This project will implement inelastic constitutive models that will yield the requisite stress-strain information necessary for graphite component design. Accurate knowledge of stress states (both elastic and inelastic) is required to assess how close a nuclear core component is to failure. Strain states are needed to assess deformations in order to ascertain serviceability issues relating to failure, e.g., whether too much shrinkage has taken place for the core to function properly. Failure probabilities, as opposed to safety factors, are required in order to capture the bariability in failure strength in tensile regimes. The current stress state is used to predict the probability of failure. Stochastic failure models will be developed that can accommodate possible material anisotropy. This work will also model material damage (i.e., degradation of mechanical properties) due to radiation exposure. The team will design tools for components fabricated from nuclear graphite. These tools must readily interact with finite element software--in particular, COMSOL, the software algorithm currently being utilized by the Idaho National Laboratory. For the eleastic response of graphite, the team will adopt anisotropic stress-strain relationships available in COMSO. Data from the literature will be utilized to characterize the appropriate elastic material constants.

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Modeling Stress Strain Relationships and Predicting Failure Probabilities For Graphite Core Components

Wider use of ceramic matrix composites (CMC) will require the development of advanced structural analysis technologies. The use of an interactive model to predict the time-independent reliability of a component subjected to multiaxial loads is discussed. The deterministic, three-parameter Willam-Warnke failure criterion serves as the theoretical basis for the reliability model. The strength parameters defining the model are assumed to be random variables, thereby transforming the deterministic failure criterion into a probabilistic criterion. The ability of the model to account for multiaxial stress states with the same unified theory is an improvement over existing models. The new model was coupled with a public-domain finite element program through an integrated design program. This allows a design engineer to predict the probability of failure of a component. A simple structural problem is analyzed using the new model, and the results are compared to existing models.

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Interactive Reliability Model for Whisker-toughened Ceramics

Confidence band estimations for distributions used in probabilistic design

Таблицы интегралов и другие математические формулы. (Tables of integrals and other mathematical data, 1961)

/pdf/a-probabilisitic-based-failure-model-for-components-5d4gp4c6vh.pdf

A probabilisitic based failure model for components fabricated from anisotropic graphite

Monte Carlo simulation techniques are used in conjunction with the pivotal quantities of the two parameter Weibull distribution (or three parameter Weibull distribution with prescribed threshold stress) to calculate confidence bands for the probability of failure of thin annular discs subjected to centrifugal loading. The theoretical predictions, assuming either volume or surface defects govern failure, are compared with experimental fracture data.

N R Cooper

Papers

Probability of failure calculations and confidence band estimates for an annular brittle disc fractured under centrifugal loading