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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.

Case studies

Mapping multiple residual stress components with PSR biaxial mapping Contour method repeatability Extending Life of Fighter Airframes Forging Residual Stress Development of the Contour Method

Technical Publications

The Contour Method (book chapter) The Slitting Method (book chapter) Fatigue Crack Growth Database for Damage Tolerance Analysis The effects of laser peening and shot peening on high cycle fatigue in 7050-T7451 aluminum alloy Correlation of one-dimensional fatigue crack growth at cold-expanded holes using linear fracture mechanics and superposition The Impact of Forging Residual Stress on Fatigue in Aluminum Repeatability of residual stress measurements Residual Stress Mapping with Multiple Slitting Measurements Forensic Determination of Residual Stresses from Fracture Surfaces Fatigue Crack Growth Behavior of TC-128-B Steel Under Variable Amplitude Loading