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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Intralaboratory Repeatability of Residual Stress Determined by the Slitting Method

This paper presents repeated slitting method measurements of the residual stress versus depth profile through the thickness of identically prepared samples, which were made to assess repeatability of the method. Measurements were made in five 17.8 mm thick blocks cut from a single plate of 316L stainless steel which had been uniformly laser peened to induce a deep residual stress field. Typical slitting method techniques were employed with a single metallic foil strain gage on the back face of the coupon and incremental cutting by wire EDM. Measured residual stress profiles were analyzed to assess variability of residual stress as a function of depth from the surface. The average depth profile had a maximum magnitude of −668 MPa at the peened surface. The maximum variability also occurred at the surface and had a standard deviation of 15 MPa and an absolute maximum deviation of 26 MPa. Since measured residual stress exceeded yield strength of the untreated plate, microhardness versus depth profiling and elastic–plastic finite element analysis were combined to bound measurement error from inelastic deformation.     

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.     

Incremental Computation Technique for Residual Stress Calculations Using the Integral Method

The Integral Method for determining residual stresses involves making surface deformation measurements within a sequence of small increments of material removal depth. Typically, the associated matrix equation for solving the residual stresses within each depth increment is ill-conditioned. The resulting error sensitivity of the residual stress evaluation makes it essential that data measurement errors are minimized and that the residual stress solution method be as stable as possible. These two issues are addressed in this paper. The proposed method involves using incremental deformation data instead of the total deformation data that are conventionally used. The technique is illustrated using an example ESPI hole-drilling measurement.     

Comparison Between Surface and Near-Surface Residual Stress Measurement Techniques Using a Standard Four-Point-Bend Specimen

Background

Determination of near-surface residual stresses is challenging for the available measurement techniques due to their limitations. These are often either beyond reach or associated with significant uncertainties.

Objective

This study describes a critical comparison between three methods of surface and near-surface residual stress measurements, including x-ray diffraction (XRD) and two incremental central hole-drilling techniques one based on strain-gauge rosette and the other based on electronic speckle pattern interferometry (ESPI).

Methods

These measurements were performed on standard four-point-bend beams of steel loaded to known nominal stresses, according to the ASTM standard. These were to evaluate the sensitivity of different techniques to the variation in the nominal stress, and their associated uncertainties.

Results

The XRD data showed very good correlations with the surface nominal stress, and with superb repeatability and small uncertainties. The results of the ESPI based hole-drilling technique were also in a good agreement with the XRD data and the expected nominal stress. However, those obtained by the strain gauge rosette based hole-drilling technique were not matching well with the data obtained by the other techniques nor with the nominal stress. This was found to be due to the generation of extensive compressive residual stress during surface preparation for strain gauge installation.

Conclusion

The ESPI method is proven to be the most suitable hole-drilling technique for measuring near-surface residual stresses within distances close to the surface that are beyond the penetration depth of x-ray and below the resolution of the strain gauge rosette based hole-drilling method.

     

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.     

A Novel Cutting Strategy for Measuring Two Components of Residual Stresses Using Slitting Method

An exact knowledge of residual stresses that exist within the engineering components is essential to maintain the structural integrity. All mechanical strain relief (MSR) techniques to measure residual stresses rely on removing a section of material that contains residual stresses. Therefore, these techniques are destructive as the integrity of the components is compromised. In slitting method, as a MSR technique, a slot with an increasing depth is introduced to the part incrementally that results in deformations. By measuring these deformations the residual stress component normal to the cut can be determined. Two orthogonal components of residual stresses were measured using the slitting method both experimentally and numerically. Different levels of residual stresses were induced into beam shaped specimens using quenching process at different temperatures. The experimental results were then compared with those numerically predicted. It was shown that while the first component of residual stress was being measured, its effect on the second direction that was normal to the first cut was inevitable. Finally, a new cutting configuration was proposed in which two components of residual stresses were measured simultaneously. The results of the proposed method indicated a good agreement with the conventional slitting.     

MEASUREMENT OF NON-UNIFORM RESIDUAL STRESSES BY COMBINED MOIRE INTERFEROMETRY AND HOLE-DRILLING METHOD： THEORY, EXPERIMENTAL METHOD AND APPLICATIONS

Hole-drilling method is one of the most convenient methods for engineering residual stress measurement. Combined with moiré interferometry to obtain the relaxed whole-field displacement data, hole-drilling technique can be used to solve non-uniform residual stress problems, both in-depth and in-plane. In this paper, the theory of moiré interferometry and incremental hole-drilling (MIIHD) for non-uniform residual stress measurement is introduced. Three dimensional finite element model is constructed by ABAQUS to obtain the coefficients for the residual stress calculation. An experimental system including real-time measurement, automatic data processing and residual stresses calculation is established. Two applications for non-uniform in-depth residual stress of surface nanocrystalline material and non-uniform in-plane residual stress of friction stir welding are presented. Experimental results show that MIIHD is effective for both non-uniform in-depth and in-plane residual stress measurements. The project supported by the FRAMATOME ANP     

Residual stress distribution on surface-treated Ti-6Al-4V by X-ray diffraction

The x-ray diffraction technique has been used to measure surface residual stress in Ti-6Al-4V samples subjected to shot peening (SP), laser shock peening (LSP) and low plasticity burnishing (LPB). The magnitude, spatial and directional dependence and uniformity of the surface residual stresses have been investigated. The results show that residual stresses due to SP are uniform and independent of direction. LSP has been observed to produce non-uniform residual stress varying from one region to another, and also within a single laser shock. In the case of LPB, residual stresses have uniform spatial distribution but have been observed to be direction-dependent. Various components of the residual stress tensor in the LPB sample have been determined following the Dolle-Hauk method. The results of the residual stress due to three surface treatments are compared, and possible reasons for spatial and directional dependence are discussed.     

Surface integrity of inconel-718 nickel-base superalloy using controlled and natural contact length tools. part I: Lubricated

The surface integrity of inconel-718 nickel-base superalloy was investigated using orthogonal cutting at various cutting speeds, depths of cut and chip-tool contact lengths under lubricated conditions. The experimental work involved the determination of residual stress, plastic strain and microhardness distribution in the surface region and the examination of the surface and subsurface using scanning electron and optical microscopy. Both residual stresses and plastic strains decreased and the quality of the mechined surface improved with an increase in cutting speed, a decrease in depth of cut and with tools having controlled chip-tool contact lengths. The results were interpreted in terms of the variation in shear plane length and consequently the variation in tool forces with cutting conditions.     

Residual stresses in thick electrodeposits of a nickel-cobalt alloy

Some electroplated metals contain residual stresses which can cause warpage or premature failure of parts plated or electrofomed with these materials. Noticeably absent from the literature are residual-stress data for finished parts. Typically for plated or electroformed parts, residual stresses are determined independently on thin strips and then piece parts are plated. This research describes a technique which can be used to measure stress on finished parts. The method involves drilling a hole in the part and measuring the resulting change of strain in the vicinity of the hole. Viability of this technique was demonstrated by measuring the stress in a nickel-cobalt deposit plated on an aluminum cylinder. Two separate runs, one 50 deg removed from the other, provided almost identical results; stress was 160 MN/m² (23,200 psi). Two other runs in a region where plating was somewhat thinner provided slightly lower results probably because all boundary-condition requirements were not met. The computed residual-stress values compared quite favorably with independent rigid-strip measurements of 131 MN/m² (19,000 psi) obtained for the solution before and after plating of the cylinder.