This paper assesses the accuracy of fatigue crack growth (FCG) predictions for high-strength aluminum samples containing residual stress (RS) and complex two-dimensional cracks subjected to constant amplitude load. FCG predictions use linear-elastic, multi-point fracture mechanics. A first prediction includes RS estimated by the model described in Part 1; a second prediction includes RS measured by the contour method. FCG test data show a significant influence of RS. Ignoring the RS results in a +60% error in predicted FCG life (non-conservative). Including RS improves predictions of crack growth significantly (errors better than +26% (estimated RS) and -14% (measured RS)).
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.
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. This work examines its application to macro-scale specimens. 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. 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. 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.
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. 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. 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. 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. 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.
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. 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.
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.