This paper deals with the accurate measurement of the in-plane strain components on a deformed specimen using the grid method. A crossed grid transferred on the specimen surface is used for this purpose. Images of this grid are captured with a CCD camera before and after deformation. The complete strain state is deduced by processing these images with a suitable procedure described in the paper. The originality of this procedure is twofold. The first one is to determine the phase derivatives directly from the images. The second one is to compensate local variations of the grid pitch as well as local rotations of the grid, because these two phenomena may corrupt the final strain maps if they are not taken into account. The metrological performance of this procedure is assessed and discussed in terms of accuracy, measurement noise and spatial resolution. Two types of tests are used for this purpose: a translation and a rotation. These tests simulate the effect of rigid-body motion in a strain field that is rigorously equal to zero. One example finally illustrates the procedure: a tensile test performed on an open-hole specimen.

This paper deals with the accurate calculation of strain using the grid method. The strain field is first directly deduced from the fringe pattern without calculating the displacement field. This procedure is validated with two numerical examples. Two types of experiment are then carried out: a translation and a tensile test. It is observed that some additional fictitious strains appear in both cases. They are due to two main reasons which interact with each other: the grid defects and the displacement of the grid lines during testing. A suitable procedure is proposed to cancel out these fictitious strains. This procedure is successfully applied in two cases of fringe patterns.

WOSInternational audienceThe use of various deconvolution techniques to enhance strain maps obtained with the grid method is addressed in this study. Since phase derivative maps obtained with the grid method can be approximated by their actual counterparts convolved by the envelope of the kernel used to extract phases and phase derivatives, non-blind restoration techniques can be used to perform deconvolution. Six deconvolution techniques are presented and employed to restore a synthetic phase derivative map, namely direct deconvolution, regularized deconvolution, Richardson-Lucy algorithm and Wiener filtering, the last two with two variants concerning their practical implementations. Obtained results show that the noise that corrupts the grid images must be thoroughly taken into account to limit its effect on the deconvolved strain maps. The difficulty here is that the noise on the grid image yields a spatially correlated noise on the strain maps. In particular, numerical experiments on synthetic data show that direct and regularized deconvolutions are unstable when noisy data are processed. The same remark holds when Wiener filtering is employed without taking into account noise autocorrelation. On the other hand, the Richardson-Lucy algorithm and Wiener filtering with noise autocorrelation provide deconvolved maps where the impact of noise remains controlled within a certain limit. It is also observed that the last technique outperforms the Richardson-Lucy algorithm. Two short examples of actual strain fields restoration are finally shown. They deal with asphalt and shape memory alloy specimens. The benefits and limitations of deconvolution are presented and discussed in these two cases. The main conclusion is that strain maps are correctly deconvolved when the signal-to-noise ratio is high and that actual noise in the actual strain maps must be more specifically characterized than in the current study to address higher noise levels with Wiener filtering