Measurement of Structural Stresses Using Hole DrillingbyJoshua S. HarringtonB.S. Mechanical Engineering, California Polytechnic University of San Luis Obispo, 2009a thesis submitted in partial fulfillmentof the requirements for the degree ofMaster of Applied Scienceinthe faculty of graduate and postdoctorial studies(Mechanical Engineerng)The University of British Columbia(Vancouver)October 2015© Joshua S. Harrington, 2015AbstractFrom a measurement standpoint structural stresses can be divided into two broad categories:stresses that can be measured straightforwardly by adjusting loads, e.g., live loads on a bridge,and those that are much more difficult, e.g., gravitational loads and loads due to static indeter-minacy. This research focuses on the development of a method that combines the hole-drillingtechnique, a method used to measure residual stresses, and digital image correlation (DIC), anoptical method for determining displacements, to measure these difficult-to-measure structuralstresses. The hole-drilling technique works by relating local displacements caused by the re-moval of a small amount of stressed material to the material stresses. Adapting the hole-drillingtechnique to measure structural stresses requires scaling the hole size and modifying the calcu-lation approach to measure deeper into a material. DIC is a robust means to measure full-fielddisplacements and unlike other methods used to measure hole-drilling displacements, can eas-ily be scaled to different hole sizes and corrected for measurement artifacts. There are threeprimary areas of investigation: the modification of the calculation method to account for thefinite thickness of structural members, understanding the capabilities and limitations of DICfor measuring hole-drilling displacements, and evaluating the effects hole cutting has on themeasurement. Experimental measurements are made to validate the measurement method aswell as apply it to the real world problem of measuring thermally induced stresses in rail roadtracks.iiPrefaceAll of the work presented henceforth was conducted in the Renewable Resources Laboratoryat the University of British Columbia, Point Grey Campus. My supervisor, Dr. Gary Schajerassisted with concept formation and manuscript editing. I was the lead investigator for all ofthe work including concept formation, experiment building, data collection, data analysis, andmanuscript composition.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixNomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Structural Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Stress Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Hole-Drilling Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 Mathematical Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Surface Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Hole-Drilling Depth Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Digital Image Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13iv3.1 DIC Basic Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 DIC applied to Hole-Drilling Technique . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Finite Thickness (FE) Profile Development . . . . . . . . . . . . . . . . . . . . . 194.1 Model Creation and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Finite Element Interpolation Techniques . . . . . . . . . . . . . . . . . . . . . . . 244.2.1 Finite Thickness Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . 284.2.1.1 Thin Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.1.2 Intermediate Interpolation . . . . . . . . . . . . . . . . . . . . . 334.2.1.3 Poisson's Ratio Interpolation . . . . . . . . . . . . . . . . . . . . 364.2.1.4 Interpolation Assumptions . . . . . . . . . . . . . . . . . . . . . 374.3 Stress Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 DIC Capabilities/Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1 DIC Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1.1 Speckle Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.1.1.1 Speckle Creation . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 DIC Error Analysis with Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . 485.2.1 DIC Error Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2.2 DIC/Hole-Drilling Error Relationship . . . . . . . . . . . . . . . . . . . . 515.2.3 Error Relationship Verification . . . . . . . . . . . . . . . . . . . . . . . . 575.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 Cutter Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.1 Possible Cutting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.2 Finite Element Model Validity for Annulus Hole . . . . . . . . . . . . . . . . . . . 616.3 Evaluation Using Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.3.1 Interferometry Background . . . . . . . . . . . . . . . . . . . . . . . . . . 656.3.2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66v6.3.3 Tests and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.3.3.1 Initial Measurements and Drilling Methods . . . . . . . . . . . . 696.3.3.2 Artifact Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 706.3.3.3 Stress Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 746.3.3.4 Interferometry Test Summary . . . . . . . . . . . . . . . . . . . . 766.4 Evaluation Using DIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.4.1 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.4.2 Test and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.4.2.1 Initial Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.4.2.2 DIC Measurement Verification . . . . . . . . . . . . . . . . . . . 786.4.2.3 Drilling Improvements . . . . . . . . . . . . . . . . . . . . . . . . 796.4.2.4 DIC Test Summary . . . . . . . . . . . . . . . . . . . . . . . . . 816.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.2 Experimental Setup and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847.2.2 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.3 DIC/Hole-Drilling Measurement Evaluation . . . . . . . . . . . . . . . . . . . . . 897.3.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.3.2 Displacement Measurement Results . . . . . . . . . . . . . . . . . . . . . . 907.3.3 Stress Measurement Results . . . . . . . . . . . . . . . . . . . . . . . . . . 957.3.4 Experiment Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.3.4.1 Interferometry Comparison . . . . . . . . . . . . . . . . . . . . . 977.3.4.2 Existing DIC/Hole-Drilling Work Comparison . . . . . . . . . . 977.3.4.3 Least Squares Calculation . . . . . . . . . . . . . . . . . . . . . . 987.4 FE Profile Thickness Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.4.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.4.2 Stress Measurement Results and Conclusions . . . . . . . . . . . . . . . . 99vi7.5 Cutter Shape / Flat Bottom FE Profile Evaluation . . . . . . . . . . . . . . . . . 1027.5.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.5.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.5.3 Experiment Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.6 Structural Stress Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107.6.1 Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117.6.1.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . 1117.6.1.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . 1117.6.1.3 Experiment Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1137.6.2 Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.6.2.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . 1157.6.2.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . 1157.6.2.3 Experiment Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1227.6.3 Phase 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.6.3.1 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . 1227.6.3.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . 1237.6.3.3 Experiment Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1257.7 Evaluation Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1258 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1288.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1308.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132viiList of Tables5.1 Painted speckles patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.2 Speckle Spatial and Spectral Characteristics. The spatial characteristic chartsindicate the percentage of the image composed of specific speckle sizes. Thespectral characteristic images indicate the spectral content of the image based onthe spread of the central peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487.1 DIC evaluation experiment details. . . . . . . . . . . . . . . . . . . . . . . . . . 907.2 Prior research and current work comparison. . . . . . . . . . . . . . . . . . . . . . 977.3 Finite thickness FE profile evaluation experiments. . . . . . . . . . . . . . . . . . 997.4 Experiments for cutter geometry error analysis. . . . . . . . . . . . . . . . . . . . 1037.5 Experiments for residual stress profile calculation. . . . . . . . . . . . . . . . . . 1117.6 Experiments for structural stress correction analysis. . . . . . . . . . . . . . . . 1157.7 Experiments for calibration curve validation analysis. . . . . . . . . . . . . . . . . 123viiiList of Figures2.1 Hole-drilling reference configuration. . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Circular stress tensors: one isotropic stress and two shear stresses. . . . . . . . . 52.3 Stress loadings for FE profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Hole-drilling strain gauge[7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Typical 2D DIC setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Painted random speckle pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.3 DIC subset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154.1 Deformed hole cross sections for infinite and finite thickness materials with ahole. The finite model has bending around the neutral axis that contributes tothe surface displacements. This is not the case for the infinite model. . . . . . 204.2 Typical mesh used for FE calculations. This specific mesh is a through-hole meshwith a thickness of 1 radius. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 Comparison of FE model to analytical model for isotropic loading condition. Theleft plot shows the displacement in radii and right shows the % error. . . . . . . . 234.4 Comparison of FE model to analytical model for harmonic loading condition withPoisson's ratio equal to zero. The left plot shows the displacement in radii andright shows the % error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.5 Comparison of FE model to analytical model for harmonic loading conditionwith thickness equal to 0.25 radii. The left plot shows the displacement in radiiand right shows the % error. The error is slightly larger for this case because athickness of 0.25 doesn't fully match the plane stress condition of the analyticalmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24ix4.6 Set of required models for a 4 hole depth model. Each model only shows 1/4 ofthe hole for visualization purposes. The different colors indicate the stress depthsthat are acting on a hole for a specific model. . . . . . . . . . . . . . . . . . . . . 264.7 Example interpolation surface for a single radial location described by set of FEmodels incrementally calculated with changing hole depth and changing stressdepth. Each point actually has 3 surfaces to describe the possible displacements(Ur, Vr, and Vt) and each radial point on the surface of the mesh will have adifferent set of surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.8 Triangular set of profile values used for bivariate interpolation . . . . . . . . . . 274.9 Ur displacements as a function of depth over a range of thicknesses. . . . . . . . . 294.10 Vr displacements as a function of depth over a range of thicknesses. . . . . . . . . 304.11 Vt displacements as a function of depth over a range of thicknesses. . . . . . . . . 314.12 Spline interpolation to find P where spline curve is defined by four points (P ∗1 , P ∗2 , P ∗3 , P ∗4 ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.13 Intermediate thickness interpolation weighting . . . . . . . . . . . . . . . . . . . . 344.14 Intermediate thickness interpolation error for Ur profile type. . . . . . . . . . . . 354.15 Intermediate thickness interpolation error for Vr profile type. . . . . . . . . . . . 354.16 Intermediate thickness interpolation error for the Vt profile type. . . . . . . . . . 365.1 X-Direction displacement gradient used to interpolate a deformed speckle for DICerror analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2 The average measured DIC pixel displacements as a function of the applied dis-placements. The ideal measurement, indicated by the blue dashed line, is whatthe 100% accurate measurement would look like. . . . . . . . . . . . . . . . . . . 505.3 DIC measurement error as a function of displacement size. . . . . . . . . . . . . 515.4 Average Ur profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.5 Average Vr profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52x5.6 Average Vt profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.7 Hole-drilling error estimate as a function of load and pixel density for 1/4 radiushole depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.8 Hole-drilling error estimate as a function of load and pixel density for 1/2 radiushole depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.9 Hole-drilling error estimate as a function of load and pixel density for 3/4 radiushole depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.10 Hole-drilling error estimate as a function of load and pixel density for 1 radiushole depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.11 Example synthetic measurement image set. . . . . . . . . . . . . . . . . . . . . . 575.12 Error function verification. A comparison of error estimates to error measuredwith synthetic hole-drilling/DIC data. . . . . . . . . . . . . . . . . . . . . . . . . 586.1 Cutter Types. Images adapted from https://www.maritool.com, http://ecx.images-amazon.com, and http://i21.geccdn.net respectively. . . . . . . . . . . . . . . . . 606.2 Flat bottomed hole and annular FE model geometries to evaluate the effect ofannular geometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.3 Annulus vs. Hole model comparison. Plots A and C show the calculated dis-placement profiles for both hole and annular geometries. Plots B and D show theerror of the annular geometries relative to the hole geometries. . . . . . . . . . . 636.4 In-planee ESPI setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.5 Typical ESPI fringe pattern. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.6 Experimental setup of for large hole interferometry hole-drilling measurements. . 676.7 ESPI box details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686.8 Interferometry beam path using multiple beam mirrors. . . . . . . . . . . . . . . 686.9 Example of two interferometry hole-drilling measurements. Image A is an exam-ple of a bad measurement with excessive surface damage. Image B is an exampleof a good measurement where surface damage has been minimized. . . . . . . . . 70xi6.10 Four images for the same measurement taken at 1, 3, 5, and 9 minutes afterdrilling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716.11 Artifact Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 726.12 Artifact subtraction from measurements with varying thermal displacements. . . 736.13 Stress and artifact values for each of the 4 measurements. The plot on the leftshows the stress measurements and the plot on the right shows the measuredartifacts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736.14 Heat treatment setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746.15 Unloaded stress relieved 1080 plate steel hole-drilling stress measurement for bothhigh speed steel (left plot) and carbide (right plot)58” annular cutters. . . . . . 756.16 Unloaded hot rolled 1080 plate steel hole-drilling stress measurement for bothhigh speed steel (left plot) and carbide (right plot)58” annular cutters with nostress relieving. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766.17 Experimental setup of for large hole DIC hole-drilling measurements. . . . . . . 776.18 Speckle degradation due to lack of protective coat. Image on left shows damagedspeckle. Image on right shows preserved speckle using sprayed polyurethanecoating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.19 Unloaded hot rolled 1080 plate steel DIC hole-drilling stress measurement forboth12” (left plot) and1116” (right plot) HSS annular cutters. . . . . . . . . . . . . 796.20 Comparison of single depth hole-drilling stress measurements for 4 different an-nular cutters both with and without cutting oil. The relatively high stress mea-surements are likely due to the residual stresses present in the test specimens, asno stress relieving was done. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.1 Zoomed out view of experimental set up to give an idea of scale. Area shown inFigure 7.2 highlighted in yellow. . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.2 Experimental setup for DIC/ hole-drilling measurements with applied loading. . . 867.3 Hole-drilling methods used in experiments. . . . . . . . . . . . . . . . . . . . . . . 877.4 Example set of measurement images. Each column is a measurement set of an Acalculation and each row is a measurement set of a B calculation. . . . . . . . . . 89xii7.5 Channel DIC/hole-drilling displacements. One fringe is equal to ~ 3000nm. The150MPa measurement shows just how effective the LSQ calculation is at pickingout the displacements due only to stress even when the signal is tiny comparedto the complete displacement measurement. Additionally, for all the specimenstested, the artifact seen in the residual is smallest here. . . . . . . . . . . . . . . . 917.6 I-Beam DIC/hole-drilling displacements. One fringe is equal to ~ 2500nm. Themeasured displacements in these measurements show that there is a significantamount of shearing displacements, which are likely due to the specimen rotatingslightly between loading. Even with this significant shear, the displacements withthe artifacts removed still do match quite closely to the ideal displacements. . . . 927.7 Square tube DIC/hole-drilling displacements. One fringe is equal to ~ 2200nm.The artifacts seen in the error were maximum for these square tube measurementscompared to the other experiments. Even with these large artifacts, the LSQalgorithm was still able to calculate reasonable stress values as seen in Figures7.9 and 7.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937.8 Rail DIC/hole-drilling displacements. One fringe is equal to ~ 2500nm. With adistinct curve across the web of the rail, of all the measurements the rail surfacewas the farthest from flat. Despite this obvious inconsistency with the FE models,the measurement error was still minimal. . . . . . . . . . . . . . . . . . . . . . . 947.9 Stress results for the measurements described in Table 7.1 showing the appliedstress vs. the measured stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.10 Error results for the measurements described in table 7.1. The left plot shows themeasurement error in MPa and the right plot shows the absolute value of thepercent error. Additionally, the right plot shows the estimated error with dashedlines for each measurement based only on the accuracy of DIC. . . . . . . . . . . 967.11 Measured stresses vs. applied stresses for single measurement where calculationthickness was varied. This shows how incorrect stresses can be calculated byusing incorrect FE profile thicknesses. . . . . . . . . . . . . . . . . . . . . . . . . 1007.12 Stress measurement error vs. material thickness when infinitely thick FE profilesare used for calculation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xiii7.13 Stress measurement error vs. calculation thickness error for a range of materialthicknesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.14 Drilled hole geometries including chamfer width and height. . . . . . . . . . . . 1037.15 Measurement variation due stress calculation with FE profiles that account for thetool geometries for Exp. 2. The calculations with the tool chamfer use custom FEprofiles that match the tool geometry, whereas the calculations with no chamferuse interpolated FE profiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.16 Average measurement error at each calculation depth for all three experiments.The average is used here because the incorrect thickness profiles scale the mea-sured stress resulting in a constant relative measurement error independent ofapplied stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.17 Average measurement error for all three experiments as a function of F, a dimen-sionless constant, described in equation 7.1, which is a function of hole depth,hole radius, cutter chamfer height, and cutter chamfer width. . . . . . . . . . . . 1077.18 Measurement correction for Exp.2 showing the original measurements in dashedlines and the corrected measurements with solid lines. The corrected stress valuesare significantly closer to the ideal curve for each depth. . . . . . . . . . . . . . . 1087.19 Average measurement error for all Exp. 1,2,&3 showing both the uncorrected andcorrected measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1097.20 Measured stress profiles across the thickness for channel, I-beam, and square tubestructural elements. It is clear from these stress profiles that the residual stressesare both significant in magnitude and differ greatly between structure type. . . . 1127.21 A comparison of measured rail residual stresses to an existing residual stress anal-yses of rail. The image on the left shows the residual stresses of a rail determinedusing the contour method [45]. The plot on the right shows the measured residualstress profile for the rail. Note that the magnitude of the measured residual stressprofile is similar the the results from the contour method. . . . . . . . . . . . . . 1137.22 Channel calibration curve and structural stress measurement results. Plot Ashows the calibration curve. Plot B shows the measured and corrected stressesas a function of applied stress. Plot C shows the measurement error in MPa. . . 117xiv7.23 I-beam calibration curve and structural stress measurement results. Plot A showsthe calibration curve. Plot B shows the measured and corrected stresses as afunction of applied stress. Plot C shows the measurement error in MPa. . . . . 1187.24 Square tube calibration curve and structural stress measurement results. Plot Ashows the calibration curve. Plot B shows the measured and corrected stressesas a function of applied stress. Plot C shows the measurement error in MPa. . . 1197.25 Rail calibration curve and structural stress measurement results. Plot A showsthe calibration curve. Plot B shows the measured and corrected stresses as afunction of applied stress. Plot C shows the measurement error in MPa. . . . . 1217.26 Corrected measured structural stress vs. applied stress for single depth measure-ments using residual stress correction calibration curves. . . . . . . . . . . . . . . 1247.27 Error results for the corrected stress measurements in MPa. . . . . . . . . . . . 125xvNomenclatureδ Measured displacements setδθ Radial displacementsδr Radial displacementsλ Wave length[d1, ..., dn] Drilled depthsσx Normal Stress in x-directionσy Normal Stress in y-directionτxy Normal Stress in y-directionθ Angular positionθ Beam Anglea Hole radiusch Chamfer heightcw Chamfer widthD∗ Normalized drilled DepthsD∗num Normaized drilled depths normalized by thicknessE ErrorxviE Young's ModulusG Column space of LSQ equationGi,j G matrix components built with Ur, Vr and Vt profile setsH Stress depthh Hole depthP Isotropic stressPnum Tabulated profile setQ Harmonic stressr Radial positions Unknown stresses vectorT Harmonic stress rotated 45 degreest Thicknesst∗ Normalized thicknesstnum Tabulated profile thicknessu Displacement of light-dark fringe pairUr Displacement profile in radial direction for unitary P stressv Poisson's ratioVθ Displacement profile in tangential direction for unitary Q or T stressVr Displacement profile in radial direction for unitary Q or T stressw Intermediate thickenss Interpolation FunctionW1 . . .W6 Artifact shapesxviiw1 . . . w6 ArtifactsXs Displacement in x-direction due to unitary τxyXx Displacement in x-direction due to unitary σxXy Displacement in x-direction due to unitary σyYs Displacement in y-direction due to unitary τxyYx Displacement in y-direction due to unitary σxYy Displacement in y-direction due to unitary σyxviiiAcknowledgmentsFirst I would like to acknowledge my supervisor Dr. Gary Schajer, whose patience and wisdomguided me throughout my research. I could not have hoped for a more understanding, anddedicated supervisor. I would like to thank my lab colleagues Ted Angus, Darren Sutton,Samuel Melamed, Wade Gubbels, and Guillaume Richoz who shared the lab with me over thelast 2 years. Furthermore, I offer my gratitude to the faculty, staff, and fellow students in theUBC Mechanical Engineering Department for the generous support and ongoing help. Lastbut not least, I would like to thank my family for the love and support they have provided methroughout my life.xixDedicationTo JessxxChapter 1Introduction1.1 Structural StressesAccurate information regarding on-site or in-situ stresses is important in the evaluation of struc-tures, particularly when determining safety or serviceability. A measurement that is capableof assessing structural loads is useful because it provides engineers with information critical toevaluating the safety and maintenance requirements for structures, as well as a means to mon-itor if loads are within design limits. Loads on a structure historically have been categorizedas either dead loads (gravitational loads) or live loads (changing loads) [1]. This is a usefuldelineation for a structural engineer when designing a structure; however from a measurementstandpoint, it is more practical to divide the loads on a structure into two different categories:loads that when manipulated externally to the structure cause a deformation and loads thatmust be manipulated internally to cause a deformation. External loads that cause measurabledisplacements, such as cars on a bridge or a train on a railroad track, are relatively easy tomeasure because the load they impart cause a directly observable deformation that can be usedto determine the stresses in the structure. The challenge is to be able to account reliably forthe loads that do not cause any directly observable deformations. Consider the example of arailroad track firmly attached to a foundation that undergoes a temperature change. The railwill normally expand or contract due to thermal expansion, but because of the redundancy offoundation constraints the rail is fixed in place. This constrained thermal expansion causeslarge stresses in the railroad track that cause no visible deformation until failure occurs. These1hard-to-measure stresses exist in many other forms, such as dead loads, residual stresses or pre-tensioned stresses; and, due to their hidden nature are referred to as locked-in stresses. Indirectmeasurement methods are needed to identify the locked-in stresses in a structure. Presented inthis thesis is a method developed to address this need.1.2 Stress MeasurementStress is not a quantity that can actually be physically measured, rather stress is inferred from itsrelationship to something that is measurable, typically a displacement or strain. Strain gauges,the gold standard for measuring stress, measure surface strain, which, when combined withHooke's law, can be used to determine stress. Other less common methods measure changes inthe material properties of the stressed material; for example, X-ray diffraction measure crystallattice strain [2], ultrasound techniques measure changes in wave velocity [3], and magnetic tech-niques measure Barkhausen noise Villari effects [3]. These less common methods might seemlike a good choice to measure locked-in structural stresses because they do not require a physicaldisplacement, but these measurements are often limited because they only measure stresses atthe very surface of a material and typically require extensive calibration. To measure locked-instresses reliably day after day in an industrial setting, a method that is robust, repeatable, easilyscalable, and easily calibrated is necessary. This will most easily be accomplished with a mea-surement method that is similar to the classic strain gauge method: by the measurement surfacedisplacements. The challenge is how to obtain measurable surface deformations from locked-instresses. A method known as the hole-drilling method was developed for the measurement ofresidual stress, a type of locked-in stress, near a material surface. This method uses a drill toremove some stressed material, causing the loads to redistribute locally and resulting in a mea-surable surface deformation surrounding the hole. While not as simple as the direct method,these deformations can be correlated to the stress that was contained within the hole. Withsome refinement, the hole-drilling method could possibly be extended to measuring locked-instructural stresses.The elastic deformations around a hole caused by drilling are very small and require a precisemeans of measurement. The most precise way to measure small deformations is with a strain2gauge. Thus, specialized strain gauge rosettes have been developed, but these rosettes are cum-bersome to apply to a material's surface and only come in limited sizes, therefore are not easilyscalable to a range of hole sizes, nor capable of making quick and repeatable measurements inan industrial setting. To avoid the issues associated with strain gauges, interferometry methodshave been applied to hole-drilling. Interferometry measures displacement with the interferenceof two coherent light beams, making it capable of precise measurements, however this metrol-ogy is very sensitive to environmental disturbances. Thus, interferometry is primarily suitedto laboratory measurements and is not ideal for the measurement of structural stresses in thefield. Recently, a method known as digital image correlation has been applied to hole-drilling,where digital images are taken before and after drilling and then displacements are calculatedby comparing these two images. Digital image correlation is easily scalable to measure stressesfrom many different hole sizes, does not require a lengthy setup, and is capable of making fieldmeasurements, which makes it an attractive approach to explore.1.3 ObjectivesThe goal of this thesis is to develop a method that can be easily incorporated by industry tomeasure locked-in structural stresses. This will be accomplished by adapting the hole-drillingtechnique to the scale required to measure structural stresses, and by understanding the capa-bilities and limitations of digital image correlation for making hole-drilling measurements. Forhole-drilling measurements, this will involve exploring the best way to measure stresses withinthe depth of a structure by evaluating new drilling techniques as well as refining the calculationmethod. With respect to digital image correlation, the limits and considerations associated withusing this metrology for the hole-drilling method need to be determined. To validate the refinedhole-drilling method, the measurement technique will be used to measure structural stresses fora range of structure types.3Chapter 2Hole-Drilling MeasurementThe hole-drilling method is a well established and common technique for measuring residualstresses [4]. The method involves the localized removal of material by drilling a hole and thenmeasuring the subsequent deformations. This method works on locked-in stresses because themeasurable deformations are due to the redistribution of the stresses in the removed materialonto the surrounding material and is independent of whether this stress is locked-in or otherwise.The foundations of the hole drilling method were established by Mathar [5] in the early 1930'sand has advanced significantly over the last 80 years [6]. The ASTM standard E-837-13 isthe standard that currently defines how the hole-drilling method should be applied for themeasurement of residual stress [7]. This research will build upon what is established in thisstandard and explore the adoption of the hole-drilling method to measure locked-in structuralstresses.2.1 Mathematical BackgroundXY r θFigure 2.1: Hole-drilling reference configuration.4Unlike the simplicity of of a standard strain gauge stress measurement, relating the locked-in in-plane stresses (σx, σy, τxy) to surface displacements is more difficult. The deformations aroundthe hole are best represented in polar coordinates by δr (r, θ) and δθ (r, θ) with the center ofthe hole at the origin (Figure 2.1). The stresses σx, σy and τxy can then also be represented inpolar coordinates with the following conversion:P =(σx + σy)2(2.1)Q =(σx − σy)2T = τxywhere P is an isotropic stress (uniform pressure) and Q,T are shear stresses (harmonicpressure) as shown in Figure 2.2.P Q TFigure 2.2: Circular stress tensors: one isotropic stress and two shear stresses.Analytic solutions relating stresses P , Q, and T to displacements δr and δθ for a simple modelof a plate with a through hole, have been developed [8, 9, 10, 11, 12, 13] with the assumptionsof a linear elastic, isotropic, homogeneous plate with hole [14]. The displacement, δr (r), due toan isotropic stress P (Figure 2.2) uniformly distributed on the inner wall of the hole isδr(r) = P Ur (r) (2.2)whereUr (r) =1 + vEa2r(2.3)The values v, E, a, and r in equation 2.3 are Poisson's ratio, Young's modulus, hole radius,5and radial position respectively. There is only a radial displacement, because for isotropic stressradial displacement is equal for all θ values. Similarly both the radial displacement, δr (r, θ)and circumferential displacement δθ (r, θ) for shear stress Q (Figure 2.2), which is essentially apressure that changes sign everypi2 radii, are defined as follows:δr (r, θ) = QVr (r) cos (2θ) (2.4)δθ (r, θ) = QVθ (r) sin (2θ)whereVr (r) =rE(4(ar)2 − (1− v)(ar)4)(2.5)Vθ (r) = − rE(2(1− v)(ar)2+ (1 + v)(ar)4)The displacements, δr and δθ, with a harmonic load are now a function of r and θ because asthe harmonic stress varies with θ so do the displacements. The surface displacements, δr and δθ,can be completely defined for any linear combination of σx, σy, and τxy by combining equations2.2,2.3,2.4, and 2.5.δr (r, θ) = P Ur (r) +QVr (r) cos (2θ) + T Vr (r) sin (2θ) (2.6)δθ (r, θ) = QVθ (r) sin (2θ)− T Vθ (r) cos (2θ)Note that in Figure 2.2 T is just Q rotated 45 degrees counterclockwise.To make equation 2.6 valid beyond the earlier assumptions of a uniform stress distributionand a through-hole plate for the analytical solution, all that must be done is to determine Ur (r),Vr (r) cos (2θ), Vr (r) sin (2θ), Vθ (r) cos (2θ) and Vθ (r) sin (2θ) from equation 2.6 as a functionof material properties, geometries, and load location. Originally this was done by empiricalmeans, but today it is most commonly done with finite element analysis (FEA) [15, 10]. Aslong as the material is homogeneous, the harmonic nature of the loading can be exploited. It6is only necessary to determine the profiles Ur (r), Vr (r), and Vθ (r), along one radial line at θequal to zero. Doing this greatly simplifies the required FEA calculations and allows for simpleinterpolation between FEA solutions. By interpolating between these finite element solutions,several sets of FE profiles can satisfy a wide range of geometries and loading conditions [16, 17];this will be covered in detail in Chapter 4. By creating sets of profiles over a range of holedepths and then for each hole depth over a range of stress depths, as shown in Figure 2.3, whereh is hole depth and H is stress depth, the surface displacement caused by any stress betweenany two depths (H1, H2) of any hole depth (h) can be calculated as shown in equation 2.7.1,13,1 3,3n,1 n,y n,nhHhole depthstress depth2,1 2,23,2Figure 2.3: Stress loadings for FE profiles.δr (r, θ, h,H1, H2) = P (Ur (r, h,H2)− Ur (r, h,H1)) (2.7)+Q (Vr (r, h,H2)− Vr (r, h,H1)) cos (2θ)+T (Vr (r, h,H2)− Vr (r, h,H1)) sin (2θ)δθ (r, θ, h,H1, H2) = Q (Vθ (r, h,H2)− Vθ (r, h,H1)) sin (2θ)−T (Vθ (r, h,H2)− Vθ (r, h,H1)) cos (2θ)The ability to determine the contribution of a stress at a particular depth to its visiblesurface displacements allows hole-drilling to be used as a means to measure how stress changesas a function of hole depth. Although there are several methods to do this, the most commonis the integral method [4, 16, 17], which works by incrementally drilling a hole and at each7depth increment taking surface deformation measurements δr and δθ. They are then used withthe interpolated FE profiles (eq. 2.10) to solve for unknowns P , Q and T at each depth. TheequationG1,1G2,1 G2,2......Gn,1 Gn,2 Gn,nP1Q1T1P2Q2T2...PnQnTn= δr 1δθ 1 δr 2δθ 2... δr nδθ n(2.8)represents the calculation for n hole depths and is more simply displayed asGs = δ (2.9)whereGi,j = Ur i,j Vr i,j cos (2θ) Vr i,j sin (2θ)Vθ i,j sin (2θ) −Vθ i,j cos (2θ) (2.10)Ur i,j = Ur (r, i, j)− Ur (r, i, j − 1)Vr i,j = Vr (r, i, j)− Vr (r, i, j − 1)Vθ i,j = Vθ (r, i, j)− Vθ (r, i, j − 1)are the interpolated finite element profiles. The value i is the hole depth and j is the stressdepth. Equation 2.9 is solved for a best fit solution using the linear least squares method with8the following steps:Gs = δ (2.11)GTGs = GT δs =(GTG)−1GT δG is the column space that defines the possible surface deformations, based on the depthincrements drilled, for any set of stresses. Depending on the number of measurement points,the matrix G can become quite large, but the GTG term in equation 2.11 reduces the size ofthe matrix to just a 3n × 3n matrix reducing the computational burden. The GTG term alsorepresents the large amount of averaging that this calculation takes advantage of when dealingwith many measurement points.The adaptation of FE models and the interpolation methods combined with the robustnessof the least squares calculation are critical in being able to measure stresses across a largerange of geometries in an industrial environment. The mathematical background established inequations 2.8, 2.9, 2.10 and 2.11 is the basis upon which the work in this thesis was developed.2.2 Surface Measurement MethodsInitially strain gauges were used to measure the surface deformations due to drilling and they arestill widely used today. Specialized rosettes, as shown in Figure 2.4, were developed for hole-drilling residual stress measurements for holes with a diameter between 1 and 5 millimeters.Strain gauges are very sensitive to changes in strain and have proven to be effective for use inthe lab and in the field. However, there are drawbacks to using strain gauges: they only measurestrain at a few points (typically three); the size of the hole is limited by the size of the gauge;and they require a time and labor intensive setup prior to the measurement. All of these factorsmake it challenging to use strain gauges as a means to measure structural stresses.9Figure 2.4: Hole-drilling strain gauge[7]Starting in the 1990's researchers started to use interferometry as a means to measure thesurface displacements due to drilling [11, 18, 19, 20, 21, 22, 23]. Interferometry measurementsrely on the interference of two coherent light beams, typically from a laser, and how the inter-ference changes before and after a drilling operation typically captured with a charge-coupleddevice (CCD) camera. Hole-drilling with interferometry has many advantages over strain gaugesin that it is a non-contact sensor, it is a full field measurement with measurements at every pixelon the images sensor, and it is more easily scalable to a range of hole sizes. The main downsideto interferometry is its extreme sensitivity to environmental factors such as air currents, vibra-tions, or small shifts in measurement components, making interferometry measurements onlysuited to the laboratory.Digital image correlation (DIC) is the most recent metrology to be adapted to hole-drillingmeasurements [24, 9, 25, 26, 27]. DIC works by comparing an image before and after a mea-surement, where applied to the surface of the material is a random speckle pattern that canuniquely identify the position of each pixel. The surface deformations can then be computedby determining how the speckle pattern deforms. The specifics of this will be detailed furtherin Chapter 3. DIC has the drawback that the measurement resolution is not as high as eitherinterferometry or strain gauges, however DIC is less affected by environmental factors, such asair currents or small misalignment between images than interferometry and is more adaptableto different geometries as well as being easier to use than strain gauges. The reduced sensitivityof DIC is mitigated by the use of many measurement points and the averaging that takes place10in the LSQ calculation (equation 2.11) making DIC an attractive surface measurement methodto be incorporated into a hole-drilling measurement to measure structural stresses easily in thefield.2.3 Hole-Drilling Depth SensitivityMathematically, the hole-drilling technique can measure stress at any depth in a material,but practically, the a hole-drilling measurement is only sensitive to about one hole radius ofdepth. The measurable displacements due to a stress below a depth of one hole radius are sosmall compared to the stresses closer to the surface that, with the imperfections of a physicalmeasurement, the least squares solution is not capable of separating out these small stressescorrectly. Meaning that, below one hole radius, the measured displacements at the surface aretoo small to reliably measure stress. To measure residual stresses existing near the surface ofa material, only small holes were required, typically 1-4 mm radii dental drill bits are used.While holes of this size have been common practice, there is no theoretical restriction on thesize of the hole, provided that the measurements are scaled up or down accordingly. This meansthat by increasing the relative hole size, the hole-drilling technique could measure deeper into amaterial and measure locked-in stresses.2.4 ConclusionsOver the last 80 years the hole-drilling method has advanced in three main areas: the way inwhich the stresses are calculated, the way in which the deformations are measured, and the wayin which the hole is drilled [6]. Mathematical methods relating internal stresses to measurabledeformations have advanced from simple analytical models to FE models allowing for the effec-tive and accurate determination of residual stresses. In addition,drilling techniques have beendeveloped and optimized to have a minimal impact on a residual stress measurement. Finally,new advanced methods for measuring displacements have been applied to hole-drilling mea-surements, increasing measurement accuracy and allowing for new applications. The Chapters4, 6 and 5 will addresses each of these advances individually with regard to the developmentof a hole-drilling/DIC measurement method capable of measuring locked-in stresses found in11structures.12Chapter 3Digital Image CorrelationDigital image correlation (DIC) is an optical metrology technique based in image processing andcomputing, where full-field surface displacements are measured by comparing the digital imagesof the specimen surface before and after loading [28]. The foundations of DIC were establishedat the University of South Carolina in the 1980's [29, 30] and it continues to be an area offocus for many researchers around the world today, in trying both to improve DIC as well asdevelop new applications for DIC. DIC was originally developed for two-dimensional in-planemeasurements normal to the camera, known as 2D DIC with the setup shown in Figure 3.1. Tomake three dimensional measurements, 3D DIC was developed using two or more cameras andstereo-vision to determine in-plane as well as out-of-plane displacements; however, compared to2D DIC, the setup is more complicated and sensitive to disturbances (such as camera alignment).DIC methods have proven applicable to fields such as civil, mechanical, material, bio-medical,and manufacturing engineering, as well as electronics packaging, joining, and others [31]. Thework done in this thesis with respect to DIC will focus on the ability of 2D DIC to be used forhole-drilling measurements as well as more fully understanding the limitations and advantagesDIC brings to this type of measurement.13SpecimenCameraComputerXZYFigure 3.1: Typical 2D DIC setup3.1 DIC Basic PrinciplesXZYFigure 3.2: Painted random speckle patternFor DIC to work, a point in an image needs to be uniquely identified with respect to all otherpoints in the image. To accomplish this, the specimen surface must have a random intensitydistribution, or speckle pattern, most commonly done by spraying paint on the surface, as shownin Figure 3.2. Due to the randomness of the speckle pattern, a single point in the image canbe uniquely identified by the surrounding area. The surrounding area chosen to define a pointis typically referred to as a subset, as shown in Figure 3.3, where the point depicted by the redcross is uniquely defined by the surrounding area. This will allow a point in the image takenbefore deformation (reference image) to be located in the image after deformation (deformed14image) by matching the point's subset from the reference image to the subset's new location inthe deformed image.ImageSubsetFigure 3.3: DIC subsetTo determine how well a subset in the deformed image matches one in the reference image,a correlation criterion is used. A correlation criterion is simply a metric that relates how welltwo subsets match. By matching a reference subset to a set of subsets in the deformed image,the correlation criteria indicates which is the best match and thus the most probable positionthat the subset's point displaced to. Several different correlation criteria have been developedthat can make this matching of subsets immune to changes in lighting conditions, thus makingDIC measurements more robust and suited for field use.To match a reference subset to the best possible deformed subset, an iterative algorithm isgenerally used. The simplest of algorithms will define a search area within which the deformationis expected to occur, and then calculate the correlation criterion for every possible subset locationat one pixel increments within that search area. The deformed subset location can then be foundto sub-pixel accuracy by interpolating between correlation criteria values at neighboring pixellocations. This is the simplest method, but it is quite cumbersome computationally and onlytakes into account subset rigid body motion. More advanced algorithms have been developed,such as Newton-Raphson and RGDIC, that speed up the calculation with guided techniques andaccount for subset deformations other than rigid body motion, including as stretch and shear[32, 33, 34, 35, 36]. For more in-depth information regarding the specifics of DIC a review of2D DIC by [28] is an excellent resource.15The work done for this thesis uses an open source 2D DIC package for Matlab called NCORRdeveloped by Justin Blaber at the Georgia Institute of Technology [37].3.2 DIC applied to Hole-Drilling TechniqueDIC was first applied to hole-drilling by McGinnis [9] in 2005. McGinnis explored the use of3D DIC as a means to measure stresses in steel beams, with the hope of later being able toextend the work to concrete structures. The work was largely successful and showed that toan extent, DIC was capable of making hole-drilling measurements by measuring tensile stressesin steel beams on the order of 150 MPa to within 8%. This work only reported the oneDIC measurement however, and did not indicate the capable accuracy of DIC for hole-drillingmeasurements or the expected measurement error due to using the DIC metrology. A paperby Nelson [25] in 2006 built on McGinnis' work, where the measurements were scaled down,with hole sizes more typical to hole-drilling, and calibrated test specimens were used, allowingfor better control over experimental conditions. Additionally many measurements were madeto establish the repeatability of the method. As the measured stresses explored were still fairlylarge (~200MPa), the results from this paper did not fully answer many of the questions left byMcGinnis, but did mention that there was a link between an increased number of measurementpoints and a higher camera resolution, to the measurement of smaller stresses values. In 2008,Lord [38] used 2D DIC and hole-drilling to measure how stresses change with depth in shot-peened aluminum. This work showed some success in measuring an in-depth stress profile andpicking out various expected stress features associated with shot-peening, but there was a ratherhigh measurement variability and, similar to the other two works, did not fully explore how DICwould impact the hole-drilling measurement error. These three works leave two basic questionsthat this thesis attempts to answer. First, what are the capabilities and limitations of DIC forhole-drilling measurements, and second, what alterations to the measurement setup could makeDIC more effective?Two other works have been published regarding hole-drilling and DIC. First is the work doneby Schajer [27] in 2012 where DIC hole-drilling techniques were used to measure stresses in silicondiscs using a scanning electron microscope (SEM). The challenge with trying to measure the16stress in one of these discs is the scale with which the work is being done. With a field ofview of only 25µm, neither strain gauges or interferometry measurement methods were feasible,therefore with the digital images from the SEM, DIC was the ideal choice. This work didn'tanswer any questions left unanswered by prior hole-drilling/DIC papers, however it was ableto extend the use of DIC with hole-drilling by including artifact correction, not only for rigidbody motion, but also for image stretch and shear. These artifacts can be a result of specimenrotation or even uniform heating of the specimen. Lastly, a paper published by Baldi [24]in 2013 explored the use of the finite element profiles used to relate surface displacements tostresses as global shape functions for the DIC calculation. This paper looked more at the DICcalculation method rather than how DIC is applied to hole-drilling, but did show that for simple,tightly controlled, through-hole measurements, DIC is capable of making accurate hole-drillingmeasurements.To be able to accurately interpret the results of a DIC hole drilling measurement, it is criticalto understand the measurement capabilities as applied to the hole drilling measurement. Theresolution with which DIC can be measured has been discussed by many researchers [28, 31]and has generally been found to be on the order of 0.01 pixels. The expected displacementsaround a hole after drilling range between 0.001 and 0.1 pixels depending on the magnitude ofthe stress, the depth of the hole, and the size of the imaging sensor. This makes DIC incapableof measuring deformations due to hole-drilling in certain cases. To be able to fully incorporateDIC as a measurement means for hole-drilling, as strain gauges and interferometry have been,a relationship between desired stress resolution, camera sensor size, and hole depth needs to bedeveloped to inform a user of the smallest stress that their setup is capable of measuring and theminimum depth requirements for the drilled holes. Chapter 5 will explore this topic in detail.3.3 ConclusionsDIC is a metrology method that has been proven over the last three decades to be capable,robust, and easily adaptable to many different areas of research. While it is not the firstattempt at using DIC with the hole-drilling technique, the research done for this thesis exploresthe capabilities of DIC for hole-drilling and establishes parameters for using DIC with hole-17drilling. By doing this, DIC/hole-drilling measurements can be taken out of the lab and beeasily adapted to measure structural stresses in the field.18Chapter 4Finite Thickness (FE) ProfileDevelopmentWhen making a measurement with the hole-drilling technique, the depth at which it is possibleto measure stress is directly proportional to the size of the hole; it is usually around 1 holeradius. This means that a hole 1-2 mm in diameter, typical for hole-drilling measurements, iscapable of measuring stress to a depth of 0.5-1 mm. This is sufficient for measuring residualstresses close to the material surface, but not for measuring structural stresses in the middle ofa structural member. For this type of measurement a much larger hole is required. When theincreased hole radius approaches the material thickness, the behavior of the surface deformationschange and must be accounted for in the finite element models.The finite element models used with the hole-drilling measurement are the link between themeasurable displacements and the unknown stresses in the material, and are a essential elementof the calculation. When the size of the hole used in the measurement is on the same order asthat of the thickness of the material, the FE profiles developed for measuring residual stressesin infinitely thick materials are no longer adequate. Instead, finite thickness models mustbe used to take into account the effect of the bending of the material to the measured surfacedeformations as is depicted in Figure 4.1.19℄℄In inite Thickness Finite ThicknessFigure 4.1: Deformed hole cross sections for infinite and finite thickness materials with ahole. The finite model has bending around the neutral axis that contributes to the surfacedisplacements. This is not the case for the infinite model.Research has been done to attempt to account for the bending influences with an analyticapproach [39, 13], but had problems with the assumptions used not being valid beyond the verythin models. This research uses two different approaches. The first approach was to create acustom set of FE profiles for each specific measurement with the models matching the materialproperties, measurement geometries, and the specific tool geometries used to create the hole.This method will provide the most accurate FE profiles but is time intensive and not quicklyadaptable to a wide range of cutting tools. The second approach uses many different sets ofprofiles created with varying thicknesses and an interpolation technique to calculate the requiredFE profiles for a given thickness. Each of the models in this approach are simplified by modelingthem as flat bottom holes. This approach has the advantage of being able to quickly determinethe FE profiles for a given measurement over a large range of thickness, and hole sizes. Forclarity, through the rest of this document, the first approach will be referred to as the customFE profile method and the second approach will be referred to as the interpolated FE profilemethod.4.1 Model Creation and ValidationTo develop the finite element models for hole-drilling measurements across a range of thicknessesand material types, several factors must be considered: What material properties should be used?20 What spatial units best describe the geometries? What element resolution is desirable? What steps can be made to simplify the models?When measuring stresses in structures, the material is isotropic and the deformations due tohole-drilling fall into the linear elastic range. This allows for FE models that use a linear elasticelement and only need Young's modulus and Poisson's ratio to be defined. For the customFE profiles the values specific to the material are simply used. However, for the interpolatedFE profiles, Young's modulus can be set equal to unity resulting in dimensionless FE solutionswhich can be easily scaled later to match any particular Young's modulus value. To accountfor different Poisson's ratios, sets of models with different Poisson's ratios can be interpolated.This will be covered in detail in Section 4.2. For both approaches, to define the geometry boththickness and radial position are specified in terms of hole radii, allowing for models that allhave the hole radius equal to unity thus eliminating the need to create the models in terms ofstandard units such as mm or in. By taking advantage of the circular geometry of the holeas well as the harmonic nature of the loading, the models can be implemented using to a 2-Daxi-symmetric model evaluated with a harmonic element. This greatly simplifies the model andthe resulting solution.℄12 3 4 5 6 7 8 9 10Sections℄Figure 4.2: Typical mesh used for FE calculations. This specific mesh is a through-hole meshwith a thickness of 1 radius.A program feapPV [40] with a harmonic element type [41] was used for all finite elementcalculations reported. A matlab script was used to generate the text run files required by feapPVto process a given solution. Matlab was used to be able to quickly generate run files for differenthole depths, thickness, and boundary conditions as well as to compile the output of feapPV21into easily processed data structures. Figure 4.2 shows a typical mesh used for FE calculations.At the hole wall, a vertical resolution of at least 4 elements for every sixteenth of a hole radiusof thickness was used. For the horizontal resolution, the mesh was divided into ten sections,between 1 and 31 hole radii from the hole center, logarithmically increasing in size so that thesection nearest the hole is the smallest. Each of these sections is used to step down the verticalmesh resolution to decrease the mesh size. Each of the 10 sections was then split into 13, 11, 8,7, 5, 4, 3, 3, 3, and 2 elements going from the inner to outer sections respectively. Additionallyan element at the outer edge (shown in green) was added with an increased Young's modulus tocause the model, which has an inner and outer radius, to behave as an infinite plate. A singleboundary condition is placed on the outer edge at the top node to anchor the model vertical.The element resolutions both horizontally and vertically, as well as the quality of the FEsolutions, were determined through a validation process. Finite element solutions of a platewith a through-hole were compared with theoretical solutions (eq. 2.2, 2.3, 2.4, & 2.5). Theharmonic model used to solve for Vr and Vt has Poisson effects that the isotropic model does nothave. Due to this, the plane stress assumptions contained in the theoretical models had to beadjusted for, by either setting Poisson's ratio to zero or by making the model very thin. Figures4.3, 4.4 and 4.5 compare the results of the FE and the analytical solutions for three separatemodels: Figure 4.3 is the model with isotropic loading, Figure 4.4 is the model with harmonicloading and Poisson's ratio equal to zero, and Figure 4.5 is the model with harmonic loadingand the model thickness set to 0.25 radii. These figures show that the FE mesh resolutions andgeneration techniques are valid and can be used for models of intermediate hole depth that donot have simple analytical solutions.22Figure 4.3: Comparison of FE model to analytical model for isotropic loading condition. Theleft plot shows the displacement in radii and right shows the % error.Figure 4.4: Comparison of FE model to analytical model for harmonic loading condition withPoisson's ratio equal to zero. The left plot shows the displacement in radii and right shows the% error.23Figure 4.5: Comparison of FE model to analytical model for harmonic loading condition withthickness equal to 0.25 radii. The left plot shows the displacement in radii and right shows the% error. The error is slightly larger for this case because a thickness of 0.25 doesn't fully matchthe plane stress condition of the analytical model.4.2 Finite Element Interpolation TechniquesTo mitigate the computational burden of the custom FE profile approach, it is desirable tocreate a set of generic models and interpolate between them to find the Ur (r), Vr (r), and Vt (r)displacement profiles at each hole depth-stress depth combination required for the measurement.This is the essence of the interpolated FE profile approach introduced at the beginning of thischapter. For a given measurement, the geometry specifications of hole radius, material thicknessand the array of drilled depths, as well as Poisson's ratio, are the variables used to carry outthe profile interpolation.For the set of FE models describing an infinitely thick specimen, commonly used for residualstress hole-drilling measurements, an interpolation method was established by Schajer in 1988[16, 17]. The interpolation requires a set of FE models created over a range of depths (h) andfor each depth over a range of stress depths (H). Figure 4.6 shows the quarter models for theset of models with four distinct hole depths. A FE model with a normalized hole radius of 1 anda normalized Young's modulus of 1 is generated for every hole depth - stress depth combination24and allows for the generation of the interpolation surfaces generalized in Figure 4.7. Each modelis evaluated for both isotropic and harmonic loading conditions resulting in three surfaces forUr (r), Vr (r), and Vt (r) respectively. For n hole depths, a profile set consists of sets ofn(n+1)2Urn,m (r), Vrn,m (r), and Vtn,m (r) profiles, where each individual profile is defined by its holedepth (n) and stress depth (m) as show in equation 4.1. This is the same way a custom FEprofile set would be created except the values for h and H would pertain to the actual geometriesof a given measurement.profile set =Ur1,1......Urn,1 · · · Urn,n ,Vr1,1......Vrn,1 · · · Vrn,n ,Vt1,1......Vtn,1 · · · Vtn,n (4.1)The complete set of data generated from the set of FE solutions describe three interpolationsurfaces for each radial position, r, over which the displacement at that radial position for anyhole depth due to a stress to any depth can be found (Figure 4.7 shows one example surface).There are several possibilities of how to implement this interpolation and, for the purposes of thework, a bivariate interpolation previously used for hole-drilling profile interpolation was used[17]. This method requires six profile set values (A,B,C,D,E,F) taken from the interpolationsurface (Figure 4.7) to find the desired profile value at X as shown in Figure 4.8. The actualinterpolation equation is shown in equation 4.2.fx = y (y − 1) /2 fA+(1− y) (y − Y ) fB+(1− y) (1 + Y ) fC+(y − Y ) (y − Y − 1) /2 fD+(1 + Y ) (y − Y ) fE+Y (1 + Y ) /2 fF(4.2)This interpolation satisfies the need to get Ur, Vr, and Vt displacements at specific hole depthsdefined by a measurement. However, it does not take into account material thickness, a fac-tor that was not so important to measure residual stresses, but is very important when using25hole-drilling to measure structural stresses. The interpolation technique developed in this workfor measurements with finite thickness materials incorporates the described depth specific in-terpolation by nesting it within a thickness interpolation and will be covered in the followingsections.Hole depth, hStress depth, HFigure 4.6: Set of required models for a 4 hole depth model. Each model only shows 1/4 of thehole for visualization purposes. The different colors indicate the stress depths that are actingon a hole for a specific model.26Figure 4.7: Example interpolation surface for a single radial location described by set of FEmodels incrementally calculated with changing hole depth and changing stress depth. Eachpoint actually has 3 surfaces to describe the possible displacements (Ur, Vr, and Vt) and eachradial point on the surface of the mesh will have a different set of surfaces.ABD E FCXH Hhhy-YFigure 4.8: Triangular set of profile values used for bivariate interpolation274.2.1 Finite Thickness InterpolationTo develop an interpolation method that takes into account not only hole depth and stress depthbut also material thickness, it is necessary to know how the behavior of the displacements changewith varying thickness. To get an idea of this behavior, models of hole depths varying from 0radii to 2 radii over a range of thicknesses from .25 to 10 radii were created and then loadedwhere the stress depth was equal to the hole depth. Then the models were run to find the Ur,Vr, and Vt displacements at a radial position of 1. An additional model was created where thebottom edge of the material was fixed vertically to mimic an infinitely thick material. Figures4.9, 4.10, and 4.11 show the Ur (r = 1), Vr (r = 1), and Vt (r = 1) displacements, where the holedepth and stress depth are equal (the portion of the surface indicated in yellow in Figure 4.7),vs depth for this range of thicknesses. These charts only include up to a depth of 2 radii becausein general hole drilling measurements there is very little sensitivity beyond one radius of depthas is evidenced from the curves flattening off the deeper the hole is drilled. From these charts, itis easy to notice that the curves for thinner materials, between 0.25 radii and 2 radii, have muchsteeper initial slopes and the Ur curves have a distinct peak. These effects can be attributed tothe bending shown in Figure 4.1 as these bending effects cause increased displacements as thematerial becomes thinner. At a thickness above around 3 radii the curves start to have similarbehaviors and the differences between them are minimal. Additionally at thicknesses beyond 3radii, the computation of the profile all the way through the thickness requires 2500+ separateFE models and becomes impractical to calculate. For these reasons, the interpolation betweenthicknesses is split into three distinct regions: thicknesses less than 3 radii, thicknesses between3 radii and 10 radii, and thicknesses greater than 10 radii.28Figure 4.9: Ur displacements as a function of depth over a range of thicknesses.29DDFigure 4.10: Vr displacements as a function of depth over a range of thicknesses.30DDFigure 4.11: Vt displacements as a function of depth over a range of thicknesses.4.2.1.1 Thin InterpolationThe thin region is the hardest region to get an accurate interpolation between thickness modelsbecause of the unique nature of each thickness's deformations. For this region a brute forcemethod was developed where many models between the thicknesses of 0.25 radii and 3 radii anduses a spline interpolation to determine the displacements for a desired thickness. Models werecreated for thicknesses of 0.25, 0.3125, 0.375, .5, 0.5625, 0.625, 0.75, 0.9375, 1.0, 1.125, 1.25, 1.5,1.5625, 1.6875, 1.875, 2, 2.25, 2.5, 2.8125, and 3 radii using the methods established in Section4.1. The reason for the strange sequence is that in order to automate the mesh generation, thenumber of vertical nodes at the the hole had to be completely factorable by 2's, 3's, and 5'sso that the mesh resolution could be stepped down away from the hole center. A resolution ofdepth and stress increments of 0.0625 radii was chosen as this was twice the resolution of profilescalculated in prior works and the resulting profiles provided enough points for interpolation evenat low thickness values.31With the measurement geometries of hole radius (r), drilled depths, ([d1, ..., dn]), and thick-ness (t), the interpolation takes the following steps:1. All geometries are normalized with respect to hole radius. This makes the hole radiusunity (like the FE models) as well as defining the material thickness and the set of drilleddepths in terms of radii.D∗ = [d1,...,dn]rt∗ = tr(4.3)2. The profile sets (P1, P2, P3, P4) of the four thicknesses closest to the material thickness arechosen. Four sets are needed because a minimum of four points are required for a splineinterpolation. Additional profile sets could be used for the interpolation but it wouldincrease the amount of tabulated data that has to be held in memory and the additionalprofile sets would not have any significant impact on the final interpolation values.3. The drilled depths are then normalized with respect to thickness for each of the four setsindividually. This is done by dividing the drilled depth values by the material thicknessand multiplying by the thickness of the interpolation sets. This creates four sets of drilleddepths where the ratio of depth to profile set thickness is constant. Due to the normaliza-tion of the drill depths with respect to thickness, the sets of models used for interpolationmust be defined all the way through the thickness, which is the reason why models wereonly created to a maximum depth of 3 radii.D∗1 = t1D∗/t∗D∗2 = t2D∗/t∗D∗3 = t3D∗/t∗D∗4 = t4D∗/t∗(4.4)4. Separately the bivariate interpolation detailed at the beginning of the chapter (equation4.2 and Figure 4.8) is carried out for each of the individual normalized drilled depth setsusing the four respective profile sets.5. There now exist four sets of interpolated profiles sets (P ∗1 , P ∗2 , P ∗3 , P ∗4 ) where Urn,m (r),32Vrn,m (r), and Vtn,m (r) are defined for each of the four thicknesses. Each n,m combi-nation indicates a group of 4 Ur, Vr, and Vt curves to interpolate between. A splineinterpolation is used to interpolate these between groups of curves to obtain a very ac-curate and final profile set (P ) specific to the measurement geometry as shown in Figure4.12. The interpolation is implemented using Matlab's generic 1D spline interpolationfunction interp1.t t t t t*1 2 3 4P1*P2*P3*P4*Proile disp. valueThicknessPspline curveFigure 4.12: Spline interpolation to find P where spline curve is defined by four points(P ∗1 , P ∗2 , P ∗3 , P ∗4 ) .4.2.1.2 Intermediate InterpolationThe intermediate thickness region between three radii and ten radii uses the three radii thickprofiles and infinitely thick profiles where they are interpolated as described in equation 4.5.Pactual = (1− w)P3 + wP∞ (4.5)Pactual, P3, and P∞ denote the calculated profiles for the measurement thickness, the profileset of thickness three radii, and the profile set of thickness infinity respectively. The interpola-tion function, w, was determined empirically by observing the behavior of the changing profiles.Equation 4.6 shows the interpolation function used where t denotes material thickness.w =ln (t− 2)2.0794(4.6)33Figure 4.13 shows how the weighting of P3 and P∞ as the measurement thickness changes fromthree radii to ten radii thick.TWFigure 4.13: Intermediate thickness interpolation weightingTo verify the accuracy of the interpolation, several intermediate thickness profiles were de-termined with FE models and then compared to their associated interpolated values. Figures4.14, 4.15, and 4.16 show the error due to the interpolation and verifies that the interpolationhas a minimal error, with values never exceeding 2% at a depth of one radius.34DFigure 4.14: Intermediate thickness interpolation error for Ur profile type.DFigure 4.15: Intermediate thickness interpolation error for Vr profile type.35DFigure 4.16: Intermediate thickness interpolation error for the Vt profile type.At thicknesses greater than ten radii thick, the infinite thickness model is used. This isthe traditional method to measure residual stresses with the hole-drilling technique.4.2.1.3 Poisson's Ratio InterpolationWhile the FE profile sets allow easy scaling for a given material's Young's modulus, taking intoaccount Poisson's ratio provides a greater challenge. The easiest way to incorporate Poisson'sratio into the FE interpolations is to create multiple sets of profile sets for a range of Poisson'sratios that span most common materials where hole-drilling is used. This is because the materialsPoisson's ratio will affect the individual profiles Ur, Vr, and Vt differently, making a simplerelation such as scaling not possible. Three sets of profile sets were created for all the thicknessesdiscussed in Subsection 4.2.1.1 with Poisson's ratios of 0.2, 0.3, and 0.4. Similar to the waydepth (bivariate) interpolation was nested inside the finite thickness interpolation, both of theseinterpolation schemes are further nested within a basic linear interpolation to obtain the correctPoisson's ratios value.364.2.1.4 Interpolation AssumptionsThe interpolation scheme developed here is only valid for measurements with material geometriesand properties that are encompassed within the assumptions of the underlying FE models.The tool geometry chosen for a measurement needs to closely match the square hole bottomused. Chapter 7 will look into the errors due to the use of flat bottom hole models wherethe cut hole deviates from the ideal square bottom hole. If the material does not behave as ahomogeneous, isotropic, elastic material, then custom FE profiles will be needed to perform ahole drilling measurement. Materials such as composites would fall into this category. Whilethere are limitations to the interpolation scheme, it is still set up to be useful for a wide range ofmeasurements commonly used with hole-drilling, so that the custom FE analysis is not needed.4.3 Stress CalculationObtaining the correct profile set, using either the custom FE profile method or the interpolatedFE profile method, for a given the measurements material properties and geometries, is only thefirst step in solving for stresses. These profile sets need to be manipulated and used correctlyto actually find the stresses. Detailed in the following is an overview of the complete stresscalculation process:1. A set of displacement or strain measurements is taken δ = ([δ1, ..., δl]) where δ can be aset of 3 strains from a strain gauge or can be thousands of displacement measurementstaken at pixel locations on an image in both the x and y directions.2. The measurement geometries and properties are then used to establish the profile setunique to the measurement with either the custom FE profile approach or the interpolatedFE profile approach.3. The profile sets are then manipulated to match the individual measurement locations.For a DIC measurement, where measurement locations are defined at each pixel, a splineinterpolation is used to interpolate between the radial positions from the FE profiles tothe exact radial position of each pixel going from Urn,m (r), Vrn,m (r), and Vtn,m (r) toUrn,m (i, j), Vrn,m (i, j), and Vtn,m (i, j) where i, j define pixel locations.374. The profile sets are then further manipulated so that they are oriented in the direction ofthe measurement. For a DIC measurement, this means converting from profiles definedin the r and θ directions to profiles defined in the x and y directions. This is shown inequation 4.7 where θ is the angular position of the i, j pixel as defined in Figure 2.1, Xx isthe x displacement due to a unitary stress in the x direction (σx), Xy is the x displacementdue to a unitary stress in the y direction (σy), Xs is the x displacement due to a unitaryshear stress(τxy), Yx is the y displacement due to a unitary stress in the x direction (σx),Yy is the y displacement due to a unitary stress in the y direction (σy), and Ys is the ydisplacement due to a unitary shear stress (τxy).Xxn,m (i, j) =12[Urn,m (i, j) + Vrn,m (i, j) cos (2θ)]cos (θ)−12[Vtn,m (i, j) sin (2θ)]sin (θ)Xyn,m (i, j) =12[Urn,m (i, j)− Vrn,m (i, j) cos (2θ)]cos (θ)+12[Vtn,m (i, j) sin (2θ)]sin (θ)Xsn,m (i, j) =[Vrn,m (i, j) sin (2θ)]cos (θ)+[Vtn,m (i, j) cos (2θ)]sin (θ)Yxn,m (i, j) =12[Urn,m (i, j) + Vrn,m (i, j) cos (2θ)]sin (θ)+12[Vtn,m (i, j) sin (2θ)]cos (θ)Yyn,m (i, j) =12[Urn,m (i, j)− Vrn,m (i, j) cos (2θ)]sin (θ)−12[Vtn,m (i, j) sin (2θ)]cos (θ)Ysn,m (i, j) =[Vrn,m (i, j) sin (2θ)]sin (θ)− [Vtn,m (i, j) cos (2θ)] sin (θ)(4.7)6. The profile sets can now be used to define a column space where a linear combination ofprofiles will define the x and y displacements due to any combination of stresses (σx, σy, τxy)acting at the depths defined by the measurement. The linear least squares problem issolved as shown in equation 4.8.Gs = δGTGs = GT δs =[GTG]−1GT δ(4.8)38where,G =Xx1,1 Xy1,1 Xs1,1Yx1,1 Yy1,1 Ys1,1............Xxl,1 Xyl,1 Xsl,1 · · · Xxl,l Xyl,l Xsl,lYxl,1 Yyl,1 Ysl,1 · · · Yxl,l Yyl,l Ysl,ls =σx1σy1τxy1...σxlσylτxylδ =δ1xδ1y...δlxδly(4.9)For measuring structural stresses, the primary concern is to measure the longitudinal stressin the member and this, in general, will only require a measurement to one hole depth, therebygreatly reducing the size of matrix G in equation 4.9.4.4 ConclusionsFinding structural stresses by the hole-drilling technique requires relatively large diameter holes,where the size of the hole may be similar to the thickness of the material. Methods weredeveloped to establish sets of displacement profiles by either using a custom FE profile approachor by using an interpolated FE profile approach. The use of the custom profile approach isrelatively simple but is time intensive as it requires unique FE models for each measurement.39The interpolated FE profile approach uses sets of finite thickness profiles that cover the rangeof thicknesses from thin (0.25 radii) to infinitely thick. By developing an interpolation schemeamong these thicknesses it is possible to generate a set of profiles that will match not onlythe hole and depth geometries of a measurement, but also the thickness, making it easy tochange the hole size of a hole-drilling measurement. Being able to easily scale the hole-size giveshole-drilling measurements an advantage over other locked-in stress measurement methods thatcan only measure stresses near the surface of a material. Most importantly for this work, itmeans that it is now, from a calculation point of view, possible to measure structural stressesby hole-drilling.40Chapter 5DIC Capabilities/OptimizationThe incorporation of the DIC metrology to the hole-drilling measurement method involves un-derstanding how to make DIC function well for this measurement, and determining the asso-ciated capabilities and limitations of DIC for this type of measurement. Since there are no100% accurate means of making measurements with any metrology, there will always be a stressmeasurement error when using DIC for measuring hole-drilling displacements. In general, DIChas a measurement accuracy of about 0.01 pixels, but this generalization does not help to un-derstand the final contribution DIC will have to a stress measurement error. The displacementsaround the hole, after drilling, vary smoothly from location to location, so the local accuracy(at one pixel) is not necessarily the same accuracy as displacements that are measured over agradient with the averaging that exists in the least squares calculation (eq. 4.8). The goal ofthis research, in the context of incorporating the DIC measurement metrology, has two parts:to understand what is required to make a good DIC measurement, and to ascertain what thestress measurement error due to DIC is as a function of hole-drilling test parameters.5.1 DIC OptimizationThere exist many variables in a DIC measurement that can affect the quality and accuracy ofthe measurement. The easiest parameters to control are: the DIC algorithms, the pixel density,and the speckle pattern. This thesis does not attempt to construct the DIC algorithms, butrather used an open source 2D DIC package called NCORR [37]. NCORR has been proven41to be comparable in effectiveness to existing commercial 2D DIC measurement packages [42].A Canon T3i camera was chosen as the hardware for image capture. The Canon T3i has asufficiently large sensor and is at a price point that makes this imaging method easily acceptableto a range of industries. Moreover, if acceptable measurements can be made with this camera,then the specialized scientific cameras common to industry will work as well. Some of thesubsequent analyses are specific to the Canon T3i but are easily repeated for any chosen imagingmethod. While this research uses a Canon T3i, imaging methods will vary depending on scale,environment and industry, and should be left as an easily changeable variable. This leavesthe speckle pattern as the final optimization variable. It is the speckle that uniquely identifieseach pixel making speckle optimization an essential component in the refinement of a DICdisplacement measurement.5.1.1 Speckle OptimizationThe shape and size of the speckles as well as their intensity can greatly affect the quality of aDIC measurement. With the displacements due to hole-drilling being in the sub-pixel range,optimizing the speckle is critical. A paper published in 2007 by Lecompte on the generation ofoptimal speckle patterns for DIC [43] is used as a guide for the development of how to create theoptimal speckle pattern. Lecompte defines two metrics that indicate the quality of a speckle:the spatial characterization of a speckle and the spectral characterization of a speckle.The spatial characterization of a speckle indicates the size and spread of the individualelements that make up a speckle. To determine the size of the speckle components, an imagingprocessing method known as morphology is employed, which allows for image components ofcertain sizes to be removed from an image. Based on Lecompte's work, the speckle shouldbe comprised of elements that range from 1 to 5 pixels in size with a mean size of 2-3 pixels.The spectral characterization of a speckle indicates the smoothness of transition between lightand dark areas. The spectral content of an image is understood by taking the two-dimensionaldiscrete Fourier transform of the speckle image and then comparing it relative to other possiblespeckle choices. The smaller the spread and magnitude of the resulting 2D DFT, the lower thespectral characterization of the speckle. The research by Lecompte indicates that the smoothnessof transition should be maximized by using a speckle with minimal spectral content. By using a42speckle with ideal spatial and spectral characteristics, the DIC calculation has the best possiblechance of making accurate measurements.5.1.1.1 Speckle CreationThere are several possible techniques to apply a speckle to the surface of a material, such as byspraying contrasting paints on the material surface, gluing retro-reflective beads to a surface, orapplying a decal with a speckle printed on it. It was determined however, that both the retro-reflective beads and the decal would not work well for the hole drilling application. This wasevidenced by the retro-reflective beads being prone to falling off, resulting in a general specklebreakdown when drilled, making it unusable. Furthermore, a printed decal was not used becausethe resolution of common printers are on the cusp of the desired resolution, and there is concernthat the elasticity of the adhesive, common to decals, would not deform consistently with theunderlying material. Therefore the chosen method for applying a speckle is the classic methodof spraying black spots of paint onto a painted white surface. This is the most common methodused with DIC, but very few details are available about the specifics of spraying techniques toachieve optimal results.A set of 10 speckle patterns were created using black spray paint. The fineness and intensityof the speckle was controlled by altering the spray pressure, distance to the material surface,and amount of time spayed. Table 5.1 shows a set of generated speckles ranging in coarseness(large-fine) and intensity (Light-Dark).#Speckle Pattern Description1Large Light2Large Normal43#Speckle Pattern Description3Medium Light4Medium Normal5Small Light6Small Normal7Small Dark8Fine Light9Fine Normal10Fine Dark44Table 5.1: Painted speckles patterns.Each of these speckles were analyzed for their spatial and spectral characteristics shownin Table 5.2. The two desired features of a speckle pattern are that it is mostly comprisedof elements ranging between 1 and 5 radii in size and that it has a minimal spectral content.Compared to the paper published by Lecompte, the spectral characteristics of all the specklesare quite similar and thus, was much less a factor for judging the quality of a speckle than thespatial characterization. The spatial content is the characteristic that is most able to distinguishbetween speckles and indicate the best speckle for this particular imaging set up. Based on thedesired speckle element size, it is clear that the fine speckles are most suitable, with the FineNormal Speckle (#9) being best, because of the even balance of light and dark areas. Thehigh sensor resolution of the T3i camera allows for DIC to be able to make high resolutionmeasurements, but it requires a speckle to be made up of small components. To create speckle#9, black spray paint was used where the dispenser was fully depressed, creating the greatestpossible pressure, and the surface was misted for about 10 seconds from a height of 1.5ft. Thehigh pressure causes the paint to spread into droplets that are as fine as possible and the distanceand spray time result in the amount of black paint applied to the surface being evenly distributedwith equal black and white areas. Based on the speckle analysis, this speckle application methodwas used for all the subsequent DIC measurements.# Spatial Characteristic Spectral Characteristic1speckle radius (pixels)0 10 20 30Percent %020406080100×1050.511.522.533.5445# Spatial Characteristic Spectral Characteristic2speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.543speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.544speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.545speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.5446# Spatial Characteristic Spectral Characteristic6speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.547speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.548speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.549speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.5447# Spatial Characteristic Spectral Characteristic10speckle radius (pixels)0 10 20 30Percent %020406080100×10500.511.522.533.54Table 5.2: Speckle Spatial and Spectral Characteristics. The spatial characteristic charts indi-cate the percentage of the image composed of specific speckle sizes. The spectral characteristicimages indicate the spectral content of the image based on the spread of the central peak.5.2 DIC Error Analysis with Synthetic DataThe analysis used to estimate the error in a hole-drilling measurement was divided into threedistinct steps: understanding DIC measurement accuracy, applying DIC measurement accuracyto hole-drilling, and finally, verifying with synthetic hole-drilling DIC data. The first step wasto create synthetic displacements in a speckle image, defined by a displacement gradient, thatcan be processed with DIC (NCORR). This enabled the development of a relationship betweenapplied displacements and measured displacement error. Next, the displacement error relation-ship was imposed on the interpolated FE models from Chapter 4 with varying thicknesses, holedepths, stresses, and pixel densities to estimate hole-drilling stress measurement error as a func-tion of these four variables. Finally, sets of synthetic hole-drilling data were created and thenprocessed using DIC and the calculation methods from Section 4.3. The resulting measurementerrors were used to verify the hole-drilling stress measurement error relationship from the priorstep.485.2.1 DIC Error EstimationIt is necessary to know the applied displacement accurately, to be able to estimate the errorof a DIC displacement measurement . There is no easy physical way to generate known defor-mations accurate to thousandths of a pixel, so, a synthetic method of applying displacementswas chosen. Speckle # 9, from Table 5.1, was used as a reference (before deformation speckle).A displacement gradient matrix matching the pixel locations of the speckle was generated, asshown in Figure 5.1. This matrix defines the x-direction displacements imposed on the referencespeckle for displacements that range linearly between -0.08 to 0.08 pixels. Displacements wereonly defined in the x-direction so that each column of the measured displacements could beaveraged to better indicate the expected measurement error over an area. Considering there isno sensitivity direction in DIC analysis, the x-direction results equally apply to the y-direction.A 2D spline interpolation was used to shift the reference image grayscale values at each pixelby the corresponding values in the displacement gradient matrix. This resulted in a deformedspeckle that could be used for a DIC analysis.Figure 5.1: X-Direction displacement gradient used to interpolate a deformed speckle for DICerror analysis.49After processing the images with the DIC software, the measured displacements were aver-aged along the columns and compared to the applied displacements, shown in Figure 5.2. Thisfigure indicates that there is a small amount of error in the measured displacements, but ingeneral, the measurement follows the expected trend when measuring sub-pixel displacements.Figure 5.3 shows the error of the measured displacement as a function of the applied displace-ment size, where equation 5.1 shows the power law fit that mathematically estimates the DICmeasurement error.ErrorDIC = −0.005× displacement−0.73 (5.1)Figure 5.2: The average measured DIC pixel displacements as a function of the applied displace-ments. The ideal measurement, indicated by the blue dashed line, is what the 100% accuratemeasurement would look like.50Figure 5.3: DIC measurement error as a function of displacement size.A mathematical estimate of DIC error is an essential tool that can be used to help estimatethe error of any measurement based on an averaging of a DIC analysis. In this case it provideda means of estimating hole-drilling error due to DIC.5.2.2 DIC/Hole-Drilling Error RelationshipThe error (E), due to DIC in a hole-drilling measurement, is a function of four variables: materialthickness (t), hole depth (h), stress size (s), and pixel density (p). Thickness and hole depthboth are defined in units of hole radii. The stress size has units of strain because it has beennormalized with Young's modulus. Finally, the pixel density is defined in pixels per hole radiusand is directly linked to the imaging sensor size. To find the error function, E (t, h, s, p), thefollowing steps were taken:1. Over a range of material thicknesses and hole depths, displacement profiles Ur, Vr, and Vtare interpolated. For each thickness/hole depth combination, the average displacement,between r = 1.25 and r = 2.25, of each profile is calculated. These radial bounds werefound empirically to be best for DIC/hole drilling measurements because too close to thehole there is speckle deterioration and subset matching errors and too far from the holethe displacements are too small for DIC to reasonable capture. The surfaces in Figures5.4 show the behavior of the average displacements of each of the profiles Ur, Vr and Vt51as a function of t and h.HTFigure 5.4: Average Ur profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths.T HFigure 5.5: Average Vr profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths.52THFigure 5.6: Average Vt profile displacements between r = 1.25 and r = 2.25 over a range ofthicknesses and hole depths.2. The stresses being measured are defined in XY coordinates. In addition, the DIC imagesare inherently in XY coordinates because of the image sensor grid, so using equation4.7 the profiles Ur, Vr, and Vt from step one are converted to Xx, Xy, Xs, Yx, Yy, andYs displacement profiles at angles of 0, 90, 180, and 270 degrees. Absolute values ofthe displacements at each of these angles was then averaged to get average X and Ydisplacements for each stress σx, σy, and τxy at each thickness/hole depth combination.3. To factor in pixel density and get the displacements on the correct scale, the profiles Xx,Xy, Xs, Yx, Yy, and Ys were scaled with a range of pixel densities and then divided by theYoung's modulus of steel. The choice of Young's modulus is arbitrary and only used toreduce the displacements to the size expected in a hole-drilling measurement. This resultsin a set of profile sets over a range of different pixel densities.4. The load was then included by scaling the profiles over a range of loads. With the Young'smodulus of steel being used, the range of loads was chosen to be between 1 MPa and100 MPa. These loads are then divided by the Young's modulus of steel to normalize theload scale and make the error analysis apply to a range of materials. This now results in53displacements in each direction (X and Y ) for each load (σx, σy, and τxy) being definedover a range of material thicknesses, hole depths, pixel densities, and normalized loads(withunits of microstrain).5. Finally, the error function developed in the prior section can be applied. As the mea-surement of structural stresses primarily deals with the measurement of a normal stressin either the X or Y direction, the displacements associated with either the Xx or theYy profiles were used as the displacements to input into the error function. It is difficultto display the error function (E (t, h, p, s)) as it is a function of four separate variables,but for an example representation of its behavior, a set of four plots was created. Thesefour plots all use a material thickness of two radii, because the effect of thickness in therange of 0.5-3 radii on the final error is minimal and the two radii displacements are nearthe middle of this range. Each plot shows a different hole depth starting at a depth of1/4 thickness and finishing with a through hole. Within each plot there are several linesfor different pixel densities, each showing the error as a function of normalized load size.These four plots, shown in Figures 5.7, 5.8, 5.9, and 5.10, are a means to visualize how theerror changes with each variable, but are not used as a means to actually calculate errorestimates. Three relationships evident in these graphs are: the higher the pixel density,the smaller the %error (with a diminishing rate of return); the larger the load, the smallerthe %error; and, the deeper the measurement the smaller the %error. To practically esti-mate the error for a given setup, a tabulated error function would be used in matlab (orsome other programming environment) to calculate the error for specific thickness, holedepths, and pixel densities.Being able to estimate the error for a DIC/hole-drilling measurement allows the measurement tobe tailored to a minimum error requirement. As the load is not chosen, the hole radius, imagingmethod, and hole depth can all be selected to get as close as possible to a chosen error limit.By taking these steps, along with optimizing speckle prior to the physical measurement, manyof the problems that could arise are mitigated.54Figure 5.7: Hole-drilling error estimate as a function of load and pixel density for 1/4 radiushole depth.Figure 5.8: Hole-drilling error estimate as a function of load and pixel density for 1/2 radiushole depth.55Figure 5.9: Hole-drilling error estimate as a function of load and pixel density for 3/4 radiushole depth.Figure 5.10: Hole-drilling error estimate as a function of load and pixel density for 1 radius holedepth.565.2.3 Error Relationship VerificationHole-drilling data was synthetically created to verify the error relationship. Similar to themanner in which the speckle was shifted in Subsection 5.2.1, sets of hole drilling images werecreated, but the pixel shifts were dictated by FE profile values rather than a gradient. Threesynthetic measurements with identical geometries, X-direction loading conditions of 10, 50 and100 MPa and Young's modulus of steel, were developed. The material thickness was set to 1radius, the depth increments were 0.25, 0.5, 0.75, and 1.00 radii, and the pixel density was set at300 pixels per radius. Figure 5.11 shows one of the synthetically generated measurement sets.Ref. Img Def. Img 1 Def. Img 2 Def. Img 3 Def. Img 4Figure 5.11: Example synthetic measurement image set.By processing these synthetic measurements with DIC and then solving for the associatedstresses, the measurement error was found and then compared to the error function establishedin the prior section. Figure 5.12 shows the results of this verification analysis where the linescorrespond to the estimated error at different loads and the X's correspond to the synthetichole-drilling measurement error at different loads. This chart shows that the error for depthsshallower than 1/2 a hole radius are difficult to estimate. Likely, this is because the size of thedisplacements are so small that it is difficult for DIC to make a consistent measurement. Atdepths below 0.5 radii, the error estimate performs quite well and even for small loads, providesa conservative error estimate. These results indicate that it is beneficial to use a hole that isgreater than 0.5 radii in depth and to use a pixel density greater than 300 to have any accuracyat low loads.57DFigure 5.12: Error function verification. A comparison of error estimates to error measured withsynthetic hole-drilling/DIC data.5.3 ConclusionsDIC can and has been used in the past for hole-drilling measurements without the optimizationand error analysis discussed here; however, this research helps establish what is required fora good DIC/hole-drilling measurement as well as quantifying the potential error in a hole-drilling stress measurement due solely to DIC. Analyzing speckles using their spectral and spatialcharacteristics resulted in an optimized technique for the application of a speckle. This givesDIC the best possible speckle images to calculate displacements. Using a synthetically displacedoptimized speckle pattern, a mathematical error estimate over a gradient was established. Thiserror estimate was then applied to the FE models from Chapter 4 to mathematically estimate theerror of a DIC/hole-drilling measurement based on material thickness, hole depth, pixel density,and load size. The hole-drilling measurement setup can then be tailored to satisfy specific errorrequirements prior to any physical measurement being attempted. This is essential to beingable to move this type of measurement from the laboratory into industry, where a measurementneeds to be set up quickly without having to verify it's accuracy. This analysis is a significantadvance in satisfying the objective of using DIC and hole-drilling to develop a method that canbe easily incorporated by industry to measure locked-in structural stresses.58Chapter 6Cutter EvaluationDuring a machining operation, material is removed, heat is generated, and machining stresses areinduced into the remaining material. For a hole-drilling measurement, these machining inducedstresses combine with the stresses that already exist in the material and make it difficult todistinguish between the unknown locked-in stresses and the machining induced stresses. Priorresearch to determine the best cutting tools and practices for hole-drilling measurements tominimize machining stresses [44] applies specifically to the small holes and high speed drillsused for conventional ASTM E837 style measurement of residual stresses. Here, similar workneeds to be done for the large holes required for the measurement of structural stresses.6.1 Possible Cutting MethodsThere exists many ways of putting a hole in a piece of metal. While it might be possible tocreate a hole using methods such as electrical discharge machining or high pressure water jetcutting, these methods would require extremely specialized equipment and would be prohibitiveto the wide spread adaptation of this method. The development of such measurements forindustry puts several requirements on the cutting method. The cutting method needs to beeconomical, easy to perform, easily reproducible, and fast. This means that specialized cuttingequipment should be minimized and more conventional cutting methods should be adapted.The most obvious piece of equipment to use would be a drill, as substantial work has gone intothe development of drills and cutters specifically designed to make holes in steel structures.59There are three primary cutter types that are used to make holes in steel: the end mill, thetwist drill, and the annular cutter (all shown in Figure 6.1). The end mill has many variationsand is primarily used with large milling machines of very high rigidity. Without the rigidity ofa milling machine, end mills have a tendency to wander, making them impractical for use witha drill in the field. Twist drills, the most common type of drilling cutter, cut a hole centeredon the point of the drill bit tip, but due to the conical shape of the cutter, they are not suitedfor hole drilling measurements, which require as close to a flat bottom as possible. The finalcutter type, the annular cutter, is similar to the end mill, but it cuts only an annulus or ring ofmaterial. By only cutting a ring of material and having a small chamfer on the outer edge ofthe bit, the cutter stays centered. In addition, drilling is less demanding because less materialneeds to be removed. Cutting only an annulus works for hole drilling because the stresses stillredistribute as if all the material within the annulus were removed. Annular cutters are alsocommonly used in the field with mag drills and rail drills for cutting holes in steel, thereforethey make a good choice here. The evaluation of annular cutters was done in three stages: first,the validity of using square bottom FE profiles for an annulus geometry was established, second,the general cutting behavior and cutting induced stresses were investigated using interferometry,the current standard method for hole drilling measurements, and third, similar investigationswere performed with DIC to make sure that similar behavior could be captured with a DICmeasurement as well as to make refinements specific to DIC.End Mill Twist Drill Annular CutterFigure 6.1: Cutter Types. Images adapted from https://www.maritool.com, http://ecx.images-amazon.com, and http://i21.geccdn.net respectively.606.2 Finite Element Model Validity for Annulus HoleTo use the FE interpolation scheme developed in Chapter 4 with annular cutters, it is necessaryto understand the effect the annular hole shape will have on the measurement. A separate FEmodel set was built with an annular hole and was compared to the existing models with a flatbottom hole. The compared models are shown in Figure 6.2. Models at110 and12 radius holedepths were evaluated because it was expected that at shallow depths, the effect of un-removedmaterial in the middle would more greatly impact the results. The results in Figure 6.3 showthe calculated Ur, Vr, and Vt for both model geometries and the profile error relative to theideal square bottom hole.Flat Bottom Hole Annular HoleFigure 6.2: Flat bottomed hole and annular FE model geometries to evaluate the effect ofannular geometry.61RNR62RNRFigure 6.3: Annulus vs. Hole model comparison. Plots A and C show the calculated displace-ment profiles for both hole and annular geometries. Plots B and D show the error of the annulargeometries relative to the hole geometries.From the analysis, it is clear that the profile error diminishes with depth, where at halfof a hole radius of depth the error is well within a reasonable profile error. The profile errorsessentially scale the final stress values, resulting in stress values that are lower than expected.The larger shallow depth error is less of a problem than it may seem because at these depthsthe chamfer on the cutter also has a significant impact on the measurement and for accurate63results would require custom FE profiles. The measurement error due to tool chamfer will beexplored in Chapter 7. By making measurements that are sufficiently deep, below ∼ 15 of a holeradius, the profile errors are within 5% of actual, and the FE interpolation scheme is valid foruse with annular cutters.6.3 Evaluation Using InterferometryInterferometry is a metrology used with hole-drilling that relies on the interference of two co-herent light beams, typically from a laser. The high resolution, the ability to easily scalethe measurement to the desired larger hole sizes, as well as being a well established means ofmeasuring hole-drilling displacements, made interferometry the chosen method to do the initiallaboratory based cutter evaluation. The goals of this initial investigation were to: investigate theannular cutter cutting behavior, find and understand any displacement artifacts due to cutting,and establish the expected machining induced stresses. Investigation of the cutting behavior isa very tactile endeavor and varies based on material hardness, cutter material, drill settings,and many other factors. Of primary concern, was to determine the best method to make cutsthat provided the best possible measurement results. This meant looking at drill speed, chipformation, feed speed, drilling pressure, as well as measurement results. When making a cut intothe material, not all of the resulting measured displacements may be due to the redistributionof stresses. It is possible that the drilling will cause additional deformations, such as thermalexpansion, and for a successful measurement, these artifact would need to be subtracted out.Finding the cause of any artifact is critical in being able to effectively remove it from the mea-surement. Finally, after determining the drilling method and understanding any measurementartifacts, further systematic tests are needed to establish the hole-drilling measurement errorsexpected due to machining stresses from the annular cutter. Both stress-relieved as well asstock hot rolled steel plate were used for this evaluation. Using interferometry for the initialmeasurements establishes a baseline upon which later DIC measurements can be evaluated.646.3.1 Interferometry BackgroundElectronic speckle pattern interferometry (ESPI) is an interferometry technique used to mea-sure displacements on optically rough surfaces. When illuminated by coherent laser light, aninterference pattern is created that has the appearance of random speckles. When an objectis illuminated by two separate laser beams derived from the same source, they interfere in asystematic way, depending on their relative phase. This relative phase depends on the lateralposition of the measured surface. Thus, measurement of local phase changes within the mea-sured interference patterns gives a detailed 2-D map of the displacements within the imagedarea. With a measurement setup similar to Figure 6.4, it is possible to make in-plane mea-surements because as the surface displaces longitudinally, the phase of one beam will increaseand the other will decrease causing a relative phase change. When an image of the displacedspeckles is subtracted from the image of the original speckle it will result in a fringe pattern, asshown if Figure 6.5, where one dark-light fringe pair corresponds to a displacement u describedin equation 6.1. The angle θ is the beam illumination angle from Figure 6.4 and λ correspondsto the wavelength of the light being used. This interferometer is only sensitive in the directiontangential to the specimen surface in the plane of the two beams, this is called the sensitivitydirection. For the interferometer shown in Figure 6.4, measurements can only be made in thex-direction and there is no sensitivity in the y-direction,u =λ2 sin (θ)(6.1)65CameraBeam 1Beam 2SpecimenXZFigure 6.4: In-planee ESPI setup.uFigure 6.5: Typical ESPI fringe pattern.6.3.2 Experimental SetupFigure 6.6 shows the experimental setup that combines an in-plane interferometer (detailed inFigure 6.7) with a swiveling mill where the measurement bed is visible to the camera as well asaccessible for drilling by the use of a hinged mirror.66Hinged MirrorFigure 6.6: Experimental setup of for large hole interferometry hole-drilling measurements.The swiveling mill can be moved out of the way when drilling is complete and the hingedmirror can be rotated over the specimen allowing for both the viewing and drilling of thespecimen in one location.67Laser Beam Splitter Piezo Mirror Beam PathFront ViewFigure 6.7: ESPI box details.The beams that leave the ESPI box are superimposed on the specimen by using beammirrors to move the light around. These mirrors must be extremely rigid, so as not to causeany problems with the extremely sensitive nature of interferometry measurements. Figure 6.8shows the two beam paths and associated mirrors.Beam Paths Beam Mirrors Specimen ESPI BoxFigure 6.8: Interferometry beam path using multiple beam mirrors.686.3.3 Tests and Results6.3.3.1 Initial Measurements and Drilling MethodsThe initial measurements on the interferometry set up were done mainly to get an understandingof the cutting behavior of the annular cutters and to establish what is required for a goodmeasurement. This initial work was done by intuitive exploration. It was found by experiencethat a cutting speed of 500-600 rpm, which is in the range of manufacturer's cutting speedrecommendations, works well. Slower cutter speeds had problems making a cut as it resulted inhigh cutting friction and excessive vibration. The faster speeds caused tool chatter and removedmaterial too quickly, making chips that spun around on the cutter and damaged the materialsurface. The quality of an interferometry measurement is highly dependent on the materialsurface because any small disturbance to the material surface alters the surface texture anddecorrelates the speckle pattern. Figure 6.9 shows two fringe images that should appear similar:the one on the left has major fringe degradation due to surface damage, where as the one on theright is a satisfactory measurement with minimal surface impact. The main source of surfacedegradation, particularly around the hole, is from chips scratching the surface as they leave thecutter. To reduce this effect, it is desirable to keep the chips as small as possible and removethem from the cutting area as quickly as possible. A pulsing action was used on the drill feedso that the tool is only in contact with the material for short bursts of time. This breaks up thechips and stops the formation of the long curling chips that tend to scratch the surface. Removalof chips was initially done by brushing them away with a soft brush, but as this wasn't able toremove chips fast enough, canned compressed air was used. With the canned air, it is importantnot to use too much at once or else the surface cooling will destroy the measurement. The mostimportant thing for making a good measurement is that drilling have a minimal impact on thesurrounding material surface.69A BFigure 6.9: Example of two interferometry hole-drilling measurements. Image A is an exam-ple of a bad measurement with excessive surface damage. Image B is an example of a goodmeasurement where surface damage has been minimized.6.3.3.2 Artifact EvaluationAfter taking several hole-drilling measurements it became clear that there was one main arti-fact of concern. The heat generated during cutting was causing displacements due to thermalexpansion. This is not so much a factor when making hole-drilling measurements with a smallhole diameter at high speed because not enough heat is generated and held in the material tomake a significant difference in the fringe pattern. However, with a much larger hole, the energyrequired to create that hole results in large amounts of heat being generated. Figure 6.10 showsa set of 4 fringe images. Each of these images derives from the same hole-drilling measurement,but taken sequentially at 1, 3, 5, and 9 minutes after the hole was drilled. The vertical fringesbecome fewer in each sequential image, indicating that the displacement is changing with time.Temperature is the only time dependent aspect of the material and therefore must be responsiblefor these displacements. The vertical fringes correspond to a stretch in the x-direction, howeverbecause this interferometry setup is only sensitive in the x-direction, a uniform expansion due totemperature would also appear as vertical fringes. This further supports the conclusion that thisartifact is a result of thermal expansion. The challenge then, is how to eliminate this artifactfrom the stress measurement.70t= 1 t= 3 t= 5 t= 9Figure 6.10: Four images for the same measurement taken at 1, 3, 5, and 9 minutes after drilling.The paper published by Schajer in 2012 [27] details how artifact correction can be incorpo-rated into the least squares stress calculation to minimize the effect of measurement distortions.This artifact correction was designed to eliminate errors due to rigid body motion, as well asstretch and shear in both the X and Y directions. The artifact due to thermal expansion isa uniform stretch, so theoretically its effect should be eliminated with this artifact correction.The artifacts can be separated from the stress measurement by including them as additionalunknowns in the least squares calculation as shown in equation 6.2.[G]W11 W21 W31 · · · · · · · · ·· · · · · · · · · W41 W51 W61..................W1l W2l W3l · · · · · · · · ·· · · · · · · · · W4l W5l W6l[s]w11w21w31...w4lw5lw6l= δ (6.2)Where artifacts w1 . . . w6 are defined as follows:w1 : rigid body x-directionw2 : stretch x-directionw3 : shear x-directionw4 : rigid body y-directionw5 : stretch y-directionw6 : shear y-direction71and W1 . . .W6 are the normalized displacements due to an artifact at each measurementlocation. They are conceptually shown in Figure 6.11. The units associated with the artifactsare arbitrary and based on a chosen normalizing value. It is critical the normalized artifactdisplacements be on the same order as hole-drilling displacements so as not to cause round offerrors within the least squares computation. With an interferometer that is only sensitive tox-direction displacements, w1 . . . w3 are the only artifacts that need to be considered.W1 W2 W3W6W5W4Image Shape Deformed ShapeFigure 6.11: Artifact Shapes.When applying the artifact correction to the hole-drilling measurements in Figure 6.10, theartifacts can be subtracted to show the underlying displacements due to hole-drilling. This isshown in Figure 6.12 where the stretch in the x-direction is subtracted from each measureddisplacement resulting in only the displacements due to hole-drilling stresses. Notice that foreach measurement, the measured displacement and x-stretch artifacts are different but theresulting stress displacements are almost identical. Figure 6.13 shows the calculated stressvalues and artifact magnitudes for each of the 4 measurements. The stress measurements remainrelatively constant (the value is not important at this point) whereas there is a clear reductionin the x-stretch artifact over time. Even the σy values, which only has Poisson effects that aremeasurable by the interferometer (x-direction sensitivity only), only varies at most by 4 MPa.72Figure 6.12: Artifact subtraction from measurements with varying thermal displacements.MMFigure 6.13: Stress and artifact values for each of the 4 measurements. The plot on the leftshows the stress measurements and the plot on the right shows the measured artifacts.The artifact correction adapted from Schajer is clearly able to eliminate the unwanted artifactof thermal expansion due to drilling even when the signal due to stress is much smaller than thatof the artifact. In addition to eliminating the artifact due to drilling, this artifact correctionmethod, designed to eliminate image distortion errors, is also able to eliminate the effects ofsmall camera motions and other disturbances that will occur in the field causing unwanted73artifacts in the DIC images.6.3.3.3 Stress MeasurementsThe goal of the interferometry setup was to be able to measure stresses due to hole cuttingand now, after establishing a proper cutting method and a technique to remove artifacts fromthe measurement, this is possible. All the following tests were performed on hot rolled 108038” steel plate because this is a common steel alloy similar to many structural steels. To makesure that there was no load on test specimens, they were mounted to the optical table withthree bolts and were offset from the bottom by spacers around each bolt. This ensured thatno undesirable bending stresses would be present, while still holding the specimen tight enoughin place for the interferometry measurements. To set a baseline of expected stresses, it is alsodesirable to remove any residual stresses that may exist in the material. This was accomplishedby soaking the test specimens in a kiln at 650ºC for 24 hours, where the oven was slowly raisedto temperature over 4 hours and after the soak slowly cooled for 6 hours. Figure 6.14 showsthe kiln with automated controls and the test specimens used.KilnThermocoupleTest SpecimenContol UnitFigure 6.14: Heat treatment setup.Tests were performed by incrementally drilling with58” carbide and high speed steel cutters,74and then measuring displacements over a range of hole depths through the thickness of thematerial. The stresses were then calculated for each individual hole depth. Figure 6.15 showsthe stress measurement results of the heat treated steel plate measurements. From these charts,it is clear that the magnitude of all the measured stresses are consistently below 10MPa, whichis within the expected error of any hole-drilling measurement, and that the behavior of the σxand σy follow similar trends. This indicates that whatever the added stress due to machiningare, they are likely equal in both the X and Y directions. For a structural stress measurement,where there is only expected to be one primary loading direction, this means that the stressmeasured normal to the loading direction can be subtracted from the primary stress to removeany stress error due to machining. It also appears that the HSS cutter induces less stress thanthe carbide, but this difference is small and the HSS measurement was only made to a depth of4.5 mm so this was not fully verified with this measurement.Hole Depth (mm)1 2 3 4 5Stress (MPa)-15-10-5 0 5 10 15 5/8 " HSS CutterσxσyτxyHeat Treated Plate No-Load Stress MeasurementsHole Depth (mm)2 4 6 8 10Stress (MPa)-15-10-5 0 5 10 15 5/8 " Carbide CutterσxσyτxyFigure 6.15: Unloaded stress relieved 1080 plate steel hole-drilling stress measurement for bothhigh speed steel (left plot) and carbide (right plot)58” annular cutters.To verify that similar results would be obtained on a material that had not been stressrelieved, similar tests were ran on similar specimens that were not stress relieved. The resultsare shown in Figure 6.16. Below the half-way hole depth, the behavior is very similar, howevermeasurements from above the half way hole depth show some distinct differences. This result is75likely due to two causes: one, the presence of residual stresses near the material surface havinga greater impact on shallower depth measurements, and two, the discrepancies are primarily inσy, which is not in the sensitivity direction of the measurement.Hole Depth (mm)2 4 6 8 10Stress (MPa)-15-10-5 0 5 10 15 5/8 " HSS CutterσxσyτxyUntreated Plate No-Load Stress MeasurementsHole Depth (mm)2 4 6 8 10Stress (MPa)-15-10-5 0 5 10 15 5/8 " Carbide CutterσxσyτxyFigure 6.16: Unloaded hot rolled 1080 plate steel hole-drilling stress measurement for both highspeed steel (left plot) and carbide (right plot)58” annular cutters with no stress relieving.6.3.3.4 Interferometry Test SummaryThe interferometry testing successfully showed the effect that drilling large holes with annularcutters can have on a hole-drilling measurement. First, a reliable method for creating holeswith minimal surface damage was established. By using a pulsing feed to keep the chips smalland constantly blowing chips away with compressed air, the surface of the material is preservedand reliable measurements can be made. Next, additional displacements due to heating werediscovered and the calculation method was updated to remove the consequent artifacts. Byadapting the least squares calculation to include artifacts as unknowns, the displacements dueartifacts can successfully be separated from those due to stresses resulting in successful stressmeasurements, even if the artifact displacements are much larger than the displacements due tohole-drilling stresses. Finally, by performing hole-drilling measurements on stress relieved andnon-stress relieved specimens both the expected magnitude and the behavior of the machining76induced stresses were established.6.4 Evaluation Using DICInterferometry is a more precise measurement than DIC, but because of its sensitivity to noise,is not ideal for use in the field. DIC is much more robust, but because of it's lesser precision,it is critical to verify that similar behavior established with the interferometry measurementscan also be observed with DIC measurements. In addition, this phase of testing focuses on thepotential changes that can be made to the drilling method to make it more effective with DICmeasurements.6.4.1 Experiment setupThe experimental set up for the unloaded DIC measurements to evaluate the cutters was exactlythe same as for the interferometry measurements, only the interferometer and the beam-mirrorswere removed and the camera was replaced with a higher resolution camera, as shown in Figure6.17 .CameraSpecimenDepth GaugeCutterMillHinged MirrorMirror Forward ViewFigure 6.17: Experimental setup of for large hole DIC hole-drilling measurements.776.4.2 Test and Results6.4.2.1 Initial TestingAfter the first attempted hole-drilling DIC measurement, it became clear that an additionalprotective surface treatment was required because the drilling chips and metal dust caused sub-stantial speckle damage by smudging the speckled paint. This type of degradation severelyimpairs subset matching in the DIC calculations. By applying a polyurethane coating to thespeckle, the smudging can be eliminated and metal dust can be wiped away while still pre-serving the speckle quality. Figure 6.18 shows the speckle degradation due to drilling on aspecimen with no extra surface treatment versus a speckle with an added polyurethane clearcoat. The polyurethane clear coat was able to protect the speckle sufficiently and was used onall subsequent measurements.Smudged Speckle Coated SpeckleFigure 6.18: Speckle degradation due to lack of protective coat. Image on left shows damagedspeckle. Image on right shows preserved speckle using sprayed polyurethane coating.6.4.2.2 DIC Measurement VerificationWith good speckle quality both before and after drilling, it was possible to make a set ofhole-drilling measurements to verify that DIC measurements result in similar behavior to in-terferometry measurements. A set of measurements was made on the same38” steel plate usedwith interferometry, but the holes were drilled with both12” and1116” HSS annular cutters to78make sure that there was no different behavior for different of hole sizes. Figure 6.19 showsthe DIC measurements corresponding to the interferometry measurements from Figure 6.16.These measurements are noisier than their matching interferometry counter-parts but all thestresses exhibit similar behavior with only a 5-10 MPa variation. Additionally, these measure-ments show that even over a range of hole sizes, the machining stresses of an annular cutter aresimilar. These measurements demonstrate that DIC is capable of making residual stress mea-surements and that the lessons learned when doing the interferometry measurements, includingcutting method, artifact correction, and expected stresses is also applicable to DIC hole-drillingmeasurements.Hole Depth (mm)2 4 6 8 10Stress (MPa)-15-10-5 0 5 10 15 1/2 " HSS CutterσxσyτxyUntreated Plate No-Load Stress Measurements - DICHole Depth (mm)2 4 6 8 10Stress (MPa)-15-10-5 0 5 10 15 11/16 " HSS CutterσxσyτxyFigure 6.19: Unloaded hot rolled 1080 plate steel DIC hole-drilling stress measurement for both12” (left plot) and1116” (right plot) HSS annular cutters.6.4.2.3 Drilling ImprovementsFor interferometry measurements, any small disturbance to the surface, even just touching,would ruin the measurement. In contrast DIC is much more robust and as long as the speckle ispreserved, a measurement can be made. With DIC, it might be possible to improve the cuttingof the annular cutters by using cutting oil and wiping it away before a measurement image isrecorded. To understand the benefit of using a cutting oil, a series of single-depth measurements79were made with both58” and1116” carbide and HSS cutters. Based on the DIC error analysis inChapter 5, as well as the interferometry and DIC measurements from this chapter, it is desirablethat a single depth measurement be drilled to at least one half of the hole radius. To make surethat the structural stresses dominate the displacements, the hole should be drilled at least halfway through the thickness, minimizing the contribution of residual stresses near the surface. Forboth these reasons all the following tests, using 9.525 mm steel plate, were drilled to a depth of6 mm. The results for both with and with out cutting oil are shown in Figure 6.20. For eachcutter, the stress measurement results are improved by using cutting oil, in both a reduction inthe magnitude of the measured stresses as well as the range of the measured stresses. This wasexpected because use of a cutting oil makes the machining easier, produces less heat, and inducesless stress into the material. Most importantly, the speckle pattern on the material surface waspreserved when using oil, verifying that cutting oil can be used with the DIC measurement.Figure 6.20: Comparison of single depth hole-drilling stress measurements for 4 different annularcutters both with and without cutting oil. The relatively high stress measurements are likelydue to the residual stresses present in the test specimens, as no stress relieving was done.806.4.2.4 DIC Test SummaryThe DIC testing successfully proved that DIC is capable of making hole-drilling stress measure-ments and explored aspects of the drilling method that was needed or could be changed whenusing a DIC measurement. Comparative measurements using DIC displacement measurementshowed that DIC was able to measure displacements accurately enough to calculate stress be-havior similar to interferometry. With interferometry being a standard by which to judge DIC,the results show that, while the results are a little noisier, DIC is a fully viable metrology forhole-drilling measurements. Additionally, it was found that to preserve the information contentof a DIC measurement, the speckle must be protected by applying a polyurethane coating. Inturn, this protective coating then allowed for the use of cutting oil, which reduced the machininginduced stresses and made cutting easier, and could easily be wiped away after drilling.6.5 ConclusionThe way a hole is cut during a hole drilling measurement, and the tool that is used to cut thehole, have an impact on both the stress results as well as the simplicity of the test. Annularcutters were chosen to drill holes that meet the requirements for measuring structural stressesin an industrial environment. Annular cutters only remove an annulus of material and theresulting geometry, from a hole-drilling measurement perspective, still mimics a complete hole,but makes the drilling significantly easier by reducing the amount of material to be removed.Annular cutters are also easily adapted to industry because they are already widely used in theon-site construction of steel structures.By comparing the FE models used in Chapter 4 to a FE model with an annulus, it wasverified that with a hole of sufficient depth, the FE interpolation scheme using flat bottom holesis valid for holes made with annular cutters. Considering that a deep hole is required for thismeasurement method, the annulus will have a minimal effect on the measurement. This showsthe versatility of the interpolation scheme and establishes the annular cutter as a reasonabletool for the measurement method.With the choice of the annular cutter it was then necessary to evaluate the effect thatthis large cutter has on the final hole-drilling measurement. Interferometry, a well established81method for measuring hole-drilling stresses, was chosen for the initial evaluation of the annularcutters. This provided a baseline that DIC could be compared to and established the behaviorand magnitude of the expected machining induced stresses. Additionally, the interferometrymeasurements were able to show that the machining induced σx and σy should be close toequal, indicating that it might be possible to subtract out machining induced stresses from astructural stress measurement where either σx or σy should be equal to zero.Using the interferometry results as a baseline upon which to judge DIC, similar hole-drillingtest were performed using DIC. These measurements were able to show that DIC is capable ofmaking the analogous hole-drilling measurements as interferometry. These measurements alsoestablished two additional practical factors that can improve the DIC/hole-drilling measurement:one, that a protective coating is necessary for the DIC speckle to be preserved during drillingand two, that the use of cutting oil, to reduce machining stresses, does not significantly impairthe DIC measurement quality.Choosing annular cutters as the hole cutting method, and comprehensively evaluating theeffects of this cutting method on hole-drilling measurements, completes a large step necessaryto be able to measure structural stresses reliably using the hole-drilling method. These cuttersare easily adaptable to industry, satisfy the geometries needed to measure structural stresses,and the analysis shown in this chapter verifies their ability to make hole-drilling measurements.82Chapter 7Experimental Validation7.1 IntroductionThe goal of this chapter is to assess the effectiveness of the developed hole-drilling/DIC mea-surement method for measuring structural stresses. To evaluate the measurement method aseries of experiments were carried out on real structural members with tightly controlled load-ing conditions. Four focus areas were identified:1. DIC displacement measurements - This portion of testing focused on the use of DIC as ameans for making hole drilling measurements. The accuracy of both DIC individually andof the DIC/hole-drilling technique were explored. This section establishes the performanceof the DIC/hole-drilling method, how it compares to interferometry measurements, andto prior work using DIC and hole-drilling.2. Finite thickness effects - This portion of testing examined the effects of the finite thicknessFE models and the error associated with the use of incorrect thickness FE profiles.3. Cutter shape effects - This portion of testing investigated the FE profile interpolationmethod and examined the error associated with the mismatch between the geometries flathole bottom, used in the FE models to create the interpolated profiles, and the physicalgeometries of the cutting tool. The error associated with the geometrical discrepancy isevaluated and a correction method is developed.834. Structural stress measurement - This final portion of testing evaluates how the proposedDIC/hole-drilling method can be used to measure structural stresses in different structuretypes that may contain residual stresses as well as structural stresses.The results of these experiments establish the accuracy, capabilities, limitations, and benefits ofthe DIC/hole-drilling method as a means to measure locked-in stresses in structural members.7.2 Experimental Setup and Methods7.2.1 Experimental SetupThe experimental set up for measuring loaded DIC/hole-drilling measurements is shown infigures 7.2. A 300 kN capacity, Tinus Olsen, compression machine was used to apply a knownload to the specimen, effectively simulating a known locked-in load. The load was measuredwith a load cell internal to the machine and strain gauges fitted to each test specimen. Atvarying loads and hole depths, images of the test specimen were captured to be processed later.If either the camera or the test specimen are moved they can be re-referenced to one anotherwith the referencing fixture that has locating points to align the camera and specimen. This iscritical as it is necessary to either remove the camera or the specimen from the setup to drillinto the material.84Figure 7.1: Zoomed out view of experimental set up to give an idea of scale. Area shown inFigure 7.2 highlighted in yellow.85IlluminationReferencing FixtureTinus Olsen Compression MachineCameraTest SpecimenStrain Gauge ReaderFigure 7.2: Experimental setup for DIC/ hole-drilling measurements with applied loading.Figure 7.3 shows the two drilling methods that were used. With the Milling Method, thetest specimen was removed from the test fixture and a separate mill was used to drill the hole.The mill provides an accurate and repeatable setup to measure incrementally at several holedepths. With the MagDrill Method, the camera was removed from the fixture and a drill with amagnetic base was used to cut the hole. This second drilling method is much more indicative ofa measurement that would be done in the field, but with this set up, it was difficult to referencethe hole position accurately, so it was used only for single depth measurements (measurementsthat only use one hole depth). Both of these drilling methods used annular cutters as thecutting tool. The position of the hole was drilled as close as possible to the neutral plane of thespecimen. This minimizes the effect that bending stresses will have on the measurement of theuniform longitudinal forces that may arise due to imperfections in the loading of the specimen.86Milling Method MagDrill MethodFigure 7.3: Hole-drilling methods used in experiments.7.2.2 Experimental MethodsThe experiments performed were designed to take one large set of images over a range of holedepths and loads and to process those images in different ways so that the deformations due tothe applied stresses can be measured separately from the deformations due to all the stresseswithin the material. The following steps detail the actions carried out to obtain a complete setof measurement images.1. A speckle pattern was applied to the specimen, as detailed in Chapter 5, and a polyurethanecoating was applied to allow for cutting oil to be used.2. A strain gauge was attached to the specimen for verifying the applied stress.3. The test specimen was placed on the referencing fixture, and if the milling method wasused to cut the hole, a set of referencing pins were used to return the specimen to thesame position after drilling.4. The camera was aligned to the specimen in the test fixture, so that the camera viewingaxis was normal to the specimen surface.5. The top jaw of the Tinus Olsen compression machine was brought down until it just held87the specimen in place. The specimen is held by the machine but there is very little stressapplied (< 1 MPa).6. A set of images were then recorded over a sequence of stress values ranging 0 and 150MPa.7. Next, a hole was drilled into the material using one of the two drilling methods. After,either the camera or the specimen was returned to the test fixture.8. Steps 6 and 7 were then repeated for the desired number of hole depths (usually between1 and 6) and care was taken to record images at the same loads as the original set.Figure 7.4 shows an example set of images for a measurement of 3 different hole depths and 4different applied stresses (including 0MPa). With this set of images, each column is a measure-ment set similar to a standard hole-drilling measurement, where a stressed material is imaged atvarying depths and then compared to a reference with no hole. The stresses can be calculatedat each depth individually or as a profile measurement. The resulting stress values would be acombination of applied stress, residual stress, and machining stress. This first approach to ana-lyzing image data is not ideal to determine the DIC/hole-drilling measurement accuracy becausethey include unknown residual machining stresses. However, if the DIC analysis is conductedusing the images along each row of Fig 7.4 (excluding the top row), using the zero load imageas the reference, the DIC indicated deformations between images are due only to the appliedstresses. The deformations due to residual stresses and machining stresses are not present be-cause the only thing that changed between images was the applied load. This essentially mimicsa material that has no internal residual or machining stresses. By individually evaluating eachimage with respect to the zero load image, the developed methods ability to calculate stress ata given depth can be evaluated. Both of these approaches of making measurement sets are usedin the subsequent analyses. For clarity through the rest of the chapter, each approach is referedto as the following: The first approach is referred to as zero-depth reference. The second approach is referred to as zero-load reference.88An important point of note is that for all the experiments performed in this chapter only thestresses in the direction of the applied stress are reported. The transverse stress, which shouldbe equal to zero, all fell within the same error range as was found for the applied stresses.Applied Stress0 MPa 10 MPa 50 MPa 100 MPaDepth6 mm4 mm2 mm 0 mmFigure 7.4: Example set of measurement images. Each column is a measurement set of an Acalculation and each row is a measurement set of a B calculation.7.3 DIC/Hole-Drilling Measurement EvaluationThe first step in evaluating the stress measurement method is to evaluate the effectiveness ofdisplacement measurement method (DIC), on which it is based. To eliminate uncertainties, azero-load reference calculation is used so that a one-to-one comparison of applied stresses tomeasured stresses can be made. Furthermore, the custom FE profiles, which match the cuttergeometries, are used in the calculation in an attempt to eliminate any error due to incorrect FE89geometries.7.3.1 Experiment DetailsFour single depth measurements were made on separate structural elements (channel, I-beam,square tube, and rail) where sets of images were taken at loads ranging from 0 to 300 kN . Toguarantee sufficient surface displacements, the hole depths used ranged between13 and23 radii.Table 7.1 details the specifics for each measurement. The Tinus Olsen compression machine canexert a maximum force of 300,000 N which is the limiting factor for the maximum stress thatcan be applied to each element.Channel I-Beam Square Tube Railhole radius mm 6.35 8.73 8.73 7.94material thickness mm 5.25 6.75 6.25 17.45hole depth mm 4.05 3.50 3.00 4.25normalized thickness 0.828 0.773 0.716 2.200normalized depth 0.639 0.401 .344 .535pixel densitypixelmm 51.25 59.82 68.24 61.55stress range MPa 0 - 150 0 - 75 0 - 100 0 - 30# of applied loads 11 6 6 4Table 7.1: DIC evaluation experiment details.7.3.2 Displacement Measurement ResultsFigures 7.5 through 7.8 show the measured DIC displacements for each of the four structuralelements at 15MPa and at their maximum load. Each figure is set up as follows: the firstcolumn shows the displacements as measured by DIC, the second column shows the measureddisplacements with all artifacts removed, the third column shows what the ideal displacementmeasurement would look like for the applied load, and finally, the fourth column shows theresidual remaining after the theoretical solution has been subtracted from the DIC measureddisplacements. Ideally, the residual should have a random texture, but in practice, some sys-tematic features remain. The top row in each figure shows displacements in the Y-direction and90the bottom row shows displacements in the X-direction. The displacements in these figures areshown with a synthetic fringe pattern (similar to interferometry measurements) because a fringepattern is capable of showing the details and relative sizes within both the large and the smalldisplacement shapes contained within these measurements. However, the residual is shown witha colormap to preserve the sign information within the display.Meas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Channel 15MPa AppliedFringeScaleErrorScalepixelspixelsMeas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Channel 150MPa AppliedFringeScaleErrorScalepixelspixelsFigure 7.5: Channel DIC/hole-drilling displacements. One fringe is equal to ~ 3000nm. The 150MPa measurement shows just how effective the LSQ calculation is at picking out the displace-ments due only to stress even when the signal is tiny compared to the complete displacementmeasurement. Additionally, for all the specimens tested, the artifact seen in the residual issmallest here.91Meas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05I-Beam 15MPa AppliedFringeScaleErrorScalepixelspixelsMeas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05I-Beam 75MPa AppliedFringeScaleErrorScalepixelspixelsFigure 7.6: I-Beam DIC/hole-drilling displacements. One fringe is equal to ~ 2500nm. The mea-sured displacements in these measurements show that there is a significant amount of shearingdisplacements, which are likely due to the specimen rotating slightly between loading. Evenwith this significant shear, the displacements with the artifacts removed still do match quiteclosely to the ideal displacements.92Meas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Square Tube 15MPa AppliedFringeScaleErrorScalepixelspixelsMeas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Square Tube 100MPa AppliedFringeScaleErrorScalepixelspixelsFigure 7.7: Square tube DIC/hole-drilling displacements. One fringe is equal to ~ 2200nm. Theartifacts seen in the error were maximum for these square tube measurements compared to theother experiments. Even with these large artifacts, the LSQ algorithm was still able to calculatereasonable stress values as seen in Figures 7.9 and 7.10.93Meas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Rail 15MPa AppliedFringeScaleErrorScalepixelspixelsMeas. Disp.Y AxisDisp. No Art. Ideal Disp. ErrorX Axis-0.06-0.04-0.0200.020.040.06-0.0500.05Rail 30MPa AppliedFringeScaleErrorScalepixelspixelsFigure 7.8: Rail DIC/hole-drilling displacements. One fringe is equal to ~ 2500nm. With adistinct curve across the web of the rail, of all the measurements the rail surface was the farthestfrom flat. Despite this obvious inconsistency with the FE models, the measurement error wasstill minimal.For each measurement, the displacements due to artifacts dwarfs the displacements due tohole-drilling as all measurements have significant stretch, shear, and rigid body motion compo-nents. The rigid body motions alone (not shown) for each of these measurements was in excessof 10 pixels which is over 100 times the size of the displacements due to hole-drilling. These ar-tifacts are linked to several causes, some of which may be: heating due to drilling, compression,imperfect centering, and imperfect load distribution shifts. It may be possible to take steps toremove these artifacts, but it is with these large artifacts that DIC displacement measurementsshine.94The error results showing the differences between the displacement data with no artifactsand the ideal displacement data indicate that the results are not perfect. Ideally the residualwould be a random peppering of blue and red dots on a green background, but it is clear herethat while the majority of the area is still green, there is a definite shape to the error wheresome areas tend to blue and others to red (especially for the square tube). This means thatthere is likely an additional artifact in the displacement data that is not being removed and ispossibly caused by something in imaging setup or change in the viewing angle caused by rigidbody motion. However, even without adding this artifact shape to the LSQ algorithm, becausethe artifact is small (on the same order as the displacements due to hole-drilling) and there isnothing in the column space of the LSQ algorithm that matches its shape, it does not have alarge impact on the final calculated stress values. This is evident in the Figures 7.9 and 7.10that show the stress results for each of these measurements.7.3.3 Stress Measurement ResultsApplied stress (MPa)0 50 100 150Measured stress (MPa)050100150IdealChannelI-BeamSq. TubeRailFigure 7.9: Stress results for the measurements described in Table 7.1 showing the applied stressvs. the measured stress.95Figure 7.10: Error results for the measurements described in table 7.1. The left plot shows themeasurement error in MPa and the right plot shows the absolute value of the percent error.Additionally, the right plot shows the estimated error with dashed lines for each measurementbased only on the accuracy of DIC.Figures 7.9 and 7.10 show the measured stress values for each structural member as well asthe associated measurement error. It is clear that the measured stress values closely follow thelinear trend of the ideal measurement and that the error is limited to within ±5MPa. Muchof this error can be attributed to DIC, where the estimated absolute error due to DIC for eachmeasurement (from Chapter 5) is shown with a dashed lines. Any error in addition to thesevalues is likely due to imperfections in the measurement, such as speckle damage, depth readingerrors, or imperfect specimen loading. Important to notice, however, is that the general trendof the absolute measurement errors matches the estimated values, and in many cases is lower,showing the DIC error estimation to be a conservative estimate.967.3.4 Experiment Conclusions7.3.4.1 Interferometry ComparisonThe DIC measurements shown in the left column of of Figures 7.5 through 7.8 convey thatdisplacement artifacts exist on a large scale relative to the expected hole-drilling displacements.This is an experimental issue rather than a DIC issue. Experiments with artifacts of thisscale were included because they are indicative of a measurement that would be made in thefield. It would be impossible to make these measurements using interferometry because thedisplacements seen are well beyond the range that interferometry can measure. DIC however,only requires that the portion of image being analyzed be present in both images. By beingable to make accurate stress measurements, despite the large artifacts, DIC is seen to be muchmore adaptable to field use than interferometry.7.3.4.2 Existing DIC/Hole-Drilling Work ComparisonThe prior work done by McGinnis, Nelson, and Baldi [9, 25, 24]in DIC/hole-drilling research allpresent stress and error analysis that can be compared to the measurements made here. Table7.2 shows the DIC method, the stress calculation method, the measurement magnitude, and theabsolute measurement error range for each work.McGinnis Nelson Baldi Current WorkDIC Method 3D-DIC 3D-DIC 2D-iDIC 2D-DICCalculation Method LSQ (3-4 Points) LSQ Full Field iDIC LSQ Full FieldHole Size (radius) 31.75 mm 0.8 mm 2 mm 6.35-9.53 mmPixel Density (pixelradius) ~500 ~100 ~580 350-700Stress Range (MPa) 135 200 0-100 0-150Absolute Error (MPa) 9.2 12 < ~2 < ~3Table 7.2: Prior research and current work comparison.Both McGinnis and Nelson use 3D-DIC, which is a much more complex set up and requiresspecial calibration. Baldi uses 2D-iDIC, which combines both the stress calculation and DICcalculation into one operation by using the FE profiles as shape functions to fit to the the97deformed image. It is clear from this comparison that there is no obvious advantage to using3D-DIC as it does not decrease the measurement error. It does however, add to the measurementcomplexity, making the measurement less adaptable to field use. McGinnis used a simplifiedleast squares calculation using only 3-4 points in the image. While providing a straightforwardnumerical answer, this approach uses only a small fraction of the available data and thus doesnot take full advantage of the averaging benefit available using the least squares approach.This is likely the cause for increased error in McGinnis' measurement. Nelson used a full fieldmeasurement and a least squares calculation similar to this work, but only uses FE profiles inthe radial direction (Ur and Vr but not Vt). This, as well as the low pixel density of the images,are likely the cause of increased error. The smaller scale of Baldi's experiments does not impactthe actual measurement method because the pixel density is still the same, but it does allowfor increased control over experiment parameters. Specifically the illumination, loading andminimization of extraneous motion, which could all be more tightly controlled. This is likelythe reason for the decreased error in Baldi's measurements. All things considered, relative to theprevious work done with hole-drilling and DIC, the measurements made in this work comparefavorably with previous published results.7.3.4.3 Least Squares CalculationBased on these experiments, it is clear that even with imperfect displacement measurements,the LSQ calculation method is capable of measuring the applied loads. The inclusion of artifactsin the least squares analysis allows for the removal of the large artifacts that would otherwisedominate the calculation, leaving just the signal due to hole-drilling stresses and other smallartifacts. As long as nothing in the column space (defined by the FE profiles) of the LSQcalculation resembles the shape of these additional artifacts, they are effectively ignored by thecalculation. Using a full field DIC measurement, which has the advantage of averaging overmany points, the accuracy of the FE profiles used to form the column space have a relativelylarger impact on the final measurement. The closer the FE profiles can be made to match themeasurement geometries, the better the LSQ calculation can perform.987.4 FE Profile Thickness EvaluationA major factor in making the FE profiles match the actual measurement geometries, especiallyon the scale required by measurements in structures, is the finite thickness of the profiles.Chapter 4 explained the reasoning behind using finite thickness profiles, but the following setof results will illustrate why the use of finite thickness profiles is necessary. This analysis usedspecimens similar to the prior section, as well as a zero-load reference measurement, but useddifferent hole sizes to get a wider range of thicknesses.7.4.1 Experiment DetailsTabulated in Table 7.3 are the details for the individual experiments.Channel I-Beam Square Tube Railhole radius mm 9.53 8.733 6.35 7.94material thickness mm 5.25 6.75 6.15 17.45hole depth mm 5.00 3.50 5.00 4.25normalized thickness 0.551 0.773 0.969 2.200normalized depth 0.525 0.401 0.787 .535pixel densitypixelmm 50.60 59.82 75.56 61.55stress range MPa 0 - 150 0 - 75 0 - 130 0 - 30# of applied loads 4 4 4 4Table 7.3: Finite thickness FE profile evaluation experiments.7.4.2 Stress Measurement Results and ConclusionsBy varying the thickness for each measurement from the correct thickness to infinitely thick(the profiles traditionally used for hole-drilling measurements) and calculating the stress, theerror caused by the incorrect thickness choice can be determined. An example of the effectthat incorrect thickness FE profiles can have on a measurement is shown in Figure 7.11 for thesquare tube measurement. This figure clearly shows that as the thickness error increases themeasurement error also increases proportionally.99MAFigure 7.11: Measured stresses vs. applied stresses for single measurement where calculationthickness was varied. This shows how incorrect stresses can be calculated by using incorrect FEprofile thicknesses.This result is only valid for one particular thickness and does not indicate how the errorwould change for a thicker or thinner measurement. To better understand this relation, thestress for each of experiments detailed in Table 7.3 was calculated using the infinitely thickprofiles and the error was determined with respect to the known applied loads. The resultsfor these calculations are shown in Figure 7.12. The shown curve indicates the maximum errordue to incorrect thickness FE profiles over a range of thicknesses. The behavior of this curveis expected, where as the material increases in thickness the error decreases, however, it doeshighlight how large this error can be for thin measurements. This figure also shows that usinga cutoff thickness of 3 radii for the fine interpolation profile sets is reasonable, because beyonda thickness of 3 radii the measurement error due to an incorrect thickness is greatly diminished.100SNFigure 7.12: Stress measurement error vs. material thickness when infinitely thick FE profilesare used for calculation.With an established set of finite thickness FE profiles, it becomes important to know howthe measurement error is affected for any thickness error. Figure 7.13 shows the measurementerror as a function of thickness error for a range of thicknesses. These results illustrate thatsmall thickness errors can have a significant impact on the measurement error and thereforejustifies the interpolation method developed in Chapter 4, which uses many separate profile setsat small thicknesses to obtain an optimum interpolation resolution.101SFigure 7.13: Stress measurement error vs. calculation thickness error for a range of materialthicknesses.It is important to note that the results displayed in figures 7.11, 7.12, and 7.13 are for a uni-axial stress field (applied stress only in Y-direction). Results for a different stress field wouldstill exhibit the same trends, but the values would differ slightly.7.5 Cutter Shape / Flat Bottom FE Profile EvaluationThe first two sets of experiments all used the custom method for FE profile generation where thecutter geometry is factored into the FE model geometry. However, using these types of profilescomes with the added cost of increased calculation time and added computational complexity.For a measurement that needs to be carried out quickly and easily in the field, it would bebeneficial to use FE profiles that can be interpolated from a set of pre-existing FE models.The interpolated profiles sets are created with square bottom models which ignore cutter shapegeometries such as the chamfer at the tool edge. To use the interpolated FE profiles reliablywith flat bottom holes, the error due to using flat bottom models when the cutter has a chamfer102needed to be explored and a method to correct for the error needed to be established.7.5.1 Experiment DetailsSimilar to the experiments up to this point, a zero-load reference measurement calculationwas used for this analysis. Three measurements using cutters ranging from 6.35 mm to 9.52were performed. Table 7.4 provides the details of each measurements and Figure 7.14 shows thecutter geometries considered in the subsequent analyses.Exp. 1 Exp. 2 Exp. 3hole radius mm 6.35 8.73 9.53material thickness mm 6.15 5.91 5.25hole depth mm 1.00-6.15 1.5-5.91 2-5.25normalized thickness 0.969 0.667 0.5512normalized depth 0.169-0.969 0.172-0.677 0.209-0.551pixel densitypixelmm 75.56 59.82 50.60tool chamfer height (ch) mm 0.9 1.1 1.15tool chamfer width (cw) mm 2.1 2.35 2.5normalized ch 0.14 0.13 0.12normalized cw 0.33 0.27 0.26Table 7.4: Experiments for cutter geometry error analysis.Figure 7.14: Drilled hole geometries including chamfer width and height.1037.5.2 Experiment ResultsTo understand the nature of the the variation in stress measurement results due to the use theflat bottom FE profiles, the stresses for each experiment were calculated with both custom FEprofiles that match the tool geometry and interpolated FE profiles that assume a square bottomhole. Shown in Figure 7.15 are the results for Exp. 2, which highlights the differences betweenthe measured stresses when using the square bottom FE profiles as opposed to the customprofiles. The measurements that use the custom profiles line up as expected and match theresults seen in the experiments from Section 7.3, but the measurements that use the flat bottomFE profiles can have a significant error. This error is a result of the FE profile values used in theLSQ calculation being larger than they should be, because they don't account for the materialthat is contained within the chamfer. The error due to the interpolated profiles is maximumfor shallow holes and reduces with an increase in hole depth. This behavior occurs because thechamfer at the bottom of the hole gets increasingly remote from the measured surface as thehole depth increases. For a given depth, the measurement is simply scaled by FE profiles withvalues larger than they should be because of the incorrect geometry, meaning that the % errorfor a given depth is constant regardless of the load. Figure 7.16 shows the average error ateach depth for all three of the experiments. If these three curves lined up, then the error wouldsimply be a function of the hole depth and tool radius, but, as the chamfer sizes are differentfor each cutter, the error is also a function of chamfer size.104Figure 7.15: Measurement variation due stress calculation with FE profiles that account for thetool geometries for Exp. 2. The calculations with the tool chamfer use custom FE profiles thatmatch the tool geometry, whereas the calculations with no chamfer use interpolated FE profiles.105Figure 7.16: Average measurement error at each calculation depth for all three experiments. Theaverage is used here because the incorrect thickness profiles scale the measured stress resultingin a constant relative measurement error independent of applied stress.As is evident in Figure 7.16, the error due to square bottom FE profiles can be quite large,and is not acceptable for reliable stress measurements. To be able to use the flat bottomedinterpolated profiles, it is necessary to come up with a method for correcting these errors. Asthe error is both a function of depth and chamfer size, a dimensionless constant, F , describedin equation 7.1, combines both cutter radius (a), chamfer height (ch), chamfer width (cw), andhole depth (h).F =hachcw(7.1)Plotting the measurement errors from Figure 7.16, not as a function of normalized depth,but rather this dimensionless constant, F , the errors converge onto one path as seen in Figure7.17. A curve was fit to these data points and a mathematical expression derived (eq. 7.2) toestimate the error due to flat bottom FE profiles.106EFigure 7.17: Average measurement error for all three experiments as a function of F, a dimen-sionless constant, described in equation 7.1, which is a function of hole depth, hole radius, cutterchamfer height, and cutter chamfer width.%Error =100 (−F + 3)F 2 − .5F + 43 (7.2)This error estimation can be used after the LSQ calculation to correct the stress measure-ments calculated with flat bottom FE profiles. Figures 7.18 shows the corrected stress curves forExp. 2 where the dashed lines are the uncorrected stresses and the solid lines are the correctedvalues. It is clear that with the correction, the stress curves much more closely, match the idealcase. The average error, for all three experiments at each depth from figure 7.16, is comparedto the corresponding corrected errors in figure 7.19. It is clear in this figure that the error foreach measurement is reduced substantially by correcting the measured stress based on the errorestimate from equation 7.2.107Figure 7.18: Measurement correction for Exp.2 showing the original measurements in dashedlines and the corrected measurements with solid lines. The corrected stress values are signifi-cantly closer to the ideal curve for each depth.108ENFigure 7.19: Average measurement error for all Exp. 1,2,&3 showing both the uncorrected andcorrected measurements.7.5.3 Experiment ConclusionsThe use of an interpolation scheme to calculate the FE profiles can be fast, effective, and reducethe computational burden of the stress calculation. However, with the models being based on aflat bottom hole, there can be significant errors due to inconsistencies between the physical andmodeled geometries. The experiments in this section have shown that it is possible to obtainaccurate stress results within 10% at a depth of 0.2 hole radii and within 3% at a depth of 0.5hole radii, by correcting the measured values with an error estimation function. This functionestimates error as a using hole depth, hole radius, cutter chamfer height, and cutter chamferwidth as variables. If time allows, it will always be more accurate to use FE profiles thatcontain cutter geometries, but if measurements need to be made quickly, and be easily adaptedto different cutter shapes, flat bottom profiles, which are easily interpolated, can be used.1097.6 Structural Stress CalculationThe experiments shown in this chapter up to this point have all been zero-load reference mea-surements, which remove both residual stress and machining stress from the measurement, andhave dealt with proving and understanding the accuracy of the DIC/hole-drilling measurementmethod. With the capabilities of the measurement method vetted and the expected measure-ment accuracy understood, the method can now be applied to measuring the complete stressstate in structures with zero-depth reference measurements. These measurements measure thecomplete stress state in the structure, which combine structural stresses (applied loads), residualstresses, and machining stresses. To measure only the structural stresses, a method is neededthat can separate them from the residual and machining stresses. This was accomplished in thethree phases.1. Experiments were performed on each of the four structural member types, with no ap-plied load, to calculate the stress profile through the thickness of each material. Thesemeasurements provided an indication of the size and nature of the residual stresses andshowed what to expect in subsequent measurements.2. A set of experiments on each structural member type was carried out over a range of loadsand depths. The stress was then calculated at each depth individually with a series ofsingle depth calculations. These measurements allowed for accurate stress measurementsto be made at each depth/applied load combination. The results from the no appliedload measurements were then compared to those with applied load to create a correctionmethod capable of separating residual and machining stresses from the structural stresses.3. A final set of single-depth experiments were performed using the correction methods fromphase 2 to separate out the structural stresses. This showed the effectiveness of thecorrection method and the applicability of the developed DIC/hole-drilling method forthe measurement of structural stresses.1107.6.1 Phase 17.6.1.1 Experiment DetailsDue to manufacturing processes, different structural members will have different residual stressprofiles through the thickness of the material. Detailed in Table 7.5 are four experiments, onefor each structural element type, each with a no applied load. With no applied load, only theresidual and machining stresses will be measured. If the stress is calculated with a complete setof images ranging from zero to final depth, as opposed to a single depth measurement, a profileof the changing stresses across the thickness of the material can be determined.Channel I-Beam Square Tube Railhole radius mm 6.35 8.73 8.73 7.94material thickness mm 5.25 5.91 6.15 17.45hole depth mm 2.14-5.25 2.75-5.91 2-6.15 1.75-9.75normalized thickness 0.826 0.677 0.704 2.200normalized depth 0.337-0.826 0.331-0.677 0.229-0.704 0.220-1.228pixel densitypixelmm 51.25 59.82 68.24 61.55applied stress MPa 0 0 0 0Table 7.5: Experiments for residual stress profile calculation.7.6.1.2 Experiment ResultsFigure 7.20 shows the measured stress profiles across the thickness for channel, I-beam, andsquare tube structural elements. These measurements are not expected to be exact because ofthe inaccuracies in the measurement set up and the coarse depth increments, but nonetheless thestill provide a valuable indication to the magnitude and behavior of the residual stresses in eachstructure type. Both the channel and I-beam use similar extrusion processes in manufactureand thus both exhibit a compressive stress across the the thickness of the material. However,the square tube uses a different process where the tube is bent and welded into shape causing111a much different residual stress profile. These three experiments show that there is no genericstress profile that can be assumed for a variety of structural elements, and even among similarstructural elements, the magnitude of residual stress can vary significantly by changing size andshape of the element.SNFigure 7.20: Measured stress profiles across the thickness for channel, I-beam, and square tubestructural elements. It is clear from these stress profiles that the residual stresses are bothsignificant in magnitude and differ greatly between structure type.A significant amount of research has gone into understanding the residual stresses in railsbecause of the direct impact that they can have on rail safety. Due to this, of four structuretypes analyzed here only the profile calculated for the rail could be compared to any existingresults. A rail sample similar in size to the rail specimen used in this analysis was evaluatedfor residual stresses using the contour method [45], a destructive means of measuring residualstress. Figure 7.21 compares the results from the contour method to the measured residualstress profile. Across the web of the rail, the magnitude of the measured stresses matches wellto the stresses from the contour method where the stress magnitude increases from the edge tothe middle and are both within the same range of -80 to -180 MPa.112SNFigure 7.21: A comparison of measured rail residual stresses to an existing residual stress anal-yses of rail. The image on the left shows the residual stresses of a rail determined using thecontour method [45]. The plot on the right shows the measured residual stress profile for therail. Note that the magnitude of the measured residual stress profile is similar the the resultsfrom the contour method.7.6.1.3 Experiment ConclusionsThe results from the experiments highlight two main things: one, the magnitude of the residualstresses in structures are significant in magnitude, and two, there is no generic shape to theresidual stress profiles across a range of structure types. The fact that the residual stresses aresignificant in magnitude means that they cannot be ignored and that to determine structuralstresses separate from the residual stresses, a measurement correction method is required. Withno generic shape to the residual stress profiles, the correction method will need to be calibratedfor each structure type and geometry individually.1137.6.2 Phase 2There are two obvious correction methods: one, a correction that determines the residual stressin a structure by numerically modeling the manufacture process, and two, a correction thatdetermines the residual stress in a structure with a calibration measurement at a known zeroload condition. The determination of residual stresses numerically is beyond the scope of thisresearch, but has been explored for a rail with positive results [46, 47]. For this work calibrationmeasurements were made at zero load to subtract out the residual stresses from the subsequentmeasurements.The structural stress (applied stress) is constant across the thickness of the material, meaningthat regardless of depth, the same structural stress measurement should be measured, thereforemaking single depth measurements ideal for this type of measurement. Single depth measure-ments can be made faster and easier than profile measurements because only one hole depthneeds to be drilled. Moreover, single depth measurements are more stable because the LSQcalculation only has to match one set of FE profiles to one displacement measurement. If sin-gle depth measurements are to be used for the measurement of structural stresses, the simplesubtraction of residual stress at the drilled depth, as defined either by a numerical model or bya profile measurement, would not work. This is because the deformation at the surface, due toresidual stress at a given depth, is a result of not only the residual stress at that particular depthbut also the residual stress that was contained in the material above it. A calibration curve formaking single depth measurements would require a curve that provided the apparent residualstress as a function of depth. Apparent residual stress is the uniform stress value that for aparticular depth causes the same surface deformations as the combined residual stresses up tothat depth. Establishing this curve is done simply with a set of zero load measurements madeover a range of depths. Rather than performing a profile calculation that would determine theactual residual stress at each depth, by conducting a single depth measurement at each depth theapparent residual stress is determined. A set of apparent residual stress measurements can be fitto a curve and used to subtract out residual stress from subsequent single depth measurementswith a structural stress component.1147.6.2.1 Experiment DetailsThe four experiments used in phase one are again used for phase two, but, in addition tothe no load measurements, measurements with applied load are included. The details of theexperiments for phase 2 are shown in Table 7.6.Channel I-Beam Square Tube Railhole radius mm 6.35 8.73 8.73 7.94material thickness mm 5.25 5.91 6.15 17.45hole depth mm 2.14-5.25 2.75-5.91 2-6.15 1.75-9.75normalized thickness 0.826 0.677 0.704 2.200normalized depth 0.337-0.826 0.331-0.677 0.229-0.704 0.220-1.228pixel densitypixelmm 51.25 59.82 68.24 61.55applied stress MPa 0-100 0-50 0-100 0-22Table 7.6: Experiments for structural stress correction analysis.7.6.2.2 Experiment ResultsThe results for the channel, I-beam, square tube, and rail elements are all presented in Figures7.22, 7.23, 7.24, and 7.25 respectively. The three plots A, B, and C in each figure are explainedas follows:1. A - These plots show the calibration curves, created using a spline interpolation betweenthe apparent residual stress values, measured with the zero applied load image sets fromeach experiment. The scale of the y axis for each of the plots includes 0 MPa to bettershow the behavior and spread of each calibration curve.2. B - These plots show both the corrected (solid lines) and uncorrected (dashed lines) stressmeasurements as a function of applied stress for three depths across the cross-section ofthe material. To give the plots a positive slope, compressive loads are shown in these plots115as positive. The results shown in this plot can be compared to the results in Figure 7.9 inSection 7.3 of this chapter.3. C - These plots show the corrected measurement error in MPa relative to the knownapplied load. The results shown in this plot can be compared to the results in the left plotof Figure 7.10 in Section 7.3 of this chapter.116Applied stress (MPa)0 20 40 60 80 100Measured stress (MPa)020406080100120140160Bideal0.50(h/a)0.66(h/a)0.81(h/a)0.50(h/a)-Corrected0.66(h/a)-Corrected0.81(h/a)-CorrectedApplied stress (MPa)0 20 40 60 80 100Error (MPa)-5-4-3-2-1012345C0.50(h/a)-Corrected0.66(h/a)-Corrected0.81(h/a)-CorrectedFigure 7.22: Channel calibration curve and structural stress measurement results. Plot A showsthe calibration curve. Plot B shows the measured and corrected stresses as a function of appliedstress. Plot C shows the measurement error in MPa.Of all the experiments, the residual stresses for the channel element were the smallest, whichis likely related to the small cross-sectional thickness. However, it did exhibit significant variabil-ity where the calibration ranged from close to 0 MPa at both surfaces and had a magnitude ofaround 25 MPa at the mid point. The corrected measured stresses were within ±5MPa which117is quite good considering that this measurement is the result of two separate DIC/hole-drillingmeasurements, one for measuring the calibration curve, and one for measuring the uncorrectedstress.Figure 7.23: I-beam calibration curve and structural stress measurement results. Plot A showsthe calibration curve. Plot B shows the measured and corrected stresses as a function of appliedstress. Plot C shows the measurement error in MPa.118The calibration curve measured for the I-beam is the most consistent across the cross-sectionof the material, where it is linear at around −35MPa. This is likely due to the symmetricalshape of the I-beam, where compressive residual stresses are evenly distributed across the webof the I-beam and the flanges contain the balancing residual stresses that are in tension. Similarto the channel measurement, the measurement error after correction is reassuringly low.Figure 7.24: Square tube calibration curve and structural stress measurement results. Plot Ashows the calibration curve. Plot B shows the measured and corrected stresses as a function ofapplied stress. Plot C shows the measurement error in MPa.119The calibration curve for the square tube measurement had both the largest overall magni-tudes and largest variation from point to point. This is likely due to the combination of stressesthat go into the square tube element during manufacture, including flat sheet bending, welding,and straightening. Even with these very large residual stresses, the corrected structural stressmeasurement error still stayed within ±4MPa of the known applied loads.120Applied stress (MPa)0 5 10 15 20 25Measured stress (MPa)050100150Bideal0.43(h/a)0.66(h/a)0.89(h/a)0.43(h/a)-Corrected0.66(h/a)-Corrected0.89(h/a)-CorrectedFigure 7.25: Rail calibration curve and structural stress measurement results. Plot A shows thecalibration curve. Plot B shows the measured and corrected stresses as a function of appliedstress. Plot C shows the measurement error in MPa.Of the four experiments performed, the results obtained for the rail measurement were mostsatisfying. The residual stress component of each measurement was quite high (over 100MPa),the surface of the rail web is not flat but curved, making it difficult to establish a zero depthdatum, and the applied loads were relatively small with a maximum of 22MPa. Even with these121limitations, the final corrected stress values were consistently within ±2MPa, which is a similarresult to results obtained by Baldi [24] but under less ideal measurement conditions.7.6.2.3 Experiment ConclusionsThe corrected structural stress values measured with these four experiments show that it ispossible to separate structural stresses accurately from the complete stress field with the useof a calibration curve. The calibration curves were established with zero load measurements,where the apparent residual stress at each measurement depth was calculated. It is likely thatthis calibration curve could also be generated with numerical models, but this was not exploredin this analysis.7.6.3 Phase 3The limitation of the results from phase 2 is that the calibration measurement and correctedstructural stresses were both calculated from one large image set on the same test specimen. Tofully prove the validity of this correction method, accurate structural stress results need to beobtained using the calibration curves from phase 2 measurements, but with a new set of singledepth measurements on separate tests specimens. For the calibration curves from phase 2 to bevalid, each of the new test specimens should have the same geometries as the calibration test,however the cutter radii and drilled depths need not match.7.6.3.1 Experiment DetailsSimilar to all the other experiments, all four structural element types were again tested. Thegeometries of the test specimens remained the same as in phase 2, but all four measurementswere made to depths not used in phase 2 and the measurements for the channel, I-beam, andsquare tube all used different size cutters. The specifics for each experiment are detailed inTable 7.7.122Channel I-Beam Square Tube Railhole radius mm 9.53 7.94 7.94 7.94material thickness mm 5.25 5.91 6.15 17.45hole depth mm 4.00 3.25 3.25 4normalized thickness 0.55 0.74 0.77 2.20normalized depth 0.426 0.410 0.410 0.504pixel densitypixelmm 51.25 59.82 68.24 61.55applied stress MPa 0-100 0-50 0-100 0-30Table 7.7: Experiments for calibration curve validation analysis.7.6.3.2 Experiment ResultsThe stresses for each of the measurements described in Table 7.7 were calculated and thencorrected using the calibration curves from plot A in Figures 7.22, 7.23, 7.24,and 7.25. Thecorrected structural stress results and associated error of this analyses are shown in figures 7.26and 7.27 respectively. These results show the measurement correction method with each of thefour structure types and that the resulting error is only slightly worse, at ±6MPa, than the priormeasurements. The increased measurement error is likely due to the variation in the machiningstresses between the measurements used to create the calibration curves and the measurementsperformed here.123Applied stress (MPa)0 20 40 60 80 100 120Measured stress (MPa)0102030405060708090100idealchannel: depth-0.43ibeam: depth-0.41square: depth-0.41rail: depth-0.50Figure 7.26: Corrected measured structural stress vs. applied stress for single depth measure-ments using residual stress correction calibration curves.124Figure 7.27: Error results for the corrected stress measurements in MPa.7.6.3.3 Experiment ConclusionsSuccessfully measuring the stresses applied to each structural member, on separate specimensfrom those used to create the calibration curves, shows that the consistency of the stress mea-surements and that the same stresses can be calculated independent of the cutter used. Thisdemonstrates that the developed DIC/hole-drilling stress measurement method can accurately,reliably, and consistently measure structural stresses over a broad range of structure types.7.7 Evaluation ConclusionsFour sets of experiments were used to evaluate the DIC/hole drilling method and its abilityto measure structural stresses. By controlling the longitudinal loading and designing the ex-periments so the stress could be calculated either as a zero-load reference measurement or azero-depth reference measurement, the method could be independently evaluated for accuracy125both with and without residual and machining stresses. This allows for an evaluation of thedifferent factors that can affect a measurement, the understanding of the expected measurementerror, and then the application of these results to the measurement of structural stress.The first set of experiments focused on DIC measurements and the ability to use themfor hole-drilling stress calculations. The results showed that DIC can reasonably be used tomeasure hole-drilling stresses to within ±5MPa, even with significant optical artifacts in themeasurement. This result is an improvement over DIC/hole-drilling research up to this pointand highlights the critical role optical artifact correction plays in the calculation of stress withsignificant measurement noise.The second and third sets of experiments focused on the performance of the calculation usingFE models with known geometry errors. First, the use of incorrect thickness FE profiles wasevaluated. The results showed that it is critical to use FE models with the correct thickness,especially for measurements made on materials of thickness less than three hole radii. Second,the use of FE profiles created with flat bottom hole models was evaluated. It is desirable to usesimple flat bottom hole models because they can easily be incorporated into an interpolationscheme, so that custom sets of FE profiles are not needed for each measurement. The resultsfrom this analysis showed that the assumption of a flat bottom hole, when it does not match theactual hole geometry, can cause significant errors especially at shallow hole depths. However,a correction method was developed that can be used to adjust the measured stresses to within3% of their actual value. Based on these two sets of experiments, it is recommended to use FEprofiles that match as closely as possible to the actual measurement geometries, but if necessary,simplifications can be made and stress values corrected post measurement.The final set of experiments applied the developed DIC/hole drilling method to the mea-surement of structural stresses. The behavior and magnitude of residual stresses for a range ofstructure types was established by performing a series of stress profile measurements with noapplied load. These measurements showed that there was no generic behavior or magnitude tothe residual stresses, so in order to subtract out residual stress from a measurement, a calibrationfor each structure type and geometry is needed. To explore this, a second set of measurementswere made over a range of loads and depths where calibration curves of the apparent residualstress at each depth were created using a series of single depth calculations. The calibration126curves were then applied to the single depth measurements under load. The results from theseexperiments showed that calibration curves can reliably be used to measure the stress, but tofully prove the use of these calibration curves, a final set of single hole depth experiments werecarried out that used separate specimens of the same structure type and geometry as the priortest. The results of these final experiments proved that with calibration curves, the structuralstresses in a structural element can be measured to within ±6MPa, even when different cuttersand hole sizes are used for testing.To illustrate that an accuracy of ±6MPa is sufficient for measurement of structural stressesthe real world example of measuring rail neutral temperature can be examined. Rail neutraltemperature is the temperature at which a section of rail will have no stress due to thermallyinduced loads and can be determined by measuring the longitudinal stress in the rail section.It is specified that a measurement used to measure rail neutral temperature must be able tomeasure to within ±5F [3]. Using the thermal coefficient of expansion and Young's modulusof steel it is determined that a ±5F accuracy corresponds to a ±6.6MPa stress measurementaccuracy. This is greater than the ±6MPa that the developed measurement method is shownto be capable of thus indicating that this method is accurate enough for field measurements.Overall, the evaluation performed establishes the capabilities of the developed stress mea-surement method and its ability to measure hole-drilling stresses. The capabilities and advan-tages of using DIC as a displacement measurement method were established. The effects of FEprofile errors on the final stress measurement were explored and error correction methods wereestablished. Most importantly however, was proving that the method can successfully apply tothe measurement of structural stresses.127Chapter 8Conclusions8.1 ContributionsThe objective of this research, as stated in the introduction, is to develop a method that canmeasure locked-in structural stresses and can be used practically in industry. This means thatthe measurement method has to measure structural stress quickly, repeatably, and accurately,even with disturbances that could be present in an industrial setting. To realize this goal, ameasurement method combining the hole-drilling technique and digital image correlation wasdeveloped.The hole-drilling calculation was modified with the use of finite thickness FE profiles. Largeholes are required to measure stresses deep within a structure. This is because deeper thanone hole radius, the magnitude of surface deformations due to drilling are too small to reliablymake a stress measurement. The infinitely thick FE profiles, used to measure residual stressesnear the surface of materials, do not accurately model the surface deformations from these largeholes, where material thickness and hole radius have the same order of magnitude. In additionto using finite thickness FE profiles, an interpolation scheme was developed to calculate thecorrect FE profiles for a given measurement. This ensures that each measurement does notrequire a unique set of FE models and allows for the method to be adapted easily to a range ofstructure sizes and types.Digital image correlation was chosen as the deformation measurement metrology since smalldisturbances will not ruin a DIC measurement, as is the case with interferometry, and it allows128for quick and repeatable measurements. The size of the deformations due to hole-drilling are verysmall, so to give the DIC calculation the best possible images, the speckle application methodwas optimized using a morphology analysis. Additionally, a method to estimate the stressmeasurement error as a function of DIC accuracy was created. This allowed for the imagingset up and measurement parameters to be tailored to a desired measurement resolution and ameans for estimating the error bounds of a given measurement. The initial set of experimentsin Chapter 7 show that the general behavior of this estimation is accurate, making it a valuabletool for the implementation of this measurement method over a wide range of structure typesand sizes, critical for the adaptation of this method by industry.A practical cutting method needed to be found, and the effects of the cutting method onthe final measurement needed to be determined. Consequently, a study was done to explorethe use of annular cutters as a means to drill the holes, because they create a hole of similarshape to the flat bottom holes used in the interpolated FE profile scheme. Moreover, they arealready widely used in industry for the fabrication and maintenance of steel structures. Withboth interferometry and DIC measurements, it was found that the cutting action of annularcutters would likely cause ±10MPa machining stress but could be reduced to ~±5MPa withthe use of cutting oil. Final results showed that annular cutters were capable of making reliablehole-drilling measurements, but often the final measurements required a correction based oncutter geometry if flat bottom FE models were used.Finally, experiments were created where the structural stress (applied load) could be variedin a test specimen and the accuracy of the developed method established. In general, themethod was shown to be able to measure stress to within ±4MPa, but with the use of zero loadapparent residual stress curves, needed to subtract out residual stresses from the measurementthis accuracy was reduced to ±6MPa. These experiments validated the developed DIC/hole-drilling measurement method, and satisfied the objective of this work to create a means tomeasure locked-in structural stresses that can easily be adopted by industry.1298.2 LimitationsThe main limitation of the work is the required use of calibration curves to eliminate residualstresses from the measurement, as each type and size of structural element needs a separateresidual stress datum curve to be determined. To make this method better for industry, amore generic technique to subtract out residual stresses is desirable. This may be possible withnumeric calculations of residual stresses, which use models of the manufacturing processes ofdifferent structural elements. However, this is beyond the scope of this work.A second limitation was that the experiments performed could not evaluate DIC/hole-drillingstress profile calculation accuracy. This is because the zero-load reference measurements areonly capable of evaluating one depth at a time, and the zero-depth reference measurementscontained unknown residual stresses in the measurement. To evaluate the stress profile calcula-tion accuracy, test specimens, with a known stress profile and zero residual stress, would needto be made at a scale large enough to be evaluated with annular cutters, which is not an easytask.8.3 Future WorkThere are a few directions in which this work should continue:1. Take this measurement method to the field and measure real structural stresses. Thiswould involve designing and testing a fixture that a drill and camera could reference to,and could easily be fixed to a broad range of structure sizes and shapes. Doing thiswould truly show the effectiveness of the developed method and expose potential practicalchallenges that were not seen in the lab.2. Develop a better relation of how chamfer shape and size effects the measurement error,when using flat bottom FE profiles over a broader range of cutter and chamfer sizes. Thiswould likely involve a synthetic analysis and then subsequent experiments to prove theresults. A more concrete relationship between chamfer shape and error would allow forthe finite thickness profile interpolation scheme, which uses flat bottom profiles to be usedover a larger range of measurements.1303. Develop a better understanding of the behavior of residual stresses in structural elements.This can be done either through modeling or experimentation to explore the generationof stress datum curves and determine if there are any simplifications that can be made intheir creation.131Bibliography[1] Robert T. Reese and Wendell A. Kawahara. Handbook on structral testing. 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Measurement of structural stresses using hole drilling Harrington, Joshua S. 2015
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Title | Measurement of structural stresses using hole drilling |
Creator |
Harrington, Joshua S. |
Publisher | University of British Columbia |
Date Issued | 2015 |
Description | From a measurement standpoint structural stresses can be divided into two broad categories: stresses that can be measured straightforwardly by adjusting loads, e.g., live loads on a bridge, and those that are much more difficult, e.g., gravitational loads and loads due to static indeterminacy. This research focuses on the development of a method that combines the hole-drilling technique, a method used to measure residual stresses, and digital image correlation (DIC), an optical method for determining displacements, to measure these difficult-to-measure structural stresses. The hole-drilling technique works by relating local displacements caused by the removal of a small amount of stressed material to the material stresses. Adapting the hole-drilling technique to measure structural stresses requires scaling the hole size and modifying the calculation approach to measure deeper into a material. DIC is a robust means to measure full-field displacements and unlike other methods used to measure hole-drilling displacements, can easily be scaled to different hole sizes and corrected for measurement artifacts. There are three primary areas of investigation: the modification of the calculation method to account for the finite thickness of structural members, understanding the capabilities and limitations of DIC for measuring hole-drilling displacements, and evaluating the effects hole cutting has on the measurement. Experimental measurements are made to validate the measurement method as well as apply it to the real world problem of measuring thermally induced stresses in railroad tracks. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2015-10-24 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NoDerivs 2.5 Canada |
DOI | 10.14288/1.0166775 |
URI | http://hdl.handle.net/2429/55049 |
Degree |
Master of Applied Science - MASc |
Program |
Mechanical Engineering |
Affiliation |
Applied Science, Faculty of Mechanical Engineering, Department of |
Degree Grantor | University of British Columbia |
Graduation Date | 2015-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nd/2.5/ca/ |
Aggregated Source Repository | DSpace |
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