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Answer:
the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi
Explanation:
Given the data in the question;
Length of surface crack α = 0.25 mm
tip radius ρ[tex]_t[/tex] = 1.2 × 10⁻³ mm
applied stress σ₀ = 1200 MPa
the theoretical fracture strength of a brittle material = ?
To determine the the theoretical fracture strength or maximum stress at crack tip, we use the following formula;
σ[tex]_m[/tex] = 2σ₀[tex]([/tex] α / ρ[tex]_t[/tex] [tex])^{\frac{1}{2}[/tex]
where α is the Length of surface crack,
ρ[tex]_t[/tex] is the tip radius,
and σ₀ is the applied stress.
so we substitute
σ[tex]_m[/tex] = (2 × 1200 MPa)[tex]([/tex] 0.25 mm / ( 1.2 × 10⁻³ mm ) [tex])^{\frac{1}{2}[/tex]
σ[tex]_m[/tex] = 2400 MPa × [tex]([/tex] 208.3333 [tex])^{\frac{1}{2}[/tex]
σ[tex]_m[/tex] = 2400 MPa × 14.43375
σ[tex]_m[/tex] = 34641 MPa
σ[tex]_m[/tex] = ( 34641 × 145 )psi
σ[tex]_m[/tex] = 5.02 × 10⁶ psi
Therefore, the theoretical fracture strength of the brittle material is 5.02 × 10⁶ psi