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.     

Slitting Measurement of Residual Hoop Stresses Through the Wall-Thickness of a Filament Wound Composite Ring

The slitting method was used to determine residual hoop stress profile along the thickness of a filament wound carbon/epoxy ring. The method involves measuring strains at the inner surface of the ring, while a narrow axial slit is cut progressively from the outer surface. In order to calculate the residual hoop stress profile over the entire ring thickness, pulse method was used, which assumes that stress in each depth increment is uniform. Besides, Tikhonov regularization was employed to stabilize the stress results and reduce its sensitivity to strain measurement errors. Regarding the fact that Tikhonov regularization is not appropriate for computing solutions with discontinuities, pulse method coupled with Tikhonov regularization was used separately for each layer of the composite ring.     

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.     

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.     

Measurement of the Residual Stress Tensor in a Compact Tension Weld Specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens.     

Controlling the Cut in Contour Residual Stress Measurements of Electron Beam Welded Ti-6Al-4V Alloy Plates

The multiple cut contour method is applied to map longitudinal and transverse components of residual stress in two nominally identical 50 mm thick electron beam welded Ti-6Al-4V alloy plates, one in the as-welded condition and a second welded plate in a post weld heat treated (PWHT) condition. The accuracy and resolution of the contour method results are directly linked to the quality of the electro-discharge machining cut made. Two symmetric surface contour artefacts associated with cutting titanium, surface bowing and a flared edge, are identified and their influence on residual stresses calculated by the contour method is quantified. The former artefact is controlled by undertaking a series of cutting trials with reduced power settings to find optimal cutting conditions. The latter is mitigated by attaching 5 mm thick sacrificial plates to the wire exit side of the test specimen. The low level of noise in the measured stress profiles for both the as-welded and PWHT plates demonstrates the importance of controlling the quality of a contour cut and the added value of undertaking cutting trials.     

Evaluation of Errors Associated with Cutting-Induced Plasticity in Residual Stress Measurements Using the Contour Method

Cutting-induced plasticity can lead to elevated uncertainties in residual stress measurements made by the contour method. In this study plasticity-induced stress errors are numerically evaluated for a benchmark edge-welded beam to understand the underlying mechanism. Welding and cutting are sequentially simulated by finite element models which have been validated by previous experimental results. It is found that a cutting direction normal to the symmetry plane of the residual stress distribution can lead to a substantially asymmetrical back-calculated stress distribution, owing to cutting-induced plasticity. In general, the stresses at sample edges are most susceptible to error, particularly when the sample is restrained during cutting. Inadequate clamping (far from the plane of cut) can lead to highly concentrated plastic deformation in local regions, and consequently the back-calculated stresses have exceptionally high values and gradients at these locations. Furthermore, the overall stress distribution is skewed towards the end-of-cut side. Adequate clamping (close to the plane of cut) minimises errors in back-calculated stress which becomes insensitive to the cutting direction. For minimal constraint (i.e. solely preventing rigid body motion), the plastic deformation is relatively smoothly distributed, and an optimal cutting direction (i.e. cutting from the base material towards the weld region in a direction that falls within the residual stress symmetry plane) is identified by evaluating the magnitude of stress errors. These findings suggest that cutting process information is important for the evaluation of potential plasticity-induced errors in contour method results, and that the cutting direction and clamping strategy can be optimised with an understanding of their effects on plasticity and hence the back-calculated stresses.     

Measuring Multiple Residual-Stress Components using the Contour Method and Multiple Cuts

The conventional contour method determines one component of residual stress over the cross section of a part. The part is cut into two, the contour (topographic shape) of the exposed surface is measured, and Bueckner’s superposition principle is analytically applied to calculate stresses. In this paper, the contour method is extended to the measurement of multiple residual-stress components by making multiple cuts with subsequent applications of superposition. The theory and limitations are described. The theory is experimentally tested on a 316L stainless steel disk with residual stresses induced by plastically indenting the central portion of the disk. The multiple-cut contour method results agree very well with independent measurements using neutron diffraction and with a computational, finite-element model of the indentation process.     

Improvement of the Contour Method for Measurement of Near-Surface Residual Stresses from Laser Peening

A study was conducted to develop a methodology to obtain near-surface residual stresses for laser-peened aluminium alloy samples using the contour method. After cutting trials to determine the optimal cut parameters, surface contours were obtained and a new data analysis method based on spline smoothing was applied. A new criterion for determining the optimal smoothing parameters is introduced. Near-surface residual stresses obtained from the contour method were compared with X-ray diffraction and incremental hole drilling results. It is concluded that with optimal cutting parameters and data analysis, reliable near-surface residual stresses can be obtained by the contour method.     

Measurement of residual stress in the weld overlay piping components

In general industry, especially in the nuclear industry, welding overlay repair is an important repair method mainly used to rebuild piping systems suffering from intergranular stress-corrosion cracking (IGSCC).The pipe surface is mechanically ground to obtain a smooth surface after the welding overlay repair. A better understanding of the effect of repair and grinding processes on the residual stresses at the surface of weld overlay is required. To obtain this understanding, it is necessary to measure directly the distribution of residual stresses on the specimen. It is expected that compressive residual stress should be induced at the inner wall surface of the pipe for prevention of IGSCC.The performance evaluation of welding overlay repair relies on whether or not the level and characteristic of the residual stress can be measured accurately. In this study, the hole-drilling strain-gage method, using the incremental drilling technique, was adopted to estimate the residual stresses on the inner and outer walls of the weld overlay pipe. The experimental results indicate that the residual stress at the pipe inner surface is compressive while that of the outer surface is tensile. Also, it is found that the depth affected by grinding is about 1.016 mm.     

Examination of the computational model for the layer-removal method for residual-stress measurement

An analytical solution is presented to examine the accuracy of the ‘layer-removal’ method for measuring localized residual stresses. In this approach, strips, which may have been cut from a pipe or a plate, have strain-gage rosettes placed on one face and layers removed from the other face. The strain measurements are used to deduce the residual stress in the layers removed. The stress measured is that along the axis of the strip. It may vary rapidly with axial distance, as for example when the strip is taken from a welded part. The present analysis shows that the actual stress distribution may be quite different from that predicted by the computational model normally used in the layer-removal method. It shows that the difference increases as the ratio of the heighth of the strip from which a layer is removed to the half dimensiona of the localized residual-stress zone increases. It is recommended that the layer-removal method can be used for measuring residual stresses for cases in which the ratio ofh/a is less than or equal to unity.     

Fluid–structure interaction in water-filled thin pipes of anisotropic composite materials

The effects of elastic anisotropy in piping materials on fluid–structure interaction are studied for water-filled carbon-fiber reinforced thin plastic pipes. When an impact is introduced to water in a pipe, there are two waves traveling at different speeds. A primary wave corresponding to a breathing mode of pipe travels slowly and a precursor wave corresponding to a longitudinal mode of pipe travels fast. An anisotropic stress–strain relationship of piping materials has been taken into account to describe the propagation of primary and precursor waves in the carbon-fiber reinforced thin plastic pipes. The wave speeds and strains in the axial and hoop directions are calculated as a function of carbon-fiber winding angles and compared with the experimental data. As the winding angle increases, the primary wave speed increases due to the increased stiffness in the hoop direction, while the precursor wave speed decreases. The magnitudes of precursor waves are much smaller than those of primary waves so that the effect of precursor waves on the deformation of pipe is not significant. The primary wave generates the hoop strain accompanying the opposite-signed axial strain through the coupling compliance of pipe. The magnitude of hoop strain induced by the primary waves decreases with increasing the winding angle due to the increased hoop stiffness of pipe. The magnitude of axial strain is small at low and high winding angles where the coupling compliance is small.     

Multi-Axial Contour Method for Mapping Residual Stresses in Continuously Processed Bodies

This paper describes a method for extending the capability of the contour method to allow for the measurement of spatially varying multi-axial residual stresses in prismatic, continuously processed bodies. Currently, the contour method is used to determine a 2D map of the residual stress normal to a plane. This work uses an approach similar to the contour method to quantify multiple components of eigenstrain in continuously processed bodies, which are used to calculate residual stress. The result of the measurement is an estimate of the full residual stress tensor at every point in the body. The approach is first outlined for a 2D body and the accuracy of the methodology is demonstrated for a representative case using a numerical experiment. Next, an extension to the 3D case is given and the accuracy is demonstrated for representative cases using numerical experiments. Finally, measurements are performed on a thin sheet of Ti-6Al-4V with a band of laser peening down the center (assumed to be 2D) and a thick laser peened plate of 316L stainless steel to show that the approach is valid under real experimental conditions.     

Steady-state creep analysis of pressurized pipe weldments by perturbation method

The stress analysis of pressurized circumferential pipe weldments under steady state creep is considered. The creep response of the material is governed by Norton’s law. Numerical and analytical solutions are obtained by means of perturbation method, the unperturbed solution corresponds to the stress field in a homogeneous pipe. The correction terms are treated as stresses defined with the help of an auxiliary linear elastic problem. Exact expressions for jumps of hoop and radial stresses at the interface are obtained. The proposed technique essentially simplifies parametric analysis of multi-material components.     

Residual stresses near a rail end

Stress fields near a cut end of a rail containing longitudinal residual stress typical of roller-straightened rail were studied using analysis and a finite element model. For a self-equilibrating residual stress distribution with equal maximum and minimum stresses, the distance to reach 95% of the mid-rail residual stress field is from 0.7 to 1.8 times the rail height, with the finite element model predicting a length of 1.1 times the rail height. This gives a measure of the accuracy of the simpler analytical models. At the rail end, the longitudinal residual stress goes to zero, and the vertical residual stress near mid-web reaches a maximum of approximately 27 ksi (186 MPa) (1.35 times the maximum mid-rail longitudinal residual stress of 20 ksi, or 138 MPa). The maximum shear stresses are 6 ksi (41 MPa) and −8 ksi (−55 MPa) near the head-web and web-base intersections, respectively, approximately 2 in. (51 mm) from the end of a 7.3 in. (185 mm) high rail. The shear stress is zero at the cut end and in mid-rail. The worst possible end-crack is a horizontal web crack in the vertical residual stress field at the rail end. The stress intensity K_I on such a crack is estimated to reach 20 ksi√in. (22 MPa√m) for cracks 0.5 in. (13mm) long. This is already 0.4 to 0.8 times K_I for carbon and alloy rails, and about 0.5 times K_Ic for a long crack.     

P91钢中厚壁管焊接残余应力分析

针对管道试件规格不同所要求的焊接工艺不一致问题,讨论P91钢中厚壁管对接接头所要求的双人对称焊形式下的焊接残余应力分布规律．基于ANSYS分析软件,以双移动高斯热源结合单元生死技术,利用顺序耦合方法得到P91钢中厚壁管焊接残余应力．讨论热处理工艺对于P91钢中厚壁管焊接残余应力的影响．结果表明,由于焊接工艺在环向位置上的结构反对称性使得焊接残余应力在环向上呈反对称分布;即便经过较高温度的预热处理,没有焊后热处理时最大等效应力仍超过屈服极限;进行焊后整体热处理的P91钢中厚壁管焊接残余应力得到了有效的改善,平均应力数值下降了60%~70%．     

Pre-kinking of a moving crack in a magnetoelectroelastic material under in-plane loading

A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases.     

Experimental Evaluation of Residual Stresses in Pipes Manufactured by UOE and ERW Processes

Pipes are basic elements used in the construction of pipelines for the long-distance transportation of oil and gas and their derivatives. They can be manufactured by cold forming processes such as UOE and ERW, both widely used in the oil and gas industry. These processes produce high levels of non-uniform plastic deformation, which introduce a new state of residual stress into the material. In some cases, these stresses combine with mechanical stresses generated by external loads leading to service failures, interrupting the transmission line and increasing the risk of accidents. Therefore, determining in advance the residual stress distribution in pipes is an important task which involves the evaluation of the structural integrity. Six pipe samples obtained by the UOE and ERW processes were measured and evaluated using a portable optical device that combines radial in-plane digital speckle pattern interferometer (DSPI) with the incremental hole-drilling technique to measure residual stresses. The experimental results indicate a distinct residual stress distribution for each manufacturing process, while the measured residual stress distributions in the longitudinal and circumferential directions were similar at all measurement locations along an individual pipe.     

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.