An Si-O bond with a Young's modulus of 9*10¹⁰Nm^?1 have an elliptical crack of depth 7nm. The surface energy is 2.29 J. Estimate fracture stress for silica fiber.

Question

Quizplus · Accepted Answer

The fracture stress for a material with an elliptical crack can be estimated using the equation $\sigma_f = \sqrt{\frac{2E\gamma}{\pi a}}$, where $E$ is the Young's modulus, $\gamma$ is the surface energy, and $a$ is the crack depth. Substituting the given values ($E = 9 \times 10^{10} \, \text{Nm}^{-2}$, $\gamma = 2.29 \, \text{J}$, $a = 7 \, \text{nm}$), the calculation yields a fracture stress of approximately $4.32 \times 10^{19} \, \text{Nm}^{-2}$, which corresponds to choice A.

An Si-O Bond with a Young's Modulus of 9*1010Nm?1 Have an Elliptical

An Si-O Bond with a Young's Modulus of 9*10¹⁰Nm^?1 Have an Elliptical