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.
Archives: Case Studies
Repeatability of Contour Method Residual Stress Measurements for a Range of Materials, Processes, and Geometries
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.
PSR Biaxial Residual Stress Mapping Validation
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.
Mapping multiple residual stress components with PSR biaxial mapping
The contour method provides a spatially resolved two-dimensional map of the component of residual stress acting normal to a plane through a part. Hill Engineering recently developed an extension to the contour method, called PSR biaxial mapping, which generates two-dimensional maps of additional residual stress components over the same plane. When combined with traditional contour method measurements, PSR biaxial mapping is a very powerful residual stress measurement tool.
The basic steps for a PSR biaxial mapping residual stress measurement are illustrated below. First, the contour method is used to measure the residual stress component normal to a plane of interest. Next, a thin slice of material adjacent to the contour method measurement plane is removed. The residual stress in the thin slice is altered during the contour method measurement and subsequent slice removal. This change in residual stress is called the PSR stress. The residual stress in the removed thin slice is determined using a series of slitting measurements. The residual stress in the removed slice is referred to as the slice stress. The residual stress in the original configuration (prior to extracting the slice) is expressed as the sum of the slice stress (residual stress measured in the removed slice) and the PSR stress (residual stress released when the slice is removed from the body).
Figure 1 – Experimental steps used in a PSR mapping measurement
An example PSR biaxial mapping residual stress measurement is shown for a nickel alloy forging (Udimet-720Li). The forging had a diameter of approximately 151 mm (5.9 in) and a maximum height of 70 mm (2.7 in). The contour method was used to measure the hoop residual stress in the forging. Following completion of the contour method measurement, wedge shaped slices were removed adjacent to the contour measurement plane. Slitting measurements were used to develop a 2D map of the radial residual stress in the slices. The measured radial stress in the slices was combined with the PSR stress to determine the radial residual stress at the measurement plane in the original configuration.
Plots of the measured two-dimensional maps of the hoop residual stress (contour method) and radial residual stress (PSR biaxial mapping) are shown below. The hoop residual stress is tensile towards the center of the forging and near the inner diameter (maximum value of approximately 450 MPa) and has compensating compressive residual stress towards the outer diameter and along the top and bottom of the forging. The radial residual stress is also tensile near the center of the forging (maximum value of approximately 200 MPa) and compressive at the top and bottom.
Figure 2 – Two-dimensional maps of residual stress in the nickel disk forging: (a) hoop direction stress and (b) radial direction stress
PSR biaxial mapping has been used to measure 2D residual stress maps for a variety of applications including: a quenched aluminum extrusion, a stainless steel welded plate, a complex nuclear power plant nozzle mockup containing a dissimilar metal weld, an aluminum T-section, a stainless steel plate with a dissimilar metal weld, a titanium plate with an electron beam weld, and a nickel alloy forging.
Additional information about bulk residual stress measurement using PSR biaxial mapping can be found in the references below. Also, please feel free to read about other residual stress measurement techniques on our website or to contact us with additional questions.
Reference information:
M. D. Olson and M. R. Hill, “A New Mechanical Method for Biaxial Residual Stress Mapping,” Experimental Mechanics, volume 55, number 6, 2015, pp. 1139–1150.
Contour method repeatability
The contour method provides a spatially resolved two-dimensional map of the component of residual stress acting normal to a plane through a part. A typical contour method residual stress measurement involves three primary steps: 1) Cutting a part in half on the plane where residual stress is to be measured (typically using a wire EDM); 2) Measuring the resulting deformation on the cut surface caused by residual stress release; and 3) Performing an analysis to relate measured deformation to residual stress.
For this case study, the repeatability of the contour method under a variety of relevant conditions was determined. Repeatability is a measure of the precision of a measurement technique, but does not address measurement accuracy. The test specimens evaluated 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, a nickel disk forging, and an aluminum plate. These specimens were selected to encompass a range of typical materials and residual stress distributions. Each repeatability study included contour method measurements on 5 to 12 similar specimens. Following completion of the contour method measurements, an analysis was performed to determine the repeatability standard deviation of each population. In general, the results of the various contour method residual stress measurement repeatability studies are similar. The repeatability standard deviation tends to be relatively small throughout the part interior, with localized regions of higher repeatability along the part perimeter. These results provide expected precision data for the contour method over a broad range of specimen geometries, materials, and stress profiles.
Aluminum T section specimens were fabricated from bars cut from a thick 7050-T7451 aluminum plate. Prior to cutting, the aluminum plate had been stress relieved by stretching. The bars were then heat treated, including a quench, to induce high residual stress indicative of the -T74 temper. After heat treatment, T-sections were machined from the bars to represent an airframe structural member. Each T-section had a length of 254 mm (10.0 in), a height of 50.8 mm (2.0 in), a width of 82.55 mm (3.25 in), and a leg thicknesses of 6.35 mm (0.25 in).
Contour method measurements were performed at the mid-length of 10 specimens. The mean longitudinal residual stress is shown in Figure 1a. There is compressive residual stress at the left, right, and top edges with tensile stress at the center. The measured residual stress is similar between the 10 measurements and is quantified by the low repeatability standard deviation (Figure 1b). The repeatability standard deviation has a low distribution at most points (average of 5 MPa), with localized regions at the edges of the bottom and center flanges where the repeatability standard deviations is larger (95th percentile at 13 MPa).
Figure 1 – (a) Mean and (b) repeatability standard deviation for the aluminum T-section specimens
Five contour method measurements were performed on the stainless steel dissimilar metal weld specimen. The results (Figure 2a) show the mean longitudinal residual stress is tensile in the weld area and heat-affected zone (maximum = 380 MPa), and near the left and right edges of the plate (maximum = 400 MPa). There is compensating compressive residual stress toward the top of the plate at the left and right edges (minimum = -260 MPa). Most points have low repeatability standard deviations (average of 17 MPa), but there are localized regions near the part boundary where the repeatability standard deviation is larger (95th percentile at 36 MPa) as shown in Figure 2b.
Figure 2 – (a) Mean and (b) repeatability standard deviation for the stainless steel DM welded specimens
Six contour method measurements were performed on the titanium EB welded plate. The mean longitudinal stress (Figure 3a) has tensile stress in the weld area (maximum = 350 MPa) and compensating compressive stress in the heat-affected zone (minimum = -200 MPa). The repeatability standard deviation is low at most points (average of 8 MPa), with localized regions near the part boundary having higher repeatability standard deviations (95th percentile at 17 MPa) as shown in Figure 3b.
Figure 3 – (a) Mean and (b) repeatability standard deviation for the titanium EB welded plate specimens
Measurements were also performed on stainless steel forgings and a nickel disk forging, which are discussed in a more in-depth technical publication.
The results of the repeatability studies show consistent trends among samples, with low repeatability standard deviations over most of the specimen interior and localized regions of higher variability (typically along the part perimeter). The mean repeatability standard deviation ranged from 5 MPa for the aluminum T section to 35 MPa for the stainless steel forging, which represent the minimum and maximum values of the population.
The magnitude of the repeatability standard deviation increases with elastic modulus of the material, as shown in Figure 4a. The materials with the largest elastic moduli also have the largest repeatability standard deviations. Furthermore, when the repeatability standard deviation is normalized by elastic modulus (Figure 4b), the normalized repeatability standard deviation becomes consistent across all specimens, ranging from 70 x 10-6 MPa/MPa to 125 x 10-6 MPa/MPa, with an average value of approximately 100 x 10-6 MPa/MPa. Similarly, the 95th percentile of the normalized repeatability standard deviation is also relatively consistent, but covers a significantly larger range from 150 x 10-6 MPa/MPa to 275 x 10-6 MPa/MPa, with an average value of 220 x 10-6 MPa/MPa.
Figure 4 – Repeatability standard deviation (a) statistics and (b) statistics normalized by elastic modulus.
Reference information:
Repeatability of Contour Method Residual Stress Measurements for a Range of Material, Process, and Geometry, M. D. Olson, A. T. DeWald, and M. R. Hill, Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 8, Springer, Cham, 2018, pp. 101–113.
The Contour Method (book chapter)
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.
The Slitting Method (book chapter)
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 effects of laser peening and shot peening on high cycle fatigue in 7050-T7451 aluminum alloy
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.
Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition
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.
The Impact of Forging Residual Stress on Fatigue in Aluminum
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.