Estimate the theoretical fracture strength (in MPa) of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped internal crack of length 0.25 mm that has a tip radius of curvature of 0.006 mm when a stress of 1060 MPa is applied. Group of answer choices (A) 16,760 MPa

(B) 8,380 MPa

(C) 132,500 MPa

(D) 364 MPa

Theoretical fracture strength is; σ_m = 13,685 MPa

None of the options are correct

Explanation:

We are given;

Nominal applied stress; σ_o = 1060 MPa

Length of surface crack; a = 0.25 mm

Tip radius of curvature; ρ_t = 0.006 mm

Now, the formula for the theoretical fracture strength which is the maximum stress at the crack tip is given as;

σ_m = 2σ_o[a/ρ_t]^ (½)

Plugging in the relevant values, we have;

σ_m = 2 (1060) [0.25/0.006]^ (½)

σ_m = 13,685 MPa