Fracture mechanics
= Fracture mechanics
<Fracture mechanics> studies the initiation and growth of cracks under loading. It connects a defect's geometry with the local driving force for crack extension and the material's resistance. A component's average <stress> alone cannot describe the concentration of deformation near a crack tip.<Applied Mechanics of Solids by A. F. Bower>[Fracture-mechanics treatment and crack-tip fields]{ref}
In <linear elastic fracture mechanics>, a mode-I <stress intensity factor> often has the form $K_I=Y\sigma\sqrt{\pi a}$, where $a$ is a specified crack dimension and $Y$ accounts for geometry. Doubling $a$ increases $K_I$ by $\sqrt2$ at fixed nominal stress. Comparing the appropriate intensity with measured <fracture toughness> is meaningful only when the loading, geometry and small-scale yielding assumptions of the model apply.