Nano-samples give higher brittle strength by the Griffith energy principle

Area of Science:

• Materials Science
• Solid Mechanics
• Fracture Mechanics

Background:

• Traditional concepts of brittle material strength are challenged by observed size effects.
• Griffith's theory, focusing on energy, is a key framework for understanding fracture.
• Existing fracture mechanics theories struggle to explain certain experimental observations, like thermal shock resistance.

Purpose of the Study:

• To demonstrate the significant and varied size effects in brittle test samples.
• To illustrate why the concept of 'strength of brittle materials' is often unsatisfactory.
• To reconcile experimental findings with fracture mechanics theory, particularly the Griffith energy criterion.

Main Methods:

• Analysis of crack equilibrium forces considering sample geometry, crack position, and force application.
• Examination of energy terms (surface, volume, potential) driving crack propagation.
• Experimental investigation of thermal shock in ceramic tubes to observe size effects.

Main Results:

• Brittle test samples show substantial size effects, with crack force depending on dimensions or being area-independent.
• The potential energy term significantly influences crack behavior, a factor overlooked by Griffith.
• Experimental data for thermal shock in ceramic tubes reveals an inverse cubic relationship between cracking force and diameter.

Conclusions:

• The Griffith energy criterion is experimentally validated for cracking, while Galilean stress criteria fail.
• The concept of 'strength of brittle materials' is untenable for many crack testing geometries due to size effects.
• Current fracture mechanics cannot fully explain the observed thermal shock resistance in fine ceramic tubes, highlighting the importance of energy-based approaches.