A hybrid experimental and numerical investigation on the Cr2AlC-coated zirconium for accident-tolerant fuel systems

SUMMARY

This study utilized a hybrid experimental and numerical approach to investigate the failure behavior of zirconium substrates coated with Cr2AlC. The failure mechanism was determined through a series of interrupted in-situ three-point bending tests in the scanning electron microscope (SEM), covering various stress states. Stress state related parameters for the Cr2AlC element at coating fracture and zirconium at crack propagation were extracted from finite element numerical simulations. A macroscopic failure criterion was formulated and validated by running numerical simulations and comparing the simulated results with the experimental ones. This work enhances accident-tolerant fuel systems (ATFs) design in nuclear power plants by providing an effective method for characterizing and predicting the failure of zirconium substrates coated with Cr2AlC and other similar thin films.

INTRODUCTION

In response to the Fukushima Daiichi nuclear disaster, various concepts and materials systems have been proposed to improve reactor safety, with one focus on developing accident-tolerant fuel systems (ATFs), especially cladding tube concepts. To overcome the current technical limitations of conventional zirconium cladding tube systems, it is crucial to investigate the failure mechanisms and characterize the mechanical properties of zirconium cladding tubes with new coating materials. In this study, Cr2AlC is deposited on the zirconium substrate. Cr2AlC, belonging to the MAX phase materials group, is renowned for its superior machinability, substantial damage tolerance, and heightened chemical resistance [1-3]. Contrasting with various other coatings, Cr2AlC shows self-regenerative crack-healing capabilities under elevated-temperatures oxidation conditions, facilitated by the formation of a stable, well-adhering oxide characterized by relative volume expansion [4-6]. Furthermore, it is expected that the facile oxidation of the Al element will lead to the formation of a dense Al2O3 layer [5, 6]. These inherent properties position Cr2AlC as a highly prospective application candidate at elevated temperatures. To assess the performance of the Cr2AlC-coated zirconium samples, a series of in-situ three-point bending tests with various sample geometries so a wide range of stress states is covered are conducted under quasi-static conditions. The simulation incorporates the maximum principal stress criterion, the modified Bai-Wierzbicki (MBW) damage model [7-9], and the analytical Yoon2014 model [10, 11]. This investigation facilitates the accurate characterization and prediction of the plastic deformation and failure of the coated samples, contributing to the investigation and further improvement of ATF cladding tube systems.

METHODOLOGY AND EXPERIMENT

Figure 1 shows the methodological workflow and the experimental procedures in this study. Firstly, the mechanical properties of the zirconium substrate are determined through uniaxial tensile (UT) tests at quasi-static conditions using standard dog bone (SDB) samples manufactured from 0.7 mm thick zirconium sheets. Nanoindentation (NI) tests with a Berkovich indenter determine the mechanical properties of the Cr2AlC thin film. The basic mechanical properties, including Young’s modulus, Poisson’s ratio of the zirconium substrate, and the Cr2AlC coating, will be used for later numerical simulation. Notably, the flow behavior of the zirconium substrate can be fitted directly from the uniaxial tensile test result using the Swift hardening law, while the flow behavior of the Cr2AlC coating is fitted by a hybrid experimental and numerical simulation method. Specifically, a random flow curve is generated for Cr2AlC coating using the Swift hardening law initially, and this flow curve is coupled into the NI test model constructed in ABAQUS. After running NI test simulations, the simulated force-depth curve is compared with the experimental ones. The fitting of the flow behavior of the Cr2AlC coating is achieved by trial and error. The Cr2AlC film with an average thickness of 3 μm is deposited on the zirconium substrate in an argon atmosphere using the high-power pulse magnetron sputtering (HPPMS) technique. To encompass various stress states, the zirconium sheet is manufactured into four geometries, including simple without a notch, unilateral V-notch (UV), bilateral V-notch (BV), and semi-circular notch. Subsequently, a series of interrupted in-situ three-point bending tests are carried out on Cr2AlC-coated zirconium samples in a scanning electron microscope (SEM) under a quasi-static condition at room temperature. Observing the thickness direction during the bending tests aids in identifying crack initiation positions, whether within the Cr2AlC coating, the zirconium substrate, or at the interface between them. Images are taken during the tests to record sample deformation and failure process. Notably, the Cr2AlC-coated samples used for NI tests have the same thin film thickness and substrate thickness as those used for bending tests, namely 3 μm and 0.7 mm, respectively. The failure criterion for the coated samples can be calibrated by analyzing the experimental results. The thickness of the selected substrate material lies within the thickness range of the cladding tube materials used in real nuclear power plants, which is usually 0.5-1 mm, and the thickness of the coating is similar to other studies [12-14]. After all the tests are finished, finite element simulations will be carried out with the user-defined subroutine, facilitating the model parameter calibration and model validation for macroscopic failure criteria. With the calibrated failure criteria, the coated sample failure can be reproduced.

RESULTS

As observed during the in-situ three-point bending tests, for all coated samples with various geometries (simple, UV, BV, and semi-circular), the Cr2AlC coating fractured at an elongation of 1750-3500 μm, and the cracks propagated from the coating to the substrate at an elongation of 2500-6250 μm. The samples with notch failed earlier than those without, and the sharper the notch was, the earlier the sample failed. The failure mechanism of the Cr2AlC-coated zirconium samples involves cracks initiating within the Cr2AlC coatings and propagating from the coating to the zirconium substrate with further loading, as depicted in Figure 2.

To obtain the critical values of local stress and strain variables, including stress triaxiality (𝜂), Lode angle parameter (𝜃̅), equivalent plastic strain (PEEQ), and maximum principal stress (MPS), a numerical simulation method was adopted to determine the critical stress and strain values when cracks initiate and propagate. The local stress state variables were extracted at the center of the coating and at the outer surface of the zirconium substrate, as marked in the simulation model in Figure 1 with the name critical zirconium element and critical Cr2AlC element. The analytical Yoon2014 model [10, 11] listed below was coupled during the simulation to consider the strength differential effect since zirconium has a hexagonal close-packed (HCP) structure, and tension and compression exist simultaneously during bending. Temperature and strain rate effects are coupled into the analytical Yoon2014 model by Pan et al. [15], considering the environmental temperature of the nuclear power plant.

The model parameter 𝐵 is set to be zero since zirconium is considered to be pressure insensitive, and the parameters 𝐴, 𝐶 are calibrated by referring to the work of Paredes and Wierzbcki [16]. 𝜎𝑌 is the yield strength of the material. 𝐼1 is the first stress invariant, and 𝐽2, 𝐽3 are the second and third stress deviator invariant, respectively.
From the simulation results, it was found that when cracks initiated in the Cr2AlC coating, the coating fracture with very limited plastic deformation occurred since the PEEQ value of coating elements in all samples was zero or nearly zero. As a result, the maximum principal stress criterion can be applied. Considering the distribution of the MPS of all tested samples, the probabilistic concept is adopted. By sequencing the fracture MPS from all tests (total number of 𝑁) in increasing order, the failure probability in the #𝑗-th test can be calculated [17]. The total number of bending tests in this study is 10.

Then, the Weibull distribution of the fracture MPS (𝜎𝑐) shown below will be applied, and the related parameters can be fitted. The failure probability equals 0.5 (𝑃𝑓=50%) is considered in this study.

After processing with the Weibull distribution, it was found that the MPS values of all the tested samples lie within the range of 2000-8000 MPa, corresponding to a failure probability of 0-1. The large scatter of the MPS value could be attributed to the different fracture mechanisms inside the Cr2AlC coating or the residual stress resulting from the cooling process after deposition is finished, while it would need to be validated in the future with other testing techniques.
Moreover, it was found that when cracks propagate from the coating to the substrate, plastic deformation occurs in the substrate material in all samples, so the modified Bai-Wierzbicki (MBW) damage model [7-9] listed below would be adopted to characterize and predict the crack propagation.

With the collected PEEQ, 𝜂𝑎𝑣𝑔, 𝜃̅𝑎𝑣𝑔 of the zirconium element of different samples at the crack propagation moments, the damage initiation locus (DIL) for zirconium when cracks propagated from the coating to the substrate can be constructed in MATLAB, as shown in Figure 3. The experimental points representing samples with different geometries are also plotted inside for comparison. Except for the experimental point of the semi-circular sample, other experimental points align well with the DIL.

With the MPS processed with the Weibull distribution and the calibrated MBW model parameters, crack initiation and propagation could be simulated and predicted, and compared with the experimental results. Figure 4 uses the BV sample as an example, comparing the experimental and simulated force-elongation curves, the observed crack initiation and propagation in SEM, and the simulated crack initiation and propagation. The blue layer represents the zirconium substrate, and the yellow layer represents the Cr2AlC coating. When the simulated elongation was 1600 μm, the Cr2AlC coating showed a complete structure; however, when the simulated elongation reached 1625 μm, the Cr2AlC coating elements were deleted, indicating the coating fracture. With further loading, when the simulated elongation reached 3250 μm, most of the coating elements were deleted, and the crack propagated from the Cr2AlC coating to the zirconium substrate, indicated by the zirconium element deletion. Notably, the model was tilted along the width direction when capturing the images so the element deletion could be better observed and presented. Compared with the experimental observation, the simulated elongation at Cr2AlC coating fractured and crack propagation fell into the experimental ranges. The crack initiation and propagation were also simulated and predicted with satisfying accuracy for coated samples with other geometries, indicating a successful validation of the applied macroscopic criterion.

CONCLUSION

Considering the current structure of the cladding tube and its development requirement, a novel cladding tube system is proposed by depositing a Cr2AlC thin film onto a zirconium sheet. By carrying out a hybrid experimental and numerical investigation on the Cr2AlC-coated zirconium samples, the integrity of Cr2AlC-coated zirconium samples is assessed. The proposed methodology and simulation model can also be transferred to other similar cladding tube structures. Furthermore, it can be concluded that:

• The failure mechanism of the Cr2AlC-coated zirconium samples involves cracks initiate within the Cr2AlC coatings, propagating from the coating to the zirconium substrate upon further mechanical loading.
• The proposed failure criterion characterized and predicted the sample failure successfully.

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ACKNOWLEDGEMENTS

The authors gratefully acknowledge the Federal Ministry for Economic Affairs and Energy (BMWi) [grant number: 100513703] for the financial funding and the GRS funding agency for the support.

AUTHORS

Boyu Pan
Institute of Metal Forming, RWTH Aachen University
boyu.pan@ibf.rwth-aachen.de

Fuhui Shen, Markus Könemann, Sebastian Münstermann
Institute of Metal Forming, RWTH Aachen University

fuhui.shen@ibf.rwth-aachen.de; markus.koenemann@ibf.rwth-aachen.de; sebastian.muenstermann@ibf.rwth-aachen.de