Transient behavior of oxide fuels with controlled microstructure and Cr₂O₃ additive

Abstract

Microstructure and Cr₂O₃ doping profoundly impact the thermal-mechanical properties and fracture of oxides fuels. It is a challenge to study the transient behavior of nuclear fuels under loss-of-coolant-event (LOCA). In this study, the crack behavior of UO₂ pellets with controlled grain structure and Cr₂O₃ doping was tested with rapid power ramping (300−900 °C per min) mimicking a prototypical LOCA heating profile. Dense micron-sized UO₂ pellets display well-maintained integrity without cracking with the ramping up to 1500 °C at a heating rate of 8 °C per second. Fracture occurs in both pure and Cr₂O₃-doped dense nano-sized UO₂ pellets. The Cr₂O₃ doped oxide fuel pellet with a larger grain size (~ 22.2 μm) displays the best performance under LOCA testing due to its highest thermal conductivity under high temperature. FEA calculations suggest a temperature gradient across the fuel pellet during transient testing, resulting in residual stress and cracking, which can be correlated with their thermal-mechanical properties.

Introduction

UO₂ is the dominant fuel for the commercial light water reactor¹ due to its high-melting point², thermal stability, good water and oxidization resistance, dimensional stability under irradiation, compatibility with cladding materials, and low cost³. However, the fuel performance under irradiation limits the fuel lifetime. During the irradiation of UO₂ fuel, the generation and release of fission gases (FGs) plays a significant role on the fuel performance⁴. FGs, mainly xenon and krypton, have a low solubility in UO₂, forming intragranular and intergranular bubbles inside the fuel pellets⁵. The bubbles formation induces the swelling and degradation of thermal conductivity of the fuel pellets, leading to a high temperature gradient and fuel cladding interaction. In addition, fission gas released to the fuel cladding through the cracks or the surface diffusion on the fuel matrix will also degrade heat transfer from fuels to cladding as a result of lower thermal conductivities of xenon and krypton⁶. This will further increase the fuel temperature and accelerate the FG releasing rate.

To enhance the fission gas retention capabilities, doped oxide fuels are developed in which the addition of Cr₂O₃ can enlarge the grain size of the UO₂ fuels with the goal of elongating the FG atom diffusion path inside the grain and reducing the FG releasing rate. Cr₂O₃ and Al₂O₃ have been used as the dopant to accelerate the grain growth of UO₂ during the sintering^7,8,9,10. Multiple researches have been performed to investigate the influence of the doping Cr₂O₃ on the diffusion behavior of FG inside the UO₂ matrix. The irradiation tests have been done to investigate swelling and the fission gas release behavior of the 0.5 wt% Cr₂O₃ doped fuel contrasting the traditional fuel¹¹. A similar behavior was observed between the reference fuel and doped fuel, probably due to higher gas diffusion rates and lower grain boundary energies in the doped fuel. Kashibe et al.¹² investigated the diffusivity of FGs in pure and Cr₂O₃ doped fuels under different temperatures, in which the doped sample has a higher activation energy than the pure one and their diffusivities depend on the temperature. When temperature is higher than 1525 K, the diffusivity of FG in doped sample is greater; while below 1525 K, the pure sample has higher diffusivity. In addition, Cooper et al.¹³ used a cluster dynamic model to calculate the Xe diffusivity in the doped and pure UO₂ fuels and the results showed Xe diffusivity is higher in both intrinsic and irradiation-enhanced regimes for doped samples. However, in the PWR and BWR reactors, the Cr₂O₃ doped fuel with larger grain size showed improved FG retention performance with the reduction of 20 bars of fuel rod inner pressure and better viscoplasticity with less pellet flaws under the operation¹⁴. Thus, although the doping of Cr₂O₃ into UO₂ fuels may increase the diffusivity of FG, counteracting the effect of FG retention capability of larger grain sizes, the better viscoplasticity may enhance the cracking and fracture resistance of the fuel pellets and thus increase the FG retention insides the fuel matrix.

Another significant challenge for increasing burnup limit is the demonstrating the safety of the fuel rods under the loss-of-coolant accident (LOCA), particularly as the utilities are pushing the high burnup of nuclear fuels¹⁵. High burnup structure (HBS) can form which is essentially a mesoscale structure consisting of micron-sized fission gas bubbles formed inside the nano-sized grain matrix. The HBS structure could be sensitive to rapid power ramping as experienced during the LOCA event. The FG bubbles formed inside the fuel matrix maybe over pressurized contrasting with the equilibrium state¹⁶, and the FG releasing rate increases rapidly as the results of the fuel disintegration and fragmentation, further increasing the inner rod pressure¹⁷. Cladding may burst upon threshold burnup and terminal temperature, particularly upon LOCA power ramping, and the fission gas release and potential fuel loss resulting from the fracture and fragmentation into the primary loop represent significant risks for reactor operation.

However, it is a challenge to understand how different microstructure features (e.g., porosity, fission gas bubble and grain size) on the fracture and fragmentation behavior and radiation effects because of complex and coupled microstructure features in HBS UO₂ and irradiation-induced microstructure evolution and defect accumulation. Numerous transient tests including separate effect testing by thermal shock or semi-integral approaches have been conducted to investigate the transient behavior of the UO₂ fuels. Doyle et al.¹⁸ have observed the fission gas burst release from high-burnup UO₂ (77 GWd per tU) nuclear fuel through the fuel heating and visualization system (FHVS). Turnbull et al.¹⁷ investigated the temperature threshold (972 K) for pulverization of the highly irradiated fuel (71 MWd per kg U) under LOCA testing by using laser heating, and the pulverization degree can be mitigated by reducing the ramping rate and applying the hydrostatic pressure. Besides, Ortega et al. investigated the transient behavior of UO₂ samples under fast ramping and cooling tests (-10−4 K per second) with terminal temperatures (853−953 K) by a molten salt bath¹⁹. Moreover, Pontillon et al. investigated the fission gas release behavior of UO₂ fuels with up to 70 GWd per t burnup under the LOCA using the circulation with a wide range of temperature increase rates (0.2−20 K per second)²⁰. Recently, Zhao et al. developed a thermal shock testing apparatus with flexible ramping rates in mimicking prototypical thermal profiles the LOCA and reactivity induced accident (RIA) events, and fresh UO₂ displays good thermal shock stability and anti-cracking performance under LOCA thermal test²¹.

In this work, we applied the rapid testing approach²¹ to test the transient behavior of UO₂ fuels with different microstructure and chromia doping to understand the impacts of grain size and doping on the fracture behavior. The transient behavior of nano-sized UO₂ under prototypical temperature ramping conditions of LOCA events will be useful to understand the performance of doped HBS fuels. The UO₂ pellets with controllable grain size are fabricated by spark plasma sintering (SPS) as an advanced approach in manufacturing ceramic and metallic fuels with controllable grain size and microstructure^{22,23,24,25,26,27,28}. Pure and Cr₂O₃ doped UO₂ fuels fabricated by SPS with different grain sizes (from tens micron meter to nano-size) serve as the model systems to study the impacts of Cr₂O₃ doping and grain structure on the thermal-mechanical properties of oxide fuels. In addition, thermal shock tests with different ramping rates (300−900 °C per min) and target temperatures (1000 °C and 1500 °C) have been designed and conducted though special SPS tooling to measure the transient behavior of UO₂ fuels as the function of grain size and Cr₂O₃ doping. FEA has been applied to calculate the temperature gradient and stress distribution of samples during the LOCA tests. The relationship between thermal-mechanical behavior and transient performance under LOCA has been investigated. Our results highlight the important impacts of grain structure and Cr₂O₃ doping on the thermal-mechanical behavior and transient behaviors. Fresh micron grain-sized fuels are stable under the LOCA conditions, in contrast to the fracture and fragmentation of the nano-sized oxide fuels. Furthermore, our paper provide a thermal shock method based on SPS, which has a more flexible controlment on the ramping rate contrasting with the traditional thermal shock methods, such as the quenching^29,30 and traditional furnace heating³¹.

Results

Thermal and mechanical properties

The polished surfaces of UO₂ pellets are shown in Fig. 1. The micron grain-sized samples (Fig. 1a–c) are sintered from 44-cycle ball-milled powders under 1700 °C and the grain size can be controlled by adjusting the dwelling time. The pure UO₂ sample with 7.8 μm grain size is shown in Fig. 1a, and the Fig. 1b, c show the Cr₂O₃ doped UO₂ with 10.4 and 22.2 μm grain size, respectively. The 10.4 μm grain-sized sample doped by Cr₂O₃ is sintered with 5 min dwelling, and the dwelling duration elongated to 25 min increases the grain size up to 22.2 μm for the Cr₂O₃ doped UO₂ sample. The Cr₂O₃ doped UO₂ pellet shows a larger grain size and higher density than the pure one without Cr₂O₃ additive. The dissolution of Cr₂O₃ on the UO₂ grain boundary can accelerate the grain growth rate of UO₂; thus, the grain growth of Cr₂O₃ doped UO₂ is faster than the pure one sintered under 1700 °C. Additionally, for the 10.4 μm grain sized sample, a secondary phase can be observed on the grain boundary as shown in Fig. 1g and EDS mappings (Fig. 1h–j). The undissolved Cr enriched secondary phase on the grain boundaries is induced by the short dwelling. In contrast, for the 22.2 μm grain size sintered with a longer duration (25 min), all of the 1000 ppm Cr₂O₃ doping are dissolved into fuel matrix, and no secondary phase can be observed.

Fig. 1: SEM images of UO₂ pellets with different grain sizes and compositions.

a the SEM image of pure UO₂-44 cycle-7.8 μm- 93% TD; b the SEM image of Cr₂O₃ doped UO₂-44 cycle-10.4 μm-95% TD; c the SEM image of Cr₂O₃ doped UO₂-44 cycle-22.2 μm-97% TD (in a, b, and c the length of scale bar is 40 μm); d the SEM image of pure UO₂-80 cycle-292 nm-94% TD and the length of scale bar is 4 μm; e the SEM image of Cr₂O₃ doped UO₂-80 cycle-293 nm-93% TD and the length of scale bar is 2 μm; f the SEM image of pure UO₂-80 cycle-418 nm-95% TD and the length of scale bar is 4 μm; g a BSE image of Cr₂O₃ doped UO₂-44 cycle-10.4 μm-95% TD with the scale bar of 5 μm; h, i, and j are the EDS mapping results for different elements (U, O, and Cr, respectively).

Highly densified nano grain-sized UO₂ samples are sintered through a high-pressure WC die and punch under 600 °C and 700 MPa and then isothermally annealed to control the grain size. Figure 1d shows the fracture surface of pure UO₂ with 292 nm grain size, in which the transgranular fracture mechanism has been observed. Figure 1e and f show thermal-etched surfaces of Cr₂O₃ doped UO₂ and pure UO₂ respectively, annealed under the exact same condition (900 °C with 30 min of dwelling). Different from the micron-sized samples sintered from 1700 °C, the Cr₂O₃ doped nano-sized UO₂ sample has a lower physical density and smaller grain size as compared with the pure one sintered at lower temperatures. Multiple samples are sintered showing the same observation, and the different grain growth effect by Cr₂O₃ additives may be a result of a low solubility of Cr₂O₃ inside UO₂ at lower sintering temperatures. Instead of accelerating the grain growth, the nano-sized Cr₂O₃ particles on the grain boundary will drag the grain boundary movement during the sintering. To obtain a similar grain size of pure UO₂ with Cr₂O₃ doped ones, post-sintered annealing at 850 °C were performed and the microstructure was shown in Fig. 1d.

Figure 2 shows x-ray diffraction patterns of all the samples showing a dominant UO₂ phase. However, the doped 22 μm grain sized sample shows higher normalized peak intensity on (311) crystal orientation. The X-ray diffracted intensity can be determined by the formula (1)³²:

$${I}_{D}=\frac{{I}_{0}{ab}}{2}\left[\frac{1}{\mu }\left(1-\exp \left(\frac{-2\mu t}{\sin \theta }\right)\right)\right]$$

(1)

Where ${I}_{D}$ is the diffracted intensity, ${I}_{0}$ is the incident X-ray intensity, $\mu$ is the linear X-ray absorption coefficient, t is the thickness, $\theta$ is the diffraction angel, a is the volume fraction of diffracting particles of the appropriate orientation (texture compensation), and b is the fraction of X-ray intensity diffracted per unit volume. Because all of the samples have the same thickness and the X-ray diffraction was conducted under same conditions and alignment, the diffraction intensity is determined by volume fraction of diffracting particles of the appropriate orientation. Thus, the doped 22 μm grain sized sample shows a preferential (311) orientation in contrast to other samples. This result indicates that the dissolving of Cr₂O₃ has significant influence on the grain growth behavior of UO₂.

Fig. 2

XRD results of the samples with different grain sizes and compositions.

The mechanical properties of UO₂ samples with different grain sizes and compositions are shown in Fig. 3. Cr₂O₃ doping enhances the mechanical properties of UO₂ samples, especially the fracture toughness. For the micro-sized samples, the 10.4 μm doped sample has a 33% improvement in fracture toughness as compared with the 7.8 μm undoped sample with a similar grain size without the sacrifice of hardness. For the doped UO₂ sample with 22.2 μm grain size, its hardness and fracture toughness are slightly higher than the pure one, consistent with the expectation in which Cr₂O₃-doped large-grained fuels will display better elastic and plastic properties. For the nano-sized UO₂ samples, hardness slightly increases with the reduction of grain size, but fracture toughness is smaller than the micron-sized samples. The possible reason may be the low grain boundary bonding strength of the nano-sized sample due to low sintering temperature.

Fig. 3

Hardness and fracture toughness of pure and Cr₂O₃ doped (marked with rectangular) UO₂ samples with different grain size, error bar represents standard deviation (the value is mean +/− standard deviation).

Thermal diffusivities and conductivities of micron-grain-sized samples are shown in Fig. 4. Cr₂O₃ doped UO₂ sample (10.4 μm) sintered with the 5 min dwelling shows the best thermal diffusivity with a 25% improvement as compared with pure UO₂ counterpart. The increase of thermal conductivity for Cr₂O₃-doped fuels is consistent with the higher physical density of the sintered pellets than pure UO₂ fuel pellets sintered at the same condition. For the Cr₂O₃-doped 22.2 μm grain sized pellet, thermal diffusivity is slightly higher than pure UO₂ below 700 K. Above 800 K, a significant improvement in thermal diffusivity can be observed as compared with the pure UO₂ pellet. Two nano-sized pellets show the lowest thermal conductivity due to the phonon scattering from grain boundaries. These results suggest simultaneous improvements in both thermal-mechanical properties for the doped fuels with micron grain size.

Fig. 4: The thermal diffusivity and conductivity of pure and Cr₂O₃ doped UO₂ samples with different grain size.

a the thermal diffusivity, and b the thermal conductivity.

Coefficients of thermal expansion (CTEs) are also measured by DIL, and as shown in Fig. 5, UO₂ fuel pellets with different compositions and grain sizes show similar behavior, indicating similar CTEs around 10.5 × 10⁻⁶ per K, which increases with temperature accordingly. Cr₂O₃ doping into micro-sized UO₂ pellets can slightly reduce the thermal expansion of the UO₂, which could be attributed to more U vacancies upon Cr₂O₃ incorporation into the crystal¹³, inducing the smaller CTE.

Fig. 5: Linear expansion rate and CTEs for pure and Cr₂O₃ doped UO₂ pellets with different grain sizes.

a Linear expansion rate (dL per L₀), b the CTE data.

Transient testing under prototypical LOCA

Transient tests under simulated LOCA temperature ramping are performed with 9 different ramping rates (changing from 5 °C per second to 15 °C per second with 1.7 °C per second increments) and initial terminal temperature is set at 1000 °C to investigate the influence of the ramping rate on the fragmentation behavior of UO₂ samples. The cooling for all of the testing is similar within a marginal window of 15 ~ 18 °C per second. In-situ measured temperature profiles with different locations across from the center to the edge of the nano grain size pellets are shown in Fig. 6. The center temperature of the sample is slightly higher than that at the edge, and the largest temperature difference is around 90 °C at the peak position. During the thermal shocking, only the sample bottom surface has contact with the graphite die and punch, and heat is conducted though the sample bottom. The temperature difference between center and edge slightly increases with higher ramping rates. With the different ramping rates, the temperature gradient slightly changed, and the cracking occurring could be attributed to the thermal stress build-up resulting from the thermal gradient associated with thermal shock testing.

Fig. 6: In-situ temperature profiles of the pure nano-sized samples under simulated LOCA transients with different ramping rates.

a 5 °C per second, and b 15 °C per second.

Four samples, including 7.8 μm pure UO₂, 10.4 μm Cr₂O₃ doped UO₂, pure and doped nano UO₂ with similar grain sizes are selected as the model systems for thermal shock testing. These will allow to investigate the influences of grain size and Cr₂O₃ doping on the fragmentation behavior of UO₂ under simulated LOCA transient. The polished surfaces of the selected samples for the thermal shock tests are shown in Fig. 7. All the samples have 8 mm diameter and 2 mm thickness with the polished surface, and these samples are intact upon thermal shock testing at a terminal temperature 1000 °C with varied temperature ramping rates. No crack is observed even for nano-sized samples thermally shocked with 15 °C per second ramping rate despite relatively low fracture toughness. Thus, fresh fuels with different grain sizes and compositions show excellent thermal shock stability under high ramping and cooling rates with the 1000 °C target temperature. These results suggest that a higher threshold heating rate at 1000 °C or a higher terminal temperature are required to create thermal shock-induced cracking in the fresh densified fuel pellets.

Fig. 7: Sample morphologies before and after thermal shock tests.

Before thermal shock tests: a pure-7.8 μm, b doped-10.4 μm, c doped-nano, and d pure-nano; and after thermal shock tests: e pure-7.8 μm, f doped-10.4 μm, g doped-nano, and h pure-nano (the scale bar at the bottom of the sample is 1 mm per grid).

In order to further evaluate the thermal shock resistance of samples with different grain sizes and compositions, thermal shock tests are performed at a higher terminal temperature of 1500 °C and different ramping rates (5 °C per second to 8 °C per second) and the temperature profile was shown in Fig. 8. With the 8 °C per second ramping rate, cracking occurs in two nano-sized samples (for both pure and doped samples), as shown in Fig. 9. Both samples show cracks initiated at the edge of sample along the radial direction. Trans-granular fracture is observed at the beginning, and then transition to a dominant intergranular cracking is observed. In addition, the grain size increases from nanometer to micron after thermal shock testing. In addition to cracking, bubble formation is also observed on the surface of the pure nano-sized pellet upon transient testing, which may be induced by the expansion of trapped Ar gas inside the sample during fuel manufacturing and sintering.

Fig. 8

Temperature profiles at the edge of the nano-sized UO₂ samples with different ramping rates (8 ^oC per second and 5 °C per second).

Fig. 9: Morphologies and microstructure of nano-sized UO₂ fuel pellets post LOCA thermal shock testing.

a optical microscope images of thermally shocked doped nano-sized pellets; b–g SEM images on the cracks of the doped nano sample (the length of scale bar in (b) is 30 μm, c, d are 50 μm, e is 100 μm, f is 50 μm and g is 10 μm); h Optical microscope images of the thermally shocked pure nano-sized pellets; i–n SEM images of the thermally shocked pure nano sample (the scale bar length of i is 500 μm, j is 100 μm, k is 30 μm, l is 100 μm, m is 40 μm, n is 50 μm).

Discussion

For micron-sized pellets, Cr₂O₃ doping into UO₂ matrix improves its thermal-mechanical properties either by increasing the grain size and density or by forming the Cr enriched secondary phase distributed on the grain boundary. For the 22.2 μm grain-sized pellet, the larger grain size and higher density lead to improved thermal conductivity. For the 10.4 μm grain-sized pellet, the Cr-enriched secondary phase distributed on the grain boundary could be responsible for the significant improvement of its thermal conductivity. Although trace amount of the doping, the Cr enriched secondary phase along the grain boundary may act as the high thermally conducting channel covering the grain surface. The distribution of the secondary phase might play a significant effect on the thermal conductivity, and the continuous distribution of higher thermally conductive phase could be more effective to improve materials thermal conductivity as compared randomly distributed phases³³. The improvement of fracture toughness maybe induced by similar reasons. For the 10.4 μm doped UO₂ sample, the existence of secondary phase particles may absorb the fracture energy and deflect the cracking directions, and ultimately reduce the cracking length, as shown in Fig. 10b. The better fracture toughness for the 22.2 μm doped sample could be also induced by the high physical density of the samples containing less pores with smaller pore size, with less cracking initiation points. The nano-sized pellets show higher hardness, which is consistent with its higher yield strength due to the small grain size, as describing in Hall-Petch Eq. (2)³⁴:

$${\sigma }_{y}={\sigma }_{0}+k{r}^{-1/2}$$

(2)

Where ${\sigma }_{y}$ represents the yield strength, ${\sigma }_{0}$ represents the stress required for initiating dislocation movement, k is a constant relevant to the fracture initiation energy, and r is the grain size. The grain boundary may pin the dislocation climbing. Thus, pure nano-sized pellets show higher hardness than micron-sized counterparts. However, fracture toughness of nano-sized samples is lower than that of micron-sized samples, which could be due to a lower bonding energy of nano-sized sample samples grain boundary. As shown in Fig. 10, the fracture mechanism for micron-sized sample is trans-granular cracking, which transits to inter-granular fracture for nano-sized grain sized samples. This is consistent with a previous study on mechanical properties of micron- and nano-sized UO₂³⁵. The lower fracture toughness of nano-sized samples may be induced by the low grain boundary surface energy due to low sintered temperature. As shown in Eq. 3³⁶, the fracture surface energy can be expressed as a function of fracture toughness.

$$2\gamma =\frac{1-{\nu }^{2}}{E}{K}_{{IC}}$$

(3)

in which $\gamma$ represents the surface energy and $\nu$ is the Poisson’s ratio, E is Young’s modulus, and the ${K}_{{IC}}$ is the fracture toughness. Another possible reason may be induced by the lower density of nano-sized pellets, and the pores along the grain boundary may act as the cracking initiation point during the testing, decreasing the critical fracture energy.

Fig. 10: Indentation of the pure and doped samples with different grain size.

a Pure-7.8 μm, b Doped-10.4 μm, c Doped-22.2 μm, d Pure-418 nm, e Pure-280 nm, and f Doped-292 nm; the length of all the scale bar is 50 μm.

To verify the stress distribution induced by the temperature ramping, FEA are performed based on the thermal-mechanical properties of pure nano UO₂ sample, and the results are shown in Fig. 11. With 1000 °C terminal temperature and 15 °C per second ramping rate, the temperature difference between the sample center and sample edge is 93 °C (see Fig. 11a), which is consistent with in-situ temperature measurement during the thermal shocking. Tensile stress along the θ direction is 22.2 MPa at the edge surface of fuel pellets. With 1500 °C terminal temperature and 8 °C per second ramping rate, the temperature difference increases to 213 °C, resulting in a higher tensile stress (44.0 MPa) at the pellet edge.

Fig. 11: FEA calculations of temperature profiles and tensile stress in the θ direction for nano-sized pellets.

a, b Temperature and stress distributions for the samples with 1000 °C terminal temperature and 15 °C per second ramping rate during LOCA test; and c, d Temperature and stress distributions of the pellets upon LOCA testing with 1500 °C terminal temperature and 8 °C per second ramping.

As reported in literature³⁷, the fracture strength of pure micron-grain-sized UO₂ under 100 °C is around 80–165 MPa, depending on different measurement methods and different samples. However, the fracture toughness of nano-sized UO₂ and micron-sized UO₂ measured by micron-indentation was reported as 0.92 and 1.2 MPa∙m^1/2 respectively. Thus, the nano-grain-sized sample will have a lower fracture strength than the micron-grain-sized sample. Although the tensile stress at the edge position of the nano-sized pellet is lower than the fracture strength (80 MPa) under LOCA transient test up to 1500 °C, the nano-sized pellet still cracks due to the flaw of the samples, e.g., pores in the fuel matrix. The critical stress which induce the cracking at the pore is inversely proportional to the pore size, as described in formula (4)³⁸:

$${\sigma }_{F}\cong {K}_{{Ic}}{(\pi C)}^{-1/2}$$

(4)

in which ${\sigma }_{F}$ is the tensile fracture stress for the ceramic at the flaw with a diameter of C and ${K}_{{Ic}}$ is fracture toughness. As shown in Fig. 12, the pore has been observed on the fractured surface of nano-sized pure UO₂ pellets after 1500 °C thermal shocking tests, and the diameter of the pore is about 166 μm. The large-sized pores formed during the transient tests accompanying with the grain growth and a higher target temperature could result in larger grain and pore sizes. The tensile strength of at the pore with diameter of 166 μm for pure and doped nano-sized UO₂ samples are calculated as 40.2 MPa and 49.1 MPa, respectively based on the formula (6) with the experimentally measured fracture toughness. Therefore, hoop tensile stress induced by the thermal gradient and the flaw size inside the sample during the thermal shock tests play an important role impacting the fracture behavior under power transient.

Fig. 12: The pores observed on the fracture surface of nano pure UO₂ after 1500 °C thermal shock tests with heating rate of 8 °C per second.

a the fracture surface with 400 μm scale bar, b the enlarged zone of the center of the fracture surface with 100 μm scale bar.

In addition, the cracks of two nano grain-sized pellets initiate at the edge of the sample, consistent with the FEA stress analysis predicting concentrated tensile stress at the edge surface. Thus, the FEA results can be used to illustrate the temperature profile during the transient testing, and nano-sized pellets crack because the thermal stress induced by the thermal ramping is larger than the critical tensile fracture stress near the pores.

To further analyze the effect of Cr₂O₃ doping and grain size on cracking behavior, the exact same thermal loading conduction has been applied in FEA to simulate the pure and doped micron grain sized samples transient behavior under same condition. The temperature profile and thermal stress are calculated and shown in Fig. 13. The pellet with a higher thermal conductivity under high temperature shows a smaller temperature gradient under the thermal shock testing. The 22.2 μm doped pellet displays the lowest thermal gradient and stress because its’ high thermal conductivity under high temperature (>1000 °C), indicating its best LOCA tolerance among all tested samples because of its excellent thermal conductivity under high temperature contrasting with the pure sample. The pure nano UO₂ exhibits a lower temperature gradient and hoop stress compared to the doped nano UO₂, primarily due to its slightly higher thermal conductivity at elevated temperatures.

Fig. 13

FEA calculations of temperature profile and tensile stress in θ direction for different samples under 1500 °C thermal shock test.

The systematic investigation performed in this study highlights the important impacts of grain size and Cr₂O₃ doping on the thermal-mechanical properties and fracture behavior of UO₂ fuels under simulated LOCA power transients. In particular, Cr₂O₃ doping not only enhances the fracture toughness of UO₂ with different grain size, but also increases thermal conductivity of micron-sized UO₂ samples. Fresh micron grain-sized pure and doped UO₂ samples are stable without cracking under the ramping tests up to 15 °C per second at a terminal temperature of 1000 °C or tested by a temperature ramping of 8 °C per second with 1500 °C terminal temperature. Both pure and doped nano-sized pellets crack along the radial directions because of their inferior thermal conductivities and fracture toughness as compared with micron-sized counterparts. The FEA results reveal a close correlation between the residual stress induced by thermal gradient and thermal conductivity. The Cr₂O₃-doped UO₂ with an average grain size of 22 μm grain size shows the best thermal shock resistance and greater tolerance under prototypical LOCA transients. In contrast, nano-sized pellets are sensitive to cracking and fracture upon powder ramping, underscoring the importance of understanding the transient behavior of high burnup fuels. The special design of SPS tooling for thermal shock testing could be helpful to accelerate the transient testing of nuclear fuels and facilitate the evaluation and quantification of performance of future fuels.

Methods

Preparation of UO₂ micron and nano-sized powders

Different sized UO₂ powders are processed through high energy ball milling, and the powder loading process is carried inside a glove box, in which the oxygen level is lower than 10 ppm, to prevent the oxidation of UO₂ powders during the ball milling. The ball milling duration is 15 min for each cycle and then pauses for 10 min between each cycle to prevent overheating of the powders. To obtain the micron-sized powders, 44 cycles have been used and the 8 mm diameter WC balls are used as ball milling mediums. For Cr₂O₃ doped UO₂ sample, 1000 ppm (weight percent) Cr₂O₃ powders are added to the 40 cycle-ball milled UO₂ powders and then ball milled for another 4 cycles to mix the powders. To obtain the nano-sized UO₂ powders, 80 cycles ball milling of oxide powder is performed using 1.8 mm WC balls as the milling medium, and the same procedure is applied to obtain Cr₂O₃ doped nano-sized UO₂ powders.

Consolidation of UO₂ pellets with different grain sizes by SPS

Different sintering parameters and high energy ball milling durations have been applied to control the gain size of UO₂ pellets. The micron grain-sized UO₂ is sintered from 44 cycle-ball milled powder through the graphite die and punch under 1700 °C with 50 MPa. Different durations (5 and 25 min) are used to control the grain size. To sinter the nano grain-sized pellets, WC dies and punches are used under high pressure (700 MPa) and low temperature (600 °C), and then the isothermal annealing is conducted under 850–900 °C for 30 min to obtain the desired grain size (300 nm).

Microstructure and phase characterization and properties investigation

The microstructure of samples is characterized by a scanning electron microscopy, SEM (Carl Zeiss Supra 55, Germany). The phase of samples is characterized by X-ray diffraction, (XRD, Westborough, USA) with Cu-Kα radiation with a step width of 0.02° (2θ).

Thermal properties investigation

A laser flash apparatus (Micro Flash LFA-457, NETZSCH) is used to measure the thermal diffusivity of sintered pellets. Both up and lower surfaces of the sample are coated with graphite spray to eliminate the influence of reflection to obtain reliable results. Measurement is conducted at temperatures between room temperature to 1000 °C in an argon inert atmosphere at a flow rate of 150 ml/min. Half time for signal receiving is restricted to be shorter than 200 ms. The Cape-Lehman + pulse correction is applied to fit the signal–time curve to derive the value of thermal diffusivity, three data points were collected in each measurement, and the standard deviation was used as the error bar. Density is presumed to be independent of temperature and measured at room temperature based on the Archimedes’ principle using an Adams analytical scale (Danbury, NY, USA). The thermal expansion coefficient data is measured through dilatometry (DIL 402, NETZSCH), and the average CTE for the samples with different compositions and grain sizes have been measured.

Mechanical properties characterization

The indentation measurement is conducted by a LECO M-400 Micro-hardness tester on the polished surfaces under room temperature with a load of 1 KgF and the holding duration of 15 s. More than 10 indentations are generated, and the SEM images are taken to measure the indentation size according to the standard ASTM C1327. The standard deviation was used as error bar. Specifically, hardness can be calculated through formula (5), in which P is loading pressure and b is the indentations’ diagonal lengths.

$$H=1.854\frac{p}{{b}^{2}}$$

(5)

Fracture toughness can be calculated from formula (6)^39,40, in which E is Young’s modulus of the UO₂ fuels with controlled microstructure based a systematic investigation in literature³⁵ and H is hardness, P is the loading pressure and C is the crack length, which equals to the distance from the center of indentation to the tip of the crack.

$${K}_{{IC}}=0.016{\left(\frac{E}{H}\right)}^{0.5}\frac{P}{{C}^{1.5}}$$

(6)

Grain size measurement

The grain size is measured from the thermally-etched surface using a rectangular intercept procedure following ASTM E112-88 stand as shown in formula (7), in which D represents the grain size, A is the area of rectangular, N_i and N₀ are the numbers of the grains in the rectangle on the boundary of the rectangle respectively. More than 100 grains are counted for each sample based on different SEM images.

$$D=\sqrt{\frac{4A}{\pi ({N}_{i}+\frac{{N}_{0}}{2})}}$$

(7)

Thermal shock test design

The LOCA thermal shock tests are conducted on the SPS with special die and punch designs as shown in Fig. 14, following the method described in our previous study²¹. The 8 mm sample was located inside a 10 mm graphite die, and there was no pressure loading on the sample during the thermal shock tests. The temperatures of the sample at the center and edge were measured by using the thermal couple and pyrometer, respectively. Different ramping rates (300−900 °C per min) and target temperatures (1000 and 1500 °C) have been applied to investigate the transient behavior of samples, which can be controlled by power output of SPS.

Fig. 14: Thermal shock test design simulating heating profile of the LOCA by SPS.

a The whole setup, in which black parts are made from graphite, white pipe is the thermal couple, and origin color is the sample, b the cross-section of the die and sample.

Finite element analysis

FEA analysis is performed using Abaqus 2020 based on the experimentally measured thermal-mechanical properties of different samples in order to calculate the temperature and stress distribution within the fuel pellets during transient test. In the simulation, the sample bottom has a positive heat flux to simulate thermal conduction through the graphite punch during thermal shock tests, in which the flux is proportional to the power output of SPS. The heat flux for 1000 °C target temperature with 900 °C per min ramping rate thermal shock is 13 KW per m²; and for the 1500 °C thermal shock test, the heat flux is 32 KW per m². The FEA model has the same size as the sample (8 mm diameter and 2 mm thickness). The elastic mechanical property has been applied based on the experiment measured Young’s modulus³⁵. The mesh size of the model is 5 × 10^-5m and the mesh property is coupled temperature-displacement, in which the thermal stress induced by nonhomogeneous thermal expansion of the pellet can be calculated based on Hook’s law. More details about the FEA simulation can be found in our previous study²¹.