Multiphysics phase-field modeling of quasi-static cracking in urania ceramic nuclear fuel

This work presents phase-field modeling of quasi-static cracking in urania (UO₂) ceramic nuclear fuel under neutron radiation at high temperatures. Considering the tightly coupled multi-physics processes within the fuel during reactor power operation, a diffusion model including Fickian and Soret effects is used to describe the oxygen hyper-stoichiometry (x in UO_2+x), and the temperature field is given by a thermal model involving non-uniform fission-generated heat source and heat flow across fuel pellet, pellet-cladding gap and cladding to the outside heat sink. Both temperature and irradiation effects are taken into account for the basic thermo-mechanical properties and irradiation behaviors of the nuclear fuel. Especially, the acceleration of fuel thermal creep by oxygen hyper-stoichiometry is included. The fracture due to the above physical processes is approximated by a scalar phase-field variable based upon a cohesive phase-field fracture method. A granite fracture experiment is simulated to validate the thermo-fracture coupling approach. For the first time, the diffusion-thermo-mechanical-fracture coupling model is applied to UO₂ fuel pellet cracking during reactor startup, power ramp and reactor shutdown. UO₂ creep is found to play an important role on the fuel pellet fragmentation. The developed capability supports interpretation of experimental data and can guide material design of ceramic nuclear fuels.     

Construction of three-dimensional dynamic growth TGO (thermally grown oxide) model and stress simulation of 8YSZ thermal barrier coating

A three-dimensional cylindrical numerical simulation physical and geometric model of TBCs sinusoidal surface was established based on the ultrasonic C-scan results of 8YSZ coating after thermal cycling. The stress distribution and evolution law of the TGO/BC interface and sample center and edge affected by TGO growth were simulated by the finite-element method. The results show that the stress at the TGO/BC interfaces changes from compressive stress to tensile stress with the increase of the number of thermal cycles. The center of the interface is distributed with large radial, circumferential and axial tensile stresses, while the edge of the sample is affected by thermal mismatch, which shows that shear stresses are alternately distributed in the XZ direction. The tensile stress at the center and the shear stress at the edge are the main reasons for the failure of the core and edge flakes of the thermal barrier coating. The linear elasticity, creep effect, fatigue effect and stress accumulation effect of each layer of TBCs in each thermal cycle period are fully considered by the model, which reveals the reason why the core and edges of the thermal barrier coating are most likely to form cracks.     

Peridynamic-based investigation of the cracking behavior of multilayer thermal barrier coatings

Numerical simulations of the cracking behavior of the top layers of multilayer thermal barrier coatings (TBCs) can effectively reveal the failure mechanisms of the TBCs. Current finite element method (FEM)-based simulation means have been applied to solve certain simple cracking problems in TBCs; however, they cannot effectively describe complex cracking problems in TBCs such as coalescence, intersection, and interference among multiple cracks. Peridynamic (PD), a newly developed mechanical theory, has been widely studied to provide analysis for cracking problems in TBCs. In this paper, a numerical model of TBCs is built by the bond-based PD (BB-PD) theory. Complex cracking behaviors, such as spontaneous crack propagation at both interfacial and internal regions, coalescence, and interference among multiple cracks, are simulated under isothermal cooling and gradient cooling conditions. In addition, the effects of interfacial roughness and calcium–magnesium–alumina–silicate (CMAS) inclusions on the cracking behavior are discussed. The results show that the PD model accurately captures complex cracking behaviors observed via scanning electron microscopy (SEM). Given the ability of the model for analyzing discontinuities in TBCs, it can help to further clarify the fracture mechanisms of TBCs.     

Effects of TGO growth on the stress distribution and evolution of three-dimensional cylindrical thermal barrier coatings based on finite element simulations

Based on the ultrasonic C-scan results of 8YSZ coatings after thermal cycles, three-dimensional cylindrical numerical simulations of the physical geometry model of the thermal barrier coating (TBC) sinusoidal surfaces were conducted with finite elements to estimate the stress distribution and evolution law of the top coat (TC)/bond coat (BC) interface, including the centre and edge of the specimen affected by the dynamic growth of the thermally grown oxide (TGO). The results show that when a layer of TGO is grown on the TC/BC interface, compressive stress is uniformly distributed on the TGO interface, and the stress value decreases as a function of the TGO layer thickness. When the thickness of the TGO exceeds a certain value, the compressive stress of all parts of the interface gradually changes to tensile stress; meanwhile, the edges of the model affected by the crest and trough effects of the wave are reflected in the radial and circumferential directions, especially along the axial direction, with alternating concentrated tensile and compressive stresses. TGO growth imposes a minor influence on the magnitude and distributions of the radial and circumferential stresses at the BC interface. The linear elasticity, creep, fatigue, and stress accumulation effects of each layer of TBCs in each thermal cycle were fully considered in this model. The model not only interprets the crest and trough effects of the TC/BC surface interface during the growth of TGO, but also interprets the effects of the core and edge of the cylindrical model, further revealing the reason for which the core and edge of the TBC will most likely form cracks.     

Dense nanocrystalline UO2+x fuel pellets synthesized by high pressure spark plasma sintering

Nanocrystalline UO_2+x powders are prepared by high‐energy ball milling and subsequently consolidated into dense fuel pellets (>95% of theoretical density) under high pressure (750 MPa) by spark plasma sintering at low sintering temperatures (600°C‐700°C). The grain size achieved in the dense nano‐ceramic pellets varies within 60‐160 nm as controlled by sintering temperature and duration. The sintered fuel pellets are single phase UO_2+x with hyper‐stoichiometric compositions as derived by X‐ray diffraction, and micro‐Raman measurements indicate that random oxygen interstitials and Willis clusters dominate the single phase nano‐sized oxide pellets of UO_2.03 and UO_2.11, respectively. The thermal conductivities of the densified nano‐sized oxide fuel pellets are measured by laser flash, and the fuel stoichiometry displays a dominant effect in controlling thermal transport properties. A reduction in thermal conductivity is also observed for the dense nano‐sized pellets as compared with micron‐sized counterparts reported in the literature. The correlation among the SPS sintering parameters—microstructure control—properties is established, and the nano‐sized UO_2+x pellets with controlled microstructure can serve as the model systems for fundamental understandings of fuel behaviors and obtaining critical experimental data for multi‐physics MARMOT model validation.     

Simulation of thermal shock cracking in ceramics using bond-based peridynamics and FEM

The effects of moderate intensity ‘hot’ or ‘cold’ shock in brittle solids have been extensively studied, while much less is known about thermal shock response during large temperature variations. In this study, a combined finite element – peridynamics numerical procedure is proposed for the simulation of cracking in ceramic materials, undergoing severe thermal shock. Initially, Finite Element nonlinear heat transfer analysis is conducted. The effects of surface convection and radiation heat exchange are also included. Subsequently, the interpolated temperature field is used to formulate a varying temperature induced action for a bond-based peridynamics model. The present model, which is weakly coupled, is found to reproduce accurately previous numerical and experimental results regarding the case of a ‘cold’ shock. Through several numerical experiments it is established that ‘cold’ and ‘hot’ shock conditions give rise to different failure modes and that large temperature variations lead to intensified damage evolution.     

Steel spheres impact on alumina ceramic tiles: Experiments and finite element simulations

Finite element simulations can be very useful for assessing and optimizing the design of advanced armor systems, but they require capturing the mechanisms of damage and failure that occur in composite-backed ceramic tiles when subjected to shock impact. The damage that occurs, primarily by the formation of radial and conical cracks and comminution, is complex. Therefore, the first step toward understanding these mechanisms are to simplify the problem. In this work, impact experiments using spherical steel projectiles were conducted on free-standing bare alumina ceramic tiles of two different thicknesses. Observations of the damage were then used to investigate the ability of numerical codes to capture the damage mechanisms occurring in the alumina tiles at various impact velocities. Three constitutive material models, used to simulate brittle fracture in isotropic solids, were explored, using commercially available finite element hydrocode LS-DYNA. These were the popular Johnson-Holmquist model 2 for ceramic materials, the pseudo-rheological Karagozian & Case Concrete model—Release III, and the elastic bond-based peridynamics model. The numerical results obtained demonstrated the capability of each approach to capture the damage produced by the impact of steel spheres on alumina ceramic tiles.     

Design and Optimization of an Innovative Solid Oxide Fuel Cell–Gas Turbine Hybrid Cycle for Small Scale Distributed Generation

Distributed power generation and cogeneration is an attractive way toward a more rational conversion of fuel and biofuel. The fuel cell‐gas turbine hybrid cycles are emerging as the most promising candidates to achieve distributed generation with comparable or higher efficiency than large‐scale power plants. The present contribution is devoted to the design and optimization of an innovative solid oxide fuel cell–gas turbine hybrid cycle for distributed generation at small power scale, typical of residential building applications. A 5 kW planar SOFC module, operating at atmospheric pressure, is integrated with a micro gas turbine unit, including two radial turbines and one radial compressor, based on an inverted Brayton cycle. A thermodynamic optimization approach, coupled with system energy integration, is applied to evaluate several design options. The optimization results indicate the existence of optimal designs achieving exergy efficiency higher than 65%. Sensitivity analyses on the more influential parameters are carried out. The heat exchanger network design is performed for an optimal configuration and a complete system layout is proposed. An example of hybrid system integration in a common residential building is discussed.     

Damage and failure mechanism of sapphire under ballistic loading based on a modified bond-based peridynamic model

To investigate the dynamic mechanical behaviors of c-plane and a-plane sapphire, a novel anisotropic constitutive model and fracture criterion are constructed on the basis of bond-based peridynamics (BB-PD) theory. And the concept of strain is introduced in the framework of BB-PD. After that, the simulations of a- and c-planes of sapphire under spherical and cylindrical impact are conducted. In addition to capturing the distribution of strain and damage, the histories of various fracture types such as the primary fracture front and cracks are monitored for quantitative analysis. The numerical predictions are shown to agree well with previous experimental results, and further reveal the damage and failure mechanisms of sapphire. The different forms of contact between the projectile and the target strongly influence the stress waves generated and energy transferred ultimately affecting the damage development process. The crystal orientation dominates the appearance of anisotropic crack modes. Crack bending and deflection, as well as spalling-like fracture, are associated with wave reflection and intersection. Moreover, an in-depth examination of the observed wave splitting phenomenon is performed.     

Modeling the thermal shock induced cracking in ceramics

Prediction of surface cracking in ceramics due to quenching is performed numerically using either the coupled criterion or a cohesive zone model. Under such a thermal shock, a network of short cracks with minimal spacing between them initiate and propagate until some of them stop while the others continue propagating. The numerical implementation consists of a periodic array of cracks modeled by a representative volume element. It allows crack initiation, simultaneous propagation and period doubling to be predicted. The investigation of the crack period doubling allows a precise determination of the optimal crack spacing, which decreases with an increasing thermal shock amplitude. The predicted crack spacing results are in agreement with experimental measurements.     

Mid-Explosion Recovery of an Intermediate Phase of a Cylindrical Metal Shell

To understand the complex dynamic response of cylindrical metal shells under highstrain-rate loading, a mid-explosion recovery device is designed to recover cylindrical shells at an intermediary phase, chosen in this study to be the phase wherein cracks penetrate through the entire casing wall thickness. The surface dynamic processes of the expansion, fracture propagation, and rupture of a 40CrMnSiB steel cylindrical shell are measured with a high-speed framing camera for determining the appropriate inner diameter of the mid-explosion recovery device. The numerical simulation software Autodyn-3D is used to predict the influence of the device wall thickness and the maximum radial deformation of the device inner wall upon the outer fracture diameter of the casing. The casing at the desired phase is recovered by the device, and the outer diameter of the shell is found to increase by 1.77 times, while the radial deformation of the device is 5 mm. The crack distributions, the distance between the adjacent penetrating shear cracks, and the number of circumferential divisions are found to vary along the axis of the cylindrical casing.     

Dynamic crack growth mechanism and lifetime assessment in plasma sprayed thermal barrier system upon temperature cycling

Failure of plasma-sprayed thermal barrier coatings (TBCs) is very complicated upon temperature cycling, therefore, to ascertain the crack propagation behavior is beneficial to understand the failure mechanism and life prediction of TBCs. In this paper, a finite element model is developed by coupling the dynamic growth of thermally grown oxide and dynamic crack propagation to explore the failure of TBCs induced by the instability of the interface between top coat (TC) and bond coat (BC). The thermal cyclic lifetime is deduced by obtaining the thermal cycles corresponding to the occurrence of complete delamination. The influence of the non-uniformity of the interface on thermal cyclic lifetime is quantitatively evaluated. Sensitivity studies including the effects of constituent properties and crack distance to the interface on the thermal cyclic lifetime are further examined. The results show that the incipient cracks usually nucleate above the valley due to the large tensile stress, and the shear stress near the peak plays a very crucial role. The crack growth involves three stages with different fracture dominated-mode. The crack propagation behavior obtained by simulation is in line with that observed by experiments. The TBCs system with a uniform interface exhibits a longer thermal cyclic lifetime compared to the non-uniform interface. Coating optimization methods proposed in this work may provide an alternative option for developing a TBCs system with longer service lifetime.     

Modelling of a CO2-gas jet into liquid-sodium following a heat exchanger leakage scenario in Sodium Fast Reactors

Sodium-cooled Fast Reactors (SFRs) represent one of the most promising technologies in the context of generation IV nuclear power reactors. In order to avoid a reaction between sodium and water when Rankine cycles are employed, the concept of Brayton cycles using supercritical CO₂ (SCCBCs) is being investigated as alternative energy conversion cycle. However, an accidental scenario must be evaluated, since a leakage inside the CO₂-sodium heat exchanger would cause a reactive underexpanded CO₂-into-sodium jet, which in turn could lead to mechanical and thermal problems. A two-fluid approach has been investigated for the modelling of the two-phase jet: according to flow maps, mist flow has been assumed at the leak exit, where high gas volume fraction and high interfacial slip velocity exist, and bubbly flow has been assumed for lower gas volume fraction and slip velocity. An interfacial friction model has been developed. Droplet and bubble diameters have been estimated following literature experimental results and using critical Weber number. For the drag coefficients, consistent correlations have been developed. A two-phase mixture turbulence model has been added. The interfacial friction approach has been implemented into the two-fluid model of the CFD software Ansys Fluent 14.0. 3D numerical simulations of gas-into-water jets have been performed for vertical upward jets and optical probe technique has been employed for the experimental measurement of void fraction inside an underexpanded N₂-into-water jet: numerical results agree with experimental results in terms of axial and radial void fraction profile. The two-fluid approach presented here will be the base for the implementation of a chemical reaction model, in order to account for the exothermic chemical reaction between the CO₂ and the sodium.     

Model for Cyclic Fatigue of Quasi-Plastic Ceramics in Contact with Spheres

A model of contact damage accumulation from cyclic loading with spheres and ensuing strength degradation in relatively tough, heterogeneous ceramics is developed. The damage takes the form of a quasi-plastic zone beneath the contact, consisting of an array of closed frictional shear faults with attendant "wing" microcracks at their ends. Contact fatigue takes place by attrition of the frictional resistance at the sliding fault interfaces, in accordance with an empirical degradation law, allowing the microcracks to extend. At large numbers of cycles or loads the microcracks coalesce, ultimately into radial cracks. Fracture mechanics relations for the strength degradation as a function of number of cycles and contact load are derived. Indentation–strength data from two well-studied coarse-grain quasi-plastic ceramics, a micaceous glass-ceramic and a silicon nitride, are used to evaluate the model. Comparative tests in static and cyclic contact loading confirm a dominant mechanical component in the fatigue. At the same time, the presence of water is shown to enhance the fatigue. The model accounts for the broader trends in the strength degradation data, and paves the way for consideration of key variables in microstructural design for optimum fatigue resistance.     

Strain-induced stiffness-dependent structural changes and the associated failure mechanism in TBCs

Dynamic structural evolution of thermal barrier coatings (TBCs) during thermal exposure is highly important to account for the failure mechanism of TBCs. In this study, to begin with, the dynamic structural changes were investigated assisted with series of TBCs with different Young’s modulus in their top-coat. Results show that the strain-induced structural changes varied from dispersive microscopic inter-tearing to concentrated macroscopic vertical cracks, owing to the gradually stiffening top-coat. Subsequently, the associated failure mechanism of TBCs was revealed based on the stiffness-dependent structural changes. In a gradient thermal cyclic test, gradient stiffening degrees occurred across the top-coat. After certain thermal cycles, some macroscopic vertical cracks were generated in the much stiffer top zone of the top-coat. Consequently, partial delamination occurred when the large vertical cracks are connected with some interfacial cracks. This can be responsible for the failure mechanism of TBCs.     

Effect of Burnup on the Response of Stainless Steel-Qad Mixed-Oxide Fuels to Simulated Thermal Transients

Direct electrical heating experiments were performed on irradiated fuel to study the fuel and cladding response as a function of burnup during a slow thermal transient. The results indicated that the nature and extent of the fuel and cladding behavior depended on the quantity of fission gas retained in the fuel. Fission-gas-driven fuel ejection occurred as the molten cladding flowed down the stack exposing bare, radially unrestrained fuel. The fuel dispersion occurred in the absence of molten fuel and the amount of fuel ejected increased with increasing burnup. In tests with medium- and high-burnup fuel, the cladding ballooned prior to melting. In regions where the cladding remained intact, helium-filled cavities were observed on the cladding. The swelling due to the cavities increased with increasing burnup.     

Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model

Comprehensive understanding of failure mechanism of thermal barrier coatings (TBCs) is essential to develop the next generation advanced TBCs with longer lifetime. In this study, a novel numerical model coupling crack propagation and thermally grown oxide (TGO) growth is developed. The residual stresses induced in the top coat (TC) and in the TGO are calculated during thermal cycling. The stresses in the TC are used to calculate strain energy release rates (SERRs) for in-plane cracking above the valley of undulation. The overall dynamic failure process, including successive crack propagation, coalescence and spalling, is examined using extended finite element method (XFEM). The results show that the tensile stress in the TC increases continuously with an increase in an undulation amplitude. The SERRs for TC cracks accumulate with cycling, resulting in the propagation of crack toward the TC/TGO interface. The TGO cracks nucleate at the peak of the TGO/bond coat (BC) interface and propagate toward the flank region of the TC/TGO interface. Both TC cracks and TGO cracks successively propagate and finally linkup leading to coating spallation. The propagation and coalescence behavior of cracks predicted by this model are in accordance with the experiment observations. Therefore, this study proposed coating optimization methods towards advanced TBCs with prolonged thermal cyclic lifetime.     

Fabrication of CeO2 microspheres by internal gelation process using flow-focusing droplet generator

Sphere-pac fuel is an alternative nuclear fuel technology in which microspheres of two or more sizes are utilized to fill the cladding tube in place of the more conventional single-size fuel pellets. This provides leeway for adjusting the fuel pellet packing density and resulting cladding tube porosity. The current investigation makes use of a flow-focusing droplet generator made from stainless steel (S.S.) 316 L, with a channel internal diameter (I.D.) of 0.5, 0.8, 1, and 3 mm. These microspheres were supposed to be of actinide oxide but here, cerium has been chosen as a surrogate of plutonium. Detailed information about the flow-focusing droplet generator, internal gelation process, and sphere-pac fuel has been provided. The size and size distribution of ceria microspheres were investigated by varying the flow rates of the continuous and dispersed phase. The characterization of ceria microspheres has been conducted using techniques such as scanning electron microscope (SEM), X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), and Brunauer–Emmett–Teller (BET) analyses. The size of prepared monodisperse microspheres was controlled precisely (within ±2%) in the range of 498–2888 μm using four S.S. 316 L flow-focusing droplet generators with channel I.D. 0.5, 0.8, 1, and 3 mm, respectively, and the coefficient of variation of the size distribution was found to be less than 2%.     

The number of radial cracks in polymethylmethacrylate in explosion of a borehole charge

The data available on the number of main radial cracks formed in a solid coarsely fracturing medium(PMMA) upon weak and strong explosion of borehole charges are generalized. A dependence of the number of radial cracks on the loading rate of the borehole walls is obtained.Translated from Fizika Goreniya i Vzryva, Vol. 32, No. 2, pp. 143–145, March–April, 1996.     

Opportunities for Advanced Ceramics and Composites in the Nuclear Sector

Ceramics have played a crucial role in the development of fission based nuclear power, in glass & glass composite high level wasteforms, in composite cements to encapsulate intermediate level wastes (ILW) and also for oxide nuclear fuels based on UO₂ and PuO₂/UO₂ mixed oxides. They are also used as porous filters with the ability to absorb radionuclides (RN) from air and liquids and are playing a key role in the cleanup at Fukushima. Non‐oxides also find current fission applications including in graphite moderators and B₄C control rods. Ceramics will continue to be significant in the near‐term expansion of nuclear power via next‐step developments of fuels with inert matrices or based on thoria and in wasteforms using alternative composite cements or single or multiphase ceramics that can host Pu & other difficult RN. Longer term advances for Generation IV reactors, which will operate at higher temperatures & with higher fuel burn‐up require innovative fuel developments potentially via carbides & nitrides or composite fuel systems. Novel non‐thermal (cement‐like) and thermal techniques are currently being developed to treat some of the difficult legacy wastes. Non‐thermally derived wasteforms developed from geopolymers, composite cements, hydroceramics, and phosphate‐bonded ceramics and thermally derived wasteforms made by Hot Isostatic Pressing and fluidized bed steam reforming (FBSR) as well as vitrification techniques based on cold crucible melting (CCM), Joule‐heater in‐container melting and plasma melting (PM) are described. Future developments in waste treatment will be based on separation technologies for partitioning individual RN along with design & construction of RN‐containing ceramic targets for inducing transmutation reactions. Near demonstration actinide‐hosting ceramic wasteforms including multiphase Synroc systems are described. Opportunities also exist for ceramics in structural applications in Generation IV reactors such as composite SiC/SiC and C/C for fuel cladding and control rods and MAX phases and ultrahigh‐temperature ceramics (UHTCs) may find near core fuel coating and cladding applications. Uses of ceramics in fusion reactor systems will be both functional (ceramic superconductors in magnet systems for plasma control and in Li silicate breeder blankets in tokamaks) and structural including as sapphire diagnostic windows, graphite diverters, and plasma facing C and UHTCs. In all these cases, performance is limited by poorly understood radiation damage and interface controlled processes, which demands a combined modeling/experimental approach.