Measurement of residual stress by the hole-drilling method: General stress-strain relationship and its solution

When a hole is drilled at any position with respect to the gages in a thin plate, a general relationship of relieved strain as a function of residual stress is presented. A simple and explicit solution for the principal residual stresses and their directions is also presented. This solution is available for the center or off-center hole-drilling cases and for the case of which the array of gages is arbitrary.     

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.     

Measurement of residual stresses by the hole-drilling method: General stress-strain relationship and its solution

The paper Measurement of Residual Stress by the Hole-drilling Method: General Stress-strain Relationship and Its Solution by Jia-jang Wang was published in the December 1988 issue ofExperimental Mechanics,Vol. 28, No. 4, pp. 355–358.     

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.     

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.     

Measurement of residual stresses by the hole-drilling method: Influences of transverse sensitivity of the gages and relieved-strain coefficients

The general expression of the error due to the transverse sensitivity of the gages and the relieved-strain coefficients, in a determination of residual stresses by the hole-drilling method in thin plates, is given. It has been shown that the transverse sensitivity of the gages can be ignored. A moderate amount of error, however, is introduced in the measurement of residual stresses when the relieved-strain coefficients from methods other than double integration over the area of the grid are used. The error due to the use of improper relieved-strain coefficients from rigorous relationships for calculation of residual stresses has been compared with the same part of the error from nonrigorous relationships. Abandonment of the use of nonrigorous relationships is recommended.     

Determination of residual stresses by an optical correlative hole-drilling method

In conjunction with the incremental hole-drilling method, a new evaluation procedure is presented for determining the residual stress state in components. In contrast to the classical method, the whole displacement field around the drilled hole is measured using the electronic speckle pattern interferometry technique. The displacement patterns, measured without contact to the surface, are then correlated with those obtained by finite-element simulations using statistical methods. The simulated displacement patterns, used for calibration purposes, result from the application of properly defined basic loads. In this way, the values and the orientation of the residual stresses can be determined by superposition of these properly scaled and shifted basic loads. Even complex states of stress can be evaluated. The theoretical background and experimental results are presented.     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP     

Inversion of speckle interferometer fringes for hole-drilling residual stress determinations

Speckle interferometric fringe patterns record stress-relief displacements induced by the drilling of blind-holes into prestressed objects. The quantitative determination of residual stress state from such stress patterns is difficult because of the ambiguity in the order of the observed fringes. The plane stress magnitudes are provided directly from selected fringe positions using a stochastic, iterative least squares minimization approach. The inversion requires prior knowledge of the experimental geometry and an appropriate uniaxial stress-relief displacement basis function derived from three-dimensional finite element calculations. Superpositioning of the rotated and scaled displacement basis functions allows the stress-relief relaxation for any biaxial state of stress to be determined. In this paper, fringe patterns were forward modeled from a large ensemble of calculated biaxial stress-relief displacement fields. Inversion of these noise-free fringe patterns reproduced the biaxial stresses with negligible error. Analysis of more realistic fringe patterns that include speckle noise gave stress magnitude errors that diminished rapidly with the number of selected points to better than 3 percent for 100 points. Sensitivity of the optical method is influenced by a number of factors, but the ensemble of model fringe patterns studied indicates that the stress magnitudes (nomalized with respect to the material's Young's modulus) from 3×10^–4 to 10^–2 can accurately be determined with visible laser radiation. The method is amenable to automation and can easily be extended to study near surface gradients in the residual stresses or applied to other optical recording techniques such as moiré and phase-shifting interferometry.     

A new rosette design for more reliable hole-drilling residual stress measurements

A new six-element strain gage rosette is presented that can greatly improve residual stress measurement accuracy when using the hole-drilling method. The proposed rosette consists of three pairs of sector-shaped radial and circumferential gages connected as half-bridges. This rosette design increases effective strain sensitivity by a factor of 2.3 compared with a standard ASTM rectangular rosette, and can identify stresses at one-third greater depths from the measurement surface. Experimental measurements confirm theoretical strain response calculations within 3–4 percent. Apart from a small increase in time to complete the electrical connections, the practical use of the proposed rosette is identical to that of a conventional three-element rosette.     

An investigation of the hole-drilling technique for measuring planar residual stress in rectangularly orthotropic materials

The applicability of the semidestructive holedrilling technique to the experimental determination of residual stresses in relatively thin rectangularly orthotropic materials was investigated. From the exploratory work, it was determined that the similitudes, for measurements at a particular ratio of hole depth to diameter, which exist for thick materials are not present in relatively thin materials. This implies that calibration tests must be made for each combination of strain-gage size and plate thickness. As a consolation, however, it was found that there is no need to drill to an optimum depth for thin materials. That is, one may simply drill a small hole completely through the material to obtain the desired strain change.     

Nonuniform residual-stress measurement by hole-drilling method

Considering the general stress field as the summation of two terms of a power series, a method for the measurement of nonuniform stress fields in thin plates by the hole-drilling method has been devised. The relieved-strain equations for the uniform and linear terms of the assumed power series have been calculated and the related constants of these equations for a range of hole diameter have been plotted.From the relieved-strain equations, it is shown that for a linear approximation of a field, a rosette gage with at least five grid elements is needed. A special rosette is proposed for the linear approximation of the residual-stress fields. In addition the equations used to determine the uniform parts, the direction, and the slopes are given. An example of the linear approximation is presented. It is shown that for some residual-stress fields, the conventional equations based on a uniform stress field produce erroneous results. The improved equations, however, provide the correct solution.     

Use of the hole-drilling method for measuring residual stresses in highly stressed shot-peened surfaces

The same shot-peening treatment was applied to five steels with different mechanical properties. The induced residual stress profiles were analyzed using X-ray diffraction and incremental hole drilling (IHD). The results of both techniques showed that IHD can still be successfully used for measuring shot-peening residual stresses, even if these exceed the yield strength of the bulk material. Expected errors due to the plasticity effect are reduced by the strain hardening of the surface. For an assessment of the reliability of IHD data, strain-hardening variation was quantified by microhardness measurements to estimate the yield strength of the plastified layer. All the main calculation methods for IHD were applied. The results were compared and discussed with respect to the characteristics of each method.     

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.     

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.     

The alignment error of the hole-drilling method

The hole-drilling method is one technique for measuring residual stresses. All the existing equations for the calculation of residual stresses are based on the assumption that the hole is located at the rosette center. In this paper, the stress-strain relationship for the eccentric hole case has been derived and expressed in terms of the off-center distance and the polar angle. The alignment error is studied and demonstrated by two examples, namely, a uniaxial-stress field and a hydrostatic-stress field. The error analysis yielded the following typical result: ten percent of hole radius off-center will yield about five-percent measurement error for the standard rosette (EA-09-062-RE-120).     

Toward more accurate resudual-stress measurement by the hole-drilling method: Analysis of relieved-strain coefficients

In residual-stress measurement by the holedrilling technique, accuracy can be enhanced if the proper values for the relleved-strain coefficients are employed. These values are obtained by double integration of the relieved strain over the area of the grid. In this paper, several methods customarily used in the literature for the calculation of these coefficients are discussed. A comparison of the coefficients from these methods and those derived by double integration demonstrate the increased accuracy of the latter.     

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.     

Measurement of residual stress in the weld overlay piping components

In general industry, especially in the nuclear industry, welding overlay repair is an important repair method mainly used to rebuild piping systems suffering from intergranular stress-corrosion cracking (IGSCC).The pipe surface is mechanically ground to obtain a smooth surface after the welding overlay repair. A better understanding of the effect of repair and grinding processes on the residual stresses at the surface of weld overlay is required. To obtain this understanding, it is necessary to measure directly the distribution of residual stresses on the specimen. It is expected that compressive residual stress should be induced at the inner wall surface of the pipe for prevention of IGSCC.The performance evaluation of welding overlay repair relies on whether or not the level and characteristic of the residual stress can be measured accurately. In this study, the hole-drilling strain-gage method, using the incremental drilling technique, was adopted to estimate the residual stresses on the inner and outer walls of the weld overlay pipe. The experimental results indicate that the residual stress at the pipe inner surface is compressive while that of the outer surface is tensile. Also, it is found that the depth affected by grinding is about 1.016 mm.     

Measurement of residual stress in a multi-layer semiconductor heterostructure by micro-Raman spectroscopy

Si-based multilayer structures are widely used in current microelectronics. During their preparation, some inhomogeneous residual stress is induced, resulting in com-petition between interface mismatching and surface energy and even leading to structure failure. This work presents a methodological study on the measurement of residual stress in a multi-layer semiconductor heterostructure. Scanning electron microscopy (SEM), micro-Raman spectroscopy (MRS), and transmission electron microscopy (TEM) were applied to measure the geometric parameters of the multi-layer structure. The relationship between the Raman spec-trum and the stress/strain on the [100] and [110] crystal orientations was determined to enable surface and cross-section residual stress analyses, respectively. Based on the Raman mapping results, the distribution of residual stress along the depth of the multi-layer heterostructure was suc-cessfully obtained.