Hole-Drilling Residual Stress Profiling using ESPI


Supervisor:  Gary S. Schajer

Renewable Resources Laboratory
Dept. Mechanical Engineering
University of British Columbia
Vancouver BC, Canada V6T 1Z4



Residual stresses are stresses that are “locked-in” within a material, and exist without any external load. Such stresses are developed during most common manufacturing processes, for example welding, cold working and grinding. These “hidden” stresses can be quite large, and can have profound effects on engineering properties, notably fatigue life and dimensional stability.

The hole-drilling method is popular method for measuring residual stresses. It works by drilling a small hole in the material and measuring the resulting deformation in the surrounding material. Traditionally, the deformation measurements are done using strain gauges, but measurements using an optical technique such as Electronic Speckle Pattern Interferometry (ESPI) provide an attractive alternative because they give full-field, non-contact measurements and they avoid the lengthy process of attaching strain gauges.

It is relatively straightforward to measure uniform residual stresses, that is, stresses that do not vary with depth from the specimen surface. For this case, a single pair of “before” and “after” measurements is sufficient. Where the residual stresses vary with depth, a series of measurements taken at small increments of hole depth is necessary. Computation of the residual stress profile from these measurements is practical but noise prone. This project is directed to enhancing measurement accuracy and reducing the otherwise substantial sensitivity to measurement errors when doing profiling measurements.

Research Approach

Two difficulties arise when doing hole-drilling profiling, the first is that the quality of the measured data deteriorates as the measurements progress because the later measurements are increasingly separated in time from the initial reference measurement. This issue occurs because of optical drifts in the interferometer system and also because of the accumulation of surface damage caused by scratches from the chips exiting the drilled hole. The second difficulty is that stress computation method is very sensitive to small measurement errors, causing proportionally larger errors in the computed stresses. It turns out that both of these difficulties can be addressed by using an incremental referencing scheme where each ESPI image is referenced to the one measured immediately before rather than to the initial image. This procedure improves the quality of the measured data by reducing the time interval between the measurements of an ESPI image and its reference image. In addition, if there is any surface damage due to scratching from the chips exiting the drilled hole, that damage only affects a single measurement. It does not perpetuate into subsequent measurements because the reference images for those measurements are continually refreshed.

The sensitivity of the residual stress profile calculation to small measurement errors occurs because the matrix within the stress calculation has small numerical values along the diagonal and therefore is ill-conditioned. It turns out that when this matrix is reformulated to correspond to incremental referencing, the numerical values along the diagonal become proportionally larger, causing the matrix to become much better conditioned. Thus, incremental ESPI referencing improves the quality of the mathematical solution as well as the optical measurements.

Diagram (a) shows the ESPI fringe pattern measured during hole-drilling using the conventional technique of referencing the ESPI image to an initial reference image. This is the last of a set of 16 incremental images, thus the initial reference image was quite old at this stage. A prominent fringe pattern is visible, also substantial noise, as seen in the dusty appearance of the fringes and background. Diagram (b) shows the ESPI fringe pattern measured using the immediately prior (15th) incremental image. In this case, the fringe pattern is very small because very little deformation occurs between the 15th and 16th hole depth increments, but more significantly, the background noise in the image is much reduced.

Diagram (a) shows the residual stress profile (x and y in-plane stresses vs. depth) computed from ESPI data referenced to the initial ESPI image. The measurements were done on a shot-peened material, hence the initial compression on the left, near the specimen surface, then moving towards modest tension at greater depths on the right. Substantial instability can be seen in the computed stress results. Diagram (b) shows the corresponding stress results computed from ESPI data with incremental referencing. Here, much more stable results are seen, due both to the improvement in optical data quality and in mathematical stability.


Improved residual stress measurements are important because they allow these “hidden” stresses to be identified more accurately and reliably. The incremental ESPI referencing technique developed here is demonstrated substantially to improve residual stress profile evaluation stability and reliability. There is no additional experimental burden involved in its use and no “downside” characteristic has been identified. Thus, the method is recommended for general use.