Hole-Drilling Residual Stress Measurement Research Articles

Ultrasonic and conventional fatigue behavior, strain rate sensitivity, and structural design methods for wrought and cold spray Al-6061

Cold spray is an additive manufacturing process that accelerates powder particles to supersonic speeds to create repairs and bulk depositions with fine-grained microstructures, high density, and good mechanical properties. Fatigue property measurement for these novel materials is critical for their use in safety-critical components, which can be accelerated with the use of ultrasonic fatigue testing. In this work, ultrasonic (20 kHz) and conventional (20 Hz) fatigue studies were conducted on as-sprayed bulk Al-6061 and conventional wrought Al-6061-T6. Complementary fatigue studies of surface preparation (surface finish and residual stress) and fatigue specimen geometry (round versus flat), as well as hole-drilling residual stress measurements, were undertaken to minimize the influence of these confounding variables. Cold spray Al-6061 exhibits fatigue frequency sensitivity, whereas the wrought material does not. Tensile testing at varied strain rates indicates that a portion of the fatigue frequency effect can be attributed to strain rate sensitivity. Fractographic studies show that crack initiation occurs from unbonded powder particles at the surface at high stress amplitude, and transitions sub-surface at lower stress amplitude. The results of these studies were used to create frequency-corrective models of S-N data and Kitagawa-Takahashi diagrams that can be used to design for fatigue crack initiation and growth resistance.

Validation of Hole-Drilling Residual Stress Measurements in Workpieces of Various Thickness

BackgroundA recent revision to the ASTM E837 standard for near-surface residual stress measurement by the hole-drilling method describes a new thickness-dependent stress calculation procedure applicable to “thin” and “intermediate” workpieces for which strain versus depth response depends on workpiece thickness. This new calculation procedure differs from that of the prior standard, which applies only to thick workpieces with strain versus depth response independent of thickness.ObjectiveHerein we assess the new calculation procedures by performing hole-drilling residual stress measurements in samples with a range of thickness.MethodsNear-surface residual stress is measured in a thick aluminum plate containing near-surface residual stress from a uniform shot peening treatment, and in samples of different thickness removed from the plate at the peened surface. A finite element (FE) model is used to assess consistency between measured residual stress across the range of sample thickness.ResultsMeasured residual stress varies with sample thickness, with thinner samples exhibiting smaller near-surface compressive stress and a larger gradient of subsurface stress. These trends are consistent with both observed bending (curvature) of the removed samples and the trend in FE-calculated expected residual stress. The measured and expected residual stresses are in good agreement for samples of intermediate thickness, but the agreement decreases with sample thickness. Measured residual stress is invariant with gage circle diameter.ConclusionThe new thickness-dependent stress calculation procedure for hole-drilling provides meaningful improvement compared to thick-workpiece calculations.

Regularization of Hole-Drilling Residual Stress Measurements with Eccentric Holes: An Approach with Influence Functions

Regularization of Hole-Drilling Residual Stress Measurements with Eccentric Holes: An Approach with Influence Functions

Tikhonov Regularization for the Fully Coupled Integral Method of Incremental Hole-Drilling

BackgroundThe unit pulse integral method is used extensively with the incremental hole-drilling residual stress measurement technique. The ASTM E837 standard, which applies only to isotropic materials, recommends the use of Tikhonov regularization to reduce instability when many depth increments are used. In its current formulation, Tikhonov regularization requires the decoupling of stress, as is possible for isotropic materials. The fully coupled integral method is needed for residual stress determination in layered composite laminates and is currently employed without Tikhonov regularization. This causes greater sensitivity to measurement errors and consequently large stress uncertainties. An approximate method of applying Tikhonov regularization exists for biaxial composites, but is not applicable to more complex laminates.ObjectiveExtend Tikhonov regularization to the fully coupled integral method to improve residual stress determination in composite laminates.MethodsThis work investigates the use of the approximate and fully coupled regularization approaches in an angle ply composite laminate of [+45/-45/0/90]s construction. Experimental validation in a [0/+45/90/-45]s laminate is also presented where the regularized fully coupled integral method is compared to the series expansion method that includes all in-plane stress and strain directions simultaneously in a least-squares solution.ResultsThe regularized integral method produces comparable results to those of series expansion while requiring twelve times less FE computation to calculate the compliances. The optimal degree of regularization is also more convenient to determine than the optimal combination of series order required by series expansion.ConclusionsThe new method is easily applied and should find wide application in the measurement of residual stresses in composite laminates.

Hole-drilling method eccentricity error correction using a convolutional neural network

Hole eccentricity is an important error source when residual stress is measured via the hole-drilling method. The conventional ways to correct eccentricity error for hole-drilling residual stress measurement rely on complicated mathematical processes and are difficult to use. To overcome this shortcoming, this paper proposes a method that uses a convolutional neural network to correct for the hole-drilling method eccentricity error. First, the hole-drilling method measurement process in uniform biaxial stress field is simulated via the finite element method. The influence of the eccentric distance, eccentric angle, and stress ratio on the strain measurement error is discussed. Then, a convolutional neural network is trained using simulated data and the hole-drilling method strain measurement error is predicted for arbitrary eccentricity conditions. Finally, the residual stress is corrected by introducing the strain error into its equation. The simulated residual stresses of ten eccentric measurement points in predefined stress fields are corrected using this procedure to conducted numerical tests. The maximum error of simulated stresses decreased from 30.46% to −4.67% after correction. Therefore, the hole eccentricity has a significant influence on the residual stress measurement accuracy of hole-drilling method. The proposed correction method can effectively eliminate this error.

Plasticity Effects in the Hole-drilling Residual Stress Measurements in Welded Structure

Plasticity Effects in the Hole-drilling Residual Stress Measurements in Welded Structure

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

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

Circumferential Rosette Design for Extended Depth Hole-Drilling Residual Stress Measurements

The radial design for strain gauge rosettes used for hole-drilling residual stress measurements was established over 50 years ago and has remained almost unchanged since then. The design was developed to promote strain sensitivity, but was made without regard for ability to identify interior stresses. Consequently, only near-surface residual stresses can be identified. The aim of this study is to investigate rosette geometric features that may be refined to enable a significant increase in ability to identify interior stresses without significant loss of strain sensitivity. A finite element analysis was undertaken to model the influence of various geometrical factors on the depth response of a strain gauge rosette. It was found that that circumferentially oriented strain gauges allow residual stress measurements to be made to twice the depth of traditional radial strain gauges, with only minor loss in strain sensitivity. A new circumferential strain gauge rosette design based on the presented analysis is proposed for use where extended depth measurements are desired.

Efficiency of Plasticity Correction in the Hole-Drilling Residual Stress Measurement.

This paper focuses on the analysis of the plasticity effect in the measurement of the residual stress by the hole-drilling method. Relaxed strains were evaluated by the computational simulation of the hole-drilling experiment using the finite element method. Errors induced by the yielding were estimated for uniaxial tension, plane shear stress state and equi-biaxial stress state at various magnitudes of residual stress uniformly distributed along the depth. The correction of the plasticity effect in the evaluation of residual stress was realized according to the method proposed by authors from the University in Pisa, which was coded in MATLAB. Results obtained from the MATLAB script were compared to the original input data of the hole-drilling simulation and discussed. The analyses suggested that the plasticity effect is negligible at the ratio of applied equivalent stress to yield stress, being 0.6, and that the correction of the plasticity effect is very successful at the previous ratio, being 0.9. Failing to comply with the condition of the strain gauge rosette orientation according to the principal stresses directions causes an increase in the relative error of corrected stresses only for the case of uniaxial tension. It affects the relative error negligibly for the plane shear and equi-biaxial stress states.

In situ studies of full-field residual stress mapping of SS304 stainless steel welds using DIC

Large tensile residual stress is detrimental to the structural integrity of welded structures. As a result, it is very important to understand the residual formation during the welding process. In this paper, a new non-contact welding residual stress measurement technique based on digital image correlation (DIC) is proposed as a way to investigate residual stress formation. To investigate the stress evolution of the welded plate, we conduct a series of experiments by using this new method. High-temperature full-field strain obtained from DIC was computed by incremental theory to acquire stress increment. Stress evolution and residual stress were obtained by superimposing the stress increment. Hole-drilling residual stress measurements for verification were also implemented. The maximum difference, which was 37 MPa between the two methods demonstrated that this new technique was able to characterize the full-field welding residual stress during the welding process.

Compact Calibration Data for Hole-Drilling Residual Stress Measurements in Finite-Thickness Specimens

The conventional way to present Integral Method calibration data for hole-drilling residual stress measurements is in the form of a large triangular table of numbers. In the common case where 20 drilling steps are used for the hole-drilling measurement, 231 numerical coefficients are needed. While such tables are effective, their bulk inhibits their use for other than the most common experimental arrangements; the convenience and usefulness of the hole-drilling method would be much extended if the bulk of the calibration data could be reduced. Here, a two-variable polynomial formulation is proposed to represent the hole-drilling calibration data. It comprises 15 numerical coefficients and provides calibration data with average accuracy within 1%, with occasional outliers reaching around 2%. The compactness of the calibration stimulated exploration of hole-drilling response beyond the conventional “thick” specimen case, also to include finite thickness specimens down to very thin (through-hole) geometries. Tables of calibration data are provided here for ASTM E837 Type A, B and C strain gauge rosettes, for various hole diameters, for conventional “thick” specimens, and for finite thickness specimens down to the through-hole case.

Eccentricity Effect in the Hole-Drilling Residual Stress Measurement

The paper focuses on the analysis of the eccentricity effect in the measurement of the hole-drilling residual stress. Relaxed strains were evaluated by computational simulation of the hole-drilling experiment using the finite element method. Errors induced by eccentricity were estimated for elastic and elastic-plastic states in area around the drilled hole due to the stress concentration. The invariance of the stress change with depth was assumed. The correction of eccentricity and plasticity effects in evaluation of residual stresses was realized within the EVAL 7 software (SINT Technology). The analysis shows that in elastic state the eccentricity and angular position of the drilled hole have a significant effect on relative residual stress errors. Correction according to the HDM method is very effective in this case. If the relative error of 5 % is allowed, which is in engineering practice acceptable, eccentricity of ±0.05 mm could be accepted without correction. When the combination of eccentricity and plasticity occurs, the correction of plasticity is more important in method 13-EXT-UN.

Plasticity Effects in the Hole-Drilling Residual Stress Measurement in Peened Surfaces

The incremental hole-drilling technique (IHD) is a widely established and accepted technique to determine residual stresses in peened surfaces. However, high residual stresses can lead to local yielding, due to the stress concentration around the drilled hole, affecting the standard residual stress evaluation, which is based on linear elastic equations. This so-called plasticity effect can be quantified by means of a plasticity factor, which measures the residual stress magnitude with respect to the approximate onset of plasticity. The observed resultant overestimation of IHD residual stresses depends on various factors, such as the residual stress state, the stress gradients and the material’s strain hardening. In peened surfaces, equibiaxial stresses are often found. For this case, the combined effect of the local yielding and stress gradients is numerically and experimentally analyzed in detail in this work. In addition, a new plasticity factor is proposed for the evaluation of the onset of yielding around drilled holes in peened surface layers. This new factor is able to explain the agreement and disagreement found between the IHD residual stresses and those determined by X-ray diffraction in shot-peened steel surfaces.

Uncertainties of the Evaluation of the Hole Drilling Residual Stress Measurement According to the ASTM E837 Standard

The paper deals in hole drilling residual stress measurement method. The basic principles of measurement and evaluation by the uniform stress and Integral methods are described. The uncertainties of the residual stress evaluation procedure based on the ASTM E837 standard are analyzed. Examples of residual stress evaluation and comparison of different ASTM E837 standard editions are presented.

Influence of Drilling Parameters on the Accuracy of Hole-drilling Residual Stress Measurements

The objective of this research is to define drill speeds that produce acceptable results when using the hole-drilling technique for measuring residual stress. For this study, three common engineering materials; alloy 6061-T651 aluminum, 304 stainless steel, and A36 carbon steel were used. This was achieved by performing ESPI/hole-drilling stress measurement of a known applied stress in discrete rpm intervals ranging from 2-40K rpm for each material. To produce a known state of stress specimens were bent elastically in a four-point bend fixture. Stress measurements were taken using single-axis electronic speckle-pattern interferometry (ESPI). It was found that for 6061-T6 aluminum, accurate and repeatable results can be achieved between speeds of 2-40K rpm. For 304 stainless steel, result accuracy diminishes when drill speeds go below 6K rpm. The A36 steel had a large as-received stress gradient across the longitudinal dimension and was therefore removed from this study.

Hole-Drilling Residual Stress Measurement with Artifact Correction Using Full-Field DIC

A full-field, multi-axial computation technique is described for determining residual stresses using the hole-drilling method with DIC. The computational method exploits the large quantity of data available from full-field images to ameliorate the effect of modest deformation sensitivity of DIC measurements. It also provides uniform residual stress sensitivity in all in-plane directions and accounts for artifacts that commonly occur within experimental measurements. These artifacts include image shift, stretch and shear. The calculation method uses a large fraction of the pixels available within the measured images and requires minimal human guidance in its operation. The method is demonstrated using measurements where residual stresses are made on a microscopic scale with hole drilling done using a Focused Ion Beam – Scanning Electron Microscope (FIB-SEM). This is a very challenging application because SEM images are subject to fluctuations that can introduce large artifacts when using DIC. Several series of measurements are described to illustrate the operation and effectiveness of the proposed residual stress computation technique.

Surface Decoration for Improving the Accuracy of Displacement Measurements by Digital Image Correlation in SEM

In-situ straining experiments and residual stress evaluations by micromachining require accurate measurement of surface displacements. Such measurements can be conveniently done using Digital Image Correlation (DIC). Three surface decoration techniques are presented to enhance surface deformation and residual stress measurement capabilities on micron-scale samples within a Scanning Electron Microscope—Focused Ion Beam (SEM-FIB) instrument. They involve the use of Yttria-stabilized-zirconia nano particles applied chemically, nano platinum dots applied using FIB, and Focused Electron Beam (FEB) assisted deposition. The three decoration techniques create distinctive, random surface features that can be used with Digital Image Correlation to provide full field maps of surface displacements at high magnifications. A series of experiments using a FEGSEM-FIB demonstrated the effectiveness of the three surface decoration techniques for FEGSEM imaging at magnifications from 2,000× to 60,000×. The precision of the image correlation is substantially enhanced by the surface decoration, with displacement standard deviations reduced to the 0.005–0.03 pixel range, depending on the patch size used. By means of an example application, the use of surface decoration for microscopic hole-drilling residual stress measurements within a FIB-SEM is presented. The same trends in DIC uncertainty observed in the analysis of the surface decoration patterns carried through to the example application. Guidelines are given for appropriate choice of decoration method to suit various practical applications.

Dual-Axis Hole-Drilling ESPI Residual Stress Measurements

A novel dual-axis ESPI hole-drilling residual stress measurement method is presented. The method enables the evaluation of all the in-plane normal stress components with similar response to measurement errors, significantly lower than with single-axis measurements. A numerical method is described that takes advantage of, and compactly handles, the additional optical data that are available from the second measurement axis. Experimental tests were conducted on a calibrated specimen to demonstrate the proposed method, and the results supported theoretical expectations.

Hole-Drilling Residual Stress Measurements at 75: Origins, Advances, Opportunities

Since its inception by Mathar in the 1930s, the hole-drilling method has grown to be the most widely used general-purpose technique for measuring residual stresses in materials. During its history, the method has progressed greatly in both sophistication and scope, with substantial advances in all three of its main aspects. Drilling procedures have developed from the early use of a conventional low-speed drill to the modern use of high-speed orbiting endmills and, for very hard materials, abrasive machining. Deformation measurements have advanced from the use of a mechanical extensometer to strain gauges and full-field optical measurements such as Moire, ESPI and Digital Image Correlation. Computation techniques have progressed from empirical calibrations for discrete measurements within uniform stress fields to finite-element inverse solutions for multiple measurements within non-uniform stress fields. This paper gives an overview of the history and progress of all three aspects of the hole-drilling method, and indicates some promising directions for future developments.

Advances in Hole-Drilling Residual Stress Measurements

Residual stress measurements by hole-drilling have developed greatly in both sophistication and scope since the pioneering work of Mathar in the 1930s. Advances have been made in measurement technology to give measured data superior in both quality and quantity, and in analytical capability to give detailed residual stress results from those data. On the technology side, the use of multiple strain gauges, Moire, Holographic Interferometry and Digital Image Correlation all provide prolific sources of high quality data. In addition, modern analytical techniques using inverse methods provide effective ways of extracting reliable residual stress results from the mass of available data. This paper describes recent advances in both the measurement and analytical areas, and indicates some promising directions for future developments.