0
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,
AML, CNMM,
Tsinghua University,
Haidian District,
Beijing 100084, China
e-mail: jp1527@126.com

Xide Li

School of Aerospace,
Department of Engineering Mechanics,
AML, CNMM,
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kandil, F. A. , Lord, J. D. , Fry, A. T. , and Grant, P. V. , 2001, “ A Review of Residual Stress Measurement Methods: A Guide to Technique Selection,” National Physical Laboratory, Teddington, UK, NPL Report No. MATC(A)04. http://www.npl.co.uk/publications/a-review-of-residual-stress-measurement-methods-a-guide-to-technique-selection.
Lunt, A. J. G. , Baimpas, N. , Salvati, E. , Dolbnya, I. P. , Sui, T. , Ying, S. , Zhang, H. , Kleppe, A. K. , Dluhoš, J. , and Korsunsky, A. M. , 2015, “ A State-of-the-Art Review of Micron-Scale Spatially Resolved Residual Stress Analysis by FIB-DIC Ring-Core Milling and Other Techniques,” J. Strain Anal. Eng. Des., 50(7), pp. 426–444. [CrossRef]
Song, X. , Yeap, K. B. , Zhu, J. , Belnoue, J. , Sebastiani, M. , Bemporad, E. , Zeng, K. , and Korsunsky, A. M. , 2012, “ Residual Stress Measurement in Thin Films at Sub-Micron Scale Using Focused Ion Beam Milling and Imaging,” Thin Solid Films., 520(6), pp. 2073–2076. [CrossRef]
Luke, K. , Dutt, A. , Poitras, C. B. , and Lipson, M. , 2013, “ Overcoming Si3N4 Film Stress Limitations for High Quality Factor Ring Resonators,” Opt. Express, 21(19), pp. 22829–22833. [CrossRef] [PubMed]
Godeke, A. , Ten Haken, B. , Ten Kate, H. H. J. , and Larbalestier, D. C. , 2006, “ A General Scaling Relation for the Critical Current Density in Nb3Sn,” Supercond. Sci. Technol., 19(10), p. R100. [CrossRef]
Wei, A. , Wiatr, M. , Mowry, A. , Gehring, A. , Boschke, R. , Scott, C. , Hoentschel, J. , Duenkel, S. , Gerhardt, M. , and Feudel, T. , 2007, “ Multiple Stress Memorization in Advanced SOI CMOS Technologies,” IEEE Symposium on VLSI Technology, Kyoto, Japan, June 12–14, pp. 216–217.
Huang, Y. , Wu, S.-L. , Chang, S.-J. , Kuo, C.-W. , Chen, Y.-T. , Cheng, Y.-C. , and Cheng, O. , 2011, “ Origin of Stress Memorization Mechanism in Strained-Si nMOSFETs Using a Low-Cost Stress-Memorization Technique,” IEEE Trans. Nanotechnol., 10(5), pp. 1053–1058. [CrossRef]
Flükiger, R. , Flükiger, R. , Uglietti, D. , Senatore, C. , and Buta, F. , 2008, “ Microstructure, Composition and Critical Current Density of Superconducting Nb3Sn Wires,” Cryogenics, 48(7–8), pp. 293–307. [CrossRef]
Lunt, A. J. , Salvati, E. , Ma, L. , Dolbyna, I. P. , Neo, T. K. , and Korsunsky, A. M. , 2016, “ Full in-Plane Strain Tensor Analysis Using the Microscale Ring-Core FIB Milling and DIC Approach,” J. Mech. Phys. Solids, 94, pp. 47–67. [CrossRef]
Salvati, E. , and Korsunsky, A. M. , 2017, “ An Analysis of Macro-and Micro-Scale Residual Stresses of Type I, II and III Using FIB-DIC Micro-Ring-Core Milling and Crystal Plasticity FE Modelling,” Int. J. Plast., 98, pp. 123–138. [CrossRef]
Pagliaro, P. , Prime, M. B. , Swenson, H. , and Zuccarello, B. , 2010, “ Measuring Multiple Residual-Stress Components Using the Contour Method and Multiple Cuts,” Exp. Mech., 50(2), pp. 187–194. [CrossRef]
Olson, M. D. , and Hill, M. R. , 2018, “ Two-Dimensional Mapping of in-Plane Residual Stress With Slitting,” Exp. Mech., 58(1), pp. 151–166. [CrossRef]
Valentini, E. , Benincasa, A. , and Bertelli, L. , 2011, “ An Automatic System for Measuring Residual Stresses by Ring-Core Method,” Italian Stress Analysis Association, 40th National Convention, Palermo, Italy, Sept. 7–10, Paper No. AIAS 2011-145.
Keil, S. , 1992, “ Experimental Determination of Residual Stresses With the Ring‐Core Method and an on‐Line Measuring System,” Exp. Tech., 16(5), pp. 17–24. [CrossRef]
Wolf, H. , 1971, “ Das Ring‐Kern‐Verfahren Zur Messung Von Eigenspannungen Und Seine Anwendung Bei Turbinen Und Generatorwellen,” Steel Res. Int., 42(3), pp. 195–200.
Wolf, H. , W., Böhm ., and Entstehung , 1971, “ Entstehung, Messung und Beurteilung von Eigenspannungen in schweren Schmiedestücken für Turbinen und Generatoren,” Steel Res. Int., 42(7), pp. 509–513.
Nelson, D. , 2014, “ Experimental Methods for Determining Residual Stresses and Strains in Various Biological Structures,” Exp. Mech., 54(4), pp. 695–708. [CrossRef]
Wenzelburger, M. , López, D. , and Gadow, R. , 2006, “ Methods and Application of Residual Stress Analysis on Thermally Sprayed Coatings and Layer Composites,” Surf. Coat. Technol., 201(5), pp. 1995–2001. [CrossRef]
Schajer, G. S. , 1988, “ Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method—Part I: Stress Calculation Procedures,” J. Eng. Mater. Technol., 110(4), pp. 338–343. [CrossRef]
Schajer, G. S. , 1988, “ Measurement of Non-Uniform Residual Stresses Using the Hole-Drilling Method—Part II: Practical Application of the Integral Method,” J. Eng. Mater. Technol., 110(4), pp. 344–349. [CrossRef]
Prime, M. B. , and Hill, M. R. , 2006, “ Uncertainty, Model Error, and Order Selection for Series-Expanded, Residual-Stress Inverse Solutions,” J. Eng. Mater. Technol., 128(2), pp. 175–185. [CrossRef]
Li, K. , and Ren, W. , 2007, “ Application of Minature Ring-Core and Interferometric Strain/Slope Rosette to Determine Residual Stress Distribution With Depth—Part I: Theories,” ASME J. Appl. Mech., 74(2), pp. 298–306. [CrossRef]
Ren, W. , and Li, K. , 2007, “ Application of Miniature Ring-Core and Interferometric Strain/Slope Rosette to Determine Residual Stress Distribution With Depth—Part II: Experiments,” ASME J. Appl. Mech., 74(2), pp. 307–314. [CrossRef]
Salvati, E. , Sui, T. , Lunt, A. J. G. , and Korsunsky, A. M. , 2016, “ The Effect of Eigenstrain Induced by Ion Beam Damage on the Apparent Strain Relief in FIB-DIC Residual Stress Evaluation,” Mater. Des., 92, pp. 649–658. [CrossRef]
Lunt, A. J. , and Korsunsky, A. M. , 2015, “ A Review of Micro-Scale Focused Ion Beam Milling and Digital Image Correlation Analysis for Residual Stress Evaluation and Error Estimation,” Surf. Coat. Technol., 283, pp. 373–388. [CrossRef]
Sebastiani, M. , Eberl, C. , Bemporad, E. , and Pharr, G. M. , 2013, “ Residual Stresses Measurement by Using Ring-Core Method and 3D Digital Image Correlation Technique,” Meas. Sci. Technol., 24(8), p. 085604. [CrossRef]
Korsunsky, A. M. , Sebastiani, M. , and Bemporad, E. , 2009, “ Focused Ion Beam Ring Drilling for Residual Stress Evaluation,” Mater. Lett., 63(22), pp. 1961–1963. [CrossRef]
Hu, Z. , Xie, H. , Lu, J. , Zhu, J. , and Wang, H. , 2011, “ Depth-Resolved Residual Stress Analysis of Thin Coatings by a New FIB–DIC Method,” Mater. Sci. Eng.: A, 528(27), pp. 7901–7908. [CrossRef]
Giri, A. , and Mahapatra, M. M. , 2017, “ On the Measurement of Sub-Surface Residual Stresses in SS 304 L Welds by Dry Ring Core Technique,” Meas., 106, pp. 152–160. [CrossRef]
Zhu, J. G. , Xie, H. M. , Li, Y. J. , Hu, Z. X. , Luo, Q. , and Gu, C. Z. , 2014, “ Interfacial Residual Stress Analysis of Thermal Spray Coatings by Miniature Ring-Core Cutting Combined With DIC Method,” Exp. Mech., 54(2), pp. 127–136. [CrossRef]
Schajer, G. S. , and Altus, E. , 1996, “ Stress Calculation Error Analysis for Incremental Hole-Drilling Residual Stress Measurements,” J. Eng. Mater. Technol., 118(1), pp. 120–126. [CrossRef]
Zuccarello, B. , Menda, F. , and Scafidi, M. , 2016, “ Error and Uncertainty Analysis of Non-Uniform Residual Stress Evaluation by Using the Ring-Core Method,” Exp. Mech., 56(9), pp. 1531–1546. [CrossRef]
Sebastiani, M. , Massimi, F. , Merlati, G. , and Bemporad, E. , 2015, “ Residual Micro-Stress Distributions in Heat-Pressed Ceramic on Zirconia and Porcelain-Fused to Metal Systems: Analysis by FIB–DIC Ring-Core Method and Correlation With Fracture Toughness,” Dental Mater., 31(11), pp. 1396–1405. [CrossRef]
Ya, M. , Dai, F. , and Lu, J. , 2003, “ Study of Nonuniform in-Plane and in-Depth Residual Stress of Friction Stir Welding,” ASME J. Pressure Vessel Technol., 125(2), pp. 201–208. [CrossRef]
Jin, P. , Li, L. , Li, X. , Wang, Q. , and Cheng, J. , 2017, “ Residual Stress in Nb3Sn Superconductor Strand Introduced by Structure and Stoichiometric Distribution After Heat Treatment,” IEEE Trans. Appl. Superconduct., 27(5), pp. 1–9. [CrossRef]
Barber, A. H. , Cohen, S. R. , and Wagner, H. D. , 2003, “ Measurement of Carbon Nanotube–Polymer Interfacial Strength,” Appl. Phys. Lett., 82(23), pp. 4140–4142. [CrossRef]
Conrad, H. , 2003, “ Grain Size Dependence of the Plastic Deformation Kinetics in Cu,” Mater. Sci. Eng.: A, 341(1–2), pp. 216–228. [CrossRef]
Jin, P. , and Li, X. , 2015, “ Correction of Image Drift and Distortion in a Scanning Electron Microscopy,” J. Microsc., 260(3), pp. 268–280. [CrossRef] [PubMed]
Mitchell, N. , 2005, “ Finite Element Simulations of Elasto-Plastic Processes in Nb3Sn Strands,” Cryogenics, 45(7), pp. 501–515. [CrossRef]
Salvati, E. , Sui, T. , and Korsunsky, A. M. , 2016, “ Uncertainty Quantification of Residual Stress Evaluation by the FIB–DIC Ring-Core Method Due to Elastic Anisotropy Effects,” Int. J. Solids Struct., 87, pp. 61–69. [CrossRef]
Fleck, N. A. , and Hutchinson, J. W. , 1997, “ Strain Gradient Plasticity,” Adv. Appl. Mech., 33, pp. 295–361. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 3

von Mises stress field under pressure calibration

Grahic Jump Location
Fig. 4

Schematic demonstration of the simulation experiment

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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].

Grahic Jump Location
Fig. 8

A sketch of the incomplete ring

Grahic Jump Location
Fig. 9

Comparison between the results from average stress analysis and DLR analysis

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In