Research Papers

Discrete Loading Ring-Core Method for Nonuniform In-Plane Residual Stress Analysis in Micro Area

[+] Author and Article Information
Peng Jin

School of Aerospace,
Department of Engineering Mechanics,
Tsinghua University,
Haidian District,
Beijing 100084, China
e-mail: jp1527@126.com

Xide Li

School of Aerospace,
Department of Engineering Mechanics,
Tsinghua University,
Haidian District,
Beijing 100084, China
e-mail: lixide@tsinghua.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received February 11, 2018; final manuscript received May 17, 2018; published online June 14, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 85(9), 091002 (Jun 14, 2018) (12 pages) Paper No: JAM-18-1086; doi: 10.1115/1.4040332 History: Received February 11, 2018; Revised May 17, 2018

The ring-core method is often used in residual stress analysis. It is applied to macro- and microscale stress analysis and has a unique advantage of releasing the residual stress across the core instead of at a single point, which makes it possible to measure an uneven residual stress field within a limited area, especially when the area is too small to be measured by other techniques. We developed a new layer-by-layer stress analysis method based on the ring-core method to retrieve the uneven in-plane stress, in which a nonuniform load that surrounds the core is approximated by discrete loading and then used to reveal the stress distribution within the core. The displacement–stress relationship is calibrated through finite element simulation. Because of the difficulty of preparing a standard specimen with an accurate high-gradient in-plane field stress in an area of several micrometers, the performance of the method was tested by a finite element simulation experiment. Good matches were achieved when comparing the calculated stress fields and the stress fields in the simulation experiments, including the biaxial, uniaxial and high-gradient cases. The method was applied to a piece of superconductor stand with a highly nonuniform stress by using a 4 μm-diameter-area ring core cut with focused ion beam.

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Fig. 2

Sketch of stress-analysis procedures for half size of the RC specimen

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Fig. 1

Schematic diagram of symbol definitions in current configuration with i layers cut

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Fig. 3

von Mises stress field under pressure calibration

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Fig. 4

Schematic demonstration of the simulation experiment

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Fig. 5

True stress distribution and calculated stress distribution for different load cases. (a) and (b) represent the true stress P and S under biaxial loading, (c) and (d) for stress P and S under uniaxial loading, (e) and (f) for stress P and S under combined loading.

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Fig. 8

A sketch of the incomplete ring

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Fig. 7

Incremental displacement between each pair of adjacent layers. The quiver was enlarged to show the deformation field more clearly. The subsets ((a)–(f)) are ordered from the top to the deepest layer. Blue arrows denote the experimental results, whereas the green arrows show the calculated displacement field. [position unit: μm].

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Fig. 6

SEM images of FIB etched ring-core during progressive layer removal: (a) the markers when no ring was etched, ((b)–(g)) 1–6 layers were removed, (h) a 55 deg SEM image of the final configuration

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Fig. 9

Comparison between the results from average stress analysis and DLR analysis



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