The Griffith Criteria for Crack Extension in Viscoelasticity

From the above analysis we may conclude that, provided the crack is growing whenever it is open, p x, t) is non-negative. When the crack is open, p x, t) = pit) wherep t) is positive. As soon as p t) becomes negative, the crack closes entirely. Then pix,t) represents the non-negative pressure acting across the crack face. 

These results are due to Graham and Sabin (1978), who derive them by means of a more explicit method. 

It is interesting to note the fundamental qualitative differences between extending and stationary cracks. These are traceable to the fact that the dominant singular term for an extending crack comes from the delta function part of the hereditary integral, while this is not so for a stationary crack. Note that this instantaneous property of singular terms, in the case of extending cracks, leads to properties similar to those found in the elastic case, while stationary viscoelastic cracks behave quite differently to the elastic case. 

In the next section, dealing with propagation criteria, the interesting similarity between elastic and extending viscoelastic cracks is further manifested. 

In order to discuss the linear viscoelastic case, we adopt a more formal approach, which incidentally also applies to the elastic case in the limit, and illustrates Goodier s result. Following Golden and Graham (1987c), we write down an isothermal energy balance relation of the form 

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