Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 1 - Theory

Statically admissible stress distributions are necessary to evaluate lower bound limit loads. Over the last three decades, several methods have been postulated to obtain these distributions using iterative elastic finite element analyses. Some of the pioneering techniques are the reduced modulus, r-node, elastic compensation, and linear matching methods, to mention a few. A new method, called the Bounded Elastic Moduli Multiplier Technique (BEMMT), is proposed and the theoretical underpinnings thereof are explained in this paper. BEMMT demonstrates greater robustness, more generality, and better stress distributions, consistently leading to lower-bound limit loads that are closer to elastoplastic finite element analysis estimates. BEMMT also questions the validity of the prevailing power law based stationary stress distributions. An accompanying research offers several case studies to validate this claim.

Mechanical Degradation Behavior of Single Crystal LiNixMnyCozO2 Cathode in Li-ion Battery by Indentation Analysis

LiNixMnyCozO2 (NMC) is among the most promising cathode materials for commercial Li-ion batteries due to its high electrochemical performance. However, NMC composite cathode is still plagued with limited cyclic performance, which is influenced by its structural stability during the cycling process. The cathode, which comprises of the active material, polymeric binder, and porous conductive matrix, often exhibits large structural variation during the electrochemical cycling process. This inevitably increases the challenge of measuring the mechanical properties of the material. Even though single crystal NMC possesses better stability as compared to the polycrystalline NMC, the electrochemical performance degradation of single crystal NMC cathode remains relatively unexplored. Different sample preparation methods are compared systematically in accordance to the previous report, and a new method of sample preparation is proposed. Nanoindentation instrument is used to measure the elastic modulus and hardness of the single crystal NMC particles. The measured elastic modulus and hardness of NMC particles, under different electrochemical environments, are dependent on a large number of nanoindentation experiments and statistical analysis of the result obtained from the carefully prepared samples. The sample preparation method is the key factor that can significantly influence the nanoindentation experiment results of the NMC particles. This work shows that the mechanical properties of the single crystal NMC particles degrade significantly with number of electrochemical cycles. The decreasing elastic modulus with the number of electrochemical cycles can be fitted using a two-parameter logarithm model.

Failure Criteria for Brittle Notched Specimens

Recently, new failure criteria were proposed for brittle materials to predict their failure loads regardless of the shapes of a notch or a crack in the material. This paper is to further evaluate the failure criteria for different shapes of notches and different materials. A circular hole, elliptical hole or crack-like slit with a different angle with respect to the loading direction was considered. Double circular holes were also studied. The materials studied were an isotropic material like polymethyl methacrylate (PMMA) as well as laminated carbon fiber composites. Both cross-ply and quasi-isotropic layup orientations were examined. The lamination theory was used for the composite materials so that they can be modelled as an anisotropic and homogeneous material. The test results were compared to the theoretical predictions using the finite element analysis with 2-D plane stress models. Both theoretical failure stresses agreed well with the experimental data for the materials and notch geometries studied herein.

Development of a Simplified PWR Fuel Assembly Nonlinear Model

This paper proposes a computation technique to develop a simplified nonlinear model for a typical nuclear fuel assembly. Because more than a hundred fuel assemblies are packed in the reactor, simplistic model generation is critical to evaluate the motion during an anticipated event such as earthquake. Two straight beams are introduced to simplify the fuel assembly, and the beam properties are moderately defined to represent the skeleton structure and a bundle of slender fuel rods. Because nonlinearity is caused by the interaction between the rods and the spacer grids in the skeleton structure, the two beams are connected with multilinear joints that characterize the mechanical interaction between them. An equation of motion for the model is provided, and the degree of the freedom of the model can be reduced by using a few major modes of the beams. Significant mechanical parameters must be defined reasonably, so a method is proposed to identify unknown parameters through a deterministic calculation and an optimization process. All the information, including the identified parameters, are utilized to develop a nonlinear finite element model with a commercial code. The performance of the model is compared with the test results.

Modeling and Simulation of the Engraving Process in Different Life Stages of Small Caliber Guns

Effects of erosion phenomenon on the performance of a given gun barrel have been analyzed throughout numerical and experimental studies. Mainly, qualitative observations were performed. Theoretical relations between the evolution of the inner barrel profile and the provided interior ballistics are limited. This paper focuses on the development of a numerical model to predict the engraving resistance evolution in terms of the inner barrel profile in the different weapon's life stages. Four test barrels "12.7x99mm NATO" with different chamber volumes were considered. First, a Coordinate Measuring Machine (CMM) with a contact scanning probe was used to measure the inner dimension of the guns. Second, piezoelectric sensors with a special doppler radar were considered to measure the (i) pressure and (ii) the bullet velocity in the test weapons. Finally, based on the obtained experimental results, a Finite Element (FE) analysis using the commercial software LS-DYNA was developed and validated. The obtained numerical results were used as insights to quantify the relationship between the engraving resistance and the chamber volume of small caliber guns.

Allowable Cracks Related to Penetration for Part-Through Cracks in Pipes Subjected to Bending Stresses

Fully plastic collapse stresses for circumferentially part-through cracked pipes subjected to bending stresses are estimated by Limit Load Criteria provided by the ASME Code Section XI. Allowable crack depths were determined by using the Limit Load Criteria and that are tabulated in the ASME Code Section XI for different plant service level conditions. On the other hand, crack penetration bending stresses for part-through cracked pipes were estimated by using the Local Approach of Limit Load Criteria. By using these Criteria, the study presented in this paper obtained allowable crack depths at penetration for circumferentially part-through cracked pipes. Comparing the allowable crack depths obtained by both methods for each service level, it is evident that the allowable crack depths at penetration calculated by the Local Approach of Limit Load Criteria are almost always smaller than those at fully plastic collapse stresses calculated by the Limit Load Criteria. It was found that the allowable crack depths provided by the ASME Code Section XI are less conservative for crack penetrations.

Large Scale Modelling of Damage and Failure of Nuclear Graphite Moderated Reactor

The UK Advanced Gas-Cooled reactors (AGRs) have cores made of graphite bricks with dual functions: as structural elements of the core, providing space for and separating fuel and control rods; and as moderator of the nuclear reaction. Nuclear graphite is a quasi-brittle material, where the dominant mechanism for failure is cracking. While cracking of isolated bricks is expected due to operation-induced changes in graphite microstructure and stress fields, these could be tolerated as far as the overall structural function of the core is maintained. Assessment of the whole core behaviour has been previously done with whole scale models where bricks have been considered as rigid body elements connected by elastic-brittle springs. This approach does not allow for the realistic assessment of the stresses in the bricks and associated brick cracking. Reported here are results from an ongoing project, which addresses this shortcoming. The proposed model uses deformable bricks with appropriate interactions, allowing for physically realistic whole core analysis. The results are focused on the damage that a graphite moderated reactor develops during a life cycle, how this affects the behaviour of the whole core, and how changes in bricks' behaviour impacts the core integrity. The proposed methodology is a major step towards high-fidelity assessment of AGRs' fitness for service, required for supporting continuous safe operation and life-extension decisions.

Buckling Behavior of Thick Porous FGM Toroidal Shell Segments Under External Pressure and Elevated Temperature Including Tangential Edge Restraint

Owing to mathematical and geometrical complexities, there is an evident lack of stability analyses of thick closed shell structures with porosity. The present work aims to analyze the effects of porosities, elasticity of edge constraint and surrounding elastic media on the buckling resistance capacity of thick functionally graded material (FGM) toroidal shell segments subjected to external pressure, elevated temperature and the combined action of these loads. The volume fractions of constituents are varied across the thickness according to power law functions and effective properties of the FGM are determined using a modified rule of mixture. The porosities exist in the FGM through even and uneven distributions. Governing equations are based on a higher order shear deformation theory taking into account interactive pressure from surrounding elastic media. These equations are analytically solved and closed-form expressions of buckling loads are derived adopting the two-term form of deflection along with Galerkin method. Parametric studies indicate that the porosities have beneficial and deteriorative influences on the buckling resistance capacity of thermally loaded and pressure loaded porous FGM toroidal shell segments, respectively. Furthermore, tangential constraints of edges lower the buckling resistance capacity of the shells, especially at elevated temperatures.

Bounded Elastic Moduli Multiplier Technique for Limit Loads: Part 2 - Case Studies

An accompanying paper provides the theoretical underpinnings of a new method to determine statically admissible stress distributions in a structure, called Bounded elastic moduli multiplier technique (BEMMT). It has been shown that, for textbook cases such as thick cylinder, beam, etc., the proposed method offers statically admissible stress distributions better than the power law and closer to elastic-plastic solutions. This paper offers several examples to demonstrate the robustness of this method. Upper and lower bound limit loads are calculated using iterative elastic analyses using both power law and BEMMT. These results are compared with the ones obtained from elastic-plastic FEA. Consistently BEMMT has outperformed power law when it comes to estimating lower bound limit loads.

A Method for Monitoring Vibrational Fatigue of Structure and Components

A vibration fatigue monitoring system has been developed by Framatome to assess, in real time, the evolution of industrial structures, systems and components lifetime expectancy. Its originality comes from the fact that only one or a few acceleration measurements are necessary to re-construct the complete stress history in the whole structure, including on welds or bolted connections that could not have been directly instrumented. From this stress history, a fatigue analysis with a rainflow counting algorithm is conducted and the cumulative usage factor of each weld or bolt is determined. The remaining life duration is then estimated. The method has been numerically and experimentally validated in that sense that the reconstructed stress histories were successfully compared to direct stress calculations and measurements. The system was then installed on five industrial structures submitted to transient dynamic excitations. It is expected that it will soon find further applications notably in monitoring vibrations induced during power plants transients that may induce some temporary resonance of piping equipment. Finally, the vibration monitoring system can also be combined with a thermal fatigue monitoring system, many of which are already deployed, at least on nuclear power plants, and the reconstructed stresses might include both thermal and mechanical effects. Installing such a fatigue monitoring on a set of sensitive systems and components could be a valuable brick in the present trend of building digital twins of power plants or other industrial structures.