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A PROBABILISITIC BASED FAILURE MODEL FOR COMPONENTS FABRICATED FROM ANISOTROPIC GRAPHITE
Xiao, Chengfeng

2014, Doctor of Engineering, Cleveland State University, Washkewicz College of Engineering.
The nuclear moderator for high temperature nuclear reactors are fabricated from graphite. During reactor operations graphite components are subjected to complex stress states arising from structural loads, thermal gradients, neutron irradiation damage, and seismic events. Graphite is a quasi-brittle material. Two aspects of nuclear grade graphite, i.e., material anisotropy and different behavior in tension and compression, are explicitly accounted for in this effort. Fracture mechanic methods are useful for metal alloys, but they are problematic for anisotropic materials with a microstructure that makes it difficult to identify a "critical" flaw. In fact cracking in a graphite core component does not necessarily result in the loss of integrity of a nuclear graphite core assembly. A phenomenological failure criterion that does not rely on flaw detection has been derived that accounts for the material behaviors mentioned. The probability of failure of components fabricated from graphite is governed by the scatter in strength. The design protocols being proposed by international code agencies recognize that design and analysis of reactor core components must be based upon probabilistic principles. The reliability models proposed herein for isotropic graphite and graphite that can be characterized as being transversely isotropic are another set of design tools for the next generation very high temperature reactors (VHTR) as well as molten salt reactors.

The work begins with a review of phenomenologically based deterministic failure criteria. A number of this genre of failure models are compared with recent multiaxial nuclear grade failure data. Aspects in each are shown to be lacking. The basic behavior of different failure strengths in tension and compression is exhibited by failure models derived for concrete, but attempts to extend these concrete models to anisotropy were unsuccessful. The phenomenological models are directly dependent on stress invariants. A set of invariants, known as an integrity basis, was developed for a non-linear elastic constitutive model. This integrity basis allowed the non-linear constitutive model to exhibit different behavior in tension and compression and moreover, the integrity basis was amenable to being augmented and extended to anisotropic behavior. This integrity basis served as the starting point in developing both an isotropic reliability model and a reliability model for transversely isotropic materials.

At the heart of the reliability models is a failure function very similar in nature to the yield functions found in classic plasticity theory. The failure function is derived and presented in the context of a multiaxial stress space. States of stress inside the failure envelope denote safe operating states. States of stress on or outside the failure envelope denote failure. The phenomenological strength parameters associated with the failure function are treated as random variables. There is a wealth of failure data in the literature that supports this notion. The mathematical integration of a joint probability density function that is dependent on the random strength variables over the safe operating domain defined by the failure function provides a way to compute the reliability of a state of stress in a graphite core component fabricated from graphite. The evaluation of the integral providing the reliability associated with an operational stress state can only be carried out using a numerical method. Monte Carlo simulation with importance sampling was selected to make these calculations.

The derivation of the isotropic reliability model and the extension of the reliability model to anisotropy are provided in full detail. Model parameters are cast in terms of strength parameters that can (and have been) characterized by multiaxial failure tests. Comparisons of model predictions with failure data is made and a brief comparison is made to reliability predictions called for in the ASME Boiler and Pressure Vessel Code.. Future work is identified that would provide further verification and augmentation of the numerical methods used to evaluate model predictions.
Stephen Duffy, PhD (Committee Chair)
Lutful Khan, PhD (Committee Member)
Mehdi Jalalpour, PhD (Committee Member)
Miron Kaufman, PhD (Committee Member)
John Gyekenyesi, PhD (Committee Member)
Paul Bosela, PhD (Committee Member)
219 p.

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Xiao, C. (2014). A PROBABILISITIC BASED FAILURE MODEL FOR COMPONENTS FABRICATED FROM ANISOTROPIC GRAPHITE. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Xiao, Chengfeng. "A PROBABILISITIC BASED FAILURE MODEL FOR COMPONENTS FABRICATED FROM ANISOTROPIC GRAPHITE." Electronic Thesis or Dissertation. Cleveland State University, 2014. OhioLINK Electronic Theses and Dissertations Center. 23 Oct 2017.

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Xiao, Chengfeng "A PROBABILISITIC BASED FAILURE MODEL FOR COMPONENTS FABRICATED FROM ANISOTROPIC GRAPHITE." Electronic Thesis or Dissertation. Cleveland State University, 2014. https://etd.ohiolink.edu/

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