Validation of a Contour Method Single-Measurement Uncertainty Estimator

This work validates an analytical single-measurement uncertainty estimator for contour method measurement by comparing it with a first-order uncertainty estimate provided by a repeatability study. The validation was performed on five different specimen types. The specimen types cover a range of geometries, materials, and stress conditions that represent typical structural applications. The specimen types 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, and a nickel disk forging. For each specimen, the residual stress was measured using the contour method on replicate specimens to assess measurement precision. The uncertainty associated with each contour method measurement was also calculated using a recently published single-measurement uncertainty estimator. Comparisons were then made between the estimated uncertainty and the demonstrated measurement precision. These results show that the single-measurement analytical uncertainty estimate has good correlation with the demonstrated repeatability. The spatial distributions of estimated uncertainty were found to be similar among the conditions evaluated, with the uncertainty relatively constant in the interior and larger along the boundaries of the measurement plane

An Uncertainty Estimator for Slitting Method Residual Stress Measurements Including the Influence of Regularization

This paper describes the development of a new uncertainty estimator for slitting method residual stress measurements. The new uncertainty estimator accounts for uncertainty in the regularization-based smoothing included in the residual stress calculation procedure, which is called regularization uncertainty. The work describes a means to quantify regularization uncertainty and then, in the context of a numerical experiment, compares estimated uncertainty to known errors. The paper further compares a first-order uncertainty estimate, established by a repeatability experiment, to the new uncertainty estimator and finds good correlation between the two estimates of precision. Furthermore, the work establishes a procedure for automated determination of the regularization parameter value that minimizes total uncertainty. In summary, the work shows that uncertainty in the regularization parameter is a significant contributor to the total uncertainty in slitting method measurements and that the new uncertainty estimator provides a reasonable estimate of single measurement uncertainty

Measuring multiple residual-stress components using the contour method and multiple cuts

The conventional contour method determines one component of stress over the cross section of a part. The part is cut into two, the contour of the exposed surface is measured, and Bueckner's superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The stress results are validated against independent measurements using neutron diffraction. The theory has implications beyond just multiple cuts. The contour method measurements and calculations for the first cut reveal how the residual stresses have changed throughout the part. Subsequent measurements of partially relaxed stresses by other techniques, such as laboratory x-rays, hole drilling, or neutron or synchrotron diffraction, can be superimposed back to the original state of the body

Biaxial Residual Stress Mapping for a Dissimilar Metal Welded Nozzle

This paper describes a sequence of residual stress measurements made to determine a two-dimensional map of biaxial residual stress in a nozzle mockup having two welds, one a dissimilar metal (DM) weld and the other a stainless steel (SS) weld. The mockup is cylindrical, designed to represent a pressurizer surge nozzle of a nuclear pressurized water reactor (PWR), and was fabricated as part of a weld residual stress measurement and finite-element (FE) modeling round-robin exercise. The mockup has a nickel alloy DM weld joining an SS safe end to a low-alloy steel cylinder and stiffening ring, as well as an SS weld joining the safe end to a section of SS pipe. The biaxial mapping experiments follow an approach described earlier, in PVP2012-78885 and PVP2013-97246, and comprise a series of experimental steps and a computation to determine a two dimensional map of biaxial (axial and hoop) residual stress near the SS and DM welds. Specifically, the biaxial stresses are a combination of a contour measurement of hoop stress in the cylinder, slitting measurements of axial stress in thin slices removed from the cylinder wall, and a computation that determines the axial stress induced by measured hoop stress. At the DM weld, hoop stress is tensile near the OD (240 MPa) and compressive at the ID (-320 MPa), and axial stress is tensile near the OD (370 MPa) and compressive near the midthickness (-230 MPa) and ID (-250 MPa). At the SS weld, hoop stress is tensile near the OD (330 MPa) and compressive near the ID (-210 MPa), and axial stress is tensile at the OD (220 MPa) and compressive near midthickness (-225 MPa) and ID (-30 MPa). The measured stresses are found to be consistent with earlier work in similar configurations

Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator

Background: Measurement precision and uncertainty estimation are important factors for all residual stress measurement techniques. The values of these quantities can help to determine whether a particular measurement technique would be viable option. Objective: This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator. Methods: Two repeatability studies were performed on test specimens extracted from aluminum and titanium shot peened plates. Each repeatability study included 12 hole-drilling measurements performed using a bespoke automated milling machine. Repeatability standard deviations were determined for each population. The repeatability studies were replicated using a commercially available manual hole-drilling milling machine (RS-200, Micro-Measurements). An updated uncertainty estimator was developed and was assessed using an acceptance criterion. The acceptance criterion compared an expected percentage of points (68%) to the fraction of points in the stress versus depth profile where the measured stresses ± its total uncertainty contained the mean stress of the repeatability studies. Results: Both repeatability studies showed larger repeatability standard deviations at the surface that decay quickly (over about 0.3 mm). The repeatability standard deviation was significantly smaller in the aluminum plate (max ≈ 15 MPa, RMS ≈ 6.4 MPa) than in the titanium plate (max ≈ 60 MPa, RMS ≈ 21.0 MPa). The repeatability standard deviations were significantly larger when using the manual milling machine in the aluminum plate (RMS ≈ 21.7 MPa), and for the titanium plate (RMS ≈ 18.9 MPa). Conclusions: The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate

Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator

Background: Measurement precision and uncertainty estimation are important factors for all residual stress measurement techniques. The values of these quantities can help to determine whether a particular measurement technique would be viable option. Objective: This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator. Methods: Two repeatability studies were performed on test specimens extracted from aluminum and titanium shot peened plates. Each repeatability study included 12 hole-drilling measurements performed using a bespoke automated milling machine. Repeatability standard deviations were determined for each population. The repeatability studies were replicated using a commercially available manual hole-drilling milling machine (RS-200, Micro-Measurements). An updated uncertainty estimator was developed and was assessed using an acceptance criterion. The acceptance criterion compared an expected percentage of points (68%) to the fraction of points in the stress versus depth profile where the measured stresses ± its total uncertainty contained the mean stress of the repeatability studies. Results: Both repeatability studies showed larger repeatability standard deviations at the surface that decay quickly (over about 0.3 mm). The repeatability standard deviation was significantly smaller in the aluminum plate (max ≈ 15 MPa, RMS ≈ 6.4 MPa) than in the titanium plate (max ≈ 60 MPa, RMS ≈ 21.0 MPa). The repeatability standard deviations were significantly larger when using the manual milling machine in the aluminum plate (RMS ≈ 21.7 MPa), and for the titanium plate (RMS ≈ 18.9 MPa). Conclusions: The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate

Measurement Layout for Residual Stress Mapping Using Slitting

Background: Residual stress spatial mapping has been developed using various measurement methods, one such method comprising a multiplicity of one-dimensional slitting method measurements combined to form a two-dimensional (2D) map. However, an open question is how to best distribute the individual slitting measurements for 2D mapping. Objective: This paper investigates the efficacy of different strategies for laying out the individual slitting measurements when mapping in-plane residual stress in thin stainless steel slices removed from a larger dissimilar metal weld. Methods: Three different measurement layouts are assessed: independent measurements on nominally identical specimens (i.e., one slitting measurement per specimen, with many specimens), repeatedly bisecting a single slice, and making nominally sequential measurements from one side of the specimen towards the other side of the specimen. Additional comparison measurements are made using neutron diffraction. Results: The work shows little difference between the independent and bisecting slitting measurement layouts, and some differences with the sequential measurements. There is good general agreement between neutron diffraction measurement data and the data from the independent and bisecting layouts. Conclusions: This work suggests that when using slitting to create a 2D map of in-plane residual stress, a cutting layout that repeatedly bisects the specimen works well, requires a small number of specimens, and avoids potential errors from geometric asymmetry or measurement sequence