Question

Griffith theory is applicable for

• A. Perfect brittle materials
• B. All ductile materials
• C. Perfect ductile materials
• D. All materials

Hint:

Griffith theory is based on energy balance and is valid only for brittle materials with negligible plastic deformation.

Answer 1

The Correct Option is A

Griffith's criterion for the fracture stress of a cracked plate is \[ \sigma_f = \sqrt{\frac{2E\gamma_s}{\pi a}} \] where \( \gamma_s \) is the surface energy per unit area and \( a \) is the half crack length.

1. Perfect brittle materials: here \( \gamma_s \) truly represents only the surface energy of the new crack faces, so the formula predicts the fracture stress accurately.
2. Ductile materials (all or perfect): a large plastic work term would need to be added inside the bracket to account for energy lost to plastic flow, so the pure Griffith formula above no longer applies as written.
3. All materials: since most materials need that extra plastic term, the formula cannot be applied universally.

So the pure Griffith energy balance is valid only for perfect brittle materials.

Answer 2

Griffith validated his theory experimentally using fine glass fibres, a nearly ideal brittle material, and the historical basis of the theory tells us a lot about where it does and doesn't apply.

1. Perfect brittle materials: Griffith's original experiments on glass fibres, and later work on ceramics, showed excellent agreement between predicted and measured fracture stress, precisely because these materials show negligible plastic deformation near a crack.
2. All ductile materials: metals such as mild steel or aluminium show a plastic zone at the crack tip that absorbs significant energy; Griffith's original glass-fibre-based theory does not account for this, so it fails to predict ductile fracture stresses without modification (later corrected by Irwin and Orowan).
3. Perfect ductile materials: such a material would yield extensively rather than crack in the brittle sense Griffith modeled, so his glass-fibre-based theory has no direct analogue here.
4. All materials: given that ductile behaviour breaks the core assumption, the theory cannot be extended to cover every material without modification.

The experimental basis of Griffith's work confirms it is restricted to perfectly brittle materials.

Therefore, the correct answer is Perfect brittle materials.