Symbol pi

The passage around this formula

The modern formalism replaces the energy balance with a field parameter. Near the tip of a crack, the elastic stress field has a characteristic inverse-square-root singularity whose amplitude is set by a single quantity, the stress intensity factor: $K = Y\,\sigma\sqrt{\pi a}$. Here $\sigma$ is the applied stress, a the crack size, and Y a dimensionless factor capturing geometry and loading. The claim embedded in this expression is a similitude claim: two cracked bodies of different shape and size, loaded differently, have the same crack-tip conditions if they have the same K . Fracture then occurs when K reaches a material-specific critical value, the plane-strain fracture toughness $K_{\mathrm{Ic}}$ .

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