Inversion of speckle interferometer fringes for hole-drilling residual stress determinations

Speckle interferometric fringe patterns record stress-relief displacements induced by the drilling of blind-holes into prestressed objects. The quanti tative determination of residual stress states from such stress patterns is difficult because of the ambiguity in the order of the observed fringes. T he plane stress magnitudes are provided directly from selected fringe posit ions using a stochastic, iterative least squares minimization approach. The inversion requires prior knowledge of the experimental geometry and an app ropriate uniaxial stress-relief displacement basis function derived from th ree-dimensional finite element calculations. Superpositioning of the rotate d and scaled displacement basis functions allows the stress-relief relaxati on for any biaxial state of stress to be determined. In this paper, fringe patterns were forward modeled from a large ensemble of calculated biaxial s tress-relief displacement fields. Inversion of these noise-free fringe patt erns reproduced the biaxial stresses with negligible error. Analysis of mor e realistic fringe patterns that include speckle noise gave stress magnitud e errors that diminished rapidly with the number of selected points to bett er than 3 percent for 100 points. Sensitivity of the optical method is infl uenced by a number of factors, but the ensemble of model fringe patterns st udied indicates that the stress magnitudes (normalized with respect to the material's Young's modulus) from 3 x 10(-4) to 10(-2) can accurately be det ermined with visible laser radiation. The method is amenable to automation and can easily be extended to study near surface gradients in the residual stresses or applied to other optical recording techniques such as moire and phase-shifting interferometry.