Characterization of Random Composites Using Moving-Window Technique
Publication: Journal of Engineering Mechanics
Volume 126, Issue 4
Abstract
Many critical damage phenomena in composite materials, including cracking, are related to local stresses that are linked to local variations in material properties associated with composite microstructure. Relatively little research, however, has been done on the effects of randomness in microstructural configuration on the material behavior of composites. For many engineering applications, it is assumed that small-scale fluctuations in material properties are averaged when evaluating macroscopic behavior. This assumption is generally valid when evaluating quantities such as displacements, average strain, or even average stress, but this approach does not provide any information about local stresses. The analysis of local stresses requires a method of characterizing material properties in terms of material microstructure. This characterization is made more difficult by the inherent randomness in composite microstructure. A methodology is presented whereby the micromechanics model known as the generalized method of cells is used in combination with a moving-window technique to produce material property fields, for elastic and inelastic material properties, associated with the random microstructure of a composite material. In this work, it is assumed that the properties of each constituent of the composite are deterministic and that the fields are the result of randomness in microstructural configuration. Subsequent statistical and probabilistic analysis of these fields will result in a probabilistic description of each property. In this work, the moving-window methodology is applied to a numerically generated micrograph and the real micrograph of a matrix-infiltrated fiber tow.
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References
1.
Aboudi, J. (1984). “Elastoplasticity theory for porous materials.” Mech. of Mat., 3, 81–94.
2.
Aboudi, J. (1989). “Micromechanical analysis of composites by the method of cells.” Appl. Mech. Rev., 42(7), 193–221.
3.
Aboudi, J. (1995). Micromechanical analysis of thermoelastic multiphase short-fiber composites. Compos. Engrg., 5(7), 839–850.
4.
Aboudi, J., Pindera, M.-J., and Arnold, S. M. (1996). “Thermoelastic theory for the response of materials functionally graded in two directions.” Int. J. Solids and Struct., 33(7), 931–966.
5.
Baxter, S. C., and Pindera, M.-J. (1999). “Stress and plastic strain fields during constrained and unconstrained fabrication cool down of fiber reinforced IMCs.” J. Composites Engrg., 33(4), 351–375.
6.
Cherng, R. H., and Wen, Y. K. (1991). “Reliability of uncertain nonlinear trusses under random excitation. I.”J. Engrg. Mech., ASCE, 120(4), 733–747.
7.
Deodatis, G. (1990). “Bounds on response variability of stochastic finite element systems.”J. Engrg. Mech., ASCE, 116(3), 565–585.
8.
Deodatis, G., and Graham, L. ( 1997). “The weighted integral method and the variability response function as part of a SFEM formulation.” Uncertainty modeling in finite element, fatigue and stability of structures, World Scientific, River Edge, N.J., 71–116.
9.
Deodatis, G., and Graham, L. (1998). “Variability response functions for structures with multiple uncertain material and/or geometric properties.” Structural safety and reliability, N. Shiraishi, M. Shinozuka, and Y. K. Wen, eds., Vol. 2, Balkema, Rotterdam, The Netherlands, 883–890.
10.
Der Kiureghian, A., and Ke, J.-B. (1988). “The stochastic finite element method in structural reliability.” Probabilistic Engrg. Mech., Ashurst, Southampton, England, 3(2), 83–91.
11.
Ghanem, R. G., and Spanos, P. D. (1991). Stochastic finite elements: A spectral approach. Springer, New York.
12.
Gibiansky, L. V., and Torquato, S. (1995). “Geometrical-parameter bounds on the effective moduli of composites.” J. Mech. Phys. Solids, 43, 1587–1613.
13.
Graham, L., and Deodatis, G. (1998). “Weighted integral method and variability response functions for stochastic plate bending problems.” Struct. Safety (in press).
14.
Herakovich, C. T., and Baxter, S. C. (1999). “Influence of pore geometry on the effective response of porous media.” J. Am. Ceramic Soc. (in press).
15.
Liu, W. K., Mani, A., and Belytschko, T. (1987). “Finite element methods in probabilistic mechanics.” Probabilistic Engrg. Mech., 2(4), 201–213.
16.
Lutes, L. D., and Sarkani, S. (1997). Stochastic analysis of structural and mechanical vibrations. Prentice-Hall, Upper Saddle River, N.J.
17.
Mendelson, A. (1983). Plasticity: Theory and application. Krieger Publishing Co., Melbourne, Fla.
18.
Ostoja-Starzewski, M. (1994). “Micromechanics as a basis of continuum random fields.” Appl. Mech. Rev., 47(1), S221–S230.
19.
Paley, M., and Aboudi, J. (1992). “Micromechanical analysis of composites by the generalized cells models.” Mech. Mat., 14, 127–139.
20.
Pindera, M.-J., and Bednarcyk, B. A. (1999). “An efficient implementation of the generalized method of cells for unidirectional multi-phased composites with complex microstructure.” Composites Part B (Engineering), 30(1), 87–105 (see also NASA Contractor Rep. 202350, May 1997).
21.
Roberts, A. P., and Knackstedt, M. A. (1996). “Structure-property correlations in model composite materials.” Physics A, 54, 2313.
22.
Salzar, R. S., Pindera, M.-J., and Barton, F. W. (1996). “Elastic/plastic analysis of layered metal matrix composite cylinders. Part I: Theory. J. Pressure Vessel Technol., 118(1), 13–20.
23.
Shinozuka, M. (1987). “Structural response variability.”J. Engrg. Mech., ASCE, 113(6), 825–842.
24.
Takada, T. (1990). “Weighted integral method in multi-dimensional stochastic finite element analysis.” Probabilistic Engrg. Mech., 5(4), 158–166.
25.
Zhang, J., and Ellingwood, B. (1994). “Orthogonal series expansions of random fields in reliability analysis.”J. Engrg. Mech., ASCE, 120(12), 2660–2677.
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Received: Jan 22, 1999
Published online: Apr 1, 2000
Published in print: Apr 2000
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