The mechanical strength of a brittle material such as alumina depends on flaws (cracks) in the alumina surface. When a tensile stress is applied perpendicular to a deep, thin crack, the stress at the tip of the crack is greatly magnified above the applied stress. Thus, the surface condition of a brittle solid determines it strength. Surface flaws develop from abrasion, so the higher the abrasion resistance of a brittle solid the greater its practical strength. Strengths of alumina are given in Table 7.
If a solid has no surface or internal flaws (a “perfect” lattice), it should have very high strength. Various theoretical equations for this ultimate strength S of a brittle solid have been proposed; one is 
S2 = Eg/4b (4)
in which E is Young’s modulus, gis the surface energy, and b the lattice parameter. With E = 403 GPa (Table 4), g = 6.0 J m-2 [17, 18], and b = 0.177 nm, the ultimate strength S of alumina is about 58 GPa. This value is very high because of the high bond strength of alumina; for example, silicate glasses and quartz have theoretical strength values of 18 GPa or lower.
Practical strengths of brittle materials vary over wide ranges depending on their surface condition and history. For alumina, tensile or bonding strengths vary over a wide range of values because of different surface conditions, resulting in different flaw depths and flaw distributions. See  for a discussion of flaw distribution functions. The strength values for alumina are higher than for most other oxides; of course all of these strengths are far smaller than the theoretical strength, and depend strongly on the history and treatment of the samples. As the temperature increases, the strength of alumina decreases (as shown in Table 7) because of the increase of atomic vibrations and reduction in bond strength, just as for the reduction in elastic modulus with temperature. The strength of polycrystalline alumina depends strongly on its grain size, as shown by one set of strength values from . See also  for strengths of alumina machined and annealed at different temperatures. The strength also decreases as the alumina becomes more porous, as shown in Table 8; isolated pores increase the applied stress on their surfaces, and open porosity means much more surface for flaw development.
Table 7 Bend strengths of alumina in MPa
Theoretical strength 58,000 at 25°C Ref.
Single crystals (sapphire) 300-700 at 25°C 2
Polycrystals with similar treatment, 2
as a function of grain size in micrometers:
Table 8 Effect of porosity on the bend strength of polycrystalline alumina at 25°C from