Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T11:47:26.316Z Has data issue: false hasContentIssue false

Mechanical methods to determine layer compliances within multilayered composites

Published online by Cambridge University Press:  31 January 2011

J. Malzbender
Affiliation:
Forschungszentrum Jülich GmbH, Institute for Materials and Processes in Energy Systems, 52425 Jülich, Germany
R. W. Steinbrech
Affiliation:
Forschungszentrum Jülich GmbH, Institute for Materials and Processes in Energy Systems, 52425 Jülich, Germany
Get access

Abstract

A comparison of bending and compressive/tensile loading cases of multilayered composites is given. Bending perpendicular to the layer interfaces is suggested as a sensitive and experimentally convenient method for determining the elastic modulus of compliant isotropic layers within a multilayered composite. Different approaches to analyze the strain and compliance behavior of the composite and individual layers are derived. Ranking of the relevant equations with respect to strain sensitivity is made, which favors the bending test perpendicular to the layer interfaces. The derived relationships permit a prediction of the bending behavior and the flexural rigidity of the composite. Furthermore, the properties of a layer within the structure can be determined. Limitations that exist for the bending perpendicular to the layer interfaces in the case of low stiffness of the layers can be overcome using either a compressive or a tensile loading mode. Application of the formulas to buckling and interfacial delamination is considered. Materials, such as plasma-sprayed thermal barrier coatings, that are supposed to behave elastically different in tension and compression are given special consideration. Although determination of elastic moduli is the main interest, in the case of known elastic moduli, the formulas can be used to determine the thickness of individual layers within a composite structure.

Type
Articles
Copyright
Copyright © Materials Research Society 2003

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

REFERENCES

1.Scholten, H., Dortmans, L., With, G. de, Smet, B. de, and Bach, P., J. Eur. Ceram. Soc. 10, 33 (1992).CrossRefGoogle Scholar
2.Smet, B. de, Bach, P., Scholten, H.F., Dortmans, L.J.M.G., and With, G. de, J. Eur. Ceram. Soc. 10, 107 (1992).Google Scholar
3.Roark, R.J. and Young, W.C., Formulas for Stress and Strain (McGraw-Hill, Singapore, 1984).Google Scholar
4.Kucuk, A., Berndt, C.C., Senturk, U., Lima, R.S., and Lima, C.R.C., Mater. Sci. Eng. A 284, 29 (2000).CrossRefGoogle Scholar
5.Kim, S.R. and Nairn, J.A., Eng. Frac. Mech. 65, 573 (2000).CrossRefGoogle Scholar
6.Rao, M.P., Sanchez-Herencia, A.J., Beltz, G.E., McMeeking, R.M., Lange, F.F., Science 286, 102 (1999).CrossRefGoogle Scholar
7.Harok, V. and Neufuss, K., J. Thermal Spay Technol. 126, 126 (2001).CrossRefGoogle Scholar
8.Exadaktylos, G.E., Vardoulakis, I., and Kourkoulis, S.K., Int. J. Solids Struct. 38, 4091 (2001).CrossRefGoogle Scholar
9.Phillipps, A.J., Clegg, W.J., and Clyne, T.W., Acta Metall. Mater. 41, 805 (1993).CrossRefGoogle Scholar
10.Phillipps, A.J., Clegg, W.J., and Clyne, T.W., Acta Metall. Mater. 41, 819 (1993).CrossRefGoogle Scholar
11.Folsom, C.A., Zok, F.W., and Lange, F.F., J. Am. Ceram. Soc. 77, 689 (1994).CrossRefGoogle Scholar
12.Folsom, C.A., Zok, F.W., and Lange, F.F., J. Am. Ceram. Soc. 77, 2081 (1994).CrossRefGoogle Scholar
13.Malzbender, J., Steinbrech, R.W., and Singheiser, L., J. Mater. Res. 18, 929 (2003).CrossRefGoogle Scholar
14.Malzbender, J., Steinbrech, R.W., and Singheiser, L., Proceedings of the 8th International Symposium on Solid Oxide Fuel Cells (SOFC VIII), edited by Singhal, S.C. and Dekigá, M., (The Electrochemical Society, Paris, 2003), p. 1963.Google Scholar
15.Wakui, T., Malzbender, J., Steinbrech, R.W., and Singheiser, L., to be presented at the International Conference on Thermal Spraying, ITSC 2003 (Orlando, Florida, 2003).Google Scholar
16.Blandin, G., Thesis, RWTH Aachen, Germany (2001).Google Scholar
17.Townsend, P.H., Barnett, D.M., and Brunner, T.A., J. Appl. Phys. 62, 4438 (1987).CrossRefGoogle Scholar
18.Perat, O., Dorkel, J.M., Scheid, E., Boyer, P. Temple, Chung, Y.S., Peyre-Lavigne, A., Zecri, M., and Tounsi, O., Microelectronics Reliability 42, 1053 (2002).CrossRefGoogle Scholar
19.Klein, C. and Miller, R.P., J. Appl. Phys. 87, 2265 (2000).CrossRefGoogle Scholar
20.Weibull, W., J. Appl. Mech. 18, 293 (1951).CrossRefGoogle Scholar
21.Johnson, C.A., in Fracture Mechanics of Ceramics, edited by Bradt, R.C., Evans, A.G., Hasselman, D.P.H., and Lange, F.F. (Plenum, New York), Vol. 6, p. 365.Google Scholar
22.Stanley, P., Fessler, H., and Sivill, A.D., Proc. Inst. Mech. Eng. 190, 585 (1976).CrossRefGoogle Scholar
23.Timoshenko, S.P., Mechanics of Materials (VanNostrand Reinhold, New York, 1972).Google Scholar
24.Giannakopoulos, A.E., Thin Solid Films 332, 17 (1998).CrossRefGoogle Scholar
25.Charalambides, P.G., Lund, J., Evans, A.G., and McMeeking, R.M., J. Appl. Mech. 56, 77 (1989).CrossRefGoogle Scholar
26.Fleck, N.A. and Sridhar, I., Composites A 33, 353 (2002).CrossRefGoogle Scholar
27.Euler, L., Opera Omnia I, 24, 231 (1744).Google Scholar
28.Schmitt, R.W., Blank, K., and Schönbrunn, G., Sprechsaal 116, 397 (1983).Google Scholar
29.Masters, C.B. and Salomon, N.J., J. Appl. Mech. 61, 872 (1994).CrossRefGoogle Scholar
30.Chen, C., Harte, A-M., Fleck, N.A., Int. J. Mech. Science 41, 1483 (2001).CrossRefGoogle Scholar
31.Freund, L.B., J. Cryst. Growth 132, 341 (1993).CrossRefGoogle Scholar
32.Sankar, B.V., Comp. Sci. Technol. 61, 689 (2001).CrossRefGoogle Scholar
33.Freund, L.B., J. Mech. Phys. Solids, 44, 723 (1996).CrossRefGoogle Scholar
34.Giannakoupolos, A.E., Suresh, S., Finot, M., and Olsson, M., Acta. Metall. Mater. 43, 1335 (1995).CrossRefGoogle Scholar
35.Finot, M. and Suresh, S., J. Mech. Phys. Solids 44, 683 (1996).CrossRefGoogle Scholar
36.Drory, M.D., Thouless, M.D., and Evans, A.G., Acta Metall. 36, 2019 (1998).CrossRefGoogle Scholar