Advances in Materials Science and Engineering

Volume 2018, Article ID 7175083, 9 pages

https://doi.org/10.1155/2018/7175083

## On the Modelling of Thermal Aging through Neutron Irradiation and Annealing

^{1}Nuclear Research Center “Kurchatov Institute”–Central Research Institute of Structural Materials “Prometey”, Shpalernaya St., 49, 191015 Saint-Petersburg, Russia^{2}State Science Center–“Institute for Physics and Power Engineering”, Bondarenko Sq. 1, 249020 Obninsk, Kaluga Region, Russia

Correspondence should be addressed to Boris Margolin; ur.xednay@zbnilogram

Received 31 October 2017; Revised 14 May 2018; Accepted 23 May 2018; Published 2 July 2018

Academic Editor: Pavel Lejcek

Copyright © 2018 Boris Margolin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new method predicting long-term thermal embrittlement of steel caused by P segregation is verified. The method is based on the results of impact strength or fracture toughness tests using specimens after relatively short-term neutron irradiation followed by annealing. 2Cr–Ni–Mo–V steel used in reactor pressure vessels of WWER-1000 type is investigated in four conditions: initial condition, after thermal aging, after neutron irradiation, and postirradiation annealing. The results of impact strength and tensile tests and SEM investigation are presented. The brittle fracture features are considered for different material conditions. Calculative estimation on neutron irradiation effect on P diffusion in steels is carried out. Experimental data are reported which confirm an intense P diffusion acceleration under neutron irradiation.

#### 1. Introduction

Thermal aging is the dominant degradation mechanism proceeding in unirradiated component (e.g., nozzle shell) materials for WWER-type reactor pressure vessels (RPVs). Therefore, thermal aging of RPV materials during NPP operation should be predicted for an adequate structural integrity assessment of unirradiated RPV components. The WWER-1000 RPV operation temperature is 290–320°C. Lifetime for this type reactor is planed to be extended at least up to 60 years.

The prediction of thermal aging of RPV materials for 60 years is rather a complicated task. The point is that thermal aging of surveillance specimen sets proceeds at the same temperature as that of RPVs. Therefore, surveillance specimen test results are relevant only to the current condition of RPV materials (for the moment of taking out surveillance specimens). Further material aging process can be predicted only through extrapolation.

Long-term prediction of thermal aging of materials is usually based on the test results of specimens subjected to accelerated aging at temperatures higher than the RPV operation temperatures. Such an approach results from the assumption that the material aging is controlled only by diffusion processes, and the equilibrium concentration of a diffusing element on some sinks (e.g., on grain boundaries) is temperature-independent. For this case, long-term prediction of thermal aging is usually based on the Arrhenius equation [1–3]. In particular, the Hollomon parameter which determines the degree of material aging depending on exposure time and temperature is one of the most commonly used [4, 5].

The phosphorus content for unirradiated RPV component materials is up to 0.020% as per relevant technical specifications. High P contents are known to result in thermal embrittlement of metal due to P segregation at grain boundaries (GBs). The equilibrium grain boundary P concentration is a temperature-dependent parameter, decreasing with increase of temperature [2, 3, 6]. Therefore, the prediction of P aging for the WWER-type RPV materials on the basis of the results of accelerated aging at higher temperatures and the Hollomon parameter application can be inadequate and nonconservative.

The above gave impetus to the development of a new method predicting “phosphorus” embrittlement of RPV steels. This new method was reported in the paper [7]. Its main idea consists in accelerating P segregation processes by neutron irradiation at a temperature corresponding to that of RPV operation (*T*_{oper}). Unlike the acceleration of P segregation processes only due to increasing a temperature, neutron irradiation hardly affects equilibrium P segregation [8, 9]. At the same time, irradiation accelerates the kinetics of P segregation through radiation-enhanced diffusion [8–22]. This acceleration results from the fact that the P diffusion coefficient increases considerably through the generation of point defects under irradiation [8, 9, 11–14]. As can be seen, the mechanism of forming P segregations is the general mechanism of metal embrittlement under thermal aging and neutron irradiation. The P diffuses towards different intragranular interphase boundaries (e.g., interphase carbide-matrix boundaries) as well as towards GBs and forms local segregations [3, 10, 19, 23–25]. As should be noted that P segregation does not lead to material hardening as P segregates mainly on GBs and on various intragranular barriers for dislocations that exist before irradiation (e.g., carbides). It means that P does not form new additional barriers for moving dislocations. At the same time, P segregations decrease the strength of interphase boundaries (e.g., carbide-matrix boundaries) or grain boundaries that makes the initiation of cleavage microcracks or intergranular brittle microcracks easier and, as a consequence, leads to material embrittlement [3, 19, 26–29]. Since the above mechanism of material embrittlement does not result in its hardening, such an embrittlement mechanism is referred to as a nonhardening mechanism [26, 27, 30].

It is necessary to note also that P also segregates on dislocation loops and precipitations [19, 31, 32]. Such segregations hardly affect material hardening [10].

The proposed method [7] consists in determining material embrittlement after the following two-stage treatment. At the first stage, accelerated neutron irradiation for short time with high neutron flux is conducted at *T* = *T*_{oper}, which hardly changes the value of equilibrium P segregation and, at the same time, accelerates the formation of P segregations due to radiation-enhanced diffusion. At the second stage, the irradiated material is annealed at a temperature which deletes material hardening caused by neutron irradiation and leads to P dissociation from the intragranular interphase boundaries, but, at the same time, does not lead to P dissociation from GBs. For the WWER-1000 RPV materials, this annealing temperature *T*_{anneal} = 450°С [7]. In addition, for the effective P diffusion coefficient to be determined, thermal aging should be carried out at the temper brittleness temperature [7].

According to the [7] time dependence of transition temperature shift due to P thermal aging, Δ*T*_{k} (*t*) is determined on the basis of the following considerations. The dependence Δ*T*_{k} (*t*) has been deducted when using the McLean equation [6], the theory of radiation-induced diffusion [11–22], and the introduced relation between the transition temperature *T*_{k} and P concentration on the interphase boundaries and/or GBs at the current moment of time () [7]. The transition temperature is taken as the temperature at which the Charpy impact strength equals 47 J or fracture toughness for specimens with thickness of 25 mm equals 100 MPam^{1/2} for the fracture probability of 50%.

The McLean equation is presented in the formwhere , , and are the P concentrations at the interfaces and/or GBs at the given temperature at the initial moment of time (*t* = 0), at the time *t*, and at *t* = ∞, respectively; *D*_{P} is the P diffusion coefficient in general depending on temperature and neutron flux (neutron dose rate) [14]; *d* is the GB thickness; *γ* = / where is the bulk P concentration in atomic percentage.

The relation between and takes into account possible P segregations in the material in the initial condition and after thermal aging during time *t*. It is taken in the form [7].where *α* and *β* are some material constants.

Based on (1) and (2), the dependence Δ*T*_{k} (*t*) is presented in the form [7]:where is the value of at *t *=* *∞; is the value of in the initial condition; and is the effective diffusion coefficient, .

Under irradiation, the P diffusion coefficient of an element (e.g., phosphorus) is calculated taking into account the production and recombination of vacancies and interstitial atoms, annihilation of point defects on the various sinks, mainly dislocations (for more details, see Section 3). In case of no irradiation, the temperature dependence of P diffusion coefficient is calculated by the well-known equation in [3] similar to the Arrhenius equation.

After the material two-phase treatment (irradiation + annealing), the value of transition temperature *T*_{k} is determined for this material. Knowing *T*_{k0}, the value of *T*_{k} for material condition after postirradiation annealing and value of D_{eff} under irradiation, the value of corresponding to the RPV operation temperature is determined from (3) where Δ*T*_{k}* *=* T*_{k}−*T*_{k0}. The dependence Δ*T*_{k} (*t*) for unirradiated material is calculated by (3) on the basis of determined value of and calculated value of D_{eff} for *T*=* T*_{oper} when there is no irradiation [7].

So, the main idea of the method proposed in [7] is the formation of the grain boundaries P segregation during short-term irradiation due to strong acceleration of P diffusion under neutron irradiation at operation temperature of RPV. Strong acceleration of P diffusion under neutron irradiation up to now has not been proved directly. At the same time, there are some indirect proofs. In particular, it is well known that neutron irradiation leads to significant increase in the vacancies and interstitials concentrations and, as a result, to significant increase in the self-diffusion coefficient [11–22]. Experimental studies [10, 28] have also revealed that P segregations can be formed under neutron irradiation at sufficiently low temperature (*T* = 50°C) when thermodiffusion of phosphorus is very small.

Phosphorus is subsized element (atomic radius of P is less than Fe radius); therefore, P diffusion may occur by both vacancy and interstitial mechanisms. Hence, it may be expected that an increase in the vacancies and interstitials concentrations under irradiation may increase equally both the self-diffusion coefficient and P diffusion coefficient. At present, there are only theoretical justifications for this consideration [8, 9, 11–14]; however, experimental data proving it are absent.

The aim of the present work is to obtain experimental data showing strong influence of neutron irradiation on P diffusion, that is, to prove that neutron irradiation increases equally both the self-diffusion coefficient and P diffusion coefficient.

#### 2. Statement of the Problem

The effect of temperature on P diffusion and equilibrium P segregation at GBs has been studied well enough by now [3, 6, 29]. The formation of P segregations at GBs leads to intergranular brittle fracture (IBF) [2, 3, 19, 29]. With a higher P concentration at GBs, the portion of IBF increases. According to (1), the P concentration at GBs is determined by the product . Hence, the portion of IBF is controlled by the product . Then, if the basic consideration of the new method is true and the condition is met, the portion of IBF (when the nonhardening brittle fracture mechanism occurs) should be approximately the same both for thermally aged material and material after neutron irradiation and annealing. In the above condition, is the effective thermal diffusion coefficient of phosphorus, is the exposure time at a higher temperature, is the effective diffusion coefficient of phosphorus under neutron irradiation, and is the time of neutron irradiation.

Thus, the following experimental procedure may be proposed for justification of the proposed method in [7]. Two different treatments should be carried out for the investigated material. One treatment is thermal aging and the another is two-phase treatment (irradiation + annealing). The regimes for these treatments should be those for which the condition is met. Here, the parameter should be calculated with the assumption that neutron irradiation increases practically equally both the self-diffusion coefficient and P diffusion coefficient (i.e presented hereafter in Section 3). Postirradiation annealing allows one to exclude any influence of irradiation-induced defects on material embrittlement except for the influence of grain boundaries P segregations that is typical for thermal aging.

Specimens machined from thermally aged material and material after postirradiation annealing should be tested over brittle fracture temperature range, and SEM examination of fracture surfaces should be performed to compare the portions of IBF for these materials.

If the portions of IBF for these material conditions coincide, then it may be concluded that the aim of the present paper is reached and the method proposed in [7] for prediction of thermal embrittlement is verified.

#### 3. Calculative Estimation of the P Diffusion Coefficient under Neutron Irradiation

Radiation-enhanced diffusion coefficients of self-diffusion (hereinafter Fe atoms) *D*_{Fe} and impurity atoms (hereinafter P atoms) *D*_{p} can be written neglecting the correlation factors as follows [8, 9, 33]:where *C*_{v} and *C*_{i} are the average vacancy and interstitial concentrations in the bulk depending on the point defect (PD) generation rate and sink density, *d*_{n} and *d*_{pn} (*n *=* *v, i) are the Fe and P diffusivities via vacancy and interstitial mechanisms, *ξ*_{pn} accounts for the binding energies of P atoms with PD as , accounts additionally for the difference in migration energies of Fe and P atoms: , and , where is some effective binding energy. The equality *d*_{v}*C*_{v} ≈ *d*_{i}*C*_{i} corresponding to steady irradiation [33] was used in (4) and (5).

Neglecting the thermal equilibrium concentration at the irradiation temperature, one can write for the average vacancy concentration [8, 9, 33]:where is the PD production rate, is the PD sink strength, is the recombination coefficient accounting for PD recombination at the rate , and *ε* is the cascade efficiency in producing freely migrating PD (usually in the range 0.1 ÷ 1).

Equation (6) can be rewritten as follows:where the parameter .

We can consider two limiting cases:(1)PD sinks are dominated or *d*_{v} is high, . Then(2)PD recombination is dominated or *d*_{v} is low, . Then

Substituting these concentrations in (4) and (5) one can obtain the following estimates of the above two cases: for and for where *d*_{v0} is the preexponential factor of vacancy diffusivity *d*_{v}.

It is seen from (10) and (11) that *D*_{Fe1} and *D*_{P1} do not depend on *d*_{v} and *D*_{P1} decreases with increasing temperature whereas *D*_{P2} can increase if .

Here, we adopt the following parameters: *K* = 6 × 10^{−8} dPa/sec for a neutron flux of 6.07 × 10^{17} n/m^{2}·s from the relation 1 dPa per 10^{25} n/m^{2} (*E* > 0.5 MeV), *ε* = 0.1 for neutron irradiation [33], *d*_{v} = 2 × 10^{−4} exp (−1.3 eV/*kT*) m^{2}/s from [11], *μ*_{R} = 8·10^{20} m^{−2} (assuming recombination volume on the order of 100 lattice parameter), and = 0.3 eV as an effective binding energy of mixed Fe–P dumbbells [33]. The *ρ*_{s} is taken to be equal to the dislocation density for RPV steel in initial condition. The *ρ*_{s} may be assumed to be equal to 10^{14} m^{−2} [7].

Then taking into account (5) and (6) for irradiation at *T* ≈ 300°C, we obtain *D*_{p} = 1.95 × 10^{−20} m^{2}/sec. This value was used above for calculation of in Table 3 accounting for *d*^{2}*γ*^{2} **=** 4.54 × 10^{−13} m^{2} [7].

Taking into account that not much is known on the diffusion parameters of self-diffusion and P diffusion in RPV steels, justification of the above parameters is based on the following analysis.

The values taken for our estimations are following values: =1.24 eV and = 0.17 eV (binding energy of mixed Fe–P dumbbells) and *≈* 0.3 eV that were used in [34, 35] for modelling of P accumulation at GBs in dilute Fe–P alloys. The models were applied successfully to fit experimental data on P accumulation at GBs in RPVs at a dose of 0.01 dPa. Modelling of P accumulation at GBs in Fe–Ni–P alloys was performed [8, 9] taking into account radiation-enhanced P diffusion via both vacancy and interstitial mechanisms, radiation-induced segregation in the matrix near GBs and the Gibbsian adsorption at GBs. Vacancy migration energies in the range from 0.6 eV to 1.2 eV, interstitial migration energies from 0.1 eV to 0.30 eV, and binding energies between a P atom and an interstitial from 0.3 eV to 0.15 eV were considered. Later on, this model was applied successfully to fit experimental surveillance data for several units of WWER-440 [36] where radiation embrittlement enhancement has been observed at neutron fluences above (2-3) × 10^{24} n/m^{2}.

In recent years, much attention has been paid to modelling of self-diffusion and P diffusion in Fe and dilute Fe–P alloys. Molecular dynamics, ab initio, and kinetic Monte Carlo calculations are applied to elucidate the mechanisms and diffusion parameters [37–41]. Ab initio calculations reveal relatively high binding energies between P atoms and vacancies (vacancy drag effect) and very high binding energies of mixed Fe–P dumbbells on the order of 1 eV and their high mobility. In addition, a new mechanism of P atoms mobility via octahedral positions in the lattice was found as a result of interaction of a self-interstitial atom with a substitutional P atom. Formation energies and diffusivities of both mobile states are similar. However, attempts to use these diffusion parameters to fit experimental data at GB phosphorus accumulation in RPVs fail to succeed. Atomic transport via interstitials in dilute Fe–P alloys was used for modelling of GB phosphorus accumulation in RPVs [38] as applied to experimental data considered before [34, 35]. The predictions highly overestimate the data. The authors suppose that a significant portion of P atoms is trapped in stable two-P complexes or segregated on point defect clusters. Both vacancy and interstitial (via mixed Fe–P dumbbells and via octahedral positions) diffusion of P atoms were used [39, 41] to fit some experimental data on GB phosphorus accumulation in RPVs at neutron fluences up to 10^{24} n/m^{2}. For fitting the data, an unreally high PD sink strength of 2 × 10^{18} m^{−2} was adopted in calculations. Possibly, reliable data on self-diffusion and P diffusion in RPVs could be obtained in molecular dynamics modelling accounting for all most important alloying and impurity elements.

#### 4. Material, Conditions, and Results of Experiment

The material selected for investigations (2Cr–Ni–Mo–V steel) used for WWER-1000 RPVs was similar to those used previously in [7]. The chemical composition of this steel is given in Table 1. The transition temperature in the initial condition *T*_{k0} is equal to −5°C, yield strength (*σ*_{Y}) at *T *=* *20°C is equal to 585* *MPa. Several sets of Charpy specimens from the above steel were machined.