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

Summary 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. Lay description High‐resolution electron backscatter diffraction (HR‐EBSD) enables one to measure the orientations of crystals in a material with extreme precision. This data is then frequently used to estimate residual strain values and dislocation (defect) densities within the material. However, such estimates require assumptions to be made about the microscopic stress state of the material being examined. This paper examines the validity of the assumption of a traction‐free state (zero stress vector on the surface of the sample). The assumption is found to hold over inaccurate measurement of the actual sample surface orientation (measurements not occurring along the desired plane are valid as long as they are within a few degrees of the desired plane). The assumption is also found to hold even though the measurements actually occur in material just below the surface where the traction can be non‐zero, rather than on the surface. This assumption hold as long as there are no significant stress concentrations close to the surface. In short, the traction‐free assumption appears to be robust and is therefore a valid assumption to use when estimating strain values and dislocation densities.