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Nanoindentation investigation on the creep behavior of P92 steel weld joint after creep-fatigue loading
International Journal of Fatigue 134 (2020) 105506
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Nanoindentation investigation on the creep behavior of P92 steel weld joint after creep-fatigue loading
T
Zengliang Gaoa,c, Yuxuan Songa,b, Zhouxin Pana, Jianan Chena, Yi Mab,⁎ a
Institute of Process Equipment and Control Engineering, College of Mechanical Engineering Zhejiang University of Technology, Hangzhou 310014, China Institution of Micro/Nano-Mechanical Testing Technology & Application, College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China c Engineering Research Center of Process Equipment and Re-manufacturing, Ministry of Education, Hangzhou, China b
ARTICLE INFO
ABSTRACT
Keywords: Welded joint Creep-fatigue interaction Nanoindentation Hardness Creep behavior
Using nanoindentation technology, the creep behavior of P92 steel welded joint that had experienced creepfatigue (CF) loading was studied at the nanoscale. In both as-welded and CF samples, the fine-grain heat affected zone region exhibited relatively lower hardness and lower creep resistance than other regions of the welded joint. Compared to the as-welded sample, enhanced creep deformation and reduced hardness were observed in the CF sample. The strain rate sensitivity was in the range from 0.010 to 0.035 for as-welded sample and 0.052 to 0.082 for the CF sample, as the measurement region changed from base metal to weld metal regions.
1. Introduction In the quest for higher power plant efficiency the trend is to go for still higher operating pressures. The next generation of power plants will operate with steam pressures in the range of 300 bar. These are the ultra-super critical power units, that operate at temperatures of 615–630 °C. Such units are frequently subject to creep-fatigue (CF) loading at high temperature through repeated start-up and shutdown cycles. Consequently, the service life of components is significantly reduced and difficult to predict. P92 steel has been extensively utilized in the main steam piping of ultra-supercritical units due to its extremely high creep resistance, low expansion coefficient and high thermal conductivity [1]. Notwithstanding the mechanical properties of P92 steel, that are adequate to the service requirement of ultra-supercritical units, welded joints are a weak region which could be the source of failure during service. Bicego et al. performed low cyclic fatigue (LCF) test of P91, P92 and E911 steel welded joints at 600 °C, which showed a reduction factor in cyclic life about 2 compared to their base metal (BM) samples [2]. It is well known that mechanical properties such as hardness and fracture strength are often reduced during the service life in many engineering components [3–7]. The degradation rate of mechanical properties is essential in order to make residual life assessments of ultra-supercritical units. However, the mechanical properties of a material are to accurately measure in situ during service. Hence, in order to predict the residual life of ultra-supercritical thermal power units, the remnant mechanical properties and damage micro⁎
mechanisms of materials after service need to be investigated. Mariappan et al. estimated the remnant tensile properties of P91 steel after prior LCF and CF loading conditions [8]. Gopinath et al. observed the microstructure of P92 steel after CF testing, and examined the damage micro-mechanisms [9]. However, the remnant mechanical properties of welded joints were not fully studied due to their structural hierarchy and mechanical heterogeneity. Pandey et al. investigated the formation mechanism of various microstructures in different regions of a P92 steel welded joint and found that the welding process produced a heterogeneous microstructure in the heat affected zone (HAZ) of welded joint [10]. The HAZ could be divided into the fine-grain heat affected zone (FGHAZ) and coarse-grain heat affected zone (CGHAZ) based on grain size, with the nucleation and propagation of creep voids more likely to occur in the FGHAZ [11–13]. They defined this as the main reason for the premature failure of welded joint. However, the relationship between microstructure and mechanical properties in the HAZ is still not confirmed. Because of the narrow width of HAZ, the change of mechanical properties with microstructural gradient is difficult to measure using conventional methods. Nanoindentation is an efficient and high-resolution technology capable of measuring mechanical properties at the nano/micro-scale [14–16]. Nguyen et al. used nanindentation to investigate the strain rate sensitivity of SM490 and SS400 structural steel welded joints by the rate-jump method after low-cycle fatigue loading [17,18]. Pham et al. determined a constitutive equation to obtain the yield strength and the strain hardening exponent of structural steel through
Corresponding author. E-mail address: [email protected] (Y. Ma).
https://doi.org/10.1016/j.ijfatigue.2020.105506 Received 3 September 2019; Received in revised form 15 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0142-1123/ © 2020 Elsevier Ltd. All rights reserved.
International Journal of Fatigue 134 (2020) 105506
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Table 1 Chemical compositions of P92 steel and the welding consumable (wt.%). Element
C
Si
Mn
Ni
Cr
Mo
P
S
N
V
P92 P92 wire
0.106 0.095
0.235 0.150
0.361 0.610
0.108 0.680
9.220 8.360
0.374 0.940
0.017 0.011
0.008 0.007
0.061 0.041
0.182 0.020
Fig. 1. (a) Illustration of the position of the samples relative to the weld and the pipe thickness; (b) Optical macrograph of the welded joint; (c) Spatial nanoindentation hardness contour in the welded joint.
80 × 80 × 840 mm were prepared for testing. In order to produce the welded joint, two pipes sections were welded together using submerged arc welding. The welded pipe was then annealed at 760 °C for 2 h followed by air cooling. Nondestructive inspection was used to confirm that the weld joints could meet the requirements. The compositions of the P92 steel and filler wire are listed in Table 1. Fig. 1 (a) shows the layout of the CF samples both through the thickness of the pipe and in relation to the welded joint, while Fig. 1(b) shows an etched macrograph of the weld cross-section and Fig. 1(c) shows spatial nanoindentation hardness contours. The P92 steel welded joint was etched using a mixture of 92 ml water, 4 ml hydrofluoric acid and 4 ml nitric acid.
nanoindentation [19]. It has also been reported that creep deformation could be observed for high-melting point materials [20,21] at room temperature, using nanoindentation techniques. In a previous study by several of the present authors, creep deformation in different regions of SA508 Gr3 steel welded joints was clearly observed using the constantload method [22]. This paper investigates the mechanical properties in micro-regions of P92 steel welded joint after CF loading. The P92 steel welded joint was divided into four regions (welded metal (WM), base metal (BM), CGHAZ and FGHAZ regions) based on the distance from the weld center line. For as-welded and CF tested samples, the hardness and creep deformations in those four regions were measured by nanoindentation. The strain rate sensitivities of creep were also estimated to study creep mechanism.
2.2. Experiment details
2. Experimental procedures
The creep-fatigue interaction (CF) test was conducted using a high temperature electronic creep-fatigue testing machine (RPL 300). The CF experiments were performed in air at 650℃. The samples were held for 25 min at 650 °C before the test started. During the testing, the
2.1. Materials P92
pipe
sections
with
thickness,
width
and
length
of 2
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Fig. 2. Microstructures observed in the as-welded sample (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal by laser scanning confocal microscopy (LSCM).
temperature variation was kept at less than ±1 °C through three S-type thermocouples. Symmetric trapezoidal waveforms with a constant strain amplitude of 0.4% and strain rate of 0.001 s−1 and holding periods of 5 mins at maximum and minimum strains were used for CF tests. The WM, BM and HAZ samples intended for nanoindentation experiments were cut from as-welded and CF tested samples using electrodischarge machining (EDM). The microstructures in all regions of both samples were observed by laser scanning confocal microscopy (LSCM, OLYMPUS OLS4500). At first, the BM, FGHAZ, CGHAZ and WM regions were clearly distinguished at 400 times magnification through LSCM measurement. The grain sizes of WM and CGHAZ regions were approximately 3 times larger than BM and FGHAZ region. Then, several 200 × 200 μm2 areas in BM, FGHAZ, CGHAZ and WM regions were randomly chosen to calculate the grain size distribution at 1000 times magnification. The number of grains with different sizes was respectively recorded in those areas. To make sure the reliability of experimental results, 5 different areas were chosen from BM, FGHAZ, CGHAZ and WM regions, respectively. Prior to nanoindentation tests, both samples were carefully polished to a mirror surface on the Nanopoli-100 (NaiNuo, Hangzhou). Diamond abrasive at the average size of 2 μm (8000#) and polyurethane polish pad were adopted. After 60-min polishing, samples were carefully cleaned in the anhydrous alcohol by ultrasonic cleaning. Nanoindentation experiments were conducted on an Agilent Nano Indenter G200 with a standard Berkovich indenter at room temperature. Before commencing the nanoindentation creep experiment, the hardness of the four weld regions (FGHAZ, CGHAZ, BM and WM) were
obtained using the recently developed continuous stiffness measurement (CSM) method, which has attracted the attention of many researchers due to its ability to measure the stiffness during the indentation process [23,24]. A constant strain rate of 0.05 s−1 was used in the CSM measurements. During the creep test, the Berkovich indenter was held for 1000 s at a maximum load of 196 mN, and the loading rate was kept constant at 4 mN/s. The space between each two indents was kept at least 50 μm. To ensure the reliability of the nanoindentation data, 20 indentations were made in each region. The thermal drift was controlled to be less than 0.05 nm/s during experiments. Meanwhile, the load drift correction was strictly calibrated at 10% of the maximum loading after the unloading stage. 3. Results and discussion 3.1. Creep-fatigue interaction experiment The microstructures observed in various regions of welded and CF tested samples are plotted in Figs. 2 and 3. For both samples, the prior austenite grain boundary of BM, FGHAZ, CGHAZ, WM regions can be explicitly distinguished in Figs. 2(a)–(d) and 3(a)–(d). A distribution of precipitates is apparent in prior austenite grains. The precipitates that were exist inside the grains of the M23C6 type, and the grain boundaries are strengthened by distributed fine MX precipitates [25–27]. These precipitates have been reported to enhance the creep resistance of P92 steel at high temperature [8]. The CF test was continued until all four samples had ruptured in either the BM or HAZ regions. The cyclic stress responses observed 3
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Fig. 3. Microstructures observed in the CF sample (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal by laser scanning confocal microscopy (LSCM).
Fig. 4. (a) Cyclic stress relaxation observed during the creep-fatigue interaction test; (b) Creep-fatigue interaction hysteresis loop of HAI 925 sample after 1 and 2000 loading cycles.
during the strain-controlled loading are shown in Fig. 4(a). The cyclic softening phenomenon can be clearly seen. In Fig. 4(a), the softening process can be divided into three stages. During the first period, the material softened rapidly, and this is followed by a period of slower steady-state softening, before a final period of acceleration of the rate of softening that led to rupture [28,29]. Fig. 4(a) shows that the cyclic lives for the four CF samples are
significantly different and clearly depends on position through the weld thickness. The HAI925 sample ruptured after more than 2000 loading cycles, while, in contrast, the HAI922 sample survived for only 960 loading cycles. Hardness should be intrinsically connected to creep resistance, as both parameters reflect the resistance to plastic deformation [30]. The spatial distribution of nanoindentation hardness contours through the weld depth is plotted in Fig. 1(c). It can be seen 4
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Fig. 5. The schematic diagram of illustration of the four microstructures in the welded joint after the CF test (HAI 923 sample), together with the nanoindentation positions.
Fig. 6. Grain size variation in the welded joint of P92 steel (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal.
that the hardness of HAZ region was higher than that of WM or BM regions. Furthermore, a region of significantly higher hardness exists at the weld root due to the submerged arc welding process and the weld profile. The longer cyclic life of the HAI925 sample could then be caused by its initially higher hardness condition. Fig. 4(b) presents, for the HAI925 sample, the stress-strain hysteresis loops for the first and 2000th cycles of loading. It is clear that creep deformation has occurred during the holding periods in the CF test, with the amount of deformation apparently increasing with number of applied cycles. This phenomenon has led to the stress relaxation shown in Fig. 4(a). The increased plastic deformation of martensitic steels during holding time
has been previously confirmed to be correlated with sub-grain size [31]. Dubey et al. [32] also found that the cyclic softening phenomenon was partly caused by significant coarsening of the fine sub-grain structure due to accumulation of plastic strain. The CF experiment represents the overall cyclic stress response of the sample. The mechanism and extent of microstructural evolution in WM, BM, FGHAZ and CGHAZ regions are, however, quite different. Thus, the mechanical properties in each region of the welded joint should be measured in order to throw light on this aspect.
5
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Fig. 7. Measured hardness as a function of indentation depth by CSM in FGHAZ region (a) As-welded sample; (b) Sample after the CF test.
Fig. 8. Hardness obtained using the CSM method in the four different regions of (a) the as-welded sample and (b) the CF sample.
3.2. Nanoindentation hardness
cases mean values at 500 nm and 1500 nm showed similar trends.
Fig. 5 shows the microstructure in the divided nanoindentation regions of a typical welded joint after CF test. The positions of nanoindentations in the WM, BM, FGHAZ and CGHAZ regions are also shown in the schematic diagram. Fig. 6(a)–(d) plots the grain size in the WM, BM, FGHAZ and CGHAZ regions, respectively. The mean values of grain size in those regions of the as-welded sample were 21 μm (BM), 18 μm (FGHAZ), 57 μm (CGHAZ) and 50 μm (WM). These values became slightly larger in the samples that had been subject to CF testing and were measured as 24 μm (BM), 23 μm (FGHAZ), 59 μm (CGHAZ) and 52 μm (WM). Fig. 7(a) and (b) show the hardness H as a function of indentation depth in the FGHAZ region of both as-welded and CF tested samples. A clear effect of indentation size effect is observed, with hardness values reducing with increased indentation depth in both cases. In the case of aluminum and brass alloys an increased hardness observed with shallow indentations has been suggested to be caused by the presence of geometrically necessary dislocations [33]. The hardness values at indentation depths of 500 nm and 1500 nm were adopted, respectively. Fig. 8(a) and (b) show the variation in hardness across the four regions of the welded joint. Compared with the as-welded sample, CF tested sample shows a reduced hardness in all regions, with the decrease being particularly marked in going form the CGHAZ to the FGHAZ regions. The hardness of high chromium steel has been shown to decrease during the holding period due to the sub-structural recovery and coarsening of carbides [34,35]. Furthermore, the growth of precipitates was more remarkable in the FGHAZ region during creep, which could lead to the observed significant reduction of hardness [36]. In both
3.3. Nanoindentation creep behavior Fig. 9(a) shows the load P applied during the creep test as a function of time t, with a constant peak value of 196 mN and a constant loading and unloading rate of 4 mN/s. Typical creep load- indentation depth (Ph) curves for all four regions of as-welded and CF tested samples are shown in Fig. 9(b) and (c), respectively. In both cases, it was observed that the steady-state holding depth in the BM and FGHAZ regions was greater than in the other two regions for the same peak load, which is consistent with the low observed hardness values. The corresponding indentation depth creep curves during the holding period are shown in Fig. 10(a)–(d), in which creep displacements are plotted against holding time. In order to aid better interpretation of these curves, the starting points (for both holding time and creep displacement) have been set to zero. Two stages of creep deformation can then be distinguished, namely the primary creep and secondary creep. In the primary stage, the creep displacement increases relatively quickly, while the creep rate decreases rapidly [37]. In the secondary creep stage, the displacement becomes almost linear with time and the creep rate gradually becomes stable. Compared with the as-welded sample, an enhanced creep displacement was observed in the CF sample. For both samples, the creep deformations in the regions with a relatively higher hardness (WM and CGHAZ) primary creep plays a greater role than secondary creep, while in the case of the softer BM and FGHAZ regions, secondary creep plays a greater role. Fig. 11(a) shows the variation in creep displacement for all four regions of both samples. The mean values of creep displacement in the BM and FGHAZ regions can be seen to be greater than in the other 6
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Fig. 9. (a) Creep test loading curve as a function of time. (b) Representative load–displacement (P-h) curves in all regions of as-welded joint; (c) Under prior creepfatigue interaction loading condition.
Fig. 10. Representative creep curves of P92 steel welded joint (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal. 7
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Fig. 11. (a) Total creep displacement (represented by indenter depth) and (b) steady-state creep rate in the four regions of the P92 steel welded joint.
Fig. 12. (a) Fit achieved for the FGHAZ creep curve using Eq. (2); (b) Variation in strain rate deduced from Eq. (2); (c) Decrease in hardness as a function of creep time; (d) Natrual log correlation between hardness and strain rate: the SRS value can be estimated by linearly fitting the steady-state part.
two regions. Creep displacements in all regions were greater in the CF sample compared with the as-welded case. The steady-state creep rates for all four regions are given in Fig. 11(b), and it is clear that the secondary creep rates increase after the CF test, with a greater increase evident in the BM and FGHAZ regions. As the dominant creep mechanism was secondary creep in these regions, creep displacements were significantly affected by these enhanced secondary creep rates. From Fig. 11(a), it can be concluded that the creep resistance of the P92 steel welded joint became lower after the CF test, with a decline in creep resistance apparent in the softer regions such as BM and FGHAZ regions. The coarsening of precipitates and recovery of dislocations during CF testing has been reported to be responsible for the reduction in creep resistance, with those mechanisms being more active in FGHAZ
region [36]. 3.4. Strain rate sensitivity Strain rate sensitivity (SRS) plays an important role in determining the mechanical properties of a material [38]. Indentation creep has been a widely used method to study SRS, which in turn can reveal information regarding the creep mechanism of traditional metals [39]. It is known that indentation creep could be dominated by mechanisms like dislocation glide and climb, grain boundary slide, amongst other [40]. The value of strain rate sensitivity m is given by [41]:
m= 8
InH In
(1)
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excluded. For polycrystalline materials, grain boundary sliding should not exist at such a low value of m. Equally, grain boundary diffusion and the tip-sample atomic diffusion could be also eliminated due to the high creep strain rate and deep holding depth [42–44]. Dislocation movement is has been shown to be the dominant creep mechanism as m drops below 0.3 [38]. Furthermore, the nanoindentation creep mechanism of welded joints in an RPV may be dominated by dislocation motion, and grain boundary activity could hence affect the creep behavior [22]. The value of m of P92 steel welded joint is similar to the value (0.008–0.022) found for RPV welded joint. This indicates that the dominant mechanism of creep deformation could be dislocation activity. The high density of grain boundaries in FGHAZ region could lead to an enhanced m value. The stress distribution beneath the indenter was calculated by finite element modeling. The Fig. S1 shows that the width of deformation zone is larger than 20 μm, and the grain boundary activities could affect the deformation mechanism beneath indenter even the pressed depth is 2 μm. The mean values of m increase significantly in all regions after the CF test. It is well known that creep deformation related to hardness, which is defined as the ability of a material to resist plastic deformation [30]. On the other hand, under cyclic loading conditions, plastic strain would also affect the density of dislocations [35]. The decreased dislocations density after the CF test could be another reason for the increased m, and m can be expressed as a function of the dislocation cell size [18]:
Fig. 13. The observed strain rate sensitivity for the four regions in the P92 steel welded joint.
The creep curve can be fitted with high reliability (R2 > 0.99) by an empirical equation:
h (t ) = h 0 + a (t
t0 ) b + kt
(2)
where h0 and t0 are the initial holding depth and time at the beginning of holding period, and a, b, k are the fitting constants. As an example of the utility of this equation, Fig. 12(a) shows the fit achieved (R2 > 0.99) using it to describe the creep curve in the FGHAZ region of the as-welded sample. Fig. 12(b) shows the strain rate variation deduced using the fitted equation, while the variation of strain rate in secondary creep is plotted in the insert. During the primary creep stage, the creep strain rates decreased rapidly from 0.002 s−1 to 0.0003 s−1. In the secondary creep stage, the creep strain decreased more slowly from 0.0003 s−1 to around 0.0001 s−1. The decrease in hardness as function of creep time is shown in Fig. 12(c), while. Fig. 12(d) shows a natural logarithm correlation between hardness and creep strain rate. The SRS could be estimated by a linear relationship during the steady-state creep stage. Fig. 13 shows the distribution of SRS (m) in all regions of both the as-welded and CF samples. For the as-welded sample, the mean values of m were in the range from 0.010 to 0.035, and the maximum value was found in the FGHAZ region. After the CF test, the mean values of m were found to range from 0.052 to 0.082, and the maximum value also occurred in the FGHAZ region. Because the initial holding depth was > 1500 nm, the indentation size effect on creep behavior could be
m=
3 3kb T d aµbcKV
(3)
where d is the mean dislocation cell diameter, V* is the activation volume, kb is Boltzmann’s constant, T is the temperature in Kelvin, and a, μ, b, c, K are constants for a given material. It is also known that the relationship between the density of dislocations and the mean dislocation cell diameter could be described as [45,46]
d=
K (4)
Where ρ is the density of dislocations, and K is a constant for a given material. Thus the value of m can be given as a function of dislocation density:
m=
3 3 kb T 1 aµbcV
(5)
Eq. (5) indicates that the SRS is inversely proportional to the square root of the dislocation density as a, μ, b, c, K and V* are positive for a given material. In a previous study, dislocation annihilation was given
Fig. 14. The dislocation density of FGHAZ region of (a) As-welded sample (b) CF tested sample by transmission electron microscopy (TEM). 9
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as the main reason for the cyclic softening phenomenon in P92 steel observed under CF loading [36,47]. Furthermore, the low dislocation density condition of P92 steel welded joint evolves because of microstructural coarsening with more equiaxed cells and dislocation annihilation occurring during the CF test [9,35]. The relatively low dislocation density of CF tested sample also leads to the enhanced m value. A similar study of gas tungsten arc welded P91 steel [34] found that the dislocation density was significantly lower in the vicinity of the finegrained HAZ adjacent to the base metal than in other regions [36]. Fig. 14 shows the dislocation density of FGHAZ region of As-welded and CF tested samples. Thus the significantly enhanced m value in the FGHAZ reflects the lower dislocation density after CF test.
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4. Conclusions This paper presents the results of a study of the nanoindentation creep behavior in micro-regions of as-welded and creep-fatigue (CF) samples, cut from a submerged arc welded joint made in a P92 steel. The strain-controlled CF test was performed at 650 °C to investigate the relationship between cyclic life and the initial hardness condition of samples positioned in different regions across the weld. The hardness and creep displacement were obtained in BM, FGHAZ, CGHAZ and WM regions of as-welded and CF samples. The strain rate sensitivities (SRS) were estimated for all regions from the nanoindentation results. The following conclusions can be drawn: 1. Cyclic softening behavior was observed for all samples during the CF test. The HAI925 sample with the highest initial hardness showed the longest cyclic life among the four samples used in CF testing. 2. For both as-welded and CF samples, the FGHAZ and BM regions had a lower hardness and creep resistance than the other regions. Compared with the as-welded sample, a reduced hardness and enhanced creep deformation were obtained in all regions of the CF sample. The increased creep displacement observed indicated that the CF loading had a deleterious effect on the creep resistance of the P92 steel welded joint. Moreover, the deleterious effect was more pronounced in BM and FGHAZ regions than in the other two region. 3. The values (0.010–0.035) found for the SRS indicated that the nanoindentation creep mechanism in the P92 steel welded joint was most likely dominated by the dislocation activation and motion. After CF test, the enhanced SRS (0.052–0.082) observed in all regions could be explained by the reduced hardness and decreased dislocations density. Declaration of Competing Interest We declare that we have no conflict of interest. Acknowledgements The research work was supported by the National 13th five-year Key Technologies R&D Program (No. 2016YFC0801902) and Zhejiang Provincial Natural Science Foundation of China (LY18E010006) and National Natural Science Foundation of China (51575489) Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijfatigue.2020.105506. References [1] Susmel L, Taylor D. Two methods for predicting the multiaxial fatigue limits of sharp notches. Fatigue Fract Eng Mater Struct 2003;26:821–33. [2] Kannan R, Srinivasan VS, Valsan M, et al. High temperature low cycle fatigue behaviour of P92 tungsten added 9Cr steel. Trans Ind Inst Met 2010;63:571–4.
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Z. Gao, et al. [36] Watanabe T, Tabuchi M, Yamazaki M, et al. Creep damage evaluation of 9Cr–1Mo–V–Nb steel welded joints showing Type IV fracture. Int J Pres Vessel Pip 2006;83:63–71. [37] Ma Y, Peng GJ, Feng YH, et al. Nanoindentation investigation on the creep mechanism in metallic glassy films. Mater Sci Eng A 2016;651:548–55. [38] Ding ZY, Song YX, Ma Y, et al. Nanoindentation investigation on the size-dependent creep behavior in a Zr-Cu-Ag-Al bulk metallic glass. Metals 2019;5:613. [39] Johnson KL. Contact mechanics. Cambridge University Press; 1987. [40] Li WB, Henshall JL, Hooper RM, et al. The mechanisms of indentation creep. Acta Metal Mater 1999;39:3099–110. [41] Choi IC, Kim YJ, Wang YM, et al. Nanoindentation behavior of nanotwinned Cu: influence of indenter angle on hardness, strain rate sensitivity and activation volume. Acta Mater 2013;61:7313–23.
[42] Coble RL. A model for boundary diffusion controlled creep in polycrystalline materials. J Appl Phys 1963;34:1679. [43] Cao ZH, Lu HM, Meng XK, et al. Indentation size dependent plastic deformation of nanocrystalline and ultrafine grain Cu films at nanoscale. J Appl Phys 2009;105:083521. [44] Wang F, Huang P, Xu KW. Time dependent plasticity at real nanoscale deformation. Appl Phys Lett 2007;90:2715. [45] Staker MR, Holt DL. The dislocation cell size and dislocation density in copper deformed at temperatures between 25 and 700 °C. Acta Mater 1972;20:569–79. [46] Holt DL. Dislocation cell formation in metals. J Appl Phys 1970;41:3197. [47] Saad A. Crystal Plasticity and creep of power plant materials (Ph.D. thesis). UK: University of Nottingham; 2011.
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International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Nanoindentation investigation on the creep behavior of P92 steel weld joint after creep-fatigue loading
T
Zengliang Gaoa,c, Yuxuan Songa,b, Zhouxin Pana, Jianan Chena, Yi Mab,⁎ a
Institute of Process Equipment and Control Engineering, College of Mechanical Engineering Zhejiang University of Technology, Hangzhou 310014, China Institution of Micro/Nano-Mechanical Testing Technology & Application, College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310014, China c Engineering Research Center of Process Equipment and Re-manufacturing, Ministry of Education, Hangzhou, China b
ARTICLE INFO
ABSTRACT
Keywords: Welded joint Creep-fatigue interaction Nanoindentation Hardness Creep behavior
Using nanoindentation technology, the creep behavior of P92 steel welded joint that had experienced creepfatigue (CF) loading was studied at the nanoscale. In both as-welded and CF samples, the fine-grain heat affected zone region exhibited relatively lower hardness and lower creep resistance than other regions of the welded joint. Compared to the as-welded sample, enhanced creep deformation and reduced hardness were observed in the CF sample. The strain rate sensitivity was in the range from 0.010 to 0.035 for as-welded sample and 0.052 to 0.082 for the CF sample, as the measurement region changed from base metal to weld metal regions.
1. Introduction In the quest for higher power plant efficiency the trend is to go for still higher operating pressures. The next generation of power plants will operate with steam pressures in the range of 300 bar. These are the ultra-super critical power units, that operate at temperatures of 615–630 °C. Such units are frequently subject to creep-fatigue (CF) loading at high temperature through repeated start-up and shutdown cycles. Consequently, the service life of components is significantly reduced and difficult to predict. P92 steel has been extensively utilized in the main steam piping of ultra-supercritical units due to its extremely high creep resistance, low expansion coefficient and high thermal conductivity [1]. Notwithstanding the mechanical properties of P92 steel, that are adequate to the service requirement of ultra-supercritical units, welded joints are a weak region which could be the source of failure during service. Bicego et al. performed low cyclic fatigue (LCF) test of P91, P92 and E911 steel welded joints at 600 °C, which showed a reduction factor in cyclic life about 2 compared to their base metal (BM) samples [2]. It is well known that mechanical properties such as hardness and fracture strength are often reduced during the service life in many engineering components [3–7]. The degradation rate of mechanical properties is essential in order to make residual life assessments of ultra-supercritical units. However, the mechanical properties of a material are to accurately measure in situ during service. Hence, in order to predict the residual life of ultra-supercritical thermal power units, the remnant mechanical properties and damage micro⁎
mechanisms of materials after service need to be investigated. Mariappan et al. estimated the remnant tensile properties of P91 steel after prior LCF and CF loading conditions [8]. Gopinath et al. observed the microstructure of P92 steel after CF testing, and examined the damage micro-mechanisms [9]. However, the remnant mechanical properties of welded joints were not fully studied due to their structural hierarchy and mechanical heterogeneity. Pandey et al. investigated the formation mechanism of various microstructures in different regions of a P92 steel welded joint and found that the welding process produced a heterogeneous microstructure in the heat affected zone (HAZ) of welded joint [10]. The HAZ could be divided into the fine-grain heat affected zone (FGHAZ) and coarse-grain heat affected zone (CGHAZ) based on grain size, with the nucleation and propagation of creep voids more likely to occur in the FGHAZ [11–13]. They defined this as the main reason for the premature failure of welded joint. However, the relationship between microstructure and mechanical properties in the HAZ is still not confirmed. Because of the narrow width of HAZ, the change of mechanical properties with microstructural gradient is difficult to measure using conventional methods. Nanoindentation is an efficient and high-resolution technology capable of measuring mechanical properties at the nano/micro-scale [14–16]. Nguyen et al. used nanindentation to investigate the strain rate sensitivity of SM490 and SS400 structural steel welded joints by the rate-jump method after low-cycle fatigue loading [17,18]. Pham et al. determined a constitutive equation to obtain the yield strength and the strain hardening exponent of structural steel through
Corresponding author. E-mail address: [email protected] (Y. Ma).
https://doi.org/10.1016/j.ijfatigue.2020.105506 Received 3 September 2019; Received in revised form 15 January 2020; Accepted 20 January 2020 Available online 21 January 2020 0142-1123/ © 2020 Elsevier Ltd. All rights reserved.
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Table 1 Chemical compositions of P92 steel and the welding consumable (wt.%). Element
C
Si
Mn
Ni
Cr
Mo
P
S
N
V
P92 P92 wire
0.106 0.095
0.235 0.150
0.361 0.610
0.108 0.680
9.220 8.360
0.374 0.940
0.017 0.011
0.008 0.007
0.061 0.041
0.182 0.020
Fig. 1. (a) Illustration of the position of the samples relative to the weld and the pipe thickness; (b) Optical macrograph of the welded joint; (c) Spatial nanoindentation hardness contour in the welded joint.
80 × 80 × 840 mm were prepared for testing. In order to produce the welded joint, two pipes sections were welded together using submerged arc welding. The welded pipe was then annealed at 760 °C for 2 h followed by air cooling. Nondestructive inspection was used to confirm that the weld joints could meet the requirements. The compositions of the P92 steel and filler wire are listed in Table 1. Fig. 1 (a) shows the layout of the CF samples both through the thickness of the pipe and in relation to the welded joint, while Fig. 1(b) shows an etched macrograph of the weld cross-section and Fig. 1(c) shows spatial nanoindentation hardness contours. The P92 steel welded joint was etched using a mixture of 92 ml water, 4 ml hydrofluoric acid and 4 ml nitric acid.
nanoindentation [19]. It has also been reported that creep deformation could be observed for high-melting point materials [20,21] at room temperature, using nanoindentation techniques. In a previous study by several of the present authors, creep deformation in different regions of SA508 Gr3 steel welded joints was clearly observed using the constantload method [22]. This paper investigates the mechanical properties in micro-regions of P92 steel welded joint after CF loading. The P92 steel welded joint was divided into four regions (welded metal (WM), base metal (BM), CGHAZ and FGHAZ regions) based on the distance from the weld center line. For as-welded and CF tested samples, the hardness and creep deformations in those four regions were measured by nanoindentation. The strain rate sensitivities of creep were also estimated to study creep mechanism.
2.2. Experiment details
2. Experimental procedures
The creep-fatigue interaction (CF) test was conducted using a high temperature electronic creep-fatigue testing machine (RPL 300). The CF experiments were performed in air at 650℃. The samples were held for 25 min at 650 °C before the test started. During the testing, the
2.1. Materials P92
pipe
sections
with
thickness,
width
and
length
of 2
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Fig. 2. Microstructures observed in the as-welded sample (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal by laser scanning confocal microscopy (LSCM).
temperature variation was kept at less than ±1 °C through three S-type thermocouples. Symmetric trapezoidal waveforms with a constant strain amplitude of 0.4% and strain rate of 0.001 s−1 and holding periods of 5 mins at maximum and minimum strains were used for CF tests. The WM, BM and HAZ samples intended for nanoindentation experiments were cut from as-welded and CF tested samples using electrodischarge machining (EDM). The microstructures in all regions of both samples were observed by laser scanning confocal microscopy (LSCM, OLYMPUS OLS4500). At first, the BM, FGHAZ, CGHAZ and WM regions were clearly distinguished at 400 times magnification through LSCM measurement. The grain sizes of WM and CGHAZ regions were approximately 3 times larger than BM and FGHAZ region. Then, several 200 × 200 μm2 areas in BM, FGHAZ, CGHAZ and WM regions were randomly chosen to calculate the grain size distribution at 1000 times magnification. The number of grains with different sizes was respectively recorded in those areas. To make sure the reliability of experimental results, 5 different areas were chosen from BM, FGHAZ, CGHAZ and WM regions, respectively. Prior to nanoindentation tests, both samples were carefully polished to a mirror surface on the Nanopoli-100 (NaiNuo, Hangzhou). Diamond abrasive at the average size of 2 μm (8000#) and polyurethane polish pad were adopted. After 60-min polishing, samples were carefully cleaned in the anhydrous alcohol by ultrasonic cleaning. Nanoindentation experiments were conducted on an Agilent Nano Indenter G200 with a standard Berkovich indenter at room temperature. Before commencing the nanoindentation creep experiment, the hardness of the four weld regions (FGHAZ, CGHAZ, BM and WM) were
obtained using the recently developed continuous stiffness measurement (CSM) method, which has attracted the attention of many researchers due to its ability to measure the stiffness during the indentation process [23,24]. A constant strain rate of 0.05 s−1 was used in the CSM measurements. During the creep test, the Berkovich indenter was held for 1000 s at a maximum load of 196 mN, and the loading rate was kept constant at 4 mN/s. The space between each two indents was kept at least 50 μm. To ensure the reliability of the nanoindentation data, 20 indentations were made in each region. The thermal drift was controlled to be less than 0.05 nm/s during experiments. Meanwhile, the load drift correction was strictly calibrated at 10% of the maximum loading after the unloading stage. 3. Results and discussion 3.1. Creep-fatigue interaction experiment The microstructures observed in various regions of welded and CF tested samples are plotted in Figs. 2 and 3. For both samples, the prior austenite grain boundary of BM, FGHAZ, CGHAZ, WM regions can be explicitly distinguished in Figs. 2(a)–(d) and 3(a)–(d). A distribution of precipitates is apparent in prior austenite grains. The precipitates that were exist inside the grains of the M23C6 type, and the grain boundaries are strengthened by distributed fine MX precipitates [25–27]. These precipitates have been reported to enhance the creep resistance of P92 steel at high temperature [8]. The CF test was continued until all four samples had ruptured in either the BM or HAZ regions. The cyclic stress responses observed 3
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Fig. 3. Microstructures observed in the CF sample (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal by laser scanning confocal microscopy (LSCM).
Fig. 4. (a) Cyclic stress relaxation observed during the creep-fatigue interaction test; (b) Creep-fatigue interaction hysteresis loop of HAI 925 sample after 1 and 2000 loading cycles.
during the strain-controlled loading are shown in Fig. 4(a). The cyclic softening phenomenon can be clearly seen. In Fig. 4(a), the softening process can be divided into three stages. During the first period, the material softened rapidly, and this is followed by a period of slower steady-state softening, before a final period of acceleration of the rate of softening that led to rupture [28,29]. Fig. 4(a) shows that the cyclic lives for the four CF samples are
significantly different and clearly depends on position through the weld thickness. The HAI925 sample ruptured after more than 2000 loading cycles, while, in contrast, the HAI922 sample survived for only 960 loading cycles. Hardness should be intrinsically connected to creep resistance, as both parameters reflect the resistance to plastic deformation [30]. The spatial distribution of nanoindentation hardness contours through the weld depth is plotted in Fig. 1(c). It can be seen 4
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Fig. 5. The schematic diagram of illustration of the four microstructures in the welded joint after the CF test (HAI 923 sample), together with the nanoindentation positions.
Fig. 6. Grain size variation in the welded joint of P92 steel (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal.
that the hardness of HAZ region was higher than that of WM or BM regions. Furthermore, a region of significantly higher hardness exists at the weld root due to the submerged arc welding process and the weld profile. The longer cyclic life of the HAI925 sample could then be caused by its initially higher hardness condition. Fig. 4(b) presents, for the HAI925 sample, the stress-strain hysteresis loops for the first and 2000th cycles of loading. It is clear that creep deformation has occurred during the holding periods in the CF test, with the amount of deformation apparently increasing with number of applied cycles. This phenomenon has led to the stress relaxation shown in Fig. 4(a). The increased plastic deformation of martensitic steels during holding time
has been previously confirmed to be correlated with sub-grain size [31]. Dubey et al. [32] also found that the cyclic softening phenomenon was partly caused by significant coarsening of the fine sub-grain structure due to accumulation of plastic strain. The CF experiment represents the overall cyclic stress response of the sample. The mechanism and extent of microstructural evolution in WM, BM, FGHAZ and CGHAZ regions are, however, quite different. Thus, the mechanical properties in each region of the welded joint should be measured in order to throw light on this aspect.
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Fig. 7. Measured hardness as a function of indentation depth by CSM in FGHAZ region (a) As-welded sample; (b) Sample after the CF test.
Fig. 8. Hardness obtained using the CSM method in the four different regions of (a) the as-welded sample and (b) the CF sample.
3.2. Nanoindentation hardness
cases mean values at 500 nm and 1500 nm showed similar trends.
Fig. 5 shows the microstructure in the divided nanoindentation regions of a typical welded joint after CF test. The positions of nanoindentations in the WM, BM, FGHAZ and CGHAZ regions are also shown in the schematic diagram. Fig. 6(a)–(d) plots the grain size in the WM, BM, FGHAZ and CGHAZ regions, respectively. The mean values of grain size in those regions of the as-welded sample were 21 μm (BM), 18 μm (FGHAZ), 57 μm (CGHAZ) and 50 μm (WM). These values became slightly larger in the samples that had been subject to CF testing and were measured as 24 μm (BM), 23 μm (FGHAZ), 59 μm (CGHAZ) and 52 μm (WM). Fig. 7(a) and (b) show the hardness H as a function of indentation depth in the FGHAZ region of both as-welded and CF tested samples. A clear effect of indentation size effect is observed, with hardness values reducing with increased indentation depth in both cases. In the case of aluminum and brass alloys an increased hardness observed with shallow indentations has been suggested to be caused by the presence of geometrically necessary dislocations [33]. The hardness values at indentation depths of 500 nm and 1500 nm were adopted, respectively. Fig. 8(a) and (b) show the variation in hardness across the four regions of the welded joint. Compared with the as-welded sample, CF tested sample shows a reduced hardness in all regions, with the decrease being particularly marked in going form the CGHAZ to the FGHAZ regions. The hardness of high chromium steel has been shown to decrease during the holding period due to the sub-structural recovery and coarsening of carbides [34,35]. Furthermore, the growth of precipitates was more remarkable in the FGHAZ region during creep, which could lead to the observed significant reduction of hardness [36]. In both
3.3. Nanoindentation creep behavior Fig. 9(a) shows the load P applied during the creep test as a function of time t, with a constant peak value of 196 mN and a constant loading and unloading rate of 4 mN/s. Typical creep load- indentation depth (Ph) curves for all four regions of as-welded and CF tested samples are shown in Fig. 9(b) and (c), respectively. In both cases, it was observed that the steady-state holding depth in the BM and FGHAZ regions was greater than in the other two regions for the same peak load, which is consistent with the low observed hardness values. The corresponding indentation depth creep curves during the holding period are shown in Fig. 10(a)–(d), in which creep displacements are plotted against holding time. In order to aid better interpretation of these curves, the starting points (for both holding time and creep displacement) have been set to zero. Two stages of creep deformation can then be distinguished, namely the primary creep and secondary creep. In the primary stage, the creep displacement increases relatively quickly, while the creep rate decreases rapidly [37]. In the secondary creep stage, the displacement becomes almost linear with time and the creep rate gradually becomes stable. Compared with the as-welded sample, an enhanced creep displacement was observed in the CF sample. For both samples, the creep deformations in the regions with a relatively higher hardness (WM and CGHAZ) primary creep plays a greater role than secondary creep, while in the case of the softer BM and FGHAZ regions, secondary creep plays a greater role. Fig. 11(a) shows the variation in creep displacement for all four regions of both samples. The mean values of creep displacement in the BM and FGHAZ regions can be seen to be greater than in the other 6
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Fig. 9. (a) Creep test loading curve as a function of time. (b) Representative load–displacement (P-h) curves in all regions of as-welded joint; (c) Under prior creepfatigue interaction loading condition.
Fig. 10. Representative creep curves of P92 steel welded joint (a) Base metal; (b) Fine-grain heat affected zone; (c) Coarse-grain heat affected zone; (d) Weld metal. 7
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Fig. 11. (a) Total creep displacement (represented by indenter depth) and (b) steady-state creep rate in the four regions of the P92 steel welded joint.
Fig. 12. (a) Fit achieved for the FGHAZ creep curve using Eq. (2); (b) Variation in strain rate deduced from Eq. (2); (c) Decrease in hardness as a function of creep time; (d) Natrual log correlation between hardness and strain rate: the SRS value can be estimated by linearly fitting the steady-state part.
two regions. Creep displacements in all regions were greater in the CF sample compared with the as-welded case. The steady-state creep rates for all four regions are given in Fig. 11(b), and it is clear that the secondary creep rates increase after the CF test, with a greater increase evident in the BM and FGHAZ regions. As the dominant creep mechanism was secondary creep in these regions, creep displacements were significantly affected by these enhanced secondary creep rates. From Fig. 11(a), it can be concluded that the creep resistance of the P92 steel welded joint became lower after the CF test, with a decline in creep resistance apparent in the softer regions such as BM and FGHAZ regions. The coarsening of precipitates and recovery of dislocations during CF testing has been reported to be responsible for the reduction in creep resistance, with those mechanisms being more active in FGHAZ
region [36]. 3.4. Strain rate sensitivity Strain rate sensitivity (SRS) plays an important role in determining the mechanical properties of a material [38]. Indentation creep has been a widely used method to study SRS, which in turn can reveal information regarding the creep mechanism of traditional metals [39]. It is known that indentation creep could be dominated by mechanisms like dislocation glide and climb, grain boundary slide, amongst other [40]. The value of strain rate sensitivity m is given by [41]:
m= 8
InH In
(1)
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excluded. For polycrystalline materials, grain boundary sliding should not exist at such a low value of m. Equally, grain boundary diffusion and the tip-sample atomic diffusion could be also eliminated due to the high creep strain rate and deep holding depth [42–44]. Dislocation movement is has been shown to be the dominant creep mechanism as m drops below 0.3 [38]. Furthermore, the nanoindentation creep mechanism of welded joints in an RPV may be dominated by dislocation motion, and grain boundary activity could hence affect the creep behavior [22]. The value of m of P92 steel welded joint is similar to the value (0.008–0.022) found for RPV welded joint. This indicates that the dominant mechanism of creep deformation could be dislocation activity. The high density of grain boundaries in FGHAZ region could lead to an enhanced m value. The stress distribution beneath the indenter was calculated by finite element modeling. The Fig. S1 shows that the width of deformation zone is larger than 20 μm, and the grain boundary activities could affect the deformation mechanism beneath indenter even the pressed depth is 2 μm. The mean values of m increase significantly in all regions after the CF test. It is well known that creep deformation related to hardness, which is defined as the ability of a material to resist plastic deformation [30]. On the other hand, under cyclic loading conditions, plastic strain would also affect the density of dislocations [35]. The decreased dislocations density after the CF test could be another reason for the increased m, and m can be expressed as a function of the dislocation cell size [18]:
Fig. 13. The observed strain rate sensitivity for the four regions in the P92 steel welded joint.
The creep curve can be fitted with high reliability (R2 > 0.99) by an empirical equation:
h (t ) = h 0 + a (t
t0 ) b + kt
(2)
where h0 and t0 are the initial holding depth and time at the beginning of holding period, and a, b, k are the fitting constants. As an example of the utility of this equation, Fig. 12(a) shows the fit achieved (R2 > 0.99) using it to describe the creep curve in the FGHAZ region of the as-welded sample. Fig. 12(b) shows the strain rate variation deduced using the fitted equation, while the variation of strain rate in secondary creep is plotted in the insert. During the primary creep stage, the creep strain rates decreased rapidly from 0.002 s−1 to 0.0003 s−1. In the secondary creep stage, the creep strain decreased more slowly from 0.0003 s−1 to around 0.0001 s−1. The decrease in hardness as function of creep time is shown in Fig. 12(c), while. Fig. 12(d) shows a natural logarithm correlation between hardness and creep strain rate. The SRS could be estimated by a linear relationship during the steady-state creep stage. Fig. 13 shows the distribution of SRS (m) in all regions of both the as-welded and CF samples. For the as-welded sample, the mean values of m were in the range from 0.010 to 0.035, and the maximum value was found in the FGHAZ region. After the CF test, the mean values of m were found to range from 0.052 to 0.082, and the maximum value also occurred in the FGHAZ region. Because the initial holding depth was > 1500 nm, the indentation size effect on creep behavior could be
m=
3 3kb T d aµbcKV
(3)
where d is the mean dislocation cell diameter, V* is the activation volume, kb is Boltzmann’s constant, T is the temperature in Kelvin, and a, μ, b, c, K are constants for a given material. It is also known that the relationship between the density of dislocations and the mean dislocation cell diameter could be described as [45,46]
d=
K (4)
Where ρ is the density of dislocations, and K is a constant for a given material. Thus the value of m can be given as a function of dislocation density:
m=
3 3 kb T 1 aµbcV
(5)
Eq. (5) indicates that the SRS is inversely proportional to the square root of the dislocation density as a, μ, b, c, K and V* are positive for a given material. In a previous study, dislocation annihilation was given
Fig. 14. The dislocation density of FGHAZ region of (a) As-welded sample (b) CF tested sample by transmission electron microscopy (TEM). 9
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as the main reason for the cyclic softening phenomenon in P92 steel observed under CF loading [36,47]. Furthermore, the low dislocation density condition of P92 steel welded joint evolves because of microstructural coarsening with more equiaxed cells and dislocation annihilation occurring during the CF test [9,35]. The relatively low dislocation density of CF tested sample also leads to the enhanced m value. A similar study of gas tungsten arc welded P91 steel [34] found that the dislocation density was significantly lower in the vicinity of the finegrained HAZ adjacent to the base metal than in other regions [36]. Fig. 14 shows the dislocation density of FGHAZ region of As-welded and CF tested samples. Thus the significantly enhanced m value in the FGHAZ reflects the lower dislocation density after CF test.
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4. Conclusions This paper presents the results of a study of the nanoindentation creep behavior in micro-regions of as-welded and creep-fatigue (CF) samples, cut from a submerged arc welded joint made in a P92 steel. The strain-controlled CF test was performed at 650 °C to investigate the relationship between cyclic life and the initial hardness condition of samples positioned in different regions across the weld. The hardness and creep displacement were obtained in BM, FGHAZ, CGHAZ and WM regions of as-welded and CF samples. The strain rate sensitivities (SRS) were estimated for all regions from the nanoindentation results. The following conclusions can be drawn: 1. Cyclic softening behavior was observed for all samples during the CF test. The HAI925 sample with the highest initial hardness showed the longest cyclic life among the four samples used in CF testing. 2. For both as-welded and CF samples, the FGHAZ and BM regions had a lower hardness and creep resistance than the other regions. Compared with the as-welded sample, a reduced hardness and enhanced creep deformation were obtained in all regions of the CF sample. The increased creep displacement observed indicated that the CF loading had a deleterious effect on the creep resistance of the P92 steel welded joint. Moreover, the deleterious effect was more pronounced in BM and FGHAZ regions than in the other two region. 3. The values (0.010–0.035) found for the SRS indicated that the nanoindentation creep mechanism in the P92 steel welded joint was most likely dominated by the dislocation activation and motion. After CF test, the enhanced SRS (0.052–0.082) observed in all regions could be explained by the reduced hardness and decreased dislocations density. Declaration of Competing Interest We declare that we have no conflict of interest. Acknowledgements The research work was supported by the National 13th five-year Key Technologies R&D Program (No. 2016YFC0801902) and Zhejiang Provincial Natural Science Foundation of China (LY18E010006) and National Natural Science Foundation of China (51575489) Appendix A. Supplementary material Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijfatigue.2020.105506. References [1] Susmel L, Taylor D. Two methods for predicting the multiaxial fatigue limits of sharp notches. Fatigue Fract Eng Mater Struct 2003;26:821–33. [2] Kannan R, Srinivasan VS, Valsan M, et al. High temperature low cycle fatigue behaviour of P92 tungsten added 9Cr steel. Trans Ind Inst Met 2010;63:571–4.
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