Fracture mechanics and interactions across cracks

Fracture mechanics refers to the analysis of the fracture of materials by the rapid growth of pre-existing flaws or cracks. Such rapid (or even catastrophic) crack growth may occur when a system acquires sufficient stored energy that, during crack extension, the system releases more energy than it absorbs. Fracture of this type (often referred to as fast fracture) can be predicted in terms of an energy 

A crack will propagate when dU/ck 0, where dc is the increase in the crack length. Using this theory, one can derive the Griffith equation, which gives the theoretical fracture strength for brittle, linearly elastic materials  

If we define a parameter Cc = 2ys = critical strain energy release rate, then we may write the criterion for catastrophic crack growth as 

That is, fracture will occur when, in a stressed material, the crack reaches a critical size (or when in a material containing a crack of some given size, the stress reaches a critical value). 

Alternatively, we may define a parameter Kc = a.JWc= critical stress intensity factor. 

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