Stress concentration and its effect in brittle material

Stress concentration is the sudden rise of local stress near a geometric discontinuity (hole, notch, keyway, fillet, sharp change of section, crack) in a loaded member. Away from the discontinuity the stress is uniform (nominal), but at the discontinuity the stress flow lines crowd together and the peak stress becomes much higher.

The severity is measured by the stress concentration factor:

$$K_t = \frac{\sigma_{max}}{\sigma_{nominal}}$$

$K_t$ depends only on the geometry (for example, for a small circular hole in a wide plate under tension $K_t \approx 3$). It is larger for sharper corners and smaller radii.

Effect in brittle material

• A brittle material (cast iron, glass, concrete, ceramics) has no yield region, so it cannot redistribute the high local stress by plastic flow.
• When $\sigma_{max}$ reaches the ultimate strength at the notch, a crack starts there and spreads suddenly across the section. The member fails at an average (nominal) stress much lower than its strength, with no warning and very little deformation.
• Hence the full theoretical $K_t$ must be used in the design of brittle members.
• In a ductile material (mild steel), the material at the notch yields locally, the peak stress is shared with neighbouring fibres, and the effect on static strength is small. For repeated (fatigue) loading, however, stress concentration is dangerous for both.

Reducing stress concentration

Provide generous fillet radii, avoid sudden changes of section, use gradual tapers, and drill relief holes at crack tips.