Effects of the progressive damage interphase on the effective bulk behavior of spherical particulate composites
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O R I G I NA L PA P E R
N. Shen · M. Y. Peng · S.-T. Gu
· Y.-G. Hu
Effects of the progressive damage interphase on the effective bulk behavior of spherical particulate composites
Received: 22 October 2019 / Revised: 28 June 2020 / Accepted: 23 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract This work aims at investigating the effect of the progressive damage interphase on the global bulk behavior of spherical particulate composites by proposing a nonlinear stress-strain relationship. To this end, first, the modeling of a damage interphase as a damage imperfect interface is briefly presented in a mathematically rigorous manner. The relationship between the proposed interface model and the classical cohesive model is also discussed and depicted by taking the example of the bilinear shape cohesive model. Second, the elastic fields of the problem where an infinite body made of a matrix containing a spherical particle with a damage interface under a remote uniform isotropic strain boundary condition are then provided in the framework of a Cartesian coordinate system, and the critical macroscopic strain boundary associated to the initial softening of the damage interface is determined. Third, with the aid of these results, the equivalent elastic properties of a perfectly bonded spherical particle related to an imperfectly damage bonded one in an infinite matrix are derived by the replacement procedure of equivalent inclusion with the requirement of energy equality. Finally, the effective bulk of the isotropic particulate composite is obtained by using the classical generalized self-consistent scheme; its global strength is also given, and their features are discussed through some numerical examples.
1 Introduction In many practical situations, the interphase region in inhomogeneous materials exhibits properties different from its surrounding phases and is considered as an important microstructure greatly influencing the global behavior of inhomogeneous materials (see, e.g., [1–6]). In the literature, there are two kinds of models that have been used to describe the properties of the interphase in inhomogeneous materials and to predict its effects on the effective properties of inhomogeneous materials. The first kind is called as the interphase model which describes the interphase region as a thin layer with uniform or variable thickness between the inhomogeneity and the matrix (see, e.g., [7–14]). The physical properties of the interphase are supposed to be different from the matrix and the inhomogeneity. The main shortcoming of the interphase model is that it is difficult to generally mesh a thin layer in the numerical simulation (see, e.g., [15]). Thus, the second kind of model is concerned with modeling the interphase region as a zero-thick interface with appropriate conditions. The properties of the interface are described by the linear or nonlinear relations between its displacement and traction discontinuities for the elastic problem, which are referred to as interface mod
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