Optically-based interferometric techniques are finding increased application to the quantitative determination of near surface stress states. Unlike the standardized strain-gage method of hole drilling, however, some optical methods are sensitive to all three components of the displacement field produced by drilling of the stress-relieving hole. Analysis of the resulting fringe patterns necessitates a full knowledge of such motions. Here, direct formulae, which relate stress-relief displacements to radial position and azimuth, relative hole dimensions, residual or applied stress, and Poisson's ratio, are constructed from an extensive series of finite element calculations. The final formulae are derived from a large set of trial formulae that best describe the displacements according to a statistical regression analysis. The formulae are generally valid for hole depth/diameter ratios from 0.5 to 4.0, for Poisson's ratios from 0.05 to 0.45, and over radial distances from the hole axis from 2 to 20 times the hole radius, although these validity ranges can vary with hole depth. The equations are compared to an existing strain-gage hole-drilling standard and are used to forward model a speckle interferometer fringe pattern recording stress-relief displacements in an acrylic block.
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