Laser surface-contouring and spline data-smoothing for residual stress measurement

We describe non-contact scanning with a confocal laser probe to measure surface contours for application to residual stress measurement. (In the recently introduced contour method, a part is cut in two with a flat cut, and the part deforms by relaxation of the residual stresses. A cross-sectional map of residual stresses is then determined from measurement of the contours of the cut surfaces.) The contour method using laser scanning is validated by comparing measurements on a ferritic steel (BS 4360 grade 50D) weldment with neutron diffraction measurements on an identical specimen. Compared to lower resolution touch probe techniques, laser surface-contouring allows more accurate measurement of residual stresses and/or measurement of smaller parts or parts with lower stress levels. Furthermore, to take full advantage of improved spatial resolution of the laser measurements, a method to smooth the surface contour data using bivariate splines is developed. In contrast to previous methods, the spline method objectively selects the amount of smoothing and estimates the uncertainties in the calculated residual stress map.     

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.     

Mapping Multiple Components of the Residual Stress Tensor in a Large P91 Steel Pipe Girth Weld Using a Single Contour Cut

The contour method is applied in an innovative manner to measure the distribution of hoop residual stress in a large martensitic-ferritic steel pipe containing a multi-pass girth weld. First, a novel one-step wire electro-discharge machining cut is conducted to divide the pipe lengthways into two halves. The deformation of the cut halves is then measured and analysed in a way that simultaneously gives maps of hoop stress across the wall thickness on both sides of the pipe and automatically accounts for through-thickness hoop bending effects and how they may vary along the pipe. Finally the contour method results are combined with X-ray diffraction residual stress measurements using the principle of superposition to determine the distribution of the axial and radial residual stresses in the pipe. It is thereby demonstrated how the distribution of three direct components of the residual stress tensor in a welded pipe can be readily determined using a “hybrid” contour measurement approach.     

Repeatability of the Contour Method for Residual Stress Measurement

This paper describes the results of a residual stress measurement repeatability study using the contour method. The test specimen is an aluminum bar (cut from plate), with cross sectional dimensions of 50.8 mm?×?76.2 mm (2 in?×?3 in) with a length of 609.6 mm (24 in). There are two bars, one bar with high residual stresses and one bar with low residual stresses. The high residual stress configuration (±150 MPa) is in a quenched and over-aged condition (Al 7050-T74) and the low residual stress configuration (±20 MPa) is stress relieved by stretching (Al 7050-T7451). Five contour measurements were performed on each aluminum bar at the mid-length of successively smaller pieces. Typical contour method procedures are employed with careful clamping of the specimen, wire electric discharge machining (EDM) for the cut, laser surface profiling of the cut faces, surface profile fitting, and linear elastic stress analysis. The measurement results provide repeatability data for the contour method, and the difference in repeatability when measuring high or low magnitude stresses. The results show similar repeatability standard deviation for both samples, being less than 10 MPa over most of the cross section and somewhat larger, around 20 MPa, near the cross section edges. A comparison with published repeatability data for other residual stress measurement techniques (x-ray diffraction, incremental hole drilling, and slitting) shows that the contour method has a level of repeatability that is similar to, or better than, other techniques.     

A domain integral for the calculation of generalized stress intensity factors in sliding complete contacts

In this study, a procedure for calculating the generalized stress intensity factor (GSIF) for 2D sliding complete contacts is presented. The method is based on a domain integral equivalent to a path-independent integral. The domain character of the approach makes it very suitable for the post-processing of finite element solutions. The robustness and accuracy of the method are assessed through numerical examples, comparing the obtained results with other techniques, such as stress extrapolation and the path-independent contour integral. In addition, the multiplier constants for other terms in the expansion series are also computed.     

Method of determining the aerodynamic coefficients of asymmetric bodies with allowance for nonlinear body shape influence factors

The numerical method proposed makes it possible to determine the aerodynamic coefficients of asymmetric bodies of fairly arbitrary shape (including those with discontinuities of the transverse contour) at small solid angles of attack. The method allows an aerodynamically sound transition from the three-dimensional system of equations of gas dynamics to a two-dimensional system, which considerably simplifies the problem and reduces by an order the machine time required. The method takes into account the nonlinear body shape influence factors, which substantially improves the accuracy of the calculations. The efficiency and accuracy of the method are demonstrated by comparing the results of the calculations with the results of a numerical solution of the three-dimensional problem.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 121–128, March–April, 1992.     

Superposition and Destructive Residual Stress Measurements

The paper describes destructive measurement of residual stress profiles across two perpendicular planes in a single coupon. Several established destructive measurement techniques can determine the residual stress locked in a coupon of interest, but in general, only a single measurement can be taken without releasing stress and affecting subsequent measurements. However, when the first measurement determines a stress profile across an entire plane, the released stress can be determined, through a supplemental stress analysis incorporating results from the first measurement, and then accounted for in a subsequent measurement. To demonstrate the capability, we describe measurements of residual stress profiles across two perpendicular planes in aluminum compact tension coupons. Residual stress was introduced into the coupons by laser shock peening, and measurements were performed using the slitting method. For each coupon, the measured stress profile on the first plane was used to compute stress released on the second plane. By adding this released stress to measured stress for the second plane, we obtain a stress profile for the second plane in the original configuration. Results of a numerical model that predicts residual stress due to laser shock peening are presented, and agreement between the model and experimental results gives confidence in the superposition method applied.     

Follow-up of a panel restoration procedure through image correlation and finite element modeling

Residual stress estimation is an important question for structural integrity. Since residual stresses are self-balanced stress fields, a classical way to obtain information on them is to remove a part of the structure, and observe the structure displacement field arising from the stress redistribution. The hole-drilling method is such an approach. In some cases, as for the present one concerning a painted panel of cultural heritage, the hole-drilling method is not suited (a structure with a complex geometry, few tests allowed) but one can take advantage of structural modifications if they are monitored (here, a restoration act). We therefore describe in this article a model updating approach, focusing on the residual stress estimation and not on the material parameter identification.This study couples an optical non-invasive shape measurement (digital image correlation, using a projected speckle pattern on the painted panel, with luminance compensation) and a numerical approach (3D finite elements) for the model updating. The 3D stereo-correlation is used to measure a partial displacement field between three different states of the structure (at three different times of the restoration act). The numerical part concerns stress evaluation, once the model and the experiments are compared using a geometric mapping and a spatial projection of discrete fields. Using modeling and identification, the simulation is used to obtain the residual stresses in the panel, before and after the restoration.     

In-situ 3D contour measurement for laser powder bed fusion based on phase guidance

In-situ layerwise imaging measurement of laser powder bed fusion (LPBF) provides a wealth of forming and defect data which enables monitoring of components quality and powder bed homogeneity. Using high-resolution camera layerwise imaging and image processing algorithms to monitor fusion area and powder bed geometric defects has been studied by many researchers, which successfully monitored the contours of components and evaluated their accuracy. However, research for the methods of in-situ 3D contour measurement or component edge warping identification is rare. In this study, a 3D contour measurement method combining gray intensity and phase difference is proposed, and its accuracy is verified by designed experiments. The results show that the high-precision of the 3D contours can be achieved by the constructed energy minimization function. This method can detect the deviations of common geometric features as well as warpage at LPBF component edges, and provides fundamental data for in-situ quality monitoring tools.     

Assessment of Primary Slice Release Residual Stress Mapping in a Range of Specimen Types

This paper further explores the primary slice removal technique for planar mapping of multiple components of residual stress and describes application to specimens with a range of alloys, geometries, and stress distributions. Primary slice release (PSR) mapping is a combination of contour and slitting measurements that relies on decomposing the stress in a specimen into the stress remaining in a thin slice and the stress released when the slice is removed from a larger body. An initial contour method measurement determines a map of the out-of-plane stress on a plane of interest. Subsequently, removal of thin slices and a series of slitting measurements determines a map of one or both in-plane stress components. Four PSR biaxial mapping measurements were performed using an aluminum T-section, a stainless steel plate with a dissimilar metal slot-filled weld, a titanium plate with an electron beam slot-filled weld, and a nickel disk forging. Each PSR mapping measurement described herein has one (or more) complementary validation measurement to confirm the technique. Uncertainty estimates are included for both the PSR mapping measurements and the validation measurements. Agreement was found between the PSR mapping measurements and validation measurements showing that PSR mapping is a viable technique for measuring residual stress fields.     

Validation of a Contour Method Single-Measurement Uncertainty Estimator

This work validates an analytical single-measurement uncertainty estimator for contour method measurement by comparing it with a first-order uncertainty estimate provided by a repeatability study. The validation was performed on five different specimen types. The specimen types cover a range of geometries, materials, and stress conditions that represent typical structural applications. The specimen types include: an aluminum T-section, a stainless steel plate with a dissimilar metal slot-filled weld, a stainless steel forging, a titanium plate with an electron beam slot-filled weld, and a nickel disk forging. For each specimen, the residual stress was measured using the contour method on replicate specimens to assess measurement precision. The uncertainty associated with each contour method measurement was also calculated using a recently published single-measurement uncertainty estimator. Comparisons were then made between the estimated uncertainty and the demonstrated measurement precision. These results show that the single-measurement analytical uncertainty estimate has good correlation with the demonstrated repeatability. The spatial distributions of estimated uncertainty were found to be similar among the conditions evaluated, with the uncertainty relatively constant in the interior and larger along the boundaries of the measurement plane.     

Analysis of rotating solids with cracks by the boundary element method

The use of the boundary element method for the solution of linear elastic fracture mechanics problems, without body forces, is quite extensive since the method is intrinsically well suited to the analysis of high stress gradients associated with crack problems. The crack-tip stresses for rotating bodies are similar to the stresses for stationary bodies and therefore all the advantages of the boundary element procedure can be encompassed in the extension of the method to the solution of rotating bodies with cracks. In the present analysis, the additional volume integral that arises from the treatment of inertial body forces is eliminated by using the well-known particular integral procedure. The matrix ill-conditioning that results from the need to model co-planar crack surfaces of non-symmetrical cracks is avoided by using the multi-region approach. The accuracy of the numerical solutions is improved by utilizing quarter-point elements with traction singular enhancement at the crack-tip. The procedure is then applied to the solution of arbitrary cracks in two- and three-dimensional rotating bodies.     

Two-Dimensional Mapping of In-plane Residual Stress with Slitting

This paper describes the use of slitting to form a two-dimensional spatial map of one component of residual stress in the plane of a two-dimensional body. Slitting is a residual stress measurement technique that incrementally cuts a thin slit along a plane across a body, while measuring strain at a remote location as a function of slit depth. Data reduction, based on elastic deformation, provides the residual stress component normal to the plane as a function of position along the slit depth. While a single slitting measurement provides residual stress along a single plane, the new work postulates that multiple measurements on adjacent planes can form a two-dimensional spatial map of residual stress. The paper uses numerical simulations to develop knowledge of two fundamental problems regarding two-dimensional mapping with slitting. The first fundamental problem is to estimate the quality of a slitting measurement, relative to the proximity of a given measurement plane to a free surface, whether that surface is the edge of the original part or a free surface created by a prior measurement. The second fundamental problem is to quantify the effects of a prior slitting measurement on a subsequent measurement, which is affected by the physical separation of the measurement planes. The results of the numerical simulations lead to a recommended measurement design for mapping residual stress. Finally, the numerical work and recommended measurement strategy are validated with physical experiments using thin aluminum slices containing residual stress induced by quenching. The physical experiments show that two-dimensional residual stress mapping with slitting, under good experimental conditions (simple sample geometry and low modulus material), has precision on the order of 10 MPa. Additional validation measurements, performed with x-ray diffraction and ESPI hole drilling, are within 10 to 20 MPa of the results from slitting.     

A numerical implementation using mid-node collocation for the hypersingular boundary contour method

A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional problems does not require any numerical integration at all. In another development, a boundary contour implementation of a regularized hypersingular boundary integral equation (HBIE) using quadratic elements and end-node collocation was proposed and the technique is termed the hypersingular boundary contour method (HBCM). As reported in that work, the approach requires highly refined meshes in order to numerically enforce the stress continuity across boundary contour elements. This continuity requirement is very crucial since the regularized HBIE is only valid at collocation points where the stress tensor is continuous, while the computed stress at the endpoints of a boundary contour element, which is a non-conforming element, is generally not. This paper presents a new implementation of the HBCM for which the regularized HBIE is collocated at the mid-node of a boundary contour element. As the computed stress tensor is continuous at these mid-nodes, there is no need for unusually refined meshes. Some numerical tests herein show that, for the same mesh density, the HBCM using mid-node collocation has a comparable accuracy as the BCM.     

A method for reconstruction of residual stress fields from measurements made in an incompatible region

A method is introduced by which the complete state of residual stress in an elastic body may be inferred from a limited set of experimental measurements. Two techniques for carrying out this reconstruction using finite element analysis are compared and it is shown that for exact reconstruction of the stress field via this method, the stress field must be measured over all eigenstrain-containing regions of the object. The effects of error and incompleteness in the measured part of the stress field on the subsequent analysis are investigated in a series of numerical experiments using synthetic measurement data based on the NeT TG1 round-robin weld specimen. It is hence shown that accurate residual stress field reconstruction is possible using measurement data of a quality achievable using current experimental techniques.     

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.     

绘制等应力线的一种有效方法

本文提出了一种绘制受载结构等应力图的有效而简单的方法,这种方法是在开发PRSA-1专用有限元程序中逐渐改进和完善的,它能根据有限元的计算结果连续地在结构内搜索等应力点,也采用了适当的方法构造出一些等应力点。借助于AUTOCAD绘图软件包,结构的等应力图可以在计算机屏幕上自动生成,也可以用绘图仪绘出以便永久保留。     

In-plane Operating Deflection Shape Measurement of an Aluminum Plate Using a Three-dimensional Continuously Scanning Laser Doppler Vibrometer System

Background

In-plane vibration is significant to a structure and has been accurately solved by many numerical methods; however, there are still not enough studies on its experimental measurement.

Objective

This work aims to propose a non-contact and fast way to measure dense full-field in-plane vibration of a plate structure, which has high frequencies and low response magnitudes.

Methods

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs is developed to conduct full-field scanning of a plate with free boundary conditions under sinusoidal excitation to measure its 3D vibrations. Calibration among the three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles to ensure that three laser spots can continuously and synchronously move along the same two-dimensional scan trajectory on the plate. The demodulation method is used to process the measured response to obtain in-plane operating deflection shapes (ODSs) of the plate.

Results

Four in-plane ODSs are obtained in the frequency range of 0–5000 Hz. Modal assurance criterion (MAC) values between in-plane ODSs from 3D CSLDV and step-wise scanning laser Doppler vibrometer (SLDV) measurements are larger than 95%. MAC values between ODSs from 3D CSLDV measurements and corresponding mode shapes from the finite element model of the plate are larger than 91%.

Conclusions

Results from 3D CSLDV measurements have good accuracy compared to those from SLDV measurements and numerical calculation, and the 3D CSLDV system can scan much more measurement points in much less time than the SLDV system.

     

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.     

A combined experimental and numerical method for the solution of generalized elasticity problems

This work presents the method for the investigation of three-dimensionally stressed bodies with arbitrary shape which are under the action of an outside system of arbitrary forces. The combined method is based on syntheses of photoelastic experimental methods (other experimental methods may also be used) and digital methods of discrete analysis. Experimental procedures are used for defining superfluous boundary conditions. The boundary-value problem with such boundary conditions is solved by numerical methods. This approach qualitatively changes the very essence of experimental methods and essentially widens their range. It reduces the amount of measurements required and, at the same time, allows one to obtain complete stress fields throughout a body in a short time. In comparison with numerical methods, the combined method increases the accuracy of problem solutions and, at the same time, reduces the time required for complete investigations.