In: Mechanical Engineering
Compare how Griffith determined critical crack length, ac, with how the value of r*is determined in the solidification process.
Griffith proposed that when a brittle material is having microstructure cracks inside, then actual strength is less than theoretical value. A crack is propogated when elastic strain energy is at least equal to energy required for formation of new surfaces.
Solidification starts by nucleation. Here nucleation starts when the sum of total free energy( volume and surface( with respect to radius is zero. Please see figure attached for details.