Displacement damage cross section and mechanical properties calculation of an Es-Salam research reactor aluminum vessel

NUCLEAR ENERGY SCIENCE AND ENGINEERING

Displacement damage cross section and mechanical properties calculation of an Es-Salam research reactor aluminum vessel

Djillali Saad，

Hocine Benkharfia，

Mahmoud Izerrouken，

Ahmed Ali Benyahia，

Hamid Ait-Abderrahim

Nuclear Science and Techniques

Vol.28, No.11

Article number 162

Published in print 01 Nov 2017

Available online 26 Oct 2017

DOI：10.1007/s41365-017-0319-3

55000

Nuclear facility aging is one of the biggest problems encountered in nuclear engineering. Radiation damage is among one of the aging causes. This kind of damage is an important factor of mechanical proprieties deterioration. The interest of this study is on the Es-Salam research reactor aluminum vessel aging due to neutron radiation. Monte Carlo (MC) simulations were performed by MCNP6 and SRIM codes to estimate the defects created by neutrons in the vessel. MC simulations by MCNP6 have been performed to determine the distribution of neutron fluence and primary knock-on-atom (PKA) creation. Considering our boundary conditions of the calculations, the helium and hydrogen gas production in the model at a normalized total neutron flux of 6.62x10¹² n/cm².s were determined to be 2.86 x 10⁸ and 1.33 x 10⁹ atoms/cm³.s, respectively. The SRIM code was used for the simulation of defects creation (vacancies, voids) in the aluminum alloy of the Es-Salem vessel (EsAl) by helium and hydrogen with an approximate energy of 11 MeV each. The coupling between the two codes is based upon post-processing of the particle track (PTRAC) output file generated by the MCNP6. A small program based on the MatLab language is performed to condition the output file MCNP6 in the format of a SRIM input file. The concentration of silicon was determined for the vessel by the calculation of the total rate of ²⁷Al(n,γ)²⁸Si reaction. The DPA (displacement per atom) was calculated in SRIM according to R.E. Stoller recommendations; the calculated value is 0.02 at a fast neutron fluence 1.89 x10¹⁹ n/cm². RCC-MRx standard for 6061-T6 aluminum was used for the simulation of the evolution of mechanical properties for high fluence. The calculated values of nuclear parameters and DPA obtained were in agreement with the experimental results from the Oak Ridge High Flux Isotope Reactor (HFIR) reported by Farrell and coworkers.

Radiation DamageEsAl6061-T6Silicon productionDPAPKAMCNP6SRIMRCC-MRxHFIR.

1. Introduction:

Aluminum alloys (5000 & 6000 series) are well used in nuclear technology as fuel cladding, structural materials, and reactor tanks^[1,2]. During the reactor operation these alloys experience radiation damage resulting in continuous aging and limitation of its life span. Consequently, aging management of the material principally reactor vessel, which is difficult to replace, is important^[3]. For this purpose, establishment of a material properties database is needed to estimate the safety life time of the structural materials used in nuclear reactors. For our knowledge, there are not enough published papers about the irradiation behavior of aluminum alloys under the operation conditions of research reactors. Therefore, in the present investigation, we developed a method based on MCNP6^[4] and SRIM^[5] codes to calculate the displacements damage caused by N_dpa in the Es-Salam research reactor aluminum vessel. We used also RCC-MRx standards for 6061-T6 aluminum to simulate the evolution of its mechanical properties. Our aim is to predict the Es-Salam reactor vessel life time under the irradiation environments and operation condition of such a reactor.

2. Radiation displacement damage:

Radiation damage induced in the aluminum structural materials depends on the composition, manufacturing circumstances, irradiation temperature, neutron spectrum, thermal, and fast neutron. In the thermal neutron field, aluminum atoms are transmuted to silicon according to the ²⁷Al(n,γ)²⁸Si reaction. The silicon precipitates grow with increasing fluence. In the case of aluminum alloys of the 5000 series, the main alloying element, Mg, is in solution. The production of silicon under irradiation causes a precipitation of Mg₂Si, which induces an increase of mechanical strength and a loss of ductility^[6]. However, in structural alloys of the 6000 series, the main alloying elements Mg and Si are fine precipitates obtained by heat treatment, therefore only the Mg content in excess of the stoichiometric composition Mg₂Si is available for further precipitation with silicon produced by irradiation^[6].

Moreover, the solvability of Al for Si is very low so in the case of the absence of an additional alloy like Mg, silicon is precipitated by crystallization at the grain boundaries. It is seen in earlier findings that Si precipitates with a diameter of 170 Å, and a concentration of 10¹⁶ cm^-3 was observed in Al6061 irradiated to thermal and fast neutron fluence of 9.2 x10²² n.cm^-2 and of 11.6 x10²² n.cm^-2 respectively^[7]. The Si precipitates accumulation induces swelling and increases tensile strength and reduction of ductility^[7,8]. We note that the transmutation reaction due to the thermal neutron capture is the major part of the defect source in the case of thermal to fast neutron ratio higher than 400^[9]. In the later case, the Si precipitates are responsible for most of the radiation strengthening in 6061-T6 alloys.

Fast neutrons (E> 1 MeV) induce displacement via elastic scattering with target atoms and nuclear reactions, principally ²⁷Al(n,α)²⁴Na and ²⁷Al(n,p)²⁷Mg with neutron energy threshold of 6 MeV and 1.9 MeV respectively. According to Kelly^[10], approx. 300 displacements are caused in average by fast neutrons (E>1 MeV) resulting in a change of mechanical properties. Both recoil atoms, called primary knock atom, and nuclear reaction products, alpha particles (α) and proton (p), impart energy to neighboring atoms and produce large displacement cascades along their path. This is possible if the PKA energy is higher than the threshold displacement energy, E_d. For collisions in which the lattice atom receives energy less than E_d, the struck atom undergoes large amplitude vibrations within its potential well but remains in its lattice site. Once initiated by the PKA atom, collisions continue occurring until energy in excess of E_d is dissipated, typically after about 10 ps. An illustration of a typical PKA event in a simple lattice is shown in Fig. 1^[11]. Various models were proposed to calculate the number of displaced atoms produced by the recoil atom of energy E. The most widely cited model was that of Kinchin and Pease^[12]. Their model assumed that between threshold energy and energy cut-off, there is a linear relationship between the number of Frenkel pair produced and the PKA energy. Below the threshold displacement energy, no new displacements would be produced. Above the high-energy cut-off, it is assumed that the additional energy is dissipated in electronic excitation and ionization. Lindhard and coworkers^[13] developed a detailed theory for energy partitioning that could be used to compute the fraction of the PKA energy that was dissipated in the nuclear system in elastic collisions and in electronic losses. This work was used by Norgett, Robinson, and Torrens (NRT) to develop a secondary displacement model that is still used as a standard in the nuclear industry and elsewhere to compute atomic displacement rates^[14]. The NRT model is governed by the following equation:

Fig. 1:

Atomic displacement processes in energetic displacement cascade envisioned by A.Seeger in 1958.

N_{d} (T_{d}) = {\begin{matrix} 0 T_{d} < E_{d} \\ 1 E_{d} \leq T_{d} < 2 E_{d} / β \\ β T_{d} / 2 E_{d} 2 E_{d} / β \leq T_{d} < \infty \end{matrix},

(1)

where N_d(T_d) is the number of displaced atoms produced by recoil atom of energy, E, and damage energy T_d and E_d is the average threshold displacement energy^[15]. β (equal to 0.8) is known as the scattering correction factor. The damage energy (T_d) in the above expression is a function of E_PKA. The damage energy is the amount of the initial PKA energy available to cause atomic displacements, with the fraction of the PKA’s initial kinetic energy lost to electronic excitation being responsible for the difference between E_PKA and T_d. It is calculated for each recoil energy using Robinson’s analytic expression^[16]. The threshold displacement energy, E_d, is dependent on the material structure and can be determined experimentally or by molecular dynamics simulation. In the present study, a value of 25 eV is used^[15]. The displacement defects consist of point defects (vacancies and interstiels). With increasing fast neutron fluence, the vacancy clusters are developed to voids and dislocations. Mean void diameter of 370 Å and concentration of about 1.9x 10¹⁴ cm^-3 were measured in Al6061 and irradiated to thermal and fast neutron fluence of 9.2 x10²² n.cm^-2 and of 11.6 x10²² n.cm^-2, respectively, by King et al.^[7]. According to these authors, the voids generate a swelling of 0.68% at this fluence.

3. Material and Calculation method

Aluminum alloy of Es-Salam reactor vessel (EsAl) is part of the 6000 series (Al-Mg-Si) and is very close to the 6061 shades which are widely used in the manufacture of sensitive structure research reactors. However, its chemical composition is a little bit different from the latter in terms of ratio of the main components (Mg and Si) that are nearly inverted in the two aluminums^[17]. The chemical composition of the aluminum vessel of the Es-Salam research reactor is given in the Table 1.

Characteristics of the vessel material^[17]

Material	density (g/cm³)	Al(%)	Mg	Si	Fe	Cu	Ti	Zn	Cr
EsAl	2.7	⪰ 98.13	0.45-0.9	0.6-1.2	⪰ 0.2	⪯ 0.01	⪯ 0.01	⪯ 0.03	⪯ 0.03

3.1. Displacement damage calculation:

The simulation of reactor neutron induced damage in structural materials is well investigated using different methods. Jonghwa et al.^[18]. have investigated radiation damage in SiC using the combination of NJOY and SRIM cods^[18]. Heinish et al.^[19] used SPECOMP and SRIM codes to calculate the damage cross section in SIC irradiated in the fission reactor. Neutron induced damage under a variety of neutron energy spectra was also investigated by several authors using a combination of MCNP and SRIM codes^[20-22].

The generalized MC transport code, MCNP, was used to model the interaction of neutrons with material^[23]. It is specifically designed for computing accurate neutron-physics, the tracking of particles through specified problem geometry^[24]. It utilizes continuous energy nuclear cross section libraries to evaluate the likelihood of interaction at each point. MCNP6 can easily tabulate additional parameters which would be useful in a more rigorous multi-scale model of radiation damage. Such parameters include nuclear heating, internal gas production (He, H, etc.), and photon production as well as many reaction rates of interest. The MCNP6 tally that is of event-by-event nature and fit the study requirement is the PTRAC card.

The SRIM software, previously known as TRIM, has gained wide popularity in the ion irradiation community. The primary reasons are that, on one hand it is free and easy to install and use in a Windows operating system, on the other hand it can calculate ion penetration depth profiles for any kind of ion with energies from a few tens of eV to 1 GeV in any material.

The SRIM software treats the ion penetration in a material with the binary collision approximation, i.e. as a series of independent binary collisions. The SRIM calculations can be ran in two different modes: "Ion distribution and quick calculation of damage" and "Detailed calculation with full damage cascades". In the former, only the path of the incoming ion is followed. In the latter, also all knock-on atoms of all generations (primary, secondary, etc.) that have an energy above the threshold energy are followed. Stoller et al.^[25] recommended an interesting recipe for obtaining DPA values for metals using SRIM code.

The coupling between the two codes (MCNP6 and SRIM) is made using a home program based on the MatLab language in order to adjust the output file of MCNP6 to the input file of SRIM.

MCNP6 transport programs are used to calculate where neutron collisions are made in the target, and give the position, and recoil statistics for each collision atom. Then, SRIM calculates the full target recoil cascade. A file called TRIM.DAT was generated and gives radiation damage events.

3.2. Mechanical properties calculation:

To simulate the mechanical properties after irradiation, we followed the methodology of the RCC-MRx standard^[26]. The principle of this methodology is:

To obtain the yield strength after irradiation of a material, simply multiply the value of the yield strength before irradiation by a factor that supports the material behavior after irradiation. While our material EsAl is shaded very close to that of 6061-T6, we used the same factors after irradiation that are given by the RCC-MRx standard. The average yield strength at 0.2% offset $R_{p0 .2}^{after}$ are obtained by multiplying the average yield strength at 0.2% offset $R_{p0 .2}^{before}$ before irradiation by the factor $f_{p0 .2}^{ir}$ . The average tensile strengths, $R_{m}^{after}$ , are obtained by multiplying the average tensile strength, $R_{m}^{before}$ before irradiation by the factor $f_{m}^{ir}$ . The factors $f_{p0 .2}^{ir}$ and $f_{m}^{ir}$ are given as a function of the fluence, Φ_th, by the formulae in the Table 2.

factors

f_{p0 .2}^{ir}

and

f_{m}^{ir}

at T=50°C

Φ_th(10²¹ n_th/cm²)	$f_{p0 .2}^{ir}$	Φ_th(10²¹ n_th/cm²)	$f_{m}^{ir}$
Φ_th ⪯ 1.2	1	Φ_th ⪯ 1.8	1
1.2 < Φ_th ⪯300	-4.3928 + 0.1111 Ln(Φ_th)	1.8 < Φ_th ⪯300	-3.6151 + 0.0943 Ln(Φ_th)

The ductility characteristics are percentage total elongation at fracture A_t and percentage total elongation at maximum force A_gt. To simulate the evolution of elongation after irradiation according to RCC-MRx standard, the decrease of elongation fulfills a function of the form:

Elongation % = A - B Log (Φ_{th}) .

(2)

Based on the A_gt and A_t values before irradiation, the constants A and B are determined for each fluence range. A_gt and A_t are given as a function of the fluence Φ_th by the formulae in the Table 3.

A_gt and A_t after irradiation

Φ_th (10²¹ n_th/cm²)	A_gt (%)	Φ_th (10²¹ n_th/cm²)	A_t (%)
5.5 < Φ_th ⪯476	248.441 - 10.397 Log(Φ_th)	34 < Φ_th ⪯532	-3.6151 + 0.0943 Ln(Φ_th)
Φ_th > 476	2.24	Φ_th > 532	2.5

4. Results:

4.1. DPA Calculation:

A model of the Es-Salam reactor core, as well as KCODE calculation and F4 tallies, was built on the MCNP6 platform to calculate the average neutron spectrum on the wall of the vessel for three energy groups of thermal, epithermal, and fast neutrons (from zero to twenty MeV). This spectrum is subsequently applied on a model of the vessel 3 cm x 3 cm x 0.8 cm slab (Fig. 2). FMn cards have been used in the input file of MCNP6 to generate (n, γ), (n, p), and (n, α) neutron reactions.

Fig. 2

(Color online): EsAl alloy model for 3D-MCNP6 calculation.

The average total unnormalized neutron flux in the specimen is 3.7075 10^-5 n/cm².s, and normalized neutron flux is 6.62 10¹² n/cm²s. The average normalized thermal flux is 6.09 x10¹² n/cm².s (E ≤ 0.55 eV), the epithermal flux is 1.88 10¹¹ n/cm².s (0.55 eV < E ≤ 0.1 MeV), and the fast flux is 3.42x 10¹¹ n/cm².s (E ≥ 2 MeV). The total unnormalized number of PKA is 9.0732 x10^-9 atoms/cm³.s and normalized number of PKA is 1.616 x10⁹ atoms/cm³.s, which has been detexrmined by the number of scatters on the EsAl aluminum atoms in a neutron energy range from 0.1 MeV to 20 MeV. The minimum neutron energy necessary to displace the atom from the crystal lattice (PKA) is 100 keV and the threshold energy displacement (E_d) is 25 eV. The total particle production in the specimen is given in Table 4.

Nuclear reaction in the material

Target atom	Reaction & product	Unnormalized production in model (Atom/cm³s)
²⁷Al	²⁷Al(n,α)²⁴Na	1.60172 10^-9
	²⁷Al(n,p)²⁷Mg	7.47150 10^-9
	²⁷Al(n,γ)²⁸Si	6.71028 10^-6

Fig. 3 shows the PKA energy thresholds (α and p) through the thickness of the vessel. Considering the damage energy as the sum of the damage energy to target atoms and phonons^[25], it is found from the calculation that the total number of DPA generated by the proton and He in EsAl as a function of fast neutron fluence (Φ_f) can be represented by the following equation:

Fig. 3

(Color online): PKA loss energy in the target atom. (a) He PKA loss energy, (b) H PKA loss energy.

D P A_{SRIM} = 1.029 10^{- 21} Φ_{f} .

(3)

MCNP6 was also used to calculate the DPA within the aluminum vessel. The DPA was calculated using the ENDF-B VI damage cross sections (Fig. 5), which are not a part of the MCNP6 default cross section libraries. The ENDF-B VI cross sections were developed using the NRT model and combined BCA-MD method^[27]. The DPA was calculated in MCNP6 according to the equation:

Fig. 5:

²⁷Al ENDF/B-VI DPA cross-sections^[27].

D P A_{XC} = \frac{\int d v \int φ (\vec{r}, E) d E \sum_{i = 1}^{N} X_{i} σ_{i}^{dpa} (E)}{\sum_{i = 1}^{N} 2 E_{d, i}},

(4)

where $σ_{i}^{dpa} (E)$ is the displacement cross-section, $φ (\vec{r}, E)$ is the neutron flux and dv is the considered volume. The MT number of damage cross section is 444. This number is used in the FM card in MCNP6. Using this tally, MCNP6 calculated the rate of displacements per atom of 3.18 x10^-10 DPA s⁻¹. The DPA can be represented as a function of fast fluence by the following equation:

D P A_{XC} = 0.929 10^{- 21} Φ_{f} .

(5)

This result agrees well with the results already found with the coupling of the codes MCNP6 and SRIM.

Figure 4 shows the DPA evolution as a function of fast neutron fluence in the Es-Salem reactor vessel (EsAl) compared to the experimental data of Al6061-T6 irradiated at HFIR^[23]. As can be seen, Eq. (3) and (5) simulate very well the experimental DPA values.

Fig. 4:

MCNP6-SRIM calculated DPA and HFIR DATA.

4.2. Silicon production:

The concentration of silicon was determined for the EsAl vessel by the calculation of the total rate of ²⁷Al(n,γ)²⁸Si reaction. The unnormalized reaction rate of ²⁷Al(n,γ)²⁸Si from thermal and epithermal neutrons is about 6.83 10^-6 atoms/cm³.s. Taking into account the volume calculation and the atomic density of the studied material, we find a linear relationship between the created silicon content and the thermal fluence (Eq. 6). The amount of silicon produced in the Es-Salem reactor vessel using this equation is presented in Fig. 6 and compared to the Si concentration formed in Al6061-T6 irraditaed at HFIR reactor^[28]. It is clear from the figure that a good concordance is found between simulation and experimental data in the fluence range lower than 3 x10²² n.cm^-2.

Fig. 6:

Thermal fluence dependence of created silicon content in EsAl alloy

w t % {}^{28}S i = 3.18 10^{- 22} Φ_{th}

(6)

The difference in the results for the height fluences is due to the two distinct ratios (thermal flux to fast flux). Indeed, the HFIR samples were irradiated with a ratio equal to 1.66 whereas the sample of our study was simulated with a ratio of 17.81. Let us note here that most neutrons arriving at the level of the vessel are moderate. The HFIR samples were taken from the control bar tubes which is why the ratio of thermal flux to the fast flux in the case of HFIR is much less than those of the Es-Salam reactor.

Weeks, et al.^[29] study indicate that the increase in tensile strength and decrease in ductility result primarily from the thermal fluence, i.e., the transmutation of aluminum to silicon. In regions where the thermal flux is greater than the fast flux, more rapid mechanical properties degradation can be expected than in areas where fast flux is dominant.

4.3. Mechanical properties simulation:

The simulation of the mechanical properties were made using the methodology of the RCC-MRx standard^[26] described above.

Fig. 7 shows the fluence dependence of R_p0.2 and R_m of EsAl and Al6061-T6 compared with the data of 6061-T6 irradiated at HFIR^[28]. The chemical composition of the 6061 alloy was 0.87 wt% Mg and 0.58 Si. Button-headed tensile specimens of gage length 28.6 mm and gage diameter 3.2 mm were machined from cold-swaged bars and were heat treated as T6 temper. The specimens were irradiated in the peripheral target positions in HFIR in contact with the cooling water at about 55°C for periods up to 3.5 years during which they accumulated fast neutron fluences up to 1.8 10²³ n/cm² and thermal fluences up to 3.0 10²³ n/cm².

Fig. 7:

Fluence dependence of R_p0.2 and R_m of EsAl and Al6061-T6 compared with data of 6061-T6 irradiated at HFIR.

As can be seen, the calculated R_p0.2 and R_m for Al6061-T6 are approximately similar the experimental data. However, the calculated R_p0.2 and R_m value of EsAl is lower than that 6061-T6 indicating probably the higher radiation resistance of EsAl.

4.4 Ductility characteristics:

Fig. 8 shows the fluence dependence of A_t and A_gt of EsAl and Al6061-T6 compared with the data of 6061-T6 irradiated at HFIR. It is clear from the figure that the calculated A_t and A_gt for Al6061-T6 reproduce the experimental data. However, the calculated A_t and A_gt value of EsAl is higher than that 6061-T6. The calculated values of ductility show an advantage in favor of the ESAl material.

Fig. 8:

Fluence dependence of A_gt and A_t of EsAl compared with HFIR of 6061-T6.

5. Vessel lifetime Estimation:

Actually, the existing thermal and fast (E>0.1 MeV) neutron fluence at the Es-Salam research reactor vessel are, respectively, 3.37 x10²⁰ n/cm² and 1.89x 10¹⁹ n/cm². According to our calculation, at such fluence, the obtained displacement density is 0.02 dpa, and only 1.23 ppm hydrogen atoms and 0.26 ppm helium are produced in the aluminum structure. The amount of silicon produced is 0.107% wt. Fig. 9 resumes the mechanical properties evolution of the Es-Salam research reactor vessel as a function of fluence. The green vertical line represents the current state. As can be seen, the critical value for the elongation representing the end of life-value (red line) is reached at a neutron fluence of 1.57 x10²² n/cm² which corresponds to 5%wt ²⁸Si and about 1100 dpa. The wt% ²⁸Si product in the Es-Salam aluminum vessel is considerably lower than the end-of-life limit. Based on the mode of operation of 60 MW days per year^[30], the power operation of the reactor could be continued for additional 1.607x 10⁶ MWh.

Fig. 9:

Fluence dependence of mechanical properties of the vessel research reactor Es-Salam

6. Conclusion

The simulations of radiation damage in Es-Salem research reactor were carried out using the MC transport code MCNP6 and the Transport Range of Ions in Matter code SRIM. The calculations have been performed using the continuous energy MCNP6 transport code to determine the nuclear parameters in the Es-Salem research reactor vessel. The parameters include high-energy neutron fluence distribution, the defect production in form of primary knock-out atoms, and H and He atoms. On the basis of MCNP6 modeling of radiation damage in the aluminum structure of the vessel of the Es-Salem research reactor, following conclusions are made:

·　Under consideration of the total power history of the Es-Salem research reactor, the dpa number and silicon produced is too low to cause any increase in the tensile strength and reduction of ductility.

·　The change of the mechanical properties of aluminum due to the fast neutron damage is considerably low for any consequences.

However, good agreement was found between our calculated values and the experimental data. Thus we conclude that the developed model is capable of accurately determining radiation damage in any structure and location of the reactor core.

References:

F. Ozturk, A. Sisman, S. Toros et al.,

Influence of aging treatment on mechanical properties of 6061 aluminum alloy

. Mater Design 31, 972-975 (2010). doi: 10.1016/j.matdes.2009.08.017