- Email: [email protected]
An assessment of creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb (ASME grade 92) steel
Materials Science & Engineering A 640 (2015) 61–71
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
An assessment of creep deformation and rupture behaviour of 9Cr– 1.8W–0.5Mo–VNb (ASME grade 92) steel T. Sakthivel n, S. Panneer Selvi, K. Laha Mechanical Metallurgy Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
art ic l e i nf o
a b s t r a c t
Article history: Received 21 April 2015 Received in revised form 18 May 2015 Accepted 21 May 2015 Available online 27 May 2015
Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been investigated at 873 K, 923 K and 973 K over a stress range of 80–220 MPa. The absence of clear primary creep regime and prolonged secondary stage of creep deformation have been noticed under lower stress level at 973 K. The variation of minimum creep rate with applied stress obeyed Norton's power law of creep. The apparent stress exponents of 15.2, 12.3 and 5.8, and apparent activation energy of 619 kJ/mole have been estimated for creep deformation of the steel. The apparent stress exponents and activation energy have been rationalised on the basis of threshold stress. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. The threshold stress compensated true stress exponent of 4 and true activation energy of 244 kJ/mole, and threshold stress normalised by Orowan stress confirms that the lattice diffusion assisted localised climb of dislocation is the rate controlling of creep deformation in the steel. The steel obeyed Monkman and modified Monkman–Grant relationships. Damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel. & 2015 Elsevier B.V. All rights reserved.
Keywords: ASME grade 92 ferritic steel Creep Activation energy Damage tolerance factor
1. Introduction Ferritic–martensitic 9% Cr steels are considered as candidate structural materials for nuclear energy systems [1,2]. The choice is based on excellent mechanical properties at high temperatures, good weldability, low thermal expansion coefficient, high thermal conductivity, adequate corrosion and stress-corrosion cracking resistances and high inherent void swelling resistance on neutron irradiation [3–5]. The ASME grade 91 and 92 (9Cr–1.8W–0.5Mo– VNb) steels are used extensively in the advanced fossil fired power plants and is being considered for structural applications in advanced sodium cooled fast reactors [6]. The addition of 1.5–2.0 wt% tungsten and 0.001 to 0.006 wt% boron along with the reduction in molybdenum content to 0.3–0.6 wt% in grade 91 (9Cr–1Mo– VNb) steel, leads to the development of grade 92 steel [7–10]. The grade 92 steel offers about 30% higher creep rupture strength over the grade 91 steel especially at higher temperatures [10,11]. The steel is used in normalised and tempered condition and has tempered martensitic structure. The steel derives its high temperature strength from tempered martensitic lath structure, stabilisation of martensitic lath structure by chromium rich M23C6 n
Corresponding author. E-mail address: [email protected] (T. Sakthivel).
http://dx.doi.org/10.1016/j.msea.2015.05.068 0921-5093/& 2015 Elsevier B.V. All rights reserved.
type of carbide, martensite phase transformation induced high dislocation density, intra-lath MX type of V and Nb-carbonitrides, and solid solution strengthening from tungsten and molybdenum [12–15]. Fine dispersion of highly stable MX type of V and Nbcarbonitrides particles are reported to enhance creep rupture strength of the tempered martensite steel not only acting as a barrier to dislocation motion but also by stabilisation of dislocation network. The presence of tungsten in the M23C6 precipitate decreases growth rate of the precipitate during creep exposure, which in turn increases the stability of the martensitic lath structure of the steel on creep exposure [7–19]. In the present investigation, creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been studied, and analysis has been carried out by performing detailed metallography to have insight of the failure mechanism. Creep deformation has been rationalised based on the back-stress concept to the dislocation motion.
2. Experimental details The chemical composition of grade 92 (ASME Gr. 92) steel is given in Table.1. The steel plate having 12 mm thickness was normalised at 1323 K for 30 min followed by air cooling, and the steel was subsequently tempered at 1053 K for 120 min followed
62
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Table 1 Chemical composition (wt%) of ASME Gr. 92 steel. Elements
C
Cr
W
Mo
Mn
Si
V
N
Nb
Gr. 92 steel
0.10
9.2
1.9
0.51
0.36
0.27
0.22
0.050
0.07
Elements
S
P
Ni
Al
B
Ti
N/Al
Fe
Gr. 92 steel
0.002
0.010
0.060
0.010
0.001
0.002
5
Bal
by air cooling. Creep specimens having dimensions of 5 mm gauge diameter and 50 mm gauge length were fabricated. Constant load creep tests in air have been carried out at 873 K, 923 K and 973 K in the stress range of 80–220 MPa in creep machines equipped with split type furnace having three zone temperature controller. Temperature was controlled within 7 2 K ( 72 °C) along the gauge length of the specimen during creep test. Elongation of the specimen was monitored by an extensometer and digital dial gauge attachment having measuring accuracy of 70.001 mm and was continuously logged in a data logger. Scanning electron microscopic (SEM) (SE – secondary electron, BSE – back scattered electron, FEG – field emission gun) studies were carried out on the steel before and after creep tests to assess microstructural degradation and fracture behaviour on creep exposure. Immersion etching for 15 s using Villella's reagent (picric acid 5 g, HCl acid 25 ml, Ethyl alcohol 500 ml) has been employed to reveal the microstructures of the steel. Specimens were thinned down to 50 mm by mechanical polishing with emery paper under flowing water followed by electrolytic double jet thinning using 20% perchloric acid and ethanol solution for transmission electron microscopic (TEM) investigation.
3. Results and discussion 3.1. Microstructure of the steel Microstructure of the grade 92 steel in the normalised and tempered condition is shown in Fig. 1(a). The prior-austenite grain size of the steel was around 20 mm. Microstructure of the steel consists of tempered martensitic lath structure (Fig. 1(b) and (c)) with transformation induced high dislocation density about 7 1014 m 2[7]. The width of the martensitic lath structure was 400 nm. Prior-austenite grain boundaries and sub-grain boundaries were decorated with M23C6 precipitates. Average size of the M23C6 precipitate was ∼90 nm measured from TEM micrograph. The energy dispersive spectroscopy (EDS) spectrum analysis of the precipitates depicted the enrichment of tungsten about 7–8 wt% (Fig. 1(d)). Presence of tungsten is reported to reduce the coarsening rate of M23C6 precipitates at high temperatures [18]. The MX type of V and Nb-rich carbide and carbo-nitride precipitates (having size of around ∼30 nm measured from FEG–SEM micrograph) in the intra-laths region were observed in the steel. The presence of M23C6 and MX precipitates in the prior-austenite, sub-grain boundaries and intra-lath regions resists the movement of boundaries and dislocations respectively led to enhance the creep strength of grade 92 steel at high temperatures [18,26]. 3.2. Creep deformation behaviour of the steel Creep curves of grade 92 steel at 923 K over a stress range of 110–170 MPa are shown in Fig. 2(a). The variations of creep strain with creep exposure exhibited the instantaneous strain on loading, distinct primary creep, narrow region of secondary creep and
prolonged tertiary creep regimes at 923 K. Similar creep deformation behaviour has been noticed at 873 K and 973 K. Narrow region of secondary and prolonged tertiary creep regimes have generally been observed in Fe–9%Cr ferritic–martensitic steels [12,13,20–22]. However, presence of clear primary creep regime was not observed under lower stress levels at 973 K (Fig. 2(b) and (c)). Longer secondary creep regime observed at 973 K under low stress level in the steel might be due to increase in solid solution strengthening contribution from tungsten by the dissolution of Laves phase (Fe2W). Extended secondary stage creep deformation has been reported in the P92 type low carbon steel under lower stress level at 923 K [20]. The variations of creep rate with creep exposure at 873 K and 923 K over a stress range of 110–220 MPa are given in Fig. 3. Creep rate of the steel with creep exposure significantly decreases in the primary creep regime, and subsequently shows the minimum creep rate regime and followed by a faster rate of creep deformation in tertiary stage till the time of fracture. The steel spent maximum duration in the tertiary state of creep deformation at all test conditions except under low stress level at 973 K. Variation of creep rate with creep strain at various temperature and stress are given in Fig. 4. The creep rate decreases with increase in creep strain in the primary regime due to work hardening by dislocation multiplication and their interactions. Stabilised creep rate occurs in the shorter secondary strain regime where the work hardening effect is counter balanced by the recovery process such as dislocation annihilation and rearrangement. Rapid increase in creep rate in the tertiary creep strain is attributed to enhancement in recovery process, growth of precipitates and cavities [12,13,22]. However, the decreasing creep rate behaviour from initial deformation was not clearly observed under lower stress level at 973 K (Fig. 4(c)). This might be due to faster annihilation of dislocations generated in the primary creep region or increase in remobilisation of immobile dislocations due to higher temperature. Strain to reach onset of tertiary creep has varied with applied stress and test temperatures (Figs. 4 and 5), onset of tertiary creep deformation occurred at 2% and 1% to 2% creep strain at test temperatures of 873 K and 923 K respectively. However, strain to reach onset of tertiary creep decreases with decrease in stress level significantly at 923 K from 2% to 1%. The change (decrease) in dislocation density up to secondary stage of deformation is relatively higher as compared to tertiary creep regime, where change in precipitation behaviour and boundary dimensions were considerably lower up to ∼1% of creep strain or minimum creep rate regime [12,23]. Creep strain accumulation for the onset of tertiary creep about 1% has been reported in W strengthened steels at 923 K [12,22]. Creep strain for onset of tertiary creep in the range of 0.5–2.5% has been observed at 973 K (Fig. 5). The decrease and increase in creep strain accumulation to onset of tertiary creep at 923 K and 973 K respectively under lower stress level might be due to increase in recovery rate of dislocation structure at 923 K and solid solution strengthening by tungsten at 973 K. 3.3. Stress and temperature dependence of minimum creep rate The variation of minimum creep rate with applied stress at 873 K, 923 K and 973 K is shown in Fig. 6. Minimum creep rate increased with increase in applied stress and test temperature. The variation of minimum creep rate ( ϵ̇min ) with applied stress (s) followed Norton’s power law of creep as ( ϵ̇min = Aσ n ) , where A is a constant, n is the stress exponent of the matrix. The variation in n value found to represent the change in creep deformation mechanisms in the materials. Stress exponent (n)¼1 is considered as Harper–Dorn creep where the dislocation density is invariant with stress. The value of n ¼3 is considered where the dislocation glide is controlled by the rate of migration of solute atoms that are
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
63
Fig. 1. Gr. 92 steel in the normalised and tempered condition (a) SE–SEM, (b) FEG–SEM and (c) TEM micrographs depicts the prior-austenite boundaries and lath regions decorated by M23C6 and MX precipitates, and (d) EDS spectra obtained from the M23C6 precipitate.
attached to the moving dislocations (solute-drag creep). The stress exponent 5 is considered where creep occurs by the dislocation climb controlled process. This is generally been observed in the materials which shows sub-grain structure formation and power law breakdown (PLB) behaviour. The stress exponent eight is considered to be dislocation climb controlled creep, where creep deformation occurs under constant microstructure. PLB occurs due to excess vacancy generation at higher stresses, and cross slip and obstacle controlled glide [24]. In the present investigation, stress exponent values of 15.1, 12.3 and 5.8 have been observed at 873 K, 923 K and 973 K respectively (Table 2). Stress exponent (n) of this steel has not been changed with stress in the investigated stress range. However, significant breakdown of stress exponent under longer creep exposure ( 4 10,000 h) in P92 steel at 923 K has been reported [7]. The obtained stress exponent (n) values are higher than the diffusion controlled dislocation based creep deformation models [24,25]. However, observed values of n were comparable to the reported values in the literature for P92 steel [7,8]. Stress exponent (n) values of 12 and13 have been reported in P92 type steels at 923 K [15]. The decrease in n values with increase in test temperatures occurred in the steel due to extensive microstructural modifications at higher test temperatures such as formation (Laves phase) and coarsening of precipitates (Laves phase, M23C6), and decreased coherent strain between MX precipitates and matrix results in lower stress dependence of minimum creep rate [12–15,25]. The stress (s) and temperature (T) dependencies of creep rate of pure metals and single phase alloys are generally described by Bird–Mukherjee–Dorn (BMD) relationship as [26]
⎛ σ ⎞n ⎛ Q ⎞ ϵkT = A⎜ ⎟ exp⎜ − c ⎟ ⎝ RT ⎠ D0μb ⎝μ⎠
where D¼D0exp( Qc/RT)) is the diffusion coefficient, D0 is the frequency factor, Qc is the activation energy for creep deformation, R is the gas constant, T is the temperature in Kelvin, μ is the shear modulus, b is the burgers vector, k is the Boltzmann constant, n is the stress exponent, A is the dimensionless constant. The creep parameters of n and Q are used to assess the responsible operating creep mechanisms. The creep activation energy (Qc) from the ln (ϵ̇min ) versus 1/T plot was evaluated at constant stress (Fig. 7). Creep activation energy (Qc) for grade 92 steel about 619.6 kJ/ mole has been obtained from the slope of the Arrhenius plot. The apparent activation energy value obtained in this study is comparable to the reported activation energy at Fe – with various Cr concentrations [27]. Creep activation energy evaluated from the present investigation is comparable with the reported energy values of 510 kJ/mole and 510–621 kJ/mole for ferritic steels [2,26]. The observed stress exponent (n) and activation energy values are larger than the solid solution Fe-based single phase alloys because of strong interaction between precipitates and mobile dislocations, which is generally been described by threshold stress [25,26,29]. 3.3.1. Threshold stress and true creep activation energy In order to understand the interactions between precipitates and mobile dislocations in the steel, threshold stress (sth) has been evaluated. Threshold stress is generally defined as the stress below which creep deformation not occurs by a specific creep mechanism. Hence, the effective stress has been considered as responsible for creep deformation instead of applied stress where the alloy is strengthened by particles or precipitates [26]. The threshold stress (sth) can be determined using the modified version of Mukherjee– Bird–Dorn creep equation as [25,26,29]
64
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Fig. 2. Variation of creep strain (%) with time of Gr. 92 steel at (a) 873 K (600 °C) and (b) 973 K (650 °C) over stress range of 80–170 MPa, and (c) projected primary creep regime at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
Fig. 3. Variation of creep rate with time of Gr. 92 steel at (a) 873 K (600 °C) and (b) 923 K (650 °C) over stress range of 110–220 MPa.
⎛ σ − σth ⎞n ⎛ Q ⎞ ϵ min = A⎜ a ⎟ exp⎜ − c ⎟ ⎝ kT ⎠ ⎝ μ ⎠ where A is a constant, n is the matrix stress exponent, σa is the
applied stress, Qc is the creep activation energy, T is the temperature in Kelvin, m is the shear modulus, k is the Boltzmann's constant. Stress exponent value about 4, and similar activation energy for creep (QC) and lattice self diffusion (QD) have been
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
65
Fig. 4. Variation of creep rate with creep strain (%) of Gr. 92 steel at (a) 873 K (600 °C), (b) 923 K (650 °C) and (c) 973 K (700 °C) over stress range of 80–220 MPa.
Fig. 5. Variation of strain to reach onset of tertiary creep with time to reach onset of tertiary creep regime of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
observed in pure metals [25,26]. The threshold stress is evaluated from strain rate (ϵ̇1/4 ) against applied stress plot, where the stress exponent of the matrix value 4 was used (Fig. 8). The interruption of stress line values at the zero strain rates provides threshold
Fig. 6. Variation of minimum creep rate with applied stress of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
stress at various temperatures. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. It is significant to note that the threshold stress decreases with increase in temperature might be due to the
66
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Table 2 The values of stress coefficients and stress exponents for stress dependence minimum creep rate and rupture life of ASME Gr. 92 steel. Temperature (K)
873 923 973
ϵmin = Aσn
tr = Aσ1−n1
A
n
A1
n1
3.84 10 40 3.28 10 31 8.62 10 16
15.1 12.3 5.8
1.54 1038 5.75 1022 5.75 1015
15.3 9.4 6.9
Fig. 9. Variation of minimum creep rate with normalised effective stress by shear modulus [sa sth]/m for P92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
Fig. 7. Arrhenius plot of temperature dependence of minimum creep rate.
Fig. 10. Arrhenius plot of temperature dependence of threshold stress compensated minimum creep rate.
Fig. 8. Variation of minimum creep rate ϵ̇1/4 with applied stress (sa) to obtain threshold stress at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
increase in precipitates size and decrease in dislocation density on high temperature exposure. The variation of strain rate (ϵ̇min ) with normalised effective stress by shear modulus ((sa sth)/m) is shown in Fig. 9. The stress exponent 4 (3.54, 3.13 and 3.90 at 873 K, 923 K and 973 K respectively) was obtained at different temperatures. The true creep activation energy (Qc) from the ln(ϵ̇min ) against 1/T plot was evaluated at constant normalised stress ((sa sth)/m) of 4.91 10 4 as shown in Fig. 10. Creep activation energy (Qc) 244.1 kJ/mole has been obtained from the slope of the Arrhenius plot. This value is similar to the activation energy for self diffusion of α-iron, 241 kJ/ mole [25]. The true activation energy value of 244 kJ/mole has
Fig. 11. Variation of normalised minimum creep rate by activation energy with effective stress by shear modulus.
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
67
been reported for creep deformation of precipitation strengthened Fe–19Cr steel [25]. In order to validate the obtained value of threshold stress, the creep rate by activation energy and effective stress by shear modulus were normalised in order to get various data in single curve. Fig. 11 shows the variation of minimum creep rate normalised by creep activation energy with effective stress normalised by shear modulus, where the values at different temperatures collapse into a single line and slope, which is rationalised with matrix stress exponent of 4 and creep activation energy 244.1 kJ/mole [26]. 3.3.2. Creep mechanisms The following creep mechanisms were considered to explain the existence of threshold stress in precipitation strengthened metals such as (i) detachment of dislocations from precipitates, (ii) shearing of precipitates, (iii) bypassing of precipitates by Orowan dislocation looping and (iv) dislocation climb over precipitates [25,28]. The detachment of dislocations from precipitates is not likely where the coherence precipitates exist in the matrix. This mechanism is not considered in the steel since the precipitates (MX and M23C6) exits in higher degree of coherency with matrix [12–15]. The shearing of precipitates is another possible mechanism, and precipitates shearing stress can be evaluated as given below [25] 1/2
σsh =
0.81Mγ ⎛ 3πφ ⎞ ⎜ ⎟ 2b ⎝ 8 ⎠
where M ¼2.9 is the mean orientation factor for bcc matrix, b¼ 0.248 nm is the burgers vector, φ is the volume fraction of precipitates, γ is the particle–matrix interface energy. The interface energy is given as, γ =
μθb(A − lnθ ) , 4π (1 − v )
where μ is the shear modulus of
the matrix (61.6 GPa, 59.3 GPa and 57.0 GPa at 873 K, 923 K and 973 K respectively), θ is the misorientation angle, A is 0.45, v is the Poisson ratio (0.3). The interface energy has been evaluated from above equation by considering misorientation angle 1.5° at different temperatures. The interface energy was about 0.11 J/m2. The energy of interface was not changed significantly with temperature, where it changes significantly with misorientation angle. The interface energy about 0.75 J/m2 has been reported in the literature [27]. The shearing stress was evaluated for P92 steel using φ = 0. 23% for MX and 0.8% for M23C6. The shearing stresses for precipitates were evaluated such as 283 MPa, 273 MPa and 263.5 MPa for MX and 513 MPa, 495 MPa and 477 MPa for M23C6 at 873 K, 923 K and 973 K respectively. The shearing stress values were higher than the threshold stress in the steel, hence the precipitates shearing mechanism was excluded. The Orowan dislocation looping stress is given by [25]
σor =
M 0.4 μb π (1 − v)
(
ln 2
2 3
)
(R)/b
λ
where R is the radius of precipitate, λ is the distance between the precipitates, M, m, b and v are the same as mentioned previously. The precipitates size was measured from the FEG–SEM and TEM micrographs. The precipitates in the size ranges about 30 nm was considered as MX, and M23C6 precipitate size was considered about 50 nm and above. The inter-particle average distance was 175 nm. The Orowan stress at different temperatures was 177 MPa, 170.2 MPa and 163.2 MPa for MX (MX type of precipitate is mainly considered in this investigation which is generally maximum inside the laths region), and 196.5 MPa, 189.2 MPa and 181.8 MPa for M23C6 at 873 K, 923 K and 973 K respectively, and was higher than the observed threshold stress in the steel. Hence, dislocation looping of precipitates has not been considered as creep deformation mechanism in the steel. The climb of dislocations has
Fig. 12. Variation of creep rupture life with applied stress at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
been considered as another possible creep mechanism which generally occurs at below the stress required for dislocation looping of precipitate. The threshold stress arises due to increase in dislocation length during climb over the precipitates. Magnitude of threshold stress found to change with the geometry of the dislocation climbing event [28]. Threshold stress normalised with Orowan stress ranges about 0.03–0.06 and 0.4–0.7 have been considered for general and local climb of dislocation events respectively [25]. The true activation energy value of 244.1 kJ/ mole has been obtained in the steel, which is comparable to the self diffusion of the α-Fe 241 kJ/mole. The threshold stress normalised by Orowan looping stress values of 0.77, 0.48 and 0.18 have been obtained at 873 K, 923 K and 973 K respectively. The threshold stress normalised by Orowan looping stress and creep activation energy computed in the steel 0.16–0.77 and 244.1 kJ/mole respectively demonstrates the occurrence of creep deformation by lattice diffusion assisted localised climb of dislocation at 873 K and 923 K, and transformation towards lattice diffusion assisted general climb of dislocation at 973 K in P92 steel. 3.4. Creep rupture life and ductility The variation of creep rupture life with applied stress at various temperatures has been shown in Fig. 12. The rupture life (tr ) decreases with increase in applied stress (σ ) and test temperature. This variation obeyed the power law of creep similar to the variation of minimum creep rate with applied stress as tr = A1σ −n1, where A1 is the stress coefficient and n1 is the stress exponent. The stress exponent (n1) values of 15.3, 9.4 and 6.9 have been obtained at 873 K, 923 K and 973 K respectively. The stress exponent decreases with increase in test temperature and has not varied with investigated applied stress range. The creep rupture life with applied stress and test temperature is expressed as [16,29], Q tr = A1σ −n1exp( RTc1 ), where Qc1 is the apparent activation energy for creep rupture life, R is the gas constant, T is the temperature in K. The apparent activation energy for creep rupture life of 598.8 kJ/ mole has been obtained in this steel (Fig. 13). Apparent activation energy value of 624 kJ/mole for creep rupture has been reported for 9% Cr ferritic steels [16,29]. The breakdown of creep strength with applied stress has not been noticed in the investigated range of stress. However, the breakdown of creep strength under lower stress ( 410,000 h creep exposure) regime has been reported in grade 92 steel and grade 91 steels due to significant modifications in the microstructural constituents of the steels, where change in
68
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
stress exponent and activation energy have been reported [16]. The breakdown of creep strength occurs early with increase in temperature in the steel [16]. The change in creep strength of Gr. 91 steel has been observed around 50,000 h at 923 K, and it is not evident up to 100,000 h at 873 K [27]. The observed value of n and n1 in the present investigation confirms the similar operating mechanism in creep deformation and rupture process. The variation of reduction in area (%) and elongation (%) with rupture life is shown in Fig. 14. The reduction in area decreased under lower applied stress in all test temperatures. However, the decrement of reduction in area with decrease in stress occurred early with increasing test temperature (Fig. 14(a)). The reduction in area (%) increased with increase in temperature. The coarsening (Laves, M23C6) of various phases led to decrease in reduction in area under lower applied stress. The elongation (%) varied between 15% and 20%, and no systematic change has been observed in the investigated duration at various temperatures (Fig. 14(b)). However, elongation (%) showed little an increasing tendency with increase in creep exposure. The stress enhanced recovery and coarsening of precipitates might have increased the elongation (%) with creep exposure. The enhanced softening and precipitation in the stressed region have been reported in modified 9Cr–1Mo and
P92 steels [1,12,13,30]. Fracture surface examination by SEM of creep ruptured specimens at various stress and test temperatures are shown in Fig. 15. Transgranular mode of fracture has been observed in all test conditions. However, changes in size and number density of dimple were observed. At lower applied stress, extensive coalescence of micro-voids resulted in larger number density of dimples (Fig. 15(b)). The higher numbers of smaller dimples were more at higher stress level and lower temperature (Fig. 15(c) and (d)). Slip lines were observed in the dimples as a result of larger plastic deformation. Slip lines in the dimples have been reported in the low carbon Fe–9 wt% Cr steel [20]. The brittle mode of fracture accompanied by lower reduction in area and hardness have been reported in the steel under long term creep exposure (4 10,000 h) in P92 steel [16]. However, significant degradation in rupture ductility has been reported after 25,000 h at 923 K and above in P91 steel [21]. Laves phase (Fe2W) has been observed at prioraustenite and subgrain boundaries under SEM–BSE mode (Fig. 16). Presence of Laves phase from the BSE mode SEM image in which the tungsten rich Laves phase appeared as bright phase because of its higher average atomic number [19]. Creep cavities were associated with Laves phase. Cavitation occurs in the steel due to increase in stress concentration at the particles which impede the motion of dislocations. Subsequent increase in localised stress at the particle–matrix interface, which experiences the excess localised plastic deformation led to micro-cracks. 3.5. Creep rate–rupture life relationships The relationships between minimum creep rate and rupture life is given by the Monkman–Grant (MG) equation as [2,31]
ϵ αmin·tr = CMG where ϵ is the minimum creep rate, tr is the rupture time, α is the constant close to unity and C is the MG constant. The materials which fails under intergranular fracture and experiences more secondary stage of creep deformation, the product of minimum creep rate and rupture life is a measure of strain to failure, and α and C are independent of test temperature and applied stress [2]. Monkman–Grant relationship has been modified by Dobes and Milika for the materials which generally exhibit larger tertiary creep deformation and shorter secondary creep deformation regime as [2,31]
ϵ αmin· Fig. 13. Arrhenius plot of temperature dependence of creep rupture life.
tr = CMMG εf
Fig. 14. Variation of (a) reduction in area (%), and (b) elongation (%) with rupture life at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
69
Fig. 15. Fracture surface of creep ruptured specimen at various temperature and stress.
Fig. 16. SEM–BSE micrograph of Gr. 92 steel creep ruptured at 923 K (650 °C) and 120 MPa depicting the presence of Laves phase and creep cavities.
where ϵ f is the strain to failure, CMMG is the modified Monkman– Grant constant. The variation of rupture time and normalised rupture time by strain to failure with minimum creep rate has been shown in Fig. 17. Grade 92 steel obeyed the Monkman and modified Monkman–Grant relationship. The values of CMG and
CMMG are 0.029 and 0.237 respectively (Fig. 17). Lower value of CMG and CMMG depicts the existence of major creep strain accumulation from tertiary creep regime. The validity of MG and MMG relationships in the steel shows the existence of close relationship between the creep deformation and fracture mechanisms. The time to onset of tertiary stage of deformation has been obtained from the time at which creep rate accelerate from minimum or steady state creep rate. The variation of time to onset of tertiary stage (tot) of creep deformation with rupture time (tr) is given in Fig. 18. The variations of tot with tr followed linear relationships as tot ¼f tr, where f is a constant. The value of f was about 0.248, which clearly demonstrates that this steel spent maximum time in the tertiary stage of creep deformation. The extensive creep strain accumulation (lower values of CMG and CMMG) and larger creeping duration in the tertiary stage of deformation have been observed in the steel. Similar behaviour has been reported in various 9 wt% Cr ferritic steels [2]. Based on the continuum damage mechanics (CDM) approach, creep damage tolerance factor ((λ ) has been defined as the ratio of strain to failure to Monkman–Grant ductility (MGD) as [2,32]
λ=
εf
ϵtr
= 1/CMMG
Creep damage occurs by loss of cross section (external-necking and internal-cavities) and changes in the microstructural constituents such as coarsening of precipitates and substructure, and
70
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Fig. 17. Variation of (a) rupture time with minimum creep rate and (b) normalised rupture time by rupture strain with minimum creep rate at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
decrease in dislocation density [2,32]. The creep damage tolerance factor has been used to assess the creep damage mode, whose value is ranges from 1 to 20 for various structural materials. The value of λ ¼1 indicates for the materials possess lower creep strain, highest value of λ demonstrates the ability of materials to withstand strain concentrations without local cracking [2]. The value of λ in the range of 1.5–2.5 indicates that the damage occurs due to growth of cavities. The value higher than 2.5 indicates the necking dominated creep damage. The value of λ ¼ 5 and above indicates that the damages by decrease in dislocation density, and coarsening of precipitates and sub-grain structure. Creep damage tolerance factor values of 4 and 5 have been reported for grade 91 steel [2]. The creep damage tolerance factor λ ¼6 was observed in the present investigation (Fig. 19). This indicates the microstructure evolution such as coarsening of M23C6 precipitates which formed during tempering, formation and coarsening of Laves phase (Fe2W), sub-grain coarsening and decrease in dislocation density coupled with limited cavity formation have been contributed in degradation of creep strength of grade 92 steel. Fig. 18. Variation of time to onset of tertiary with rupture time of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
4. Conclusions Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo– VNb steel at 873 K, 923 K and 973 K over a stress range of 220– 80 MPa have been investigated. The following conclusions were drawn from the study.
Fig. 19. Variation of damage parameter with rupture time of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
i. The stress dependence of minimum creep rate obeyed Norton's power law with higher apparent stress exponents of 5.8–15.2 and activation energy value of 619 kJ/mole. ii. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. iii. The threshold stress compensated true stress exponent of 4 and true activation energy of 244 kJ/mole, threshold stress normalised by Orowan stress confirms that the creep deformation in the steel occurred by lattice diffusion assisted localised climb of dislocations over the precipitates. iv. The apparent stress exponents of 6.9–15.3 and apparent activation energy value of 598.8 kJ/mole obtained for creep rupture shows that the similar operating mechanism in creep deformation and rupture behaviour in Gr. 92 steel. v. The steel obeyed Monkman–Grant and modified Monkman– Grant relationships.
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
vi. Creep damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel.
Acknowledgements The authors wish to thank Dr. P.R. Vasudeva Rao, Director, Indira Gandhi Centre for Atomic Research, Dr. T. Jayakumar, Director, Metallurgy and Materials Group and Dr. A.K. Bhaduri, Associate Director, Materials Development and Technology Group, for their keen interest in the work and encouragement. The support extended by Mr. Syamala Rao Polaki in microstructural investigation is gratefully acknowledged. Experimental assistance provided by Mr. N. S. Thampi and Mr. M. Govindasamy in conducting creep tests are acknowledged.
References [1] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Igarashi, J. Nucl. Mater. 433 (2013) 23–29. [2] Triratna Shrestha, Mehdi Basirat, Indrajit Charit, Gabriel P. Potirniche, Karl K. Rink, Mater. Sci. Eng. A 565 (2013) 382–391. [3] A. Bhattacharya, E. Meslin, J. Henry, C. Pareige, B. Décamps, C. Genevois, D. Brimbal, A. Barbu, Acta Mater. 78 (2014) 394–403. [4] Leyun Wang, Meimei Li, Jonathan Almer, Acta Mater. 62 (2014) 239–249. [5] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Yoshizawa, M. Igarashi, Mater. Lett. 63 (2009) 2423–2425. [6] Meimei Li, Leyun Wang, Jonathan D. Almer, Acta Mater. 76 (2014) 381–393. [7] P.J. Ennis, A. Zielinska-Lipiec, O. Wachter, A. Czyrska-Filemonowicz, Acta Mater. 45 (1997) 4901–4907. [8] P.J. Ennis, A. Zielinska-Lipiec, A. Czyrska-Filemonowicz, Mater. Sci. Technol. 16
71
(2000) 1226–1232. [9] K. Maruyama, K. Sawada, J. Koike, Iron Steel Inst. Jpn. Int. 41 (2001) 641–653. [10] V. A. V´yrostkov´a, J. Homolov´a, Pecha, M. Svoboda, Mater. Sci. Eng. A 480 (2008) 289–298. [11] Lj Milovic, T. Vuherer, I. Blacic, M. Vrhovac, M. Stankovic, Materi. Des. 46 (2013) 660–667. [12] Valeriy Dudko, Andrey Belyakov, Dmitri Molodov, Rustam Kaibyshev, Metall. Mater. Trans. A 44A (2013) 162–172. [13] Irina Fedorova, Alla Kipelova, Andrey Belyakov, Rustam Kaibyshev, Metall. Mater. Trans. A 44A (2013) 128–135. [14] Fujio Abe, Mater. Sci. Eng. A 319–321 (2001) 770–773. [15] K. Sawada, K. Kubo, F. Abe, Mater. Sci. Eng. A 319–321 (2001) 784–787. [16] Jae Seung Lee, Hassan Ghassemi Armaki, Kouichi Maruyama, Taro Muraki, Hitoshi Asahi, Mater. Sci. Eng. A 428 (2006) 270–275. [17] Yin Zhong Shen, Sung Ho Kim, Chang Hee Han, Hai Dong Cho, Woo Seog Ryu, J. Nucl. Mater. 384 (2009) 48–55. [18] S.S. Wang, D.L. Peng, L. Chang, X.D. Hui, Mater. Des. 50 (2013) 174–180. [19] T. Sakthivel, M. Vasudevan, K. Laha, P. Parameswaran, K.S. Chandravathi, S. Panneer Selvi, V. Maduraimuthu, M.D. Mathew, Mater. Sci. Eng. A 591 (2014) 111–120. [20] I. Fedorova, A. Belyakov, P. Kozlov, V. Skorobogatykh, I. Shenkova, R. Kaibyshev, Mater. Sci. Eng. A 615 (2014) 153–163. [21] K. Kimura, H. Kushima, K. Sawada, Mater. Sci. Eng. A 510–511 (2009) 58–63. [22] O. Prat, J. Garcia, D. Rojas, G. Sauthoff, G. Inden, Intermetallics 32 (2013) 362–372. [23] A. Kostka, K.-G. Tak, R.J. Hellmig, Y. Estrin, G. Eggeler, Acta Mater. 55 (2007) 539–550. [24] Oleg D. Sherby, Eric M. Taleff, Mater. Sci. Eng. A 322 (2002) 89–99. [25] Nhon Q. Vo, Christian H. Liebscher, Michael J.S. Rawlings, Mark Asta, David C. Dunand, Acta Mater 71 (2014) 89–99. [26] Triratna Shrestha, Mehdi Basirat, Indrajit Charit, Gabriel P. Potirniche, Karl K. Rink, Uttara Sahaym, J. Nucl. Mater. 423 (2012) 110–119. [27] K. Maruyama, H. Ghassemi Armaki, R.P. Chen, K. Yoshimi, M. Yoshizawa, M. Igarashi, Int. J. Press. Vessels Pip. 87 (2010) 276–281. [28] J. Čadek, Creep in Metallic Materials, Elsevier, Amsterdam, 1988. [29] S. Spigarelli, Int. J. Press. Vessels Pip. 101 (2013) 64–71. [30] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Igarashi, Mater. Sci. Eng. A 527 (2010) 6581–6588. [31] Hassan Osman Ali, Mohd Nasir Tamin, J. Nucl. Mater. 433 (2013) 74–79. [32] B.F. Dyson, T.B. Gibbons, Acta Mater. 35 (1987) 2355.
Contents lists available at ScienceDirect
Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
An assessment of creep deformation and rupture behaviour of 9Cr– 1.8W–0.5Mo–VNb (ASME grade 92) steel T. Sakthivel n, S. Panneer Selvi, K. Laha Mechanical Metallurgy Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, India
art ic l e i nf o
a b s t r a c t
Article history: Received 21 April 2015 Received in revised form 18 May 2015 Accepted 21 May 2015 Available online 27 May 2015
Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been investigated at 873 K, 923 K and 973 K over a stress range of 80–220 MPa. The absence of clear primary creep regime and prolonged secondary stage of creep deformation have been noticed under lower stress level at 973 K. The variation of minimum creep rate with applied stress obeyed Norton's power law of creep. The apparent stress exponents of 15.2, 12.3 and 5.8, and apparent activation energy of 619 kJ/mole have been estimated for creep deformation of the steel. The apparent stress exponents and activation energy have been rationalised on the basis of threshold stress. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. The threshold stress compensated true stress exponent of 4 and true activation energy of 244 kJ/mole, and threshold stress normalised by Orowan stress confirms that the lattice diffusion assisted localised climb of dislocation is the rate controlling of creep deformation in the steel. The steel obeyed Monkman and modified Monkman–Grant relationships. Damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel. & 2015 Elsevier B.V. All rights reserved.
Keywords: ASME grade 92 ferritic steel Creep Activation energy Damage tolerance factor
1. Introduction Ferritic–martensitic 9% Cr steels are considered as candidate structural materials for nuclear energy systems [1,2]. The choice is based on excellent mechanical properties at high temperatures, good weldability, low thermal expansion coefficient, high thermal conductivity, adequate corrosion and stress-corrosion cracking resistances and high inherent void swelling resistance on neutron irradiation [3–5]. The ASME grade 91 and 92 (9Cr–1.8W–0.5Mo– VNb) steels are used extensively in the advanced fossil fired power plants and is being considered for structural applications in advanced sodium cooled fast reactors [6]. The addition of 1.5–2.0 wt% tungsten and 0.001 to 0.006 wt% boron along with the reduction in molybdenum content to 0.3–0.6 wt% in grade 91 (9Cr–1Mo– VNb) steel, leads to the development of grade 92 steel [7–10]. The grade 92 steel offers about 30% higher creep rupture strength over the grade 91 steel especially at higher temperatures [10,11]. The steel is used in normalised and tempered condition and has tempered martensitic structure. The steel derives its high temperature strength from tempered martensitic lath structure, stabilisation of martensitic lath structure by chromium rich M23C6 n
Corresponding author. E-mail address: [email protected] (T. Sakthivel).
http://dx.doi.org/10.1016/j.msea.2015.05.068 0921-5093/& 2015 Elsevier B.V. All rights reserved.
type of carbide, martensite phase transformation induced high dislocation density, intra-lath MX type of V and Nb-carbonitrides, and solid solution strengthening from tungsten and molybdenum [12–15]. Fine dispersion of highly stable MX type of V and Nbcarbonitrides particles are reported to enhance creep rupture strength of the tempered martensite steel not only acting as a barrier to dislocation motion but also by stabilisation of dislocation network. The presence of tungsten in the M23C6 precipitate decreases growth rate of the precipitate during creep exposure, which in turn increases the stability of the martensitic lath structure of the steel on creep exposure [7–19]. In the present investigation, creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo–VNb steel have been studied, and analysis has been carried out by performing detailed metallography to have insight of the failure mechanism. Creep deformation has been rationalised based on the back-stress concept to the dislocation motion.
2. Experimental details The chemical composition of grade 92 (ASME Gr. 92) steel is given in Table.1. The steel plate having 12 mm thickness was normalised at 1323 K for 30 min followed by air cooling, and the steel was subsequently tempered at 1053 K for 120 min followed
62
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Table 1 Chemical composition (wt%) of ASME Gr. 92 steel. Elements
C
Cr
W
Mo
Mn
Si
V
N
Nb
Gr. 92 steel
0.10
9.2
1.9
0.51
0.36
0.27
0.22
0.050
0.07
Elements
S
P
Ni
Al
B
Ti
N/Al
Fe
Gr. 92 steel
0.002
0.010
0.060
0.010
0.001
0.002
5
Bal
by air cooling. Creep specimens having dimensions of 5 mm gauge diameter and 50 mm gauge length were fabricated. Constant load creep tests in air have been carried out at 873 K, 923 K and 973 K in the stress range of 80–220 MPa in creep machines equipped with split type furnace having three zone temperature controller. Temperature was controlled within 7 2 K ( 72 °C) along the gauge length of the specimen during creep test. Elongation of the specimen was monitored by an extensometer and digital dial gauge attachment having measuring accuracy of 70.001 mm and was continuously logged in a data logger. Scanning electron microscopic (SEM) (SE – secondary electron, BSE – back scattered electron, FEG – field emission gun) studies were carried out on the steel before and after creep tests to assess microstructural degradation and fracture behaviour on creep exposure. Immersion etching for 15 s using Villella's reagent (picric acid 5 g, HCl acid 25 ml, Ethyl alcohol 500 ml) has been employed to reveal the microstructures of the steel. Specimens were thinned down to 50 mm by mechanical polishing with emery paper under flowing water followed by electrolytic double jet thinning using 20% perchloric acid and ethanol solution for transmission electron microscopic (TEM) investigation.
3. Results and discussion 3.1. Microstructure of the steel Microstructure of the grade 92 steel in the normalised and tempered condition is shown in Fig. 1(a). The prior-austenite grain size of the steel was around 20 mm. Microstructure of the steel consists of tempered martensitic lath structure (Fig. 1(b) and (c)) with transformation induced high dislocation density about 7 1014 m 2[7]. The width of the martensitic lath structure was 400 nm. Prior-austenite grain boundaries and sub-grain boundaries were decorated with M23C6 precipitates. Average size of the M23C6 precipitate was ∼90 nm measured from TEM micrograph. The energy dispersive spectroscopy (EDS) spectrum analysis of the precipitates depicted the enrichment of tungsten about 7–8 wt% (Fig. 1(d)). Presence of tungsten is reported to reduce the coarsening rate of M23C6 precipitates at high temperatures [18]. The MX type of V and Nb-rich carbide and carbo-nitride precipitates (having size of around ∼30 nm measured from FEG–SEM micrograph) in the intra-laths region were observed in the steel. The presence of M23C6 and MX precipitates in the prior-austenite, sub-grain boundaries and intra-lath regions resists the movement of boundaries and dislocations respectively led to enhance the creep strength of grade 92 steel at high temperatures [18,26]. 3.2. Creep deformation behaviour of the steel Creep curves of grade 92 steel at 923 K over a stress range of 110–170 MPa are shown in Fig. 2(a). The variations of creep strain with creep exposure exhibited the instantaneous strain on loading, distinct primary creep, narrow region of secondary creep and
prolonged tertiary creep regimes at 923 K. Similar creep deformation behaviour has been noticed at 873 K and 973 K. Narrow region of secondary and prolonged tertiary creep regimes have generally been observed in Fe–9%Cr ferritic–martensitic steels [12,13,20–22]. However, presence of clear primary creep regime was not observed under lower stress levels at 973 K (Fig. 2(b) and (c)). Longer secondary creep regime observed at 973 K under low stress level in the steel might be due to increase in solid solution strengthening contribution from tungsten by the dissolution of Laves phase (Fe2W). Extended secondary stage creep deformation has been reported in the P92 type low carbon steel under lower stress level at 923 K [20]. The variations of creep rate with creep exposure at 873 K and 923 K over a stress range of 110–220 MPa are given in Fig. 3. Creep rate of the steel with creep exposure significantly decreases in the primary creep regime, and subsequently shows the minimum creep rate regime and followed by a faster rate of creep deformation in tertiary stage till the time of fracture. The steel spent maximum duration in the tertiary state of creep deformation at all test conditions except under low stress level at 973 K. Variation of creep rate with creep strain at various temperature and stress are given in Fig. 4. The creep rate decreases with increase in creep strain in the primary regime due to work hardening by dislocation multiplication and their interactions. Stabilised creep rate occurs in the shorter secondary strain regime where the work hardening effect is counter balanced by the recovery process such as dislocation annihilation and rearrangement. Rapid increase in creep rate in the tertiary creep strain is attributed to enhancement in recovery process, growth of precipitates and cavities [12,13,22]. However, the decreasing creep rate behaviour from initial deformation was not clearly observed under lower stress level at 973 K (Fig. 4(c)). This might be due to faster annihilation of dislocations generated in the primary creep region or increase in remobilisation of immobile dislocations due to higher temperature. Strain to reach onset of tertiary creep has varied with applied stress and test temperatures (Figs. 4 and 5), onset of tertiary creep deformation occurred at 2% and 1% to 2% creep strain at test temperatures of 873 K and 923 K respectively. However, strain to reach onset of tertiary creep decreases with decrease in stress level significantly at 923 K from 2% to 1%. The change (decrease) in dislocation density up to secondary stage of deformation is relatively higher as compared to tertiary creep regime, where change in precipitation behaviour and boundary dimensions were considerably lower up to ∼1% of creep strain or minimum creep rate regime [12,23]. Creep strain accumulation for the onset of tertiary creep about 1% has been reported in W strengthened steels at 923 K [12,22]. Creep strain for onset of tertiary creep in the range of 0.5–2.5% has been observed at 973 K (Fig. 5). The decrease and increase in creep strain accumulation to onset of tertiary creep at 923 K and 973 K respectively under lower stress level might be due to increase in recovery rate of dislocation structure at 923 K and solid solution strengthening by tungsten at 973 K. 3.3. Stress and temperature dependence of minimum creep rate The variation of minimum creep rate with applied stress at 873 K, 923 K and 973 K is shown in Fig. 6. Minimum creep rate increased with increase in applied stress and test temperature. The variation of minimum creep rate ( ϵ̇min ) with applied stress (s) followed Norton’s power law of creep as ( ϵ̇min = Aσ n ) , where A is a constant, n is the stress exponent of the matrix. The variation in n value found to represent the change in creep deformation mechanisms in the materials. Stress exponent (n)¼1 is considered as Harper–Dorn creep where the dislocation density is invariant with stress. The value of n ¼3 is considered where the dislocation glide is controlled by the rate of migration of solute atoms that are
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
63
Fig. 1. Gr. 92 steel in the normalised and tempered condition (a) SE–SEM, (b) FEG–SEM and (c) TEM micrographs depicts the prior-austenite boundaries and lath regions decorated by M23C6 and MX precipitates, and (d) EDS spectra obtained from the M23C6 precipitate.
attached to the moving dislocations (solute-drag creep). The stress exponent 5 is considered where creep occurs by the dislocation climb controlled process. This is generally been observed in the materials which shows sub-grain structure formation and power law breakdown (PLB) behaviour. The stress exponent eight is considered to be dislocation climb controlled creep, where creep deformation occurs under constant microstructure. PLB occurs due to excess vacancy generation at higher stresses, and cross slip and obstacle controlled glide [24]. In the present investigation, stress exponent values of 15.1, 12.3 and 5.8 have been observed at 873 K, 923 K and 973 K respectively (Table 2). Stress exponent (n) of this steel has not been changed with stress in the investigated stress range. However, significant breakdown of stress exponent under longer creep exposure ( 4 10,000 h) in P92 steel at 923 K has been reported [7]. The obtained stress exponent (n) values are higher than the diffusion controlled dislocation based creep deformation models [24,25]. However, observed values of n were comparable to the reported values in the literature for P92 steel [7,8]. Stress exponent (n) values of 12 and13 have been reported in P92 type steels at 923 K [15]. The decrease in n values with increase in test temperatures occurred in the steel due to extensive microstructural modifications at higher test temperatures such as formation (Laves phase) and coarsening of precipitates (Laves phase, M23C6), and decreased coherent strain between MX precipitates and matrix results in lower stress dependence of minimum creep rate [12–15,25]. The stress (s) and temperature (T) dependencies of creep rate of pure metals and single phase alloys are generally described by Bird–Mukherjee–Dorn (BMD) relationship as [26]
⎛ σ ⎞n ⎛ Q ⎞ ϵkT = A⎜ ⎟ exp⎜ − c ⎟ ⎝ RT ⎠ D0μb ⎝μ⎠
where D¼D0exp( Qc/RT)) is the diffusion coefficient, D0 is the frequency factor, Qc is the activation energy for creep deformation, R is the gas constant, T is the temperature in Kelvin, μ is the shear modulus, b is the burgers vector, k is the Boltzmann constant, n is the stress exponent, A is the dimensionless constant. The creep parameters of n and Q are used to assess the responsible operating creep mechanisms. The creep activation energy (Qc) from the ln (ϵ̇min ) versus 1/T plot was evaluated at constant stress (Fig. 7). Creep activation energy (Qc) for grade 92 steel about 619.6 kJ/ mole has been obtained from the slope of the Arrhenius plot. The apparent activation energy value obtained in this study is comparable to the reported activation energy at Fe – with various Cr concentrations [27]. Creep activation energy evaluated from the present investigation is comparable with the reported energy values of 510 kJ/mole and 510–621 kJ/mole for ferritic steels [2,26]. The observed stress exponent (n) and activation energy values are larger than the solid solution Fe-based single phase alloys because of strong interaction between precipitates and mobile dislocations, which is generally been described by threshold stress [25,26,29]. 3.3.1. Threshold stress and true creep activation energy In order to understand the interactions between precipitates and mobile dislocations in the steel, threshold stress (sth) has been evaluated. Threshold stress is generally defined as the stress below which creep deformation not occurs by a specific creep mechanism. Hence, the effective stress has been considered as responsible for creep deformation instead of applied stress where the alloy is strengthened by particles or precipitates [26]. The threshold stress (sth) can be determined using the modified version of Mukherjee– Bird–Dorn creep equation as [25,26,29]
64
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Fig. 2. Variation of creep strain (%) with time of Gr. 92 steel at (a) 873 K (600 °C) and (b) 973 K (650 °C) over stress range of 80–170 MPa, and (c) projected primary creep regime at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
Fig. 3. Variation of creep rate with time of Gr. 92 steel at (a) 873 K (600 °C) and (b) 923 K (650 °C) over stress range of 110–220 MPa.
⎛ σ − σth ⎞n ⎛ Q ⎞ ϵ min = A⎜ a ⎟ exp⎜ − c ⎟ ⎝ kT ⎠ ⎝ μ ⎠ where A is a constant, n is the matrix stress exponent, σa is the
applied stress, Qc is the creep activation energy, T is the temperature in Kelvin, m is the shear modulus, k is the Boltzmann's constant. Stress exponent value about 4, and similar activation energy for creep (QC) and lattice self diffusion (QD) have been
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
65
Fig. 4. Variation of creep rate with creep strain (%) of Gr. 92 steel at (a) 873 K (600 °C), (b) 923 K (650 °C) and (c) 973 K (700 °C) over stress range of 80–220 MPa.
Fig. 5. Variation of strain to reach onset of tertiary creep with time to reach onset of tertiary creep regime of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
observed in pure metals [25,26]. The threshold stress is evaluated from strain rate (ϵ̇1/4 ) against applied stress plot, where the stress exponent of the matrix value 4 was used (Fig. 8). The interruption of stress line values at the zero strain rates provides threshold
Fig. 6. Variation of minimum creep rate with applied stress of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
stress at various temperatures. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. It is significant to note that the threshold stress decreases with increase in temperature might be due to the
66
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Table 2 The values of stress coefficients and stress exponents for stress dependence minimum creep rate and rupture life of ASME Gr. 92 steel. Temperature (K)
873 923 973
ϵmin = Aσn
tr = Aσ1−n1
A
n
A1
n1
3.84 10 40 3.28 10 31 8.62 10 16
15.1 12.3 5.8
1.54 1038 5.75 1022 5.75 1015
15.3 9.4 6.9
Fig. 9. Variation of minimum creep rate with normalised effective stress by shear modulus [sa sth]/m for P92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
Fig. 7. Arrhenius plot of temperature dependence of minimum creep rate.
Fig. 10. Arrhenius plot of temperature dependence of threshold stress compensated minimum creep rate.
Fig. 8. Variation of minimum creep rate ϵ̇1/4 with applied stress (sa) to obtain threshold stress at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
increase in precipitates size and decrease in dislocation density on high temperature exposure. The variation of strain rate (ϵ̇min ) with normalised effective stress by shear modulus ((sa sth)/m) is shown in Fig. 9. The stress exponent 4 (3.54, 3.13 and 3.90 at 873 K, 923 K and 973 K respectively) was obtained at different temperatures. The true creep activation energy (Qc) from the ln(ϵ̇min ) against 1/T plot was evaluated at constant normalised stress ((sa sth)/m) of 4.91 10 4 as shown in Fig. 10. Creep activation energy (Qc) 244.1 kJ/mole has been obtained from the slope of the Arrhenius plot. This value is similar to the activation energy for self diffusion of α-iron, 241 kJ/ mole [25]. The true activation energy value of 244 kJ/mole has
Fig. 11. Variation of normalised minimum creep rate by activation energy with effective stress by shear modulus.
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
67
been reported for creep deformation of precipitation strengthened Fe–19Cr steel [25]. In order to validate the obtained value of threshold stress, the creep rate by activation energy and effective stress by shear modulus were normalised in order to get various data in single curve. Fig. 11 shows the variation of minimum creep rate normalised by creep activation energy with effective stress normalised by shear modulus, where the values at different temperatures collapse into a single line and slope, which is rationalised with matrix stress exponent of 4 and creep activation energy 244.1 kJ/mole [26]. 3.3.2. Creep mechanisms The following creep mechanisms were considered to explain the existence of threshold stress in precipitation strengthened metals such as (i) detachment of dislocations from precipitates, (ii) shearing of precipitates, (iii) bypassing of precipitates by Orowan dislocation looping and (iv) dislocation climb over precipitates [25,28]. The detachment of dislocations from precipitates is not likely where the coherence precipitates exist in the matrix. This mechanism is not considered in the steel since the precipitates (MX and M23C6) exits in higher degree of coherency with matrix [12–15]. The shearing of precipitates is another possible mechanism, and precipitates shearing stress can be evaluated as given below [25] 1/2
σsh =
0.81Mγ ⎛ 3πφ ⎞ ⎜ ⎟ 2b ⎝ 8 ⎠
where M ¼2.9 is the mean orientation factor for bcc matrix, b¼ 0.248 nm is the burgers vector, φ is the volume fraction of precipitates, γ is the particle–matrix interface energy. The interface energy is given as, γ =
μθb(A − lnθ ) , 4π (1 − v )
where μ is the shear modulus of
the matrix (61.6 GPa, 59.3 GPa and 57.0 GPa at 873 K, 923 K and 973 K respectively), θ is the misorientation angle, A is 0.45, v is the Poisson ratio (0.3). The interface energy has been evaluated from above equation by considering misorientation angle 1.5° at different temperatures. The interface energy was about 0.11 J/m2. The energy of interface was not changed significantly with temperature, where it changes significantly with misorientation angle. The interface energy about 0.75 J/m2 has been reported in the literature [27]. The shearing stress was evaluated for P92 steel using φ = 0. 23% for MX and 0.8% for M23C6. The shearing stresses for precipitates were evaluated such as 283 MPa, 273 MPa and 263.5 MPa for MX and 513 MPa, 495 MPa and 477 MPa for M23C6 at 873 K, 923 K and 973 K respectively. The shearing stress values were higher than the threshold stress in the steel, hence the precipitates shearing mechanism was excluded. The Orowan dislocation looping stress is given by [25]
σor =
M 0.4 μb π (1 − v)
(
ln 2
2 3
)
(R)/b
λ
where R is the radius of precipitate, λ is the distance between the precipitates, M, m, b and v are the same as mentioned previously. The precipitates size was measured from the FEG–SEM and TEM micrographs. The precipitates in the size ranges about 30 nm was considered as MX, and M23C6 precipitate size was considered about 50 nm and above. The inter-particle average distance was 175 nm. The Orowan stress at different temperatures was 177 MPa, 170.2 MPa and 163.2 MPa for MX (MX type of precipitate is mainly considered in this investigation which is generally maximum inside the laths region), and 196.5 MPa, 189.2 MPa and 181.8 MPa for M23C6 at 873 K, 923 K and 973 K respectively, and was higher than the observed threshold stress in the steel. Hence, dislocation looping of precipitates has not been considered as creep deformation mechanism in the steel. The climb of dislocations has
Fig. 12. Variation of creep rupture life with applied stress at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
been considered as another possible creep mechanism which generally occurs at below the stress required for dislocation looping of precipitate. The threshold stress arises due to increase in dislocation length during climb over the precipitates. Magnitude of threshold stress found to change with the geometry of the dislocation climbing event [28]. Threshold stress normalised with Orowan stress ranges about 0.03–0.06 and 0.4–0.7 have been considered for general and local climb of dislocation events respectively [25]. The true activation energy value of 244.1 kJ/ mole has been obtained in the steel, which is comparable to the self diffusion of the α-Fe 241 kJ/mole. The threshold stress normalised by Orowan looping stress values of 0.77, 0.48 and 0.18 have been obtained at 873 K, 923 K and 973 K respectively. The threshold stress normalised by Orowan looping stress and creep activation energy computed in the steel 0.16–0.77 and 244.1 kJ/mole respectively demonstrates the occurrence of creep deformation by lattice diffusion assisted localised climb of dislocation at 873 K and 923 K, and transformation towards lattice diffusion assisted general climb of dislocation at 973 K in P92 steel. 3.4. Creep rupture life and ductility The variation of creep rupture life with applied stress at various temperatures has been shown in Fig. 12. The rupture life (tr ) decreases with increase in applied stress (σ ) and test temperature. This variation obeyed the power law of creep similar to the variation of minimum creep rate with applied stress as tr = A1σ −n1, where A1 is the stress coefficient and n1 is the stress exponent. The stress exponent (n1) values of 15.3, 9.4 and 6.9 have been obtained at 873 K, 923 K and 973 K respectively. The stress exponent decreases with increase in test temperature and has not varied with investigated applied stress range. The creep rupture life with applied stress and test temperature is expressed as [16,29], Q tr = A1σ −n1exp( RTc1 ), where Qc1 is the apparent activation energy for creep rupture life, R is the gas constant, T is the temperature in K. The apparent activation energy for creep rupture life of 598.8 kJ/ mole has been obtained in this steel (Fig. 13). Apparent activation energy value of 624 kJ/mole for creep rupture has been reported for 9% Cr ferritic steels [16,29]. The breakdown of creep strength with applied stress has not been noticed in the investigated range of stress. However, the breakdown of creep strength under lower stress ( 410,000 h creep exposure) regime has been reported in grade 92 steel and grade 91 steels due to significant modifications in the microstructural constituents of the steels, where change in
68
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
stress exponent and activation energy have been reported [16]. The breakdown of creep strength occurs early with increase in temperature in the steel [16]. The change in creep strength of Gr. 91 steel has been observed around 50,000 h at 923 K, and it is not evident up to 100,000 h at 873 K [27]. The observed value of n and n1 in the present investigation confirms the similar operating mechanism in creep deformation and rupture process. The variation of reduction in area (%) and elongation (%) with rupture life is shown in Fig. 14. The reduction in area decreased under lower applied stress in all test temperatures. However, the decrement of reduction in area with decrease in stress occurred early with increasing test temperature (Fig. 14(a)). The reduction in area (%) increased with increase in temperature. The coarsening (Laves, M23C6) of various phases led to decrease in reduction in area under lower applied stress. The elongation (%) varied between 15% and 20%, and no systematic change has been observed in the investigated duration at various temperatures (Fig. 14(b)). However, elongation (%) showed little an increasing tendency with increase in creep exposure. The stress enhanced recovery and coarsening of precipitates might have increased the elongation (%) with creep exposure. The enhanced softening and precipitation in the stressed region have been reported in modified 9Cr–1Mo and
P92 steels [1,12,13,30]. Fracture surface examination by SEM of creep ruptured specimens at various stress and test temperatures are shown in Fig. 15. Transgranular mode of fracture has been observed in all test conditions. However, changes in size and number density of dimple were observed. At lower applied stress, extensive coalescence of micro-voids resulted in larger number density of dimples (Fig. 15(b)). The higher numbers of smaller dimples were more at higher stress level and lower temperature (Fig. 15(c) and (d)). Slip lines were observed in the dimples as a result of larger plastic deformation. Slip lines in the dimples have been reported in the low carbon Fe–9 wt% Cr steel [20]. The brittle mode of fracture accompanied by lower reduction in area and hardness have been reported in the steel under long term creep exposure (4 10,000 h) in P92 steel [16]. However, significant degradation in rupture ductility has been reported after 25,000 h at 923 K and above in P91 steel [21]. Laves phase (Fe2W) has been observed at prioraustenite and subgrain boundaries under SEM–BSE mode (Fig. 16). Presence of Laves phase from the BSE mode SEM image in which the tungsten rich Laves phase appeared as bright phase because of its higher average atomic number [19]. Creep cavities were associated with Laves phase. Cavitation occurs in the steel due to increase in stress concentration at the particles which impede the motion of dislocations. Subsequent increase in localised stress at the particle–matrix interface, which experiences the excess localised plastic deformation led to micro-cracks. 3.5. Creep rate–rupture life relationships The relationships between minimum creep rate and rupture life is given by the Monkman–Grant (MG) equation as [2,31]
ϵ αmin·tr = CMG where ϵ is the minimum creep rate, tr is the rupture time, α is the constant close to unity and C is the MG constant. The materials which fails under intergranular fracture and experiences more secondary stage of creep deformation, the product of minimum creep rate and rupture life is a measure of strain to failure, and α and C are independent of test temperature and applied stress [2]. Monkman–Grant relationship has been modified by Dobes and Milika for the materials which generally exhibit larger tertiary creep deformation and shorter secondary creep deformation regime as [2,31]
ϵ αmin· Fig. 13. Arrhenius plot of temperature dependence of creep rupture life.
tr = CMMG εf
Fig. 14. Variation of (a) reduction in area (%), and (b) elongation (%) with rupture life at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
69
Fig. 15. Fracture surface of creep ruptured specimen at various temperature and stress.
Fig. 16. SEM–BSE micrograph of Gr. 92 steel creep ruptured at 923 K (650 °C) and 120 MPa depicting the presence of Laves phase and creep cavities.
where ϵ f is the strain to failure, CMMG is the modified Monkman– Grant constant. The variation of rupture time and normalised rupture time by strain to failure with minimum creep rate has been shown in Fig. 17. Grade 92 steel obeyed the Monkman and modified Monkman–Grant relationship. The values of CMG and
CMMG are 0.029 and 0.237 respectively (Fig. 17). Lower value of CMG and CMMG depicts the existence of major creep strain accumulation from tertiary creep regime. The validity of MG and MMG relationships in the steel shows the existence of close relationship between the creep deformation and fracture mechanisms. The time to onset of tertiary stage of deformation has been obtained from the time at which creep rate accelerate from minimum or steady state creep rate. The variation of time to onset of tertiary stage (tot) of creep deformation with rupture time (tr) is given in Fig. 18. The variations of tot with tr followed linear relationships as tot ¼f tr, where f is a constant. The value of f was about 0.248, which clearly demonstrates that this steel spent maximum time in the tertiary stage of creep deformation. The extensive creep strain accumulation (lower values of CMG and CMMG) and larger creeping duration in the tertiary stage of deformation have been observed in the steel. Similar behaviour has been reported in various 9 wt% Cr ferritic steels [2]. Based on the continuum damage mechanics (CDM) approach, creep damage tolerance factor ((λ ) has been defined as the ratio of strain to failure to Monkman–Grant ductility (MGD) as [2,32]
λ=
εf
ϵtr
= 1/CMMG
Creep damage occurs by loss of cross section (external-necking and internal-cavities) and changes in the microstructural constituents such as coarsening of precipitates and substructure, and
70
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
Fig. 17. Variation of (a) rupture time with minimum creep rate and (b) normalised rupture time by rupture strain with minimum creep rate at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
decrease in dislocation density [2,32]. The creep damage tolerance factor has been used to assess the creep damage mode, whose value is ranges from 1 to 20 for various structural materials. The value of λ ¼1 indicates for the materials possess lower creep strain, highest value of λ demonstrates the ability of materials to withstand strain concentrations without local cracking [2]. The value of λ in the range of 1.5–2.5 indicates that the damage occurs due to growth of cavities. The value higher than 2.5 indicates the necking dominated creep damage. The value of λ ¼ 5 and above indicates that the damages by decrease in dislocation density, and coarsening of precipitates and sub-grain structure. Creep damage tolerance factor values of 4 and 5 have been reported for grade 91 steel [2]. The creep damage tolerance factor λ ¼6 was observed in the present investigation (Fig. 19). This indicates the microstructure evolution such as coarsening of M23C6 precipitates which formed during tempering, formation and coarsening of Laves phase (Fe2W), sub-grain coarsening and decrease in dislocation density coupled with limited cavity formation have been contributed in degradation of creep strength of grade 92 steel. Fig. 18. Variation of time to onset of tertiary with rupture time of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
4. Conclusions Creep deformation and rupture behaviour of 9Cr–1.8W–0.5Mo– VNb steel at 873 K, 923 K and 973 K over a stress range of 220– 80 MPa have been investigated. The following conclusions were drawn from the study.
Fig. 19. Variation of damage parameter with rupture time of Gr. 92 steel at 873 K (600 °C), 923 K (650 °C) and 973 K (700 °C).
i. The stress dependence of minimum creep rate obeyed Norton's power law with higher apparent stress exponents of 5.8–15.2 and activation energy value of 619 kJ/mole. ii. The threshold stress values of 137.5 MPa, 83.3 MPa and 29.7 MPa were obtained at 873 K, 923 K and 973 K respectively. iii. The threshold stress compensated true stress exponent of 4 and true activation energy of 244 kJ/mole, threshold stress normalised by Orowan stress confirms that the creep deformation in the steel occurred by lattice diffusion assisted localised climb of dislocations over the precipitates. iv. The apparent stress exponents of 6.9–15.3 and apparent activation energy value of 598.8 kJ/mole obtained for creep rupture shows that the similar operating mechanism in creep deformation and rupture behaviour in Gr. 92 steel. v. The steel obeyed Monkman–Grant and modified Monkman– Grant relationships.
T. Sakthivel et al. / Materials Science & Engineering A 640 (2015) 61–71
vi. Creep damage tolerance factor of 6 in the steel demonstrates that the microstructural degradation such as coarsening of precipitates and subgrain structure is the dominant creep damaging mechanism in the steel.
Acknowledgements The authors wish to thank Dr. P.R. Vasudeva Rao, Director, Indira Gandhi Centre for Atomic Research, Dr. T. Jayakumar, Director, Metallurgy and Materials Group and Dr. A.K. Bhaduri, Associate Director, Materials Development and Technology Group, for their keen interest in the work and encouragement. The support extended by Mr. Syamala Rao Polaki in microstructural investigation is gratefully acknowledged. Experimental assistance provided by Mr. N. S. Thampi and Mr. M. Govindasamy in conducting creep tests are acknowledged.
References [1] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Igarashi, J. Nucl. Mater. 433 (2013) 23–29. [2] Triratna Shrestha, Mehdi Basirat, Indrajit Charit, Gabriel P. Potirniche, Karl K. Rink, Mater. Sci. Eng. A 565 (2013) 382–391. [3] A. Bhattacharya, E. Meslin, J. Henry, C. Pareige, B. Décamps, C. Genevois, D. Brimbal, A. Barbu, Acta Mater. 78 (2014) 394–403. [4] Leyun Wang, Meimei Li, Jonathan Almer, Acta Mater. 62 (2014) 239–249. [5] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Yoshizawa, M. Igarashi, Mater. Lett. 63 (2009) 2423–2425. [6] Meimei Li, Leyun Wang, Jonathan D. Almer, Acta Mater. 76 (2014) 381–393. [7] P.J. Ennis, A. Zielinska-Lipiec, O. Wachter, A. Czyrska-Filemonowicz, Acta Mater. 45 (1997) 4901–4907. [8] P.J. Ennis, A. Zielinska-Lipiec, A. Czyrska-Filemonowicz, Mater. Sci. Technol. 16
71
(2000) 1226–1232. [9] K. Maruyama, K. Sawada, J. Koike, Iron Steel Inst. Jpn. Int. 41 (2001) 641–653. [10] V. A. V´yrostkov´a, J. Homolov´a, Pecha, M. Svoboda, Mater. Sci. Eng. A 480 (2008) 289–298. [11] Lj Milovic, T. Vuherer, I. Blacic, M. Vrhovac, M. Stankovic, Materi. Des. 46 (2013) 660–667. [12] Valeriy Dudko, Andrey Belyakov, Dmitri Molodov, Rustam Kaibyshev, Metall. Mater. Trans. A 44A (2013) 162–172. [13] Irina Fedorova, Alla Kipelova, Andrey Belyakov, Rustam Kaibyshev, Metall. Mater. Trans. A 44A (2013) 128–135. [14] Fujio Abe, Mater. Sci. Eng. A 319–321 (2001) 770–773. [15] K. Sawada, K. Kubo, F. Abe, Mater. Sci. Eng. A 319–321 (2001) 784–787. [16] Jae Seung Lee, Hassan Ghassemi Armaki, Kouichi Maruyama, Taro Muraki, Hitoshi Asahi, Mater. Sci. Eng. A 428 (2006) 270–275. [17] Yin Zhong Shen, Sung Ho Kim, Chang Hee Han, Hai Dong Cho, Woo Seog Ryu, J. Nucl. Mater. 384 (2009) 48–55. [18] S.S. Wang, D.L. Peng, L. Chang, X.D. Hui, Mater. Des. 50 (2013) 174–180. [19] T. Sakthivel, M. Vasudevan, K. Laha, P. Parameswaran, K.S. Chandravathi, S. Panneer Selvi, V. Maduraimuthu, M.D. Mathew, Mater. Sci. Eng. A 591 (2014) 111–120. [20] I. Fedorova, A. Belyakov, P. Kozlov, V. Skorobogatykh, I. Shenkova, R. Kaibyshev, Mater. Sci. Eng. A 615 (2014) 153–163. [21] K. Kimura, H. Kushima, K. Sawada, Mater. Sci. Eng. A 510–511 (2009) 58–63. [22] O. Prat, J. Garcia, D. Rojas, G. Sauthoff, G. Inden, Intermetallics 32 (2013) 362–372. [23] A. Kostka, K.-G. Tak, R.J. Hellmig, Y. Estrin, G. Eggeler, Acta Mater. 55 (2007) 539–550. [24] Oleg D. Sherby, Eric M. Taleff, Mater. Sci. Eng. A 322 (2002) 89–99. [25] Nhon Q. Vo, Christian H. Liebscher, Michael J.S. Rawlings, Mark Asta, David C. Dunand, Acta Mater 71 (2014) 89–99. [26] Triratna Shrestha, Mehdi Basirat, Indrajit Charit, Gabriel P. Potirniche, Karl K. Rink, Uttara Sahaym, J. Nucl. Mater. 423 (2012) 110–119. [27] K. Maruyama, H. Ghassemi Armaki, R.P. Chen, K. Yoshimi, M. Yoshizawa, M. Igarashi, Int. J. Press. Vessels Pip. 87 (2010) 276–281. [28] J. Čadek, Creep in Metallic Materials, Elsevier, Amsterdam, 1988. [29] S. Spigarelli, Int. J. Press. Vessels Pip. 101 (2013) 64–71. [30] H. Ghassemi-Armaki, R.P. Chen, K. Maruyama, M. Igarashi, Mater. Sci. Eng. A 527 (2010) 6581–6588. [31] Hassan Osman Ali, Mohd Nasir Tamin, J. Nucl. Mater. 433 (2013) 74–79. [32] B.F. Dyson, T.B. Gibbons, Acta Mater. 35 (1987) 2355.