Fracture toughness

Remarks

Example: if a steel has $K_{Ic} = 50 \, \mathrm{MPa}\sqrt{\mathrm{m}}$, a through crack of length $2a = 2 \, \mathrm{cm}$ in a wide plate grows at the remote stress $\sigma = K_{Ic} / \sqrt{\pi a} = 50 / \sqrt{0.01 \pi} \approx 282 \, \mathrm{MPa}$. Non-example: the tensile strength of a material is not a fracture toughness. It is a critical stress measured on an uncracked specimen, and it does not involve a crack. For a linear elastic isotropic material with Young's modulus $E$ and Poisson's ratio $\nu$, the critical energy release rate is $G_{Ic} = K_{Ic}^2 (1 - \nu^2) / E$. Thin specimens, which are closer to plane stress, show a larger apparent toughness, which is why the plane-strain value is the reference.