Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

Park, Jun-Sang; Lienert, U.; Dawson, Paul R.; Miller, Matthew P.

doi:10.1007/s11340-013-9771-0

Cited by 27 publications

(10 citation statements)

References 44 publications

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“…These micro-strains measured within the grains provide the elastic strain response of each phase. This elliptical deviation from a circle with a strain-free radius provides the deviatoric micro-strain tensor for that lattice plane 36 . To measure the directional strain within the measurement plane, radial measurements of an individual ring are conducted around the azimuth angle, and compared with this strain-free radius, R o , as described by Diaz et al 29 and shown in Fig.…”

Section: Methodsmentioning

confidence: 99%

Strain response of thermal barrier coatings captured under extreme engine environments through synchrotron X-ray diffraction

et al. 2014

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The mechanical behaviour of thermal barrier coatings in operation holds the key to understanding durability of jet engine turbine blades. Here we report the results from experiments that monitor strains in the layers of a coating subjected to thermal gradients and mechanical loads representing extreme engine environments. Hollow cylindrical specimens, with electron beam physical vapour deposited coatings, were tested with internal cooling and external heating under various controlled conditions. High-energy synchrotron X-ray measurements captured the in situ strain response through the depth of each layer, revealing the link between these conditions and the evolution of local strains. Results of this study demonstrate that variations in these conditions create corresponding trends in depth-resolved strains with the largest effects displayed at or near the interface with the bond coat. With larger temperature drops across the coating, significant strain gradients are seen, which can contribute to failure modes occurring within the layer adjacent to the interface.

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Section: Methodsmentioning

confidence: 99%

Strain response of thermal barrier coatings captured under extreme engine environments through synchrotron X-ray diffraction

et al. 2014

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“…(It is possible to interrogate individual diffraction volumes along z L by placing a set of slits downstream of the sample in the path of the diffracted beam. 17,23 )…”

Section: Materials and Experimental Techniquesmentioning

confidence: 99%

“…Residual stress analysis methods at opposite ends of the complexity spectrum—a traditional, widely used, sin 2 Ψ method, which considers lattice strain measurements from one family of planes for a stress solution at one material point (cf. Hauk 13 ) and a recently developed bi-scale optimization methodology that simultaneously considers lattice strain measurements from multiple sets of planes at multiple locations within the workpiece to compute a spatially varying residual stress field 16–18 —were used with high-fidelity synchrotron X-ray data. The intent is not to declare which method is better or worse, but rather to illustrate the range of stress solutions that are possible with the same set of lattice strain data.…”

Section: Introductionmentioning

confidence: 99%

Determination of residual stress in a microtextured α titanium component using high-energy synchrotron X-rays

Park

Ray

Dawson

et al. 2016

The Journal of Strain Analysis for Engineering Design

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A shrink-fit sample is manufactured with a Ti-8Al-1Mo-1V alloy to introduce a multiaxial residual stress field in the disk of the sample. A set of strain and orientation pole figures are measured at various locations across the disk using synchrotron high-energy X-ray diffraction. Two approaches-the traditional sin 2 C method and the bi-scale optimization method-are taken to determine the stresses in the disk based on the measured strain and orientation pole figures, to explore the range of solutions that are possible for the stress field within the disk. While the stress components computed using the sin 2 C method and the bi-scale optimization method have similar trends, their magnitudes are significantly different. It is suspected that the local texture variation in the material is the cause of this discrepancy.

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“…For residual stress, an understanding of the macroscopic stress distribution is the goal. Using multiple sets of SPFs taken at many points within the component, the spatially heterogeneous macroscopic stress field within an engineering component can be determined [18][19][20]. The spatial interdependence of stress that arises due to equilibrium is now exploited as a constraint on the solution using a finite element discretization of the component.…”

Section: Determining Distributions Of Residual Stressmentioning

confidence: 99%

“…In the end, nearly 1,000,000 measurements were made over the quarter disk in the ''2D'' experiments [18]. We also made a 3D sample by tapering the hole in the disk, producing a variation of stress through the disk thickness [20]. At each location, a conical slit setup was used to crystals.…”

Section: Determining Distributions Of Residual Stressmentioning

confidence: 99%

Understanding local deformation in metallic polycrystals using high energy X-rays and finite elements

Miller

Dawson

2014

Current Opinion in Solid State and Materials Science

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a b s t r a c tA methodology for understanding the stress and elastoplastic deformation responses within a loaded polycrystal is presented along with illustrative examples. High energy synchrotron X-rays are used to penetrate bulk metallic samples and produce diffracted intensity from each deforming crystal -revealing the evolving internal structure. A virtual representation of the microstructure is constructed using the finite element method (FEM) to simulate the evolution of the elastoplastic deformations, stress fields, and lattice orientations within the deforming crystals as the polycrystal is loaded. Simulations are compared directly to experimental diffraction data. In the case of powder experiments, lattice strain pole figures (SPFs) measured experimentally are compared to SPFs calculated by projecting X-rays through the finite element mesh. During in situ loading experiments, the stress states are found to differ from one crystal to the next and to vary from the stress being applied at the macroscale. A SPF/FEM-based methodology for quantifying residual stress fields within processed polycrystalline components is described. SPFs were measured at many points within a shrink-fit sample. Finite element discretizations of both the sample and orientation space of each diffraction volume were used to formulate an optimization for the distribution of the stress tensor within the sample. A different experiment, one in which the X-ray beam and the crystals are closer to the same size, is used to investigate the aggregate crystal by crystal. The Debye-Scherrer rings reduce to a set of spots associated with each crystal within the diffraction volume. This method is demonstrated by tracking deformation of four grains within a deforming BCC titanium aggregate loaded in situ within the elastic regime to determine the single crystal elastic moduli. Plastic deformation can also be investigated by monitoring the size and shape of individual diffraction spots. Each spot contains geometrically exact information regarding the internal structure of the crystal. Instead of reconstructing the crystal structure by inverting the diffraction data, virtual diffraction experiments are performed on the finite element mesh and the resulting simulated diffraction patterns are compared directly to the experimental results. Once the experimental/simulation methodology is validated, the approximation of the subgrain distribution of stress and lattice orientation from the finite element model can be used to construct theories for failure phenomena such as microcrack initiation. As opposed to other methods of discretizing a polycrystalline aggregate, the finite element framework enables a seamless transition to analyses associated with mechanical design.

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Quantifying Three-Dimensional Residual Stress Distributions Using Spatially-Resolved Diffraction Measurements and Finite Element Based Data Reduction

Cited by 27 publications

References 44 publications

Strain response of thermal barrier coatings captured under extreme engine environments through synchrotron X-ray diffraction

Strain response of thermal barrier coatings captured under extreme engine environments through synchrotron X-ray diffraction

Determination of residual stress in a microtextured α titanium component using high-energy synchrotron X-rays

Understanding local deformation in metallic polycrystals using high energy X-rays and finite elements

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