Particle model craze formation

The so-called structure particle model explains craze formation and crack formation by microcracks along the interface of structural units ( particles ) of the morphology. The formation of microcracks is determined by the interface energy between these particles. Microcracks develop if a critical deformation limit, which depends on the interface energy, is exceeded. This model primarily provides a quantitative description of the effect of liquid or gaseous media on stress crack formation. 

Some of the models used to rationalize the toughening effect associated with plastic deformation of the matrix and second-phase particle at the crack tip are represented in Fig. 1. This deformation is achieved through crack pinning and broadening, particle bridging and cavitation, crack path deflection, shear band formation and crazing or microcracking for stress relaxation at a crack tip. 

In the first attemped quantitative model proposed by Lazzeri and Bucknall [52], it was predicted that only particles >0.25 p diameter were capable of cavitating imder a given set of conditions, lending some support to the concept that there is an optimum rubber particle size for the toughening. They also showed that cavitated rabber particles can initiate crazes and dilatational bands in the matrix. They propose that the sudden conversion of rubber particles into the mechanical equivalent of voids (by cavitation) has the indirect effect of accelerating the volume expansion in the matrix through the formation of dilatational shear bands. 

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