Analysis of traction-free assumption in high-resolution EBSD measurements

The effects of using a traction-free (plane-stress) assumption to obtain the full distortion tensor from high-resolution EBSD measurements are analyzed. Equations are derived which bound the traction-free error arising from angular misorientation of the sample surface; the error in recovered distortion is shown to be quadratic with respect to that misorientation, and the maximum 'safe' angular misorientation is shown to be 2.7 degrees. The effects of localized stress fields on the traction-free assumption are then examined by a numerical case study, which uses the Boussinesq formalism to model stress fields near a free surface. Except in cases where localized stress field sources occur very close to sample points, the traction-free assumption appears to be admirably robust.