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23 April, 07:58

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

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  1. 23 April, 08:15
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    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
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