Granule Strength and Breakage

Fracture toughness defines the stress distribution in the body just before fracture and is given by 

The process zone is a measure of the yield stress or plasticity of the material in comparison to its brittleness. Yielding within the process zone may take place either plastically or by diffuse microcracking, depending on the brittleness of the material. 

For plastic yielding, is also referred to as the plastic zone size. The critical strain energy release rate is the energy equivalent to fracture toughness, first proposed by Griffith (58). They are related by 

In the case of indentation fracture, one determines hardness H from the area of the residual plastic impression, and fracture toughness from the lengths of cracks propagating from the indent as a function of indentation load F (59). Hardness is a measure of the yield strength of the material. Toughness and hardness in the case of indentation are given by 

The process zone plays a large role in determining the mechanism of granule breakage (56), with mechanisms such as those previously presented in Table 1. 

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