Marie-Christine Baietto

Modelling of Corrosion Induced Stresses during Zircaloy-4 Oxidation in Air

In the frame of its research work on nuclear fuel safety, the French “Institut de Radioprotection et de Sûreté Nucléaire” (IRSN) has highlighted the importance of cladding tube oxidation on its thermomechanical behavior. The occurrence of radial cracking and spallation has been observed as the main mechanisms for the zirconia layer degradation during transient experiments. A study of these two mechanisms has been jointly launched by IRSN and Areva-NP. Thus laboratory air oxidations of fully recrystallized or stress-relieved low-tin Zircaloy-4 cladding tubes have been performed. Representative oxide layer thicknesses varying from 10 to 100 0m have been obtained. SEM micrographs of the obtained oxidised samples show that short circumferential cracks are periodically distributed in the oxide thickness. For specimens with oxide film thickness greater than 30 0m, radial cracks are initiated from the outer surface of the oxide layer and propagated radially. Veins characterised by the lack of circumferentially orientated crack are evidenced. All these phenomena are mainly linked to high compressive stress levels in the zirconia layer. A model describing the stress evolution in the oxide and in the cladding has been developed. This model takes into account the influence of elasticity, cladding creep, oxide growth and thermal expansion. Deflection tests data [15] are used to calibrate the oxide growth modelling. The model enables the evaluation of strain or stress profile in the oxide layer and in the base metal. Numerical results are in good agreement with a large set of axial and circumferential strains measurements. Further a better understanding of cracking mechanisms is achieved considering the good agreement between experimental and numerical analysis.

An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

Abstract: A 3D graded coating/substrate model based on multigrid techniques within a finite difference frame work is presented. Localized refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for (i) a homogeneous material and (ii) a graded material. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < E-c/E-s < 10) of the coating on the contact parameters (P-h, a). Three-dimensional examples are then presented to illustrate the efficiency and the large range of possibilities of the model. The influence of different gradations of Youngs modulus, constant, linear and sinusoidal, through the coating thickness on the maximum tensile stress is analyzed, showing that the sinusoidal gradation best accommodates the property mismatch of two successive layers. A final case is designed to show that full 3D spatial property variations can be accounted for. Two spherical inclusions of different size made from elastic solids with Youngs modulus and Poissons ratio are embedded within an elastically mismatched finite domain and the stress field is computed.

Modeling of inter- and transgranular stress corrosion crack propagation in polycrystalline material by using phase field method

Abstract A coupled multiphysics phase field framework is proposed to model anodic dissolution induced by stress corrosion fracture growth at microstructual level. The effects of electrochemical-mechanical processes (including crystal anisotropy) are all taken into account. This new model is based upon: (i) an anisotropic phase transformation model based on a variational formulation to describe material dissolution along preferential directions; (ii) an efficient description of grain boundaries as a smeared cohesive zone; (iii) an explicit approximation to model the different electrochemical behaviors between grain boundary and grain interior. Both intergranular and transgranular stress corrosion cracking is simulated in an efficient manner. The abilities of the proposed model are illustrated through several numerical examples involving a full prediction of complex crack network growth induced by stress corrosion cracking within 2D polycrystaline models.

Coupled Experimental/Numerical Approach to Determine the Creep Behavior of Zr-4 Cladding Under LOCA Condition

The thermo-mechanical behavior of Zircaloy-4 fuel rods under Loss-Of-Coolant Accident (LOCA) conditions is investigated. A custom experimental setup is dedicated to the high-temperature creep ballooning study of 90mm long cladding samples. Creep tests were performed under an inert environment (argon), for temperatures from 750 to 850°C and internal pressures ranging from 1 to 5 MPa. As the high-temperature creep of metals is strongly influenced by the temperature, the setup allow for a heterogeneous thermal distribution along the specimen. A unique test provides a rich database about the steady-state creep of the alloy. A first campaign is dedicated to bare Stress Relieved Annealed Zr-4.

Friction of Rough Soft Matter Contacts: Local Investigations Through Image Correlation Technique

The friction induced in contacts is a key feature concerning functionality of mechanisms, reliability of systems, energy consumption… Friction on soft matter occurs in many applications (tire/road contacts, touch-sensitive exploration, micro-manipulation of biological items…) as well as in nature. The latter offers various examples of how a topographic surface pattern may control friction. The result is a complex combination of phenomena: adhesion, elastic ratio of bodies in contact, viscous flow, plasticity occurrence, and topography interaction. The role of this latter phenomenon essentially lies in the splitting of the contact area between the two contacting materials and plays an important role on friction response when coupled with adhesion.© 2014 ASME

A comparative study of multiaxial high-cycle fatigue criteria applied to rough rolling contacts

Rolling contacts are a major topic in scientific studies as they are highly exposed to fatigue damage. Indeed, the applied loads generate periodic stresses and the surface roughness generates stress concentrations close to the surface. The combination of these two phenomena facilitates fatigue damage. Many multi-axial criteria have been created to explain and predict this type of damage. Furthermore, a large number of papers compare the different fatigue criteria based on combined bending and torsion tests [1,2]. However, these studies are not representative of the stress gradients found in rough contacts, close to the surface. Hence the current work, which proposes a comparative study of several fatigue criteria with a combined experimental and numerical approach.Copyright

Three-Dimensional Voronoi and Multigrid Model for Microstructure Contact Problem

The prediction of both the tribological behaviour and mechanical analysis of the wear resistance are still of great research interest in order to improve the lifetime of material surfaces. This concerns both bulk and coated materials although coating processes have been often developed in order to protect substrates from tribological solicitations. The wear resistance of coated materials has been the subject of many studies which show that it is possible to protect and improve significantly the durability of substrates. A straightforward discretisation of the multi-scale problem of graded coatings on substrates exceed the memory and CPU capacity of current (and next generation) computers. The authors have proposed an efficient numerical model that can handle this multi-scale problem: using billion points and locally refined grids.Copyright

Normal and Tangential Contact Between Anisotropic Materials With an Anisotropic Coating

A contact model using semi analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics, with strong potential for inelastic, inhomogeneous or anisotropic problems. Recent developments aim to quantify displacements and stresses of an anisotropic half space with an anisotropic coating which is in contact with a rigid sphere. The influence of symmetry axes on the contact problem solution will be more specifically analyzed.Copyright

Contact Analyses for Anisotropic Half Space With an Anisotropic Coating

For most composite and mono-crystal materials their compositions or the elaboration and manufacturing processes imply that it exists one or two main directions or even a general anisotropy. Moreover, coatings are often used to prevent or control wear. Coatings do not have, generally, the same properties as the substrate and may have various thicknesses. The influence of the anisotropy orientations (in the coating and in the substrate) have to be taken into account to better predict the distribution of the contact pressure and the subsurface stress-field in order to optimize the service life of industrial components. A contact model using semi analytical methods, relying on elementary analytical solutions, has been developed. It is based on numerical techniques adapted to contact mechanics. Recent developments aim to quantify displacements and stresses of a layered anisotropic elastic half space which is in contact with a rigid sphere. The influence of material properties and layer thickness on the contact problem solution will be more specifically analyzed.© 2012 ASME

A 3D Multigrid Solver for the Elastic Contact Problem: Application to Graded Materials

The actual contact between solid surfaces is generally rough and time dependent. The stresses induced by the rough contact can only be correctly described using a detailed 3D model. Even finer details are required in the case of surface coatings. Consequently, the rough coated contact problem is strongly multi-scale: the characteristic dimensions of the contact, the coating and the roughness range from the millimeter to the nanometer. A straightforward discretisation of this multi-scale problem would exceed the memory and CPU capacity of current (and next generation) computers. This paper proposes an efficient numerical model that can handle this multi-scale problem: using 109 points and locally refined grids. The proposed model is based on multigrid techniques within a finite difference frame work. Localised refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for simple cases. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < Ec /Es < 10) of the coating on the contact parameters (Ph , a). A linear graded coating, used as a solution to avoid interfacial problems, is then compared to a coating with constant properties. A quantitative analysis of the evolution of the maximum tensile stress with depth is conducted in both cases.Copyright