The contour method provides a spatially resolved two-dimensional map of the component of residual stress acting normal to a plane through a part. A typical contour method residual stress measurement involves three primary steps: 1) Cutting a part in half on the plane where residual stress is to be measured (typically using a wire EDM); 2) Measuring the resulting deformation on the cut surface caused by residual stress release; and 3) Performing an analysis to relate measured deformation to residual stress.

For this case study, the repeatability of the contour method under a variety of relevant conditions was determined. Repeatability is a measure of the precision of a measurement technique, but does not address measurement accuracy. The test specimens evaluated include: an aluminum T section, a stainless steel plate with a dissimilar metal slot-filled weld, a stainless steel forging, a titanium plate with an electron beam slot-filled weld, a nickel disk forging, and an aluminum plate. These specimens were selected to encompass a range of typical materials and residual stress distributions. Each repeatability study included contour method measurements on 5 to 12 similar specimens. Following completion of the contour method measurements, an analysis was performed to determine the repeatability standard deviation of each population. In general, the results of the various contour method residual stress measurement repeatability studies are similar. The repeatability standard deviation tends to be relatively small throughout the part interior, with localized regions of higher repeatability along the part perimeter. These results provide expected precision data for the contour method over a broad range of specimen geometries, materials, and stress profiles.

Aluminum T section specimens were fabricated from bars cut from a thick 7050-T7451 aluminum plate. Prior to cutting, the aluminum plate had been stress relieved by stretching. The bars were then heat treated, including a quench, to induce high residual stress indicative of the -T74 temper. After heat treatment, T-sections were machined from the bars to represent an airframe structural member. Each T-section had a length of 254 mm (10.0 in), a height of 50.8 mm (2.0 in), a width of 82.55 mm (3.25 in), and a leg thicknesses of 6.35 mm (0.25 in).

Contour method measurements were performed at the mid-length of 10 specimens. The mean longitudinal residual stress is shown in Figure 1a. There is compressive residual stress at the left, right, and top edges with tensile stress at the center. The measured residual stress is similar between the 10 measurements and is quantified by the low repeatability standard deviation (Figure 1b). The repeatability standard deviation has a low distribution at most points (average of 5 MPa), with localized regions at the edges of the bottom and center flanges where the repeatability standard deviations is larger (95th percentile at 13 MPa).

Five contour method measurements were performed on the stainless steel dissimilar metal weld specimen. The results (Figure 2a) show the mean longitudinal residual stress is tensile in the weld area and heat-affected zone (maximum = 380 MPa), and near the left and right edges of the plate (maximum = 400 MPa). There is compensating compressive residual stress toward the top of the plate at the left and right edges (minimum = -260 MPa). Most points have low repeatability standard deviations (average of 17 MPa), but there are localized regions near the part boundary where the repeatability standard deviation is larger (95th percentile at 36 MPa) as shown in Figure 2b.

Six contour method measurements were performed on the titanium EB welded plate. The mean longitudinal stress (Figure 3a) has tensile stress in the weld area (maximum = 350 MPa) and compensating compressive stress in the heat-affected zone (minimum = -200 MPa). The repeatability standard deviation is low at most points (average of 8 MPa), with localized regions near the part boundary having higher repeatability standard deviations (95th percentile at 17 MPa) as shown in Figure 3b.

Measurements were also performed on stainless steel forgings and a nickel disk forging, which are discussed in a more in-depth technical publication.

The results of the repeatability studies show consistent trends among samples, with low repeatability standard deviations over most of the specimen interior and localized regions of higher variability (typically along the part perimeter). The mean repeatability standard deviation ranged from 5 MPa for the aluminum T section to 35 MPa for the stainless steel forging, which represent the minimum and maximum values of the population.

The magnitude of the repeatability standard deviation increases with elastic modulus of the material, as shown in Figure 4a. The materials with the largest elastic moduli also have the largest repeatability standard deviations. Furthermore, when the repeatability standard deviation is normalized by elastic modulus (Figure 4b), the normalized repeatability standard deviation becomes consistent across all specimens, ranging from 70 x 10-6 MPa/MPa to 125 x 10-6 MPa/MPa, with an average value of approximately 100 x 10-6 MPa/MPa. Similarly, the 95th percentile of the normalized repeatability standard deviation is also relatively consistent, but covers a significantly larger range from 150 x 10-6 MPa/MPa to 275 x 10-6 MPa/MPa, with an average value of 220 x 10-6 MPa/MPa.

**Reference information:**

Repeatability of Contour Method Residual Stress Measurements for a Range of Material, Process, and Geometry, M. D. Olson, A. T. DeWald, and M. R. Hill, Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8, Springer, Cham, 2018, pp. 101–113.