. The fracture toughness of polycrystalline alumina (Young’s modulus 306GPa) is about 4MPa m1/2 while the toughness of MgO partially stabilized zirconia (PSZ) (Young’s modulus 138GPa) is about 10MPa...

. The fracture toughness of polycrystalline alumina (Young’s modulus 306GPa) is about 4MPa m1/2 while the toughness of MgO partially stabilized zirconia (PSZ) (Young’s modulus 138GPa) is about 10MPa m1/2.

a. Estimate the fracture surface energy of (i) alumina and (ii) PSZ assuming these toughness values were obtained under conditions of plane stress.

b. Polycrystalline ceramics often have intergranular cracks in them due to thermal expansion mismatch. Their strength is therefore limited by these cracks whose size is on the order of the grain size. Calculate the maximum strength you would expect to observe in (i) alumina with a 20-mm-diameter grain size and (ii) PSZ with a 50-mm-diameter grain size. Model the cracks as internal circular cracks with the same size as the grains.