Error analysis of 3D shearography using finite-element modelling

Abstract

ABSTRACT: This paper describes the development of an opto-mechanical simulation of a complete shearography system, including the shearography instrument, the samples and the test environment. This simulation is applied to the measurement of 3D strains in engineering samples. The samples are a cylinder loaded by internal pressure and a flat plate under axial load. Finite elements models are used to obtain the displacements fields. A 3D shearography instrument consisting of a laser and four cameras has been simulated using the optical model. Combining the finite elements and optical simulations allows phase maps to be generated, which are the predictions for measurements using the complete test setup. Errors due to sample material properties, loading inaccuracy and dimensional tolerances are included in the model and this allows the calculation of phase maps at the minimum and maximum error limits. The simulation through path lengths and the simulation by inverted shearography processing provide similar results and the difference is associated with the approximation introduced by the sensitivity vector. \\ 7. CONCLUSIONS: Two simulation approaches for a 3D shearography system have been explained. The first method uses displacement data from the FEM to calculate displacement gradient. Sensitivity vector are calculated and are used to estimate the phase map. The second method uses displacements from the FE model to estimate the object surface position before and after loading. The difference of path length is used to estimate the phase map. The difference between the methods is seen as a measurement of the influence of the approximations made on the sensitivity vector. For the shearography instrument configuration analyzed on this paper, we found that the approximation causes a difference of 2 π (one fringe) on the phase map when a working distance of 200 mm is used. The approximation is greatly improved when the working distance is increased as expected from the shearography theory. A comparison of simulation methods with real shearography measurements is the subject of on-going research. Two test samples, a flat plate loaded axially and a cylinder loaded by internal pressure were simulated. Included errors are associated with the sample’s material properties uncertainty, loading inaccuracy and manufacturing tolerances. These uncertainties causes an error of 4 π (two fringe) on the central area of the phase maps.