hand, a crack introduces a stress concentration modeled by Inglis's equation
: (For sharp cracks)where:
: is the loading stress,
: is half the length of the crack, and
: is the radius of curvature at the crack tip.

Putting these two equations together gets
:

Sharp cracks (small ) and large defects (large ) both lower the fracture strength of the material.

As of 2010 scientists discovered supersonic fracture, the phenomenon of crack propagation faster

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