​Compressive strength of sapphire crystals

Compressive strength of sapphire crystals

Compression strength is 2 GPa (3•105 psi).

 psi).Young's modulus (Elasticity modulus) is the value opposite to flexibility: E=1/S33. For different crystallographic directions, this value is E[0001]=1 /S33, E[11 2 0]=1/S11. Listed below are Young's modulus (GPa)[1] tested by various authors:

The values of Young's modulus are temperature dependent: E[0001]=435 GPa (63•106 psi) temperature 323 K, E[0001]=386 GPa (56•106psi) temperature 1,273 K. Now, the longest use The calculated Young's modulus value is 345

GPa(50•106 psi).( 1 megapascal (MPa)=145 pounds/inch 2(psi)=10.2 kg/cm 2(kg/cm2)

Compression modulus is 250 GPa (5-10•104 psi).

Shear modulus (Rigidity modulus) is 145 GPa (21•106psi) -175 GPa (26•106psi).

Rupture modulus is 350-690 MPa (5-10•104psi).

Weibull modulus is the probability of brittle fracture of a material under pressure beyond its ultimate strength σS. If P0 is the probability of material failure per unit volume, then the failure probability for a sample with volume V can be obtained by the following formula

(1-P0)V = 1-P (2.6)

 The expression for 1-P0 is the probability of existence of a material per unit volume at pressure σS; 1-P is the probability of existence of the entire sample with volume V at the same pressure.

 Webster's theory describes the cumulative failure P as a function of applied tension σ and the probability of tension-induced rupture at a strength-limited surface crack. Depending on the surface state (even the end state) and the history of the sample, the Webster modulus may be in the range of 5.38 ( growth) and 6.35 (annealing) [71] to 6.07 [72] and even 9.79 [73] based on chemical-mechanical polishing.

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