If the surface energy of a magnesium oxide - nickel oxide (MgO-NiO) solid solution is 1.05 J/m2 and its elastic modulus is 198 GPa, what is the maximum length of an internal elliptical flaw, in mm, if the ceramic part must survive an applied tensile stress of 27 MPa normal to this elliptical flaw

The maximum length is 3.897*10^-5 mm

Explanation:

Extension = surface energy/elastic modulus

surface energy = 1.05 J/m^2

elastic modulus = 198 GPa = 198*10^9 Pa

Extension = 1.05/198*10^9 = 5.3*10^-12 m

Strain = stress/elastic modulus = 27*10^6/198*10^9 = 1.36*10^-4

Length = extension/strain = 5.3*10^-12/1.36*10^-4 = 3.897*10^-8 m = 3.897*10^-8 * 1000 = 3.897*10^-5 mm