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.     

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

Experimental Techniques -     

Multiple trenching: a simple self-calibrating method of residual-stress measurement

A simple semidestructive residual-stress-measurement technique, particularly suitable for measurement parallel to edges or on outside radii of components, is presented. The nature of the technique obviates reliance upon calibration constants such as have been obtained for the hole-drilling and ring-cutting methods for residual-stress measurement. Use of such calibration constants might seriously underestimate stress values for relatively shallow surface stresses such as may be produced by, for example, grinding or thermochemical treatment.     

A direct method to evaluate hole-alignment error in residual-stress measurement

In this paper, a direct method based on the Sandifer and Bowie theory was derived to take hole-alignment error into account in residual-stress measurement. The principal stresses and their orientation are calculated directly from this method when the relaxed strains, hole diameter, eccentricity and orientation are known. It is more convenient to use than other iterative methods.     

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.     

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

Experimental Techniques -     

A consistent-splitting model for experimental residual-stress analysis

Destructive laboratory procedures for measuring through-thickness residual stresses in metals frequently involve some combination of three types of cutting steps. Deformation data, recorded after each step, are used in back-computation procedures to produce an estimate of the original residual-stress distribution. Questions arise concerning the applicability of simplifying assumptions embodies in existing back-computation schemes for each of the three types of steps. This paper focuses on one of these steps generally called the splitting step. Two existing back-computation schemes were evaluated. One existing scheme, applied to a typical spliting problem, estimated residual stresses that were in error by as much as 35,000 psi. In another case, the second existing back-computation scheme led to errors of about 30 percent. An improved back-computation scheme is developed for the splitting step based on a ‘consistent-splitting model’. Verifications and applications of the model are presented. In the verification studies, results obtained from the consistent-splitting model for two cases showed excellent agreement with finite-element reference solutions.     

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.     

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.     

Nondestructive residual-stress measurement on the inside surface of stainless-steel pipe weldments

The instrumentation, technique, and procedures are described for the nondestructive measurement of residual stresses on the inside surface of pipe as small as 10 in. in diam. The instrument is based upon a unique position-sensitive scintillation X-ray detector which provides for the most compact X-ray stress-measurement instrument available since the introduction of film cameras four decades ago. This instrument is capable of applying the single-exposure technique of X-ray stress measurements which results in unprecedented rapidity of stress measurement consistent with excellent precision and accuracy. The results of testing the precision and accuracy of the instrument on a zero-stress powder and four-point-bend specimen are given. Residual stresses in four austenitic stainless-steel girth-welded pipes are presented illustrating the effects of the different welding procedures. The results from the pipes confirm the beneficial residual-stress condition of heat-sink-welding procedures.     

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.     

Comparison of three residual-stress measurement methods on a mild steel bar

The objective of this investigation was to ascertain the surface residual-stress condition of a specially thermal-mechanically treated mild steel bar. Three methods of residual-stress measurement were used—two of them accurate, well-verified approaches and the third an experimental one. The first two were stress-relief blind-hole drilling (SRT) and X-ray diffraction (XRD), and the third was Barkhausen noise analysis (BNA). It is difficult to make direct comparisons between these methods since they each sample a different volume of material at different depths into the surface. However, the SRT data, when extrapolated to shallow depths sampled by the XRD, show excellent agreement with that nondestructive method. The BNA results show poor correlation with the XRD and SRT even with extrapolation to similar depths. The major reason for the poor BNA results seems to be its sensitivity to the microstructural conditions of the sample. All of the measurements, with the exception of one set of BNA measurements, indicate that tensile stresses existed in the surface of the specimen.     

Polychromatic X-ray method for residual-stress measurements in a subsurface layer

The classical sin² method with characteristic X-rays is widely used to measure residual stress nondestructively in the steel members of a structure or a machine. With this method it is, however, difficult to measure the three-dimensional stress distribution with a steep gradient that occurs along the depth direction in a subsurface layer of the material after surface treatment such as grinding or cold rolling. This paper presents a new polychromatic X-ray method for residual-stress measurements in a subsurface layer. The relationship between the diffracted beam peak of the polychromatic X-ray and the strain along the depth direction in a subsurface layer was obtained by theoretical analysis. It was modeled by numerical simulation to obtain probable values of the parameters, and these were used along with experimental X-ray data to derive an experimental value for the stress gradient. This was compared with the values predicted from plate bending theory.Paper was presented at the 1994 SEM Spring Conference on Experimental Mechanics held in Baltimore, MD on June 6–9.     

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.     

Nondestructive residual-stress measurement in a wide-flanged rolled beam by acoustoelasticity

X-ray stress analysis is a standard nondestructive stress-measurement technique, but its use is limited in the sense that only a surface layer is surveyed. Recently, acoustoelasticity has emerged as a technique for nondestructive stress analysis. Acoustoelasticity makes use of stress-induced acoustic-birefringent effects. It gives stress distributions averaged through the thickness of a specimen. This technique is attractive because it does not require a transparent plastic model as photoelasticity does. However, much should be done before this method is established as a standard nondestructive technique of stress analysis. The most important among them is to separate stress-induced birefringence from that introduced by texture structure. For special cases, such as axisymmetric stress distributions and when a stress-free region is knowna priori, residual-stress distributions can be evaluated nondestructively. In this paper, we measured residual-stress distribution in a wide-flanged rolled beam by using a recently developed T-type transducer. The results were compared to those obtained from conventional destructive methods.     

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.     

A computational method for dislocation-precipitate interaction

A new computational method for the elastic interaction between dislocations and precipitates is developed and applied to the solution of problems involving dislocation cutting and looping around precipitates. Based on the superposition principle, the solution to the dislocation-precipitate interaction problem is obtained as the sum of two solutions: (1) a dislocation problem with image stresses from interfaces between the dislocation and the precipitate, and (2) a correction solution for the elastic problem of a precipitate with an initial strain distribution. The current development is based on a combination of the parametric dislocation dynamics (PDD) and the boundary element method (BEM) with volume integrals.The method allows us to calculate the stress field both inside and outside precipitates of elastic moduli different from the matrix, and that may have initial coherency strain fields. The numerical results of the present method show good convergence and high accuracy when compared to a known analytical solution, and they are also in good agreement with molecular dynamics (MD) simulations. Sheared copper precipitates (2.5 nm in diameter) are shown to lose some of their resistance to dislocation motion after they are cut by leading dislocations in a pileup. Successive cutting of precipitates by the passage of a dislocation pileup reduces the resistance to about half its original value, when the number of dislocations in the pileup exceeds about 10. The transition from the shearable precipitate regime to the Orowan looping regime occurs for precipitate-to-matrix elastic modulus ratios above approximately 3-4, with some dependence on the precipitate size. The effects of precipitate size, spacing, and elastic modulus mismatch with the host matrix on the critical shear stress (CSS) to dislocation motion are presented.     

A computational method for first-excursion reliability

An efficient computational method is suggested for the first-excursion reliability assessment of nonstationary process. In the proposed method, the nonlinear performance function is linearized at the Hasofer-Lind point obtained by an iterative algorithm. The problem of the nonstationary processes is solved by the discrete-time method, in which the precision can be controlled by choosing the steps of discretization. The derived formulae can be conveniently degraded to calculate both the first-excursion reliability with linear performance function of stationary processes and the time-independent reliability. The suggested method is useful for the analysis of components and systems with nonstationary responses in structural design where some uncertainties are represented by a vector of nonstationary processes. Examples are given to demonstrate the fast convergency and effectiveness of the presented method. The project supported by the National Natural Science Foundation of China     

A computational method for the hydrodynamics of fractured-porous media

A numerical method based on the boundary-fitted finite difference method (BFDM) is presented in this paper. The boundaries are external (the boundary of the physical domain) and internal (which corresponds to the fracture network). The difference between this approach and the usual one lies in the inclusion of discrete fractures in the volume that represents the porous medium. The numerical model has been used in the prediction of the flow pattern in several internationally recognized verification cases and applied to the solution of hypothetical problems of interest to us in the field of nuclear waste repository modelling. The results obtained show that the numerical approach considered gives accurate and reliable predictions of the hydrodynamics of fractured-porous media, thus justifying its use for the above-mentioned studies.