Improved Calibration Coefficients for the Hole-Drilling Method Considering the Influence of the Poisson Ratio

For residual stress analyses with the incremental hole-drilling method adequate evaluation formalisms in order to transform the measured strains into stresses are required. The Integral Method is the most important theory used for analyses of nonlinear residual stress depth distributions. It is based on a calibration, which is carried out by Finite-Element-Analyses. For the sake of simplicity the used numerical models often represent an ideally cylindrical hole and ideal elastic material behavior with fixed elastic constants. The adaption of the calibration coefficients from the numerical simulations to the real experimental state is often performed by simple correction factors or is ignored completely. The following investigation highlights the influence of the Poisson ratio on the calibration coefficients for the most commonly used strain gage rosettes geometries, which are standardized by ASTME837-08. It comes out that the application of existing simple correction factors is only valid within a small range and better approximations can be obtained by alternative strategies.     

On the measurement of residual-stress gradients in aluminum-alloy specimens

The assessment or prediction of fatigue life or strength improvement due to residual stresses requires knowledge of their magnitude and distribution. This paper presents an extension of the modified hole-drilling technique (MHDT) to the measurement of stress gradients in a biaxial-residual-stress field. This is achieved by taking a series of ‘point’ measurements and evaluating the stress profile with due consideration to the effects of hole location, the interaction between holes and the redistribution of stress due to hole drilling. An application to the measurement of residual stresses induced in 2024-T3 aluminum-alloy specimens by edge-dimpling technique is described and the method of compensation for the effect of redistribution of stress is explained. The experimental results are shown to be in good agreement with those obtained elsewhere by an analytic-numerical solution.     

Measurement of residual-stress distribution by the incremental hole-drilling method

The hole-drilling method is widely used to measure residual stresses in mechanical components. Recent developments have shown that strains measured on the surface during an incremental drilling can be related to residual-stress distribution. Researchers throughout the world have proposed different calibration methods which lead to more or less accurate results.The present paper discusses different approaches used. A new calibration method is proposed. We also show how finite-element analysis can be used to determine the correlation coefficients. The variation of the strains measured on the surface for each increment is due to, first, the residual stresses in the layer and, second, the change of the hole geometry. Most authors do not consider the latter aspect. Our results show that this causes a significant error in the experimental data. The finite-element method has been used to compute the coefficients for all types of strain-gage rosettes when the hole diameter is predetermined.Another problem of the hole-drilling method is the selection of the drilling tool. Two systems have been studied: ultra-high-speed air turbine and conventional milling machine. The method has been applied on both shot-peened and water-quenched test specimens. The results are successfully compared with the bending-deflection and the X-ray method.     

Modifications to the hole-drilling technique of measuring residual stresses for improved accuracy and reproducibility

The hole-drilling technique is a relatively well established and straightforward semidestructive method for measuring residual stresses in fabricated components. However, a number of factors can have a marked influence on the accuracy of this technique. Some of the factors evaluated in the present work were the method of drilling the hole, the size and shape of the hole, and the equations used to calculate the principal residual stresses from the relaxed-strain measurements. In this investigation, air-abrasive hole drilling using a 0.062-in.-ID stationary nozzle gave the most reproducible and accurate results. Of the three approaches used to calculate the residual stresses, one method proved to be superior, especially in a biaxial-stress field.     

On residual-stress measurements in light truck wheels using the hole-drilling method

An investigation of the effect of drilling speed, milling-cutter wear, drilling mode, and applied drilling force on residual-stress measurements in a light truck wheel using a milling guide manufactured by Measurements Group, Inc. is described. The milling variables chosen were used to minimize the residual stresses induced by the introduction of a hole into the wheel material. An improved hole-drilling procedure was developed and found to be successful in the residual-stress measurements for a light truck wheel.     

Optimal calculation steps for the evaluation of residual stress by the incremental hole-drilling method

The integral method is a suitable calculation procedure for the determination of nonuniform residual stresses by semidestructive mechanical methods such as the hole-drilling method and the ring-core method. However, the high sensitivity to strain measurement errors due to the ill conditioning of the equations has hindered its practical use. the analysis of the influence of the strain measurment error on the computed stresses carried out in the present work has showed that, given both maximum hole depth and number of total steps, the error sensitivity depends on the particular depth increment distribution used. By means of the matrix formulation, the depth increment distribution that optimizes the numerical conditioning is investigated. Numerical simulations and an experimental test have corroborated the best performance of the proposed step distribution with respect to the constant or increasing distributions commonly used.     

Hole-drilling method using grating rosette and Moiré interferometry

The hole-drilling method is one of the most wellknown methods for measuring residual stresses. To identify unknown plane stresses in a specimen, a circular hole is first drilled in the infinite plate under plane stress, then the strains resulting from the hole drilling is measured. The strains may be acquired from interpreting the Moire signature around the hole. In crossed grating Moire interferometry, the horizontal and vertical displacement fields （u and v） can be obtained to determinate two strain fields and one shearing strain field. In this paper, by means of Moire interferometry and three directions grating （grating rosette） developed by the authors, three displacement fields （u, v and s） are obtained to acquire three strain fields. As a practical application, the hole-drilling method is adopted to measure the relief strains for aluminum and fiber reinforced composite. It is a step by step method; in each step a single laminate or equivalent depth is drilled to find some relationships between the drilling depth and the residual strains relieved in the fiber reinforced composite materials.     

The accuracy of residual stress measurement by the hole-drilling method

This paper describes the verification of the accuracy of residual stress measurement by the hole-drilling method. The strain measurement is simulated by the use of the indirect fictitious-boundary integral method. As an example, a finite rectangular plate subjected to initial stress is treated, and a simulated measurement of the residual stress is made using the strain relieved during hole drilling. The accuracy of residual stress measurement is estimated by comparing the simulated measured residual stress with the actual residual stress, i.e., the given initial stress. The results are shown for various distances and angles of strain gages. Also, the influences of the eccentricity of the hole from the center of the strain gages and the effect of a boundary near the hole are examined.     

Enhanced sensitivity residual-stress measurements using taper-hole drilling

A novel method for enhancing the strain sensitivity of the hole-drilling method for measuring uniform residual stresses is examined. Such enhanced strain sensitivity is important because it improves the accuracy of the residual-stress evaluation. The new method involves enlarging the effective hole size by drilling a reverse taper hole. A simple practical technique for drilling reverse taper holes is described. The strain sensitivity for this new method is compared with that of the conventional hole-drilling method. Experimental results show excellent correspondence with theoretical results. The reasons for the sensitivity improvement are explained.     

Determination of residual-stress variation with depth by the hole-drilling method

The hole-drilling method is a residual-stress measurement technique in which a blind hole (usually 1.6 mm or 3.2 mm in diameter) is drilled into a material and the strain perturbances around the hole are measured by surfacemounted strain gages. The conventional hole-drilling-method procedure is to analyze the net strain changes due to the drilling of the full-depth hole (usually about 100 percent of hole diameter) and to interpret the resulting stress calculations insofar as they represent the average stresses through the hole depth. It has been determined that this procedure may lead to significant errors, particularly where there are large stress variations through the hole depth. Such errors may be difficult to detect simply by observing the strain data. This paper describes a finite-element procedure which was used to develop calibration constants to allow measurements of residual-stress variation with depth to be routinely performed by the hole-drilling method.     

Incremental Hole Drilling for Residual Stress Analysis of Thin Walled Components with Regard to Plasticity Effects

The incremental hole-drilling method is widely used in residual stress depth distribution analysis. However, two specific difficulties with the generalization of the incremental method exist, including the consideration of the sample thickness and residual stress states close to the local material’s yield strength. The stress concentration effect of the hole can lead to plastic deformation in the vicinity of the hole, which results in an overestimation of residual stresses. Typically, the effect of the component’s thickness and the plasticity effects are analyzed separately and correction approaches are proposed. In the current paper, we analyze the combined effects of plasticity and thickness on residual stress analysis using the incremental hole-drilling method. A systematic study was performed on steel samples with (i) isotropic and (ii) anisotropic elastic and elasto-plastic material behavior with varying thicknesses ranging between 1 mm and 4 mm. Electronic speckle pattern interferometry (ESPI) hole-drilling experiments were conducted on beam samples loaded using a 4-point bending fixture. Finite element simulations were conducted to gain insight into the effects of incremental hole-drilling. The results indicate that reducing the component’s thickness increases the plastic deformation in the vicinity of the hole and results in significant stress deviations. Thin components bend during hole-drilling as a result of the loss of stiffness, which amplifies the plasticity effect.     

A finite-element technique to analyze the data measured by the hole-drilling method

A finite-element technique to analyze the data obtained by the hole-drilling strain-gage method is presented. In this study, residual stresses are assumed as initial stresses existing in the structural material or component. It is also assumed that the elimination of the initial stresses in the region of the drilled hole changes the measured strains. After putting initial stresses into displacement finite-element equations and comparing the stiffness matrix and the initial stresses matrix with those of the previous increment, equations relating unknown initial stresses and measured strains were obtained. By solving these equations, residual stresses were obtained. In this paper three examples are studied. In the first two examples, calibration constants C1 to be used in determining residual stress were calculated which varied with depth. In the third example, the data obtained by using the hole-drilling method are analyzed. All examples show good agreement with previous studies. Using the present method allows greater flexibility of choice of specimen shape, materials, and experimental procedure than would be possible if only analytic solutions were used.     

Three-dimensional stress-relief displacements from blind-hole drilling: a parametric description

Optically-based interferometric techniques are finding increased application to the quantitative determination of near surface stress states. Unlike the standardized strain-gage method of hole drilling, however, some optical methods are sensitive to all three components of the displacement field produced by drilling of the stress-relieving hole. Analysis of the resulting fringe patterns necessitates a full knowledge of such motions. Here, direct formulae, which relate stress-relief displacements to radial position and azimuth, relative hole dimensions, residual or applied stress, and Poisson's ratio, are constructed from an extensive series of finite element calculations. The final formulae are derived from a large set of trial formulae that best describe the displacements according to a statistical regression analysis. The formulae are generally valid for hole depth/diameter ratios from 0.5 to 4.0, for Poisson's ratios from 0.05 to 0.45, and over radial distances from the hole axis from 2 to 20 times the hole radius, although these validity ranges can vary with hole depth. The equations are compared to an existing strain-gage hole-drilling standard and are used to forward model a speckle interferometer fringe pattern recording stress-relief displacements in an acrylic block.     

3D numerical simulation of drilling residual stresses

Drilling can affect the integrity of the surface of a mechanical component and reduce its fatigue life. Thus, drilling parameters such as lubrication or drilling velocity must be optimized to ensure a satisfactory residual mechanical state of the hole surfaces. Unfortunately, experimental tests are time consuming and it is not easy to observe the cutting process because of the confinement of the drill zone. The literature does not exhibit any numerical simulation capable of simulating 3D thermomechanical phenomena in the drill zone for large depth holes. Therefore, residual stresses cannot be easily simulated by means of the sole drilling parameters. The aim of this article is to propose a new numerical approach to compute drilling residual stresses for large-depth holes. A first simulation is developed to simulate heat transfer by means of a 3D thermoviscoplastic simulation in a new Rigid-ALE framework allowing the use of large calculation time steps. Then, a time interpolation and a spatial projection are implemented to rebuild the Lagrangian thermal history of the machined component. Finally, a thermo-elastoplastic simulation is carried out to compute residual stresses in the final workpiece. In this paper, the method is applied to a 316L austenitic stainless steel in the case of an unlubricated hole. The computed residual stresses are compared to experimental measurements.     

Residual Stress Analysis on Thick Film Systems by the Incremental Hole-Drilling Method – Simulation and Experimental Results

The residual stress state in thick film systems, as for example thermal spray coatings, is crucial for many of the component’s properties and for the evaluation of the integrity of the coating under thermal and/or mechanical loading. Therefore it is necessary to be able to determine the local residual stress distribution in the coating, at the interface and in the substrate. The incremental hole-drilling method is a widely used method for measuring residual stress depth profiles, which was already applied for thermally sprayed coatings. But so far no reliable hole-drilling evaluation method exists for layered materials having a stress gradient in depth. The objective was to investigate, how far existing evaluation methods of the incremental hole-drilling method that are only valid for residual stress analysis of homogenous material states can be applied to thick film systems with coating thicknesses between 50 μm and 1000 μm and to point out the application limits for these already existing methods. A systematic Finite Element (FE) study was carried out for coating systems with an axisymmetric residual stress state σ₁?=?σ₂. It is shown that conventional evaluation methods developed for homogeneous, non-layered material states can be successfully applied for a stress evaluation in the substrate and the coating for small and for sufficiently large coating thicknesses, respectively, regardless of the type of evaluation algorithm used i.e. the differential or the integral method. The same accounts for material combinations that have a Young’s modulus ratio close to one, between 0.8 and 1.2. The studies indicated that outside the given ranges case specific calibration must be applied to calculate reliable results. Further, calibration data were determined case specifically for a selected model coating system. The accuracy of a residual stress determination using these case specific calibration data was examined and the sensitivity of the evaluation with respect to an accurate knowledge of the boundary conditions of the coating system i.e. the coating thickness and the Young modulus was studied systematically. Finally, the calibration data were applied on a thermally sprayed aluminium coating on a steel substrate analysis and the results for using the incremental hole drilling method were compared to results from X-ray stress analysis.     

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 takes advantage of 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.     

Brief investigation of induced drilling stresses in the center-hole method of residual-stress measurement

Results of experiments to measure induced drilling stresses in the center-hole method of residual-stress measurement are described. Five specimens of different metals were specially prepared in an attempt to relieve malerial residual stress. Surface-residual-stress measurements were then performed by the center-hole method with a conventionally used (low-speed) end mill and an ultra-high-speed drill. For each specimen, the relieved strains due to the hole drilling were significantly higher for the low-speed end mill than for the ultra-high-speed drill. Preliminary conclusions are that the ultra-high-speed drill would be much superior to the conventional low-speed end mill in the measurement of residual stress by the center-hole method.     

Approximated Repair Methods for Outlier Strain Data from Hole-Drilling Residual Measurements

The current ASTM E 837 standard gives the standardized procedure for the evaluation of uniform and non uniform residual stresses, that is, stresses that do not vary and vary significantly with depth from the specimen surface, respectively. For non uniform stresses, the standard states that many small increments should be done in order to have a stable calculation of the residual stress profile. In addition, it states that irregularities as well as outlier strain points should be investigated and if necessary, the hole-drilling test should be repeated. In some applications outside the laboratory, the availability to repeat a test with outlier points is not possible. In these cases, the standard does not show the more appropriated way which should be followed to use only valid measured data (without outliers). For this reason, a stress profile corresponding to a shot peening test was simulated and one hole step was included in different hole depths as outlier point in order to evaluate the feasibility of some proposed ways of computation. These ways were: (a) following the ASTM procedure but replacing outlier strain points by linear interpolation of neighboring good ones, (b) following the ASTM procedure but replacing outlier strain points by a parabola interpolation of neighboring good ones and (c) using cumulative relaxation strain functions and only good measured points. Statistical criteria were also introduced and developed in order to identify outlier points. Results show a practical procedure to detect outlier points in experimental strain data.     

Residual-stress measurement in orthotropic materials using the hole-drilling method

The hole-drilling method is used here to measure residual stresses in an orthotropic material. An existing stress-calculation method adapted from the isotropic case is shown not to be valid for orthotropic materials. A new stress-calculation method is described, based on the analytical solution for the displacement field around a hole in a stressed orthotropic plate. The validity of this method is assessed through a series of experimental measurements. A table of elastic compliances is provided for practical residual-stress measurements in a wide range of orthotropic materials.     

Solution of the moiré hole drilling method using a finite-element-method-based approach

The moiré hole drilling method in a biaxially loaded infinite plate in plane stress is an inverse problem that exhibits a dual nature: the first problem results from first drilling the circular hole and then applying the biaxial loads, while the other problem arises from doing the opposite, i.e., first applying the biaxial load and then drilling the circular hole. The first problem is hardly ever addressed in the literature but implies that either separation of stresses or material property identification may be achieved from interpreting the moiré signature around the hole. The second is the well-known problem of determination of residual stresses from interpreting the moiré fringe orders around the hole. This paper addresses these inverse problem solutions using the finite element method as the means to model the plate with a hole, rather than the typical approach using the Kirsch solution, and a least-squares optimization approach to resolve for the quantities of interest. To test the viability of the proposed method three numerical simulations and one experimental result in a finite width plate are used to illustrate the techniques. The results are found to be in excellent agreement. The simulations employ noisy data to test the robustness of this approach. The finite-element-method-based inverse problem approach employed in this paper has the potential for use in applications where the specimen shape and boundary conditions do not conform to symmetric or well-used shapes. Also, it is a first step in testing similar procedures in three-dimensional samples to assess the residual stresses in materials.