Estimate the theoretical fracture strength of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.15 mm and that has a tip radius of curvature of 0.002 mm when a stress of 1370 MPa is applied.

The theoretical fracture strength of the brittle material is 11864.5 MPa

Explanation:

Fracture strength is the ability of a material to withstand fracture. It is also known as the breaking stress, it is the stress at which the material fails as a result of fracture. It usually determined from the stress-strain curve after performing a tensile test.

Given that:

Length (L) = 0.15 mm = 0.15 × 10⁻³ m

radius of curvature (r) = 0.002 mm = 0.002 × 10⁻³ m

Stress (s₀) = 1370 MPa = 1370 × 10⁶ Pa

theoretical fracture strength (s) = ?

The theoretical fracture strength is given as:

Substituting values:

s = 11864.5 MPa

The theoretical fracture strength of the brittle material is 11864.5 MPa

Theoretical fracture strength(σ) = 11,865 Mpa

Explanation:

We are given;

L = 0.15 mm

r = 0.002 mm

σ_o = 1370 MPa

Fracture strength, also known as breaking strength, is the stress at which a specimen fails via fracture. This is usually determined for a given specimen by a tensile test, which charts the stress–strain curve. The final recorded point is the fracture strength. However, it can be calculated theoretically as follows;

σ = σ_o√(L/r)

σ = 1370√(0.15/0.002) ≈ 11,865 Mpa

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