Micromechanics of creep deformation of two-phase composites and porous materials

A local-field theory and a mean-field theory are developed to predict the transient creep behavior of a metal-matrix composite with unidirectionally aligned and randomly oriented inclusions, respectively. The matrix and inclusion phases may both undergo the primary and the secondary creep, where the creep rate depend nonlinearly on the stress. The proposed method is based upon Eshelby's (17) inclusion theory, Mori-Tanaka's (32) mean-field theory and Luo and Weng's (31) local solution of a three-phase cylindrically concentric solid. While the local theory can be used to a somewhat higher concentration, the mean-field one is suitable only for a composite with low volume fraction of inclusions. The theoretical predictions are found to be in reasonable agreement with the experimental data.In order to extend the theory to a higher concentration and a large creep strain, Mori-Tanaka's (32) method is extended into the Laplace domain to examine the linearly viscoelastic behavior of two types of composite materials: a transversely isotropic one with aligned spheroidal inclusions and an isotropic one with randomly oriented inclusions. The results coincide with some exact solutions for the composite sphere and cylinder assemblage models and, with spherical voids or rigid inclusions, the effective shear property also lies between Christensen's (9) bounds. Comparison with the experimental data indicates the that theory is remarkably accurate.With this newly developed theory in the Laplace space, the nature of void growth for the general class of linear viscoelastic matrix is studied at a non-dilute concentration range. Special attention is paid on the self-similar void growth, transient void growth and the asymptotic shapes with unidirectionally aligned spheroidal voids, where both the elastic strain and the transient creep may be also present. The established condition is found to be universal regardless of the specific viscoelastic model, thereby also containing the result of Budiansky et al. (7) who studied the growth of a single void in a linear viscous matrix with a rigid elastic response and...