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

Abstract

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 holedrilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator. Methods: Two repeatability studies were performed on test specimens extracted from an aluminum and titanium shot peened plate. 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 2 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.

Peen forming and stress peen forming of rectangular 2024–T3 aluminium sheets: Curvatures, natural curvatures and residual stresses

“…Olson et al [ 38 ] performed a detailed study on the repeatability on the shot peened aluminium for 12 hole drilling measurements and found that the repeatability standard deviation was max ≈15 MPa and root mean square ≈ 6.4 MPa for the aluminium alloy which the authors considered. Therefore, we would assume the one point measurement is sufficient in this study.…”

Residual Stress Measurements in Extreme Environments for Hazardous, Layered Specimens

“…Selecting the amount of regularization and calculating uncertainties is challenging for data analysis that uses an inverse solution and has been studied recently [48][49][50][51].…”

“…Because the work here uses displacements instead of strains and allows for stress discontinuities, none of the previous methods were precisely applicable. After trial and error, an adaptation of the Olson method for incremental hole drilling [50] proved to be the most robust approach. The amount of regularization was chosen by varying the regularization parameter β over more than 10 orders of magnitude.…”

“…Uncertainty in β, regularization uncertainty, is a "model error" associated with the inverse solution and is a significant source of uncertainty [48]. The regularization uncertainty was calculated by varying β plus and minus two orders of magnitude from the chosen value and calculating the standard deviation in the stresses at every point [50]. The two uncertainty sources are combined in quadrature at every point in the stress profile to give the total uncertainty.…”

A calibration bench to validate systematic error compensation strategies in hole drilling measurements

“…Latest release of ASTM E837 standard includes a procedure to estimate random errors (namely, errors which affect every strain measurement randomly, such as electrical noise) and to filter them through Tikhonov regularization [9]. As observed in [10] and [11], strains are also affected by systematic errors which are not included in the estimation since they affect all measurements in a strongly correlated fashion, such as errors in the rosette gage factors or in the identification of the zero-depth point. In Fig.…”