Keywords: damage identification, speckle shearography, modal response, high order spatial derivatives.

The need for the development of global methods for damage detection has been primarily motivated by applications in the automotive and aviation industries. The superior performance requirement of the materials has stimulated the increased use of composite materials. Despite its superior strength to weight ratio in relation to metals, composite structures are more sensitive to damage and the inspection techniques available today are not completely effective. This has motivated the search for new non-destructive inspection techniques applied to damage identification in composite structures. The analysis of perturbations in the modal curvature field is presented in the literature as the most promising technique. Also, the fourth order spatial derivative of mode shapes has been proposed. In practice, these derivatives can only be obtained by numerical differentiation of experimental displacements and rotations fields. Moreover, the high frequency experimental noise is amplified and propagated through the numerical differentiation process, becoming dominant relative to the signal. Also, the application of low-pass filters leads to suppression of important signal components required for the representation of local perturbations arising from the damage. Two strategies to minimise the effect of the noise propagation are proposed. The first is based on measurements of the modal rotation fields with high spatial resolution and low level noise, whereas the second involves minimising the number of mathematical operations before the differentiation. The damage localisation method is based on the identification of the perturbations in the second, third and fourth order derivatives of the modal displacement fields. The speckle shearography and stroboscopic illumination with phase-shifting are used for non-contact and full-field measurements of the phase maps of the modal rotation fields. This process allows the reduction of one order of the number of numerical differentiation needed. The second, third and fourth order derivatives of the mode shapes are obtained by numerically differentiating the experimental phase maps instead of the continuous rotation field, thereby, avoiding the propagation of noise caused by post-processing the phase maps. The study was carryout in a laminated composite plate, which was used in previous studies. Internal damage at two different locations were introduced by low velocity impacts. The phase maps of the first nine modal rotation fields for the plate in free-free condition were measured. This allows the identification of a local perturbation near the region of the higher energy impact. These perturbations are amplified by the numerically differentiation, and can be easily identified in all of the first nine mode shapes. The full-field spatial derivatives present high amplitudes close to the damaged region. This methodology proves to be more effective relative to the others proposed in previous studies, with the advantage of not needing the description of the undamaged structural behaviour.

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