The tensile strength of brittle materials may be determined using a variation of Equation 8.1. Compute the critical crack tip radius for an Al2O3 specimen that experiences tensile fracture at an applied stress of 275 MPa (40,000 psi). Assume a critical surface crack length of 2 × 10−3 mm and a theoretical fracture strength of E/10, where E is the modulus of elasticity.

0.39 nM

Explanation:

The critical crack tip radius from the equation

attached below

for fracture to occur the бm will have to reach the fracture strength of material

i.e.  бm =  E/10

from equation 2 attached below

St = ( 400 * a * бo^2 ) / E^2 ------ 3

Given : a = 2*10^-3 mm , бo = 275 MPa, E = 393 * 10^3 MPa ( gotten from table)

Input given values into equation 3

St = 3.9 * 10^-7 ≈ 0.39 nM

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answer:

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