Background Hole drilling is a measurement technique used to determine near surface residual stresses and has been codified in ASTM E837-20. In ASTM E837-20, the minimum allowable distance to a free edge is prescribed as 1.5 times the gauge circle diameter. Objective This work examines the effect arising from the distance from a free edge on a hole drilling measurement and provides an approach to determine residual stress for measurements where the edge distance is closer than that currently permitted by ASTM E837-20. Methods Numerical experiments were performed to understand how the compliance matrices change when the distance from a hole drilling measurement to a free edge varies. In addition, a series of hole drilling measurements were performed at various distances from a free edge using a shot peened aluminum plate with a nominally equibiaxial stress state to demonstrate the approach. Results The numerical experiments determined that the use of corrected compliance matrices is appropriate when the edge distance is as small as 0.35 times the gauge circle diameter. Physical measurements supported the use of custom compliance matrices for a given free edge distance and specimen thicknesses.

The objective of this paper is to validate a measurement-driven, model-based approach to estimate residual stress (RS) in samples machined from quenched aluminum stock. Model input is derived from measurement of RS in the parent stock. Validation is performed for prismatic T-sections removed from bars at different locations. We find RS predicted agrees with RS measured, by contour and neutron diffraction methods, with root-mean-square model-measurement difference of 22 MPa. Follow-on work (in Part 2) applies the RS estimation to samples representative of aircraft structures and examines the effects of RS on fatigue crack growth in the RS-bearing samples.

Background There are various experimental measurement techniques used to measure residual stress and this work describes one such method, the slotting method, and its application to measure near surface residual stresses. Objective This work examines its application to macro-scale specimens. Methods A series of numerical experiments were performed to understand the size required to assume that the specimen is infinitely large, namely the thickness, width, and height. To assess measurement repeatability, 12 slotting measurements were performed in a shot peened aluminum plate. Results The numerical experiments determined the specimen should have a thickness greater than or equal to 21.6 mm (0.85 in), a total specimen width (normal to the slot length) greater than or equal to 44.5 mm (1.75 in), and total height (parallel to the slot) greater than or equal to 38.1 mm (1.5 in) for the specimen to be assumed to be infinite. Slotting measurement repeatability was found to have a maximum repeatability standard deviation of 30 MPa at the surface that decays rapidly to 5 MPa at a depth of 0.3 mm from the surface. Comparison x-ray diffraction measurements were performed. Conclusions Infinite plate dimensions and slot length were determined as well as measurement repeatability. Slotting was shown to have significantly better repeatability than X-ray diffraction with layer removal for this application.

Background Residual stress spatial mapping has been developed using various measurement methods, one such method comprising a multiplicity of one-dimensional slitting method measurements combined to form a two-dimensional (2D) map. However, an open question is how to best distribute the individual slitting measurements for 2D mapping. Objective This paper investigates the efficacy of different strategies for laying out the individual slitting measurements when mapping in-plane residual stress in thin stainless steel slices removed from a larger dissimilar metal weld. Methods Three different measurement layouts are assessed: independent measurements on nominally identical specimens (i.e., one slitting measurement per specimen, with many specimens), repeatedly bisecting a single slice, and making nominally sequential measurements from one side of the specimen towards the other side of the specimen. Additional comparison measurements are made using neutron diffraction. Results The work shows little difference between the independent and bisecting slitting measurement layouts, and some differences with the sequential measurements. There is good general agreement between neutron diffraction measurement data and the data from the independent and bisecting layouts. Conclusions This work suggests that when using slitting to create a 2D map of in-plane residual stress, a cutting layout that repeatedly bisects the specimen works well, requires a small number of specimens, and avoids potential errors from geometric asymmetry or measurement sequence.

This paper describes the development of a new uncertainty estimator for slitting method residual stress measurements. The new uncertainty estimator accounts for uncertainty in the regularization-based smoothing included in the residual stress calculation procedure, which is called regularization uncertainty. The work describes a means to quantify regularization uncertainty and then, in the context of a numerical experiment, compares estimated uncertainty to known errors. The paper further compares a first-order uncertainty estimate, established by a repeatability experiment, to the new uncertainty estimator and finds good correlation between the two estimates of precision. Furthermore, the work establishes a procedure for automated determination of the regularization parameter value that minimizes total uncertainty. In summary, the work shows that uncertainty in the regularization parameter is a significant contributor to the total uncertainty in slitting method measurements and that the new uncertainty estimator provides a reasonable estimate of single measurement uncertainty.

This paper describes the development of an uncertainty estimate for slitting residual stress measurement. The uncertainty estimate includes a newly developed uncertainty estimate related to the smoothing used in the stress calculation procedure called the regularization uncertainty. This work describes the approach to define the regularization uncertainty, shows the usefulness of the uncertainty estimate in a numerical experiment. The uncertainty estimate is shown to meet an acceptance criterion that compares the calculated (measured) stress ± its uncertainty estimate to the true value for the numerical experiment. This works shows the regularization uncertainty estimate to be a necessary contributor to the uncertainty in slitting and additionally the uncertainty estimate developed here reasonably predicts the uncertainty present in slitting method measurements.

Measurement precision and uncertainty estimation are important factors for all residual stress measurement techniques. The values of these quantities can help to determine whether a particular measurement technique would be viable option. This paper determines the precision of hole-drilling residual stress measurement using repeatability studies and develops an updated uncertainty estimator. Two repeatability studies were performed on test specimens extracted from aluminum and titanium shot peened plates. Each repeatability study included 12 hole-drilling measurements performed using a bespoke automated milling machine. Repeatability standard deviations were determined for each population. The repeatability studies were replicated using a commercially available manual hole-drilling milling machine (RS-200, Micro-Measurements). An updated uncertainty estimator was developed and was assessed using an acceptance criterion. The acceptance criterion compared an expected percentage of points (68%) to the fraction of points in the stress versus depth profile where the measured stresses ± its total uncertainty contained the mean stress of the repeatability studies. Both repeatability studies showed larger repeatability standard deviations at the surface that decay quickly (over about 0.3 mm). The repeatability standard deviation was significantly smaller in the aluminum plate (max ≈ 15 MPa, RMS ≈ 6.4 MPa) than in the titanium plate (max ≈ 60 MPa, RMS ≈ 21.0 MPa). The repeatability standard deviations were significantly larger when using the manual milling machine in the aluminum plate (RMS ≈ 21.7 MPa), and for the titanium plate (RMS ≈ 18.9 MPa). The single measurement uncertainty estimate met a defined acceptance criterion based on the confidence interval of the uncertainty estimate.

In this study, the relationship between SCC growth rate and Vickers hardness for Type 316 stainless steel at various temperatures in simulated PWR primary water was investigated. In addition, IGSCC growth measurements were conducted using so-called functionally graded cold-rolled specimens made of Type 316 stainless steel, in simulated PWR primary water. Residual stress measurements were performed using the contour and slitting methods on the functionally graded cold-rolled specimens. The contour method measurements found highly tensile stress (350 MPa) toward the surface of the side with a larger thickness reduction and low-magnitude stress elsewhere. The purpose of these latter specimens was to evaluate the effect of heavily cold-worked layers on the inner surface of components made of Type 316 stainless steel on the possibility that IGSCC could penetrate through the wall thickness. The test data showed that the work-hardened inner surface does not always have a detrimental effect on SCC susceptibility. However, if any surface cracks exist within the work-hardened inner surface layer of any components, the stress at the crack tip becomes very large and SCC easily initiates. Nevertheless, even if IGSCC initiates from a heavily cold-worked layer at the inner surface, IGSCC growth rate in Type 316 stainless steel was found to eventually become negligibly small or arrests in the soft base material.

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.

This paper further explores the primary slice removal technique for planar mapping of multiple components of residual stress anddescribes 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.

This article describes the use of complementary residual stress measurements to quantify cold-work stress relief in die forgings used for monolithic unitized aerospace components. Two specimens were used, being nominally identical, but measured at different processing stages: one that was die forged and quenched (high residual stress state) and one having a post-quench, cold-work stress relief (low residual stress state). Multi-component residual stress maps were developed using multiple techniques along a single measurement plane (axes of this plane run parallel to the nominal long-transverse [x-direction] and short-transverse directions [y-direction]). The measurement techniques were energy dispersive X-ray diffraction (EDXRD), neutron diffraction (ND), and primary slice removal (PSR) biaxial mapping. Good agreement was found between the EDXRD and PSR biaxial mapping measurements. In the high-stress specimen, measured stress normal to the measurement plane (z-direction [L]) is highly compressive along the part exterior (-300 MPa) and highly tensile toward the center (250 MPa), as typical of quenched aluminum. Stress along the x-direction has a similar spatial distribution but smaller magnitude (-200 MPa to 130 MPa). The measured stresses in the cold-worked, low-stress specimen are significantly lower, with z-direction and x-direction stresses ranging between -130 MPa and 75 MPa.

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.

This paper describes a sequence of residual stress measurements made to determine a two-dimensional map of biaxial residual stress (weld direction and transverse to the weld direction) in a mockup with a partial arc excavation and weld repair (EWR), as well as three additional maps of one component of residual stress. The mockup joins two dissimilar metal plates (SA-508 low alloy steel and Type 316L stainless steel) with a nickel alloy weld metal (Alloy 82/182). A partial groove is then excavated and filled in with SCC resistant Alloy 52M weld metal. The mockup was fabricated to investigate the effectiveness of the EWR mitigation methodology being investigated through the development of ASME Code Case N-847 to address stress corrosion cracking problems in reactor coolant system butt welds. The biaxial stress map is determined using a newly developed technique called primary slice removal (PSR) mapping, which uses both contour method and slitting measurements. In this case, the technique requires measuring the longitudinal stress along a plane and the long transverse stress remaining in a slice removed adjacent to that plane. This paper includes descriptions of the experiments and data analysis. The measured residual stresses follow expected trends and compare favorably to the results of computational weld residual stress modeling.

Residual stresses were measured in rectilinear aluminium bars quenched using an aqueous polyoxyethylene glycol (PAG) solution or cold-water. Residual stresses were measured with neutron diffraction and a superposition-based method using mechanical strain release measurements. Three orthogonal stress components were measured along two transverse lines using neutron diffraction. The longitudinal residual stresses were mapped over a transverse cross-section using the contour technique. A primary slice removal technique mapped three orthogonal residual stresses over a transverse cross-section in the PAG extrusion. Residual stresses were found to vary from biaxial compressive in the part boundaries to triaxial tensile in the interiors. There was close correlation between the neutron diffraction and mechanical strain release techniques. PAG quenching demonstrated lower residual stresses. This paper is part of a Themed Issue on Measurement, modelling and mitigation of residual stress.

This paper describes a residual stress measurement approach that determines a two-dimensional map of biaxial residual stress. The biaxial measurement is a combination of contour method, slitting method measurements on a thin slices removed adjacent to the contour plane, and a computation to account for the effects of slice removal. The measurement approach uses only mechanical stress release methods, which is advantageous for some measurement articles. The measurement approach is verified with independent confirmation measurements. Biaxial mapping measurements are performed in a long aluminum bar (77.8 mm width, 51.2 mm thickness, and 304.8 mm length) that has residual stresses induced with quenching. The measured stresses are consistent with quench induced residual stress, having peak magnitude of 150 MPa and a distribution that is tensile toward the center of the bar and compressive around the boundary. The validating confirmation measurement results have good agreement with results from the biaxial mapping approach.

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 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 results of the numerical simulation 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 has precision on the order of 10 MPa.

This paper describes a newly developed uncertainty estimate for contour method residual stress measurements and presents results from two experiments where the uncertainty estimate was applied. The uncertainty estimate includes contributions from random error sources including the error arising from noise in displacement measurements and the smoothing of the displacement surfaces. The output is a two-dimensional, spatially varying uncertainty estimate such that every point on the cross-section where residual stress is determined has a corresponding uncertainty value. The current paper describes the use of the newly developed uncertainty estimate in a quenched aluminum bar with a cross section of 51 × 76 mm and a stainless steel weld plate with a cross-section of 25.4 × 152.4 mm, with a 6.35 mm deep groove, filled with a multi-pass weld. The estimated uncertainty in the quenched aluminum bar is approximately 5 MPa over the majority of the cross-section, with localized areas of higher uncertainty, up to 10 MPa. The estimated uncertainty in the welded stainless steel plate is approximately 22 MPa over the majority of the cross-section, with localized areas of higher uncertainty, over 50 MPa.

The paper describes measurements of residual stress in nozzles with dissimilar metal (DM) welds typical of those found in the primary cooling loop of a pressurized water reactor (PWR). Experimental data were developed for several assets in a sustained program lasting several years, during which residual stress measurement techniques were refined and improved. Residual stress technique refinement used building block studies to assess residual stress measurement capability and define measurement precision. By applying a wide range of techniques in the building block studies, ranging from simple (surface hole drilling) to complex (neutron diffraction), it was possible to select a small number of techniques that were judged appropriate for use in measurements on larger mockup, prototype, and ex-plant configurations. A novel combination of two established mechanical stress release techniques, the contour method and the slitting method, provided for two-dimensional spatial mapping of the biaxial stress near typical nozzle DM welds. The biaxial map comprises measurements of both the hoop and axial weld residual stress components, and their spatial variation with radial and axial position in the nozzle wall. The paper provides weld residual stress mapping data for three assets with DM welds: mockup of a PWR pressurizer safety and relief nozzle; mockup of a PWR pressurizer surge nozzle; and, a PWR pressurizer safety and relief nozzle removed from a cancelled plant.

This paper describes a sequence of residual stress measurements made to determine a two-dimensional map of biaxial residual stress in a stainless steel weld. A long stainless steel (316L) plate with an eight-pass groove weld (308L filler) was used. The biaxial stress measurements follow a recently developed approach, comprising a combination of contour method and slitting measurements, with a computation to determine the effects of out-of-plane stress on a thin slice. The measured longitudinal stress is highly tensile in the weld- and heat-affected zone, with a maximum around 450 MPa, and compressive stress toward the transverse edges around −250 MPa. The total transverse stress has a banded profile in the weld with highly tensile stress at the bottom of the plate (y = 0) of 400 MPa, rapidly changing to compressive stress (at y = 5 mm) of −200 MPa, then tensile stress at the weld root (y = 17 mm) and in the weld around 200 MPa, followed by compressive stress at the top of the weld at around −150 MPa. The results of the biaxial map compare well with the results of neutron diffraction measurements and output from a computational weld simulation.

Tensile weld residual stress (WRS) in the presence of primary water has been identified as a main driver for stress corrosion cracking in dissimilar metal welds found in the cooling circuit of pressurized water reactors. Thus, WRS data are needed to support plant management decisions, and so are of interest to a broad range of stakeholders in pressure vessel technology. In an effort to validate predictive WRS models and quantify modeling uncertainty, the U.S. Nuclear Regulatory Commission (NRC) and the Electric Power Research Institute (EPRI) have cooperatively organized a research program on WRS. This paper is a follow-up to earlier work, which described a series of WRS data analysis methods that provide a range of figures of merit, from simple (e.g., root mean square difference from a benchmark) to complex (e.g., comparison of predicted crack growth behavior), that can be used to judge WRS data quality. The present work applies those methods to assess model outputs developed during the second NRC/EPRI international round robin study (Phase 2b) on WRS modeling. The results of exercising the data analysis methods are presented, and compared to results obtained from an analysis of data from the previous round robin (Phase 2a).