PSI - Issue 5

J. V. Araújo dos Santos et al. / Procedia Structural Integrity 5 (2017) 1198–1204 J.V. Araújo dos Santos et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

Shearography is an optical method, allowing non-contact, full-field and high resolution measurements. It relies on the speckle phenomenon, which occurs in diffuse and rough surfaces whenever they are illuminated by coherent light. It is one of several speckle interferometry methods and its origin can be traced back to the works of Leendertz and Butters (1973), Vlasov and Presnyakov (1973) and Hung and Taylor (1974). Shearography is nowadays an appropriate technique for the quantitative analysis of damage. Indeed, besides measuring directly the gradients or derivatives of the displacement fields, with the use of digital devices and image processing algorithms, the quality of the measurements has improved significantly in relation to the ones using analog systems and visual inspection. The subtraction of the phase of laser light, which is the most common type of coherent light used, coming from the reflection of two neighboring points in the surface is the basis of shearography. Usually, any two points are aligned in a specific direction, called shearing direction, and the distance between the points defines the shearing amount. This process is equivalent to the application of forward or backward finite differences to the displacement field, where the step in the formulas is the distance between the two points, and thus will be equal to the shearing amount. The shearing amount allows the adjustment of the measurement sensitivity, such that large sensitivities are obtained with high values of shearing amounts. However, in this case, one observes the smoothing of the displacement derivative we want to measure. Therefore, and in terms of the analysis of structural damage, the increase of the shearing amount results in a larger perturbation of the rotation field in the damaged area, although at the expense of the smoothing of the derivative. In the context of a combination of mechanical models, holography and shearography for the quantitative detection of defects, Li et al. (2002) stated that good approximate results are obtained when the shearing amount is considerably smaller than the dimension of the view field. A study of the quantitative analysis of an inside crack of pipeline by Kim et al. (2003) showed that when the crack size was equal to the amount of shearing, the crack size was determined accurately and was also closely related with the shearing direction. The influence of shearing amount on detecting size and location of crack-shaped internal defect was also studied by Kang et al. (2006). The influence of large shearing amounts on flaw detection is discussed by Xu et al. (2014) and it is found that large shearing amounts will involve the fringes of the displacement derivative and of the displacement. In view of the difficulties in finding a perfect value for the shearing amount, which will gives us the best measurement accuracy and rich contrast of the phase maps, Steinchen et al. (1998) stated that by learning the shearing amount should not be smaller than 1% of the investigated area. The aim of this paper is to report a study on damage identification using shearography with different shearing amounts. The main objective of the study is the establishment of a range of shearing amounts that can lead to correct localizations of structural damage in beams using modal response. A free-free aluminum beam is discretized by finite elements and the modes shapes, i.e. the modal displacement and rotation fields, are obtained in both undamaged and damaged states. Modal curvature fields obtained directly from the finite element analysis and obtained by simulating shearography are used to compute damage indicators. The damage indicators computed using the data from the simulation of shearography show a great dependency on the shearing amount. In fact, for large shearing amounts, it seems that the damage is spread across a larger area than the actual one. Also, the peak values of the damage indicators present an attenuation and the damage area also increases with the shearing amount. Thus, it is advisable to take these finding into consideration whenever we analyze results coming from shearography with the objective of localizing damage.

2. Description of method

This Section contains the description of the simulation of shearography as well as the description of the way the curvatures are computed.

2.1. Simulation of shearography

The most important Equations describing the use of shearography to obtain out-of-plane related measurements are defined in Araújo dos Santos and Lopes (2017) as: