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.
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Authors’ version at LANL
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.
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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.
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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.
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Author’s version
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.
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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.
Repeatability of Residual Stress Measurements
This paper describes the use of slitting to form a two-dimensional spatial map of one component of residual stress in the plane of a two-dimensional body. Slitting is a residual stress measurement technique that incrementally cuts a thin slit along a plane across a body, while measuring strain at a remote location as a function of slit depth.
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Residual stresses can be a main cause of fractures, but forensic failure analysis is difficult because the residual stresses are relaxed after fracture because of the new free surface. In this paper, a method is presented for a posteriori determination of the residual stresses by measuring the geometric mismatch between the mating fracture surfaces. Provided the fracture is not overly ductile, so that plasticity may be neglected, a simple, elastic calculation based on Bueckner’s principle gives the original residual stresses normal to the fracture plane. The method was demonstrated on a large 7000 series aluminum alloy forging that fractured during an attempt to cut a section into two pieces. Neutron diffraction measurements on another section of the same forging convincingly validated the residual stresses determined from the fracture surface mismatch. After accounting for closure, an analysis of the residual stress intensity factor based on the measured residual stress agreed with the material’s fracture toughness and fractographic evidence of the failure initiation site. The practicality of the fracture surface method to investigate various failures is discussed in light of the required assumptions.
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Preprint (at LANL)