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.     

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.     

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.     

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.     

Applications of the incremental hole-drilling method for measurement of residual-stress distribution

Experimental Techniques -     

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.     

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.     

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).     

Refined analysis of the relieved strain coefficients for the off-center hole-drilling case

This paper presents the numerical and analytical expressions for the relieved strain coefficients to take account of the size of the gage grid when a drilled hole is off center with respect to the rosette center. It also presents a simple method for calculation of these coefficients involving the reduction of the resistances of the side filaments.     

A new approach for determining the induced drilling stresses in the hole-drilling method of residual-stress measurement

Experimental Techniques -     

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.     

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 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.     

Measurement of residual stress by the hole-drilling method: On the direction of maximum residual stress

A rigorous and analytical criterion for determining the direction of maximum residual stress is presented. Based on this criterion, a simple intuitive method which is independent—not only of the reference coordinate, but also of the order of gage numbers—is also presented to determine the direction of maximum residual stress.     

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.     

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.     

Comparison of residual-stress variation with depth-analysis techniques for the hole-drilling method

Numerous data-analysis techniques have been developed to determine residual-stress information from strain data obtained from the hole-drilling method. The most commonly used technique for data analysis was developed by Rendler and Vigness (which forms the basis of the standard described in ASTM E837-85). A numerical development which was a model of the hole-drilling procedure has been used to determine stress variation with depth. A rigorous finite-element method to specifically analyze stresses in discrete hole increments has been developed. To evaluate these data-analysis techniques, three different computer-simulated stress fields are compared. The stress fields include a uniaxial stress that is constant with depth, a bending stress that varies linearly with depth, and a subsurface stress reversal. (The basis for this comparison is a finite-element developed technique. Its accuracy will be discussed later.) All data-analysis techniques showed excellent agreement for the uniaxial stress constant with depth test case. However, for the other two stress fields, significant discrepancies were apparent. Results are compared and discussed.     

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.     

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     

Determining micrometer-zero settings when making residual-strain measurements using the hole-drilling strain-gage method

Experimental Techniques -