Asteel having a yield strength of 1,450 mn/m² and a fracture toughness of 55 mn/m3/2 is placed into service. quality control indicates that brittle inclusions, which fractured during the manufacturing of the steel, are present in the steel and that the maximum dimension of these inclusions is about 20 microns. this dimension can be considered to be the length of an existing interior crack in the steel. a thick disk of this plate is placed into service. a) show that the steel will yield plastically before cracks associated with the inclusions propagate through the material. take the value for parameter & = 1.05. b) what size would the inclusions have to be in order to have the material fracture before it yielded plastically? [ref: mechanical behavior of materials, courtney, 2000) hint: stress required to propagate a crack through is estimated by og = where c is the crack length (or 2c for an interior crack length), a is a constant on the order of unity and dependent on the crack geometry, k is the material property called the fracture toughness. f/2