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X-ray analysis of steep residual stress gradients: The 2θ-derivative method

  • Thomas Erbacher and Alexander Wanner
Published/Copyright: June 11, 2013
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International Journal of Materials Research
From the journal International Journal of Materials Research Volume 99 Issue 10

Abstract

Machined ceramics and other hard materials exhibit very steep subsurface gradients of residual stresses. X-ray analysis enables the non-destructive assessment of the distributions of these residual stresses versus the distance from the surface via variation of the penetration depth of the X-rays. Conventional evaluation procedures are based on continuous or piecewise defined polynomial functions of stress versus distance, which are fitted to the X-ray data by means of complex solution schemes. These solution schemes are, however, in many cases unstable and difficult to handle. We have developed an entirely novel evaluation procedure which is based on polynomials fitted to the “2θ vs. sin2 ψ” plots obtained from the X-ray measurements. It is shown that the residual stress profiles can be computed explicitly from these polynomials without any further assumptions. The evaluation procedure is described in detail and demonstrated in a case study on ground alumina ceramics.

Keywords: Residual stress analysis; X-ray diffraction; Stress gradients; Alumina ceramic; Grinding
* Correspondence address, Dr.-Ing. Thomas ErbacherE.ON Kernkraft GmbHAbteilung EKK-TTKTresckowstraße 5, D-30457 Hannover, GermanyTel.: +49 511 439 28 21Fax: +49 511 439 43 77E-mail: , Prof. Dr. Alexander WannerInstitut für Werkstoffkunde IUniversität Karlsruhe (TH)Kaiserstr. 12, Geb. 10.91, D-76131 Karlsruhe, GermanyTel.: +49 721 608 23 45Fax: +49 721 608 80 44E-mail: alexander.wanner@kit.edu

References

[1] B.Eigenmann, B.Scholtes, E.Macherauch: Mat.-wiss.u. Werkstofftech.21 (1990) 257–265.10.1002/mawe.19900210705Search in Google Scholar

[2] B.Eigenmann, B.Scholtes, E.Macherauch, in: H.Fujiwara, T.Abe, K.Tanaka (Eds.), Residual Stresses III, Elsevier Applied Science, London, New York, (1992) 601–606.Search in Google Scholar

[3] T.Erbacher, M.H.Ott, T.Beck, O.Vöhringer: Mat. Sci. Forum490–491 (2005) 485–490.10.4028/www.scientific.net/MSF.490-491.485Search in Google Scholar

[4] R.Hessert: Bearbeitungseigenspannungen, Randschichtschädigungen und Festigkeiten geschliffener Al2O3- und ZrO2-Keramiken, Doctoral Thesis, Universität Karlsruhe, Karlsruhe, Germany. Published by: Shaker Verlag, Aachen (1998).Search in Google Scholar

[5] A.Kämpfe, B.Eigenmann, D.Löhe: Z. Metallkd.91 (2000) 967–975.Search in Google Scholar

[6] T.Leverenz, B.Eigenmann, E.Macherauch: Z. Metallkd.87 (1996) 616–625.Search in Google Scholar

[7] W.Pfeiffer, M.Rombach: Adv. X-Ray Anal.41 (1997) 493–500.Search in Google Scholar

[8] T.Erbacher: Eigenspannungen, Festigkeiten und Schädigungsverhalten von Aluminiumoxid unter thermischer und friktiver Randschichtbeanspruchung, Doctoral Thesis, Universität Karlsruhe, Karlsruhe, Germany. Published by: Shaker Verlag, Aachen (2006).Search in Google Scholar

[9] E.Macherauch, P.Müller: Z. Angew. Physik13 (1961) 305–312.Search in Google Scholar

[10] B.Ballard, X.Zhu, P.Predecki, D.Braski: Adv. X-Ray Anal.41 (1994) 1133–1143.Search in Google Scholar

[11] T.Dümmer, B.Eigenmann, M.Stüber, H.Leiste, D.Löhe, O.Vöhringer: Z. Metallkd.90 (1999) 780–787.Search in Google Scholar

[12] B.Eigenmann, B.Scholtes, E.Macherauch: Mat.-wiss.u. Werkstofftech.21 (1990) 257–265.10.1002/mawe.19900210705Search in Google Scholar

[13] T.Ely, P.K.Predecki, I.C.Noyan: Adv. X-Ray Anal.41 (1999) 467–478.Search in Google Scholar

[14] P.D.Evenschor: Z. Metallkde.73 (1982) 387–390.Search in Google Scholar

[15] C.Genzel: Phys. Stat. Sol. A156 (1996) 353–364.10.1002/pssa.2211560213Search in Google Scholar

[16] T.C.Huang, P.K.Predecki: Adv. X-Ray Anal.40 (1996) 61–69.Search in Google Scholar

[17] A.K.KämpfeP.Predecki, B.Eigenmann: Proc. Micro Mat., Berlin: DVM, (1997) 1074–1076.Search in Google Scholar

[18] G.Lim, W.Parrish, C.Ortiz, M.Belloto, M.Hart: J. Mater. Res.2 (1987) 471–478.10.1557/JMR.1987.0471Search in Google Scholar

[19] H.Ruppersberg, I.Detemple, J.Krier: Z. f. Kristallographie195 (1991) 189–203.10.1524/zkri.1991.195.3-4.189Search in Google Scholar

[20] H.Behnken, V.Hauk: Mat. Sci. Eng. A300 (2001) 41–51.10.1016/S0921-5093(00)01791-3Search in Google Scholar

[21] I.N.Bronstein, K.A.Semendjajew (Eds.): Taschenbuch der Mathematik. Stuttgart: Teubner Verlagsgesellschaft (1991).Search in Google Scholar

[22] I.C.Noyan, J.B.Cohen: Residual Stress – Measurement by Diffraction and Interpretation, Berlin: Springer (1987) 121–122.Search in Google Scholar

[23] Y.Yoshioka, T.Sasaki, M.Kuramoto: Adv. X-Ray Anal.28 (1985) 225–264.Search in Google Scholar

[24] A.K.KämpfeB.Eigenmann, D.Löhe: Z. Metallkd.91 (2000) 967–975.Search in Google Scholar

[25] H.Wern, P.Klein, G.Marchand: Adv. X-Ray Anal.45 (2002) 206–211.Search in Google Scholar

[26] J.Reinshagen: Korrelation zwischen Partikelwechselwirkungen und Grünkörpereigenschaften nassgeformter Keramiken. Doctoral Thesis, Universität Karlsruhe, Karlsruhe, Germany. Appeared in: Karlsruhe: Schriftenreihe des Instituts für Keramik im Maschinenbau, IKM, Vol. 47 (2006).Search in Google Scholar

[27] E.DörreH.Hübner: Alumina: Processing, Properties, and Applications. Berlin: Springer Verlag (1984).10.1007/978-3-642-82304-6Search in Google Scholar

[28] „Landolt-Börnstein, Physikalisch-Chemische Tabellen“, III/11, III/18. Berlin: Springer Verlag (1984).Search in Google Scholar

[29] B.Eigenmann, B.Scholtes, E.Macherauch: Mat.-wiss. u. Werkstofftech.20 (1989) 314–325.10.1002/mawe.19890200908Search in Google Scholar

[30] R.Hessert: Bearbeitungseigenspannungen, Randschichtschädigungen und Festigkeiten geschliffener Al2O3- und ZrO2-Keramiken. Doctoral Thesis, Universität Karlsruhe, Karlsruhe, Germany. Aachen: Shaker Verlag (1998).Search in Google Scholar

[31] T.Erbacher, M.H.Ott, T.Beck, O.Vöhringer: Mat. Sci. Forum490–491 (2005) 485–490.10.4028/www.scientific.net/MSF.490-491.485Search in Google Scholar

[32] B.Okolo, A.Wanner: Int. J. Mater. Res.97 (2006) 1415–1424.10.3139/146.101386Search in Google Scholar

[33] B.Eigenmann: Röntgenographische Analyse inhomogener Spannungszustände in Keramiken, Keramik-Metall-Fügeverbindungen und dünnen Schichten, Doctoral Thesis, Universität Karlsruhe, Karlsruhe, Germany, Appeared in: Karlsruhe: Schriftenreihe des Instituts für Keramik im Maschinenbau, IKM, Vol. 5 (1992).Search in Google Scholar

[34] A.Kumar, U.Welzel, E.J.Mittemeijer: J. Appl. Cryst.39 (2006) 633–646.10.1107/S0021889806023417Search in Google Scholar

[35] T.Erbacher, A.Wanner, T.Beck, O.Vöhringer: J. Appl. Cryst.41 (2008) 377–385.10.1107/S0021889807066836Search in Google Scholar

Received: 2008-3-31
Accepted: 2008-7-6
Published Online: 2013-06-11
Published in Print: 2008-10-01

© 2008, Carl Hanser Verlag, München

Articles in the same Issue

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  2. Contents
  3. Editorial
  4. To Professor Dr.-Ing. Karl-Heinz Zum Gahr on the occation of his 65th birthday
  5. Review
  6. Innovative materials for energy technology
  7. STAU – a review of the Karlsruhe weakest link finite element postprocessor with extensive capabilities
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  11. Investigation of surface fatigue of thermally sprayed micro- and nanocrystalline cylinder wall coatings by means of cavitation testing
  12. Thermal, mechanical and fretting fatigue of silicon nitride
  13. Effect of phase stability and composition on hydrogen diffusion in the binary systems Ti–Mo and Ti–V and related Ti-base alloys
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  18. Microstructural and acoustic damage analysis and finite element stress simulation of air plasma-sprayed thermal barrier coatings under thermal cycling
  19. The running-in of amorphous hydrocarbon tribocoatings: a comparison between experiment and molecular dynamics simulations
  20. Development of multifunctional thin films using high-throughput experimentation methods
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https://doi.org/10.3139/146.101739
Keywords for this article
Residual stress analysis; X-ray diffraction; Stress gradients; Alumina ceramic; Grinding

Articles in the same Issue

  1. Contents
  2. Contents
  3. Editorial
  4. To Professor Dr.-Ing. Karl-Heinz Zum Gahr on the occation of his 65th birthday
  5. Review
  6. Innovative materials for energy technology
  7. STAU – a review of the Karlsruhe weakest link finite element postprocessor with extensive capabilities
  8. Basic
  9. “Evolution” of microstructure in materials
  10. X-ray analysis of steep residual stress gradients: The 2θ-derivative method
  11. Investigation of surface fatigue of thermally sprayed micro- and nanocrystalline cylinder wall coatings by means of cavitation testing
  12. Thermal, mechanical and fretting fatigue of silicon nitride
  13. Effect of phase stability and composition on hydrogen diffusion in the binary systems Ti–Mo and Ti–V and related Ti-base alloys
  14. Determination of v–K curves from lifetime tests with reloaded survivals
  15. Mechanical properties of a single gecko seta
  16. Applied
  17. Influence of Fe–F-co-doping on the dielectric properties of Ba0.6Sr0.4TiO3 thick-films
  18. Microstructural and acoustic damage analysis and finite element stress simulation of air plasma-sprayed thermal barrier coatings under thermal cycling
  19. The running-in of amorphous hydrocarbon tribocoatings: a comparison between experiment and molecular dynamics simulations
  20. Development of multifunctional thin films using high-throughput experimentation methods
  21. A transmission electron microscopy procedure for in-situ straining of miniature pseudoelastic NiTi specimens
  22. Recent developments in micro ceramic injection molding
  23. σ-phase morphologies and their effect on mechanical properties of duplex stainless steels
  24. Development of high power density cathode materials for Li-ion batteries
  25. Notification
  26. DGM News
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