Blind-hole residual stress determination using optical interferometry

The in-plane method and the out-of-plane method are used to analyze blind-hole residual stress as measured by optical interferometry. The in-plane method, which constructs a relation between the in-plane displacement field and the residual stress released from blind-hole drilling, is applicable when the sensitivity vector of the interferometer used in the measuring system is parallel to the object surface. Three in-plane displacements obtained from one interference pattern are sufficient to determine the residual stress. The out-of-plane method, which establishes a new relation between the out-of-plane displacement field and the released residual stress, is suggested when the sensitivity vector is perpendicular to the object surface. Two relative out-of-plane displacements extracted from one interference pattern are sufficient to determine the residual stress. With the adoption of these two methods, interpolating calculation is not needed to determine the fringe order of each data point, since the selections of the required data points are flexible using these two methods. Two experiments, one for the in-plane method and the other for the out-of-plane method, were carried out to illustrate the applicability and usefulness of these two methods.     

基于大型炉体焊接残余应力测试的盲孔法研究

为提高炉体焊接残余应力测试精度,对传统的盲孔法进行改进,即在测点打孔后多次扩孔并增加孔深;通过对SM400ZL钢焊接残余应力测试时的应变释放系数A,B进行实验标定,得出多组应变释放系数值,计算可得残余应力的估算值,并对不同状况下的残余应力值进行比较.通过大拉力标定试验得出SM400ZL钢盲孔的孔边塑性变形对测量精度的影响和塑性修正公式.结果表明,改进的盲孔法能够更准确地测得焊接残余应力值,测量结果经塑性修正,最大误差减小到2%以下.测试方法和结果可直接在相关的工程实际中应用.     

Two holographic blind-hole methods for measuring residual stresses

The relationship between the displacements and stresses relieved from blind-hole drilling is introduced via an easily understandable concept in this paper. Combining this concept with holographic interferometry, two holographic blind-hole methods for measuring residual stresses are established. The first is a new technique which requires measuring three out-of plane displacements; and the second is a modification of another technique which requires measuring two out-of plane displacements. Each of the two methods needs only one interference fringe pattern and is demonstrated by using it to measure a known residual stress in an aluminum specimen.     

Investigation of shrinkage-induced stresses in stereolithography photo-curable resins

An experimental study has been undertaken to investigate the shrinkage characteristics of acrylic-based and epoxy-based stereolithography (SL) photopolymer resin systems after they have been laser cured and post-cured under ultraviolet (UV), and thermal exposure. The induced residual stresses and strains were determined by the shadow moiré and the hole-drilling strain-gage methods. Out-of-plane displacements (warpage) of acrylic-based post-cured resin plates were recorded by means of the shadow moiré method and correlated to the shrinkage strains by theoretical analysis. The induced residual stresses in the epoxy-based cylindrical resin specimens were determined from strains of three-element strain-gage rosettes of the blind-hole drilling method. Results are presented for the shrinkage stresses and strains for both material systems as a function of the post-curing process (UV, thermal). It was found that the shrinkage strains in the acrylic-based photopolymer resin were of considerable magnitude, while thermal post-curing resulted in higher shrinkage stresses for both material systems. The values of the shrinkage stresses compare well with those of the existing literature.     

反应堆贯穿件J形焊缝残余应力研究1）

焊接残余应力是引起应力腐蚀开裂的主要原因,准确地掌握残余应力的分布是对结构完整性评定的关键.为了探明反应堆压力容器顶盖控制棒驱动机构（control rod drive mechanism,CRDM）贯穿件J形焊缝残余应力的分布,本研究加工两个CRDM贯穿件实验模拟件,采用盲孔法测试两个J形接头的焊接残余应力.通过实验探明了CRDM贯穿件焊缝残余应力的分布规律,为反应堆压力容器结构完整性的研究提供必要参考.     

A New Procedure to Measure Near Yield Residual Stresses Using the Deep Hole Drilling Technique

Mechanical strain relief techniques for estimating the magnitude of residual stress work by measuring strains or displacements when part of the component is machined away. The underlying assumption is that such strain or displacement changes result from elastic unloading. Unfortunately, in components containing high levels of residual stress, elastic-plastic unloading may well occur, particularly when the residual stresses are highly triaxial. This paper examines the performance of one mechanical strain relief technique particularly suitable for large section components, the deep hole drilling (DHD) technique. The magnitude of error is calculated for different magnitudes of residual stress and can be substantial for residual stress states close to yield. A modification to the technique is described to allow large magnitudes of residual stress to be measured correctly. The new technique is validated using the case of a quenched cylinder where use of the standard DHD technique leads to unacceptable error. The measured residual stresses using the new technique are compared with the results obtained using the neutron diffraction technique and are shown to be in excellent agreement.     

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.     

Residual stress by blind-hole method with off-center hole

Application of the blind-hole drilling technique to measurement of residual stresses in areas too restricted for drilling guides is now possible by using a set of equations derived to account for off-center drilled holes. Prior technique required the hole to be drilled concentric with the gage center within ±0.001 in (0.0254 mm), thus requiring the use of a precision locating and drilling guide. The equations apply to commercially available 0-, 90- and 225-deg strain-gage rosettes, but can be easily modified or scaled for different arrays. Details of a hand-drilling procedure are presented, along with examples. Potential errors and data interpretation are discussed.     

Full field methods and residual stress analysis in orthotropic material. I Linear approach

This work analyzes the problem of residual stress determination in an orthotropic material using the hole drilling technique combined with non-contact, full field optical methods. Due to the complex behavior of the material, first a solution algorithm for the isotropic case is analyzed, then the procedure is extended to solving the more complex problem. In the first part of the work, the simplified Smith–Schajer solution to the through-hole problem for an orthotropic material is analyzed, showing that the same linear least square approach used in the isotropic case applies to a large set of orthotropic materials; based on this analysis a simple residual stress measurement algorithm is developed using either analytical or numerically estimated calibration coefficients.In the second part of the work, the general solution is discussed: since in this case the simplified Smith–Schajer solution cannot be used, the Lekhnitskii’s analysis of the through-hole plate in tension is introduced and extended to handle residual stresses. On this basis a solution algorithm using the nonlinear fit of the theoretical displacement field capable of treating all the orthotropic materials at the cost of a more complex numerical procedure is proposed. The performances of both algorithms are tested against numerically generated noisy fields and experimental ones and show a good reliability and accuracy.     

Displacement Determination by Holographic Interferometry for Residual Stress Analysis in Elastic Bodies

A method is developed for determining the three displacement components by the method of holographic interferometry from two interferograms used to measure residual stresses by hole drilling. The displacements are determined at the intersection points of the principal axes and the hole boundary. The method is experimentally validated by measuring the stress state of a plate under uniaxial tension __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 111–117, August 2005.     

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.     

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.     

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.     

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.     

Full field methods and residual stress analysis in orthotropic material. II: Nonlinear approach

This paper is the second part of a work that analyses the problem of residual stress determination in an orthotropic material by the hole drilling technique combined with full field optical methods. Due to the complex behaviour of the material, two theoretical formulations capable of describing the displacement field in an infinite plate in tension with a hole have been proposed: a simplified one, which can treat only a subset of all orthotropic materials, and a general, much more complex one. In the first part of this work, it has been shown that by using the simplified formulation, it is possible to develop a linear least square approach to the residual stress identification problem capable of treating a large class of orthotropic materials. This second part shows that the same approach can be extended to the general case providing that a somewhat more complex, nonlinear algorithm, is acceptable.     

Investigation of displacement fields in an abrasive waterjet drilling process: Part 2. Numerical analysis

In this paper, the displacement fields associated with the abrasive waterjet (AWJ) drilling process were simulated using the finite element method. A threedimensional finite element model was established, and justifiable pressure loads were used in the numerical model to simulate the AWJ drilling process. It was assumed that the pressure load in the AWJ could be resolved into three components, such as impact jet pressure, shear and normal pressure. The effect of these three pressure loads and their magnitudes on the surface displacement were investigated as a function of the jet penetration depth through numerical modeling. Using the hybrid experimental-numerical stress analysis approach, the transient state of stress and strain associated with the notch crest of the jet-induced hole at the impingement zone of the target material during AWJ piercing can be modeled numerically. It was found that the shear contributed the most in shaping the displacement contour patterns and that the jet pressure did not play a dominant role in determining theu field displacement. The jet pressure and shear had the most effect on thev field displacement contour pattern. It was demonstrated that the principal stresses at the bottom of the cavity increase as the depth of the hole increases.     

Propagation behavior of Love waves in a functionally graded half-space with initial stress

The propagation behavior of Love waves in a functionally graded material layered non-piezoelectric half-space with initial stress is taken into account. The Wentzel–Kramers–Brillouin (WKB) technique is adopted for the theoretical derivations. The analytical solutions are obtained for the dispersion relations and the distributions of the mechanical displacement and stress along the thickness direction in the layered structure. First, these solutions are used to study the effects of the initial stress on the dispersion relations and the group and phase velocities, then the influences of the initial stress on the distributions of the mechanical displacement and shear stresses along the thickness direction are discussed in detail. Numerical results obtained indicate that the phase velocity of the Love waves increases with the increase in the magnitude of the initial tensile stress, while decreases with the increase in the magnitude of the initial compression stress. The effects on the dispersion relations of the Love wave propagation are negligible as the magnitudes of the initial stress are less than 100 MPa. Some other results are obtained for the distributions of field quantities along thickness direction. The results obtained are not only meaningful for the design of functionally graded structures with high performance but also effective for the evaluation of residual stress distribution in the layered structures.     

Residual-stress determination through combined use of holographic interferometry and blind-hole drilling

Holographic interferometry is used to determine in-plane radial displacements due to release of residual stresses by hole drilling. A method is derived for relating radial displacements measured in three directions of illumination to the state of residual stress, analogous to relations used in the conventional strain-rosette technique. Residual stress is produced by an interference fit of two circular tubes. Agreement between stress determined holographically with a computed value and with that determined by the conventional technique is good. Advantages of the holographic technique in overcoming various shortcomings of the conventional technique are discussed. A modification of the holographic technique involving data collection in only two directions of illumination is described.     

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.     

Validation of Mechanical Strain Relaxation Methods for Stress Measurement

Most validation studies of mechanical strain relaxation (MSR) methods for residual stress measurement rely on using the saw-tooth residual stress distribution resulting from four point bending and elastic–plastic deformation. Validation studies using simple applied stress profiles in rectangular steel beams are used in this work, together with beams subjected to elastic–plastic bending. Two MSR methods are explored, deep-hole drilling (DHD) and incremental centre hole drilling (ICHD). As well as a series of experiments, finite element analyses are conducted to determine the accuracy in the inversion of measured deformation to reconstruct stress. The validation tests demonstrated that apart from the applied stresses, the initial residual stresses also contribute even when samples are expected to be stress free. The uncertainty in measurement for the two MSR methods is determined, with the uncertainty in near surface measurement found to be significantly larger than uncertainty for interior measurement. In simple loading cases (and simple stress profiles) the uncertainty in measurement and hence the degree of validation is shown to be within about ±50 MPa for steel for “known” stress up to about 140 MPa. However, if the residual stress distribution is more complex there arises increased uncertainty in the predicted residual stress and lack of confidence between measurements methods.