Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-19T04:06:59.123Z Has data issue: false hasContentIssue false
  • English
  • Français

In Situ Elastic Strain Measurements—Diffraction and Spectroscopy

Published online by Cambridge University Press:  31 January 2011

R. Spolenak ,
W. Ludwig ,
J.Y. Buffiere  and
J. Michler
Get access

Abstract

Understanding the mechanical properties of materials is crucial for their reliable application as bulk materials as well as in a miniaturized form. The deformation of materials is usually non-uniform and, hence, needs to be characterized on a local level. The following article focuses on the in-Situ determination of mechanical stresses in crystalline materials during deformation. This can be achieved by both diffraction as well as spectroscopical methods, where the elastic strain is the parameter measured, which is subsequently converted into stresses by the application of Hooke's law. As in Situ measurements require rapid data acquisition in conjunction with reasonable penetration depths, we will focus on x-rays. However, the different techniques described can be applied to any other diffraction probe as well. The description of diffraction techniques, which span the range from averaging techniques to 2D and 3D strain mapping, is complemented by a section on Raman spectroscopy as an alternative method for stress determination for non-metallic materials. Local stresses also can be correlated to local defect densities.

Type
Research Article
Information
MRS Bulletin , Volume 35 , Issue 5: In Situ Mechanical Testing of Biological and Inorganic Materials at the Micro- and Nanoscales , May 2010 , pp. 368 - 374
Copyright
Copyright © Materials Research Society 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Warren, B.E., Averbach, B.L., Phys. Rev. 86 (4), 656 (1952).Google Scholar
2.Noyan, I.C., Cohen, J.B., Residual Stress (Springer, New York, 1987).CrossRefGoogle Scholar
3.Hommel, M., Kraft, O., Acta Mater. 49 (19), 3935 (2001).CrossRefGoogle Scholar
4.Kraft, O., Hommel, M., Arzt, E., Mater. Sci. Eng. A 288 (2) 209 (2000).Google Scholar
5.Gianola, D.S., Van Petegem, S., Legros, M., Brandstetter, S., Van Swygenhoven, H., Hemker, K.J., Acta Mater. 54 (8), 2253 (2006).CrossRefGoogle Scholar
6.Wanner, A., Dunand, D.C., Appl. Synchrotron Radiat. Tech. Mater. Sci. V 590, 157 (2000).Google Scholar
7.Bohm, J., Gruber, P., Spolenak, R., Stierle, A., Wanner, A., Arzt, E., Rev. Sci. Instrum. 75 (4), 1110 (2004).CrossRefGoogle Scholar
8.Gruber, P.A., Bohm, J., Onuseit, F., Wanner, A., Spolenak, R., Arzt, E., Acta Mater. 56 (10), 2318 (2008).CrossRefGoogle Scholar
9.Gruber, P.A., Olliges, S., Arzt, E., Spolenak, R., J. Mater. Res. 23 (9), 2406 (2008).CrossRefGoogle Scholar
10.Olliges, S., Gruber, P.A., Auzelyte, V., Ekinci, Y., Solak, H.H., Spolenak, R., Acta Mater. 55 (15), 5201 (2007).Google Scholar
11.Frank, S., Handge, U.A., Olliges, S., Spolenak, R., Acta Mater. 57 (5), 1442 (2009).CrossRefGoogle Scholar
12.Korsunsky, A.M., Wells, K.E., Withers, P.J., Scripta Mater. 39 (12), 1705 (1998).Google Scholar
13.Hung, Y.C., Bennett, J.A., Garcia-Pastor, F.A., Di Michlel, M., Buffiere, J.Y., Doel, T.J.A., Bowen, P., Withers, P.J., Acta Mater. 57 (2), 590 (2009).CrossRefGoogle Scholar
14.Sinclair, R., Preuss, M., Maire, E., Buffiere, J.Y., Bowen, P., Withers, P.J., Acta Mater. 52 (6), 1423 (2004).CrossRefGoogle Scholar
15.Kao, H.K., Cargill, G.S., Giuliani, F., Hu, C.K., J. Appl. Phys. 93 (5), 2516 (2003).CrossRefGoogle Scholar
16.Kao, H.K., Cargill, G.S., Hu, C.K., J. Appl. Phys. 89 (5), 2588 (2001).Google Scholar
17.Zhang, H., Cargill, G.S., Ge, Y., Maniatty, A.M., Liu, W., J. Appl. Phys. 104 (12), 123533 (2008).CrossRefGoogle Scholar
18.Yan, H.F., Murray, C.E., Noyan, I.C., Appl. Phys. Lett. 90 (9), 091918 (2007).Google Scholar
19.Riekel, C., Muller, M., Vollrath, F., Macromolecules 32 (13), 4464 (1999).Google Scholar
20.Ice, G.E., Chung, J.S., Larson, B.C., Budai, J.D., Tischler, J.Z., Tamura, N., Lowe, W., Synchrotron Radiat. Instrum. 521, 19 (2000).CrossRefGoogle Scholar
21.Tamura, N., Celestre, R.S., MacDowell, A.A., Padmore, H.A., Spolenak, R., Valek, B.C., Chang, N.M., Manceau, A., Patel, J.R., Rev. Sci. Instrum. 73 (3), 1369 (2002).Google Scholar
22.Barabash, R.I., Ice, G.E., Tamura, N., Valek, B.C., Bravman, J.C., Spolenak, R., Patel, J.R., J. Appl. Phys. 93 (9), 5701 (2003).CrossRefGoogle Scholar
23.Gruber, P.A., Solenthaler, C., Arzt, E., Spolenak, R., Acta Mater. 56 (8), 1876 (2008).Google Scholar
24.Spolenak, R., Brown, W.L., Tamura, N., MacDowell, A.A., Celestre, R.S., Padmore, H.A., Valek, B., et al., Phys. Rev. Lett. 90 (9), 096102 (2003).CrossRefGoogle Scholar
25.Nyilas, R.D., Kobas, M., Spolenak, R., Acta Mater. 57 (13), 3738 (2009).CrossRefGoogle Scholar
26.Budiman, A.S., Nix, W.D., Tamura, N., Valek, B.C., Gadre, K., Maiz, J., Spolenak, R., Patel, J.R., Appl. Phys. Lett. 88 (23), 233515 (2006).CrossRefGoogle Scholar
27.Valek, B.C., Bravman, J.C., Tamura, N., MacDowell, A.A., Celestre, R.S., Padmore, H.A., Spolenak, R., Brown, W.L., Batterman, B.W., Patel, J.R., Appl. Phys. Lett. 81 (22), 4168 (2002).CrossRefGoogle Scholar
28.Valek, B.C., Tamura, N., Spolenak, R., Caldwell, W.A., MacDowell, A.A., Celestre, R.S., Padmore, H.A., et al. J. Appl. Phys. 94 (6), 3757 (2003).CrossRefGoogle Scholar
29.Larson, B.C., Yang, W., Ice, G.E., Budai, J.D., Tischler, J.Z., Nature 415 (6874), 887 (2002).CrossRefGoogle Scholar
30.Larson, B.C., Yang, W., Tischler, J.Z., Ice, G.E., Budai, J.D., Liu, W., Weiland, H., Int. J. Plast. 20 (3), 543 (2004).Google Scholar
31.Poulsen, H.F., Three-Dimensional X-ray Diffraction Microscopy. Mapping Polycrystals and their Dynamics. Springer Tracts in Modern Physics (Springer, Berlin, 2004).CrossRefGoogle Scholar
32.Martins, R.V., Margulies, L., Schmidt, S., Poulsen, H.F., Leffers, T., Mater. Sci. Eng. A 387–89, 84 (2004).Google Scholar
33.West, S.S., Schmidt, S., Sorensen, H.O., Winther, G., Poulsen, H.F., Margulies, L., Gundlach, C., Jensen, D.J., Scripta Mater. 61 (9), 875 (2009).CrossRefGoogle Scholar
34.Sutton, M.A., Wolters, H., Peters, W.H., Ranson, W.F., McNeill, S.R., Image Vision Comput. 1 (3), 133 (1983).Google Scholar
35.Limodin, N., Rethore, J., Buffiere, J.Y., Gravouil, A., Hild, F., Roux, S., Acta Mater. 57 (14), 4090 (2009).Google Scholar
36.Haldrup, K., Nielsen, S.F., Wert, J.A., Exp. Mech. 48 (2), 199 (2008).CrossRefGoogle Scholar
37.Nielsen, S.F., Poulsen, H.F., Beckmann, F., Thorning, C., Wert, J.A., Acta Mater. 51 (8), 2407 (2003).Google Scholar
38.Bay, B.K., Smith, T.S., Fyhrie, D.P., Saad, M., Exp. Mech. 39 (3), 217 (1999).Google Scholar
39.Roux, S., Hild, F., Viot, P., Bernard, D., Composites Part A 39 (8), 1253 (2008).CrossRefGoogle Scholar
40.Toda, H., Sinclair, I., Buffiere, J.Y., Maire, E., Khor, K.H., Gregson, P., Kobayashi, T., Acta Mater. 52 (5), 1305 (2004).Google Scholar
41.Verhulp, E., van Rietbergen, B., Huiskes, R., J. Biomech. 37 (9), 1313 (2004).CrossRefGoogle Scholar
42.Rannou, J., Limodin, N., Rethore, J., Gravouil, A., Baietto-Dubourg, M.-C., Buffiere, J.Y., Combescure, A., Hild, F., Roux, S., Methods Appl. Mech. Eng. (2009); doi:10.1016/j.cma.2009.09.013.Google Scholar
43.Ludwig, W., Reischig, P., King, A., Herbig, M., Lauridsen, E.M., Johnson, G., Marrow, T.J., Buffiere, J.Y., Rev. Sci. Instrum. 80 (3), 033905 (2009).CrossRefGoogle Scholar
44.Grasselli, J.G., Bulkin, B.J., Analytical Raman Spectroscopy (Wiley, New York, 1991).Google Scholar
45.Weber, W.H., Merlin, R., Raman Scattering in Materials Science (Springer, New York, 2000).CrossRefGoogle Scholar
46.Gogotsi, Y., Miletich, T., Gardner, M., Rosenberg, M., Rev. Sci. Instrum. 70, 4612 (1999).CrossRefGoogle Scholar
47.Anastassakis, E., Cardona, M., in High Pressure in Semiconductor Physics II. Semiconductors and Semimetals 55, Suski, T., Paul, W., Eds. (Academic Press, San Diego, 1998), p. 117.Google Scholar
48.Wasmer, K., Wermelinger, T., Bidiville, A., Spolenak, R., Michler, J., J. Mater. Res. 23, 3040 (2008).CrossRefGoogle Scholar
49.Webster, S., Batchelder, D.N., Smith, D.A., Appl. Phys. Lett. 72, 1478 (1998).CrossRefGoogle Scholar
50.Wessel, J., J. Opt. Soc. Am. B 2, 1538 (1985).Google Scholar
51.Fleischmann, M., Hendra, P.J., McQuillan, A.J., Chem. Phys. Lett. 26, 163 (1974).Google Scholar
52.Albrecht, M.G., Creighton, J.A., J. Am. Chem. Soc. 99, 5215 (1977).CrossRefGoogle Scholar
53.Jeanmaire, D.L., Van Duyne, R.P., J. Electroanal. Chem. 84, 1 (1977).CrossRefGoogle Scholar
54.Michler, J., Von Kaenel, Y., Stiegler, J., Blank, E., J. Appl. Phys. 83, 187 (1998).CrossRefGoogle Scholar
55.Anderson, M.S., Appl. Phys. Lett. 76, 3130 (2000).CrossRefGoogle Scholar
56.Pettinger, B., Picardi, G., Schuster, R., Ertl, G., Electrochemistry 68 (12), 942 (2000).Google Scholar
57.Stöckle, R.M., Suh, Y.D., Deckert, V., Zenobi, R., Chem. Phys. Lett. 318, 131 (2000).Google Scholar
58.Becker, M., Sivakov, V., Andrä, G., Geiger, R., Schreiber, J., Hoffmann, S., Michler, J., Milenin, A.P., Werner, P., Christiansen, S.H., Nano Lett. 7 (1), 75 (2007).Google Scholar
59.Becker, M., Sivakov, V., Gösele, U., Stelzner, T., Andrä, G., Reich, H.J., Hoffmann, S., Michler, J., Christiansen, S.H., Small 4 (4), 398 (2008).Google Scholar
60.Christiansen, S.H., Becker, M., Fahlbusch, S., Michler, J., Sivakov, V., Andrä, G., Geiger, R., Nanotechnology 18, 035503 (2007).Google Scholar
61.Maass, R., Van Petegem, S., Grolimund, D., Van Swygenhoven, H., Kiener, D., Dehm, G., Appl. Phys. Lett. 92 (7), 071905 (2008).Google Scholar
62.Maass, R., Van Petegem, S., Van Swygenhoven, H., Derlet, P.M., Volkert, C.A., Grolimund, D., Phys. Rev. Lett. 99 (14), 145505 (2007).Google Scholar
63.Wermelinger, T., Borgia, C., Solenthaler, C., Spolenak, R., Acta Mater. 55, 4657 (2007).Google Scholar
64.Wermelinger, T., Spolenak, R., J. Raman Spectrosc. 40, 679 (2009).Google Scholar
65.Yan, H.F., Kalenci, O., Noyan, I.C., Maser, J., J. Appl. Phys. 104 (2), 023506 (2008).Google Scholar