J.Mech.Phys.Sol. 45, 1281-1302, 1997


T. Reiter¹², G.J.Dvorak¹, and V. Tvergaard³

¹Center for Composite Materials and Structures,
Rensselaer Polytechnic Institute, Troy, NY
²Institute of Lightweight Structures and Aerospace Engineering,
TU Wien, Vienna, Austria
³Department of Solid Mechanics
Technical University of Denmark, Lyngby, Denmark

Abstract - Elastic response of selected plane-array models of graded composite microstructures is examined under both uniform and linearly varying boundary tractions and displacements, by means of detailed finite element studies of large domains containing up to several thousand inclusions. Models consisting of piecewise homogeneous layers with equivalent elastic properties estimated by Mori-Tanaka and self-consistent methods are also analysed under similar boundary conditions. Comparisons of the overall and local fields predicted by the discrete and homogenized models are made using a C/SiC composite system with very different Young's moduli of the phases, and relatively steep compositional gradients.
The conclusions reached from these comparisons suggest that in those parts of the graded microstructure which have a well-defined continuous matrix and discontinuous second phase, the overall properties and local fields are well predicted by Mori-Tanaka estimates. On the other hand, the response of graded materials with a skeletal microstructure in a wide transition zone between clearly matrix phases is better approximated by the self-consistent estimates. Certain exceptions are noted for loading by overall transverse shear stress. The results suggest that the averaging methods originally developed for statistically homogeneous aggregates may be selectively applied, with a reasonable degree of confidence, to aggregates with composition gradients, subjected to both uniform and nonuniform overall loads.