ADVANCED MATERIALS & PROCESSES | NOVEMBER/DECEMBER 2024 14 the measurement plan. As with every measurement system, getting accurate and precise data at the same time may be either challenging, costly, or both. Furthermore, each measurement methodology comes with various assumptions, strengths, and limitations. In general, residual stress measurements are used in one of the following applications: a) residual stress predictive model validation or calibration; b) failure investigation; c) process opti- mization; d) component life assessment; and e) quality control. In the case of model calibration and validation, failure analysis, and component life assessment, accuracy is important; whereas, precision is more relevant in process optimization and quality control[1]. OVERVIEW OF RESIDUAL STRESS MEASUREMENT METHODS It is important to clarify that none of the residual stress measurement methods measure residual stress directly. All measurement methods rely on the measurement of a feature resulting from the presence of residual stress, and use physics-based models or calibrations to convert that feature into residual stress values given various assumptions. It is important to note that stress, and therefore residual stress, is defined by a tensor. To define the complete strain tensor, at least six stress components must be measured. Given time and resource restrictions or measurement method limitations, the residual stress state is assumed to be uniaxial, biaxial, or pseudo-triaxial. Regardless of underlying assumptions, each method uses Hooke’s law to convert strain into residual stresses. DIFFRACTION-BASED METHODS Residual stress measurement by diffraction methods is based on the fact that x-ray or neutron diffraction methods can measure distances between atomic planes, also called d-spacings. The resulting diffraction beam angle 2θ may be measured relative to the angle of the incident beam, which can be directly related to the atomic d-spacing using Bragg’s law, nλ = 2d sin θ. Here, λ is the wavelength of the incident x-rays or neutrons, d is the atomic plane spacing, and 2θ is the angle subtended by the incident and diffracted beams. Figure 3a illustrates a diffraction experiment in a stressfree material where for a given d-spacing and incident x-ray wavelength, λ, the diffracted beam is measured at a 2θ angle from the incident beam. Figure 3b shows that in the presence of residual or applied stresses the material will experience a change in the d-spacing which results in a shift of the diffraction peak angle relative to stress-free state. Figure 3c shows the diffraction peak shift resulting from the presence of residual or applied stresses can be measured in a diffractogram[2-6]. Note that electron diffraction can also be used to measure residual stress, but due to the localized nature of electron diffraction this technique can only capture type III stress/strains. This method is generally used to determine the geometrically necessary dislocations (GND). When using laboratory x-ray diffraction systems, a variety of configurations and techniques can be used including the sin2φ, cos α, and multiple hkl approaches, as well as single crystal and epitaxial thin film methods[1,2]. When using a synchrotron source of x-rays, residual stress measurements may be performed in either energy dispersive or angular dispersive set-ups[3-6]. Specialized techniques to characterize type II and III stresses include high energy diffraction microscopy (HEDM), three-dimensional x-ray diffraction (3DXRD)[7], point- focused high energy diffraction microscopy (PF-HEDM)[8], and dark field x-ray microscopy (DFXM)[9]. Neutron diffraction residual stress measurements can be collected in either continuous beam or time-pulsed beam[10-13]. Diffraction-based measurement methods have several variations based on the type of radiation used and diffraction conditions. Laboratory-based methods generally have a relatively shallow (few microns in metals) penetration depth; therefore, probing residual stresses deeper into the sample requires material removal. Correspondingly, this material removal is generally considered either destructive or semi- destructive since the final product must be physically altered locally. However, Fig. 3 — Simplified illustration of the impact on measured diffraction peak in the presence of residual or applied stresses. (a) Diffraction from a stress-free material. (b) Diffraction shift due to applied or residual stress. (c) Diffractogram of stress-free and stressed material where, due to tensile stress present, diffraction peak shifts from the stress-free diffraction peak position. (a) (b) (c)
RkJQdWJsaXNoZXIy MTYyMzk3NQ==