or KI . For Stage I, the crack growth rate or DHC velocity (DHCV) sensitively changes at a small KI just above KIH under which the crack cannot grow. For Stage II, DHCV becomes constant independent of KI when it becomes considerably larger than KIH and for Stage III, it abruptly increases, leading to an unstable fracture when KI exceeds KIC as shown in Fig. 1. It should be noted that this cracking mechanism applies to stress corrosion cracking and hydrogen induced cracking of steels and other metals [1]. Dutton et al. suggested that at low KI as with Stage I, the hydride could grow in excess of a small plastic zone [2,3]. According to Dutton’s hypothesis [2], part of the hydride would be exposed to the elastic stress field of a crack ahead of the plastic ∗
Tel.: +82 42 868 2359; fax: +82 42 868 8346. E-mail address: [email protected] (Y.S. Kim). 1 Present address: InterPower Engineering & Consulting Co. Ltd., Zip code 137-130, 4th floor, Namgoong Bldg. 90-8, Yangjae-Dong, Seocho-ku, Seoul, Korea. 0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.11.197
zone, causing the local hydrostatic stress at the hydride tip to sensitively change with KI . Since a hydrostatic stress is assumed to be a driving force for diffusion growth of the hydride, it accounts for a rapid increase in the crack growth rate with KI . Dutton et al. also suggested that at large KI as with Stage II, a large hydride could grow within a larger plastic zone with a lesser dependency of the hydrostatic stress with KI , leading the crack growth rate to have a lesser dependency on KI when compared to that in Stage I. It should be noted that Dutton’s DHC model [2,3] has made two unrealistic assumptions: a hydride growth in an elastic field of the zirconium matrix and an autocatalytic precipitation of hydrides upon hydrogen entering into the plastic zone even in an isothermal condition. The hydride growth in the elastic zone as assumed by Dutton et al [2,3] contradicts Westlake’s observation [4] where an applied stress less than the yield strength had no effect on the cooling soluvs but a 5% plastic strain only raised the cooling solvus temperature by 10 K in NbH. Contrary to Dutton’s assumption, precipitation of hydrides cannot occur in an isothermal condition [5] but it can do in a thermal cycle with some undercooling [6–8]. Yan and Eadie [9] also suggested a hypothesis to explain the Stage I and II behaviors of DHCV with KI under the same assumption as Dutton’s. Using the experimentally measured
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Fig. 1. Schematic diagram illustrating the three stages of delayed hydride cracking velocity when plotted as a function of the applied stress intensity factors.
critical hydride length, lc over which hydrides fractured at different KI , they calculated the time, tc for a hydride to grow to that critical hydride length at a fixed KI with Dutton’s assumption that the hydrostatic stress is the driving force for diffusion growth of a hydride. Then, the DHCV dependency of KI was obtained by plotting the velocity defined as lc over tc at different KI . However, this model has some imperfections because, first, hydrides cannot precipitate in an isothermal condition by a difference in the hydrostatic stress [10,11], second, the velocity defined as lc over tc by their definition is an instantaneous DHCV, corresponding to the first stage where the DHCV sensitively changes with KI , not the DHCV in the second stage. The weakest point of all the previous DHC models is that they failed to provide a feasible explanation for the flat crack growth rate in zirconium alloys independent of KI at the second stage. This failure results from their assumption that the hydrostatic stress is the driving force for diffusion of hydrogen towards the crack with a higher tensile stress. With Kim’s DHC model [12–14] that a difference in hydrogen concentration or C due to stress-induced precipitation of hydrides at the crack tip is the driving force for DHC, a constant DHCV in zirconium alloys independent of KI can be understood. When the applied KI is large enough to cause stress-induced precipitation [12,15–17], the crack tip has a decreased hydrogen concentration to the terminal solid solubility for dissolution of hydrogen (TSSD) (point C in Fig. 2) when compared to the bulk region of the supersaturated hydrogen concentration (point B in Fig. 2). Thus, C corresponding to the distance BC as shown in Fig. 2 is created between the crack tip and the bulk region, which is the driving force for DHC. This leads DHCV to depend, not on KI but on C between the crack tip and the bulk region as suggested by Kim’s DHC model [12–14]. Though Kim’s DHC model can account for the flat DHCV independent of KI in the second stage as shown in Fig. 1, it has yet to explain a KI dependency of DHCV and lc in the first stage. In essence, all the DHC models proposed to date failed to provide a feasible rationale of why the critical hydride length, lc and DHCV in zirconium alloys are affected by an applied KI , which is the aim of this study. To this end, we conducted DHC tests to determine the threshold stress intensity factor, KIH for the onset of delayed hydride cracking in a cold-worked Zr–2.5Nb tube in the load increasing mode.
Fig. 2. (a) The solvus lines of hydrogen during a thermal cycle to which the Zr–2.5Nb with 60 ppm H is subjected in the DHC tests. The driving force for DHC is a difference in the hydrogen concentration or C accompanied by nucleation of the hydrides at the crack tip under a tensile stress, which corresponds to 29 ppm H at 250 ◦ C, equal to the distance BC.
2. Experimental procedures 2.1. Specimen preparation Seventeen millimeter compact tension specimens shown in Fig. 3a were used to determine the KIH in the axial direction of a cold worked and stress relieved Zr–2.5Nb pressure tube with a strong tangential texture with most of
Fig. 3. (a) Schematic drawing of the curved compact tension specimens and (b) thermal cycle treatments applied for determining the threshold stress intensity factor, KIH for the onset of delayed hydride cracking in CANDU Zr–2.5Nb tube.
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the (0 0 0 1) basal poles oriented towards the tangential direction [18]. Hydrogen of 60–100 ppm was charged electrolytically into the specimen to form a thick hydride layer on the surface followed by an annealing in a salt bath which can control the specimen temperature to within ±0.5 ◦ C. More details of the hydrogen charging procedure are reported elsewhere [19]. The hydrogen content of the specimen was obtained by averaging five different values measured with a LECO RH 404 analyzer. A pre-fatigue crack of 1.7 mm was introduced using an Instron 8501 to have a ratio of the fatigue length and the CT length (=a0 /W) equal to 0.5. The applied stress intensity factor or KI was 15 MPa m−1/2 at the initiating stage of the pre-fatigue crack and it decreased to 7 MPa m−1/2 after the fatigue crack grew to 1.7 mm.
2.2. Delayed hydride cracking tests Compact tension (CT) specimens were subjected to a constant load in a creep machine while the initiation of a crack was monitored by a dc potential drop method. Fig. 3b shows a typical thermal cycle to which the CT specimens were subjected in the DHC tests. The CT specimens were heated to a peak temperature by 0.5–1 ◦ C/min, held there for 1 h and cooled down to the test temperature followed by applying a load from 30 min after reaching the test temperature. The peak temperature was set at 10 ◦ C higher than the terminal solid solubility for dissolution (TSSD) temperature to dissolve all the charged hydrogen in the zirconium matrix. At the test temperatures ranging from 160 to 280 ◦ C, the initial applied load was increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 in the load increasing mode when the crack did not grow within 24 h. The KIH was defined as the maximum stress intensity factor to cause a crack to grow within 24 h. More than two measured data sets were obtained at each test temperature for the reliability of the KIH data. The crack length was determined on the fractured surface by dividing the area of the DHC crack calculated by an image analyzer by the width.
3. Results Since DHC is a discontinuous process of crack growth, the critical hydride length, lc should correspond to the spacing of the striation lines that can be determined from the fracture surfaces of the Zr–2.5Nb CT specimens [12,20,21]. To identify a correlation of lc and KI , we determined the striation spacing on the fracture surfaces with the striation line sequences. Fig. 4 shows the striation spacing with the striation line sequence for the Zr–2.5Nb CT specimens that were determined from the fracture surfaces after DHC tests at 250 ◦ C in the load increasing mode. The striation spacing was the largest at the first striation line and then it decreased rapidly to around 25–30 m at the ninth striation line despite some scattering of the striation spacing with the line sequence. Similar patterns were observed not only at 250 ◦ C but also at 200 and 280 ◦ C, as shown in Fig. 5, where the striation spacing rapidly decreased for the first few striation line sequences and then leveled off to a constant. Since the striation spacing corresponds to lc over which the hydrides can crack at an applied KI , based on the striation spacing data shown in Figs. 4 and 5, the lc was represented as a function of an instantaneous KI as shown in Fig. 6. Here, the instantaneous KI was obtained using a KI correlation for the CT specimens in accordance with ASTM E399 [22]. The lc was the largest at as
Fig. 4. (a) Striation lines and (b) striation spacing with the striation line sequence for the fracture surfaces of the Zr–2.5Nb CT specimen that was subjected to the DHC tests at 250 ◦ C in the load increasing mode.
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over 9 MPa m−1/2 where an instantaneous plastic zone, γ p , as expressed according to Eq. (1), exceeds lc : KI 2 γp = 0.23 (1) σYS
Fig. 5. Change of the striation spacing with the striation line sequence for the Zr–2.5Nb CT specimens that were subjected to the DHC tests at temperatures ranging from 200 to 280 ◦ C in the load increasing mode.
Fig. 6. Critical hydride length (or lc ) and the plastic zone size formed at the crack tip with an applied stress intensity factor, KI for the Zr–2.5Nb tube that was subjected to DHC tests in the load increasing mode. Here, the lc corresponds to the striation spacing.
low a KI as just above KIH with its drastic decrease to a constant or 30 m above 9 MPa m−1/2 , especially at 250 ◦ C. Here, all the crack fronts must have a sharp DHC crack except for the crack front at the first striation line. Despite the same crack front, the hydride did not fracture at a low KI until it grew to a larger lc (corresponding to point A) but it fractured upon growing to a smaller lc of 30 m at a higher KI , as shown in Fig. 6. It should be noted that the KI dependency of lc shown in Figs. 5 and 6 agrees with that in the Zr–2.5Nb tubes reported by Shek et al. [21] though the striation spacing data in Stage II shown in Fig. 5 are much closer to those of the CANDU Zr–2.5Nb tube determined by a round robin test on delayed hydride cracking velocity of Zr–2.5Nb tubes [23] when compared to those given by Shek et al. [21]. 4. Discussion 4.1. Constant lc in the second stage of DHCV in Zr–2.5Nb tube The results shown in Figs. 4 and 6 showed that in the load increasing mode, lc became constant at a larger KI of
where γ p is a plastic zone at the crack tip formed by an instantaneous deformation, KI an applied stress intensity factor (MPa m−1/2 ) and σ YS the yield strength (MPa) in the tangential direction of the Zr–2.5Nb tube. This finding demonstrates that it is not until hydrides precipitating at the crack tip grow to a constant lc that they fracture, leading the DHC crack to advance, and that cracking of the hydrides is not governed by the applied KI as long as it becomes much larger than KIH . In other words, a critical condition for cracking of the hydrides is not an applied stress but their size. Hence, as cracking of the hydrides is assumed to occur in accordance with Kim’s hypothesis that hydrides fracture by an interaction of the hydrides and dislocation twins at the crack tip, the hydrides will fracture by twins upon their reaching the lc in the plastic zone, γ p which is larger than the lc . This can account for a constant lc and, hence a constant DHCV when the applied KI is large enough to exceed KIH . It should be noted that DHCV is inversely dependent on the lc which governs the hydrogen concentration gradient at the crack tip [12–15]. Consequently, the KI dependency of DHCV in Stages I and II as shown in Fig. 1 is concluded to be caused by a KI dependency of the lc as shown in Fig. 6. The plausibility of our argument that hydrides fracture by their interaction with twins is provided by correlating a rapid increase of KIH in CANDU Zr–2.5Nb pressure tubes at temperatures over 300 ◦ C with the temperature dependency of the twins [24]. The rapid increase in the KIH at temperatures over 300 ◦ C contributes to a decreased DHC velocity, according to Kim’s DHC model [12–15,24], thus leading to a cessation of DHC at 350 ◦ C as observed by Sagat and Puls [25]. 4.2. Change of lc with KI in the first stage of DHCV At a low KI just above KIH , corresponding to Stage I of DHCV, the lc was larger than that in Stage II with the applied KI over 9 MPa m−1/2 as shown in Fig. 6. This increased lc is the cause of the reduced DHCV in the first stage when compared to that in the second stage. When compared to the plastic zone, γ p due to an instantaneous plastic deformation, according to Eq. (1), however, the lc in the first stage is much larger as illustrated in Fig. 6. When an instantaneous deformation only occurs at the crack tip without creep as with the second stage of DHCV, the hydrides precipitated in the plastic zone are too small to fracture even by their interaction with twins. Thus, the fact that the measured lc is much larger than the instantaneous plastic zone, γ p as with Stage I demonstrate that the plastic zone where the hydrides can precipitate must have grown to the lc by a time dependent deformation such as creep. As the increased plastic zone of lc is fully covered with hydrides, the hydrides grow to the lc over the instantaneous plastic zone, γ p . Then, the enlarged hydrides to the lc in length would have fractured easily by their interaction with twins if the twins were still working at the crack
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tip. However, since the creep promotes dislocation slips and suppresses twins, cracking of the hydrides by their interaction with twins will be restrained. This causes the hydrides to become resistant to cracking, thus leading to a larger lc in Stage I when compared to that in Stage II. Evidence for this argument is provided by Sagat’s experiment where the crept Zr–2.5Nb specimens had a higher KIH than that of the Zr–2.5Nb with no creep [26]. This can account for why the hydrides do not fracture until they grow to a larger lc , leading to a lower DHCV in the first stage and why, in the second stage, hydrides fracture at a reduced lc , leading to a higher and constant DHCV. The amount of creep required for γ p to grow to the critical hydride length lc will be inversely proportional to the applied KI . The creep effect on an increased KIH or lc becomes greater at a smaller KI but it becomes zero at a larger KI where a larger instantaneous plastic zone over the critical hydride length is produced without creep. Thus, a rapid drop of lc at a low KI as shown in Fig. 6 is likely to be due to a change in the amount of creep with KI by which γ p can grow to lc . The transition between Stages I and II of DHCV with KI may occur at the KI by which γ p increases to over lc (corresponding to point C as shown in Fig. 6). 5. Conclusions DHC in a Zr–2.5Nb tube occurred discontinuously where the hydrides fractured upon their growth to over the lc . In the load increasing mode where the applied KI increased step-wise by 0.5 MPa m−1/2 from 4.5 MPa m−1/2 using Zr–2.5Nb compact tension specimens, the lc was the largest at as low a KI as just above KIH with its drastic decrease to a constant and reduced value at a larger KI as with Stage II. This finding was observed independent of the test temperatures ranging from 200 to 280 ◦ C. Since DHCV is inversely governed by the lc according to Kim’s DHC model, it is concluded that the KI dependency of DHCV is caused by a KI dependency of the lc . In the second stage where a larger KI is applied to create a larger instantaneous plastic zone at the crack tip without creep, the hydrides growing in the plastic zone fractured upon their growth to over the lc , likely due to an interaction of the hydrides and twins. In the first stage where a smaller γ p is instantaneously formed at a lower KI , creep must occur to extend the plastic zone to the measured lc from a smaller γ p . Hence, a larger lc in the first stage is suggested to be due to a creep effect on the increased KIH which is experimentally supported by Sagat’s results. The rationale why the creep deformation increases the KIH or lc as with the first stage is provided using Kim’s hypothesis that cracking of the hydrides occurs by their interaction with twins.
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