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Equation 11 · Part 6 · Why Materials Fail: Fracture, Flaws and the Inspection Interval

=

K=Y σπa.K = Y\,\sigma\sqrt{\pi a}.
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

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 σπaK = Y\,\sigma\sqrt{\pi a}. Here σ\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 KIcK_{\mathrm{Ic}} .

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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