A generalized reliability model was developed for use in the design
of structural components made from brittle, homogeneous anisotropic
materials such as single crystals. The model is based on the
Weibull distribution and incorporates a variable strength
distribution and any equivalent stress failure criteria. In
addition to the reliability model, an energy based failure
criterion for elastically anisotropic materials was formulated. The
model is different from typical Weibull-based models in that it
accounts for strength anisotropy arising from fracture toughness
anisotropy and thereby allows for strength and reliability
predictions of brittle, anisotropic single crystals subjected to
multiaxial stresses. The model is also applicable to elastically
isotropic materials exhibiting strength anisotropy due to an
anisotropic distribution of flaws. In order to develop and
experimentally verify the model, the uniaxial and biaxial strengths
of a single crystal nickel aluminide were measured. The uniaxial
strengths of the and crystal directions were measured in three and
four-point flexure. The biaxial strength was measured by subjecting
plates to a uniform pressure in a test apparatus that was developed
and experimentally verified. The biaxial strengths of the single
crystal plates were estimated by extending and verifying the
displacement solution for a circular, anisotropic plate to the case
of a variable radius and thickness. The best correlation between
the experimental strength data and the model predictions occurred
when an anisotropic stress analysis was combined with the normal
stress criterion and the strength parameters associated with the
crystal direction.
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