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.     

Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring

A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost complete overview of residual stress states in the component during each production step. To reduce the measurement time in the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process. Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well.     

Measurement and Prediction of Residual Stresses in Quenched Stainless Steel Components

Austenitic stainless steel cylinders and rings are spray water quenched to create residual stresses at or greater than the yield strength. The residual stresses are measured using neutron diffraction, and two mechanical strain relaxation methods: deep hole drilling and incremental centre hole drilling. This paper compares the measurements with predictions of quenching using finite element analysis. Also finite element analysis is used to mimic deep hole and incremental centre hole drilling methods and to reconstruct residual stresses as if they have been measured. The measurements reveal similar trends to the predictions but there is only limited agreement between their magnitudes. However, there is better agreement between the reconstructed stresses and the measurements. Both the two mechanical strain relaxation methods reveal that large discrepancies occur between measurements and predictions arise because of plasticity. Irrespective of this and surprisingly there is good agreement between deep hole drilling and neutron diffraction measurements.     

Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition

The traditional contour method maps a single component of residual stress by cutting a body carefully in two and measuring the contour of the cut surface. The cut also exposes previously inaccessible regions of the body to residual stress measurement using a variety of other techniques, but the stresses have been changed by the relaxation after cutting. In this paper, it is shown that superposition of stresses measured post-cutting with results from the contour method analysis can determine the original (pre-cut) residual stresses. The general superposition theory using Bueckner’s principle is developed and limitations are discussed. The procedure is experimentally demonstrated by determining the triaxial residual stress state on a cross section plane. The 2024-T351 aluminum alloy test specimen was a disk plastically indented to produce multiaxial residual stresses. After cutting the disk in half, the stresses on the cut surface of one half were determined with X-ray diffraction and with hole drilling on the other half. To determine the original residual stresses, the measured surface stresses were superimposed with the change stress calculated by the contour method. Within uncertainty, the results agreed with neutron diffraction measurements taken on an uncut disk.     

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.     

Residual Stress Analysis of Orthotropic Materials by the Through-hole Drilling Method

The present study deals with the development and the application of the through-hole drilling method for the residual stress analysis in orthotropic materials. Through a systematic theoretical study of the stress field present on orthotropic plates with a circular hole, the relationships between the relaxed strains measured by a rectangular strain gauge rosette and the Cartesian components of the unknown residual stresses are obtained. The theoretical formulas of each influence coefficient allow the user an easy application of the method to the analysis of uniform-residual stresses on a generic homogeneous orthotropic material. Furthermore, to extend the method to the analysis of the residual stresses on orthotropic laminates, caused by initial in-plane loadings, an alternative formulation is implemented. The accuracy of the proposed method has been assessed through 3D numerical simulations and experimental tests carried out on unidirectional, cross-ply and angle-ply laminates.     

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.     

Computation of Bending Stress in Pipes Using Weighted Hole-Drilling and DSPI Measurements

Pipelines usually operate under bending and axial stresses, caused by external loads, combined with residual stress distributions (manufacturing stresses), which affect the mechanical behavior of the pipe. Despite its semi-destructive nature, the hole drilling technique and digital speckle pattern interferometry (DSPI) can be applied to determine combined stresses along a cross-section. To achieve this, a set of equally-spaced angular points spread along the cross-section perimeter are measured. For non-uniform stress computations the hole drilling technique frequently gives a detailed stress distribution which is related to the external layer (1 mm) of the pipeline. In order to obtain a representative and unique value for the stress acting at each point, a novel approach can be used to evaluate a weighted average stress from each available stress distribution and to identify possible outlier measured points. In accordance with this approach, weighting coefficients are calculated using some particular features found in the residual stress profiles of pipelines. A reference bending test bench was used to evaluate the proposed methodology and it verified good agreement between the reference and computed stresses.     

钻孔法测量残余应力过程中钻孔附加应变

本文叙述了钻孔法测量残余应力过程中的附加应变.研究应力水平对附加应变的影响是在单向应力条件下进行的,结果表明,钻孔条件、材料状态以及残余应力达到一定值时,附加应变为零.     

Residual Stress Measurement in Composite Laminates Using Incremental Hole-Drilling with Power Series

Current methods for incremental hole-drilling in composite laminates have not been successfully applied in laminates of arbitrary construction or where significant variation of residual stress exists within a single ply. This work presents a method to overcome these limitations. Series expansion is applied to each ply orientation separately so that the discontinuities in the residual stresses at ply interfaces can be correctly captured. Temperature variations described by power series are used to set up eigenstrains and consequent stresses which vary in the through-thickness direction. The calibration coefficients at each incremental hole depth are calculated through the use of finite element modelling. The inverse solution employs a least-squares approach which makes the resulting solution insensitive to measurement uncertainty. Robust uncertainties in the residual stress distributions are determined using Monte Carlo simulation. The residual stress distribution is found from that combination of series orders in the different ply orientations that has the lowest RMS uncertainty, selected only from those combinations that have converged. The method is demonstrated on a GFRP laminate of [0₂/+45/?45]_s construction where it is found that transverse cracking of the plies at the inner surface of the hole may have impacted on the accuracy of the results.     

Experimental Methods for Determining Residual Stresses and Strains in Various Biological Structures

Over the years, an assortment of methods for determining residual stresses has been developed in the field of experimental mechanics. Adaptations of those methods to study residual strains and stresses in various biological structures found in humans, other mammals, viruses and an insect are reviewed. Methods considered include deflections from release of residual stresses, hole drilling and ring coring, strains upon dissection, the contour method, slitting (crack compliance), X-ray diffraction, photoelasticity, and membrane and shell displacements. Sources of residual stresses and strains are summarized and examples of their physiological role noted.     

Improvements in Residual Stress Measurement by the Incremental Centre Hole Drilling Technique

This paper presents results which advance and improve the usefulness, accuracy and efficiency of incremental centre hole drilling as a method of measuring near surface residual stress fields. Particular emphasis is placed on providing optimal values for the number of drilling step increments to be used and their corresponding size. Guidelines on the optimal values for the number and size of steps to use during measurements are presented for various ratios of hole radius to strain gauge rosette radius in the form of tabulated data. These guidelines are subsequently incorporated into a new data analysis program which permits very near surface residual stress fields to be accurately determined in real components. The benefits of the new approach are highlighted by reporting the results of measurements made on three industrial components, each of which has been subjected to a well-known engineering process. These components are a shot-peened spring-steel, a friction stir welded aluminium alloy, and a titanium alloy subjected to three different machining processes. The results reveal that the improvements to the incremental centre hole drilling technique can provide measured residual stresses from depths ranging from about 10 m to 1 mm.     

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.     

A modified hole-drilling technique for determining residual stresses in thin plates

This paper presents a modified hole-drilling technique for measuring residual stresses in sheet and thin-plate materials. The primary advantage of the modification is that it eliminates the necessity for calibration of each experimental hole-gage assembly. The relaxation coefficients are calculated from theory, and the strain components which are extraneous to the true relaxation strains are determined and separated from the measured relaxation strains. Experiments were conducted on 0.050-in. (1.27-mm) and 0.125-in. (3.175-mm)-thickness aluminum-alloy specimens. Sources of extraneous strain components are analyzed and values for these strain components resulting from machining residual stresses and localized plastic yielding are determined. Finally, the recommended range of the nondimensional ratio of hole diameter to distance between hole center and strain-gage center is determined by the maximum permissible error in residual-stress estimates. The modified technique appears to be accurate within ±5 percent or better and is, therefore, comparable in precision with the X-ray technique.     

Residual Stress Determination Using Hole Drilling and 3D Image Correlation

In recent years, the hole drilling method for determining residual stresses has been implemented with optical methods such as holographic interferometry and ESPI to overcome certain limitations of the strain rosette version of hole drilling. Although offering advantages, the interferometric methods require vibration isolation, a significant drawback to their use outside of the laboratory. In this study, a 3D image correlation approach was used to measure micron-sized surface displacements caused by the localized stress relief associated with hole drilling. Residual stresses were then found from the displacements using non-dimensional relations previously derived by finite element analysis. A major advantage of image correlation is that it does not require interferometric vibration isolation. Experiments were performed to check the ability of this new approach for uniaxial and equi-biaxial states of stress. Stresses determined by the approach were in good agreement with computed values and those determined by hole drilling using holographic interferometry.     

A New Procedure for the Evaluation of Non-Uniform Residual Stresses by the Hole Drilling Method Based on the Newton-Raphson Technique

The hole drilling method is one of the most used semi-destructive techniques for the analysis of residual stresses in mechanical components. The non-uniform stresses are evaluated by solving an integral equation in which the strains relieved by drilling a hole are introduced. In this paper a new calculation procedure, based on the Newton-Raphson method for the determination of zeroes of functions, is presented. This technique allows the user to introduce complex and effective forms of stress functions for the solution of the problem. All the relationships needed for the evaluation of the stresses are obtained in explicit form, eliminating the need to use additional mathematical tools. The technique is based on a rather general theory that allows to obtain the formulations of various existing techniques as particular cases.     

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.     

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.     

Thermal Stress Measurement in Continuous Welded Rails Using the Hole-Drilling Method

The absence of expansion joints in Continuous Welded Rail has created the need for the railroad industry to determine the in-situ thermal stress levels for rail buckling and breakage prevention. This paper explores the hole-drilling method as a possible solution to this problem. A new set of calibration coefficients to compute the stress field relieved by fine hole depth increments required by the high strength steel was determined. The new calibration coefficients were experimentally validated on an aluminum plate subjected to a known uniaxial load. The thermal stress levels of constrained rails were estimated after compensation for the residual stress components, based on statistical relationships developed experimentally between the longitudinal and the vertical residual stresses. The results showed that the hole-drilling procedure, with appropriate calibration coefficients and residual stress compensation, can estimate the in-situ rail thermal stresses with an expected accuracy that is within the industry acceptable levels.