Cladding Failure Modelling for Lead-Based Fast Reactors: A Review and Prospects

: Lead-cooled fast reactors (LFRs) are considered one of the most promising technologies to meet the requirements introduced for advanced nuclear systems. LFRs have higher neutron doses, higher temperatures, higher burnup and an extremely corrosive environment. The failure studies of claddings play a vital role in improving the safety criteria of nuclear reactors and promoting research on advanced nuclear materials. This paper presented a comprehensive review of the extreme environment in LFRs based on the fuel performance analyses and transient analyses of reference LFRs. It provided a clear image of cladding failure, focusing on the underlying mechanisms, such as creep, rupture, fatigue, swelling, corrosion, etc., which are resulted from the motions of defects, the development of microcracks and accumulation of ﬁssion products to some extent. Some fundamental parameters and behavior models of Ferritic/Martensitic (F/M) steels and Austenitic stainless (AuS) steels were summarized in this paper. A guideline for cladding failure modelling was also provided to bridge the gap between fundamental material research and realistic demands for the application of LFRs.


Introduction
Today's nuclear energy system is the result of a fifty-year development during which this technology has reached industrial maturity and become a reliable resource for our electricity needs. Nuclear energy plays a more and more important role in decarbonization strategy and the energy crisis worldwide. Nevertheless, the further development of nuclear energy relies on the solution of two key issues: the high use of nuclear fuels and the safe disposal of nuclear waste [1,2].
The International Generation IV Initiative (GEN-IV) was established in 2000 to foster the research and development necessary to underpin the development of a new generation of nuclear energy systems. The GEN-IV nuclear systems, which comprise both the reactors and their associated fuel-cycle facilities, are intended to deliver significant advances compared with current light water reactors (LWRs) in respect of economics, safety, environmental performance, and proliferation resistance [3][4][5][6][7].
Lead-cooled fast reactors (LFRs) are considered one of the most promising technologies to meet the requirements introduced for GEN-IV nuclear systems [8][9][10][11]. LFRs feature a fast neutron spectrum, high-temperature operation and cooling by relatively inert molten lead or lead-bismuth eutectic (LBE). Based on a closed fuel cycle for efficient conversion of fertile uranium and characteristics of a fast spectrum and compact facility, LFRs are envisioned for missions in extensive and multi-purpose power supply with efficient and the safe utilization of nuclear fuels [12]. Furthermore, Accelerator Driven Systems (ADSs) have been proposed to transmute minor actinides (MAs) and long-lived fission products

Overview of LFRs and ADSs
From the early 1960s to 1995, LBE-cooled fast reactors were designed and built in the Soviet Union for submarine propulsion, providing an estimated 80 reactor years of operating experience. While significant differences exist between these reactors and currently considered GEN-IV LFRs, the operational experience built a strong base for understanding the technology and identifying solutions to the technical challenges [34]. Research and design activities related to LFRs are ongoing in Europe, the U.S., Russia, China and other countries after GEN-IV [35,36]. Russia has pursued two initiatives, SVBR-100 and BREST-300 [37,38]. The SVBR-100 is generally considered a follow-on technology to the prior submarine propulsion technology. It is a small reactor cooled by LBE, and BREST-300 is a medium-sized reactor cooled by pure lead. In Europe, the ELSY project was initiated in 2006 to define the main options of LFRs of industrial size with a power of 1500 MWth and 600 MWe [39]. The following LEADER project is continuing the study of an industrial-sized reactor under the name ELFR and also is examining a demonstrator LFR of power 100 MWe called ALFRED [40][41][42]. Additionally, the conceptual design of Swedish SEALER has been conducted by Kungliga Tekniska Högskolan (KTH) and LeadCold Reactors to meet the demands for commercial power production in Arctic regions [43]. The U.S. LFR program is focused on developing a small transportable reactor system known as the Small Secure Transportable Autonomous Reactor (SSTAR) with a power of 45 MWth and 20 MWe [44].
Compared with LFRs, ADSs intend to achieve a high transmutation efficiency of MAs and LLFPs, where a subcritical mostly LBE-cooled fast reactor is driven by a proton accelerator. LBE is not only the coolant, but also the neutron source of spallation activated by a proton beam [45,46]. The Integrated Project (IP) EUROTRANS proposed two ADS design routes, the XT-ADS and the EFIT. The XT-ADS is designed to demonstrate the feasibility of the ADS concept, while the long-term EFIT development aims at a generic conceptual design of an industrial-scale transmuter [17,47,48]. In Belgium, SCK CEN intends to develop MYRRHA, a multi-purpose hybrid research reactor for high-tech applications, which can operate in both critical and subcritical dual-modes [49]. Furthermore, the Chinese Academy of Sciences (CAS) has proposed a step-wise roadmap. China initiative Accelerator Driven System (CiADS) is the proof-of-principle facility in the first phase [50]. Tentative specifications and main parameters of LFRs and ADSs are presented in Table 1. The schematics of a fuel pin, an ADS and an LFR are shown in Figure 1. Inside the reactor core, the fuel pin suffers from the most extreme environment for a long time. In general, fuel pins will service for several equivalent full power years and experience three cycles in the core. The design burnup of LFR fuels could be more than 8 a.t.% before refueling, while some small modular LFRs intended to use for remote areas or special purposes have higher burnup. Moreover, a series of transient scenarios could cause severe damage to some extent. Reactor dynamics and accident sequences depend on the specific design and safety potential of different LFRs, which bring more complicated issues to materials because of a fast-changing environment. Hence, transient analyses and in-pile experiments are necessary to provide realistic conditions for research on nuclear materials. design and safety potential of different LFRs, which bring more complicated issues to materials because of a fast-changing environment. Hence, transient analyses and in-pile experiments are necessary to provide realistic conditions for research on nuclear materials.

Long-Term Steady Operation
Given the inaccessible experiment data of LFRs, the fuel performance modelling and transient analyses of LFRs are helpful for understanding the relatively realistic environment inside the reactor core and provide a clear image for material applications. Here, we took ALFRED and ELSY as reference to illustrate the long-term operating environment for fuel pins.
Fuel performance codes (FPCs) can be utilized to provide essential guidance on the behaviors of fuel and cladding materials. The fuel performance analysis of ALFRED was carried out using the extended TRANSURANUS code, and a modified version of the fuel performance code FEMAXI-SCK-1 was adapted for ELSY [51,52]. Figure 2 illustrates the long-term conditions for fuel pins of ALFRED and ELSY. ALFRED is a small-size (300 MWth) pool-type LFR, but it has a relatively higher linear power of the hottest fuel pin than ELSY. A five-batch cycle without reshuffling with a 5-year fuel residence time was expected, i.e., 365 equivalent full power days (EFPD) per cycle leading to a total 1825 EFPD and a burnup of 9.4 a.t.%, as shown in Figure 2a. The linear power decreased from 36.7 kW/m to 26.4 kW/m from the beginning of life (BoL) to the end of life (EoL), considering the variations of fission nuclides and reactivity swings. Refueling between two cycles was foreseen to last about 15 days [53]. ELSY is an industrial LFR with a thermal power of 1500 MW. As can be seen in Figure 2b, the long-term behaviors of the hottest ELSY fuel pin under the nominal conditions were simulated for a period of 2190 EFPDs, and the total operation period was subdivided into six one-year cycles with one-month shutdown pe-

Long-Term Steady Operation
Given the inaccessible experiment data of LFRs, the fuel performance modelling and transient analyses of LFRs are helpful for understanding the relatively realistic environment inside the reactor core and provide a clear image for material applications. Here, we took ALFRED and ELSY as reference to illustrate the long-term operating environment for fuel pins.
Fuel performance codes (FPCs) can be utilized to provide essential guidance on the behaviors of fuel and cladding materials. The fuel performance analysis of ALFRED was carried out using the extended TRANSURANUS code, and a modified version of the fuel performance code FEMAXI-SCK-1 was adapted for ELSY [51,52]. Figure 2 illustrates the long-term conditions for fuel pins of ALFRED and ELSY. ALFRED is a small-size (300 MWth) pool-type LFR, but it has a relatively higher linear power of the hottest fuel pin than ELSY. A five-batch cycle without reshuffling with a 5-year fuel residence time was expected, i.e., 365 equivalent full power days (EFPD) per cycle leading to a total 1825 EFPD and a burnup of 9.4 a.t.%, as shown in Figure 2a. The linear power decreased from 36.7 kW/m to 26.4 kW/m from the beginning of life (BoL) to the end of life (EoL), considering the variations of fission nuclides and reactivity swings. Refueling between two cycles was foreseen to last about 15 days [53]. ELSY is an industrial LFR with a thermal power of 1500 MW. As can be seen in Figure 2b, the long-term behaviors of the hottest ELSY fuel pin under the nominal conditions were simulated for a period of 2190 EFPDs, and the total operation period was subdivided into six one-year cycles with one-month shutdown periods in between for maintenance. The linear power of the ELSY fuel pin was 23 kW/m, and the peak burnup of about 8.5 a.t.% (and the peak cladding damage of 82 dpa) was achieved at the end of the operation.  Figure 2c shows the temperatures of the fuel, the cladding and the coolant of AL-FRED. The maximum temperature of the fuel was close to 2200 °C and occurred nearly at half of the first cycle, and then kept dropping before steady state. This peculiarity resulted from the trade-off between the fission gas release rate and the gap size reduction. At the beginning of the nominal operation, the decrease in the fuel temperature resulted from the initial outward deformation caused by activated creep, relocation and accumulated swelling. After that, the fission gas released into the plenum decreased the gap conductance and, hence, the fuel temperature increased. When the fuel temperature reached the maximum, the heat transfer was enhanced due to the gradually decreasing gap width until contact, and at that time, the fuel temperature was a constant almost. By contrast, the evolutions of the fuel and cladding temperatures for ELSY are illustrated in Figure 2d. As we can see from Figure 2c,d, the temperature evolution of the ELSY fuel during the previous five cycles was similar to that of the ALFRED fuel during the first two cycles, but the evolution of ELSY was much slower and stretched because of lower linear power and  [51,52]. Figure 2c shows the temperatures of the fuel, the cladding and the coolant of ALFRED. The maximum temperature of the fuel was close to 2200 • C and occurred nearly at half of the first cycle, and then kept dropping before steady state. This peculiarity resulted from the trade-off between the fission gas release rate and the gap size reduction. At the beginning of the nominal operation, the decrease in the fuel temperature resulted from the initial outward deformation caused by activated creep, relocation and accumulated swelling. After that, the fission gas released into the plenum decreased the gap conductance and, hence, the fuel temperature increased. When the fuel temperature reached the maximum, the heat transfer was enhanced due to the gradually decreasing gap width until contact, and at that time, the fuel temperature was a constant almost. By contrast, the evolutions of the fuel and cladding temperatures for ELSY are illustrated in Figure 2d. As we can see from Figure 2c,d, the temperature evolution of the ELSY fuel during the previous five cycles was similar to that of the ALFRED fuel during the first two cycles, but the evolution of ELSY was much slower and stretched because of lower linear power and temperature. The maximum fuel temperature of ELSY was 1618 • C. It is notable from Figure 2c,d that both the cladding temperatures of ALFRED and ELSY were more than 500 • C, and temperature variations were less than 100 • C, where large stresses will not occur in the cladding. Therefore, we can conclude that the cladding corrosion over 500 • C is the dominant failure mechanism before fuel-cladding contact under long-term operation for LFRs. Figure 2e displays the pressure evolutions of the ALFRED fuel pin. The gap size is driven by deformation caused by thermal expansion, densification, swelling, creep, dislocation, etc. At the end of the second cycle (4 a.t.%), the gap closure and fuel-cladding mechanical interaction (FCMI) occurred, with the contact pressure starting to increase. The maximum contact pressure was 55.6 MPa at last, and meanwhile, the final plenum pressure of 2.16 MPa mainly resulted from the fission gas release. The FCMI occurred at 6.4 a.t.% in ELSY, and the maximum contact pressure was 44.2 MPa in Figure 2f. It is possible that once the contact occurs, everything will become complicated. This is because large stresses induced by ongoing contact will accelerate creep and make microcracks grow fast until failure, especially with degradation of cladding mechanical performance due to irradiation and corrosion.

Transients and Reactor Dynamics
During the long-term steady operation, LFRs could experience a series of transient accidents, in which the reactor parameters change intensely in a short time and may exceed safety limits. Therefore, the safety principles and guidelines have to be elaborated for LFRs. The LFR designs with the safety objectives are structured along three basic conditions: (1) the design basis conditions (DBC-structured into four categories); (2) design extension conditions (DEC-limiting events, complex sequences and severe accidents); (3) residual risk situations [54]. For innovative reactor systems such as GEN-IV LFRs, transient analyses play an important role and provide references of the relatively realistic in-pile environments for research and experiments on nuclear materials. In this paper, transient analyses of DBCs for EFIT and CiADS were summarized and compared [55][56][57], including beam-trip transients, unprotected beam overpower (UBOP), unprotected loss of flow (ULOF), unprotected and protected loss of heat sink (ULOHS and PLOHS). The "protected" for ADSs without control rods means a beam interruption is triggered at the beginning of accident sequences.
Transient analyses for EFIT have been carried out with SIMMER-III which is a twodimensional, multi-phase, multi-component, fluid-dynamics system code coupled with structural models and a neutron dynamics model [58,59]. Figure 3 depicts temperature variations under different transients in EFIT. Frequent beam trips could occur due to the instability of the proton accelerator. As shown in Figure 3a, 10 s beam-trip started 2 s later than the initial steady state, and then the temperatures decreased immediately. When the beam was on again after the 10 s interval, the temperatures returned to their initial values within about 30 s. During this 10 s beam-trip process, the maximal fuel, cladding and coolant temperatures dropped by 743 • C, 88 • C and 65 • C, respectively. In addition, there is a possibility that the beam current may increase instantly from its nominal value to a certain high level. For the EFIT core, a beam overpower to 120% at hot full power conditions was defined as a transient case for investigating its safety features. Figure 3b shows that the temperatures increased immediately and then kept steady. In this case, the maximum temperatures of the fuel, the cladding and the coolant were 1597 • C, 545 • C and 507 • C, respectively. Therefore, fatigue due to alternating stresses should be the most important issue under frequent beam transients in ADSs.
actor vessel auxiliary cooling system (RVACS). However, all these operations and protections are insufficient to remove the core decay heat. After 50,000 s of PLOHS, the temperatures still increased continuously, and even the coolant temperature reached 970 °C, which is unacceptable for the safety of LFRs. Under this circumstance, the cladding temperature increased to a very high value, where all the failure-related behaviors will be accelerated, like corrosion, creep and rupture. Transient analyses for CiADS using the extended BELLA code are shown in Figure 4 [56,60]. Compared with the industrial EFIT design, CiADS is a 10 MW LBE-cooled subcritical reactor designed to demonstrate the engineering feasibility of the ADS concept. It is notable from Figure 3 to Figure 4 that the reactor dynamics are similar between EFIT and CiADS under these transient scenarios. As shown in Figure 4, the maximum temperatures of the fuel and the cladding dropped by 52 °C and 38 °C under 10 s beam-trip. As for the UBOP case, the beam current was assumed to increase instantly from the nominal value to a double higher value at 10 s and then hold for 50 s. The peak temperatures of the fuel and the cladding were 549 °C and 466 °C due to a low reactor power. However, some risks tended to occur under ULOF and ULOHS for the reason that both the coolant temperatures exceeded the design limit of 550 °C, where the accelerated LBE corrosion combined with accumulated creep could be severe. In the ULOF case, the primary pump was designed to stop within 1 s, leading to the overshooting of temperatures, as shown in Figure 3c. Although the pump head became zero, the coolant mass flow rate in the core was finally stabilized at 30% due to the natural convection in the system. With the remaining coolant removing capacity, the fuel, cladding and coolant peak temperatures finally kept steady at 1552 • C, 730 • C and 685 • C. As for the PLOHS in Figure 3d, the loss of heat sink was expressed as a stopped heat exchange through the heat exchangers accompanied by the beam interruption and the activated reactor vessel auxiliary cooling system (RVACS). However, all these operations and protections are insufficient to remove the core decay heat. After 50,000 s of PLOHS, the temperatures still increased continuously, and even the coolant temperature reached 970 • C, which is unacceptable for the safety of LFRs. Under this circumstance, the cladding temperature increased to a very high value, where all the failure-related behaviors will be accelerated, like corrosion, creep and rupture.
Transient analyses for CiADS using the extended BELLA code are shown in Figure 4 [56,60]. Compared with the industrial EFIT design, CiADS is a 10 MW LBE-cooled subcritical reactor designed to demonstrate the engineering feasibility of the ADS concept. It is notable from Figure 3 to Figure 4 that the reactor dynamics are similar between EFIT and CiADS under these transient scenarios. As shown in Figure 4, the maximum temperatures of the fuel and the cladding dropped by 52 • C and 38 • C under 10 s beam-trip. As for the UBOP case, the beam current was assumed to increase instantly from the nominal value to a double higher value at 10 s and then hold for 50 s. The peak temperatures of the fuel and the cladding were 549 • C and 466 • C due to a low reactor power. However, some risks tended to occur under ULOF and ULOHS for the reason that both the coolant

Limits of Fuel Design for LFRs
Note that the temperature variations of different reference LFRs above were all pronounced, which brings significant challenges to nuclear materials. On the one hand, the fuel temperature will rise or drop from the coolant operating temperature of about 400 °C to the peak fuel temperature of more than 2000 °C during reactor start-up or shut-down. On the other hand, the frequent fast-changing conditions and temperatures above the safety limits under transients will cause cladding failures, such as fatigue, creep rupture, ratcheting and serious FCMI. Additionally, the corrosion and swelling of LFR fuel pins under long-term operation should be of great concern. Figure 5 depicts the oxide thicknesses of ELSY and CiADS [52,61]. The protective oxide layers seem too thick at the end of life, which may influence heat conduction and structural stability of claddings.

Limits of Fuel Design for LFRs
Note that the temperature variations of different reference LFRs above were all pronounced, which brings significant challenges to nuclear materials. On the one hand, the fuel temperature will rise or drop from the coolant operating temperature of about 400 • C to the peak fuel temperature of more than 2000 • C during reactor start-up or shut-down. On the other hand, the frequent fast-changing conditions and temperatures above the safety limits under transients will cause cladding failures, such as fatigue, creep rupture, ratcheting and serious FCMI. Additionally, the corrosion and swelling of LFR fuel pins under long-term operation should be of great concern. Figure 5 depicts the oxide thicknesses of ELSY and CiADS [52,61]. The protective oxide layers seem too thick at the end of life, which may influence heat conduction and structural stability of claddings. Although there are no widely acknowledged and fixed design limits for LFRs, some indicative limits from open studies and reports may be constructive. Under ALFRED conditions, some limits have been summarized for fatigue analyses and could provide some references for LFRs in general [51,53,62,63]. The design limits, presented in Table 2 for reference, mainly focus on the maximum temperatures and unrecoverable deformation of claddings, which are worthy of concern.

Cladding Materials and Failure
The extreme environment brings great challenges to materials for GEN-IV LFRs, especially the cladding and structural materials. Two kinds of candidate materials for claddings have been studied for near-term deployment, namely Ferritic/Martensitic (F/M) steels and Austenitic stainless (AuS) steels [64]. One of the most intensively investigated F/M steels is the 9Cr-1Mo grade (e.g., T91 and HT-9), while the 316ss and 15-15Ti (e.g., DIN 1.4970) grades are among the most thoroughly investigated AuS steels [65][66][67]. However, such a unique and balanced nuclear material capable of resisting so many kinds of extreme environments in LFRs does not exist. Other materials, such as oxide-dispersionstrengthened (ODS) steels, the MAX (Mn+1AXn) phase, SiCf/SiC (i.e., SiC fibre-reinforced Although there are no widely acknowledged and fixed design limits for LFRs, some indicative limits from open studies and reports may be constructive. Under ALFRED conditions, some limits have been summarized for fatigue analyses and could provide some references for LFRs in general [51,53,62,63]. The design limits, presented in Table 2 for reference, mainly focus on the maximum temperatures and unrecoverable deformation of claddings, which are worthy of concern.

Cladding Materials and Failure
The extreme environment brings great challenges to materials for GEN-IV LFRs, especially the cladding and structural materials. Two kinds of candidate materials for claddings have been studied for near-term deployment, namely Ferritic/Martensitic (F/M) steels and Austenitic stainless (AuS) steels [64]. One of the most intensively investigated F/M steels is the 9Cr-1Mo grade (e.g., T91 and HT-9), while the 316ss and 15-15Ti (e.g., DIN 1.4970) grades are among the most thoroughly investigated AuS steels [65][66][67]. However, such a unique and balanced nuclear material capable of resisting so many kinds of extreme environments in LFRs does not exist. Other materials, such as oxide-dispersion-strengthened (ODS) steels, the MAX (M n+1 AX n ) phase, SiC f /SiC (i.e., SiC fibre-reinforced SiC) composites and refractory metals have some appealing properties and, thus, have been studied [68][69][70]. Some compositions of F/M steels and AuS steels are listed in Table 3.
In particular, recent progress in ODS steels produced by mechanical alloying techniques allows them to be used as fuel cladding in SFRs. The thermally stable oxide particles dispersed in the ferritic matrix improve the radiation resistance and creep resistance at high temperature [68,71,72]. Refractory metals and alloys offer attractive and promising hightemperature strength, good thermal conductivity, and compatibility with most liquid metal coolants, many of which are suitable for applications in nuclear environments. However, significant issues related to low-temperature irradiated mechanical property degradation at even low neutron fluences restrict the use of refractory metals [73]. Advanced ceramic composites, such SiC and Si3N4, have outstanding characteristics of high thermal conductivity, low thermal expansion and exceptional resistance to thermal shock and to corrosion in aggressive environments at high temperatures. However, this implies a few inadequate characteristics for structural applications, such as low fracture toughness, high sensitivity to the presence of microstructural flaws, brittle behavior and lack of reliability. Reinforcing with continuous SiC-based fibers allows these weaknesses to be overcome [69,74,75].
3.1. Candidate Cladding Materials 3.1.1. F/M Steels F/M steels with a body-centred cubic (bcc) crystal structure have abundant advantages: the mechanical properties of F/M steels are excellent, and it is easier to process and manufacture; furthermore, F/M steels are the ideal nuclear material candidate to achieve high fuel burnups contributed to their high thermal conductivity, low thermal expansion and superior resistance to void swelling [76,77]. The chemical compositions and microstructures of this type of steel are tailored to form austenite during normalizing and then martensite after quenching. Tempering these steels at about 760 • C can transform the martensite to ferrite and make them remain excellent ductility and fracture toughness at the same time. Their excellent void swelling resistance mainly results from numerous martensitic lath boundaries decorated with fine carbide and carbonitride particles, and a high density of dislocations, all of which serve as effective sinks for irradiation-induced defects [64]. However, these steels somewhat lack long-term creep resistance, limiting their service temperature below 600 • C. Irradiation embrittlement below 400-450 • C may also be a performance-limiting factor, leaving a relatively narrow temperature 'window' suitable for long-term service in a reactor [78,79]. Despite these concerns, T91 and other F/M steel grades were initially recommended for claddings in ELSY, EFIT, SSTAR and MYRRHA. The thermal and mechanical parameters of HT9 are listed in Table 4 for reference. Table 4. Thermal and mechanical parameters of HT9 [80,81].

AuS Steels
316L AuS steels with the face-centred cubic (fcc) crystal structure exhibit good performance under fast neutron irradiation at the relatively low temperatures (350-475 • C) of reactors such as EBR-II [64]. However, their service lifetime is limited by irradiationinduced void swelling at high irradiation doses. Consequently, in order to improve swelling resistance, AISI 316 steel grade has been updated to a wide variety. The main modification is adjusting their chemical compositions by slightly increasing the Ni to Cr ratio and adding small amounts of Si and Ti. These new versions of AuS steels are often called "Ti-modified" or "Ti-stabilized" stainless steels [82]. In the case of 15-15Ti steels, one may notice that the main alloying elements are Mo, Mn, Si and Ti. Mo improves the high-temperature mechanical properties, while Si binds vacancies and removes impurities. Ti is added to promote the formation of TiC precipitates. The interfaces between TiC precipitates and the austenite matrix act as sinks for irradiation-induced defects, thereby delaying void swelling. The interface sink efficiency (defect annihilation) is determined by the recombination of point defects at the interface, which is contributed to the high elastic energy stored at the interface and low migration energy barriers of the point defects [83,84]. Moreover, some steels of the 15-15Ti type are micro-alloyed with Nb, V, Zr and Ta, which impart additional phase stability. Thermal and mechanical parameters of 15-15Ti are listed in Table 5 for reference. Table 5. Thermal and mechanical parameters of 15-15Ti [51].

Parameter Correlation
Thermal

Cladding Failure Mechanisms
In addition to satisfying materials design criteria based on in-pile performance, cladding materials for current and proposed future nuclear energy systems must provide adequate resistance to three additional overarching environmental degradation phenomena: temperature dependence, radiation damage and chemical compatibility [85,86]. In Section 2, we discussed the extreme environments in LFRs. On the one hand, temperatures in the core will experience large increments or decrements during reactor start-up and shut-down, and swing under a long-term operation due to the reactivity changes. On the other hand, transient scenarios occurring suddenly cause instant temperature variations, which may exceed the safety limits with potentially serious consequences. All these steady-state and dynamic processes lead to high temperatures and large temperature gradients and hence induce considerable thermal stresses. Some macroscopical failure behaviors of claddings, such as thermal creep, cyclic fatigue, rupture and ratcheting between fuels and claddings, are temperature-dependent. Furthermore, the amount of radiation damage produced in materials from exposure to neutrons created by the nuclear reactions is quantified by the international standardized parameter of displacements per atom (dpa), which means each atom of the matrix has been displaced from its lattice site once [87,88]. According to the current evaluation, the maximum dpa of LFRs ranges from 100 dpa to 150 dpa. Radiation damage can produce pronounced irradiation creep, void swelling and hardening due to high densities of nanoscale defects and fission products. Some fission products will diffuse from the free surface and enter into the coolant, while others form clusters and reduce the yield strength of the cladding [89,90]. Other failure phenomena of LFR claddings can be attributed to chemical compatibility issues, such as lead or LBE corrosion and fuel-cladding chemical interaction (FCCI). These behaviors change the interface state of claddings and influence the cladding integrity and structural strength.

Creep
The time-dependent permanent deformation is termed as 'creep' due to outer load or stress. Creep is slow-motion plastic deformation, but would be expected at stresses and temperatures much lower than those required for plastic flow at high strain rates. In fact, there is no distinct temperature below which a solid does not exhibit process. Rather, creep is found to be an activated process. The creep phenomenon is more pronounced in nuclear materials subjected to high temperatures for long periods, and irradiation can accelerate the creep processes. It is because creep behaviors are related to microstructure and defects of materials. In view of the large variety of mobile defects in a solid, more than ten kinds of creep mechanisms have been proposed. Most materials have the capacity to deform by several alternative and independent mechanism, such as stress-induced vacancy migration (diffusional creep) and climb-controlled dislocation motion. Based on the idea of deformation-mechanism maps, which particular mechanism is dominant depends on the current stress and temperature [21,91]. Materials may fail by creep at stresses far below their yield strengths. Creep failure usually experiences three stages of deformation: (a) primary creep, (b) secondary creep and (c) tertiary creep leading to failure [92].
In order to simulate the creep of claddings and integrated into the thermo-mechanical coupling, based on the experiment data, the formula to evaluate the creep behaviors of the 15-15Ti type is presented by [93,94]: where . ε th is the equivalent Von Mises thermal creep rate in %h −1 , R is the gas constant (8.314 J·mol −1 ·K −1 ), T is the temperature in K, and σ eq is the equivalent stress in MPa.
The irradiation-induced creep of 15-15Ti is described by means of the following correlation [51]: where . ε ir is the equivalent Von Mises irradiation creep rate in %h −1 , E is the mean neutron energy in MeV and ϕ is the neutron flux in n·cm −2 ·s −1 .
In comparison, thermal and irradiation creep models for HT9 are given by [80]: . ε ir are equivalent Von Mises thermal and irradiation creep rate in %s −1 , respectively, R is the gas constant (1.987 cal·mol −1 ·K −1 ), T is the temperature in K, σ eq is the equivalent stress in MPa and ϕ is the neutron flux in 10 22 n·cm −2 ·s −1 .

Swelling
The void swelling tends to be more serious for cladding steels in fast reactors due to a higher irradiation [95]. This quantity, defined as the volume increase over the initial volume, is mainly influenced by the neutron fluence and the temperature. As for AuS steels, swelling is usually modelled considering an incubation period (at low dpa) where no swelling occurs [96]. Afterwards, the swelling starts increasing exponentially or linearly with the neutron fluence. It was observed and proved that the intricate interaction of swelling rate, creep and stress state exist indeed, but in view of their complex relations, no model or detailed description is suitable to explain the mechanism. Therefore, this effect is unconsidered in most experiments and modelling [51]. As contrast, F/M steels have excellent resistance to void swelling. Since there are no suitable swelling models for  in the open literature, a data-driven approach has been pursued in the study for ALFRED, consisting of the derivation of a correlation based on experimental data available for this kind of steel [51,97]. The swelling model for "generalized" 15-15Ti is given by: where ∆V V is the volumetric swelling rate in %, T is the temperature in°C, and Φ is the neutron fluence in 10 22 n·cm −2 .
The irradiation-induced volumetric swelling model for HT9 is based on the experiments in EBR-II and is presented by [98]: where ∆V V is the volumetric swelling rate in %, R is the steady-state swelling rate percentage in 10 −22 cm 2 , ϕ is the neutron flux in 10 22 n·cm −2 ·s −1 , t is the time in s, and T is the temperature in K.

Rupture
Creep rupture of materials refers to the failure that has been subjected to stresses and temperatures well below the yield stress for long periods. The deformation of the metal occurs by creep rather than the nearly instantaneous plastic deformation characteristic. Unlike brittle fracture, creep rupture does not occur suddenly upon applying stress but as a result of long-term stress. In order to evaluate the rupture time due to creep under in-pile ever-changing conditions, a cumulative damage function (CDF) approach based on the Larson-Miller parameter (LMP) is used widely in fuel performance codes (FPC), where CDF more considerable than one means that creep rupture has occurred [99]. Adopting AuS steels as cladding material ensures a better creep behavior concerning the use of F/M steels, but the thermal creep cladding failure can be of concern under FCMI conditions, resulting from the rising stress. The relative CDF can be denoted in terms of rupture time as: where ∆t is the lasting time under current conditions, and t r represents the time-to-rupture in hour.

Hardening
Neutron irradiation can produce pronounced hardening at low and intermediate temperatures due to the production of high densities of nanoscale defect clusters (dislocation loops, helium bubbles, etc.), which serve as obstacles to dislocation motion [100]. When hardening occurs, stress-dependent strains decrease and fracture toughness reduces. Radiation hardening, along with reductions in elongation and fracture toughness, typically become apparent at damage levels exceeding 0.1 dpa and are predominantly noticeable for homologous irradiation temperatures below 0.35T M , where T M represents the absolute melting temperature. Both materials display substantial irradiation-induced increasements in yield and ultimate tensile stress, significant reductions in elongation (particularly uniform elongation), and diminished strain hardening capacity. The decreases in elongation and strain hardening capacity are often ascribed to flow localization mechanisms, such as dislocation channeling, and strain hardening exhaustion. In addition to the reduced elongation, neutron irradiation at lower temperatures also generally leads to a decrease in fracture toughness [85]. The yield stress model and the ultimate tensile strength (UTS) model for 15-15Ti without considering irradiation are given by [51]: where σ y,0.2% is the initial yield stress in MPa, σ UTS is the initial yield stress in MPa and T is the temperature in°C. The yield stress model and the UTS model for HT9 are given by [81]:

Corrosion
Lead or LBE corrosion is a potentially severe structural materials degradation effect restricting the lifetime of claddings in LFRs. The principal corrosion mechanisms affecting the in-service performance of nuclear steels are oxidation, dissolution and erosion. Oxidation occurs when steel is brought into contact with an oxygen-containing liquid lead or LBE. Compared with other kinds of corrosion mechanisms, controlled oxidation is an effective way to prevent the further corrosion. Based on the oxygen controlling technology, the dense oxide layers covering the cladding surface will preventing the direct coolant attack and protect the steel bulk. But once the protective oxide layers are too thick, they will influence the thermal conductivity and structural strength of cladding as well. Dissolution corrosion takes place in the absence of oxide scales, where the matrix of steels dissolves into the coolant accompanied by the coolant penetration into the steel bulk. Erosion is always caused by the cross flow of the high-density and high-velocity coolant [64].
To prevent the severe lead or LBE corrosion, protected oxide layers technology is proposed and adopted in LFRs to prevent intense direct dissolution. The oxygen concentration and the flow velocity are the two most important factors that affect the oxide layer properties. The long-term behavior of the oxide layers model with an oxygen-controlled system has been developed to evaluate the status of claddings [101,102]. This model predicts the thickness of the double oxide layers (Fe 3 O 4 magnetite layer and spinel layer) considering growth and removal. Based on the mass balance, the kinetics of the magnetite layer is expressed by: where Fe 3 O 4 , St, Sp, LBE denote the magnetite layer, the steel, the spinel layer and LBE; δ is the thickness; ρ is the density; F is the mass fraction of Fe; k p is the oxidation constant of the steel; R m is the mass transfer rate.
As for the kinetics of the spinel layer growth, it depends on the real operating conditions: The spinel layer can be expressed by the parabolic law before the magnetite layer is completely removed: If the corrosion rate or the iron-removal rate by the flow is less than that of the iron diffusion rate through the spinel layer, the thickness of the spinel can be calculated by the linear growth law: With the thickness of the spinel layer increasing, the iron-diffusion rate through the spinel and the iron mass transfer rate by the liquid metal at the oxide/liquid interface are equal to each other, then Tedmon equation is applied: where t 0 is the time when outer magnetite layer has been totally removed; R Sp is the scale removal rate of the spinel layer.

Cladding Failure Modelling
Claddings, as the first barrier to contain radioactive nuclear fuels, is a key part of the fuel element and it is designed to keep its integrity and tightness in nominal and off-normal conditions. Therefore, the research and analyses of claddings are tightly related to fuel behaviors and even the overall reactor conditions, which brings more complexities and difficulties. The fuel element is the critical component of nuclear reactors, and its servicing performance does not only restrict the safety, reliability and economics of LFRs but also hinders the pace of engineering application. In particular, suffering from high temperatures, severe irradiation and corrosion in LFRs, fuel elements will evolve from the atomic scale to the macroscopic scale. In addition, the multi-physics phenomena occurring in the fuel range from microseconds to several years, leading to complex material behaviors and multiform cladding fatigue of fuel elements. Mixed oxide (MOX) fuel (U,Pu)O 2 is considered a reference fuel in GEN-IV LFRs. In terms of MOX fuels, multi-physics phenomena occur and interact with each other during long-term operation, such as thermo-mechanical coupling, fuel restructuring, constituent redistribution, swelling and fission gas release, cracking, corrosion, FCCI and FCMI, etc. [103]. Additionally, the mechanical behaviors of fuels and claddings tend to be multiform under high temperatures and radiation damage. Multiphysics behaviors of the LFR fuel pin are depicted in Figure 6.
fuel behaviors and even the overall reactor conditions, which brings more complexities and difficulties. The fuel element is the critical component of nuclear reactors, and its servicing performance does not only restrict the safety, reliability and economics of LFRs but also hinders the pace of engineering application. In particular, suffering from high temperatures, severe irradiation and corrosion in LFRs, fuel elements will evolve from the atomic scale to the macroscopic scale. In addition, the multi-physics phenomena occurring in the fuel range from microseconds to several years, leading to complex material behaviors and multiform cladding fatigue of fuel elements. Mixed oxide (MOX) fuel (U,Pu)O2 is considered a reference fuel in GEN-IV LFRs. In terms of MOX fuels, multi-physics phenomena occur and interact with each other during long-term operation, such as thermomechanical coupling, fuel restructuring, constituent redistribution, swelling and fission gas release, cracking, corrosion, FCCI and FCMI, etc. [103]. Additionally, the mechanical behaviors of fuels and claddings tend to be multiform under high temperatures and radiation damage. Multiphysics behaviors of the LFR fuel pin are depicted in Figure 6. Dedicated computer codes and some open-source or commercial finite element method (FEM) software are usually used to conduct fuel performance modelling. Fuel performance codes (FPCs) exist for many fuel types and are used for various purposes, including design optimization, experiment planning and interpretation and safety analysis [104]. The behaviors and interactions of fuel and cladding are complicated, where we have to consider the thermo-mechanical coupling, and even the effects of restructuring, constituent migrations, corrosion, fission gas release and so on. It is assumed that the axial temperature gradient is much smaller than the radial temperature gradient. As a result, a Dedicated computer codes and some open-source or commercial finite element method (FEM) software are usually used to conduct fuel performance modelling. Fuel performance codes (FPCs) exist for many fuel types and are used for various purposes, including design optimization, experiment planning and interpretation and safety analysis [104]. The behaviors and interactions of fuel and cladding are complicated, where we have to consider the thermo-mechanical coupling, and even the effects of restructuring, constituent migrations, corrosion, fission gas release and so on. It is assumed that the axial temperature gradient is much smaller than the radial temperature gradient. As a result, a majority of the codes (e.g., LIFE, FEMAXI, TRANSURANUS) represent the cylindrical fuel rod in a so-called one-and-a-half dimension (1.5D) and are capable of conducting performance analyses for the whole fuel pin under nominal and off-normal conditions. Table 6 collects most of the FPCs for fast reactors worldwide [105][106][107][108][109][110][111][112][113][114][115].
Except for these 1.5D FPCs, 2D or even 3D FEM software, such as ANSYS, COMSOL, ABAQUS and BISON based on MOOSE, is used to deal with the local phenomena [80,116]. Heat generated by nuclear fission throughout the fuel is conducted to the cladding tube and then to the surrounding coolant. Due to the cylindrical pellets, there is a parabolic temperature distribution in the pellets, and a near linear temperature distribution in the cladding due to the excellent thermal conductivity. The maximum temperature is located in the centerline of the fuel. The existence of temperature gradients induces the large thermal stresses and elastic or elastoplastic strains, accompanied by thermal expansion. Once the expansion of the pellet is more than the gap width, the fuel and cladding mechanical interaction (contact) occurs. Figure 7 shows the structural details and deformation of the claddings. The cracks are induced by the large thermal stress gradients during start-up and transients. The difference of the radial thermal expansion of pellets leads to the socalled bamboo-like shape of the cladding with regularly spaced ridges. Furthermore, the ballooning effect of claddings will occur due to axial temperature distribution. All these issues are related to the cladding failure modes and have to be focused [117].

Summary and Outlook
In view of the undocumented experiments and ongoing demonstrations of GEN-IV LFRs, the review of cladding failure has to be focused on the modelling and takes references from separated effects. However, we must admit that cladding failure behaviors under a long-term operation and transient conditions are major safety concerns for LFRs

Summary and Outlook
In view of the undocumented experiments and ongoing demonstrations of GEN-IV LFRs, the review of cladding failure has to be focused on the modelling and takes references from separated effects. However, we must admit that cladding failure behaviors under a long-term operation and transient conditions are major safety concerns for LFRs and deserve more attention. Compared with LWRs, LFRs have higher neutron doses, higher temperatures, higher burnup and an extremely corrosive environment. These complicated and extreme environments inside the reactor core bring significant challenges to nuclear materials and critical structures, especially claddings, the first barriers containing radioactive nuclear fuels.
The fuel performance modelling and transient analyses of LFRs are helpful for understanding the relatively realistic environment inside the reactor core and providing a clear image for material applications. In this paper, we took ALFRED and ELSY as reference to illustrate the long-term operating environment for fuel pins. According to the demands of LFRs, the fuel pin will service more than five equivalent full power years and the burnup will exceed 8 a.t.%, while some small modular LFRs intended to use for remote areas or special purposes have higher burnups. The maximum dpa of LFRs ranges from 100 dpa to 150 dpa and causes severe irradiation damage to claddings. Temperatures in the core will experience large increments or decrements during reactor start-up and shut-down, and swing under a long-term operation due to the reactivity changes. The fuel performance analyses of ALFRED indicate that the maximum temperature of the fuel is close to 2200 • C under nominal conditions, and the maximum contact pressure is 55.6 MPa at last because of FCMI, where accelerated creep rupture could occur.
During the long-term steady operation, LFRs could experience a series of transient accidents, in which the reactor parameters change intensely in a short time and may exceed safety limits. Therefore, the safety principles and guidelines have to be elaborated for LFRs. In this paper, transient analyses of DBCs for EFIT and CiADS were summarized and compared, including beam-trip transients, UBOP, ULOF, ULOHS and PLOHS. During frequent 10 s beam-trip of EFIT, the temperature variations of the fuel, the cladding and the coolant were 743 • C, 88 • C and 65 • C, respectively, which is inclined to induce the thermal cyclic fatigue of claddings. Furthermore, under ULOF and ULOHS for both EFIT and CiADS, the coolant temperatures exceeded the design limit of 550 • C with a consequence of irreversible damage of claddings caused by accelerated LBE corrosion.
In addition to satisfying materials design criteria based on in-pile performance, candidate cladding materials for current and proposed future nuclear energy systems must provide adequate resistance to three additional overarching environmental degradation phenomena: temperature dependence, radiation damage and chemical compatibility. Some macroscopical failure behaviors of claddings, such as thermal creep, cyclic fatigue, rupture and ratcheting between fuels and claddings, are temperature-dependent. Radiation damage can produce pronounced irradiation creep, void swelling and hardening due to high densities of nanoscale defects and fission products. Other failure phenomena of LFR claddings can be attributed to chemical compatibility issues, such as lead or LBE corrosion and fuel-cladding chemical interaction (FCCI).
Based on the modelling results, some critical issues need to be addressed in the future: (i) The fuel cladding mechanical interaction (FCMI) plays an important role in cladding failure, and it is effective to consider delaying FCMI from the initial design of LFRs. In reality, the cladding temperature in LFRs and its variation are relatively low under long-term steady operation, which will not induce large thermal stresses in the cladding before contact. The dominant failure mechanism should be cladding corrosion, and any mechanical effects are not obvious for certain. But once the contact occurs, everything will become complicated. Because large stresses induced by ongoing contact will accelerate creep and make microcracks growing fast until failure, especially with the degradation of cladding mechanical performance due to irradiation and corrosion.
(ii) Which failure mechanism is dominant under different scenarios should be figured out. With regard to frequent beam-trips in ADSs, fatigue under alternating stresses should be the most important issue, and the ratcheting between fuel and cladding tends to be serious after FCMI. But as for ULOF and ULOHS, the cladding temperature increases to a very high value, where all the failure-related behaviors will be accelerated.
(iii) Cladding failure modelling is elaborated with experimental support and performed using FPCs and commercial FEM software. The highly sophisticated descriptions of cladding behaviors should include theoretical knowledge and nonlinear material models. Those unconsidered fatigue mechanisms in this paper, such as liquid metal embrittlement (LME), ratcheting effects, FCCI, either lack suitable mathematical descriptions to couple with multi-physics behaviors or cannot be explained by specifical theories. All of them deserve further research to support quantified simulation and couple with other phenomena. Most importantly, a systematic and demand-driven deployment needs to be conducted from fundamental research to engineering application.

Acknowledgments:
We thank Jinxiong Zhou of Xi'an Jiaotong University for providing us with guidance.

Conflicts of Interest:
The authors declare that they have no known competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.