Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator
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RESEARCH PAPER
Precision of Hole-Drilling Residual Stress Depth Profile Measurements and an Updated Uncertainty Estimator M.D. Olson 1
&
A.T. DeWald 1 & M.R. Hill 2
Received: 26 August 2020 / Accepted: 5 November 2020 # Society for Experimental Mechanics 2020
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 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. Keywords Residual stress . Uncertainty . Hole-drilling . Precision . Repeatability . Regularization
Abbreviations p, q, t P, Q, T N ν E ε
Numerical calibration coefficient matrices Strain invariant vectors Stress invariant vectors Number of rows in the invariant vectors Poisson’s ratio Elastic modulus Measured strain
* M. D. Olson [email protected] 1
Hill Engineering, LLC, 3083 Gold Canal Drive, Rancho Cordova, CA, USA
2
Department of Mechanical and Aerospace Engineering, University of California, One Shields Avenue, Davis, CA, USA
z h σ τ β C α b p;b q, and bt Uσ,ε Uε e Uσ, reg Uσ, tot pstd, qstd, tstd prms, qrms, trms
Average cut depth Cut depth Normal stress Shear stress Regulation parameter penalization matrix Regulation parameter Fitted strain invariants Stress uncertainty from strain uncertainty Strain uncertainty Lower limit of strain uncertainty Stress uncertainty from regularization uncertainty Tota
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