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Figure 15. Linear dependency between Nmax and the number of cracked finite elements.

Figure 15. Linear dependency between Nmax and the number of cracked finite elements.

from which we can obtain the structure critical number of AE events Nmax. An energy parameter describing the damage level of the structure can be defined as the following ratio:

where Tae = fractal acoustic emission energy density; and Nmax is evaluated at the peak stress, ou. Eq. (5) predicts a volume effect on the maximum number of AE events for a specimen tested to failure.

The extent of structural damage can be worked out from the AE data recorded on a reference specimen (subscript r) obtained from the structure and tested to failure. Naturally, the fundamental assumption is that the damage level observed in the reference specimen is proportional to the level reached in the entire structure before monitoring is started.

N being the number of AE events currently recorded by the monitoring apparatus.

Now, we can assume that the number of AE is also proportional to the number of Gauss points subjected to cracking in the finite element model. Therefore, the number of AE and the number of cracks in the finite element model should show the same exponent with respect to the considered volume. In fact, this is what we can substantially observe from Figure 14.

The linear relation between the number of cracked elements (or Gauss points) in the finite element model, and the AE is put into evidence also in Figure 15, where the two quantities are plotted in a direct comparison.

In fact, the calculated coefficient of linear regression is equal to 0.93.

Finally, let us observe that the slope of this linear relation depends on the discretization of the finite element model. On the other hand, refining the mesh (e.g. dividing by two the linear size of each element) does not change sensibly the exponent in Figure 14.

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