Microstructure evolution and yield strength of CLAM steel in low irradiation condition

Materials Science & Engineering A 682 (2017) 563–568

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Microstructure evolution and yield strength of CLAM steel in low irradiation condition

MARK

⁎

Chenchong Wanga, Chi Zhanga, , Jijun Zhaob, Zhigang Yanga, Wenbo Liua a

Key Laboratory of Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China State Key Laboratory of Materials Modification by Laser, Electron, and Ion Beams, School of Physics and Optoelectronic Technology and College of Advanced Science and Technology, Dalian University of Technology, Dalian 116024, China

b

A R T I C L E I N F O

A BS T RAC T

Keywords: Microstructure evolution Yield strength Irradiation High temperature

The microstructure and yield strength of China low activation martensitic (CLAM) steel were observed and tested. The evolution of defects, including He bubbles and dislocation loops, and MC carbides were analyzed. According to the microstructure observation results, a two-step simulation model was established to analyze the relationship between microstructure and strength. For the first step, a rate theory model was used to simulate the evolution of defects (He bubbles and dislocation loops). The incubation, nucleation and growth stage of defects were shown by simulation results. For the second step, the simulation results of defect evolution were added into a superposition strengthening model, which combined different strengthening methods, to simulate the yield strength of CLAM steel in high temperature and irradiation condition. Based on both experimental and simulation results, the effect of high temperature and irradiation on microstructure and strength was discussed in CLAM steels. The simulation results of yield strength were basically consistent with experimental results.

1. Introduction Reduced activation ferritic/martensitic (RAFM) steels are considered as potential materials for first wall and blanket structure in fusion reactors [1–3]. China low activation martensitic (CLAM) steel, as one of RAFM steels, is considered as the primary Chinese test blanket module of International Thermonuclear Experimental Reactor (ITER) and in the designs of FDS series PbLi blankets for the future fusion reactors [4–6]. So, the mechanical properties of CLAM steel were paid much attention by researchers [7,8]. As well known, the microstructure can greatly affect the mechanical properties of steels [9,10]. In order to enhance the safety of the fusion reactors, many previous works focused on the relationship between microstructure and mechanical properties in CLAM steels. In the irradiation condition, the most important microstructure evolution is the formation of dislocation loops and He bubbles for CLAM steels. However, it is difficult and costly to obtain the number density and mean size of different defects in steels by experiment. Especially for the small displacement damage, the defects are usually too small to be found by experiment methods. In order to analyze the evolution of dislocation loops and He bubbles, many simulation models were established, including molecular dynamics, phase field, rate theory, etc [11–13]. Recently, rate theory models, which use rate

⁎

equations to simulate defect evolution from the initial stage of irradiation was widely used to calculate the number density and size of dislocation loops and He bubbles, due to its low computational cost [14]. For the precipitation, several models were also established by irradiation-enhanced diffusion theory to simulate the nucleation and growth of the carbides in irradiation condition [15,16]. However, these models only considered about the microstructure. In order to simulate the yield strength of the steels in irradiation and high temperature conditions, more mechanical models should be built based on the microstructure simulation results. For a long time, yield strength simulation in metal materials were studied by many experts and several classical models were built, including Peierls-Nabarro model [17], Hall-Petch model [18], Orowan dislocation looping model [19], Friedel's shear cutting model [20], Kocks-Mecking model [21]. etc. Peierls-Nabarro model was used to simulate friction stress of lattice. Hall-Petch model mainly expressed the grain refinement. Orowan's and Friedel's model were used for dispersion strengthening. Kocks-Mecking model was dislocation theory. So, every classical model had its own function and using limit. In order to enhance the application range of yield strength simulation, a superposition model, which combined different classical models, was established and used to simulate the yield strength of gear steels [22]. However, this superposition model can only be used in normal

Corresponding author. E-mail address: [email protected] (C. Zhang).

http://dx.doi.org/10.1016/j.msea.2016.11.057 Received 7 October 2016; Received in revised form 16 November 2016; Accepted 17 November 2016 Available online 18 November 2016 0921-5093/ © 2016 Elsevier B.V. All rights reserved.

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4. Simulation methods

condition (room temperature without irradiation). For high temperature strength simulation, a dislocation theory model was established to simulate the relationship between temperature and yield strength of tungsten [23]. However, no irradiation effect or other strengthening methods, except for dislocation strengthening was considered in the model. In general, strength simulation of RAFM steels in irradiation and high temperature condition was a complicated problem, which consisted of many different factors. In this paper, the microstructure of CLAM steel was observed. A two-step model was established to simulate the yield strength of CLAM steel. For the first step, rate theory model was used to simulate the evolution of dislocation loops and He bubbles in small displacement damage (0–0.02 dpa). For the second step, the results in first step were added into a superposition strengthening model, which contained different strengthening methods and the effect of irradiation and temperature. The simulation results of yield strength were compared with the experimental results.

Based on the observation in Part.3, it was clear that the microstructure of CLAM steels after irradiation mainly included dislocation, precipitation, He bubbles, dislocation loops, etc. Therefore, a model contained both microstructure and strengthening simulation was established to simulate the yield strength of CLAM steels in high temperature and irradiation condition. The main factor chart of the simulation was shown in Fig. 3. As Fig. 3, different factors were considered in the model, including dislocation, solid solution element, precipitation, friction stress of lattice, shear modulus, interface bonding, He bubbles and dislocation loops. Especially for the size/number density of He bubbles/dislocation loops in the condition of <0.1 dpa, which could hardly be observed by experiment, a rate theory model was used to obtain reasonable simulation results of the He bubbles/ dislocation loops evolution. 4.1. Rate theory model

2. Material and methods

As the observation results (Fig. 2), defects like He bubbles would form during the irradiation in CLAM steel. He bubbles and dislocation loops played the most important role on irradiation hardening of RAFM steels [28,29]. However, for a small irradiation condition( < 0.1 dpa), the defects could hardly be observed by experiment methods because their sizes were even smaller than the microscope resolution. So, in order to simulate the yield strength of CLAM steel in low irradiation condition( < 0.1 dpa), simulation method should first be used to express the evolution of He bubbles and dislocation loops. Because rate theory was now widely used and proved to be a good method to simulate the evolution of defects in RAFM steels [11,12], in this work, a rate theory model, which included several types of defects (self-interstitials (I), vacancies (V), helium atoms (He), self-interstitial clusters (IC), void (VC), vacancy-helium pairs (V, He), bubbles (B)) was used. The model contained the main assumptions as follows: (1) only helium, vacancy and interstitials were mobile; (2) vacancy-helium pair and one vacancy with one He atom inside were not included in bubbles; (3) thermal dissociation was considered for vacancy-helium pairs. According to these assumptions, the concentration of self-interstitials, vacancies and helium atoms was described by Eqs. (1)–(3).

The samples studied in this work were taken from a 12 mm thick CLAM steel plate, which was hot-forged and rolled by a 20 kg ingot. The heat treatment process was normalizing at 980 °C for 30 min, followed by air quenching. Then, the samples were tempered at 760 °C for 90 min (post-irradiation annealing), followed by air quenching. The main composition of the steel was shown in Table 1. Irradiation was carried out in China high flux reactor to a displacement damage value of both 2 dpa and 0.02 dpa, nominally at 250 °C with the irradiation flux of 5× 10−5 dpa/s. Then tensile testing was carried out at 15, 100, 200 and 350 °C for the samples with 0.02 dpa. The tensile samples were GR3 circular scale sample for High temperature tensile test (GB/T 4338—1995), with the length of 51 mm and the standard segment size of ϕ4 × 20 mm. Samples for transmission electron microscope(TEM) were cut to thin foils and ground to 50 µm in thickness. Then, electropolished in a perchloric acid-ethanol solution at −30 to −40 °C. Microstructure observation was carried out by JEOL JEM2011(Japan Electron Optics Ltd., Tokyo) with an accelerated voltage of 120 kV.

dCI dt

3. Microstructure observation results

= PI (1 − εR )(1 − εI ) − 2ZI , I MI CI2 − ZI , V (MI + MC ) CI CV − ZI , IC MI CI SI − ZI , VC MI CI SV − ZI , B MI CI SB − ZI , VHe MI CI CV , He − MI CI CS − NI PIC (1)

In order to obtain clear results of the defects formed in CLAM steels, samples with higher irradiation flux (2 dpa) were used for TEM observation. Fig. 1 showed the observation results of microstructure in CLAM steel. As the main reinforcement, MC carbides with the mean radius of 30 nm were founded in the martensite matrix (Fig. 1(a)). The diffraction pattern of MC was shown in Fig. 2(b). In previous works, MC carbides were studied in details and the observation results about MC carbides in this work were basically consistent with the previous results [24–26]. Also, a great amount of dislocation was found in the matrix of CLAM steel (Fig. 1(c)). Fig. 2 showed the He bubbles founded in CLAM steel with the condition of 2 dpa. He bubbles could form both at the interface and inside the grain. However, the observation results showed that He bubbles had higher number density at the grain boundary than inside the grain. These observation results of the distribution of He bubbles were consistent with the previous observation and simulation results [27].

dCV dt

= PV (1 − εR )(1 − εV ) − 2ZV , V MV CV2 − ZI , V (MI + MC ) CI CV − ZHe, V MHe CV CHe − ZV , V MV CV SV − ZV , IC MV CV SI − ZV , B MV CV SB − ZV , He MV CV CHe − ZV , He MV CV CV , He + MHe TV , He CV , He + ZI , VHe MI CI CV , He − MV CV CS − NV PVC (2)

dCHe dt

= PHe − ZHe, V MHe CV CHe − ZHe, V MHe CHe SV − ZHe, B MHe CHe SB − ZHe, V MHe CHe CV , He + ZI , VHe MI CI CV , He + MHe TV , He CV , He

− MHe CHe CS

(3)

where P was the production rate of defects; T was the probability of dissociation of helium from a vacancy; M and S were described by Eqs. (4)–(7). 1/3

Table 1 Main composition of CLAM steel used in this work(wt%).

2 SV = (48π 2RV CVC )

(4)

SI = 2(πRI CIC )1/2

(5)

1/3 (48π 2RV , He CB2 )

Element

C

Cr

W

V

Ta

Mn

Si

Fe

SB =

Content(wt%)

0.12

8.91

1.44

0.2

0.15

0.49

0.11

Bal.

M = ν exp(−Em /kt ) 564

(6) (7)

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Fig. 1. Microstructure in CLAM steel at 0 dpa: (a) MC carbide; (b)diffraction pattern of MC carbide; (c) dislocation in matrix.

The nucleation process of dislocation loops, voids, vacancy-helium pairs and bubbles were expressed by Eqs. (8)–(11).

dCIC 2 = PIC (1 − εR ) εI / NI + ZI , I MI CI2 − kL2 CIC dt

(8)

dCVC = PVC (1 − εR ) εV / NV + ZV , V MV CV2 − MHe CHe SV dt

(9)

dCV , He dt

= ZHe, V MHe CV − ZV , VHe MV CV CV , He − ZI , VHe MI CI CV , He − MHe TV , He CV , He − ZMHe CHe CV , He

dCB = ZV , He MV CV CV , He + ZHe, VC MHe CHe CVC + ZHe, VHe MHe CHe CV , He dt

(10) Fig. 3. Main factor chart of the two-step simulation.

(11)

dRB dt

Also, the growth of defects was expressed by Eqs. (12)–(14). The value of the parameters used in this model was listed in Table 2.

dRI = ZI , IC MI CI SI − ZV , IC MV CV SI + NI PIC dt

= ZV , B MV CV SB − ZI , B MI CI SB + ZHe, VC MHe CHe SV × + ZHe, VHe MHe CHe CV , He

RV CVC

(14)

(12) 4.2. Strengthening model

dRV R = ZV , VC MV CV SV − ZI , VC MI CI SV + NV PVC − ZHe, VC MHe CHe SV × V dt CVC

According to the microstructure observation results (Fig. 1), both precipitation and large amount of dislocation were found, which

(13)

Fig. 2. He bubbles in CLAM steel at 2 dpa: (a) He bubbles around M23C6; (b) He bubbles at the grain boundary and matrix.

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of MC carbides in CLAM steel. The CRSS for solid-solution strengthening of CLAM steels was expressed by Eq. (21).

Table 2 Parameters used in rate theory model. Parameter

Value

Unit

P PIC PVC

1.2× 10−10 1.2× 10−2 1.2× 10−2 0.3

dpa/s dpa/s dpa/s eV

1.5

eV

0.08

eV

0.7 0.2 0.2 10−6 10−6 1 0.15 45 40.4 40 27 4 6× 10–22

1 1 1 defects/atom defects/atom 1 1 1 1 1 1 1 m3/s

10–13

s−1

I EM V EM He EM

εR εI εV CS CSHe ZI,I ZV,V ZI,VZI, VHeZHe,VZV, HeZV, ZI, ICZI, VC ZV, ICZV, VCZI,BZV,BZHe,B ZHe, VC NINV

VHeZHe, VHe

kL2 ν

⎞1/2 ⎛ τss = ⎜⎜∑ kss2 , i ci⎟⎟ ⎠ ⎝ i

where kss, i was the solid solution coefficient of element i in martensite. ci was the mole fraction of i in martensite. The Hall–Petch stress, which expressed the grain refinement, was expressed by Eq. (22) 1

σH − P = KH − P d − 2

where K0 was the Hall-Petch constant in normal condition (room temperature without irradiation); kirr , kT and aT were constant. For the Peierl-Nabarro stress, modified P-N model [32] was used as Eqs. (24) and (25).

⎡ kB T ln(γṗ / ε )̇ ⎤2 ⎥ σP − N = σf ⎢1 − 2Hk ⎣ ⎦ σf = M

wL =

⎛ 2w R ⎞ 2Kb ln ⎜ D MC ⎟ ⎠ wL RMC ⎝ b

(15)

πwq φMC

− 2wr

−1 ⎛ 1 1 ⎞ + wD = ⎜ ⎟ ⎝ wL 2wr ⎠

K=

μ (T ) 1 4π 1−ν

⎡ μ (T ) 2πds ⎤ exp ⎢ − ⎥ ⎣ b (1 − ν ) ⎦ 1−ν

(25)

Δσirr (T , ϕ) = λMμ (T ) b Ndl (ϕ) ddl (ϕ) + βMμ (T ) bdH (ϕ) NH (ϕ)2/3

(26)

5. Results and discussion

(16)

2wD RMC ) b wL RMC ln( b )

(24)

where γṗ , Hk and ds represented the strain rate, double kink activation enthalpy and the spacing of the slip planes, respectively; ε̇ was mean shear rate. Also, the irradiation enhanced stress was calculated by Eq. (26), based on Friedel-Kroupa-Hirsch model [20] and dispersed barrier hardening model [33]. The value of the parameters used in this strengthening model was listed in Table 3.

where α was a constant of order unity; hd (T ) was the dislocationdislocation interaction strength, which was set as linear with a slope of −4× 10−4 and a constant of 0.38 [23]; μ (T ) was also set as linear with a slope of −5.37× 107 Pa/K and a constant of 77 GPa based on the simulation results by first principle method [31]. Based on the observation results, MC, the main reinforcement in CLAM steels, was about 30 nm in radius, which was much larger than the critical value for dislocation shear cutting. So, modified Orowan bypass model was used to calculate CRSS for dispersion strengthening by Eqs. (17)–(20).

τp = Y

(23)

KH − P = K0 + kirr ϕ + kT exp(aT ΔT )

where M was the Taylor factor for CLAM steel; τd , τss and τp were critical-resolved shear stress(CRSS) for dislocation strengthening, solid-solution strengthening and dispersion strengthening, respectively; σH − P was for the stress of grain refinement; σP − N was for the friction stress of lattice; Δσirr was for the stress enhancement by dislocation loops and He bubbles. For dislocation strengthening, the CRSS could be calculated by Eq. (16) based on Kocks-Mecking model [30].

τd = αμ (T ) b hd (T ) ρ

(22)

where d was the packet size of martensite; Hall-Petch constant was expressed by Eq. (23)

indicated that CLAM steel contained a variety of strengthening methods. So, different strengthening models should be combined by superposition laws to express the yield strength of CLAM steel. The yield strength was described by Eq. (15). 1⎤ ⎡ σy = M ⎢τd + (τssk + τpk ) k ⎥ + σH − P + σP − N + Δσirr ⎣ ⎦

(21)

Fig. 4 showed the simulation results of He bubble evolution. The simulation results showed that the number density of He bubbles increased significantly with the increasing of displacement damage (dpa), but the size of He bubbles just began to increase when the damage was up to 0.01 dpa. So, in low damage condition ( < 0.01 dpa), the evolution of He bubble had a stage of incubation. In the incubation stage, both the amount and size of He bubbles remain a stable value. In middle damage condition (0.01–0.02 dpa), the evolution of He bubbles had a significant stage of nucleation. In the nucleation stage, the amount of He bubbles increased quickly with a stable size. These

ln(

Table 3 Parameters used in strengthening model.

(17)

Parameter

Value

Parameter

Value

(18)

k d − He ρ0 b

0.2 nm/dpa 5× 1012 m−3 0.248 nm

ε̇ α γṗ

10−3 s−1 0.4 3.71× 1010 s−1

(19)

Y wr wq φMC RMC

0.65 0.82 0.75 0.5% 30 nm 1.8 82.7 MPa 0.7

Hk ν M kirr kT aT β ccr

1.65× 10–19 J 0.3 2.5 200 1.5× 104 0.01 0.22 8.3%

(20)

k

where Y was dispersion distribution parameter; wr and wq were the mean radius and area for the particle intersection in the glide plane; ν was Poisson's ratio; φMC and RMC were the volume fraction and radius

k ss, Cr λ

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Fig. 6. Simulation results of yield strength in high temperature and irradiation condition.

Fig. 4. Simulation results of He bubble evolution.

results were similar with previous simulation results by phase field [12]. In the simulation results of phase field, not only incubation and nucleation, but a growth stage in high damage condition was shown. Because only the damage condition of ≤ 0.02 dpa was studied in our work, the growth stage in high damage condition was not shown in the results of this rate theory model. The simulation results showed that the size of He bubbles was less than 0.1 nm in the condition of 0.02 dpa, so it can hardly been observed by TEM. Fig. 5 showed the simulation results of dislocation loop evolution by rate theory model. In a relatively lower damage condition ( < 0.001 dpa), the evolution of dislocation loop also showed a stage of incubation, which was similar with the evolution of He bubbles. However, the nucleation stage of dislocation loop was not significant. Instead of nucleation, a growth stage of dislocation loop was shown in the condition of 0.001–0.02 dpa. These results were also similar with other simulation results by rate theory in RAFM steels [13]. The simulation results of rate theory were added into the strengthening model as input parameters. The simulation results of yield strength of CLAM steel were shown in Fig. 6. Yield strength in only high temperature condition and in both irradiation and high temperature condition were calculated and compared with experimental results. The simulation results clearly showed the softening by high temperature and the irradiation hardening phenomenon in CLAM steel. With the temperature increased from 15 to 350 °C, the yield strength of CLAM steel decreased for about 100 MPa. With the damage increased from 0 to 0.02 dpa, the yield strength of CLAM steel increased for about 150 MPa. The simulation results in Fig. 6 also showed that, for the conditions of 0–350 °C+0 dpa and 0–200 °C+0.02 dpa, the error between simula-

tion results and experiment results of yield strength was less than 25 MPa ( < 7% of the total yield strength). However, in the condition of 350 °C+0.02 dpa, the error between simulation results and experiment results was up to 50 MPa. It was probably because we ignored the effect of temperature on the defect evolution. The mobility or diffusion coefficient of element or defects (interstitials, vacancies, helium atoms) in metal alloys was usually a temperature-dependent parameter. With the increasing of temperature, the diffusion rate of defects would probably be enhanced. Therefore, the formation of dislocation loops or He bubbles would probably become faster than the situation of room temperature. If the effect of temperature was added into the rate theory model, the simulation results of the number density and size of defects would probably be larger than the recent value. So, we could obtain a more reasonable simulation result of yield strength, which would be closer to the experiment value in the condition of 350 °C+0.02 dpa. In the condition of 0–200 °C and 0–0.02 dpa, the effect of temperature on defects evolution was not significant, so the simulation results were consistent with experimental results. 6. Conclusion The microstructure and yield strength of CLAM steel in high temperature and irradiation condition was observed and tested. Then a two-step simulation model was established to simulate the evolution of defects and yield strength in CLAM steels. (1) MC carbides, dislocation and He bubbles were observed in CLAM steel. It indicated that different strengthening methods, including dispersion strengthening, dislocation strengthening, irradiation enhanced strengthening, etc, should be considered during the simulation of yield strength in high temperature and irradiation condition. (2) A rate theory model was used to simulate the evolution of defects. With the increasing of displacement damage from 0 to 0.02 dpa, the incubation and nucleation stage of He bubbles were shown by simulation results. The incubation and growth stage was shown in the simulation of dislocation loop. (3) The results of rate theory model were added into the strengthening model. The softening by high temperature and the irradiation hardening phenomenon in CLAM steel were simulated. The simulation results of yield strength in irradiation and high temperature condition for CLAM steels were basically consistent with experimental results. Acknowledgements This work was financially supported by National Basic Research

Fig. 5. Simulation results of dislocation loop evolution.

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Programs of China (No. 2015CB654802 and No. 2015GB118001). Greatly acknowledged the financial support provided by the National Natural Science Foundation of China (Grant No. 51471094). The authors acknowledge the assistance of FDS group in Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, with the mechanical property test.

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