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 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 article examines the precision of the contour method using five residual stress measurement repeatability studies. The test specimens evaluated include the following: 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. These specimens were selected to encompass a range of typical materials and residual stress distributions. Each repeatability study included contour method measurements on five to ten similar specimens. Following completion of the residual stress measurements, an analysis was performed to determine the repeatability standard deviation of each population. In general, the results of the various repeatability studies are similar. The repeatability standard deviation tends to be relatively small throughout the part interior, and there are localized regions of higher repeatability standard deviations along the part perimeter. The repeatability standard deviations over much of the cross section range from 5 MPa for the aluminum T-section to 25 MPa for the nickel disk forging. There is a strong correlation between the elastic modulus of the material and the repeatability standard deviation. These results demonstrate the precision of the contour method over a broad range of specimen geometries, materials, and stress states.
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.
Chapter 5 of Practical Residual Stress Measurement Methods.
The contour method, which is based upon solid mechanics, determines residual stress through an experiment that involves carefully cutting a specimen into two pieces and measuring the resulting deformation due to residual stress redistribution. The measured displacement data are used to compute residual stresses through an analysis that involves a finite element model of the specimen. As part of the analysis, the measured deformation is imposed as a set of displacement boundary conditions on the model. The finite element model accounts for the stiffness of the material and part geometry to provide a unique result. The output is a two-dimensional map of residual stress normal to the measurement plane. The contour method is particularly useful for complex, spatially varying residual stress fields that are difficult (or slow) to map using conventional point wise measurement techniques. For example, the complex spatial variations of residual stress typical of welds are well-characterized using the contour method. A basic measurement procedure is provided along with comments about potential alternate approaches, with references for further reading.
Chapter 4 of Practical Residual Stress Measurement Methods.
The slitting method is a technique for measuring through thickness residual stress normal to a plane cut through a part. It involves cutting a slit (i.e., a thin slot) in increments of depth through the thickness of the work piece and measuring the resulting deformations as a function of slit depth. Residual stress as a function of through thickness position is determined by solving an inverse problem using measured deformations. The chapter describes practical measurement procedures, provides a number of example applications, and summarizes efforts to determine the quality of the residual stress information obtained with the method.
The high cycle fatigue performance of 7050-T7451 aluminum was investigated for untreated as-machined, laser peened, and shot peened conditions. Constant amplitude, smooth (Kt=1) fatigue tests were conducted in four-point bending at a stress ratio of R=0.1. Results show that laser peening induces a layer of compressive residual stress more than three times deeper than for shot peening. Both treatments significantly increase fatigue performance.
This work assesses the ability of linear elastic fracture mechanics (LEFM) with superposition to correlate the growth of one-dimensional fatigue cracks at cold-expanded open holes under constant amplitude loading. Care is taken in the work to accurately: control the test setup to ensure one-dimensional crack growth, determine residual stress in the coupons, measure crack growth, determine the fatigue crack growth rate (FCGR), compute stress intensity factors, and correlate fatigue crack growth rate with stress intensity factor range ΔK and stress ratio R.
Large aluminum forgings are seeing increased application in aerospace structures, particularly as an enabler for structural unitization. These applications, however, demand an improved understanding of the forging process induced bulk residual stresses and their impact on both design mechanical properties and structural performance. In recent years, significant advances in both computational and experimental methods have led to vastly improved characterization of residual stresses.
Residual stresses are of interest from an engineering perspective because they can have a significant influence on material performance. For example, fatigue initiation, fatigue crack growth rate, stress corrosion cracking, and fracture are all influenced by the presence of residual stress. Current design methods for aerospace structure typically assume that the material is residual stress-free.