A uniform remote stress does not imply a uniform local stress when geometry contains holes, grooves, shoulders or sharp notches. Such features disturb the load path and create a stress concentration.

For an elastic component, define the theoretical stress-concentration factor

$$K_t=\frac{\sigma_{\max}}{\sigma_{\mathrm{nom}}}.$$

If a plate carrying nominal tensile stress $80,\mathrm{MPa}$ has $K_t=2.5$, the elastic peak is

$$\sigma_{\max}=2.5(80)=200,\mathrm{MPa}.$$

$K_t$ is primarily geometric: sharper notches and smaller fillet radii generally produce larger peaks. It is not itself a material strength or a safety factor.

The linear-elastic peak also cannot grow without limit in a ductile material. If the predicted local stress exceeds yield, a small plastic zone can redistribute stress, so an elastic $K_t$ no longer describes the full local field.

A crack is an extreme case. Treating a crack simply by an ever-larger $K_t$ becomes unhelpful because an ideal sharp crack has a singular elastic stress field. Fracture mechanics therefore characterizes cracks with stress-intensity or energy quantities instead of an ordinary finite peak stress.