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.

Hole drilling residual stress measurement method

This week, we have uploaded a new vlog to Hill Engineering’s YouTube channel revolving around a particularly handy residual stress measurement technique. The hole drilling measurement method is one of our most popular residual stress measurement options, and involves the incremental drilling of a small hole into the surface of a specimen. Watch the video below and read on to learn more about the hole drilling method. Continue reading Hole drilling residual stress measurement method

Case Study: Contour Method Repeatability

Recently, Hill Engineering posted a new case study detailing our research into contour method repeatability. In the case study, we performed contour method measurements on multiple similar specimens belonging to six different specimen types: aluminum T-section, stainless steel plate with dissimilar metal slot-filled weld, stainless steel forging, titanium plate with electron beam slot-filled weld, nickel disk forging, and aluminum plate. Continue reading Case Study: Contour Method Repeatability

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.

Tensile test

A tensile test is a standard method used by material scientists and engineers to determine important material strength and ductility properties. For example, tensile tests can be used to measure the yield strength of a material, which is defined as the stress at which a material begins to deform plastically. Hill Engineering has ample experience performing tensile tests, and other mechanical property tests, in pursuit of our passion to maximize the potential of materials. Continue reading Tensile test

How We Work

Maintaining the high quality of our work is our top priority. That’s why it’s important that our office environment promotes efficiency and qualitative communication here at Hill Engineering. From a project’s inception until its close, we strive to keep a workflow that handles our customer’s needs with consistent attention and care. Continue reading How We Work

Cold expansion

Fatigue is one important failure mode that guides the design and engineering of aircraft structure. As we have discussed previously aircraft are often manufactured using rivets and fasteners, which require drilling many holes in the structure during assembly. The holes act as stress concentrations, which tend to be locations where fatigue cracks are found. Compressive residual stresses act to hold cracks shut and result in improved fatigue performance. This residual compressive stress can provide substantial benefits in terms of performance, safety, cost, and inspection requirements. To take advantage of the benefits of compressive residual stress, cold expansion is often applied to aircraft fastener holes. Continue reading Cold expansion

Fracture surfaces evaluation

Aircraft undergo complex loading during their operation and lifecycle. For example, take off, landing, turbulence, and flight/ground maneuvers are all instances where significant loading occurs. The cyclic loading and unloading activates a failure mechanism called fatigue, which is most prevalent at the highest stressed regions. Continue reading Fracture surfaces evaluation

Failure analysis of high strength nuts

Fracture and fatigue are important material performance issues that Hill Engineering examines on a regular basis. Hill Engineering recently contributed to a publication titled “Investigating and interpreting failure analysis of high strength nuts made from nickel-base superalloy.” The publication includes a detailed review of work performed to understand the failure of these fracture critical nuts. The abstract text is copied below. A temporary link to download a pdf of the publication is provided at the bottom. Continue reading Failure analysis of high strength nuts

Opening Up with the Interns

Every summer, Hill Engineering hires university students as interns; aiming to give them insight into industry jobs and provide them with the experience they’ll need to develop their careers post-graduation. We pride ourselves on involving interns in projects which utilize and further explore the concepts they have learned in school. In the past, we’ve had many positive outcomes from our internship program. The interns have delivered fresh perspective on our projects and a few have even transferred to full-time employment at Hill Engineering. This year, we welcome three students into our summer internship program. Continue reading Opening Up with the Interns