Fracture Energy definition

Kinloch and Hunston [163, 167] and others used the concept of time-temperature superpositioning, and separated the effect of changing the volume fraction and the properties of the matrix phase. No definite relationship between fracture energy and volume fraction of rubber was observed. The maximal value of volume fraction that can be achieved is about 0.2-0.3. Attempts to produce higher volume fraction result in phase inversion and loss of mechanical fracture properties. Though in most of the studies [168, 169], phase inversion was reported at a volume fraction >20%, in some recent studies inversion has been reported [170,171] at a very low volume fraction ( 2%) of rubber. 

Mathematical Analysis in the Mechanics of Fracture by James R. Rice, from Vol. II of Fracture edited by G. Sih, Academic Press, New York New York, 1968. Rice s account of fracture remains, in my opinion, one of the definitive statements of many of the key ideas in the subject. Section E on Energy Variations and Associated Methods is especially pertinent to our discussion on configurational forces and gives an in depth application of these ideas in the fracture context. 

There are two principal theories, or models, that attempt to describe what happens during brittle fracture, the Griffith fracture theory and the Irwin model. Both assume that fracture takes place through the presence of preexisting cracks or flaws in the polymer and are concerned with what happens near such a crack when a load is applied. Each leads to the definition of a fracture-toughness parameter and the two parameters are closely related to each other. The Griffith theory is concerned with the elastically stored energy near the crack, whereas the Irwin model is concerned with the distribution of stresses near the crack. Both theories apply strictly only for materials that are perfectly elastic for small strains and are therefore said to describe linear fracture mechanics. 

The fundamental principle on which fracture mechanics is based is that cracklike defects exist in all materials and that when critical conditions are attained at the crack tip, the crack will begin to propagate and the material will fracture. In linear elastic fracture mechanics (LEFM) the assumption is made that the material deforms elastically (i.e. is Hookean) at all times, thereby greatly simplifying definition of the elastic energy stored in the material prior to fracture. The most... 

Even if a crack is stationary, because the critical value, Gc, at which fracture takes place has not been attained, Eq. (10.13) is still a useful definition of the rate, G, at which energy would be available from the strained specimen. For a tensile strip with an edge cut, it yields... 

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