Recent research conducted under NASA LaRC's Creativity and
Innovation Program has led to the development of an initial
approach for a hierarchical fracture mechanics. This methodology
unites failure mechanisms occurring at different length scales and
provides a framework for a physics-based theory of fracture. At the
nanoscale, parametric molecular dynamic simulations are used to
compute the energy associated with atomic level failure mechanisms.
This information is used in a mesoscale percolation model of defect
coalescence to obtain statistics of fracture paths and energies
through Monte Carlo simulations. The mathematical structure of
predicted crack paths is described using concepts of fractal
geometry. The non-integer fractal dimension relates geometric and
energy measures between meso- and macroscales. For illustration, a
fractal-based continuum strain energy release rate is derived for
inter-and transgranular fracture in polycrystalline metals.
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