Fracture toughness measures a material's resistance to crack extension, not its resistance to ordinary yielding.

In linear elasticity, Mode-I toughness is reported as $K_{Ic}$. The corresponding energy resistance is related approximately by

$$G_c=\frac{K_{Ic}^2}{E'},$$

where $E'=E$ in plane stress and $E'=E/(1-\nu^2)$ in plane strain.

Crack-tip plastic zone

Even when most of a component remains elastic, stresses very near a crack tip can exceed yield. A rough Mode-I plastic-zone scale is

$$r_p\sim \frac{1}{2\pi}\left(\frac{K_I}{\sigma_y}\right)^2$$

for plane stress; constraint reduces the zone under plane strain.

If this zone is small compared with crack size, ligament dimensions and specimen thickness, linear-elastic fracture mechanics can still be useful. Large-scale yielding requires elastic-plastic fracture parameters instead.

Toughening mechanisms

A material can resist fracture by consuming or shielding crack-driving energy. Mechanisms include plastic deformation near the tip, crack deflection, bridging behind the tip, transformation of material near the crack and microcracking. Ceramics, polymers, metals and composites achieve toughness through different combinations of these mechanisms.

A high yield strength therefore does not automatically imply high fracture toughness. Engineering material design must often balance strength, ductility and resistance to flaw growth.