Short note: Griffith theory

Griffith theory (A. A. Griffith, 1920) explains why the actual fracture strength of brittle materials is far below the theoretical strength. It states that every real material contains microscopic cracks or flaws, which magnify the local stress at their tips.

Principle

A crack extends only if the elastic strain energy released by its growth is at least equal to the surface energy needed to create the new crack surfaces. For a thin plate with an internal crack of length $2a$, the critical (fracture) stress is

$$\sigma_c = \sqrt{\frac{2E\gamma}{\pi a}}$$

where $E$ is the modulus of elasticity, $\gamma$ is the surface energy per unit area and $a$ is half crack length.

Conclusions

• Larger flaws give lower fracture strength.
• Brittle materials (glass, ceramics, concrete) fail by crack propagation under tension, and are much stronger in compression, where cracks close.
• For ductile materials, plastic work at the crack tip also adds to the energy needed (Irwin-Orowan modification).

The theory is the base of fracture mechanics.